diff --git "a/batch_s000023.csv" "b/batch_s000023.csv" new file mode 100644--- /dev/null +++ "b/batch_s000023.csv" @@ -0,0 +1,10332 @@ +source,target +obtained 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 $1.2\,\sigma$." + 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 $L_\mathrm{Aa}/L_\mathrm{Ab} +\approx 1.3$ and mass ratio $M_\mathrm{Aa}/M_\mathrm{Ab} \approx 1.1$ of the $\delta$ Vel A pair." + 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." + 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." + 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." + 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." + 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. + 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}) )." + 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)." + 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." + With the advent of speckle interferometry (Tango et al. 1979)), With the advent of speckle interferometry (Tango et al. \cite{tango79}) ) + 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. + 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};" + Lenzen et al. 1998)), Lenzen et al. \cite{lenzen98}) ) + and the N-band camera VLT/VISIR (Lagage et al. 2004))., and the N-band camera VLT/VISIR (Lagage et al. \cite{lagage04}) ). + 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." + 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}. + 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}) )" +for NACO and 75+| mmas/pixel for VISIR., for NACO and $75 \pm 1$ mas/pixel for VISIR. + 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}) )," + 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. + 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." + 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. + 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}) )" + in his Table 5. that includes 17epochs between 1895 and 1999.," in his Table 5, that includes 17epochs between 1895 and 1999." + 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}) ) + 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." + Transforming the Tango et al., Transforming the Tango et al. + 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." + 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}." + The corresponding orbital elements are listed in Table 6.., The corresponding orbital elements are listed in Table \ref{tab:AB_orbit}. + 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 $\pi = 39.8 \pm 0.4$ ." +"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. +" 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." + 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). +" 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 $\Delta +d_{av}$, after stochastically culling the synthetic clusters to the same number of sources available in the observed clusters (see Table 2)." +" 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." +" 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." + The solar type disc dispersal timescales are kept fixed at 2 Myr., The solar type disc dispersal timescales are kept fixed at 2 Myr. +" We note that in our very simplified model, what"," We note that in our very simplified model, what" + ," \citep[see e.g.][]{SandersMirabel, BarnesHernquist, Genzel, DiMatteo, Hopkins06}." +"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." +" 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." +" 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." + 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. + 2003; optical - Gerssen et al., 2003; optical - Gerssen et al. + 2004; near-IR - Max et al., 2004; near-IR - Max et al. +" 2005, 2007; Scoville et al."," 2005, 2007; Scoville et al." + 2000; Tecza et al., 2000; Tecza et al. + 2000; Engel et al., 2000; Engel et al. + 2010; mid-IR - Armus et al., 2010; mid-IR - Armus et al. + 2006; mm - Tacconi et al., 2006; mm - Tacconi et al. +" 1999; radio - Gallimore Beswick 2004, Hagiwara et al."," 1999; radio - Gallimore Beswick 2004, Hagiwara et al." + 2011)., 2011). +" 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." + 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}. +" 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." +" 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}) )." +"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" +"power spectrum estimates are expected to be underevolved by roughly AY1.,conversion of the jet energy to thermal energy suggests that $0 \ge M \ge 1$. + Constraints 1-3 reduce to GV+1)//N=0.360.03., Constraints 1-3 reduce to $(M+1)/N=0.36 \pm 0.03$. + Constraints 4 and 5 give NV=3.14£0.34.," Constraints 4 and 5 give $N=3.14 \pm +0.34$." + 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." + In round numbers. N=3 and M=0.," In round numbers, $N=3$ and $M=0$." + What should verv high red shift (2~10) GRBs look like?, What should very high red shift $z \sim 10$ ) GRBs look like? + 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." +" 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 $P_{256}$." + 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 $E_{peak} \sim 200 keV$ ." +ippenetal.(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}. +. 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." +" 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. + 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. (" +This 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. + as shown in Figure 2.), as shown in Figure 2.) + 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." + 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." +" 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. +" 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." +" The value of Zi, is approximately constant for all bursts.", The value of $E_0$ is approximately constant for all bursts. + 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. + Thus itnow seems, Thus itnow seems +the GC candidate list. but some coutaminatioun still remains.,"the GC candidate list, but some contamination still remains." + Section 3.6 describes how we quantify the contamination level.," Section \ref{section:contamination} + describes how we quantify the contamination level." + 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. + 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." + 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. + 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." + 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}." + 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. + 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. + 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. +" 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. + 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." + 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." + 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." + 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. + 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." + 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. + 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. + The, The +for overdense regions to condcuse out.,for overdense regions to condense out. + 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." + 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 $q \sim 1$. +" We take the Dexavitational potential to be Deiven by -u ↴∖↴⋯∪∪↑∐⊓⋅⋜⋯↴∖↴↕↑↕∪∐∙ : uSeay outer .forrrotkpepe 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). +HST 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.” + 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." + 1995: Faber et al, 1995; Faber et al. +" 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. + 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." + 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." + 1995): we use such values in our nuuerical results of 8333.1., 1995); we use such values in our numerical results of 3.1. + 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." + 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 $r +\gsim \rt$ while it is predominantly that of the black hole for $r +\lsim \rt$ , where the transition radius is (for $r_b \rightarrow 0$ ) 0.05 )." + 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 $\sigma +\approx 300$ km $^{-1}$ in the Virgo cluster, a distance $\approx 20$ Mpc away, $\rt$ corresponds to $\approx 0.5$ arcsec." + 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)." + 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 $r_s$. + Rewriting equations (2))-(2]) vields Ü —L. where V= aud ," Rewriting equations \ref{mdot}) \ref{energy}) ) yields v =, where N = and D = 1 -." +"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." +"≺∏∐⋅∪∏↑↸∖↥⋅↴⋝≺∏⋯≺↧⋜∐⋅⋅↖↽↸⊳∪∐≼∐↑↕∪∐↴∖↴↑∪↴⋝↸∖↴∖↴⋉∖↸⊳↕∏↸∖≼⇂ 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 $\ro$." +" 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, $\dot M(r_s)$." + 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. +" 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 $^{-3}$, $\sigma +\approx 300$ km $^{-1}$, $c_o \approx \sigma$ (e.g., Stewart et al." + 1981) aud AFzm3<10?AZ. (Ianus et al., 1984) and $M \approx 3 \times 10^9 M_\odot$ (Harms et al. + 1991: Ford et al., 1994; Ford et al. + 199L: AMacchoetto ct al., 1994; Macchetto et al. + 1997)., 1997). + In. MS8T. AL ds inferred to decrease from 10M.srtats TU kpe to ~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." + 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." + 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." + The V-band CLE slope in the range LO!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 $\omega \tau_{c_0} += 1$, see Paper I), and the red edge of the strip with $\tau_{c_0} = +1300 \s$ (when the $1000 \s$ period mode becomes invisible at the surface, $\omega \tau_{c_0} = 10 \gg 1$, see Paper I)." + 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}. + 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. + 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. + A number of practical cdilliculties may arise. in the actual analysis., A number of practical difficulties may arise in the actual analysis. + 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." + In the following sections. we apply our results ignoring these dilliculties.," In the following sections, we apply our results ignoring these difficulties." + 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" +strongly suggests that these are noise artifacts.,strongly suggests that these are noise artifacts. +" 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." + 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. + 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. + 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. +" 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." + 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. + 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. + 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. + 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. +" 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 $\sim500~\mbox{km s}^{-1}$." + 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. +" 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." + 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. + 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. +" The line is extremely weak and so potentially unreliable, however."," The line is extremely weak and so potentially unreliable, however." +" '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." +" 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." + 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. +" 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." + The SiIV, The SiIV +unWw,\ref{Choice}. + 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. + The On-The-Fly (OTF) mapping mode of Mopra. was used., The On-The-Fly (OTF) mapping mode of Mopra was used. + 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. + 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. + The scan rate was yper secoud., The scan rate was per second. + 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." +" 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." + 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." + A single OFF position was observed for every two scan rows., A single OFF position was observed for every two scan rows. + 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." +" 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 ." +". 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. + Weather conditions were variable., Weather conditions were variable. + 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. +" 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." + 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." + 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." + 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)." + 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." + 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}. + iis particularly prevaleut in cold gas (2).., is particularly prevalent in cold gas \citep[][]{Hirota:1998}. + ootten shows iufall signatures aud outflow wines (6.8. ?7)..," often shows infall signatures and outflow wings \citep[e.g.,][]{Rawlings:2004, Fuller:2005}." + These stroug lines cau all be optically thick., These strong lines can all be optically thick. + 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. (" +(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. + 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. +" 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}." + 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. + 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." + 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)). + The maps were reduced using the andpackages!?., The maps were reduced using the and. +. 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. + uses lis output to construct a uniformly eridded cube., uses this output to construct a uniformly gridded cube. + Both polavizations were averaged together., Both polarizations were averaged together. + 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." +" This choice of parameters xoduces an effective heain size of FWIIM =72"".", This choice of parameters produces an effective beam size of FWHM =. +. 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." + The data are presented on fjio antenna temperature scale , The data are presented on the antenna temperature scale$_{A}^{*}$ ). +"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 $_{mb}$ ). + All the data, All the data +objects.,objects. + 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. + 'There are two sub-DLAs in the spectrum of this QSO., There are two sub-DLAs in the spectrum of this QSO. +" 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}." +. This field was observed in the griz filters., This field was observed in the $griz$ filters. + Exposure times are given in Table 1.., Exposure times are given in Table \ref{Tab:Obs}. . +" 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}." +" 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." +" 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." +" 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)." + 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}. . + The software package was usedtodetermine a photometric redshift of zpno¢=0.79+ 0.08., The software package was usedtodetermine a photometric redshift of $z_{phot}=0.79\pm0.08$ . +have often been rejected as unfeasible for the most massive black holes A10M...,"have often been rejected as unfeasible for the most massive black holes $M > 10^9 +\Msun$." + 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." + 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 $t_Q > 2 +\times 10^8$ yr by revisiting the results shown in Fig \ref{fig3}." + 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 $M \simeq 10^{10} +\Msun$ requires mass accretion rates which rapidly approach $100 +{\rm M_{\odot} yr^{-1}}$." + 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." + 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} + provides good evidence that the most massive black holes are not accreting matter at a rate significantly in excess of $10 {\rm M_{\odot} yr^{-1}}$." + ‘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 $10^9 \Msun$." +" 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 $10 {\rm M_{\odot} yr^{-1}}$." + 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 $\simeq +2 - 20 {\rm M_{\odot} yr^{-1}}$ ) or by the physics of galaxy formation (e.g. Archibald et al." + 2002: Cuanato ct al., 2002; Granato et al. + 2001. 2003).," 2001, 2003)." + 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)." + 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 $0.10.4 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 $q < 0.5\,$." + 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. + 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." + We will also examine cores with different masses., We will also examine cores with different masses. + 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." + 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)." + 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 $5.4 M_{\odot}$." + The initial ratio of thermal to gravitational energy is cina= 0.45., The initial ratio of thermal to gravitational energy is $\alpha_{\rm therm} = 0.45$ . + 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)." +" 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. +"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." + 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}." + 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}. +. 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." + 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." + 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. + 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 $\sim 2 M_{\odot}$." +" 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." + 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." +" 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." + 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. + 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." + 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." + 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." +" 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." + 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." + 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." + 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." + 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." + (Westetal.2008).. Schiuuidtetal.2010b)..,"\citep[e.g.][]{boo10} \citep{west08}. \citep{H02, west04, west05, + bootem, schmidt_sam}, \citep{west04,west08, kowalski09, + kruse10,hilton10}," + 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}." +. 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. + 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, + 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)." + 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}." +. 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." + 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." + 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}. + 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}." +ev2009).. 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} + decreased with height in the Galactic disk (a proxy for age)." + 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 local +increasing fraction of (he cloud mass starts to expand.,increasing fraction of the cloud mass starts to expand. + Such expansion costs energy., Such expansion costs energy. + 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." + 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." + This is ihe Donnor-Ebert density contrast., This is the Bonnor-Ebert density contrast. + 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}." +. We recall. however. (hat this instability arises [rom perturbations of a cloudFemperature.," We recall, however, that this instability arises from perturbations of a cloud." + In. contrast. our sequence has varving effective sound speed.," In contrast, our sequence has varying effective sound speed." + The DBonner-Ebert contrast no longer marks a stability transition., The Bonner-Ebert contrast no longer marks a stability transition. + 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." + 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." + 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." + 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." + 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. + Returning to dimensional notation. equation (ALO) stated where L is the luminosity.," Returning to dimensional notation, equation (A10) stated where $L$ is the luminosity." + 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." + 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, $(3/2)\int\!P\,dV$." + Using equation (3) for P. this integral becomes (3/2).«5.," Using equation (3) for $P$, this integral becomes $(3/2) M_\circ\,a_T^2$." + 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" +A 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. +" 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, $dY/dZ$." +" 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 $1.1\pm 1.4$. +" 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 $\delta Y_p\simeq 0.002-0.004$." +" 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." + 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. + 1992: Olive et al., 1992; Olive et al. + 1997: Peimbert et al., 1997; Peimbert et al. + 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." + 2003)» with the aid of Dig-Dang nucleosvuthesis, 2003) with the aid of Big-Bang nucleosynthesis. + 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. + We suspect that (his mieht not represent properly the error including svstematics., We suspect that this might not represent properly the error including systematics. + 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. + In (his paper we are particularly concerned with the effect induced by, In this paper we are particularly concerned with the effect induced by +Puzia (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." + 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." + 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. ( +2003. 2004).,"2003, 2004)." + 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. + 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. + 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. + 1994)., 1994). + 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. ( +2008). 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." + show a very good correlation (r 0.9: Fig., show a very good correlation (r $\simeq$ 0.9; Fig. + 1)., 1). + 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. + 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. +" We initiallv excluded the observations corresponding to C117 because the values of Riga, and _h$ for this GC are significantly higher than those of all other GCs. + We started with the, We started with the +The 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 ." +. 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 . +. 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." + The inpainting problem can be defined as follows., The inpainting problem can be defined as follows. + 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)." + In short. we have: Y= LX.," In short, we have: $Y = L X$ ." + lupaiutiug cousists in recovering VY kuowine Y aud £L., Inpainting consists in recovering $X$ knowing $Y$ and $L$. + 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. + 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." + More details can be found in(?)., More details can be found in. +. In this paper. the choscu ‘dictionary’ is the spherical harmonic domain.," In this paper, the chosen `dictionary' is the spherical harmonic domain." +" 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" +The 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." + 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)." + 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. + 1997). has provided new opportunities for accurate estimates of this distance scale., 1997) has provided new opportunities for accurate estimates of this distance scale. + Various authors (Reid 1997: Gratton et al., Various authors (Reid 1997; Gratton et al. + 19975: Pont et al., 1997b; Pont et al. + 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. + 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." + 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)." + 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." + Fernley ct al. (, Fernley et al. ( +1997) 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." + 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." + 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. + 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. +the 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." + 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." +" 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)." + 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}) )." + Most points have values of :<2., Most points have values of $z < 2$. + 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." + 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 $z$." + Nevertheless. a few OAs with high redshift are detected in the simulation.," Nevertheless, a few OAs with high redshift are detected in the simulation." +" 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." + 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 $\theta_{\rm j}$. + 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. + 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." + 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." +" 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). +" 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." +" 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." + 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. + 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. + 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." + 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." + 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). + 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." + 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." +" 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}." +. The chances of observing the change in magnitudes will hus be Imited., The chances of observing the change in magnitudes will thus be limited. +" 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." + 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)." + 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." + The time of detection is considerably arecr for OAs., The time of detection is considerably larger for OAs. + 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." + 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." + 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)." + 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}." +. 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}. ." +. 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}. ." + Thus. we added," Thus, we added" +garect. 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}) )." + 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." + 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." + 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." + ]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." + 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. + This equation was first applied by Fablman et al. (, This equation was first applied by Fahlman et al. ( +1994) 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." + 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. + 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. + 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." + 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." +" 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)." + 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. (" +Llere 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 $\exep=1/g^{\ast}$ .) + 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. + 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." + 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 $(1-\kappa_{\rm s})$." + 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}) ).]" + 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. + 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 $N\rightarrow\infty$. + 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." + 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}) )." + 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 (see +a 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}) )." +" 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}. + 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." +⋅⋅⋪ 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. +↽∕∏↓⋜↧↑⋜⋯∪↥⋅↴⋝↕↑⋜↧↕↴∖↴↕∩⊾∐⋜↧↕↸∖↘↕↴∖↴↑↴∖↴↕∐≺∐↸⊳⋜↧↑↸∖↴∖↴↑∐⋜↧↑↑∐↸∖↴∖↴↖↽↴∖↴↑↸∖⋯ not face-on., That an orbital signal exists indicates that the system is not face-on. + 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" +"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)." + The nucleus hosts a highly variable continuum and line emission source., The nucleus hosts a highly variable continuum and line emission source. + Conünuunm variability. first reported by Fitch et al. (," Continuum variability, first reported by Fitch et al. (" +1967). 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." + 1995). UV. (Clavel et al.," 1995), UV (Clavel et al." + 1990). and optical (Lyutyi 1972).," 1990), and optical (Lyutyi 1972)." + 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)." + 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. + 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. (" +1987). Edelson et al. (,"1987), Edelson et al. (" +1987). and ce ]xool Begelman (1989).,"1987), and de Kool Begelman (1989)." + 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. (" +1990) (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." + 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." +" 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 $>0.1\arcsec$." + Observations show that the mil-IK emission in NGC 4151 is compact., Observations show that the mid-IR emission in NGC 4151 is compact. +" 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. + 1987)., 1987). + 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. +" 1987. also did. not detect. any extended emission with resolutions =6"".", 1987 also did not detect any extended emission with resolutions $\gtrsim 6\arcsec$. + Observations by ISO (Infrared Space Observatory: Rodviquez-Espinosa οἱ al., Observations by ISO (Infrared Space Observatory; Rodriquez-Espinosa et al. + 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). +" These observations however were at a resolution of 180"".", These observations however were at a resolution of $180\arcsec$. + 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." + 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. + 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." + 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 $% +\micro n and 18 $\micron$ ." +The 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. + 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}) ). +" 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. + 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. + 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. + 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 $M_{\odot}$ $^{-3}$. + 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}) ). + This is to be expected: a study by Sensui et al. (, This is to be expected: a study by Sensui et al. ( +2000) 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. + 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. + 2002. 2009).," 2002, 2009)." +" 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. + 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. + 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." + 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}) ). + The tidal disruption timescale is much shorter (han that for merging., The tidal disruption timescale is much shorter than that for merging. + 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." + 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." + 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." + 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. + Tidal shreclding is à form of shearing bv differential rotation., Tidal shredding is a form of shearing by differential rotation. + 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. + 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 along +ionizing influence of the QSOs.,ionizing influence of the QSOs. +" 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." +" 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." +" 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=, 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 = $, and $f_{cont}$ is determined by stellar synthesis models fit to the photometric data." + 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). +"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." + 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. + 2006; Songaila 2004)., 2006; Songaila 2004). +" 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." +" 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." + 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. + 2006) and a lognormal optical depth distribution (Becker et al., 2006) and a lognormal optical depth distribution (Becker et al. +" 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 $\tau_{GP}^{eff}$." +" 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." +" 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." +" 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)." + The observing details for these data are discussed elsewhere (Frye et al., The observing details for these data are discussed elsewhere (Frye et al. + 2007)., 2007). + 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. +" 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)." + '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. +" 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." +" 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." + Thus we restrict our parameterspace to E(B—V)€0.1., Thus we restrict our parameterspace to $E(B-V) \leq 0.1$. + 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}. +". 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." +" 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." +" 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." +" For each 7, three parameters remain"," For each $\tau$ , three parameters remain" +"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." + 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." +" 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." +" 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). + 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. + 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}," + Ramaty et al. 1996))., Ramaty et al. \cite{Rama96}) ). + 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}," + Molaro et al. 1997..," Molaro et al. \cite{MBCP97}," + Thorburn Tobbs 1996..Wc Pruuas 1906 Carctaa Lóppez et al. 1998))," Thorburn Hobbs \cite{TH96}, Primas \cite{Pri96} + a Lóppez et al. \cite{Gar98}) )" + as shown by Vaugioni-Fluu et al. (199 1))., as shown by Vangioni-Flam et al. \cite{VLC94}) ). + 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." +" 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”)." +" 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." + 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." + 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 this + 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." + 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 $(u=r/t)$. + 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)." + 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. + 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." + 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." + 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." + 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)." + 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." + 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." + Their results were confirmed. by an independent semi-analvtical study (Popov 1993)., Their results were confirmed by an independent semi-analytical study (Popov 1993). + 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." + 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." + 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" + 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" +Both 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. + 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." + 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." + 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 $w=p/\rho=-1$." +" 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." +" 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: ${\theta}=\Omega_{\Lambda}$." + 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}. . + The best-fit value of the parameter is: Q4=0.85(rl., The best-fit value of the parameter is: $\Omega_\Lambda=0.85^{+0.11}_{-0.18}$. + 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 $\sigma$ )." + 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." +" 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." + 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. + 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" +the phase-averaged flux.,the phase-averaged flux. + 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)." + 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." + 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. + 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. + 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}. +. 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-peaked +as opposed to the quasi-sinusoidal profiles of \tfe\ and \ett, +see][]{gk02}." + SGR bursts on the other hand show no correlation with pulse phase., SGR bursts on the other hand show no correlation with pulse phase. + 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. + 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." + 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. + 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." + 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." + 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. + 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." +" 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. + 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" +coellicient 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." + 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: $\xi_c(t)=P_c(t)/(\rho_0 V_{sh}(t)^2)$. +" 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." + 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." + 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." + 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 $\xi_c(t)$." + 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." + 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. + 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." + 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-resonant +In 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}. + 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. +" 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)." + 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}) )." + 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}) ). + 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 $\phi_{0}*u$." + We will show that, We will show that +All 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. + 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." + Ring eccentricilies are sel (o zero in their analvsis., Ring eccentricities are set to zero in their analysis. + 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. + 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." + 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." + 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." + 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." + 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." + 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." + 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. + 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." + 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}." + 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." + The computation of Z(«) is described in relinca.., The computation of $I(a)$ is described in \\ref{inca}. . + Finally. in," Finally, in" +seen all right at a first glance.,seem all right at a first glance. + 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 $\omega$?" + We do not know., We do not know. + 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}) )." + 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." + What else can one imagine for δω=Q0)?, What else can one imagine for $\delta\omega (J=0)$? + Currently. we lack imagination for other possibilities of confusion.," Currently, we lack imagination for other possibilities of confusion." + 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. + 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." +both 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 $T_{\rm eff}$." + 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 $q<13.5\,{\rm arcsec^{-1}}$ ." + 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." + 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}. ." + 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}. ." +" 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}) ). +" 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 $a_{\rm + gr}$, but it becomes independent of $a_{\rm gr}$ at longer wavelengths (see \\ref{sed-Ow92-a0-qext}) )." + 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. +" 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 $a_{\rm gr}$." + 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. + 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 $\lambda \la 2\,{\rm\mu m}$." + 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 $a_{\rm + gr} \ga 0.12\,{\rm\mu m}$ 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 $a_{\rm gr} = 0.1\,{\rm\mu m}$." + 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." + 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). + 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 $2.11\,{\rm + \mu m}$ visibility." + 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 $\lambda>2\,{\rm\mu m}$." + 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 $2.11\,{\rm +\mu m}$ decreases." + 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}) )." + 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." + The curvature changes its sign at about ανν—«0.1gn.," The curvature changes its sign at about $a_{\rm gr}<0.1\,{\rm\mu m}$." + This behaviour reflects the changes of the spatial intensity. distribution., This behaviour reflects the changes of the spatial intensity distribution. + 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}) )." + 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" +PAH emission exists around NGC 5529.,PAH emission exists around NGC 5529. + The Inset to Fig., The Inset to Fig. + 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." +" 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)." +" 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)." +" 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." + 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?" + As indicated in Sect. 4.1..," As indicated in Sect. \ref{band_contributions}," + 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." +" 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." + 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. + 6bb (Inset. grey curve).," \ref{slices_fig}b b (Inset, grey curve)." +" 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)." + 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." +" 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)." + 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." + 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." +" 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)." +" 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)." + 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)." + As indicated in Sect. 2..," As indicated in Sect. \ref{ngc5529}," + 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." + 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." + 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." + 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." + This is shown in the two overlays of Fig. 7.., This is shown in the two overlays of Fig. \ref{iso_halpha}. + In Fig., In Fig. + 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." + 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." + The are (see Sect. 4.3)), The arc (see Sect. \ref{halo_emission}) ) + 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." + Fig., Fig. + 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." + 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." +" 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 $\approx$ $^\circ$ $^\prime$ $^{\prime\prime}$." + Similarities on the south-west side of the disk are also apparent., Similarities on the south-west side of the disk are also apparent. + 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}) )," + 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." + 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. + 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." + 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." + 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." + 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. + 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." + Few statistics exist on the presence of PAHs in galaxy halos., Few statistics exist on the presence of PAHs in galaxy halos. + 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}) )." + Tacconi-Garman et al. (, Tacconi-Garman et al. ( +2005) 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." + 2006)., 2006). + 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" +Fig 9..,Fig \ref{SFH_p2}. + shows that P-mode generates potential vorticity with a positive sign., shows that P-mode generates potential vorticity with a positive sign. +" 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." +" 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." + 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}) ). +" 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." +" 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." + Fig., Fig. + 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. +" 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 $\eta$." +" 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." + 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. + 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. + 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. + 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. + 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. + 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 different +4765-f01-1504 (Carrascoetal.2006).,4765-f01-1504 \citep{camein2006}. +. 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}. +" 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." + 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}. . +" 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." +" 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." +" 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." +" 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." +" 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." + 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. +" 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." + The final exposures used are given in Table 1.., The final exposures used are given in Table \ref{tbl:obslog}. +" 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." + 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. +" 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. + 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}) ). + 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. +" 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." +" 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." +" 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)." +" 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}." +". 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." +" 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." + 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. +" 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}." +". 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 $\sim$ $'$." + 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}. + 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}. +". 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. + 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. +" 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)." + 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}. +. X-ray data were reduced with the taskzrtpipeline version 0.12.1., X-ray data were reduced with the task version 0.12.1. +" 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." + We also calculated the confidence interval of the detection., We also calculated the confidence interval of the detection. +" 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." + 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. + 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. + 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}. +". 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." + 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}. +" 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)." + 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. + 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}. +. The images have a FWHM of the PSF of about 122., The images have a FWHM of the PSF of about 2. +" 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." +" 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." + 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 bright +sullicienthy 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. + 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." + 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." + This condition. as derived in section 20 is peὃνομις.," This condition, as derived in section \ref{anal_sect} + is $pc\gg eA_\|u_{\rm sh}$." + 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 ( )." +260) 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." + 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,." +3T) 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}. +". Por &+ ion-cvclotron resonance takes over and the growth rate 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 $t>0$." + 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}." + 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 $H^1_{loc}(\R\times [0,+\infty))$." + 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. + 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 $(\rho^+-\rho^-)$." + 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." + In this section we consider the case where the three-dimensional material is a slab with boundary conditions where 7€IE is a [ixed constant (see Figure 4)).," In this section we consider the case where the three-dimensional material is a slab $\Omega= (-1,1)\times \R^2$ with boundary conditions where $\tau\in\R$ is a fixed constant (see Figure \ref{f4}) )." + In that ease. we ean check (hat the solution to the equation (2.9)) on O supplemented with boundary conditions (3.15)). is And then [rom the evolution equation (2.7)). we see that in the case 7>0. the positive dislocations move to the right aud the negative dislocations move to the left.," In that case, we can check that the solution to the equation \ref{eq::9}) ) on $\Omega$ supplemented with boundary conditions \ref{eq::10}) ), is And then from the evolution equation \ref{eq::2}) ), we see that in the case $\tau>0$, the positive dislocations move to the right and the negative dislocations move to the left." + In order to take into account the short range dynamics with aceumulations of dislocations on the boundary of the material. Groma. Czikor and Zaiser [0| have proposed to modify equation (2.7)) into the following equation (GCZ model)," In order to take into account the short range dynamics with accumulations of dislocations on the boundary of the material, Groma, Czikor and Zaiser \cite{GCZ} have proposed to modify equation \ref{eq::2}) ) into the following equation (GCZ model)" +fraction significantly after t>1x107yr.,fraction significantly after $t\gtrsim1\times10^{7}\ {\rm yr}$. + 'The dependence of time evolution of SFR on the ISM density around SN is presented in Figure 9.., The dependence of time evolution of SFR on the ISM density around SN is presented in Figure \ref{SFevo2}. +" We can see that after t~5x107yr higher density around SNe progenitors results in lower molecular fraction, and hence lower star formation efficiency."," We can see that after $t\sim5\times10^{7}\ {\rm yr}$ higher density around SNe progenitors results in lower molecular fraction, and hence lower star formation efficiency." +" The SFR, W(t), is independent of ngn before t~5x107 yr, because Hy forms predominantly in the gas phase."," The SFR, $\Psi(t)$ , is independent of $n_{\rm SN}$ before $t\sim5\times10^{7}\ {\rm yr}$ , because ${\rm H}_{2}$ forms predominantly in the gas phase." +" In the model without reverse shock destruction, the SFR increases from ~105yr and saturates around 5x10?yr."," In the model without reverse shock destruction, the SFR increases from $\sim10^{8}\ {\rm yr}$ and saturates around $5\times10^{8}\ {\rm yr}$." + This is because the gas is consumed by the star formation., This is because the gas is consumed by the star formation. +" In model A10m9 (ngx=10 cm-?), SFR is suppressed until t~0.8x10?yr."," In model A10m9 $n_{\rm SN}=10\ {\rm cm^{-3}}$ ), SFR is suppressed until $t\sim0.8\times10^{9}\ {\rm yr}$." +" We should note that it is probably that ngn1cm? for Pop III stars in the mass range of 20—40 Mo, since Pop III stars are massive and can photoevaporate the clouds in which they form, and that ionized flows evacuate the dense gas around the stars to well below ngx=1επιὉ (Whalenetal.2004;Kitayama 2004)."," We should note that it is probably that $n_{\rm SN}<1\ {\rm cm}^{-3}$ for Pop III stars in the mass range of $20-40\ {\rm M}_{\odot}$ , since Pop III stars are massive and can photoevaporate the clouds in which they form, and that ionized flows evacuate the dense gas around the stars to well below $n_{\rm SN}=1\ {\rm cm}^{-3}$ \citep{Wha04, Kit04}." +". In this case, considering circumstellar densities of 10cm~? and greater is not relevant to dust evolution in the SN remnant."," In this case, considering circumstellar densities of $10\ {\rm cm}^{-3}$ and greater is not relevant to dust evolution in the SN remnant." +" In this paper, we consider ngy>5cm? for completeness."," In this paper, we consider $n_{\rm SN}>5\ {\rm cm}^{-3}$ for completeness." +" If the stars are forming at lower redshift and are enriched, they will have stellar winds that also sweep away circumstellar gas to low densities."," If the stars are forming at lower redshift and are enriched, they will have stellar winds that also sweep away circumstellar gas to low densities." +" We note that in usual star formation recipe in both numerical simulations and analytic models, SFRis assumed to increase with the local gas density and our results show that the SFR is"," We note that in usual star formation recipe in both numerical simulations and analytic models, SFRis assumed to increase with the local gas density and our results show that the SFR is" +Transiting Extrasolar planets are relatively rare among all known planet discoveries (69 transiting planets out of 429 known planetarysvstems)!.,Transiting Extrasolar planets are relatively rare among all known planet discoveries (69 transiting planets out of 429 known planetary. +. However. transits are unique in that Chev allow for the direct measurement of the radius of (he transiting planet relative {ο the host star.," However, transits are unique in that they allow for the direct measurement of the radius of the transiting planet relative to the host star." + Combined with radial velocity data. il is possible to determine the density of the transiting planet as well.," Combined with radial velocity data, it is possible to determine the density of the transiting planet as well." + Ixnowledge of the heating of the star can allow models of the bulk properties of these planets to be formulated and then compared (to observation (Lor example. Daraffe et al.," Knowledge of the heating of the star can allow models of the bulk properties of these planets to be formulated and then compared to observation (for example, Baraffe et al." + 2008: Fortney et al., 2008; Fortney et al. + 2007: Burrows et al 2007)., 2007; Burrows et al 2007). + since (he depth of the (transit is directly. related (ο its radius. the size of a (ransiline planet is one of (he easiest parameters to measure.," Since the depth of the transit is directly related to its radius, the size of a transiting planet is one of the easiest parameters to measure." + This makes transiting planets especially interesting to discover and study in detail. however this method becomes increasingly difficult," This makes transiting planets especially interesting to discover and study in detail, however this method becomes increasingly difficult" +" likestructuresthatmayarisef rombipolaroutflows, itisverylikel ythath dima extiéyhajhtind¢{Gati","structures that may arise from bipolar outflows, it is very likely that the unusually high [N ]/[O ] ratios stem from shock interactions of these structures with surrounding material." +"pnsi ofs NGC 6369ockinteractionso f thes [N τῇ, and [O 11] images and ratio maps."," To investigate the structure of these features in more detail, we show in Figure \ref{fig.shocks} a radial profile across a particularly bright filament of the eastern extension extracted from the $\alpha$, [N ], and [O ] images and ratio maps." +" The comparison of the surface brightness profiles indicates that the peak of all these three emission lines are almost coincident, but the spatial profile of the [O ΠΠ] line is noticeable broader."," The comparison of the surface brightness profiles indicates that the peak of all these three emission lines are almost coincident, but the spatial profile of the [O ] line is noticeable broader." +" The inner shoulder of this profile, closer to the central star (negative offsets in Fig. 13)),"," The inner shoulder of this profile, closer to the central star (negative offsets in Fig. \ref{fig.shocks}) )," + can be explained as the result of a higher photo-excitation., can be explained as the result of a higher photo-excitation. +" The shoulder of the line farther away from the nebula, however, cannot be explained in this way and it very likely reveals the presence of a forward shock propagating onto a lower density medium."," The shoulder of the line farther away from the nebula, however, cannot be explained in this way and it very likely reveals the presence of a forward shock propagating onto a lower density medium." + The [O 111|/Ha ratio profile in the lower-panel of Fig., The [O $\alpha$ ratio profile in the lower-panel of Fig. +" 13 allows us to derive a quantitative value for the spatial extent of this post-shock region, ~172."," \ref{fig.shocks} allows us to derive a quantitative value for the spatial extent of this post-shock region, $\simeq1\farcs2$." +" At the distance of 1,550 pc, this corresponds to 3x10!8 cm, comparable to the post-shock cooling widths determined from modelling of shocks2005)."," At the distance of 1,550 pc, this corresponds to $\sim$ $\times$ $^{16}$ cm, comparable to the post-shock cooling widths determined from modelling of shocks." +. There is a growing number of PNe in the literature that show knots or blobs of emission well separated from their main nebular shells that do not form a halo., There is a growing number of PNe in the literature that show knots or blobs of emission well separated from their main nebular shells that do not form a halo. +" In some cases, the kinematics of these knots imply high-velocity collimated outflows, e.g., Fleming 1 or 1182000),, while in some others, e.g., 446342008),, the velocity of the knots is close to the systemic velocity, may be due to motions close to the plane of the sky."," In some cases, the kinematics of these knots imply high-velocity collimated outflows, e.g., Fleming 1 or 18, while in some others, e.g., 4634, the velocity of the knots is close to the systemic velocity, may be due to motions close to the plane of the sky." +" As for 66369, we note that one of the blobs located outside its inner shell and envelope is detected in the Ha and [N ΠΠ] emission lines at the slit position #11 (Fig. 4))."," As for 6369, we note that one of the blobs located outside its inner shell and envelope is detected in the $\alpha$ and [N ] emission lines at the slit position 1 (Fig. \ref{slits.img}) )." +" This blob, at an offset of ~70” ffrom 66369 central star, has a relatively small velocity shift, ~+17 km s!, with respect to the systemic velocity, and its velocity width is small, FWHM~26kms! in Ho and c21 km s! in [N rr]."," This blob, at an offset of $\sim$ from 6369 central star, has a relatively small velocity shift, $\sim$ +17 km $^{-1}$ , with respect to the systemic velocity, and its velocity width is small, $\rm FWHM\simeq26\,km\,s^{-1}$ in $\alpha$ and $\simeq21$ km $^{-1}$ in [N ]." + 'The kinematical properties of this outer condensation make 66369 closer to the case of the lower velocity knots of 44634 thanto a case of high-velocity collimated, The kinematical properties of this outer condensation make 6369 closer to the case of the lower velocity knots of 4634 thanto a case of high-velocity collimated +We expect low-count-rate SSSs for two reasons.,We expect low-count-rate SSSs for two reasons. + First. the intrinsic SSS luminosity function of some SSSs is dominated by low-L sources.," First, the intrinsic SSS luminosity function of some SSSs is dominated by low-L sources." + The luminosity of nuclear-burning WDs. e.g.. Increases with increasing WD mass. with L nearing the Eddington limit and 47 perhaps in excess of 100 eV. as the WD mass approaches the Chandrasekhar mass.," The luminosity of nuclear-burning WDs, e.g., increases with increasing WD mass, with $L$ nearing the Eddington limit and $k\, T$ perhaps in excess of $100$ eV, as the WD mass approaches the Chandrasekhar mass." + Since. however. WDs with lower mass are more common. most nuclear-burning WDs should be less luminous.," Since, however, WDs with lower mass are more common, most nuclear-burning WDs should be less luminous." + In addition. Greiner et al. (," In addition, Greiner et al. (" +"1999) and Greiner 11999, established that there 1s a lower-luminosity extension of the class of SSSs. which presumably corresponds to nuclear-burning WDs of even lower mass than those in the systems first observed with andROSAT.","1999) and Greiner 1999, established that there is a lower-luminosity extension of the class of SSSs, which presumably corresponds to nuclear-burning WDs of even lower mass than those in the systems first observed with and." + The number of systems in our Galaxy capable of appearing as such lower-luminosity SSSs may be approximately 10.000. Second. the effects of absorption on the radiation emitted by SSSs is severe.," The number of systems in our Galaxy capable of appearing as such lower-luminosity SSSs may be approximately $10,000.$ Second, the effects of absorption on the radiation emitted by SSSs is severe." + The 18.5 ksee observation of M104 was likely to only detect those SSSs on the outer edge of the side of the disk and bulge nearest to us., The $18.5$ ksec observation of M104 was likely to only detect those SSSs on the outer edge of the side of the disk and bulge nearest to us. + In spite of the numerical dominance of the low count rate SSSs. SSSs are also well represented among the most luminous SSSs.," In spite of the numerical dominance of the low count rate SSSs, SSSs are also well represented among the most luminous SSSs." + Three of the 12 brightest M104 X-ray sources are SSSs—these include one of the brightest non-nuclear sources. X82.," Three of the $12$ brightest M104 X-ray sources are SSSs--these include one of the brightest non-nuclear sources, X82." + X82 is an SSS located in the bulge of MIOA., X82 is an SSS located in the bulge of M104. + The spectral fit is shown in Figure 3., The spectral fit is shown in Figure 3. + The spectral parameters (Table 2) are: kT2180 eV. Ly28.9<10 erg so). Nj20.925S107 em.," The spectral parameters (Table 2) are: $k\, T = 180$ eV, $L_X = 8.9 \times 10^{38}$ erg $^{-1}$, $N_H = 0.9^{+4.6}_{-0.9} \times 10^{20}$ $^{-2}$." + This fit cannot provide a unique physical interpretation., This fit cannot provide a unique physical interpretation. + It is. however. consistent with the model of an intermediate-mass BH.," It is, however, consistent with the model of an intermediate-mass BH." + Consider a geometrically thin but optically thick accretion disk. and identify the inner edge of the disk with the last stable orbit around an acecreting BH.," Consider a geometrically thin but optically thick accretion disk, and identify the inner edge of the disk with the last stable orbit around an accreting BH." + If we assume an emission efficiency of 10% (1.e.. that 10% of the rest energy of matter falling into the BH is radiated by the disk). then Por the spectral parameters derived in the fit. we find that the mass of the BH would be ~400...," If we assume an emission efficiency of $10\%$ (i.e., that $10\%$ of the rest energy of matter falling into the BH is radiated by the disk), then For the spectral parameters derived in the fit, we find that the mass of the BH would be $\sim 400\, M_\odot$." + This 1s likely to be a lower limit. since spectral hardening effects.M orientation. effects. and spin would all tend to increase the derived value of the mass.," This is likely to be a lower limit, since spectral hardening effects, orientation effects, and spin would all tend to increase the derived value of the mass." + There is a clear over density of SSSs in the region near the nucleus: 4 SSSs are located within ~1 kpe of the galaxy center. and an additional 3 SSSs are located within 1.5 kpe of the center.," There is a clear over density of SSSs in the region near the nucleus: $4$ SSSs are located within $\sim 1$ kpc of the galaxy center, and an additional $3$ SSSs are located within $1.5$ kpc of the center." + Since this places 1/3 of the SSSs in roughly 2% of the area containing SSSs. it is clear that this overdensity implies that some of these 7 SSSs are physically close to the nucleus.," Since this places $1/3$ of the SSSs in roughly $2\%$ of the area containing SSSs, it is clear that this overdensity implies that some of these $7$ SSSs are physically close to the nucleus." + In M31 there are SSSs within several parsecs of the nucleus. and members of the bulge population are among the most luminous SSSs in the galaxy.," In M31 there are SSSs within several parsecs of the nucleus, and members of the bulge population are among the most luminous SSSs in the galaxy." + While it is possible that all or most of these sources are simply descended from the stellar populations that inhabit the bulge. the presence of SSS very close to the nucleus of M31 has suggested that some bulge SSSs may be the stripped cores of stars that have been tidally disrupted by à central BH.," While it is possible that all or most of these sources are simply descended from the stellar populations that inhabit the bulge, the presence of SSS very close to the nucleus of M31 has suggested that some bulge SSSs may be the stripped cores of stars that have been tidally disrupted by a central BH." + If this is so. then galaxies with massive BHs. such as M104. with an estimated BH mass of 10°... should have a central overdensity of SSS.," If this is so, then galaxies with massive BHs, such as M104, with an estimated BH mass of $10^9 M_\odot$, should have a central overdensity of SSS." + Given the small numbers of SSSs observed near the disk. coupled with the large size of the bulge. it is difficult to definitely identify SSSs as members of a disk population.," Given the small numbers of SSSs observed near the disk, coupled with the large size of the bulge, it is difficult to definitely identify SSSs as members of a disk population." + Indeed. SSSs in or near the disk are the ones most likely to be subject to absorption.," Indeed, SSSs in or near the disk are the ones most likely to be subject to absorption." + The locations of X21 (9 counts). X37 (9 counts). ΧΕΙΘΟ (15 counts). and possibly X102 (20 counts) are consistent with membership in the disk.," The locations of X21 (9 counts), X37 (9 counts), X110 (15 counts), and possibly X102 (20 counts) are consistent with membership in the disk." + Indeed the distributions of counts in S. M. and H for at least 3 of these sources (X37. X110. and X102) would be consistent with what is expected for a highly luminous. highly absorbed source with kT~100 eV. One of the most exciting aspects of the M104 observations is that for the first time. we can unambiguously identify SSSs located out of the disk of a spiral galaxy. (," Indeed the distributions of counts in S, M, and H for at least $3$ of these sources (X37, X110, and X102) would be consistent with what is expected for a highly luminous, highly absorbed source with $k\, T \sim 100$ eV. One of the most exciting aspects of the M104 observations is that for the first time, we can unambiguously identify SSSs located out of the disk of a spiral galaxy. (" +See also eet 2003a. on M31.),"See also et 2003a, on M31.)" + The 2 softest sources. X71. and X86. are each located >4 kpe away (north and south. respectively) from the galactic disk.," The $2$ softest sources, X71, and X86, are each located $> 4$ kpc away (north and south, respectively) from the galactic disk." + Neither is associated with a known GC or with any other optical counterpart on the DSS image., Neither is associated with a known GC or with any other optical counterpart on the DSS image. + From neither source have we received photons with energies >1.1 keV. The estimated luminosity of X71 is L4«I0 erg s. while for X86 we derive 1.6«1075 erg s7!. (," From neither source have we received photons with energies $> 1.1$ keV. The estimated luminosity of X71 is $1.4 \times 10^{37}$ erg $^{-1}$, while for X86 we derive $1.6 \times 10^{38}$ erg $^{-1}$. (" +These estimates use a model with kT=125 eV and Nj25«10°? em.),"These estimates use a model with $k\, T = 125$ eV and $N_H = 5 \times 10^{20}$ $^{-2}$ .)" + If these are not foreground or background objects. they may be good candidates for the NBWD model.," If these are not foreground or background objects, they may be good candidates for the NBWD model." + Since such systems should not have experienced prior supernova explosions. they are unlikely to have been ejected from the disk.," Since such systems should not have experienced prior supernova explosions, they are unlikely to have been ejected from the disk." + They are therefore likely descendants of an old halo stellar population., They are therefore likely descendants of an old halo stellar population. + A particularly interesting SSS is X35. which ts ina GC. (," A particularly interesting SSS is X35, which is in a GC. (" +From its position alone. it could be part of the bulge or halo.),"From its position alone, it could be part of the bulge or halo.)" + This source does emit photons between 1.1 and 2 keV. The source properties are consistent with those of a BH accretor with mass equal to 50M (See equation (2))., This source does emit photons between 1.1 and 2 keV. The source properties are consistent with those of a BH accretor with mass equal to $\sim 50 M_\odot$ (See equation (2)). + This is similar to the situation we have ..found in NGC 4472. where at least 5 SSSs are associated with GCs. several amenable to a similar interpretation (Friedman et al.," This is similar to the situation we have found in NGC 4472, where at least $5$ SSSs are associated with GCs, several amenable to a similar interpretation (Friedman et al." + 2002. eet 2003b).," 2002, et 2003b)." + In the region covered by the $3 CCD. 249 PNe have been identified.," In the region covered by the S3 CCD, $249$ PNe have been identified." + None of these is near enough to an X-ray source to suggest a physical association., None of these is near enough to an X-ray source to suggest a physical association. + The fact that no PNe are associated with SSSs is interesting., The fact that no PNe are associated with SSSs is interesting. + Because SSSs emit highly ionizing radiation., Because SSSs emit highly ionizing radiation. + Indeed. one SSS in the Magellanic Clouds is a PN (Wang 1991).," Indeed, one SSS in the Magellanic Clouds is a PN (Wang 1991)." + SSSs that are binary systems can ionize the interstellar medium in which they are embedded., SSSs that are binary systems can ionize the interstellar medium in which they are embedded. + Those located in regions in which the ISM has a density greater than ~| atom em. can create circumstellar ionization nebulae with very large (radiation-limited) radii (>10 pe) (Rappaport et al.," Those located in regions in which the ISM has a density greater than $\sim 1$ atom $^{-3}$ , can create circumstellar ionization nebulae with very large (radiation-limited) radii $>10$ pc) (Rappaport et al." + 1994)., 1994). + CAL 83. located in the Magellanic Clouds 1s embedded in such a nebula (Remillard. Rappaport. Maeri 1995).," CAL 83, located in the Magellanic Clouds is embedded in such a nebula (Remillard, Rappaport, Macri 1995)." + With two of twelve Magellanic Cloud SSSs associated with nebulae. and with ~1000 SSSs predicted in galaxies such as ΜΟΙ. we might expect there to be dozens of such associations.," With two of twelve Magellanic Cloud SSSs associated with nebulae, and with $\sim 1000$ SSSs predicted in galaxies such as M31, we might expect there to be dozens of such associations." + The nebulae could be and would likely be included among PNe lists by surveys using the methodology Ford et al (1996) used to identify PNe in M104Stefano. Paerels. Rappaport 1995).," The nebulae could be and would likely be included among PNe lists by surveys using the methodology Ford et al (1996) used to identify PNe in M104, Paerels, Rappaport 1995)." + Because only a small fraction of all SSSs can be detected. the number of observable PN/SSS may be only 1—10% of the number of physical associations.," Because only a small fraction of all SSSs can be detected, the number of observable PN/SSS may be only $1-10\%$ of the number of physical associations." + We might expect some matches for M104Stefano. Paerels. Rappaport 1995).," We might expect some matches for M104, Paerels, Rappaport 1995)." + The laek of anysuch associations may mean that SSSs are, The lack of anysuch associations may mean that SSSs are +,reaction. +," The error in 3 is also due to BBN uncertainties, in this case the $d(p,\gamma)\he3$ and $\he3(d,p)\he4$ reactions dominate the uncertainty." +," About half of the uncertainty in the CMB + BBN prediction of D is due to BBN errors, where again $d(p,\gamma)\he3$ is important, as well as $p(n,\gamma)d$ and $d(d,n)\he3$." +," We encourage intensified efforts to obtain high-precision measurements of these reactions, and their uncertainties." +," In closing, it is impressive that our now-exquisite understanding of the universe at $z \sim 1000$ also confirms our understanding of the universe at $z \sim 10^{10}$." +," This agreement lends great confidence in the soundness of the hot big bang cosmology, and impels our search deeper into the early universe." +," We thank Benjamin Wandelt for helpful conversations, and Ken Nollett for useful discussions regarding the differences between our BBN predictions." +, The work of K.A.O. was partially supported by DOE grant DE–FG02–94ER–40823. +, The work of B.D.F. and R.H.C. was supported by the National Science Foundation under grant AST-0092939. + , +order of magnitude more luminous than the bright resolved RSN in the nearby starburst ealaxyv M82 (see next subsection).,order of magnitude more luminous than the bright resolved RSN in the nearby starburst galaxy M82 (see next subsection). + The most plausible interpretation is that all the detectable sources in Arp 220 are voung. and consequently buminous.," The most plausible interpretation is that all the detectable sources in Arp 220 are young, and consequently luminous." + Given the apparent rate of appearance of new sources. and (he total number of sources detected. the turnover rate of sources in a uniform population would imply that the oldest objects are likely to be al most a few decades old.," Given the apparent rate of appearance of new sources, and the total number of sources detected, the turnover rate of sources in a uniform population would imply that the oldest objects are likely to be at most a few decades old." + However. the population is clearly heterogeneous. aud there is evidence that the brighter sources tend to decay slowly.," However, the population is clearly heterogeneous, and there is evidence that the brighter sources tend to decay slowly." + More information is needed in order to reliably estimate ages., More information is needed in order to reliably estimate ages. + Recently. our team has detected several of the point sources al 2.3. 5 and 8.4 GlIIz (Conway et al. in prep): preliminary. analvsis indicates (hat they exhibit a range of spectral indices. from flat to steep.," Recently, our team has detected several of the point sources at 2.3, 5 and 8.4 GHz (Conway et al, in prep); preliminary analysis indicates that they exhibit a range of spectral indices, from flat to steep." + Further analvsis and interpretation will be provided in the forthcoming paper., Further analysis and interpretation will be provided in the forthcoming paper. + In the absence of external free-Iree absorption. RSN which are no longer in the rising phase al 15011 are expected to exhibit steep spectra characteristic of optically {hin svnchrotron emission.," In the absence of external free-free absorption, RSN which are no longer in the rising phase at 18cm are expected to exhibit steep spectra characteristic of optically thin synchrotron emission." + There is considerable evidence. however. for significant [ree-[ree optical cepts at 18cm in Che nuclei of powerful ULIRGs (e.g. Condon et al.," There is considerable evidence, however, for significant free-free optical depths at 18cm in the nuclei of powerful ULIRGs (e.g. Condon et al." + 1991). which would likely manifest itself as spatially correlated fLIattening of RSN spectra across regions of ihe Arp 220 nuclei.," 1991), which would likely manifest itself as spatially correlated flattening of RSN spectra across regions of the Arp 220 nuclei." +" Any interpretation of the star-forming environment in the nuclei. based on our 18cenronlv RSN measurements. must take into account (he possibility. that radio luminosities, RSN counts. and rates of new source appearances may all be underestimatec."," Any interpretation of the star-forming environment in the nuclei, based on our 18cm-only RSN measurements, must take into account the possibility that radio luminosities, RSN counts, and rates of new source appearances may all be underestimated." +" The (wo nuclei of Arp 220. though strikinely similar in many properties (numerous Πρ, strong compact OII meeamaser emission. strong diffuse continuum emission). display differimg properties wilh regard to (he point sources."," The two nuclei of Arp 220, though strikingly similar in many properties (numerous RSN, strong compact OH megamaser emission, strong diffuse continuum emission), display differing properties with regard to the point sources." + The (wo principal differences are: (a) the point sources are svstematically stronger in the west (ie. the Iumninosity. Iunctions are different as can be seen in Figure 3): and. (b) the sources are confined to a somewhat more compact region in the west.," The two principal differences are: (a) the point sources are systematically stronger in the west (i.e. the luminosity functions are different as can be seen in Figure 3); and, (b) the sources are confined to a somewhat more compact region in the west." + We can quantilv the difference in Iuminositv functions by applving a Ixolmogorov-Smirnov test to the thax density data., We can quantify the difference in luminosity functions by applying a Kolmogorov-Smirnov test to the flux density data. + A simple comparison vields a probability of 0.001 that the samples are drawn Irom the same population. primarily due to ihe much higher mean flux density in the west.," A simple comparison yields a probability of 0.001 that the samples are drawn from the same population, primarily due to the much higher mean flux density in the west." + An obvious hypothesis to explain this result is that the eastern nucleus population is just a lainter replica of that in the west., An obvious hypothesis to explain this result is that the eastern nucleus population is just a fainter replica of that in the west. + A simple model relating expected RSN luminosities to (he far intrarecl luminosity can be constructed. using a/? decay profile where 5=1.3 (Smith οἱ al.," A simple model relating expected RSN luminosities to the far infrared luminosity can be constructed, using a $t^{-\gamma}$ decay profile where $\gamma = 1.3$ (Smith et al." +" 1998a.b). and translating Zj;, into a relative star formation rate and hence a supernova. rate."," 1998a,b), and translating $L_{fir}$ into a relative star formation rate and hence a supernova rate." +" This leads to mean RSNages proportional to Ll. and RSN fluxes S44,x Ly."," This leads to mean RSNages proportional to $L_{fir}^{-1}$ , and RSN fluxes $S_{rsn} \propto +L_{fir}^{\gamma}$ ." + The, The +and the bolometric off-peaks huminositv of COM J1911—5958A. This implies that the modulation due to the heating effect (A(mag)=2.5log[1+(9/2)(£3/£1)]. where 7<1 is the elliciency of the process) should be negligible (AGuag)©0.001) and in fact no flix enhancement is detected around phase 0.75. when (he side of the companion facing (he pulsar is visible.,"and the bolometric off-peaks luminosity of COM $-$ 5958A. This implies that the modulation due to the heating effect $\Delta{\rm +(mag)}=2.5\log[1+(\eta/2)(\xi_2/\xi_1^2)]$ , where $\eta<1$ is the efficiency of the process) should be negligible $\Delta{\rm +(mag)}\lapp 0.001$ ) and in fact no flux enhancement is detected around phase 0.75, when the side of the companion facing the pulsar is visible." + Ellipsoidal variations due to the tidal deformation of the companion are known to produce a lisht curve wilh two peaks at quadratures (see for example the case of PSR J1140—5340 in NGC 6397. Ferraro et al.," Ellipsoidal variations due to the tidal deformation of the companion are known to produce a light curve with two peaks at quadratures (see for example the case of PSR $-$ 5340 in NGC 6397, Ferraro et al." + 2001). but the light curve is expected to have maxima of equal amplitude aud clear minima (of unequal depth) al conjunctions.," 2001), but the light curve is expected to have maxima of equal amplitude and clear minima (of unequal depth) at conjunctions." + Moreover. tidal deformations are expected to be insignificant for a companion whose radius is ~20 {imes smaller than the radius of its Roche lobe.," Moreover, tidal deformations are expected to be insignificant for a companion whose radius is $\sim 20$ times smaller than the radius of its Roche lobe." + Accretion of matter onto a compact object can generate a varietv of modulated optical emission (e.g. Frank. Ning Raine 2002). but neither the neutron star nor the Ile-WD in this svslem can be suitable sources of plasma [feeding accretion-related. processes al the present epoch.," Accretion of matter onto a compact object can generate a variety of modulated optical emission (e.g. Frank, King Raine 2002), but neither the neutron star nor the He-WD in this system can be suitable sources of plasma feeding accretion-related processes at the present epoch." + The timing stability and the extension of the time span of the radio observations of (Corongiu et al., The timing stability and the extension of the time span of the radio observations of (Corongiu et al. + 2006) tend also to exclude the existence of a residual accretion disk around the pulsar or the presence of a third optically faint body which is now pouring mass in the binary., 2006) tend also to exclude the existence of a residual accretion disk around the pulsar or the presence of a third optically faint body which is now pouring mass in the binary. +" One may wonder if the optical modulation can be intrinsic to (the ΠοΑΕ,", One may wonder if the optical modulation can be intrinsic to the He-WD. + Non-radial pulsations of WDs can produce optical [uctuations at a level of ~0.2 mag. but for a star with Zurse11.000A the expected modulation occurs at periods significantly shorter (han 0.84 days (e.g. Bergeron οἱ al.," Non-radial pulsations of WDs can produce optical fluctuations at a level of $\sim 0.2$ mag, but for a star with $T_{\rm eff}\approx +11,000~K$ the expected modulation occurs at periods significantly shorter than 0.84 days (e.g. Bergeron et al." + 2004)., 2004). + However. a few high magnetic field (105 G) isolated WDs (see e.g. PG 10314-234. Piirola Reiz 1992. and EUVE J0317—855. Barstow et al.," However, a few high magnetic field $\sim 10^8$ G) isolated WDs (see e.g. PG 1031+234, Piirola Reiz 1992, and EUVE $-$ 855, Barstow et al." + 1995) display variations of ©0.3 mag at the supposed rotational period of the star., 1995) display variations of $\lapp 0.3$ mag at the supposed rotational period of the star. + In the framework of an oblique rotator model for the WD. these photometric modulations have been interpreted with changes with (he rotational phase of the mean magnetic field streneht over (he visible stellar surface (which in turn affects Che opacity along the line of sight: Ferrario et al.," In the framework of an oblique rotator model for the WD, these photometric modulations have been interpreted with changes with the rotational phase of the mean magnetic field strenght over the visible stellar surface (which in turn affects the opacity along the line of sight: Ferrario et al." + 1997)., 1997). + A suitable geometry. (leading to an alternate exposure of both the magnetic polar caps of the WD) maa in principle produce a double peaked lisht curve. but we note that all the aforementionedeffects have been observed. only in relatively massive," A suitable geometry (leading to an alternate exposure of both the magnetic polar caps of the WD) may in principle produce a double peaked light curve, but we note that all the aforementionedeffects have been observed only in relatively massive" +The infrared surface brightness method is a modification of the visual surface brightness technique developed bv Barnes et al. (,The infrared surface brightness method is a modification of the visual surface brightness technique developed by Barnes et al. ( +1977). and thus shares the same computational aleorithm.,1977) and thus shares the same computational algorithm. + Because solution of the equations is (he important issue. we introduce (he equations in some detail.," Because solution of the equations is the important issue, we introduce the equations in some detail." + Useful discussions of previous work have been given by Gieren. Barnes Alolfett. (1993). Fouqué Gieren (1997). Norderen et al. (," Useful discussions of previous work have been given by Gieren, Barnes Moffett (1993), Fouqué Gieren (1997), Nordgren et al. (" +2002). Foueué.. Storm. Gieren (2003). ancl Barnes et al. (,"2002), Fouqué,, Storm, Gieren (2003), and Barnes et al. (" +2003).,2003). +" Barnes Evans (1976). and Barnes. Evans. Parsons (1976). defined a visual surface brightness parameter Fy as and also as. where V, is the stellar visual magnitude corrected. [or interstellar extinction. o is the stellar angular ciameter expressed in milliarcseconds. 7; is (he elfective temperature and BC is the bolometrie correction."," Barnes Evans (1976) and Barnes, Evans, Parsons (1976) defined a visual surface brightness parameter $F_V$ as and also as, where $V{\rm _0}$ is the stellar visual magnitude corrected for interstellar extinction, $\phi$ is the stellar angular diameter expressed in milliarcseconds, $T_e$ is the effective temperature and $BC$ is the bolometric correction." +" They demonstrated (hat Fi is well correlated with Johnson color index (V.—HR), lor a very wide range of stellar tvpes.", They demonstrated that $F_V$ is well correlated with Johnson color index $(V-R){\rm _0}$ for a very wide range of stellar types. + equation (3)) is called the visual surface brightness relation., equation \ref{eq:basiceq}) ) is called the visual surface brightness relation. + These relations led Barnes et al. (, These relations led Barnes et al. ( +LOTT) to infer a clistance scale lor Cepheids as follows.,1977) to infer a distance scale for Cepheids as follows. +" At each time /in the pulsation of the Cepheid. equations (1)) ancl (3)) may be combined to obtain the angular diameter variation of the star. o(/). In addition we infer the Cepheid's linear radius variation A2) about the mean radius from an integration of the radial velocity curve. V, (4)."," At each time $t$in the pulsation of the Cepheid, equations \ref{eq:fparameter}) ) and \ref{eq:basiceq}) ) may be combined to obtain the angular diameter variation of the star, $\phi(t)$, In addition we infer the Cepheid's linear radius variation ${\Delta}R(t)$ about the mean radius from an integration of the radial velocity curve, $V_r(t)$ ," +the solution for each chip nailed down. we fouud the global linear parameters that mapped both chips iuto a convenient ineta-chip reference frame.,"the solution for each chip nailed down, we found the global linear parameters that mapped both chips into a convenient meta-chip reference frame." +" Iu Paper I we derived a 3""Lorder polynomial solution for the GD for filters F225W. E275W aud F336W: bere our ait iu this section is to obtain the polyuouial solution for seven other filters for which suitable observations are available. namely: F390W. ΕΩΡΑ, F252W. F606W. ETTSW. ΕΡΤΙΑΝ aud FSSOLP."," In Paper I we derived a $^{\rm rd}$ -order polynomial solution for the GD for filters F225W, F275W and F336W; here our aim in this section is to obtain the polynomial solution for seven other broad-band filters for which suitable observations are available, namely: F390W, F438W, F555W, F606W, F775W, F814W and F850LP." + Whereas in Paper I we had to use au astrometric reference catalog that was taken several years prior in order to extract the CD solutiou. we cau now perform a sell-calibratiou of the GD thanks to the improvect uumber of images at differeut roll angles offered by the new data set.," Whereas in Paper I we had to use an astrometric reference catalog that was taken several years prior in order to extract the GD solution, we can now perform a self-calibration of the GD thanks to the improved number of images at different roll angles offered by the new data set." + Sell-calibratious can often be more accurate thau calibratious that reference a staudard field. since stars in standard fields cau move due to proper motious aud since the brightuess rauge where stars in the catalog are well measured nay uot correspond to the brightuess[n] range where stars in the calibration exposures are well measured.," Self-calibrations can often be more accurate than calibrations that reference a standard field, since stars in standard fields can move due to proper motions and since the brightness range where stars in the catalog are well measured may not correspond to the brightness range where stars in the calibration exposures are well measured." + Furthermore. the images may have different. crowding issues aud measurement qualities [rom the catalog.," Furthermore, the images may have different crowding issues and measurement qualities from the catalog." + We followed the prescriptions given in Auderson Wine (2003) for WEPC2 aud subsequentLy used by the same authors to derive the GD correction for the ACS/HRC (Anderson Wing 2001) aud for the ACS/WEC (AWKOG)., We followed the prescriptions given in Anderson King (2003) for WFPC2 and subsequently used by the same authors to derive the GD correction for the ACS/HRC (Anderson King 2004) and for the ACS/WFC (AK06). + The same strategy was also used by two of us to calibrate a erouncd-based instriuneut (see Bellini Bedin 2010 for details)., The same strategy was also used by two of us to calibrate a ground-based instrument (see Bellini Bedin 2010 for details). + Briefly. we started with the F336W CD-solution of Paper Las first guess to correct star posltious for the seven recward of FB36W (from F390W to FSSOLP) aud created a master frame for each filter tudepenclently.," Briefly, we started with the F336W GD-solution of Paper I as first guess to correct star positions for the seven redward of F336W (from F390W to F850LP) and created a master frame for each filter independently." + We then performed the iterative procedure described in Paper [to improve the polynomial coefficients., We then performed the iterative procedure described in Paper I to improve the polynomial coefficients. + With a better GD solution. we then re-coustructed the master frames aud repeated the entire process three times.," With a better GD solution, we then re-constructed the master frames and repeated the entire process three times." + A lourth repetition of the procedure provided. negligible improvement., A fourth repetition of the procedure provided negligible improvement. + The 3-order polynomial coellicients for all LO of the broad-band filters are, The $^{\rm rd}$ -order polynomial coefficients for all 10 of the broad-band filters are +"model we used was the standard model. A. from Ford.etal.(2003).. that is. C—I. A,/Ny25.6x10magen? and M—3x10M,vr.","model we used was the standard model, A, from \citet{for03}, that is, $G_0=1$ , $A_v/N_H=5.6\times 10^{-22}\,{\rm mag\, cm^{2}}$ and $\dot M = 3 \times 10^{-5}\, {\rm M_{\odot}\, yr^{-1}}$." +| Given a spatial distribution for the formaldehyde. we can caleulate (he excitation conditions ol the molecule and the line strengths of various transitions.," Given a spatial distribution for the formaldehyde, we can calculate the excitation conditions of the molecule and the line strengths of various transitions." + For these caleulations. we enmploved the Large Velocity Gradient (LVG) code of Neuleld&Παππάς(1993).," For these calculations, we employed the Large Velocity Gradient (LVG) code of \citet{NK93}." +. The LVG code uses the escape probability method to solve the equations of statistical equilibrium for the energy. levels of formaldehyde., The LVG code uses the escape probability method to solve the equations of statistical equilibrium for the energy levels of formaldehyde. + We used the same parameters for the cireumstellar conditions as Melnicketal.(2001).. listed here in Table 6..," We used the same parameters for the circumstellar conditions as \citet{mel01}, listed here in Table \ref{CSEparams}." + We obtained the formaldehyde Linstein-À coefficients and the οποιον levels from Jaruschewskiοἱal.(1986)... ancl the collisional coefficients Irom Green(1991).," We obtained the formaldehyde Einstein-A coefficients and the energy levels from \citet{jar86}, and the collisional coefficients from \citet{gre91}." +. Given an assumed abundance and spatial distribution for formaldehyde. the LVG program caleulates both the total line strength for various transitions. ancl (for each transition) the amount of line Iuminosity. dL. produced in a given radial interval. dr. as a funetion of r. where r is the astrocentrie radius.," Given an assumed abundance and spatial distribution for formaldehyde, the LVG program calculates both the total line strength for various transitions, and (for each transition) the amount of line luminosity, $dL$, produced in a given radial interval, $dr$, as a function of $r$, where $r$ is the astrocentric radius." + We have a third program which uses the tabulated 4L(r)/dr to caleulate the Formaldehyde line strength and shape after convolution with the telescope beam and Gaussian microturbulence., We have a third program which uses the tabulated $dL(r)/dr$ to calculate the formaldehyde line strength and shape after convolution with the telescope beam and Gaussian microturbulence. +" The IRAM 30m telescope has a frequenev-dependent. ZPDW of 17"" at 1H0 GlIz (near the 24»—ly transition of formaldehyde). 16"" at 150 GIIz (near the 244—ly transition of formaldehyde) and 10"" around 240 Gllz."," The IRAM 30m telescope has a frequency-dependent $HPBW$ of $17\arcsec$ at $140\,$ GHz (near the $2_{12}-1_{11}\>$ transition of formaldehyde), $16\arcsec$ at $150\,$ GHz (near the $2_{11}-1_{10}\>$ transition of formaldehyde) and $10\arcsec$ around $240\,$ GHz." + The convolution program is similar to the line shape program of Fordetal.(2003).. except that this program also allows calculations of lime streneths al offset. positions.," The convolution program is similar to the line shape program of \citet{for03}, except that this program also allows calculations of line strengths at offset positions." + We can compare the output of the convolution program directly to our observations., We can compare the output of the convolution program directly to our observations. +" In comparing our models wil our observations. we will rely primarily on the 150.495 Gllz 24,—ly transition of formaldehyde. [ον reasons we detail below."," In comparing our models with our observations, we will rely primarily on the $150.498\,$ GHz $2_{11}-1_{10}\>$ transition of formaldehyde, for reasons we detail below." + In order to accurately determine the abundance of formaldehyde around IRC+10216. we must first determine its radial distribution. since any abundance determination will depend on the excitation conditions of formaldehyde. which in turn depends on formaldehyde's radial distribution.," In order to accurately determine the abundance of formaldehyde around IRC+10216, we must first determine its radial distribution, since any abundance determination will depend on the excitation conditions of formaldehyde, which in turn depends on formaldehyde's radial distribution." + Fortunately. our offset observations are ideally suited to distinguishing whether formaldehyde has a compact or extended source in IRC+10216.," Fortunately, our offset observations are ideally suited to distinguishing whether formaldehyde has a compact or extended source in IRC+10216." +" We find. based on our ""average off-center position”. that the ratio of (f T\dejoyp. the integrated antenna temperature at the position. ΜΕ the integrated antenna temperature at the central position is 0.40£0.03 at the 150.498 GIIz 24,—lag transition and0.51+0.02 at the 140.840 GiTIz 245—144 Uransition."," We find, based on our “average off-center position”, that the ratio of $(\int T_A^*dv)_{off}$ , the integrated antenna temperature at the off-center position, to $(\int T_A^*dv)_{cent}$, the integrated antenna temperature at the central position is $0.40 \pm 0.03$ at the $150.498\,$ GHz $2_{11}-1_{10}\>$ transition and$0.51 \pm 0.02$ at the $140.840\,$ GHz $2_{12}-1_{11}\>$ transition." + Here we are quoting statistical errors only (lo). and we point out that the 215—144 Uransitionmay be partly contaminated by (he CsI doublet.," Here we are quoting statistical errors only $1\sigma$ ), and we point out that the $2_{12}-1_{11}\>$ transitionmay be partly contaminated by the $_5$ H doublet." + The contamination from, The contamination from +l.,1. + This procedure vields he set of 14 WB tracks that we have used to compute the imteerated spectra., This procedure yields the set of 14 HB tracks that we have used to compute the integrated spectra. + The niasses of these interpolated tracks together with their corresponding ZAIID effective temperatures are eiven in columus (2) aud (1) of Table 1., The masses of these interpolated tracks together with their corresponding ZAHB effective temperatures are given in columns (2) and (4) of Table 1. + The relative wmmber of UB stars at cach mass. as taken from the nass distribution iu Fig.," The relative number of HB stars at each mass, as taken from the mass distribution in Fig." +e.oO la of DDDE. is iudicaed by the quantity iii column (3|.," 4a of DDDF, is indicated by the quantity $n$ in column (3)." + Since the location of a star along its IID track is uot known a priori. we wave decided to represcut contribution of the ΠΟ stars of a particular mass to integrated spectrum by averaging their spectra over IIB phase.," Since the location of a star along its HB track is not known a priori, we have decided to represent the contribution of the HB stars of a particular mass to the integrated spectrum by averaging their spectra over the HB phase." + To do lis. we first convert cach TB track iuto a probability diagram. by dividing the IIR. diagram iuto cells of (Alogy. A Tig) iu the surface eravity aud effective temperature.," To do this, we first convert each HB track into a probability diagram by dividing the HR diagram into cells of $\Delta \log g$, $\Delta$ ) in the surface gravity and effective temperature." + Each cell / is assigned a weight equal to time spent in that particular cell Ar; inultiplied. by corresponding bolometric huninosity L;., Each cell $i$ is assigned a weight equal to the time spent in that particular cell $\Delta \tau _{i}$ multiplied by the corresponding bolometric luminosity $L_{i}$. + The weight thus provides the contribution of cach cell to the total fiux enütted by stars on that track., The weight thus provides the contribution of each cell to the total flux emitted by stars on that track. + If the track is sulxivi iuto v cells. the average light. L4;(A) at the waveleneth A. enmütted bv a star of lass AM in the IID phase is given by: where πΕΠΑ) is the monochromatic flux. aud oTAy; is the bolometric dux of cell /..," If the track is subdivided into $n$ cells, the average light, $_{M}(\lambda)$ at the wavelength $\lambda$, emitted by a star of mass $M$ in the HB phase is given by: where $\pi F_{i} (\lambda)$ is the monochromatic flux, and $\sigma {\rm T}_{{\rm eff},i}^{4}$ is the bolometric flux of cell $i$ ." +" The integrated light £(À ) from a stellar system with a nass distribution Nay is then the weighted stun of these contributions: where Na, is the wmuber of IID stars with mass M. aud Soy,Nay is the total umuber of ITB stars iu the ITUT slit."," The integrated light $L$ $\lambda$ ) from a stellar system with a mass distribution $N_M$ is then the weighted sum of these contributions: where $N_M$ is the number of HB stars with mass $M$, and ${\sum_MN_M}$ is the total number of HB stars in the HUT slit." + The sunmunation is taken over the range from 0.5001. ((ZATIB ~ 20.500 IS) to 0.6639 (ZAIB σε &.000 Is). as listed in Table 1.," The summation is taken over the range from 0.5001 (ZAHB $\simeq$ 29,500 K) to 0.6639 (ZAHB $\simeq$ 8,000 K), as listed in Table 1." + Table 1 also gives the time averaged values ofTi4.. logg. aud £ along cach track.," Table 1 also gives the time averaged values of, $\log g$, and $L$ along each track." + The probability diagrams cover the range in logy from 3.0 to 5.5 in steps of 0.5 dex and the range in roni 8.000 to 35.000 Ix. The step size in Zig depended ou he temperature as follows: ATi == 500Ix for 8.000 Ix <Των 13.000 I: 1.000 Is for 13.000 It $ 35,000 K (see later)." + This predictive approach will not work for the post-IID stars because there are so few of them., This predictive approach will not work for the post-HB stars because there are so few of them. + The IB litetime is 5ο]0) Alvr compared to a xost-IID. litetimie of 15-20 Myr so bv time-scale arguimeuts. there should be only 3-6 post-OB stars present oein the IIUT slit.," The HB lifetime is $\approx$ 100 Myr compared to a post-HB lifetime of 15-20 Myr, so by time-scale arguments, there should be only 3-6 post-HB stars present in the HUT slit." + Even though he post-IID. stars may be few in nuniber. they caunot v0 Jenored because of their high hunuinosities - up to an order of maegnitude brighter than the IIB stars (Fig.," Even though the post-HB stars may be few in number, they cannot be ignored because of their high luminosities - up to an order of magnitude brighter than the HB stars (Fig." + 1)., 1). + Compounding the problem is the fact that the post-IID ghase is a tumultuous iue. m which a sar traverses a arge area ofthe TR diagram as it undergoes nuucrous Te Hashes.," Compounding the problem is the fact that the post-HB phase is a tumultuous time, in which a star traverses a large area of the HR diagram as it undergoes numerous He flashes." + Since it is impossible to predict the most probable ocations of the vost-B stars. we let the observed WUT spectrum itsef euide our selection of canclidae post-IID stars.," Since it is impossible to predict the most probable locations of the post-HB stars, we let the observed HUT spectrum itself guide our selection of candidate post-HB stars." + That is. we first model the contribution of the IID stars. which are nuucerous enough that they cau be treated in a statistical fashion.," That is, we first model the contribution of the HB stars, which are numerous enough that they can be treated in a statistical fashion." + We then use the residual between the observed spectriuui aud the WB component to ascertain the propertics of the remaining stars., We then use the residual between the observed spectrum and the HB component to ascertain the properties of the remaining stars. + We used IJurucz (1993) LTE model atmospheres for logZ/Z. = -l.5 aud the spectrum svutlesis code. SYNSPEC (Παρα oet al.," We used Kurucz' (1993) LTE model atmospheres for $\log Z/\zsun$ = -1.5 and the spectrum synthesis code, SYNSPEC (Hubeny et al." + 1991) to Senerate the theoretical spectra. TFA).," 1994) to generate the theoretical spectra, $\pi F(\lambda )$." + In the spectrum svutlesis. the metal abundances were scaled to aloeZ/Z..=1.53 with a 0.1 dexenhancement of à process elements (Q. Ne. Me. Si. S. Ca. and Ti) ," In the spectrum synthesis, the metal abundances were scaled to a $\log Z/\zsun = -1.53$ with a 0.4 dexenhancement of $\alpha-$ process elements (O, Ne, Mg, Si, S, Ca, and Ti) ." +A anicroturbulent velocity. e;= 2kmn/s was adopted. consistent with the," A microturbulent velocity, $v_{{\rm t}}=2$ km/s was adopted, consistent with the" +indicate in both the maximum density over all times and the mean of the time-dependent maximum density.,indicate in both the maximum density over all times and the mean of the time-dependent maximum density. + The maximum scale-dependent density in NS simulations is very similar at 64? and at 128°., The maximum scale-dependent density in NS simulations is very similar at $64^3$ and at $128^3$. + This quantity is nevertheless very sensitive to the low-number statistics of the concentration events., This quantity is nevertheless very sensitive to the low-number statistics of the concentration events. + A more robust measure is the mean of the maximum density., A more robust measure is the mean of the maximum density. + This measure increases somewhat from 64? to 1283., This measure increases somewhat from $64^3$ to $128^3$. + It is also evident from that major concentration events have a higher temporal filling factor at 128°., It is also evident from that major concentration events have a higher temporal filling factor at $128^3$. + Whether this is intrinsic to the streaming instability dynamics or just an effect of running simulations for too short time is not possible to discern., Whether this is intrinsic to the streaming instability dynamics or just an effect of running simulations for too short time is not possible to discern. + The apparent linear decrease of logarithmic density with logarithmic scale implies max(pp)οςL* as a good model for the scale-dependence of the maximum density., The apparent linear decrease of logarithmic density with logarithmic scale implies ${\rm max}(\rho_{\rm p}) \propto L^{-\alpha}$ as a good model for the scale-dependence of the maximum density. + Two limits can immediately be put on a., Two limits can immediately be put on $\alpha$. +" The lowest value would stem from a razor-thin particle mid-plane layer of uniform density, with M«L?’, giving max(pp)«M/D?οL'! and thus a=1."," The lowest value would stem from a razor-thin particle mid-plane layer of uniform density, with $M \propto L^2$, giving ${\rm max}(\rho_{\rm p}) +\propto M/L^3 \propto L^{-1}$ and thus $\alpha=1$." + Concentration of all particles in a single point would yield the upper limit of a=3., Concentration of all particles in a single point would yield the upper limit of $\alpha=3$. +" We overplot in with a thin black line the power law max(oy)οςL, fitted to match the mean density of the box at L=0.2H."," We overplot in with a thin black line the power law ${\rm +max}(\rho_{\rm p}) \propto L^{-2}$, fitted to match the mean density of the box at $L=0.2 H$." + The α=2 power law follows the data extremely well., The $\alpha=2$ power law follows the data extremely well. +" This implies that M«L, tthat the particles primarily concentrate either in 1-D filaments or in spherically symmetric clouds of density p(r)ος1/17, known in star formation as the singular isothermal spheresolution (e.g.Shu, 1977)."," This implies that $M \propto L$, that the particles primarily concentrate either in 1-D filaments or in spherically symmetric clouds of density $\rho(r) +\propto 1/r^2$, known in star formation as the singular isothermal spheresolution \citep[e.g.][]{Shu1977}." +. In we show the particle density around the densest grid point in SI128.ee0.3.NNS at t=327.," In we show the particle density around the densest grid point in NS at $t=32 +T_{\rm orb}$." + The overdense structure appears elongated along the y-direction with the density falling rapidly towards all directions (although slower along y)., The overdense structure appears elongated along the $y$ -direction with the density falling rapidly towards all directions (although slower along $y$ ). +" Simulations without collisions (bottom panel of 9)) show similar trends as the simulations with NS collisions, but there is a marked decrease in the maximum density over the smallest shared scale between 64? and 1283."," Simulations without collisions (bottom panel of ) show similar trends as the simulations with NS collisions, but there is a marked decrease in the maximum density over the smallest shared scale between $64^3$ and $128^3$." + Nevertheless the mean of the maximum density agrees between the two resolutions., Nevertheless the mean of the maximum density agrees between the two resolutions. + The convergence in scale-dependent maximum density shows that the dynamics of the streaming instability concentration events is well-resolved and independent of dissipation scale and viscosity., The convergence in scale-dependent maximum density shows that the dynamics of the streaming instability concentration events is well-resolved and independent of dissipation scale and viscosity. +" This is in contrast to turbulent concentration in driven isotropic turbulence which, for a given particle size, appears on lengthscales that are fixed relative tothe Kolmogorov (viscous) scale (Hogan&Cuzzi,2007;Panetal.,2011)."," This is in contrast to turbulent concentration in driven isotropic turbulence which, for a given particle size, appears on lengthscales that are fixed relative tothe Kolmogorov (viscous) scale \citep{HoganCuzzi2007,Pan+etal2011}." +. In contrast the streaming instability is fixed relative to the sub-Keplerian scale nr~0.05H., In contrast the streaming instability is fixed relative to the sub-Keplerian scale $\eta r\sim0.05 H$. +" At €~0.0016H, probed only at 128?, the maximum density in simulations with NS collisions reaches more than three thousand times the gas density."," At $\ell \sim 0.0016 H$, probed only at $128^3$, the maximum density in simulations with NS collisions reaches more than three thousand times the gas density." +" Higher resolution simulations will be needed to test if the particle density continues to follow the max(py)οςL? trend, or eventually finds a smallest scale."," Higher resolution simulations will be needed to test if the particle density continues to follow the ${\rm max}(\rho_{\rm p})\propto L^{-2}$ trend, or eventually finds a smallest scale." + The 2-D streaming instability simulations of Bai&Stone(2010a) converged in density statistics at between 512? and 1024? grid cells., The 2-D streaming instability simulations of \cite{BaiStone2010a} converged in density statistics at between $512^2$ and $1024^2$ grid cells. +" Reaching those resolutions in 3-D is very computationally demanding, but should be an important priority for the future."," Reaching those resolutions in 3-D is very computationally demanding, but should be an important priority for the future." +" The gravitational potential field of the particles is found by mapping the particle density on the grid, using a second order spline interpolation scheme, and solving the Poisson equation using a fast Fourier transform method (Johansenetal., 2007)."," The gravitational potential field of the particles is found by mapping the particle density on the grid, using a second order spline interpolation scheme, and solving the Poisson equation using a fast Fourier transform method \citep{Johansen+etal2007}." +. The gravitational acceleration is interpolated back to the particle positions using second order spline interpolation., The gravitational acceleration is interpolated back to the particle positions using second order spline interpolation. +" The strength of the gravity is defined by the non-dimensional parameter which is related to the thin-disc self-gravity parameter Q through ο~1.66G-! (Safronov,1960;Toomre,1964)."," The strength of the gravity is defined by the non-dimensional parameter which is related to the thin-disc self-gravity parameter $Q$ through $Q \approx +1.6 \tilde{G}^{-1}$ \citep{Safronov1960,Toomre1964}." +". The solar nebula of Hayashi(1981) has 6~0.04 at 3 AU from the sun, the parameter depending weakly on the distance."," The solar nebula of \cite{Hayashi1981} has $\tilde{G}\approx0.04$ at 3 AU from the sun, the parameter depending weakly on the distance." +" We use G=0.1 as a reference choice in the simulations, but experiment with G down to 0.02.The total particle mass in the box is where the mass unit My=Hpo depends on the temperature and location in the disc [H] and the strength of the self-gravity [po=! (4nG)GQ?]."," We use $\tilde{G}=0.1$ as a reference choice in the simulations, but experiment with $\tilde{G}$ down to 0.02.The total particle mass in the box is where the mass unit $M_0 = H^3 \rho_0$ depends on the temperature and location in the disc $H$ ] and the strength of the self-gravity $\rho_0=(4 \pi G)^{-1} +\tilde{G} \varOmega^2$ ]." +" While the expression in does not depend on G, in units where H=po 1, the physical mass unit does."," While the expression in does not depend on $\tilde{G}$ , in units where $H=\rho_0=1$ , the mass unit does." +" In a nebula with the scale-height given by Hayashi (1981),, we have at r=3AU with G-0.1 α mass unit of Mo«1.3x1027g and M,« 2.8Mcaes."," In a nebula with the scale-height given by \cite{Hayashi1981}, , we have at $r=3\,{\rm AU}$ with $\tilde{G}=0.1$ a mass unit of $M_0 \approx 1.3 \times +10^{27}\,{\rm g}$ and $M_{\rm p} \approx 2.8 M_{\rm Ceres}$ ." +satisfies Consider contour integration over the rectangleο(.Re +2=0. Rez —a and z—vcdiY (0Z(X) associated with the z;and absolute summabilitv of the 5,."," whence The result now follows in the limit as $k$ approaches infinity, taking into account the residue sum $e^{-\frac{\lambda}{2}}Z(\lambda)$ associated with the $z_k$and absolute summability of the $\gamma_k$." + Following the expanded Euler identity (7)). we define for all z away [rom the τε. its Fourier transform on «a>sup e. and the coefficients," $\Box$ Following the expanded Euler identity \ref{EQN_B2}) ), we define for all $z$ away from the $z_k$ , its Fourier transform on $a>\sup a_k$ , and the coefficients" +(hat can explain svstematic offsets of 0.1 mag.,that can explain systematic offsets of $\sim$ 0.1 mag. + Nevertheless. in our case. (he stability of our equipment and procedures along with our many independent calibrations and cross checks eives us sirong confidence (hat our results are reliable.," Nevertheless, in our case, the stability of our equipment and procedures along with our many independent calibrations and cross checks gives us strong confidence that our results are reliable." + It is always possible to postulate some arbitrary facing and brightening caused by whatever mechanism has previously macle Nereid a variable. such that the light curves in Figure 1 are produced. without. changing the surface texture.," It is always possible to postulate some arbitrary fading and brightening caused by whatever mechanism has previously made Nereid a variable, such that the light curves in Figure 1 are produced without changing the surface texture." + Nevertheless. such postulated changes appear to be correlated with the Earth's position due to the low-phase differences being centered on opposition and due to the return to the same magnitude on five occasions when the phase is 0.471$ GeV. This is due to the distribution of the number density in the main acceleration region, where the photons of $E>$ 1 GeV are emitted." + Figure 9. shows the average charge density (Lilled-circle) and the resultant charge density in the main acceleration region (circle)., Figure \ref{rho_phi} shows the average charge density (filled-circle) and the resultant charge density in the main acceleration region (circle). + Phe average charge density and therefore the number density in the main acceleration region acquire the maximum vale at polar angle around 2407. which corresponds to the pulse phase around 0.3.," The average charge density and therefore the number density in the main acceleration region acquire the maximum vale at polar angle around $^{\circ}$, which corresponds to the pulse phase around 0.3." + We have discussed the clleets of the distributions of f. fyfhe and 1.gi; on the shape of the energy dependent light curves.," We have discussed the effects of the distributions of $f$, $h_1/h_2$ and $1-g_1$ on the shape of the energy dependent light curves." +" As discussed in section 3.2.2.. the distribution of thickness ratio h,/ho moinlv allects the light curve of £x1 GeV energy bands. and it makes a bump at. pulse phase arounc 0.25 in the light curve below1 GeV. The shape of bridge emission in the light curves above 1 GeV are mainly alfecte by theazimuthal distributions of the fractional thickness f and of the number density 1. gi."," As discussed in section \ref{gapthick}, the distribution of thickness ratio $h_1/h_2$ mainly affects the light curve of $E\le 1$ GeV energy bands, and it makes a bump at pulse phase around 0.25 in the light curve below1 GeV. The shape of bridge emission in the light curves above 1 GeV are mainly affected by theazimuthal distributions of the fractional thickness $f$ and of the number density $1-g_1$ ." + We demonstrated. the third-peak-like structure can be produced by the azimutha structure of f. hiπο and lo qi.," We demonstrated the third-peak-like structure can be produced by the azimuthal structure of $f$ , $h_1/h_2$ and $1-g_1$ ." + Figure LO shows the pulsed profiles calculated by taking into account the azimuthal distributions for all f. hi/h» anc l gi.," Figure \ref{edlc_3dis} shows the pulsed profiles calculated by taking into account the azimuthal distributions for all $f$ , $h_1/h_2$ and $1-g_1$ ." + Me can see in Figure 10. that there is a bump, We can see in Figure \ref{edlc_3dis} that there is a bump +"show the fraction of companions that was correctly identified (position and flux ratio) as a function of the flux ratio (i.e., the detection “completeness”).","show the fraction of companions that was correctly identified (position and flux ratio) as a function of the flux ratio (i.e., the detection “completeness”)." +" The agreement with the y? analysis is excellent in the case of tau Cet, while the blind test suggests a sensitivity slightly better than expected from the y? analysis in the case of Fomalhaut."," The agreement with the $\chi^2$ analysis is excellent in the case of tau Cet, while the blind test suggests a sensitivity slightly better than expected from the $\chi^2$ analysis in the case of Fomalhaut." +" In the latter case, the median sensitivity within the mmas region would be around instead of the expected0."," In the latter case, the median sensitivity within the mas region would be around instead of the expected." +23%.. The right-hand side plots display the measured flux ratios of the best-fit binary models as a function of the true flux ratios., The right-hand side plots display the measured flux ratios of the best-fit binary models as a function of the true flux ratios. + These plots demonstrate the absence of bias in the determination of the companion brightness., These plots demonstrate the absence of bias in the determination of the companion brightness. +" They also confirm that the flux ratio of false detections generally does not exceed and0.35%,, respectively, for Fomalhaut and tau Cet."," They also confirm that the flux ratio of false detections generally does not exceed and, respectively, for Fomalhaut and tau Cet." +" A similar analysis was performed for Regulus, with contrasts ranging from to for the fake companions."," A similar analysis was performed for Regulus, with contrasts ranging from to for the fake companions." +" Because the u,v plane coverage is less dense in this case, several replica of the fake companions introduced in the data sets appear frequently in the y? cubes, at various positions in the search region."," Because the $u,v$ plane coverage is less dense in this case, several replica of the fake companions introduced in the data sets appear frequently in the $\chi^2$ cubes, at various positions in the search region." + These can be seen as the side lobes of the instrumental PSF achieved during this snapshot., These can be seen as the side lobes of the instrumental PSF achieved during this snapshot. +" Due to the statistical noise and systematic errors (which are not fully averaged out due to the low number of OBs/files), the most significant minimum in the Y? cube does not always correspond to the actual positionof the companion."," Due to the statistical noise and systematic errors (which are not fully averaged out due to the low number of OBs/files), the most significant minimum in the $\chi^2$ cube does not always correspond to the actual positionof the companion." +" In Fig. 6,,"," In Fig. \ref{fig:blind_regulus}," +" we have therefore used two definitions of the completeness level: a “detection” is reported when a significant minimum (i.e., at more that 3c"") is observed in the y? cube at the companion position, while the “position” of the companion is deemed found only when the global minimum in the cube is located less than mmas away from the actual companion position."," we have therefore used two definitions of the completeness level: a “detection” is reported when a significant minimum (i.e., at more that $3\sigma$ ) is observed in the $\chi^2$ cube at the companion position, while the “position” of the companion is deemed found only when the global minimum in the cube is located less than mas away from the actual companion position." + The left-hand side plot of Fig., The left-hand side plot of Fig. +" illustrates a behaviour that was already noted in the case of del Aqr: even when the detection is (very) clear, the companion position generally remains ambiguous due to the limited u,v plane coverage, and the global best fit is not always found at the right position."," \ref{fig:blind_regulus} illustrates a behaviour that was already noted in the case of del Aqr: even when the detection is (very) clear, the companion position generally remains ambiguous due to the limited $u,v$ plane coverage, and the global best fit is not always found at the right position." + This is also the reason for the presence of filled red dots in the right-hand side plot for contrasts ranging from to0.9%:: the estimated companion position is generally wrong in this contrast range., This is also the reason for the presence of filled red dots in the right-hand side plot for contrasts ranging from to: the estimated companion position is generally wrong in this contrast range. +" Nonetheless, the results of the blind test in terms of pure detection (disregarding position) are fully compatible with the y? analysis."," Nonetheless, the results of the blind test in terms of pure detection (disregarding position) are fully compatible with the $\chi^2$ analysis." +" Overall, we have thus used three different approaches to evaluate the sensitivity levels, which all give similar results: The agreement between the various approaches further validates the sensitivity levels and confirms that 3c is a reasonable significance level for identifying candidate companions."," Overall, we have thus used three different approaches to evaluate the sensitivity levels, which all give similar results: The agreement between the various approaches further validates the sensitivity levels and confirms that $3\sigma$ is a reasonable significance level for identifying candidate companions." + It also validates a posteriori our assumption of Gaussian statistics for our data sets., It also validates a posteriori our assumption of Gaussian statistics for our data sets. + Fomalhaut is a bright A4V star located at ppc., Fomalhaut is a bright A4V star located at pc. +" Near-infrared interferometric observations with VLTI/VINCI have recently revealed a K-band excess emission close to the photosphere, with a flux ratio of 8.8x10?+1.2 (?).."," Near-infrared interferometric observations with VLTI/VINCI have recently revealed a K-band excess emission close to the photosphere, with a flux ratio of $8.8\times 10^{-3} \pm 1.2\times 10^{-3}$ \citep{Absil09}." +" In that paper, it was argued that the excess emission most probably comes from an extended source, rather than from a point-like companion."," In that paper, it was argued that the excess emission most probably comes from an extended source, rather than from a point-like companion." +" The absence of closure phase signal in our PIONIER data further confirms this conclusion, and allows the presence of any companion with a flux ratio greater than 2.8x10? to be rejected at 30 with a completeness level on a mmas field-of-view."," The absence of closure phase signal in our PIONIER data further confirms this conclusion, and allows the presence of any companion with a flux ratio greater than $2.8\times 10^{-3}$ to be rejected at $3\sigma$ with a completeness level on a mas field-of-view." +" According to the models of ?,, this corresponds to a mass limit around 0.175Mo for an age of MMyr (?).."," According to the models of \citet{Baraffe98}, this corresponds to a mass limit around $0.175M_{\odot}$ for an age of Myr \citep{DiFolco04}." + We therefore confirm that the previously detected excess emission at K band comes from an extended (and mostly point-symmetric) source., We therefore confirm that the previously detected excess emission at K band comes from an extended (and mostly point-symmetric) source. +" This G8 main sequence star located at ppc is also known to have a K-band excess emission, with a flux ratio of 9.8x10?+2.1 derived from high-precision visibility measurements at the CHARA array with the FLUOR instrument (?).."," This G8 main sequence star located at pc is also known to have a K-band excess emission, with a flux ratio of $9.8\times 10^{-3} \pm 2.1\times 10^{-3}$ derived from high-precision visibility measurements at the CHARA array with the FLUOR instrument \citep{DiFolco07}." +" As in the case of Fomalhaut, our PIONIER observations confirm the absence of low-mass companion within the first mmas around tau Cet, with a completeness level of 4.5x107? at 3σ."," As in the case of Fomalhaut, our PIONIER observations confirm the absence of low-mass companion within the first mas around tau Cet, with a completeness level of $4.5\times 10^{-3}$ at $3\sigma$." +" According to the models of ?,, this corresponds to a mass limit around 0.09M5 for an age of GGyr (?);; however, the significance of the best-fit binary model for the tau Cet data set is rather close to 3c, so that the possibility that a faint companion is actually"," According to the models of \citet{Baraffe98}, this corresponds to a mass limit around $0.09M_{\odot}$ for an age of Gyr \citep{DiFolco04}; however, the significance of the best-fit binary model for the tau Cet data set is rather close to $3\sigma$ , so that the possibility that a faint companion is actually" +that this scaling matters most for the faintest objects that are observed.,that this scaling matters most for the faintest objects that are observed. + However. the value of πο is not significantly changed if rather we assume S/N xIuxE? as would occur if the observations were photon-limited.," However, the value of $\bar{n}_{\rm eff}$ is not significantly changed if rather we assume $S/N \propto\,$ $^{1/2}$ as would occur if the observations were photon-limited." + The solid. curves from top to bottom are mar for 2=2.3. and 4.," The solid curves from top to bottom are $\bar{n}_{\rm eff}$ for $z=2, ~3,$ and $4$." + These curves illustrate that it will be challenging to (1) measure the 3D Lye forest at z3 because of the fallol£ in the total abundance of quasars or (2) obtain mar210E Alpe> at any redshift’ because of the shallow faint-enc slope of the luminosity function., These curves illustrate that it will be challenging to (1) measure the $3$ D $\alpha$ forest at $z> 3$ because of the falloff in the total abundance of quasars or (2) obtain $\bar{n}_{\rm eff} \gg 10^{-3}~$ $^{-2}$ at any redshift because of the shallow faint-end slope of the luminosity function. + Table 4. tabulates may as various redshifts and limiting magnitudes. andit also gives the conversion [rom 7 to 7 units.," Table \ref{table:neff} tabulates $\bar{n}_{\rm eff}$ as various redshifts and limiting magnitudes, andit also gives the conversion from $^{-2}$ to $^{-2}$ units." + The dashed curves in Figure 1. show the total number of quasars brighter than map., The dashed curves in Figure \ref{fig:Neff} show the total number of quasars brighter than $m_{\rm AB}$. + Phe elfective number density ab nbb is always a factor of a few smaller than the total number of quasars. with the cillerence decreasing with redshift.," The effective number density at $m_{\rm AB}^{1A}$ is always a factor of a few smaller than the total number of quasars, with the difference decreasing with redshift." + See Appendix A for an analytic understanding of this suppression for power-law luminosity functions., See Appendix \ref{ap:powerlaw} for an analytic understanding of this suppression for power-law luminosity functions. + BOSS will achieve a D-band magnitude limit of 22002=2 (mSz21 at 2— 3) and also achieve mille 22., BOSS will achieve a B-band magnitude limit of $m^{\rm lim}_{\rm AB} \approx 22$ at $z=2$ $m^{\rm lim}_{\rm AB} \approx 21$ at $z=3$ ) and also achieve $m_{\rm AB}^{1A} \approx 22$ . + ‘These numbers vield nar=(03OS).107 Alpe7 4dTdeg FP at 2=3., These numbers yield $\bar{n}_{\rm eff} = (0.3 -0.8) \times 10^{-3}~$ $^{-2}$ $4-7~$ $^{-2}$ ] at $z=2-3$. + BigBOSS aims to achieve one magnitude fainter than BOSS. which results in nar= Alpe Pats=2?3.," BigBOSS aims to achieve one magnitude fainter than BOSS, which results in $\bar{n}_{\rm eff} = (1 -2) \times 10^{-3}~$ $^{-2}$ at $z=2-3$." + For these nay and at &z0.1 Alpeο. SAN scales linearly with roy such that BigBOSS will be a few times more sensitive than BOSS.," For these $\bar{n}_{\rm eff}$ and at $k \gtrsim 0.1~$ $^{-1}$, $S/N$ scales linearly with $\bar{n}_{\rm eff}$ such that BigBOSS will be a few times more sensitive than BOSS." + Figure 2. is a contour plot of nj as a function of n/t and mkb., Figure \ref{fig:Neffcont} is a contour plot of $\bar{n}_{\rm eff}$ as a function of $m^{\rm lim}_{\rm AB}$ and $m_{\rm AB}^{1A}$. + The solid contours are caleulatecl assuming 0.1 Alpe1 and ave labeled in units of 10.7 7., The solid contours are calculated assuming $k_{\parallel} = 0.1~$ $^{-1}$ and are labeled in units of $10^{-3}~$ $^{-2}$. + These curves illustrate that op is maximized roughly when milssmyp 0.5., These curves illustrate that $\bar{n}_{\rm eff}$ is maximized roughly when $m^{\rm lim}_{\rm AB} \approx m_{\rm AB}^{1A}-0.5$ . + Little is gained by observing fainter quasars than mk0.5 or hy integrating longer on the same quasars once inbzeml| 0.5., Little is gained by observing fainter quasars than $m_{\rm AB}^{1A} - 0.5$ or by integrating longer on the same quasars once $m_{\rm AB}^{1A} \approx m^{\rm lim}_{\rm AB} + 0.5$ . + Lhe dashed contours are the same but at —0.5> 1 fat which Pus is a factor of 0.6 smaller in our| model)). demonstrating that the &( dependence of these conclusions is weak.," The dashed contours are the same but at $k_{\parallel} = 0.5~$ $^{-1}$ (at which $P_{\rm los}$ is a factor of $0.6$ smaller in our model), demonstrating that the $k_{\parallel} $ dependence of these conclusions is weak." +" llow much is gained by weighting by iw,relative toa uniform weighting scheme?", How much is gained by weighting by $w_n$relative to a uniform weighting scheme? + Let us take a luminosity with power-law index 2. a form discussed in. Appendix A.," Let us take a luminosity with power-law index $-2$, a form discussed in Appendix \ref{ap:powerlaw}." + We assume that S/Nxπαν. Lain{λος=1 (equivalent to SAND=2: Table 3)). where Paus is the noise power spectrum for quasars at the survey limiting magnitude.," We assume that $S/N \propto {\rm flux}$, $P_{\rm N, lim}/P_{\rm los} = 1$ (equivalent to $[S/N]_{1A} \approx 2$; Table \ref{table:SNR}) ), where $P_{\rm N, lim}$ is the noise power spectrum for quasars at the survey limiting magnitude." + This case results in only a improvement in the value of relative to à simple uniform weighting., This case results in only a improvement in the value of $P_{\rm tot} - P_{\rm F}$ relative to a simple uniform weighting. + For Pau/{Ίων=0.5 (0.3). the improvement is 40% (60%).," For $P_{\rm N, lim}/P_{\rm los} = 0.5 \,(0.3)$ , the improvement is $40\%$ $60\%$ )." +" Thus. weighting only olfers a significant improvement when a large fraction of the quasars have PNa4,<1."," Thus, weighting only offers a significant improvement when a large fraction of the quasars have $P_{\rm N, n}/P_{\rm los} < 1$." + One can define an cllective volume for Lya forest. surveys analogous to the ellective volume in galaxy surveys (?).., One can define an effective volume for $\alpha$ forest surveys analogous to the effective volume in galaxy surveys \citep{feldman94}. +" In particular. in the galaxy survey case the ellective volume is which becomes in the Lya forest survey caseIn equation (15)) and (16)). V, is the actualvolume of the galaxy survey. 2 is the galaxy power spectrum. moa is the number density of galaxies. and £ is the line-of-ight dimension of the Lya survey."," In particular, in the galaxy survey case the effective volume is which becomes in the $\alpha$ forest survey caseIn equation \ref{eqn:Veffg}) ) and \ref{eqn:Veff}) ), $V_{\rm g}$ is the actualvolume of the galaxy survey, $P_{\rm g}$ is the galaxy power spectrum, $\bar{n}_{\rm g, 3D}$ is the number density of galaxies, and $L$ is the line-of-sight dimension of the $\alpha$ survey." + Phe major ciffercnee between these two effective. volumes is just thatin the Lya case the shot noise is in the plane of the sky. and thisterm is modulated by the line-of-sight power., The major difference between these two effective volumes is just thatin the $\alpha$ case the shot noise is in the plane of the sky and thisterm is modulated by the line-of-sight power. + ligure 3. plots a generalization of the the cllective volume. Var(Af AL]. for nap=1031.7.10. 7. and 103 7. in order ofincreasing dash length.," Figure \ref{fig:Veff} plots a generalization of the the effective volume, $V_{\rm eff, \mu}(k)/[{\cal A} \, L]$ , for $\bar{n}_{\rm eff} = 10^{-1}, ~10^{-2}, ~10^{-3}$ , and $10^{-4}~$ $^{-2}$ , in order ofincreasing dash length." + We define Vou(A) to be Var(&) but averaged. over a shell in À- such that Var(&)=2.ALD. DLE where," We define $V_{\rm eff, \mu}(k)$ to be $V_{\rm eff}(\bfk)$ but averaged over a shell in $k$ -space such that $V_{\rm eff, \mu}(k) \equiv 2 \, {\cal A} L \, P_{\rm F, \mu}^2/\delta P_{\rm F, \mu}^2$ , where" +frame.,frame. + Our results make this the most comprehensive polarinetric calibration of NIC? to date (aud quite likely the last) for direct nuaenme., Our results make this the most comprehensive polarimetric calibration of NIC2 to date (and quite likely the last) for direct imaging. + We sugeest this quantitative characterization of the NIC2 polarimetric system supersede the previous post-NCS era polarimetric calibrations., We suggest this quantitative characterization of the NIC2 polarimetric system supersede the previous post-NCS era polarimetric calibrations. + As the techniques usec here require extremely precise photometry. there are many potential sources contributing to the wnecrtaimtics in determuning p aud 0.," As the techniques used here require extremely precise photometry, there are many potential sources contributing to the uncertainties in determining $p$ and $\theta$." + Wighly precise photometric repeatability is limited by temporal. thermal. and metrologic optical instabilities iu the ZZST|NICMOS iustymmenutal system affecting the PSF. as well as spatial quantization and performance defects in the NIC2 detector and readout electronics.," Highly precise photometric repeatability is limited by temporal, thermal, and metrologic optical instabilities in the +NICMOS+ instrumental system affecting the PSF, as well as spatial quantization and performance defects in the NIC2 detector and readout electronics." + The measurement dispersions introduced by these (aud perhaps other svsteniatic) effects are carried through the SA99 analysis to determine o(p) aud σ(0)., The measurement dispersions introduced by these (and perhaps other systematic) effects are carried through the SA99 analysis to determine $\sigma(p)$ and $\sigma(\theta)$. + However. as we have been able to determine revised values for ty aud fio) du 19 cases. We can assign uucertaimties to these cocficicnts.," However, as we have been able to determine revised values for $t_0$ and $t_{120}$ in 13 cases, we can assign uncertainties to these coefficients." + By propagating these uncertaiuties through the polarimetric analysis we find that they dominate over the errors derived following SA99., By propagating these uncertainties through the polarimetric analysis we find that they dominate over the errors derived following SA99. +" For example. applying the new cocffideuts to VRsle we find p=L3S40.1.0=12645"" following SA99. but by propae: the uncertainties in fj we find p=L610.7..—O.6)%.1266110. 21)."," For example, applying the new coefficients to VR84c we find $p=1.3\pm0.4, \theta=126\pm5\degr$ following SA99, but by propagating the uncertainties in $t_k$ we find $p=1.3(+0.7,-0.6)\%, \theta=126(+10,-24)\degr$ ." + The remaining uncertainties i the derived transmission cocficicuts do indeed dominate the statistical uncertainties from the photometry., The remaining uncertainties in the derived transmission coefficients do indeed dominate the statistical uncertainties from the photometry. + What affect— do these unecrtaimtics have— ou the observationally determined values of δω and ος, What affect do these uncertainties have on the observationally determined values of $p_{ins}$ and $\theta_{ins}$? + Could these uncertainties be responsible for the observed iustruimnental/ polarization?, Could these uncertainties be responsible for the observed instrumental polarization? + As can be secu from) Table L. deviations between πι.ο aud £ (tha in an ideal detector would be invariant) are no greater than ~2% which corresponds to a lo error m p;44 of ouly," As can be seen from Table \ref{tab:rollsnic2}, deviations between $I_1, I_2$ and $I_3$ (that in an ideal detector would be invariant) are no greater than $\sim2\%$ which corresponds to a $1\sigma$ error in $p_{ins}$ of only." + Tlowever. a more accurate wav to determine Pins requires obscrvatious of an unpolarized παπαατς star across the whole detector area to map any fiele dependence in the polarization.," However, a more accurate way to determine $p_{ins}$ requires observations of an unpolarized standard star across the whole detector area to map any field dependence in the polarization." + As our results have been derived from dithered observatious. if there is a field dependence in the polarization. then that couk niniüc an imstruneutal polarization on our data.," As our results have been derived from dithered observations, if there is a field dependence in the polarization, then that could mimic an instrumental polarization on our data." +" Such a study. cannot be done with the current data. so it is uot possible to assert p;,; at such a level."," Such a study cannot be done with the current data, so it is not possible to assert $p_{ins}$ at such a level." + IDustead. it js Inore appropriate to prescut the value as an instrumental upper luit: pip. could indeed be zero.," Instead, it is more appropriate to present the value as an instrumental upper limit; $p_{ins}$ could indeed be zero." +" What then happens to the rest of our analvsis if pi, is indeed zero?", What then happens to the rest of our analysis if $p_{ins}$ is indeed zero? + To test this. we have re-derived the values of f; without subtracting pj. in the (Q. 0) plane.," To test this, we have re-derived the values of $t_k$ without subtracting $p_{ins}$ in the $Q,U$ ) plane." +" Takingthis approach we find fy=OQ.asl+0.008. and του=0,505+0.003 which is eutirelv consistent with he results taken from the iustrumentally subtracted (Q.U)."," Takingthis approach we find $t_0=0.884\pm0.008$ and $t_{120}=0.838\pm0.003$ which is entirely consistent with the results taken from the instrumentally subtracted $(Q,U)$." + So. again we find that the errors in fj dominate he uncertainties in the measured values of p and 0.," So, again we find that the errors in $t_k$ dominate the uncertainties in the measured values of $p$ and $\theta$." + As these uncertaiuties have been derived frou 13 separate observations. that are all subjected to the photometric uncertainties theniselves. we are left with he uuderstaudius that this calibration is limited bv he photometric repeatability of individual observations.," As these uncertainties have been derived from 13 separate observations, that are all subjected to the photometric uncertainties themselves, we are left with the understanding that this calibration is limited by the photometric repeatability of individual observations." + This includes all of the known affects presented in ?7.., This includes all of the known affects presented in \ref{obs}. +" When comparing the new parallel transmission coefficients with the old it can be seen that ου is consistent with both calibrations: oulv fy has needed to be changed. albeit ""onlv by ~0.5%."," When comparing the new parallel transmission coefficients with the old it can be seen that $t_{120}$ is consistent with both calibrations; only $t_0$ has needed to be changed, albeit “only” by $\sim0.5\%$." + Applving this correction to previous studies ofhighly polarized targets will therefore not alter the results by απ significant amounts., Applying this correction to previous studies of polarized targets will therefore not alter the results by any significant amounts. +" BHowever. when applied to targets with low polarization this ""tweak"" has a tremendous affect."," However, when applied to targets with low polarization this ��tweak” has a tremendous affect." + Iu the cases where the target is spatially resolved. aud does nof contain a strong point source. then observers should bin their data to 3«23 pixels (in order to mect the diffraction lint of the iustruucenut).," In the cases where the target is spatially resolved, and does not contain a strong point source, then observers should bin their data to $3\times3$ pixels (in order to meet the diffraction limit of the instrument)." + Ditheriug cau be used iu the usual way to increase spatial resolution as well as to uutigate bad pixel affects., Dithering can be used in the usual way to increase spatial resolution as well as to mitigate bad pixel affects. +" IToxcever. signal to noise will still amit the accuracy of p aud 0 determinations. especially in tareets whose surface brightucsscs vary sienificautly on small spatial scales. i.c.. comparable to. or sinaller than. the diffraction ΙΤ,"," However, signal to noise will still limit the accuracy of $p$ and $\theta$ determinations, especially in targets whose surface brightnesses vary significantly on small spatial scales, i.e., comparable to, or smaller than, the diffraction limit." + The case of a spatially unresolved source is not so straightforward., The case of a spatially unresolved source is not so straightforward. +" As explained above. the uncertainties i| f, do dominate the accuracy of po and @."," As explained above, the uncertainties in $t_k$ do dominate the accuracy of $p$ and $\theta$." + However. as this study las shown. uou-repeatabilitics ij aperture photometry (iu the absence of well observations) suggest that unideutified outliers can readily bias polariuctric analysis independent of he intrinsic accuracy of the polariuuetric calibration.," However, as this study has shown, non-repeatabilities in aperture photometry (in the absence of well-dithered observations) suggest that unidentified outliers can readily bias polarimetric analysis independent of the intrinsic accuracy of the polarimetric calibration." + The data have been carefully inspected to identity photometrically deficient pixels by compare cach individual profile to the dispersion in the photometry neasured from ~12 poiutiugs., The data have been carefully inspected to identify photometrically deficient pixels by comparing each individual profile to the dispersion in the photometry measured from $\sim12$ pointings. + This study has shown hat ~10% of all target pointings (even those avoiding shown photometrically deficicut areas of the detector like he coronagraphic hole) will include uncorrectable bad Xxels that affect the measured polarization., This study has shown that $\sim10\%$ of all target pointings (even those avoiding known photometrically deficient areas of the detector like the coronagraphic hole) will include uncorrectable bad pixels that affect the measured polarization. + A method o robustly detect. and reject. photometric nieasures degraded by such effects is to perform a target raster witli a dither pattern with three or more poiutiues.," A method to robustly detect, and reject, photometric measures degraded by such effects is to perform a target raster with a dither pattern with three or more pointings." + The step size should be more than three times ercater than the FWIIM of the PSF to avoid persistence., The step size should be more than three times greater than the FWHM of the PSF to avoid persistence. + Encircled οςον: (intensitv) profiles should be derived indepeudently from. each observation (dither point)., Encircled energy (intensity) profiles should be derived independently from each observation (dither point). + With a sufficiently larec munber of dither poiuts. a sigma clip can then be used to determine whether an individual profile is deviant or not.," With a sufficiently large number of dither points, a sigma clip can then be used to determine whether an individual profile is deviant or not." + The greater mmuber of dithers used. the more accurate this clip will be.," The greater number of dithers used, the more accurate this clip will be." + For small ummbers of dither points (not optimally recommended) medianing can be used to coarsely reject outliers., For small numbers of dither points (not optimally recommended) medianing can be used to coarsely reject outliers. + The average of the remaiming profiles can then be used to derive p and @ from the coefficients presented in Table 7.., The average of the remaining profiles can then be used to derive $p$ and $\theta$ from the coefficients presented in Table \ref{tab:newcoeffs}. . + This study has shown that the affects of the IPRFs are larecly mitigated by effective. dithering., This study has shown that the affects of the IPRFs are largely mitigated by effective dithering. +" Towever. the uncertzüntv in the calibration of fj, ultimately"," However, the uncertainty in the calibration of $t_k$ ultimately" +Dufouretal.(2007) Diy~ Dig~ found long ago strong sunilaurities between the partial ionization regions and associated superficial convection zones of white chwarf models with IL. ου. and C-dominated atinospheres/euvelopes.,"\citet{dufournat} $\sim $ $\Te \sim$ $\Te \sim$ found long ago strong similarities between the partial ionization regions and associated superficial convection zones of white dwarf models with H-, He-, and C-dominated atmospheres/envelopes." + Theoretical cousiderations thus suggested that some of the Hot DO white dwarfs. because they are located in a narrow range of effective temperature around 20.000 kk (Dufouretal.2007.2008).. could possibly pulsate.," Theoretical considerations thus suggested that some of the Hot DQ white dwarfs, because they are located in a narrow range of effective temperature around 20,000 K \citep{dufournat,dufour08}, could possibly pulsate." + Following this. a systematic search for pulsations iu carbon-atimosphere white dwarfs carried out by Mouteomeryctal.(2008) successfully discovered the first pulsating carbou-donmünated atimosphere white dwarf SDSS J112625.71]575218.3. (hereafter SDSS J1126|5752).," Following this, a systematic search for pulsations in carbon-atmosphere white dwarfs carried out by \citet{montgomery08} successfully discovered the first pulsating carbon-dominated atmosphere white dwarf: SDSS J142625.71+575218.3 (hereafter SDSS J1426+5752)." + Thev uncovered a single pulsation (and its first harmonic) with a period of 117 s in that star., They uncovered a single pulsation (and its first harmonic) with a period of 417 s in that star. + Tn parallel with this observational effort. Fontaineotal.(2008). carried out the first detailed stability study. based on the full nonacdiabatic approach. to investigate the asteroseinological potential of carbou-atimosphere white dwarfs.," In parallel with this observational effort, \citet{fontaine08} carried out the first detailed stability study, based on the full nonadiabatic approach, to investigate the asteroseismological potential of carbon-atmosphere white dwarfs." + They showed that pulsational iustabilities in the range of effective temperature where the Tot DOs are found are indeed possible. but only if a fair amount of helium is present in the atiuosphiere/euvelope compositional mixture.," They showed that pulsational instabilities in the range of effective temperature where the Hot DQs are found are indeed possible, but only if a fair amount of helium is present in the atmosphere/envelope compositional mixture." + White dwirf models with pure carbon cuvelopes are found to pulsate. but only at much higher temperatures than those characterizing Tot DO's discovered up to now.," White dwarf models with pure carbon envelopes are found to pulsate, but only at much higher temperatures than those characterizing Hot DQ's discovered up to now." + Towever. the SDSS spectra analvzed in Dufourctal.(2008).. even though quite noisy. rule out large amounts of helm (frou the absence of the Πο ALITL line) for alb objects except SDSS J1126|5752 which. because of its higher surface eravity and lower effective teniperature. could perhaps have an Πού abundance ratio as high as0.5.," However, the SDSS spectra analyzed in \citet{dufour08}, even though quite noisy, rule out large amounts of helium (from the absence of the He $\lambda$ 4471 line) for all objects except SDSS J1426+5752 which, because of its higher surface gravity and lower effective temperature, could perhaps have an He/C abundance ratio as high as0.5." + So. according to the full uonadiabatic models.," So, according to the full nonadiabatic models," +"lgnoring anv recombinations. the radius /2, of the Stvomuiumeren sphere of a quasar of age {ο is such that the number of hydrogen atoms in the sphere equals the total nunber of ionizing photons produced by Che source: (CLL). where 72, is in proper (not comoving) units. (257) is the mean hydrogen density within R,. and Non is emission rate of ionizing photons from the quasar.","Ignoring any recombinations, the radius $R_{\rm s}$ of the Strömmgren sphere of a quasar of age $t_Q$ is such that the number of hydrogen atoms in the sphere equals the total number of ionizing photons produced by the source: (CH), where $R_{\rm s}$ is in proper (not comoving) units, $\langle n_H \rangle$ is the mean hydrogen density within $R_{\rm s}$, and $\dot N_{\rm ph}$ is emission rate of ionizing photons from the quasar." + For (155). we have adopted ihe mean IGM density at 2=6.28 with OQ)=0.04. and Non=1.3x10%s! is calibrated from the observed flux of SDSS LO30+0524. extrapolating its continuum to energies above 13.6eV using a standard quasar template spectrum (Elvis et al.," For $\langle n_H \rangle$, we have adopted the mean IGM density at $z=6.28$ with $\Omega_{\rm b}=0.04$, and $\dot +N_{\rm ph}=1.3\times 10^{57}~{\rm s^{-1}}$ is calibrated from the observed flux of SDSS 1030+0524, extrapolating its continuum to energies above 13.6eV using a standard quasar template spectrum (Elvis et al." + 1994. which agrees well with ihe more recent SDSS template in Vanclen Berk οἱ al.," 1994, which agrees well with the more recent SDSS template in Vanden Berk et al." + 2001. hereafter VdD).," 2001, hereafter VdB)." +" Adopting the same template spectrum. and assuming further that (he BIL powering this quasar is shining al its Eddington luminosity. the mass of the BIL is f[ound to be Af),=2xLO?M..."," Adopting the same template spectrum, and assuming further that the BH powering this quasar is shining at its Eddington luminosity, the mass of the BH is found to be $M_{\rm bh}=2\times10^9~{\rm M_\odot}$." + We have used (his mass to convert equation (1)) into equation (2))., We have used this mass to convert equation \ref{eq:Rt1}) ) into equation \ref{eq:Rt2}) ). + In an evolving and chumpy cosmological density lield around a quasar. ionizing photons are lost to recombinations. and the size of the HI] region can be reduced relative to the prediction of equation (2)).," In an evolving and clumpy cosmological density field around a quasar, ionizing photons are lost to recombinations, and the size of the HII region can be reduced relative to the prediction of equation \ref{eq:Rt2}) )." +" We need to then solve (he equation for (he radius of the ionization front. ἐς. taking into account all relevant effects including recombination. density evolution and cosmological effects as follows: where //(z) is the Hubble constant al 2. C=οGry)? is the mean chimping factor ol ionized gas within /24,. ancl ay is the hydrogen recombination coefficient."," We need to then solve the equation for the radius of the ionization front, $R_{\rm s}$, taking into account all relevant effects including recombination, density evolution and cosmological effects as follows: where $H(z)$ is the Hubble constant at $z$, $C\equiv\langle n_H^2 \rangle / +\langle n_H \rangle^2$ is the mean clumping factor of ionized gas within $R_{\rm s}$, and $\alpha_B$ is the hydrogen recombination coefficient." + The three terms on the right side of equation (3)) account for the Hubble expansion. the ionizations by newly produced. photons. and. recombinations. respectively (Shapiro Giroux 1937: IHaiman Loeb 1997).," The three terms on the right side of equation \ref{eq:Ri}) ) account for the Hubble expansion, the ionizations by newly produced photons, and recombinations, respectively (Shapiro Giroux 1987; Haiman Loeb 1997)." + Although equation (2)) is accurate for low clumping factors ancl quasar ages (CoS10. lgCS105 ves). the results presented. here are based on a numerical solution of equation (3)).," Although equation \ref{eq:Rt2}) ) is accurate for low clumping factors and quasar ages $C\la 10$, $t_Q\la 10^8$ yrs), the results presented here are based on a numerical solution of equation \ref{eq:Ri}) )." + In general. a quasar has an intrinsic Lya emission line. which is reprocessed along the line of sight to the observer by (he opacity of the intervening neutral IGM as well as," In general, a quasar has an intrinsic $\alpha$ emission line, which is reprocessed along the line of sight to the observer by the opacity of the intervening neutral IGM as well as" +supported systems) are preferentially found. as satellites to the Milky Way ancl M31. whereas chwarl irregular. galaxies (ecnerally eas rich. rotating systems) are preferentially founcl as isolated systems.,"supported systems) are preferentially found as satellites to the Milky Way and M31, whereas dwarf irregular galaxies (generally gas rich, rotating systems) are preferentially found as isolated systems." + This position-morpholoeyv relation was [first highlighted by Einasto.Ixaasik.&Saar(1974) and suggests that the environment of a dwarf galaxy plays a fundamental role in driving its evolution., This position-morphology relation was first highlighted by \citet{1974Natur.250..309E} and suggests that the environment of a dwarf galaxy plays a fundamental role in driving its evolution. + Mayerctal.(2001a.b.2006) suggest that tidal clleets and ram pressure stripping of dwarf galaxies in the halo of large galaxies may be sullicient to turn a rotationally supported system into a pressure supported. svstem.," \citet{2001ApJ...559..754M,2001ApJ...547L.123M,2006MNRAS.369.1021M} suggest that tidal effects and ram pressure stripping of dwarf galaxies in the halo of large galaxies may be sufficient to turn a rotationally supported system into a pressure supported system." + Isolated dwarf spheroidals are. therefore. particularly interesting as they would have been immune for the shaking and stirring that has occurred. to most chwarf svstems and hence may represent the dwarf galaxies in their most pristine form.," Isolated dwarf spheroidals are, therefore, particularly interesting as they would have been immune for the shaking and stirring that has occurred to most dwarf systems and hence may represent the dwarf galaxies in their most pristine form." + However. such isolated dwarf spheroidal galaxies are rare within the Local Group. with two cwarfs not. currently a satellite of either. the Milky. Way and M31: Cetus andLucana’.," However, such isolated dwarf spheroidal galaxies are rare within the Local Group, with two dwarfs not currently a satellite of either the Milky Way and M31; Cetus and." +. Determining the cdsnamical properties and orbital history of such galaxies can help determine the role of interactions in governing a dwarf egalaxy’s morphology., Determining the dynamical properties and orbital history of such galaxies can help determine the role of interactions in governing a dwarf galaxy's morphology. + Discovereded by Whiting.Hau.&IrIrwin(1999)(1999). in an eve-ball survey of photographic plates. the Cetus dwarf galaxy is seen to lie at a distance of 755+ 23kpe (AleConnachicetal.2005.assuming(3132 0029): it is almost as remote from M31. with a separation of 6S0kpc.," Discovered by \citet{1999AJ....118.2767W} in an eye-ball survey of photographic plates, the Cetus dwarf galaxy is seen to lie at a distance of $755\pm23$ kpc \citep[][ assuming $E(B-V)=0.029$]{2005MNRAS.356..979M}; it is almost as remote from M31, with a separation of 680kpc." + LHencoe. unlike the vast majority. of cwarl svstems within the Local Group. Cetus does not appear to be part of the entourage of either the Milky Way or Andromeda Galaxy. and apparently. represents an isolated member of the local dwarf population.," Hence, unlike the vast majority of dwarf systems within the Local Group, Cetus does not appear to be part of the entourage of either the Milky Way or Andromeda Galaxy, and apparently represents an isolated member of the local dwarf population." + Furthermore. an analysis of the stellar distribution in this cwarl reveal it to. possess a hall-light radius of more than 300pc. and a tidal radius of6.6kpe7.. making it the largest radial extent dwarl within the local population (AleConnachic&Irwin.2006)..," Furthermore, an analysis of the stellar distribution in this dwarf reveal it to possess a half-light radius of more than 300pc, and a tidal radius of, making it the largest radial extent dwarf within the local population \citep{alaninprep}." + Such a large physical extent suggests that Cetus has not undergone a significant interaction with other members of the Local Group and. hence provides an ideal testhecl for kincmatic analvsis., Such a large physical extent suggests that Cetus has not undergone a significant interaction with other members of the Local Group and hence provides an ideal testbed for kinematic analysis. + To this end. a reanalysis of the INE/WEC data obtained by MeConnachiectal.(2005) was undertaken to search for any evidence of tidal disruption due to any previous interactions.," To this end, a reanalysis of the INT/WFC data obtained by \citet{2005MNRAS.356..979M} was undertaken to search for any evidence of tidal disruption due to any previous interactions." + This was coupled with a spectroscopic survey of the Cetus cdwarl galaxy which was undertaken with Deimos on the eck I0m telescope with the goal of determining its kinematic and dark matter properties., This was coupled with a spectroscopic survey of the Cetus dwarf galaxy which was undertaken with Deimos on the Keck 10m telescope with the goal of determining its kinematic and dark matter properties. +" The details of the observations are presented in Section ?7.. while a discussion of the results appears in Section οον,"," The details of the observations are presented in Section \ref{observations}, while a discussion of the results appears in Section \ref{results}." + his paper closes with Section ?? which presents the implications and conclusions of this stucdv., This paper closes with Section \ref{conclusions} which presents the implications and conclusions of this study. + The photometric observations were obtained: with the INT/WEC on the 2.5m Isaac Newton Telescope on La Palma ancl were originally presented by MeConnachieetal.(2005)., The photometric observations were obtained with the INT/WFC on the 2.5m Isaac Newton Telescope on La Palma and were originally presented by \citet{2005MNRAS.356..979M}. + As noted in this previous work. the V and beolour magnitucde diagram of the Cetus dwarl clearly reveals the presence of a red-giant branch below L=20.5.," As noted in this previous work, the V and I colour magnitude diagram of the Cetus dwarf clearly reveals the presence of a red-giant branch below I=20.5." + Furthermore. the presence of the dwarf is clearly revealed in stellar density. as apparen in Figure 1..," Furthermore, the presence of the dwarf is clearly revealed in stellar density, as apparent in Figure \ref{fig1}." + Hence. this photometric data was used to selec targets for spectroscopic followup with the Ixeck telescope.," Hence, this photometric data was used to select targets for spectroscopic followup with the Keck telescope." + The stars were chosen to lie within 0.15mags of the Ree Giant Branch (ROB) between 22.0«&£«20.5: the selection box is overlaid on the CMD presented in Figure 2 an the spatially clistribution of stars appears in Figure 1.., The stars were chosen to lie within $\sim0.15$ mags of the Red Giant Branch (RGB) between $22.0»0.," For any assumed value of $n$, an upper limit to the age of the pulsar, and thus the remnant, is provided in the limit $P_0 \rightarrow 0$." + À bralkine iudex well below η=1.5 would be highlv unusual. so that ~LO kyr is a reasonable upper luit ou the age of1.," A braking index well below $n = 1.5$ would be highly unusual, so that $\sim 40$ kyr is a reasonable upper limit on the age of." +0.. Hacks the bright X-ray PWN expected from an energetic pulsar: it is only the second example (of some 20) of a pulsu with EZ1«1079 ere 3 unaccompanied by a PWN of comparable briehtuess. Fpwx/Fpan<1. defving the trend preseuted in Cotthelf (2001).," lacks the bright X-ray PWN expected from an energetic pulsar: it is only the second example (of some 20) of a pulsar with $\dot E +\simgt 4\times 10^{36}$ erg $^{-1}$ unaccompanied by a PWN of comparable brightness, $F_{\rm PWN}/F_{\rm PSR}\simgt 1$, defying the trend presented in Gotthelf (2004)." +" As such. it is sunilar to (Coni 11998). the GO 1us pulsar with E=1.6«10% ere st, Bo=31ν107? G. aud rz.=8&1 kw."," As such, it is similar to (Torii 1998), the 69 ms pulsar with $\dot E = 1.6 +\times 10^{37}$ erg $^{-1}$, $B_s = 3.1 \times 10^{12}$ G, and $\tau_c = 8.1$ kyr." + The nuderliminous PWNe in these cases remain unexplained., The underluminous PWNe in these cases remain unexplained. + Iu other respects. however. the X-ray PAWN around nuiuav not be so unusual.," In other respects, however, the X-ray PWN around may not be so unusual." + The semi-major axis of the elliptical clongation around the unresolved source ds approximately 6” length. represcuting a physical dimension of 9«1011inDyy cu.," The semi-major axis of the elliptical elongation around the unresolved source is approximately $6\arcsec$ in length, representing a physical dimension of $9\times10^{17} \ D_{10}$ cm." + For comparison. the Vela PWN’s N-ray “outer arc lies at a distance dos1017 cm frou the pulsar in the ecometric model of (2001)..," For comparison, the Vela PWN's X-ray “outer arc” lies at a distance $1\times10^{17}$ cm from the pulsar in the geometric model of \citet{2001ApJ...556..380H}. ." +The probabilities for a 2 Lila detection and a 2556 detection are A similar result is seen for 20-30 and for 10-20 random positions.,The probabilities for a $>$ $\sigma$ detection and a $>$ $\sigma$ detection are A similar result is seen for 20-30 and for 10-20 random positions. + Thus we conclude that the detected: mean gu flux is real., Thus we conclude that the detected mean $\mu$ m flux is real. + We performed simulations to verify how reliable the average detections were., We performed simulations to verify how reliable the average detections were. + We assumed that the star formation rate is proportional to restframe Za DIuuimositv. with different ratios for differeut classes of objects.," We assumed that the star formation rate is proportional to restframe $L_V$ luminosity, with different ratios for different classes of objects." + We found that systematic errors occur at the level of 0.1-0.2 Jy for the average fluxes., We found that systematic errors occur at the level of 0.1-0.2 mJy for the average fluxes. + For the DRGs and EROs this is not a concern. but for the fainter objects (c.g.. the non-DRGs with average flux 0.1L Jv) this iuplies that the systematic errors are at least as large as the detections.," For the DRGs and EROs this is not a concern, but for the fainter objects (e.g., the non-DRGs with average flux 0.14 mJy) this implies that the systematic errors are at least as large as the detections." + The systematic problems are due to a conibination of effects; iuchiding the negative “sidelobes” in the beam pattern. which cause the total flux of the map to be zero. aud can reduce the flux for the faint. but abundant nou-DRC aud superpositions ofobjects.," The systematic problems are due to a combination of effects, including the negative “sidelobes” in the beam pattern, which cause the total flux of the map to be zero, and can reduce the flux for the faint, but abundant non-DRGs, and superpositions of objects." + Obviously. simil observationss. of other fields would help to constrain the errors for the DRGs: but it is unclear whether such measurements will ever constrain the flux from the faint uon-DRCs.," Obviously, similar observations of other fields would help to constrain the errors for the DRGs; but it is unclear whether such measurements will ever constrain the flux from the faint non-DRGs." + The average SER of the DRCs can be estimated roni the average subuun flux assmnuius an SED aud an initial mass function (IME)., The average SFR of the DRGs can be estimated from the average submm flux assuming an SED and an initial mass function (IMF). + As the subnun aud ‘ar-intrared (FIR) SED of the DRGs ijs uuknown. we use the SED description for dusty starburst ealaxies from Yun&Carilli(2002) for calculating he FIR luminosity.," As the submm and far-infrared (FIR) SED of the DRGs is unknown, we use the SED description for dusty starburst galaxies from \citet{YunCar02} for calculating the FIR luminosity." +" Because of the laree negative A-correction dn. the παατα, the observed 850,an flux densifv ds essentially coustaut between redshift ] ixl 8 for a gen luuinositv."," Because of the large negative $k$ -correction in the submm, the observed $\mu$ m flux density is essentially constant between redshift 1 and 8 for a given luminosity." + For the DRG 2) 2] B3.5semple.theaverage FIRluiminositgisl.2«1032 LL. which is comparable to the luninosity of the local ultraluniinous infrared ealaxy (ULIRG) 2220.," For the DRG $<$ $z$ $<$ 3.5 sample, the average FIR luminosity is $1.2\times10^{12}$ $_\odot$, which is comparable to the luminosity of the local ultraluminous infrared galaxy (ULIRG) 220." + Firthermore. we base the conversion between FIR huuimositv and SER ou Ποσο(1998).. where a Salpeter TIF iu the mass range MINI. is assumed.," Furthermore, we base the conversion between FIR luminosity and SFR on \citet{kennicutt98}, where a Salpeter IMF in the mass range $_\odot$ is assumed." + However. we asstuned a lean age of the stellar population of αντ aud a constant star formation dure that time. which lowers the couversion by a factor of 1.5:ILpnS|L.," However, we assumed a mean age of the stellar population of 1Gyr and a constant star formation during that time, which lowers the conversion by a factor of 1.5:." +[. We assmned thisSFR\AL longer meant\= age since modcling of the optical-Near IR SEDs suggest ages of 1-2 Cyr (FS01)., We assumed this longer mean age since modeling of the optical-Near IR SEDs suggest ages of 1-2 Gyr (FS04). + We obtain au average SER of 159XE12MM | for 2«<045. where the error reflects the accuracy of the subnuu detection.," We obtain an average SFR of $159\pm42$ $_\odot$ $^{-1}$ for $20 corresponds to an outward directed $(F_{\rm M})_r$ (Eq." + 4)., 4). + A critical lag weit is thus defined as the maxinum value of the lag that the available pinning forces can sustain., A critical lag $\omega_{\rm crit}$ is thus defined as the maximum value of the lag that the available pinning forces can sustain. + For larger assumed values of the lag. w>wey. however stationary pinning conditions may nol be realized. aud (he spinning down of the superfluid occurs as in the absence of any pinning. whileaff of the vorlices move and are influenced by (he existing external forces. instantaneouslv.," For larger assumed values of the lag, $\omega \geq \omega_{\rm +crit}$, however stationary pinning conditions may not be realized, and the spinning down of the superfluid occurs as in the absence of any pinning, while of the vortices move and are influenced by the existing external forces, instantaneously." + In contrast. when w«wey. which is the case of interest here. vortices might be still released [rom (heir pinning sites.though partially ancl temporarily. due to other unpinning," In contrast, when $\omega< \omega_{\rm crit}$, which is the case of interest here, vortices might be still released from their pinning sites,though partially and temporarily, due to other unpinning" +AIS is grateful for UCL/MSSL. support.,MS is grateful for UCL/MSSL support. + FPhanks to Simon Dve for his help with the BLAST data., Thanks to Simon Dye for his help with the BLAST data. + In order to use the CLLAO® L-T relation. which uses colour. instead. of SED peak wavelength. we establish a conversion between the two quantities.," In order to use the CHA09 L-T relation, which uses colour, instead of SED peak wavelength, we establish a conversion between the two quantities." + Using our fitted SED templates. we calculate rest-frame Lboo/Lioo colour (C) for the 27 local IIpSCz ULIRGs (where Ly is in W/Lz for direct comparison with the € — log (fou /fiow) where fy is in Jv] definition used in CILXAOO9).," Using our fitted SED templates, we calculate rest-frame $_{60}$ $_{100}$ colour (C) for the 27 local IIFSCz ULIRGs (where $_{\lambda}$ is in W/Hz for direct comparison with the C [= log $_{60}$ $_{100}$ ) where $_{\lambda}$ is in Jy] definition used in CHA09)." + As expected. C and Aja follow a one to one relationship which can be fit with the following equation (using a biweight estimator): where C—log (Lig /Ling). A2..," As expected, C and $\lambda_{\rm peak}$ follow a one to one relationship which can be fit with the following equation (using a biweight estimator): where C=log $_{60}$ $_{100}$ \ref{fig:fig9}." +but have not yet beenfirmed?.,but have not yet been. +". The putative TTVs for HAT-P-13 have been challenged by Fultonetal.(2011),, who presented observations of ten transits over two observing seasons."," The putative TTVs for HAT-P-13 have been challenged by \citet{Fulton+11aj}, who presented observations of ten transits over two observing seasons." +" They found that a linear ephemeris was an acceptable match to all transit timing measurements, with the exception of the first of the two obtained by Szabóetal.(2010).."," They found that a linear ephemeris was an acceptable match to all transit timing measurements, with the exception of the first of the two obtained by \citet{Szabo+10aa}." +" The physical properties of the HAT-P-13 system have been derived by Bakosetal.(2009) and Winnetal.(2010b),, who used the same light curves."," The physical properties of the HAT-P-13 system have been derived by \citet{Bakos+09apj2} and \citet{Winn+10apj2}, who used the same light curves." + Since these studies a wealth of new photometric data has been gathered., Since these studies a wealth of new photometric data has been gathered. +" This has been used to investigate putative TTVs, but has not been brought to bear on improving the physical properties of the system."," This has been used to investigate putative TTVs, but has not been brought to bear on improving the physical properties of the system." + In this work we present new photometry covering four transits and use all available high-quality photometry to measure refined physical properties of HAT-P-13., In this work we present new photometry covering four transits and use all available high-quality photometry to measure refined physical properties of HAT-P-13. +" Two full transits of HAT-P-13 were observed with the BFOSC imager mounted on the mm CCassini at Loiano Observatory, Italy."," Two full transits of HAT-P-13 were observed with the BFOSC imager mounted on the m Cassini at Loiano Observatory, Italy." + We used a Gunn filter and autoguided throughout., We used a Gunn $i$ filter and autoguided throughout. +" We had to reject a small numberi of datapoints in both transits, as they were affected by pointing jumps which compromised the data quality."," We had to reject a small number of datapoints in both transits, as they were affected by pointing jumps which compromised the data quality." + A summary of our observations is given in reftab:obslog and the full data can be found in reftab:lc.., A summary of our observations is given in \\ref{tab:obslog} and the full data can be found in \\ref{tab:lc}. +" The telescope was defocussed so the point spread functions (PSFs) resembled annuli of widths 15—25 pixels, in order to reduce the light from the target and comparison stars to a maximum of roughly 350000 counts per pixel."," The telescope was defocussed so the point spread functions (PSFs) resembled annuli of widths 15–25 pixels, in order to reduce the light from the target and comparison stars to a maximum of roughly 000 counts per pixel." + This approach reduces the susceptibility of the data to flat-fielding noise and increases the efficiency of the observations., This approach reduces the susceptibility of the data to flat-fielding noise and increases the efficiency of the observations. +" A detailed description of the defocussing method can be found in Southworthetal.(2009a,b)., and an instance of its use with the Cassini telescope in Southworthal. (2010).."," A detailed description of the defocussing method can be found in \citet{Me+09mn,Me+09mn2}, and an instance of its use with the Cassini telescope in \citet{Me+10mn}." +" Several images were taken with the telescope properly focussed, and used to verify that there were no faint stars within the defocussed PSF of HAT-P-13."," Several images were taken with the telescope properly focussed, and used to verify that there were no faint stars within the defocussed PSF of HAT-P-13." + Data reduction was undertaken using standard methods pertaining to aperture photometry., Data reduction was undertaken using standard methods pertaining to aperture photometry. + Software aperture positions were specified by hand but shifted to account for pointing, Software aperture positions were specified by hand but shifted to account for pointing +should be applied to early PC data when the count rate is higher than ~0.6 count s~ in order to get correct X-ray lightcurve and spectra.,should be applied to early PC data when the count rate is higher than $\sim 0.6$ count $^{-1}$ in order to get correct X-ray lightcurve and spectra. + We made this correction by fitting a King function profile to the point spread function (PSF) to determine the radial point at which the measured PSF deviates from the model., We made this correction by fitting a King function profile to the point spread function (PSF) to determine the radial point at which the measured PSF deviates from the model. +" The counts were extracted using an annular aperture that excluded the affected ~4 pixel core of the PSF, and the count rate was corrected according to the model."," The counts were extracted using an annular aperture that excluded the affected $\sim$ 4 pixel core of the PSF, and the count rate was corrected according to the model." + We also considered the most recent calibration and exposure maps., We also considered the most recent calibration and exposure maps. +" reffig:XRT1 shows the 0.3-10 keV X-ray lightcurve, which can be well modeled with a doubly broken power-law which is equivalent with a broken power-law with a jump transition at ~500 s. For a doubly broken power-law, the fitted parameters are: ay=—1.75+0.04 (x?=152.4 for 119), th1~310 s, a2=—0.70+0.13 (x?=13.7 for 18), ty~2.9x10? s, a3=—1.24+0.03 (x?=38.9 for 54)."," \\ref{fig:XRT1} shows the 0.3-10 keV X-ray lightcurve, which can be well modeled with a doubly broken power-law which is equivalent with a broken power-law with a jump transition at $\sim$ 500 s. For a doubly broken power-law, the fitted parameters are: $\alpha_1 = -1.75 \pm 0.04$ $\chi^2=152.4$ for 119), $t_{\rm b1} \sim 310$ s, $\alpha_2 = -0.70 \pm 0.13$ $\chi^2=13.7$ for 18), $t_{\rm b2} \sim 2.9 \times 10^3$ s, $\alpha_3 += -1.24 \pm 0.03$ $\chi^2=38.9$ for 54)." + The integrated spectra of the above first and third segments are shown in reffig:SED.., The integrated spectra of the above first and third segments are shown in \\ref{fig:SED}. +" In detail, the spectral power-law indices are 6; 0.05, 83=—1.27+0.10, and {2 is in the middle."," In detail, the spectral power-law indices are $\beta_1= +-0.74\pm0.05$ , $\beta_3=-1.27\pm0.10$, and $\beta_2$ is in the middle." + The Swift Ultraviolet and Optical Telescope (UVOT) began observing at ~150 after the trigger and found no optical counterpart down to ~18s mag (Immleretal. 2008))., The Ultraviolet and Optical Telescope (UVOT) began observing at $\sim$ 150 s after the trigger and found no optical counterpart down to $\sim$ 18 mag \citealt{Immler08}) ). +" Ground-based observations of the afterglow of 0081109A were carried out with the REM telescope at La Silla (Zerbietal2001;Chincarinietal2003;Covinoal. 2004)) equipped with the ROSS optical spectrograph/imager and the REMIR near-infrared camera on 2008 Nov 09, starting about 52 seconds after the burst(D’Avanzo 2008))."," Ground-based observations of the afterglow of 081109A were carried out with the REM telescope at La Silla \citealt{Zerbi01,Chincarini03,Covino04}) ) equipped with the ROSS optical spectrograph/imager and the REMIR near-infrared camera on 2008 Nov 09, starting about 52 seconds after the burst\citealt{DAvanzo08}) )." +" The night was clear, with a seeing of about 2.0""."," The night was clear, with a seeing of about $2.0''$ ." +model b has a sienilicantlv sharper change at the edge of the flux rope than is the case for model a. and its angle is consistently smaller over much of the fIux rope volume. indicating a more sheared field.,"model b has a significantly sharper change at the edge of the flux rope than is the case for model a, and its angle is consistently smaller over much of the flux rope volume, indicating a more sheared field." + In model d almost all of the angle changes are concentrated at the center and the edge of the flix rope., In model d almost all of the angle changes are concentrated at the center and the edge of the flux rope. + Here there is a concentration of highlv sheared field al the center of the flix rope. outside which the anele has a plateau between 607 and. 707. finally increasing sharply to 90° at the edge.," Here there is a concentration of highly sheared field at the center of the flux rope, outside which the angle has a plateau between $60^{\circ}$ and $70^{\circ}$, finally increasing sharply to $90^{\circ}$ at the edge." + In the other models the distribution of angle changes is more even., In the other models the distribution of angle changes is more even. + The clamping of angle contours near (he edge of each fIux rope in models b. c and d is an elfect of the total field strength there - small changes in /? cause large changes in the angle there.," The clumping of angle contours near the edge of each flux rope in models b, c and d is an effect of the total field strength there - small changes in $f^2$ cause large changes in the angle there." + Chromospheric fibrils as observed in Hla are believed to delineate magnetic [lux tube, Chromospheric fibrils as observed in $\alpha$ are believed to delineate magnetic flux tube +munber of fundamental Cepheid calibrators and bring the uncertainties down to £2% We discuss each of these steps in (urn. and give an overview of some preliminary results based on our current analysis ofSpAzer data.,"number of fundamental Cepheid calibrators and bring the uncertainties down to $\pm$ We discuss each of these steps in turn, and give an overview of some preliminary results based on our current analysis of data." + Two relatively recent developments have dramatically changed the landscape regarding a recalibration of the extragalactic distance scale., Two relatively recent developments have dramatically changed the landscape regarding a recalibration of the extragalactic distance scale. + First. Benedict (2007) used the Fine Guidance Sensors (FGS) on LST to provide the first high-precision. geometric parallaxes {ο 10 nearby Galactic Cepheids having periods ranging from 4 to 35 days.," First, Benedict (2007) used the Fine Guidance Sensors (FGS) on HST to provide the first high-precision, geometric parallaxes to 10 nearby Galactic Cepheids having periods ranging from 4 to 35 days." + Second. Freedman: (2008) demonstrated (using Spilzer/SAGE legacy data for the LMC from Meixner 2006) the small dispersion in the mid-infrared Period-Luminosity. (PL) relations (hereafter relerred (o as the Leavitt Law) at mid-infrared wavelengths. even for single (not. observations of Cepheids.," Second, Freedman (2008) demonstrated (using /SAGE legacy data for the LMC from Meixner 2006) the small dispersion in the mid-infrared Period-Luminosity (PL) relations (hereafter referred to as the Leavitt Law) at mid-infrared wavelengths, even for single (not phase-averaged) observations of Cepheids." + Mid-inlrared observations of Cepheids offer a host of advantages over shorter wavelength data., Mid-infrared observations of Cepheids offer a host of advantages over shorter wavelength data. + Most. important is the reduced sensiüvitv of lone-waveleneth data (o. line-ol-sieht interstellar extinction (both Galactic and extragalactic)., Most important is the reduced sensitivity of long-wavelength data to line-of-sight interstellar extinction (both Galactic and extragalactic). + The interstellar extinction law at mid-infrared wavelengths has now been measured by a number of authors (Rieke Lebolsky 1985: 2005: 2007: 2007: 2009)., The interstellar extinction law at mid-infrared wavelengths has now been measured by a number of authors (Rieke Lebofsky 1985; 2005; 2007; 2007; 2009). +" Thev find that the shape of the extinction curve varies somewhat between dilferent sightlines. where the observed range of 3A, is 0.0580.071 al 3.6 jim. and 0.0230.060 al 4.5 jan. However. the most important point is that the extinction measured in magnitudes in (he mid-IB. as compared to optical V-band data. for example. is reduced by [actors of 14-17 ad 3.6 jan. and 16-43 al 4.5 jm. In practice then. for Ay\~ 0.20 mae.5 with an uncertaintv in the reddeninge5 of (cL(D—V) = £0.02) mag (giving eM] of £0.06 mag). at mic-IR wavelengths this reduces (0 clau, = 0.0128 0.004 mag: that is. the correction to a V-band distance transforms [rom to a correction of only in distance at 3.6 pam. and it drops the uncertainty on the distance from in the visual down to a statistically insignificant level of only 40.2%. at 3.6 qum. In addition. because stellar surface brightness in the mid-infrared is so insensitive to temperature (being on (he Havleigh-Jeans portion of the spectral energy. distribution). the observed. evelical variation in à Cepheid's huminosity at 2.6 sam is almost completely dominated by the comparatively small racial (1.e.. surface area) variations."," They find that the shape of the extinction curve varies somewhat between different sightlines, where the observed range of $A_{\lambda}/A_V$ is 0.058–0.071 at 3.6 $\mu$ m, and 0.023–0.060 at 4.5 $\mu$ m. However, the most important point is that the extinction measured in magnitudes in the mid-IR, as compared to optical $V$ -band data, for example, is reduced by factors of 14-17 at 3.6 $\mu$ m, and 16-43 at 4.5 $\mu$ m. In practice then, for $A_V \sim$ 0.20 mag, with an uncertainty in the reddening of $\epsilon$ $E(B-V)$ = $\pm$ 0.02) mag (giving $\epsilon$ $_V$ ] of $\pm$ 0.06 mag), at mid-IR wavelengths this reduces to $A_{3.6\mu m}$ = $\pm$ 0.004 mag; that is, the correction to a V-band distance transforms from to a correction of only in distance at 3.6 $\mu$ m, and it drops the uncertainty on the distance from in the visual down to a statistically insignificant level of only $\pm$ at 3.6 $\mu$ m. In addition, because stellar surface brightness in the mid-infrared is so insensitive to temperature (being on the Rayleigh-Jeans portion of the spectral energy distribution), the observed, cyclical variation in a Cepheid's luminosity at 3.6 $\mu$ m is almost completely dominated by the comparatively small radial (i.e., surface area) variations." + The slope of the Period-Luminosity relation in the mil-IR. then becomes virtually equivalent to the, The slope of the Period-Luminosity relation in the mid-IR then becomes virtually equivalent to the +field along the disk. ο)=οἱ)ο”.,"field along the disk, $B_\phi(r)=2I_d(r)/cr$." +" Close to the disk. rB., is approxinatelv coustaut along a magnetic field line."," Close to the disk, $rB_\phi$ is approximately constant along a magnetic field line." +" The three components of the initial maeuetic field on the disk are shown in Figure 1,", The three components of the initial magnetic field on the disk are shown in Figure 4. + To escape rapid twisting of the maguetic field due to the difference between the azimuthal velocities ofthe disk aud the corona. we supposed that the corona iitially rotates with an angular velocity which is constant on cvluders r=coust and equal to eg/r of the disk.," To escape rapid twisting of the magnetic field due to the difference between the azimuthal velocities of the disk and the corona, we supposed that the corona initially rotates with an angular velocity which is constant on cylinders $r=$ const and equal to $v_K/r$ of the disk." + As a result of this rotation the corona is not in equilibrium iu the +-direction., As a result of this rotation the corona is not in equilibrium in the $r$ -direction. + However. this lack of initial equilibriun does not disrupt the evolution of outflows froin the disk. aud it does not affect the final stationary states where the flaw reaches equilibrium.," However, this lack of initial equilibrium does not disrupt the evolution of outflows from the disk, and it does not affect the final stationary states where the flow reaches equilibrium." + The lower boundary of our sinulatiou region is the disk which is perfectly conducting aud rotates at the I&eperiau vate., The lower boundary of our simulation region is the disk which is perfectly conducting and rotates at the Keperian rate. +" Thus the tangential component of the electric field im the svstem of coordinates rotating with the disk is zero. at 2=0. where v;=ege, and v is the fluid velocity just above the disk."," Thus the tangential component of the electric field in the system of coordinates rotating with the disk is zero, at $z=0$, where ${\bf v}_d = v_K {\bf e}_\phi$, and $\bf v$ is the fluid velocity just above the disk." + This condition means that in this system of coordinates the poloidal velocity is parallel to the poloidal magnetic field at 2=0., This condition means that in this system of coordinates the poloidal velocity is parallel to the poloidal magnetic field at $z=0$. + The magnetic field is frozen iuto the disk so that DB.=Date) whereBy. is a eiven function of + and is determined by the :-comiponeut of the imitial monopole maenectic field.," The magnetic field is frozen into the disk so that $B_z=B_{dz}(r)$, where$B_{dz}$ is a given function of $r$ and is determined by the $z$ -component of the initial monopole magnetic field." +" Notice that the two other field compoucuts. D, aud D,,. ave not fixed on the disk aud change with time so as to satisfy the MIID equations in the computational reelon."," Notice that the two other field components, $B_r$ and $B_\phi$, are not fixed on the disk and change with time so as to satisfy the MHD equations in the computational region." + We suppose that the density aud cutropy on the disk surface are fixed. p=par).οο) with ο) and Sur) given functions of ¢ which follow from equations (29) ancl (31).," We suppose that the density and entropy on the disk surface are fixed, $\rho=\rho_d(r),~S=S_d(r)$ with $\rho_d(r)$ and $S_d(r)$ given functions of $r$ which follow from equations (29) and (31)." + Note that in the present work. the velocity of outflow from the disk is a free variable.," Note that in the present work, the velocity of outflow from the disk is a free variable." + This is different frou our earlicr work (Ustvusova cet al., This is different from our earlier work (Ustyugova et al. + 1995)., 1995). + When the velocity of outflow from the disk is less than the slow mmaguetosonic speed. then the nuuber of boundary conditions we have is sufficient.," When the velocity of outflow from the disk is less than the slow magnetosonic speed, then the number of boundary conditions we have is sufficient." + ILowever. if the outflow velocity is super slow maguctosouic. then there should be an additional houndary condition.," However, if the outflow velocity is super slow magnetosonic, then there should be an additional boundary condition." + Because we do not have this additional boundary conditiou. we suppose that the amplitudes of the correpouding outgoing waves are equal to zero.," Because we do not have this additional boundary condition, we suppose that the amplitudes of the correponding outgoing waves are equal to zero." + This is equivalent to the fact that we use the values of calculated parameters in the cells just above the disk., This is equivalent to the fact that we use the values of calculated parameters in the cells just above the disk. + Ou the : axis. all fluxes normal to this axisare equal to zero.," On the $z-$ axis, all fluxes normal to this axisare equal to zero." +" On the outer boundaries. ΞBu OF 2=Zu the “free” boundary couditions =0 were used for all variables exchiding B,,."," On the outer boundaries, $r=R_{max}$ or $z=Z_{max}$, the “free” boundary conditions $\partial F_j/{\partial n}=0$ were used for all variables excluding $B_\phi$." +" Were.Συ 0/0» is the derivative perpendicukw to the boundary —lp.f(5)ey. Co.USB,.Be}."," Here, $\partial/{\partial n}$ is the derivative perpendicular to the boundary, $F_j=\{\rho,~ f(S),~ v_r,$ $v_\phi,~ v_z,~ B_r,~ B_z\}$." + Our earlier simulation£F; study (Romanova et al., Our earlier simulation study (Romanova et al. +" 1997) showed that the coudition 12,δη=0 can lead to wnplysical results.", 1997) showed that the condition $\partial B_\phi/{\partial n}=0$ can lead to unphysical results. +" The outer boundary coucition on D,, is considered in detail in 81.", The outer boundary condition on $B_\phi$ is considered in detail in 4. + If the process of outflow formation is strougly nou-stationary. then the problem of the iuflueuce of outer boundary conuditious nay not appear.," If the process of outflow formation is strongly non-stationary, then the problem of the influence of outer boundary conditions may not appear." + This is because it is difficult to separate the influence of boundary conditions from effects. connected with non-stationaritv., This is because it is difficult to separate the influence of boundary conditions from effects connected with non-stationarity. + Towever. when the flow goes to a steady-state. we observed that the stationary flow pattern can depend on the iuposed outer boundary conditions aud iu some cases ou the shape of the simulation region.," However, when the flow goes to a steady-state, we observed that the stationary flow pattern can depend on the imposed outer boundary conditions and in some cases on the shape of the simulation region." + It is nuportaut to elinuinate the influence of boundary conditions., It is important to eliminate the influence of boundary conditions. + It is possible. if (1) the flow is supersonic (uper fast magnetosonic) aud it isperpendicular to the outer boundaries (then information flows out of the simulation region). or (2) the correct boundary conditions are close by some method.," It is possible, if (1) the flow is supersonic (super fast magnetosonic) and it is to the outer boundaries (then information flows out of the simulation region), or (2) the correct boundary conditions are chosen by some method." + The first condition camnot be realized diving the stage of establishing of the flow. because initially. the flow is subsonic.," The first condition cannot be realized during the stage of establishing of the flow, because initially, the flow is subsonic." + If the flow is supersonic. but is not perpendicular to the boundary. then the Mach cones may be partially directed inside the simulation region aud even supersonic flow may influence the flow inside the region.," If the flow is supersonic, but is not perpendicular to the boundary, then the Mach cones may be partially directed inside the simulation region and even supersonic flow may influence the flow inside the region." + The orieutatiou of the Mach cones depends iu eoncral on the shape of simulation region., The orientation of the Mach cones depends in general on the shape of simulation region. + The second condition cau be realized onlv in some approximation., The second condition can be realized only in some approximation. + The “best” outer boundary couditious are those which influence oulv the vicinity of the bomudarics and not the central part of the simulation region., The “best” outer boundary conditions are those which influence only the vicinity of the boundaries and not the central part of the simulation region. + This involves all flow variables. but we will cliscuss only the outer houndary condition ou δι. because we fouud that this condition had the strongest influeuce ou the calculated flows.," This involves all flow variables, but we will discuss only the outer boundary condition on $B_\phi$, because we found that this condition had the strongest influence on the calculated flows." +" The final flow may depend on both the Mach cone oricutation at the boundaries (shape of the region) aud ou the outer boundary condition ou D,,.", The final flow may depend on both the Mach cone orientation at the boundaries (shape of the region) and on the outer boundary condition on $B_\phi$. + Iu differeut situations oue of these factors may be more niportant than the other., In different situations one of these factors may be more important than the other. +" To separate their influence ou the final flow pattern. we discuss im §L.1 simulations for a fixed. simulation region. but with ditfercut outer boundary couditious on D,,."," To separate their influence on the final flow pattern, we discuss in 4.1 simulations for a fixed simulation region, but with different outer boundary conditions on $B_\phi$ ." +" Next. in $L2 we fixed the boundary condition on D, and investigated the depeudeuce of the flow on the shape of"," Next, in 4.2 we fixed the boundary condition on $B_\phi$ , and investigated the dependence of the flow on the shape of" +first-order differential equatious to solve for the photon trajectories.,first-order differential equations to solve for the photon trajectories. + This improves the accuracy of the calculation aud increases its speed (e.g. Rauch Blaucllord 1991: Dexter Agol 2009: see. however. Broderick 2006: Doleuce et 22009 for dilfereut approaches).," This improves the accuracy of the calculation and increases its speed (e.g., Rauch Blandford 1994; Dexter Agol 2009; see, however, Broderick 2006; Dolence et 2009 for different approaches)." + The Ixerr iuetric is very particular both in the seuse that it is completely described by ouly two parameters (the mass aud the spin of the compact object) aud that orbits within this metric are characterized by the Carter constant. (see. e.g.. discussion in Will 2009).," The Kerr metric is very particular both in the sense that it is completely described by only two parameters (the mass and the spin of the compact object) and that orbits within this metric are characterized by the Carter constant (see, e.g., discussion in Will 2009)." + Introducing auy deviatiou [rom the Ixerr metric. while satis{vine the vacuum Elustein field) equations. does not preserve its Petrov-type D character and the Carter constant is uo longer conserved aloug geodesies (see. e.g. Glampedakis Babak 2006: Cair. Li. Nlaudel 2008).," Introducing any deviation from the Kerr metric, while satisfying the vacuum Einstein field equations, does not preserve its Petrov-type D character and the Carter constant is no longer conserved along geodesics (see, e.g., Glampedakis Babak 2006; Gair, Li, Mandel 2008)." + As a result. ray tracing in a non-Ixerr metric cannot be performed entirely using iutegrals of motious but requires integrating the secoucd-order differential equatious for incividual geocdesies.," As a result, ray tracing in a non-Kerr metric cannot be performed entirely using integrals of motions but requires integrating the second-order differential equations for individual geodesics." + There are at least two clistinet astroplivsical settiugs for which ray tracing iu a metric that deviates [rom the err solution is important., There are at least two distinct astrophysical settings for which ray tracing in a metric that deviates from the Kerr solution is important. + First. the exterual spacetime of a neutron star spiuulng at ~300—600 Hz. which is typical of X-ray. bursters in low-1nass N-ray binaries. is not accurately described by the Ixerr inetric.," First, the external spacetime of a neutron star spinning at $\simeq +300-600$ Hz, which is typical of X-ray bursters in low-mass X-ray binaries, is not accurately described by the Kerr metric." + Effects related to the oblateness of the star (Morsiuk et 22007) as well as to deviatious of the quadrupole moment of its spacetime [rom the Ixerr value (Hartle Thorne 1968: see also Laarakkers Poisson 1999: Berti Stergioulas 2001) are not negligible at these spin frequencies., Effects related to the oblateness of the star (Morsink et 2007) as well as to deviations of the quadrupole moment of its spacetime from the Kerr value (Hartle Thorne 1968; see also Laarakkers Poisson 1999; Berti Stergioulas 2004) are not negligible at these spin frequencies. + Matching the theoretical mocels to the level of accuracy reached with current. observatious of spinuine[n] neutron stars can ouly be achieved by conskleriug at least the deviation of the quadrupole moments of their spacetimes from the herr values., Matching the theoretical models to the level of accuracy reached with current observations of spinning neutron stars can only be achieved by considering at least the deviation of the quadrupole moments of their spacetimes from the Kerr values. + Secoud. calculating the observatioual appearance of black holes with arbitrary quadrupole —ος=jents can be used iu testing the uo-hair theorem with astrophysical observatious (Joliaunsen Psaltis 2010a. 2010b. 20106).," Second, calculating the observational appearance of black holes with arbitrary quadrupole moments can be used in testing the no-hair theorem with astrophysical observations (Johannsen Psaltis 2010a, 2010b, 2010c)." + The absence of additional ‘hair’ ensures that all runoments of a black hole spacetime that are higher than the dipole have a particular clepeuceuce ou the mass aud the W.pin of the black bole., The absence of additional `hair' ensures that all moments of a black hole spacetime that are higher than the dipole have a particular dependence on the mass and the spin of the black hole. + In particular. the quadrupole moment q of a black hole W.spacetime has to epeud ou itsH spinH a accordingH to the relationH g=>—«7. where all quantitiesm have been normalizedH with appropriate powers of the mass M. of the black hole.," In particular, the quadrupole moment $q$ of a black hole spacetime has to depend on its spin $a$ according to the relation $q=-a^2$, where all quantities have been normalized with appropriate powers of the mass $M$ of the black hole." + Allowing for the quadrupole moment ol the spacetime to take arbitrary values ancl using observatious to test the validity of the above relation between the quadrupole aud the spin of the black hole constitutes a formal quantitative test of the no-hair theorem (Ryau 1995)., Allowing for the quadrupole moment of the spacetime to take arbitrary values and using observations to test the validity of the above relation between the quadrupole and the spin of the black hole constitutes a formal quantitative test of the no-hair theorem (Ryan 1995). + Here we present a uew ray-tracing algorithun for calculating the observational appearance of spiuniug compact objects with arbitrary quadrupole moments., Here we present a new ray-tracing algorithm for calculating the observational appearance of spinning compact objects with arbitrary quadrupole moments. + We employ the metric of Clampecdakis Babak (2006). which is characterized by three parameters: tle mass aud spin of the compact object and its quadrupole moment.," We employ the metric of Glampedakis Babak (2006), which is characterized by three parameters: the mass and spin of the compact object and its quadrupole moment." + In the algorithm. we integrate two first-order clillerential equations that arise [rom integrals of motion as well as two second-order differential equations for two components of the geodesic equatious in order to compute the trajectories of pliotons in," In the algorithm, we integrate two first-order differential equations that arise from integrals of motion as well as two second-order differential equations for two components of the geodesic equations in order to compute the trajectories of photons in" +0.024ΧΚ for a subsample of 54 galaxies.,$\times R$ for a subsample of 54 galaxies. + The color-magnitude diagram is shown in Fig. 3.., The color-magnitude diagram is shown in Fig. \ref{fig:3}. +" From the photometric catalog, we considered as “likely cluster members” those galaxies lying within 0.25 mag of the CMR."," From the photometric catalog, we considered as “likely cluster members” those galaxies lying within 0.25 mag of the CMR." + Fig., Fig. + 4 shows a zoomed region of the contour map for the likely members (734 galaxies within the whole ~ region)., \ref{fig:4} shows a zoomed region of the contour map for the likely members (734 galaxies within the whole $\sim$ region). +" The galaxy distribution reveals two significant peaks ~5’ (~0.5 Mpc) far: the NNE peak, coincident with the BCG, and the SSW peak, with no dominant galaxy, at R.A.=04°59™05$4, Dec.=+08°45’06” (J2000.0)."," The galaxy distribution reveals two significant peaks $\sim +5\arcm$ $\sim 0.5$ Mpc) far: the NNE peak, coincident with the BCG, and the SSW peak, with no dominant galaxy, at $04^{\mathrm{h}}59^{\mathrm{m}}05\dotsec4$, $+08\degree +45\arcmm 06\arcs$ (J2000.0)." +" The SSW peak has the higher density and a larger population — by factors of 1.2 and 2.7 according to the 2D adaptive—kernel method (2D DEDICA, Pisani 1996))."," The SSW peak has the higher density and a larger population – by factors of 1.2 and 2.7 according to the 2D adaptive–kernel method (2D DEDICA, Pisani \cite{pis96}) )." +" Figure 3 also shows the 105 galaxies of the photometric sample within a radius of from the SSW peak, whose properties can be accurately described by the above CMR, too, suggesting that both clumps are at a similar redshift."," Figure \ref{fig:3} also shows the 105 galaxies of the photometric sample within a radius of from the SSW peak, whose properties can be accurately described by the above CMR, too, suggesting that both clumps are at a similar redshift." + Ebelingetal.1998 report a cluster X-ray luminosity in the 0.1-2.4 keV band of 1.07 x 10“ erg/sec (after cosmological corrections)., \cite{ebe98} report a cluster X-ray luminosity in the 0.1-2.4 keV band of 1.07 $\times$ $^{44}$ erg/sec (after cosmological corrections). + Bohringeretal.2000 report a slightly lower value of 0.9 x 10“ erg/sec., \cite{boe00} report a slightly lower value of 0.9 $\times$ $^{44}$ erg/sec. + The hot ICM (see Fig. 1)), The hot ICM (see Fig. \ref{fig:1}) ) + is clearly bimodal in agreement with the optical galaxy distribution., is clearly bimodal in agreement with the optical galaxy distribution. +" However, a clear shift between the galaxies and gas distribution is present (see Fig. 5))"," However, a clear shift between the galaxies and gas distribution is present (see Fig. \ref{fig:5}) )" + and the BCG is not coincident with the X-ray peak., and the BCG is not coincident with the X-ray peak. + The SSW structure is more extended and shows an irregular shape., The SSW structure is more extended and shows an irregular shape. + The NNE clump is more compact and regular., The NNE clump is more compact and regular. +" The bright source, visible in the X-ray map at R.A.=0459™37 Dec.=+08°45’50” (J2000.0) is identified with a discrete unrelated$7, radio source."," The bright source, visible in the X-ray map at $04^{\mathrm{h}}59^{\mathrm{m}}37\dotsec7$, $+08\degree +45\arcmm 50\arcs$ (J2000.0) is identified with a discrete unrelated radio source." +" We conclude that optical and X-ray data that we have presented indicate a merging cluster structure, where the main cluster is identified with the SSW structure."," We conclude that optical and X-ray data that we have presented indicate a merging cluster structure, where the main cluster is identified with the SSW structure." +" This cluster as shown by its irregular shape and lack of a dominant galaxy, was not in a relaxed stage, and is now strongly interacting (major merging) with a more compact cluster (the NNE structure) dominated by a bright BCG."," This cluster as shown by its irregular shape and lack of a dominant galaxy, was not in a relaxed stage, and is now strongly interacting (major merging) with a more compact cluster (the NNE structure) dominated by a bright BCG." + We present in Fig., We present in Fig. +" 6 the plot of the total radio power and X-ray luminosity for radio halos as shown by Giovanninietal.2009,, where we have included 0217+70 and A523."," \ref{fig:6} the plot of the total radio power and X-ray luminosity for radio halos as shown by \cite{gio09}, where we have included 0217+70 and A523." +" The dots refer to classical powerful radio halos in X-ray luminous clusters, which have been found to show a correlation between the radio power and the X-ray luminosity."," The dots refer to classical powerful radio halos in X-ray luminous clusters, which have been found to show a correlation between the radio power and the X-ray luminosity." +" The red triangles are outliers, i.e. they refer to the few known radio halos that are overluminous in radio with respect to the empirical radio - correlation."," The red triangles are outliers, i.e. they refer to the few known radio halos that are overluminous in radio with respect to the empirical radio - X-ray correlation." +substitution can be computed from the convolution of the filter with an auxiliary map w(r). which has a value | inside the range of valid data and 0 in the zero-padded region.,"substitution can be computed from the convolution of the filter with an auxiliary map $w(\vec{r})$, which has a value 1 inside the range of valid data and 0 in the zero-padded region." +" Because the A- filter (2), has to fulfil the two it has to be split into the positive and negative filter parts for the computation of the normalisation errors.", Because the $\Delta$ -variance filter $\bigodot_l$ has to fulfil the two it has to be split into the positive and negative filter parts for the computation of the normalisation errors. + The sums extend over the map of valid data., The sums extend over the map of valid data. + In total four convolution integrals need to be evaluated to compute the A-variance where fpi Stands for the map with the additional zero-padded boundary region., In total four convolution integrals need to be evaluated to compute the $\Delta$ -variance where $f\sub{padded}$ stands for the map with the additional zero-padded boundary region. + the convolution integrals can be easily computed in Fourier space involving a fast Fourier transform and a map multiplication., the convolution integrals can be easily computed in Fourier space involving a fast Fourier transform and a map multiplication. +" The full map convolved with the A-variance filter truncated at the map edges is then It is only defined where the normalisation parameters W,coe and W,any are both different from zero."," The full map convolved with the $\Delta$ -variance filter truncated at the map edges is then It is only defined where the normalisation parameters $W\sub{{\it l}, core}$ and $W\sub{{\it l}, ann}$ are both different from zero." + In the computation of the A-variance spectrum one has to take into account the reduced significance of the data values in the convolved maps produced by the fact that the applied filter becomes more and more distorted relative to the optimum filter when it is truncated., In the computation of the $\Delta$ -variance spectrum one has to take into account the reduced significance of the data values in the convolved maps produced by the fact that the applied filter becomes more and more distorted relative to the optimum filter when it is truncated. + Using the normalisation parameters of the truncated filters as d neasure for their significance one can add a significance weighting to the A-variance analysis., Using the normalisation parameters of the truncated filters as a measure for their significance one can add a significance weighting to the $\Delta$ -variance analysis. + We define the A-variance no longer as the variance of the convolved map but weight with The sum covers the whole (extended) convolved data field., We define the $\Delta$ -variance no longer as the variance of the convolved map but weight with The sum covers the whole (extended) convolved data field. + The definition of the significance function às. the product of both normalisation factorsis somewhat arbitrary but reproduces the desired behaviour that changes 1n the positive and negative part of the filter contribute equally., The definition of the significance function as the product of both normalisation factors is somewhat arbitrary but reproduces the desired behaviour that changes in the positive and negative part of the filter contribute equally. + We have tested different powers of the product but found the best agreement with the theoretical behaviour in fBm data sets for an exponent of just unity., We have tested different powers of the product but found the best agreement with the theoretical behaviour in fBm data sets for an exponent of just unity. + Figure 3. demonstrates the effect of the edge treatment in the example of an fBm structure which is periodic and for a non-periodie sub-map from a larger fBm structure., Figure \ref{fig_edgeexample} demonstrates the effect of the edge treatment in the example of an fBm structure which is periodic and for a non-periodic sub-map from a larger fBm structure. + We have used three different ways to compute the A-variance., We have used three different ways to compute the $\Delta$ -variance. + First we assume that the maps are periodic. neglecting all wrap-around effects.," First we assume that the maps are periodic, neglecting all wrap-around effects." + For the periodic fBm this is. of course. the best assumption which should reproduce exactly the properties of the power spectrum used to generate the fBm.," For the periodic fBm this is, of course, the best assumption which should reproduce exactly the properties of the power spectrum used to generate the fBm." + It is. however. rarely useful when dealing with observed data as they are in general not periodic.," It is, however, rarely useful when dealing with observed data as they are in general not periodic." + The second approach creates periodicity by mirroring the map along both axes as discussed by Stutzkietal.(1998) so that a larger periodic map is produced and wrap- effects can be neglected., The second approach creates periodicity by mirroring the map along both axes as discussed by \citet{Stutzki} so that a larger periodic map is produced and wrap-around effects can be neglected. + This approach. however. still results in discontinuities in the first derivatives at the mirror axes.," This approach, however, still results in discontinuities in the first derivatives at the mirror axes." + The third approach uses the truncated filter as described above., The third approach uses the truncated filter as described above. +ραασαν tue of NGC 6626/NGC 6638 and NGC 6558/NGC 6569. which occupy. useful locations in the Ser coordinate system (6X...) ~ (353.-2) and ~ (351.5). respectively).,"particularly true of NGC 6626/NGC 6638 and NGC 6558/NGC 6569, which occupy useful locations in the Sgr coordinate system $(\Lambda_{\odot},B_{\odot}$ ) $\sim$ (353,-2) and $\sim$ (351,5), respectively)." + The nearest clusters in our ACS program to the Ser core. other than (hose in Table 2. are NGC 6656. 6717 and 6723 (marked as open circles in Figure 12)).," The nearest clusters in our ACS program to the Sgr core, other than those in Table 2, are NGC 6656, 6717 and 6723 (marked as open circles in Figure \ref{f:2masscomp}) )." + ILowever. none of these clusters show any indication of Ser debris.," However, none of these clusters show any indication of Sgr debris." + This is expected given the relatively high I. positions of the clusters (-4.1. -6.1. and +7.5. respectively).," This is expected given the relatively high $B_{\odot}$ positions of the clusters (-4.1, -6.1, and +7.5, respectively)." + Figure 14 compares the density of Ser main sequence stars (παν) measured in our five ACS fields against the power law-+eore density model fit to M giants from Table |. of MO3., Figure \ref{f:sgrdencomp} compares the density of Sgr main sequence stars $N_{\rm Sgr}$ ) measured in our five ACS fields against the power law+core density model fit to M giants from Table 1 of M03. + The relative density level has been scaled to minimize the 47 of the comparison without altering the core radius. ellipticitv or index of the M02 power law mocel.," The relative density level has been scaled to minimize the $\chi^2$ of the comparison without altering the core radius, ellipticity or index of the M03 power law model." + Four of the fields show consistent relative densities within 1-3 σ of the prediction., Four of the fields show consistent relative densities – within 1-3 $\sigma$ of the prediction. + NGC! 6652. however. represented in Figure 14. by an open square. is significantly (7 0) olf from the prediction. despite its proximity to NGC 6637. which is at a similar radial distance and is the closest to the model prediction.," NGC 6652, however, represented in Figure \ref{f:sgrdencomp} by an open square, is significantly (7 $\sigma$ ) off from the prediction, despite its proximity to NGC 6637, which is at a similar radial distance and is the closest to the model prediction." + Removing NGC 6652 from (he fit would reduce the 4? from 31 to 3.9 (dashed line in Figure 14))., Removing NGC 6652 from the fit would reduce the $\chi^2$ from 31 to 3.9 (dashed line in Figure \ref{f:sgrdencomp}) ). + We explored whether a change to the MO3 model could bring the NGC 6652 data point back into line., We explored whether a change to the M03 model could bring the NGC 6652 data point back into line. + Five data points are insullicient to constrain either a King or exponential density model., Five data points are insufficient to constrain either a King or exponential density model. +" Llowever. we compared (he data points to a series of “lov models"" using the power law and core model from. MOS with a variety. of core radii. power law indices and elliplicilies."," However, we compared the data points to a series of “toy models"" using the power law and core model from M03 with a variety of core radii, power law indices and ellipticities." + The data were insensilive to the core radius aud [avored a slightly. shallower power law index (han (hat of M03 (2.4-2.5. compared (to. MO2's 2.6).," The data were insensitive to the core radius and favored a slightly shallower power law index than that of M03 (2.4-2.5, compared to M03's 2.6)." + We also found. that the data favored a slishtlv higher ellipticity (han MO3's 0.62 of 0.67 (with NGC 6652) or 0.65 (without)., We also found that the data favored a slightly higher ellipticity than M03's 0.62 of 0.67 (with NGC 6652) or 0.65 (without). + However. even these changes only mareinally improved the fit of the model. with and without NGC 6652. to 4? values of 29 and 3.6. respectively.," However, even these changes only marginally improved the fit of the model, with and without NGC 6652, to $\chi^2$ values of 29 and 3.6, respectively." + No simple exponential model could bring NGC! 6652 into line with the other background features., No simple exponential model could bring NGC 6652 into line with the other background features. + What could be the cause of the discrepancy in NGC 6652?, What could be the cause of the discrepancy in NGC 6652? + Completeness is not an issue: the artificial star tests described in Paper V show that all five clusters have completeness levels (ο 51Η=23., Completeness is not an issue; the artificial star tests described in Paper V show that all five clusters have completeness levels to $F814W=23$. + Ht is unlikely that any of our fields suffer [rom significant contamination from the foreground Galactic stars. despite their proximity to (he midplane.," It is unlikely that any of our fields suffer from significant contamination from the foreground Galactic stars, despite their proximity to the midplane." +ddata and subtracting fits to the continua [rom all spectra. we were able to eross-correlate the absorption spectrum of wwith. our template (Tonryu Davis. 1979).,"data and subtracting fits to the continua from all spectra, we were able to cross-correlate the absorption spectrum of with our template (Tonry Davis 1979)." +. We. corrected the resulting radial velocities by the svstemic velocity. of the template starτν Evans 1979) and fitted them with a circular function: Orbital phases were adopted. relative to the corrected CCR ephemeris. where Oy corresponds το superior conjunction of the white dwarf.," We corrected the resulting radial velocities by the systemic velocity of the template star; Evans 1979) and fitted them with a circular function: Orbital phases were adopted relative to the corrected CCF ephemeris, where $\phi_0$ corresponds to superior conjunction of the white dwarf." + 5 represents the systemic, $\gamma$ represents the systemic +although the slopes are similar from about 5 Cwr onwards.,"although the slopes are similar from about $5\,$ Gyr onwards." + For the 6822 mocel clusters we see that more mass is lost by any particular time if the cluster was initially closer to filling its tidal radius (noting that NI is the upper of the solid lines).," For the $\,6822$ model clusters we see that more mass is lost by any particular time if the cluster was initially closer to filling its tidal radius (noting that N1 is the upper of the solid lines)." + This corresponds to the finding of Cieles jaumegardt (2008) that clusters that are initially well within the tidal radius take a much greater. number of half-mass relaxation times to lose half of their mass than clusters that Gill their tidal radius., This corresponds to the finding of Gieles Baumgardt (2008) that clusters that are initially well within the tidal radius take a much greater number of half-mass relaxation times to lose half of their mass than clusters that fill their tidal radius. + Following Ciersz Hegegie (1997) an expression for the mass-Ioss rate can be written as: where In.V is the Coulomb logarithm and we take A=0.4N., Following Giersz Heggie (1997) an expression for the mass-loss rate can be written as: where $\ln \Lambda$ is the Coulomb logarithm and we take $\Lambda = 0.4 N$. + For their N-bocky models of N=500 stars Ciersz Lleeeic (1997) found a value of 1.3 for Av., For their $N$ -body models of $N = 500$ stars Giersz Heggie (1997) found a value of 1.3 for $k_{\rm e}$. + In Figure S. we plot A as a [function of the number of hall-mass relaxation times that ave elapsed., In Figure \ref{f:fig8} we plot $k_{\rm e}$ as a function of the number of half-mass relaxation times that have elapsed. + We see that the behaviour for all of the clusters hat initially fill their tidal raclit is similar. in particular N3 ollows MI. ancl that & decreases as the clusters become more evolved.," We see that the behaviour for all of the clusters that initially fill their tidal radii is similar, in particular N3 follows M1, and that $k_{\rm e}$ decreases as the clusters become more evolved." + We also see that & is lower for clusters with smaller initial rj/ri. a result that is preclicted analytically w Cicles Baumgardt (2008) and previously demonstrated » the Monte Carlo models of Spitzer Chevalier (1973).," We also see that $k_{\rm e}$ is lower for clusters with smaller initial $r_{\rm h} / r_{\rm t}$, a result that is predicted analytically by Gieles Baumgardt (2008) and previously demonstrated by the Monte Carlo models of Spitzer Chevalier (1973)." + In this work we use Eq., In this work we use Eq. + 3. and Figure S. simply as a wav of comparing the mass-loss evolution of the various models., \ref{e:dmdt} and Figure \ref{f:fig8} simply as a way of comparing the mass-loss evolution of the various models. + A detailed. examination of how dissolution times lor star clusters in tidal fields can be expected to scale with cluster parameters can be found in Baumgardt Alakino (2003) and Cieles Daumgardt (2008)., A detailed examination of how dissolution times for star clusters in tidal fields can be expected to scale with cluster parameters can be found in Baumgardt Makino (2003) and Gieles Baumgardt (2008). + We also remind the reader at this stage that the values of rj are based on threc-dimoensional data., We also remind the reader at this stage that the values of $r_{\rm h}$ are based on three-dimensional data. + LH instead we calculated the half-mass radii from a. two-dimensional projection a reduction of about 25 per cent. would result (Fleck et al., If instead we calculated the half-mass radii from a two-dimensional projection a reduction of about 25 per cent would result (Fleck et al. + 2006)., 2006). + Furthermore. Hurlev (2007) showed that projected. hall-light radii could be as much as half that of the corresponding half-mass radii for dynamically evolved clusters.," Furthermore, Hurley (2007) showed that projected half-light radii could be as much as half that of the corresponding half-mass radii for dynamically evolved clusters." + In. Table 2 we show both the half-light. (two climensional) and half-mass (threc-dimensional) raclit for the models at an age of 12€vr.," In Table \ref{t:table2} we show both the half-light (two dimensional) and half-mass (three-dimensional) radii for the models at an age of $12\,$ Gyr." + The errors in both values are also shown., The errors in both values are also shown. +" Most obvious is that the errors in ry) are greater than in yy, rellecting that the former quantity Ductuates on a short timescale resulting from a sensitivity to the movement of massive stars in combination with events such as the evolution of bright giants to become dim white chvarls."," Most obvious is that the errors in $r_{\rm h,l}$ are greater than in $r_{\rm h}$ reflecting that the former quantity fluctuates on a short timescale resulting from a sensitivity to the movement of massive stars in combination with events such as the evolution of bright giants to become dim white dwarfs." + We can find particular times when ma is as low as that of ry.," We can find particular times when $r_{\rm h,l}$ is as low as that of $r_{\rm h}$." + However. on average the reduction is in the range.," However, on average the reduction is in the range." + It might also be expected that the my ry ratio would be smaller for more evolved clusters with a greater degree of niwss-segreeation (sav MI compared to N3) but overall we see only a weak trend for this.," It might also be expected that the $r_{\rm h,l}$ $r_{\rm h}$ ratio would be smaller for more evolved clusters with a greater degree of mass-segregation (say M1 compared to N3) but overall we see only a weak trend for this." + We have shown with our model N3 that clusters in the outer regions of a galaxy such as 6822 can naturally evolve to have large half-mass radii provided they begin by filling their tidal radii.," We have shown with our model N3 that clusters in the outer regions of a galaxy such as $\,6822$ can naturally evolve to have large half-mass radii provided they begin by filling their tidal radii." + Ehe hal(-light radii in projection can exceed 15 pe which is within the range observed for extended clusters.," The half-light radii in projection can exceed $15\,$ pc which is within the range observed for extended clusters." + Furthermore. extended: clusters are observed. out to 11 κρο in projection from the centre of 6822 which corresponds to à three-dimensional {ος of ~15 kpe.," Furthermore, extended clusters are observed out to $\sim 11\,$ kpc in projection from the centre of $\,6822$ which corresponds to a three-dimensional $R_{\rm gc}$ of $\sim 15\,$ kpc." + Our models were evolved. at Rue=IO kpe νο following equation 1. we can scale the tidal radius by a factor of 1.5 and potentially the half-mass and half-light radii by a similar factor.," Our models were evolved at $R_{\rm gc} = 10\,$ kpc so following equation \ref{e:rtide} we can scale the tidal radius by a factor of 1.5 and potentially the half-mass and half-light radii by a similar factor." + Thus half-light. radii in excess of 20 are possible.," Thus half-light radii in excess of $20\,$ pc are possible." + Also consider that our models started with peNo=100000 and have a mass of about 30000A7. remaining at 12 Give.," Also consider that our models started with $N = 100\,000$ and have a mass of about $30\,000 \, M_\odot$ remaining at $12\,$ Gyr." + Lf, If +wp) 5,) . +17 For L—A and nau~AG and mildly nonlinear density contrast Onay~ 1. this implies on~(3D).," For $L\sim\lambda$ and $n_{\rm clump}\sim \lambda^{-3}$ and mildly nonlinear density contrast $\delta_{\rm max}\sim 1$ , this implies $\epsilon_{\rm vort}\sim (3\Gamma)^{-1}$." +" The collisions of and compression in accelerated plasma shells (Bell2004.2005) may amplify the density contrast into the strongly nonlinear regime dja,“>I. but we do not attempt to estimate the magnitude of this effect."," The collisions of and compression in accelerated plasma shells \citep{Bell:04,Bell:05} may amplify the density contrast into the strongly nonlinear regime $\delta_{\rm max}\gg 1$, but we do not attempt to estimate the magnitude of this effect." + If vorticity is generated on scales A<Aras, and Oven)>Ag as well as Tra7SI7c/R."," The fastest growing mode has wavelength and growth rate = e, For nonlinear density contrast production on scales $\lambda_{\rm fast}$ we need $\xi(x_{\rm cool})> \lambda_{\rm fast}$ and $\xi(x_{\rm rel}) > \lambda_{\rm fast}$ as well as $\Upsilon_{\rm fast} > 8\Gamma^2 c/R$." + However. the wavelength of the fastest growing mode Is very small if B is the microgauss field typical of the interstellar medium.," However, the wavelength of the fastest growing mode is very small if $B$ is the microgauss field typical of the interstellar medium." + All longer wavelengths A>Ag also grow on rates Μο., All longer wavelengths $\lambda > \lambda_{\rm fast}$ also grow on rates ). +..(36) This seems to suggest that a reversing field may be generated on a wide range of scales., This seems to suggest that a reversing field may be generated on a wide range of scales. + The instability has enough time to reach nonlinear growth only when the growth rate exceeds the inverse crossing time of the shock precursor YANG7) To evaluate(Gi the growth)r rate. we substitute equations (13: coherent field) with A2R/8T- and (2.49) in equation (2.4)) to obtain YXQGA)(," The instability has enough time to reach nonlinear growth only when the growth rate exceeds the inverse crossing time of the shock precursor ) To evaluate the growth rate, we substitute equations \ref{eq:density_of_delta}; coherent field) with $\Delta=R/8\Gamma^2$ and \ref{eq:bell_fast}) ) in equation \ref{eq:bell_rate}) ) to obtain )." +"38) Where eg, parametrizes the strength of the pre-existing coherent field. not to be confused with the same symbol expressing strength of the length scale-dependent tangled field in previous sections."," Where $\epsilon_{B_0}$ parametrizes the strength of the pre-existing coherent field, not to be confused with the same symbol expressing strength of the length scale-dependent tangled field in previous sections." +" The condition for nonlinear growth in equation (2.4)) is then fulfilled when 2(qtm p (39) which suggests( thatag)! nonlinear growth is very broadly expected on scales ASGnasR/ST- when =-""relerit-"," The condition for nonlinear growth in equation \ref{eq:Upsilon_condition}) ) is then fulfilled when ) , which suggests that nonlinear growth is very broadly expected on scales $\lambda\lesssim \xi_{\rm max} \sim R/8\Gamma^2$ when $\gamma_{p,{\rm max}} \lesssim \gamma_{\rm rel,crit}$." + When pinayne nonlinear growth is panaxstill. expected on scales smaller than R/8U~ but still much larger than the plasma skin depth.," When $\gamma_{p,{\rm max}}\gg \gamma_{\rm rel,crit}$, nonlinear growth is still expected on scales smaller than $R/8\Gamma^2$ but still much larger than the plasma skin depth." + The complexity of the structure of ultrarelativistic collisionless shocks stems from the multiscale nature of plasma self-organization., The complexity of the structure of ultrarelativistic collisionless shocks stems from the multiscale nature of plasma self-organization. + This and the preceding analytical and numerical analysis have identified organization on various spatial scales between the proton plasma skin ef~2«107em and the width of the blastwave in the upstream frame R/8I7~107210?em., This and the preceding analytical and numerical analysis have identified organization on various spatial scales between the proton plasma skin $c/\omega_{\rm p}\sim 2\times10^7\textrm{ cm}$ and the width of the blastwave in the upstream frame $R/8\Gamma^2\sim 10^{12}-10^{18}\textrm{ cm}$. + While the dynamical organization of the plasma on different scales is interdependent. our understanding of the scale interdependence in the precursors of ultrarelativistie collisionless shocks is still in its infancy.," While the dynamical organization of the plasma on different scales is interdependent, our understanding of the scale interdependence in the precursors of ultrarelativistic collisionless shocks is still in its infancy." + Motivated by the present and other preliminary investigations (see.e.g..Milosavljevió&Nakar2006:Katzetal.2007:Keshetetal.2008;Spitkovsky 2008b).. we propose several possible regions within the structure of an ultrarelativistic shock precursor in which the physical processes that drive plasma organization. change character as a function. of distance from the shock.," Motivated by the present and other preliminary investigations \citep[see, e.g.,][]{Milosavljevic:06,Katz:07,Keshet:08,Spitkovsky:08}, we propose several possible regions within the structure of an ultrarelativistic shock precursor in which the physical processes that drive plasma organization change character as a function of distance from the shock." + We. however. caution that not all of these regions have to be present in all—or perhaps any—of the blastwave precursors.," We, however, caution that not all of these regions have to be present in all—or perhaps any---of the blastwave precursors." + Similarly. we are not able to determine the relative ordering of the regions. with respect to their distance from the shock transition. with any degree of certainty.," Similarly, we are not able to determine the relative ordering of the regions, with respect to their distance from the shock transition, with any degree of certainty." + In a shock that produces a power-law spectrum of accelerated nonthermal particles (see $1. for potential limitations of this key assumption). we propose thatthe shock precursor may contain the following concentric regions: |].," In a shock that produces a power-law spectrum of accelerated nonthermal particles (see \ref{sec:intro} for potential limitations of this key assumption), we propose thatthe shock precursor may contain the following concentric regions: 1." +" An outermost region extending to the maximum possible radial distance from the shock. measured in the reference frame of the shock upstream. of ~ R/8I"".that is causally associated with the explosion."," An outermost region extending to the maximum possible radial distance from the shock, measured in the reference frame of the shock upstream, of $\sim R/8\Gamma^2$ ,that is causally associated with the explosion." + This region contains a low density of nonthermal protons in the high-energy tail of, This region contains a low density of nonthermal protons in the high-energy tail of +xedieted. and the emitted radio fixes should be of the order of 10 those of Jupiter.,"predicted, and the emitted radio fluxes should be of the order of $10^{5}$ those of Jupiter." +" The peak of the cmitted spectrin should fall at frequencies of a few or several eus of MIIz depending ou the streneth of the planetary naenctic field (sec.ο,Steveus2005:Zarka2007:&Zarka2011.andreferences therem).."," The peak of the emitted spectrum should fall at frequencies of a few or several tens of MHz depending on the strength of the planetary magnetic field \citep[see, e.g., ][ and references therein]{Stevens05,Zarka07,JardineCameron08,Lanza09,HessZarka11}." + A siguificaut Hux at microwave frequencies 1s expected if hieli-energy articles spiral along the kC magnetic fields of the spots in the stellar photosphere. but to attribute the emission o SPMIT it is necessary to detect its modulation with he orbital or the svuodic period.," A significant flux at microwave frequencies is expected if high-energy particles spiral along the kG magnetic fields of the spots in the stellar photosphere, but to attribute the emission to SPMI it is necessary to detect its modulation with the orbital or the synodic period." + Ou the other haud. radio emission iu the MIIZ range is characteristic of he planetary fields and its detection would provide information on the streneth of the planetary magnetic fields.," On the other hand, radio emission in the MHz range is characteristic of the planetary fields and its detection would provide information on the strength of the planetary magnetic fields." + Most of the models cousidered above dealt with analogics§f or differences between the solar-planct aud the star-lancet interactions. or focussed on specific issues stich as he phase lag between the chromospheric hot spot aud he planet.," Most of the models considered above dealt with analogies or differences between the solar-planet and the star-planet interactions, or focussed on specific issues such as the phase lag between the chromospheric hot spot and the planet." +" Nevertheless. only some of them considered he problemi of clissipating a power of the order of 1030au] qu : ↓∩−↓∖↖↑∪⋯⊳⋯∏↕↑↕∪↥⋅↑∐∖↸∖∐↸∖↥⋅∩⊾↖↽∐⋅↥⋅⋜⊔∐⋜↧↑↸∖≺↧⋝↖↽ Oo, ⋅ he chromospleric hot spots of Shkoluiketal.(2005)."," Nevertheless, only some of them considered the problem of dissipating a power of the order of $10^{20}-10^{21}$ W to account for the energy irradiated by the chromospheric hot spots of \citet{Shkolniketal05}." +. Tn their MIID simulations. Tpetal.(2001) were able o obtain powers of the order of 3.«102? W adopting a maenetic field of 0.1 CG aud a size of the interaction area of 5 Jupiter radii at the maeuctopause between he planctary Seld aud the stellar coronal field with au orbital velocity of the planet of 280 kins+.," In their MHD simulations, \citet{Ipetal04} were able to obtain powers of the order of $3 \times 10^{19}$ W adopting a magnetic field of $0.1$ G and a size of the interaction area of 5 Jupiter radii at the magnetopause between the planetary field and the stellar coronal field with an orbital velocity of the planet of $280$ km $^{-1}$." + However. vpical surface fields in WD 179919 ave of the order of 10 € at most and even im the case of the remarkably active host IID 1597323. they do uot exceed ~ LOG (Moutouctal.2007).," However, typical surface fields in HD 179949 are of the order of $10$ G at most and even in the case of the remarkably active host HD 189733 they do not exceed $\sim 40$ G \citep{Moutouetal07}." +. Since the field maeneticstrength decreases at least as (r/R)P. where ris the distance from the ceutre of the star aud its radius. we expect field streneths B~0.02)0.08 Coat a distauce of SR. typical of most of the svsteis with hiuts of SPMI.," Since the magnetic field strength decreases at least as $(r/R)^{-3}$, where $r$ is the distance from the centre of the star and $R$ its radius, we expect field strengths $B \simeq 0.02-0.08$ G at a distance of $8R$, typical of most of the systems with hints of SPMI." + Since the dissipated power is proportional to B7. the field streneth is too low to account for the cucrev raciated in the chromospheric hot spots.," Since the dissipated power is proportional to $B^{2}$, the field strength is too low to account for the energy radiated in the chromospheric hot spots." + A power at least two or three orders of mmaenitude larger is required., A power at least two or three orders of magnitude larger is required. + Lanza(2009) proposed that the enerev needed to explain the hot spot comes frou the whole magnetic structure connecting the planet with the star and is released at a closer distance than the planet orbital radius., \citet{Lanza09} proposed that the energy needed to explain the hot spot comes from the whole magnetic structure connecting the planet with the star and is released at a closer distance than the planet orbital radius. + His considerations were based ou models borrowedll from solar plysics to explain the budget of solar flares and Tere. we introduce some intuitive ideas for such a kind of models bv means of a simple cartoon (sec Fig. 5)).," His considerations were based on models borrowed from solar physics to explain the budget of solar flares and Here, we introduce some intuitive ideas for such a kind of models by means of a simple cartoon (see Fig. \ref{coronal_sketch}) )." + We consider a late-tvpe star with a hot Jupiter whose orbital motion is not svuchrouous with stellar rotation., We consider a late-type star with a hot Jupiter whose orbital motion is not synchronous with stellar rotation. + At the beeinnine of the process. a long coronal loop reconnects with the plauctary maguetosphere releasing a anodest amount of energv. with a characteristic dissipated power of the order of 1011 W for a time scale of the order of Lfey. where L is the size of the interaction region and c4 the Alfven velocity.," At the beginning of the process, a long coronal loop reconnects with the planetary magnetosphere releasing a modest amount of energy, with a characteristic dissipated power of the order of $10^{17}$ W for a time scale of the order of $L/v_{\rm A}$, where $L$ is the size of the interaction region and $v_{\rm A}$ the Alfven velocity." + Once the reconnection process is over. the relative orbital motion of the planct with respect to the loop footpoiuts produces a bending of the loop on a timescale of the order of the dav.," Once the reconnection process is over, the relative orbital motion of the planet with respect to the loop footpoints produces a bending of the loop on a timescale of the order of the day." + The stress of the field) accumulates enerey into the loop aud the field is no louger potential as indicated by the curvature of the field lines in the outer corona., The stress of the field accumulates energy into the loop and the field is no longer potential as indicated by the curvature of the field lines in the outer corona. + This energy cau be released closer to the star when the curved field lues interact with shorter loops. as iu the final sketch of the cartoon.," This energy can be released closer to the star when the curved field lines interact with shorter loops, as in the final sketch of the cartoon." + Since the interaction site is closer to the star. the magnetic field intensity is remarkably lavecr there. while the relative velocity field. that scales roughly as Πο is still of the order of several tens of kins 1.," Since the interaction site is closer to the star, the magnetic field intensity is remarkably larger there, while the relative velocity field, that scales roughly as $(r/R)$, is still of the order of several tens of km $^{-1}$." + Considering a field streneth B=1 G at the interaction site. a typical size of the interacting region of £=R. aud a relative velocity e=30 lui s.|; we lave a released power of: where 0o56. even in ULIRGs whose large amounts of dense star-Iorming molecular are intrinsically luminous in such lines.," This can yield faint CO $\rightarrow $ J lines for $\geq $ 6, even in ULIRGs whose large amounts of dense star-forming molecular are intrinsically luminous in such lines." + Such high optical depths can easily account for the so-called [CT] line IJuminosity delicity known to exists in such svstenis., Such high optical depths can easily account for the so-called [CII] line luminosity deficity known to exists in such systems. +" 2,", 2. + Similar conditions max be present in high redshilt galaxies. vielding deceptively “cool” CO SLEDs at high Irequencies even in extreme slarbursts such as Che subimillimeter galaxies.," Similar conditions may be present in high redshift galaxies, yielding deceptively “cool” CO SLEDs at high frequencies even in extreme starbursts such as the submillimeter galaxies." + 3., 3. + Global dust emission SEDs cannot unambigiouslv distinguish between high dust optical depths at far-IR/submun wavelengths or large amounts of cold dust. as they. can both contribute to the Fu-IB/subnmm part of the dust emission SED in a similar fashion.," Global dust emission SEDs cannot unambigiously distinguish between high dust optical depths at far-IR/submm wavelengths or large amounts of cold dust, as they can both contribute to the far-IR/submm part of the dust emission SED in a similar fashion." + 4., 4. + The very low COand HCN line excitation in 1193 demonstrates that low global eas excitation remains possible even in vigorously stu-Iorming LIRGs., The very low CO HCN line excitation in 193 demonstrates that low global gas excitation remains possible even in vigorously star-forming LIRGs. +but the values are correlated.,but the values are correlated. + Wowever. for the larger clusters (roy2930 arcsec) the correlation breaks dow and the differcuce eau amount to factors of several.," However, for the larger clusters $r_{90} > 30$ arcsec) the correlation breaks down and the difference can amount to factors of several." + This differences arises from the extrapolation of the profile to radii larger than those for which our data provide good constraimts and the iuplication of significant inounuts of licht at large radius. which of course dives roy upwards.," This differences arises from the extrapolation of the profile to radii larger than those for which our data provide good constraints and the implication of significant amounts of light at large radius, which of course drives $r_{90}$ upwards." + Due to the truncated nature of Nine profiles. we prefer those in determining roy because there is less potential for those profiles to “runaway at large radii.," Due to the truncated nature of King profiles, we prefer those in determining $r_{90}$ because there is less potential for those profiles to “run away"" at large radii." + The differences between the models are less marked when comparing estimates of à. (Figure 9))., The differences between the models are less marked when comparing estimates of $r_c$ (Figure \ref{fig:cr Plot}) ). + Iu the SAIC. Wall&Zaritsky(2006) had noted a small. but interesting sub-class of clusters that appear rime-like.," In the SMC, \cite{hz} had noted a small, but interesting sub-class of clusters that appear ring-like." + We Πα similar clusters iu the LMC aud show such clusters in Figure 10.., We find similar clusters in the LMC and show such clusters in Figure \ref{fig:Ring Clusters}. . + From our visual iuspection of the xofiles (FigureOo 3.. we classify 78 as rueC» clusters (~7 of our sample).," From our visual inspection of the profiles (Figure \ref{fig:Sample Profiles}, we classify 78 as ring clusters $\sim 7$ of our sample)." + The nature of these clusters remains a nsterv that detailed kinematics Πο! help resolve., The nature of these clusters remains a mystery that detailed kinematics might help resolve. + We plot their projected distribution. as well as all other clusters. in the LMC in Figure 11. but find no telltale difference im the distribution of the ring clusters.," We plot their projected distribution, as well as all other clusters, in the LMC in Figure \ref{fig:LMC dist} but find no telltale difference in the distribution of the ring clusters." + We compare the profile structural paramcters. more specifically roy. core radius and cluster concentration. for our LAIC and the published SAIC cluster populations (IBll&Zarit," We compare the profile structural parameters, more specifically $r_{90}$, core radius and cluster concentration, for our LMC and the published SMC cluster populations \citep{hz}." +sky2006).. Iu Figure 12 we compare the roy values., In Figure \ref{fig:R90 Comparison} we compare the $r_{90}$ values. + We find that the distributious are very similar for rog15 pc. but that there is a significaut drop in the fraction ofclusters with roy715 pe iu the," We find that the distributions are very similar for $r_{90} < 15$ pc, but that there is a significant drop in the fraction ofclusters with $r_{90} > 15$ pc in the" +maenituces than earlier galaxies (Hicaleo-Gamimez 2001: ναι der Berel 2008).,magnitudes than earlier galaxies (Hidalgo-Gámmez 2004; van der Bergh 2008). + Moreover. barred ealaxies teud to be larger than nou-bar'ed galaxies of the same My (Hidalgo-Crámuinez 2001).," Moreover, barred galaxies tend to be larger than non-barred galaxies of the same $_b$ (Hidalgo-Gámmez 2004)." + The main clifference resides in the gas deusity surface. with a strong correlation [or barred. galaxies. while noue for non-barred.," The main difference resides in the gas density surface, with a strong correlation for barred galaxies, while none for non-barred." + The reason or such cdiffereuce is not well uuderstood vet., The reason for such difference is not well understood yet. + It night. be related with some clynamical processes ¢X the bar acting ou the gas mass distribution., It might be related with some dynamical processes of the bar acting on the gas mass distribution. + Or it is just a problem of poor sampling with a sima| rauge in values of the eraclient., Or it is just a problem of poor sampling with a small range in values of the gradient. + Figures 7-10 can also be used to check tie reliability of the gradieut of the individual galaxies, Figures 7-10 can also be used to check the reliability of the gradient of the individual galaxies. + Adopting the delinition of dwarf spira ealaxy by Hidaleo-Gaminez (2001) aud Figures Ta aud Sa. dwarf spirals uuelit show slopes larger van —0.15 dex/kpe. which are in agreement with the results presented here.," Adopting the definition of dwarf spiral galaxy by Hidalgo-Gámmez (2004) and Figures 7a and 8a, dwarf spirals might show slopes larger than $-0.15$ dex/kpc, which are in agreement with the results presented here." + As said above. he values lor VOC 6205 aud UGC 5296 seem to be too large.," As said above, the values for UGC 6205 and UGC 5296 seem to be too large." + Ciradients of about —0.2 dex/Ekp«: [or LGC 6205 and between —0.2 and —0.3 dex/kpe for κας 5296 melt fit all the correlations presented here while. consiering the uucertaiuties in the eradient. the value for UGC 6377 seems to be quite good.," Gradients of about $-0.2$ dex/kpc for UGC 6205 and between $-0.2$ and $-0.3$ dex/kpc for UGC 5296 might fit all the correlations presented here while, considering the uncertainties in the gradient, the value for UGC 6377 seems to be quite good." +" The fitting of the only. barred galaxy iu our sample. UOC 5212. is very good for the relatiouship with the My, and the . while the eas surlace density is very large for its gradient."," The fitting of the only barred galaxy in our sample, UGC 5242, is very good for the relationship with the $_b$ and the ), while the gas surface density is very large for its gradient." + Therefore. it can be concluded that despite all the uncertainties aid caveats. the gradieut for these four particular dwarf spirals are really quite steep aud th ey follow the same relatiouship as late-type spirals: that is. smaller. auc less brigller £ealaxies have larger gracieuts. regardless of their gas mass.," Therefore, it can be concluded that despite all the uncertainties and caveats, the gradient for these four particular dwarf spirals are really quite steep and th ey follow the same relationship as late-type spirals; that is, smaller, and less brighter galaxies have larger gradients, regardless of their gas mass." + The abuidance gradient [or four chwarl spiral galaxies |ave been obtaiued. none of them previously stidied.," The abundance gradient for four dwarf spiral galaxies have been obtained, none of them previously studied." + Contrary to expected. the three non-barred galaxies show very steep gradients. larger than —0.2 dex/kpe. while the barred galaxy UGC [252 5lows a shallower one. of ouly —0.10 dex/kpce.," Contrary to expected, the three non-barred galaxies show very steep gradients, larger than $-0.2$ dex/kpc, while the barred galaxy UGC 4252 shows a shallower one, of only $-0.10$ dex/kpc." + Therefore. it seems that bared. dwarf galaxies lave sualler slopes than non-barred oues. as previously discussed.," Therefore, it seems that barred, dwarf galaxies have smaller slopes than non-barred ones, as previously discussed." + Although the gradients look very stee> compared with the values for the Milky Way. they follow the treud deli1ος] wy other late-type. uxr-dwarf galaxies.," Although the gradients look very steep compared with the values for the Milky Way, they follow the trend defined by other late-type, non-dwarf galaxies." + The gradients for ας 6205 and UGC 5296 are. at leas|. of —0.2 and —0-:) dexspc. respectively.," The gradients for UGC 6205 and UGC 5296 are, at least, of $-0.2$ and $-0.3$ dex/kpc, respectively." + In order to obtain a conclusive answer. more late-tvpe. «Wal “aud non-dwarf are jeecled.," In order to obtain a conclusive answer, more late-type, dwarf and non-dwarf are needed." +. The increase of the slope wih Hubje type has beer reported before and it is confirmed with these new gradients of very sina| spiral galaxies., The increase of the slope with Hubble type has been reported before and it is confirmed with these new gradients of very small spiral galaxies. + There are indications than the dwarfer the galaxy ds. the steeper the gracieut.," There are indications than the dwarfer the galaxy is, the steeper the gradient." + This uight be a very important conclusion., This might be a very important conclusion. +" As concluded in Hidalgo-Ctámunez (2001) it seems tliat cw""rf spiral galaxies do uot share the same properties as their normal-size counterparts.", As concluded in Hidalgo-Gámmez (2004) it seems that dwarf spiral galaxies do not share the same properties as their normal-size counterparts. + Actally. heir luminosity fLLictious aid star formation processes resemble more those lor irregular galaxies‘ (Reyes-Pérrez 200:): Reves-Pérrez Hidaleo-CGamunez. in preparation).," Actually, their luminosity functions and star formation processes resemble more those for irregular galaxies (Reyes-Pérrez 2009; Reyes-Pérrez Hidalgo-Gámmez, in preparation)." + Therelore. it woul be very interesting to asX why normal irregular galaxies. which are similar to ονα Sim galaxies 1 Linany other aspects. do uo have strong gradients in oxygen abundance?," Therefore, it would be very interesting to ask why normal irregular galaxies, which are similar to dwarf Sm galaxies in many other aspects, do not have strong gradients in oxygen abundance?" +sources are detailed in ?..,sources are detailed in \citet{6df}. + For the purpose of this paper. we are interested in those selected. from theROSAT ALL Sky Survey (?)..," For the purpose of this paper, we are interested in those selected from the All Sky Survey \citep{rass}." + ltedshifts were measured from the 6dEXGS spectra using the RUNZ package (originally written by W. Sutherland. 7)) and assigned a quality. Q. based on the reliability of the redshift.," Redshifts were measured from the 6dFGS spectra using the RUNZ package (originally written by W. Sutherland, \citealt{2001MNRAS.328.1039C}) ) and assigned a quality, $Q$, based on the reliability of the redshift." + X quality Q= 1 or 2 denotes a unreliable redshift. Q= 3 signifies a probable redshift. and (9= 4 implies a certain redshift.," A quality $Q=$ 1 or 2 denotes a unreliable redshift, $Q=$ 3 signifies a probable redshift, and $Q=$ 4 implies a certain redshift." + Galactic sources were assigned a quality (= 6 (2), Galactic sources were assigned a quality $Q=$ 6 \citep{6df}. + During the redshifting process. unusual spectra or features were [lagged. with comments.," During the redshifting process, unusual spectra or features were flagged with comments." + These comments appear in the final catalogue ancl are explained in more detail in Section 6.1.., These comments appear in the final catalogue and are explained in more detail in Section \ref{comments}. + There are a total of 3405 LASS sources used. as input targets for the Gdk Galaxy Survey. here defined. as the RASSθα ‘full catalogue’.," There are a total of 3405 RASS sources used as input targets for the 6dF Galaxy Survey, here defined as the RASS–6dFGS `full catalogue'." +" Of those sources. 2224 (65.3% ) were observed as part of 64 ancl form. the ""observed sample."," Of those sources, 2224 $\%$ ) were observed as part of 6dFGS and form the `observed sample'." + Investigating the quality of cach redshift (Table 11). revealed that there are a total of 1715 (77.1! RASSσα sources with reliable redshifts (Qé= 3).," Investigating the quality of each redshift (Table \ref{qualitytab}) ), revealed that there are a total of 1715 $\%$ ) RASS–6dFGS sources with reliable redshifts $Q\geq3$ )." + This subset forms the ‘spectroscopic sample’., This subset forms the `spectroscopic sample'. + Figure 1. shows the fraction of sources observed. binned by 5 magnitude. along with the fraction of sources with reliable redshifts.," Figure \ref{completenessbmagfig} shows the fraction of sources observed, binned by $b_{\rm J}$ magnitude, along with the fraction of sources with reliable redshifts." + Of the 1478 optically bright objects (54 17.5) in the observed sample. 1333 A) have reliable redshift. measurements (marked by the dashed line in Figure 1)).," Of the 1478 optically bright objects $b_{\rm J} \leq 17.5$ ) in the observed sample, 1333 $\%$ ) have reliable redshift measurements (marked by the dashed line in Figure \ref{completenessbmagfig}) )." + As expected. the number of sources in the spectroscopic sample. decreases as the objects become optically fainter.," As expected, the number of sources in the spectroscopic sample decreases as the objects become optically fainter." + Phe selection of observed targets were not dependant on optical magnitucle. but assigned. according to where there were spare fibres on the Gd spectrograph.," The selection of observed targets were not dependant on optical magnitude, but assigned according to where there were spare fibres on the 6dF spectrograph." + There are 108 objects that were observed twice by Gal ancl S objects observed three times., There are 108 objects that were observed twice by 6dF and 8 objects observed three times. + A decision was mace based on the quality of the redshifts as to which observation appears in the final catalogue such that cach object is only listed. once., A decision was made based on the quality of the redshifts as to which observation appears in the final catalogue such that each object is only listed once. + LE both observations resulted. in poor quality redshifts the first catalogue line was chosen. otherwise the observation with the highest quality appears in the final catalogue.," If both observations resulted in poor quality redshifts the first catalogue line was chosen, otherwise the observation with the highest quality appears in the final catalogue." + In all cases but one. sources with more than one good quality spectrum had identical redshifts so once again the first line was chosen.," In all cases but one, sources with more than one good quality spectrum had identical redshifts so once again the first line was chosen." + ¢1446036-025346 was observed on 2 occasions and has redshifts of 2=-—0.0772. Q=3 and >=0.0000. Q=6 listed for each observation.," g1446036-025346 was observed on 2 occasions and has redshifts of $z=0.0772$, $Q=3$ and $z=0.0000$, $Q=6$ listed for each observation." + The spectrum suggests that this source is an active Mestar so the z=0 redshift was included in the final catalogue., The spectrum suggests that this source is an active M-star so the $z=0$ redshift was included in the final catalogue. + Some example 6dEGS spectra are shown in Figure 2.., Some example 6dFGS spectra are shown in Figure \ref{spectrafig}. + Of the sources in the observed sample. there are 238 Galactic sources (10.6%).," Of the sources in the observed sample, there are 238 Galactic sources $\%$ )." + The majority of these are either typical E. or G type stars (~45%). implving either a misidentification or à foreground star dominating the spectrum. or active stars (~30%. See Figure 2)).," The majority of these are either typical F or G type stars $\sim 45\%$ ), implying either a misidentification or a foreground star dominating the spectrum, or active M-stars $\sim 30\%$, See Figure \ref{spectrafig}) )." + There are also a number of cataclysmic variable (CV) stars clisplavine strong Balmer emission and white cwarfs (Listed with comments “WD in the final data catalogue)., There are also a number of cataclysmic variable (CV) stars displaying strong Balmer emission and white dwarfs (listed with comments `WD' in the final data catalogue). + A small number of objects have =0 nebula emission. characterised by typical nebula emission lines such as the forbidden OLI] A5007 Line.," A small number of objects have $z=0$ nebula emission, characterised by typical nebula emission lines such as the forbidden [OIII] $\lambda 5007$ line." + This is generally cue to foreground. nebula emission dominating the spectrum., This is generally due to foreground nebula emission dominating the spectrum. + Due to the 6dEGS survey limit. all of these sources have |b|107. but 55% of these objects have 10<|b]30°," Due to the 6dFGS survey limit all of these sources have $|b|>10^{\circ}$, but $\%$ of these objects have $10^{\circ}<|b|<30^{\circ}$." + In aclelition to sources marked. as possible BL-Lacs during the redshifting process. spectra with poor quality redshifts (ic. sources in the observed. sample. but not in the spectroscopic sample) were checked. individually by eve to search for possible BL-Lac objects.," In addition to sources marked as possible BL-Lacs during the redshifting process, spectra with poor quality redshifts (i.e. sources in the observed sample, but not in the spectroscopic sample) were checked individually by eye to search for possible BL-Lac objects." + These were identified by a featureless optical spectrum with a strong continuum., These were identified by a featureless optical spectrum with a strong continuum. + An example spectrum is shown in Figure 2.., An example spectrum is shown in Figure \ref{spectrafig}. +" Only sources with b,x17.5 were inspected as bevond this magnitude it is nud to distinguish if the spectrum is featureless because it is à DL-Lac object or because of low signal to noise.", Only sources with $b_{\rm J} \leq 17.5$ were inspected as beyond this magnitude it is hard to distinguish if the spectrum is featureless because it is a BL-Lac object or because of low signal to noise. + There are a total of 55 (3.7%) sources llagged as possible BL-Lacs. oit. Further observational follow up is required to confirm his classification.," There are a total of 55 $\%$ ) sources flagged as possible BL-Lacs, but further observational follow up is required to confirm this classification." + There are 31 sources that have reliable redshifts and vet have still been flagged as possible BL-Lacs., There are 31 sources that have reliable redshifts and yet have still been flagged as possible BL-Lacs. + This is because weak features were able to be distinguished (cenerallv narrow ionised oxvgen emission. lines) but the spectrum was still tvpical of a BL-Lac object.," This is because weak features were able to be distinguished (generally narrow ionised oxygen emission lines), but the spectrum was still typical of a BL-Lac object." + Of these 86 sources. 42 (49%) also have radio counterparts in either the," Of these 86 sources, 42 $\%$ ) also have radio counterparts in either the" +Vila-Costas Excuiunds (1992) found out that the gradient is related with the total mass of ealaxy for non-barre ealaxies aud any morphological type.,Vila-Costas Edmunds (1992) found out that the gradient is related with the total mass of the galaxy for non-barred galaxies and any morphological type. + They also obtained correlatious w he absolute magnitude. when all the morphological types and barred galaxies are included.," They also obtained correlations with the absolute magnitude, when all the morphological types and barred galaxies are included." + AL Zaritsky et al. (," Also, Zaritsky et al. (" +1991 found out a good correlation between the eraclieut. aud the morpholoegi ype. with lareer slopes for late spirals.,"1994) found out a good correlation between the gradient and the morphological type, with larger slopes for late spirals." + Here. we are golig to explore the relatiouship among the gracieit and other characteristic or late-type spirals oils.," Here, we are going to explore the relationship among the gradient and other characteristics for late-type spirals only." + Lu order to do this. information on the optica radius. surface brightness. absolute μας]tude aud gas mass aucl density has been obtaiued for five late-tyye (Sd or later 1o0n-barred spit‘al galaxies ancl four barred galaxies rom cliflerent authosonas Webster et al. (," In order to do this, information on the optical radius, surface brightness, absolute magnitude and gas mass and density has been obtained for five late-type (Sd or later), non-barred spiral galaxies and four barred galaxies from different authors, as Webster et al. (" +198 Ιόςαἱ et al. C,"1983), McCall et al. (" +LOSS). Zaritsky et al. (,"1985), Zaritsky et al. (" +1991). va1 Zee et al. (,"1994), van Zee et al. (" +"1997) aud Hπω""ο.imez (2001) a ‘eferences therein.",1997) and Hidalgo-Gámmez (2004) and references therein. + Noue of these parameters excep itea »olute maguitucle were studied by Ech1iuis (1992) or Zaritsky et al. (, None of these parameters except the absolute magnitude were studied by Vila-Costas Edmunds (1992) or Zaritsky et al. ( +1991).,1994). + The results are shown in Figures [rom Jaa to 10aa for non-ldeuwred galaxies aud in Figures frolu í o LObb for barred ones., The results are shown in Figures from \ref{fig7}a a to \ref{fig10}a a for non-barred galaxies and in Figures from \ref{fig7}b b to \ref{fig10}b b for barred ones. + Iu these figures. the stars COLTesp(dLd to the galaxies in the literatile euxd triaugles represent the galaxies in this study warf spiral galaxies).," In these figures, the stars correspond to the galaxies in the literature and triangles represent the galaxies in this study (dwarf spiral galaxies)." + Also. the solid line is tle [ittiug to th e non-dwarl galaxies sample while the Mted iue is the fitting to all the galaxies. iuclucliD>oO he dwarf oues.," Also, the solid line is the fitting to th e non-dwarf galaxies sample while the dotted line is the fitting to all the galaxies, including the dwarf ones." + The regressioue coellicients of e fonjer are shown at the top-right corner of eac1 figure., The regression coefficients of the former are shown at the top-right corner of each figure. + The largest value of the regression coellicient fco non-barred galaxies are those for the My aud le optical radius. indicatiug hat the eracdiei τοιOL-dwarL late-type spirals shows a treud witli lese (wo pal‘ammeters.," The largest value of the regression coefficient for non-barred galaxies are those for the $_b$ and the optical radius, indicating that the gradient of non-dwarf, late-type spirals shows a trend with these two parameters." + There is also a weak ος119laion with the gas mass (total 4 —0.61) but ιοί tred at all for he gas surface density. wit La regressiou coellicient of —0.:)).," There is also a weak correlation with the gas mass (total $_g$ = $-0.61$ ) but not trend at all for the gas surface density, with a regression coefficient of $-0.3$." + Wieu cbwarf spirals are include. the regression c«velielf‘ients clo uot Change much. although the slopes |)ecame shallower Or all je cases.," When dwarf spirals are included, the regression coefficients do not change much, although the slopes became shallower for all the cases." + ΤΙere might yO several reasois Fcx the sinall regressiou coellicient in Figure 10aa as a luch sinaller j1umber of daa-points., There might be several reasons for the small regression coefficient in Figure \ref{fig10}a a as a much smaller number of data-points. + Also. as the values of the dS are determined averagiug he gas mass over the area of a disc aud not cousidering au specific disc iuodel. there mus be ciffereices between the dS auc ile Sin gas sur‘ace density.," Also, as the values of the dS are determined averaging the gas mass over the area of a disc and not considering an specific disc model, there must be differences between the dS and the Sm gas surface density." + In any case. the value obtained for |QC 6205 seeius to be similar to tle olier five Sin galaxies. but uot LGC 5296 where the surface deisity is much smaller.," In any case, the value obtained for UGC 6205 seems to be similar to the other five Sm galaxies, but not UGC 5296 where the surface density is much smaller." + In order to e non-dwarl treds. both UGC 6205 and UGC 5296 might have lower gradients. between —0.] d —0.30 dex/ke».," In order to fit the non-dwarf trends, both UGC 6205 and UGC 5296 might have lower gradients, between $-0.15$ and $-0.30$ dex/kcp." + They are. in any case. larger thar those values for non-cwarl galaxies.," They are, in any case, larger than those values for non-dwarf galaxies." + They bot also seem to hiwe very low content of the gas mass., They both also seem to have very low content of the gas mass. + Jes Tbb to LObb slOW he same as Figwes Yaa to LOaa. but lor barred galaxies. with ‘four galaxies from the literature (NGC 1395. NGC 925. NCC 1313. and NGC 5068) aud jaugle).," Figures \ref{fig7}b b to \ref{fig10}b b show the same as Figures \ref{fig7}a a to \ref{fig10}a a, but for barred galaxies, with a total of four galaxies from the literature (NGC 4395, NGC 925, NGC 1313, and NGC 5068) and UGC 5242 (triangle)." + Now. tle absolute magultuce (rg = —0.93) aud the gas surface deusity. (rj 10w a correlation with tle eracient.," Now, the absolute magnitude $_g$ = $-0.93$ ) and the gas surface density $_g$ = $-0.73$ ) show a correlation with the gradient." + restts presentec bere seem to be iu agreement with previous investigations., The results presented here seem to be in agreement with previous investigations. + The correlatiou ol the gracieuts with both. the radius aud the absolute maguituce muelt be related. with the correlation with the morphological type.," The correlation of the gradients with both, the radius and the absolute magnitude might be related with the correlation with the morphological type." + The late-type galaxies teud to be sinaller auc with larger, The late-type galaxies tend to be smaller and with larger +since the discovery. of the first cxoplanet around. a solar-like star by 7.. the cxoplanct field has bloomed with over 400 currently known.,"Since the discovery of the first exoplanet around a solar-like star by \cite{mayor95}, the exoplanet field has bloomed with over 400 currently known." + While the majority of exoplanets have been discovered through racial velocity measurements of the Doppler wobble ellect. it is the svstems that exhibit transits that are most highly. prized.," While the majority of exoplanets have been discovered through radial velocity measurements of the Doppler wobble effect, it is the systems that exhibit transits that are most highly prized." + “Phese planets are crucial for determining exoplanet bulk densities (via radii ancl mass measurements) as well as their atmospheric properties (via infrared. measurements of their dav/night variations and Lransmission spectroscopy, These planets are crucial for determining exoplanet bulk densities (via radii and mass measurements) as well as their atmospheric properties (via infrared measurements of their day/night variations and transmission spectroscopy). + ‘Transiting exoplanets.). however. also oller the opportunity to detect other planets within the system. since an additional planet may alter the period. of the observed. transits.," Transiting exoplanets, however, also offer the opportunity to detect other planets within the system since an additional planet may alter the period of the observed transits." + This can occur in two wavs., This can occur in two ways. + In the first case the gravitational inlluence of the perturbing body can can alter the orbital period. of the transiting exoplanet clirecthy., In the first case the gravitational influence of the perturbing body can can alter the orbital period of the transiting exoplanet directly. +" This. effect. is particularly strong for planets. in mean motion resonances and can even allow Earth-masseed objects to. be detected. while ""exo-moons! orbiting the ransiting planet itself also induce a similar effect (ee. 2))."," This effect is particularly strong for planets in mean motion resonances and can even allow Earth-massed objects to be detected, while `exo-moons' orbiting the transiting planet itself also induce a similar effect (e.g. \citealt{simon07}) )." + In the second case. a perturbing mass in a wider orbit can cause the transiting planet / star system to wobble around 10 barvcentre. again altering the observed transit times out. by changing the light travel-time.," In the second case, a perturbing mass in a wider orbit can cause the transiting planet / star system to wobble around the barycentre, again altering the observed transit times but by changing the light travel-time." +" Although searching for transit) timing variations (hereafter. PPVs) can potentially uncover the existence of Earth-mass objects (see 2: οι ?:5 ?:5 Ἐν, and references wrein for recent observational studies). there are other ellects that can lead to PPVs."," Although searching for transit timing variations (hereafter, TTVs) can potentially uncover the existence of Earth-mass objects (see \citealt{gibson10}; \citealt{rabus09}; \citealt{bean09}; \citealt{gibson09}; \citealt{millerricci08}, and references therein for recent observational studies), there are other effects that can lead to TTVs." + These include the precession of orbits due to general relativistic cllects (?)). tidal issipation. torques due to the spin-induced: quadrupole moment of the host star (2)). perturbations of transit times ue Lo star spots. as well as reorientation of the planetary orbit with respect to the Earth as a result of proper motion (?)).," These include the precession of orbits due to general relativistic effects \citealt{pal08}) ), tidal dissipation, torques due to the spin-induced quadrupole moment of the host star \citealt{miralda02}) ), perturbations of transit times due to star spots, as well as reorientation of the planetary orbit with respect to the Earth as a result of proper motion \citealt{rafikov09}) )." + Llowever. there is a wealth of observations of many ilferent. eclipsing binary stars (e.g. 2: 2: 2: Pe 75 7: Pes ?5 Tu 7u P)) that have shown quasi-periodic variations in eclipse times over timescales of vears to decades that are comparable to. or larger than. the elfects being searched for amongst transiting exoplanets.," However, there is a wealth of observations of many different eclipsing binary stars (e.g. \citealt{hall80}; \citealt{glownia86}; \citealt{bond88}; \citealt{warner88}; \citealt*{baptista92}; \citealt{echevarria93}; \citealt{wolf93}; \citealt*{baptista00}; \citealt{baptista02}; \citealt{baptista03}; \citealt{borges08}) ) that have shown quasi-periodic variations in eclipse times over timescales of years to decades that are comparable to, or larger than, the effects being searched for amongst transiting exoplanets." + The favoured explanation for these observed: variations in the orbital. periods of eclipsing binary stars is known as, The favoured explanation for these observed variations in the orbital periods of eclipsing binary stars is known as +Our study benefits from the recent explosion in KBO surveys.,Our study benefits from the recent explosion in KBO surveys. +" Our simulations incorporated three different populations of source bodies, representing three different populations of KBOs."," Our simulations incorporated three different populations of source bodies, representing three different populations of KBOs." + We relied on the models of Kavelaarsetal.(2008) and Kavelaarsetal.(2009) to disentangle these populations in the face of the many observational biases that affect measurements of KBO populations (seealsoBrown2001;Trujillo&2001).," We relied on the models of \citet{kave08} and \citet{kave09} to disentangle these populations in the face of the many observational biases that affect measurements of KBO populations \citep[see also][]{brow01, truj01}." +. The source populations we assumed are as follows: Figure 1 illustrates these three assumed source populations., The source populations we assumed are as follows: Figure \ref{fig:initial} illustrates these three assumed source populations. +" We assigned 25,000 particles to each of them."," We assigned 25,000 particles to each of them." +" For comparison, Liou&Zook(1999) assumed that all of their source bodies were in orbits with semimajor axes 45 or 50 AU."," For comparison, \citet{lz99} assumed that all of their source bodies were in orbits with semimajor axes 45 or 50 AU." +" Moro-Martin&Malhotra(2002) assumed all source bodies had orbits with semimajor axes equal to 45 AU, or that the source body semimajor axes were distributed uniformly from 35-50 AU."," \citet{mm1} assumed all source bodies had orbits with semimajor axes equal to 45 AU, or that the source body semimajor axes were distributed uniformly from 35–50 AU." + Holmesetal.(2003) assumed all their source bodies had approximately Pluto-like orbits., \citet{holm03} assumed all their source bodies had approximately Pluto-like orbits. +" Note that although we assigned equal numbers of particles to each source population, we assigned each dust population a different relative dust production rate in the collisional grooming algorithm, as described above cold, hot, plutinos)."," Note that although we assigned equal numbers of particles to each source population, we assigned each dust population a different relative dust production rate in the collisional grooming algorithm, as described above cold, hot, plutinos)." +" Many of the source particles have resonant orbits, by chance."," Many of the source particles have resonant orbits, by chance." +" But except for the plutinos, we did not attempt to capture the detailed resonant dynamics of the KB in our source"," But except for the plutinos, we did not attempt to capture the detailed resonant dynamics of the KB in our source" +The carly KASC cata releases lec to the discovery of the nineteen candidate dS5ct stars listed in Table. 1:: many more have been found in subsequent data. releases. and. ground-based studies. of these stars are now in progress.,"The early KASC data releases led to the discovery of the nineteen candidate $\delta$ Sct stars listed in Table \ref{tab1}; many more have been found in subsequent data releases, and ground-based studies of these stars are now in progress." + Laterestingly. many objects show periodograms with frequencies both in the mmocde ὁ SSct and. nimode DDor domains. Le.. they are candidate hybrid. pulsators (Crigahcenectal.2010).," Interestingly, many objects show periodograms with frequencies both in the mode $\delta$ Sct and mode $\gamma$ Dor domains, i.e., they are candidate hybrid pulsators \citep{griga10}." +. Dedicated. short-cacleneeNepler data for. the most promising hybrid. candidates will of exploited. for seismic studies of these stars., Dedicated short-cadence data for the most promising hybrid candidates will be exploited for seismic studies of these stars. + To his end it is extremely important to constrain the undamoental parameters of the stars(elective temperature dig. surface eravity logg. projected. rotational velocity resin’. luminosity log L/L.) in order to limit the range of models.," To this end it is extremely important to constrain the fundamental parameters of the stars(effective temperature $T_{\rm eff}$, surface gravity $\log g$, projected rotational velocity $v \sin i$, luminosity $\log L/{\rm L}_\odot$ ) in order to limit the range of models." + Measurement of resins is essential to constrain the rotational velocity of the mocels., Measurement of $v \sin i$ is essential to constrain the rotational velocity of the models. + Stellar fundamenta parameters can be obtained by using photometry. e.g. in the Strómmegren system. or by means of mid- or high-resolution spectroscopic observations.," Stellar fundamental parameters can be obtained by using photometry, e.g., in the Strömmgren system, or by means of mid- or high-resolution spectroscopic observations." + Very few of the 19Acpler 0 Sse stars have previously been observed spectroscopically and no reliable estimates of the stellar parameters can be derive from the existing data., Very few of the 19 $\delta$ Sct stars have previously been observed spectroscopically and no reliable estimates of the stellar parameters can be derived from the existing data. + For this reason. we undertook a systematic spectroscopic study of theseA'epler targets ane report our results here.," For this reason, we undertook a systematic spectroscopic study of these targets and report our results here." + This work fits in the eround-base observational efforts of I.ASC' with the aim to characterize allAcpíer pulsators (Uxvtterhoevenetal.2010a.b).," This work fits in the ground-based observational efforts of KASC with the aim to characterize all pulsators \citep{uytte10a,uytte10b}." +. The spectra used. in our analysis were acquired. with. two different instruments: The reduction of spectra. which included. the subtraction of the bias frame. trimming. correcting for the Dat-iekd and the seattered light. the extraction of the orders. and the wavelength calibration. was done hy using the NOAO/IRAEpackaget.," The spectra used in our analysis were acquired with two different instruments: The reduction of spectra, which included the subtraction of the bias frame, trimming, correcting for the flat-field and the scattered light, the extraction of the orders, and the wavelength calibration, was done by using the NOAO/IRAF." +. The amount of scattered light correction was about LOAADU., The amount of scattered light correction was about ADU. +" Phe S/N ratio of the spectra was at least ~ 1130 ancl SO for Loiano and OACT observatories. respectively,"," The S/N ratio of the spectra was at least $\sim$ 130 and 80 for Loiano and OACT observatories, respectively." + Complete StrOmmeren-Crawlord oveby photometry is available for seven objects in our sample (stars with an 7e in column 5 of roftabl)) while veby data are present for three additional objects (stars with a 75 in column 5 of , Complete Strömmgren-Crawford $uvby\beta$ photometry is available for seven objects in our sample (stars with an $a$ ” in column 5 of \\ref{tab1}) ) while $uvby$ data are present for three additional objects (stars with a $b$ ” in column 5 of \\ref{tab1}) ). +Phe source of both the Strómmegren and Strómmegren-C'rawford. data is Hauck&Moermillod.(1998)., The source of both the Strömmgren and Strömmgren-Crawford data is \citet{hauck}. +". For the other six objects (identified with a ve"" in column 5 of reftabl)) plusthe three stars in 66866. only Johnson photometry is available. mainly in DV. filters."," For the other six objects (identified with a $c$ ” in column 5 of \\ref{tab1}) ) plusthe three stars in 6866, only Johnson photometry is available, mainly in $BV$ filters." + For these stars we used the values reported byAD., For these stars we used the values reported by. + In the near-infrared. JA photometry of good quality is present in the 2MLASS catalogue (Skrutskieetal.1996). [or all the targets.," In the near-infrared, $JHK$ photometry of good quality is present in the 2MASS catalogue \citep{2mass} for all the targets." +" For the seven stars with weby photometry, E(b y) can be estimated by using the calibration by Moon(1985).. using the106 codeUvBYBETA."," For the seven stars with $uvby\beta$ photometry, $E(b-y)$ can be estimated by using the calibration by \citet{moon}, using the code." +. “Phe result is reported. in ‘Table 1.. where we have used the transformation (DV)=Εςο) (Cardellietal.1989).," The result is reported in Table \ref{tab1}, , where we have used the transformation $E(B-V)=1.4\,E(b-y)$ \citep{cardelli89}." +. For the three stars without 2 indices we used the equivalent spectral type derived in Section 3.2. to derive the intrinsic (by) τοι the relation between (μυ and spectral type (Voigt2006)., For the three stars without $\beta$ indices we used the equivalent spectral type derived in Section \ref{parameters_from_spectroscopy} to derive the intrinsic $(b-y)$ from the relation between $(b-y)_0$ and spectral type \citep{born06}. +. Similarlv. for five stars with (5.V) colours. we adopted the intrinsic (2Vou colours as a function. of spectral tvpe (Sehmidt-haler 1982).," Similarly, for five stars with $(B-V)$ colours, we adopted the intrinsic $(B-V)_0$ colours as a function of spectral type \citep{schmidt}." +. We assigned a larger error to these values than those based. on weby3 photometry., We assigned a larger error to these values than those based on $uvby\beta$ photometry. + The remaining four variables are cluster members. three belong to NGC 6866 and one to NGC 6811.," The remaining four variables are cluster members, three belong to NGC 6866 and one to NGC 6811." + The reddenings of these two clusters were adopted from Dutra&Biea(2000). for NGC 6866 and Glushkovaetal.(1999) and Luo for NGC 6811., The reddenings of these two clusters were adopted from \citet{dutra} for NGC 6866 and \citet{Glushkova} and \citet{luo} for NGC 6811. + Values of Z;4;and logg were estimated. [rom co and 2 using the data erid by Moon&Doretsky (1985)..., Values of $T_{\rm eff}$and $\log g$ were estimated from $c_0$ and $\beta$ using the data grid by \citet{moondwo}. . + Evpical photometrie errors. (0.015. and 0.03mmasg in 2 and co. respectively) have been assumed.," Typical photometric errors (0.015 and mag in $\beta$ and $c_0$, respectively) have been assumed." + The derived: values of Zi and logg are reported in νοας (columns 6 and. 10. respectively).," The derived values of $T_{\rm eff}$ and $\log g$ are reported in \\ref{tab2} (columns 6 and 10, respectively)." + In calculating the uncertainties. we conservatively assumed an error of Kis ancl 0.3ddex for Zi and logg. respectively.," In calculating the uncertainties, we conservatively assumed an error of K and dex for $T_{\rm eff}$ and $\log g$ , respectively." + “Phe values of Tog and logg derived. from. spectroscopy (see Section 3.2 below) anc seby are in good agreement. with all the cilferences less than 3o.," The values of $T_{\rm eff}$ and $\log g$ derived from spectroscopy (see Section \ref{parameters_from_spectroscopy} below) and $uvby\beta$ are in good agreement, with all the differences less than $\sigma$ ." + Only 005724440 1187234) showsa dilference in temperature close to the edge of this limit., Only 05724440 187234) showsa difference in temperature close to the edge of this limit. + We discussthis object in Section 3.3.., We discussthis object in Section \ref{individuals}. . + An additional photometric estimate of Z;ijp can be obtained [rom the calibrations by Masanaetal.(20060)., An additional photometric estimate of $T_{\rm eff}$ can be obtained from the calibrations by \citet{masana06}.. +recovered fractions.,recovered fractions. + The f?°coveed() is quite low in the inner regions and then rises slowly and peaks at around 100 kpc., The $f^{\rm recovered}_{\rm unbound}(r)$ is quite low in the inner regions and then rises slowly and peaks at around 100 kpc. + This rise coincides with fall of fraction frecovere?(r).," This rise coincides with a fall of fraction $f^{\rm + recovered}_{\rm bound}(r)$." +" This is due to the atwo facts a) low ε (circularity of orbit) are more likely to followingbe unbound than circular events since they pass close to the center, b) low ε events are more likely to be found at the apocenter and their apocenter is further away than that of an high e event of similar energy."," This is due to the following two facts a) low $\epsilon$ (circularity of orbit) are more likely to be unbound than circular events since they pass close to the center, b) low $\epsilon$ events are more likely to be found at the apocenter and their apocenter is further away than that of an high $\epsilon$ event of similar energy." + The black line representing frecovered shows that the outer halo (beyond 60 kpc) is highly structuredg(r) whereas the inner halo (less than 40 kpc) which contains about of the material (as shown by the red line) has very little material which can be recovered as structures., The black line representing $f^{\rm recovered}_{\rm bound+unbound}(r)$ shows that the outer halo (beyond 60 kpc) is highly structured whereas the inner halo (less than 40 kpc) which contains about of the material (as shown by the red line) has very little material which can be recovered as structures. + This implies that in the inner regions strong phase mixing greatly limits the amount of material that can be recovered as structures in 3-d configuration space., This implies that in the inner regions strong phase mixing greatly limits the amount of material that can be recovered as structures in 3-d configuration space. +" The analysis also suggests that for a given survey the fraction of material in groups will depend sensitively upon the contribution of the inner halo to the survey, which in turn is determined by the geometry and the depth of the survey."," The analysis also suggests that for a given survey the fraction of material in groups will depend sensitively upon the contribution of the inner halo to the survey, which in turn is determined by the geometry and the depth of the survey." + A few other issues which can affect the fraction of material in groups are as follows., A few other issues which can affect the fraction of material in groups are as follows. +" We have here considered only the 3-d configuration space, additional information in the form of velocities should help detect more groups and increase the fraction of material in groups."," We have here considered only the 3-d configuration space, additional information in the form of velocities should help detect more groups and increase the fraction of material in groups." +" Also, the choice of photometric selection function can decrease or increase the fraction of material in groups depending upon the contribution of the smooth component to the sample of stars in the survey (see for further details)."," Also, the choice of photometric selection function can decrease or increase the fraction of material in groups depending upon the contribution of the smooth component to the sample of stars in the survey (see for further details)." + Issues related to our choice of the clustering scheme which can affect the fraction of material in groups are discussed in6., Issues related to our choice of the clustering scheme which can affect the fraction of material in groups are discussed in. +"2.. In this section we apply the group-finder to our more realistic synthetic surveys of stellar halos (data sets $2-S5), compare their sensitivity to different accretion events and assess their ability to distinguish accretion histories."," In this section we apply the group-finder to our more realistic synthetic surveys of stellar halos (data sets S2–S5), compare their sensitivity to different accretion events and assess their ability to distinguish accretion histories." +" We apply the group-finder with k=30 and selecting 9 according to to account for the difference in the sample sizes, to all seventeen stellar halo models within each data set."," We apply the group-finder with $k=30$ and selecting $S_{\rm Th}$ according to to account for the difference in the sample sizes, to all seventeen stellar halo models within each data set." +" summarizes our results by plotting the number fraction of accretion events recovered as a function of accretion time, where each symbol a 1 Gyr interval."," summarizes our results by plotting the number fraction of accretion events recovered as a function of accretion time, where each symbol represents a 1 Gyr interval." +" As expected, our idealized survey S1 representsrecovers the largest fraction of events at all times, and the SDSS MSTO survey (S5), which covers less than of the volume of any of"," As expected, our idealized survey S1 recovers the largest fraction of events at all times, and the SDSS MSTO survey (S5), which covers less than of the volume of any of" +In addition. measuring surface brigh(ness. especially of faint and diffuse objects. is difficult both in definition and in practice.,"In addition, measuring surface brightness, especially of faint and diffuse objects, is difficult both in definition and in practice." + For a large and complicated Galactic nebula. for instance. where is the center?," For a large and complicated Galactic nebula, for instance, where is the center?" + If that cannot. be defined. then neither can one define a central surface brightness.," If that cannot be defined, then neither can one define a central surface brightness." + Η the object is not of some regular form. then the apparatus developed for comparing elliptical galaxies (sav) is not of mich use.," If the object is not of some regular form, then the apparatus developed for comparing elliptical galaxies (say) is not of much use." + In spite of all this. it is possible to obtain some measurement of how faint an object the eve-plate combination could detect.," In spite of all this, it is possible to obtain some measurement of how faint an object the eye-plate combination could detect." + To this end. the [Iux within a section of each candidate was measured (using the IRAF routine polvphot). an area roughly one are minute in diameter containing the brightest parts.," To this end, the flux within a section of each candidate was measured (using the IRAF routine polyphot), an area roughly one arc minute in diameter containing the brightest parts." + Stars were excluded as much as possible (which was difficult near (he Galactic Plane). as were the bright nuclei of face-on galaxies (which appear starlike on the plates).," Stars were excluded as much as possible (which was difficult near the Galactic Plane), as were the bright nuclei of face-on galaxies (which appear starlike on the plates)." + The intention was (to measure as Closely as possible what (he eve responded {ο in the survev field., The intention was to measure as closely as possible what the eye responded to in the survey field. + Then two (sometimes more) sections of blank sky were likewise measured. irving to bracket the object sideways to the remaining flat-field gradients: these were averaged and subtracted from the object flux.," Then two (sometimes more) sections of blank sky were likewise measured, trying to bracket the object sideways to the remaining flat-field gradients; these were averaged and subtracted from the object flux." + The counts per pixel were transformed into magnitudes per square are second using photometric solutions derived fom Landolt stancards taken the same night., The counts per pixel were transformed into magnitudes per square arc second using photometric solutions derived from Landolt standards taken the same night. + An uncertaintv was derived using both the variation in the skv readings and the uncertainty in the photometric solution., An uncertainty was derived using both the variation in the sky readings and the uncertainty in the photometric solution. + The sky subtraction dominated most measurements. even on non-photometric nights.," The sky subtraction dominated most measurements, even on non-photometric nights." + In several cases (he same object was measured on different runs; the results agree to within our stated errors. though it was clear that the uncertainties are not overstalec.," In several cases the same object was measured on different runs; the results agree to within our stated errors, though it was clear that the uncertainties are not overstated." + The measurements were all done in A2. because only in that band do we have data on all objects.," The measurements were all done in $R$, because only in that band do we have data on all objects." + This is a result of looking for the tip of the Red Giant Branch. which is easiest {ο detect there.," This is a result of looking for the tip of the Red Giant Branch, which is easiest to detect there." + Unfortunately. most surface brightness estimates and measurements are given in V: Chis must be borne in mind when making comparisons.," Unfortunately, most surface brightness estimates and measurements are given in $V$; this must be borne in mind when making comparisons." + The combined histogram for all candidate objects is shown in Figure &.., The combined histogram for all candidate objects is shown in Figure \ref{total}. + Clearly we are reliably detecting things out to about 24 mag arc 7., Clearly we are reliably detecting things out to about 24 mag arc $^{-2}$. + The reduction in number per brightness bin bevond that point could be interpreted as Cae onset of incompleteness. (hough if we're seeing a significant. number fainter than 25 it’s hard to understand why we would be missing many a full magnitude brighter.," The reduction in number per brightness bin beyond that point could be interpreted as the onset of incompleteness, though if we're seeing a significant number fainter than 25 it's hard to understand why we would be missing many a full magnitude brighter." + Ii order (ο transform Che graph into something «quantitative. we need some model for (he underlying distribution of surface brightness. (," In order to transform the graph into something quantitative, we need some model for the underlying distribution of surface brightness. (" +1I we were dealing withοί brightness we could apply geometric argumentis. but for the distances we are dealing with. surface brightness is constant.),"If we were dealing with brightness we could apply geometric arguments, but for the distances we are dealing with, surface brightness is constant.)" + While these do exist [or ealaxies. modelling such a thing lor Galactic nebulositv is a daunting thought.," While these do exist for galaxies, modelling such a thing for Galactic nebulosity is a daunting thought." + For this reason we plot the two classes of object separately in Figure 9.. ll, For this reason we plot the two classes of object separately in Figure \ref{gal_xgal}. +ere (he peak and faint-end falloff of the Galactic nebulosiües are clearly Iaànter than (he corresponding features [or extragalactic objects., Here the peak and faint-end falloff of the Galactic nebulosities are clearly fainter than the corresponding features for extragalactic objects. + This indicates (hat much of the decrease, This indicates that much of the decrease +correspond to larger temperatures in the external mantle. in favour of a more cllicient IBI.,"correspond to larger temperatures in the external mantle, in favour of a more efficient HBB." + Figure 2 shows the evolution of the C-O core mass during the TP-AGB phase of models with dilferent. initial masses and/or input. proseriptions., Figure \ref{mcore} shows the evolution of the C-O core mass during the TP-AGB phase of models with different initial masses and/or input proscriptions. + The BIL and 2 moclels (Lull squares and open triangles) evolve to smaller core masses. as a result of the higher mass loss in their carly ολα phase.," The BH and BC models (full squares and open triangles) evolve to smaller core masses, as a result of the higher mass loss in their early TP-AGB phase." + In the left panel we see that in the less massive BL and XC models the mass of the remnant is almost independent of the adopted opacity. being only slightly higher. as expected. in the DII case.," In the left panel we see that in the less massive BH and BC models the mass of the remnant is almost independent of the adopted opacity, being only slightly higher, as expected, in the BH case." + Whenthe Stranieroetal.(2006) Dass loss rate is used (SOGLL and S06€ models) the masses of the remnant cdiller more significantly (see coL3 of Table 2)). the discrepancy consisting in 2A.~Q.OSAL. lor M= 2M..," Whenthe \citet{oscar2} mass loss rate is used (S06H and S06C models) the masses of the remnant differ more significantly (see col.3 of Table \ref{yields}) ), the discrepancy consisting in $\delta M_{\rm c} \sim 0.08M_{\odot}$ for $M=2M_{\odot}$ ," +eres +t.,erg $^{-1}$. + These values. although just upper Buts. compare favorably with the the ecneral trend recognizable in Fie.," These values, although just upper limits, compare favourably with the the general trend recognizable in Fig." + 3. where we have plotted the optical huuinositv of the wine pulsus known to have an optical counterpart (see e.g. Mignuani. 1998) as a function of their characteristic age.," 3, where we have plotted the optical luminosity of the nine pulsars known to have an optical counterpart (see e.g. Mignani, 1998) as a function of their characteristic age." + In particular. a turnover iu the optical huuinositv secius to occur for pulsars aging around 105 ves.," In particular, a turnover in the optical luminosity seems to occur for pulsars aging around $10^{4}$ yrs." + For older objects. the scenario appears more complicated by the ouset of thermal cussion from the neutron star surface which. as in the case of the middle-aged PSBRO0656|11 (Pavlov ct al.," For older objects, the scenario appears more complicated by the onset of thermal emission from the neutron star surface which, as in the case of the middle-aged PSR0656+14 (Pavlov et al." + 1997) and. Cenmunea (AGenani ct al., 1997) and Geminga (Mignani et al. + 1998). can significantly. if not complitelv. accorit for the overall optical huninosity.," 1998), can significantly, if not complitely, account for the overall optical luminosity." + NarrSFRXMMusMUEP Mupg ⋔≽∖∖⊽∐↾↭↾∐↕↾∖↴⋂↕⋠∖↕⋝↕↭↜↕⋠∖↕⋠∖↾↰↕⋠⊲≻↸⋉⊳∖∖⋝↕∙⋠∖∖⊽⋠⇝↕↕⋠∖⋠↕↾∐↕↾v IK-Slaw:Sclinidt1959:Kennicutt1998).," $\Sigma_{\rm SFR}\propto\Sigma_{\rm gas}^n$ $\Sigma_{\rm SFR}$ $\Sigma_{\rm gas}$ \citep[hereafter, K-S law:][]{schmidt59, kennicutt98}." +".It eas Xj, than with that of total Is) gas Xrrun (οιο,,Wong&Blitz2002)."," gas $\Sigma_{\rm H_2}$ than with that of total $_2$ ) gas $\Sigma_{\rm HI + H_2}$ \citep[e.g.,][]{wong02}." +. Because alinost all of the existing studies ou the EI&- law have been carried out based ou CO observations of kpc-scale resolution or disk-averaged data (6...I&o-imueietal 2005).. not much is known about the validity of the I&-S law for smaller molecular structures such as giant molecular associatious (GALAs) and eiaut molecular clouds (CAICS).," Because almost all of the existing studies on the K-S law have been carried out based on CO observations of kpc-scale resolution or disk-averaged data \citep[e.g.,][]{komugi05}, not much is known about the validity of the K-S law for smaller molecular structures such as giant molecular associations (GMAs) and giant molecular clouds (GMCs)." + Receuth. I&eunicuttetal.(2007) investigated Ίν-ο law in M51 down to a linear scale of 500ppe aud cloud mass scales of LO°107 AL... : ⊱⇪↕↴⋉∖↥⋯∐↑⋜," Recently, \citet{kennicutt07} investigated K-S law in M51 down to a linear scale of pc and cloud mass scales of $10^6\textendash10^7\mo$ ." +⋯∖⋜↧⋜⋯≼↧∣⇀⋍⋤↕∖↕↴∖↑∐↸∖↴∖↿∐↕⋜↧↸⊳↸∖≼∐∖∐↴∖↕↑⋅↖∪↕∶↴∙⋜↧↴∖∙ : o ⊺↕∐↴∖↴↥⋅↸∖↕⋜↧↑, They found that the nonlinear K-S law can be extended down to that scale. +"↕∪∐↴∖↴∐∏≻↕↴∖↴↨↘↽∐∪↖↖↽∐⋜↧↴∖↴↑↕∐∖↕↘⊽↸∖∐∐↕↸⊳∏↑↑≓≋↸⊳↕∐⊔↕≼∐⋜∏↖↽ 1 xKS"" I MM M ,4abl» i: RNBU neacal "", uMHu(hereafter. has ""e beiE» (tr) | bau1 Lon."" 0 scale‘ iu M5I."," \citet{bigiel08} revealed that the K-S law is applicable at the 750-pc scale for seven spiral galaxies, and that it holds down to the 250-pc scale in M51." + 4Verleyct1IDal.(2 aujwe shown» that aaa loose correlation⋅ exists⋅⋅ even in the I80-pc scale iuDO M33. where a strong correlation was found on the global scale (leveretal.2001).," \citet{verley10} have shown that a loose correlation exists even in the 180-pc scale in M33, where a strong correlation was found on the global scale \citep{heyer04}." +.. Because most of. the molecular gas is coufined. within molecular clouds aud virtually all of the GAIC's are sites of star formation in the Millkv Wav. GAICs) play an nuportaut. role in. star formation.," Because most of the molecular gas is confined within molecular clouds and virtually all of the GMCs are sites of star formation in the Milky Way, GMCs play an important role in star formation." +:⋅⋅ It ⋅⋅is Huportant to understand how star formation at GAIC scales is linked to the I&-S law. which is valid for “oe," It is important to understand how star formation at GMC scales is linked to the K-S law, which is valid for kpc-scales." +One wav to address this ∙∙issue is. to conduct a high-.spatialresolution mapping of cutive molecular gas disks in the nearest ealaxies., One way to address this issue is to conduct a high-spatial-resolution mapping of entire molecular gas disks in the nearest galaxies. + The recent improvements in the : ∙∙∙ ⋅∙ ⋅∙ ∙ ↓∢⊲↓∙⊲⋅↜≱↓ telescopes have mace such observational studies feasible.," The recent improvements in the resolution, sensitivity, and observation efficiency of radio telescopes have made such observational studies feasible." + AD is the best target for this purpose., M33 is the best target for this purpose. + It is one ofthe nearest spiral. ealaxics. (Ώ=slo.kpe:Freedinanctal. im inwwhichh individual CMCsCENICS cauc be ⇁∖resoh«d usedne present-day liiustrüiuents., It is one of the nearest spiral galaxies \citep[$\rm D=840$ kpc;][]{freedman91} in which individual GMCs can be resolved using present-day instruments. + Furthermore. because its disk," Furthermore, because its disk" + (p.a) (Delivannis.Ixawaler1990:Pinsonneanlt1997).. (Delivannis&Pinsonneault1997.herealt," $\alpha$ \citep{ddk, p97}, \citep[][hereafter DP97]{dp97}." +erDP97).. (1002720 (7002550. ," $\pm$ \citet{boes86} + $\pm$ " +The interstellar medium is highly turbulent and the evolution of interstellar clouds.,The interstellar medium is highly turbulent and the evolution of interstellar clouds. + The turbulent pressure is partially able to support them against gravitational collapse (Klessenetal..200001: turbulent shocks create and dissolve dense clumps in molecular clouds or even whole clouds (Ballesteros-Paredesetal...1999).. the turbulent mass transport modifies their chemical evolutio (Décamp&LeBourlot. 2002).. and the irregular turbulet structure determines their penetration by UV radiation (Zielinskyetal.. 2000).," The turbulent pressure is partially able to support them against gravitational collapse \citep{Klessen}; turbulent shocks create and dissolve dense clumps in molecular clouds or even whole clouds \citep{Javier}, the turbulent mass transport modifies their chemical evolution \citep{LeBourlot}, and the irregular turbulent structure determines their penetration by UV radiation \citep{PDR}." +. Thus. the complex dynamic structure on all scales resulting from turbulence has important implicatios for many aspects of the astrophysics of the interstellar matter.," Thus, the complex dynamic structure on all scales resulting from turbulence has important implications for many aspects of the astrophysics of the interstellar matter." + Whereas many observations reveal the complexity of the structure of the interstellar medium. most models of interstellar clouds are still based on simple geometrical configurations.," Whereas many observations reveal the complexity of the structure of the interstellar medium, most models of interstellar clouds are still based on simple geometrical configurations." + A first step towards a better understanding of interstellar turbulence anc towards building more realistic models of interstellar clouds is to identify model structures characterised by a limited set of parameters which can be quantified by comparison with observed cloud images., A first step towards a better understanding of interstellar turbulence and towards building more realistic models of interstellar clouds is to identify model structures characterised by a limited set of parameters which can be quantified by comparison with observed cloud images. + As many aspects of observed interstellar clouds can be described by fractal properties (Combes.2000)... a promising first approach to à parametric description is given by exponents of scaling relations.," As many aspects of observed interstellar clouds can be described by fractal properties \citep{Combes}, a promising first approach to a parametric description is given by exponents of scaling relations." + Motivated by the similarity of observed interstellar cloud images with the structure of (fBm. see Sect. 2.2.1) ," Motivated by the similarity of observed interstellar cloud images with the structure of (fBm, see Sect. \ref{sect_pertestdata}) )" +fractals. which are characterised by the single number of the exponent of the power spectrum. Stutzkietal.(1998) developed the A-variance analysis as a tool to measure the structural scaling behaviour of observed images.," fractals, which are characterised by the single number of the exponent of the power spectrum, \citet{Stutzki} + developed the $\Delta$ -variance analysis as a tool to measure the structural scaling behaviour of observed images." + The A-variance is a type of averaged wavelet transform that measures the variance in a structure f(7) on a given scale | by filtering it by a spherically symmetric down-up-down function of size / (Zielinsky Stutzki 1999)., The $\Delta$ -variance is a type of averaged wavelet transform that measures the variance in a structure $f(\vec{r})$ on a given scale $l$ by filtering it by a spherically symmetric down-up-down function of size $l$ (Zielinsky Stutzki 1999). + The A-variance analysis was successfully applied to several observational data sets: Stutzkietal.(1995) studied a CO map of the Outer Galaxy. Benschetal.(2001) investigated a series of nearby star-forming clouds and a number of nested maps in different CO isotopes from the Polaris Flare. Huber(2002) performed a systematic study of a large set of Galactic CO maps. and power-law A-variance spectra with exponents between 0.5 and 1.3.," The $\Delta$ -variance analysis was successfully applied to several observational data sets: \citet{Stutzki} studied a CO map of the Outer Galaxy, \citet{Bensch} + investigated a series of nearby star-forming clouds and a number of nested maps in different CO isotopes from the Polaris Flare, \citet{Huber} performed a systematic study of a large set of Galactic CO maps, and power-law $\Delta$ -variance spectra with exponents between 0.5 and 1.3." + Mac Low Ossenkopf (2000) and Ossenkopf (2002) applied the A-variance analysis to simulations of interstellar turbulence to compare the scaling behaviour of the simulations with that of observed maps., Mac Low Ossenkopf (2000) and Ossenkopf (2002) applied the $\Delta$ -variance analysis to simulations of interstellar turbulence to compare the scaling behaviour of the simulations with that of observed maps. + It became however obvious that. aside from the spectral index. deviations from a power law on particular scales should be studied as well because they provide significant information on the physical processes on these scales.," It became however obvious that, aside from the spectral index, deviations from a power law on particular scales should be studied as well because they provide significant information on the physical processes on these scales." +" Thus the A-variance analysis is to be optimised with respect to its capabilities of the corresponding scale detection,", Thus the $\Delta$ -variance analysis is to be optimised with respect to its capabilities of the corresponding scale detection. + We propose in this paper a number of improvements to the A-variance optimising its sensitivity. Its applicability to arbitrary data sets. and the speed of its computation.," We propose in this paper a number of improvements to the $\Delta$ -variance optimising its sensitivity, its applicability to arbitrary data sets, and the speed of its computation." + The critical quantity for the detection of pronounced scales in a structure is the shape of the wavelet filter funetion., The critical quantity for the detection of pronounced scales in a structure is the shape of the wavelet filter function. + The spherically symmetric down-up-down function introduced by Stutzkietal.(1998) 1s an obvious first choice., The spherically symmetric down-up-down function introduced by \citet{Stutzki} is an obvious first choice. + However. other wavelet shapes offer attractive alternatives.," However, other wavelet shapes offer attractive alternatives." + For infinitely extended or for periodic structures the fastest way of numerically calculating the A-variance is given by a Fourier transform of the image., For infinitely extended or for periodic structures the fastest way of numerically calculating the $\Delta$ -variance is given by a Fourier transform of the image. + However. observed maps typically have a finite size. often even cutting the observed clouds at the map boundary. and Fourier-based methods run into the well known problems of artificial structure being introduced by these edge effects.," However, observed maps typically have a finite size, often even cutting the observed clouds at the map boundary, and Fourier-based methods run into the well known problems of artificial structure being introduced by these edge effects." + Benschetal.(2001) thus implemented the A-variance by a numerical treatment in the spatial domain., \citet{Bensch} thus implemented the $\Delta$ -variance by a numerical treatment in the spatial domain. + Calculating a two-dimensional convolution in the spatial domain. however. results in a rather slow computation.," Calculating a two-dimensional convolution in the spatial domain, however, results in a rather slow computation." + An additional complicationin observed data comes from the fact that the signal-to-noise ratio is often not uniform across the mapped area., An additional complicationin observed data comes from the fact that the signal-to-noise ratio is often not uniform across the mapped area. +V1,5. + The sample of 8 GGCs in Ferraro et al. (, The sample of 8 GGCs in Ferraro et al. ( +2000) covers a wide range in metallicity despite its small size.,2000) covers a wide range in metallicity despite its small size. +" While our sample is a little larger. comprising 11 GGC's. it covers a limited range in metallicity,"," While our sample is a little larger, comprising 11 GGCs, it covers a limited range in metallicity." + Therefore. (he combined data set increases the sample of GGC'Ss to 16 and covers a wider range in metallicity (han (hat of the sample GGCs of our work.," Therefore, the combined data set increases the sample of GGCs to 16 and covers a wider range in metallicity than that of the sample GGCs of our work." + We have found clear relations between GGC metallicity and luminosity of the RGB bump. as shown in Figure 5.," We have found clear relations between GGC metallicity and luminosity of the RGB bump, as shown in Figure 5." + By taking error-weighted mean averages for the 3 common GGCs and combining (he remaining data we have (he reduced regression equations (Ga) aud (6b) and we plot the results in Figure 5 as solid lines., By taking error-weighted mean averages for the 3 common GGCs and combining the remaining data we have the reduced regression equations (6a) and (6b) and we plot the results in Figure 5 as solid lines. + Dashed lines ave [rom equations given in Figure 13 of Ferraro et al. (, Dashed lines are from equations given in Figure 13 of Ferraro et al. ( +2000) (ranslormect into the 241ASS svstem and dot-dashed lines are from equations (5a) and (5b).,2000) transformed into the 2MASS system and dot-dashed lines are from equations (5a) and (5b). + Although dashed lines and dot-dashed lines are not exactly coincident with each other. their forms ave very similar.," Although dashed lines and dot-dashed lines are not exactly coincident with each other, their forms are very similar." + The first terms of equations (6a) and (6b) are negligible if (he errors in the parameters are considered., The first terms of equations (6a) and (6b) are negligible if the errors in the parameters are considered. + Therefore solid lines are nearly linear ancl deviate from the dashed lines slightly at the metal rich ends., Therefore solid lines are nearly linear and deviate from the dashed lines slightly at the metal rich ends. + This is due to metallicity revision of NGC 6553 and NGC 6523., This is due to metallicity revision of NGC 6553 and NGC 6528. + Their original values in Ferraro et al. (, Their original values in Ferraro et al. ( +2000). which were extrapolated to be |Fe/Il]ecoz =—0.44 and —0.38. and [MI/1 =—0.36 and —0.31. respectively. have been revised to |Fe/Il]ecoz =—0.06 and 0.07. and ΑΗ = 0.08 and 0.22. respectively.,"2000), which were extrapolated to be $_{\rm CG97}$ $= -0.44$ and $-0.38$ , and [M/H] $= -0.36$ and $-0.31$, respectively, have been revised to $_{\rm CG97}$ $= -0.06$ and 0.07, and [M/H] $=$ 0.08 and 0.22, respectively." + The overall trend. for the RGB bump positions of GGCs to become brighter with decreasing metallicity has been supported by many theoretical models derived [rom the first such model established by Sweigart (1978)., The overall trend for the RGB bump positions of GGCs to become brighter with decreasing metallicity has been supported by many theoretical models derived from the first such model established by Sweigart (1978). + However. there is also a moderate helium abundance dependeney. (Sweigart 1978) and a weak age dependency (Ferraro et al 1999; Yi et al.," However, there is also a moderate helium abundance dependency (Sweigart 1978) and a weak age dependency (Ferraro et al 1999; Yi et al." + 2001) of RGB bump positions for a given metallicity., 2001) of RGB bump positions for a given metallicity. + According to Yi et al. (, According to Yi et al. ( +2001) and Ferraro et al. (,2001) and Ferraro et al. ( +1999). the RGB bump Inminosity varies with metallicity by roy = 0.96 in the metallicity range |Fe/I1I] = —2.3 ~ 0.0 and in the age range of T Gyr ~ 16 Gyr.,"1999), the RGB bump luminosity varies with metallicity by $\Delta{M_{V}} \over \Delta{\rm [Fe/H]}$ $\approx$ 0.96 in the metallicity range [Fe/H] $=$ $-2.3$ $\sim$ 0.0 and in the age range of 7 Gyr $\sim$ 16 Gyr." + Yun Lee (1979) found that RGB bump bolometric Iuminosity varied with |Fe/II] according to a nearly constant relation in the helium abundance range Y — Q.1 ~ 0.3., Yun Lee (1979) found that RGB bump bolometric luminosity varied with [Fe/H] according to a nearly constant relation in the helium abundance range $Y$ $=$ 0.1 $\sim$ 0.3. + in the theoretical luminosity finction analvsis of 46 RGB models of Sweigart Gross (1978)., in the theoretical luminosity function analysis of 46 RGB models of Sweigart Gross (1978). + Therefore. we assume that the RGB bump luminosity varies with |Fe/1l]constantly by AireAAti] = 0.96 in the metallicity range |Fe/II] = —2.3 ~ 0.0. in the age range," Therefore, we assume that the RGB bump luminosity varies with [Fe/H]constantly by $\Delta{M_{V}} \over \Delta{\rm [Fe/H]}$ $\approx$ 0.96 in the metallicity range [Fe/H] $=$ $-2.3$ $\sim$ 0.0, in the age range" +CPB 37A (also called G348.5|0.1. IX(2000)=17LOG Dec.(2000)2.3872:yf ) was discovered by Clark.Caswell&Green(1975). in the radio band and has a shell-tvpe morphology with an angular size of 15 arcmin.,"CTB 37A (also called G348.5+0.1, $\rmn{RA}(2000)=17^{\rmn{h}} 14^{\rmn{m}} 06^{\rmn{s}}$ $\rmn{Dec.}~(2000)=-38\degr 32\arcmin$ ) was discovered by \citet{b5} in the radio band and has a shell-type morphology with an angular size of 15 arcmin." + From Very Large Array observations at wavelengths of 6. 20. and 90 cm. ]xassim.Daum&Weiler(1991) reported that this supernova remnant (SNIU is expanding in an inhomogeneous region. and is part of a complex. composed of three SNRs: CPB BTA. G348.710.8 (also called CPB 37B). and €2348.5-0.0," From Very Large Array observations at wavelengths of 6, 20, and 90 cm, \citet{b6} reported that this supernova remnant (SNR) is expanding in an inhomogeneous region, and is part of a complex composed of three SNRs: CTB 37A, G348.7+0.3 (also called CTB 37B), and G348.5-0.0." + From the Galactic plane survey data of G348.5|0 Yamauchietal.(2¢JOS) found that the X-ray spectra of the SNI was heavily absorbed by interstellar matter with Ig22107 em? and the size of X-ray cniission was coniparable to its radio structure.," From the Galactic plane survey data of G348.5+0.1, \citet{b28} found that the X-ray spectra of the SNR was heavily absorbed by interstellar matter with $N_{\rm H}\sim2\times10^{22}$ ${\rm +cm^{-2}}$ and the size of X-ray emission was comparable to its radio structure." + Frailοἱal.ee detected OLI masers with velocities at ve 20 and60 km s+. in the direction of ςΕν 37A at 1720. MlIIz.," \citet{b31} detected OH masers with velocities at about 20 and 60 km $^{-1}$, in the direction of CTB 37A at 1720 MHz." + Revnoso&Mangum(2000) the environment of this remnant with associated OLL NAM1720 MlIz masers in the CO J—1-) transition with the 12 Meter Telescope of the NRAO., \citet{b53} surveyed the environment of this remnant with associated OH 1720 MHz masers in the CO J=1-0 transition with the 12 Meter Telescope of the NRAO. + They reported that à number of molecular clouds are interacting with the SNA. shock fronts., They reported that a number of molecular clouds are interacting with the SNR shock fronts. + Aharonianetal.(2008). using. and data showed the presence of thermal ravs from the Northeast part. an extended non-thermal X-rav source. CXOU J171419.8-383023 in the Northwest part and a 5-rav source. LIESS 1714-385. coincident with the remnant.," \citet{b20} using and data showed the presence of thermal X-rays from the Northeast part, an extended non-thermal X-ray source, CXOU J171419.8-383023 in the Northwest part and a ${\gamma}$ -ray source, HESS J1714-385, coincident with the remnant." + They found a high. absorbing column density. of Nao~31077 em?., They found a high absorbing column density of $N_{\rm H}\sim3\times10^{22}$ ${\rm cm^{-2}}$. + Thev claimed that. the observed X-ray morphology was a result. of interaction with the inhomogeneous medium surrounding the remnant and. this inhomogencity was also responsible for the break-out raclio morphology., They claimed that the observed X-ray morphology was a result of interaction with the inhomogeneous medium surrounding the remnant and this inhomogeneity was also responsible for the break-out radio morphology. +" Castro&Slane(2010) using observations with the Fermi-LAT. have revealed 5 -ravy emission from this SNR: the spectrum of the source coincident with CPB 387A was fitted by a power-law (PL) model with an exponential cutoll at energy £24,442 GeV. Considering the lack of evidence for contribution by a pulsar and the presence of maser emission for the remnant they proposed that *-ravs result from molecular clouds interactions."," \citet{b51} using observations with the Fermi-LAT, have revealed ${\gamma}$ -ray emission from this SNR; the spectrum of the source coincident with CTB 37A was fitted by a power-law (PL) model with an exponential cutoff at energy $E_{\rm +cut}$ =4.2 GeV. Considering the lack of evidence for contribution by a pulsar and the presence of maser emission for the remnant they proposed that ${\gamma}$ -rays result from SNR-molecular clouds interactions." + The distance to the CPB 387A has been estimated fron 2] em absorbtion measurement to be in between6.7-13.7 kpe by Caswellctal.(1975)associated., The distance to the CTB 37A has been estimated from 21 cm absorbtion measurement to be in between 6.7-13.7 kpc by \citet{b52}. + From velocity. measurements of molecular clouds with the remnant.HRevnoso& adopted a distance of 11.3 kpe.," From velocity measurements of molecular clouds associated with the remnant,\citet{b53} adopted a distance of 11.3 kpc." + So we will use d—11.3 kpe for our calculationsthroughout this work., So we will use d=11.3 kpc for our calculationsthroughout this work. + The location. of CPB 37X containing Oll. maser, The location of CTB 37A containing OH maser +"and 5;"" is the flux density measured on the image with the 2D parabolic fit, g is the gain coefficient calculated by the post-facto gain calibration and p; and oo,,; are respectively the mean and RMS surface brightness of an annular region around the source.","and $S^{raw}_i$ is the flux density measured on the image with the 2D parabolic fit, $g$ is the gain coefficient calculated by the post-facto gain calibration and $\rho_i$ and $\sigma_{bg,i}$ are respectively the mean and RMS surface brightness of an annular region around the source." +" The weighting factor of 1/02 captures both the noise level in the surrounding region and the absolute flux density calibration error, from the MGPS-2 and SUMSS catalogues, assumed to be 5 per cent."," The weighting factor of $1/\sigma_i^2$ captures both the noise level in the surrounding region and the absolute flux density calibration error, from the MGPS-2 and SUMSS catalogues, assumed to be 5 per cent." +" For a source with a peak flux density at the detection limit of 14mJybeam σι is dominated by the background RMS term and has a ο,typical value of3mJy."," For a source with a peak flux density at the detection limit of $14\unit{mJy~beam^{-1}}$, $\sigma_i$ is dominated by the background RMS term and has a typical value of." +" For a source with flux density of 100mJybeam""! the flux density calibration term dominates and results in a typical error of o;~6mJy.", For a source with flux density of $100\unit{mJy~beam^{-1}}$ the flux density calibration term dominates and results in a typical error of $\sigma_i \simeq 6 \unit{mJy}$. +" To determine whether a source is variable or not, we work from the null hypothesis that all sources are static with added Gaussian measurement error."," To determine whether a source is variable or not, we work from the null hypothesis that all sources are static with added Gaussian measurement error." +" Applying the measured X& to the analytic X? cumulative distribution function (CDF) yields the probability of rejecting the null hypothesis, ie. the probability that the source is genuinely variable, which we write as P(x7.)."," Applying the measured $\chi^2_{\mathrm{lc}}$ to the analytic $\chi^2$ cumulative distribution function (CDF) yields the probability of rejecting the null hypothesis, i.e. the probability that the source is genuinely variable, which we write as $P(\chi^2_{\mathrm{lc}})$." +" Working with probabilities rather than x? values also enables us to compare the statistics of light curves with differing number of measurements, which is absorbed in the CDF."," Working with probabilities rather than $\chi^2$ values also enables us to compare the statistics of light curves with differing number of measurements, which is absorbed in the CDF." + Those light curves whose probability exceeds a certain threshold can be classified as variable., Those light curves whose probability exceeds a certain threshold can be classified as variable. +" Past investigations such as those of ?,, ? and ? applied a probability threshold of 99 per cent to derive a set of"," Past investigations such as those of \citet{kesteven1977.2.7GHzvariability}, \citet{gregory1986radiopatrol} and \citet{seilstad1983.10.8GHz} applied a probability threshold of 99 per cent to derive a set of" +"a method to derive the SZ temperature that does not require symmetry and so is suitable for merging clusters,",a method to derive the SZ temperature that does not require symmetry and so is suitable for merging clusters. + In this paper. we extend the previous studies by introducing a method to derive the standard temperature deviation and temperature variance along the line-of-sight for revealing the 3D temperature structure for relatively cool merging galaxy clusters with temperatures less than 10 keV. We focus on relatively cool merging galaxy clusters because it is easier to measure their standard temperature deviation and temperature variance owing to lower order SZ corrections.," In this paper, we extend the previous studies by introducing a method to derive the standard temperature deviation and temperature variance along the line-of-sight for revealing the 3D temperature structure for relatively cool merging galaxy clusters with temperatures less than 10 keV. We focus on relatively cool merging galaxy clusters because it is easier to measure their standard temperature deviation and temperature variance owing to lower order SZ corrections." + Shock-heated regions have been found by Chandra in numerous galaxy clusters in the range from galaxy groups with temperatures of = | keV. such a HGC 62 (Gitti et al.," Shock-heated regions have been found by Chandra in numerous galaxy clusters in the range from galaxy groups with temperatures of $\approx$ 1 keV, such a HGC 62 (Gitti et al." + 2010). to the most massive galaxy clusters with temperatures of = 15 keV. such as the Bullet cluster (Markeviteh et al.," 2010), to the most massive galaxy clusters with temperatures of $\approx$ 15 keV, such as the Bullet cluster (Markevitch et al." + 2002)., 2002). + In this paper. we show that the temperature variance along the line-of-sight is an useful quantity. which allows us to reveal shocks in galaxy clusters. and demonstrate how to reveal a merger shock by analvzing a relatively cool simulated galaxy cluster.," In this paper, we show that the temperature variance along the line-of-sight is an useful quantity, which allows us to reveal shocks in galaxy clusters, and demonstrate how to reveal a merger shock by analyzing a relatively cool simulated galaxy cluster." + We also propose an extension of our method to make it suitable for hot galaxy clusters (in the temperature range of 10 keV — |5 keV)., We also propose an extension of our method to make it suitable for hot galaxy clusters (in the temperature range of 10 keV – 15 keV). + We calculate the temperature variance along the line-of-sight for a simulated hot galaxy cluster to demonstrate how this quantity can be derived from multi-frequency observations of the SZ effect., We calculate the temperature variance along the line-of-sight for a simulated hot galaxy cluster to demonstrate how this quantity can be derived from multi-frequency observations of the SZ effect. + Studying the presence of gas inhomogeneities along the of-sight by means of the SZ eftect is important to improve our knowledge of the 3D temperature structure of merging galaxy clusters., Studying the presence of gas inhomogeneities along the line-of-sight by means of the SZ effect is important to improve our knowledge of the 3D temperature structure of merging galaxy clusters. + This will permit us to improve the deprojection analysis of galaxy clusters by comparing the derived values of the standard temperature deviation along the line-of-sight with those calculated from the deprojection maps., This will permit us to improve the deprojection analysis of galaxy clusters by comparing the derived values of the standard temperature deviation along the line-of-sight with those calculated from the deprojection maps. + An analysis of maps of the gas temperature variance along the line-of-sight will provide us with an interesting approach to reveal merger shocks., An analysis of maps of the gas temperature variance along the line-of-sight will provide us with an interesting approach to reveal merger shocks. + This approach is alternative to that based on the projected X-ray surface brightness maps (e.g. Markevitch et al., This approach is alternative to that based on the projected X-ray surface brightness maps (e.g. Markevitch et al. + 2002)., 2002). + The layout of the paper is as follows., The layout of the paper is as follows. + We calculate the SZ intensity maps of the simulated galaxy cluster at frequencies of 150 GHz and 217 GHz in the framework of the Wright formalism in Sect., We calculate the SZ intensity maps of the simulated galaxy cluster at frequencies of 150 GHz and 217 GHz in the framework of the Wright formalism in Sect. + 2., 2. + We propose a method to derive the temperature variance along the line-of-sight for relatively cool galaxy clusters and apply this method to the simulated galaxy cluster in Sect., We propose a method to derive the temperature variance along the line-of-sight for relatively cool galaxy clusters and apply this method to the simulated galaxy cluster in Sect. + 3. using the derived SZ intensity maps.," 3, using the derived SZ intensity maps." + We also propose a method to reveal merger shocks in the simulated galaxy cluster in Sect., We also propose a method to reveal merger shocks in the simulated galaxy cluster in Sect. + 3., 3. + We present our discussion on how to improve the proposed method and calculate the temperature variance for a simulated hot galaxy cluster in Sects., We present our discussion on how to improve the proposed method and calculate the temperature variance for a simulated hot galaxy cluster in Sects. + 4 and 5. respectively.," 4 and 5, respectively." + We present our conclusions in Sect., We present our conclusions in Sect. + 6., 6. + In this section. we calculate the SZ intensity maps at frequencies of 150 GHz and 217 GHz in the framework of the relativistic Wright formalism for the merging galaxy cluster simulated by Dubois et al. (," In this section, we calculate the SZ intensity maps at frequencies of 150 GHz and 217 GHz in the framework of the relativistic Wright formalism for the merging galaxy cluster simulated by Dubois et al. (" +2010) and previously analyzed by means of the SZ effect by Prokhorov et al. (,2010) and previously analyzed by means of the SZ effect by Prokhorov et al. ( +2010b).,2010b). + The derived SZ intensity maps will be used in the next section to calculate the temperature variance along the line-of-sight., The derived SZ intensity maps will be used in the next section to calculate the temperature variance along the line-of-sight. + The galaxy cluster simulations of Dubois et al. , The galaxy cluster simulations of Dubois et al. ( +2010). which we use in this paper. are run with the Adaptive Mesh Refinement (AMR) code RAMSES (Teyssier 2002).,"2010), which we use in this paper, are run with the Adaptive Mesh Refinement (AMR) code RAMSES (Teyssier 2002)." + The simulation follows the gas dynamics using a second-order unsplit Godunov scheme for the Euler equations with a Total Variation Diminishing scheme for extrapolation of fluid quantities at the cell interface from their cell centre values., The simulation follows the gas dynamics using a second-order unsplit Godunov scheme for the Euler equations with a Total Variation Diminishing scheme for extrapolation of fluid quantities at the cell interface from their cell centre values. + Particles are evolved with a particle-mesh solver for gravity and using a Cloud-In-Cell interpolation., Particles are evolved with a particle-mesh solver for gravity and using a Cloud-In-Cell interpolation. + The simulation includes gas cooling from a. primordial sus composition of Hydrogen and Helium with a UV heating background following Haardt Madau (1996)., The simulation includes gas cooling from a primordial gas composition of Hydrogen and Helium with a UV heating background following Haardt Madau (1996). + The reionization redshift is set up at z=8.5., The reionization redshift is set up at $z=8.5$. + Star formation proceeds in high gas- regions with p>0.1Hem? (Rasera Teyssier 2006. Dubois Teyssier 2008).," Star formation proceeds in high gas-density regions with $\rho>0.1 \, \rm H\, \rm cm^{-3}$ (Rasera Teyssier 2006, Dubois Teyssier 2008)." + Though feedback from supernovae is not included. we take into account the feedback from Active Galactic Nuclei following the model from Dubois et al. (," Though feedback from supernovae is not included, we take into account the feedback from Active Galactic Nuclei following the model from Dubois et al. (" +2010). which is the dominant source of energy in massive objects such as galaxy clusters.,"2010), which is the dominant source of energy in massive objects such as galaxy clusters." + The simulation is performed assuming a flat ACDM cosmology (Spergel et al., The simulation is performed assuming a flat $\Lambda$ CDM cosmology (Spergel et al. + 2003)., 2003). +" A zoom technique is employed with a 128? coarse grid in a 50 A4, Mpe box size. and with wo nested grids with a 20 hy Mpe and a 6 hy Mpe radius or a 2565 and 512° equivalent grid respectively. where πω=Hyf/000kms!Mpe !). This leads to a minimum dark matter mass of Mp=4.5x10M.."," A zoom technique is employed with a $128^3$ coarse grid in a 80 $h^{-1}_{100}$ Mpc box size, and with two nested grids with a 20 $h^{-1}_{100}$ Mpc and a 6 $h^{-1}_{100}$ Mpc radius for a $256^3$ and $512^3$ equivalent grid respectively, where $h_{100}=H_{0}/(100\, \rm km\, \rm s^{-1}\, \rm Mpc^{-1})$ This leads to a minimum dark matter mass of $M_{\rm DM}=4.5\times 10^8\, +\rm M_{\odot}$." + The grid is dynamically refined down o level 16. reaching 1.19 hy kpe.," The grid is dynamically refined down to level $16$, reaching 1.19 $h^{-1}_{100}$ kpc." + The zoom region tracks the ormation of a galaxy cluster with a 1:1 major merger occurring at z — 0.8., The zoom region tracks the formation of a galaxy cluster with a 1:1 major merger occurring at z = 0.8. + This z = 0.8 major galaxy merger drives the cluster gas to emperatures twice the virial temperature thanks to violent shock waves., This z = 0.8 major galaxy merger drives the cluster gas to temperatures twice the virial temperature thanks to violent shock waves. + The projected mass-weighted temperature map is shown in Fig., The projected mass-weighted temperature map is shown in Fig. + 2., 2. + For further details of the simulation. see Dubois et al. (," For further details of the simulation, see Dubois et al. (" +2010).,2010). + Using the Wright formalism. we have previously calculated he SZ intensity maps at frequencies of 128 GHz and 369 GHz for he simulated cluster at z=0.74 (see Prokhorov et al.," Using the Wright formalism, we have previously calculated the SZ intensity maps at frequencies of 128 GHz and 369 GHz for the simulated cluster at z=0.74 (see Prokhorov et al." + 2010b)., 2010b). + These Tequencies correspond to minimum and maximum values of the SZ intensity in the the Kompaneets approximation (Kompaneets 1957)., These frequencies correspond to minimum and maximum values of the SZ intensity in the the Kompaneets approximation (Kompaneets 1957). + The ratio of these SZ intensities has allowed us to derive he SZ-temperature from mock SZ observations., The ratio of these SZ intensities has allowed us to derive the SZ-temperature from mock SZ observations. + The derived SZ-temperature is shown in Fig., The derived SZ-temperature is shown in Fig. + 2. (top left-hand panel) and demonstrates how the prominent structures on the 2D projected emperature map of the merging cluster can be unveiled., \ref{Fig1} (top left-hand panel) and demonstrates how the prominent structures on the 2D projected temperature map of the merging cluster can be unveiled. + The mass-weighted temperature map (in keV) of the simulated. cluster is Lotted in Fig., The mass-weighted temperature map (in keV) of the simulated cluster is plotted in Fig. + 2. (top right-hand panel) for a comparison.," \ref{Fig1} + (top right-hand panel) for a comparison." + The gas amperature maps have prominent “arc-like™ structures. which have a high temperature compared with other simulated cluster regions.," The gas temperature maps have prominent “arc-like” structures, which have a high temperature compared with other simulated cluster regions." +" The average temperature of the ""arc-like"" structures is 25 keV and. therefore. we can use this simulated cluster as an example of a relatively low temperature galaxy cluster."," The average temperature of the “arc-like” structures is $\approx$ 5 keV and, therefore, we can use this simulated cluster as an example of a relatively low temperature galaxy cluster." + Below. we briefly describe how to calculate the SZ intensity maps in the framework of the Kompaneets and Wright formalisms.," Below, we briefly describe how to calculate the SZ intensity maps in the framework of the Kompaneets and Wright formalisms." + The CMB intensity distortion caused by the SZ effect on a non-relativistic electron population in the framework of the Kompaneets approximation is given by (for a review. see Birkinshaw 1999) where fy=2hPoy)(Ute. xοPoy. and the spectral shape of the SZ distortion is described by the spectral function The subscript ‘nr’ denotes that Eq.CL ," The CMB intensity distortion caused by the SZ effect on a non-relativistic electron population in the framework of the Kompaneets approximation is given by (for a review, see Birkinshaw 1999) where $I_{\mathrm{0}}=2 (k_{\mathrm{b}} T_{\mathrm{cmb}})^3 / +(hc)^2$, $x=h\nu/k_{\mathrm{b}} T_{\mathrm{cmb}}$, and the spectral shape of the SZ distortion is described by the spectral function The subscript $`\mathrm{nr}' $ denotes that Eq.\ref{Inr}) )" +was obtained for a non- electron population in the Kompaneets approximation., was obtained for a non-relativistic electron population in the Kompaneets approximation. +" The Comptonization parameter v4, is given by", The Comptonization parameter $y_{\mathrm{gas}}$ is given by + these simulations pertain to the evolution of he trans-Neptunian region over + Gyr in the framework of the ice model (Tsiganis et al..," these simulations pertain to the evolution of the trans-Neptunian region over 4 Gyr in the framework of the Nice model (Tsiganis et al.," + 2005: Gomes et al..," 2005; Gomes et al.," + 2005)., 2005). + to compute the contribution of the TNO region to the HIHQ Centaur A last. fourth set of simulations were similar to the third set apart from the fact that the classical Oort cloud was used ie. the Oort cloud that was formed in the current Galactic environment rather than during the Sun's birth cluster (e.g. Dones et al..," to compute the contribution of the TNO region to the HIHQ Centaur A last, fourth set of simulations were similar to the third set apart from the fact that the classical Oort cloud was used i.e. the Oort cloud that was formed in the current Galactic environment rather than during the Sun's birth cluster (e.g. Dones et al.," + 2004)., 2004). + These simulations were performed to determine whether the classical Oort cloud could dominate the inner Oort cloud as the source of HIHQ Centaurs., These simulations were performed to determine whether the classical Oort cloud could dominate the inner Oort cloud as the source of HIHQ Centaurs. + The data was taken from Brasser et al. (, The data was taken from Brasser et al. ( +2010) at 250 Myr and simulated for the remaining 3.8 Gyr.,2010) at 250 Myr and simulated for the remaining 3.8 Gyr. + Only particles that were already in the Oort cloud were used., Only particles that were already in the Oort cloud were used. + Once again. the Galactic tide. passing stars and the planets were included.," Once again, the Galactic tide, passing stars and the planets were included." + In this section the results from our numerical simulations are presented., In this section the results from our numerical simulations are presented. + The probability of finding a HIHQ Centaur is essentially given by the product of the fraction of particles that ever enter the HIHQ Centaur phase multiplied by particle's fractional lifetime in the HIHQ Centaur state., The probability of finding a HIHQ Centaur is essentially given by the product of the fraction of particles that ever enter the HIHQ Centaur phase multiplied by particle's fractional lifetime in the HIHQ Centaur state. + Using the TNO simulations from Lykawka et al. (, Using the TNO simulations from Lykawka et al. ( +2009) (set I) and the ones from set 2. we computed the probability of a body being in the HIHQ Centaur state.,"2009) (set 1) and the ones from set 2, we computed the probability of a body being in the HIHQ Centaur state." +" The probability for HIHQ Centaur production turned out to be 1.2«10."" for objects withq€15.30] AU.α<100 AU ands> 65°."," The probability for HIHQ Centaur production turned out to be $1-2 \times 10^{-5}$ for objects with$q \in [15,30]$ AU,$a<100$ AU and $i>65^\circ$ ." +eclipse timings (7O) as compared to predicted: timines “C™) that would be expected. from. a linear. ephemeris.,eclipse timings (“O”) as compared to predicted timings (“C”) that would be expected from a linear ephemeris. + Dx plotting a simple ο6 diagram. they show that the O—€' residuals for HU. Aqr contain two evclical signals superposecL on a longer-period curvature.," By plotting a simple $O-C$ diagram, they show that the $O-C$ residuals for HU Aqr contain two cyclical signals superposed on a longer-period curvature." + Lach signal can »e modelled as a Ixeplerian orbit to determine the planetary xwameters., Each signal can be modelled as a Keplerian orbit to determine the planetary parameters. + We reproduce the parameter estimates of Qianetal.(2011). in Table 1.., We reproduce the parameter estimates of \citet{Qian2011} in Table \ref{planetparams}. + Xs for planets detected with by racial-velocity method. only the radial component of the jxanet's inlluence on the host star is detectable.," As for planets detected with by radial-velocity method, only the radial component of the planet's influence on the host star is detectable." + Here. only he line-ol-sieht light-travel time differences are observed. so the mass estimates for the HU Acqr planets are given as minimum values.," Here, only the line-of-sight light-travel time differences are observed, so the mass estimates for the HU Aqr planets are given as minimum values." + Qianetal.(2011) note that the HEU Aqr system inclination is S5. so. if the planets orbit in the same plane as the stars. their true masses would. only be larger than the minimum values given in Table 1..," \citet{Qian2011} note that the HU Aqr system inclination is $85^{\circ}$, so, if the planets orbit in the same plane as the stars, their true masses would only be larger than the minimum values given in Table \ref{planetparams}." + In order to examine the potential dynamical stability of the two planets suggested for the LLU Aqr system. we performer a large number of detailed dynamical simulations using the integrator within the /IN-body. dynamical. package (Chambers1999).," In order to examine the potential dynamical stability of the two planets suggested for the HU Aqr system, we performed a large number of detailed dynamical simulations using the integrator within the $N$ -body dynamical package \citep{Chambers99}." +. Following the strategy employec to analyse the stability of the HIU 8799 svstem (Marshall. 2010)... we held. the orbit. of the inner planet constant (with @=3.6Al and e= 0.0). an varied the orbital elements of the outer planet across a range corresponding to c3 times the discoverv letters. quotec uncertainties in the semi-major axis. e. and eccentricity. c.," Following the strategy employed to analyse the stability of the HR 8799 system \citep{Marshall2010}, , we held the orbit of the inner planet constant (with $a = 3.6~AU$ and $e = 0.0$ ), and varied the orbital elements of the outer planet across a range corresponding to $\pm$ 3 times the discovery letter's quoted uncertainties in the semi-major axis, $a$, and eccentricity, $e$." + We initially considered. the scenario. described in. Qianetal. (2011)... where the planets are considered to be co-," We initially considered the scenario described in \citet{Qian2011}, where the planets are considered to be co-planar." + In other words. we set the orbital inclinations. 7. of the two planets to be OF at the start of our integrations.," In other words, we set the orbital inclinations, $i$, of the two planets to be $^{\circ}$ at the start of our integrations." + We treat the central stars. a 0:95 white cwarl anc a Q.2 secondary. as a single point mass.," We treat the central stars, a 0.88 white dwarf and a 0.2 secondary, as a single point mass." + Since the stars orbit cach other with a period of only 2.08. hours (ic. with a separation of 0.004. AW). and. the bodies. of interest are believed to orbit at distances of 3.6 and 5.4 AU. js treatment is dvnamically justified.," Since the stars orbit each other with a period of only 2.08 hours (i.e. with a separation of 0.004 AU), and the bodies of interest are believed to orbit at distances of 3.6 and 5.4 AU, this treatment is dynamically justified." + We give each. plane 10 Minimum mass estimated. in Qianetal.(2011)., We give each planet the minimum mass estimated in \citet{Qian2011}. +.. We note in passing that. if the masses of the proposed. planets are significantly ereater than those detailed in Qianet (2011).. then this could only have a deleterious elfect on the gaability of their proposed orbits.," We note in passing that, if the masses of the proposed planets are significantly greater than those detailed in \citet{Qian2011}, then this could only have a deleterious effect on the stability of their proposed orbits." + Fixing the orbit of the inner planet. we simulated a otal of 9261 planetary svstems.," Fixing the orbit of the inner planet, we simulated a total of 9261 planetary systems." + In cach simulated. svsteni. 1 inner planet began on the same orbit. but the orbital elements. of the outer planet were chosen such that each simulation sampled a unique set of possible parameters.," In each simulated system, the inner planet began on the same orbit, but the orbital elements of the outer planet were chosen such that each simulation sampled a unique set of possible parameters." + We listributecl the orbital. elements. of the outer planet such ju we tested 21 values of semi-major axis. spread. evenly across c3-7 [rom the value (@=5.4 AU) given in Qianeal.(2011).," We distributed the orbital elements of the outer planet such that we tested 21 values of semi-major axis, spread evenly across $\pm$ $\sigma$ from the value $a=5.4$ AU) given in \citet{Qian2011}." +. For cach value of semi-major axis. we tested 2 values of orbital eccentricity. again spread evenly across d 6 from the value (e=0.51). given in that work.," For each value of semi-major axis, we tested 21 values of orbital eccentricity, again spread evenly across $\pm$ $\sigma$ from the value $e=0.51$ ), given in that work." + Finally. a each of these 441 (e.ο) locations we carried out 21 tests. with the initial location of the planet distributed across a range of 3-0 from the nominal mean anomaly of the outer plane (calculated. from Fig.," Finally, at each of these 441 $(a,e)$ locations we carried out 21 tests, with the initial location of the planet distributed across a range of $\pm$ $\sigma$ from the nominal mean anomaly of the outer planet (calculated from Fig." + 2 of Qianetal.(2011)))., 2 of \citet{Qian2011}) ). + Fhese 926 unique models. based on the LIU Aqr system. parameters. were integrated. using the integrator. within for a period of 100. Myr. following the evolution an final fates of the two postulated. planets in the system.," These 9261 unique models, based on the HU Aqr system parameters, were integrated using the integrator within for a period of 100 Myr, following the evolution and final fates of the two postulated planets in the system." + A planet was deemed. ejected. from the system upon reaching a distance of 1000 AU from the barveentre. and all mutua collisions were recorded.," A planet was deemed ejected from the system upon reaching a distance of 1000 AU from the barycentre, and all mutual collisions were recorded." + Vhis vielded a lifetime from each incliviclual integration in the range 0 - LOO Myr. defined. as the time until one or other of the planets was removed from. the system through either collision or ejection.," This yielded a lifetime from each individual integration in the range 0 - 100 Myr, defined as the time until one or other of the planets was removed from the system through either collision or ejection." + To explore the 1-7. parameter range in greater detail. we launched. à second. suite of integrations. again using 9261 test systems.," To explore the $\sigma$ parameter range in greater detail, we launched a second suite of integrations, again using 9261 test systems." + The set-up. was performed. exactly as described above. except that the orbital parameters of the outer planet were varied within a 1-7 range. rather than the 3-7 distribution carried out.previously.," The set-up was performed exactly as described above, except that the orbital parameters of the outer planet were varied within a $\sigma$ range, rather than the $\sigma$ distribution carried outpreviously." + These two suites of integrations vielded. 17493 clistinet tests of the stability of the HU. Aqr system. with 9261 of these performed. in the central Ἔλ-σ of the element space described in Qianetal.(2011).. ancl the other 8232 distributed in the range 1-0 to 3-0.," These two suites of integrations yielded 17493 distinct tests of the stability of the HU Aqr system, with 9261 of these performed in the central $\pm$ $\sigma$ of the element space described in \citet{Qian2011}, and the other 8232 distributed in the range $\sigma$ to $\sigma$." + The results of these integrations are shown in Fig 1.., The results of these integrations are shown in Fig \ref{coplanar}. . + Once these simulations had been completed. we carried out. equivalent suites for scenarios where the outer planet was moving on an orbit inclined to that of the inner planet.," Once these simulations had been completed, we carried out equivalent suites for scenarios where the outer planet was moving on an orbit inclined to that of the inner planet." + Following the procedure detailed above. we tested svstems in which the outer planets orbit was inclined by 57. 15° and 45° with respect to the inner's orbit. in order to examine the influence of mutual orbital inclinations on the stability of the svstem.," Following the procedure detailed above, we tested systems in which the outer planet's orbit was inclined by $^{\circ}$, $^{\circ}$ and $^{\circ}$ with respect to the inner's orbit, in order to examine the influence of mutual orbital inclinations on the stability of the system." + We then considered. further scenarios. in which the outer planet. was moving in a retrograde sense. with respect to the inner body. with inclinations of 135° ancl 1807.," We then considered further scenarios in which the outer planet was moving in a retrograde sense, with respect to the inner body, with inclinations of $^{\circ}$ and $^{\circ}$." + For simplicity. we kept the masses of the two planets constant through these runs at the lowest values sugeested in Qianetal.(2011).," For simplicity, we kept the masses of the two planets constant through these runs at the lowest values suggested in \citet{Qian2011}." +.. Although it is true that significantly. inclined. orbits for the planets would. result. in larger real masses for them. we note that a significant mutual inclination between the planets does not necessarily mean that it is the outermost planet that is inclined to the line of sight. while the innermost is in that plane.," Although it is true that significantly inclined orbits for the planets would result in larger real masses for them, we note that a significant mutual inclination between the planets does not necessarily mean that it is the outermost planet that is inclined to the line of sight, while the innermost is in that plane." + Rather than attempt to shift the planetary mass by the free parameter of potential inclination. we instead took the lowest masses possible.," Rather than attempt to shift the planetary mass by the free parameter of potential inclination, we instead took the lowest masses possible." + We remind the reader that this essentially means that we have allowed the planetary svstem the best. possible chance of being stable - as the mass of the planets increases. so does their gravitational reach. increasing the strengthof anv mutual interactions.," We remind the reader that this essentially means that we have allowed the planetary system the best possible chance of being stable - as the mass of the planets increases, so does their gravitational reach, increasing the strengthof any mutual interactions." + The results. of our // —0 (Le. coplanar) dynamical integrations are shown in Vie 1. , The results of our $i=$ $^{\circ}$ (i.e. coplanar) dynamical integrations are shown in Fig \ref{coplanar}. . +Each colourbox in that figure shows the median. lifetime obtained. from 21 independent integrations performed: with the outer planet placed on an orbit with that particular combination of e and, Each colourbox in that figure shows the median lifetime obtained from 21 independent integrations performed with the outer planet placed on an orbit with that particular combination of $a$ and +We have simulated magnetocentrifugally driven. conical jets over a range in distance of 1000 times the initial jet radius. in both 3D and axisymmetric 2.5D. The calculations extend to a factor of about 5-10 beyond the surface.,"We have simulated magnetocentrifugally driven, conical jets over a range in distance of 1000 times the initial jet radius, in both 3D and axisymmetric 2.5D. The calculations extend to a factor of about 5–10 beyond the surface." + The 3D jets developed non-axisymmetric instabilities of the kink kind., The 3D jets developed non-axisymmetric instabilities of the kink kind. + The violence of the instabilities depends on the rotation profile applied at the base., The violence of the instabilities depends on the rotation profile applied at the base. + With a rigid rotation (oR) profile. the perturbations grow to much larger amplitudes than with a Keplerian (oR7!'*) profile.," With a rigid rotation $\proptoo R$ ) profile, the perturbations grow to much larger amplitudes than with a Keplerian $\proptoo R^{-1/2}$ ) profile." + We suspect that the reason for the differing behavior lies in the magnetic shear. defined as the variation of the magnetic pitch with distance to the axis.," We suspect that the reason for the differing behavior lies in the magnetic shear, defined as the variation of the magnetic pitch with distance to the axis." + In the rigid rotation case. there is virtually no shear as opposed to the Keplerian case. for which the pitch increases with distance from the axis. see Fig. 5..," In the rigid rotation case, there is virtually no shear as opposed to the Keplerian case, for which the pitch increases with distance from the axis, see Fig. \ref{fig:pitch}." + A shear-free configuration is expected to be unstable to non-resonant modes. whereas a configuration with increasing pitch is expected to be unstable to modes with a resonant surface inside the jet (22)..," A shear-free configuration is expected to be unstable to non-resonant modes, whereas a configuration with increasing pitch is expected to be unstable to modes with a resonant surface inside the jet \citep{2000Appl,2000Lery}." + This fits well with what we observe in the simulations. viz.," This fits well with what we observe in the simulations, viz." + that the kink is confined inside the jet in the Keplerian case., that the kink is confined inside the jet in the Keplerian case. + Heuristically speaking. the differing behavior could be attributed to the fact that the outer (high 2) layers of the jet. which are more stable (higher magnetic pitch). damp internally arising modes in the Keplerian case.," Heuristically speaking, the differing behavior could be attributed to the fact that the outer (high $\vartheta$ ) layers of the jet, which are more stable (higher magnetic pitch), damp internally arising modes in the Keplerian case." + In both cases. the longitudinal wavelength of the instabilities is ~5 times larger than the value of the magnetic pitch near the axis.," In both cases, the longitudinal wavelength of the instabilities is $\simm5$ times larger than the value of the magnetic pitch near the axis." + The relation is qualitatively consistent with the findings of ?. for a cylindrical jet., The relation is qualitatively consistent with the findings of \citet{2000Appl} for a cylindrical jet. + The growth time of the instabilities is on the order of the crossing time., The growth time of the instabilities is on the order of the crossing time. + The exact relation is difficult to determine. because the crossing time as well as the location of the resonant surface can only be estimated.," The exact relation is difficult to determine, because the crossing time as well as the location of the resonant surface can only be estimated." + As the azimuthal magnetic field strength and with it the azimuthal speed decrease past the surface. opposing parts of the jets become causally disconnected from each other.," As the azimuthal magnetic field strength and with it the azimuthal speed decrease past the surface, opposing parts of the jets become causally disconnected from each other." + Thus. the jet expands too fast for mode instabilities to grow.," Thus, the jet expands too fast for mode instabilities to grow." + The effect is amplified if the jet is diverging., The effect is amplified if the jet is diverging. + Recollimation. on the other hand. should boost the growth of instabilities.," Recollimation, on the other hand, should boost the growth of instabilities." + As found in other studies. the conversion of magnetic enthalpy (Poynting flux) to kinetic energy is fairly efficient. on the order70%.," As found in other studies, the conversion of magnetic enthalpy (Poynting flux) to kinetic energy is fairly efficient, on the order." +. Dissipation of magnetic fields by internal instabilities is expected to contribute additional acceleration of the flow (?).., Dissipation of magnetic fields by internal instabilities is expected to contribute additional acceleration of the flow \citep{2002Drenkhahn}. + The calculations do not show a clear signature of this process., The calculations do not show a clear signature of this process. + It seems that either the observed region ts too small. and/or the numerical dissipation of magnetic fields is too weak.," It seems that either the observed region is too small, and/or the numerical dissipation of magnetic fields is too weak." + Also. from a macroscopic point. of view. the instabilities were not violent enough to bring together fields with an antiparallel component. as is necessary for magnetic reconnection to occur.," Also, from a macroscopic point of view, the instabilities were not violent enough to bring together fields with an antiparallel component, as is necessary for magnetic reconnection to occur." + Moreover. most of the magnetic enthalpy was already converted in the magnetocentrifugal acceleration process.," Moreover, most of the magnetic enthalpy was already converted in the magnetocentrifugal acceleration process." + Therefore. even if there was magnetic dissipation. the effect would not be dramatic.," Therefore, even if there was magnetic dissipation, the effect would not be dramatic." + Nevertheless. we found that the magnetic field gets significantly distorted by the instabilities.," Nevertheless, we found that the magnetic field gets significantly distorted by the instabilities." + This should facilitate magnetic. field. dissipation further downstream but it may be necessary to extend the calculations to larger distances to see the effect., This should facilitate magnetic field dissipation further downstream but it may be necessary to extend the calculations to larger distances to see the effect. + It is tempting to compare the instability-related structures in the simulations with structures in observed jets., It is tempting to compare the instability-related structures in the simulations with structures in observed jets. + The 3D Jet structure in. Fig. 4..," The 3D jet structure in Fig. \ref{fig:rhot}," + for example. is reminiscent of the semi-regular patterns seen in images taken of outflows from young stellar objects (YSO) like HH 34 (?)..," for example, is reminiscent of the semi-regular patterns seen in images taken of outflows from young stellar objects (YSO) like HH 34 \citep{2002Reipurth}." + There are. however. other possible interpretations. of the observed structure.," There are, however, other possible interpretations of the observed structure." + The wiggles in YSO jets could also be the result of a precessing or orbitally moving source (?.andreferences therein)..," The wiggles in YSO jets could also be the result of a precessing or orbitally moving source \citep[and references +therein]{2002Masciadri}. ." + The symmetric nature of structures often seen in jet and counterjet (e.g.HH212?) suggests a modulation of the outflow speed or mass flux originating at the source of the outflow rather than an instability developing further away., The symmetric nature of structures often seen in jet and counterjet \citep[e.g. HH 212][]{2001Wiseman} suggests a modulation of the outflow speed or mass flux originating at the source of the outflow rather than an instability developing further away. + The irregularities caused by the instabilities studied here are possibly more important for internal magnetic energy release inside the jet than for major observable structures like the knots and wiggles in YSO jets. though they are likely to contribute to these at some levelas well.," The irregularities caused by the instabilities studied here are possibly more important for internal magnetic energy release inside the jet than for major observable structures like the knots and wiggles in YSO jets, though they are likely to contribute to these at some levelas well." +validate the discussed scenario.,validate the discussed scenario. + Ouly a few recent nunericeal works lave focused ou the interaction of a CME with a realistic maguetic structure obtained from maguetogram measurements (BRoussevetal.2011).," Only a few recent numerical works have focused on the interaction of a CME with a realistic magnetic structure obtained from magnetogram measurements \citep[]{Roussev:2007, Lugaz:2010a, Cohen:2010, Evans:2011}." +. Other suuulatious have usually relied ou au ideal representation of the corona with a single dipolar or quadrupolu active region in a dipolar Sun (asinShiotaetal.2010.for example)..," Other simulations have usually relied on an ideal representation of the corona with a single dipolar or quadrupolar active region in a dipolar Sun \citep[as in][for example]{Manchester:2003, Lynch:2009, Jacobs:2009, Shiota:2010}." +. Were. the interaction of the dux rope with the backerouud maguetic Seld is different from both these ideal cases aud the realistic cases previously studied because of the aucmone nature of the active region.," Here, the interaction of the flux rope with the background magnetic field is different from both these ideal cases and the realistic cases previously studied because of the anemone nature of the active region." + The topology is differeut from the solar iiuiumuui cases studied before with an isolated AR rot surrounded by equatorial coronal holes (Cohenetal.2010:Evansetal.2011) aud also different from the wo solar maximum case studies of Roussevetal.(2007) and Lugazetal.(2010) with complex connectivity )tween multiple ARs.," The topology is different from the solar minimum cases studied before with an isolated AR not surrounded by equatorial coronal holes \citep[]{Cohen:2010, Evans:2011} and also different from the two solar maximum case studies of \citet{Roussev:2007} and \citet{Lugaz:2010a} with complex connectivity between multiple ARs." + Receuth. Titovetal.(2008) studied in great detail the magnetic topology of the corona before and during the evolution phase leading o the 1997 Mav 12 CAE.," Recently, \citet{Titov:2008} studied in great detail the magnetic topology of the corona before and during the evolution phase leading to the 1997 May 12 CME." + Their study was also for a relatively simple magnetic topologv without iuflueuce roni equatorial coronal holes., Their study was also for a relatively simple magnetic topology without influence from equatorial coronal holes. + The evolution of the CME is altered by the aueimonue mature of the active region. ie. by the presence of nuipolay magnetic field around it.," The evolution of the CME is altered by the anemone nature of the active region, i.e. by the presence of unipolar magnetic field around it." + We find that the vositive footpoiut of the flux rope does not reconnect away from the active region since there is α very iuited negative polarity maguctic flux around it., We find that the positive footpoint of the flux rope does not reconnect away from the active region since there is a very limited negative polarity magnetic flux around it. + As a consequence. the flux rope remains line-fied at its )ositive. footpoiut.," As a consequence, the flux rope remains line-tied at its positive footpoint." + Iu contrast. the negative footpoiut reconnects quickly and extensively with the positive naenetic flux. partly from the positive spot of AR 10798 aud partly from the neighborime coronal hole.," In contrast, the negative footpoint reconnects quickly and extensively with the positive magnetic flux, partly from the positive spot of AR 10798 and partly from the neighboring coronal hole." + The reconnection is a 2-phase process as illustrated iu Figure 5., The reconnection is a 2-phase process as illustrated in Figure 5. + In the first phase (top pancls). all of the twisted closed field lines of the fux rope (dark blue) recounect with the streamer maguetic field (ereeu).," In the first phase (top panels), all of the twisted closed field lines of the flux rope (dark blue) reconnect with the streamer magnetic field (green)." + It results in erupting field lues connecting the positive footpoiut of the flux rope with the streamer. shown in vellow and post-flare loops in fushia.," It results in erupting field lines connecting the positive footpoint of the flux rope with the streamer, shown in yellow and post-flare loops in fushia." + In the second phase (bottoni panels). the newly formed (vellow) crupting field lines reconnect with open field lines to form (orange) open and twisted erupting field lines.," In the second phase (bottom panels), the newly formed (yellow) erupting field lines reconnect with open field lines to form (orange) open and twisted erupting field lines." + Below. we describe the detailed recounection process aud the chaneec m magnetic topologv durius the eruption.," Below, we describe the detailed reconnection process and the change in magnetic topology during the eruption." + The reconnection involves two phases: the first onc. when the negative footpoiut of the fiux rope recounects outside the fan surface (top paucls of Figure 5) aud the second one. When some of the eruptiug field lines open up (bottom panels of Figure 5).," The reconnection involves two phases: the first one, when the negative footpoint of the flux rope reconnects outside the fan surface (top panels of Figure 5) and the second one, when some of the erupting field lines open up (bottom panels of Figure 5)." + The detailed reconnection process of this first phase goes as follows: first. the (dark blue) Ποια lines of the flux rope reconnect with overlviug anenmone ficld (pink) to form twisted (light blue) field lues counecting the positive foopoiut of the flux rope with the negative main spot of the active region (top eft paucl of Figure 5).," The detailed reconnection process of this first phase goes as follows: first, the (dark blue) field lines of the flux rope reconnect with overlying anemone field (pink) to form twisted (light blue) field lines connecting the positive foopoint of the flux rope with the negative main spot of the active region (top left panel of Figure 5)." + This reconnection lappeus at he bald patch., This reconnection happens at the bald patch. + Iu a second step. the newly formed field ines (light blue) reconnect with closed (ereen) field lines outside of the fan surface to form the (vellow) field lines connecting the positive footpoiut of the flux rope with he streamer (top right panel).," In a second step, the newly formed field lines (light blue) reconnect with closed (green) field lines outside of the fan surface to form the (yellow) field lines connecting the positive footpoint of the flux rope with the streamer (top right panel)." + This reconnection occurs at the null point., This reconnection occurs at the null point. + The two steps of the first phase are early simultaneous aud overlying closed field lines from he streamer belt flux svstem (ereen field les) recounect away., The two steps of the first phase are nearly simultaneous and overlying closed field lines from the streamer belt flux system (green field lines) reconnect away. + During the reconnection process. a null poiut forms (low the fux rope aud there is a separator linking he bald patch aud this null poiut.," During the reconnection process, a null point forms below the flux rope and there is a separator linking the bald patch and this null point." + This separator is siuilar to the bald patch-bald patch separator or the quasi-eparatrix laver discussed for example iu Titov&Démoulin(1999) and. Aulanieretal.(2010) and it is shown in metallic blue in the middle left panel of Figure 5., This separator is similar to the bald patch-bald patch separator or the quasi-separatrix layer discussed for example in \citet{Titov:1999} and \citet{Aulanier:2010} and it is shown in metallic blue in the middle left panel of Figure 5. + A current sheet forms in association with he separator and it is shown as a purple surface in he bottom left panel of Figure 5., A current sheet forms in association with the separator and it is shown as a purple surface in the bottom left panel of Figure 5. + The current shect ades a sigmoidal shape. which is very commuon from flux enmereenuce aud shearing motions (Manchesteretal.200I:Titovetal.2008:Απο2010) but it can also o the result of reconnection with adjaceut fiux svstenis and due to the pre-event topology as is found here.," The current sheet takes a sigmoidal shape, which is very common from flux emergence and shearing motions \citep[]{Manchester:2004c,Titov:2008, Aulanier:2010} but it can also be the result of reconnection with adjacent flux systems and due to the pre-event topology as is found here." + During the first phase. which lasts about 510 iuinutes. he fux rope expands to a height of 1 BR... above the solar surface.," During the first phase, which lasts about 5–10 minutes, the flux rope expands to a height of 1 $_\odot$ above the solar surface." + Due to the CME expansion. the null point is pushed castward along the outer spine by about 3° and its height increases by about 0.01 ...," Due to the CME expansion, the null point is pushed eastward along the outer spine by about $^\circ$ and its height increases by about 0.04 $_\odot$." + At the end of lis phase. the flux rope remains composed of closed field ines but it appears totally disconnected from its original jegative footpoiut (see top right panel of Figure 6).," At the end of this phase, the flux rope remains composed of closed field lines but it appears totally disconnected from its original negative footpoint (see top right panel of Figure 6)." + Open feld lines Qvhite) from the leading positive spot reconnect at the separator below the flux rope with ancmone feld lines to fox uew open feld lines (shown in brown) passing at proximity of the null omt., Open field lines (white) from the leading positive spot reconnect at the separator below the flux rope with anemone field lines to form new open field lines (shown in brown) passing at proximity of the null point. + Separator reconnection is described iun Parucll&Galseaard(2001). for example., Separator reconnection is described in \citet{Parnell:2004} for example. + This is illustrated iu he iiddle left pauel of Figure 5., This is illustrated in the middle left panel of Figure 5. + A similar type of reconnection following the cruption of a fux rope has (oen previously cliscussed in Mackay&vanDallegooi-jen (2006)., A similar type of reconnection following the eruption of a flux rope has been previously discussed in \citet{MacKay:2006}. +. Due to the reconnection of the auemone fiux system and the streamer belt aud due to the formation of the separator. the magnetic topology changes quite drastically from the pre-event topology.," Due to the reconnection of the anemone flux system and the streamer belt and due to the formation of the separator, the magnetic topology changes quite drastically from the pre-event topology." + The uull point )clow the flux rope separates the anenione flux svsteni and open field lines originating from the leading (vhito) and trailine (brown) positive spots (uiddle left paucl of Fieure 5)., The null point below the flux rope separates the anemone flux system and open field lines originating from the leading (white) and trailing (brown) positive spots (middle left panel of Figure 5). + The outer spine of this svsteni is open., The outer spine of this system is open. + Such an opemime of a similar topology duriug a dependent process was shown iu Edioucdsouoetal. (2010)., Such an opening of a similar topology during a time-dependent process was shown in \citet{Edmondson:2010}. +.. The easteru null point separates the crupting (vellow) magnetic field and the closed feld originating from the positive trailing spot., The eastern null point separates the erupting (yellow) magnetic field and the closed field originating from the positive trailing spot. + The outer spine connects the positive trailing spot and the positive footpoiut of the flux rope through the flux rope., The outer spine connects the positive trailing spot and the positive footpoint of the flux rope through the flux rope. + The full maguetic topologv with all the differeut type of ficld lines discussed here is shown iu the middle right panel of Figure 5., The full magnetic topology with all the different type of field lines discussed here is shown in the middle right panel of Figure 5. + The presence of two null points separating different but overlapping flux svstenis. as shown here. is only possible in a fully 3-D simulation as is the case here.," The presence of two null points separating different but overlapping flux systems, as shown here, is only possible in a fully 3-D simulation as is the case here." + The secoud phase of reconnection happens when the fiux rope is not, The second phase of reconnection happens when the flux rope is not +to reach their final masses before exhausting their nuclear fuel Useto&Wood2006).,to reach their final masses before exhausting their nuclear fuel \citep{ketoetal06}. +.. The result is eravitational instability duriug collapse. leading to the formation of dense eas filuueuts in the rotating. collapsing flow. along with dozens of accommpauving stars (Paper D.," The result is gravitational instability during collapse, leading to the formation of dense gas filaments in the rotating, collapsing flow, along with dozens of accompanying stars (Paper I)." + The strougest sources of ionizing radiation orbit throueh the dense filaments repeatedly. accreting lass efficicutly when they do.," The strongest sources of ionizing radiation orbit through the dense filaments repeatedly, accreting mass efficiently when they do." + The filaments absorb the lonizing radiation locally. though. when this happens. shiclding the rest of the rregiou for long οποιο] for it to recombine.," The filaments absorb the ionizing radiation locally, though, when this happens, shielding the rest of the region for long enough for it to recombine." + As a result. the size of the observed iregion relaius independent of the age of the ionizing star until the surrounding secoudary star formation cuts off accretion on to the primary and a compact iregion begius to erow around it.," As a result, the size of the observed region remains independent of the age of the ionizing star until the surrounding secondary star formation cuts off accretion on to the primary and a compact region begins to grow around it." + Iu this paper we cousider iu more detail than in Paper 1 whether our models of ionization interacting with a evavitationally unstable accretion flow can reproduce the observations of ultracompact 1regious sununarized at the begimuiug of this section., In this paper we consider in more detail than in Paper I whether our models of ionization interacting with a gravitationally unstable accretion flow can reproduce the observations of ultracompact regions summarized at the beginning of this section. + We show how rregious fluctuate in size as their ceutral stars pass through censity fluctuations. aud demonstrate that our models qualitatively reproduce all miorphologies observed for ultracompact 1reglons. even Giving general quantitative agreement witli the distribution of different morphologics observed byWood&Churclwell(1989) aud I&urtzetal.(199D.," We show how regions fluctuate in size as their central stars pass through density fluctuations, and demonstrate that our models qualitatively reproduce all morphologies observed for ultracompact regions, even giving general quantitative agreement with the distribution of different morphologies observed by\citet{woodchurch89} and \citet{kurtzetal94}." +. Our models also offer a natural explanation for the observed clusteriug of ultracompact rregious., Our models also offer a natural explanation for the observed clustering of ultracompact regions. + We further demoustrate that they reproduce observed SEDs. aud provide natural explanations for the anomalous SEDs observed for some ultracompact rregious (Lizano2008:Beutherctal.2001:Netoet 2008).," We further demonstrate that they reproduce observed SEDs, and provide natural explanations for the anomalous SEDs observed for some ultracompact regions \citep{lizano08,beuthetal04,ketoetal08}." +. Iu refsecinmuueries we describe our methods for modeling ultracompact rregious aud sumnulatiug observations. while in rofseciesults we describe the results of our work relevant for this paper.," In \\ref{sec:numerics} we describe our methods for modeling ultracompact regions and simulating observations, while in \\ref{sec:results} we describe the results of our work relevant for this paper." + Finally. in refseciconclusions we draw conclusions.," Finally, in \\ref{sec:conclusions} we draw conclusions." + We present three-duinensional gas dyanunic. siauulatiouns with —radiation feedback from= ioniziug— aud non-ioniziug radiation.," We present three-dimensional, gas dynamic, simulations with radiation feedback from ionizing and non-ionizing radiation." + We use the FLASID adaptive-mesh code (Frvselletal.2000).. modified to iuclude a hvbrid-clharacteristies ravtracius method (Rijkhorstetal.2006). to solve the radiative transfer problem.," We use the FLASH adaptive-mesh code \citep{fryxell00}, modified to include a hybrid-characteristics raytracing method \citep{rijk06} to solve the radiative transfer problem." + The protostars are modeled by sink particles (Federrathal.2010). that are coupled to the radiation module via a protostellar iiodoel (Paper I)., The protostars are modeled by sink particles \citep{federrathetal09} that are coupled to the radiation module via a protostellar model (Paper I). + We simulate the collapse of a massive core with a mass of 1000. AZ...," We simulate the collapse of a massive core with a mass of $1000\ +M_\odot$ ." +" The core las coustant density within the sphere with r«0.5 pc. while further out the density falls off as r.7, "," The core has constant density within the sphere with $r < 0.5\,$ pc, while further out the density falls off as $r^{-3 / 2}$." +The eas temperature is initially T— 30K. The core begius iu solid body rotation with a ratio of rotational to gravitational energy 2=0.05.," The gas temperature is initially $T = 30\,$ K. The core begins in solid body rotation with a ratio of rotational to gravitational energy $\beta = 0.05$." + We use an adaptive mesh with a cell size at the highest refinement level of 98 AU.," We use an adaptive mesh with a cell size at the highest refinement level of $98\,$ AU." + Sink particles are inserted at a cut-off density of poy=7«10Meco ? and accrete all gas above Poss Within an accretion radius of ri5900 AU if it is eravitationally bound to the particle.," Sink particles are inserted at a cut-off density of $\rho_\mathrm{crit} = 7 \times 10^{-16}\,$ $^{-3}$ and accrete all gas above $\rho_\mathrm{crit}$ within an accretion radius of $r_\mathrm{sink} = 590\,$ AU if it is gravitationally bound to the particle." + We analyze two siaulatious., We analyze two simulations. + In the first simulation (run Aj. we only follow the evolution of a single star and suppress the formation of auv secondary stars.," In the first simulation (run A), we only follow the evolution of a single star and suppress the formation of any secondary stars." + We do this by introducing a dynamical temperature floor with Newton's constant G. mean molecular weight ji. Doltziiuuu's coustaut Ay. local gas density p. aud cell size Av.," We do this by introducing a dynamical temperature floor with Newton's constant $G$, mean molecular weight $\mu$, Boltzmann's constant $\kb$, local gas density $\rho$, and cell size $\Delta x$." + This temperature floor euarantees that the Jeans leneth is always resolved with » cells., This temperature floor guarantees that the Jeans length is always resolved with $n$ cells. + We must sot 0I| to prevent artificial fragimoeutation (Truclove1997)., We must set $n \geq 4$ to prevent artificial fragmentation \citep{truelove97}. +. Iu the second simulation (run D). we do not apply the temperature fioor. instead allowing the formation of secondary sink particles.," In the second simulation (run B), we do not apply the temperature floor, instead allowing the formation of secondary sink particles." + More details on the simulation method as well as a detailed description of the simulation results cau be found in Paper I. Radio coutimmuun ciuission frou rregious around massive stars at waveleugths Az0.3 cm (vyxLot Tz) is predominantly: caused bv frec-free cluission from ionized hydrogen (Cordon&Sorocheuko2002).," More details on the simulation method as well as a detailed description of the simulation results can be found in Paper I. Radio continuum emission from regions around massive stars at wavelengths $\lambda \geq 0.3\,$ cm $\nu \leq 10^{11}\,$ Hz) is predominantly caused by free-free emission from ionized hydrogen \citep{gorsor02}." +. Since scattering cau be neglected for this problem (Kraus1966:Cordon&Sorocheuko2002).. the equatiou of radiative trausfer can be readilv iutegrated.," Since scattering can be neglected for this problem \citep{kraus66,gorsor02}, the equation of radiative transfer can be readily integrated." + First. we calculate the free-free absorption cocticient of atomic hydrogen with unnber density of free electrons ps4. electron temperature T; aud frequency v7.," First, we calculate the free-free absorption coefficient of atomic hydrogen with number density of free electrons $\nel$, electron temperature $T_{\mathrm{e}}$ and frequency $\nu$." + Since the electrons thermalize quickly (Dwsou&Willams1980).. we can take the eas temperature f=Ti.," Since the electrons thermalize quickly \citep{dysonetal80}, we can take the gas temperature $T = T_{\mathrm{e}}$." + Caven the absorption cocfiicicut. the optical depth at distance + from the edge of the domain is then The radiative trauster equation in the Ravleigh-Jeaus Iuuit then leads to the brightuess temperature The resulting map of brightuess teniperatures can be convertedto flux densities with the solid angle subtended by the beam Qs of the telescope via Following the aleorithia described in MacLowctal. (1991b).. we couvolve the resulting image with the beam width aud add some noise according to the telescope parameters.," Given the absorption coefficient, the optical depth at distance $r$ from the edge of the domain is then The radiative transfer equation in the Rayleigh-Jeans limit then leads to the brightness temperature The resulting map of brightness temperatures can be convertedto flux densities with the solid angle subtended by the beam $\Omega_\mathrm{S}$ of the telescope via Following the algorithm described in \citet{maclowetal91}, , we convolve the resulting image with the beam width and add some noise according to the telescope parameters." + The parameters for the Very Large Array, The parameters for the Very Large Array +"where 73,1, is given by wi,=(τὸ2(0/ο)λικΕτη).","where $\tau_{0,1n}^*$ is given by $w_{1n}^*=2(b/c)\lambda_{1n}F(\tau_{0,1n}^*)$." +" The ratios 71,Ly8/Ti,.Lya and Ti,Lyy/Ti,Lya from the simulation with RT are shown in the upper panel of Fig. 16.."," The ratios $\tau_{l,{\rm Ly\beta}}/ \tau_{l,{\rm Ly\alpha}}$ and $\tau_{l,{\rm Ly\gamma}}/ \tau_{l,{\rm Ly\alpha}}$ from the simulation with RT are shown in the upper panel of Fig. \ref{fig:tauHILynpLya}." + A rise in both ratios occurs at redshifts z<4 once rreionization begins., A rise in both ratios occurs at redshifts $z<4$ once reionization begins. + The inferred values of the characteristic ooptical depth Τίγα are shown in thebottom panel., The inferred values of the characteristic optical depth $\tau^*_{\rm Ly\alpha}$ are shown in thebottom panel. +" The corresponding predicted values of 71,Ly+/Ti,Lya (upper panel) lie close to, but somewhat below, the values measured from the simulation, suggesting the single parameter separable model for the line distribution provides a good description of the line blanketing, but becomes less accurate at large values of Tiyq-"," The corresponding predicted values of $\tau_{l,{\rm Ly\gamma}}/ \tau_{l,{\rm Ly\alpha}}$ (upper panel) lie close to, but somewhat below, the values measured from the simulation, suggesting the single parameter separable model for the line distribution provides a good description of the line blanketing, but becomes less accurate at large values of $\tau^*_{\rm Ly\alpha}$." +" For a homogeneous radiation field, the ratio of the tto ooptical depths per pixel is where Ny; and Nyerr are the aand ccolumn densities,respectively, and byr and Όμοι the corresponding Doppler parameters."," For a homogeneous radiation field, the ratio of the to optical depths per pixel is where $N_{\rm HI}$ and $N_{\rm HeII}$ are the and column densities,respectively, and $b_{\rm HI}$ and $b_{\rm HeII}$ the corresponding Doppler parameters." +" For pure thermal broadening, buen= bx1/2, while for velocity-broadened lines, buerr= bur."," For pure thermal broadening, $b_{\rm + HeII}=b_{\rm HI}/2$ , while for velocity-broadened lines, $b_{\rm + HeII}=b_{\rm HI}$ ." + For metagalactic, For metagalactic +population characterized by our calculated mean log(CN/O). error. and standard deviation.,"population characterized by our calculated mean log(N/O), error, and standard deviation." + In other words. some additional scatter is needed to explain the observed spread inN/O'*.," In other words, some additional scatter is needed to explain the observed spread in." +. In order to estimate the magnitude of this additional scatter. we recalculated reduced Vesquare values lor the 52 plateau objects numerous times. each Gime adding intrinsic scatter to (he measurement errors in quadrature to simulate real scatter among the objects. with a larget value for the reduced \-square of unity.," In order to estimate the magnitude of this additional scatter, we recalculated reduced $\chi$ -square values for the 52 plateau objects numerous times, each time adding intrinsic scatter to the measurement errors in quadrature to simulate real scatter among the objects, with a target value for the reduced $\chi$ -square of unity." + Such a value was reached when σ for the intrinsic component was 0.024. or about 1/3 of the magnitude of the standard deviation ancl the typical statistical uncertainties in column (4) of Table 6..," Such a value was reached when $\sigma$ for the intrinsic component was 0.024, or about 1/3 of the magnitude of the standard deviation and the typical statistical uncertainties in column (4) of Table \ref{bigtable}." + Therefore. the implication of (his \-square analvsis is that only a small portion of the scatter observed lor the plateau objects is intrinsic.," Therefore, the implication of this $\chi$ -square analysis is that only a small portion of the scatter observed for the plateau objects is intrinsic." + Considering (hat the many of the uncertainties associated with the line strengths taken from the literature for our analvsis are only estimated and not determined in a rigorous fashion. we cannot conclude with anv confidence (hat a significant portion of the vertical scatter in N/O is real.," Considering that the many of the uncertainties associated with the line strengths taken from the literature for our analysis are only estimated and not determined in a rigorous fashion, we cannot conclude with any confidence that a significant portion of the vertical scatter in N/O is real." + Rather. the issue can only be decided by using better measurements including well-determined uncertainties in the abundances.," Rather, the issue can only be decided by using better measurements including well-determined uncertainties in the abundances." + This paper has been devoted to a detailed review of the method [or deriving N ancl QO abundances in low mass emission-line galaxies wilh 12 + log(O/IL)« 8.1., This paper has been devoted to a detailed review of the method for deriving N and O abundances in low mass emission-line galaxies with 12 + $\leq$ 8.1. + These low metalliitv svstems are classified in the literature as dwarl irregular galaxies. blue compact ealaxies. or IL II galaxies.," These low metallicity systems are classified in the literature as dwarf irregular galaxies, blue compact galaxies, or H II galaxies." + The principal motivation for our work was to estimate the contribution of the N/O uncertainties to the scatter among N/O plateau objects in the log(N/O) versus diagram., The principal motivation for our work was to estimate the contribution of the N/O uncertainties to the scatter among N/O plateau objects in the log(N/O) versus diagram. + To carry out this studs. we selected a sample of 68 objects [rom the literature ancl used their published de-reddened: emission-line strengths (o calculate a homogeneous set of abundances. paving special attention to the determination of [N II] and. {O HI] electron temperatures for which the necessary but weak auroral lines are usually absent from the data.," To carry out this study, we selected a sample of 68 objects from the literature and used their published de-reddened emission-line strengths to calculate a homogeneous set of abundances, paying special attention to the determination of [N II] and [O II] electron temperatures for which the necessary but weak auroral lines are usually absent from the data." + In such cases these temperatures. which are needed (to compute the abundances of (heir associated ions (Nand ). must be inferred from parametric relations in terms of the more accessible [O III] temperature.," In such cases these temperatures, which are needed to compute the abundances of their associated ions $^+$ and $^+$ ), must be inferred from parametric relations in terms of the more accessible [O III] temperature." + We established theoretical relations for the relevant. temperatures based on sinele-star IL 1I region simulations (modeled with CLOUDY)) ancl emploving our own input stellar spectra (modeled with PIIOENIX))., We established theoretical relations for the relevant temperatures based on single-star H II region simulations (modeled with ) and employing our own input stellar spectra (modeled with ). + These, These +This value is very close to (he highest possible energv of the accelerated protons. thus ihe Fermi upper limits basically exclude the possibility of a proton spectrum sienilicantlv steeper than dLV/dExE7.,"This value is very close to the highest possible energy of the accelerated protons, thus the Fermi upper limits basically exclude the possibility of a proton spectrum significantly steeper than ${\rm d}N/{\rm d}E\propto E^{-2}$." + since the VILE spectrum obtained [rom 002294200 seems to show no significant changes on a vearly (ime scale. i.e. on a (ime scale much longer than the one defined by the cooling time (see Eq. 4)).," Since the VHE spectrum obtained from 0229+200 seems to show no significant changes on a yearly time scale, i.e. on a time scale much longer than the one defined by the cooling time (see Eq. \ref{eq:cooling}) )," + the proton spectrum is expected to be steady., the proton spectrum is expected to be steady. + A steady proton distribution with power-law index p—2 can be formed in two different wavs: (1) with an almost mono-energetic continuous proton injection (e.g. through converter mechanism) in the regime: and Gi) wilh a conventional acceleration spectrum in the regime., A steady proton distribution with power-law index $p=2$ can be formed in two different ways: (i) with an almost mono-energetic continuous proton injection (e.g. through converter mechanism) in the regime; and (ii) with a conventional acceleration spectrum in the regime. + A very hard steady proton distribution with p=—0.5 requires can be formed in the when an acceleration mechanism similar (o converter mechanism is responsible for the particle acceleration., A very hard steady proton distribution with $p=-0.5$ requires can be formed in the when an acceleration mechanism similar to converter mechanism is responsible for the particle acceleration. + The resultinge model parameters are summarized in Table 1 and the eorresponcdinege curves (Fits 1-3) are shown in Fig. 3.., The resulting model parameters are summarized in Table \ref{table:parameters} and the corresponding curves (Fits 1-3) are shown in Fig. \ref{fig:0229}. + In the case of the EBL level F1.0. the de-absorbed VILE spectrum has a photon index close to Dic1.5.," In the case of the EBL level F1.0, the de-absorbed VHE spectrum has a photon index close to $\Gamma_{\rm int}\simeq1.5$." + For a proton distribution with p—2. the proton svnchrotron radiation below the peak has a photon index close to 1.5. ie. formally it can explain the VUE data points without invoking internal absorption.," For a proton distribution with $p=2$, the proton synchrotron radiation below the peak has a photon index close to $1.5$, i.e. formally it can explain the VHE data points without invoking internal absorption." + Thus. in this case the key question is whether (he internal absorption scenario can provide a consistent explanation of the X-ray component.," Thus, in this case the key question is whether the internal absorption scenario can provide a consistent explanation of the X-ray component." + Given the strict upper limits provided by Fermi. which are at the level of the extrapolation in the HIE band of the E4471.5 VILE spectrum. the available energy," Given the strict upper limits provided by Fermi, which are at the level of the extrapolation in the HE band of the $\Gamma_{\rm int}\simeq1.5$ VHE spectrum, the available energy" +stucdving not only the median values of metallicity. A(Mgb/ 5) and age. but the whole distribution of these parameters in bins of a.,"studying not only the median values of metallicity, $\Delta$ $\langle$ $\rangle$ ) and age, but the whole distribution of these parameters in bins of $\sigma_v$." + We show these distributions in Fie. S..," We show these distributions in Fig. \ref{fig:hist}," + where we have split our galaxy samples in three bins ol central velocity dispersion., where we have split our galaxy samples in three bins of central velocity dispersion. +" Using the 2-sided Ixolmogorov-Smirnov (INS) test. we find that the bulges of quiescent spirals are more metal-rich than elliptical galaxies at fixed 70, with high confidence (probability of the two samples to be drawn from the same distribution P~10. 7)."," Using the 2-sided Kolmogorov-Smirnov (KS) test, we find that the bulges of quiescent spirals are more metal-rich than elliptical galaxies at fixed $\sigma_v$ with high confidence (probability of the two samples to be drawn from the same distribution $P\sim10^{-3}$ )." + Ehe dillerence in the median values is at the level of ~0.07 dex., The difference in the median values is at the level of $\sim 0.07$ dex. +" While there are some dillerences in a enhancement and age (at least in some of the e, bins). their statistical significance is not large. so phwsical interpretation is unnecessary. especially considering the typical uncertainties allecting the measurements."," While there are some differences in $\alpha-$ enhancement and age (at least in some of the $\sigma_v$ bins), their statistical significance is not large, so physical interpretation is unnecessary, especially considering the typical uncertainties affecting the measurements." + Gallazzictal.(2008) identified the systematic uncertainties allectine the derivation of the stellar population parameters., \citet{anna08} identified the systematic uncertainties affecting the derivation of the stellar population parameters. + Phe main contributions to the error budget in the case of metallicity are the lack of variation of a/c] in BCO3 models. and to the choice of priors according o which the model library produces a galaxv'sSELL.," The main contributions to the error budget in the case of metallicity are the lack of variation of $\alpha$ /Fe] in BC03 models, and to the choice of priors according to which the model library produces a galaxy's." +.. A combination of both factors can add an error of up to 0.046 ex in. Z/H]. which is more than half of the difference we ind between passive spirals and ellipticals.," A combination of both factors can add an error of up to 0.046 dex in [Z/H], which is more than half of the difference we find between passive spirals and ellipticals." +" However. the act that we see the same trend. in all bins of a, and the ilferent shape of the distributions in Fig."," However, the fact that we see the same trend in all bins of $\sigma_v$ and the different shape of the distributions in Fig." + S make us believewt there is a physical difference between the two galaxy samples., \ref{fig:hist} make us believethat there is a physical difference between the two galaxy samples. + Moreover. we have shown that a/EFe] of spiral xilees ancl cllipticals are indistinguishable at fixed. velocity ispersion. thus any bias introduced by afke would. alfect wir total metallicity in a similar way and have negligible elect on our cillerential analysis.," Moreover, we have shown that $\alpha$ /Fe] of spiral bulges and ellipticals are indistinguishable at fixed velocity dispersion, thus any bias introduced by $\alpha$ /Fe would affect their total metallicity in a similar way and have negligible effect on our differential analysis." + So far. we have performed a dilferential analysis of 10 stellar populations in the of spiral and liptical galaxies. but we can not guarantee that all the LIÉeht in the SDSS spectrograph fiber does indeed come from 10 bulge.," So far, we have performed a differential analysis of the stellar populations in the of spiral and elliptical galaxies, but we can not guarantee that all the light in the SDSS spectrograph fiber does indeed come from the bulge." + In order to minimize this potential contamination rom disk light we have chosen to work only with galaxies josting disks. with stellar populations more similar," In order to minimize this potential contamination from disk light we have chosen to work only with galaxies hosting disks, with stellar populations more similar" +NS aud the companions matter flowing through the Lagrangian point.,NS and the companion's matter flowing through the Lagrangian point. + Theoretical models iudicate that the material lost by the companion star may take somewhat different shapes. ranging from a bow shock to au regular annular region iu the Roche lobe of the NS. depending on radio pulsar wind properties aud the rate aud aneular moment of the mass loss frou the companion star (Tavani Brookshaw 1993).," Theoretical models indicate that the material lost by the companion star may take somewhat different shapes, ranging from a bow shock to an irregular annular region in the Roche lobe of the NS, depending on radio pulsar wind properties and the rate and angular momentum of the mass loss from the companion star (Tavani Brookshaw 1993)." + i iav be as large as 0.1 (Tava 1991) aud the shock DIuuinuositv can be expressed as ομως=gLu2«10744BSP.2.5|eresD o(upoη10.1).," $\eta$ may be as large as 0.1 (Tavani 1991) and the shock luminosity can be expressed as $L_{\rm shock}=\eta\,L_{\rm sd}\sim 2\times 10^{32}\,\eta_{-1}\,B^2_8 +\,P_{2.5\,{\rm ms}}^{-4}\ergs$ $\eta\sim \eta_{-1}\,0.1$ )." + The huuinosity ratio across the transitiou from the propeller to thi! rotation powered reeime cau be approximated as (Stella et al., The luminosity ratio across the transition from the propeller to the rotation powered regime can be approximated as (Stella et al. + 1991: Campana e al., 1994; Campana et al. + 19982) where es—G is the eravitational radius.," 1998a) ( , where $r_{\rm g}=G\,M/c^2$ is the gravitational radius." +" The euergy spec‘trim due to shock enission is expected to be a power law with photon index of ~1Db2 that extends froma ~10 eV to ~100 keV. with both energy. boundaries shifting as ByDP,2.053 (Tavani Arons 1997: Campana et al."," The energy spectrum due to shock emission is expected to be a power law with photon index of $\sim 1.5-2$ that extends from a $\sim 10$ eV to $\sim 100$ keV, with both energy boundaries shifting as $B_8\,P_{\rm 2.5 ms}^{-3}$ (Tavani Arons 1997; Campana et al." + 19982)., 1998a). + Observationally. the nature of the two spectral compoucuts observed during the quiescent state of SNRTs is a matter of debate.," Observationally, the nature of the two spectral components observed during the quiescent state of SXRTs is a matter of debate." + One possibility is that some matter leaks through the centrifugal barrier accreting outo the NS surtace aud produces iu turn the observed soft component. whereas the hard compoucut arises in an ADAF ≺∑∐⋜⋯∶↴∙⊾↸∖⋜↧," One possibility is that some matter leaks through the centrifugal barrier accreting onto the NS surface and produces in turn the observed soft component, whereas the hard component arises in an ADAF (Zhang et al." +↕∙⊽⋂∩≺∖∖∶⋀∖↕↸∖∐∪∏↸∖↑⋜↧↕↕≝, 1998; Menou et al 1999). +↭≝⊔⋅∐∪↖↖⇁↸∖↖↽↸∖↥⋅⋜↧↸⊳↕↸∖⋜∐⋅⋜↧↴∖↴↴∖↴↸∖↴∖↴↴∖↴↕⊔↸∖∐↑∪↕⋟↑∐↴∖↴↴∖↴↻↸∖↸⊳⊓⋅⋜↧ ⋯∪≼∐∖⊔⋯↴∖↴∐∪↑↴⋝↸∖↸∖∐↸⊳⋜∐⋅↥⋅↕↸∖≺↧⋯↑∙↖⇁↸∖↑⋅∐∪↥⋅↴∖↴↸∖↕⋟⊣⊳∪∐↴∖↴↕↴∖↴," However a clear assessment of this spectral model has not been carried out yet, nor self-consistent ADAF models for NSs exist." +↑↸∖∐↑⊀≚↕≻⋎⇪⋯∪≺∐∖↕↴∖↴↕⋡∪↥⋅⋀∖⊽≋↴∖↴↸∖⊼↕↴∖↴↑∙ The other possibility complains a cooling NS? ⋖↖↖↽↕∐↸⊳⊔⊳∪∐↥⋅∏⋝∏↑↸∖↴∖↴↑∪∐↸∖↴∖↴∪↕⋟↑↸⊳∪∐∏⋯∐↸∖∐∩↖↖⇁∪↥⋅↨↘↽↕∐∶↴⋁⋜↧↴∖↴⋜⋃⋅⋜∥∐∪↴∏∏↴∖↴⋜∐⋅∙↑∐∖↥⋅↸∖↕⋜↧↑↕↖⇁↕↴∖↴ wind of which seuerates a shock power law spectrum (Campana ct al.," The other possibility complains a cooling $\,$ (which contributes to the soft component) working as a radio pulsar, the relativistic wind of which generates a shock power law spectrum (Campana et al." + 1998a)., 1998a). +" This is. at least qualitatively,| in aereciuentS with the hard power law like Xrav ↸⊳∪∐∏⋯∐↸∖↕↑∪↴⋝↴∖↴↸∖↥⋅↖⇁↸∖≼⊔∐∐↸∖≺∏↕↸∖↴∖↴↸⊳↸∖∐↑⊸∖⊽↥⋅⋜↧⋅↖↽↴∖↴↻↸∖↸⊳⊓⋅⋯⊔∪↕≯≼⊲↸∖∐ δι Agl N-1 anc X 1732ο01."," This is, at least qualitatively, in agreement with the hard power law like X–ray component observed in the quiescent X–ray spectrum of Cen X-4, Aql X-1 and X 1732–304." + The extended power law spectrum expected frou shock. emission is also in agreement with the recently determined residual UV»sectrum of Con which shows no evidence for a turnover down to lowest nieasured UV energies (~7.5 ev: MeChliutock Remillard 2000) aud matches quite weIthe extrapolation of the (power law) X.rav spectrum.," The extended power law spectrum expected from shock emission is also in agreement with the recently determined residual UV spectrum of Cen X-4, which shows no evidence for a turnover down to lowest measured UV energies $\sim 7.5$ eV; McClintock Remillard 2000) and matches quite wellthe extrapolation of the (power law) X–ray spectrum." +equivalent curves [rom the Paper | analysis as dashed lines on the plots.,equivalent curves from the Paper I analysis as dashed lines on the plots. + Although. both sets of curves give nearly the same time delays. the curves associated with the combiued data sets slow much clearer minima.," Although both sets of curves give nearly the same time delays, the curves associated with the combined data sets show much clearer minima." + We have taken the inediaun values of the columus in Table 3. to be the best-fit time delays aud relative magnifications as determined οι the data., We have taken the median values of the columns in Table \ref{tab_combdisp} to be the best-fit time delays and relative magnifications as determined from the data. + These values are given in Table {.., These values are given in Table \ref{tab_results}. + The meciau time delays are 7344=31.5 d. rpc=36.0 d. aud 755=17.0 d. The time clelay ratios are (τητην)=2.14 and (rpp/rgc)=2.11.," The median time delays are $\tau_{BA} = +31.5$ d, $\tau_{BC} = 36.0$ d, and $\tau_{BD} = 77.0$ d. The time delay ratios are $(\tau_{BD} / \tau_{BA}) = 2.44 $ and $(\tau_{BD} / \tau_{BC}) = 2.14$." + These agree well with the values obtained in Paper I. We performed several cousisteucy checks ou the derived delays., These agree well with the values obtained in Paper I. We performed several consistency checks on the derived delays. + First. we computect all possible delays between a leadiug component aud a trailing component. using the dispersion metlocls listed in Table 3..," First, we computed all possible delays between a leading component and a trailing component, using the dispersion methods listed in Table \ref{tab_combdisp}." + The inediau values obtained for these delays were τις=2.5 d. ray=15.5 d. aud Top=1.0 d. These delays are cousisteut within the uucertainties πμ ΟΠ willl hel hreedelayscalculaledabove.," The median values obtained for these delays were $\tau_{AC} = 2.5$ d, $\tau_{AD} = 45.5$ d, and $\tau_{CD} = +44.0$ d. These delays are consistent within the uncertainties \\ref{sec_mc}) ) with the three delays calculated above." + Secondly. wecoiniypuledthedelaysbelweencomponentBandtheolhert! techuique described in Paper L which requires that the input light curves be interpolatect onto a reeularly-spaced eric.," Secondly, we computed the delays between component B and the other three components using the $\chi^2$ -minimization technique described in Paper I, which requires that the input light curves be interpolated onto a regularly-spaced grid." + The \7-minimization results were consistent with the dispersion uethod values. but had more scatter about the median values.," The $\chi^2$ -minimization results were consistent with the dispersion method values, but had more scatter about the median values." + The increased scatter is probably due o stuall biases introduced by the various methods of interpolating the input light curves., The increased scatter is probably due to small biases introduced by the various methods of interpolating the input light curves. + The final check was to combine the input light curves by shifting the A.C. and D curves by the appropriate tune delays ancl maguificatious and then combining them with the uushilted B light curve.," The final check was to combine the input light curves by shifting the A, C, and D curves by the appropriate time delays and magnifications and then combining them with the unshifted B light curve." + The 'esultiug composite curves are shown in Figures [-—6.., The resulting composite curves are shown in Figures \ref{fig_compos_af310}- \ref{fig_compos_ab922}. + The composite curves show that the major eatures. and many of the minor features. in each of the individual light curves are reproduced iu he other light curves at the proper times. giving additional confidence that the measured delays are the correct ones.," The composite curves show that the major features, and many of the minor features, in each of the individual light curves are reproduced in the other light curves at the proper times, giving additional confidence that the measured delays are the correct ones." + We have estimatecl the uucertaiuties on the time delays and relative inagnifications through loute Carlo simulatious., We have estimated the uncertainties on the time delays and relative magnifications through Monte Carlo simulations. + This is the same methocl that was used in Paper I. To summarize. we sinoothecd each of the composite curves (Figures 1-—6)) to create the input “true” light. curves or the stimulations.," This is the same method that was used in Paper I. To summarize, we smoothed each of the composite curves (Figures \ref{fig_compos_af310}- \ref{fig_compos_ab922}) ) to create the input “true” light curves for the simulations." + One “true” light curve was generated for each season. usiug the best-fit 'elative maguilicatious appropriate for that season.," One “true” light curve was generated for each season, using the best-fit relative magnifications appropriate for that season." + The delays used for each season were the global ime delays derived. from the combined analysis (see Table { for the input delays ancl relative [un—agnilications)., The delays used for each season were the global time delays derived from the combined analysis (see Table \ref{tab_results} for the input delays and relative magnifications). + The sinoothing method used to generate the “true” curves from tle composites was e varlable-width boxcar techuique described in Paper I. with five points in the smoothing window.," The smoothing method used to generate the “true” curves from the composites was the variable-width boxcar technique described in Paper I, with five points in the smoothing window." + The simulated light curves were created by addiug a Craussian-distributed raudom: uoise term to e points ou the “true? curves., The simulated light curves were created by adding a Gaussian-distributed random noise term to the points on the “true” curves. + The widths of the Gaussian distributions. e. were determined from e olfsets between the measured composite curves aud their smoothed counterparts.," The widths of the Gaussian distributions, $\sigma$ , were determined from the offsets between the measured composite curves and their smoothed counterparts." + The values, The values +the same distance from us. and monitored with the same observational set-up. the relative rate depends only on the ratio of the square root of their masses. and on the ratio of their transverse speeds.,"the same distance from us, and monitored with the same observational set-up, the relative rate depends only on the ratio of the square root of their masses, and on the ratio of their transverse speeds." + The results are shown in the third column of Table 1., The results are shown in the third column of Table 1. + To compute these ratios. we have assumed that the transverse speeds of all M dwarfs. L dwarfs. T dwarfs. WDs. and BHs are the same.," To compute these ratios, we have assumed that the transverse speeds of all M dwarfs, L dwarfs, T dwarfs, WDs, and BHs are the same." + Observations of pulsars. however. clearly show that the typical speeds of neutron stars are higher. presumably due to kicks associated with the supernova explosions that spawned them.," Observations of pulsars, however, clearly show that the typical speeds of neutron stars are higher, presumably due to kicks associated with the supernova explosions that spawned them." + Although the initial velocity distribution of neutron stars is highly uncertain. one widely accepted model is that of Arzoumanian et al. (," Although the initial velocity distribution of neutron stars is highly uncertain, one widely accepted model is that of Arzoumanian et al. (" +2002).,2002). + The velocity distribution consists of two Maxwellians., The velocity distribution consists of two Maxwellians. + One of these contains 40% of the neutron stars and is peaked at 127 km s': the second. including the rest of the stars. is peaked at 707 km H )," One of these contains $40\%$ of the neutron stars and is peaked at $127$ km $^{-1}$; the second, including the rest of the stars, is peaked at $707$ km $^{-1}$ .)" + 15% of all neutron stars have speeds in excess of 1000 km s., $15\%$ of all neutron stars have speeds in excess of $1000$ km $^{-1}$. + To take into account the relatively higherspeed of NSs. we use for them a transverse speed that is five times larger than the transverse speeds used for the other stellar lenses.," To take into account the relatively higher speed of NSs, we use for them a transverse speed that is five times larger than the transverse speeds used for the other stellar lenses." + For this reason. Table | indicates that an individual NS lens can produce an event rate that is larger than that produced by a BH lens. even though the BH is more massive.," For this reason, Table 1 indicates that an individual NS lens can produce an event rate that is larger than that produced by a BH lens, even though the BH is more massive." + The duration of the NS-generated events would tend to be shorter. however.," The duration of the NS-generated events would tend to be shorter, however." + On average. If we are monitoring a single lens. the time between events would be shortest for generated events and longest for T-dwarf-generated events.," On average, if we are monitoring a single lens, the time between events would be shortest for NS-generated events and longest for T-dwarf-generated events." + If we are monitoring a large region. without prior knowledge of individual lenses in the foreground. we must use the expression for the total rate in (4). which includes the relative densities.," If we are monitoring a large region, without prior knowledge of individual lenses in the foreground, we must use the expression for the total rate in (4), which includes the relative densities." + The results for different stellar lenses. relative to M dwarfs. are shown in the fourth column of Table I.," The results for different stellar lenses, relative to M dwarfs, are shown in the fourth column of Table 1." + These results indicate that the ratio between the number of M-dwarf events and the total number of events caused by all other stellar lenses is roughly 2 to 1., These results indicate that the ratio between the number of M-dwarf events and the total number of events caused by all other stellar lenses is roughly 2 to 1. + If. therefore. there are even a modest number of M-dwarf lensing events in a data set. the data set is very likely to also include events caused by compact objects and by brown dwarfs.," If, therefore, there are even a modest number of M-dwarf lensing events in a data set, the data set is very likely to also include events caused by compact objects and by brown dwarfs." + Note that we have assumed that the spatial distributions of these different classes of lenses are similar., Note that we have assumed that the spatial distributions of these different classes of lenses are similar. + If each population can be modeled by a spatial distribution that falls off exponentially with height from the Galactic midplane. and also with radial distance from the Galaxy center. then differences among the populations are quantifiable through differences among the exponents applicable for each population.," If each population can be modeled by a spatial distribution that falls off exponentially with height from the Galactic midplane, and also with radial distance from the Galaxy center, then differences among the populations are quantifiable through differences among the exponents applicable for each population." + When these population differences are integrated over a distance of a kpe. relevant for nearby lenses. they tend to change the relative results by a factor of at most a few.," When these population differences are integrated over a distance of a kpc, relevant for nearby lenses, they tend to change the relative results by a factor of at most a few." + Table 2 is designed to predict the rates of events caused by nearby lenses in optical monitoring programs of the past. present. and future.," Table 2 is designed to predict the rates of events caused by nearby lenses in optical monitoring programs of the past, present, and future." + To generate the rates shown in Table 2 we used 4., To generate the rates shown in Table 2 we used 4. + We assume three different types of observational set-up., We assume three different types of observational set-up. +" The set-up labeled ""past"" simulates the first generation of microlensing monitoring surveys."," The set-up labeled “past"" simulates the first generation of microlensing monitoring surveys." +" We take fy=0.34. and (,,=2.5"". """," We take $f_T = 0.34$, and $\theta_{mon}=2.5''$. “" +"Present"" labels the observational set-up that is similar to the one presently used to monitor M31.","Present"" labels the observational set-up that is similar to the one presently used to monitor M31." +" In this case. fr20.1. and 0,,,,=1""."," In this case, $f_T = 0.1$, and $\theta_{mon}=1''$." +" The moniker ""Future"" refers to the type of monitoring that will be conducted with Pan-STARRS and LSST."," The moniker “Future"" refers to the type of monitoring that will be conducted with Pan-STARRS and LSST." +" Specifically. we take fy=0.02. and 0,,,,20.5""."," Specifically, we take $f_T = 0.02$, and $\theta_{mon}=0.5''$." + In the second. third. and fourth columns of Table 2. we compute the rate per decade per square degree.," In the second, third, and fourth columns of Table 2, we compute the rate per decade per square degree." + In the fourth column. we compute the rate per decade per 150 square degrees.," In the fourth column, we compute the rate per decade per $150$ square degrees." + This angular area is à conservative estimate of the area of the sky over which the combination of Pan-STARRS and LSST will be able to discover lensing events., This angular area is a conservative estimate of the area of the sky over which the combination of Pan-STARRS and LSST will be able to discover lensing events. + Each entry of Table 2 consists of three numbers., Each entry of Table 2 consists of three numbers. +" The number. which is always the smallest. is the rate rf Dj"" "," The left-most number, which is always the smallest, is the rate if $D_L^{max}$ " +"gap opening to occur later in the growth of Jupiter, i.e., for a higher value of m;.","gap opening to occur later in the growth of Jupiter, i.e., for a higher value of $m_J$." + Using the criterion for gap opening derived by Crida et al. (, Using the criterion for gap opening derived by Crida et al. ( +"2006): where q=my/Mo, Ry=aj(my/3Mo)!? is the Hill radius of Jupiter and R=a,Q.J/Y is the Reynolds number, we indeed predict that gap opening should occur for m;>0.23 M; in run I1 and for m;>0.35 M; in model I5.","2006): where $q=m_J/M_\odot$, $R_H=a_J(m_J/3M_\odot)^{1/3}$ is the Hill radius of Jupiter and ${\cal R}=a_J^2\Omega_J/\nu$ is the Reynolds number, we indeed predict that gap opening should occur for $m_J>0.23$ $M_J$ in run I1 and for $m_J> 0.35$ $M_J$ in model I5." +" Thus, for a higher viscosity, Jupiter's gap grows later and its type II migration is faster."," Thus, for a higher viscosity, Jupiter's gap grows later and its type II migration is faster." +" This means that, when Saturn's gas accretion starts, the Jupiter-Saturn separation is larger for the case of a higher viscosity."," This means that, when Saturn's gas accretion starts, the Jupiter-Saturn separation is larger for the case of a higher viscosity." +" Indeed, for run I5 the two planets are significantly farther apart than for run I1, just interior to the 2:1 resonance."," Indeed, for run I5 the two planets are significantly farther apart than for run I1, just interior to the 2:1 resonance." +" For even higher viscosities (higher values of a), Saturn's core would be pushed beyond the 2:1 resonance with Jupiter such that subsequent evolution could involve temporary capture in this resonance (as in run I4 discussed above)."," For even higher viscosities (higher values of $\alpha$ ), Saturn's core would be pushed beyond the 2:1 resonance with Jupiter such that subsequent evolution could involve temporary capture in this resonance (as in run I4 discussed above)." +" In model I5, the early stages of Saturn's growth involve convergent migration of the two planets followed by trapping in the 3:2 resonance."," In model I5, the early stages of Saturn's growth involve convergent migration of the two planets followed by trapping in the $3:2$ resonance." +" Here, reversal of migration occurs for slightly higher planet masses than seen previously — m;0.8 M, and m,=0.3 M; - but the final outcome is the same, namely sustained outward migration with the planets maintaining their 3:2 commensurability."," Here, reversal of migration occurs for slightly higher planet masses than seen previously – $m_J=0.8$ $M_J$ and $m_s=0.3$ $M_J$ – but the final outcome is the same, namely sustained outward migration with the planets maintaining their $3:2$ commensurability." +" We also find that the outward migration is slower for higher a because Jupiter’s gap becomes shallower as the viscosity increases, in agreement with the results of Morbidelli Crida (2007)."," We also find that the outward migration is slower for higher $\alpha$ because Jupiter's gap becomes shallower as the viscosity increases, in agreement with the results of Morbidelli Crida (2007)." + We tested the effect of the disk's aspect ratio h=H/r from h=0.03 (run I6) to Ah=0.05 (run I7)., We tested the effect of the disk's aspect ratio $h = H/r$ from $h=0.03$ (run I6) to $h=0.05$ (run I7). + Fig., Fig. + 11 shows the evolution these runs as compared with our fiducial case., \ref{fig:vary_h} shows the evolution these runs as compared with our fiducial case. + From Eq., From Eq. + 3 we know that lower-mass planets can open gaps in thinner disks., 3 we know that lower-mass planets can open gaps in thinner disks. +" Thus, for =0.03, Saturn's core is trapped at the edge of Jupiter's gap early in the simulation, and Saturn's core is pushed outward as Jupiter's mass increases and as its gap widens; this episode of outward migration of Saturn's core is apparent between 1000 and 2000orbits in Fig."," Thus, for $h=0.03$, Saturn's core is trapped at the edge of Jupiter's gap early in the simulation, and Saturn's core is pushed outward as Jupiter's mass increases and as its gap widens; this episode of outward migration of Saturn's core is apparent between $1000$ and $2000$orbits in Fig." +" 11 (A=0.03, second panel)."," \ref{fig:vary_h} $h=0.03$, second panel)." + The planets' orbital separation reaches a peak value just outside the 2:1 resonance (see bottom panel of Fig. 11))., The planets' orbital separation reaches a peak value just outside the 2:1 resonance (see bottom panel of Fig. \ref{fig:vary_h}) ). +" For this run (4= 0.03) accretion onto Saturn’s core is switched on at t—1900 orbits such that during the early stages of its growth, Saturn still follows Jupiter's gap through the action of the corotation torque."," For this run $h=0.03$ ) accretion onto Saturn's core is switched on at $t\sim 1900$ orbits such that during the early stages of its growth, Saturn still follows Jupiter's gap through the action of the corotation torque." +" At later times, the interaction with the disk becomes non-linear and Saturn passes through both Jupiter's gap, is captured in the 3:2 resonance with Jupiter, and the two planets migrate outward."," At later times, the interaction with the disk becomes non-linear and Saturn passes through both Jupiter's gap, is captured in the 3:2 resonance with Jupiter, and the two planets migrate outward." +" Because Jupiter's gap is deeper than in the fiducial case I1, the outward migration is faster for model I6 (see also Morbidelli Crida 2007)."," Because Jupiter's gap is deeper than in the fiducial case I1, the outward migration is faster for model I6 (see also Morbidelli Crida 2007)." + In run I7 the disk was thicker (h= 0.05) and this resulted in a different mode of evolution., In run I7 the disk was thicker $h=0.05$ ) and this resulted in a different mode of evolution. +" As before, Saturn's core was captured at the edge of Jupiter's gap and pushed outward as the gap widened, this time beyond the 2:1 resonance with Jupiter."," As before, Saturn's core was captured at the edge of Jupiter's gap and pushed outward as the gap widened, this time beyond the 2:1 resonance with Jupiter." +" Once Saturn accreted enough gas to cancel the effect of the corotation torque, it became trapped in the 2:1 resonance."," Once Saturn accreted enough gas to cancel the effect of the corotation torque, it became trapped in the 2:1 resonance." +" This is because Jupiter's gap is shallower for the thicker disk, causing slower convergent migration of the two planets."," This is because Jupiter's gap is shallower for the thicker disk, causing slower convergent migration of the two planets." +" Thus, Saturn is unable to cross the 2:1 resonance (see also Rein et al."," Thus, Saturn is unable to cross the 2:1 resonance (see also Rein et al." + 2010)., 2010). +" Of course, disruption of the 2:1 resonance followed by capture in the 3:2 resonance on longer timescales can not be ruled out."," Of course, disruption of the 2:1 resonance followed by capture in the 3:2 resonance on longer timescales can not be ruled out." +" Indeed, Pierens Nelson (2008) showed that, for a scenario close to the setup of model I7, the system is temporarily locked in the 2:1 resonance but the resonance is broken and the planets are evenrually trapped in 3:2 resonance."," Indeed, Pierens Nelson (2008) showed that, for a scenario close to the setup of model I7, the system is temporarily locked in the 2:1 resonance but the resonance is broken and the planets are evenrually trapped in 3:2 resonance." +" We now test the effect of the disk's radial surface density profile, where the surface density X varies with orbital radius Ras X«R?."," We now test the effect of the disk's radial surface density profile, where the surface density $\Sigma$ varies with orbital radius $R$ as $\Sigma \propto R^{-\sigma}$." + We compare two runs with σ=3/2 (models I8 and I9) with our standard models that have c=1/2 (II and I4)., We compare two runs with $\sigma=3/2$ (models I8 and I9) with our standard models that have $\sigma = 1/2$ (I1 and I4). +" We note that a σ=1/2 profile corresponds to disks with constant accretion rates and 6=1, whereas sub-mm measurements of young protoplanetary disks appear to favor σ50.5—1 (e.g., Mundy et al."," We note that a $\sigma = 1/2$ profile corresponds to disks with constant accretion rates and $\beta=1$, whereas sub-mm measurements of young protoplanetary disks appear to favor $\sigma \approx 0.5-1$ (e.g., Mundy et al." + 2000; Andrews Williams 2007) and different interpretations of the minimum-mass solar nebula model (Weidenschilling 1977; Hayashi 1981) yields values of o between 1/2 (Davis 2005) and 2 (Desch 2007)., 2000; Andrews Williams 2007) and different interpretations of the minimum-mass solar nebula model (Weidenschilling 1977; Hayashi 1981) yields values of $\sigma$ between 1/2 (Davis 2005) and 2 (Desch 2007). + Eq., Eq. +" 1 predicts that for σ=1.5, Jupiter and Saturn's cores should migrate at the same rate (in an isothermal disk) rather than undergoing convergent migration."," \ref {eq:taumig} predicts that for $\sigma=1.5$, Jupiter and Saturn's cores should migrate at the same rate (in an isothermal disk) rather than undergoing convergent migration." +" The consequence is that, in contrast with models in which c= 1/2, the cores are"," The consequence is that, in contrast with models in which $\sigma=1/2$ , the cores are" +wav Rauchetal.1997:MeDonald&Aliralela-Escucdé POOL).,"way \citealt{Rauch97,McDonaldMiraldaEscude01}) )." + We will use this later to constrain the softness parameter of the UVB., We will use this later to constrain the softness parameter of the UVB. + For the effective optical depth the central values from the fitting formula of Schayectal.(2003). have been used., For the effective optical depth the central values from the fitting formula of \cite{Schaye03} have been used. + The corresponding uncertainties have been estimated by binning the le errors given in table 5 of into recdshift bins of width As= 0.1., The corresponding uncertainties have been estimated by binning the $1\sigma$ errors given in table 5 of \cite{Schaye03} into redshift bins of width $\Delta z = 0.1$ . + Aleasurements of the effective optical depth. tHe. are more cillieult. to obtain: finding QSOs which have relatively clear lines-ol-sieht anc which are bright enough in the far-UY to enable the detection of absorption spectra is challenging.," Measurements of the effective optical depth, $\tau_{\rm HeII}$, are more difficult to obtain; finding QSOs which have relatively clear lines-of-sight and which are bright enough in the far-UV to enable the detection of absorption spectra is challenging." + Only six QSO spectra are known to show intergalactic absorption. and only four have vielded opacity measurements.," Only six QSO spectra are known to show intergalactic absorption, and only four have yielded opacity measurements." + Lt is therefore not clear to what extent the available data provides a statistically representative measure of the opacity., It is therefore not clear to what extent the available data provides a statistically representative measure of the opacity. + Nevertheless. observational stuclics of the forest. have met with impressive. success in recent vears. in particular with high resolution studies made using STIS and the," Nevertheless, observational studies of the forest have met with impressive success in recent years, in particular with high resolution studies made using STIS and the." +(FUSE). Figure 2 shows a compilation of optical depth measurements taken from the literature., Figure \ref{fig:tau} shows a compilation of optical depth measurements taken from the literature. + The data are from Q0302003 (Jakobsenetal.1994:etal.1997:Heapct 20000). PINS 1935692 1996:Xndersonetal. 1999).). HS 1700|64 (Davidsenetal. 1996)) and LIE 2347.4342 (Reimersetal.LOOT:Weissοἱ2001:Zhengetal. 2004b)) with uncertainties shown where applicable.," The data are from $\rm Q0302-003$ \citealt{Jakobsen94,Hogan97,Heap00}) ), $\rm PKS$ $1935-692$ \citealt{Jakobsen96,Anderson99}) ), $\rm HS$ $1700+64$ \citealt{Davidsen96}) ) and $\rm HE$ $2347-4342$ \citealt{Reimers97,Kriss01,Zheng04b}) ) with uncertainties shown where applicable." + Phe solid curve in figure 2. shows the fit we use as the mean ellective optical depth for our artificial spectra. given by: Note that this fit only provides a general description for 1¢ global evolution of the cllective optical depth.," The solid curve in figure \ref{fig:tau} shows the fit we use as the mean effective optical depth for our artificial spectra, given by: Note that this fit only provides a general description for the global evolution of the effective optical depth." + The forest opacity exhibits strong fluctuations which increase rapidlv with increasing redshift: the metagalactic ionization rate is obviously not spatially uniform. (Reimersetal.2004:ShullctZheng2004b)).," The forest opacity exhibits strong fluctuations which increase rapidly with increasing redshift; the metagalactic ionization rate is obviously not spatially uniform \citealt{Reimers04,Shull04,Zheng04b}) )." + The error bars attached to the solid circles. in figure 2.— provide an estimate of the variationin the opacity using a simple model for a Hluctuating UVB due to emission from QSOs.," The error bars attached to the solid circles in figure \ref{fig:tau} + provide an estimate of the variationin the opacity using a simple model for a fluctuating UVB due to emission from QSOs." +" ‘Phe error bars show the 25'4 and 75"" percentiles of THe For each set of 1024 spectra at the relevant redshift.", The error bars show the $25^{\rm th}$ and $75^{\rm th}$ percentiles of $\tau_{\rm HeII}$ for each set of $1024$ spectra at the relevant redshift. + We will turn to the details of modelling jose UVB Uuctuations in section 3.., We will turn to the details of modelling these UVB fluctuations in section \ref{sec:toymodel}. + Aw cdiscussech by Vheunsοἱal.(1998) and Boltonetal.(2005). inferring the metagalactiec ionization rate by reproducing the observed effective. optical depth: with artificial forest spectra stretches present-dayv numerical capabilities cue to the wide range of physical scales involved.," As discussed by \cite{Theuns98} and \cite{Bolton05}, inferring the metagalactic ionization rate by reproducing the observed effective optical depth with artificial forest spectra stretches present-day numerical capabilities due to the wide range of physical scales involved." + ]t is thus important to perform numerical convergence tests., It is thus important to perform numerical convergence tests. + We have used the simulations listed in Table 1. for à mass resolution and box size study.," We have used the simulations listed in Table \ref{tab:sims} + for a mass resolution and box size study." + Lhe 400° simulations are only run to z=3: they were too computationally demanding to enable a practical study below this redshift., The $400^{3}$ simulations are only run to $z=3$; they were too computationally demanding to enable a practical study below this redshift. + However. the >=3 data should provide a good indication of how close the simulations are to convergence.," However, the $z=3$ data should provide a good indication of how close the simulations are to convergence." + As box size ds inereased. larecr voids can he accommodated within the simulation. reducing the mean absorption and altering the ILrand.— gas distribution in a similar manner.," As box size is increased, larger voids can be accommodated within the simulation, reducing the mean absorption and altering the and gas distribution in a similar manner." + There is an 8 per cent reduction in both the and ionization rates inferred from the 30.200 model compared to the 1500 run with the same mass resolution. with a further 3 per cent reduction for the 60400 data.," There is an $8$ per cent reduction in both the and ionization rates inferred from the $30-200$ model compared to the $15-100$ run with the same mass resolution, with a further $3$ per cent reduction for the $60-400$ data." + Note that the ratio of the inferred ionization rates for the two species depends little on box size., Note that the ratio of the inferred ionization rates for the two species depends little on box size. + As noted by Theunsctal.(1998).. convergence of the opacity requires higher numerical resolution than the opacity.," As noted by \cite{Theuns98}, convergence of the opacity requires higher numerical resolution than the opacity." + Increasing the mass resolution of a simulation will resolve smaller haloes. transferring more optically thin eas [rom the low density. LGAL into optically thick. high cnsity regions. decreasing the mean absorption.," Increasing the mass resolution of a simulation will resolve smaller haloes, transferring more optically thin gas from the low density IGM into optically thick, high density regions, decreasing the mean absorption." + The reduction of the effective optical cepth resulting from this re-cistribution of the low density eas is partially [set by the increased contribution to the opacity [rom the high. density regions., The reduction of the effective optical depth resulting from this re-distribution of the low density gas is partially offset by the increased contribution to the opacity from the high density regions. + For Hle u. which is optically lick down to much lower gas densities. this ollset is less 1xonounced. 1producingo a >greater overall changee in the etfective optical depth for increased. mass resolution.," For He $\rm \scriptstyle II$ , which is optically thick down to much lower gas densities, this offset is less pronounced, producing a greater overall change in the effective optical depth for increased mass resolution." + The ionization rate inferred from the 15200 moclel is S per cent lower compared to the value of the 15100 run. with a further drop of S per cent for the 15400model.," The ionization rate inferred from the $15-200$ model is $8$ per cent lower compared to the value of the $15-100$ run, with a further drop of $8$ per cent for the $15-400$model." + The LIL opacity has only marginally converged at 2= 3., The HI opacity has only marginally converged at $z=3$ . + As expected the ionization rate shows a greater reduction in magnitude withincreasing mass resolution. exhibiting a 20 per cent reduction between the 15200 and 15—400 models and a 33 per cent drop for the 30.200 and 980400 simulations.," As expected the ionization rate shows a greater reduction in magnitude withincreasing mass resolution, exhibiting a $20$ per cent reduction between the $15-200$ and $15-400$ models and a $33$ per cent drop for the $30-200$ and $30-400$ simulations." + Note that the stricter resolution requirement, Note that the stricter resolution requirement +formation and evolution of the TNb and the outer Solar System.,formation and evolution of the TNb and the outer Solar System. +he middle between two stars.,the middle between two stars. + For wnequal-mass uuaries. on the other hind. we have a couple of equations. Equation (35)) for «=1 aud 2. for two xuwanmeters of the orbital augular velocity aud the ocation of the ceuter of mass.," For unequal-mass binaries, on the other hand, we have a couple of equations, Equation \ref{eq:forcebalance}) ) for $a=1$ and 2, for two parameters of the orbital angular velocity and the location of the center of mass." + Iu the previous papers (Tanienchi&Coureoulhon2002b.2003).. hose paraiueters were determined by solving the couple of equations as stated in Section IT D of Tanienchi&Courgoulhon(2002a).," In the previous papers \citep{tan02b,tan03}, those parameters were determined by solving the couple of equations as stated in Section II B of \citet{tan02a}." +. This method works for Newtonian binary systems (Taniguchi&Courgoulhon2002a) aud :so in the case that the difference iu mass of the neutron stars is αμα. for general relativistic binary svstenis., This method works for Newtonian binary systems \citep{tan02a} and also in the case that the difference in mass of the neutron stars is small for general relativistic binary systems. + ILowever. if he difference ii mass of the neutron stars is senificautlv huge. the coupled equations. Equation (35)) for α=1 and 2. would uo ο suultauecouslv satisfied at earlier steps of conrputational iteration because he state of the üuarv neutron stars is far from equilibriui. auk as a result. the computation would fail to achieve he convergence to a solution.," However, if the difference in mass of the neutron stars is significantly large, the coupled equations, Equation \ref{eq:forcebalance}) ) for $a=1$ and 2, would not be simultaneously satisfied at earlier steps of computational iteration because the state of the binary neutron stars is far from equilibrium, and as a result, the computation would fail to achieve the convergence to a solution." + To avoid such crush of computation for smal lass ratios. MSALNAp<-0.8 ∖↽∖⋅∖wher: ARB≓∖⊽↴⊣⇣↕(a=--1.2) denotes the Arnowitt-Desecr-Misuner (ADAI) uass for a spherical star «@ in isolation. we adopt the same method as used or black hole-jieutron star binaries. described in Touiguchietal.(2006.2007. 2008).. to cetermune the location of the center of mass: we require hat the linear nuomienutuim of the svstenmi vanishes Tere we have assumed maximal slicing condition. v=0.," To avoid such crush of computation for small mass ratios, $M_{\rm ADM}^{\rm NS 1}/M_{\rm ADM}^{\rm NS 2} < 0.8$ where $M_{\rm ADM}^{\rm NS a}~(a=1,2)$ denotes the Arnowitt-Deser-Misner (ADM) mass for a spherical star $a$ in isolation, we adopt the same method as used for black hole-neutron star binaries, described in \citet{tan06,tan07,tan08}, to determine the location of the center of mass; we require that the linear momentum of the system vanishes Here we have assumed maximal slicing condition, $K=0$." + 0uce the location of the ceuter of mass is determined in an iteration step. we move the position of cach star. keeping the separation. iu order for the ceuter of mass of the binary system. to locate on the Z-axis.," Once the location of the center of mass is determined in an iteration step, we move the position of each star, keeping the separation, in order for the center of mass of the binary system to locate on the $Z$ -axis." + For the computation of the orbital angular velocity. we keep the method that Equation (35)) ds satisfied.," For the computation of the orbital angular velocity, we keep the method that Equation \ref{eq:forcebalance}) ) is satisfied." + As the readers may realize. Equation (35)) gives two values of he orbital aneular velocity for the unequal-nass case because there are two equations iu Equation (35)).," As the readers may realize, Equation \ref{eq:forcebalance}) ) gives two values of the orbital angular velocity for the unequal-mass case because there are two equations in Equation \ref{eq:forcebalance}) )." + Even though those values of the orbital angular velocity are very close (the relative difference is within the convergence level). they are slightly different because of numerical error.," Even though those values of the orbital angular velocity are very close (the relative difference is within the convergence level), they are slightly different because of numerical error." + In the preseut paper. we just take au average of the two values.," In the present paper, we just take an average of the two values." + It nav be worthy to conunent on another method for determining the orbital augular velocity., It may be worthy to comment on another method for determining the orbital angular velocity. + While our method for calculatingBi O is to require the force balance. Equation. (35)). it is possible to obtain @ by requiring the euthalpy at two points ou the neutron stars surface to be equal. ie. -—1 on the surface.," While our method for calculating $\Omega$ is to require the force balance Equation \ref{eq:forcebalance}) ), it is possible to obtain $\Omega$ by requiring the enthalpy at two points on the neutron star's surface to be equal, i.e., $h=1$ on the surface." + We confiui that the results of those two methods coincide withiu the convergence level of the euthalpy., We confirm that the results of those two methods coincide within the convergence level of the enthalpy. + A sequence of binary neutron stars should be constructed for a fixed barvon rest mass of each star. as the orbital separation decreases.," A sequence of binary neutron stars should be constructed for a fixed baryon rest mass of each star, as the orbital separation decreases." + This is vecatise we regard the barvou rest mass as conserved as the orbital separation decreases due o the emission of gravitational waves., This is because we regard the baryon rest mass as conserved as the orbital separation decreases due to the emission of gravitational waves. + Along such a constaut-barvon-rest-nuass sequence. we hen monitor three elobal quantities the ADM uas. the Tomar mass. aud the total angular uonmentun. as well as a sensitive mass-hedcaiug indicator of a star (sce Equation (19))).," Along such a constant-baryon-rest-mass sequence, we then monitor three global quantities: the ADM mass, the Komar mass, and the total angular momentum, as well as a sensitive mass-shedding indicator of a star (see Equation \ref{eq:defchi}) ))." + The ADAM mass in isotropic Cartesian coordinates is written as If we use Equation (15)) aud Cass” theorem. the ADM amass can be written in terms of volue integral as Both of Equations (38)) aud (39)) eive the same results relative to the convergence level of the colputation.," The ADM mass in isotropic Cartesian coordinates is written as If we use Equation \ref{eq:psi}) ) and Gauss' theorem, the ADM mass can be written in terms of volume integral as Both of Equations \ref{eq:admsurf}) ) and \ref{eq:admvol}) ) give the same results relative to the convergence level of the computation." + The omar nass is written as where we use the fact that the shift vector falls off rapidly chough to be neglected from Equation (103)., The Komar mass is written as where we use the fact that the shift vector falls off rapidly enough to be neglected from Equation \ref{eq:Komarsurf}) ). + Using the boundary conditions that @=1 , Using the boundary conditions that $\Phi=1$ +and between pairs of binaries based on the FewBody integrator developed by Fregeauetal.(2004): (1) it replaces the treatment of the escape process in the static tidal field based on (2001) by one in accordance the theory proposed by FokushigeΠοσσίο (2000).,and between pairs of binaries based on the FewBody integrator developed by \citet{FCZR2004}; (ii) it replaces the treatment of the escape process in the static tidal field based on \citet{Ba2001} by one in accordance the theory proposed by \citet{FH2000}. +".. The escape process is not instantaneous any more. an object needs time to find its way around the Lagrangian points £L, and L» to escape."," The escape process is not instantaneous any more, an object needs time to find its way around the Lagrangian points $L_1$ and $L_2$ to escape." + The MOCCA code incorporates most of the processes which are important during stellar system evolution e.g.: the relaxation process. the main engine ofdynamical cluster evolution: stellar evolution according to Hurley.Pols.&Tout(2000). for the evolution of single stars. supplemented by the methods of Hurley.Tout.&Pols(2002) for internal evolution of binary stars (BSE code) and also simple approach for colliding stars according to McScatter interface to BSE by Heggie.Porte-giesZwart.&Hurley (2006): the escape process in the static tidal field of the parent galaxy: direct few body integrator to follow interactions between binaries and single stars and other binaries: mass segregated initial cluster configuration according to Baumgardt.DeMarchi.&Kroupa(2008) and Subr.Kroupa&Baumgardt (Q008).," The MOCCA code incorporates most of the processes which are important during stellar system evolution e.g.: the relaxation process, the main engine ofdynamical cluster evolution; stellar evolution according to \citet{Hu2000} for the evolution of single stars, supplemented by the methods of \citet{Hu2002} for internal evolution of binary stars (BSE code) and also simple approach for colliding stars according to McScatter interface to BSE by \citet{HPH2006}; the escape process in the static tidal field of the parent galaxy; direct few body integrator to follow interactions between binaries and single stars and other binaries; mass segregated initial cluster configuration according to \citet{BDK2008} and \citet{SKB2008}." +. There are several factors which motivate this work., There are several factors which motivate this work. +" Star clusters are the focus of many intensive observational campaigns (e.g.Bedinetal.2001:Bedin.Piotto2003:Grind-etal.201I.andreferences therein). which are now turning to the examination. of the parameters of their populations. of different kinds of binaries. BSS and other ""peculiar"" objects."," Star clusters are the focus of many intensive observational campaigns \citep[e.g.][and references therein] {bedinetal2001,bedinetal2003,grindlayetal2001,piottoetal2002, +kaliarietal2003,kafkaetal2004,richeretal2004,andersonetal2006,miloneetal2011}, which are now turning to the examination of the parameters of their populations of different kinds of binaries, BSS and other ""peculiar"" objects." + Dynamical models are needed for the design and interpretation of observational programmes: how is the period distribution and the spatial distribution of binaries affected by dynamical evolution?, Dynamical models are needed for the design and interpretation of observational programmes: how is the period distribution and the spatial distribution of binaries affected by dynamical evolution? + What is the influence of environment and dynamical evolution on the formation of “peculiar” objects?," What is the influence of environment and dynamical evolution on the formation of ""peculiar"" objects?" + Understanding the abundance. spatial distribution and channels of formation of BSS can only be attempted by a technique which follows simultaneously both BSS dynamics and internal evolution.," Understanding the abundance, spatial distribution and channels of formation of BSS can only be attempted by a technique which follows simultaneously both BSS dynamics and internal evolution." + While A’-body technique may ultimately be the method of choice for such studies. systems of the size of most globular clusters are likely to remain beyond reach for some years. simply because of the number of stars and the size of the binary population.," While $N$ -body technique may ultimately be the method of choice for such studies, systems of the size of most globular clusters are likely to remain beyond reach for some years, simply because of the number of stars and the size of the binary population." + After all. it is only recently that the “hardest” open clusters M67 (Hurleyetal.2005) and “easiest”. loosely bound and distant globular cluster Palomar 14 CZonoozietal.2011) have been modelled at the necessary level of sophistication.," After all, it is only recently that the “hardest"" open clusters M67 \citep{Hurleyetal2005} and “easiest"", loosely bound and distant globular cluster Palomar 14 \citep{Zonoozietal2011} have been modelled at the necessary level of sophistication." + To efficiently compute detailed models of large star clusters and to investigate the influence of initial parameters on a cluster’s global and local observational properties we need a technique which is much faster than the N-bodv code and at the same time can give he same level of information about every object in the cluster as he N-body code does., To efficiently compute detailed models of large star clusters and to investigate the influence of initial parameters on a cluster's global and local observational properties we need a technique which is much faster than the N-body code and at the same time can give the same level of information about every object in the cluster as the N-body code does. + The MOCCA code is such a technique., The MOCCA code is such a technique. + One of the drawbacks of the non direct techniques (also the Tonte Carlo one) compared to the N-body model is à necessity of use of free parameters which try to describe the complexity of johysieal processes naturally covered in the direct code., One of the drawbacks of the non direct techniques (also the Monte Carlo one) compared to the N-body model is a necessity of use of free parameters which try to describe the complexity of physical processes naturally covered in the direct code. +" The mos important free parameters (from the point of view of MOCCA) are connected with the relaxation process ( coefficient in the Coulomb ogarithm). escape process in the static tidal field and dynamica interactions between different objects Gwhere the parameter. 1,5. is the maximum pericentre distance between interacting objects for which few-body interactions are calculated explicitly)."," The most important free parameters (from the point of view of MOCCA) are connected with the relaxation process $\gamma$ coefficient in the Coulomb logarithm), escape process in the static tidal field and dynamical interactions between different objects (where the parameter, $r_{pmax}$, is the maximum pericentre distance between interacting objects for which few-body interactions are calculated explicitly)." + The usua method to determine the free parameters is a comparison with the results of N-body simulations., The usual method to determine the free parameters is a comparison with the results of N-body simulations. + For the previous version of the Monte Carlo code the comparison was done only for small A’ systems (up to N=24000)., For the previous version of the Monte Carlo code the comparison was done only for small $N$ systems (up to $N = 24000$ ). + The code was successfully used to simulate evolution of real star clusters: M67 (Giersz.Heggie.Hurley2008).. M4 (Heggie&Giersz2008a).. NGC6397 Heggie2009:Hegzgie&Giersz2009) and 47Tuc (Giersz&Heggie2011).," The code was successfully used to simulate evolution of real star clusters: M67 \citep{GHH2008}, , M4 \citep{HG2008}, NGC6397 \citep[][]{GH2009,HG2009} and 47Tuc \citep{GH2011}." +. Despite those successes there were some doubts connected with the NV sealing of the escape process. which implementation was based on Baumgardt(2001).," Despite those successes there were some doubts connected with the $N$ scaling of the escape process, which implementation was based on \citet{Ba2001}." +. To fully trust the MOCCA code it has to be tested for larger N. and not only for the global parameters like evolution of the total cluster mass or Lagrangian radii. but also against the properties and spatial distributions of binaries and BSS.," To fully trust the MOCCA code it has to be tested for larger N, and not only for the global parameters like evolution of the total cluster mass or Lagrangian radii, but also against the properties and spatial distributions of binaries and BSS." + That kind of comparison will show how far we can trust results of Monte Carlo simulations and which processes cannot be properly described in the framework of the MOCCA code., That kind of comparison will show how far we can trust results of Monte Carlo simulations and which processes cannot be properly described in the framework of the MOCCA code. + This paper begins in Sec.2. with a summary of the features which have been added to the Monte Carlo scheme during the construction of the new version of the code. the MOCCA code.," This paper begins in Sec.2 with a summary of the features which have been added to the Monte Carlo scheme during the construction of the new version of the code, the MOCCA code." + We also show there how we calibrate the free parameters of the MOCCA code with results of N-body simulations., We also show there how we calibrate the free parameters of the MOCCA code with results of $N$ -body simulations. + Next (Sec., Next (Sec. + 3) we describe the similarities and differences between MOCCA and N-body simulation and discuss the possible reasons for that., 3) we describe the similarities and differences between MOCCA and N-body simulation and discuss the possible reasons for that. + The final section summarises our conclusions. and discusses some limitations and future developments of the MOCCA code.," The final section summarises our conclusions, and discusses some limitations and future developments of the MOCCA code." + The MOCCA code (Hypki&Giersz2011). is an updated version of the Monte Carlo code developed in Giersz(1998.2001.2006):Giersz.Heggie.&Hurley (2008).," The MOCCA code \citep{HyG2011} is an updated version of the Monte Carlo code developed in \citet{Gi1998,Gi2001,Gi2006,GHH2008}." +. In addition to the description of the relaxation process which is responsible for the dynamical system evolution it includes synthetic stellar evolution of single and binary stars using prescriptions described by Hurley.Pols.&Tout(2000) and Hurley.Tout.&Pols(2002) and direct integration procedures for small No subsystems based on the FewBody code Fregeauetal.(2004)., In addition to the description of the relaxation process which is responsible for the dynamical system evolution it includes synthetic stellar evolution of single and binary stars using prescriptions described by \citet{Hu2000} and \citet{Hu2002} and direct integration procedures for small $N$ subsystems based on the FewBody code \citet{FCZR2004}. +.. One of the more important updates is a better description of the escape process according to (Fokushige&Heggie2000)., One of the more important updates is a better description of the escape process according to \citep{FH2000}. +. Now the escape of an object from the system is not instantaneous anymore. but time delayed.," Now the escape of an object from the system is not instantaneous anymore, but time delayed." + The theory of Fokushige&Heggie(2000) incorporates a number of parameters which they had to determine empirically. and which depend on the system under consideration: here we shall determine these parameters by comparing the results with those of N-body simulations.," The theory of \citet{FH2000} incorporates a number of parameters which they had to determine empirically, and which depend on the system under consideration; here we shall determine these parameters by comparing the results with those of N-body simulations." + In the N-body code formation of binaries and subsequent their interactions follow naturally from the movement of stars in the system under the mutual gravitational force., In the N-body code formation of binaries and subsequent their interactions follow naturally from the movement of stars in the system under the mutual gravitational force. + In the MOCCA code first we need to check if the interaction is due be computing its probability and then if it is so we execute the direct integration procedure for small No (3- or 4-body) subsystem to find out the outcome of the interaction., In the MOCCA code first we need to check if the interaction is due be computing its probability and then if it is so we execute the direct integration procedure for small $N$ (3- or 4-body) subsystem to find out the outcome of the interaction. + The interaction probability depends. among others. on the maximum value of the pericentre distance. Myre.," The interaction probability depends, among others, on the maximum value of the pericentre distance, $r_{pmax}$." + The larger this distance the larger the number of interactions. which are weaker on average.," The larger this distance the larger the number of interactions, which are weaker on average." + Choosing a proper value Of risus IS crucial for a balance between code efficiency and its accuracy. e.g. thenumber of BSS observed in the system strongly depends on rios.," Choosing a proper value of $r_{pmax}$ is crucial for a balance between code efficiency and its accuracy, e.g. thenumber of BSS observed in the system strongly depends on $r_{pmax}$ ." + As it was pointed out in Fokushige&Heggie(2000) and Baumgardt(2001). the process of escape from a cluster in a steady, As it was pointed out in \citet{FH2000} and \citet{Ba2001} the process of escape from a cluster in a steady + Iu receut vears diffuse ionized eas (DIC) frequently also called. wari ionized medium (WIM) has been ideutibied as an nmuportaut component of the ISAL iu particular with regard to the influence of SE ou the laree scale distribution and physical properties of the ISAL.," In recent years diffuse ionized gas (DIG) frequently also called warm ionized medium (WIM) has been identified as an important component of the ISM, in particular with regard to the influence of SF on the large scale distribution and physical properties of the ISM." + This eas colpouent typically las a τον low electron deusity of7 \,\sim 0.08\,\rm{cm^{-3}}$ (in the disk) which decreases exponentially towards the halo and is characterized through a temperature of $T=$ K. For a detailed review on recent developments concerning the disk–halo connection, which is briefly described below, we refer to Dettmar \cite{De95}) ) or Dahlem \cite{Da97b}) )." + Iu our own galaxy DIG was first detected as an extraplanar eas laver (Ilovle Ellis 1963)) bv radio observations., In our own galaxy DIG was first detected as an extraplanar gas layer (Hoyle Ellis \cite{HoEl63}) ) by radio observations. +" Iu the carly seventies Πα observations were performed which also showed an extraplauar laver. (sce RRevnolds 1981)) which is now known as the ""Bevuüolds lwer."," In the early seventies $\alpha$ observations were performed which also showed an extraplanar layer, (see Reynolds \cite{Re84}) ) which is now known as the `Reynolds layer'." + Ouly as receutlv as 1990 this gas coniponeut has been detected iu external galaxies outside traditional regious (Dettmar 1990: Rand et al. 1990)), Only as recently as 1990 this gas component has been detected in external galaxies outside traditional regions (Dettmar \cite{De90}; Rand et al. \cite{Ra90}) ) + Since the DIC is traced bw Πα ClUSSION. several studies have been dedicated to detect eDICC in external ealaxies with the use of narrowband Πα CCD imagine. prefercutially in οσοon galaxies. where the halo separates from the disk PPildis et al. 1991:," Since the DIG is traced by $\alpha$ emission, several studies have been dedicated to detect eDIG in external galaxies with the use of narrowband $\alpha$ CCD imaging, preferentially in edge–on galaxies, where the halo separates from the disk Pildis et al. \cite{Pi94};" + Rane et al. 1992:, Rand et al. \cite{Ra92}; + Rand. 1996:: this work)., Rand \cite{Ra96}; this work). + About two dozen ealaxics have jn detected up to now that show signs of diskhalo interaction (DIIT)., About two dozen galaxies have been detected up to now that show signs of disk–halo interaction (DHI). + Subsequent loneslit spectroscopy las been performed for a few galaxies including 8891 (Dettimar Schulz 1992:: Keppel et al. ουνι, Subsequent longslit spectroscopy has been performed for a few galaxies including 891 (Dettmar Schulz \cite{DeSc}; Keppel et al. \cite{Ke91}; + Baud 1997: Rand L998)). 11631 (Colla et al. 1996)).," Rand \cite{Ra97}; Rand \cite{Ra98}) ), 4631 (Golla et al. \cite{GoDo}) )," + 22188 (Domeorrecn Dettimar 1997)]. 11963 33001 (Tillhnann Doettinar 2000)). zunong a few others.," 2188 (Domgörrgen Dettmar \cite{DoDe}) ), 1963 3044 (Tülllmann Dettmar \cite{TuDe}) ), among a few others." + DIC doetectious in starburst galaxies seein to be a «ώμο. feature. as it was evidenced bv an investigation by Lehnert Ueckman (1995)).," DIG detections in starburst galaxies seem to be a common feature, as it was evidenced by an investigation by Lehnert Heckman \cite{LeHe}) )." + DIC typically reaches scaleheights iu οσοon galaxies of ~1 2kkpc. but as in the case of 5501. spectroscopic investigations have shown that DIC even cau be detected at oxtraplanar distances of up to Skkpe (Rand 1997)).," DIG typically reaches scale–heights in edge–on galaxies of $\sim$ kpc, but as in the case of 891 spectroscopic investigations have shown that DIG even can be detected at extraplanar distances of up to kpc (Rand \cite{Ra97}) )." + The most likely process for ionizing the DIC is photoionization (Mathis 1986: Domeorreca Mathis 1991))., The most likely process for ionizing the DIG is photoionization (Mathis \cite{Ma86}; Domgörrgen Mathis \cite{DoMa}) ). + Althoueh photoiouization bv OD stars MMiller. Cox 1995: Dove Shull 19901)) is regarded as the primary process. other mechanisms have been invoke such as shock-ionization (Clievalier Cleeeoo 1985)3. aud turbulent mixing lavers (Slavin et al. 19933) ," Although photoionization by OB stars Miller Cox \cite{MiCo}; Dove Shull \cite{DoSh}) ) is regarded as the primary process, other mechanisms have been invoked such as shock-ionization (Chevalier Clegg \cite{ChCl}) ), and turbulent mixing layers (Slavin et al. \cite{SlSh}) )" +to account for the observed emission line ratios., to account for the observed emission line ratios. + Ainechanisin for the transport of gas and radiation iuto the halo has been foxinulated iu the late cightics, Amechanism for the transport of gas and radiation into the halo has been formulated in the late eighties +For the wavelengths. the confusion limits are given hy the photometric,"For the wavelengths, the confusion limits are given by the photometric." +criterion! With quiu;—5. they are about 447. 200. 79.4. 22-4 and 11.2 mJy at 350. 550. 850. 1380 and 2097 jin respectively (for detection only. qui; —3 is better ancl leads to the following confusion limits: 251. 112. 44.7. 14.1 and 6.31 at 350. 550. 850. 1380 ane 2097 [am respectively).," With $_{phot}$ =5, they are about 447, 200, 79.4, 22.4 and 11.2 mJy at 350, 550, 850, 1380 and 2097 $\mu$ m respectively (for detection only, $_{phot}$ =3 is better and leads to the following confusion limits: 251, 112, 44.7, 14.1 and 6.31 at 350, 550, 850, 1380 and 2097 $\mu$ m respectively)." + The confusion. limit. (with ρω). is above the 5o instrumental noise at. 350 jin. comparable at 550 yam and then below at longer wavelengths.," The confusion limit (with $_{phot}$ =5) is above the $\sigma$ instrumental noise at 350 $\mu$ m, comparable at 550 $\mu$ m and then below at longer wavelengths." + It can be compared to the values given in the. Vable 2.1.," It can be compared to the values given in the, Table 2.1." + In this Table. the confusion limits have been computed: using © rather than {f(0.b\déds in Eq. 12..," In this Table, the confusion limits have been computed using $\Omega$ rather than $\int f^2(\theta, \phi) d\theta d\phi$ in Eq. \ref{eq_sigma}." + This leads to a systematic overestimates of toony bv a factor 1.33., This leads to a systematic overestimates of $\sigma_{conf}$ by a factor 1.33. + Correcting for this factor. the ratio of those estimates to the present ones increases from 350 to 2097 jim from 1.2 to 3.," Correcting for this factor, the ratio of those estimates to the present ones increases from 350 to 2097 $\mu$ m from 1.2 to 3." +" To compute the number of sources expected. in the Planck survey. we use a cut in Dux equal to 57, such as: where eo,rp LorPlanck is given by toonp = Stim £D."," To compute the number of sources expected in the survey, we use a cut in flux equal to $\sigma_{tot}$ such as: where $\sigma_{conf}$ for is given by $\sigma_{conf}$ = $_{lim}$ /5." +" Cael is an adclitonal noise clue to unresolved sources with [uxes between Syj,,, and Soja: This additional term is only present when the 5a;,,.; is greater than the confusion limit (as for example for theSPIRE verv-laree Final sensitivities on point sources. together with the number of detected: sources forPlanck are given in Table 7.."," $\sigma_{add}$ is an additonal noise due to unresolved sources with fluxes between $_{lim}$ and $\sigma_{inst}$: This additional term is only present when the $\sigma_{inst}$ is greater than the confusion limit (as for example for the very-large Final sensitivities on point sources, together with the number of detected sources for are given in Table \ref{Planck-tbl}." + At all wavelengths. the sensitivity of the survey is in the euclidian part of the number counts.," At all wavelengths, the sensitivity of the survey is in the euclidian part of the number counts." +Planch will not be able to constrain. with the resolved sources. the evolution of the subnum galaxies but it will give an absolute calibration of the bright number counts. that will not be provided by any other planned instruments.," will not be able to constrain, with the resolved sources, the evolution of the submm galaxies but it will give an absolute calibration of the bright number counts, that will not be provided by any other planned instruments." + Moreover. by covering the whole sky. it will probably detect the most spectacular clusty. object of the observable Universe. as the hyperluminous or the strongly. lensed starburst or AGN galaxies. as well as extreme sources not included in the Note however that the sensitivities have been computed with an instrumental noise derived from a mean integration time.," Moreover, by covering the whole sky, it will probably detect the most spectacular dusty object of the observable Universe, as the hyperluminous or the strongly lensed starburst or AGN galaxies, as well as extreme sources not included in the Note however that the sensitivities have been computed with an instrumental noise derived from a mean integration time." + With thePlanck scanning strategy. some high latitudes regions (where the cirrus contamination is low) will be surveved: more. deeply. leading to an instrumental noise about 3 times lower.," With the scanning strategy, some high latitudes regions (where the cirrus contamination is low) will be surveyed more deeply, leading to an instrumental noise about 3 times lower." + In such high redundaney. parts of the sky. survey will be limited by the confusion noise (except at 2007. pam where the instrumental ancl confusion noises are on the same order).," In such high redundancy parts of the sky, survey will be limited by the confusion noise (except at 2097 $\mu$ m where the instrumental and confusion noises are on the same order)." + In those regions.Planck will produce unique maps of the CLB fluctuations.," In those regions, will produce unique maps of the CIB fluctuations." + CID anisotropies are maink contributed. by moderate to high redshift’ star-forming galaxies. whose clustering properties and evolutionary. histories are currently unknown.," CIB anisotropies are mainly contributed by moderate to high redshift star-forming galaxies, whose clustering properties and evolutionary histories are currently unknown." +PLanck observations will thus complement the future fer-LR and submum telescopes from ground and space that will perform deep surveys over small area., observations will thus complement the future far-IR and submm telescopes from ground and space that will perform deep surveys over small area. + These surveys will resolve a substantial fraction of the CIB but will. probably not investigate the clustering of the submm ealaxies since it peculres SULVOVS OVOE much larger ALCAS., These surveys will resolve a substantial fraction of the CIB but will probably not investigate the clustering of the submm galaxies since it requires surveys over much larger areas. + Since the far-LR and subnini sources (1) are often associated with mergers or interacting galaxies and (2) their energy ouput is dominated by high. luminosity sources at high redshift’ (which might be related to the optical where the output is dominated. by high. brightness sources at. high redshift (Lanzetta et al., Since the far-IR and submm sources (1) are often associated with mergers or interacting galaxies and (2) their energy ouput is dominated by high luminosity sources at high redshift (which might be related to the optical where the output is dominated by high brightness sources at high redshift (Lanzetta et al. + 2002)). they have to be studied in detail in the long wavelength range ancl at high reclshilt (2223) as à tool to understand the merging process and the phiysies of the first non linear Two kinds of requirements have to be meet by the postSIRE. Herschel and Planck surveys: To quantify the first. requirement. we compute the surface needed to detect more. than 100. sources. with uminosities o£ 3 107 and 3 1077 L. in each redshift range (Table sj).," 2002)), they have to be studied in detail in the long wavelength range and at high redshift $\geq$ 3) as a tool to understand the merging process and the physics of the first non linear Two kinds of requirements have to be meet by the post, and surveys: To quantify the first requirement, we compute the surface needed to detect more than 100 sources with luminosities of 3 $^{11}$ and 3 $^{12}$ $_{\odot}$ in each redshift range (Table \ref{sfce_pred}) )." + At. high. redshift. we need surveys of about iiuncdred: of square degrees to find. enough high. Luminous objects to do statistical studies.," At high redshift, we need surveys of about hundred of square degrees to find enough high luminous objects to do statistical studies." + Lf enough area is covered. we need moreover a high sensitivitv. for example we have o reach 0.21 mJy at S50 jim for L=3 107 L. galaxies (dominating the LF at z~1) and 1.9 mJy at 850. pam (or 19 my at 1300 yan) for L=3 1077 L. galaxies (dominating he LE at Z2).," If enough area is covered, we need moreover a high sensitivity, for example we have to reach 0.21 mJy at 850 $\mu$ m for L=3 $^{11}$ $_{\odot}$ galaxies (dominating the LF at $\sim$ 1) and 1.9 mJy at 850 $\mu$ m (or 0.9 mJy at 1300 $\mu$ m) for L=3 $^{12}$ $_{\odot}$ galaxies (dominating the LF at $>$ 2)." + The fluxes of typical 3 1017 L. galaxies at high-z are just. for the single-antenna telescopes. at he confusion limit.," The fluxes of typical 3 $^{12}$ $_{\odot}$ galaxies at high-z are just, for the single-antenna telescopes, at the confusion limit." + With the future wide-field. imaging instruments on these telescopes. for exampleSCUBA-2 (Llolland et al.," With the future wide-field imaging instruments on these telescopes, for example (Holland et al." + 2001) ancBOLOCAAL (Glenn et al., 2001) and (Glenn et al. + 1998). πιάνου of square degrees at the Lo my level at 1300. sam could bemapped in a reasonable amount of time.," 1998), hundred of square degrees at the 1 mJy level at 1300 $\mu$ m could bemapped in a reasonable amount of time." + However. with10/15 arsecbeam. it will be very cillicult to make optical identifications and. follow-up observations at other," However, with10/15 arsecbeam, it will be very difficult to make optical identifications and follow-up observations at other" +The calculations described here are similar to the unheated flow presented in Brighenti Mathews (2003). where the reader may find a description of the thermal evolution of the flow.,"The calculations described here are similar to the unheated flow presented in Brighenti Mathews (2003), where the reader may find a description of the thermal evolution of the flow." + Recently. Guo Oh (2007) have also discussed simulations of the ICM in a T4 keV cluster.," Recently, Guo Oh (2007) have also discussed simulations of the ICM in a $T\sim 4$ keV cluster." + The results of our calculations are in qualitative agreement with those in the two aforementioned papers., The results of our calculations are in qualitative agreement with those in the two aforementioned papers. + As the σας cools in the central region. it slowly flows inward to approximately preserve equilibrium.," As the gas cools in the central region, it slowly flows inward to approximately preserve equilibrium." + A positive temperature gradient develops and the density profile steepens., A positive temperature gradient develops and the density profile steepens. + At the end of the simulations the temperature profile agrees nicely with typical observed cool core clusters (Figure 1). while the computed density is somewhat flatter.," At the end of the simulations the temperature profile agrees nicely with typical observed cool core clusters (Figure 1), while the computed density is somewhat flatter." +" This ean be understood with the long initial central cooling time (see above). which makes the ""radiative age"" of our models rather young. even after ~10 Gyr."," This can be understood with the long initial central cooling time (see above), which makes the “radiative age” of our models rather young, even after $\sim 10$ Gyr." + After about one cooling time the gus in the centre cools to very low temperature. this is the onset of the so-called cooling catastrophe.," After about one cooling time the gas in the centre cools to very low temperature, this is the onset of the so-called cooling catastrophe." + The mass cooling rate grows with time. reaching an approximate steady-state after few cooling times (see Brighenti Mathews 2003. 2006).," The mass cooling rate grows with time, reaching an approximate steady-state after few cooling times (see Brighenti Mathews 2003, 2006)." + In the caleulations presented here the mass cooling rates are still increasing at the end of the simulations. due to the rather long initial cooling times.," In the calculations presented here the mass cooling rates are still increasing at the end of the simulations, due to the rather long initial cooling times." + At |=13.7 Gyr we find ALool&TO (40). AL. Ayr for the hot (cold) cluster., At $t=13.7$ Gyr we find $\dot M_{\rm cool}\approx 70$ $(40)$ $M_\odot$ /yr for the hot (cold) cluster. + A total mass of ~Ll.1013 37. and ~1.3OHAL. is cooled below X-ray temperature in the hot and cold. cluster respectively., A total mass of $\sim 1.1 \times 10^{11}$ $M_\odot$ and $\sim 1.3\times 10^{11} M_\odot$ is cooled below X-ray temperature in the hot and cold cluster respectively. + This is at odd with observations. which show tight constraints on the cooling rate (e.g. Peterson Fabian 2006) a blatant manifestation of the cooling flow problem.," This is at odd with observations, which show tight constraints on the cooling rate (e.g. Peterson Fabian 2006) -- a blatant manifestation of the cooling flow problem." + We do not attempt to solve this problem here (see MeNamara Nulsen 2007 for a recent review on this subject)., We do not attempt to solve this problem here (see McNamara Nulsen 2007 for a recent review on this subject). + Rather. we are interested in the formation of the cool core following the assembly of the cluster or the last major merging.," Rather, we are interested in the formation of the cool core following the assembly of the cluster or the last major merging." + The way in which the heating necessary to halt radiative cooling influences the density and temperature profiles is not well known., The way in which the heating necessary to halt radiative cooling influences the density and temperature profiles is not well known. + Here we take the position that the average thermal structure of the ICM is not greatly affected by the heating process., Here we take the position that the average thermal structure of the ICM is not greatly affected by the heating process. + This appears justified by the reasonable agreement shown in Figure | below between observed and simulated. purely radiative temperature profile (see Brighenti Mathews 2006 and Guo Oh 2007 for models in which the variables profiles are not significantly modified by jet heating).," This appears justified by the reasonable agreement shown in Figure 1 below between observed and simulated, purely radiative temperature profile (see Brighenti Mathews 2006 and Guo Oh 2007 for models in which the variables profiles are not significantly modified by jet heating)." + Following this assumption we neglect the gravity from the unrealistic accumulation of cold gas in the centre of our models. which would generate a strong temperature peak (Brighenti Mathews 2000).," Following this assumption we neglect the gravity from the unrealistic accumulation of cold gas in the centre of our models, which would generate a strong temperature peak (Brighenti Mathews 2000)." + The radial protiles of the gas temperature. density and surface brightness are obtained at temporal steps of 0.2 Gyr starting from the cosmic time of 3 Gyr. corresponding to >—2.11 for the assumed cosmology. and reaching +=O after 10.7 Gyr.," The radial profiles of the gas temperature, density and surface brightness are obtained at temporal steps of 0.2 Gyr starting from the cosmic time of 3 Gyr, corresponding to $z=2.11$ for the assumed cosmology, and reaching $z=0$ after 10.7 Gyr." + These profiles are plotted in Fig. |.., These profiles are plotted in Fig. \ref{fig:prof}. + When we refer to the age of the structure. we mean the cosmic time at which the physical quantity is observed the cosmic time at which the strueture started its evolution. i.e. 3 Gyr.," When we refer to the age of the structure, we mean the cosmic time at which the physical quantity is observed the cosmic time at which the structure started its evolution, i.e. 3 Gyr." + In the same figure. we present the profiles normalized at the values observed at 0.2/?»04 in a cool-core (A1835 rom Morandi Ettori 2007 and A1795. for the inner regions. rom Ettori et al.," In the same figure, we present the profiles normalized at the values observed at $0.2 R_{200}$ in a cool-core (A1835 from Morandi Ettori 2007 and A1795, for the inner regions, from Ettori et al." + 2001) and a non-cool-core CA665. Morandi Ettori 2007) massive cluster.," 2001) and a non-cool-core (A665, Morandi Ettori 2007) massive cluster." + The profiles follow the predicted behaviour in particular of the gas density and surface brightness distribution., The profiles follow the predicted behaviour in particular of the gas density and surface brightness distribution. + Larger deviations are observed in the temperature orofile that depend strongly on the reference global value adopted o normalize the profile., Larger deviations are observed in the temperature profile that depend strongly on the reference global value adopted to normalize the profile. + We present in Fig., We present in Fig. + 2. the relative variation of the temperature. density and surface brightness as function of the age of the objects. both as ratios between the quantities estimated at fixed fractions of {ους Ge. 0.01ogy. that lies well within the cluster core. and 0.22509. radius at which the cooling is not effective anymore) and as relative changes per Gyr at 0.01.0.1.0.272505.," \ref{fig:dq_age} the relative variation of the temperature, density and surface brightness as function of the age of the objects, both as ratios between the quantities estimated at fixed fractions of $R_{200}$ (i.e. $0.01 R_{200}$, that lies well within the cluster core, and $0.2 R_{200}$, radius at which the cooling is not effective anymore) and as relative changes per Gyr at $0.01, 0.1, 0.2 R_{200}$." + The expected behaviour is contirmed for all the quantities under exam with the added value that we are now in condition to quantify the magnitude of the variations., The expected behaviour is confirmed for all the quantities under exam with the added value that we are now in condition to quantify the magnitude of the variations. + The temperature decreases rapidly at first. with relative changes between 5 and 20 per cent per Gyr when measured at 0.0172»050.," The temperature decreases rapidly at first, with relative changes between 5 and 20 per cent per Gyr when measured at $0.01 R_{200}$ ." + After —7 Gyr the temperature profile of the two objects reaches a quasi-steady state., After $\sim 7$ Gyr the temperature profile of the two objects reaches a quasi-steady state. + This results in a ratio Cr=0.01/2505)/2(e=0.245095) equals to —0.4 after 10 Gyr of pure cooling flow evolution., This results in a ratio $T (r=0.01R_{200}) / T (r=0.2R_{200})$ equals to $\sim0.4$ after 10 Gyr of pure cooling flow evolution. + The gas densityrises at a rate of about 15-20 per cent per Gyr when measured at 0.017»; and of | per cent when the increase is evaluated at 0.272555., The gas densityrises at a rate of about 15-20 per cent per Gyr when measured at $0.01 R_{200}$ and of 1 per cent when the increase is evaluated at $0.2 R_{200}$. + After 10 Gyr. the ratio between these values is about 35. a factor ~4+5 larger than the ratio measured at the beginning of the formation of the cooling core.," After 10 Gyr, the ratio between these values is about 35, a factor $\sim 4-5$ larger than the ratio measured at the beginning of the formation of the cooling core." + The surface brightness. roughly proportional to the integral along the line of sight of the squared density. amplities the variations. observed in the density profile and is observed to increase with a mean rate of 16 and | per cent per Gyr at 0.01 and 02ους. respectively. with a ratio that rises from 10 to 60-70 at the present time. both in cool and hot systems.," The surface brightness, roughly proportional to the integral along the line of sight of the squared density, amplifies the variations observed in the density profile and is observed to increase with a mean rate of 16 and 1 per cent per Gyr at $0.01$ and $0.2 R_{200}$, respectively, with a ratio that rises from 10 to 60–70 at the present time, both in cool and hot systems." + To characterize the evolution of the cooling core. we consider the results of the modelization of the radial profiles of the X-ray quantities as function of the cosmic time.," To characterize the evolution of the cooling core, we consider the results of the modelization of the radial profiles of the X-ray quantities as function of the cosmic time." +" We model the gas temperature. density and surface brightness profiles shown in Figure | with analytic formulae commonly used in the literature. which provide a good description of both observed and simulated profiles: where ry and.r, are the radius rescaled for the corresponding scale radius (e.g. rg=αυ or rfíb, or ου)."," We model the gas temperature, density and surface brightness profiles shown in Figure \ref{fig:prof} with analytic formulae commonly used in the literature, which provide a good description of both observed and simulated profiles: where $x_0$ and $x_1$ are the radius rescaled for the corresponding scale radius (e.g., $x_0=r/a_0$ or $r/b_0$ or $r/c_0$ )." + To avoid some degeneracy among the parameters describing the temperature oofile. we fix the inner scale radius. ay. to 0.052544.," To avoid some degeneracy among the parameters describing the temperature profile, we fix the inner scale radius, $a_0$, to $0.05 R_{200}$." + A least squares fit is then performed between 0.010ου and 0.54200. where the numerical simulations provide more robust results. wopagating a relative. error comparable to. the. observational constraints (without any significant change in the best-fit results. we have adopted errors in the range of few per cent on the surface brightness. 5-15 per cent on the gas density. [0-20 per cent on the emperature values).," A least squares fit is then performed between $0.01 R_{200}$ and $0.5 R_{200}$, where the numerical simulations provide more robust results, propagating a relative error comparable to the observational constraints (without any significant change in the best-fit results, we have adopted errors in the range of few per cent on the surface brightness, 5-15 per cent on the gas density, 10-20 per cent on the temperature values)." + In general. single power-laws provides a good description of hese profiles over partial sections of the radial profile. suggesting hat cooling alone is not able to reproduce an emission shaped with an inner. well-detined core.," In general, single power-laws provides a good description of these profiles over partial sections of the radial profile, suggesting that cooling alone is not able to reproduce an emission shaped with an inner, well-defined core." + For instance. while a single -7 model well reproduces the outskirts of the gas density and surface brightness profile. a second inner component. either a power-law as in equation.," For instance, while a single $\beta-$ model well reproduces the outskirts of the gas density and surface brightness profile, a second inner component, either a power-law as in equation." + |. or an additive 2. model. is characterized by very small core radii. of the order of the lower end of the investigated radial range of0.01 Aoou. and a factor between 5 and 10 lower than the external core radius.," \ref{eq:fit} or an additive $\beta-$ model, is characterized by very small core radii, of the order of the lower end of the investigated radial range of$0.01 R_{200}$ , and a factor between 5 and 10 lower than the external core radius." + A power-law | constant describes properly the gas entropy profile. A=Zn22/45 H," A power-law $+$ constant describes properly the gas entropy profile, $K=T_{\rm gas}/n_{\rm gas}^{2/3}$ ," + A power-law | constant describes properly the gas entropy profile. A=Zn22/45 H»," A power-law $+$ constant describes properly the gas entropy profile, $K=T_{\rm gas}/n_{\rm gas}^{2/3}$ ," + A power-law | constant describes properly the gas entropy profile. A=Zn22/45 H»c," A power-law $+$ constant describes properly the gas entropy profile, $K=T_{\rm gas}/n_{\rm gas}^{2/3}$ ," +with the best fitting values and 68.3 per cent. confidence intervals for Aosoo from(2008).,with the best fitting values and 68.3 per cent confidence intervals for $M_{2500}$ from. +.. We fit à power-law to the data using the err algorithm of(2007).. assuming independent. log-normal measurement The resulting best fit. shown inClI.. has a slope of 1.91x 0.19.," We fit a power-law to the data using the algorithm of, assuming independent, log-normal measurement The resulting best fit, shown in, has a slope of $1.91\pm0.19$ ." +are determined from the sample of 34 V. band. sources in common between the and the Weck frames.,are determined from the sample of 34 $V$ band sources in common between the and the Keck frames. + Due to USTs high spatial resolution. we are confident that the vast majority of sources that appear in the final list are GCs and hence use them to refine our Weck canclicdate list.," Due to 's high spatial resolution, we are confident that the vast majority of sources that appear in the final list are GCs and hence use them to refine our Keck candidate list." + The following criteria. were applied to the 615 objects in common between the Keck 2. V and. J frames: (a) 21.5«V25.0. (b) 2.5$ $^{\circ}$, $^{\circ}$ and $^{\circ}$ respectively to be physically possible $_{corot}>$ 0)." + A summary of the limitations on the inclination of the pulsational axis is given in Table 1., A summary of the limitations on the inclination of the pulsational axis is given in Table 1. + From this table it can be seen which are the physically possible values of i ancl inclination that we are unable (o test due to the FAMILIAS model restrictions., From this table it can be seen which are the physically possible values of $m$ and inclination that we are unable to test due to the FAMIAS model restrictions. +" However. these ""holes? can be mitigated by the fact that at lower inclinations than those imposed by the model limits. the v value. ancl hence the Coriolis lorce. becomes laree enough that the pulsations surface deformations begin to be limited to an equatorial waveguide (Townsend2003)."," However, these “holes” can be mitigated by the fact that at lower inclinations than those imposed by the model limits, the $\nu$ value, and hence the Coriolis force, becomes large enough that the pulsations surface deformations begin to be limited to an equatorial waveguide \citep{To03}." +. In these cases just the regions about (he equator are varving. bul we would be viewing the star [rom low inclinations.," In these cases just the regions about the equator are varying, but we would be viewing the star from low inclinations." + This means that only a small area of the visible surface would be experiencing pulsation ancl (he radial velocity amplitude would be expected to be low when compared will observed racial velocity amplitudes in other ? DDor stars., This means that only a small area of the visible surface would be experiencing pulsation and the radial velocity amplitude would be expected to be low when compared with observed radial velocity amplitudes in other $\gamma$ Dor stars. + To give an example of this. i£ /=20° and the mode was i50 (hen approximately one quarter of the full surface variability is visible since more than half the pulsation amplitude is constrained to within 35° of the equator.," To give an example of this, if $i$ $^{\circ}$ and the mode was $m$ =0 then approximately one quarter of the full surface variability is visible since more than half the pulsation amplitude is constrained to within $^{\circ}$ of the equator." + In contrast. the + frequency in question has an amplitude of 1.09 ss.| which is comparable to the radial velocity amplitudes of the strongest mode in other 5 DDor stars e.g. 1.3 ! in + DDoradus (Dalonaetal.1996)... 0.35 ! in ILD49434 (Uvtterhoevenetal.2008)... 1.45 ! in HIDIS9631 and 0.49 ! in ΗΤΟ (Alaisonnenveetal.2010).," In contrast, the $^{-1}$ frequency in question has an amplitude of 1.09 $^{-1}$ which is comparable to the radial velocity amplitudes of the strongest mode in other $\gamma$ Dor stars e.g. 1.3 $^{-1}$ in $\gamma$ Doradus \citep{Bl96}, 0.35 $^{-1}$ in HD49434 \citep{Ut08}, 1.45 $^{-1}$ in HD189631 and 0.49 $^{-1}$ in HD40745 \citep{Ms10}." +. Therefore. it is unlikely that we are dealing with a strong Coriolis force and hence a high ν΄ value for a given mm value.," Therefore, it is unlikely that we are dealing with a strong Coriolis force and hence a high $\nu$ value for a given $m$ value." + Because of this the inclination “holes” mentioned previously. which are associated with hieh v values. can be considered as unlikely solutions.," Because of this the inclination “holes” mentioned previously, which are associated with high $\nu$ values, can be considered as unlikely solutions." + All (€ and m. combinations from (=0 to (=3 were tested keeping in mind the restrictions [rom Table 1., All $\ell$ and $m$ combinations from $\ell$ =0 to $\ell$ =3 were tested keeping in mind the restrictions from Table 1. + Higher values of / were not considered because the 1.9875 d! Is a slrong photometric frequency found in (he data ol Zerbietal.(1999) and modes with f ; 3arehardtodeteetinsuchg. basedpholomelricsludiesduelogeamelriccancellatione |feels, Higher values of $\ell$ were not considered because the 1.9875 $^{-1}$ is a strong photometric frequency found in the data of \cite{Ze99} and modes with $\ell$ $>$ 3 are hard to detect in such ground-based photometric studies due to geometric cancellation effects. + PheinpulparametersloP AALAS wereperin, The input parameters to FAMIAS were permitted to vary as shown in Table 2. + , The two best fitting modes with different $\ell$ +115..65..71.. 39.. 105.. 1,", L45. ," +17.. 111.. 318.. 25.. 117.. ," 174.," +193.. LL. 207.. 171.22...13.. 517. 9.. [," 547. , [" +25| MfcAlister IT. A. & ITartkopf W.,25] McAlister H. A. & Hartkopf W. +"or equivalentIv For a universe with Q4,=0.3. Oy=0.7. and Ly)=50 km ! |. ? find the best-fit parameters to be 9,=3.41. %=1.58. hy=1.36. à=-0.27. Mj,=—22.65. and ο)—0.36x10."" * ","or equivalently For a universe with $\Omega_M = 0.3$ , $\Omega_\Lambda = 0.7$ , and $H_0 = +50$ km $^{-1}$ $^{-1}$, \citet{twodf:lf} find the best-fit parameters to be $\beta_1 = 3.41$, $\beta_2 = 1.58$, $k_1 = 1.36$, $k_2 = +-0.27$, $M_B^\ast = -22.65$, and $\phi^\ast = 0.36\times +10^{-6}$ $^{-3}$ $^{-1}$." +With the above functional form of the Iuminositv finetion. the observed magnification distribution can be written in terms of a hypergeometric function: to be the ratio of the sample flux limit to the characteristic luminosity of the luminosity function. Z(2)=L.(z)/L5(z). In practice. the normalization constant for this equation can be easily computed numerically by integrating pi(qiz)dp.," With the above functional form of the luminosity function, the observed magnification distribution can be written in terms of a hypergeometric function: where I have defined $R(z)$ to be the ratio of the sample flux limit to the characteristic luminosity of the luminosity function, $R(z) = +L_s(z)/L_B^\ast(z)$ In practice, the normalization constant for this equation can be easily computed numerically by integrating $p_s(\mu;z)\,d\mu$." + Ol course.the observed. luminosity ΠΟΙΟ itself. will be slightly. modified. from the intrinsic form. because of lensing.," Of course,the observed luminosity function itself will be slightly modified from the intrinsic form because of lensing." +" IQ, is large enough to cause significant lensing. then the intrinsic humninositv function will have a steeper slope (han what is actually observed (?7?).."," If $\Omega_c$ is large enough to cause significant lensing, then the intrinsic luminosity function will have a steeper slope than what is actually observed \citep{lens:vietri,lens:schneider-ext-source}." +" For the purposes of calculating the flux ratio (2) aud the amplification bias. il is assumed that these chanees in the Iuminosity functions slope are of second order in O,."," For the purposes of calculating the flux ratio $R(z)$ and the amplification bias, it is assumed that these changes in the luminosity function's slope are of second order in $\Omega_c$." + Since it is already. believed from ? μα O.<0.1. the effect on the luminosity [function would be negligible.," Since it is already believed from \citet{lens:dalcanton} that $\Omega_c < 0.1$, the effect on the luminosity function would be negligible." + If in fact the intrinsic luminosity function were steeper. (hen (the amplification bias would be greater: hence. ignoring the effects of lensing on the luminosity finetion leads lo more conservative Constraints on O..," If in fact the intrinsic luminosity function were steeper, then the amplification bias would be greater; hence, ignoring the effects of lensing on the luminosity function leads to more conservative constraints on $\Omega_c$." +" For a survey wilh an apparent D magnitude limit m. the flux ratio (2) can be expressed as follows: where d,(2)=(142)?DCz) is the luminosity distance. and the last term is the IX correction for an object with spectral energy distribution f,xv"". a fairly good approximation to the quasar UV/optical continuum."," For a survey with an apparent $B$ magnitude limit $m_s$, the flux ratio $R(z)$ can be expressed as follows: where $d_\ell(z) = (1+z)^2 D(z)$ is the luminosity distance, and the last term is the K correction for an object with spectral energy distribution $f_\nu \propto \nu^{-\alpha}$, a fairly good approximation to the quasar UV/optical continuum." + ? find that a=0.5 for quasars drawn [rom SDSS data., \citet{sdss:qso-composite} find that $\alpha = 0.5$ for quasars drawn from SDSS data. +" As discussed later in Section 3.1.. the SDSS quasar magnitude limit is expressed in /* rather than D: 1 compensate by adding a constant colortemmD—;=0.35 to the 7* limit to obtain m,inthe above equation (?).. Figure 3. plots the flux ratio as a Iunction of redshift for the SDSS Quasar Catalog and using the 2dF huninosity. function."," As discussed later in Section \ref{sec:edr}, the SDSS quasar magnitude limit is expressed in $\iband$ rather than $B$; I compensate by adding a constant colorterm$B-i = 0.35$ to the $\iband$ limit to obtain $m_s$ in the above equation \citep{sdss:edr-qsocat}.. Figure \ref{fig:Rz} plots the flux ratio as a function of redshift for the SDSS Quasar Catalog and using the 2dF luminosity function." +and potentially break the degeneracy with an expansion replicating dark energy.,and potentially break the degeneracy with an expansion replicating dark energy. + It also highlights the possibility of searching for signatures of modified gravity in current data by looking for changes in the growth of structure., It also highlights the possibility of searching for signatures of modified gravity in current data by looking for changes in the growth of structure. +" However, even if we do have a plethora of new and viable physical principles that explain dark energy naturally we might want a way to quantify how these models affect this growth signature."," However, even if we do have a plethora of new and viable physical principles that explain dark energy naturally we might want a way to quantify how these models affect this growth signature." + If we do not have the models we might just want to test the influx of data for of something unusual., If we do not have the models we might just want to test the influx of data for of something unusual. + Either way it is possible to parameterise this extra growth., Either way it is possible to parameterise this extra growth. + This notion of parameterising growth is analogous to the familiar parameterisation of the background expansion into wo and Wa., This notion of parameterising growth is analogous to the familiar parameterisation of the background expansion into $w_{0}$ and $w_{a}$. + This is sufficient in describing and restricting the multitude of possible dark energy models and expansion histories., This is sufficient in describing and restricting the multitude of possible dark energy models and expansion histories. + It is now common procedure to examine data and convert it into constraints on various cosmological parameters including wo and wa., It is now common procedure to examine data and convert it into constraints on various cosmological parameters including $w_{0}$ and $w_{a}$. + We might therefore like to extend this parameter space and allow for the additional signatures of gravity., We might therefore like to extend this parameter space and allow for the additional signatures of gravity. +" One possible parameterisation for growth is given by y in Equation and was first introduced by ? and ? and later discussed in ?,, ?,, ? and ?.."," One possible parameterisation for growth is given by $ \gamma $ in Equation and was first introduced by \citet{Peebles08} and \citet{Lahav91} and later discussed in \citet{Wang98}, \citet{linder05}, , \citet{HutererLinder07} and \citet{linderCahn07}." + By once again looking at Figure 1 we can see that the growth factor g(a) is affected by the expansion history and by the gravitational framework., By once again looking at Figure \ref{fig:growths} we can see that the growth factor g(a) is affected by the expansion history and by the gravitational framework. +" It is worth noting that the y parameterisation distinguishes the two contributions to the growth, encapsulating the latter in isolation."," It is worth noting that the $\gamma$ parameterisation distinguishes the two contributions to the growth, encapsulating the latter in isolation." + This is due to the impact from the expansion being absorbed into Qm(a) thus leaving Υ to pick out any remaining remaining contribution., This is due to the impact from the expansion being absorbed into $\Omega_{m}(a)$ thus leaving $\gamma$ to pick out any remaining remaining contribution. + It is in this way that y has become known as a modified gravity or beyond-Einstein parameter., It is in this way that $\gamma$ has become known as a modified gravity or beyond-Einstein parameter. + It is easy to see why given that it detects changes to the growth not associated with expansion., It is easy to see why given that it detects changes to the growth not associated with expansion. +" This could be down to a change in the force law acting on matter represented, for example, by the extra factor in Equation(9)."," This could be down to a change in the force law acting on matter represented, for example, by the extra factor in Equation." +" And as we alluded to earlier, evident in Figure 1,, this allows us to distinguish between dark energy and modified gravity."," And as we alluded to earlier, evident in Figure \ref{fig:growths}, this allows us to distinguish between dark energy and modified gravity." +" However, as highlighted in ? there exists an interesting caveat."," However, as highlighted in \citet{KunzSapone07} there exists an interesting caveat." + They found that contrary to Figure 1 one could force some arbitrary and generic dark energy to replicate the growth of DGP., They found that contrary to Figure \ref{fig:growths} one could force some arbitrary and generic dark energy to replicate the growth of DGP. + This was achieved by allowing for dark energy models with lower sound speeds (cj# 1) which in turn induce clustering in the fluid., This was achieved by allowing for dark energy models with lower sound speeds $c_{s}^{2} \neq 1$ ) which in turn induce clustering in the fluid. + The clustering instigates a deepening of the gravitational potential wells thus leading to a magnification in the metric perturbations and subsequently an increase in the growth., The clustering instigates a deepening of the gravitational potential wells thus leading to a magnification in the metric perturbations and subsequently an increase in the growth. + In addition the existence of anisotropic stress was permitted which had the effect of suppressing growth., In addition the existence of anisotropic stress was permitted which had the effect of suppressing growth. + With a careful balance between stress and sound speed they succeeded in replicating g(a) for DGP., With a careful balance between stress and sound speed they succeeded in replicating g(a) for DGP. +" Now although highly fine tuned it is worth keeping in mind that observationally detecting some non-LCDM growth factor, or -y, would therefore not necessarily constitute modified gravity."," Now although highly fine tuned it is worth keeping in mind that observationally detecting some non-LCDM growth factor, or $\gamma$, would therefore not necessarily constitute modified gravity." +" In this way, unless one allows for only smooth non-clustering dark energy the growth parameter is not just a modified gravity parameter."," In this way, unless one allows for only smooth non-clustering dark energy the growth parameter is not just a modified gravity parameter." + Instead it has the ability to pick up on clustered dark energy and modified gravity both of which would be interesting., Instead it has the ability to pick up on clustered dark energy and modified gravity both of which would be interesting. + Given the above it is therefore our intention to test the growth parameter and see whether current data or a future probe can pick out this subtle but potentially important effect., Given the above it is therefore our intention to test the growth parameter and see whether current data or a future probe can pick out this subtle but potentially important effect. +" Indeed there exists a few early attempts, including constraints from peculiar velocity measurements from low redshift Supernovae (?)) as well as future survey forecasts from ?,, ? and ?.."," Indeed there exists a few early attempts, including constraints from peculiar velocity measurements from low redshift Supernovae \citealt{Abate08}) ) as well as future survey forecasts from \citet{AmendolaKunzSapone07}, \citet{HutererLinder07} and \citet{HeavensKitchingVerde07}." + Figure 3 demonstrates the result of varying this parameter on the linear growth factor., Figure \ref{fig:gamma_growths} demonstrates the result of varying this parameter on the linear growth factor. + The growth for standard LCDM corresponds to y=0.55 whereas for flat DGP it corresponds to y=0.68., The growth for standard LCDM corresponds to $\gamma = 0.55$ whereas for flat DGP it corresponds to $\gamma=0.68$. + In this way it is clear that a higher growth parameter results in a suppression of growth., In this way it is clear that a higher growth parameter results in a suppression of growth. + It is worthwhile noting that other attempts at parameterising modified gravity have been made which aspire to encapsulate the properties of gravity similar to the Parameterised Post-Newtonian (PPN) parameters for local gravity constraints (7))., It is worthwhile noting that other attempts at parameterising modified gravity have been made which aspire to encapsulate the properties of gravity similar to the Parameterised Post-Newtonian (PPN) parameters for local gravity constraints \citealt{Will93}) ). +" For example, these include parameterising the relationship between the two metric potentials (ó and w) and/or quantifying any modification to the Poisson equation (E.g. ?,, ?,, ?,, ?,, ? and ?))."," For example, these include parameterising the relationship between the two metric potentials $\phi$ and $\psi$ ) and/or quantifying any modification to the Poisson equation (E.g. \citet{AmendolaKunzSapone07}, \citet{HuSawicki07b}, \citet{IshakUpadhyeSpergel05}, \citet{Jain07}, \citet{Daniel08} and \citet{BertschingerZukin08}) )." + In fact these observations lead us on to the final modified gravity signature and characteristicwe must consider before our analysis with weak lensing., In fact these observations lead us on to the final modified gravity signature and characteristicwe must consider before our analysis with weak lensing. + For any deviation in the Poisson equation or between the metric potentials causes a, For any deviation in the Poisson equation or between the metric potentials causes a +observed at the VLA we used the VLA coordinates of the radio core.,observed at the VLA we used the VLA coordinates of the radio core. + In case the radio core was not detected we used the WENSS positions of the radio sources and we found it useful to overlay the VLA radio maps. when available. on our IR frames.," In case the radio core was not detected we used the WENSS positions of the radio sources and we found it useful to overlay the VLA radio maps, when available, on our IR frames." + For positioning the radio structure over our IR images. we needed astrometric information for our IR images.," For positioning the radio structure over our IR images, we needed astrometric information for our IR images." + This was obtained using stellar objects in common between our images and R-band CCD images for which the astrometric work was already done (Rengelink and Snellen. private communications). or. when these were not available. using optical sky maps extracted from the digitized sky survey (DSS) plates available at the Space Telescope Science Institute.," This was obtained using stellar objects in common between our images and $R$ -band CCD images for which the astrometric work was already done (Rengelink and Snellen, private communications), or, when these were not available, using optical sky maps extracted from the digitized sky survey (DSS) plates available at the Space Telescope Science Institute." + The accuracy of our astrometric work depends on several factors: the uncertainties in the optical right ascension and declination positions; the errors in the radio positions: the accuracy in the radio/IR overlay procedure., The accuracy of our astrometric work depends on several factors: the uncertainties in the optical right ascension and declination positions; the errors in the radio positions; the accuracy in the radio/IR overlay procedure. + The accuracy of the optical positions from the DSS plates is about | to 2 aresec. depending on the distance of the object from the center of the Schmidt plate.," The accuracy of the optical positions from the DSS plates is about 1 to 2 arcsec, depending on the distance of the object from the center of the Schmidt plate." + The positional errors in the VLA radio maps are about | aresee or better., The positional errors in the VLA radio maps are about 1 arcsec or better. + The WENSS radio coordinates (used for some USS sources lacking VLA radio maps) have a 1 sigma error on the position better than 5 aresec., The WENSS radio coordinates (used for some USS sources lacking VLA radio maps) have a 1 sigma error on the position better than 5 arcsec. + For double sources that do not show an obvious radio core component. the extent of the radio source introduces an additional indetermination in the position of the IR counterpart.," For double sources that do not show an obvious radio core component, the extent of the radio source introduces an additional indetermination in the position of the IR counterpart." + Finally. the accuracy of our radio/IR overlay procedure is about 0.5 aresec.," Finally, the accuracy of our radio/IR overlay procedure is about 0.5 arcsec." + Taking into account all these uncertainties. we have accepted as good identifications those for which the distance between the radio and IR position ts less than 1.5 to 5 aresec. depending on the astrometric information available.," Taking into account all these uncertainties, we have accepted as good identifications those for which the distance between the radio and IR position is less than 1.5 to 5 arcsec, depending on the astrometric information available." + Tables |. 2. 3 list the coordinates of the IR counterparts.," Tables 1, 2, 3 list the coordinates of the IR counterparts." + In many cases. our IR detections provided us with an useful tool in order to confirm the identification of the fainter optical sources and to find the counterparts of the sources still lacking optical identifications.," In many cases, our IR detections provided us with an useful tool in order to confirm the identification of the fainter optical sources and to find the counterparts of the sources still lacking optical identifications." + Figure | shows the A- and J-band images of the sources for which we have an IR counterpart. even if uncertain.," Figure 1 shows the $K$- and $J$ -band images of the sources for which we have an IR counterpart, even if uncertain." + For all the IR counterparts. we measured the magnitudes using circular apertures with the minimum diameter which includes all the detected object flux.," For all the IR counterparts, we measured the magnitudes using circular apertures with the minimum diameter which includes all the detected object flux." + We tested this procedure by making several measurements with different aperture diameters., We tested this procedure by making several measurements with different aperture diameters. + In a few cases we adjusted the photometric aperture to correspond to that used for the same object on the optical image by Snellen., In a few cases we adjusted the photometric aperture to correspond to that used for the same object on the optical image by Snellen. + The size of the apertures and the measured magnitudes. corrected for galactic foreground extinction. are listed in Tables 1. 2 and 3 for the three samples respectively.," The size of the apertures and the measured magnitudes, corrected for galactic foreground extinction, are listed in Tables 1, 2 and 3 for the three samples respectively." + The photometric accuracy given in Tables |. 2. 3 has been evaluated from the measured fluctuations of the sky background around the source for measurement apertures equivalent to that used for source itself.," The photometric accuracy given in Tables 1, 2, 3 has been evaluated from the measured fluctuations of the sky background around the source for measurement apertures equivalent to that used for source itself." + If no IR counterpart is detected we give 30 upper limit based on the background fluctuations., If no IR counterpart is detected we give $\sigma$ upper limit based on the background fluctuations. + The J9A colours which we obtain for the USS sources and for the galaxies in the GPS sample are within the range of those observed for distant radio galaxies (e.g. Lilly Longair 1984)).01144331., The $J-K$ colours which we obtain for the USS sources and for the galaxies in the GPS sample are within the range of those observed for distant radio galaxies (e.g. Lilly Longair \cite{lilly}) ). + The object is resolved but round in A-band and has two companions at 4.5 aresee to the south-east which are not included in our photometry., The object is resolved but round in $K$ -band and has two companions at 4.5 arcsec to the south-east which are not included in our photometry. +0115502. The IR counterpart is at 3 aresec to the west of the central radio component., The IR counterpart is at 3 arcsec to the west of the central radio component. +0125344. We give as a tentative identification a faint object at 4 aresec to the south-east of the radio source which ts visible also in the /-band., We give as a tentative identification a faint object at 4 arcsec to the south-east of the radio source which is visible also in the $R$ -band. + 01274350.. We give as a tentative identification a compact object near the eastern component of the northeri radio lobe., We give as a tentative identification a compact object near the eastern component of the northern radio lobe. +01294-353.. Our identification Is at 3.6 arcsec to the south-west of the radio position., Our identification is at 3.6 arcsec to the south-west of the radio position. +01334320.. The faint object visible in 7. but not in WV corresponds to the optical identification (Rengelink. private communication).," The faint object visible in $J$ but not in $K$ corresponds to the optical identification (Rengelink, private communication)." +01354311.. Our tentative identification corresponds to a faint object in the /7-band., Our tentative identification corresponds to a faint object in the $R$ -band. + 01364-325.. We give the magnitude of the object at 3 aresec to the east of the central radio component., We give the magnitude of the object at 3 arcsec to the east of the central radio component. + It is visible also in the R-band., It is visible also in the $R$ -band. +01364333.. We have measured the object which ts at about half way between the two radio lobes., We have measured the object which is at about half way between the two radio lobes. +01394-375.. We give the magnitude of the object at 4 aresec to the south of the radio position., We give the magnitude of the object at 4 arcsec to the south of the radio position. +01404+323.. Our identification is at 6 aresec to the south of a brighter galaxy., Our identification is at 6 arcsec to the south of a brighter galaxy. +"01434360.. Our tentative identification is at + aresee to the north of the radio position,01484330.", Our tentative identification is at 4 arcsec to the north of the radio position. +. We have measured the three object shown in the figure., We have measured the three object shown in the figure. + The most likely but still uncertain identification ts the object number 3., The most likely but still uncertain identification is the object number 3. +"02024-300.. We give as a tentative identification the extended object visible only in .7 at 3 aresec to the north-west of the radio position,17024604.", We give as a tentative identification the extended object visible only in $J$ at 3 arcsec to the north-west of the radio position. +. The identification is just to the north of the southern radio lobe and corresponds to the galaxy visible in the #-band. for which the redshift has been measured (Bremer. private communicatio19134672.," The identification is just to the north of the southern radio lobe and corresponds to the galaxy visible in the $R$ -band, for which the redshift has been measured (Bremer, private communication)." +.. Our tentative identification is 2.5 aresee to the north-west of the radio position., Our tentative identification is 2.5 arcsec to the north-west of the radio position. +"23214223.. Our tentative identification is at 3 aresec to the north of the radio position,23344154.", Our tentative identification is at 3 arcsec to the north of the radio position. +. Of the 3 objects to the east of the radio position. we give as a tentative identification the closest one.," Of the 3 objects to the east of the radio position, we give as a tentative identification the closest one." +23344313... Our tentative identification ts the central object of the 3 around the radio position., Our tentative identification is the central object of the 3 around the radio position. +23514103.. The object has two components in both - and A- which we measured separately. 19584615., The object has two components in both $J$ - and $K$ -bands which we measured separately. . + The quasar ts at 3 arcsec to the north-west of a star (Snellen. PhD thesis).," The quasar is at 3 arcsec to the north-west of a star (Snellen, PhD thesis)." +contraction to planetesimal densities.,contraction to planetesimal densities. + But the important point remains. that by leaplrogeine intermediate size regimes. GI avoids the rapid inspiral of meter-sized boclies.," But the important point remains, that by leapfrogging intermediate size regimes, GI avoids the rapid inspiral of meter-sized bodies." + Unfortunatelv. a powerful argument has been developed against the GI scenario. which has led largely to its abandonment by modera workers in the field (Weidenschilling1995).," Unfortunately, a powerful argument has been developed against the GI scenario, which has led largely to its abandonment by modern workers in the field \citep{wei95}." +. A review of the difficulty is necessary before before we can justify a renewed attack on the basic idea., A review of the difficulty is necessary before before we can justify a renewed attack on the basic idea. + Even in an otherwise quiescent disk. midplane (urbulence may develop (o stir the particulate laver (oo vigorously to allow sufficient solid settling to the midplane.," Even in an otherwise quiescent disk, midplane turbulence may develop to stir the particulate layer too vigorously to allow sufficient solid settling to the midplane." + Without such settling the criterion (2)) cannot be satisfied., Without such settling the criterion \ref{Roche}) ) cannot be satisfied. + The problem lies in the vertical shear possessed bv disks with a highly stratified vertical distribution of solid to gas., The problem lies in the vertical shear possessed by disks with a highly stratified vertical distribution of solid to gas. + The particulate- sub-disk. which possesses near-INeplerian rotation. revolves somewhat faster than the surrounding gas disk. which has non-vanishing support against the inward pull of the sun from gas pressure in addition to centrifugal effects.," The particulate-dominated sub-disk, which possesses near-Keplerian rotation, revolves somewhat faster than the surrounding gas disk, which has non-vanishing support against the inward pull of the Sun from gas pressure in addition to centrifugal effects." +" The magnitude of the resulting velocity differential. No,=yeyΙΟ. is proportional to η, which roughly equals the ratio ol thermal to kinetic energy of the gas: where 2 is the gas pressure and ce, is the isothermal sound speed."," The magnitude of the resulting velocity differential, $\Delta v_\phi = \eta v_{\rm K} = \eta r \Omega$, is proportional to $\eta$, which roughly equals the ratio of thermal to kinetic energy of the gas: where $P$ is the gas pressure and $c_{\rm g}$ is the isothermal sound speed." +" In the popular model of the minimum solar nebula (hereafter MSN. see relseciprop)). 4c2xLOΑΙή, and Av,c50m/s al r=1 AU (Hayashi. 1981)."," In the popular model of the minimum solar nebula (hereafter MSN, see \\ref{sec:prop}) ), $\eta \simeq 2 \times 10^{-3} +(r/\mathrm{AU})^{1/2}$, and $\Delta v_\phi \simeq 50 +\,\mathrm{m/s}$ at $r=1$ AU (Hayashi 1981)." +" 'Turbulent eddies with a characterise velocity equal to the available velocity differential. ~ελ, would then prevent GI. since the Toomre ( criterion requires that the particle random velocity be much smaller: ej<7cm/sNo. lor instability. (Weidenschilling 1995)."," Turbulent eddies with a characteristic velocity equal to the available velocity differential, $\sim\Delta v_\phi$, would then prevent GI, since the Toomre $Q$ criterion requires that the particle random velocity be much smaller: $c_{\rm +p} < 7 \cm/{\mathrm s} \ll \Delta v_\phi$, for instability (Weidenschilling 1995)." + These general arguments are supported by nunerical simulations (Cuzzi.Dobrovol-skis.&Champnev1993) which calculate the steady state properties of (wo-plase (gas and parüculate) turbulence in the midplane of a MSN disk., These general arguments are supported by numerical simulations \citep{cdc93} which calculate the steady state properties of two-phase (gas and particulate) turbulence in the midplane of a MSN disk. + Particulates with internal densities ol normal rock and with sizes from LO to GOem (which are assumed {ο have grown by other mechanisms and are moderately coupled to gas motions) acquire space densities too low for GI by an order of magnitude or more., Particulates with internal densities of normal rock and with sizes from $10$ to $60 \cm$ (which are assumed to have grown by other mechanisms and are moderately coupled to gas motions) acquire space densities too low for GI by an order of magnitude or more. + Their computational methods use a mixing length prescription to relate diffusivity ancl velocity shear through an extrapolation lrom laboratory studies of boundary Iavers., Their computational methods use a mixing length prescription to relate diffusivity and velocity shear through an extrapolation from laboratory studies of boundary layers. + While quite sophisticated. this approach does not directly address ihe mechanism by which the existence of the vertical shear generates turbulence.," While quite sophisticated, this approach does not directly address the mechanism by which the existence of the vertical shear generates turbulence." + Using a linear stability analvsis. Sekiva(1998). confirmed that GI in a turbulent dust," Using a linear stability analysis, \citet{sek98} confirmed that GI in a turbulent dust" +disk total luminosity Logj;4; is half the accretion luminosity and each [ace of the disk radiates μι.,disk total luminosity $L_{disk}$ is half the accretion luminosity and each face of the disk radiates $L_{disk}/2$. +" This is so. because the matter at the inner edge ol the disk (r22 R,) retains the remaining accretion energy in the form of kinetic energy. as 1 rotates at Keplerian speed."," This is so, because the matter at the inner edge of the disk $r \approx R_*$ ) retains the remaining accretion energy in the form of kinetic energy, as it rotates at Keplerian speed." + The effective surface temperature of such a disk is given by 1981): where i=r/fi. and σ the Stefan-Doltzmann constant.," The effective surface temperature of such a disk is given by \citep{sha73,lyn74,pri81}: where $x=r/R_*$, and $\sigma$ the Stefan-Boltzmann constant." + For practical purpose the last relation is usually written From this it is seen (hat accretion disks arouncl WD stars emit their energv in (he optical and UV., For practical purpose the last relation is usually written From this it is seen that accretion disks around WD stars emit their energy in the optical and UV. +" The above relation is obtained by assuming a no-shear boundary condition. QQ/Or=0. al the stellar surface r=2, (Pringle1981)."," The above relation is obtained by assuming a no-shear boundary condition, $\partial \Omega / \partial r =0$, at the stellar surface $r=R_*$ \citep{pri81}." +. Therefore. this model does not take into account the relatively slow rotation of the WD. and it gives a disk temperature T—0E (!)," Therefore, this model does not take into account the relatively slow rotation of the WD, and it gives a disk temperature T=0K (!)" +" at the stellar surface (r= R,). and a maximum temperature ως=0.48870 at c=1.36."," at the stellar surface $r=R_*$ ), and a maximum temperature $T_{max}=0.488 T_0$ at $x=1.36$." + This model also neglects the spin up of the star bv the disk., This model also neglects the spin up of the star by the disk. + This relation. however. gives a good approximation of the effective surface temperature in the disk al larger radii (5>> 4).," This relation, however, gives a good approximation of the effective surface temperature in the disk at larger radii $r>>R_*$ )." + For a typical high mass accretion rate οἱ /vr. the maximum temperature in the inner disk reaches about 50.000Ix-100.000]. and the inner disk become (he strongest emission source of the svstem in the UV.," For a typical high mass accretion rate of $\dot{M}= 1 \times 10^{-8}M_{\odot}$ /yr, the maximum temperature in the inner disk reaches about 50,000K-100,000K, and the inner disk become the strongest emission source of the system in the UV." +" During the low state of NLs (or quiescent state of DNs) the mass mass accretion rate decreases down to Mc10.AL, /vr. while the maximum temperature drops to less than 210.000. making the disk peak in the optical and barely emit any flux in the UV."," During the low state of NLs (or quiescent state of DNs) the mass mass accretion rate decreases down to $\dot{M} \approx 10^{-12} M_{\odot}$ /yr, while the maximum temperature drops to less than $\approx$ 10,000K, making the disk peak in the optical and barely emit any flux in the UV." + The standard disk moclel is a good approximation for rk22A. but in the inner disk region. one needs to moclel the BL between the slowly rotating stellar surface and its Ixeplerian accretion disk.," The standard disk model is a good approximation for $r>>R_*$, but in the inner disk region, one needs to model the BL between the slowly rotating stellar surface and its Keplerian accretion disk." + We would like also to note here that contrary (ο accreting neutron stars. (he irradiation of the disk by the heated WD and DL is negligible in accreting WDs (vanParaclijs&AleClintock 1993).. and one does not need (o take it into account when modeling accretion disks in CVs.," We would like also to note here that contrary to accreting neutron stars, the irradiation of the disk by the heated WD and BL is negligible in accreting WDs \citep{van94,sha98,kin98}, , and one does not need to take it into account when modeling accretion disks in CVs." +Furthermore. large-scale simulations are computationally costly (even when they sacrifice completeness for speed by ignoring hydrodynamic processes) and thus are inefficient in large parameter studies.,"Furthermore, large-scale simulations are computationally costly (even when they sacrifice completeness for speed by ignoring hydrodynamic processes) and thus are inefficient in large parameter studies." + On the other hand. analytic models. while more approximate. are fast and can provide physical insight into the import of various processes.," On the other hand, analytic models, while more approximate, are fast and can provide physical insight into the import of various processes." + However. analytical models are hard-pressed to go beyond the linear regime. and beyond making fairly simple predictions such as the mean 21-em signal (2).. the probability density function (PDF: ?)) and power spectrum (?2)..," However, analytical models are hard-pressed to go beyond the linear regime, and beyond making fairly simple predictions such as the mean 21-cm signal \citep{Furlanetto06}, the probability density function (PDF; \citealt{FZH04_21cmtop}) ) and power spectrum \citep{PF07, Barkana09}." + The 21-em tomographie signal should be rich in information. accommodating many additional. higher-order statistical probes. such as the bi-Palyectrum (Pritchard et al..," The 21-cm tomographic signal should be rich in information, accommodating many additional, higher-order statistical probes, such as the bi-spectrum (Pritchard et al.," + in preparation). the difference PDF (?).. ete.," in preparation), the difference PDF \citep{BL08}, etc." + In this paper. we follow a path of compromise. attempting to reserve the most useful elements of both analytic and numeric approaches.," In this paper, we follow a path of compromise, attempting to preserve the most useful elements of both analytic and numeric approaches." +re We introduce a self-consistent. simulation. specifically optimized to predict the high-redshift 2|-em signal.," We introduce a self-consistent, simulation, specifically optimized to predict the high-redshift 21-cm signal." + Through a combination of the excursion-set ormalism and perturbation theory. our code can generate full 3D realizations of the density. ionization. velocity. spin temperature. and ultimately 21-em brightness temperature fields.," Through a combination of the excursion-set formalism and perturbation theory, our code can generate full 3D realizations of the density, ionization, velocity, spin temperature, and ultimately 21-cm brightness temperature fields." + Although he physical processes are treated with approximate methods. our results agree well with a state-of-the-art hydrodynamic simulation of reionization.," Although the physical processes are treated with approximate methods, our results agree well with a state-of-the-art hydrodynamic simulation of reionization." + However. unlike numerical simulations. realizations are computationally cheap and can be generated in a matter of minutes on a single processor. with modest memory requirements.," However, unlike numerical simulations, realizations are computationally cheap and can be generated in a matter of minutes on a single processor, with modest memory requirements." + Most importantly. our code is publicly available at httpz/Awww.astro.princeton.edu/- mesinger/Sim.html.," Most importantly, our code is publicly available at $\sim$ mesinger/Sim.html." + We name our simulation2/cmFAST., We name our simulation. +" Semi-Numerical approaches have already proved invaluable in reionization studies (22222?,)., "," Semi-Numerical approaches have already proved invaluable in reionization studies \citep{Zahn05, MF07, GW08, Alvarez09, CHR09, Thomas09}." +Indeed. 21e6mFAST is a more specialized. version. of our previous code. DexM (?:: hereafter MFO07).," Indeed, 21cmFAST is a more specialized version of our previous code, DexM \citealt{MF07}; hereafter MF07)." + The difference between the two is that 2IemFAST bypasses the halo finding algorithm. resulting in a faster code with a larger dynamic range and more modest memory requirements.," The difference between the two is that 21cmFAST bypasses the halo finding algorithm, resulting in a faster code with a larger dynamic range and more modest memory requirements." + In this work. we also introduce some new additions to our code. mainly to compute the spin temperature.," In this work, we also introduce some new additions to our code, mainly to compute the spin temperature." + In $2.. we compare predictions from 21emFAST with those from hydrodynamic simulations of the various physical components comprising the 21-em signal in the post heating regime.," In \ref{sec:post_heat}, we compare predictions from 21cmFAST with those from hydrodynamic simulations of the various physical components comprising the 21-cm signal in the post heating regime." + Density. ionization. peculiar velocity gradient. and full2|-em brightness temperature fields are explored in 32.1.. $2.2. $2.3... 82.4... respectively.," Density, ionization, peculiar velocity gradient, and full21-cm brightness temperature fields are explored in \ref{sec:den}, \ref{sec:ion}, \ref{sec:dvdr}, \ref{sec:21cm_cmp}, respectively." + In. $3... we introduce our method for computing the spin temperature fields. with results from the complete caleulation (including the spin temperature) presented in $3.3..," In \ref{sec:heating}, we introduce our method for computing the spin temperature fields, with results from the complete calculation (including the spin temperature) presented in \ref{sec:results}." +" Finally in δι, we summarize our findings."," Finally in \ref{sec:conc}, we summarize our findings." + Unless stated otherwise. we quote all quantities in comoving units.," Unless stated otherwise, we quote all quantities in comoving units." + We adopt the background cosmological parameters (OV. Os. OQ. η. σε. Loy 0.046. 0.96. (072.028.0.82. 70 km s.1 +). matching the five-year results of the satellite (2)..," We adopt the background cosmological parameters $\Omega_\Lambda$, $\Omega_{\rm M}$, $\Omega_b$, $n$, $\sigma_8$, $H_0$ ) = (0.72, 0.28, 0.046, 0.96, 0.82, 70 km $^{-1}$ $^{-1}$ ), matching the five–year results of the satellite \citep{Komatsu09}." + Our ultimate goal is to compute the 21 em background. which requires a number of physies components.," Our ultimate goal is to compute the 21 cm background, which requires a number of physics components." + To identify them. note that the offset of the 21-em brightness temperature from the CMB temperature. 7-. along a line of sight (LOS) at observed frequency V. can be written as (c.f. 2)):," To identify them, note that the offset of the 21-cm brightness temperature from the CMB temperature, $\Tcmb$, along a line of sight (LOS) at observed frequency $\nu$ , can be written as (c.f. \citealt{FOB06}) ):" +" where 75 is the gas spin temperature. Τι, is the optical depth at the 2|-em frequeney Vy. (x.2)—pspLis the evolved (Eulerian) density contrast. //(2) is the Hubble parameter. de,dr is the comoving gradient of the line of sight component of the comoving velocity. and all quantities are evaluated at redshift >=μήν1."," where $T_S$ is the gas spin temperature, $\tau_{\nu_0}$ is the optical depth at the 21-cm frequency $\nu_0$ , $\delNL({\bf x}, z) \equiv \rho/\bar{\rho} - 1$ is the evolved (Eulerian) density contrast, $H(z)$ is the Hubble parameter, $dv_r/dr$ is the comoving gradient of the line of sight component of the comoving velocity, and all quantities are evaluated at redshift $z=\nu_0/\nu - 1$." +" The final approximation makes the assumption that that de,ff. which is generally true for the pertinent redshifts and /scales. though we shall return to this issue in $2.3."," The final approximation makes the assumption that that $dv_r/dr \ll H$ , which is generally true for the pertinent redshifts and scales, though we shall return to this issue in \ref{sec:dvdr}." + For tiducial astrophysical models. this is likely a safe assumption during the bulk of reionization (2272)..," For fiducial astrophysical models, this is likely a safe assumption during the bulk of reionization \citep{Furlanetto06, CM08, Santos08, Baek09}." + We will however revisit this assumption in $3.. where we introduce our method for computing the spin temperature field.," We will however revisit this assumption in \ref{sec:heating}, where we introduce our method for computing the spin temperature field." + The remaining components of eq., The remaining components of eq. +" |. are the density. 2j. the ionization. «yy. and the velocity gradient. do,fdr."," \ref{eq:delT} are the density, $\delNL$, the ionization, $\nf$, and the velocity gradient, $dv_r/dr$." + Below. we study these in turn. comparing 2lemFAST to the hydrodynamic cosmological simulation of 2..(ICs).," Below, we study these in turn, comparing 21cmFAST to the hydrodynamic cosmological simulation of \citet{TCL08},." +" We perform ""by-eve"" comparisons at various redshifts/stages of reionization. as well as one and two-point statistics: the PDFs (smoothed on several scales). and the power spectra."," We perform “by-eye” comparisons at various redshifts/stages of reionization, as well as one and two-point statistics: the PDFs (smoothed on several scales), and the power spectra." + Since our code is designed to simulate the cosmological 21-em signal from neutral hydrogen. we study the regime before the likely completion of reionization. >—1 (though present data is even consistent with reionization completing at 2 <6: 22).," Since our code is designed to simulate the cosmological 21-cm signal from neutral hydrogen, we study the regime before the likely completion of reionization, $z\gsim7$ (though present data is even consistent with reionization completing at $z\lsim$ 6; \citealt{Lidz07, Mesinger09}) )." +" The simulations of ? are the current. ""state-of-the-art"" reionization simulations.", The simulations of \citet{TCL08} are the current “state-of-the-art” reionization simulations. +" They include simultaneous treatment of dark matter (DM) and gas. five-frequeney radiative transfer (RT) onal2? grid. and they resolve My,2ο ionizing sources with —40 DM particles ina 143 Mpc box."," They include simultaneous treatment of dark matter (DM) and gas, five-frequency radiative transfer (RT) on a $^3$ grid, and they resolve $M_{\rm halo}\gsim10^8 \Msun$ ionizing sources with $\gsim 40$ DM particles in a 143 Mpc box." + We calculate the evolved density field in the same fashion as in the “parent” code. DexM. outlined in ΜΕΟΖ.," We calculate the evolved density field in the same fashion as in the “parent” code, DexM, outlined in MF07." + In short. we generate density and velocity ICs in initial (Lagrangian) space. in roughly the same manner as numerical cosmological simulations.," In short, we generate density and velocity ICs in initial (Lagrangian) space, in roughly the same manner as numerical cosmological simulations." + We then approximate gravitational collapse by moving each initial matter particle (whose mass is the total mass in the corresponding IC cell) according to first-order perturbation theory (2)..., We then approximate gravitational collapse by moving each initial matter particle (whose mass is the total mass in the corresponding IC cell) according to first-order perturbation theory \citep{ZelDovich70}. + First-order perturbation theory is very computationally convenient as the displacement field is a separable function of space and time. so the spatial component need only be computed once for each realization/box.," First-order perturbation theory is very computationally convenient as the displacement field is a separable function of space and time, so the spatial component need only be computed once for each realization/box." + There is no separate treatment of baryons and DM., There is no separate treatment of baryons and DM. + Readers interested in more details concerning this approach are encouraged to checkMFQ7., Readers interested in more details concerning this approach are encouraged to checkMF07. + Thisapproach to generating large-scale density fields was also adopted by ? and ?.. who briefly showed that the resulting fields at high-z traced the DM distribution from an N-body code fairly well.," Thisapproach to generating large-scale density fields was also adopted by \citet{CHR09} and \citet{Santos09}, , who briefly showed that the resulting fields at $z$ traced the DM distribution from an N-body code fairly well." + Here we perform more extensive comparisons., Here we perform more extensive comparisons. + The Lagrangian, The Lagrangian +and a concentration parameter e=fogtfr)0.94.,and a concentration parameter $c = log(r_t / r_c) = 0.94$. + A Paclova evolutionary model (Girardietal.2000) was chosen with log(ege(gr))=10.10 and Fe/H]—1.98., A Padova evolutionary model \citep{leo} was chosen with $\log(age(yr)) = 10.10$ and $[Fe/H] = -1.98$. + The simulated: cluster is placed. 10.8&pe away [rom the Sun with no recdcdening. for simplicity.," The simulated cluster is placed $10.8 kpc$ away from the Sun with no reddening, for simplicity." + We adopt à Ixroupa ME and choose not to include mass segregation., We adopt a Kroupa IMF and choose not to include mass segregation. + The adopted fraction of binaries for this simulations is of ., The adopted fraction of binaries for this simulations is of . +. Phe tical tails extend 1Ape in each direction. with a position angle of 45° and an angle with the plane of the sky of 207.," The tidal tails extend $1~kpc$ in each direction, with a position angle of $45^\circ$ and an angle with the plane of the sky of $20^\circ$." + The chosen tidal tails width is 16'=50pe., The chosen tidal tails width is $16 \arcmin = 50pc$. +" The simulated globular cluster has ~2105 stars with of them belonging to the tidal tail,"," The simulated globular cluster has $\sim 2\,10^4$ stars with of them belonging to the tidal tail." + The simulation was carried out. using the g and ¢ passbands from. DIES., The simulation was carried out using the $g$ and $r$ passbands from DES. + A 20deg? region of the Galaxy Liclel stars was simulated usingTrilegal., A $20 deg^2$ region of the Galaxy field stars was simulated using. +. These stars were uniformly spread. in a 24deg region around the simulated star cluster., These stars were uniformly spread in a $24 deg^2$ region around the simulated star cluster. + Photometric errors were added: based on SDSS + magnitudes. which is consistent with a photometric detection limit of à23.0.," Photometric errors were added based on SDSS $r$ magnitudes, which is consistent with a photometric detection limit of $r\sim23.0$." + This limit is also consistent with the observations of NGC 2298 (see $4.1 [or details)., This limit is also consistent with the observations of NGC 2298 (see \ref{sec:2298data} for details). + Since we know which stars belong to the simulated: cluster. it is fairly easy to build.. the same is true for.," Since we know which stars belong to the simulated cluster, it is fairly easy to build, the same is true for." + We applied the ALP to four tical tails with cillerent densities. (3200). (1600). (S00). and (160) of the total number of simulated: cluster stars.," We applied the MF to four tidal tails with different densities, (3200), (1600), (800), and (160) of the total number of simulated cluster stars." + This was done by randomly removing stars from the simulated tail., This was done by randomly removing stars from the simulated tail. + Furthermore. we compared the ME. results with a simpler method. of quantifving the simulated. tidal tail. based on simple star counts.," Furthermore, we compared the MF results with a simpler method of quantifying the simulated tidal tail, based on simple star counts." + In this alternative method we compute star counts at cach spatial bin. evaluate the expected average background counts. and subtract this later [rom the former.," In this alternative method we compute star counts at each spatial bin, evaluate the expected average background counts, and subtract this later from the former." + Figure 1. shows the on-sky distribution of simulated stars compared. to the ALP results., Figure \ref{sim} shows the on-sky distribution of simulated stars compared to the MF results. + Lt is clear that. the matched-filter improves the contrast of the tail relative to the feld stars when compared. to a direct. star. counting method., It is clear that the matched-filter improves the contrast of the tail relative to the field stars when compared to a direct star counting method. + Yet. the comparison of the left and right. columns in the figure reveal that the ALP does not recover all the structure and extension in the tails. specially in the sparser cases.," Yet, the comparison of the left and right columns in the figure reveal that the MF does not recover all the structure and extension in the tails, specially in the sparser cases." + In figure 2. we compare. for the two methods. the resulting cluster counts to the actual number of simulated ‘Luster stars.," In figure \ref{matchalpha} we compare, for the two methods, the resulting cluster counts to the actual number of simulated cluster stars." + The matched-filter clearly recluces the noise in this scatter. plot. by a factor of 1.92/0.72=2.67. and rerclore the contrast with the background. when compared to simple star counts method.," The matched-filter clearly reduces the noise in this scatter plot by a factor of $1.92 / 0.72 = 2.67$, and therefore the contrast with the background, when compared to simple star counts method." + We conclude that the our implementation. of the matched-filter works well for this simulated. set., We conclude that the our implementation of the matched-filter works well for this simulated set. + 1n order to further validate our algorithm: we have chosen the halo elobular cluster Palomar 5., In order to further validate our algorithm we have chosen the halo globular cluster Palomar 5. + “Phis cluster has the most prominent tical tail known to date. making it à good test case for anv detection algorithm.," This cluster has the most prominent tidal tail known to date, making it a good test case for any detection algorithm." + Our analysis was carried out using the Sloan Digital Sky Survey (SDSS) Data Release 7 (DIT) (Abazajian 2009)., Our analysis was carried out using the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) \citep{dr7}. +. SDSS is a large survey. covering up to 10000 square degrees of the northern and part of the southern galactic cap. using 5 filters (πο ές).," SDSS is a large survey, covering up to 10000 square degrees of the northern and part of the southern galactic cap, using 5 filters $ugriz$ )." + Hs large continuous area coverage and photometric homogeneity make it a veryuseful data set for the discovery. of tidal tails or any other larec scale sub-structure in the Galaxy., Its large continuous area coverage and photometric homogeneity make it a veryuseful data set for the discovery of tidal tails or any other large scale sub-structure in the Galaxy. +''here is no reason to believe that the universe is infinite.,There is no reason to believe that the universe is infinite. + While general relativity specifies the local curvature of spacetime. the global ecometry of the universe remains unspecified.," While general relativity specifies the local curvature of spacetime, the global geometry of the universe remains unspecified." + From this point of view. an infinite universe is assumed. only to simplify theoretical calculations and is subject to observational verification.," From this point of view, an infinite universe is assumed only to simplify theoretical calculations and is subject to observational verification." + Although inflation would. push topology scales. Lar out of. view. recent observations (Spinradetal.1997:Garnavich1998) suggest that the curvature of the universe may deviate fron lat sulliciently to be measurable.," Although inflation would push topology scales far out of view, recent observations \cite{open2,open1} suggest that the curvature of the universe may deviate from flat sufficiently to be measurable." + Lf curvature is observable. hen how can we assume topology is not?," If curvature is observable, then how can we assume topology is not?" + As it represents the largest. volume observable. the Cosmic Microwave Background (€M) is uniquely sensitive o the global geometry of the universe.," As it represents the largest volume observable, the Cosmic Microwave Background (CMB) is uniquely sensitive to the global geometry of the universe." + Already the Cosmic Backeround Explorer. (COBL) results have been used o place constraints on Lat topologies and limited: open opologies that are orders of magnitude better than other approaches (Cott1980:Sokoloy1993:Stevens.Scott.&1997:Levin.Scannapieco.&Silk 1998).. hereafter. LSS).," Already the Cosmic Background Explorer (COBE) results have been used to place constraints on flat topologies and limited open topologies that are orders of magnitude better than other approaches \cite{flat1,flat2,sss,star,lum1,lum2,costa,lbbs,us}, hereafter LSS)." + The increased. sensitivity of the next. generation of CMD experiments has inspired renewed. interest. in the search for topology1998)., The increased sensitivity of the next generation of CMB experiments has inspired renewed interest in the search for topology. + In LSS. we were able to quantify the effects of topology on the €CMD by considering all possible compactifications of [lat space.," In LSS, we were able to quantify the effects of topology on the CMB by considering all possible compactifications of flat space." + We solved. for the spectrum. of [uctuations explicitly which allowed: us to create realizations of finite universes and compare typical angular power spectra to the COBE data., We solved for the spectrum of fluctuations explicitly which allowed us to create realizations of finite universes and compare typical angular power spectra to the COBE data. + Here we extend those results by. computing the ensemble-averaged angular power spectrum. as opposed to just obtaining realizations.," Here we extend those results by computing the ensemble-averaged angular power spectrum, as opposed to just obtaining realizations." + Since we know the moces explicitly from LSS. our task here is to reduce the angular power spectrum to a simple analytic expression. for each of the six orientable topologies.," Since we know the modes explicitly from LSS, our task here is to reduce the angular power spectrum to a simple analytic expression for each of the six orientable topologies." + Generic features in the spectrum can then be identified without ambiguity., Generic features in the spectrum can then be identified without ambiguity. + The primary cause of CAIB temperature [luctuations is lumps in the geometry of spacetime at the time of decoupling., The primary cause of CMB temperature fluctuations is lumps in the geometry of spacetime at the time of decoupling. + “Phe fluctuations can be decomposed into cigenmodes and written in any compact. Hat spacetime as (GN ).(1) with Ay the conformal time between today and decoupling.," The fluctuations can be decomposed into eigenmodes and written in any compact, flat spacetime as k ) with $\Delta \eta $ the conformal time between today and decoupling." + On a compact manifold. the usual continuous spectrum of eigenvalues becomes discretized. hence the sum in 1..," On a compact manifold, the usual continuous spectrum of eigenvalues becomes discretized, hence the sum in \ref{eq1}." + The dr are primordiallv seeded Gaussian amplitudes that obey. the reality condition be=φ'r and a set of relations that depend on the topology (LSS)., The $\hat \Phi_{\vec k}$ are primordially seeded Gaussian amplitudes that obey the reality condition $\hat \Phi_{\vec k}=\hat \Phi_{-\vec k}^*$ and a set of relations that depend on the topology (LSS). + With this decomposition we can construct the, With this decomposition we can construct the +sphereRm) aud thus offers uo advantages over the ptre spectral imethod used here.,sphere and thus offers no advantages over the pure spectral method used here. +" We find that all Ct,fom With mm greater than the maximum agin1iab wavevector of the stochastic forcing vanish. hence the spectral expansion cai be severely truncated1 by restricting ML without loss of accuracy."," We find that all $c_{\ell_1 \ell_2 m}$ with $m$ greater than the maximum azimuthal wavevector of the stochastic forcing vanish, hence the spectral expansion can be severely truncated by restricting $M \ll L$ without loss of accuracy." + This results in substanial speed-up aid a recductiou in the required memory., This results in substantial speed-up and a reduction in the required memory. + Moreover. only a subset of the possible coeficients of the qt⋜∥∐⋅⋜↕⋃∢∙∐∩∐∐∐≺↵⋜⋃⋅⋯≺↵⊳∖⋅∁⊽⋅⋅. ⋅⋅⋅ ⋉⊏⊐ and C'J⋅⋅∕⋅ with [ indices appear in Eq.," Moreover, only a subset of the possible coefficients of the quadratic nonlinearities, $C^{(-)}_{\ell; \ell_1 m; \ell_2 m}$ and $C^{(+)}_{\ell_1; \ell 0; \ell^\prime m}$, with 4 indices appear in Eq." + 15 'esulting in reduced memory usage., \ref{ceom2} resulting in reduced memory usage. + Finally we note that the coce implemeutiug thi DNS and DSS (via CE2) is written in the Objective-C++ programuniug laiguage and ruis on Apple computers (OS X 10.6) utilizing aud graud central clispatcl (ecd) for efficient SNP. parallelis., Finally we note that the code implementing both DNS and DSS (via CE2) is written in the Objective-C++ programming language and runs on Apple computers (OS X 10.6) utilizing C-blocks and grand central dispatch (gcd) for efficient SMP parallelism. + We stress that the DSS cau run an order of magnitude or mo'e faster than DNS., We stress that the DSS can run an order of magnitude or more faster than DNS. + In the absence of clamping and driviug forces. the EOM lor the cunulauts. like the EOM for the vorticity and magnetic potential have a uumyer of conservation laws.," In the absence of damping and driving forces, the EOM for the cumulants, like the EOM for the vorticity and magnetic potential have a number of conservation laws." + For example. in the hydrodyuamite case. kinetic energy. eustrophy aid augular —101nentuim are couserved. whilst for the MHD case 11e conserved quantities are augular mouentum. total energy. cross-helicity. and. the lueali squalrec potential.," For example, in the hydrodynamic case, kinetic energy, enstrophy and angular momentum are conserved, whilst for the MHD case the conserved quantities are angular momentum, total energy, cross-helicity, and the mean squared potential." + Moreover. for stochastic forcing restricted to wavevectors |(|>0. the case considered here. the angular moineutuim in the CE2 ‘elnaius exactly zero. in contrast to DNS.," Moreover, for stochastic forcing restricted to wavevectors $| \ell | > 0$, the case considered here, the angular momentum in the CE2 remains exactly zero, in contrast to DNS." + Just as or direct numerical simulations utilisiug sjxherical harmonics there are convenient expressions o {the average values of various quantiti ers of the low-order cumulauts., Just as for direct numerical simulations utilising spherical harmonics there are convenient expressions of the average values of various quantities in terms of the low-order cumulants. + For exaimple the neal Cross-helicity is given by: where the two layers are labelled explicitly in tle final line., For example the mean cross-helicity is given by: where the two layers are labelled explicitly in the final line. + Similar expressions are available for the averages of other quadratic quantities., Similar expressions are available for the averages of other quadratic quantities. + The models are formulated on the unit sphere with a timescale such that the sj»here complete a [ull rotation iu oue day of model time., The models are formulated on the unit sphere with a timescale such that the sphere complete a full rotation in one day of model time. + All model j»arameters may be defined iu terms of these leneth aud time scales: lor instance Q=25., All model parameters may be defined in terms of these length and time scales; for instance $\Omega = 2 \pi$. + Fricticoi removes energy at long leieth scales aud is parameterized by rate &., Friction removes energy at long length scales and is parameterized by rate $\kappa$. + The hyperviscosity 7» tlat appears in Eq. (16)), The hyperviscosity $\nu_2$ that appears in Eq. \ref{EOM}) ) + is iucluclecl solely to absorb enstrophiy at the sinallest resolved scales., is included solely to absorb enstrophy at the smallest resolved scales. + Consequently it is rescaled with he eric size or spectral cutoll so that, Consequently it is rescaled with the grid size or spectral cutoff so that +on thecenter-ol-mass energy. \/s.andthose of hyperons having only one common,"with the projectile, such as $\Sigma^-, \Xi^0$and $\Xi^-$ in $pA$ collisions, depend on $\sqrt{s}$ ." + quark, The target +of these cases(Vézquez-Semadenietal.2006:Hennebelle 2007). synthetic H spectra are computed to study the effect of turbulence.,"of these \citep{nref3,nref2}, synthetic H spectra are computed to study the effect of turbulence." + In general. these analytical and numerical works predict a Kolmogorov-like turbulence in two-phase neutral ISM.," In general, these analytical and numerical works predict a Kolmogorov-like turbulence in two-phase neutral ISM." + Hennebelleetal.(2007) also report. based on simulation results. a power law scaling o7-x/? consistent with our observation.," \citet{nref2} also report, based on simulation results, a power law scaling $\sigma^2_v \propto l^{0.8}$ consistent with our observation." + Now. since fractional ionization couples the H to the magnetic field. the turbulence is expected. to. be magnetohydrodynamic (MHD) in. nature.," Now, since fractional ionization couples the H to the magnetic field, the turbulence is expected to be magnetohydrodynamic (MHD) in nature." + Though simple and ingenious models (e.g.Goldreich&Sridhar1995)— of incompressible MHD turbulence have been proposed. most of the insights into incompressible and compressible MHD turbulence again come from numerical simulations (Choetal.2002.andreferences therein)...," Though simple and ingenious models \citep[e.g.][]{gs95} of incompressible MHD turbulence have been proposed, most of the insights into incompressible and compressible MHD turbulence again come from numerical simulations \citep[][and references therein]{ch02}. ." + Models (likeGoldreich&Sridhar1995) predict a Kolmogorov-like energy spectrum. £(A)x&77. for incompressible MHD turbulence and this is supported by both numerical simulations and observations (see Choetal.(2002). for details).," Models \citep[like][]{gs95} predict a Kolmogorov-like energy spectrum, $E(k) \propto k^{-5/3}$, for incompressible MHD turbulence and this is supported by both numerical simulations and observations (see \citet{ch02} for details)." + In ease of compressible MHD turbulence. Alfvén modes are least susceptible to damping mechanisms (Minter&1997) and hence the energy transfer in Alfvén waves is of mayor interest.," In case of compressible MHD turbulence, $\acute{e}$ n modes are least susceptible to damping mechanisms \citep{mi97} and hence the energy transfer in $\acute{e}$ n waves is of major interest." + Again. numerical simulations show that the energy spectra of Alfvén modes follow a Kolmogorov-like spectrum.," Again, numerical simulations show that the energy spectra of $\acute{e}$ n modes follow a Kolmogorov-like spectrum." + In a situation where the bulk of the energy transfer is via Alfvén waves. the non-thermal velocity dispersion 9v is related to the magnetic perturbation amplitude 077 and H number density ng ας dr=Df/Azpingnmg ¢Arons&Max1975: where j/=1.4 is the effective mass of an H+He gas with cosmic abundance. ng is the mass of the hydrogen atom and it is usually assumed that οὐ)~2.," In a situation where the bulk of the energy transfer is via $\acute{e}$ n waves, the non-thermal velocity dispersion $\delta v$ is related to the magnetic perturbation amplitude $\delta B$ and H number density $n_H$ as $\delta v = \delta B/\sqrt{4\pi\mu n_{\rm H}m_{\rm H}}$ \citep{am75,ar07} where $\mu=1.4$ is the effective mass of an H+He gas with cosmic abundance, $m_{\rm H}$ is the mass of the hydrogen atom and it is usually assumed that $\delta B \sim B$." +" Using this relation. the magnetic field is found to be of the order of few jG (column density weighted mean and median values are 11.7 and 10.2 ο respectively) with no significant trend related to ""cloud"" size."," Using this relation, the magnetic field is found to be of the order of few $\mu$ G (column density weighted mean and median values are 11.7 and 10.2 $\mu$ G respectively) with no significant trend related to “cloud” size." + We note that there are various uncertainties to the derived equipartition magnetic field., We note that there are various uncertainties to the derived equipartition magnetic field. + But our estimate is broadly consistent with the observed magnetic field in the diffuse neutral ISM and matches. within a factor of 2. with the median magnetic field estimated for a sub-sample of these components using Zeeman splitting measurements Troland 2005).," But our estimate is broadly consistent with the observed magnetic field in the diffuse neutral ISM and matches, within a factor of 2, with the median magnetic field estimated for a sub-sample of these components using Zeeman splitting measurements \citep{ht05}." +. The break that is clearly seen in Figure (23) requires some attention., The break that is clearly seen in Figure \ref{fig:2}) ) requires some attention. + This change in the power law index can not be explained just in terms of lower signal to noise on the physical quantities at low Nui Ts end., This change in the power law index can not be explained just in terms of lower signal to noise on the physical quantities at low $_{\rm HI}$ $_{\rm S}$ end. + However. as shown in the figure. the data are well fit by a model in which the line width is overestimated by about ~60 K. There are three systematic effects that may contribute to the overestimation of the line width without much affecting Nut and Ts: (i) the finite spectral resolution. (i1) blending of two or more narrow components and (il) velocity (but not Ts) fluctuations in the gas within the Arecibo beam.," However, as shown in the figure, the data are well fit by a model in which the line width is overestimated by about $\sim +60$ K. There are three systematic effects that may contribute to the overestimation of the line width without much affecting $_{\rm HI}$ and $_{\rm S}$: (i) the finite spectral resolution, (ii) blending of two or more narrow components and (iii) velocity (but not $_{\rm S}$ ) fluctuations in the gas within the Arecibo beam." + The contribution from the first effect is quantified by estimating the width of a Gaussian signal after smoothing it to a spectral resolution of 0-4 km ! and adding noise similar to that in the actual spectra., The contribution from the first effect is quantified by estimating the width of a Gaussian signal after smoothing it to a spectral resolution of 0.4 km $^{-1}$ and adding noise similar to that in the actual spectra. + The effect is found to be almost negligible because of the high spectral resolution., The effect is found to be almost negligible because of the high spectral resolution. + A similar numerical exercise with two Gaussian components was done to check the effect of blending of narrow components and ambiguities in Gaussian fitting., A similar numerical exercise with two Gaussian components was done to check the effect of blending of narrow components and ambiguities in Gaussian fitting. + In this ease.the effect is most significant when the blended lines are of comparable amplitudes and have separations comparable to their widths.," In this case,the effect is most significant when the blended lines are of comparable amplitudes and have separations comparable to their widths." + For example. blending of components with Tymer=60 K (width of the Gaussian ~0.7 km s.I) with a separation of —1.2 km ¢ results in typically 20 — 30 K overestimation of TyΗταν”.," For example, blending of components with $_{\rm K}max = 60$ K (width of the Gaussian $\sim 0.7$ km $^{-1}$ ) with a separation of $\sim 1.2$ km $^{-1}$ results in typically 20 – 30 K overestimation of $_{\rm K}max$." + When the amplitudes of two Gaussian profiles are comparable. the line width is overestimated by upto 60 K. The third possibility. that is. a fine scale structure in the velocity (but not in the temperature) has been proposed earlier (e.g.Broganetal.2005:Roy2006). to explain the observed fine scale H opacity fluctuations (Dieteretal.1976:Cro-visieretal. 1985).," When the amplitudes of two Gaussian profiles are comparable, the line width is overestimated by upto $\sim 60$ K. The third possibility, that is, a fine scale structure in the velocity (but not in the temperature) has been proposed earlier \citep[e.g.][]{br05,nr06} to explain the observed fine scale H opacity fluctuations \citep{di76,cr85}." +. Such velocity fluctuations within the Arecibo beam will also cause an overestimation of Tymer., Such velocity fluctuations within the Arecibo beam will also cause an overestimation of $_{\rm K}max$. + We. however. note that the scale length (inferred from Nyy and Tz) of the components below the break is very small.," We, however, note that the scale length (inferred from $_{\rm HI}$ and $_{\rm S}$ ) of the components below the break is very small." + Although the existence of tiny “clouds” is supported by observations and. numerical simulations (Braun&Kanekar2005:StanimiroviéHeiles&Audit2007. e.g... their origin and physical properties are still unknown.," Although the existence of tiny “clouds” is supported by observations and numerical simulations \citep[e.g.]{bk05,st05,na06,nref3, +nref1}, their origin and physical properties are still unknown." + The evaporation timescale for these clouds are ~1 Myr., The evaporation timescale for these clouds are $\sim 1$ Myr. + These structures can survive if either the ambient pressure around the clouds is much higher than the standard ISM pressure or they are formed continuously with a comparable timescale., These structures can survive if either the ambient pressure around the clouds is much higher than the standard ISM pressure or they are formed continuously with a comparable timescale. + While we have presented plausible arguments for the break that We See not corresponding to a physical phenomena. the lack of detailed understanding of these tiny H structures means that we can not rule out the possibility of some physical phenomenon being responsible for the break.," While we have presented plausible arguments for the break that we see not corresponding to a physical phenomena, the lack of detailed understanding of these tiny H structures means that we can not rule out the possibility of some physical phenomenon being responsible for the break." + For a multi-phase medium if the turbulent velocity dispersion sealing is similar for coexisting phases. then this scaling relation can be exploited to get a handle on the physical temperature of the gas that is detected only in H emission but not in absorption.," For a multi-phase medium if the turbulent velocity dispersion scaling is similar for coexisting phases, then this scaling relation can be exploited to get a handle on the physical temperature of the gas that is detected only in H emission but not in absorption." + Since one only has a lower limit on Ts for these components. they lie. as expected. systematically on the top left side of the fit to the components detected in both emission and absorption (Figure (33).," Since one only has a lower limit on $_{\rm S}$ for these components, they lie, as expected, systematically on the top left side of the fit to the components detected in both emission and absorption (Figure \ref{fig:3}) ))." +" For these components we define a proxy temperature Tj, that will restore the component back to this power law correlation.", For these components we define a proxy temperature $_{\rm L}$ that will restore the component back to this power law correlation. +" Given the measured Ng, and Ty, from the emission spectra. one can uniquely compute this proxy temperature."," Given the measured $_{\rm HI}$ and $_{{\rm K}max}$ from the emission spectra, one can uniquely compute this proxy temperature." +" Since Τι, corresponds to the velocity widthafter correction for the turbulent velocity. it is a better estimate of the actual physical temperature of the cloud than that of Tha..."," Since $_{\rm L}$ corresponds to the velocity widthafter correction for the turbulent velocity, it is a better estimate of the actual physical temperature of the cloud than that of $_{{\rm K}max}$ ." +" Note that since most of the components in Figure (35) line beyond the break in the fitted function the derived Τι, is independent of the whether the break arises due to some underlying physical reason.", Note that since most of the components in Figure \ref{fig:3}) ) line beyond the break in the fitted function the derived $_{\rm L}$ is independent of the whether the break arises due to some underlying physical reason. +this absorption. it can account for a signilicant fraction of the currently missing barvons. implied by big bang nucleosvuthesis 2001).. the observed aungular power spectrum of the cosmic microwave background radiation and the Thomson opacity interred [rom its polarization 2010).,"this absorption, it can account for a significant fraction of the currently missing baryons, implied by big bang nucleosynthesis , the observed angular power spectrum of the cosmic microwave background radiation and the Thomson opacity inferred from its polarization ." +. Of these barvons. in the local universe only ~50% are present in (he galaxies. galaxy clusters and UV-optical IGM line svstems known to date2007).," Of these baryons, in the local universe only $\sim 50\%$ are present in the galaxies, galaxy clusters and UV-optical IGM line systems known to date." +. Furthermore. if of the barvons are in the IGM. and if the diffuse low-z IGM metallicity is indeed ~0.2—0.4 solar as we postulate here. then the IGM contains the bulk of the metals in the present-day universe. compared (o. say. solar metallicity in stars and galaxies that comprise only of the barvons.," Furthermore, if of the baryons are in the IGM and if the diffuse $z$ IGM metallicity is indeed $\sim 0.2 - 0.4$ solar as we postulate here, then the IGM contains the bulk of the metals in the present-day universe, compared to, say, solar metallicity in stars and galaxies that comprise only of the baryons." + The presence of absorption in GRBs and RLQs. that both harbor powerful jets. but less in RQQs. also raises the possibility Chat the absorption effect has something to do with the jet.," The presence of absorption in GRBs and RLQs, that both harbor powerful jets, but less in RQQs, also raises the possibility that the absorption effect has something to do with the jet." + It was discovered by that high-z RLQs are much more absorbed in the A-ravs (han ROGQs. which seems (o support a jet effect.," It was discovered by that $z$ RLQs are much more absorbed in the s than RQQs, which seems to support a jet effect." + On the other hand. (hese authors also realized the absorplion (if imürinsic) mereases with z and not with luminosity. which argues against a jel-plivsics origin.," On the other hand, these authors also realized the absorption (if intrinsic) increases with $z$ and not with luminosity, which argues against a jet-physics origin." + The fact that local RLQs generally do not have the high column densities that are found in (he hieh-: sources has been confirmed recently bytherein)., The fact that local RLQs generally do not have the high column densities that are found in the $z$ sources has been confirmed recently by. +. Indeed. ascribing photo-electrie absorption to the jet is counter-intuitive. as (he jet is not expected to comprise atomic material with bound electrons. ancl especially nol metals. that produce (he observed. oopacitv.," Indeed, ascribing photo-electric absorption to the jet is counter-intuitive, as the jet is not expected to comprise atomic material with bound electrons, and especially not metals, that produce the observed opacity." + Moreover. the little scatter of the observed optical depth found in (his paper. and even more the tendency to an asvanptotic opacity al hieh z that require a putative intrinsic column to scale approximately with (1+2)?? to offset the decreasing cross section. calls into question the realistic role jets ean play in determining the soft oopacllv.," Moreover, the little scatter of the observed optical depth found in this paper, and even more the tendency to an asymptotic opacity at high $z$ that require a putative intrinsic column to scale approximately with $(1+z)^{2.5}$ to offset the decreasing cross section, calls into question the realistic role jets can play in determining the soft opacity." + Turning to the trends of intergalactic line absorption towards GRBs and quasars in the optical band does not provide a clear-cut answer to the uniqueness of absorption towards jelled sources either., Turning to the trends of intergalactic line absorption towards GRBs and quasars in the optical band does not provide a clear-cut answer to the uniqueness of absorption towards jetted sources either. + On one hand. the number of UI intervening absorption svstenis towards GRBs and blazars is a [ew times vigher than that towards RQQs.," On one hand, the number of II intervening absorption systems towards GRBs and blazars is a few times higher than that towards RQQs." + As there is no obvious reason for line sights towards GRBs to be different [rom Chose towards quasars. il would require metals to be entrained in the jets of GRBs and RLOs.," As there is no obvious reason for line sights towards GRBs to be different from those towards quasars, it would require metals to be entrained in the jets of GRBs and RLQs." + On the other hand. line sights towards high-: RLOs seem to have a similar number density of intervening DLA svstems as those towards opticallv-selected (again. mostly RQQs) samples2001).," On the other hand, line sights towards $z$ RLQs seem to have a similar number density of intervening DLA systems as those towards optically-selected (again, mostly RQQs) samples." +. Prospectively. (here is a clear way to disünguish a well confined absorber Irom a cosmologically," Prospectively, there is a clear way to distinguish a well confined absorber from a cosmologically" +"stars with an age in excess of ~8 MMyr, of the same type as those that we discovered in the field around 119874 in the LMC (see II).","stars with an age in excess of $\sim 8$ Myr, of the same type as those that we discovered in the field around 1987A in the LMC (see I)." + The physical parameters of the bona-fide PMS stars that we have identified are obtained as explained in the following., The physical parameters of the bona-fide PMS stars that we have identified are obtained as explained in the following. +" The radius R, comes from the luminosity and effective temperature of the stars, which in turn follow from the observed colour (V—J) and magnitude (V), properly corrected for interstellar extinction as explained in refredde.."," The radius $R_*$ comes from the luminosity and effective temperature of the stars, which in turn follow from the observed colour $(V-I)$ and magnitude $V$ ), properly corrected for interstellar extinction as explained in \\ref{redde}." +" The stellar mass M. and age were derived by comparing the location of each star in the Russell (H-R) diagram of reffig6 with the PMS evolutionary tracks and corresponding isochrones, via interpolation over a finer grid than the one shown in the "," The stellar mass $M_*$ and age were derived by comparing the location of each star in the Hertzsprung--Russell (H–R) diagram of \\ref{fig6} with the PMS evolutionary tracks and corresponding isochrones, via interpolation over a finer grid than the one shown in the figure." +"We followed the interpolation procedure developed by figure.Romaniello (1998), which does not make assumptions on the properties of the population, such as the functional form of the IMF."," We followed the interpolation procedure developed by Romaniello (1998), which does not make assumptions on the properties of the population, such as the functional form of the IMF." +" As for the theoretical models, we adopted those of the Pisa group (Degl'Innocenti et al."," As for the theoretical models, we adopted those of the Pisa group (Degl'Innocenti et al." + 2008; Tognelli et al., 2008; Tognelli et al. +" 2011), for metallicity Z=0.002 or about Zo /8."," 2011), for metallicity $Z=0.002$ or about $Z_\odot/8$ ." + These new PMS tracks were specifically computed for the mass range from 0.45 to with an updated version of the FRANEC evolutionary code (see Chieffi Straniero 1989 and Degl'Innocenti et al., These new PMS tracks were specifically computed for the mass range from $0.45$ to with an updated version of the FRANEC evolutionary code (see Chieffi Straniero 1989 and Degl'Innocenti et al. + 2008 for details and Cignoni et al., 2008 for details and Cignoni et al. + 2009 for an application)., 2009 for an application). +" reveals that the masses of the bona-fine PMS stars span over a decade, from «0.45 for the coolest objects to ~4 for the hottest ones."," \\ref{fig6} reveals that the masses of the bona-fine PMS stars span over a decade, from $< 0.45$ for the coolest objects to $\sim 4$ for the hottest ones." +" As mentioned above, some of the objects with Teg>10000 KK and W.q(Ha)>—50 could be Be stars and we have marked all objects of this type with squares to distinguish them from the rest."," As mentioned above, some of the objects with $T_{\rm eff} > 10\,000$ K and $W_{\rm eq}(H\alpha) > +-50$ could be Be stars and we have marked all objects of this type with squares to distinguish them from the rest." + reffig6 also provides a more quantitative characterisation of the age difference between the two populations of PMS stars that we identified earlier in the CMD reffig5)).," \\ref{fig6} + also provides a more quantitative characterisation of the age difference between the two populations of PMS stars that we identified earlier in the CMD \\ref{fig5}) )." +" The isochrones in the figure, corresponding from right to left to ages of 0.125, 0.25, 0.5, 1, 2, 4, 8, 16 and MMyr, show that the young population has a median age of ~ 1MMyr, whereas the older bona-fide PMS stars span a wider age range from ~ 10MMyr to 30MMyr, with a broad peak around MMyr."," The isochrones in the figure, corresponding from right to left to ages of $0.125$, $0.25$, $0.5$, 1, 2, 4, 8, 16 and Myr, show that the young population has a median age of $\sim 1$ Myr, whereas the older bona-fide PMS stars span a wider age range from $\sim 10$ Myr to Myr, with a broad peak around Myr." +" We derived a reliable measure ofthe mass and age for all stars indicated as thick dots in reffig6,, except for the coolest objects that would have"," We derived a reliable measure ofthe mass and age for all stars indicated as thick dots in \\ref{fig6}, , except for the coolest objects that would have" +IT is the local scale height. and a is then an efficiency actor with a value <1.,"$H$ is the local scale height, and $\alpha$ is then an efficiency factor with a value $\leq$ 1." + The magnitude of turbulent velocity fiuctuatious depends both on the value of a and ou how this efiicicucy factor is apportioned between he sound speed and the scale height., The magnitude of turbulent velocity fluctuations depends both on the value of $\alpha$ and on how this efficiency factor is apportioned between the sound speed and the scale height. +" If. for example. he najortv of the power in turbulent fluctuations occurs at the leneth of the scale height. the velocity Huctuations can be as sinall as ae, (perhaps augimoenutec wea geometric factor of a few)."," If, for example, the majority of the power in turbulent fluctuations occurs at the length of the scale height, the velocity fluctuations can be as small as $\alpha c_s$ (perhaps augmented by a geometric factor of a few)." + On the other laud. if the xoportionalitv factor a applies evenly to the length iux velocity scales in the problem. the turbulent fluctuations could be as laree as Nes (again possibly modifie wea ecolmetric factor).," On the other hand, if the proportionality factor $\alpha$ applies evenly to the length and velocity scales in the problem, the turbulent fluctuations could be as large as $\sqrt{\alpha} c_s$ (again possibly modified by a geometric factor)." + Since there is no evidence of shocks that would point to sonic or supersonic turbulence in ciremustellu disks. it is unlikely that the turbuleu velocity fluctuations would be much larger thaw VILAM ," Since there is no evidence of shocks that would point to sonic or supersonic turbulence in circumstellar disks, it is unlikely that the turbulent velocity fluctuations would be much larger than $\sqrt{\alpha} c_s$." +It is clear that shewmiug box simulations of MIID turbulence with zero uct maenetic field flux do no eive reliable values of the viscosity parameter a due to nunercal dissipation. which results iu values of à tha depend ou resolution (??)..," It is clear that shearing box simulations of MHD turbulence with zero net magnetic field flux do not give reliable values of the viscosity parameter $\alpha$ due to numerical dissipation, which results in values of $\alpha$ that depend on resolution \citep{pes07,fro07}." + This is unütigated by the use of more realistic siiimlation conditions iucluding vertical stratification (ce...2277).. but the resulting depeudence of à aud therefore turbuleut velocity fluctuations ou the uaenitude of the magnetic field is troublesome. since naenetic field streneths and geometries in circuitcllar disks are uncoustrained by observations (c.e.. 7)..," This is mitigated by the use of more realistic simulation conditions including vertical stratification \citep[e.g.,][]{sto96,fle03,dav10,fla10}, but the resulting dependence of $\alpha$ and therefore turbulent velocity fluctuations on the magnitude of the magnetic field is troublesome, since magnetic field strengths and geometries in circumstellar disks are unconstrained by observations \citep[e.g.,][]{hug09b}. ." + The inclusion of vertical eravitv has also been shown to cad to convergence (e.c.2?)..," The inclusion of vertical gravity has also been shown to lead to convergence \citep[e.g.][]{dav10,fla10}." + It is perhaps iustiuctive o investigate how o may be related. to the observed urbulent linewidth iu the context of shearime-box simulations., It is perhaps instructive to investigate how $\alpha$ may be related to the observed turbulent linewidth in the context of shearing-box simulations. +" Quantities typically reported for shearing oxes include the shear stress LB,B,/Ez. where D, aud D, ave the magnetic field along the . aud y directions. respectively: Revuolds stress pe,ócy. where p is deusity. v. is the 2 component of velocity. and de, is the y coniponeut of velocity without shear: and the magnitude of velocity fluctuations alone the different dinenusious of the simulation. pez,../2."," Quantities typically reported for shearing boxes include the shear stress $-B_x B_y / 4 +\pi$, where $B_x$ and $B_y$ are the magnetic field along the $x$ and $y$ directions, respectively; Reynolds stress $\rho v_x \delta v_y$, where $\rho$ is density, $v_x$ is the $x$ component of velocity, and $\delta v_y$ is the $y$ component of velocity without shear; and the magnitude of velocity fluctuations along the different dimensions of the simulation $\rho +v_{x,y,z}^2/2$." + Each of these quantities is routinely normalized by the initial midplane pressure. Dy(see.ce.22).," Each of these quantities is routinely normalized by the initial midplane pressure, $P_0$\citep[see, e.g.,][]{sto96,dav10}." + The total stress 2 is then the sum of the Maxwell and Revuolds stresses. and is directly proportional to the viscosity paramcter à. according to the relationship T—ape. where eds the sound. speed.," The total stress $T$ is then the sum of the Maxwell and Reynolds stresses, and is directly proportional to the viscosity parameter $\alpha$, according to the relationship $T = \alpha \rho c_s^2$ , where $c_s$ is the sound speed." + It is then straightforward to relate a to the turbulent velocity as a function of sound speed: where Cra ds the measured turbulent linewidth (typically the FWHAL calculated from €. which is the 1/¢ half-width) and / is the disk inclination.," It is then straightforward to relate $\alpha$ to the turbulent velocity as a function of sound speed: where $v_\mathrm{turb}$ is the measured turbulent linewidth (typically the FWHM calculated from $\xi$, which is the $1/e$ half-width) and $i$ is the disk inclination." + Using reported values of the relevant simulation parameters from ον ανὈμμ]ος for a face-ou disk. aud a~LCCfee)? for an edge-on disk.," Using reported values of the relevant simulation parameters from \citet{dav10}, $\alpha \sim 3 (v_\mathrm{turb}/c_s)^2$ for a face-on disk, and $\alpha \sim 1.5 (v_\mathrm{turb}/c_s)^2$ for an edge-on disk." +" For the value of a~0.01 ynderived in ον, this predicts a midplane turbulent linewidth of roughly of the sound speed. depending on the source geonietry."," For the value of $\alpha \sim 0.01$ derived in \citet{dav10}, this predicts a midplane turbulent linewidth of roughly of the sound speed, depending on the source geometry." + Observational attempts at coustrainiug the value of a in ciretuustellar disks. while generally quite uncertain. secni to cluster near values of 7. with large scatter (e.g...27).," Observational attempts at constraining the value of $\alpha$ in circumstellar disks, while generally quite uncertain, seem to cluster near values of $^{-2}$, with large scatter \citep[e.g.,][]{har98,and09a}." + TE the velocity fluctuations are estimated as VIL this result would nuplv velocity fluctuations up to of the sound speed near the midplaue. although this global value is likely to varywidely depeudiug ou local conditions that affect the ionizatiou fraction aud the coupling of ions and neutrals.," If the velocity fluctuations are estimated as $\sqrt{\alpha} c_s$, this result would imply velocity fluctuations up to of the sound speed near the midplane, although this global value is likely to varywidely depending on local conditions that affect the ionization fraction and the coupling of ions and neutrals." + A theoretical comparison between circuuustellar disks aud the Tavlor-Couctte flow by ?/— finds that the i turbulent linewidth (of order <30% of the sound speed) derived frou low spectral resolution observations of DAL Tau by 2? are on par with expectations frou laboratory measurements bv ?.., A theoretical comparison between circumstellar disks and the Taylor-Couette flow by \citet{her05} finds that the $^{-1}$ turbulent linewidth (of order $\lesssim$ of the sound speed) derived from low spectral resolution observations of DM Tau by \citet{gui98} are on par with expectations from laboratory measurements by \citet{dub04}. . + There is someevideuce. both from the study of FU Ori objects (2)— and global MIID.simulations of stratified disks (e.g. 2).. that the turbulent linewidth may," There is someevidence, both from the study of FU Ori objects \citep{har04} and global MHDsimulations of stratified disks \citep[e.g.][]{fro06}, , that the turbulent linewidth may" +"have a luminosity of ~2Lea, unless viewed at very. hieh inclination.",have a luminosity of $\sim 2L_{\rm Edd}$ unless viewed at very high inclination. + This agrees with observations of RS Oph. as does the outburst duration implied by (6)).," This agrees with observations of RS Oph, as does the outburst duration implied by \ref{tvisc}) )." + The rise of RS Oph to maximum. was very rapid 1 day)., The rise of RS Oph to maximum was very rapid $\la 1$ day). + This follows from the dwarl nova picture given here also., This follows from the dwarf nova picture given here also. +" To brighten from an accretion. luminosity of 10""ores| to 107eres requires the disc. instability heating| [ront⋅ to move from⋅ cisc⋆ radius⋆ Z4;~10Lou em to the white chwarf radius. which is about LO times smaller."," To brighten from an accretion luminosity of $10^{37}~{\rm erg\, s^{-1}}$ to $10^{38}~{\rm erg\, s^{-1}}$ requires the disc instability heating front to move from disc radius $R_d\sim 10^{10}$ cm to the white dwarf radius, which is about 10 times smaller." +" Eqn (51) of Lasota (2001) shows that the disc instability must be of ""insideout type. as the opposite would require a mass transfer rate greater than about +107 d i.c. comparable with the outburst accretion rate."," Eqn (51) of Lasota (2001) shows that the disc instability must be of `inside–out' type, as the opposite would require a mass transfer rate greater than about $4\times 10^{20}$ $^{-1}$, i.e. comparable with the outburst accretion rate." +" Forsuch outbursts the [ront moves with a velocity. $056, so the rise time is Using the disc central temperature given by Frank et al.."," Forsuch outbursts the front moves with a velocity $\la \alpha_h c_s$, so the rise time is Using the disc central temperature given by Frank et al.," +" 2002 (eqn 5.49) to estimate c, we find fi,23 hours.", 2002 (eqn 5.49) to estimate $c_s$ we find $t_{\rm rise} \ga 3$ hours. + Thus far the dwarf nova model gives a consistent representation of the outburst of RS Oph., Thus far the dwarf nova model gives a consistent representation of the outburst of RS Oph. + However we need one modification of the usual picture., However we need one modification of the usual picture. + A normal cdwarl nova outburst would end. not. after a viscous time. but. after a local thermal time. which is considerably. shorter.," A normal dwarf nova outburst would end not after a viscous time, but after a local thermal time, which is considerably shorter." + The crucial dillerence in RS Oph is the very large size of the accretion disc., The crucial difference in RS Oph is the very large size of the accretion disc. + Phis means that irracliation by the central source (temperature xd1/2 ) must dominateR local viscousR energy release (temperature x.42 771) at large cise racii where most of the dise mass is.," This means that irradiation by the central source (temperature $\propto R^{-1/2}$ ) must dominate local viscous energy release (temperature $\propto R^{-3/4}$ ) at large disc radii, where most of the disc mass is." + Phe outburst then resembles those of soft Xoray transients: the disc is trapped in the hot outburst state until central accretion drops because most of the heated. mass has been accreted (xing Ritter 1998)., The outburst then resembles those of soft X–ray transients: the disc is trapped in the hot outburst state until central accretion drops because most of the heated mass has been accreted (King Ritter 1998). +" For a disc heated by a central point source of luminosity L, the irradiation temperature Zi(2?) is given by (cf King Ritter. 1998) where & is the StefanBoltzmann constant. g is a ecometric factor of order 0.2. and 44/1?~0.04 is the disc aspect ratio."," For a disc heated by a central point source of luminosity $L_c$ the irradiation temperature $T_{\rm + irr}(R)$ is given by (cf King Ritter, 1998) where $\sigma$ is the Stefan–Boltzmann constant, $g$ is a geometric factor of order 0.2, and $H/R \sim 0.04$ is the disc aspect ratio." + This gives an irradiation temperature of order that is. the central accreting white dwarf keeps the disc sellconsistently in the hot state (Li2 Z4) out to a radius Hy107 em at the start of the outburst.," This gives an irradiation temperature of order that is, the central accreting white dwarf keeps the disc self–consistently in the hot state $T_{\rm irr} > T_H$ ) out to a radius $R_h\sim 10^{12}$ cm at the start of the outburst." + In this case the outburst must evolve on the local hotstate viscous time. and decay exponentially or linearly in time depending on whether irradiation keeps the whole disc in the hot state or not (xine Ritter. 1998).," In this case the outburst must evolve on the local hot–state viscous time, and decay exponentially or linearly in time depending on whether irradiation keeps the whole disc in the hot state or not (King Ritter, 1998)." +" As £2, is smaller than the full cise outer racius. the outburst decay should be (bolomoetricallv) linear over à viscous timescale."," As $R_h$ is smaller than the full disc outer radius, the outburst decay should be (bolometrically) linear over a viscous timescale." + This is consistent with observation (Page et ab.," This is consistent with observation (Page et al.," + 2008. Fig.l) between cays 50 to 100.," 2008, Fig.1) between days 50 to 100." + )etween. outbursts we expec we disc to refill. with little or no accretion on to the white cdwarl.," Between outbursts we expect the disc to refill, with little or no accretion on to the white dwarf." + This. olfers a natural explanation for the faintness of the system between outbursts. in particular in Xrays (Alukai 2009).," This offers a natural explanation for the faintness of the system between outbursts, in particular in X–rays (Mukai 2009)." + We conclude that the main features of the outbursts of LS Oph are successfully explained in terms of an instability in a disc irradiated by the central accreting white cbwart., We conclude that the main features of the outbursts of RS Oph are successfully explained in terms of an instability in a disc irradiated by the central accreting white dwarf. + We have suggested above that the outburst behaviour of RS Oph is explicable in terms of instabilities in an irradiated disc., We have suggested above that the outburst behaviour of RS Oph is explicable in terms of instabilities in an irradiated disc. + Until now the usual interpretation of RS Oph and other recurrent novae is that matter accumulates on the surface of the white dwarf until it reaches the base pressure Poi~B2010710 dyne cm72 required+ to ignite. as a runaway thermonuclear event., Until now the usual interpretation of RS Oph and other recurrent novae is that matter accumulates on the surface of the white dwarf until it reaches the base pressure $P_{\rm crit} \sim 2 \times 10^{19}$ dyne $^{-2}$ required to ignite as a runaway thermonuclear event. + We note that the presence of processcc material in the outbursts is not per se proof of nuclear burning in the outburst. since the companion star is evolved.," We note that the presence of processed material in the outbursts is not per se proof of nuclear burning in the outburst, since the companion star is evolved." + Thus any material transferred to the white ονα zux subsequently expelled in an aceretiondriven outburst came originally Crom the convective envelope of the red. giant. where it mixed with products of the nuclearburning shel around the degenerate core.," Thus any material transferred to the white dwarf and subsequently expelled in an accretion–driven outburst came originally from the convective envelope of the red giant, where it mixed with products of the nuclear–burning shell around the degenerate core." + Is composition therefore does not differ greatly. from that of matter partially burnt anc ected from the white cwarl surface in a classical nova., Its composition therefore does not differ greatly from that of matter partially burnt and ejected from the white dwarf surface in a classical nova. + This picture has several dilliculties. which we list below.," This picture has several difficulties, which we list below." + 1., 1. + Phe presence of jets requires an aceretion disc. and is very hard to reconcile with a thermonuclear model. as noted in the Introduction.," The presence of jets requires an accretion disc, and is very hard to reconcile with a thermonuclear model, as noted in the Introduction." + The nuclear energy. vield from burning hvdrogenrich matter considerably exceeds its gravitational binding energv at the surface of a white dwarf., The nuclear energy yield from burning hydrogen–rich matter considerably exceeds its gravitational binding energy at the surface of a white dwarf. + Hence a thermonuclear explosion would. inevitably blow away the inner parts of any accretion clisc., Hence a thermonuclear explosion would inevitably blow away the inner parts of any accretion disc. + 2., 2. +" Even assuming a mass M, close to the Chancrasckhar limit. the white dwarf has to acerete at a rate AL=πμ...10M.wr5 in order to. accumulate enough mass to =ignite the outbursts (here Z2, is the white dwarl radius. and fou2720 vr is the duration of quiesence)."," Even assuming a mass $M_1$ close to the Chandrasekhar limit, the white dwarf has to accrete at a rate $\dot M = P_{\rm + crit}R_1^4/GM_1t_{\rm qu} \ga 10^{-8}\msun~{\rm yr}^{-1}$ in order to accumulate enough mass to ignite the outbursts (here $R_1$ is the white dwarf radius, and $t_{\rm qu} \simeq 20$ yr is the duration of quiesence)." + 3ut the aceretion rate AZ210“AL.ve tis hard to reconcile with the lack ofN.rays observed from RS Oph in quicscence., But the accretion rate $\dot M \ga 10^{-8}\msun~{\rm yr}^{-1}$ is hard to reconcile with the lack of X–rays observed from RS Oph in quiescence. + Alukai (2009) considers various possible wavs out of this conclusion. including combinations of very high. intrinsic absorption columns and. totally optically thick boundary lavers. and concludes that none are convincing.," Mukai (2009) considers various possible ways out of this conclusion, including combinations of very high intrinsic absorption columns and totally optically thick boundary layers, and concludes that none are convincing." + In particular. CVs with boundary laver emission always in practice have a surface laver optically thin enough to produce hard X.rays (Patterson Raymond. 1985). Le. an optically thin region where accretion energy. is released.," In particular, CVs with boundary layer emission always in practice have a surface layer optically thin enough to produce hard X–rays (Patterson Raymond, 1985), i.e. an optically thin region where accretion energy is released." + 3., 3. + The very wide binary orbit of RS Oph suggests that its disc is likely to be unstable. thus reduce central accretion severely below the value Aland710.“AL.vr1 required. for the thermonuclear model.," The very wide binary orbit of RS Oph suggests that its disc is likely to be unstable, and thus reduce central accretion severely below the value $\dot M \ga 10^{-8}\msun~{\rm yr}^{-1}$ required for the thermonuclear model." + To avoid this the outer dise radius must be smaller than 2«10.2e. where α is the binary separation.," To avoid this the outer disc radius must be smaller than $\sim + 2\times 10^{-3}a$, where $a$ is the binary separation." + This is ruled out if the giant. fills its Roche lobe. and very unlikely even if mass transfer is via stellar wind capture. since the wind speed is rather less than the orbital velocity of the giant conipanion.," This is ruled out if the giant fills its Roche lobe, and very unlikely even if mass transfer is via stellar wind capture, since the wind speed is rather less than the orbital velocity of the giant companion." + We note finally that the chwarl novatype outbursts considered in Section 2 imply a mean white cdwarl accretion rate Ady<710MAL.ve‘of20 vr (note that mass loss during the outburst makes this an upper limit).," We note finally that the dwarf nova–type outbursts considered in Section 2 imply a mean white dwarf accretion rate $\dot M_0 \la +7\times 10^{-8}\msun\, {\rm yr}^{-1}$ yr (note that mass loss during the outburst makes this an upper limit)." + With a non.extreme white dwarl mass one might then speculate on a thermonuclear nova occurring alter a few outbursts., With a non–extreme white dwarf mass one might then speculate on a thermonuclear nova occurring after a few outbursts. + However the ultimate source of mass is not the disc. but the companion star.," However the ultimate source of mass is not the disc, but the companion star." + Unless this transfers mass at a rate 2 My. the dise will run out of mass and the outbursts will recur more slowly.," Unless this transfers mass at a rate $\ga \dot M_0$ , the disc will run out of mass and the outbursts will recur more slowly." + This is another way of saving that (as always) the nova recurrence, This is another way of saying that (as always) the nova recurrence +Rotationally supported disks account for only a small fraction of the mass in the local Universe. but they contain most of the angular momentum (hereafter AM).,"Rotationally supported disks account for only a small fraction of the mass in the local Universe, but they contain most of the angular momentum (hereafter AM)." +" The way disks acquire anc redistribute their AM represents one of the most challenging problems for models of galaxy formation and evolution,", The way disks acquire and redistribute their AM represents one of the most challenging problems for models of galaxy formation and evolution. + According to the current cosmological paradigm. baryons anc dark halos in galaxies aequire their spin through tidal torques exerted by adjacent structures at early times.," According to the current cosmological paradigm, baryons and dark halos in galaxies acquire their spin through tidal torques exerted by adjacent structures at early times." + This AM ts ther redistributed among the different galaxy components through a number of internal and external processes as the galaxy evolves., This AM is then redistributed among the different galaxy components through a number of internal and external processes as the galaxy evolves. + Among the internal processes. bars. lopsidedness. spiral patterns and other coherent structures are efficient in redistributing AM in galaxies. as many studies have shown (e.g..222)..," Among the internal processes, bars, lopsidedness, spiral patterns and other coherent structures are efficient in redistributing AM in galaxies, as many studies have shown \citep[e.g.,][]{athanassoula205,debattista206,minchev210}." + These stellar asymmetries can be stimulated or strengthened by external processes. such as accretion of a few M« yr! of gas from cosmological filaments (see??) or tidal interactions and mergers (???)..," These stellar asymmetries can be stimulated or strengthened by external processes, such as accretion of a few $_{\odot}$ $^{-1}$ of gas from cosmological filaments \citep[see][]{bournaud205a,bournaud205b} or tidal interactions and mergers \citep{jogM206,mapelliMBH208,reichard209}." +" In particular. during an interaction orbital AM is converted into internal rotation, in an outside-1n manner: the components which first interact are the most extended ones. while the more tightly bound components experience strong tidal effects only in the final phases of the merging process (22?).."," In particular, during an interaction orbital AM is converted into internal rotation, in an outside-in manner: the components which first interact are the most extended ones, while the more tightly bound components experience strong tidal effects only in the final phases of the merging process \citep{barnes192,dimatteo208a,dimatteo209}." + Many studies have shown that major mergers have a catastrophic impact on the ordered motion of the pre-existing galaxies., Many studies have shown that major mergers have a catastrophic impact on the ordered motion of the pre-existing galaxies. + If the progenitors have disks. they are usually destroyed by the strong energy and AM redistribution taking place during the interaction (?????).. unless peculiar orbital configurations are chosen (??)..," If the progenitors have disks, they are usually destroyed by the strong energy and AM redistribution taking place during the interaction \citep{toomre177,bendo200, naabB203,bournaudJC205,jesseit209}, , unless peculiar orbital configurations are chosen \citep{puerari201,crocker209}." + The fraction of gas present in the progenitor disks can also influence the morphology and kinematics of the final remnant (e.g..?).. but this depends as well on the gas physics implemented in the models (e.g..?)..," The fraction of gas present in the progenitor disks can also influence the morphology and kinematics of the final remnant \citep[e.g.,][]{hopkins209}, but this depends as well on the gas physics implemented in the models \citep[e.g.,][]{bournaud210}." + In the case of pressure-supported progenitors. in turn. the tidal torques exerted by the companion can be strong enough to produce high rotational support (v/c> 1) at large radit. even in merger remnants having an elliptical-like morphology (?)..," In the case of pressure-supported progenitors, in turn, the tidal torques exerted by the companion can be strong enough to produce high rotational support $v/\sigma>1$ ) at large radii, even in merger remnants having an elliptical-like morphology \citep{dimatteo209}." + More attention has been given to the study of the impact of AM redistribution in major mergers than in minor mergers (with mass ratios «0.10., More attention has been given to the study of the impact of AM redistribution in major mergers than in minor mergers (with mass ratios $\le$ 0.1). + This despite the fact that minor mergers are expected to be much more common than major mergers (?) and that many traces of ongoing or past interactions are visible both in the Milky Way (see?.forarecentreview).. our neighbor galaxy Andromeda (??) and other galaxies in the local Universe (2)..," This despite the fact that minor mergers are expected to be much more common than major mergers \citep{fakhouriM208} and that many traces of ongoing or past interactions are visible both in the Milky Way \citep[see][for a recent review]{klement210}, our neighbor galaxy Andromeda \citep{ibata201,mcconnachie209} and other galaxies in the local Universe \citep{martinez-delgado210}." + ?. pointed out that the AM redistribution during minor mergers also have an impact on the kinematics of stellar disks and may explain the distribution of the orbital eccentricities of stars in the solar neighborhood., \citet{dimatteo210} pointed out that the AM redistribution during minor mergers also have an impact on the kinematics of stellar disks and may explain the distribution of the orbital eccentricities of stars in the solar neighborhood. + Understanding how AM ts redistributed during such episodes is fundamental to the understanding of how disks can be maintained. how their kinematies can be affected. and what the signatures are of these processes on the dynamical properties of different stellar populations.," Understanding how AM is redistributed during such episodes is fundamental to the understanding of how disks can be maintained, how their kinematics can be affected, and what the signatures are of these processes on the dynamical properties of different stellar populations." + This paper is the second of a series where we study. by means of numerical simulations. the impact of minor mergers on AM redistribution in galaxies.," This paper is the second of a series where we study, by means of numerical simulations, the impact of minor mergers on AM redistribution in galaxies." + In? (hereafter Paper 1). we investigated the impact of dissipationless minor mergers on disk galaxies. showing in particular that the initially non-rotating dark matter halo of the primary galaxy always gains AM and that the specific AM of the stellar component always decreases.," In \cite{quDM210a} (hereafter Paper I), we investigated the impact of dissipationless minor mergers on disk galaxies, showing in particular that the initially non-rotating dark matter halo of the primary galaxy always gains AM and that the specific AM of the stellar component always decreases." + We also showed that this decrease in AM ts accompanied by a change in stellar velocity anisotropy as the stellar orbits become less tangentially dominated as the merger advances., We also showed that this decrease in AM is accompanied by a change in stellar velocity anisotropy as the stellar orbits become less tangentially dominated as the merger advances. + In this paper. we aim to advance this analysis by studying simulations of dissipative minor mergers. exploring a range of gas fractions and morphological parameters for the primary galaxy and the satellite.," In this paper, we aim to advance this analysis by studying simulations of dissipative minor mergers, exploring a range of gas fractions and morphological parameters for the primary galaxy and the satellite." + Star formation and feedback from supernovae explosions are included in the models. and we are able to trace the AM redistribution of all the galaxy components: dark matter. gas. old stars (1.e.. those already in the galaxies before the interactior starts) and new stars (1.e.. those formed from the gas during the interaction).," Star formation and feedback from supernovae explosions are included in the models, and we are able to trace the AM redistribution of all the galaxy components: dark matter, gas, old stars (i.e., those already in the galaxies before the interaction starts) and new stars (i.e., those formed from the gas during the interaction)." + In particular. we aim to understand if dissipative minor nergers still slow down the stellar disk of the primary galaxy and if stellar populations of different ages show a different AM content and different dynamical properties in the final (1.9... post-merger) disk.," In particular, we aim to understand if dissipative minor mergers still slow down the stellar disk of the primary galaxy and if stellar populations of different ages show a different AM content and different dynamical properties in the final (i.e., post-merger) disk." + The paper is organized as follows: the numerical code. the initial galaxy models and orbital conditions adopted for the runs are described in ??..," The paper is organized as follows: the numerical code, the initial galaxy models and orbital conditions adopted for the runs are described in \ref{model}." + Section 2? presents the main results. in particular how the AM content of gas and the old and new stellarpopulations is affected by a single and by two," Section \ref{results} presents the main results, in particular how the AM content of gas and the old and new stellarpopulations is affected by a single and by two" +An ordinary cilferential equation (ODL) solver derived by Shu ancl Osher (1988) is used. to solve Ίσα (1911.,An ordinary differential equation (ODE) solver derived by Shu and Osher (1988) is used to solve Eq \ref{runge}) ). + Lt is à third order Runec-Wutta that does not increase the total variation of the numerical solution ancl preserves the conservation form of the schemoe., It is a third order Runge-Kutta that does not increase the total variation of the numerical solution and preserves the conservation form of the scheme. + Gravity is included in the gas evolution through the source termi . τον. in Eq. (15)).," Gravity is included in the gas evolution through the source term , ${\bf s}_{i,j,k}$, in Eq. \ref{runge}) )." + This term includes the eradient of the gravitational potential which is produced by the total mass distribution. gas plus dark matter.," This term includes the gradient of the gravitational potential which is produced by the total mass distribution, gas plus dark matter." + The procedure used to solve Poisson's equation (4)) is described in Sec., The procedure used to solve Poisson's equation \ref{poisson1}) ) is described in Sec. + 2.4., 2.4. + The criteria to select the time step is very. important and. it) must be considered. elobally with other time constrains that are unrelated to the gas part., The criteria to select the time step is very important and it must be considered globally with other time constrains that are unrelated to the gas part. + Phorefore. we will cliscuss it in the forthcoming section 2.5.," Therefore, we will discuss it in the forthcoming section 2.5." + The dark matter is treated as a collisionless system of particles., The dark matter is treated as a collisionless system of particles. + Each of these particles evolves obeving the following equations: where X. v—απ=hy.(hyp.0). and oó(f.Xx) are. respectively. the Eulerian coordinates. the peculiar velocity. and the peculiar Newtonian gravitational potential.," Each of these particles evolves obeying the following equations: where ${\bf x}$, ${\bf v}=a(t)\frac{d{\bf x}}{dt}= (v_x, v_y, v_z)$, and $\phi(t,{\bf x})$ are, respectively, the Eulerian coordinates, the peculiar velocity, and the peculiar Newtonian gravitational potential." + When ó(f.x) is known. the position and. velocities of each one of the dark matter particles can be updated from the previous time step.," When $\phi(t,{\bf x})$ is known, the position and velocities of each one of the dark matter particles can be updated from the previous time step." + In our code we solved. these equations using a Lax-Weneroll scheme which is second. order., In our code we solved these equations using a Lax-Wendroff scheme which is second order. + We summarize the steps to eo from time stepn7. where all the variables areknown. to the step on| 1. using an intermediate step E Áoil-gqAX4," We summarize the steps to go from time step$n$, where all the variables areknown, to the step $n+1$ , using an intermediate step $t^{n+{1\over2}}=t^n + {{\Delta t}\over2}$ :" +of interest. ny~107to 10?emο 6gL to 10lan/s. Bo110 15μα vioo1 to 10.,"of interest, $n_0\sim 10^2$to $10^3~\mathrm{cm^{-3}}$ , $v_0\sim 1$ to $10~\mathrm{km/s}$ , $B_0\sim 1$ to $15~\mathrm{\mu G}$, $\chi_{i0} \sim 1$ to $10$." + Henceforth. we shall adopt ionization-recombination equilibrium aud use n;xnte1/2 so that r;=r.1/2 aud Equation (27)) governs steady Cshocks.," Henceforth, we shall adopt ionization-recombination equilibrium and use $n_i\propto n_n^{1/2}$ so that $r_i = r_n^{1/2}$, and Equation \ref{govEq}) ) governs steady Cshocks." + For any given set of parameters ng. vy. Bo. aud \jo. Equation (27)) cau be integrated to obtain a steady C shock solution.," For any given set of parameters $n_0$, $v_0$, $B_0$, and $\chi_{i0}$, Equation \ref{govEq}) ) can be integrated to obtain a steady C shock solution." + However. it is also useful to obtain estimates of the dependence of the C shock thickuess ou the basic flow parameters.," However, it is also useful to obtain estimates of the dependence of the C shock thickness on the basic flow parameters." + This parameterization is potentially useful iu diagnosing magnetic field strenetls from observations., This parameterization is potentially useful in diagnosing magnetic field strengths from observations. + Iu addition. it provides a helpful guide to assessiug tle scales at which ambipolar diffusion becomes importaut in CMS domiuated by stroug turbulence.," In addition, it provides a helpful guide to assessing the scales at which ambipolar diffusion becomes important in GMCs dominated by strong turbulence." + Lf by appropriate simplificatious we can integrate the governing ODE of Equation (27)) analytically. we cau obtain au approximate expression for the shock thickness as a function of rp. vg. Bu. aud yjo.," If, by appropriate simplifications we can integrate the governing ODE of Equation \ref{govEq}) ) analytically, we can obtain an approximate expression for the shock thickness as a function of $n_0$, $v_0$, $B_0$, and $\chi_{i0}$." + Note that. since the governing equatious for oblique shocks are qualitatively similar to the simplified case applied here. the oblique shock thickuess cau be approached using the same methods discussed in this section (see Appendix. A)).," Note that, since the governing equations for oblique shocks are qualitatively similar to the simplified case applied here, the oblique shock thickness can be approached using the same methods discussed in this section (see Appendix \ref{sec:appendix}) )." + From nunerical integrations of Equation (27)) with a rauge of parameters. we have fouud that rafrg drops very quickly at the beginning. becomes flat in the central region. thet increases rapidly uear the other edge of the shock (see bottom panels of Fig.," From numerical integrations of Equation \ref{govEq}) ) with a range of parameters, we have found that $r_n/r_B$ drops very quickly at the beginning, becomes flat in the central region, then increases rapidly near the other edge of the shock (see bottom panels of Fig." + 2. aud 3))., \ref{ana_thick1} and \ref{ana_thick2}) ). + This behavior cau be used to define the thickness of C-type shocks., This behavior can be used to define the thickness of C-type shocks. +" Since the minimum of r,/rg depends on the parameters (see Equation (39)) below). we should ensure that our thickuess clefinition is insensitive to this value."," Since the minimum of $r_n/r_B$ depends on the parameters (see Equation \ref{rndrBmin}) ) below), we should ensure that our thickness definition is insensitive to this value." + Based ou these cousideratious. we adopt the following definition of shock thickness for exact numerical solutions: Note that for some weak shocks. μη is always larger than 0.95.," Based on these considerations, we adopt the following definition of shock thickness for exact numerical solutions: Note that for some weak shocks, $r_n/r_B$ is always larger than $0.95$." + Therefore this definition also provides limitations in the parameter space to exclude shocks which are not stroug and thus do not satisfy our stroug shock analysis., Therefore this definition also provides limitations in the parameter space to exclude shocks which are not strong and thus do not satisfy our strong shock analysis. + We have integrated the shock ODE for a rauge of parameters. aud computed the shockthickuess according to the definition in Equation ) (30)).," We have integrated the shock ODE for a range of parameters, and computed the shockthickness according to the definition in Equation \ref{thickDef}) )." + This is the dataset of exact solutions of C shock thickuessH over a parameter gridH withH 410 values ofH ni equally spaced between 4107> aud 410u ciu7. 411 values of e equally spaced between 2 and 15 kin/s. Lf valuesof By equally spacedbetween 2 aud 15 pC. and 11 values of vig equally spaced between 1 and 21.," This is the dataset of exact solutions of C shock thickness over a parameter grid with $10$ values of $n_0$ equally spaced between $10^2$ and $10^3$ $\mathrm{cm^{-3}}$, $14$ values of $v_0$ equally spaced between $2$ and $15$ $\mathrm{km/s}$ , $14$ valuesof $B_0$ equally spacedbetween $2$ and $15$ $\mu\mathrm{G}$ , and $11$ values of $\chi_{i0}$ equally spaced between $1$ and $21$ ." + The range of C shock thickness is 0.1 to 20 pe in this parameter rauge., The range of C shock thickness is $0.1$ to $20$ pc in this parameter range. + Note that all parts of this parameter space are not necessarily, Note that all parts of this parameter space are not necessarily +source count rates of 0.620£0.006s.! and 0.5342€0.005s+ for the two observations.,"source count rates of $0.620 \pm 0.006\mbox{ +s}^{-1}$ and $0.534\pm 0.005\mbox{ s}^{-1}$ for the two observations." + For precision timing analvses we were [forced (to account separately for the charee-(ransler time. (hat is. (he approximately 4 s it takes for the charge packets produced by each X-ray photon [rom the source to be read out from the center of the ACIS-83 chip.," For precision timing analyses we were forced to account separately for the charge-transfer time, that is, the approximately 4 s it takes for the charge packets produced by each X-ray photon from the source to be read out from the center of the ACIS-S3 chip." + We made this correction in (wo different wavs: first. by following an approximate prescription related to us by the AA-rav Center Helpdesk stalk aud. second. by executing a shell script provided to us by Allyn Tennant of the Marshall Space FlightCenter?.," We made this correction in two different ways: first, by following an approximate prescription related to us by the X-ray Center Helpdesk staff; and second, by executing a shell script provided to us by Allyn Tennant of the Marshall Space Flight." +. Results of the two approaches were identical: however. we note (hat the latter approach is superior in (hat it incorporates corrections lor the dither-motion and flexure of the observatory over the course of the observation: (hese corrections will make a difference for analyses requiring significantly more precision (han ours.," Results of the two approaches were identical; however, we note that the latter approach is superior in that it incorporates higher-order corrections for the dither-motion and flexure of the observatory over the course of the observation; these corrections will make a difference for analyses requiring significantly more precision than ours." + rrealtime dala were processed according to the protocols described on the wwebsite’:: note that the ppointing was offset from bby 20 aremin (ο reduce contamination [rom the bright source GRS 19154105. resulting in a [actor of 1.5 decrease in count rates relative to direct-pointing observations due to reduced collimator efficiency.," realtime data were processed according to the protocols described on the web; note that the pointing was offset from by 20 arcmin to reduce contamination from the bright source GRS 1915+105, resulting in a factor of 1.5 decrease in count rates relative to direct-pointing observations due to reduced collimator efficiency." + The spectrum was (particle) background-dominated al high energies. so (ming analvses were performed on 260 keV data only.," The spectrum was (particle) background-dominated at high energies, so timing analyses were performed on 2–60 keV data only." + Our spectral analvsis locused first on the ddata., Our spectral analysis focused first on the data. +" We extracted the events in a large background region and used the CXC tool to bin the source aud background event data and generate (he appropriate response files,", We extracted the events in a large background region and used the CXC tool to bin the source and background event data and generate the appropriate response files. + We then fit the data using the andSherpa packages independently., We then fit the data using the and packages independently. + As a caveat to the results reported below. we note that the continuous-clocking mode of ACIS has not vet been independently calibrated for spectral purposes: our analysis depends on the calibration ol the timed-exposure “Faint” mode of ACIS 5-3. which telemeters an equivalent. quantity of information about each event (3x3 pixel islands).," As a caveat to the results reported below, we note that the continuous-clocking mode of ACIS has not yet been independently calibrated for spectral purposes; our analysis depends on the calibration of the timed-exposure “Faint” mode of ACIS S-3, which telemeters an equivalent quantity of information about each event $3\times 3$ pixel islands)." +" To the extent that photon interaction limes in (he CCD substrate are negligible compared to the CC single-row clocking (ime οἱ 2,85 ms. we expect this calibration to be accurate."," To the extent that photon interaction times in the CCD substrate are negligible compared to the CC single-row clocking time of 2.85 ms, we expect this calibration to be accurate." +where ο equals Newton's gravitational constant. and g is the gravitational acceleration of the star at radius R: where op ts the Stefan-Boltzmann constant.,"where $G$ equals Newton's gravitational constant, and $g$ is the gravitational acceleration of the star at radius $R$: where $\sigma_\mathrm{R}$ is the Stefan-Boltzmann constant." + provide two mass estimates. one for a theoretical calibration Gyispi) and one for an observational calibration Gy).," provide two mass estimates, one for a theoretical calibration $m_\mathrm{MSH1}$ ) and one for an observational calibration $m_\mathrm{MSH2}$ )." + Instead of using spectral type calibrations. a more direct way to derive spectroscopic. masses Is by carefully fitting model atmospheres to high-resolution spectra. where both s. and are determined simultaneously?).," Instead of using spectral type calibrations, a more direct way to derive spectroscopic masses is by carefully fitting model atmospheres to high-resolution spectra, where both $g$, and are determined simultaneously." +. Together with its absolute magnitude it is possible to arrive at a mass using Eqs. (6)), Together with its absolute magnitude it is possible to arrive at a mass using Eqs. \ref{eq:M_spec}) ) + and (7)., and \ref{eq:M_R}) ). + A sample of spectroscopic masses derived with this method will also be compared with dynamical and model masses., A sample of spectroscopic masses derived with this method will also be compared with dynamical and model masses. + Although the results presented here cover a large parameter space. they involve some caveats.," Although the results presented here cover a large parameter space, they involve some caveats." + First of all. both the employed stellar evolution models. as well as the MSHOS5 stellar atmospheres. which define our spectral classes. only cover solar metallicity (z = 0.02).," First of all, both the employed stellar evolution models, as well as the MSH05 stellar atmospheres, which define our spectral classes, only cover solar metallicity (z = 0.02)." + Metallicity is known to have a very strong influence on the evolution and atmospheres of (O) stars via their metallicity-dependent winds., Metallicity is known to have a very strong influence on the evolution and atmospheres of (O) stars via their metallicity-dependent winds. + The newly developed spectral type definitions for LMC and SMC metallicities are a first step to loosen these limitations. but are not as thoroughly based as the MSHOS work for solar metallicity.," The newly developed spectral type definitions for LMC and SMC metallicities are a first step to loosen these limitations, but are not as thoroughly based as the MSH05 work for solar metallicity." + Table | shows the spectral evolution of a series of massive stellar models of different metallicities using the spectral type definitions in Table 1.., Table \ref{tab:MM03z20} shows the spectral evolution of a series of massive stellar models of different metallicities using the spectral type definitions in Table \ref{tab:LTgrid}. + While these spectral type definitions are based on solar netallicity atmospheres or empirical calibrations (for z= 0.008 and z= 0.004). considerable differences in the evolution are noticeable.," While these spectral type definitions are based on solar metallicity atmospheres or empirical calibrations (for z= 0.008 and z= 0.004), considerable differences in the evolution are noticeable." + Another relevant aspect for the evolution of massive stars concerns binary evolution., Another relevant aspect for the evolution of massive stars concerns binary evolution. + Because many (if not most) massive stars are part of a binary system. often with considerable secondary masses(2222??). they could be capable of influencing each other's. evolution in. a. profound. manner.," Because many (if not most) massive stars are part of a binary system, often with considerable secondary masses, they could be capable of influencing each other's evolution in a profound manner." + Because all observations presented in Table 2. involve eclipsing binaries. all the objects must form tight pairs with reasonably large stars. and therefore binary evolution is bound to be important. but it is à non-trivial matter to account for it.," Because all observations presented in Table \ref{tab:dyn} + involve eclipsing binaries, all the objects must form tight pairs with reasonably large stars, and therefore binary evolution is bound to be important, but it is a non-trivial matter to account for it." + Ás was mentioned in the introduction. an. additional potential prime source for errors in the mass determination concerns the atmosphere and wind parameters. as well as the mass-loss prescription employed in the evolutionary models.," As was mentioned in the introduction, an additional potential prime source for errors in the mass determination concerns the atmosphere and wind parameters, as well as the mass-loss prescription employed in the evolutionary models." + In recent years. observational techniques allowed us to measure masses of very massive stars directly by observing the orbits of massive eclipsing binaries.," In recent years, observational techniques allowed us to measure masses of very massive stars directly by observing the orbits of massive eclipsing binaries." + In Table 2. the dynamical mass estimates for 33 very massive stars are listed., In Table \ref{tab:dyn} the dynamical mass estimates for 33 very massive stars are listed. + The majority of the stars (22) are from a compilation by?.. who provides three lists with massive binaries from the literature.," The majority of the stars (22) are from a compilation by, who provides three lists with massive binaries from the literature." + His first list shows detached systems. the second one non-eclipsing binaries (with lower mass limits only) and the third systems. which are either dynamically evolved (semi-detached or contact systems) or contain giants or supergiants.," His first list shows detached systems, the second one non-eclipsing binaries (with lower mass limits only) and the third systems, which are either dynamically evolved (semi-detached or contact systems) or contain giants or supergiants." + All but two systems from the first list are included in Table 2 as are three systems form the third list. two of them are given as being before the interaction stage and the supergiant V729 Cys.," All but two systems from the first list are included in Table \ref{tab:dyn} as are three systems form the third list, two of them are given as being before the interaction stage and the supergiant V729 Cyg." + The systems with lower limits only and the ones which are dynamically evolved are not suitable for the current study and are therefore not included., The systems with lower limits only and the ones which are dynamically evolved are not suitable for the current study and are therefore not included. + The remaining eclipsing binaries except one are from literature published after the list. but which contain the necessary data for this study.," The remaining eclipsing binaries except one are from literature published after the list, but which contain the necessary data for this study." + The exception is WR22 B. which is not covered in because the primary is a Wolf-Rayet star.," The exception is WR22 B, which is not covered in because the primary is a Wolf-Rayet star." + The dynamical masses from Table 2. involve present-day nasses instead of initial masses., The dynamical masses from Table \ref{tab:dyn} involve present-day masses instead of initial masses. + This ts accounted for by not only comparing the evolving parameters with the luminosity and grid. but by simultaneously keeping track of the initial nass.," This is accounted for by not only comparing the evolving parameters with the luminosity and grid, but by simultaneously keeping track of the initial mass." + Therefore. in Table + the initial stellar mass for a spectral type is given as well as the possible minimal and maximal nass when the stars enter and leave the respective spectral type.," Therefore, in Table \ref{tab:Orot} the initial stellar mass for a spectral type is given as well as the possible minimal and maximal mass when the stars enter and leave the respective spectral type." + Additionally. the minimal and maximal age is given when the nodels enter and leave aspectral type.," Additionally, the minimal and maximal age is given when the models enter and leave aspectral type." + In addition to dynamical mass determinations. several spectroscopic masses exist for O-type stars.," In addition to dynamical mass determinations, several spectroscopic masses exist for O-type stars." + Table 3 shows a compilation of these spectroscopic masses taken from ?," Table \ref{tab:spec} shows a compilation of these spectroscopic masses taken from ," + Table 3 shows a compilation of these spectroscopic masses taken from ?.," Table \ref{tab:spec} shows a compilation of these spectroscopic masses taken from ," + Table 3 shows a compilation of these spectroscopic masses taken from ?..," Table \ref{tab:spec} shows a compilation of these spectroscopic masses taken from ," +probability law: where P is the probability. / represents the CAIRD element. m is the synthetic (1ocel) CMRD. and nis the observed CAIRD.,"probability law: where $P$ is the probability, $i$ represents the CMRD element, $m$ is the synthetic (model) CMRD, and $n$ is the observed CMRD." + Maximizing this value for an unchanging observed (ΑΠΛΟ is the equivalent of minimizing the Poisson equivalent of 47., Maximizing this value for an unchanging observed CMRD is the equivalent of minimizing the Poisson equivalent of $\chi^2$. +" By determining the combination of cluster formation rates and mass function slope that minimizes this equation. as well as the acceptable range of values surrounding the minimum. we can thus determine these values empirically,"," By determining the combination of cluster formation rates and mass function slope that minimizes this equation, as well as the acceptable range of values surrounding the minimum, we can thus determine these values empirically." + We also anticipate being able to constrain the cluster radius distribution., We also anticipate being able to constrain the cluster radius distribution. + Once we have compiled sulflicient data. we will also attempt to constrain the lower-mass cutoff (or anv slope change) in the mass function.," Once we have compiled sufficient data, we will also attempt to constrain the lower-mass cutoff (or any slope change) in the mass function." + Details of the statistics. including a derivation of this formula. an explanation of why V cannot be used with Poisson-distributed data. importance of using noiseless synthetic CAIRDs. and techniques for evaluating the quality of the best lit and uncertainties in the parameters are found in Dolphin(2002): we do not wish to duplicate the lenetly discussion of statistics here and instead refer (he reader to that paper.," Details of the statistics, including a derivation of this formula, an explanation of why $\chi^2$ cannot be used with Poisson-distributed data, importance of using noiseless synthetic CMRDs, and techniques for evaluating the quality of the best fit and uncertainties in the parameters are found in \citet{dol02b}; we do not wish to duplicate the lengthy discussion of statistics here and instead refer the reader to that paper." + Belore concluding our example analvsis of NGC 3627. we wish to demonstrate the effecliveness of our analysis technique via application to a simulated galaxy.," Before concluding our example analysis of NGC 3627, we wish to demonstrate the effectiveness of our analysis technique via application to a simulated galaxy." + To make the results of this exercise directly comparable to our NGC 3627 study. we will use (he parameters producing the best fit to NGC 3627's cluster population.," To make the results of this exercise directly comparable to our NGC 3627 study, we will use the parameters producing the best fit to NGC 3627's cluster population." +" These values are shown as the ""ónpul values in Table 1..", These values are shown as the “input” values in Table \ref{tab_synthfit}. + Our first test was to determine the parameters (hat produced the best fit to the synthetic data., Our first test was to determine the parameters that produced the best fit to the synthetic data. + A comparison between these values and those used io create the svnthetie data will test our technique for any biases., A comparison between these values and those used to create the synthetic data will test our technique for any biases. + While some difference is expected (because (he simulated observed CMBRD was randomly populated). one expects that the differences between the," While some difference is expected (because the simulated observed CMRD was randomly populated), one expects that the differences between the" +models are therefore unsuitable for applications to neutron stars as pointed out by 2..,models are therefore unsuitable for applications to neutron stars as pointed out by \citet{glendenning-00}. + In order to reproduce the properties of finite nuclei and infinite nuclear matter with the same level of accuracy as the non-relativistic elfective forces discussed in Section 9.. other mesons must be included.," In order to reproduce the properties of finite nuclei and infinite nuclear matter with the same level of accuracy as the non-relativistic effective forces discussed in Section \ref{sect.examples}, other mesons must be included." + Besides non-linear self-meson interactions must be introduced. (see for instance chapter 4 of ?))., Besides non-linear self-meson interactions must be introduced (see for instance chapter 4 of \citealt{glendenning-00}) ). + For the present time. we will restrict the discussion of the entrainment elfects to the a mocel.," For the present time, we will restrict the discussion of the entrainment effects to the $\sigma-\omega$ model." + Phe mocdels considered by ? can be significantly improved (keeping in mind the inherent limitations of such models) by simply refitting the parameters., The models considered by \citet{comer-03} can be significantly improved (keeping in mind the inherent limitations of such models) by simply refitting the parameters. + With only two free parameters e; and e. only two of the symmetric infinite nuclear matter properties listed in Table 3. can be fitted exactly.," With only two free parameters $c_\sigma$ and $c_\omega$, only two of the symmetric infinite nuclear matter properties listed in Table \ref{table.forces.properties} can be fitted exactly." +" We have constructed three new parameter sets BLI-BL3 by fixing the saturation density to ny=0.16 fm5 and (1) the binding energy per nucleon to e.=16 MeV for DLI. (ii) the Dirac effective mass to mp=0.7m for DL2. (ii) the svmametry energy to e,=28 MeV for BL3 (the fitting procedure did not converge for e,=30 MeV)."," We have constructed three new parameter sets BL1-BL3 by fixing the saturation density to $n_0=0.16$ $^{-3}$ and (i) the binding energy per nucleon to $a_v=-16$ MeV for BL1, (ii) the Dirac effective mass to $m_D=0.7 m$ for BL2, (iii) the symmetry energy to $a_s=28$ MeV for BL3 (the fitting procedure did not converge for $a_s=30$ MeV)." + The parameters of these new models are given in Table 4.., The parameters of these new models are given in Table \ref{table.meson.couplings}. + As can be seen in comparing Table 5 and 3.. the overall agreement with empirical nuclear data is still very poor rellecting the lack of llexibilitv of these @dw models.," As can be seen in comparing Table \ref{table.rmf.properties} and \ref{table.forces.properties}, the overall agreement with empirical nuclear data is still very poor reflecting the lack of flexibility of these $\sigma-\omega$ models." + Phe most important constraint for application to neutron stars is to reproduce at least the equation of state of neutron matter., The most important constraint for application to neutron stars is to reproduce at least the equation of state of neutron matter. + We have thus constructed the parameter set BL4 hy fitting the realistic equation of state of ?.., We have thus constructed the parameter set BL4 by fitting the realistic equation of state of \citet{akmal-98}. + Phe result of the fit is shown in Figure 1E. as well as the predictions of the other mean field. models.," The result of the fit is shown in Figure \ref{fig:eos_pnm_rmf}, as well as the predictions of the other mean field models." + This should be compared with the results of non-relativistic elective forces in Figure L.., This should be compared with the results of non-relativistic effective forces in Figure \ref{fig:eos_pnm}. + Note that the parameter sets GLL GLEE ane BLS predict incorrectly the existence of bound neutron matter.," Note that the parameter sets GLI, GLII and BL3 predict incorrectly the existence of bound neutron matter." + From these four niodels. it seems that the best compromise is achieved for the parameter set BL2. vielding reasonable values of the saturation density. compression modulus. Dirac effective mass (which is an important quantity for entrainment cllects as discussed in Section 9)) together with a fairly good fit of the neutron matter equation of state.," From these four models, it seems that the best compromise is achieved for the parameter set BL2, yielding reasonable values of the saturation density, compression modulus, Dirac effective mass (which is an important quantity for entrainment effects as discussed in Section \ref{sect.examples}) ) together with a fairly good fit of the neutron matter equation of state." + Note however that this mocdel is still very crude compared to the ον or LNS Skyrme forces presented in Section 9.., Note however that this model is still very crude compared to the SLy4 or LNS Skyrme forces presented in Section \ref{sect.examples}. + In particular. the values of the svnimetry energy ας and the binding energy. per nucleon e. which are two basic nuclear matter properties. are unrealistic.," In particular, the values of the symmetry energy $a_s$ and the binding energy per nucleon $a_v$, which are two basic nuclear matter properties, are unrealistic." + We have applied the general expressions derived by ? within the @αἱ mean field models. to evaluate the entrainment parameters and to compare the results with those obtained using the non-relativistic elfective energy. density. functional theory.," We have applied the general expressions derived by \citet{comer-03} within the $\sigma-\omega$ mean field models, to evaluate the entrainment parameters and to compare the results with those obtained using the non-relativistic effective energy density functional theory." + We have greatly improved the models considered by ο (i) by refitting the meson coupling constants leading to a better agreement with nuclear data as discussed: previously. ancl (ii) by including muons which allect the composition of neutron star core and contribute to the pressure.," We have greatly improved the models considered by \citet{comer-03} (i) by refitting the meson coupling constants leading to a better agreement with nuclear data as discussed previously, and (ii) by including muons which affect the composition of neutron star core and contribute to the pressure." + Leptons are treated as ideal relativistic Fermi gases as discussed in Section 9.., Leptons are treated as ideal relativistic Fermi gases as discussed in Section \ref{sect.examples}. + Phe parameters Ay and Ay in the expansion of the master function A. introduced in Section 4.. are given by where Jy and Aly are given by Eqs.(63) and. (AS) respectively in the paper of ?..," The parameters $\lambda_0$ and $\lambda_1$ in the expansion of the master function $\Lambda$, introduced in Section \ref{sect.rel.hydro}, are given by where ${\cal A}\vert_0$ and $\Lambda\vert_0$ are given by Eqs.(63) and (A8) respectively in the paper of \citet{comer-03}." + Note that we have added the muon contribution in the Lagrangian density., Note that we have added the muon contribution in the Lagrangian density. + Using the nucleon chemical potentials given by Eqs.(A9) and. (ALO) of that paper. together with the lepton chemical potentials defined by £20.(23)). we have determined the equilibrium composition of the neutron star core assuming co-moving particles as discussed in Section 7..," Using the nucleon chemical potentials given by Eqs.(A9) and (A10) of that paper, together with the lepton chemical potentials defined by \ref{eq.muX}) ), we have determined the equilibrium composition of the neutron star core assuming co-moving particles as discussed in Section \ref{sect.composition}." + Results are shown in Figure 13. for the parameter set BL2., Results are shown in Figure \ref{fig:BL2_core} for the parameter set BL2. + “Phe proton fraction is very small at low densities unlike that predicted by non-relativistic effective forces., The proton fraction is very small at low densities unlike that predicted by non-relativistic effective forces. + As discussed in Section 9.. this can be understood from the very small (incorrect) value of the symmetry energy ας at saturation density (see Table 5)).," As discussed in Section \ref{sect.examples}, this can be understood from the very small (incorrect) value of the symmetry energy $a_s$ at saturation density (see Table \ref{table.rmf.properties}) )." + As can be seen in Figure 6.. the equation of state is however similar to that obtained for the non-relativistic ellective nucleon-nucleon interactions.," As can be seen in Figure \ref{fig:eos}, the equation of state is however similar to that obtained for the non-relativistic effective nucleon-nucleon interactions." + “Phe reason is that matter in neutron star core is almost pure neutron matter and all mocels SLy4. LNS ancl BL2 reproduce reasonably well the neutron matter equation of state (see Figure 1 anc 14)).," The reason is that matter in neutron star core is almost pure neutron matter and all models SLy4, LNS and BL2 reproduce reasonably well the neutron matter equation of state (see Figure \ref{fig:eos_pnm} and \ref{fig:eos_pnm_rmf}) )." +"hyvdrocvuamic equations of motion to lowest order in ///H. where =c,/€ is the disk scale height (c; is the isothermal sound speed ancl O is the local rotation lvequency) and H is the local radius.","hydrodynamic equations of motion to lowest order in $H/R$, where $H = c_s/\Omega$ is the disk scale height $c_s$ is the isothermal sound speed and $\Omega$ is the local rotation frequency) and $R$ is the local radius." + See Naravanetal.(1987). [or a description., See \cite{ngg87} for a description. + Adopting a local Cartesian coordinate svstem where the vr axis is oriented parallel to (he radius vector and the y axis points forward in azimuth. the equations of motion become where X and J? are the two-dimensional density ancl pressure. v is the fluid velocity ancl ddl is (he Lagrangian derivative.," Adopting a local Cartesian coordinate system where the $x$ axis is oriented parallel to the radius vector and the $y$ axis points forward in azimuth, the equations of motion become where $\Sigma$ and $P$ are the two-dimensional density and pressure, $\bld{v}$ is the fluid velocity and $d/dt$ is the Lagrangian derivative." + The third ancl fourth terms in equation (2)) represent the Coriolis and centrifugal forces in the local model expansion. where q=—(1/2)dlnO2/dInr is (he shear parameter.," The third and fourth terms in equation \ref{EQ2}) ) represent the Coriolis and centrifugal forces in the local model expansion, where $q = -(1/2) \, d\ln\Omega^2/d\ln r$ is the shear parameter." + We will assume throughout that q=3/2. corresponding to a Neplerian shear profile.," We will assume throughout that $q = 3/2$, corresponding to a Keplerian shear profile." + We close the above equations wilh an isothermal equation of state where c; is constant in lime and space., We close the above equations with an isothermal equation of state where $c_s$ is constant in time and space. + Equations (1)) through (3)) can be combined to show that the vertical component of potential vorlicity is a constant of (he motion: i.e.. the potential vorticitv of [Inid elements in (wo dimensions is conserved.," Equations \ref{EQ1}) ) through \ref{EQ3}) ) can be combined to show that the vertical component of potential vorticity is a constant of the motion; i.e., the potential vorticity of fluid elements in two dimensions is conserved." + An equilibrium solution to the equations of motion is, An equilibrium solution to the equations of motion is +"maximum 7.;g/ obtained with S-Method is 45 kK, while the Τε values from Z-Method get as high as 50 kK. The results shown in this paper concerning Ίεῃ/ and U/ are strongly dependent on the kind of atmosphere model used to the grid of models.","maximum / obtained with S-Method is 45 kK, while the / values from Z-Method get as high as 50 kK. The results shown in this paper concerning / and / are strongly dependent on the kind of atmosphere model used to compute the photoionization grid of models." +" In MSBMO3/, we computediscuss in detail the photoionizationmajor differences between, for instance, WM-Basic/ and CMFGEN! (Hillier&Miller1998),, in sofar as the determination of Τεμ/ is concerned."," In /, we discuss in detail the major differences between, for instance, / and / \citep{HM98}, in sofar as the determination of / is concerned." +" Using the CMFGEN! instead of WM-Basic/ atmosphere models would certainly lead to a globally lower Τε (MSBMO3/), and perhaps different gradients."," Using the / instead of / atmosphere models would certainly lead to a globally lower / /), and perhaps different gradients." +" The increase of 7.g/ with Z found here is in contradiction with the theoretical predictions of e.g. Schalleretal.(1992), and if confirmed it might have profond implications for the study of the upper mass end of the IMF."," The increase of / with $Z$ found here is in contradiction with the theoretical predictions of e.g. \citet{SSMM92}, and if confirmed it might have profond implications for the study of the upper mass end of the IMF." +" However, more extensive studies will be needed to check whether the use of different atmospheres codes will confirm the gradients found here or generate genuine gradients."," However, more extensive studies will be needed to check whether the use of different atmospheres codes will confirm the gradients found here or generate genuine gradients." +" Our results, nevertheless, show the importance of taking properly into account the variation in the stellar SEDs with metallicity in any attempt to determine a reliable 7.;/ from Π/ regions."," Our results, nevertheless, show the importance of taking properly into account the variation in the stellar SEDs with metallicity in any attempt to determine a reliable / from / regions." + Based on WM-Basic/ atmosphere models we have computed a large set of photoionisation models., Based on / atmosphere models we have computed a large set of photoionisation models. + From these models we have built excitation diagnostic diagrams based on III/II]/ and IV/TII|/ (mid-IR lines) excitation ratios., From these models we have built excitation diagnostic diagrams based on / and / (mid-IR lines) excitation ratios. + ISO observations of galactic Π/ regions are superimposed to these diagrams., ISO observations of galactic / regions are superimposed to these diagrams. +" According to their metallicity, Teg/ and U/ are determined for every Π/ region."," According to their metallicity, / and / are determined for every / region." +" A correlation between Τε and Ne/Neo/, and an anti-correlation between U/ and Ne/Nec/, have been found, without evidence of any correlation between both Τεµ/ and U/ versus Rga/. The determination of Top;/ is strongly dependent on the changes in stellar SEDs due to the radial metallicity gradient within the Galaxy, while the results found concerning the behaviour of U/ are globally insensitive to this effect."," A correlation between / and /, and an anti-correlation between / and /, have been found, without evidence of any correlation between both / and / versus /. The determination of / is strongly dependent on the changes in stellar SEDs due to the radial metallicity gradient within the Galaxy, while the results found concerning the behaviour of / are globally insensitive to this effect." + The gaseous excitation sequence is therefore mainly driven by the effects of metallicity on the stellar SEDs., The gaseous excitation sequence is therefore mainly driven by the effects of metallicity on the stellar SEDs. + A global increase of Te;/ with metallicity appears nevertheless to be , A global increase of / with metallicity appears nevertheless to be present. +More investigation using different atmosphere codespresent. will be needed to confirm that our conclusions are not unduly biased toward the use of WM-Basic/ models., More investigation using different atmosphere codes will be needed to confirm that our conclusions are not unduly biased toward the use of / models. + Comparison with Τεμ/ determined from direct observations of ionizing stars can also help to evaluate the robustness of the method presented in this work., Comparison with / determined from direct observations of ionizing stars can also help to evaluate the robustness of the method presented in this work. + I am gratefull to Luc Binette and Manuel Peimbert for useful comments and a critical reading of the manuscript., I am gratefull to Luc Binette and Manuel Peimbert for useful comments and a critical reading of the manuscript. + This work was partly supported by the CONACyT (Méxxico) grant 40096-F., This work was partly supported by the CONACyT (Méxxico) grant 40096-F. +detection limits may provide interesting constraints on theory as we describe in Section 5..,detection limits may provide interesting constraints on theory as we describe in Section \ref{sec:conc}. + To select He WD candidates for observation we generally select only those WDs with logg<7.6 (a mass «0.45 M.) and 7.000—1 at high z is the earlier growth of the matter fluctuations."," In the CDM cosmologies with dynamic dark energy, the main consequence of having $w>-1$ at high $z$ is the earlier growth of the matter fluctuations." +" This determines a higher number density of haloes in the quintessence universe than in the standard cosmology at a fixed epoch (see,e.g.Maioetal.2006)."," This determines a higher number density of haloes in the quintessence universe than in the standard cosmology at a fixed epoch \citep[see, e.g.][]{Maio2006}." +". Thereby, the presence of a dark energy component might affect the reionization process, requiring a different ionization efficiency to fully ionize the IGM at a given redshift."," Thereby, the presence of a dark energy component might affect the reionization process, requiring a different ionization efficiency to fully ionize the IGM at a given redshift." +" In this work, we use an analytic approach to investigate how reionization proceeds in quintessence cosmologies."," In this work, we use an analytic approach to investigate how reionization proceeds in quintessence cosmologies." +" In doing this, we consider two different cosmological models for which we assume that the redshift dependence of the equation of state parameter w(z) follows the self-interacting potentials proposed by Peebles&Ratra(2003) and Brax&Martin(2000)."," In doing this, we consider two different cosmological models for which we assume that the redshift dependence of the equation of state parameter $w(z)$ follows the self-interacting potentials proposed by \citet{peebles2003} and \citet{brax2000}." +". The predicted scenario obtained by “painting” the evolution of the HII regions through the (Furlanetto&Oh2005,hereafterFOS) analytic model, is compared to that expected for a ACDM universe."," The predicted scenario obtained by “painting” the evolution of the HII regions through the \cite[][hereafter F05]{furlanetto2005} analytic model, is compared to that expected for a $\Lambda$ CDM universe." + The paper is organized as follows., The paper is organized as follows. + In Section 2 we briefly outline the quintessence cosmologies considered here., In Section \ref{sect:qd} we briefly outline the quintessence cosmologies considered here. + In Section 3 we review the main features of the FOS model., In Section \ref{sect:model} we review the main features of the F05 model. + Section 4 contains the results on the evolution of the ionized bubbles and their properties., Section \ref{sect:res} contains the results on the evolution of the ionized bubbles and their properties. + The final Section 5 summarises our main conclusions., The final Section \ref{sect:conclu} summarises our main conclusions. + The main aim of this paper is to investigate the process of cosmic reionization in quintessence cosmologies and compare to the predicted scenario for a standard flat ACDM universe., The main aim of this paper is to investigate the process of cosmic reionization in quintessence cosmologies and compare to the predicted scenario for a standard flat $\Lambda$ CDM universe. +" Thus, the ACDM cosmology will be our referencecase, for which we assume that the contributions to the present density parameter from cosmological constant, matter, and baryons are Qo,=0.7, Qom=0.3 and Qon=0.046, respectively; the Hubble constant is Ho=70 km/s/Mpc (i.e. h=0.7 in units of 100 km/s/Mpc)."," Thus, the $\Lambda$ CDM cosmology will be our referencecase, for which we assume that the contributions to the present density parameter from cosmological constant, matter, and baryons are $\Omega_{0\Lambda}=0.7$, $\Omega_{\rm 0m}=0.3$ and $\Omega_{\rm +0b}=0.046$, respectively; the Hubble constant is $H_{0}=70$ km/s/Mpc (i.e. $h=0.7$ in units of 100 km/s/Mpc)." + We also fix the normalization of the power spectrum of the matter fluctuations according to og=0.9 and the spectral index is n=1., We also fix the normalization of the power spectrum of the matter fluctuations according to $\sigma_{8}=0.9$ and the spectral index is $n=1$. + These parameters are in agreement with the WMAP first-year data (Spergeletal.2003)., These parameters are in agreement with the WMAP first-year data \citep{spergel2003}. +. We recall that the more recent analysis of the WMAP three-year data (Spergeletal.2007) suggests slightly different values (in particular a lower og and a smaller Qom).," We recall that the more recent analysis of the WMAP three-year data \citep{spergel2007} suggests slightly different values (in particular a lower $\sigma_{8}$ and a smaller $\Omega_{\rm +0m}$ )." +" Our parameter choice, which is done to allow a direct comparison with the similar analysis made by F05, can have some small quantitative effect on some of the results, but cannot alter the general conclusions of our analysis, which is aimed at discussing the expected differences between models where the dark energy component is provided by a cosmological constant or by a dynamic quintessence."," Our parameter choice, which is done to allow a direct comparison with the similar analysis made by F05, can have some small quantitative effect on some of the results, but cannot alter the general conclusions of our analysis, which is aimed at discussing the expected differences between models where the dark energy component is provided by a cosmological constant or by a dynamic quintessence." +" Thus, the dark energy models we consider are cosmological scenarios in which the dynamic dark energy component is characterized by a self-interacting scalar field ®, evolving under the effects of the potential V(9)."," Thus, the dark energy models we consider are cosmological scenarios in which the dynamic dark energy component is characterized by a self-interacting scalar field $\Phi$, evolving under the effects of the potential $V(\Phi)$." +" Here we summarize the main features of these models (seePeebles&Ratra2003,formoredetails).", Here we summarize the main features of these models \citep[see][for more details]{peebles2003}. + The potential has to satisfy the Klein-Gordon equation: where H(z) represents the redshift evolution of the Hubble constant given by the usual Friedmann equation., The potential has to satisfy the Klein-Gordon equation: where $H(z)$ represents the redshift evolution of the Hubble constant given by the usual Friedmann equation. + The corresponding z-evolution of the quintessence parameter w is provided by the equation of state such that w——1 if 6?0.5—0.6 mag. which is obviously larger than the averaged value (1,5~0.2 obtained from a large sample of GRB optical afterglows (e.g.. Ixann et al."," Generally speaking, the required extinctions $A_V>0.5-0.6$ mag, which is obviously larger than the averaged value $\langle A_V\rangle\sim0.2$ obtained from a large sample of GRB optical afterglows (e.g., Kann et al." + 2007)., 2007). +" In fact. a tvpical dust extinction ly~1 mag is identified for some optically ""dark"" GRDs (e.g.. Perlev et al."," In fact, a typical dust extinction $A_V\sim1$ mag is identified for some optically “dark” GRBs (e.g., Perley et al." + 2009)., 2009). + Recent near infrared observations indicate that the line-ol-sight of alterelow of “dark” 0030325 shows heavy exünction wilh an amount ly>2 mag (IHashimoto et al., Recent near infrared observations indicate that the line-of-sight of afterglow of “dark” 080325 shows heavy extinction with an amount $A_V>2$ mag (Hashimoto et al. + 2010)., 2010). + We compile a sample of 18 GRB alterelows with nmulti-wavelength. detections from radio to optical bands., We compile a sample of 18 GRB afterglows with multi-wavelength detections from radio to optical bands. + Comparing (he alterglows with Blazars shows that the afterglows are well consistent with the firmly established Blazar sequence (e.. the (κ) απο The alterglows are only distributed at the low luminosity end of the sequence. which suggests that the GRB alterglows have similar emission mechanism with the high [requency-peaked DL Lac objects.," Comparing the afterglows with Blazars shows that the afterglows are well consistent with the firmly established Blazar sequence (i.e., the $\nu L_{\nu}(\mathrm{5GHz})$ $\alpha_{\mathrm{RO}}$ The afterglows are only distributed at the low luminosity end of the sequence, which suggests that the GRB afterglows have similar emission mechanism with the high frequency-peaked BL Lac objects." + The implication on “dark” GIRDs is also discussed., The implication on “dark” GRBs is also discussed. + The authors would like to thank the anonymous referee lor his/her comments that improve (he paper., The authors would like to thank the anonymous referee for his/her comments that improve the paper. + This work was supported by the National Science Foundation of China (under grant. 10803003)and by (he National Basie Research Program of China (grant 2000252500]., This work was supported by the National Science Foundation of China (under grant 10803008)and by the National Basic Research Program of China (grant 2009CB824800). +A similar result. is found with the variation of the maximum FWIAL with radio size. shown in Figure 4..,"A similar result is found with the variation of the maximum FWHM with radio size, shown in Figure \ref{fwhmsize}." + These two parameters are anti-correlated. at. greater than the significance. level (Spearmann Hank test). with the four sources lving in the ‘shock’ region of the line diagnostic diagram. (Figure 1)) having clearly the highest values.," These two parameters are anti-correlated at greater than the significance level (Spearmann Rank test), with the four sources lying in the `shock' region of the line diagnostic diagram (Figure \ref{linediag}) ) having clearly the highest values." + This latter point is made more clearly. in Figure where the FWLIAL of the OL] 3 emission can be seen to be inversely correlated with the CLL] CCL] 1900 emission line ratio. at the significance level using a Spearmann Rank correlation test.," This latter point is made more clearly in Figure \ref{cratfwhm} + where the FWHM of the [OII] 3727 emission can be seen to be inversely correlated with the CIII] CII] 1909 emission line ratio, at the significance level using a Spearmann Rank correlation test." + The kinematical and ionisation properties of these galaxies are fundamentally connected., The kinematical and ionisation properties of these galaxies are fundamentally connected. + It is not only the kinematics of the eas that evolve with the radio source size. but also the physical extent ancl th luminosity of the line emission.," It is not only the kinematics of the gas that evolve with the radio source size, but also the physical extent and the luminosity of the line emission." + Figure 6 shows the variation of the equivalent width of the OH] 3727 emission line with increasing size of the radio source., Figure \ref{EWsize} shows the variation of the equivalent width of the [OII] 3727 emission line with increasing size of the radio source. + Although this correlation is less strong significance in à Spearmann Rank test). it is apparent that the small sources in the ‘shockdominated? region of Figure 1. show enhanced OL] 3727 equivalent widths.," Although this correlation is less strong significance in a Spearmann Rank test), it is apparent that the small sources in the `shock–dominated' region of Figure \ref{linediag} show enhanced [OII] 3727 equivalent widths." + A more accurate description of Figure 6 is not that there is an inverse correlation between the equivalent width of the ΟΠ) emission and radio size. but rather that at large (κ150 kkpce) radio sizes the distribution of equivalent widths is fairly Dat. and at small sizes there is often a factor of 2 to 3 excess emission relative to this level.," A more accurate description of Figure \ref{EWsize} is not that there is an inverse correlation between the equivalent width of the [OII] emission and radio size, but rather that at large $\gta 150$ kpc) radio sizes the distribution of equivalent widths is fairly flat, and at small sizes there is often a factor of 2 to 3 excess emission relative to this level." + This enhancement of the line of small racio sources with respect to large sources implies an even &reater boosting of their linehaminosilies. lor two reasons.," This enhancement of the line of small radio sources with respect to large sources implies an even greater boosting of their line, for two reasons." + First. the optical continuum emission of small radio sources is more luminous than that of large sources. as indicated by Jost shorteitebest6a.. decreasing the apparent increase in the emission line equivalent width.," First, the optical continuum emission of small radio sources is more luminous than that of large sources, as indicated by Best \\shortcite{bes96a}, decreasing the apparent increase in the emission line equivalent width." + Second. the equivalent width is determined. from the extracted. 1.dimensional spectrum from a spatial region along the slit of about kkpe (see Paper D): the physical extent of the emission line regions of small racio sources is greater than that of large racio sources. as shown in Figure 7..," Second, the equivalent width is determined from the extracted 1–dimensional spectrum from a spatial region along the slit of about kpc (see Paper 1); the physical extent of the emission line regions of small radio sources is greater than that of large radio sources, as shown in Figure \ref{emissize}." + Excluding ὃς200. which is an exceptional source in many wavs (e.g. see discussion in Jost 11997). the emission line regions of radio sources with sizes <200 kkpe have total extents of up to about kkpe kkpe racius. i£ symmetrical).," Excluding 3C265, which is an exceptional source in many ways (e.g. see discussion in Best 1997), the emission line regions of radio sources with sizes $\gta 200$ kpc have total extents of up to about kpc kpc radius, if symmetrical)." + Smaller radio sources. however. have emission line regions ranging from this size up to about kkpe. a size comparable to the extent of the radio source.," Smaller radio sources, however, have emission line regions ranging from this size up to about kpc, a size comparable to the extent of the radio source." + 1n other words. line emission at clistances from the AGN of 30 to 5SOkkpe generally is only seen at the stage of radio source evolution when the hotspots are passing. or have just passed. through this region.," In other words, line emission at distances from the AGN of 30 to kpc generally is only seen at the stage of radio source evolution when the hotspots are passing, or have just passed, through this region." + A number of results have been derived in. the previous sections and these are summarised here for clarity., A number of results have been derived in the previous sections and these are summarised here for clarity. + Ae[ore discussing the interpretation ο these correlations. first a comparison is made to see if such results also hold for low redshift radio galaxies.," Before discussing the interpretation of these correlations, first a comparison is made to see if such results also hold for low redshift radio galaxies." + Jaum studied the ionisation and kinematics of a sample of 40 radio galaxies with redshifts z£0.2., Baum \\shortcite{bau92} studied the ionisation and kinematics of a sample of 40 radio galaxies with redshifts $z \lta 0.2$. + Their sample contained a large mixture of radio source types. including both Fanarolf. Riley (1974: hereafter. class Land Lb as well as sources with intermediate structures.," Their sample contained a large mixture of radio source types, including both Fanaroff Riley (1974; hereafter \nocite{fan74} class I and II as well as sources with intermediate structures." + Many dillerences are now known to exist between the FRI and FRAIL sources besides the large dillerences at racio wavelengths. such as the luminosity and environments of their host. galaxies (?:7:?).. the luminosity of their emission line gas (2).. dilferences in the cust properties (?).. ancl possibly a dillerent mode of accretion on to the central black hole (?)..," Many differences are now known to exist between the I and II sources besides the large differences at radio wavelengths, such as the luminosity and environments of their host galaxies \cite{hil91,bau95,led96}, the luminosity of their emission line gas \cite{zir95}, differences in the dust properties \cite{dek99}, and possibly a different mode of accretion on to the central black hole \cite{rey96}." + aum aalso found a significant difference in the host. galaxy kinematics between the (wo radio source types., Baum also found a significant difference in the host galaxy kinematics between the two radio source types. +" They classified. the kinematics of the radio galaxies into three classes. ""rotators'. ""calm nonrotators and ‘violent nonrotators'."," They classified the kinematics of the radio galaxies into three classes, `rotators', `calm non–rotators' and `violent non--rotators'." + Thev found that almost all of the IL sources fell into the rotator or violent non-rotator classes: most of the FRAIL ancl intermediate tvpe sources were calm. non-, They found that almost all of the II sources fell into the rotator or violent non-rotator classes; most of the I and intermediate type sources were calm non-rotators. + All of the Ες had strong emission lines with a relatively high ionisation parameter. whilst the FRU and," All of the II's had strong emission lines with a relatively high ionisation parameter, whilst the I and" +M33 (??)..,"M33 \citep{2003ApJ...599..258R,2005ASSL..327..287B}." + We use 30% larger cloud radii for M33 data to overcome the difference in the size measurement technique with the Milky Way data pointed out by ?.., We use $\%$ larger cloud radii for M33 data to overcome the difference in the size measurement technique with the Milky Way data pointed out by \citet{2003ApJ...599..258R}. + The above relation fits the data over two orders of magnitude i1 radius. from | to 100 pc. and it is shown by the continuous line in the three panels of Figure 4..," The above relation fits the data over two orders of magnitude in radius, from 1 to 100 pc, and it is shown by the continuous line in the three panels of Figure \ref{fig:size}." + In the same Figure we plot the data for M33 GMCs (open symbols) (??) and for clouds relative to HII regions in our survey (filled circles).," In the same Figure we plot the data for M33 GMCs (open symbols) \citep{1990ApJ...363..435W,2003ApJ...599..258R} + and for clouds relative to HII regions in our survey (filled circles)." + Cloud sizes derived using a uniform intrinsic line ratio Rz0.5 (bottom panel) are too large to satisfy the observed size-linewidth. relation., Cloud sizes derived using a uniform intrinsic line ratio R=0.5 (bottom panel) are too large to satisfy the observed size-linewidth relation. + Furthermore. cloud masses are too large to be compatible with previous surveys and the median volume density 15 lower by more than a factor 10 than the value in the Milky Way.," Furthermore, cloud masses are too large to be compatible with previous surveys and the median volume density is lower by more than a factor 10 than the value in the Milky Way." + Considering the outer envelope of the clouds in hydrostatic equilibrium with the ISM. we estimate higher densities.," Considering the outer envelope of the clouds in hydrostatic equilibrium with the ISM, we estimate higher densities." + However we cannot derive the parameters of the cloud using only this assumption but their limiting values., However we cannot derive the parameters of the cloud using only this assumption but their limiting values. +" To overcome this limitation. we assume that the size-linewidth relation observed in the Milky Way anc in the GMCs of M33 holds for gravitationally bound cloud cores. and that there is an average scaling factor of the core size with respect to the maximum cloud size D""""* (given i1 Table 5 and plotted with asterisk symbols in the middle panel)."," To overcome this limitation, we assume that the size-linewidth relation observed in the Milky Way and in the GMCs of M33 holds for gravitationally bound cloud cores, and that there is an average scaling factor of the core size with respect to the maximum cloud size $^{max}$ (given in Table 5 and plotted with asterisk symbols in the middle panel)." +" By minimizing the dispersion around the plotted size-linewidth relation. we derive core sizes which are a factor 4 smaller thar D'""*,"," By minimizing the dispersion around the plotted size-linewidth relation, we derive core sizes which are a factor 4 smaller than $^{max}$." + These are shown in the middle panel of Figure 4. by filled circles., These are shown in the middle panel of Figure \ref{fig:size} by filled circles. + In the top panel of the figure we plot cloud sizes relative to the radially varying co model (Table 6)., In the top panel of the figure we plot cloud sizes relative to the radially varying $_{CO}$ model (Table 6). + We can see that despite the large scatter the average cloud size 1s smaller than that of GMCs and not much different than what the linewidth relation predicts., We can see that despite the large scatter the average cloud size is smaller than that of GMCs and not much different than what the size-linewidth relation predicts. + In the previous Section we have seen that we were able to detect CO in most star forming regions and in the proximity of some evolved stars. even though CO lines are generally weaker in the latter case.," In the previous Section we have seen that we were able to detect CO in most star forming regions and in the proximity of some evolved stars, even though CO lines are generally weaker in the latter case." + We shall now examine whether newly born clusters can be distinguished from evolved stars using IRAC color-color diagrams., We shall now examine whether newly born clusters can be distinguished from evolved stars using IRAC color-color diagrams. + Previous studies on closer objects (like the LMC and SMC galaxies) used IRAC color-color diagrams to separate Young Stellar Objects (hereafter YSOs) from stars or from evolved AGBs. and AGBs from HII regions (?????)..," Previous studies on closer objects (like the LMC and SMC galaxies) used IRAC color-color diagrams to separate Young Stellar Objects (hereafter YSOs) from stars or from evolved AGBs, and AGBs from HII regions \citep{2007ApJ...669..327S,2007MNRAS.374..979C,2008AIPC.1001..331M,2009AJ....138.1597B, +2009ApJS..184..172G}." + Models indicate that star formation regions at different stages of the protostar to star evolutionary sequence occupy different areas of the color-color diagrams. even though there is overlapping and not a well defined separation between the various areas (?)..," Models indicate that star formation regions at different stages of the protostar to star evolutionary sequence occupy different areas of the color-color diagrams, even though there is overlapping and not a well defined separation between the various areas \citep{2006ApJS..167..256R}." + Similarly ? have shown that there is no simple diagnostic in color-color or color-magnitude diagrams that can be used to uniquely separate YSOs from AGB stars., Similarly \citet{2009ApJS..184..172G} have shown that there is no simple diagnostic in color-color or color-magnitude diagrams that can be used to uniquely separate YSOs from AGB stars. + Evolved stars of different types (Carbon-rich versus Oxygen-rich for example) lie in separate regions of the IRAC color-color diagram but HII regions are found to lie everywhere (2).., Evolved stars of different types (Carbon-rich versus Oxygen-rich for example) lie in separate regions of the IRAC color-color diagram but HII regions are found to lie everywhere \citep{2009AJ....138.1597B}. + For AGB stars the [3.6]-[8.0] and [3.5]-[4.5] colors are used to separate carbon stars from stars with silicate envelopes due to the presence of silicate and Π.Ο features in the spectra., For AGB stars the [3.6]-[8.0] and [3.5]-[4.5] colors are used to separate carbon stars from stars with silicate envelopes due to the presence of silicate and $H_2 O$ features in the spectra. + These feature affect the [3.6]-[8.0] color excess which seems to correlate with the, These feature affect the [3.6]-[8.0] color excess which seems to correlate with the +" Relsdal1964:Turneretal.1984:Fukugita1992:Nochanek1993:Chaeetal.2004:Mitchell2005:York2005)) Nochanek2005;Chae2005:Treuetal.2006:Koopmans2006) ~90 Myersetal.2003)) 2001)) Oeurietal.2006)) Quy. ου i, Chaeetal.2002:2003:Mitchell2005))"," \citealt{Ref64, TOG84, Fuk92, Koc93, Cha02, Cha03, Cha04a, +Mit05, Yor05}) \citealt{KKS97,MS98,Kee01,KW01,CM03,Ofe03,RK05,Cha05,Tre06,Koo06,Cha06}) \citealt{KP05,KP06}) $\sim 90$ \citealt{Mye03,Bro03}) \citealt{Win01}) \citealt{Ogu06}) $\Om$ $\Ox$ $w_x$ \citealt{Cha02, Cha03, Mit05})" +formation aud is younger.,formation and is younger. + The short boxy/bulge bar was primarily identified iu the IR observations oL evolved stars aud lacks 6.7—C6Hz methanol maser emission. thereby indicatiug it traces an older. more evolved population.," The short boxy/bulge bar was primarily identified in the IR observations of evolved stars and lacks 6.7–GHz methanol maser emission, thereby indicating it traces an older, more evolved population." + Heuce. our observatious agree with the implied age dichotomy iu the bars (e.g.?)..," Hence, our observations agree with the implied age dichotomy in the bars \citep[e.g.][]{lopez01}." + The (near) 3-kpe arm was originally discovered by ? as ali absorption feature with a radial velocity of appximately. —50 Lat oF longitude., The (near) 3–kpc arm was originally discovered by \citet{vanwoerden57} as an absorption feature with a radial velocity of approximately $-$ $^{-1}$ at $^{\circ}$ longitude. + It. was uamed by ? based on the perceived taieet point at longitude —22* corresponding to a Galactocentric racius of 3kkpc (when tle solar «listauce is skpe)., It was named by \citet{oort58} based on the perceived tangent point at longitude $-$ $^{\circ}$ corresponding to a Galactocentric radius of kpc (when the solar distance is kpc). + At this loneituce the clistinet feature bleuds with spiral arii emission., At this longitude the distinct feature blends with spiral arm emission. + Subsedqently tie negative longitude tangent has also been inferred as the cause lor peaks iu the longituclial brig—ltliess jxrofile of radio continnuu at low frequencies (e.g. ? analysis of ?? 108 MHz clea). 2.1 inu eljssion (e.g. 2)). OH/IR star kinematics (e.g.?) aud IR star counts (e.g.2)..," Subsequently the negative longitude tangent has also been inferred as the cause for peaks in the longitudinal brightness profile of radio continuum at low frequencies (e.g. \citet{beuermann85} analysis of \citet{haslam81,haslam82} 408 MHz data), 2.4 $\mu$ m emission (e.g. \citealt{hayakawa81}) ), OH/IR star kinematics \citep[e.g.][]{sevenster99b} and IR star counts \citep[e.g.][]{churchwell09}." + However tle WOr sof? showed that he peak was not evident iu ugher [frequency radio coutinuui1 emissiOll. SUL thas at 1.1 GHz (e.g.7)1 and 5 GHz (e.g.we?2)..," However the work of \citet{hayakawa81} showed that the peak was not evident in higher frequency radio continuum emission, such as at 1.4 GHz \cite[e.g.][]{mathewson62} and 5 GHz \cite[e.g.][]{lockman79}." + A »ositive longitude taugejit has never been clealv observed., A positive longitude tangent has never been clearly observed. + ? infer'ed a tangent at 22.67. (with a velocity o “~110kkimss 5) by ο[n]) a ring-like structure. based ou the riug fit of ? for heHI data across the ougitude range 355° to 6°.," \citet{bania80} inferred a tangent at $^{\circ}$ (with a velocity of $\sim$ $^{-1}$ ) by assuming a ring-like structure, based on the ring fit of \citet{cohen76} for the data across the longitude range $^{\circ}$ to $^{\circ}$." + They found CO emission at <110kkimss 5 out d was1ot distinct from the rest of he Galactic emission.," They found CO emission at $\le$ $^{-1}$, but it was not distinct from the rest of the Galactic emission." + The question remains as to why we clo not see a clear positive longitude t:uigeut., The question remains as to why we do not see a clear positive longitude tangent. + One possible explaiation is that it could be due O greater ¢oscuration aoug the liue of sielit. with a lareer leugth of the Carina-Sagittarius aud Crux-Seutui) ΑΡΗΣ present. compared wih the negaeive tangent (Wwiere the spiral aris have au orientation aliuost perpexlicular to the liie. of sight).," One possible explanation is that it could be due to greater obscuration along the line of sight, with a larger length of the Carina-Sagittarius and Crux-Scutum arms present, compared with the negative tangent (where the spiral arms have an orientation almost perpendicular to the line of sight)." + Recently ? discovered the long spectlated far 3—ipe arm coune‘part in CO emission. traciug both arms betwee c1» longitude.," Recently \citet{dame08} discovered the long speculated far 3–kpc arm counterpart in CO emission, tracing both arms between $\pm$ $^{\circ}$ longitude." + Fort:üv-ive 6.7-CHz nethanol nuers were associated with these parallel structres (??) and one «X tjese. the briehtest kuow1 —vethanol maser 9.621+0.196. has a distance of 5.2+0.6 kkpe determine by astrometric parallax (?)..," Forty-five 6.7–GHz methanol masers were associated with these parallel structures \citep{green09b, caswell10mmb1} and one of these, the brightest known methanol maser 9.621+0.196, has a distance of $\pm$ kpc determined by astrometric parallax \citep{sanna09}." + This places the maser at a CGalactocentric cisance of kkpce. concurring with ow expectatio15 (see previous section) for the Calactocentrie racius of the 3-kpe arus.," This places the maser at a Galactocentric distance of kpc, concurring with our expectations (see previous section) for the Galactocentric radius of the 3–kpc arms." +" The astromeric observaious alsc» sliowed the source to have a velocity component in a radial direction from 11e Galactic centre lj and a velocity component counter to the authors chosen inodel of Galactic rotation (—60kkmss! relative to a [lat rotation curve with circular velocity of η,", The astrometric observations also showed the source to have a velocity component in a radial direction from the Galactic centre $^{-1}$ ) and a velocity component counter to the authors chosen model of Galactic rotation $-$ $^{-1}$ relative to a flat rotation curve with circular velocity of $^{-1}$ ). +"All the data in our possession indicate that some of these stars have a metallicity very close (within 0.03 dex; note that also their Li abundance is comparable; see previous Section) to the Sun, they have a very similar temperature (within 50 K), as well as a comparable age to the Sun, and they are true main sequence stars.","All the data in our possession indicate that some of these stars have a metallicity very close (within 0.03 dex; note that also their Li abundance is comparable; see previous Section) to the Sun, they have a very similar temperature (within 50 K), as well as a comparable age to the Sun, and they are true main sequence stars." + To the best of our knowledge they are the best candidates in M67 to be the closest analogues to our star., To the best of our knowledge they are the best candidates in M67 to be the closest analogues to our star. + In Figure 8 we compare the GIRAFFE spectrum of the Sun with the sum of the spectra of the 10 best stars analogues and of the 5 best analogues in a portion of the spectra which includes Ha and in another including the Li lines., In Figure \ref{fig:solar_twins_comp_Sun} we compare the GIRAFFE spectrum of the Sun with the sum of the spectra of the 10 best stars analogues and of the 5 best analogues in a portion of the spectra which includes $\alpha$ and in another including the Li lines. + The extremely small difference between the solar spectrum and these co-added spectra confirm quantitatively the very close resemblance of these stars to the Sun., The extremely small difference between the solar spectrum and these co-added spectra confirm quantitatively the very close resemblance of these stars to the Sun. + At the request of the referee we performed also a direct comparison between the solar spectrum and the spectrum of our solar analogs., At the request of the referee we performed also a direct comparison between the solar spectrum and the spectrum of our solar analogs. +" We used a y? minimization using a Doppler shift and a re-adjustment of the continuum of the stars of M67 as free parameters, in order to match the observed spectra to the observed GIRAFFE solar spectrum."," We used a $\chi^2$ minimization using a Doppler shift and a re-adjustment of the continuum of the stars of M67 as free parameters, in order to match the observed spectra to the observed GIRAFFE solar spectrum." +" The reduced Y? of the fit, or the associated probability, then provides a mean to rank the M67 stars."," The reduced $\chi^2$ of the fit, or the associated probability, then provides a mean to rank the M67 stars." + We restricted the comparison to a range of 10 ccentered on Ha., We restricted the comparison to a range of 10 centered on $\alpha$. +" While in the fitting of the synthetic spectra the core of the line was excluded from the fitting range, it was here included."," While in the fitting of the synthetic spectra the core of the line was excluded from the fitting range, it was here included." + The LTE synthetic spectra fail to reproduce the core of Ha due to the presence of a chromosphere (absent in the model atmospheres employed by us) and to NLTE effects., The LTE synthetic spectra fail to reproduce the core of $\alpha$ due to the presence of a chromosphere (absent in the model atmospheres employed by us) and to NLTE effects. +" Instead, the sought-for solar analogs must behave exactly like the Sun, including in the core of Ha."," Instead, the sought-for solar analogs must behave exactly like the Sun, including in the core of $\alpha$." +" With this method the three M67 stars which are most similar to the Sun are the stars 1194, 1101 and 637."," With this method the three M67 stars which are most similar to the Sun are the stars 1194, 1101 and 637." +" The result is thus very similar to what obtained by comparing the observed spectra to synthetic spectra, confirming that the stars we selected are very similar to the Sun."," The result is thus very similar to what obtained by comparing the observed spectra to synthetic spectra, confirming that the stars we selected are very similar to the Sun." +" We prefer the method based on synthetic spectra, since the direct comparison to the solar spectrum is affected by the noise present in the latter."," We prefer the method based on synthetic spectra, since the direct comparison to the solar spectrum is affected by the noise present in the latter." +" We would like finally to use the observed B—V colour of the solar analogues to derive in an independent way the B—V colour of the Sun, and this requires to evaluate the cluster reddening."," We would like finally to use the observed $B-V$ colour of the solar analogues to derive in an independent way the $B-V$ colour of the Sun, and this requires to evaluate the cluster reddening." +" The reddening towards M67 has been evaluated by many authors in the last 50 years, and a thorough discussion is given by Taylor(2007)."," The reddening towards M67 has been evaluated by many authors in the last 50 years, and a thorough discussion is given by \cite{Taylor2007}." +". M67 reddening is evaluated by this author in E(B—V)=0.041+0.004, which is accidentally the same value obtained by Anetal.(2007) as the average point of the traditionally accepted range for the cluster."," M67 reddening is evaluated by this author in $E(B-V)=0.041\pm0.004$, which is accidentally the same value obtained by \cite{An2007} as the average point of the traditionally accepted range for the cluster." + We will therefore adopt this value., We will therefore adopt this value. + This implies that the de-reddened colour for the average of our 10 solar analogues is (B—V)o=0.651., This implies that the de-reddened colour for the average of our 10 solar analogues is $(B-V)_{\odot}=0.651$. +" The value is in excellent agreement with what found by inverting the fit of all the stars using the ΤΕΕ, which would have predicted (B—V)g=0.659 and the value obtained by inverting the fit of TH*, which would give (B—V)o=0.651."," The value is in excellent agreement with what found by inverting the fit of all the stars using the $T^{\rm LDR}$ which would have predicted $(B-V)_{\odot}=0.659$ and the value obtained by inverting the fit of $T^{\rm H{\alpha}}$, which would give $(B-V)_{\odot}=0.651$." + It is not simple to evaluate a realistic error estimate for this colour., It is not simple to evaluate a realistic error estimate for this colour. +" This should include: the spread (0.020 mag) around our determination, the uncertainty in the cluster reddening, plus other systematics originating from stellar evolution and photometry."," This should include: the spread (0.020 mag) around our determination, the uncertainty in the cluster reddening, plus other systematics originating from stellar evolution and photometry." + We evaluate the evolutionary effects by investigating the expected variations of the solar color with age and metallicity by using evolutionary models., We evaluate the evolutionary effects by investigating the expected variations of the solar color with age and metallicity by using evolutionary models. + Photometric uncertainties are estimated by comparing Yadav et al. (, Photometric uncertainties are estimated by comparing Yadav et al. ( +2008) photometry with what obtained for this cluster by other groups.,2008) photometry with what obtained for this cluster by other groups. + We use the tracks from Girardietal.(2000) for analyzing differential evolutionary effects., We use the tracks from \cite{Girardi2000} for analyzing differential evolutionary effects. +" Because our stars have a similar effective temperature to the Sun, age has no influence: for stars younger than 5 Gyr of solar Teg, the visual absolute magnitudes and colours do not change in any appreciable way."," Because our stars have a similar effective temperature to the Sun, age has no influence: for stars younger than 5 Gyr of solar $T_{\rm eff}$, the visual absolute magnitudes and colours do not change in any appreciable way." +" If M67 were younger than the Sun,the only effect would be that"," If M67 were younger than the Sun,the only effect would be that" +Typically (his exponential sensitivity is accompanied by a very small rate. so that it is nol very important for stellar evolution.,"Typically this exponential sensitivity is accompanied by a very small rate, so that it is not very important for stellar evolution." + ο bursts arise [from the thermonuclear burning of hydrogen. ancl helium. accreted onto the surface of a neutron star in a binary svstem (see WallaceanclWoosley(1981)))., X-ray bursts arise from the thermonuclear burning of hydrogen and helium accreted onto the surface of a neutron star in a binary system (see \cite{woosrp}) ). +" Characteristic temperatures during burning are a few hundred keV. and characteristic densities are py)&10""g/em?."," Characteristic temperatures during burning are a few hundred keV, and characteristic densities are $\rho Y_e\approx +10^6 {\rm g/cm^3}$." + The creation of nuclei heavier than A240 occurs via the rp-process. in which nuclei undergo (p.5) reactions until (μον approach the proton drip line and/or ;2./ec decay intervenes.," The creation of nuclei heavier than ${\rm +A}\approx 40$ occurs via the process, in which nuclei undergo $({\rm p,\gamma})$ reactions until they approach the proton drip line and/or $\beta^+/{\rm ec}$ decay intervenes." + The time for burning along the rp-process path is set lo some extent by the » {ος liletàime of a few important wailing point nuclei., The time for burning along the process path is set to some extent by the $\beta^+/$ ec lifetime of a few important waiting point nuclei. + Here we present a lew examples ol important rates., Here we present a few examples of important rates. + Three important waiting point nuclei with A0 in Figure 10aa. In differentially-rotating flows, the Keplerian frequency increases with decreasing r even more rapidlythan the sound speed, leading to a decreasing scale-height H [see equation (14))]."," This results in a larger radial velocity gradient $d |u^r_2| / dr>0$ in Figure \ref{fig:global-2}a a. In differentially-rotating flows, the Keplerian frequency increases with decreasing $r$ even more rapidlythan the sound speed, leading to a decreasing scale-height $H$ [see equation \ref{eq:H}) )]." +" The dependence of these two quantities, Ωμ and ος, on the radius in the downstream flow"," The dependence of these two quantities, $\Omega_K$ and $c_s$ , on the radius in the downstream flow" +field.,field. + In Section 5 the projection aud fitting methods are described., In Section 5 the projection and fitting methods are described. + Finally. Section 6 coutains the results aud section 7 the conclusions.," Finally, Section 6 contains the results and section 7 the conclusions." + We analyse in detail a numerical simulation of a star cluster with initial mass My=LOM. on a civeular orbit in an analytic Milkv Way poteutial., We analyse in detail a numerical simulation of a star cluster with initial mass $M_0=10^4\msun$ on a circular orbit in an analytic Milky Way potential. + It is the fiducia cluster sinulation (run 10) discussed in Just et al. (, It is the fiducial cluster simulation (run 10) discussed in Just et al. ( +2009).,2009). + We have chosen this cluster. because if is a fvpica representative for the high-mass end of the observed OC's.," We have chosen this cluster, because it is a typical representative for the high-mass end of the observed OCs." + Since the total mass of the cluster svsteni is doninuatec bv the highauass cud. the correction of biases iu the lnass deteruimation are nost inportaut in that parameter reenne.," Since the total mass of the cluster system is dominated by the high-mass end, the correction of biases in the mass determination are most important in that parameter regime." + The cluster is set up as a Hj=6 Wine node with a halfinass radius of 8ppc., The cluster is set up as a $W_0=6$ King model with a half-mass radius of pc. + The extension of the cluster initially exceeds the Roche lobe imitially leacling to zu Chhaneced mass loss in the first Car., The extension of the cluster initially exceeds the Roche lobe initially leading to an enhanced mass loss in the first Gyr. + We used a Salpeter IME and included mass loss by stellar evolution., We used a Salpeter IMF and included mass loss by stellar evolution. + The total ifctime of he cluster at a circular orbit with Reo= shkkpe is €x., The total lifetime of the cluster at a circular orbit with $R_C=8.5$ kpc is Gyr. + For details of the evolution see Just et al. (, For details of the evolution see Just et al. ( +2009).,2009). + For the ligh-resolution simulation of a dissolving star cluster with jN=10101 particles in the tidal field of the Alilkv Way the direct N-body code oGRAPE! (arfst et al., For the high-resolution simulation of a dissolving star cluster with $N=40404$ particles in the tidal field of the Milky Way the direct $N$ -body code $\phi$ (Harfst et al. + 2007) has been used in combination wit the special-purpose hardware at the Astrononmisches Recheu-Iustitut CARI) inU, 2007) has been used in combination wit the special-purpose hardware at the Astronomisches Rechen-Institut (ARI) in. +eidelbere?.. οὐ is an acrouviu for Parallel Wermute Inteeration withGRAPE., $\phi$ is an acronym for Parallel Hermite Integration with. + The code is written in and uses a fourth-order Termite scheme (Malkino Aarseth 1992) for the orbit integration., The code is written in and uses a fourth-order Hermite scheme (Makino Aarseth 1992) for the orbit integration. + It is parallelized aud uses he MPI library for communication between the processors., It is parallelized and uses the MPI library for communication between the processors. + The force computatious are executed on the fast special-purpose hardwareGRAPE., The force computations are executed on the fast special-purpose hardware. + The special-purpose hardware cards are especially desigued to calculate eravitational forces iu N-body sunulatious very fast usine parallelization with Xpelimiugc» (see IEufst et al., The special-purpose hardware cards are especially designed to calculate gravitational forces in $N$ -body simulations very fast using parallelization with pipelining (see Harfst et al. + 2007 and references therein)., 2007 and references therein). + The code oGRAPE does no use regularization as the codes or (Aarsetl 1999. 2003: Spuzenm 1999) but a standard πο type N-body eravitational softening.," The code $\phi$ does not use regularization as the codes or (Aarseth 1999, 2003; Spurzem 1999) but a standard Plummer type $N$ -body gravitational softening." + The softening leneth iu the model used for the curreut work was €=10? pe., The softening length in the model used for the current work was $\epsilon=10^{-3}$ pc. +" We tested with different softening leugths e=105,10 Land 107 pe that there are no significant differences regarding shape evolution aud star cluster mass loss."," We tested with different softening lengths $\epsilon= 10^{-3}, 10^{-4}$ and $10^{-5}$ pc that there are no significant differences regarding shape evolution and star cluster mass loss." + For the simulation of a star cluster in the tidal feld of the Calaxy the |/N-body woblem is solved im an analytic background potential., For the simulation of a star cluster in the tidal field of the Galaxy the $N$ -body problem is solved in an analytic background potential. + We use au axi-sviuunetric JS-conrponuent imodel. where bulge. dise aud halo are described by Plhuuunuer-INuzuiiu iuodels (Alivamoto Nagai 1975) with the potential The paramcters αν aud AL of the Ally Wav imiodel are given in Table 1. for the three compoucuts.," We use an axi-symmetric 3-component model, where bulge, disc and halo are described by Plummer-Kuzmin models (Miyamoto Nagai 1975) with the potential (R,z) = - The parameters $a, b$ and $M$ of the Milky Way model are given in Table \ref{tab:gal-par} + for the three components." + The top panel of Figure 1. shows the rotation curve of the 3-component model of the Milky Way., The top panel of Figure \ref{fig:frequ} shows the rotation curve of the 3-component model of the Milky Way. + The parameters of the 3-compoucut model are chosen such that the rotation curve matches that of the Milky Way(Dauphole Colin 1995)., The parameters of the 3-component model are chosen such that the rotation curve matches that of the Milky Way(Dauphole Colin 1995). + At the solar radius Ry=8.0 kpe. whichwas," At the solar radius $R_0=8.0$ kpc, whichwas" +Also note that the linear density field is only accurate on large scales 10 Mpc at z~ 7).,Also note that the linear density field is only accurate on large scales $\gsim$ 10 Mpc at $z\sim7$ ). + Thus care should be taken in applying tools (>which rely on the linear density field (such as the standard excursion set formalism) at smaller scales., Thus care should be taken in applying tools which rely on the linear density field (such as the standard excursion set formalism) at smaller scales. +" Nevertheless, we include in 21cmFAST a feature to evolve the density field using fully linear evolution, instead of the perturbation approach discussed above."," Nevertheless, we include in 21cmFAST a feature to evolve the density field using fully linear evolution, instead of the perturbation approach discussed above." + This allows one to generate extremely large boxes at low resolution., This allows one to generate extremely large boxes at low resolution. +" When using this feature, one should make sure that the chosen cell size is indeed in the linear regime at the redshift of interest."," When using this feature, one should make sure that the chosen cell size is indeed in the linear regime at the redshift of interest." + Some results making use of this feature are presented below., Some results making use of this feature are presented below. +" In Fig. 2,,"," In Fig. \ref{fig:filter_den_pdfs}," +" we show the PDFs of the density fields smoothed on scale Reiter, computed from the gas curves), DM curves), and 21cmFAST curves) fields, at z= 20, 15, 10, 7 bottom)."," we show the PDFs of the density fields smoothed on scale $R_{\rm filter}$, computed from the gas ), DM ), and 21cmFAST ) fields, at $z=$ 20, 15, 10, 7 )." +" From the left panel (Reiter=0.5 Mpc), we see that as structure formation progresses, we tend to increasingly over-predict the abundance of small scale underdensities, and under-predict the abundance of large-scale overdensities."," From the left panel $R_{\rm filter}=0.5$ Mpc), we see that as structure formation progresses, we tend to increasingly over-predict the abundance of small scale underdensities, and under-predict the abundance of large-scale overdensities." +" However, even at z=7, our PDFs are accurate at the percent level to over a dex around the mean density."," However, even at $z=7$, our PDFs are accurate at the percent level to over a dex around the mean density." +" Understandably, the agreement between the PDFs becomes better with increasing scale (see the right panel corresponding to Reiter=5 Mpc)."," Understandably, the agreement between the PDFs becomes better with increasing scale (see the right panel corresponding to $R_{\rm filter}=5$ Mpc)." +" Interestingly, the DM distributions match the gas quite well, although this is somewhat of a coincidence, as we shall see from the power spectra below."," Interestingly, the DM distributions match the gas quite well, although this is somewhat of a coincidence, as we shall see from the power spectra below." +" In Figure 3,, we present the density power spectra, defined as A3s(k,2)=K3/(2x?V)(Jó(k,z)|?)x."," In Figure \ref{fig:den_ps}, we present the density power spectra, defined as $\Delta^2_{\rm \delta\delta}(k, z) = k^3/(2\pi^2 V) ~ \langle|\delta({\bf k}, z)|^2\rangle_k$." +" The solid red, dotted green, and dashed blue curves correspond to the gas, DM, and 2|cmFAST fields, respectively."," The solid red, dotted green, and dashed blue curves correspond to the gas, DM, and 21cmFAST fields, respectively." +" On small scales (k>5 Mpc""), the three fields have different power."," On small scales $k \gsim 5$ $^{-1}$ ), the three fields have different power." +" The collapse of gas is initially delayed with respect to the pressureless DM, resulting in less small scale power."," The collapse of gas is initially delayed with respect to the pressureless DM, resulting in less small scale power." +" The perturbation theory approach of 21cmFAST is closer in spirit to the DM evolution, but does not capture virialized structure."," The perturbation theory approach of 21cmFAST is closer in spirit to the DM evolution, but does not capture virialized structure." +" In fact the close agreement at z=7 between the gas and 21cmFAST density power spectra is a coincidence, with the scale flattening of the 21cmFAST power attributable to “shell-crossing” by the matter particles in the Zel’Dovich approximation."," In fact the close agreement at $z=7$ between the gas and 21cmFAST density power spectra is a coincidence, with the small-scale flattening of the 21cmFAST power attributable to ``shell-crossing'' by the matter particles in the Zel'Dovich approximation." +" During reionization, the evolution of the gas is very complicated, since the power spectrum on small scales is sensitive to the thermal history of the reionization model (e.g. ?))."," During reionization, the evolution of the gas is very complicated, since the power spectrum on small scales is sensitive to the thermal history of the reionization model (e.g. \citealt{HG97}) )." +" On large scales (k<0.5 Mpc~'), all three power spectra agree remarkably at all epochs."," On large scales $k\lsim0.5$ $^{-1}$ ), all three power spectra agree remarkably at all epochs." +" To put this into perspective, neither the MWA nor LOFAR have sufficient signal to noise to detect the 21-cm signal beyond k>2 Mpc~! (e.g. ?))."," To put this into perspective, neither the MWA nor LOFAR have sufficient signal to noise to detect the 21-cm signal beyond $k\gsim2$ $^{-1}$ (e.g. \citealt{McQuinn06}) )." +"There are two possibilities for (7/(E7.Vu»D""n(HN.Ov}p naunely Iu the first subcase d iust equal one. so that NY=X54<$5.","There are two possibilities for $(h^q(\P^2,V))_{q=0}^2=(h^i(X,\O_X))_{i=1}^3$, namely In the first subcase $d$ must equal one, so that $X=\tilde{X}=S_1\times S_2$." + Iu the second subcase d must equal two. so that Nis a double cover of X.," In the second subcase $d$ must equal two, so that $\tilde{X}$ is a double cover of $X$." + The next two lemunas could have been proved earlier. but we did not need them until now: first some notation.," The next two lemmas could have been proved earlier, but we did not need them until now; first some notation." + Let ACT2 be the degeneracy locus which: ↻⋜∐⋅⋜⊔⊔↸∖⊓⋅↕∑↸∖↴∖↴↴∖↴↕↕↓∶↴∙⊾↿↕↕⋜↧↥⋅∏↴⋝↥⋅↸∖↴∖↴≺≻↕⊼∶⊸∖≻∏⊾−∙⋜⋯≼⊔↸∖↑≀∶∏↼−∆↴⋝↸∖↕↑↴∖↴↸⊳∪∐∏≻↕↸∖⋯↸∖∐↑∙⋅ . . :io -2 ⋅ ⊟≻↥," Let $\Delta\subset\P^2$ be the degeneracy locus which parametrizes singular fibres of $\pi:X\rightarrow\P^2$, and let $U=\P^2\backslash\Delta$ be its complement." +⋅⊺∠⊂≀⊽↖↖⇁↸∖∐⋜∏⇁↸∖⋜↧↸⊳⋜⋯∪∐↕↸⊳⋜↧↕↕↴∖↴∪⋯∪↥⋅↻↕∐↴∖↴⋯ aud thus We now return to the two subcases of this section., For $t\in U$ we have a canonical isomorphism and thus We now return to the two subcases of this section. +bv an aceretion disc.,by an accretion disc. + Initially the mass of the disc. is comparable to. anc often. greater than the mass of the central object.," Initially the mass of the disc is comparable to, and often greater than the mass of the central object." + Thus. the disc is prone to the appearance of gravitational instabilities which. in most cases. result in the fragmentation of the disc into one or more protostellar objects Bonnell 1994: Bonnell Bate 1994: Burkert. Date Bocenheimer 1997: Whitworth et al.," Thus, the disc is prone to the appearance of gravitational instabilities which, in most cases, result in the fragmentation of the disc into one or more protostellar objects (Bonnell 1994; Bonnell Bate 1994; Burkert, Bate Bodenheimer 1997; Whitworth et al." + 1995)., 1995). + Phe formation of this first. star generally occurs in the lowest of the local potential minima., The formation of this first star generally occurs in the lowest of the local potential minima. + Surrounding condensations with slightly lower gas densities form. additional stars (e.g. in the filaments whose intersection generated the first. dense dump)., Surrounding condensations with slightly lower gas densities form additional stars (e.g. in the filaments whose intersection generated the first dense clump). + Both the stars and the residual gas are attracted bv their mutual gravitational forces ancl [all towards cach other., Both the stars and the residual gas are attracted by their mutual gravitational forces and fall towards each other. + The interactions between the gas and the protostars dissipate some of the kinetic energy of the latter (Bonnell et al., The interactions between the gas and the protostars dissipate some of the kinetic energy of the latter (Bonnell et al. + 1997). allowing the stellar objects to rapidly come close to the initial star ancl its clise-born companions to form a high-density sub-cluster containing from 2 up to S stars: à small cluster.," 1997), allowing the stellar objects to rapidly come close to the initial star and its disc-born companions to form a high-density sub-cluster containing from 2 up to 8 stars: a $N$ cluster." + This process repeats itself in other parts of the eloud., This process repeats itself in other parts of the cloud. + Given the size of the eloud we have modelled Canel consequently. the number of Jeans masses initially. present in the system). no more than 32 of these star-forming sites are ever produced.," Given the size of the cloud we have modelled (and consequently, the number of Jeans masses initially present in the system), no more than 3 of these star-forming sites are ever produced." + Subsequently. sub-clusters are attracted to each other and merge to form the final mini-cluster.," Subsequently, sub-clusters are attracted to each other and merge to form the final mini-cluster." + Thus. the star formation process is hierarchical in nature. as has been vividly illustrated. (for a 1000. M. cloud) by Bonnell. Date Vine (2003).," Thus, the star formation process is hierarchical in nature, as has been vividly illustrated (for a 1000 $_\odot$ cloud) by Bonnell, Bate Vine (2003)." +"LX ""These sub-clusters bear much similarity with the No elusters modelled. by Delgado-Donate.. Clarke Bate (2003: henceforth DCBO3) in the sense that. initially. the cluster Components are arranged in a dynamically unstable configuration."," These sub-clusters bear much similarity with the $N$ clusters modelled by Delgado-Donate, Clarke Bate (2003; henceforth DCB03) in the sense that, initially, the cluster components are arranged in a dynamically unstable configuration." + As the systems seeks to attain stability. the cluster breaks up: the most. massive components [orm a ierarchical multiple (typically a binary or a triple system) whilst the low mass components are ejected. either to large separations or from the cloud. altogether.," As the systems seeks to attain stability, the cluster breaks up: the most massive components form a hierarchical multiple (typically a binary or a triple system) whilst the low mass components are ejected, either to large separations or from the cloud altogether." + In contrast. with he DC€D03 simulations. the number of stellar seeds is not ixed and therefore further star formation events can take ace. introducing dvnamical instability again in the system.," In contrast with the DCB03 simulations, the number of stellar seeds is not fixed and therefore further star formation events can take place, introducing dynamical instability again in the system." + Sub-cluster merging provides an additional complication to he simple small-N cluster picture. as a multiple system can » driven to the proximity of another one so that. further interactions take place.," Sub-cluster merging provides an additional complication to the simple $N$ cluster picture, as a multiple system can be driven to the proximity of another one so that further interactions take place." + The fact that low mass components are the prime candidates to be ejected means that. eiven the high stellar density of cach sub-cluster and the tencdeney of sub-clusters to interact with each other. few bound pairs involving a low mass Component — Le. low mass ratio. wide or low mass pairs can survive the interaction with other cluster members.," The fact that low mass components are the prime candidates to be ejected means that, given the high stellar density of each sub-cluster and the tendency of sub-clusters to interact with each other, few bound pairs involving a low mass component – i.e. low mass ratio, wide or low mass pairs – can survive the interaction with other cluster members." + The binding energy of these pairs is too low., The binding energy of these pairs is too low. + In addition. in he present simulations accretion discs surround most of the stellar objects formed. and when surrounding a binary. tend o drive the mass ratio g to high values (Bate Bonnell 1997).," In addition, in the present simulations accretion discs surround most of the stellar objects formed, and when surrounding a binary, tend to drive the mass ratio $q$ to high values (Bate Bonnell 1997)." + After sub-cluster merging. a new process comes into av: exchange of binary components (Valtonen Alikkola 1991).," After sub-cluster merging, a new process comes into play: exchange of binary components (Valtonen Mikkola 1991)." + Thus. the lightest companions are exchanged by more massive ones and hence. the probability for the surviving rinaries to have nearly equalamass components is enhanced (see also Date. Bonnell Dromnm 2002b).," Thus, the lightest companions are exchanged by more massive ones and hence, the probability for the surviving binaries to have nearly equal-mass components is enhanced (see also Bate, Bonnell Bromm 2002b)." + Lo addition. where quadruples are formed. involving binarv-binary pairs. the surrounding circum-quacdruple disc will tend. to drive the otal masses of cach binary to similar values.," In addition, where quadruples are formed involving binary-binary pairs, the surrounding circum-quadruple disc will tend to drive the total masses of each binary to similar values." + A large fraction of the bodies ejected from the unstable sub-clusters become sub-stellar objects., A large fraction of the bodies ejected from the unstable sub-clusters become sub-stellar objects. + This is so because the ejected objects are typically the low mass components of the system ancl because. after being ejected from the dense region in which the multiple system sits. the ejected. body is largely deprived of further accretion (Reipurth Clarke 2001: Date. Bonnell Bromm 2002a).," This is so because the ejected objects are typically the low mass components of the system and because, after being ejected from the dense region in which the multiple system sits, the ejected body is largely deprived of further accretion (Reipurth Clarke 2001; Bate, Bonnell Bromm 2002a)." + Hence. taking into account that all the objects in these simulations start. with a mass close to the opacity limit (a lew Jupiter masses). it is not surprising that many of the ejectae become brown οπε," Hence, taking into account that all the objects in these simulations start with a mass close to the opacity limit (a few Jupiter masses), it is not surprising that many of the ejectae become brown dwarfs." + The spatial distribution of stars and brown cwarts within each multiple (henceforth the configuration) is shown in Table 1., The spatial distribution of stars and brown dwarfs within each multiple (henceforth the ) is shown in Table 1. + For cach simulation. the column contains two rows: the upper one refers to the internal structure of the multiples at /=0.5 Myr. Le. at the end of the hverodvnamic. caleulation. (hereafter configuration): and the bottom row corresponds to f=10.5 Alvr. Le at the end of the N-bocky integration.," For each simulation, the column contains two rows: the upper one refers to the internal structure of the multiples at $t = +0.5$ Myr, i.e. at the end of the hydrodynamic calculation (hereafter ); and the bottom row corresponds to $t = 10.5$ Myr, i.e at the end of the $N$ -body integration." + All the other columns. except the first two. also refer to both the hivelrodynamic aad: N-body results.," All the other columns, except the first two, also refer to both the hydrodynamic and N-body results." + ]t can be seen from theconfigurations that he basic building blocks of the multiples! internal hierarchy are binary stars., It can be seen from the that the basic building blocks of the multiples' internal hierarchy are binary stars. + This property rellects the origin of these ryotuncl svstems as byproducts of a hierarchical formation srocess. in which the ἱνρίσα outcome of a small cluster disintegration is a tightly bound: binary star.," This property reflects the origin of these bound systems as byproducts of a hierarchical formation process, in which the typical outcome of a $N$ cluster disintegration is a tightly bound binary star." + Subsequent merging of several small-N clusters bind two or more ünaries into one single multiple svstem., Subsequent merging of several $N$ clusters bind two or more binaries into one single multiple system. +" Column 3 (Nu, N.D shows on the left the number of stars and brown dwarfs that remain in multiple svstems at. the. end. of he simulations: in the case that more than one mutually Unbound multiple system is formed. the membership number of cach is separated by commas within brackets."," Column 3 $_{\rm +m}$; $_{\rm s}$ ]) shows on the left the number of stars and brown dwarfs that remain in multiple systems at the end of the simulations; in the case that more than one mutually unbound multiple system is formed, the membership number of each is separated by commas within brackets." + On the right is shown the number of stellar objects that escaped. from the cloud., On the right is shown the number of stellar objects that escaped from the cloud. + Overall. the ratio of unbound to bound objects is approximately 2/3 at 0.5 Myr.," Overall, the ratio of unbound to bound objects is approximately 2/3 at 0.5 Myr." + At an age of 0.5 Myr. of the stars and brown chwarls are locked in 12 multiple systems. with about a third of the components being low-mass. weakly bound outlicrs.," At an age of 0.5 Myr, of the stars and brown dwarfs are locked in 12 multiple systems, with about a third of the components being low-mass, weakly bound outliers." + Exclucing these outliers and unbound singles. of the remaining objects are in pure binaries (2 svstemis). are in quadruples (2 systems). are in quintuples (4 systems). are in sextuples (3 svstems) and are in multiples with seven components (1 svstem).," Excluding these outliers and unbound singles, of the remaining objects are in pure binaries (2 systems), are in quadruples (2 systems), are in quintuples (4 systems), are in sextuples (3 systems) and are in multiples with seven components (1 system)." + Figure 1 shows the value of the mass ratio q (loft panel) ancl semi-major axis e (right panel) of the resulting multiples as a function of primary mass (see figure caption for an explanation of the symbols)., Figure 1 shows the value of the mass ratio $q$ (left panel) and semi-major axis $a$ (right panel) of the resulting multiples as a function of primary mass (see figure caption for an explanation of the symbols). + It can be seen that no binary star withprimary mass larger than <=0.2 M. is formed. despite the initial mass of the components being 200 smaller.," It can be seen that no binary star withprimary mass larger than $\approx 0.2$ $_\odot$ is formed, despite the initial mass of the components being $200 \times$ smaller." + In acclition. all except one binary have q larger than 0.5.," In addition, all except one binary have $q$ larger than 0.5." + The exception appears in the region located between the solid ancl dashed lines. where binaries with brown dwarf companions are found.," The exception appears in the region located between the solid and dashed lines, where binaries with brown dwarf companions are found." + Apart from this binary. brown dwarf companions are only found as wide components of high-order multiples.," Apart from this binary, brown dwarf companions are only found as wide components of high-order multiples." + The right panel illustrates two trends., The right panel illustrates two trends. + Firstly. ANO multiples are typically wider than low-N multiples.," Firstly, $N$ multiples are typically than $N$ multiples." +dillerences. are detected. for the time-scales. ranging from 10% to 40%.,"differences are detected for the time-scales, ranging from $10\%$ to $40\%$." + As cliscussecl above. the ages of simulated discs. are in relatively good agreement with observational results.," As discussed above, the ages of simulated discs are in relatively good agreement with observational results." + However. observations reveal a ereat variety. of clisc-bulec systems and the estimation of their ages still sulfers fron large uncertainties.," However, observations reveal a great variety of disc-bulge systems and the estimation of their ages still suffers from large uncertainties." + As a result. the scatter in disc and bulge ages obtained observationally is large. and ages cover almost the whole possible range between 2 Car and. the Llubble time.," As a result, the scatter in disc and bulge ages obtained observationally is large, and ages cover almost the whole possible range between 2 Gyr and the Hubble time." + Pheoretically. it is however expected that disces erow significantly at. low redshifts. because they are easily disrupted. and they have higher survival probability if they orm late. during more cuiescent evolutionary periods.," Theoretically, it is however expected that discs grow significantly at low redshifts, because they are easily disrupted and they have higher survival probability if they form late, during more quiescent evolutionary periods." + In this context. our simulated. disces are perhaps older han expected or. alternatively. not massive enough. while »ulges are too massive.," In this context, our simulated discs are perhaps older than expected – or, alternatively, not massive enough, while bulges are too massive." + As shown in Table 3.. the cdisc-to- ratios are of the order of 0.2 (kinematicallv-defined) or 40.7 (photomoetricallv-defined).," As shown in Table \ref{table_ages}, the disc-to-total ratios are of the order of $0.2$ (kinematically-defined) or $0.4-0.7$ (photometrically-defined)." + Reeent estimations for he mass of the bulge and the disc of our Milkv Way are ~2LOM ML. and ~65107 ML respectively. (Sofue. llonma Omodaka 2009).," Recent estimations for the mass of the bulge and the disc of our Milky Way are $\sim 2\times 10^{10}$ $_\odot$ and $\sim 6\times 10^{10}$ $_\odot$, respectively (Sofue, Honma Omodaka 2009)." + This translates into a csc-to-otal mass ratio of 0.75 (ignoring the mass in the stellar alo which anywav contributes very little to the total mass)., This translates into a disc-to-total mass ratio of $0.75$ (ignoring the mass in the stellar halo which anyway contributes very little to the total mass). + In simulations. the formation of overly massive bulges and ess massive disces might be due to a number of causes that nave been already. discussed in the literature: inappropriate modelling of the involved physical processes (e.g. Piontek Steinmetz 2010: Agertz. Teyssier Moore 2010). insullicient resolution (e.g. Governato et al.," In simulations, the formation of overly massive bulges and less massive discs might be due to a number of causes that have been already discussed in the literature: inappropriate modelling of the involved physical processes (e.g. Piontek Steinmetz 2010; Agertz, Teyssier Moore 2010), insufficient resolution (e.g. Governato et al." + 2007). or even a failure in the cosmological model (e.g. Sommoer-Larsen Dolgov 2001: Alaver. Governato Ixaufmann 2008).," 2007), or even a failure in the cosmological model (e.g. Sommer-Larsen Dolgov 2001; Mayer, Governato Kaufmann 2008)." + In particular. Agertz et al. (," In particular, Agertz et al. (" +2010) claim that the inability to formi massive clises is due to the adoption of strong feedback combined with high star formation elliciencies.,2010) claim that the inability to form massive discs is due to the adoption of strong feedback combined with high star formation efficiencies. + Note however that although their simulations produce massive discs. they convert baryons into stars with an overall elliciency which is much too high to be consistent with a AC DAL cosmology (e.g. Guo et al.," Note however that although their simulations produce massive discs, they convert baryons into stars with an overall efficiency which is much too high to be consistent with a $\Lambda$ CDM cosmology (e.g. Guo et al." + 2010)., 2010). + In models where supernova feedback. is the main regulating mechanism of star formation. the early formation of very massive bulges may be responsible of the inability to form massive discs later on.," In models where supernova feedback is the main regulating mechanism of star formation, the early formation of very massive bulges may be responsible of the inability to form massive discs later on." + This is because feedback at high redshift drives a wind [rom the inner regions where star formation is taking place. leaving less eas available for late star formation.," This is because feedback at high redshift drives a wind from the inner regions where star formation is taking place, leaving less gas available for late star formation." + This occurs in our mioclel. and is illustrated in Fig. 3::," This occurs in our model, and is illustrated in Fig. \ref{baryonic_mass_evol}:" + the stellar masses (dotted-dashed lines) grow rapidly at carly times. leaving little cold. gas (dotted lines) at late times.," the stellar masses (dotted-dashed lines) grow rapidly at early times, leaving little cold gas (dotted lines) at late times." + Most. of the gas (gas masses are typically 1.54 times lower than the stellar masses) is hot (dashed. lines). and formis gaseous haloes with typical temperatures of 107 Ix. Much gas is also expelled from our haloes. as rellected in the barvon fractions we find. which are in the range 0.07 and 0.10. substantially smaller than the cosmic barvon fraction assumed (Table 1)).," Most of the gas (gas masses are typically $1.5-4$ times lower than the stellar masses) is hot (dashed lines), and forms gaseous haloes with typical temperatures of $10^7$ K. Much gas is also expelled from our haloes, as reflected in the baryon fractions we find, which are in the range $0.07$ and $0.10$, substantially smaller than the cosmic baryon fraction assumed (Table \ref{simulations_table}) )." + Finally. another possible reason for the seenerallv low SEHs at low redshifts ds that our mocoel does not. include the ellects of gas reurn from low- and intermediate-mass stars (Vinsley 1974).," Finally, another possible reason for the generally low SFRs at low redshifts is that our model does not include the effects of gas return from low- and intermediate-mass stars (Tinsley 1974)." + The gas return fraction of a stellar population of given age over the Llubble time can be as high as 40—50%. depending on the LME. and. less strongly. on the metallicity (Jungwiert. Combes Palous 2001).," The gas return fraction of a stellar population of given age over the Hubble time can be as high as $40-50\%$, depending on the IMF and, less strongly, on the metallicity (Jungwiert, Combes Palouš 2001)." + This gas can in principle be added to the disc and formi new stars., This gas can in principle be added to the disc and form new stars. + Thus. up to about half of the stellar mass forming at recishift 2o2 may be returned in the form of gas by 2=0 and be available to make new dise stars (Martig DBournaud 2009).," Thus, up to about half of the stellar mass forming at redshift $z\sim 2$ may be returned in the form of gas by $z=0$ and be available to make new disc stars (Martig Bournaud 2009)." + Llowever. if gas return comes from stars in the bulge. this ellect cannot build extended disces. since such stars have low angular momentum.," However, if gas return comes from stars in the bulge, this effect cannot build extended discs, since such stars have low angular momentum." +stellar population changes. by a factor of approximately 1.1-1.2 from blue to near-infrared (JX-band).,"stellar population changes, by a factor of approximately 1.1-1.2 from blue to near-infrared $K$ -band)." + This would correspond. to a factor of about 1.03-1.06 from g to z., This would correspond to a factor of about 1.03-1.06 from $g$ to $z$. + Since these numbers are very small. a very accurate analysis is needed to derive conclusions from the SDSS database.," Since these numbers are very small, a very accurate analysis is needed to derive conclusions from the SDSS database." + Our results seem to first order in agreement with these numbers., Our results seem to first order in agreement with these numbers. + The derived. scale lenghts ancl our presentation of the transformation coellicients. for. converting observed. scale lengths from one SDSS band to another. furthermore. are meant to be useful tools to test the results of cosmological ealaxy formation models. whether numerical. or semi-analytical.," The derived scale lenghts and our presentation of the transformation coefficients for converting observed scale lengths from one SDSS band to another, furthermore, are meant to be useful tools to test the results of cosmological galaxy formation models, whether numerical, or semi-analytical." + In the future. we plan to add the stored. paranietors orm the Galaxy project to obtain a larger sample with morphological classifications (at this stage. detailed morphologics are not available). but also compare scale οποία as a function. environment. nuclear activity. and colour gradients (e.g.comparingthesamplewiththatofLatziminaoglouetal...2005).," In the future, we plan to add the stored parameters form the Galaxy project to obtain a larger sample with morphological classifications (at this stage, detailed morphologies are not available), but also compare scale length as a function environment, nuclear activity, and colour gradients \citep[e.g., comparing the sample with that of ][]{Chatzimi05}." +. Many. more parameters can »e further investigated. and with the data and the derived parameters at hand. we now have the capability to continue his project in various and potentially unforesecable directions.," Many more parameters can be further investigated, and with the data and the derived parameters at hand, we now have the capability to continue this project in various and potentially unforeseeable directions." + This work made use of EUIRO-VO software. tools and services.," This work made use of EURO-VO software, tools and services." + The EEURO-VO has been funded by the European Commission through contract numbers B1031675. (DCA) and. 011892 (VO-TECLII) under the 6th. Framework Programme and contract number 212104 (AIDA) under the πια Framework Programme., The EURO-VO has been funded by the European Commission through contract numbers RI031675 (DCA) and 011892 (VO-TECH) under the 6th Framework Programme and contract number 212104 (AIDA) under the 7th Framework Programme. + We also acknowledge the use of NASA's SkyView facility. (http://skyvvieweslenasa.gov) located at NASA Cocldarel Space Flight Center. the usage of the Hyperbeda database (http:leda.univ-lvondfr). and the TOCAT software (http:wwwestarlink.ac.uk/topcat/).," We also acknowledge the use of NASA's SkyView facility (http://skyview.gsfc.nasa.gov) located at NASA Goddard Space Flight Center, the usage of the HyperLeda database (http://leda.univ-lyon1.fr), and the TOCAT software (http://www.starlink.ac.uk/topcat/)." + KE acknowledges. support from the Swedish Research Council (Vetenskapsradet). ancl the hospitality. of LESO-Garching where parts of this work were done.," KF acknowledges support from the Swedish Research Council det), and the hospitality of ESO-Garching where parts of this work were done." + Kk also acknowledges support [rom Sergio Gelato for computer support. and fruitful discussions with Robert Cumming and Genoveva Alicheva.," KF also acknowledges support from Sergio Gelato for computer support, and fruitful discussions with Robert Cumming and Genoveva Micheva." + Finally we thank the referee Erederic Bournaucl for insightful ancl encouraging comments which rclped improve our manuscript., Finally we thank the referee Frederic Bournaud for insightful and encouraging comments which helped improve our manuscript. + Funding for the SDSS and SDSS-LE has been provided » the Alfred DP. Sloan Foundation. the Participating Institutions. the National Science. Foundation. the US Department of Enerev. the National Aeronautics and Space Administration. theJapanese Monbukagakusho. the Max Janck Society. and the Higher Ecdueation Funding Council or England.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." + “Phe SDSS Web site is http:wav.sclss.0re The SDSS is managed. by the Astrophysical Research Consortium for the Participatingὃν Institutions., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. + The 'articipating lnstitutions are the American Museumof (ανα {Πρίουν. Astrophysical Institute. Potsdam. University of Basel. University of Cambridge. CaseWestern leserve University. University of Chicago. Drexel University. Fermilab. the Institute. for Advanced Study. the Japan Participation Croup. Johns Hopkins University. the Joint Institute for Nuclear Astrophysics. the Ixavli Institute for Particle Astrophysics ancl Cosmology. the korean Scientist Croup. the Chinese Academy of Sciences (LAMOST). Los Alamos National Laboratory. the Max Planck Institute for Astronomy (AIPLA). the Max. Planck lnstitute for Astrophysics (AIPA). NewAlexico State University. Ohio State University. University of Pittsburgh. University of. Portsmouth. Princeton University. the United. States Naval Observatory. and the University of Washington.," The Participating Institutions are the American Museumof Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, CaseWestern Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max Planck Institute for Astronomy (MPIA), the Max Planck Institute for Astrophysics (MPA), NewMexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington." +(irige@er efficiency has not been well studied. which presents an additional clilliciliv.,"trigger efficiency has not been well studied, which presents an additional difficulty." + We show that by studving the logN. logP? distributions of the aand bbursts. we can justify (hie usage of the heterogeneous redshift sample and set detection thresholds for measuring luminosity functions.," We show that by studying the $\log N$ $\log P$ distributions of the and bursts, we can justify the usage of the heterogeneous redshift sample and set detection thresholds for measuring luminosity functions." + We present the huminositv functions using the heterogeneous redshift sample. where we adopt a cosmology of [fy=70kms.!Mpef. Qj=0.3. and O4=0.7.," We present the luminosity functions using the heterogeneous redshift sample, where we adopt a cosmology of $H_0 = 70~\rm{km~s^{-1}~Mpc^{-1}}$ , $\Omega_{\rm m} = 0.3$, and $\Omega_{\Lambda}= 0.7$." + We use the Sie7ff--BAT GRB catalog published in Sakomoto οἱ al. (, We use the -BAT GRB catalog published in Sakomoto et al. ( +2008).,2008). + The sample consists of 237 bbiursts detected before 2007 June 10., The sample consists of 237 bursts detected before 2007 June 16. + All the bursts are triggered by the BAT instriunent on boardο, All the bursts are triggered by the BAT instrument on board. +"ἱ, The Sweff--BAT catalog contains a number of basic properties of the bursts such as the burst duration. spectral index. and peak photon fIux in several bands."," The -BAT catalog contains a number of basic properties of the bursts such as the burst duration, spectral index, and peak photon flux in several bands." + There are 229 bursts wilh peak photon flux estimates in the 15150 keV band. with a minimum value of 0.23!.," There are 229 bursts with peak photon flux estimates in the 15–150 keV band, with a minimum value of 0.23." +". Of these 229 bursts. 210 bursts can be identified as long bursts and 15 as short bursts. where we divide the sample at 74,=2 s. In this paper. we focus on these 210 long bursts."," Of these 229 bursts, 210 bursts can be identified as long bursts and 15 as short bursts, where we divide the sample at $T_{90} = 2$ s. In this paper, we focus on these 210 long bursts." + To compare with the bburst sample. we use the long bburst sample [rom Ixommers et al. (," To compare with the burst sample, we use the long burst sample from Kommers et al. (" +2000). which consists of 2176 long GRBs from both online andl off-line searches.,"2000), which consists of 2176 long GRBs from both online and off-line searches." + We plot the log logP? distributions of the aand bbursts in Figure 1.., We plot the $\log N$ $\log P$ distributions of the and bursts in Figure \ref{fig:np}. . + We use the >50% coded field of view of Oow]=1.4 str lor the DAT and a flight time of Tswift=2.49 vr until 2007 June 16 to calculate the burst rate for the ssample., We use the $>50$ coded field of view of $\Omega_{\swift}=1.4$ str for the BAT and a flight time of $T_{\swift}=2.49$ yr until 2007 June 16 to calculate the burst rate for the sample. + For the ssaniple. we adopt the values from IxXommers οἱ ((2000) with Tjqpsp=1.33x105 s and a niean field of view of 25455j=0.67x4x str.," For the sample, we adopt the values from Kommers et (2000) with $T_{\batse} = 1.33\times10^{8}$ s and a mean field of view of $\Omega_{\batse} = 0.67*4\pi$ str." + We also correct Lor the band pass differences between the BAT (15150 keV) and ((50300 keV) instruments. where we use thespectral fits provided by Sakamotoet ((2003) for the," We also correct for the band pass differences between the BAT (15–150 keV) and (50–300 keV) instruments, where we use thespectral fits provided by Sakamotoet (2008) for the" +Solar flares are processes of magnetic reconnection accompanied by violent release of accumulated magnetic free energy in the solar atmosphere.,Solar flares are processes of magnetic reconnection accompanied by violent release of accumulated magnetic free energy in the solar atmosphere. + Recently. increasing observational evidence has shed new light on the flare associated magnetic field change. which occurs. not only in the corona as expected. but also extends down to the dense photosphere where the magnetic fields were assumed anchored and insusceptible to coronal eruption (e.g..Kopp&Pneuman1976;ChoudharyGary 1999)..," Recently, increasing observational evidence has shed new light on the flare associated magnetic field change, which occurs not only in the corona as expected, but also extends down to the dense photosphere where the magnetic fields were assumed anchored and insusceptible to coronal eruption \citep[e.g.,][]{Kopp+Pneuman1976SoPh...50...85K, Choudhary+Gary1999SoPh..188..345C}." + Early low cadence vector magnetograph observations have hinted at possible flare-related changes of photospheric transverse field and magnetic shear near the flared neutral lines (Wang1992;Hagyardetal.1999:Li 2000)..," Early low cadence vector magnetograph observations have hinted at possible flare-related changes of photospheric transverse field and magnetic shear near the flared neutral lines \citep{WangH1992SoPh..140...85W, Ambastha+etal1993SoPh..148..277A, Wang+etal1994ApJ...424..436W, Chen+etal1994SoPh..154..261C, Hagyard+etal1999SoPh..184..133H, Li+etal2000PASJ...52..483L}." + When continuous high cadence line-of-sight (LOS) photospheric magnetograms become available. rapid and permanent magnetic flux changes are found spatially and temporally associated with flare occurrence (Spirocketal.2002;Wang 2006).. ," When continuous high cadence line-of-sight (LOS) photospheric magnetograms become available, rapid and permanent magnetic flux changes are found spatially and temporally associated with flare occurrence \citep{Spirock+etal2002ApJ...572.1072S, Wang+etal2002ApJ...576..497W, Yurchyshyn+etal2004ApJ...605..546Y, Sudol+Harvey2005ApJ...635..647S, WangH2006ApJ...649..490W}." +The interpretations of those impulsive flux changes in different flare events were inconclusive then., The interpretations of those impulsive flux changes in different flare events were inconclusive then. +" On the other hand. from white-light (WL) observations. rapid outer penumbral decay and central (1.e.. near flaring neutral line; throughout this letter. the term ""central"" always refers to near flaring neutral line) structure darkening are found quite commonly in complex ó sunspots right after major flares (Wangetal.2004:Deng2005:Liu2005;Chenetal. 2007).."," On the other hand, from white-light (WL) observations, rapid outer penumbral decay and central (i.e., near flaring neutral line; throughout this letter, the term “central” always refers to near flaring neutral line) structure darkening are found quite commonly in complex $\delta$ sunspots right after major flares \citep{WangH+etal2004ApJ...601L.195W, Deng+etal2005ApJ...623.1195D, LiuC+etal2005ApJ...622..722L, ChenW+etal2007ChJAA...7..733C}." + Since sunspots are magnetic in. nature and their structure is closely related to the local magnetic field configuration. the authors interpret the sudden change of sunspot structure as the manifestation of magnetic field restructuring at the photosphere.," Since sunspots are magnetic in nature and their structure is closely related to the local magnetic field configuration, the authors interpret the sudden change of sunspot structure as the manifestation of magnetic field restructuring at the photosphere." + In particular. Liuetal.(2005.Fig.12) present a schematic reconnection picture that explains most of the observational aspects. where the original fanning out field lines of opposite polarities get connected over the neutral line and plunged downward after the flare. resulting 1n. more vertical fields in the outer part and more horizontal fields in the central region compared to pre-flare configuration.," In particular, \citet[][Fig.12]{LiuC+etal2005ApJ...622..722L} present a schematic reconnection picture that explains most of the observational aspects, where the original fanning out field lines of opposite polarities get connected over the neutral line and plunged downward after the flare, resulting in more vertical fields in the outer part and more horizontal fields in the central region compared to pre-flare configuration." + Recent precise vector magnetic field measurements endorse the concept of this reconnection picture., Recent precise vector magnetic field measurements endorse the concept of this reconnection picture. + For instance. Lietal.(2009). find that the mean inclination angle (with respect to surface normal) in the outer decayed penumbral regions decreases (1.e.. becomes more vertical) while that in the central darkened areas increases (1.e.. becomes more inclined) after a major flare.," For instance, \citet{Li+etal2009ScChG..52.1702L} find that the mean inclination angle (with respect to surface normal) in the outer decayed penumbral regions decreases (i.e., becomes more vertical) while that in the central darkened areas increases (i.e., becomes more inclined) after a major flare." + Focusing on the flare-induced changes in horizontal magnetic fields. Wangetal.(2009) detected substantial strengthening of horizontal magnetic field in the central region and weakening in patches in the outskirts of à à sunspot group.," Focusing on the flare-induced changes in horizontal magnetic fields, \citet{WangJ+etal2009ApJ...690..862W} detected substantial strengthening of horizontal magnetic field in the central region and weakening in patches in the outskirts of a $\delta$ sunspot group." + The clearly observed flare-associated photospheric magnetic field changes have— also drawn the— attention of theorists., The clearly observed flare-associated photospheric magnetic field changes have also drawn the attention of theorists. + Quantitatively assessing the change of Lorentz force that needs to be rebalanced during magnetic eruptions. Hudsonetal.(2008) and Fisheretal.(2010) conclude that the photospherie magnetic fields near the flaring neutral line should undergo a collapse (1e.. become more horizontal) along with a downward (inward) jerk resulting from drastic coronal magnetic reconfigurations.," Quantitatively assessing the change of Lorentz force that needs to be rebalanced during magnetic eruptions, \citet{Hudson+Fisher+Welsch2008ASPC..383..221H} and \citet{Fisher+etal2010arXiv1006.5247F} conclude that the photospheric magnetic fields near the flaring neutral line should undergo a collapse (i.e., become more horizontal) along with a downward (inward) jerk resulting from drastic coronal magnetic reconfigurations." + This is in. principle consistent with the reconnection picture presented by Liuetal. (2005).., This is in principle consistent with the reconnection picture presented by \citet{LiuC+etal2005ApJ...622..722L}. + Wang&Liu(2010) synthesized the vector and LOS magnetic field observations covering major flares and find that 23 out of 24 events showed signatures of collapsed, \citet{Wang+Liu2010ApJ...716L.195W} synthesized the vector and LOS magnetic field observations covering major flares and find that 23 out of 24 events showed signatures of collapsed +The TLUSTY (IInbenv 1933) and SYNSPEC (IInbeny Lanz 1995) codes were used to create model spectra of white clwarl stellar aàimospheres.,The TLUSTY (Hubeny 1988) and SYNSPEC (Hubeny Lanz 1995) codes were used to create model spectra of white dwarf stellar atmospheres. + Solar abundances were asstunecl., Solar abundances were assumed. + Wade IHubenys (1998) optically thick disk model grid was the source of model accretion disks., Wade Hubeny's (1998) optically thick disk model grid was the source of model accretion disks. + We then used IUEFIT. which is a 4? minimization routine. to calculate a. 4? value and a seale factor for each of our models.," We then used IUEFIT, which is a $\chi^{2}$ minimization routine, to calculate a $\chi^{2}$ value and a scale factor for each of our models." + The scale factor 5 is defined in terms of the stellar radius R. and distance d bv: F(Au.) = 9 HO) where 8 = Επ] P)., The scale factor S is defined in terms of the stellar radius R and distance by: $\lambda_{obs}$ ) = S $\lambda_{model}$ ) where S = $\pi$ $^2$ $^2$ ). + The scale factor is normalized {ο one kiloparsec for the distance and one solar radius for the radius., The scale factor is normalized to one kiloparsec for the distance and one solar radius for the radius. +" Thus. for a photosphere the distance d is given by: d= 1000pc (R,;/R..)/ S."," Thus, for a photosphere the distance is given by: = 1000pc $_{wd}$ $_{\sun}$ )/ $^{0.5}$." +" since the accretion disk model fluxes are normalized to a distance of 100 pc. for an accretion disk fit. the distance is given bv:d = 100/S""pe"," Since the accretion disk model fluxes are normalized to a distance of 100 pc, for an accretion disk fit, the distance is given by: = $^{0.5}$ pc." + We also carried out combination fits utilizing both the best-fitting accretion disk moclel and the best-litting photosphere model., We also carried out combination fits utilizing both the best-fitting accretion disk model and the best-fitting photosphere model. + With this fit. we were able to obtain (he relative contributions of the accretion disk and the white dw.," With this fit, we were able to obtain the relative contributions of the accretion disk and the white dwarf." + The spectra were prepared [for fitting by masking regions with negative [Iux., The spectra were prepared for fitting by masking regions with negative flux. + For SWP54454 we masked1190-1223À.. along with1737-1793À.," For SWP54454 we masked, along with." +. For SWDP07950 we masked wavelengths <1228AÀ.. as well as1925-1927À.," For SWP07950 we masked wavelengths $<$, as well as." +. First. we carried out. accretion clisk-only fits to the data.," First, we carried out accretion disk-only fits to the data." + We ran models with white dwarl masses of0.350. 0.550. 0.300. 1.030 and 1.210 solar masses.," We ran models with white dwarf masses of 0.350, 0.550, 0.800, 1.030 and 1.210 solar masses." + There was also a range of log M. values fromall-8.0 up to -10.5 in increments of 0.5., There was also a range of log $\dot{M}$ values from -8.0 up to -10.5 in increments of 0.5. + The disk inclination angle4 was kept fixed at 187 in of the fits to be consistent with the evidence that V841 Oph is a very low inclination svstem., The disk inclination angle was kept fixed at $\degr$ in all of the fits to be consistent with the evidence that V841 Oph is a very low inclination system. + The parameters of the best-fitting aceretion disk models are summarizedin Table3., The parameters of the best-fitting accretion disk models are summarized in Table 3. + For (he same white dwarf mass of0.8 M... the best-fitting cisk-only model to SWDP07950 is displaved in fie.," For the same white dwarf mass of 0.8 $_\sun$, the best-fitting disk-only model to SWP07950 is displayed in fig." + 1 while the best-fitting disk model to SWP54454 is displaved in fig., 1 while the best-fitting disk model to SWP54454 is displayed in fig. + 2., 2. + For a fixed white dwarl mass of 1.0 M... (he best-flitting disk-onlyv models to SWP07950 and SWP54454 are displaved in fies.," For a fixed white dwarf mass of 1.0 $_\sun$, the best-fitting disk-only models to SWP07950 and SWP54454 are displayed in figs." + 3 ancl 4. respectively.," 3 and 4, respectively." +" The best-fitting accretion disk models to both spectra have the same accretion rate. 23x10. I ML,/vi. and the scale [actors ofthese best-fits place V841 Oph within 200 pe of the sun."," The best-fitting accretion disk models to both spectra have the same accretion rate, $\sim$ $\times$ $^{-11}$ $_\sun$/yr, and the scale factors ofthese best-fits place V841 Oph within 200 pc of the sun." +the presence of differential reddening across the cluster. as recently found also by Yadav Sagar As a working hypothesis. we shall consider as cancliclate cluster members the stars having £(21) = 0.52z0.07. ancl investigate how they distribute in. the reddening corrected CMDs.,"the presence of differential reddening across the cluster, as recently found also by Yadav Sagar As a working hypothesis, we shall consider as candidate cluster members the stars having $E(B-V)$ = $\pm$ 0.07, and investigate how they distribute in the reddening corrected CMDs." + In Fig., In Fig. + T we plot the reddening correctecl CAIDs in the planes V.(BVo. (loft. panel) anel io(0 Dmfight panel) using the same symbols as in Fie., 7 we plot the reddening corrected CMDs in the planes $V_o - (B-V)_o$ (left panel) and $V_o - (U-B)_o$ (right panel) using the same symbols as in Fig. + 5. and by provisionally adopting Ay=3.0 (Feinstein et al. 1980).," 5, and by provisionally adopting $R_V~=~3.0$ (Feinstein et al 1980)." +" All the stars brighter than Y,«11.5 define a nice sequence.", All the stars brighter than $V_o < 11.5$ define a nice sequence. + There is just one exception. which is the star 2118S (Grubissich numbering) which has a very large reddening.," There is just one exception, which is the star 18 (Grubissich numbering) which has a very large reddening." + Phe analysis of its colours (sec Table 2) seems to support the idea that this star is actually a blend of two stars. a blue supergiant with a red companion (see also the discussion in Feinstein et al (1980).," The analysis of its colours (see Table 2) seems to support the idea that this star is actually a blend of two stars, a blue supergiant with a red companion (see also the discussion in Feinstein et al (1980)." +" Further sprectra are necessary to better clarily this Below Vi, = 11.5 stars having smaller recldening start to mix with stars having larger reddening.", Further sprectra are necessary to better clarify this Below $V_o$ = 11.5 stars having smaller reddening start to mix with stars having larger reddening. +" We interpret this fact in the sense that up to V, = 11.5 Trumpler 15 clearly emerges from the background. whereas below this magnitude it smoothly merges with the general Galactic disk field."," We interpret this fact in the sense that up to $V_o$ = 11.5 Trumpler 15 clearly emerges from the background, whereas below this magnitude it smoothly merges with the general Galactic disk field." + This fact was not evident in previous photometry which were not sullicienthy deep., This fact was not evident in previous photometry which were not sufficiently deep. + A final check is to look at the spatial cüstribution of members and non-moenibers in the field. of the cluster., A final check is to look at the spatial distribution of members and non-members in the field of the cluster. + “Phis is presented in Fig., This is presented in Fig. + S. where again filled. circles represent. candidate members and open squares indicate candidate non-memboers.," 8, where again filled circles represent candidate members and open squares indicate candidate non-members." + It seems that our selection criterion. of members. and. non-members worked fine. since member stars. as expected. tend to concentrate in the cluster core. whereas. non-members preferentially distribute in the cluster In conclusions. we suggest that the 90 stars having HRBV)=052£0.07 are probable members. whereas all the other stars having (51)=0.92+022 are fielcl stars.," It seems that our selection criterion of members and non-members worked fine, since member stars, as expected, tend to concentrate in the cluster core, whereas non-members preferentially distribute in the cluster In conclusions, we suggest that the 90 stars having $E(B-V)~=~0.52\pm0.07$ are probable members, whereas all the other stars having $E(B-V)~=~0.92\pm0.22$ are field stars." + Leis worth noticing here that in a recent work DeCGiola-Eastwood et al (2001) found that the field: stars in a region close to y have indeed a reddening οVV)x1.0. Alorrell et al (1988). provide spectral. classification of 2] stars in the field. of Trumpler 15., It is worth noticing here that in a recent work DeGioia-Eastwood et al (2001) found that the field stars in a region close to $\eta$ have indeed a reddening $E(B-V) \approx 1.0$ Morrell et al (1988) provide spectral classification of 21 stars in the field of Trumpler 15. + We have combined 16 common stars (16) to obtain absolute magnitudes ancl ‘colors and. derive. another estimate of the cluster mean reddening., We have combined the common stars (16) to obtain absolute magnitudes and colors and derive another estimate of the cluster mean reddening. + These stars are listed. in Table 2., These stars are listed in Table 2. +" We derive je reddening £(2VV) by adopting the intrinsic color indices of OB giants. supergiants ancl dwarf stars in the ~""DVRIJHINLAL system provided by Wegner (1994)."," We derive the reddening $E(B-V)$ by adopting the intrinsic color indices of OB giants, supergiants and dwarf stars in the $UBVRIJHKLM$ system provided by Wegner (1994)." + For yw 16 stars in Table 2 we obtain £(BV)=0.52250.06. in perfect agreement with the mean reddening derived from 1ο analysis of the color-color diagram.," For the 16 stars in Table 2 we obtain $E(B-V)~=~0.52\pm0.06$, in perfect agreement with the mean reddening derived from the analysis of the color-color diagram." + This result makes us confident when using the photometric probable candidate members above derived., This result makes us confident when using the photometric probable candidate members above derived. + As already outlined. the large reddening spread: visible in Kies 5 and 6 can be due to the presence of dillerential reddening across the cluster.," As already outlined, the large reddening spread visible in Figs 5 and 6 can be due to the presence of differential reddening across the cluster." + This possibility has been already discussed. by Yadav and Sagar (2001). bv using data from the literature. and confirmed by the mid-infrared observations obtained by Smith et al (2000. fig.," This possibility has been already discussed by Yadav and Sagar (2001) by using data from the literature, and confirmed by the mid-infrared observations obtained by Smith et al (2000, fig." + 2) with the ALSX satellite. which show how the region of Trumpler 15 is unevenly It is interesting to look for a possible relation of the color excess of cach candidate member with its position on the plane of the sky. which would confirm the presence of patchy absorption.," 2) with the $MSX$ satellite, which show how the region of Trumpler 15 is unevenly It is interesting to look for a possible relation of the color excess of each candidate member with its position on the plane of the sky, which would confirm the presence of patchy absorption." + To this aim. we plotted in Fig.," To this aim, we plotted in Fig." + 9 the distribution of colour excesses across the cluster., 9 the distribution of colour excesses across the cluster. + In. this figure the size of the points is proportional to the color excess., In this figure the size of the points is proportional to the color excess. + By inspective this plot one can readily recognizes how the obscuration toward Trumpler 15 is really irregular., By inspective this plot one can readily recognizes how the obscuration toward Trumpler 15 is really irregular. + There is some disagreement in the literature whether the extinction toward this cluster is normal (fy) —3.0. Feinstein et al 1980) or anomalous (larger Z. Tapia ct al A recent estimate of £4 = 4.0 is reported by. Patriarch et al (2001). but is based. on just one star 18) which," There is some disagreement in the literature whether the extinction toward this cluster is normal $R_V$ =3.0, Feinstein et al 1980) or anomalous (larger $R_V$, Tapia et al A recent estimate of $R_V$ = 4.0 is reported by Patriarchi et al (2001), but is based on just one star 18) which" +and the aspect ratio(s) b=LjLe.,"and the aspect ratio(s) $\Gamma =L_{x,y}/L_z$." + The microscopic diffusivities are included in the original equations. (49)) to. regularize the system by allowing [or dissipation ancl irmeversibilitv., The microscopic diffusivities are included in the original equations \ref{eq:HRBorig}) ) to regularize the system by allowing for dissipation and irreversibility. + However. note that the periodic boundary conditions forbid. the formation of boundary. lavers. so it may be conjectured that the macroscopic statistical properties. of the turbulent convection should. be well defined: ancl independent. of ν and 5 in the limits Rax (Spiegel 1971).," However, note that the periodic boundary conditions forbid the formation of boundary layers, so it may be conjectured that the macroscopic statistical properties of the turbulent convection should be well defined and independent of $\nu$ and $\kappa$ in the limits ${\rm Ra}\to\infty$ (Spiegel 1971)." + Furthermore. we may expect the turbulence to be statistically steady and homogeneous. although. anisotropic.," Furthermore, we may expect the turbulence to be statistically steady and homogeneous, although anisotropic." + These. properties have been argued to be more relevant to convection in astrophysical systems than standard RavleighDénnard convection., These properties have been argued to be more relevant to convection in astrophysical systems than standard Rayleigh–Bénnard convection. + The URB model may therefore provide. a suitable local model of convection deep. inside a star or planct., The HRB model may therefore provide a suitable local model of convection deep inside a star or planet. + On dimensional grounds. the rms turbulent velocity. for example. must be expressible in the form where f is à climensionless function.," On dimensional grounds, the rms turbulent velocity, for example, must be expressible in the form where $f$ is a dimensionless function." + According to the discussion above. f should tend to à non-zero function of E alone in the limit Rax.," According to the discussion above, $f$ should tend to a non-zero function of $\Gamma$ alone in the limit $\mathrm{Ra}\to\infty$." + Hoods tempting to conjecture hat f also becomes independent of E in the limit oflarge aspect ratio. Ex.," It is tempting to conjecture that $f$ also becomes independent of $\Gamma$ in the limit oflarge aspect ratio, $\Gamma\to\infty$." + This would imply that the vertical ength-scale. L. plavs a fundamental role in determining he saturation level of the turbulent convection. presumably »v limiting the size of coherent structures. Ceddies).," This would imply that the vertical length-scale $L_z$ plays a fundamental role in determining the saturation level of the turbulent convection, presumably by limiting the size of coherent structures (`eddies')." + For convection deep inside a star or planet. it is the pressure scale-height that imposes a characteristic vertical scale on he turbulence (see Section 5)): in the local model. the vertical extent of the box plays an equivalent. role.," For convection deep inside a star or planet, it is the pressure scale-height that imposes a characteristic vertical scale on the turbulence (see Section \ref{sec:anelastic}) ); in the local model, the vertical extent of the box plays an equivalent role." + In oactice. owing to some peculiarities of the HIU system discussed below. the role of the aspect ratio in the behaviour of the solutions is not so straightforward.," In practice, owing to some peculiarities of the HRB system discussed below, the role of the aspect ratio in the behaviour of the solutions is not so straightforward." + Applving our closure model to HD. and noting that all statistical averages are now independent of position. we obtain the system. of ODEs for the temporal evolution of the seconc-order correlations {ει P; and (Q:[4 where we have ignored for simplicity contributions from terms including C». C; and ων which do not contribute to the hish-Bavleigh number dynamics of HIUD convection.," Applying our closure model to HRB, and noting that all statistical averages are now independent of position, we obtain the system of ODEs for the temporal evolution of the second-order correlations $\bar +R_{ij}$ , $\bar F_i$ and $\bar Q$: where we have ignored for simplicity contributions from terms including $C_\nu$, $C_\kappa$ and $C_{\nu\kappa}$ which do not contribute to the high-Rayleigh number dynamics of HRB convection." +" Note that the resulting equation for £2 is so that these equations consist. of a main. svstem. for GI.IBQ). decoupled systems for (2,E.) and GusP). and prognostic equations for ζειly, and i."," Note that the resulting equation for $\bar R$ is so that these equations consist of a main system for $(\bar R,\bar +R_{zz},\bar F_z,\bar Q)$, decoupled systems for $(\bar R_{xz},\bar +F_x)$ and $(\bar R_{yz},\bar F_y)$, and prognostic equations for $\bar +R_{xx}, \bar R_{yy}$ and $\bar R_{xy}$." + While selecting £ as the distance to the wall is a natura choice for wall-bouncded convection or shear lows. a dilferen approach must be used for triply periodic Hows.," While selecting $L$ as the distance to the wall is a natural choice for wall-bounded convection or shear flows, a different approach must be used for triply periodic flows." +" Phe larges eddy size in this case is limited by the horizontal anc vertical scales in the box. so that £ can be assumed to be proportional to min(GL,.Ly.L.)."," The largest eddy size in this case is limited by the horizontal and vertical scales in the box, so that $L$ can be assumed to be proportional to $\min(L_x,L_y,L_z)$." + Lt is important to note that the selection of a dilleren L implies a potential rescaling of the (655 coelIicients., It is important to note that the selection of a different $L$ implies a potential rescaling of the $\{C_i\}$ coefficients. + For example. had: we selected £=2/2 in the wall-bouncdec case instead of £=2. then the estimated C5. CS. Cis and C would all be half the values (quoted in Section 3.4 since these parameters enter the model in the combinations οεν ote.," For example, had we selected $L = z/2$ in the wall-bounded case instead of $L=z$, then the estimated $C_1$ , $C_2$, $C_6$ and $C_7$ would all be half the values quoted in Section \ref{s:calibration} + since these parameters enter the model in the combinations $C_1/L$, etc." + Nevertheless. the ratios of any pairs of constants within the group (C'1.CS. should. (presumably) be preserved.," Nevertheless, the ratios of any pairs of constants within the group $\{C_1,C_2,C_6,C_7\}$ should (presumably) be preserved." +" Following these C5.considerations.C7) we elect to keep the estimated values of the [6] given in equations (46)) and (48)). and calibrate instead the value of the proportionality constant 2 in the expression £=0min(L,.L,. L.)."," Following these considerations, we elect to keep the estimated values of the $\{C_i\}$ given in equations \ref{eq:C1C2}) ) and \ref{eq:C6C7}) ), and calibrate instead the value of the proportionality constant $\delta$ in the expression $L= \delta +\min(L_x,L_y,L_z)$ ." + A search for non-trivial fixed pointsof the dynamical system (53)) (with &2 0) reveals they are the (positive) solutions ofa quartic equation., A search for non-trivial fixed pointsof the dynamical system \ref{hrb}) ) (with $\bar R > 0$ ) reveals they are the (positive) solutions of a quartic equation. +In the limit of large Ha it can be shown,In the limit of large Ra it can be shown +It therefore seems apparent that in the case of GRB 090102 the high polarization signal requires the presence of large-scale ordered magnetic fields in the relativistic outflow (Figure 4(a)).,It therefore seems apparent that in the case of GRB 090102 the high polarization signal requires the presence of large-scale ordered magnetic fields in the relativistic outflow (Figure 4(a)). + As the measurement was obtained while the reverse-shock emission was dominant in GRB 090102. the detection of significant polarization provides the first direct evidence that such magnetic fields are present when significant reverse shock emission is produced.," As the measurement was obtained while the reverse-shock emission was dominant in GRB 090102, the detection of significant polarization provides the first direct evidence that such magnetic fields are present when significant reverse shock emission is produced." + Magnetization of the outflow can be expressed as a ratio of magnetic to kinetic energy flux. 7.," Magnetization of the outflow can be expressed as a ratio of magnetic to kinetic energy flux, $\sigma$." + The degree of magnetization cannot be sufficient for the jet to be completely Poynting flux dominated (σ>1) since this would be expected to suppress a reverse shock?.., The degree of magnetization cannot be sufficient for the jet to be completely Poynting flux dominated $\sigma>1$ ) since this would be expected to suppress a reverse \cite{mga09}. + We can therefore reconcile the detection of polarization in GRB 090102 and our previous non-detection in GRB 060418 in a unified manner if GRB jets have magnetization of c~1., We can therefore reconcile the detection of polarization in GRB 090102 and our previous non-detection in GRB 060418 in a unified manner if GRB jets have magnetization of $\sigma \sim 1$. +" In the GRB 060418 case, the jet would have had slightly higher magnetization than unity, resulting in the suppression of a reverse shock, while GRB 090102 would have o slightly smaller than unity, which is optimal to produce bright reverse shock emission."," In the GRB 060418 case, the jet would have had slightly higher magnetization than unity, resulting in the suppression of a reverse shock, while GRB 090102 would have $\sigma$ slightly smaller than unity, which is optimal to produce bright reverse shock emission." + Of course due to the small sample (only two objects). we can not rule out a possibility that cach GRB jet had very different magnetization.," Of course due to the small sample (only two objects), we can not rule out a possibility that each GRB jet had very different magnetization." +" Finally we note that a high degree of polarization is also predicted for the prompt -ray emissionH inH the presence of> large-scale ordered magneticH 3,VF fields-7..."," Finally we note that a high degree of polarization is also predicted for the prompt $\gamma$ -ray emission in the presence of large-scale ordered magnetic \cite{gran03, fan09}. ." + Recent claimsH of> rapidlyH (~10 9) variable 5-ray polarization from less than to (+25%)) in the prompt emission of GRB 041219A* lend further support to models with magnetized outflows and offer the possibility that the peak optical polarization trom GRB 0901012 could have been even higher than that measured inour 60 second exposure., Recent claims of rapidly $\sim10$ s) variable $\gamma$ -ray polarization from less than to $\pm$ ) in the prompt emission of GRB \cite{gotz09} lend further support to models with magnetized outflows and offer the possibility that the peak optical polarization from GRB 0901012 could have been even higher than that measured inour 60 second exposure. +We shall use the structure function to characterize CRB lighteuve variability.,We shall use the structure function to characterize GRB lightcurve variability. + First we review other statistical nieasures of variability that have been eiiploved in GRB studies., First we review other statistical measures of variability that have been employed in GRB studies. + We then motivate our choice of the structure function., We then motivate our choice of the structure function. + Beloborodoy. Stern. Svensson (2000: hereafter. BSS) studied the power density spectra (PDS). Py=Fy where ΓΕ is the Fourier transform of the peak-normalized lighteurve. F(t). of BATSE CRBs.," Beloborodov, Stern, Svensson (2000; hereafter BSS) studied the power density spectra (PDS), $P_f=F_fF_f^*$ where $F_f$ is the Fourier transform of the peak-normalized lightcurve, $F(t)$, of BATSE GRBs." + Their sample of about 500 bursts was defined by requiring that Του. the tune to accumulate from to of the total fiueuce in the 1 BATSE enerev channels was ercater than 20 s. that the peak couut rate in chaunels 213 (55-110 aud 110-320 keV) was 2100 counts per 0.06 [s time bin. and that the total flucuce was greater than 32 times that of the peak time biu.," Their sample of about 500 bursts was defined by requiring that $T_{90}$, the time to accumulate from to of the total fluence in the 4 BATSE energy channels was greater than 20 s, that the peak count rate in channels 2+3 (55-110 and 110-320 keV) was $>100$ counts per 0.064 s time bin, and that the total fluence was greater than 32 times that of the peak time bin." + They concluded the PDS of bursts was well-described by a power law. PgXfYS foy foc1 Hz.," They concluded the PDS of bursts was well-described by a power law, $P_f\propto f^{-5/3}$ for $f<1$ Hz." + They also found evidence for a break. in the power law at higher frequencies. such that the PDS declined more rapidly.," They also found evidence for a break in the power law at higher frequencies, such that the PDS declined more rapidly." + The PDS inethod based on the Fourier transform has cisadvantaeges because GRBs are aperiodic aud trausieut signals. with varvine durations.," The PDS method based on the Fourier transform has disadvantages because GRBs are aperiodic and transient signals, with varying durations." +" To adjust the PDS of cach burst to a uniform frequency range. BSS added artificial zero flux portions to the lishteurve so that the total duration was 1015 s. As they comunent. this ""zero padding” introduces an artificial. fluctuating contribution to the PDS that cau dominate the true signal at low frequencics,"," To adjust the PDS of each burst to a uniform frequency range, BSS added artificial zero flux portions to the lightcurve so that the total duration was 1048 s. As they comment, this “zero padding” introduces an artificial, fluctuating contribution to the PDS that can dominate the true signal at low frequencies." +" Shen Song (2003) analyzed the variability of a similar sample of bright. long-duration GRBs by calculating the variation power defined as P(r)=ΔΝ↽-jx?yam,imn)Di£77. where Εν2H—94Le.roe Nis a counting+ series. obtained. οι. the time history of the observed pliotous with a time step 7. includiug backeround phlotous."," Shen Song (2003) analyzed the variability of a similar sample of bright, long-duration GRBs by calculating the variation power defined as $P(\tau)=(1/N)\Sigma_{i=1}^{N} (m_i - \bar{m})^2/\tau^2$, where $m_i, \:i=1,...,N$ is a counting series obtained from the time history of the observed photons with a time step $\tau$ , including background photons." + The power density is calculated via pit)=Pim)το)τοm).," The power density is calculated via $p(\tau) = P(\tau_1) - +P(\tau_2)/(\tau_2-\tau_1)$." + The power density was calculated for a noise series for cach burst aud then subtracted from ptr)., The power density was calculated for a noise series for each burst and then subtracted from $p(\tau)$. + Shen Song found the timescale at which p was a i1iaxiuimua for cach burst and claimed evidence for a bimedal distribution iu these peak timescales. with roughly half the bursts peaking at 7ls and half peaking at 7>1s. We performed this method of analysis ona similar sample of BATSE CRBs (our main sample). finding there were a siguificaut uunmber of bursts where the peak of p(7) was at the mininuun timescale set by the BATSE time resolution of 6 lus.," Shen Song found the timescale at which $p$ was a maximum for each burst and claimed evidence for a bimodal distribution in these peak timescales, with roughly half the bursts peaking at $\tau<1$ s and half peaking at $\tau>1$ s. We performed this method of analysis on a similar sample of BATSE GRBs (our main sample), finding there were a significant number of bursts where the peak of $p(\tau)$ was at the minimum timescale set by the BATSE time resolution of 64 ms." + Also many bursts had a relatively broad and flat-peaked power density. which is uot refiected in the single value of the timescale ofthe peak.," Also many bursts had a relatively broad and flat-peaked power density, which is not reflected in the single value of the timescale of the peak." + For these reasons we have preferred to use our structure function analysis. described below.," For these reasons we have preferred to use our structure function analysis, described below." +" Borgonovo (2001) studied the discrete autocorrelation fiction (ACF. the Fourier transform of the PDS}. defined as EN=hAT)—NyeiisidR=1 NL. where e; is the uuuber of counts in a given finie bin after subtraction of backerouud(yq. b; aud. ly—=δαNV1,2ο(0;|5;). of a sample of GRBs with optical afterelows and known redshifts. focusing mainly on those with BATSE data (as in our ÀA-GRD sample)."," Borgonovo (2004) studied the discrete autocorrelation function (ACF, the Fourier transform of the PDS), defined as $A(\tau = k\Delta T) = +\Sigma_{i=0}^{N-1} c_ic_{i+k}/A_0,\:k=1,...,N-1$ , where $c_i$ is the number of counts in a given time bin after subtraction of background $b_i$ and $A_0\equiv \Sigma_{i=0}^{N-1} c_i^2 - (c_i+b_i)$, of a sample of GRBs with optical afterglows and known redshifts, focusing mainly on those with BATSE data (as in our A-GRB sample)." + He considered the half width at half maximaun of the ACE (corrected for cosmic redshift). claiming evidence for a bimodality iu the distribution.," He considered the half width at half maximum of the ACF (corrected for cosmic redshift), claiming evidence for a bimodality in the distribution." + However. differences in this width ofthe ACT depend quite seusitivelv on the finite duration of the bursts. which are influenced by observational selection effects; and less scusitively on the actual variability properties at a fixed. timescale.," However, differences in this width of the ACF depend quite sensitively on the finite duration of the bursts, which are influenced by observational selection effects, and less sensitively on the actual variability properties at a fixed timescale." + Reichart et al. (, Reichart et al. ( +2001) studied the variability of bursts with kuown redshifts by looking at the (116201 unanied squared) difference between the observed lishteurve aud the same liehteurve simoothed on a particular timescale. proportional to the burst duration.,"2001) studied the variability of bursts with known redshifts by looking at the (mean summed squared) difference between the observed lightcurve and the same lightcurve smoothed on a particular timescale, proportional to the burst duration." + Using 11 bursts with measured variabilitics aud isotropic peak Iuninosities. the value of the smoothing timescale was optimized to eive the largest chanee iu isotropic peak Iunuinositv for a given chauge in variability.," Using 11 bursts with measured variabilities and isotropic peak luminosities, the value of the smoothing timescale was optimized to give the largest change in isotropic peak luminosity for a given change in variability." + By this iethod a significant correlation between this measure of variability and luminosity was found., By this method a significant correlation between this measure of variability and luminosity was found. + One important feature of this method is the use of smoothing timescales that are proportional to burst duration rather than a fixed timescale., One important feature of this method is the use of smoothing timescales that are proportional to burst duration rather than a fixed timescale. + Reichart et al. (, Reichart et al. ( +2001) noted that if fixed timescales were used then uo correlation was foucl.,2001) noted that if fixed timescales were used then no correlation was found. + GRD hebtcurves have also been studied by decomposition iuto pulses of a particular functional form (e.g. Norris ct al., GRB lightcurves have also been studied by decomposition into pulses of a particular functional form (e.g. Norris et al. + 1996: Riunirez-Ruiz Fenimore 2000: Lee. Bloom Petrosian 2000: Nakar Pirau 2002: Quilligan et al.," 1996; Ramirez-Ruiz Fenimore 2000; Lee, Bloom Petrosian 2000; Nakar Piran 2002; Quilligan et al." + 2003)., 2003). + This inethiod suffers because it requires an arbitrary specification of the functional form of the pulses. but has the advantage that once this assumption has been made. relatively good statistics ou pulse properties cau be obtained from a given sot of burst data.," This method suffers because it requires an arbitrary specification of the functional form of the pulses, but has the advantage that once this assumption has been made, relatively good statistics on pulse properties can be obtained from a given set of burst data." + Ramurez-Ruiz Fenimore (2000) looked at pulse width evolution within GRBs fiudiug that pulses did not appear to get broader over the course of bursts. contrary to the simplest models of production in external shocks.," Ramirez-Ruiz Fenimore (2000) looked at pulse width evolution within GRBs finding that pulses did not appear to get broader over the course of bursts, contrary to the simplest models of production in external shocks." + Lee et al. (, Lee et al. ( +2000) found that pulse timescales tend to be shorter in CRBs with ligher peak fluxes. as expected from cosmic time dilation. although there is also tentative evidence for a coutrinition fron processes intrinsic to the bursts.,"2000) found that pulse timescales tend to be shorter in GRBs with higher peak fluxes, as expected from cosmic time dilation, although there is also tentative evidence for a contribution from processes intrinsic to the bursts." +" We use the first-order structure ""unction (Butinan 1978). defined as Dir) sj) is based on an average of 500correlations."," We use the first-order structure function (Rutman 1978), defined as ) ) is based on an average of 500correlations." + Di(r=61τις) is based on an average of 999correlations., $D^1(\tau=64\:{\rm ms})$ is based on an average of 999correlations. + Large Charge," Recently there has been an increasing interest in higher derivative $N=2$ black holes \cite{r2entropy,mohauptreview,r2stabeq,r2simple,r2interpolation,SJR,nonsusy1,nonsusy2}." + Four-Dimensional Non, In this work we consider $N=2$ supergravity in four dimensions with small $R^2$ curvature corrections. +-Extremal N 2Black Holes with R?," We construct large charge non-extremal black hole solutions in all space, with either a supersymmetric or a non-supersymmetric extremal limit, and analyze their thermodynamic properties." +-Terms EvAL Gruss Ra, The extremal limits were discussed in \cite{allrpaper}. +ymond and Beverly Sackler Sc, The horizon geometry and entropy of small near-extremal black holes were discussed in \cite{r2ne}. +hool ofPhysics a, Non-extremal black holes without $R^2$ -terms were discussed in \cite{nonextremal}. +nd Astronomy. Το University.," When considering the Bekenstein-Hawking entropy one notices that it has the same form as that of the extremal black holes, with the charges being replaced by a specific function of the charges and the non-extremality parameters." + Tel-Aviv 00978. Israel.," With $R^2$ -terms, the entropy is no longer given by the Bekenstein-Hawking arealaw, but is given in general by the Wald formula \cite{wald}." + Abstract I rop, A natural question to ask is whether the above property holds for the $R^2$ -corrected black hole entropy. +erties. This generalizes some ," Indeed, we will provide evidence that this is the case for a class of non-extremal black holes with a supersymmetric extremal limit." +of the extremal solutions presentedin farNiv:0902.083 1].," A relation between the indexed entropy of the BPS $N=2$ black holes and the topological string partition function, evaluated at the attractor point (horizon) has been proposed in \cite{osv} + We suggest that one may still use the relation \ref{top}) ) for the above class of non-extremal $N=2$ black holes, with the replaced charges." + The incexed e, This may be so at least to first order in the non-extremality parameter. +utropyof the non-extremal extension oft," If correct, one gets all the perturbative $F$ -terms corrections to the non-extremal or near-extremal $N=2$ black holes entropy using the topological string partition function." +he supersviunetric blackhole.has the form ofthe extremal e," We note that this is not correct in general, as in the case of small black holes \cite{r2ne}, and in the case of black holes with a non-supersymmetric extremal limit, discussed later." +ntropy., Both do not exhibit the entropy structure discussed above. + withthe charges, Note that the $R^2$ -terms considered in this paper are $F$ -terms. + replacedbya function of thechar," One generally expects also $D$ -term corrections, which are not taken into account here." +ges. the moduliat infinity andthe nou-e," For supersymmetric black holes, it is conjectured that such terms do not contribute to the entropy \cite{osv}." +xtreimality parameter.This isthe same behaviorasin the case with," For extremal non-supersymmetric black holes, it is conjectured that the mass-charge ratio is decreased by higher curvature corrections \cite{mass_charge}. ." +out /--teruis. February200, It is interesting to consider the behavior for +out /--teruis. February2009, It is interesting to consider the behavior for +"Over the last several vears. the possibility of observing both the eravitational-wave (GAV) ancl electromagnetic: (EM) emission signatures of coalescing supermassive black hole (SMDID) binaries has received intense attention (Holz&&Moenou2008:Dottiet 2006: for specific. proposed mechanisms for LEAL signatures. see Armitage&Natara-jan2002 ancl Milosavljevió&Phinney2005.. as well as recent reviews by Llaimanetal.2009— and Schnit""Atian 2011)).","Over the last several years, the possibility of observing both the gravitational-wave (GW) and electromagnetic (EM) emission signatures of coalescing supermassive black hole (SMBH) binaries has received intense attention \citealt{HH05, Kocsis+06, Kocsis+07, Kocsis+08, + Dotti+06}; for specific proposed mechanisms for EM signatures, see \citealt{AN02} and \citealt{MP05}, as well as recent reviews by \citealt{Haiman+09} and \citealt{Schnittman11}) )." + The bursts of GWs emitted. by such systems. can now be predicted by numerical eeneral relativity2006).. ancl are expected. to be observed. by current and. future detectors.," The bursts of GWs emitted by such systems can now be predicted by numerical general relativity, and are expected to be observed by current and future detectors." + The temporal evolution of the gravitational waveform. can be used to extract the luminosity distance. help constrain the location of the source on the sky. and. determine the masses and spins of the SALBUs.," The temporal evolution of the gravitational waveform can be used to extract the luminosity distance, help constrain the location of the source on the sky, and determine the masses and spins of the SMBHs." + Loan EAL signature of the coalescence can also be identified. this would allow for a determination of the source redshift. turning merging black holes into “standard sirens” for probing cosmic loSuch multi-messenger. observations. would also enable astronomical investigations of SMDlIIs whose masses. spins," If an EM signature of the coalescence can also be identified, this would allow for a determination of the source redshift, turning merging black holes into “standard sirens” for probing cosmic Such multi-messenger observations would also enable astronomical investigations of SMBHs whose masses, spins" +SAL. star (100 Myr).,"$8\,{\rm M}_\odot$ star (100 Myr)." + This is similar to a model preseuted in Thacker&Couchiman(2000)., This is similar to a model presented in \cite{thacker}. +. For SNe IL. the moetallicity-dependent stellar vields of Woosley&Weaver(1995) are adopted.," For SNe II, the metallicity-dependent stellar yields of \cite{ww} are adopted." +For low- aud mass stars. we use the stellar vields of vandeuTock&Crocuwegeu(1997).,"For low- and intermediate-mass stars, we use the stellar yields of \cite{vanden}." +. We adopt SNe Ta model of Ikobavashi.Tsujiuoto.&Nomoto(2000).. aud the vields of Iwamotoetal.(1999).," We adopt SNe Ia model of \cite{kobayashi}, and the yields of \cite{iwamoto}." +. The initial conditions are two galaxies with exponential eas disks. embedded in dark matter halos.," The initial conditions are two galaxies with exponential gas disks, embedded in dark matter halos." + These are created using CGalactICS (I&uijkeu&Dubiuski 1995)). aud are esseutiallv stable iu the that their density profiles. potential. and velocity ellipsoids will not change significantly when individual galaxies are evolved.," These are created using GalactICS \citealt{dubinski}) ), and are essentially stable in the that their density profiles, potential, and velocity ellipsoids will not change significantly when individual galaxies are evolved." + CalactICS uses the lowered Evans model for the dark matter halo. which leads to a coustaut-«deusitv core.," GalactICS uses the lowered Evans model for the dark matter halo, which leads to a constant-density core." + Auuuerical simulationssugecst that halos have a cuspy ceutral deusity profile (Navarro.Frenk.&WhiteMooreetal1999:Clüguaal.2000:Jine&SutoIXIvpiu 2001).," Numerical simulationssuggest that halos have a cuspy central density profile \citep{nfw96,nfw97,mooreetal99,ghignaetal00,js00,klypinetal01}." +. However. these results are in couflict with many observations. so we prefer to use a constaut-deusitv core.," However, these results are in conflict with many observations, so we prefer to use a constant-density core." + Ii iui case. our results should not be sensitive to the details of the central density profile. since the core contaius ouly a sunall fraction ofthe total nass.," In any case, our results should not be sensitive to the details of the central density profile, since the core contains only a small fraction of the total mass." + The laveer galaxy las total mass of 5.«10HNL..., The larger galaxy has total mass of $5\times10^{11}{\rm M}_\odot$. + The nass ratio is 2:1. disk scale lougths are 15 and 3.1 kpc. and cach las barvou fraction of 17%.," The mass ratio is 2:1, disk scale lengths are 4.5 and 3.1 kpc, and each has baryon fraction of $\%$." + Each galaxy consists of 10.000 barvonie aud 100.000 dark matter particles.," Each galaxy consists of 40,000 baryonic and 100,000 dark matter particles." + The zinall galaxy approaches with its orbital aueular momentum vector Inclined to that of the laree galaxy., The small galaxy approaches with its orbital angular momentum vector inclined to that of the large galaxy. + Both galaxies have prograde rotation with respect to the angular momentum of the svstem. the orbital cucrey ofthe system is «10H. eres.," Both galaxies have prograde rotation with respect to the angular momentum of the system, the orbital energy of the system is $\times 10^{44}$ ergs." + The system is bound. aud the spin parameter (ratio of orbital cherey to binding energv) is A=0.01.," The system is bound, and the spin parameter (ratio of orbital energy to binding energy) is $\lambda=0.04$." + The eas disks evolve aud fori stars prior to the merecr. aud have gas fractions of fy—ως(Meas1Mau)=091 at the tine of the merger.," The gas disks evolve and form stars prior to the merger, and have gas fractions of $f_g\equiv M_{\rm gas}/(M_{\rm gas}+M_{\rm stars})=0.91$ at the time of the merger." + Cas is given ai initial metallicity oflog(Z/Z..)— l aud |a/Fe]=0.35.," Gas is given an initial metallicity of $\log(Z/Z_{\odot})=-4$, and $\rm[\alpha/Fe]=0.35$." +" We follow the simulation for 1.5 Gyrs,", We follow the simulation for 1.5 Gyrs. + The eas-rich merecr results in a final galaxy with disk morphology., The gas-rich merger results in a final galaxy with disk morphology. + Figure 1. shows the D-baud ποσατν map of the resultaut ealaxy after 1.5 Cors of the simulation. where we employ the simple stellar population of Kodama.&Avimoto(1997).," Figure \ref{final} shows the B-band luminosity map of the resultant galaxy after 1.5 Gyrs of the simulation, where we employ the simple stellar population of \cite{kodama}." +. Shown. both face ou (upper panels) and edee on (ower panels) are all stars Gieht paucl). what we will callstars. which are those formed before aud diving the merger (11iddle panel). audsfars. which are those that form after the merger (eft paucl).," Shown, both face on (upper panels) and edge on (lower panels) are all stars (right panel), what we will call, which are those formed before and during the merger (middle panel), and, which are those that form after the merger (left panel)." + From the facc-ou view. it is evident that the remmaut of this particular merecr simulation is a ring galaxy. which indicates that prograde eas-rich disk-disk mereers can produce ring galaxies.," From the face-on view, it is evident that the remnant of this particular merger simulation is a ring galaxy, which indicates that prograde gas-rich disk-disk mergers can produce ring galaxies." + We fiud this especially interesting in helt of 1).. who found that the incidence of times increases rapidly with redshitt.," We find this especially interesting in light of \cite{Lavery}, who found that the incidence of rings increases rapidly with redshift." + We will study this further in our future papers., We will study this further in our future papers. + The DB-baud huninosity profiles are shown in Figure 2.. and used to determine scale-leugths of 5.1 iux 1.1 kpe respectively for the merger auc disk stars;," The B-band luminosity profiles are shown in Figure \ref{struct}, and used to determine scale-lengths of 5.1 and 4.1 kpc respectively for the merger and disk stars." +" A bulge component. within the inner ονΌρο, is apparent from the surface density profile. which is best fit with a bulge. disk. aud thick disk."," A bulge component, within the inner $\sim3{\rm kpc}$, is apparent from the surface density profile, which is best fit with a bulge, disk, and thick disk." + This is cousisteut with the merger reminant depicted in Figure 2 of Robertsonetal.(2006)., This is consistent with the merger remnant depicted in Figure 2 of \citet{robertson06}. +. We note that our idealized initia disks do not have spheroid stellay components, We note that our idealized initial disks do not have spheroid stellar components. + Auy stars in such component would end up in a splieroida conrponeut in the final ealaxy. auc thus the idealized initial conditions are partially respousible for the lack of a significant spheroidal component in the final galaxy.," Any stars in such component would end up in a spheroidal component in the final galaxy, and thus the idealized initial conditions are partially responsible for the lack of a significant spheroidal component in the final galaxy." + Our results remain valid so long as any initia spheroid component is of low chough mass not to effect the dynamics of the merger., Our results remain valid so long as any initial spheroid component is of low enough mass not to effect the dynamics of the merger. + The star formation rate. Figure 3.. shows a starburst which peaks at around 380MLvrὃν during the moreer.," The star formation rate, Figure \ref{sfr}, shows a starburst which peaks at around $380\,{\rm M}_\odot{\rm yr}^{-1}$, during the merger." + The end of this starburst is used to divide stars iuto merecr aud disk stars., The end of this starburst is used to divide stars into merger and disk stars. + Prior to tle merger. star formation is around 30 AL +.," Prior to the merger, star formation is around 30 $_\odot$ $^{-1}$." + After the merger event. the star formation rate drops below 10Myr+ after around a Corr. although this is affected by our idealized iuitial coucitious that asses a deuse eas disk.," After the merger event, the star formation rate drops below $10{\rm M}_\odot{\rm yr}^{-1}$ after around a Gyr, although this is affected by our idealized initial conditions that assumes a dense gas disk." +" The lass of stars born before. diving. and after the merecr. are 6.3« 100, 33:& 107. and 19\ΤΟΔΕ, respectively."," The mass of stars born before, during, and after the merger, are $6.3\times10^9$ , $33\times 10^9$ , and $19\times10^9{\rm M}_\odot$ respectively." +"Unfortunately, there is no single model which can reproduce the observational properties of the cluster.","Unfortunately, there is no single model which can reproduce the observational properties of the cluster." +" Instead, there are several models which can equally well produce reasonable fit to the observations (Figs. 19,, 20,, 21,, 22,, a 23))"," Instead, there are several models which can equally well produce a reasonable fit to the observations (Figs. \ref{fig:m67_2000.1}, , \ref{fig:m67_2000.5}, , \ref{fig:m67_2000.7}, \ref{fig:m67_2000.9}, \ref{fig:m67_2001.3}) )" +" In general from very low values of arr, i.e. 0.1, up to the canonical value, 1.3, the agreement with observations is reasonably good."," In general from very low values of $\alpha_{IMF}$, i.e. 0.1, up to the canonical value, 1.3, the agreement with observations is reasonably good." +" For some models the luminosity function is modelled better, while for others the surface density profile is better."," For some models the luminosity function is modelled better, while for others the surface density profile is better." + The initial parameters of the best models and the parameters at 4 Gyr are summarised in Tab. 6.., The initial parameters of the best models and the parameters at 4 Gyr are summarised in Tab. \ref{table:new_m67}. + The other model parameters are close to those chosen by Hurleyetal. (2005)., The other model parameters are close to those chosen by \citet{hurleyetal2005}. +. The free parameters of the Monte Carlo code are exactly as determined in the previous Sections., The free parameters of the Monte Carlo code are exactly as determined in the previous Sections. +" For the purpose of the following comparison with the Monte Carlo simulations, weshall focus on the surface density profile given in Bica&Bonatto(2005),, corrected as above for the background stars."," For the purpose of the following comparison with the Monte Carlo simulations, weshall focus on the surface density profile given in \citet{bb2005}, corrected as above for the background stars." +" Clearly, the models show reasonably good agreement with the observations (see Figs 19 - 23 (top panel))."," Clearly, the models show reasonably good agreement with the observations (see Figs \ref{fig:m67_2000.1} - \ref{fig:m67_2001.3} (top panel))." + Use of the corrected observational data brings the surface density profile for the large radii into much better agreement with the simulations (see for comparison Fig. 13))., Use of the corrected observational data brings the surface density profile for the large radii into much better agreement with the simulations (see for comparison Fig. \ref{fig:m67_sd}) ). +" The special treatment of the tide in the Monte Carlo model plays only a minor role: the effective tidal radius, is only reduced by about 1596 in comparison to the true rt.,;,tidal radius, Τε."," The special treatment of the tide in the Monte Carlo model plays only a minor role: the effective tidal radius, $r_{t_{eff}}$, is only reduced by about $15 \%$ in comparison to the true tidal radius, $r_t$." +" It seems that, despite the large latitude of M67, the contamination of the observed surface density profile by background stars plays an important role, at large radii."," It seems that, despite the large latitude of M67, the contamination of the observed surface density profile by background stars plays an important role, at large radii." + 'The comparison between the luminosity functions from the Monte Carlo models and observations is given in the same figures as for the surface density profiles., The comparison between the luminosity functions from the Monte Carlo models and observations is given in the same figures as for the surface density profiles. +" The luminosity functions are in reasonable agreement with observations, except that the modelled luminosity function has an excess for V>16 mag, in comparison with observations."," The luminosity functions are in reasonable agreement with observations, except that the modelled luminosity function has an excess for $V > 16$ mag, in comparison with observations." + Of course there are also noticeable differences for the high-luminosity end connected with the relative lack of blue stragglers in the Monte Carlo models., Of course there are also noticeable differences for the high-luminosity end connected with the relative lack of blue stragglers in the Monte Carlo models. +" It could be argued that the excess of low-luminosity stars cannot be explained by supposing that not all low-mass stars are observed, because the observational field of M67 is high-latitude, not heavily contaminated and sparse, and so all stars with V~18 mag should be observed."," It could be argued that the excess of low-luminosity stars cannot be explained by supposing that not all low-mass stars are observed, because the observational field of M67 is high-latitude, not heavily contaminated and sparse, and so all stars with $V \sim 18$ mag should be observed." +" On the other hand the authors themselves (Montgomery,Marschall&Janes1993) declared that the determination of the luminosity function “is a difficult procedure because of the presence of background stars"".", On the other hand the authors themselves \citep{montgomeryetal1993} declared that the determination of the luminosity function “is a difficult procedure because of the presence of background stars”. +" Their background correction has been applied in the observational data shown in these figures, and they did it in the following way."," Their background correction has been applied in the observational data shown in these figures, and they did it in the following way." +" The background was estimated by counting stars in an area of the colour-magnitude diagram just blue of the main sequence, and equal in area to the assumed boundaries of the main sequence."," The background was estimated by counting stars in an area of the colour-magnitude diagram just blue of the main sequence, and equal in area to the assumed boundaries of the main sequence." +" But photometric errorsin thecolours rise abruptly by V— 15, and the resulting spread in the main sequence"," But photometric errorsin thecolours rise abruptly by $V = 15$ , and the resulting spread in the main sequence" +frames taken on a given night.,frames taken on a given night. + The resulting nightly flattields were normalised and divided into the individual frames., The resulting nightly flatfields were normalised and divided into the individual frames. + The routine was then used to exclude areas of the frames affected by astronomical objects and the generation of the nightly average flatfield repeated., The routine was then used to exclude areas of the frames affected by astronomical objects and the generation of the nightly average flatfield repeated. + Division of the individual frames by these improved flatfields produced good results for both PSF-star and target frames. but low-level structure in the sky was still visible at the | per cent level.," Division of the individual frames by these improved flatfields produced good results for both PSF-star and target frames, but low-level structure in the sky was still visible at the 1 per cent level." + The tinal step in the flattielding involved rerunning the routine on the flattielded frames and then generating a 20-clipped average of the 9 (63) frames in each PSF- (target) sequence., The final step in the flatfielding involved rerunning the routine on the flatfielded frames and then generating a $\sigma$ -clipped average of the 9 (63) frames in each PSF-star (target) sequence. + Division of each frame by the resulting tinal flattield reduced the structure in the sky to ὃς0.3 per cent., Division of each frame by the resulting final flatfield reduced the structure in the sky to $\la 0.3$ per cent. + The master PSF-star (target) image was generated from a Sa- clipped average of the 9 (63) frames. emploving the appropriate XY-offsets for the dither pattern.," The master PSF-star (target) image was generated from a $\sigma$ -clipped average of the 9 (63) frames, employing the appropriate XY-offsets for the dither pattern." + A bad-pixel mask. derived from the dark frames and the variance of the nightly flattield frames. was employed to exclude bad pixels from the averaging.," A bad-pixel mask, derived from the dark frames and the variance of the nightly flatfield frames, was employed to exclude bad pixels from the averaging." + The resulting frames were both cosmetically clean and showed no detectable structure in the sky., The resulting frames were both cosmetically clean and showed no detectable structure in the sky. + The combined image was then clipped to retain just the central fully-exposed 536«536 pixel (49. 49”) region.," The combined image was then clipped to retain just the central fully-exposed $536 \times 536$ pixel $49\arcsec +\times 49\arcsec$ ) region." + In order to identify faint galaxies with small projected separations from the quasars. subtraction of the quasar images was undertaken using the standard sequence of routines (Stetson1987) inIRAP. ," In order to identify faint galaxies with small projected separations from the quasars, subtraction of the quasar images was undertaken using the standard sequence of routines \citep{1987PASP...99..191S} in." +A 21 pixel (1799) radius aperture was used o define the PSFs and also for the quasar image subtractions., A 21 pixel 9) radius aperture was used to define the PSFs and also for the quasar image subtractions. + The PSF-star images were analysed using the routine to produce a ibrary of template-PSFs., The PSF-star images were analysed using the routine to produce a library of template-PSFs. + All the PSF-star images were best-fit by a Toffat profile. usually with 3--=1.5. although the images obtained in the poorest seeing typically produced a best-fit with 7=2.5.," All the PSF-star images were best-fit by a Moffat profile, usually with $\beta=1.5$, although the images obtained in the poorest seeing typically produced a best-fit with $\beta=2.5$." + The target frames were then inspected visually and additional emplate-PSFs were constructed using the routines. where a single stellar image brighter than missas|0.5 was oresent in the frame.," The target frames were then inspected visually and additional template-PSFs were constructed using the routines, where a single stellar image brighter than $m_{quasar}+0.5$ was present in the frame." + The number of target frames for which two or more such suitable stars were present was small but in such cases a single template-PSF was constructed., The number of target frames for which two or more such suitable stars were present was small but in such cases a single template-PSF was constructed. + Care was taken to ensure that none of the stellar images possessed peak counts taking them into he non-linear exposure-count regime of UFTI., Care was taken to ensure that none of the stellar images possessed peak counts taking them into the non-linear exposure–count regime of UFTI. + The subtraction of the quasar images was undertaken using the routine., The subtraction of the quasar images was undertaken using the routine. +" As expected. the template-PSFs derived from a sarticular target frame produced the most satisfactory subtractions or the target quasar,"," As expected, the template-PSFs derived from a particular target frame produced the most satisfactory subtractions for the target quasar." + Where such a template-PSF was not available. a suitable template-PSF was chosen from the full library based on he seeing. ellipticity and orientations of fainter stellar images in the arget frame.," Where such a template-PSF was not available, a suitable template-PSF was chosen from the full library based on the seeing, ellipticity and orientations of fainter stellar images in the target frame." + Table |.. Col.," Table \ref{tab:obs}, Col." + 9 indicates whether the adopted subtraction employed a library (L) or target frame (F) PSF., 9 indicates whether the adopted PSF-subtraction employed a library (L) or target frame (F) PSF. + The results of all the subtractions were examined visually and a series of tests carried out to verify the reliability of the quasar-image removal., The results of all the subtractions were examined visually and a series of tests carried out to verify the reliability of the quasar-image removal. +" In cases where a faint image was revealed by the subtraction. other stellar images (when present) in the target frame were also processed to ensure that similar ""images? were not revealed."," In cases where a faint image was revealed by the subtraction, other stellar images (when present) in the target frame were also processed to ensure that similar `images' were not revealed." +" Similarly. when low-level systematic residuals. usually of the ""butterfly? or ""elover-leaf type. werepresent.. other stellar images were processed to ascertain that the same form of residual persisted."," Similarly, when low-level systematic residuals, usually of the `butterfly' or `clover-leaf' type, were, other stellar images were processed to ascertain that the same form of residual persisted." + In all cases. irrespective of whether faint images or residuals were apparent. a number of different PSF-templates were tested to check that the results of the image subtraction was not strongly dependent on the exact PSF-template used.," In all cases, irrespective of whether faint images or residuals were apparent, a number of different PSF-templates were tested to check that the results of the image subtraction was not strongly dependent on the exact PSF-template used." + Fig., Fig. + | shows the pre- and best post-subtracted quasar images for the 30 quasars and the tive control quasars., 1 shows the pre- and best post-subtracted quasar images for the 30 quasars and the five control quasars. + Each image pair shows a 1570« region centred on the quasar. with the pre-subtraction image presented on the right-hand side.," Each image pair shows a $15\farcs0 \times +15\farcs0$ region centred on the quasar, with the pre-subtraction image presented on the right-hand side." + A scale-bar is shown in the op right-hand panel of each page., A scale-bar is shown in the top right-hand panel of each page. + The combination of the UFTI instrument. with its small 00091 pixels. and an observing strategy in which high signal-o-noise ratio target and PSF-star observations were obtained was designed to maximise the accuracy ofthe PSF characterisation.," The combination of the UFTI instrument, with its small 091 pixels, and an observing strategy in which high signal-to-noise ratio target and PSF-star observations were obtained was designed to maximise the accuracy of the PSF characterisation." + The resulting image subtractions were well-behaved with the form of he residuals showing consistent behaviour among multiple stars within the same frame. and as a function of the degree of similarity between the PSF-templates and the image profiles.," The resulting image subtractions were well-behaved with the form of the residuals showing consistent behaviour among multiple stars within the same frame, and as a function of the degree of similarity between the PSF-templates and the image profiles." + However. the magnitude range of the quasars. 15.4.5Av16.9. causes a significant variation to exist in the magnitude of the faintest galaxies that may be detected reliably. as the PSF-subtraction is limited in accuracy by a constant percentage of the quasar flux.," However, the magnitude range of the quasars, $15.4 \le K \le 16.9$, causes a significant variation to exist in the magnitude of the faintest galaxies that may be detected reliably, as the PSF-subtraction is limited in accuracy by a constant percentage of the quasar flux." + To determine the effectiveness of the PSF-subtraction a series of simulations were undertaken using the package withinIRAP., To determine the effectiveness of the PSF-subtraction a series of simulations were undertaken using the package within. + Synthetic galaxies. modelled pessimistically as pure exponential disks. were blurred to match the seeing using a Moffat profile.," Synthetic galaxies, modelled pessimistically as pure exponential disks, were blurred to match the seeing using a Moffat profile." + To match the appearance of galaxies in the images. these synthetic galaxies were constructed with intrinsic half-light radii of LI to 0/225. corresponding to spatial half-light diameters of ~2- Skkpe. and a range of apparent magnitude 19.05A20.0.," To match the appearance of galaxies in the images, these synthetic galaxies were constructed with intrinsic half-light radii of 1 to 25, corresponding to spatial half-light diameters of $\sim$ kpc, and a range of apparent magnitude $19.0 \le K \le 20.0$." + The synthetic galaxies were then added to the actual frames of absorber and control quasars that were not found to possess close companion galaxies., The synthetic galaxies were then added to the actual frames of absorber and control quasars that were not found to possess close companion galaxies. + Three quasar-galaxy separations of A@=ο0.075 and 170 were explored. using quasar images covering the full magnitude range of quasars present in the sample.," Three quasar-galaxy separations of $\Delta\theta=0\farcs0, 0\farcs5$ and $1\farcs0$ were explored, using quasar images covering the full magnitude range of quasars present in the sample." + The results of the simulations were encouraging., The results of the simulations were encouraging. + A separations A@z170 the galaxy images are visible in the pre-PSF-subtracted images for all but the brightest quasars. and al galaxies as faint as /y=20.0 are recovered.," At separations $\Delta\theta \ge 1\farcs0$ the galaxy images are visible in the pre-PSF-subtracted images for all but the brightest quasars, and all galaxies as faint as $K=20.0$ are recovered." + Down to separations of A@&075 all galaxies with A'=19.5 are revealed via the PSF-subtraction., Down to separations of $\Delta\theta \ge 0\farcs5$ all galaxies with $K=19.5$ are revealed via the PSF-subtraction. + Fainter than ἐν=19.5. galaxies can be detected down to ἐν=20.0 only for the faintest third of the quasar images GN. 16.5).," Fainter than $K=19.5$, galaxies can be detected down to $K=20.0$ only for the faintest third of the quasar images $K \ge 16.5$ )." +" The recovery rate for essentially zero-separations. Ad=025, is poor."," The recovery rate for essentially zero-separations, $\Delta\theta \la 0\farcs25$, is poor." + Galaxies with A19.5 cannot be recovered for any of the quasars and galaxies with 19.0:fy<19.5 can only be recovered for quasars with A:16.0., Galaxies with $K \ge 19.5$ cannot be recovered for any of the quasars and galaxies with $19.0 \le K < 19.5$ can only be recovered for quasars with $K \ge 16.0$. +" The rapid degredation in the ability to recover faint galaxies at the very smallest separations comes about primarily because of the presence of the characteristic ‘butterfly’ or ""clover-leaf residuals. which are caused by very small differences in the PSFs and potential confusion from the cores of quasar host galaxies."," The rapid degredation in the ability to recover faint galaxies at the very smallest separations comes about primarily because of the presence of the characteristic `butterfly' or `clover-leaf' residuals, which are caused by very small differences in the PSFs and potential confusion from the cores of quasar host galaxies." + In summary. the PSF-subtraction is capable of recovering galaxies with percentage fluxes of the quasar of 1. 1.5 and 7 per cent at separations of A@=170.075. and (70 respectively.," In summary, the PSF-subtraction is capable of recovering galaxies with percentage fluxes of the quasar of 1, 1.5 and 7 per cent at separations of $\Delta\theta=1\farcs0, 0\farcs5$, and $0\farcs0$ respectively." + Notes regarding the results of the PSF-subtraction for a small number of quasars are included in Appendix 7.., Notes regarding the results of the PSF-subtraction for a small number of quasars are included in Appendix \ref{sec:app}. + The high-resolution of the raw images. necessary for the image subtractions. was not optimal for the detection of faint low-surface brightness images within the target exposures.," The high-resolution of the raw images, necessary for the image subtractions, was not optimal for the detection of faint low-surface brightness images within the target exposures." + Image catalogues. including the detection. of the target quasar or quasartclose_ccompanion. were constructed by applying," Image catalogues, including the detection of the target quasar or companion, were constructed by applying" +thus the concentration. log(7;/75)) to increase svstemalicallyalong with JH. to a lesser extentas stars with fainter and fainter magnitudes were included to define the observed density profile.,"thus the concentration, $\log\,(r_t/r_0)$ ) to increase systematically—along with $R_h$, to a lesser extent—as stars with fainter and fainter magnitudes were included to define the observed density profile." + This is primarily because stars with g'Z19 20 in our sample are somewhat depleted. relative to the brighter stars. in the innermost ~2 3* of NGC 6791.," This is primarily because stars with $g^\prime \ga 19$ –20 in our sample are somewhat depleted, relative to the brighter stars, in the innermost $\sim\!2\arcmin$ $3\arcmin$ of NGC 6791." + However. il is not clear whether this is a physical effect (e.g.. due to mass segregation) or an artifact of crowcding and image blending in the core of the eluster.," However, it is not clear whether this is a physical effect (e.g., due to mass segregation) or an artifact of crowding and image blending in the core of the cluster." +" The total luminosity of all stars with ο<22 in our catalogue is Li,25500 6500L.. (assumingS D=4.0 kpe. corrected for ;15=0.55 magS of extinction. and dependingS on whether or not the Iuminosities are weighted by 2)."," The total luminosity of all stars with $g^\prime<22$ in our catalogue is $L_{\rm tot}\approx 5500$ $6500~L_{\odot,g^{\prime}}$ (assuming $D=4.0$ kpc, corrected for $A_{\rm g^{\prime}}=0.55$ mag of extinction, and depending on whether or not the luminosities are weighted by $P_\mu$ )." +" Adopting a theoretical 9! stellar mass- relation [rom (he Padova isochrones (Marigoetal.2008) implies a total mass of AL,25000AL. For the observed stars."," Adopting a theoretical $g^\prime$ stellar mass-luminosity relation from the Padova isochrones \citep{mar08} + implies a total mass of $M_{\rm tot}\approx5000~M_\odot$ for the observed stars." + This is a lower limit to the cluster mass because we have not attempted corrections for stellar binarity or incompleteness., This is a lower limit to the cluster mass because we have not attempted corrections for stellar binarity or incompleteness. +" We note that. if a Wine(1966) model with e=0.74 and Ry,=5 pe accurately describes the internal mass profile of NGC 6791. then the projected. one-dimensional velocity dispersion averaged within the effective radius should be (0);20.36(GALHj,jl""gg(75kms!"," We note that, if a \citet{kin66} model with $c=0.74$ and $R_h=5$ pc accurately describes the internal mass profile of NGC 6791, then the projected, one-dimensional velocity dispersion averaged within the effective radius should be $\langle\sigma\rangle_h \simeq 0.36\,\left(GM_{\rm tot}/R_h\right)^{1/2} + \approx 0.75~{\rm km~s}^{-1}$." +" This corresponds (o an intrinsic proper-motion dispersion of o,20.04(D/4kpc)masvrwhich is much smaller (han the formal uncertainties in our proper motions."," This corresponds to an intrinsic proper-motion dispersion of $\sigma_\mu \approx + 0.04\,\left(D/4\,{\rm kpc}\right)^{-1}~{\rm mas~yr}^{-1}$, which is much smaller than the formal uncertainties in our proper motions." + It is also significantly lower (han the raclial-velocity dispersion of &2kms.l reported for about a dozen red giants by Carraro (2006).. suggesting either that the Carraroetal... dispersion may be spuriously hieh. or that NGC: 6791 may not be in virial equilibrium.," It is also significantly lower than the radial-velocity dispersion of $\approx\!2~{\rm km~s}^{-1}$ reported for about a dozen red giants by \citet{car06}, suggesting either that the \citeauthor{car06} + dispersion may be spuriously high, or that NGC 6791 may not be in virial equilibrium." +" Perhaps related to the second option. we note that a 5000 M. cluster in a Qalactic orbit with a pericenter of 3 kpe aud an apocenter ol ~10 kpe (Bedinοἱal.2006) is expected to have a tidal radius of r7;zz13pe~11 al pericenter. and 1,2228pcz24 αἱ apocenteras against a value of r,Z23! suggested by our Ixing-mocdel fitting of NGC 6791."," Perhaps related to the second option, we note that a 5000 $M_\odot$ cluster in a Galactic orbit with a pericenter of $\simeq\!3$ kpc and an apocenter of $\simeq\!10$ kpc \citep{bed06} is expected to have a tidal radius of $r_t\approx 13~{\rm pc}\simeq11\arcmin$ at pericenter, and $r_t\approx28~{\rm pc}\simeq24\arcmin$ at apocenter—as against a value of $r_t\ga 23\arcmin$ suggested by our King-model fitting of NGC 6791." + Deciding the true dvnamical state of this cluster will require much more comprehensive and hieher-precision proper-motion and radial-velocity survevs. to obtain the lightest possible constraints on ils orbit ancl (ο delineate accurately ils internal kinematics.," Deciding the true dynamical state of this cluster will require much more comprehensive and higher-precision proper-motion and radial-velocity surveys, to obtain the tightest possible constraints on its orbit and to delineate accurately its internal kinematics." + Even a casual inspection of the cluster sCMD reveals an unusually broad RGB on the order of A(g’=r!) ~0.1 mag. while the formal uncertainties in the colors of these stars do not exceed ~0.02 mag.," Even a casual inspection of the cluster's CMD reveals an unusually broad RGB – on the order of $\Delta(g'-r')\sim$ 0.1 mag, while the formal uncertainties in the colors of these stars do not exceed $\sim$ 0.02 mag." + There is a variely of potential sources of increased scatter in the CMD. such as instrumental effects including (he limitations of aperture photometrv in crowded fields. presence of field stars. differential reddening. binarity of stars. metallicity variations. and possible ellects on color/luminosity of RGB stars by variable mass loss suggested by," There is a variety of potential sources of increased scatter in the CMD, such as instrumental effects including the limitations of aperture photometry in crowded fields, presence of field stars, differential reddening, binarity of stars, metallicity variations, and possible effects on color/luminosity of RGB stars by variable mass loss suggested by" +of targets in SDSS QSO survey (Ménnard et al.,of targets in SDSS QSO survey (Ménnard et al. + 2008)., 2008). + In sample $1.65 QSOs have not been selected on the basis of their colours but have been selected on the basis of their radio or X-ray properties or have been serendipitously detected.," In sample S1, 65 QSOs have not been selected on the basis of their colours but have been selected on the basis of their radio or X-ray properties or have been serendipitously detected." + We have constructed composite of this sample (NCS65 sample) and also of the sample of the rest of the 1019 colour selected QSOs (CS1019 sample) in sample S1., We have constructed composite of this sample (NCS65 sample) and also of the sample of the rest of the 1019 colour selected QSOs (CS1019 sample) in sample S1. + The relative E(CD12) of the NCS65 with respect to CSI0I9 is 0.0027., The relative $E(B-V)$ of the NCS65 with respect to CS1019 is 0.0027. + The emission redshift distributions of these two samples are however different. KS test giving the probability that the two sets of redshifts to be drawn from the same distribution close to zero. the (51019 sample having higher redshifts.," The emission redshift distributions of these two samples are however different, KS test giving the probability that the two sets of redshifts to be drawn from the same distribution close to zero, the CS1019 sample having higher redshifts." + Thus the relative reddening could partly be due to the difference in emission redshifts of the two samples (e.g. see samples 13 and [4 in tables | and 3)., Thus the relative reddening could partly be due to the difference in emission redshifts of the two samples (e.g. see samples 13 and 14 in tables 1 and 3). +" We therefore selected QSOs from the colour selected sample of 1019 systems €CSIOI9) which have z,,,, and m; values close to those of the QSOs in the sample which were not colour selected (NCS65). using the procedure described in section 2."," We therefore selected QSOs from the colour selected sample of 1019 systems (CS1019) which have $_{em}$ and $_i$ values close to those of the QSOs in the sample which were not colour selected (NCS65), using the procedure described in section 2." +" This new sample of 65 colour selected QSOs (CS65) has similar distribution of Zo, and m; as that for the sample of QSOs which are no colour selected (NCS63). KS test yielding the probability for the distributions to be same to be > 0.93."," This new sample of 65 colour selected QSOs (CS65) has similar distribution of $_{em}$ and $_i$ as that for the sample of QSOs which are not colour selected (NCS65), KS test yielding the probability for the distributions to be same to be $>$ 0.93." + The relative (D.—V) of NCS65 with respect to CS65 is 0.0020., The relative $E(B-V)$ of NCS65 with respect to CS65 is 0.0020. + So the QSOs selected by methods other than colour selection appear to be more reddened as compared to the colour selected QSOs., So the QSOs selected by methods other than colour selection appear to be more reddened as compared to the colour selected QSOs. + We have plotted composites for CS65 and NCS65 in the bottom panel of Fig.7., We have plotted composites for CS65 and NCS65 in the bottom panel of Fig.7. + We note that only 4 systems are common in NCS65 and $23., We note that only 4 systems are common in NCS65 and S23. + We next studied the absorption lines in the composite spectra in order to examine any correlation with absorber and QSO properties., We next studied the absorption lines in the composite spectra in order to examine any correlation with absorber and QSO properties. + The arithmetic mean composite of the sample SI is shown in Fig.8., The arithmetic mean composite of the sample S1 is shown in Fig.8. + The equivalent widths of absorption lines for this spectrum are given in Table 4., The equivalent widths of absorption lines for this spectrum are given in Table 4. + The table also includes equivalent widths of the sample | (full sample) of YO06., The table also includes equivalent widths of the sample 1 (full sample) of Y06. + The DLA systems appear to have lower ionization compared to the full sample of YO6 as seen from the considerably lower equivalent widths of C IV and ΑΙ III lines., The DLA systems appear to have lower ionization compared to the full sample of Y06 as seen from the considerably lower equivalent widths of C IV and Al III lines. + In order to study the dependence of line strengths on the absorber and QSO properties we have plotted in Fig.9 lines of several species for some of the subsamples from Table |., In order to study the dependence of line strengths on the absorber and QSO properties we have plotted in Fig.9 lines of several species for some of the subsamples from Table 1. + Lines for two subsamples (in red and in black) are plotted in each row: the details of the subsamples are given in the last column of that row., Lines for two subsamples (in red and in black) are plotted in each row; the details of the subsamples are given in the last column of that row. + Also plotted in green. are the | c errors in flux of the composite spectra.," Also plotted in green, are the 1 $\sigma$ errors in flux of the composite spectra." + As expected. lines of higher ionization are somewhat weaker and those of lower ionization are somewhat stronger in the subsample having higher H I column density.," As expected, lines of higher ionization are somewhat weaker and those of lower ionization are somewhat stronger in the subsample having higher H I column density." +" Subsample S11 with higher z,,;, seems to have somewhat weaker lines of higher ionization species as compared to the corresponding subsample S12 at lower redshift.", Subsample S11 with higher $_{ab}$ seems to have somewhat weaker lines of higher ionization species as compared to the corresponding subsample S12 at lower redshift. + The difference is not very signiticant for οἱ IV lines., The difference is not very significant for Si IV lines. + The difference is not likely to be due to the slight difference in the average H I column densities in these subsamples., The difference is not likely to be due to the slight difference in the average H I column densities in these subsamples. + If true this may indicate a change in the ionizing radiation., If true this may indicate a change in the ionizing radiation. + Line strengths do seem to depend on 1ο limiting values of A(g and more strongly on Wy as seen from the atl “and ο)”H rows in Fig.9., Line strengths do seem to depend on the limiting values of $\Delta(g-i)$ and more strongly on $_{\rm SiII}$ as seen from the $^{th}$ and $^{th}$ rows in Fig.9. + In the third from bottom pane of the figure we have compared lines for subsamples S16 and $22., In the third from bottom panel of the figure we have compared lines for subsamples S16 and S22. + The equivalent widths of lines of subsamples having A(g7)<01 (S16) and A(gP)<0.8 (S22) are very similar., The equivalent widths of lines of subsamples having $\Delta(g-i)<-0.01$ (S16) and $\Delta(g-i)<0.3$ (S22) are very similar. + The relative (01) between these two subsamples 1s 0.007 (see Table 3)., The relative $E(B-V)$ between these two subsamples is 0.007 (see Table 3). + This indicates that the systems with A(g—7)< 0.3are basically a similar and it is only a few systems with A(g—i)>0.3 that have larger equivalent widths and also higher H I column densities (see Table |)., This indicates that the systems with $\Delta(g-i)<0.3$ are basically all similar and it is only a few systems with $\Delta(g-i)\ge0.3$ that have larger equivalent widths and also higher H I column densities (see Table 1). + Only 13 systems are common between samples S21 and $23., Only 13 systems are common between samples S21 and S23. + Removing hese systems from S21 makes the line strengths the same as those or S2? (indicating that the higher A(g—7) in rest of the systems in S21 may not originate in the intervening absorbers and could be intrinsic to the quasar). while removing these systems from S23 still leaves lines significantly stronger than those for S24.," Removing these systems from S21 makes the line strengths the same as those for S22 (indicating that the higher $\Delta(g-i)$ in rest of the systems in S21 may not originate in the intervening absorbers and could be intrinsic to the quasar), while removing these systems from S23 still leaves lines significantly stronger than those for S24." + Thus we conclude that the line strengths are most sensitive to Wai.," Thus we conclude that the line strengths are most sensitive to $_{\rm +SiII}$." + S23 orms ~ of the DLA sample., S23 forms $\sim$ of the DLA sample. + Some of these could be the dusty. vigh abundance systems found at high redshifts as mentioned in section 3.1.," Some of these could be the dusty, high abundance systems found at high redshifts as mentioned in section 3.1." + In the second from bottom panel of the figure we have compared lines for subsamples $19 and S23., In the second from bottom panel of the figure we have compared lines for subsamples S19 and S23. + Lines of $23 seem to be stronger than those for S19., Lines of S23 seem to be stronger than those for S19. + In the bottom panel of Fig.9. we have plotted lines for the sample of QSOs based on colour selection and not based on colour selection (NCS65 and CS65 as described in section 3.1.3).," In the bottom panel of Fig.9, we have plotted lines for the sample of QSOs based on colour selection and not based on colour selection (NCS65 and CS65 as described in section 3.1.3)." + Lines of C and Al are weaker in the colour selected sample. those of Si are of similar strength. while all lines of Fe IT (only one of which is included in Fig.9) are stronger in this sample.," Lines of C and Al are weaker in the colour selected sample, those of Si are of similar strength, while all lines of Fe II (only one of which is included in Fig.9) are stronger in this sample." + The lines O TAL302 and Si ITAI304 are exceptionally weak in CS65 which can not be real in view of the strength of οἱ IIA1526 line., The lines O $\lambda1302$ and Si $\lambda1304$ are exceptionally weak in CS65 which can not be real in view of the strength of Si $\lambda1526$ line. + We believe this may be caused by the fact that the samples are small and for almost half of the samples these lines lie in the Lyman alpha forest and thus may be severely affected., We believe this may be caused by the fact that the samples are small and for almost half of the samples these lines lie in the Lyman alpha forest and thus may be severely affected. +" The average Nu, of both samples differ by only ~ 0.1 dex.", The average $_{\rm HI}$ of both samples differ by only $\sim$ 0.1 dex. + The composite spectra thus may indicate lower abundances in the colour selected sample and higher depletion of Fe and possibly Si in the sample not selected on the basis of colour., The composite spectra thus may indicate lower abundances in the colour selected sample and higher depletion of Fe and possibly Si in the sample not selected on the basis of colour. + This is consistent with higher dust content of the DLAs along lines of sight to QSOs which are not colour selected., This is consistent with higher dust content of the DLAs along lines of sight to QSOs which are not colour selected. + Comparison of several absorption lines in the composite spectra of a number of subsamples. detined in Table |. constructed on the basis of absorber and QSO properties.," Comparison of several absorption lines in the composite spectra of a number of subsamples, defined in Table 1, constructed on the basis of absorber and QSO properties." + The lines for the ful sample are plotted in the top panel., The lines for the full sample are plotted in the top panel. + Each row shows different lines in the composite spectra of the same two subsamples (one in red and the other in black). which are detailed in the last column ofeach row.," Each row shows different lines in the composite spectra of the same two subsamples (one in red and the other in black), which are detailed in the last column of each row." + Each column contains lines of the same species. indicated in the top row of that column. the wavelength of which is indicated below each column.," Each column contains lines of the same species, indicated in the top row of that column, the wavelength of which is indicated below each column." + One o errors in the flux of the composite spectra are shown in green for each pixel., One $\sigma$ errors in the flux of the composite spectra are shown in green for each pixel. + Scales are identical for al rows of a given column. except for the second from bottom panel. for which y axis scale goes to smaller values because of the stronger lines for the subsamples plotted in that row.," Scales are identical for all rows of a given column, except for the second from bottom panel, for which y axis scale goes to smaller values because of the stronger lines for the subsamples plotted in that row." + The tick marks on the y axis are 0.1 units apart., The tick marks on the y axis are 0.1 units apart. + The x axis spans 10 in all columns., The x axis spans 10 in all columns. +" For the weakest lines in the composite spectrum. the least affected by saturation. the equivalent widths in the full YO6 sample and those of SI are nearly the same (see Table 4). implying the typical column densities are similar (to within factors of 2) while the average column density of Ng, differs by a of factor5 (log «Ng> = 20.72 for SI and equals 20.00 for the full sample of YO6)."," For the weakest lines in the composite spectrum, the least affected by saturation, the equivalent widths in the full Y06 sample and those of S1 are nearly the same (see Table 4), implying the typical column densities are similar (to within factors of 2) while the average column density of $_{\rm H +I}$ differs by a factor of 5 (log $<$ $_{\rm H I}>$ = 20.72 for S1 and equals 20.00 for the full sample of Y06)." + Evidently. all of the involved species (Si II. Zn II. Cr IT. Fe IT. Mn ID) are more deficient compared to HT ita the sample S1 of this paper.," Evidently, all of the involved species (Si II, Zn II, Cr II, Fe II, Mn II) are more deficient compared to H I in the sample S1 of this paper." + The composite spectrum thus impies lower abundance of heavy elements. in general. at high redshifts than at lower redshifts in the regions probed by QSO absorption systems.," The composite spectrum thus implies lower abundance of heavy elements, in general, at high redshifts than at lower redshifts in the regions probed by QSO absorption systems." + In Table 5 we have given the abundances obtained from weakest lines of the species mentioned above. assuming tem to be on the linear part of the curve of growth.," In Table 5 we have given the abundances obtained from weakest lines of the species mentioned above, assuming them to be on the linear part of the curve of growth." + The abundances are about of the solar values. with Fe and Mn having somewhat lower abundances.," The abundances are about of the solar values, with Fe and Mn having somewhat lower abundances." + The abundances are consistent with the oredictions of chemical, The abundances are consistent with the predictions of chemical +thick disce of hydrogeuaich circtuustellar material around the SN Ia progenitor.,thick disc of hydrogen-rich circumstellar material around the SN Ia progenitor. + If such a circumstellar torus were present around the majority of progenitors of SNe Ta. one would likely expect to observe livdrogenu iu their spectra. though to date less than of SNe Ta have shown any sienature of associated Lydrogen (seee.2..Tan&Podsi- 2006).," If such a circumstellar torus were present around the majority of progenitors of SNe Ia, one would likely expect to observe hydrogen in their spectra, though to date less than of SNe Ia have shown any signature of associated hydrogen \citep[see e.g.,][]{HP06}." +. Tan&Podsiadlowski(2001) investigated SNe Ia progenitors froiu WD | MS aud WD | evolved binaries with very specific binary configurations using population svuthesis., \citet{HP04} investigated SNe Ia progenitors from WD + MS and WD + evolved binaries with very specific binary configurations using population synthesis. + Iu that work. they do not preseut rates of SNe Ta derived from other possible formation chanucls of SNe Ta so we cannot compare DDS rates.," In that work, they do not present rates of SNe Ia derived from other possible formation channels of SNe Ia so we cannot compare DDS rates." + The Galactic rate of SDS SNe Ia for their model which most closely matches our standard (Model 1) parameters is ~6«10far d, The Galactic rate of SDS SNe Ia for their model which most closely matches our standard (Model 1) parameters is $\sim 6 \times 10^{-4}$ $^{-1}$. +" This value is an order of maguitude above our SDS spia galaxy Model 1 rate of —6«10/7 Ἐν though is stil nearly an order of maenitude lower than the empirical SN Ia Galactic vate of Cappollaroetal.(1999.Lx10Fy Ἡ,"," This value is an order of magnitude above our SDS spiral galaxy Model 1 rate of $\sim 6 \times 10^{-5}$ $^{-1}$, though is still nearly an order of magnitude lower than the empirical SN Ia Galactic rate of \citet[][$4 \times 10^{-3}$ $^{-1}$." + The rate for the Wan&Pocdsiadlowski(2001) mode which most closely matches Model 2 is ~10.7 SNe Ta Lo which is close (though still below) the Calactic rates of Cappellaroetal.(1999).. aud is a factor of 5 nues higher than our Model 2 SDS rates (~2«10 ly ," The rate for the \citet{HP04} model which most closely matches Model 2 is $\sim 10^{-3}$ SNe Ia $^{-1}$, which is close (though still below) the Galactic rates of \citet{CET99}, and is a factor of 5 times higher than our Model 2 SDS rates $\sim 2 \times 10^{-4}$ $^{-1}$ )." +It was pointed out bv Tan&Podsiadlowski(2001) hat their prescription for hydrogen accunmmlation is more efficieut than that used by other authors (.c..Yungel-son&Livio 1998).," It was pointed out by \citet{HP04} that their prescription for hydrogen accumulation is more efficient than that used by other authors \citep[i.e.,][]{YL98}." +. It is also more efücient than the xescription we have adopted in this study., It is also more efficient than the prescription we have adopted in this study. + The range of wdrogen accretion rates onto WDs which leads to stable nurnnug (sce section 2) aud cficient mass acctuuulation js uncertain. and it is possible that stable lydrogen nurnnug nav occur for a wider rauge of accretion rates. in turn allowing for higher SNe Ia rates followine your the SDS chanuel as allowed in Tan&Podsiad-oeski(200 1).," The range of hydrogen accretion rates onto WDs which leads to stable burning (see section 2) and efficient mass accumulation is uncertain, and it is possible that stable hydrogen burning may occur for a wider range of accretion rates, in turn allowing for higher SNe Ia rates following from the SDS channel as allowed in \citet{HP04}." +. However. comparison of model hiycdrogeu- WDs on the IER. diagram with supersoft X- sources (Nomotoetal.2007) indicates that the wescription for stable hydrogen burning iu a thiu shell (and adopted here) is consistent with observations.," However, comparison of model hydrogen-accreting WDs on the H-R diagram with supersoft X-ray sources \citep{Nom07} indicates that the prescription for stable hydrogen burning in a thin shell (and adopted here) is consistent with observations." + Tt is worth notius that the delay time distributions of Cregeio(2005).. derived using analytical formulations. produce a DDS DTD shape which is similar to ours: peaked at short (<1 Cyr) delay times. followed by a smooth drop-off as a function of time. due to the dependence of the delay time on the timescale associated with eravitational wave eniüssion.," It is worth noting that the delay time distributions of \citet{Gre05}, derived using analytical formulations, produce a DDS DTD shape which is similar to ours: peaked at short $< 1$ Gyr) delay times, followed by a smooth drop-off as a function of time, due to the dependence of the delay time on the timescale associated with gravitational wave emission." + A simile trend is also found for the delay times of DDS progenitors iu Yuusclson&Livio(2000.Fig., A similar trend is also found for the delay times of DDS progenitors in \citet[][Fig. 2]{YL00}. +2).. The Cregeio(2005) study also deteriuned that the shape of the DTD arising frou SDS progenitors was more flat than when compared to that of the DDS. aud that the SDS delay time depended upon the main sequence lifetime of the SCcondarv star (see their section 5). which is cousisteut with our fiudiues.," The \citet{Gre05} study also determined that the shape of the DTD arising from SDS progenitors was more flat than when compared to that of the DDS, and that the SDS delay time depended upon the main sequence lifetime of the secondary star (see their section 5), which is consistent with our findings." + Delay times of SNe Ia were caleulated by Belezvuskial (2005)., Delay times of SNe Ia were calculated by \citet{BBR05}. +. It was found that the merger of two white dwarfs was cousisteut with an ορΊσα] delay time estimate of ~3 Cyr (Strolecretal.2001)(1998)... and that WDs accreting from non-degencrate stars could potentially explain the observed delay times if a low common euvolope efficiency is used (age5°;e.g.,Cognardetal.2011;Keithetal.2011;Ransom 2011)."," Spectacularly, many radio MSPs have recently been discovered in such searches at high Galactic latitudes \citep[$|b|>5\arcdeg$; e.g.,][]{cgj+11,kjr+11,rrc+11}." +. Here we report on the first pulsar to be discovered at low Galactic latitude that is responsible for a formerly unidentified 1FGL source., Here we report on the first pulsar to be discovered at low Galactic latitude that is responsible for a formerly unidentified 1FGL source. +" iin ((also 2FGL J2030.0+3640), discovered with the NRAO Green Bank Telescope (GBT), is also the first non-MSP gamma-ray pulsar identified in radio searches of IFGL sources."," in (also 2FGL J2030.0+3640), discovered with the NRAO Green Bank Telescope (GBT), is also the first non-MSP gamma-ray pulsar identified in radio searches of 1FGL sources." +" Consistent with the properties of known gamma-ray pulsars, our first IFGL search targets are non-variable and have spectra consistent with exponentially-cutoff power laws."," Consistent with the properties of known gamma-ray pulsars, our first 1FGL search targets are non-variable and have spectra consistent with exponentially-cutoff power laws." +" In this initial small radio survey at the GBT we aimed to search along the Galactic plane, indicating a relatively high search frequency (=1 GGHz) in order to minimize deleterious propagation effects in the interstellar medium and the background due to Galactic synchrotron emission."," In this initial small radio survey at the GBT we aimed to search along the Galactic plane, indicating a relatively high search frequency $\ga 1$ GHz) in order to minimize deleterious propagation effects in the interstellar medium and the background temperature due to Galactic synchrotron emission." +" At the 2GGHz temperaturefrequency used, the GBT beam is 3’ HWHM, and the 1FGL sources to be searched should therefore, ideally, have ros confidence level error radii) below that, after accounting for the combined statistical and estimated systematic positional uncertainties."," At the GHz frequency used, the GBT beam is $3'$ HWHM, and the 1FGL sources to be searched should therefore, ideally, have $r_{95}$ confidence level error radii) below that, after accounting for the combined statistical and estimated systematic positional uncertainties." +" These are strict criteria, and we searched total of only three sources."," These are strict criteria, and we searched a total of only three sources." +" For each we provide A,a (a,6,ros), which are respectively the R.A. and decl."," For each we provide $\alpha,\delta,\Delta_{\theta},r_{95}$ ), which are respectively the R.A. and decl." +" of theobserved position, its offset from the IFGL position (we observed in late 2009, based on an interim version of the catalog), and ros for the gamma-ray source: 1IFGL J0224.06201c (36°00,62°04, 1’,4’), where the “c” indicates that the measured properties of this source (including position) may not be reliable; IFGL J1746.7—3233 (266270,—32°61,3’, 3’); and ((307°52,36°68,1’, 3’)."," of the position, its offset from the 1FGL position (we observed in late 2009, based on an interim version of the catalog), and $r_{95}$ for the gamma-ray source: 1FGL J0224.0+6201c $36\fdg00,62\fdg04,1',4'$ ), where the “c” indicates that the measured properties of this source (including position) may not be reliable; 1FGL J1746.7–3233 $266\fdg70,-32\fdg61,3',3'$ ); and $307\fdg52,36\fdg68,1',3'$ )." + We observed each source for hhr using the GUPPI at a central frequency of GGHz., We observed each source for hr using the GUPPI at a central frequency of GHz. +" Each of 512 polarization-summed frequency channels, spanning a bandwidth of MMHz, were sampled every mms before writing to disk."," Each of 512 polarization-summed frequency channels, spanning a bandwidth of MHz, were sampled every ms before writing to disk." +" The flux limit of these searches, converted to a standard search densityfrequency of GGHz, was approximately mmjy, for an assumed pulsar duty cycle of and spin period larger than a few tens of milliseconds."," The flux density limit of these searches, converted to a standard search frequency of GHz, was approximately mJy, for an assumed pulsar duty cycle of and spin period larger than a few tens of milliseconds." +" We analyzed the data with standard pulsar search in PRESTO (Ransom2001),, selecting trial techniquesdispersion implementedmeasures so as to maintain ideal sensitivity up to twice the maximum Galactic DM predicted in each direction by the Cordes&Lazio(2002) electron distribution model."," We analyzed the data with standard pulsar search techniques implemented in PRESTO \citep{ran01}, selecting trial dispersion measures so as to maintain ideal sensitivity up to twice the maximum Galactic DM predicted in each direction by the \citet{cl02} electron distribution model." + The data sets retained significant sensitivity to (possibly binary) MSPs up to DM=100cem?..," The data sets retained significant sensitivity to (possibly binary) MSPs up to $\mbox{DM} +\approx 100$." +" We therefore did the analysis intwo passes, including one where we allowed for a modest amount of unknown constant acceleration (parameterized in PRESTO by zmax= 50)."," We therefore did the analysis intwo passes, including one where we allowed for a modest amount of unknown constant acceleration (parameterized in PRESTO by $\mbox{zmax}=50$ )." +" In the ddata, collected on 2009 November 27, we discovered on Christmas day an obvious pulsar with period P=0.200 ss and DM=247?."," In the data, collected on 2009 November 27, we discovered on Christmas day an obvious pulsar with period $P=0.200$ s and $\mbox{DM}=247$." +. We began regular timing observations of the new pulsar at GBT on 2010 January 8., We began regular timing observations of the new pulsar at GBT on 2010 January 8. +" Observing parameters were identical to those used in the search observation, although with much shorter integration times, typically 5 minutes."," Observing parameters were identical to those used in the search observation, although with much shorter integration times, typically 5 minutes." + In this manner we measured pulse times of arrival (TOAs) on 28 separate days through 2011 April 11., In this manner we measured pulse times of arrival (TOAs) on 28 separate days through 2011 April 11. + Using these with we obtain a phase-connected rotational ephemeris with mms rms residual., Using these with we obtain a phase-connected rotational ephemeris with ms rms residual. +" After 5 months of radio timing, the solution was sufficient to yield an initial detection of gamma-ray pulsations (see Section 2.3))."," After 5 months of radio timing, the solution was sufficient to yield an initial detection of gamma-ray pulsations (see Section \ref{sec:gamma}) )." +" The DM measurement was improved with the aid of one additional observation centered at GGHz, and implies an uncertainty in the alignment of radio and gamma-ray pulses of only mms."," The DM measurement was improved with the aid of one additional observation centered at GHz, and implies an uncertainty in the alignment of radio and gamma-ray pulses of only ms." +" In order to determine the polarization characteristics ofJ2030--3641,, we have used GUPPI to make three flux- full-Stokes observations of the pulsar, one each at central frequencies of GGHz (lasting for hhr), GGHz hhr), and GGHz hhr)."," In order to determine the polarization characteristics of, we have used GUPPI to make three flux-calibrated full-Stokes observations of the pulsar, one each at central frequencies of GHz (lasting for hr), GHz hr), and GHz hr)." +" We analyzed the data with PSRCHIVE (Hotanetal.2004),, and show the resulting GGHz profiles in Figure 1.."," We analyzed the data with PSRCHIVE \citep{hvm04}, and show the resulting GHz profiles in Figure \ref{fig:pol}." +" The profiles at the other two frequencies are comparable, with a possible slight hint of interstellar scattering visible at GGHz."," The profiles at the other two frequencies are comparable, with a possible slight hint of interstellar scattering visible at GHz." +" The Faraday rotation measure is RM=+514rrad mm, which implies an average electron-weighted Galactic magnetic field strength along the line of sight of 2.6µΟ. The radio spectral index, based on the three flux density measurements, is (where S,ος v; see Table 1))."," The Faraday rotation measure is $\mbox{RM}=+514$ $^{-2}$ which implies an average electron-weighted Galactic magnetic field strength along the line of sight of $2.6\,\mu$ G. The radio spectral index, based on the three flux density measurements, is $\alpha = -1.7\pm0.1$ (where $S_{\nu} +\propto \nu^{\alpha}$ ; see Table \ref{tab:parms}) )." +" We used “Pass 6 diffuse""-class LLAT events (having the highest probability of being gamma- photons),excluding those with zenith angles >100° to"," We used “Pass 6 diffuse”-class LAT events (having the highest probability of being gamma-ray photons),excluding those with zenith angles $>100\arcdeg$ to" +"nearly οσοicrate mi nass, as the mass of the th inodo is approximately equal to (Ale: for any />0.","nearly degenerate in mass, as the mass of the $i$ -th mode is approximately equal to $i M_C$ for any $i > 0$." + The KE tower of excited gauge bosons is expected to be truucated at the masses of the order of the new CUT scale (~100 TeV). where new owesies (e.g... brane dvuaimics) should take over.," The KK tower of excited gauge bosons is expected to be truncated at the masses of the order of the new GUT scale $\sim 100$ TeV), where new physics (e.g., brane dynamics) should take over." + Finally. i the Randa]-Suucimua 1οςοἱ he zeroth Wk mode of the gravitou renisdns massless. while the hieher modes have nasses spaceLas subsequent zeros of the Bessels fiuction JA.," Finally, in the Randall-Sundrum model the zeroth KK mode of the graviton remains massless, while the higher modes have masses spaced as subsequent zeros of the Bessel's function $J_1$." + If the lnass of the first excited. unocde of the eraviton is A4. the μιibsequeut excitalons would have masses of 1.5334. 2.6644). 18M. L30AAL «te.," If the mass of the first excited mode of the graviton is $M_1$, the subsequent excitations would have masses of $M_1$, $M_1$, $M_1$, $M_1$, etc." + T16 spacius vetween the adjacent IKE excitatious decreases at ligji dnassess, The spacing between the adjacent KK excitations decreases at high masses. + The zeroth excitation is coupled to the ΠΕ teusor witli thο erantational sreneth GCy. while each of the higher excitations couples wit1 the sreneth ~AZ.3. Lo. comparable to the EW coupling strenetji.," The zeroth excitation is coupled to the energy-momentum tensor with the gravitational strength $G_N$, while each of the higher excitations couples with the strength $\sim 1/\Lambda_\pi^2$, i.e., comparable to the EW coupling strength." + The excites modes are prestunably truccated. at masses Mp whiere brane excitations would nioify the discussed behavior.," The excited modes are presumably truncated at masses $\sim M_{\rm Pl}$, where brane excitations would modify the discussed behavior." + Since IKK eravitous couple o the energvanonientuni tensor. they eau be added to zuiv verex or liue of aiv SM Fevunan diagram accessible at colliders.," Since KK gravitons couple to the energy-momentum tensor, they can be added to any vertex or line of any SM Feynman diagram accessible at colliders." + Consequellv. to probe the ADD model οἱ1e could look for direct ciission of KE οταν]ous. e.g.. In the qq»gí5|Guy process. which results im a single jet or ploou or monophoton) i the observable final state.," Consequently, to probe the ADD model one could look for direct emission of KK gravitons, e.g., in the $q \bar q \to g/\gamma + G_{\rm KK}$ process, which results in a single jet or photon or ) in the observable final state." + The experimental signature for such eveuts is an apparent transverse monientuni uon-conservation aid an overall cuhaucement of the tail of t1ο jet/photon transverse energy ossectriun., The experimental signature for such events is an apparent transverse momentum non-conservation and an overall enhancement of the tail of the jet/photon transverse energy spectrum. + Another type o| effect. observalbk| iu ligh-cncrey collisions is an eubaicement of Drell-Yan or dibosou spectrum at lüeh invariant lnasses due to additional diagrams involving virtual KK eravion exchauge., Another type of effect observable in high-energy collisions is an enhancement of Drell-Yan or diboson spectrum at high invariant masses due to additional diagrams involving virtual KK graviton exchange. + Searches for virtua eraviton effects are couplemieutary to those for direct eyaviton enuüssion. since t1e former depend on the ultraviolet cuuoff of the IKE spectrum. Mg. whie the latter depends directly ou the fuuanenta Plauck scale Mp.," Searches for virtual graviton effects are complementary to those for direct graviton emission, since the former depend on the ultraviolet cutoff of the KK spectrum, $M_S$, while the latter depends directly on the fundamental Planck scale $M_D$." + While direct eravitou eMISSION cross section 1s We] defined 2.10).. the cross section for virtual eravito1 excliuige depends on a particular rCpresenation of he interaction Lagraugiai aud the definition of the ultraviole cuteXE Mag.," While direct graviton emission cross section is well defined \cite{Peskin,GRW}, the cross section for virtual graviton exchange depends on a particular representation of the interaction Lagrangian and the definition of the ultraviolet cutoff $M_S$." + We will consider two such represchtations |2.11]..," We will consider two such representations \cite{GRW,HLZ}." + Iu bot rof them. 1ο effec‘ts of ED are parameterized via a siiele variable je;= F/ALE. where F is a dimeisionless xuwanmeter of order one reflecting he dependence o [virtual Cux exchange on he nuuber of extra dimeions.," In both of them, the effects of ED are parameterized via a single variable $\eta_G = {\cal F}/M_S^4$ where ${\cal F}$ is a dimensionless parameter of order one reflecting the dependence of virtual $G_{\rm KK}$ exchange on the number of extra dimensions." + Ref., Ref. + |2| simply fixes F at Lowule an attempt o resolve the i-depeudeu “OS Lac ein [LL].," \cite{GRW} simply fixes ${\cal F}$ at 1, while an attempt to resolve the $n$ -dependence is made in \cite{HLZ}." + Iu both cases the iiterference with he SM cdiaeriuusC» is assumed to lx! coustructive., In both cases the interference with the SM diagrams is assumed to be constructive. + LEP experiueuts have pionecree searches for large extra din5sions at colliders in both direct eraviton οἱnissiou in the e!«>>Z|Gy Channel auc via virtual eraviton effects in fermion pair. as well as in diboson ]xoduction.," LEP experiments have pioneered searches for large extra dimensions at colliders in both direct graviton emission in the $e^+ e^- \to \gamma/Z + G_{\rm KK}$ channel and via virtual graviton effects in fermion pair, as well as in diboson production." + The best seusitvitv is achieved inthe «!¢»5|Gig and iu thee!έ2C|€ channels., The best sensitvity is achieved in the $e^+ e^- \to \gamma + G_{\rm KK}$ and in the $e^+ e^- \to e^+ e^-/\gamma\gamma$ channels. + For a review of LEP limits sec.eg. Refs. 6.191.," For a review of LEP limits see,e.g., Refs. \cite{EDreviews,LEPcomb}. ." +apparent spectral shape.,apparent spectral shape. + Here. we use the Cousins parameters., Here we use the Cousins parameters. + In Fig., In Fig. + 6 we plot the broadband spectra from S nights. 2002 May. 1. 4. 11. 13. 14. 19 June 1. 7 (LIJD 396. 399. 406. 405. 409. 414. 427 432).," 6 we plot the broadband spectra from 8 nights, 2002 May 1, 4, 11, 13, 14, 19 June 1, 7 (HJD 396, 399, 406, 408, 409, 414, 427 432)." + Also shown is à curve representing a power law approximation to the emission from an optically thick. X-rav heated disc.," Also shown is a curve representing a power law approximation to the emission from an optically thick, X-ray heated disc." + The distribution is given bv the equation ByoxA3ebeEOS hore FA ds the reddened. [ux at wavelength A and zl is the wavelength dependent reddening correction toward the source.," The distribution is given by the equation $F_{\lambda} \propto \lambda^{-3}e^{-A_{\lambda } +/1.086}$ where $F_{\lambda }$ is the reddened flux at wavelength $\lambda $ and $A_{\lambda }$ is the wavelength dependent reddening correction toward the source." + Phe amplitude is arbitrary and he spectrum is reddened. assuming interstellar extinction ely=0.42., The amplitude is arbitrary and the spectrum is reddened assuming interstellar extinction $A_{V}=0.42$. + This value is scaled. from the estimated: value ely=0.68 for SAX JISOS.43658 (Wane et ab.," This value is scaled from the estimated value $A_{V}=0.68$ for SAX J1808.4–3658 (Wang et al.," + 2001) using he integrated. column densities. Nyx1.3Oem> or SAN 1505.3658 (Cilfanov et ab.," 2001) using the integrated column densities, $N_H \approx 1.3 \times 10^{20} cm^{-2}$ for SAX J1808.4–3658 (Gilfanov et al.," + 1998) and Nyzx7.6«107em> for XTE 20929.314 (Juett et al.," 1998) and $N_H +\approx 7.6 \times 10^{20} cm^{-2}$ for XTE J0929–314 (Juett et al.," + 2003)., 2003). + A similar value for cy is obtained by using the relationship rctwveen ely and Ny given by Predebl Schmitt (1995)., A similar value for $A_{V}$ is obtained by using the relationship between $A_{V}$ and $N_H$ given by Predehl Schmitt (1995). + We have no information on the Lux in for the first night (1LJD 396) but it is clear that the spectrum was heavily reddened on that occasion., We have no information on the flux in for the first night (HJD 396) but it is clear that the spectrum was heavily reddened on that occasion. + On subsequent nights the spectra were generally steeper ancl hack an approximately power law clistribution., On subsequent nights the spectra were generally steeper and had an approximately power law distribution. + There was. however. a highly: variable red excess above the power law.," There was, however, a highly variable red excess above the power law." + The excesses are not sensitive to the assumed value of ely., The excesses are not sensitive to the assumed value of $A_{V}$. + On ILJD 399 the excess was near zero (similar to the canonical disc power law distribution) and. as noted in section 3.3. the spectrum was anomalouslvy blue.," On HJD 399 the excess was near zero (similar to the canonical disc power law distribution) and, as noted in section 3.3, the spectrum was anomalously blue." + On LLJD 409 (and possibly LEJD 432 although with less statistical significance) the band was strongly enhanced consistent with strong Balmer line (440) emission., On HJD 409 (and possibly HJD 432 although with less statistical significance) the band was strongly enhanced consistent with strong Balmer line $H\alpha$ ) emission. + Balmer emission cannot however account for the variable excesses in/., Balmer emission cannot however account for the variable excesses in. + Measurements errors were relatively laree for the last two nights in Fig., Measurements errors were relatively large for the last two nights in Fig. + 6 (LIJD 427 and 432) but it is clear that the red. excess had. disappeared. and that the spectra were steeper (bluer) than during earlier observations., 6 (HJD 427 and 432) but it is clear that the red excess had disappeared and that the spectra were steeper (bluer) than during earlier observations. + Several features distinguish Ες 0029314 [rom SAN JISQS.43658., Several features distinguish XTE J0929–314 from SAX J1808.4–3658. + Firstly. the maximum of the orbital period moculation occurs at phase 0.19320.05 rather than at phase zero.," Firstly, the maximum of the orbital period modulation occurs at phase $0.19 \pm 0.05$ rather than at phase zero." + This points to an origin of N-rav heating in SAN JISNQN.43658 but the situation is more complex in NTIZ J09209314., This points to an origin of X-ray heating in SAX J1808.4–3658 but the situation is more complex in XTE J0929–314. + Galloway. ct al. (, Galloway et al. ( +2002b) have shown that the 'ompanion in NPE 0929314 is probably a very low mass (0.00847.) helium white dwarf.,"2002b) have shown that the companion in XTE J0929–314 is probably a very low mass $\sim 0.008 +M_{\odot}$ ) helium white dwarf." + The companion in SAX JISOS.43658 is believed. to be a ~0.057. brown cwarf (Bildsten Chakrabarty. 2001).," The companion in SAX J1808.4–3658 is believed to be a $\sim 0.05M_{\odot}$ brown dwarf (Bildsten Chakrabarty, 2001)." + The Roche lobe radii of the companion stars will therefore dilfer by almost an order of magnitude substantially reducing. the X-ray. radiation reprocessed by the companion in SPE J0929.314., The Roche lobe radii of the companion stars will therefore differ by almost an order of magnitude substantially reducing the X-ray radiation reprocessed by the companion in XTE J0929–314. + We have estimated the amplitude £o of optical modulation due to heating of the companion star in NTE J0929314 using the relation Loy=Lxa/LxgidpidVGLRe)Log where Log is the optical modulation observed. for SAX 1505.3658 (Giles et al. 1999). Lyi/Lxg is the ratio of the X-ray fluxes (CGilfanov ct ab.," We have estimated the amplitude $L_{OA}$ of optical modulation due to heating of the companion star in XTE J0929–314 using the relation $L_{OA} = L_{XA}/L_{XB}(d_B/d_A)^{2}(R_A/R_B)^{2}L_{OB}$ where $L_{OB}$ is the optical modulation observed for SAX J1808.4--3658 (Giles et al, 1999), $L_{XA}/L_{XB}$ is the ratio of the X-ray fluxes (Gilfanov et al.," + 1998. Juett et al.," 1998, Juett et al.," + 2003). αμάν is the ratio of distances between the neutron stars ancl their companions and Waffle is the ratio of the Roche Lobe raclii for the two svstems.," 2003), $d_B/d_A$ is the ratio of distances between the neutron stars and their companions and $R_A/R_B$ is the ratio of the Roche Lobe radii for the two systems." + The estimated orbital modulation is 25 per cent of that observed. suggesting that. if it is eencrated thermally. much of the emission. comes from a hot spot on the disc.," The estimated orbital modulation is $\sim 25$ per cent of that observed suggesting that, if it is generated thermally, much of the emission comes from a hot spot on the disc." + This provides an explanation for the observed: maximum phase which lies mid-way between that expected from heating of the companion and from hot spot emission., This provides an explanation for the observed maximum phase which lies mid-way between that expected from heating of the companion and from hot spot emission. + ‘Turning to the spectral eharacteristies the broadband spectra from SAN JLS08.43658 are well fitted by smoothly varving functions derived from a thermal disc model (Wang et al..," Turning to the spectral characteristics the broadband spectra from SAX J1808.4–3658 are well fitted by smoothly varying functions derived from a thermal disc model (Wang et al.," + 2001)., 2001). + However. there are signifiant. time dependent.R& band excesses in our XE 0929.314 spectra.," However, there are signifiant, time dependent, band excesses in our XTE J0929–314 spectra." + Nothing like this has been reported for SAN JISOS4.3658 although Wane et al. (, Nothing like this has been reported for SAX J1808.4–3658 although Wang et al. ( +2001) reported a strong near HU excess on one occasion and this may well have extended to optical wavelengths.,2001) reported a strong near IR excess on one occasion and this may well have extended to optical wavelengths. + We have insullicient information to explain our observed spectral variability., We have insufficient information to explain our observed spectral variability. + As noted in section 3.5. variable Balmer emission may be responsible for the band excesses but cannot contribute to the excesses in.," As noted in section 3.5, variable Balmer emission may be responsible for the band excesses but cannot contribute to the excesses in." +7. The remarkable changes in the red. excesses between LLJD. 396 and 399 and between LEJD 409 and 414 might perhaps be due to cillusion inwards of cool matter from a brief enhancement of mass transfer onto the disc from the companion star., The remarkable changes in the red excesses between HJD 396 and 399 and between HJD 409 and 414 might perhaps be due to diffusion inwards of cool matter from a brief enhancement of mass transfer onto the disc from the companion star. + Alternatively. the red. excesses may be due to. transient svnchrotron emission from matter Lowing out of the system," Alternatively, the red excesses may be due to transient synchrotron emission from matter flowing out of the system" +"is redshift dependent: more distant sources have higher rest-frame frequencies and, therefore should have a smaller core radius and shorter rest-frame delay.","is redshift dependent: more distant sources have higher rest-frame frequencies and, therefore should have a smaller core radius and shorter rest-frame delay." + This effect can potentially be studied in more detail using a larger sample subdivided into high- and low-redshift bins., This effect can potentially be studied in more detail using a larger sample subdivided into high- and low-redshift bins. +" Since a distribution of different delay values is expected, we do not estimate an error range on the detected peak."," Since a distribution of different delay values is expected, we do not estimate an error range on the detected peak." + The value should only be taken as a typical one for the AGNs in peakour sample., The peak value should only be taken as a typical one for the AGNs in our sample. + In Figure 2 we plot the integrated 0.1—100 GeV -ray photon flux against the 15 GHz VLBA core flux density for data in which the measurement leads the radio measurementpairs by 2.540.2 y-raymonths in the observer’s frame., In Figure \ref{f:flux-flux} we plot the integrated $0.1-100$ GeV $\gamma$ -ray photon flux against the 15 GHz VLBA core flux density for data pairs in which the $\gamma$ -ray measurement leads the radio measurement by $2.5 \pm 0.2$ months in the observer's frame. +" The formal probability of a chance correlation is 5x10"".", The formal probability of a chance correlation is $5\times10^{-6}$. +" If we drop the points with photon flux greater than 1077 ph cm? s!, the correlation is still present at a high level of significance."," If we drop the points with photon flux greater than $4\times10^{-7}$ ph $^{-2}$ $^{-1}$, the correlation is still present at a very high level of significance." + We also note the span over one veryorder of in the fluxes for a radio flux density., We also note the span over one order of magnitude in the $\gamma$ -ray fluxes for a given radio flux density. +" Several magnitudefactors can y-raycontribute to this givenscatter: the shape of the K-correction effects, different seed photons, and y-raydifferent spectrum,Doppler boosting levels in the y-ray and radio domains (Lister2007)."," Several factors can contribute to this scatter: the shape of the $\gamma$ -ray spectrum, K-correction effects, different seed photons, and different Doppler boosting levels in the $\gamma$ -ray and radio domains \citep{Lister_MC}." +". Although radio loud AGN are generally known to have twin structures, the sources in our have a one-sidedjet parsec-scale morphology sample(Listerettypicallyal.2009b),, selection effects and of the jet implyingemission."," Although radio loud AGN are generally known to have twin jet structures, the sources in our sample typically have a one-sided parsec-scale morphology \citep{MOJAVE}, implying strong selection effects and Doppler boosting of the jet emission." +strong Localization of the y-ray Doppleremission boostingregion within the AGN radio structure and its production mechanism(s) remain topics of active debate., Localization of the $\gamma$ -ray emission region within the AGN radio structure and its physical production mechanism(s) remain topics of active debate. +" physicalThere are three for the site of the emission: (a) only within the possibilitiesunresolved radio core, (b) high-energyonly in the resolved (downstream) jet region, (c) both in the core and jet."," There are three possibilities for the site of the high-energy emission: (a) only within the unresolved radio core, (b) only in the resolved (downstream) jet region, (c) both in the core and jet." +" Repeating the same analysis as in 3.1 for the total VLBA flux density, we found that the corresponding correlation coefficients agree within the errors with those found for the core flux densities."," Repeating the same analysis as in \ref{s:rg_core} for the total VLBA flux density, we found that the corresponding correlation coefficients agree within the errors with those found for the core flux densities." +" Thus, no firm conclusions can be drawnout of this comparison."," Thus, no firm conclusions can be drawnout of this comparison." +" Indeed, the sources in our are highly core dominated, with a median value of Score/Svipasample=0.71, where Score and Syipa are the core and total VLBA flux respectively."," Indeed, the sources in our sample are highly core dominated, with a median value of $S_\mathrm{core}/S_\mathrm{VLBA}=0.71$, where $S_\mathrm{core}$ and $S_\mathrm{VLBA}$ are the core and total VLBA flux density, respectively." +" By contrast, when the jet flux densities density,(Sy;pA— Score) are used, the correlation coefficients are significantly lower, making scenario (b) less probable."," By contrast, when the jet flux densities $S_\mathrm{VLBA}-S_\mathrm{core}$ ) are used, the correlation coefficients are significantly lower, making scenario (b) less probable." + To reduce the uncertainty in the jet flux density estimations we excluded sources with a high (>0.9) core dominance., To reduce the uncertainty in the jet flux density estimations we excluded sources with a high $>0.9$ ) core dominance. +" Nevertheless, the correlation between the jet flux densities measured quasi-simultaneously with the y-ray photon flux is still significant."," Nevertheless, the correlation between the jet flux densities measured quasi-simultaneously with the $\gamma$ -ray photon flux is still significant." + This could be the result of both radio and being boosted by similar beaming factors (Lister-rayetregimesal.2009a;Kovalev2009;Savolainenetal.," This could be the result of both radio and $\gamma$ -ray regimes being boosted by similar beaming factors \citep{MF1,MF2,MF4}." +" 2010).. Assuming the same factor for the jet and the core (opaque jet base), we would Dopplerexpect a weak but correlation between the flux density and integral y-ray significantemission."," Assuming the same Doppler factor for the jet and the core (opaque jet base), we would expect a weak but significant correlation between the jet flux density and integral $\gamma$ -ray emission." +" Alternatively, it is jetpossible that for some low-redshift sources, y-ray emission may also be produced outside the radio core, as could be the case in 884 (Abdoetal. 2009b),, where radio flare accompanying the y-ray activity was detected in the innermost jet region."," Alternatively, it is possible that for some low-redshift sources, $\gamma$ -ray emission may also be produced outside the radio core, as could be the case in 84 \citep{3C84_Fermi}, where radio flare accompanying the $\gamma$ -ray activity was detected in the innermost jet region." + We note that Kovalev(2009) found a correlation between the LAT 0.1—100 GeV photon flux from the integration and 8 GHz radio flux density simultaneously measured the VLBA., We note that \cite{Kovalev_Fermi_assoc} found a correlation between the LAT $0.1-100$ GeV photon flux from the three-month integration and 8 GHz radio flux density measured by the VLBA. +" The of this correlation in this highly variableby population further presencesuggests that Doppler beaming is the likely cause, and that the Doppler"," The presence of this correlation in this highly variable population further suggests that Doppler beaming is the likely cause, and that the Doppler" +fitted the lieht curve by changing the iuchnation anele. be. Ξ 307. 157. 507. 557. GOP. 657. 667. 677. 687. 697. and 707.,"fitted the light curve by changing the inclination angle, i.e., $i=30\arcdeg$ , $45\arcdeg$ , $50\arcdeg$, $55\arcdeg$ , $60\arcdeg$ , $65\arcdeg$ , $66\arcdeg$, $67\arcdeg$, $68\arcdeg$, $69\arcdeg$ , and $70\arcdeg$." + Some of them are plotted iu Figure 2.., Some of them are plotted in Figure \ref{vmag1370va1_v394cra1987}. +" The visual naguitude of the 1987 outburst can be reproduced when he inclination angle is between 65° aud TO"" except for he first day of the outburst.", The visual magnitude of the 1987 outburst can be reproduced when the inclination angle is between $65\arcdeg$ and $70\arcdeg$ except for the first day of the outburst. + It is almost certain that the visual light during the first dav exceeds the Eddington iut because our optically thick wind solutious do not xoduce super Eddingtou luminosities., It is almost certain that the visual light during the first day exceeds the Eddington limit because our optically thick wind solutions do not produce super Eddington luminosities. + Based ou the best fitted. solutions. we have estimated he envelope mass at the optical maxinuun as AA=DasςLO SAL... which indicates a mass accretion rate of Mie=15<10TAL t during the quiescent phase vetween the 1919 aud 1987 outbursts if uo WD matter as been dredeed up.," Based on the best fitted solutions, we have estimated the envelope mass at the optical maximum as $\Delta M= 5.8 \times 10^{-6} M_\odot$ , which indicates a mass accretion rate of $\dot M_{\rm acc}= 1.5 \times 10^{-7} M_\odot$ $^{-1}$ during the quiescent phase between the 1949 and 1987 outbursts if no WD matter has been dredged up." + About (L5«10 SAL.) of the envelope mass has been blown off in the outburst wiud while the residual (1.3.10. SAL.) has been left and added to the helium laver of the WD., About $4.5 \times 10^{-6} M_\odot$ ) of the envelope mass has been blown off in the outburst wind while the residual $1.3 \times 10^{-6} M_\odot$ ) has been left and added to the helium layer of the WD. + Thus. the net nass Increasing rate of the WD is AN=O3L10TAL |.," Thus, the net mass increasing rate of the WD is $\dot M_{\rm He}= 0.34 \times 10^{-7} M_\odot$ $^{-1}$." + The distance to V391 CrÀ is estimated to be 6.1 kpe for uo absorption (ντ= 0)., The distance to V394 CrA is estimated to be 6.1 kpc for no absorption $A_V=0$ ). + We discuss the distance to V39l CrA iu more detail. in the next section. to solve the discrepancy of the distance estimations between iu quiescence aud in bursting pliases.," We discuss the distance to V394 CrA in more detail, in the next section, to solve the discrepancy of the distance estimations between in quiescence and in bursting phases." + Iu a quiescent phase. we lave adopted the same binary model in the 1987 outburst phase except for the disk shape (see Fie. 3)).," In a quiescent phase, we have adopted the same binary model in the 1987 outburst phase except for the disk shape (see Fig. \ref{v394cra_fig_quiescent}) )," +" that is. we assume the WD iass as AMwp= L37al... the accretion buuinositv of the WD as (e.c... Staxrfieldetal. 1988)) aud the viscous Iunuinositv aud the irradiation effect of the ACDE as (e... Schaudletal. 1997)). where Lyyp and Zip, are the total audintrinsic luninositics of the WD. respectively. G the gravitational constant. AL is the mass accretionrate of the WD. Bp=0.00328... is the radius of the 1.9: M...WD. o is the Stetau-Boltzimauu constant. Tisaia is the surface teiiperature of the ACDE. ris the distance from the ceuter of the WD. and cos? is the incident angle of the surface."," that is, we assume the WD mass as $M_{\rm WD}= 1.37 M_\odot$ , the accretion luminosity of the WD as (e.g., \cite{sta88}) ) and the viscous luminosity and the irradiation effect of the ACDK as (e.g., \cite{sch97}) ), where $L_{\rm WD}$ and $L_{\rm WD,0}$ are the total and intrinsic luminosities of the WD, respectively, $G$ the gravitational constant, $\dot M_{\rm acc}$ is the mass accretionrate of the WD, $R_{\rm WD}= 0.0032 R_\odot$ is the radius of the $1.37 M_\odot$ WD, $\sigma$ is the Stefan-Boltzmann constant, $T_{\rm ph, disk}$ is the surface temperature of the ACDK, $r$ is the distance from the center of the WD, and $\cos\theta$ is the incident angle of the surface." + The accretion huuiuositv of the WD is as large as 1000L.. for AL1.510AL. |., The accretion luminosity of the WD is as large as $\sim 1000 L_\odot$ for $\dot M_{\rm acc} \sim 1.5 \times 10^{-7} M_\odot$ $^{-1}$. + The unheated temperatures are asstuned to be [000 I& at the disk ria aud 5000 Ts at the MS photosphere., The unheated temperatures are assumed to be 4000 K at the disk rim and 5000 K at the MS photosphere. +" Figure L shows the observational points (open circles) by Schaefer (1990) together with our calculated 5 light curve (thick solid line) for the suggested mass accretion rate of To fit our theoretical light curves with Sceliaefers (1990) observational points. we have calculated £ light curves by chaugiug the parameters of à=0.5 1.0 by 0.1 step. JF=0.05 0.50 by 0.05 step. Tuis 30006000 Iv by 1000 I& step. νο=3000 and. LOOO IX at the disk rim. νου=0 1000 Εν by 100 £L. step and 5000 Εν by 1000 L.. step aud /—60. FO"" by 1? step aud seck for the best fit model for cach mass accretion rate."," Figure \ref{mix_lum_bv} shows the observational points (open circles) by Schaefer (1990) together with our calculated $B$ light curve (thick solid line) for the suggested mass accretion rate of To fit our theoretical light curves with Schaefer's (1990) observational points, we have calculated $B$ light curves by changing the parameters of $\alpha=0.5$ —1.0 by 0.1 step, $\beta=0.05$ —0.50 by 0.05 step, $T_{\rm ph, MS}= 3000$ —6000 K by 1000 K step, $T_{\rm ph, disk}= 3000$ and 4000 K at the disk rim, $L_{\rm WD,0}=0$ —1000 $L_\odot$ by 100 $L_\odot$ step and 1000---5000 $L_\odot$ by 1000 $L_\odot$ step and $i=60$ $70\arcdeg$ by $1\arcdeg$ step and seek for the best fit model for each mass accretion rate." + The best fit parameters obtained are shown in the figures (also see Table 1. for the other mass accretion rates of 410“AL. Hj, The best fit parameters obtained are shown in the figures (also see Table \ref{v394cra_quiescence} for the other mass accretion rates of $\times 10^{-7} M_\odot$ $^{-1}$ ). + Then we have calculated the theoretical color iudex (D.V). for these best ft modols., Then we have calculated the theoretical color index $(B-V)_c$ for these best fit models. +" Hore. we explain oulv the case of HM=4.5«10TAL. ο, "," Here, we explain only the case of $\dot M_{\rm acc}= 1.5 \times 10^{-7} M_\odot$ $^{-1}$." +because. the 1987 outburst model suggestsa average mass accretion rate of ~1.5 \simeq <2 \pi \Sigma_* R^2 / \dot{M}> \simeq \dot{M}_{*}/\dot{M}$ . + The iuportant poiut for he elobal comparison is that he derived mass accretion rates for almost all sample galaxies lie iu he range between ~0.1 M πμ... whereas the star formation rates vary between LY Mox ο and 3 Mosv +.," The important point for the global comparison is that the derived mass accretion rates for almost all sample galaxies lie in the range between $\sim 0.1$ $_{\odot}$ $^{-1}$ and $0.6$ $_{\odot}$ $^{-1}$, whereas the star formation rates vary between $0.1$ $_{\odot}$ $^{-1}$ and $3$ $_{\odot}$ $^{-1}$." + In the following we show why the mass accretion rate shows this yvchavior., In the following we show why the mass accretion rate shows this behavior. + Using v=Crarbfariy du Eq., Using $\nu=v_{\rm turb}l_{\rm driv}$ in Eq. + 1 leads to The expressiou for the mass accretion rate theu becomes Asstuning typical values at Ros/2. Chon=10 la=100 pe. €=10 M.pe 7. vields a nass acerction rate of AL=0.07 |l.," \ref{eq:energyflux} leads to The expression for the mass accretion rate then becomes Assuming typical values at $R_{25}/2$, $v_{\rm turb}=10$ $^{-1}$ , $l_{\rm driv}=100$ pc, $\Sigma=10$ $_{\odot}$ $^{-2}$, yields a mass accretion rate of $\dot{M}=0.07$ $_{\odot}$ $^{-1}$." + For an error estimate we use the observational uncertainties elven in Sec. 3.1.., For an error estimate we use the observational uncertainties given in Sec. \ref{sec:data}. +" Because of the large uncertainties associated with the molecular eas. we estimate the error of the mass accretion rate af ealactic radi larger than A55,/2 where the gas is predominantly iu atomic form."," Because of the large uncertainties associated with the molecular gas, we estimate the error of the mass accretion rate at galactic radii larger than $R_{25}/2$ where the gas is predominantly in atomic form." +" We assume X=10 .pe 7. DAL.pe 2.8.=5«10MAL 2vr 1, AM,=2.5«10MAL pe Aye locus=]d0lanss 1 boand Ava,= ο,"," We assume $\Sigma=10$ $_{\odot}$ $^{-2}$, $\Delta \Sigma=1$ $_{\odot}$ $^{-2}$ , $\dot{\Sigma}_{*}=5 \times 10^{-10}$ $_{\odot}$ $^{-2}$ $^{-1}$, $\Delta \dot{\Sigma}_{*}=2.5 \times 10^{-10}$ $_{\odot}$ $^{-2}$ $^{-1}$, $v_{\rm turb}=10$ $^{-1}$, and $\Delta v_{\rm turb}=3$ $^{-1}$." + Τ]ὰς leads to logM(Maroij-0.5 30.5. Le. we obtain au uucertaiutv of about a factor of 3.," This leads to $\log(\dot{M} ({\rm M}_{\odot}{\rm yr}^{-1}))=-0.5 \pm 0.5$ , i.e. we obtain an uncertainty of about a factor of 3." + The inspection of Figs. 1.. 2.," The inspection of Figs. \ref{fig:radialprofilesKM05}, \ref{fig:radialprofilesVB03}," + and 5 gives he cousisteut auswer that oulv the less massive ealaxies (logAAD.)Z 10) can sustain the eas oss due to star formation by radial gas transport within the ealactic disks., and \ref{fig:sfrmdot} gives the consistent answer that only the less massive galaxies $\log M_{*} ({\rm M}_{\odot}) \la 10$ ) can sustain the gas loss due to star formation by radial gas transport within the galactic disks. + These galaxies cau even rave access fo their gas reservoir bevond the optical radius., These galaxies can even have access to their gas reservoir beyond the optical radius. + Ou the other hand. the radial gas rausport in the massive spiral galaxies muelt rot be suticient to balance the eas loss due o star formation.," On the other hand, the radial gas transport in the massive spiral galaxies might not be sufficient to balance the gas loss due to star formation." + This implies that. whereas a lnassive galaxy needs spherical iufall from a outative eas halo or las to wait for iufall with an aneular momentum close to that of its disk o replenish its gas content. a less massive galaxy can live with large angular momentum accretion. )ecause Its dass accretion rate even at R>R3 is large. enough for using this gas to sustain its star formation rate.," This implies that, whereas a massive galaxy needs spherical infall from a putative gas halo or has to wait for infall with an angular momentum close to that of its disk to replenish its gas content, a less massive galaxy can live with large angular momentum accretion, because its mass accretion rate even at $R > R_{25}$ is large enough for using this gas to sustain its star formation rate." + The star formation rate of le Inassive ealaxics is thus set by the amount of external accretion., The star formation rate of the massive galaxies is thus set by the amount of external accretion. + In the absence of such an external eas accretion galaxies will slowly coustuue 111 gas. the eas surface density will decrease. the Toomme parameter Q of the eas will increase. and je star formation. rate will.," In the absence of such an external gas accretion galaxies will slowly consume their gas, the gas surface density will decrease, the Toomre parameter $Q$ of the gas will increase, and the star formation rate will." +decline?.. Examples iu. our suple mieht be NGC 3351 ux NGC 2811., Examples in our sample might be NGC 3351 and NGC 2841. + Given that most of the nassive galaxies of our sample do not show this behavior suggests that these galaxies experieuce ass accretion with rates comparable to thei star formation rates (1-9 Myr |) from a putative spherical halo of ionized eas or from satellite accretion leading to a temporarily enhanced mass accretion rate within the disk., Given that most of the massive galaxies of our sample do not show this behavior suggests that these galaxies experience mass accretion with rates comparable to their star formation rates (1-3 $_{\odot}$ $^{-1}$ ) from a putative spherical halo of ionized gas or from satellite accretion leading to a temporarily enhanced mass accretion rate within the disk. + The theory of chuupy gas disks (VDU3) provides analytic expressious for large-scale and siunall-scale properties of galactic gas disks., The theory of clumpy gas disks (VB03) provides analytic expressions for large-scale and small-scale properties of galactic gas disks. + Large-scale xoperties cousidered are the gas surface deusity. density. disk height. turbulent driving leneth scale. velocity dispersion. σας viscosity. volume filling factor. aud molecular fraction.," Large-scale properties considered are the gas surface density, density, disk height, turbulent driving length scale, velocity dispersion, gas viscosity, volume filling factor, and molecular fraction." + Small-scale oxoperties are the mass. size. deusitv. turbulent. Too-fall. molecular formation timescales of the uost massive selferavitatiug gas clouds.," Small-scale properties are the mass, size, density, turbulent, free-fall, molecular formation timescales of the most massive selfgravitating gas clouds." +" These quantities depend on the stellar surface density. he augular velocity ο, the disk radius R. aud 1 ree parameters. which are the Toonme parameter Q of the eas. the mass accretion rate AT. the ratio 8 vetween the daiving leugth scale of turbulence aud he cloud size. aud the radius. at which the local star formation timescale is uo longer he cloud yec-fall timescale. but the molecule formation nuescale."," These quantities depend on the stellar surface density, the angular velocity $\Omega$, the disk radius $R$, and 4 free parameters, which are the Toomre parameter $Q$ of the gas, the mass accretion rate $\dot{M}$, the ratio $\delta$ between the driving length scale of turbulence and the cloud size, and the radius, at which the local star formation timescale is no longer the cloud free-fall timescale, but the molecule formation timescale." + We determine these free parameters using three independent measurements of the radial profiles of the (1) neutral gas (111). molecular eas (CO). and star formation rate (FUV | 21444).," We determine these free parameters using three independent measurements of the radial profiles of the (i) neutral gas ), molecular gas (CO), and star formation rate (FUV + 24 $\mu$ m)." + A sample ofLS mostly spiral galaxies from Leroy is used diu the analysis., A sample of18 mostly spiral galaxies from \citet{Leroy} is used in the analysis. +Dased ou the simultancous VDUS model fitting of the radial profiles of the total gas surface density.,"Based on the simultaneous VB03 model fitting of the radial profiles of the total gas surface density," +dependent on the seeing conditions and on the instrument design.,dependent on the seeing conditions and on the instrument design. +" The straylieht point spread functions can be approximated from fitting observations of the solar limb (aurcolas, see, e.g. Sobotka et al."," The straylight point spread functions can be approximated from fitting observations of the solar limb (aureolas, see, e.g., Sobotka et al." +" 1993) or from fitting the profiles of planetary limbs during transits (see, e.g.. Bonet et al."," 1993) or from fitting the profiles of planetary limbs during transits (see, e.g., Bonet et al." + 1995; Mathew et al., 1995; Mathew et al. + 2009; Wedemeyer-Bóhhm Rouppe van der Voort 2009)., 2009; Wedemeyer-Böhhm Rouppe van der Voort 2009). +" Since we do not have these auxiliary data, we applied a rough estimation, assuming that the biggest amount of the straylight stems from regions within 1.6"" around the respective positions (approximately the tenfold of the spatial resolution of the data), 1.c.. we approximated the straylight point spread function with a Gaussian of 1.6"" width."," Since we do not have these auxiliary data, we applied a rough estimation, assuming that the biggest amount of the straylight stems from regions within $1.6\varcsec$ around the respective positions (approximately the tenfold of the spatial resolution of the data), i.e., we approximated the straylight point spread function with a Gaussian of $1.6\varcsec$ width." + For deconvolving the images we used the Wiener filter given in Sobotka et al. (, For deconvolving the images we used the Wiener filter given in Sobotka et al. ( +"1993) and applied a slight modification, so that it has the shape where MTP is the modulation transfer function (the modulus of the Fourier transform of the point spread function), & is the spatial wavenumber and c is a free parameter which defines the straylight contribution that has to be deconvolved.","1993) and applied a slight modification, so that it has the shape where MTF is the modulation transfer function (the modulus of the Fourier transform of the point spread function), $k$ is the spatial wavenumber and $c$ is a free parameter which defines the straylight contribution that has to be deconvolved." + F(A) for different choices of c is plotted in Fig., $F(k)$ for different choices of $c$ is plotted in Fig. + 3., 3. + The advantage of the present form of the filter compared to the one used in Sobotka et al. (, The advantage of the present form of the filter compared to the one used in Sobotka et al. ( +"1993) is that it converges to unity for large &, 1.c., it does not affect the small-scale structures of the images.","1993) is that it converges to unity for large $k$, i.e., it does not affect the small-scale structures of the images." +" In the present study the value of parameter c has been chosen equal to 2.0, so that the resulting quiet Sun rms image contrast for the continuum point (att=4,—300 .)) of the best scan increases from in the original image to in the deconvolved image, which is closer to, but still somewhat smaller than the contrast obtained from data at a similar wavelength that are much less contaminated by straylight (continuum at 5250.4 .1n IMaX/Sunrise observations, see Martínnez Pillet et al."," In the present study the value of parameter $c$ has been chosen equal to 2.0, so that the resulting quiet Sun rms image contrast for the continuum point (at $\lambda = \lambda_0 - 300$ ) of the best scan increases from in the original image to in the deconvolved image, which is closer to, but still somewhat smaller than the contrast obtained from data at a similar wavelength that are much less contaminated by straylight (continuum at 5250.4 in IMaX/Sunrise observations, see nez Pillet et al." + 2011)., 2011). +" We finally used this conservative choice, although we also tested other straylight functions, including broad Gaussians with widths up to 16""."," We finally used this conservative choice, although we also tested other straylight functions, including broad Gaussians with widths up to $16\varcsec$." +" The results of using stronger straylight removal (larger c) or broader Gaussians, remained similar, but provided stronger downflows and, for larger c, also stronger contrast."," The results of using stronger straylight removal (larger $c$ ) or broader Gaussians, remained similar, but provided stronger downflows and, for larger $c$, also stronger contrast." +" Stronger straylight removal also led to bigger""e scatter in the velocities and somewhat more distorted line profiles, which was another reason to keep to the conservative value of straylight."," Stronger straylight removal also led to bigger scatter in the velocities and somewhat more distorted line profiles, which was another reason to keep to the conservative value of straylight." +" We selected a 13”x13"" field in the quiet Sun to compare velocities before and after straylight removal.", We selected a $13\varcsec\times13\varcsec$ field in the quiet Sun to compare velocities before and after straylight removal. + Results are shown in Fig., Results are shown in Fig. + 4., 4. +" The redshift in inter-granular lanes increases disproportionately through straylight removal (see panels (b), (c) and (d) of Fig."," The redshift in inter-granular lanes increases disproportionately through straylight removal (see panels (b), (c) and (d) of Fig." + 4., 4. + Downflows are particularly affected by straylight because they are narrower and are present in darker features., Downflows are particularly affected by straylight because they are narrower and are present in darker features. + The fact that the downflows remain weaker than upflows also after our standard straylight removal confirms that we have been conservative in the removed amount of straylight., The fact that the downflows remain weaker than upflows also after our standard straylight removal confirms that we have been conservative in the removed amount of straylight. +commonly divided into that of scold’ absorption (i.e. by neutral material) and warm! absorption (ie. bv ionized material).,commonly divided into that of `cold' absorption (i.e. by neutral material) and `warm' absorption (i.e. by ionized material). + The warm absorption has already. been discussed. in Sections 2.3.2 and 2.3.3., The warm absorption has already been discussed in Sections 2.3.2 and 2.3.3. + Xs previously mentioned. variability studies have [ed to a two-zone model for this absorber.," As previously mentioned, variability studies have led to a two-zone model for this absorber." + ‘Table 3 summarizes the properties of these two absorbing regions based on modeling with the photoionization cocle (Ferlancl 1991)., Table 3 summarizes the properties of these two absorbing regions based on modeling with the photoionization code (Ferland 1991). +" Once the ellect of the warm absorber has been mocoeled. the A-ray spectrum can be examined [for evidence of additional cold absorption in excess to that expected. from our own Galaxy (the Galactic column density along the line of sight to this source is Nowy=4.1.107""em. =)."," Once the effect of the warm absorber has been modeled, the X-ray spectrum can be examined for evidence of additional cold absorption in excess to that expected from our own Galaxy (the Galactic column density along the line of sight to this source is $N_{\rm Gal}=4.1\times 10^{20}\pcmsq$ )." + Describing the warm absorber with a simple one-zone photoionization model computed by the code (see Fabian et al., Describing the warm absorber with a simple one-zone photoionization model computed by the code (see Fabian et al. +" 1994 for a detailed description of this warm absorber model). the spectrum suggests an excess cold column density of No=Laqdn""107""em"," 1994 for a detailed description of this warm absorber model), the spectrum suggests an excess cold column density of $N_{\rm H}=1.7^{+0.4}_{-0.3}\times +10^{20}\pcmsq$." + Quoted: errors are statistical in nature and stated. at the 90 per cent confidence. level [or one interesting parameter GN?=27)., Quoted errors are statistical in nature and stated at the 90 per cent confidence level for one interesting parameter $\Delta\chi^2=2.7$ ). +" It. has been suggested that the low energy calibration of the41504 SIS is incorrect so as to over-estimate the cold absorption by 107""em (e.g. see discussion in Cappi et al.", It has been suggested that the low energy calibration of the SIS is incorrect so as to over-estimate the cold absorption by $\times 10^{20}\pcmsq$ (e.g. see discussion in Cappi et al. + 1997)., 1997). + Phus. within these calibration uncertainties. our result may be consistent with there being negligible cold absorption excess to the Galactic column.," Thus, within these calibration uncertainties, our result may be consistent with there being negligible cold absorption excess to the Galactic column." +" Fitting the same simple mocel to theROSAT PSPC spectrum suggests an excess column density of Ng=(1920)107""emτν in good agreement with the result."," Fitting the same simple model to the PSPC spectrum suggests an excess column density of $N_{\rm H}=(1.9\pm 0.3)\times +10^{20}\pcmsq$, in good agreement with the result." + Comparing the results. of Sections 3.13.4. reveals an apparent contradiction., Comparing the results of Sections 3.1–3.4 reveals an apparent contradiction. + X-ray. observations show that. the column density of cold (neutral) gas along the line of sight to he primary X-ray source is Ny£25107em.>., X-ray observations show that the column density of cold (neutral) gas along the line of sight to the primary X-ray source is $N_{\rm H}\approxlt 2\times 10^{20}\pcmsq$. + However. xh the optical continuum source and the DLIS are highly recdened.," However, both the optical continuum source and the BLR are highly reddened." + On the basis of local (Galactic) studies. we would expect à cold. gas column density of Nyz2.6107em.? o be associated with the dust responsible for the reddening.," On the basis of local (Galactic) studies, we would expect a cold gas column density of $N_{\rm +H}\approxgt 2.6\times 10^{21}\pcmsq$ to be associated with the dust responsible for the reddening." + ‘This is more than an order of magnitude above the X-ray imits., This is more than an order of magnitude above the X-ray limits. + Since the X-ray emission is thought to occur deeper within the central engine than either the optical continum. or optical line emission. this result is somewhat surprising.," Since the X-ray emission is thought to occur deeper within the central engine than either the optical continuum or optical line emission, this result is somewhat surprising." + This discrepancy for 6-30-15 was first hinted a w Pineda et al. (, This discrepancy for $-$ 6-30-15 was first hinted at by Pineda et al. ( +1980) ancl explicitly commented: upon » Revnolds Fabian (1995) on the basis of cata drawn rom the literature.,1980) and explicitly commented upon by Reynolds Fabian (1995) on the basis of data drawn from the literature. + A similar discrepancy. has been founc or HUXS 13349| 2438 (Brandt. Fabian Pounds 1996). an infrared. luminous quasar which also displavs a prominen warm absorber.," A similar discrepancy has been found for IRAS $+$ 2438 (Brandt, Fabian Pounds 1996), an infrared luminous quasar which also displays a prominent warm absorber." + These authors discuss various resolutions of his discrepancy., These authors discuss various resolutions of this discrepancy. + To summarize these discussions. it is fou hat the only way to reconcile this result with a plausible geometry and. a physically reasonable gas-to-clust ratio is o sugeest that the cust resides in the gas tha constitutes the warm absorber.," To summarize these discussions, it is found that the only way to reconcile this result with a plausible geometry and a physically reasonable gas-to-dust ratio is to suggest that the dust resides in the gas that constitutes the warm absorber." + The soft. X-ray opacity of his material is less than that of cold material primarily due o the almost complete ionization of hydrogen ancl helium., The soft X-ray opacity of this material is less than that of cold material primarily due to the almost complete ionization of hydrogen and helium. + The dusty warm absorber hypothesis has also been explore w Revnolds (1997) in the context of a sample of Sevfer ealaxics., The dusty warm absorber hypothesis has also been explored by Reynolds (1997) in the context of a sample of Seyfert galaxies. + We now cliscuss clusty warm absorbers in more cetail., We now discuss dusty warm absorbers in more detail. + In this section we explore the idea of a dusty warm absorber in more detail than any. of the above previous work., In this section we explore the idea of a dusty warm absorber in more detail than any of the above previous work. + In particular. we construct photoionization models of dusty warm absorbers and explicitly fit these mocels to the clata.," In particular, we construct photoionization models of dusty warm absorbers and explicitly fit these models to the data." + Dust erains are highly cllicient radiators and hence can thermally decouple from the surrounding hot gas., Dust grains are highly efficient radiators and hence can thermally decouple from the surrounding hot gas. + Under the, Under the +summarized in 2.. the number of single white dwarfs with known field strength is 108.,"summarized in \citet{wickramasinghe+ferrario00-1}, the number of single white dwarfs with known field strength is 108." + Our current census of polars is 76. of which some measure of the surface field is available for a subset of 53.," Our current census of polars is 76, of which some measure of the surface field is available for a subset of 53." + reff-fielddist shows the distribution of the measured (mean or typical) field strengths in the single white dwarfs and in polars., \\ref{f-fielddist} shows the distribution of the measured (mean or typical) field strengths in the single white dwarfs and in polars. + For the latter. the quoted field strength is preferentially that of the main acereting pole as determined from the spacing of cyclotron lines. replaced by Zeeman detections where no cyclotron measurement ts available.," For the latter, the quoted field strength is preferentially that of the main accreting pole as determined from the spacing of cyclotron lines, replaced by Zeeman detections where no cyclotron measurement is available." + It is likely that this distribution is biased against the detection of both high and low field strengths. because the high-field systems have weak spectral features in the optical range and the low-field systems often display a cyclotron continuum with all lines washed out.," It is likely that this distribution is biased against the detection of both high and low field strengths, because the high-field systems have weak spectral features in the optical range and the low-field systems often display a cyclotron continuum with all lines washed out." + We suspect that most of the 23 polars with no field measurement and all of the 40 confirmed or suspected intermediate polars in the 2003 edition of the ? catalogue have field strengths typically in the ΜΜ range. given that the minimum field strength which allows a magnetic CV to synchronize is of the order of 110MMG.," We suspect that most of the 23 polars with no field measurement and all of the 40 confirmed or suspected intermediate polars in the 2003 edition of the \citeauthor{ritter+kolb03-1} catalogue have field strengths typically in the MG range, given that the minimum field strength which allows a magnetic CV to synchronize is of the order of MG." + The lack of high-field polars has been a long-standing puzzle., The lack of high-field polars has been a long-standing puzzle. + ? suggested that for strong fields (B> 40MMG) the wind of the secondary may couple to the magnetic field lines of the white dwarf rather to those of the secondary. and. as a consequence of the large magnetospheric radius of the white dwarf. magnetic braking would be much more efficient than in non-magnetic CVs — in fact so efficient that the mass transfer would be thermally unstable. with a correspondingly very short life time of such systems.," \citet{hameuryetal89-3} suggested that for strong fields $B>40$ MG) the wind of the secondary may couple to the magnetic field lines of the white dwarf rather to those of the secondary, and, as a consequence of the large magnetospheric radius of the white dwarf, magnetic braking would be much more efficient than in non-magnetic CVs – in fact so efficient that the mass transfer would be thermally unstable, with a correspondingly very short life time of such systems." + ? and ? alternatively argued that in high-field polars the magnetic field lines of the secondary will form closed loops or connect to the field lines of the white dwarf. reducing the magnetic flux in open field lines.," \citet{wickramasinghe+wu94-1} and \citet{lietal94-1} alternatively argued that in high-field polars the magnetic field lines of the secondary will form closed loops or connect to the field lines of the white dwarf, reducing the magnetic flux in open field lines." + Therefore. their prediction is that the angular momentum loss and mass transfer rates in strongly magnetic CVs should be lower compared to non- ones. and they predict à maximum field strength of —70— I00MMG. above which mass transfer will be suppressed completely (see. however. the discussion by ?)).," Therefore, their prediction is that the angular momentum loss and mass transfer rates in strongly magnetic CVs should be lower compared to non-magnetic ones, and they predict a maximum field strength of $\sim70-100$ MG, above which mass transfer will be suppressed completely (see, however, the discussion by \citealt{kingetal94-1}) )." + Our determination of a white dwarf magnetic field strength of B—150MMG in JJ1554 raises the number of high-field polars (B>1OOMMG) to three — which makes these objects a rare but no longer exceptional species., Our determination of a white dwarf magnetic field strength of $B\simeq150$ MG in J1554 raises the number of high-field polars $B>100$ MG) to three – which makes these objects a rare but no longer exceptional species. +" UUMa (B=~200MMG. Ps,=Hl6mmin) and HHer (8—150MMQG. Pap= 113mmin) are both below the period gap. and JJ1554 (B—145 MMQG. P4=152 mmin) is right in the middle of the gap — re. all known high-field polars have periods below 3hh. It seems. however. premature to draw any conclusion based on three systems only."," UMa $B\simeq200$ MG, $\Porb=116$ min) and Her $B\simeq150$ MG, $\Porb=113$ min) are both below the period gap, and J1554 $B\simeq145$ MG, $\Porb=152$ min) is right in the middle of the gap – i.e. all known high-field polars have periods below h. It seems, however, premature to draw any conclusion based on three systems only." + One property that at least UUMa and RXJJI554 share is that they are frequently. encountered in states of low mass transfer (22222). while the long-term variability of HHer is less well documented.," One property that at least UMa and J1554 share is that they are frequently encountered in states of low mass transfer \citep{remillardetal94-2, schmidtetal96-1, schmidtetal99-1, +tovmassianetal01-2, thorstensen+fenton02-1}, while the long-term variability of Her is less well documented." + Assuming that frequent low states are a general property of high-field polars it is likely that a considerable fraction of these systems have evaded discovery so far., Assuming that frequent low states are a general property of high-field polars it is likely that a considerable fraction of these systems have evaded discovery so far. +" The exact causes of low states in polars are not yet fully understood. possible mechanisms that could decrease the mass transfer rate on time scales of years include starspots moving across the Z, point (?2) and the swinging dipole model by ?.."," The exact causes of low states in polars are not yet fully understood, possible mechanisms that could decrease the mass transfer rate on time scales of years include starspots moving across the $L_1$ point \citep{king+cannizzo98-1, hessmanetal00-1} and the swinging dipole model by \citet{andronov87-1}." + Detailed long-term monitoring of the accretion activity of polars in general. and high-field polars in particular. would be desirable to establish a measure of their accretion rates following the approach of ?..," Detailed long-term monitoring of the accretion activity of polars in general, and high-field polars in particular, would be desirable to establish a measure of their accretion rates following the approach of \citet{hessmanetal00-1}." + ? believe that the maximum 1n the distribution of single white dwarfs near 20MMG is real., \citet{schmidtetal03-1} believe that the maximum in the distribution of single white dwarfs near MG is real. + Taking into account the selection effects for identifying magnetic CVs in the first place. and measuring the magnetic fields of their white dwarfs in the second place. it seems possible that the intrinsic distribution of magnetic field strengths in CV white dwarfs is not dissimilar from the one of single white dwarfs.," Taking into account the selection effects for identifying magnetic CVs in the first place, and measuring the magnetic fields of their white dwarfs in the second place, it seems possible that the intrinsic distribution of magnetic field strengths in CV white dwarfs is not dissimilar from the one of single white dwarfs." + 11554 is one example of the systems not readily recognisable as high-field polars by optical means. and systems with white dwarfs of still higher field strength possibly may exist but appear no different than ordinary polar.," 1554 is one example of the systems not readily recognisable as high-field polars by optical means, and systems with white dwarfs of still higher field strength possibly may exist but appear no different than ordinary polar." + BTG was supported by a PPARC Advanced Fellowship., BTG was supported by a PPARC Advanced Fellowship. +" Additional support was provided through NASA grant GO- from the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. Ine.. under NASA contract NAS 5-26555,"," Additional support was provided through NASA grant GO-9357 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555." +continued to appear tu the pair of spots due to the teudeucy of entrained material to attempt to escape.,continued to appear in the pair of spots due to the tendency of entrained material to attempt to escape. + Towards the later stages of the simulation. however. the frequency (aud size) of light bridges climinishecl together with the amount of entrained material available for light bridge formation.," Towards the later stages of the simulation, however, the frequency (and size) of light bridges diminished together with the amount of entrained material available for light bridge formation." + Together with previous mocels of umbral convection (5chüssler&Vógler2006) and sunspot simulatious (Heinemannetal.2007:Rempel2009a.b) suggest that uiubral dots. pentumbral filaments and light bridges are all mauifestatious of overturning magnetocouvectlou.," Together with previous models of umbral convection \citep*{Schuessler:UmbralConvection} and sunspot simulations \citep{Heinemann:PenumbraFineStructure,Rempel:PenumbralStructure,Rempel:SunspotStructure} suggest that umbral dots, penumbral filaments and light bridges are all manifestations of overturning magnetoconvection." + In this paper. we preseted the first radiative MHD simulation of the birth of an AR on the solar surface.," In this paper, we presented the first radiative MHD simulation of the birth of an AR on the solar surface." + To mimic the emergence of magnetic [lis from the convection zoue to the photosphere. a magnetic seimitorus was kirematically advected upward through the bottom boundary. which is ocated at 7.5 Mu below the photospheric owe.," To mimic the emergence of magnetic flux from the convection zone to the photosphere, a magnetic semitorus was kinematically advected upward through the bottom boundary, which is located at $7.5$ Mm below the photospheric base." + Here is a list of interestiug findiugs regarding the slivsics of how AR formatio OCCULS ln the simulation., Here is a list of interesting findings regarding the physics of how AR formation occurs in the simulation. + The maguetic field streeth B oft Jerμας: Plasma in the emereine flux regiou roughly follow he scaling relation B.x2o!/7. whe οσο is {1e 1nass density.," The magnetic field strength $B$ of the rising plasma in the emerging flux region roughly follow the scaling relation $B \propto \varrho^{1/2}$, where $\varrho$ is the mass density." + This scaling relation is consistent. witli he scenario that rising plasua prefereitlaly exyancl in the horizontal directions., This scaling relation is consistent with the scenario that rising plasma preferentially expand in the horizontal directions. + This 10rizontal expausion cisperses field over a la‘oe |orizontal area., This horizontal expansion disperses field over a large horizontal area. + As time progresses. the dispersed inagnetic raginents coalesce iuto gradually arger CO1cent‘atious (in terms of flux content).," As time progresses, the dispersed magnetic fragments coalesce into gradually larger concentrations (in terms of flux content)." + Wher compact uaguetic concentrations attain a flux of ~ELO!6 Nix or more. they appear as dark pores i1n ---Wensily linages.," When compact magnetic concentrations attain a flux of $\sim 10^{19}$ Mx or more, they appear as dark pores in intensity images." + Iu order for dispersed field to become compact agaln. excess Wass niist be remover [rom the original emereing structure.," In order for dispersed field to become compact again, excess mass must be removed from the original emerging structure." + This is [aciitated by couvective dowullows. wl.ich act on horizon.tal field o form U-Ioops anchored below the strlace.," This is facilitated by convective downflows, which act on horizontal field to form U-loops anchored below the surface." + Magnetic recounectiou witliu these |OOps tralsports lass away from risiug field lines., Magnetic reconnection within these loops transports mass away from rising field lines. + This physical meclianisim is tlie same as tle oue suggested Vv lor explaining how the mass Is clischareed [rom the rising magnetic Held i observed ene'?lne UN reglolls., This physical mechanism is the same as the one suggested by \citet{Lites:SpaceScienceReviews} for explaining how the mass is discharged from the rising magnetic field in observed emerging flux regions. + It is [οι idthat the azimut!ally-averaged [lows around the developing uagnetic concenrations (correspoucliig Lo spots) contriblle o the erosion of iaguetic lux., It is found that the azimuthally-averaged flows around the developing magnetic concentrations (corresponding to spots) contribute to the erosion of magnetic flux. + Howeve* correlatious betwee1 the fIuctuatios of velociy aud magnetic fields result ju net luward migratio1 of magnetic flux wih the same sig as that of the spot.," However, correlations between the fluctuations of velocity and magnetic fields result in net inward migration of magnetic flux with the same sign as that of the spot." + We emphasize that tese streaming magnetic polarities are more aki1 {ο the inovii[n]0 dipolar features (MDFs.Bernasconi found in emerginge flux regionse (Strousοἱal.1996:Schlichenmaier2010) thal," We emphasize that these streaming magnetic polarities are more akin to the moving dipolar features \citep[MDFs,][]{Bernasconi:EmergingFlux} found in emerging flux regions \citep{StrousZwaan:HorizontalDynamics,Schlichenmaier:PenumbraFormation} than" +Given that dark matter halos in simulatious (and presumably in nature) are not perlectly spherical. cleanly delineated objects. it is intriguing that the moclel coustructed iu tliis paper works as well as it does at matching the simulation results.,"Given that dark matter halos in simulations (and presumably in nature) are not perfectly spherical, cleanly delineated objects, it is intriguing that the model constructed in this paper works as well as it does at matching the simulation results." + Nevertheless. this analytic mocdel provides a good qualitative αμα quantitative description over the eutire rauge of scales covered by the simulation. and it can be used to make predictious beyond these scales.," Nevertheless, this analytic model provides a good qualitative and quantitative description over the entire range of scales covered by the simulation, and it can be used to make predictions beyond these scales." + This is the first model prescription that successfully reproduces both two- and three-poiut mass correlations., This is the first model prescription that successfully reproduces both two- and three-point mass correlations. + We believe that it will prove to be a generally useful framework., We believe that it will prove to be a generally useful framework. + We have enjoyed stimulating discussions with John Peacock aud David. Weiuberg., We have enjoyed stimulating discussions with John Peacock and David Weinberg. + We thauk Επ. Bertschiuger for valuable comments aud for providing the //=—2 scale-free simulatiou., We thank Edmund Bertschinger for valuable comments and for providing the $n=-2$ scale-free simulation. + Computing time for this work is provided by the National Scalable Cluster Project aud the Intel Eniac2000 Project at the University of Peuusylvania., Computing time for this work is provided by the National Scalable Cluster Project and the Intel Eniac2000 Project at the University of Pennsylvania. + C.-P. M. acknowledges support of an Alfred P. Sloan Foundation Fellowship. a Cottrell Scholars Award from the Research Corporation. a Peuu Research Foundation Award. and NSF grant AST 090723161.," C.-P. M. acknowledges support of an Alfred P. Sloan Foundation Fellowship, a Cottrell Scholars Award from the Research Corporation, a Penn Research Foundation Award, and NSF grant AST 9973461." +that the model could be extended so as to clarify this issue also.,that the model could be extended so as to clarify this issue also. + Work on these extensions is currently in. progress., Work on these extensions is currently in progress. + LJS wishes to. thank Department of Applicc Mathematics anc Vheorctical Physics at the University of Cambridge for the award of a Crighton fellowship. for partial support of this research., LJS wishes to thank the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge for the award of a Crighton fellowship for partial support of this research. + She would. also like to acknowledge the financial assistance she received. via the Chaire dExcellence award to -rofessor Steve Balbus at the Ecole Normale Supérrieure in Paris., She would also like to acknowledge the financial assistance she received via the Chaire d'Excellence award to Professor Steve Balbus at the Ecole Normale Supérrieure in Paris. + We thank Steve Houghton for his earlier contributions to the numerical code. Douglas Cough for his helpful comments in the early stages of this work .and Paul Bushby for many useful discussions.," We thank Steve Houghton for his earlier contributions to the numerical code, Douglas Gough for his helpful comments in the early stages of this work ,and Paul Bushby for many useful discussions." + Finally. we wish to thank the referee for helpful and constructive comments.," Finally, we wish to thank the referee for helpful and constructive comments." +536. the mean residuals show that for each magnitude or color of interest. zero points Lor the project data are coherent [rom cluster to cluster at the FAI level.,"3–6, the mean residuals show that for each magnitude or color of interest, zero points for the project data are coherent from cluster to cluster at the FM level." + Both the SCIDS protocol and the FM standard. have. proved to be controversial., Both the SCIDS protocol and the FM standard have proved to be controversial. + In part. this problem is due to two durable axioms.," In part, this problem is due to two durable axioms." + According to one of them (noted in 87.3 of Tavlor&Joner 2006)). the FM standard is rendered meaningless by a lower limit of about 1020 mmag on the precision and accuracy of photometry.," According to one of them (noted in 7.3 of \citealt{tj06}) ), the FM standard is rendered meaningless by a lower limit of about 10–20 mmag on the precision and accuracy of photometry." + According to the other axiom (noted in 84.4 of TJJ). there is an inescapable danger (hat photometric transformations will compromise data accuracy.," According to the other axiom (noted in 4.4 of TJJ), there is an inescapable danger that photometric transformations will compromise data accuracy." + The second axiom is relevant here because SCIDS can be applied only to input data on a common photometric svstem., The second axiom is relevant here because SCIDS can be applied only to input data on a common photometric system. + For (hat reason. transformations nisl be applied to some of those data before they are analvzed.," For that reason, transformations must be applied to some of those data before they are analyzed." + To put such issues in perspective. we note [ist that the zero point projects are based on a stricilv Baconian outlook (see Bacon1620.. Second Book. aphorism 10).," To put such issues in perspective, we note first that the zero point projects are based on a strictly Baconian outlook (see \citealt{b1620}, Second Book, aphorism 10)." + To paraphrase a relevant aphorism [from thal source: “We must not imagine or invent. but discover the properties of [the data themselves].," To paraphrase a relevant aphorism from that source: “We must not imagine or invent, but discover the properties of [the data themselves].”" + That is done solely by applying statistical analysis to them., That is done solely by applying statistical analysis to them. + Iu contrast. no authority is conceded (o axioms like those cited just above.," In contrast, no authority is conceded to axioms like those cited just above." + To see where the Daconian protocol leads. readers are invited (o consult the first. two paris of 811 of TJJ.," To see where the Baconian protocol leads, readers are invited to consult the first two parts of 11 of TJJ." + That discussion vields some pertinent conclusions., That discussion yields some pertinent conclusions. + For one (hing. no 1020 mmae mit that would rule out the use of the EM standard exists.," For one thing, no 10–20 mmag limit that would rule out the use of the FM standard exists." +" Moreover. transformations need nol compronise data accuracy, even al (he EM level."," Moreover, transformations need not compromise data accuracy, even at the FM level." + In (heir Table 14. TJJ display photometric data whose zero points cohere at that level.," In their Table 14, TJJ display photometric data whose zero points cohere at that level." + Additional examples ol this sort awe cited in 2.3. 3.5. and 3.7. (," Additional examples of this sort are cited in 3.3, 3.5, and 3.7. (" +For further evidence supporting the relevance of the FAL stanclard. readers are invited to consult 87.3 of Tavlor&Joner 2006..),"For further evidence supporting the relevance of the FM standard, readers are invited to consult 7.3 of \citealt{tj06}. .)" + In the papers produced by the projects. offsets derived by applving SCIDS are quoted repeatedly.," In the papers produced by the projects, offsets derived by applying SCIDS are quoted repeatedly." + Quite often. results of tests for scale factor differences are reported as well.," Quite often, results of tests for scale factor differences are reported as well." + With one exception. however (see Table 5 of Tavlor&Joner 2005)). no such differences are detected.," With one exception, however (see Table 5 of \citealt{tj05}) ), no such differences are detected." + In response. only results from zero point tests are summarized here for the sake of brevilv.," In response, only results from zero point tests are summarized here for the sake of brevity." + Let, Let +The formation of binary and multiple systems seems to be à common phenomenon in star formation (e.g..?)..,"The formation of binary and multiple systems seems to be a common phenomenon in star formation \citep[e.g.,][]{Mathieuetal2000}." + Surveys of young star-forming regions with high spatial resolution allow a statistical description of the binary parameters and a comparison between regions of various ages and with different environments (e.g..??)..," Surveys of young star-forming regions with high spatial resolution allow a statistical description of the binary parameters and a comparison between regions of various ages and with different environments \citep[e.g.,][]{Leinertetal1993, Ducheneetal2007}." + Binarity has been studied also in young stellar clusters of various ages to investigate its relation to the evolution of protoplanetary disces (e.g..22).," Binarity has been studied also in young stellar clusters of various ages to investigate its relation to the evolution of protoplanetary discs \citep[e.g.,][]{ClarkePringle1991a, Bouwmanetal2006}." + Different scenarios have been proposed to explain. the formation of binary systems., Different scenarios have been proposed to explain the formation of binary systems. + The standard scenario supports the hypothesis that a binary or multiple system forms when the core of a molecular cloud fragments during its gravitational collapse., The standard scenario supports the hypothesis that a binary or multiple system forms when the core of a molecular cloud fragments during its gravitational collapse. + The fragmentation process can be divided into two main classes: direct (e.g..22) and rotational fragmentation (e.g..222?)..," The fragmentation process can be divided into two main classes: direct \citep[e.g.,][]{BossBodenheimer1979, BateBurkert1997} and rotational fragmentation \citep[e.g.,][]{Bonnell1994, BonnellBate1994a, BonnellBate1994b, Burkertetal1997}." + While the direct fragmentation strongly depends on the initial density distribution in the molecular cloud. this is not the case for rotational fragmentation. which ts caused by asymmetric instabilities 1n a rotating disc or ring.," While the direct fragmentation strongly depends on the initial density distribution in the molecular cloud, this is not the case for rotational fragmentation, which is caused by asymmetric instabilities in a rotating disc or ring." + If the proto-binary accretes (only) gas with low angular momentum. a dise is formed only around the primary star while the secondary may have none.," If the proto-binary accretes (only) gas with low angular momentum, a disc is formed only around the primary star while the secondary may have none." + If instead the secondary developed tts own disc. also the primary will have a disc (?)..," If instead the secondary developed its own disc, also the primary will have a disc \citep{BateBonnell1997}." + According to the two different. scenarios of binary formation. the resulting circumstellar discs may have different inclinations.," According to the two different scenarios of binary formation, the resulting circumstellar discs may have different inclinations." + When the binary ts formed via rotational fragmentation the discs are expected to be preferentially aligned., When the binary is formed via rotational fragmentation the discs are expected to be preferentially aligned. + If. however. the stellar components anc their own disces form directly from a collapsing core (promptinitialfrag-mentation’: 2). this can lead to two misaligned dises (?)..," If, however, the stellar components and their own discs form directly from a collapsing core \citep[`prompt initial fragmentation';][]{Pringle1989}, this can lead to two misaligned discs \citep{Bateetal2000}." + Under more complicated initial conditions even a small cluster can be formed from such a core., Under more complicated initial conditions even a small cluster can be formed from such a core. + Moreover. interactions in these clusters between stars with dises can cause a dissipative encounter (e.g..2)..," Moreover, interactions in these clusters between stars with discs can cause a dissipative encounter \citep[e.g.,][]{ClarkePringle1991a}." + This may lead to the formation of binary or multiple systems via capture and thus to binaries with misaligned dises., This may lead to the formation of binary or multiple systems via capture and thus to binaries with misaligned discs. + In dense star-forming regions. a massive accretion disc may even cause the capture of a passing star (?)..," In dense star-forming regions, a massive accretion disc may even cause the capture of a passing star \citep[][]{ClarkePringle1991b}." + On the other hand. strong tidal interactions can lead to aligned disces.," On the other hand, strong tidal interactions can lead to aligned discs." + Another possibility to have misaligned dises is that the gravitational interaction of a passing object causes the dise’s tilt (and hence also the direction of a possible jet) in a binary system (?).., Another possibility to have misaligned discs is that the gravitational interaction of a passing object causes the disc's tilt (and hence also the direction of a possible jet) in a binary system \citep[][]{Bateetal2000}. + ? estimated that in one million years. in a small cluster. a few percent of the stellar systems can experience a tilt of a few degrees during the star encounters.," \cite{Heller1993} estimated that in one million years, in a small cluster, a few percent of the stellar systems can experience a tilt of a few degrees during the star encounters." + The effect of stellar encounters in different cluster environments has been investigated by ?.., The effect of stellar encounters in different cluster environments has been investigated by \citet[][]{Olczaketal2010}. + They found that the encounter rate remains unaffected by the size of the stellar population. while it strongly depends on the cluster density: in clusters less dense and less massive than the ONC. massive stars dominate the encounter-induced disc-mass loss. whereas in denser and more massive clusters the disc-mass removal is controlled by low-mass stars.," They found that the encounter rate remains unaffected by the size of the stellar population, while it strongly depends on the cluster density: in clusters less dense and less massive than the ONC, massive stars dominate the encounter-induced disc-mass loss, whereas in denser and more massive clusters the disc-mass removal is controlled by low-mass stars." + In systems near the end of their accretion phase. the infall of a small amount of material with à different angular momentum to the orbit can cause a misalignment of dises originally aligned (e.g..?)..," In systems near the end of their accretion phase, the infall of a small amount of material with a different angular momentum to the orbit can cause a misalignment of discs originally aligned \citep[e.g.,][]{Bateetal2000}." + Therefore. from the alignment of circumstellar discs it is possible to understand the dynamics that most likely took place during the star-formation process.," Therefore, from the alignment of circumstellar discs it is possible to understand the dynamics that most likely took place during the star-formation process." + Studying disc alignment requires observations of protoplanetary dises around young binary stars with high spatial resolution., Studying disc alignment requires observations of protoplanetary discs around young binary stars with high spatial resolution. + Previous studies determined the inclination by means of polarimetry (e.g..2?2).. orientation. of the jets (e.g..22).. and direct observations of the dises (e.g..?2)..," Previous studies determined the inclination by means of polarimetry \citep[e.g.,][]{Moninetal1998, Wolfetal2001, Moninetal2006}, orientation of the jets \citep[e.g.,][]{Eisloffeletal1996, Davisetal1997}, and direct observations of the discs \citep[e.g.,][]{Koresko1998, Stapelfeldtetal1998a}." + Another technique. that allows to directly measure size. inclination and orientation of the inner parts of protoplanetary dises is long-baseline interferometry at infrared wavelengths.," Another technique, that allows to directly measure size, inclination and orientation of the inner parts of protoplanetary discs is long-baseline interferometry at infrared wavelengths." + A recent interferometric study of T Tau showed that the three dises in this triple system are misaligned (?).., A recent interferometric study of T Tau showed that the three discs in this triple system are misaligned \citep{Ratzkaetal2009}. + Therefore. the formation process ofT Tau probably has been highly dynamic.," Therefore, the formation process of T Tau probably has been highly dynamic." + We present im this. paper a multi-wavelength. high-resolution observational survey of the young binary system Haro 6-10 (GV Tau. IRAS 0426342426).," We present in this paper a multi-wavelength, high-resolution observational survey of the young binary system Haro 6-10 (GV Tau, IRAS 04263+2426)." + Haro 6-10 is a T Tauri binary system residing within the L-1524 molecular cloud., Haro 6-10 is a T Tauri binary system residing within the L-1524 molecular cloud. + It is composed of an optically visible source. Haro," It is composed of an optically visible source, Haro" +previous studies individual observational samples have been analyzed by different authors who used ciffereut methods of analysis.,previous studies individual observational samples have been analyzed by different authors who used different methods of analysis. + In the current situation where the cluster clustering results from different studies do not agree. it is nuportant to reanalyze and compare all preciouslv studied seuples iu an impartial wav.," In the current situation where the cluster clustering results from different studies do not agree, it is important to reanalyze and compare all preciously studied samples in an impartial way." + Tn this paper we apply methods of calculating aud characterizing the CFs to all cluster samples ii a same way to remove any relative biases., In this paper we apply methods of calculating and characterizing the CFs to all cluster samples in a same way to remove any relative biases. + It is hoped that in this objective aud consistent wav of analysis we could find the common characteristics of. and iutriusic differences iu the spatial distributions of various cluster saluples.," It is hoped that in this objective and consistent way of analysis we could find the common characteristics of, and intrinsic differences in the spatial distributions of various cluster samples." + Ou the other hand. rich clusters of galaxies often have diffuse iutracluster gas trapped in their poteutial wells.," On the other hand, rich clusters of galaxies often have diffuse intracluster gas trapped in their potential wells." + The thermal X-ray flux from the intracluster gas. which is heated to temperature of a few 10*K. is proportional to the square of the ion deusity. and thus is more confined to the ceuter ofthe clusters than the projected galaxy distribution.," The thermal X-ray flux from the intracluster gas, which is heated to temperature of a few $10^7\;{\rm K}$, is proportional to the square of the ion density, and thus is more confined to the center of the clusters than the projected galaxy distribution." + Therefore.the X-rav selected clusters are expected to lave neeligible projection effects (Bricl&Heury1993: Ebelingοἳal. 19061).," Therefore,the X-ray selected clusters are expected to have negligible projection effects \cite{bri93}; \cite{ebe96}) )." + Ebeliug et al. (, Ebeling et al. ( +1996) have cross-correlated the clusters in the ACO catalog CAbelletal. 1989)) with the Νταν sources (Tritmper 1993)) aud created tle N-vay-Brightest Abell-type Clusters of galaxies (XBACS)} catalog.,1996) have cross-correlated the clusters in the ACO catalog \cite{abe89}) ) with the X-ray sources \cite{tru93}) ) and created the X-ray-Brightest Abell-type Clusters of galaxies (XBACs) catalog. + More recently. Ebeling et al. (," More recently, Ebeling et al. (" +1998) have published the Brightest Clusters Sample (BCS) which is a true X-ray selected sample from theROSAT Αγδν Survey.,1998) have published the Brightest Clusters Sample (BCS) which is a true X-ray selected sample from the All-Sky Survey. + It should be interesting to compare the clustering streneths of these X-ray cluster samples with those of optically sclected samples to further extend our knowledge ou the clustering properties of clusters of ealaxies., It should be interesting to compare the clustering strengths of these X-ray cluster samples with those of optically selected samples to further extend our knowledge on the clustering properties of clusters of galaxies. + Postiman et al (, Postman et al. ( +1992) have published a complete redshitt catalog of 351 Abell clusters with richness class RC2 (0. declination 6= 2175. aud tenth-rauked,"1992) have published a complete redshift catalog of 351 Abell clusters with richness class $RC \ge 0$ declination $\delta \ge -27\fdg5$ , and tenth-ranked" +With the availabilitw of more computational resources. numerical models are able to take into account the (hermocdvnamic processes in (he solar interior ancl atmosphere. aud,"With the availability of more computational resources, numerical models are able to take into account the thermodynamic processes in the solar interior and atmosphere, and produce a realistic convection zone overlaid by a self-consistent upper atmosphere \citep[]{vogler2005,stein2006,hansteen2006,abbett2007,gudiksen2011}." + such realistic simulations reveal a wealth of complex clvnamic interactions between the magnetic field and the convective flows., Such realistic simulations reveal a wealth of complex dynamic interactions between the magnetic field and the convective flows. + ?? study the rise of buovant magnetic [hux tubes from the near-surface convection zone into the photosphere and chromosphere aud find the fundamental role of convective flows in the emergence of the magnetic flux. ad the photosphere.," \cite{cheung2007,tortosa2009} study the rise of buoyant magnetic flux tubes from the near-surface convection zone into the photosphere and chromosphere and find the fundamental role of convective flows in the emergence of the magnetic flux at the photosphere." + ??? simulate an emerging [lux (tube. which increases the size of the photospheric granules and alters the chromospheric structure.," \cite{cheung2007,martinez2008,martinez2009} simulate an emerging flux tube, which increases the size of the photospheric granules and alters the chromospheric structure." + More discussion on the interaction between the magnetic field and the convective flows can be found in ??..," More discussion on the interaction between the magnetic field and the convective flows can be found in \cite{fan2004,nordlund2009}." + Raciative MILD simulations on a larger scale (22). report the formation of the sunspots and active regions.," Radiative MHD simulations on a larger scale \citep[]{rempel2009,cheung2010} report the formation of the sunspots and active regions." + ?2?. [ind outflows in the pemuubral structure driven by the Lorentz forces al (he surface and by the convective flows in the deeper lavers.," \cite{rempel2009,rempel2011} find outflows in the penumbral structure driven by the Lorentz forces at the surface and by the convective flows in the deeper layers." + ? simulates the formation of a pair of sunspols in an active region with a magnetic seni-torus advected (through the bottom of the domain and finds the mass removal in the magnetic flux driven bv the reconnection. and the migration of the flux due to horizontal flows.," \cite{cheung2010} simulates the formation of a pair of sunspots in an active region with a magnetic semi-torus advected through the bottom of the domain and finds the mass removal in the magnetic flux driven by the reconnection, and the migration of the flux due to horizontal flows." + With the inclusion of turbulent convection (?).. it is shown that the transport of energy. into the corona becomes even more critical as downdralts return much of the magnetic energy back below the photosphere.," With the inclusion of turbulent convection \citep[]{fang2010}, it is shown that the transport of energy into the corona becomes even more critical as downdrafts return much of the magnetic energy back below the photosphere." + This sinmlation treats the emergence of a weak axial [lux of 3.3x1015 Mx. which is quickly shredded and dispersed (o the intereranular lanes by the convection motions.," This simulation treats the emergence of a weak axial flux of $3.3\times10^{19}$ Mx, which is quickly shredded and dispersed to the intergranular lanes by the convection motions." + These radiative MIID simulations illustrate the importance of turbulent convective flows in (he emergence of the magnetic structures., These radiative MHD simulations illustrate the importance of turbulent convective flows in the emergence of the magnetic structures. + In light of (hese previous resul(s. we expand upon the work of ? bv simulating the emergence of a larger twisted magnetic flux rope emerging Iron deeper in the convection zone. and study the energetics during its rise," In light of these previous results, we expand upon the work of \cite{fang2010} by simulating the emergence of a larger twisted magnetic flux rope emerging from deeper in the convection zone, and study the energetics during its rise" +Several very cool white dwarfs with suspected Tagmo015001 have been discovered receutly (Faribi2005:INilicetal.Cratesοἳ2001:visctal. 1999).,"Several very cool white dwarfs with suspected $T_{\rm eff}\rm \wig< 4500 \, K$ have been discovered recently \citep{FAR,KM,G,OPP,Harris01,HOD,Ibata00,HR2}." +. Most of them are thought to posses helimu-rich atmosphneres with au very hieh ΠοΠz10? ratio (Bergeronetal.2005:etal2001:Ποάσαιal. 2000).," Most of them are thought to posses helium-rich atmospheres with an very high $\rm He/ H \wig> 10^{3}$ ratio \citep{BAL,KM,G,BL,Bergeron01,OPP,HOD}." + Iu most cases. however. current atimosphere models fail to reproduce the observed. spectra and photometry of these peculiar stars.," In most cases, however, current atmosphere models fail to reproduce the observed spectra and photometry of these peculiar stars." + The reason. aud there may be more than one. for this shortcoming of the models is ΠΙΟ.," The reason, and there may be more than one, for this shortcoming of the models is presently unknown." +" eurmeut models meseutlyextreme physical However,atmospheric conditions for predictsuch stars. reaching deusities of up to23ooan?cu’."," However, current models predict extreme physical atmospheric conditions for such stars, reaching densities of up to $\rm 2-3 \ g/cm^{3}$." +" UnderDEY theseuuo conditions.(cT; then niosthd] ideal eas constitutive plivsies used in published atmosphere models is demonstrably inadequate,"," Under these conditions, the mostly ideal gas constitutive physics used in published atmosphere models is demonstrably inadequate." +" A carefil look at the dense matter effects on d1ο equation|ti of statstate;Y cliemistry.heist opacities.‘"" modificationai radiativeUU transfer| is Ut to necessary]compute pastesplivsicallv realistic models of these stars."," A careful look at the dense matter effects on the equation of state, chemistry, opacities, and radiative transfer is necessary to compute physically realistic models of these stars." + Several of these effects lave been studied. previously such as refractive radiative transfer (I&owalslà&Samuou 2001)... the effects of Suid correlations on Πο roe-free and He Rayleigh scattering (IKowalskietal.2005:Telesiaset2002). . and the ionization of warm. dense helinm (I&owalskietal.2005:Berecronetal.," Several of these effects have been studied previously, such as refractive radiative transfer \citep{KS04}, the effects of fluid correlations on $\rm He^-$ free-free and He Rayleigh scattering \citep{KSM05,IRS}, and the ionization of warm, dense helium \citep{KSM05,BSW}." + 1995).. In this contribution we resent an additional correction that arises in the dense fluid: The solution for the dissociation of nolecular lvdrogen in dense fluid helium. in the iui Πω=~1.," In this contribution we present an additional correction that arises in the dense fluid: The solution for the dissociation of molecular hydrogen in dense fluid helium, in the limit $\rm He/H>>1$." + The relative duportance of hese corrections varies cousiderablv. even more so when they are combined.," The relative importance of these corrections varies considerably, even more so when they are combined." + As several mere cease natter effects remain unexplored. it is premature o ponder their implications for the analysis of he coolest white dwarfs known aud whether they will result iu qodels that reproduce the data.," As several more dense matter effects remain unexplored, it is premature to ponder their implications for the analysis of the coolest white dwarfs known and whether they will result in models that reproduce the data." + Nouctheless. incorporating adequate coustitutive ovsies iu atmosphere models is a necessary step o reach a proper understauding. of. these peculiar. tars," Nonetheless, incorporating adequate constitutive physics in atmosphere models is a necessary step to reach a proper understanding of these peculiar stars." + We introducenou-ideal-ide: effects: iuto the equilixiua dissociation.⋅⋅ of. inoleculuw hydrogen through a of⋅⋅⋅ the⋅ chemical poteutials⋅ of. IT1us aud IL (section ⋅⊀2).," We introduce non-ideal effects into the equilibrium dissociation of molecular hydrogen through a modification of the chemical potentials of $\rm H \, \textrm{\scriptsize{I}}$ and $\rm H_2$ (section 2)." + We ⇁⋅find that the strong interactions, We find that the strong interactions + We ⇁⋅find that the strong interactions⋅, We find that the strong interactions +variability is understood.,variability is understood. +" Indeed, while it is tempting to conflate the process of discovery with classification, by making sequential the two decisions, different machineries can be brought to bear on each."," Indeed, while it is tempting to conflate the process of discovery with classification, by making sequential the two decisions, different machineries can be brought to bear on each." +" The literature on autonomous classification, by various computational techniques, has been growing rapidly; indeed a wide range of machine-learning techniques have been applied to classification of large astronomical datasets (see Mahabaletal.2008 and Bloom&Richards2011 for review)."," The literature on autonomous classification, by various computational techniques, has been growing rapidly; indeed a wide range of machine-learning techniques have been applied to classification of large astronomical datasets (see \citealt{2008AIPC.1082..287M} and \citealt{2011arXiv1104.3142B} for review)." +" Aside from domain-specific classification (microlensing and supernovae), most work concerns classification of variables stars on historical datasetsretrospect, where analysis is performed after most of the data have been collected and cleaned (e.g., 2010))."," Aside from domain-specific classification (microlensing and supernovae), most work concerns classification of variables stars on historical datasets, where analysis is performed after most of the data have been collected and cleaned (e.g., \citealt{2006A&A...446..395S,2007A&A...475.1159D,2011rich,2007arXiv0712.2898W,2009A&A...494..739S,2010arXiv1008.3143B}) )." +" We are interested in a related, but more urgent challenge: classification on streaming data, where analysis is performed while the data are still being accumulated."," We are interested in a related, but more urgent challenge: classification on streaming data, where analysis is performed while the data are still being accumulated." +" At a logistical level, keeping up with classification (and discovery) assures that the survey producing the data can be continually informed of the progress, allowing the survey to change course midstream if scientifically warranted."," At a logistical level, keeping up with classification (and discovery) assures that the survey producing the data can be continually informed of the progress, allowing the survey to change course midstream if scientifically warranted." +" But at a more fundamental level, the reason for real-time classification is that the vast majority of science conducted with time-variable objects, especially one-off transients, comes when more data are accumulated about the objects of interest."," But at a more fundamental level, the reason for real-time classification is that the vast majority of science conducted with time-variable objects, especially one-off transients, comes when more data are accumulated about the objects of interest." +" Enabling intelligent follow-up, then, becomes a main driver for rapid classification."," Enabling intelligent follow-up, then, becomes a main driver for rapid classification." +" Ultimately, one can view Given this view of real-time classification, the advantages of a computational (rather than human-centric) approach become clear:"," Ultimately, one can view Given this view of real-time classification, the advantages of a computational (rather than human-centric) approach become clear:" +maegnetosphere.,magnetosphere. + We beein (to address (his question in the following section., We begin to address this question in the following section. + In order to (rack the magnetic flux in time and determine how the changes in connectivity occur we examine some parücular ancl so begin by briefly discussing their motivation., In order to track the magnetic flux in time and determine how the changes in connectivity occur we examine some particular and so begin by briefly discussing their motivation. +" Recall that an ideal evolution of the magnetic field is one salislvine the curl of which gives In such a situation the magnetic field and a line element have same evolution equation and so flux is ""Irozen-in. to the plasma and (he magnetic topology is conserved.", Recall that an ideal evolution of the magnetic field is one satisfying the curl of which gives In such a situation the magnetic field and a line element have same evolution equation and so flux is `frozen-in' to the plasma and the magnetic topology is conserved. + A real plasma evolution has where IN. represents some non-ideal term (such as J in a resistive MIID evolution ) which is typically localised to some region of space., A real plasma evolution has where $\mathbf{N}$ represents some non-ideal term (such as $\eta \mathbf{J}$ in a resistive MHD evolution ) which is typically localised to some region of space. + I this paper the effect of the non-ideal term is modelled by the addition of a magnetic [lux ring., In this paper the effect of the non-ideal term is modelled by the addition of a magnetic flux ring. + Even with the inclusion of the non-ideal term we may sometimes still lind a velocity w with respect to which the magnetic flux is frozen-in if can bewritten as where ® is an arbitrary. function. since taking the curl again and using Faradays law eives an equation of the form (6)..," Even with the inclusion of the non-ideal term we may sometimes still find a velocity $\mathbf{w}$ with respect to which the magnetic flux is frozen-in if can bewritten as where $\Phi$ is an arbitrary function, since taking the curl again and using Faraday's law gives an equation of the form ." +The collision of the supersonic solar wind with the interstellar plasma [low results in,The collision of the supersonic solar wind with the interstellar plasma flow results in +contemporaneous SCIDAR measurement in order to ensure the aperture is at the correct. plane.,contemporaneous SCIDAR measurement in order to ensure the aperture is at the correct plane. + We are grateful to the Science and Technology. Facilities Committee (SPEC) for. financial support (JO)., We are grateful to the Science and Technology Facilities Committee (STFC) for financial support (JO). + RA acknowledecs financial. support from CONACPE and PAPIIT through erants number 58291 and IN107109-2., RA acknowledges financial support from CONACyT and PAPIIT through grants number 58291 and IN107109-2. +cllusters.,lusters. +balanced by radiative losses. i.e. the radiation reaction limit.,"balanced by radiative losses, i.e. the radiation reaction limit." + Under (he assumption that the accelerating electric fieldE is a fraction 7)<1 of themagnetic field 5. the acceleration gain is ecD. with e is the electron charge.," Under the assumption that the accelerating electric field$E$ is a fraction $\eta \leq 1$ of themagnetic field $B$, the acceleration gain is $ec\eta B$, with $e$ is the electron charge." +" The radiation reaction limit is then reached if: ec. NB 2.=230, gua where the losses due to curvature radiation are given on (he right side."," The radiation reaction limit is then reached if: e c B = _b^4 ( )^2, where the losses due to curvature radiation are given on the right side." +" Using ((2.1)) it follows from ((2.1)) that ((3)* e (08)?1(3) The radius of curvature. A, canbeexpressed inunits of the light evlinder Hj. &cDP/(2x). where P is the period of the pulsar ancl £ is a dimensionless scaling parameter."," Using \ref{01}) ) it follows from \ref{00}) ) that = ( c ( The radius of curvature $R_c$ canbeexpressed inunits of the light cylinder $R_L$,$R_c = \xi R_L = \xi c P/ ( 2 \pi)$ , where $P$ is the period of the pulsar and $\xi$ is a dimensionless scaling parameter." + I. furthermore. D isreplaced by the radial distribution of the magnetic field of a dipole B=Bxs(Rxs/R)!. where Bus is the magnetic field on the surface of the neutrons star and Ryy the starOs surface. then it follows that: (an). EMUp2/4 150 — 5 UL (BT) -," If, furthermore, $B$ isreplaced by the radial distribution of the magnetic field of a dipole $B = B_{NS} (R_{NS}/R)^3$, where $B_{NS}$ is the magnetic field on the surface of the neutrons star and $R_{NS}$ the starÕs surface, then it follows that: = (3 = = = (3 =9 10^7 = 3 10^7 ." + I. furthermore. D isreplaced by the radial distribution of the magnetic field of a dipole B=Bxs(Rxs/R)!. where Bus is the magnetic field on the surface of the neutrons star and Ryy the starOs surface. then it follows that: (an). EMUp2/4 150 — 5 UL (BT) --," If, furthermore, $B$ isreplaced by the radial distribution of the magnetic field of a dipole $B = B_{NS} (R_{NS}/R)^3$, where $B_{NS}$ is the magnetic field on the surface of the neutrons star and $R_{NS}$ the starÕs surface, then it follows that: = (3 = = = (3 =9 10^7 = 3 10^7 ." + I. furthermore. D isreplaced by the radial distribution of the magnetic field of a dipole B=Bxs(Rxs/R)!. where Bus is the magnetic field on the surface of the neutrons star and Ryy the starOs surface. then it follows that: (an). EMUp2/4 150 — 5 UL (BT) --υ," If, furthermore, $B$ isreplaced by the radial distribution of the magnetic field of a dipole $B = B_{NS} (R_{NS}/R)^3$, where $B_{NS}$ is the magnetic field on the surface of the neutrons star and $R_{NS}$ the starÕs surface, then it follows that: = (3 = = = (3 =9 10^7 = 3 10^7 ." + I. furthermore. D isreplaced by the radial distribution of the magnetic field of a dipole B=Bxs(Rxs/R)!. where Bus is the magnetic field on the surface of the neutrons star and Ryy the starOs surface. then it follows that: (an). EMUp2/4 150 — 5 UL (BT) --υα," If, furthermore, $B$ isreplaced by the radial distribution of the magnetic field of a dipole $B = B_{NS} (R_{NS}/R)^3$, where $B_{NS}$ is the magnetic field on the surface of the neutrons star and $R_{NS}$ the starÕs surface, then it follows that: = (3 = = = (3 =9 10^7 = 3 10^7 ." + I. furthermore. D isreplaced by the radial distribution of the magnetic field of a dipole B=Bxs(Rxs/R)!. where Bus is the magnetic field on the surface of the neutrons star and Ryy the starOs surface. then it follows that: (an). EMUp2/4 150 — 5 UL (BT) --υαῃ," If, furthermore, $B$ isreplaced by the radial distribution of the magnetic field of a dipole $B = B_{NS} (R_{NS}/R)^3$, where $B_{NS}$ is the magnetic field on the surface of the neutrons star and $R_{NS}$ the starÕs surface, then it follows that: = (3 = = = (3 =9 10^7 = 3 10^7 ." +proceediues) aud redshift space distortions will provide further counstraiuts on the density parameter Oy aud b.,proceedings) and redshift space distortions will provide further constraints on the density parameter $\Omega_0$ and $b$. + Clues to the plivsies of galaxy formation will be provided by studving the huninosity fiction aud clustering of galaxies separated by colour. morphology and other intrinsic galaxy properties.," Clues to the physics of galaxy formation will be provided by studying the luminosity function and clustering of galaxies separated by colour, morphology and other intrinsic galaxy properties." + Photometric redshifts [3] will make the Sloan dataset au extremely powerful oue for studving ealaxy evolution over a range of redshifts bevoud that reached by the spectroscopic survey., Photometric redshifts \cite{c95} will make the Sloan dataset an extremely powerful one for studying galaxy evolution over a range of redshifts beyond that reached by the spectroscopic survey. + We also plan to search for low surface brightuess (LSB) ealaxics in the Sloan imaging data., We also plan to search for low surface brightness (LSB) galaxies in the Sloan imaging data. + The diift-scan observing mode means that detection of LSB objects is limited bv photon statistics rather than flat-ficldine errors. and we expect to detect ealaxics with a ceutral surface brehtuess as low as jug0yo27.5 mag aresec.7 2in the +? baud.," The drift-scan observing mode means that detection of LSB objects is limited by photon statistics rather than flat-fielding errors, and we expect to detect galaxies with a central surface brightness as low as $\mu_0 \approx 27.5$ mag $^{-2}$ in the $r'$ band." + One- of: the survey products will. be a lsE binned sky map. from which we will be able to find galaxies to a surface brightuess of vet four times less.," One of the survey products will be a $4 \times 4$ binned sky map, from which we will be able to find galaxies to a surface brightness of yet four times less." + ca . ol. NH . MM∙∙ MED ‘ MLLOW TONCL of TALS. MAL(~20 inCrab dn. the ADVONαιαοσν rauge) have been detected with a relatively eood accuracy ou the estimated position (1.5 / offset for 519 Table 23).,"From the analysis of each individual pointing, sources with a relatively low level of flux $\sim 20$ mCrab in the $-$ energy range) have been detected with a relatively good accuracy on the estimated position (1.8 $^{\prime}$ offset for $-$ 549 Table \ref{tab:offset}) )." + This level of flux seenis to be the sensitivity lint of ISGRI at the cureut stage of (see also pa 1)., This level of flux seems to be the sensitivity limit of ISGRI at the current stage of (see also paper 1). + Note that for large augles frou the center of the FOV.XT the flux of a source is still rather uncertain at this carly stage of the mission.," Note that for large angles from the center of the FOV, the flux of a source is still rather uncertain at this early stage of the mission." + Fainter sources can be detected with longer exposure ↑↕⋯↸∖↴∖↴∙⋜↧↴∖↴↸∖∙∶↴⋁∙∐⋮↽⊔⋅↱⊐∙↕∢∔⊔↕∙↖↖⇁↕∐↸⊳∐∙∐⋜↕↴∖↴⋜↧∐⋜↧↖⇁↸∖↥⋅⋜↧∶↴⋁↸∖≼↧ flux of about 30 uCrab. over the four poiutiugs where it is in the FOV.," Fainter sources can be detected with longer exposure times, as e.g. $-$ 6141, which, has an averaged flux of about 20 mCrab, over the four pointings where it is in the FOV." + Some slight offset (up to 3.5 7) is still forud between the estimated positions aud the catalogue ones., Some slight offset (up to 3.5 $^{\prime}$ ) is still found between the estimated positions and the catalogue ones. + It is worth noting that the offset depeuds on two factors: the distance from the center of the FOV. and the source flux (thus the significance ofits detection).," It is worth noting that the offset depends on two factors: the distance from the center of the FOV, and the source flux (thus the significance of its detection)." + As the source is far from the centre. the offset increases (Table 2j. while for bright sources (sources detected with ligher significance) the location accuracy usually increases (see Cros et al.," As the source is far from the centre, the offset increases (Table \ref{tab:offset}) ), while for bright sources (sources detected with higher significance) the location accuracy usually increases (see Gros et al." + 2003. Walter ct al.," 2003, Walter et al." + 20031 and paper 1)., 2003b and paper 1). + In the, In the +What can be learned about the +—2 radio galaxies and sub-millimetre galaxies from their inferred location on this diagram?,What can be learned about the $z \simeq 2$ radio galaxies and sub-millimetre galaxies from their inferred location on this diagram? +" First. we note that most (but not all) of the +~2 radio galaxies already lie on the local galaxy locus. with project stellar mass densities of στο210""M.kpe7."," First, we note that most (but not all) of the $z \simeq 2$ radio galaxies already lie on the local galaxy locus, with project stellar mass densities of $\sigma_{50} \simeq 10^9\,{\rm M_{\odot} kpc^{-2}}$." + This is interesting. but perhaps not unexpected given their moderately large sizes and apparently dynamically relaxed stellar populations.," This is interesting, but perhaps not unexpected given their moderately large sizes and apparently dynamically relaxed stellar populations." + Four of the radio galaxies have higher surface mass densities., Four of the radio galaxies have higher surface mass densities. + This might be telling us that their stellar masses have been over-estimated. or their half-light radii under-estimated. but the two obvious cases of an AGN contribution have already been removed and are not plotted in Fig. 9..," This might be telling us that their stellar masses have been over-estimated, or their half-light radii under-estimated, but the two obvious cases of an AGN contribution have already been removed and are not plotted in Fig. \ref{surface1}." + Alternatively these objects could really be destined to evolve further. in which case the dry-merging tracks shown in Fig.," Alternatively these objects could really be destined to evolve further, in which case the dry-merging tracks shown in Fig." + 9 would imply that they will land onthe present day locus with stellar masses =2.3.1077AL..," \ref{surface1} would imply that they will land onthe present day locus with stellar masses $\simeq 2-3 \times 10^{12} \,{\rm M_{\odot}}$." + This is in fact not unreasonable. given that they are already among the most massive galaxies known at 2&2. und vet still appear somewhat more compact than the most massive elliptical galaxies in the present-day universe.," This is in fact not unreasonable, given that they are already among the most massive galaxies known at $z \simeq 2$, and yet still appear somewhat more compact than the most massive elliptical galaxies in the present-day universe." + Interestingly. and unlike the lower-luminosity star-forming Lyman-break ealaxies. most of the sub-millimetre galaxies also appear to lie 207above the local galaxy locus. .in the same general regime as the moderately compact quiescent galaxies.," Interestingly, and unlike the lower-luminosity star-forming Lyman-break galaxies, most of the sub-millimetre galaxies also appear to lie above the local galaxy locus, in the same general regime as the moderately compact quiescent galaxies." + Thus. while the morphological evidence suggests the sub-millimetre galaxies are star-forming discs. in terms of surface muss density they can clearly evolve into high-redshift quiescent galaxies without significant size evolution.," Thus, while the morphological evidence suggests the sub-millimetre galaxies are star-forming discs, in terms of surface mass density they can clearly evolve into high-redshift quiescent galaxies without significant size evolution." + Also. if they subsequently follow the dry-merger evolutionary tracks indicated in Fig. 9..," Also, if they subsequently follow the dry-merger evolutionary tracks indicated in Fig. \ref{surface1}," + they are ultimately destined to evolve into present-day massive elliptical galaxies with Alay25»107ML.," they are ultimately destined to evolve into present-day massive elliptical galaxies with $M_{star} > 5 \times 10^{11}\,{\rm M_{\odot}}$." + There are 5 sub-millimetre galaxies which appear to have lower surface mass densities. and thus lie within the locus defined by present-day galaxies and high-redshift DRGs and Lyman-break galaxies.," There are 5 sub-millimetre galaxies which appear to have lower surface mass densities, and thus lie within the locus defined by present-day galaxies and high-redshift DRGs and Lyman-break galaxies." + Both of the radio unidentitied sub-millimetre galaxies lie within this subsample. suggesting either that they have been mis-identified. or (not unreasonably) that strong radio emission is an indicator for the densest starbursts.," Both of the radio unidentified sub-millimetre galaxies lie within this subsample, suggesting either that they have been mis-identified, or (not unreasonably) that strong radio emission is an indicator for the densest starbursts." + In summary. Fig.," In summary, Fig." + 9. supports the conclusion that. while the sub-millimetre galaxies appear Cat the epoch of observation) to be best described as star-forming discs. their stellar masses and stellar mass surface densities indicate that they are capable of evolving rapidly into dense. quiescent galaxies at 21.5. and ultimately into present-day massive ellipticals.," \ref{surface1} supports the conclusion that, while the sub-millimetre galaxies appear (at the epoch of observation) to be best described as star-forming discs, their stellar masses and stellar mass surface densities indicate that they are capable of evolving rapidly into dense, quiescent galaxies at $z > 1.5$, and ultimately into present-day massive ellipticals." + We have obtained deep. high-quality A -band images of complete subsamples of powerful radio and sub-millimetre galaxies at redshifts 2 2.," We have obtained deep, high-quality $K$ -band images of complete subsamples of powerful radio and sub-millimetre galaxies at redshifts $z \simeq 2$ ." + The data were obtained in the very best available seeing (FWHM ~ aaresee) through the queue-based, The data were obtained in the very best available seeing (FWHM $\simeq$ arcsec) through the queue-based +We have identified 269 old stellar clusters in the FSR catalogue of possible cluster candidates.,We have identified 269 old stellar clusters in the FSR catalogue of possible cluster candidates. +" For the 63 known globular clusters and 147 known open clusters we extracted parameters (distance, reddening, age) from the literature."," For the 63 known globular clusters and 147 known open clusters we extracted parameters (distance, reddening, age) from the literature." + For the remaining 27 known open clusters and 32 so far unclassified FSR cluster candidates we determine parameters here using isochrone fitting., For the remaining 27 known open clusters and 32 so far unclassified FSR cluster candidates we determine parameters here using isochrone fitting. +" Additionally, we determine the parameters of all clusters homogeneously by the same set of data (2MASS JHK photometry), the same data analysis method and the same set of isochrones (Girardi et al. (2002)))."," Additionally, we determine the parameters of all clusters homogeneously by the same set of data (2MASS JHK photometry), the same data analysis method and the same set of isochrones (Girardi et al. \cite{2002A&A...391..195G}) )." +" This will allow us, in particular for the open clusters, to analyse and compare the distribution of the parameters of our sample of old stellar clusters along the entire Galactic Plane."," This will allow us, in particular for the open clusters, to analyse and compare the distribution of the parameters of our sample of old stellar clusters along the entire Galactic Plane." +" We will in the following only discuss the open cluster parameters, if not stated otherwise."," We will in the following only discuss the open cluster parameters, if not stated otherwise." + In refnotes we provide some notes for all newly identified old open clusters and for the known ones when their parameters differ significantly from the literature values., In \\ref{notes} we provide some notes for all newly identified old open clusters and for the known ones when their parameters differ significantly from the literature values. + Here we will briefly mention some of the notable discoveries and their properties., Here we will briefly mention some of the notable discoveries and their properties. +" 00039 is a GGyr old, highly reddened cluster."," 0039 is a Gyr old, highly reddened cluster." + With just 4.6kkpc from the Galactic Centre it is one of the rare old inner Galaxy clusters., With just kpc from the Galactic Centre it is one of the rare old inner Galaxy clusters. + 00313 881) shows a large number of giants but no main sequence., 0313 81) shows a large number of giants but no main sequence. +" This indicates that it might be an old, massive cluster about 10kpc from the Galactic Centre."," This indicates that it might be an old, massive cluster about 10kpc from the Galactic Centre." +" Both, 00412 33) and 00460 are very distant kkpc) and old (1.2GGyr) clusters."," Both, 0412 3) and 0460 are very distant kpc) and old Gyr) clusters." +" Very nice examples of newly discovered clusters (or objects with parameters determined for the first time) are 00134, 0177 552), 0275, 0342, 0972 (NGC22429), 1404 555), 1463, 1565 119), 1670 11101) which show a number of red giants and main sequence stars, while for 00170, 0329 992), 1521, 1559 1106) only red giants are detected."," Very nice examples of newly discovered clusters (or objects with parameters determined for the first time) are 0134, 0177 52), 0275, 0342, 0972 2429), 1404 55), 1463, 1565 19), 1670 1101) which show a number of red giants and main sequence stars, while for 0170, 0329 92), 1521, 1559 106) only red giants are detected." +" Since we aim to investigate the old clusters in the FSR catalogue, we have to analyse the age distribution of our sample."," Since we aim to investigate the old clusters in the FSR catalogue, we have to analyse the age distribution of our sample." + This is shown in refdistrage.., This is shown in \\ref{distrage}. + There the red dotted histogram shows the age distribution as obtained for the known open clusters using the literature values., There the red dotted histogram shows the age distribution as obtained for the known open clusters using the literature values. + The black solid histogram shows the distribution of the ages determined in the paper for all open clusters., The black solid histogram shows the distribution of the ages determined in the paper for all open clusters. +" In both cases there is a clear peak at about GGyr (which is also the average of the distribution), and more than older than MMyrs."," In both cases there is a clear peak at about Gyr (which is also the average of the distribution), and more than older than Myrs." +" This shows that our selection of clusters with a clear RGB or a main sequence and red giants, was successful in picking out old stellar systems."," This shows that our selection of clusters with a clear RGB or a main sequence and red giants, was successful in picking out old stellar systems." +" However, it still selects a few younger clusters."," However, it still selects a few younger clusters." +" Most likely these are more massive, hence showing a larger, and thus observable number of red (super) giants earlier in their evolution."," Most likely these are more massive, hence showing a larger, and thus observable number of red (super) giants earlier in their evolution." +" Some of the clusters with lower ages (based on the literature) have, according to our isochrone fits, an older age."," Some of the clusters with lower ages (based on the literature) have, according to our isochrone fits, an older age." +" This is caused by the fact that we try to include potential giant stars in the fit of the cluster isochrone, generally leading to a slightly larger age."," This is caused by the fact that we try to include potential giant stars in the fit of the cluster isochrone, generally leading to a slightly larger age." + For a large fraction of clusters we can compare our determined parameters with the values obtained from the literature., For a large fraction of clusters we can compare our determined parameters with the values obtained from the literature. + This will allow us to estimate the uncertainties of the isochrone fitting for the clusters without known parameters., This will allow us to estimate the uncertainties of the isochrone fitting for the clusters without known parameters. + At first we check the position accuracy of the cluster candidates., At first we check the position accuracy of the cluster candidates. + We determine the difference of our coordinates and the literature coordinates for the known clusters., We determine the difference of our coordinates and the literature coordinates for the known clusters. +" For the generally highly concentrated globular clusters the average difference is 0.5’, while for the open clusters we find an average positional difference of 2’."," For the generally highly concentrated globular clusters the average difference is 0.5', while for the open clusters we find an average positional difference of 2'." + This rather large value seems to be caused by erroneous coordinates of some not well investigated clusters in SIMBAD., This rather large value seems to be caused by erroneous coordinates of some not well investigated clusters in SIMBAD. + See refproperties to check the differences for each individual cluster., See \\ref{properties} to check the differences for each individual cluster. +" Except in some cases the distance, age and reddening estimates from the literature and our isochrone fitting are in agreement."," Except in some cases the distance, age and reddening estimates from the literature and our isochrone fitting are in agreement." + In the refnotes we will discuss in detail the clusters with large differences in the parameters., In the \\ref{notes} we will discuss in detail the clusters with large differences in the parameters. + On average the cluster distances show a scatter of about log(age) values an agreement of about agree to within the metallicity., On average the cluster distances show a scatter of about log(age) values an agreement of about agree to within the metallicity. +" Hence, we generally used solar values, except if a different value was available from the literature."," Hence, we generally used solar values, except if a different value was available from the literature." +" In some cases it was, however, only possible to obtain a fit to the CMDs and CCDs with non-solar values."," In some cases it was, however, only possible to obtain a fit to the CMDs and CCDs with non-solar values." + See refproperties for the metallicities used for our best fitting isochrone., See \\ref{properties} for the metallicities used for our best fitting isochrone. +" Please note that if the cluster has a lower metallicity than used here, the estimated reddening would be higher and the distances lower."," Please note that if the cluster has a lower metallicity than used here, the estimated reddening would be higher and the distances lower." + Similarly the cluster age would be influenced systematically., Similarly the cluster age would be influenced systematically. +" However, if the metallicity is changed by less than a few tenth of a dex, then the parameters will stay within the above mentioned uncertainties."," However, if the metallicity is changed by less than a few tenth of a dex, then the parameters will stay within the above mentioned uncertainties." + It is much more important to identify the cluster red giants and main sequence turn off with high accuracy., It is much more important to identify the cluster red giants and main sequence turn off with high accuracy. +in the envelope.,in the envelope. + Therefore. a large value of this parameter. i.e... Q20.1. can be related to a hiehlv inhomogeneous mass loss process. as well as to a high mass loss rate.," Therefore, a large value of this parameter, i.e., $Q \ga 0.1$, can be related to a highly inhomogeneous mass loss process, as well as to a high mass loss rate." + Soker Iarpaz (1992) argued that the characteristics of AGB stellar pulsations depend on the thermal and dynamical time scales., Soker Harpaz (1992) argued that the characteristics of AGB stellar pulsations depend on the thermal and dynamical time scales. + They used the thermal time scale of only the upper envelope. and for the dvnamical (me scale thev took the pulsation period.," They used the thermal time scale of only the upper envelope, and for the dynamical time scale they took the pulsation period." + The star starts to contract before it leaves the AGB., The star starts to contract before it leaves the AGB. +" The initial contraction is slow. and the stellar racdius during the early contraction phase can be approximated by where τα A,4, are (he stellar radius and envelope mass when the contraction starts."," The initial contraction is slow, and the stellar radius during the early contraction phase can be approximated by where $R_m$ and $M_{\rm env-m}$ are the stellar radius and envelope mass when the contraction starts." + For the model used by Soker (1992) relation (7)) holds for an envelope mass of 0.001.3MaSsOAL. with 920.2 for most of the time., For the model used by Soker (1992) relation \ref{rad1}) ) holds for an envelope mass of $0.001 \la M_{\rm env} \la 0.1 M_\odot$ with $\delta \simeq 0.2$ for most of the time. + Then 6 increases more and more rapidly until it reaches a verv huge value when the star contracts by (wo order of magnitude for a tiny change in the envelope mass (Schónnberner 1983)., Then $\delta$ increases more and more rapidly until it reaches a very large value when the star contracts by two order of magnitude for a tiny change in the envelope mass (Schönnberner 1983). + Qualitativelv similar behavior is found for other core masses. but at different envelope masses (Schonnberner 1983: Frankowski 2003).," Qualitatively similar behavior is found for other core masses, but at different envelope masses (Schönnberner 1983; Frankowski 2003)." + Using equation (7)) to express the stellar radius in equation (6)) gives for the contracting-AGB phase Duringe the contracting-AGDe phase the luminosity and mass do not changee much. and the derivative of equation (8)}) can be written as Alonge the entire AGB AQI is negativee (beside temporal variations. e.g..e after therma pulses).," Using equation \ref{rad1}) ) to express the stellar radius in equation \ref{chi1}) ) gives for the contracting-AGB phase During the contracting-AGB phase the luminosity and mass do not change much, and the derivative of equation \ref{chi2}) ) can be written as Along the entire AGB $\Delta Q$ is negative (beside temporal variations, e.g., after thermal pulses)." + It is very positive during the fast contraction along the post-AGD track (again. beside temporal variations).," It is very positive during the fast contraction along the post-AGB track (again, beside temporal variations)." + The transition from AQ<0 to AQ>0 can mark the beginning of the post-AGD phase. (, The transition from $\Delta Q <0$ to $\Delta Q>0$ can mark the beginning of the post-AGB phase. ( +Note that the envelope mass decreases with time. and therefore when AQ«0 then Q increases with time.),"Note that the envelope mass decreases with time, and therefore when $\Delta Q <0$ then $Q$ increases with time.)" + Namely. the star is said to terminate the AGB when CQ is at ils maximunr value: (his occurs after the contraction started and (Q=Qe.," Namely, the star is said to terminate the AGB when $Q$ is at its maximum value; this occurs after the contraction started and $Q=Q_C$." +" If there is no change in (he density profile then d1n2./dInM,=0 and AQe changes sien when 9=0.4.", If there is no change in the density profile then $d \ln \beta_s/d \ln M_{\rm env} = 0$ and $\Delta Q_C$ changes sign when $\delta = 0.4$. + This is when more or less the rapid contraction starts., This is when more or less the rapid contraction starts. +" However. during the contracting-AGD phase the clensity profile becomes steeper (e.g.. Soker 1992). and >, "," However, during the contracting-AGB phase the density profile becomes steeper (e.g., Soker 1992), and $\beta_s$ " +"statistics,",statistics. + We therefore leave the question. without au answer but add two relevaut remarks without further conumuient: sone very τος stars have uo detectable disk. for exauple TD 116512 (ASV. 320 My). HD 20630 (65V. 300 Ny). ΠΟ 3739E (STV. 320 Myr) and soie old stars have retained their disk: examples: ITD 10700. (GS. 7.2 Car). HD 75732 (65V. 5.0 Car) and WD 207129 (GOV. LL Cyr the last case has heen studied im detail (JourdainAbuizonetal. 1999).," We therefore leave the question without an answer but add two relevant remarks without further comment: some very young stars have no detectable disk, for example HD 116842 (A5V, 320 Myr), HD 20630 (G5V, 300 Myr), HD 37394 (K1V, 320 Myr) and some old stars have retained their disk; examples: HD 10700 (G8V, 7.2 Gyr), HD 75732 (G5V, 5.0 Gyr) and HD 207129 (G0V, 4.4 Gyr); the last case has been studied in detail \citep{jour:99}." +. The age effect is shown eraphically in Fig. 7:5, The age effect is shown graphically in Fig. \ref{fig:cumul_just_model}; + it displavs the cunulative distribution of stars with a disk., it displays the cumulative distribution of stars with a disk. + The x-axis is the iudex of a star after all stars have been sorted by age., The x-axis is the index of a star after all stars have been sorted by age. + At a given age the local slope of the curve in this diagram gives the probability that stars of that age have a disk., At a given age the local slope of the curve in this diagram gives the probability that stars of that age have a disk. + The two liue segmoeuts shows how the cumulative umber increases when of the disks disappear eradually iu the first 0.4 Cir aud the remaimine eraduallv in the 12 Cyr thereafter., The two line segments shows how the cumulative number increases when of the disks disappear gradually in the first 0.4 Gyr and the remaining gradually in the 12 Gyr thereafter. + lu section 5.6 we will review the evidence that at about [00 Myr after the formation of the Sun a related phenomenon took place in the solar svstei., In section 5.6 we will review the evidence that at about 400 Myr after the formation of the Sun a related phenomenon took place in the solar system. +" Tn ""Veea-like circmnstellar disks the dust particles have a life-time much shorter than the age ofthe star.", In “Vega-like” circumstellar disks the dust particles have a life-time much shorter than the age of the star. + Within 1 Myr they will disappear via radiation pressure aud the Povutiug-Robertson effect (Ammannοal.1981)., Within 1 Myr they will disappear via radiation pressure and the Poynting-Robertson effect \citep{auma:84}. +. Au upper lait of 109 year is given for dust aroundA-type stars bv Povutine-Robertson drag (Durusetal.1979:Dackniau&Paresce 1993): the actual life time will be smaller: for Pie. Artvinowicz&Clampin(1997) fiud ouly 1000 vears.," An upper limit of $10^6$ year is given for dust aroundA-type stars by Poynting-Robertson drag \citep{burn:79,back:93}; the actual life time will be smaller: for $\beta$ Pic, \citet{arty:97} find only 4000 years." + Coutinuouslv new eraius have to replace those that disappear., Continuously new grains have to replace those that disappear. + A plausible mechanisin that cau supply these new erains at a high enough rate and for a sufficicut long time are the collisions between asteroids and planctesimals., A plausible mechanism that can supply these new grains at a high enough rate and for a sufficient long time are the collisions between asteroids and planetesimals. + Direct detectionof such larger bodies is rot vet possible although the existence of comets around jJ Piciss eeested by the rapidly appearing aud cisappearing coniponeuts of the Call I-absorption line (Ferletet1987)., Direct detection of such larger bodies is not yet possible although the existence of comets around $\beta$ Pic is suggested by the rapidly appearing and disappearing components of the CaII K-absorption line \citep{ferl:87}. +. The total mass of the dust that ISO detected is about that of the Moon., The total mass of the dust that ISO detected is about that of the Moon. + To produce the dust for £00 Nr uuch more mass must be presen in invisible form. that of asteroids or “plauctesimals”.," To produce the dust for 400 Myr much more mass must be present in invisible form, that of asteroids or “planetesimals”." + Thus the disappearance of the infrared excess on a timescale of Myr does not race the removal of the dust grams. butdust.," Thus the disappearance of the infrared excess on a timescale of Myr does not trace the removal of the dust grains, but." + Yu the solar svstein the same may have happened: see below., In the solar system the same may have happened; see below. + When a star has a companion or a planet the eravitational field will have a time-variable compoucut., When a star has a companion or a planet the gravitational field will have a time-variable component. + Will this component destroy the disk?, Will this component destroy the disk? + Not uecessarily so: the auets Jupiter and Saturn have both a dust disk aud nauv satellites., Not necessarily so: the planets Jupiter and Saturn have both a dust disk and many satellites. + On purpose we did not select marrow biuaries: we rejected stars within 1 arcuin from a target star. unless lis other star was at least 5 maenitudesOo fainter iu the V-baud.," On purpose we did not select narrow binaries: we rejected stars within 1 arcmin from a target star, unless this other star was at least 5 magnitudes fainter in the $V$ -band." + This criterium accepts wide multiple-stirs aud indecd these occur., This criterium accepts wide multiple-stars and indeed these occur. + We used the Uipparcos Catalogue to check all 8b stars from Table 2. for multiplicity., We used the Hipparcos Catalogue to check all 84 stars from Table \ref{tab:stars} for multiplicity. + Forty-cight stars have an cutry in the “Catalogue of courpauious of double aud iultiple stars” (=CCDAD). see Douunanect&Nvs (1991).," Forty-eight stars have an entry in the “Catalogue of companions of double and multiple stars” (=CCDM), see \citet{domm:94}." +.. Amone the Ll stars with a disk there are seven wide iuultiple-stars., Among the 14 stars with a disk there are seven wide multiple-stars. + Tn one case (IID22019) the star is part of an astrometric double: we ignore the object., In one case (HD22049) the star is part of an astrometric double; we ignore the object. + That leaves us with six stars that have both a disk and stellar companions., That leaves us with six stars that have both a disk and stellar companions. + The couclision is therefore that colupanions do not uccessarily destroy a disk., The conclusion is therefore that companions do not necessarily destroy a disk. + Table 9. contains information on these six stars with both a disk aud (at least) one companion., Table \ref{tab:multiple} contains information on these six stars with both a disk and (at least) one companion. +" Iu column (1) the nune appears. in coluuu (2) the IID-umuber ancl in column (3) the ονπο iu the CCDAL column (1) gives the total uunber of companions given in the CCDAL cohuun (5) eives the distance. r. between A aud D in astronomical units aud column (6) the magnitude difference in the V-baud between the first aud the secoud component (7À aud ""D. respectively)."," In column (1) the name appears, in column (2) the HD-number and in column (3) the entry-number in the CCDM; column (4) gives the total number of companions given in the CCDM, column (5) gives the distance, $r$, between A and B in astronomical units and column (6) the magnitude difference in the $V$ -band between the first and the second component (“A” and “B”, respectively)." + There are at least two remarkable Cases in Table 9.., There are at least two remarkable cases in Table \ref{tab:multiple}. + One is Vega CID 172167) with four companions: its briehtest companion ix at 190 AU. but its closest companion at only 200 AU. just outside of Veea’s disk.," One is Vega (HD 172167) with four companions; its brightest companion is at 490 AU, but its closest companion at only 200 AU, just outside of Vega's disk." + The other is p? Cue that has a disk (Dominiketal.1905: 2000).. a planet (Butleretal.1997) and a stellar companion.," The other is $\rho^1$ Cnc that has a disk \citep{domi:98, + tril:98, jaya:00}, , a planet \citep{butl:97} and a stellar companion." +"scales with the dust-to-gas ratio Dyw and the FUX radiation flux Umw as In the opposite regime of large Uww, the shielding by dust is expected to dominate over self-shielding, because self-shielding is a gradual function of the gas column density and may not be able to provide the required shielding for sufficiently large UV fluxes.","scales with the dust-to-gas ratio $\D$ and the FUX radiation flux $\U$ as In the opposite regime of large $\U$, the shielding by dust is expected to dominate over self-shielding, because self-shielding is a gradual function of the gas column density and may not be able to provide the required shielding for sufficiently large UV fluxes." +" In this regime, Equation (B]) becomes and the exponential factor is now large, so the characteristic density for the atomic-to-molecular transition is Thus, as mention, in the regime where dust shielding dominates, the dependence of the characteristic column on the FUV flux Umw is logarithmic."," In this regime, Equation \ref{eq:h2bal}) ) becomes and the exponential factor is now large, so the characteristic density for the atomic-to-molecular transition is Thus, as mention, in the regime where dust shielding dominates, the dependence of the characteristic column density on the FUV flux $\U$ is only logarithmic." + densityThere is no way to convert onlybetween the characteristic column density and the physical gas density easily., There is no way to convert between the characteristic column density and the physical gas density easily. +" Nevertheless, the following simple fitting formula captures the of the atomic-to-molecular transition on the averagedust-to-gas ratio dependenceand the FUV flux in our simulations: where x is given by Here n,=25cm?, A is and g is a fudge factor to approximately account for the transition between the two regimes: g~1 when self-shielding dominates and g« when dust shielding dominates."," Nevertheless, the following simple fitting formula captures the average dependence of the atomic-to-molecular transition on the dust-to-gas ratio and the FUV flux in our simulations: where $x$ is given by Here $n_{\ast}=25\dim{cm}^{-3}$, $\Lambda$ is and $g$ is a fudge factor to approximately account for the transition between the two regimes: $g\approx 1$ when self-shielding dominates and $g \propto \D^{-1}$ when dust shielding dominates." + We adopt the followingDy fitting formula for the quantity g: where and describes thetransition to the regime when formation of H5 via the reactions dominates., We adopt the following fitting formula for the quantity $g$: where and describes thetransition to the regime when formation of $\H2$ via the gas phase reactions dominates. +" Figure gasD| phaseshows the value of the total (molecular, atomic, and ionized - although the contribution of ionized gas in all equations in this section is completely negligible) hydrogen at which molecular fraction reaches fy,=0.5 (x= density0)."," Figure \ref{fig:nthfit} shows the value of the total (molecular, atomic, and ionized - although the contribution of ionized gas in all equations in this section is completely negligible) hydrogen density at which molecular fraction reaches $f_\H2=0.5$ $x=0$ )." + Our fitting formulae give the following approximate expression for this density: This equation is a better approximation than the the simple step-function ansatz proposed in (?)., Our fitting formulae give the following approximate expression for this density: This equation is a better approximation than the the simple step-function ansatz proposed in . +. Figure[2] demonstrates, Figure \ref{fig:nthfit} demonstrates +"filter set in the UVOT is different from that of the OOM, and the above values should not be directly compared with the OM measurements in XMM1 above.","filter set in the UVOT is different from that of the OM, and the above values should not be directly compared with the OM measurements in XMM1 above." + Grupeetal.(2008a) measured an offset between the magnitudes from the two instruments of Wlom—Wiuvor=0.78 by comparing several field stars in the images of the AGN Mkn 335.," \citet{grkoga2008} + measured an offset between the magnitudes from the two instruments of $W1_{\rm OM} - W1_{\rm UVOT} = 0.78$ by comparing several field stars in the images of the AGN Mkn 335." +" With this taken into account, there seems to be little variability in the UV between the two epochs."," With this taken into account, there seems to be little variability in the UV between the two epochs." + The optical and IR counterpart candidates of the source from the USNO B1.0 and 2MASS Point Source Catalogs are given in Table 2.., The optical and IR counterpart candidates of the source from the USNO B1.0 and 2MASS Point Source Catalogs are given in Table \ref{tbl:counterpart}. +" The optical counterpart, the galaxy IC 4765-f01-1504, is shown in Figure 1 (Carrascoetal."," The optical counterpart, the galaxy IC 4765-f01-1504, is shown in Figure \ref{fig:optimg} + \citep{camein2006}." +" Our fits of the V- and I-band images using a 2006).Sérrsic model give integrated magnitudes of 16.99+0.01 and 15.62+0.02, effective radii of 2/552-E0""004 and 2/994-0""009, Sérrsic indices of 3.54+0.06 and 4.14+0.13, and apparent axis ratios of 0.238+0.003 and 0.27140.003, respectively."," Our fits of the V- and I-band images using a Sérrsic model give integrated magnitudes of $\pm$ 0.01 and $\pm$ 0.02, effective radii of $\pm$ 04 and $\pm$ 09, Sérrsic indices of $\pm$ 0.06 and $\pm$ 0.13, and apparent axis ratios of $\pm$ 0.003 and $\pm$ 0.003, respectively." +" This galaxy may be an elliptical galaxy, which typically has a Sérrsic index of 4."," This galaxy may be an elliptical galaxy, which typically has a Sérrsic index of 4." + The axis ratios above would imply a high inclination of this galaxy if its intrinsic ellipticity is low., The axis ratios above would imply a high inclination of this galaxy if its intrinsic ellipticity is low. + Figure 2 shows the spectrum of IC 4765-f01-1504 from the Gemini South Telescope., Figure \ref{fig:optspec} shows the spectrum of IC 4765-f01-1504 from the Gemini South Telescope. +" No clear emission lines were detected, supporting the identification as an elliptical galaxy."," No clear emission lines were detected, supporting the identification as an elliptical galaxy." +" A redshift of z=0.0353+0.0001 was obtained from both the cross-correlation method, with R=12.80, and the absorption line fit method, indicating a perfect agreement between them."," A redshift of $z$ $\pm$ 0.0001 was obtained from both the cross-correlation method, with $R=12.80$, and the absorption line fit method, indicating a perfect agreement between them." +" This redshift disagrees with the value of 0.0869 obtained by Carrascoetal. which used the cross-correlation method (as there(2006),, were no significant emission lines detected)."," This redshift disagrees with the value of 0.0869 obtained by \citet{camein2006}, which used the cross-correlation method (as there were no significant emission lines detected)." +" Considering that our new spectrum has much better quality, we adopt this new redshift."," Considering that our new spectrum has much better quality, we adopt this new redshift." + We measured a 3-0 upper limit of [ΟΠΠ 5007 oof 0.9x1077? erg s! cm?., We measured a $\sigma$ upper limit of [OIII] 5007 of $\times$$10^{-15}$ erg $^{-1}$ $^{-2}$. +" Assuming a flat universe with the Hubble constant Hp=73 km s! Mpc! and the matter density O;—0.27, this redshift corresponds to a comoving radial distance of 143.9 Mpc and a luminosity distance of 149.0 Mpc, which will be used in this paper."," Assuming a flat universe with the Hubble constant $H_0$ =73 km $^{-1}$ $^{-1}$ and the matter density $\Omega_{\rm M}$ =0.27, this redshift corresponds to a comoving radial distance of 143.9 Mpc and a luminosity distance of 149.0 Mpc, which will be used in this paper." +" The absolute V and K magnitudes of this galaxy are -19.2 and -21.6, respectively, after the Galactic extinction correction (Schlegeletal."," The absolute V and K magnitudes of this galaxy are -19.2 and -21.6, respectively, after the Galactic extinction correction \citep{scfida1998}." +" Based on the BH mass vs. bulge luminosity relations 1998).from Graham(2007),, Laueretal.(2007) and Marconi&Hunt(2003),, the above magnitudes imply the mass of the SMBH in IC 4765-f01-1504 to be about 10’ and 109 iif the bulge/total luminosity ratio is 1 or 0.1, respectively."," Based on the BH mass vs. bulge luminosity relations from \citet{gr2007}, \citet{lafari2007} and \citet{mahu2003}, the above magnitudes imply the mass of the SMBH in IC 4765-f01-1504 to be about $^7$ and $^6$ if the bulge/total luminosity ratio is 1 or 0.1, respectively." +" Because the sample of galaxies in the above studies were generally brighter than IC 4765-f01-1504 and these relations have large intrinsic scattering, these mass estimates might have an uncertainty as large as one order of magnitude."," Because the sample of galaxies in the above studies were generally brighter than IC 4765-f01-1504 and these relations have large intrinsic scattering, these mass estimates might have an uncertainty as large as one order of magnitude." +the peak of star formation at ;23. where optical/UV emission can attenuate the >LOGGeV photons. just as the IR background can attenuate the Τον cussion of blazars at lower +. c.g. aud references therein.,"the peak of star formation at $z\approx 2-3$, where optical/UV emission can attenuate the $>$ GeV photons, just as the IR background can attenuate the TeV emission of blazars at lower $z$, e.g. \citet{dka05} and references therein." + Of course. there ix also attenuation from the host. photon field and. in principle. from the intervening z=1.89 ealaxy.," Of course, there is also attenuation from the host photon field and, in principle, from the intervening z=1.89 galaxy." + These contributions will make it dificult to extract constraints on the extragalactic background photon field from this (or any one) object., These contributions will make it difficult to extract constraints on the extragalactic background photon field from this (or any one) object. + However. statistical studies of high red-shift blazars with GLAST (Chen.Reyes&Ritz2001).. should still be able to extract elobal coustraints ou the extragalactic backeround light aud its evolution.," However, statistical studies of high red-shift blazars with GLAST \citep{crr04}, should still be able to extract global constraints on the extragalactic background light and its evolution." +CLO4 vields. is essentially indistinguishable after ~5 Crs. while the discrepant. nature of the models emploving the WOG vields is seltcobvious.,"CL04 yields, is essentially indistinguishable after $\sim$ 5 Gyrs, while the discrepant nature of the models employing the K06 yields is self-obvious." + We have not shown the moclels using the KWOG bypernovac vielcs. as their impact for the evolution of FC ο is negligible.," We have not shown the models using the K06 hypernovae yields, as their impact for the evolution of $^{12}$ $^{13}$ C is negligible." + In the case of 78 each of the vield compilations results in fairly sell-consistent evolutionary trends. although the hypernovae do. reduce he predicted. ratio bv a factor of two relative to models neglecting them.," In the case of $^{32}$ $^{34}$ S, each of the yield compilations results in fairly self-consistent evolutionary trends, although the hypernovae do reduce the predicted ratio by a factor of two relative to models neglecting them." + From Fig. 5..," From Fig. \ref{fig:iso_timeevolution}," + we also note the existence of predicted yositivenm radial. gradients. in+ both FC2 MA ο1 and Ba ;5 S/S.1 reflecting both the inside-out. galaxy formation framework and the consequent increased. importance of the secondary xoduction of C in the inner regions of the galactic model (c.g. tMO3).," we also note the existence of predicted positive radial gradients in both $^{12}$ $^{13}$ C and $^{32}$ $^{34}$ S, reflecting both the inside-out galaxy formation framework and the consequent increased importance of the secondary production of $^{13}$ C in the inner regions of the galactic model (e.g. RM03)." + From the lower panel of Fig. 5..," From the lower panel of Fig. \ref{fig:iso_timeevolution}," + we Can see hat «ur template dual-infall model is consistent with the extant galactic BSS data (solar svstem and local ISM): he lower value observed at z-0.80 (M06) can be partially reconciled with it being nearer its respective ealaxys centre han the solar a point to which we return in 4.2., we can see that our template dual-infall model is consistent with the extant galactic $^{32}$ $^{34}$ S data (solar system and local ISM); the lower value observed at z=0.89 (M06) can be partially reconciled with it being nearer its respective galaxy's centre than the solar a point to which we return in 4.2. + Previous galactic models for OC ο (e.g. ΗΛΙΟ). while consistent with the local SM. predicted. an increase. in OSC over the past 5-5-10 Covers. driven in part by the use of the older van den Llock Groenewegen (1997) vields.," Previous galactic models for $^{12}$ $^{13}$ C (e.g. RM03), while consistent with the local ISM, predicted an increase in $^{12}$ $^{13}$ C over the past 5-10 Gyrs, driven in part by the use of the older van den Hoek Groenewegen (1997) yields." + To amicliorate that apparent discrepancy. MOS introduced an important acditional source of PC. in the form of novac.," To ameliorate that apparent discrepancy, RM03 introduced an important additional source of $^{13}$ C, in the form of novae." + While successful in recovering the decline in DP with time. the overproduction of IC resulted in a significant mismatch between the model and the observations. as shown in Fig. 6..," While successful in recovering the decline in $^{12}$ $^{13}$ C with time, the overproduction of $^{13}$ C resulted in a significant mismatch between the model and the observations, as shown in Fig. \ref{fig:rm03}," + which required an à posteriori re-scaling of the model to the solar svstenr value., which required an a posteriori re-scaling of the model to the solar system value. + Conversely. the predicted. decline in + MUS over the vast 5-10. Caves in our model is naturally consistent. with he observed. solar value ane that of the local 981.," Conversely, the predicted decline in $^{12}$ $^{13}$ C over the past 5-10 Gyrs in our model is naturally consistent with the observed solar value and that of the local ISM." + Ες schaviour is driven by the new IWLOT vields (which obviously XAIO8 did not have access to) without the need of recourse o any additional C novae contribution., This behaviour is driven by the new KL07 yields (which obviously RM03 did not have access to) without the need of recourse to any additional $^{13}$ C novae contribution. +" The putative need or novae might even be exacerbated if one were to include. or example. “horn again"" (Le. re-ignited) stars such as Sakurai's Object: it has been suggested recently that such objects might be the dominant source of C in the Universe (Llajeduk et al."," The putative need for novae might even be exacerbated if one were to include, for example, “born again” (i.e., re-ignited) stars such as Sakurai's Object; it has been suggested recently that such objects might be the dominant source of $^{13}$ C in the Universe (Hajduk et al." + 2005)., 2005). + In the future. a phenomenological reatment of both novae and. such born-again objects will » implemented withinGEtool.," In the future, a phenomenological treatment of both novae and such born-again objects will be implemented within." + As alluded to earlier. it can be seen in Fig.," As alluded to earlier, it can be seen in Fig." + 5. that it is dillicult. for our template model to reproduce the isotopic ratios observed in the spiral galaxy at 250590., \ref{fig:iso_timeevolution} that it is difficult for our template model to reproduce the isotopic ratios observed in the spiral galaxy at z=0.89. + JXedamittecdly. the IxX06. vields appear to provide a better fit to FC τς ab (5.7 Gar (upper panel) although. at the same time. they are less successful for n 78/78. We have examined. two possible alternatives to our template solar neighbourhood model which could explain the lower values observed at high-redshift: (i) varving the ealactocentric distance of the mocel: (ii) varving the LME.," Admittedly, the K06 yields appear to provide a better fit to $^{12}$ $^{13}$ C at t=5.7 Gyr (upper panel) although, at the same time, they are less successful for $^{32}$ $^{34}$ S. We have examined two possible alternatives to our template solar neighbourhood model which could explain the lower values observed at high-redshift: (i) varying the galactocentric distance of the model; (ii) varying the IMF." +" First. as noted earlier. the data of ALOG probes a galactocentric distance closer to 4.5 kpe. rather than the solar galactocentric distance of 8.5 kpe: our template Milky Way model for this radial ""bin"" would. prediet a πο ο evolution olfset by ~20% from the solar. neighbourhoo: value. as shown in Fig. 5.."," First, as noted earlier, the data of M06 probes a galactocentric distance closer to 4.5 kpc, rather than the solar galactocentric distance of 8.5 kpc; our template Milky Way model for this radial “bin” would predict a $^{12}$ $^{13}$ C evolution offset by $\sim$ from the solar neighbourhood value, as shown in Fig. \ref{fig:iso_timeevolution}." + Vhis is. however. insullicient to reproduce the observed. values.," This is, however, insufficient to reproduce the observed values." + second. we explored. the dependence of the predictec isotope ratios upon the relative proportion of massive stars in the IAIF by [lattening (significantlv) the high-mass ene of the IME (representing the LME by a single. power-law of slope 0.9).," Second, we explored the dependence of the predicted isotope ratios upon the relative proportion of massive stars in the IMF by flattening (significantly) the high-mass end of the IMF (representing the IMF by a single power-law of slope 0.9)." + Figure 7 shows the time evolution of the C/C and © S/S isotope ratios using both this massive-star biased LAIF ane the cleault WE IME., Figure \ref{fig:imf} shows the time evolution of the $^{12}$ $^{13}$ C and $^{32}$ $^{34}$ S isotope ratios using both this massive-star biased IMF and the default KTG IMF. + The immediate. conclusion to be drawn is that both ratios decrease dramatically (by a factor of approximately four) when adopting the massive star-biasecl IME., The immediate conclusion to be drawn is that both ratios decrease dramatically (by a factor of approximately four) when adopting the massive star-biased IMF. + Llaving said that. it is important to be aware that in large part. this," Having said that, it is important to be aware that in large part, this" +pixel mask was use to exclude bad pixels from the final summed images.,pixel mask was used to exclude bad pixels from the final summed images. + Absolute photometric transformations were derived from the observatious of Persson (1998) HST stanclaὉ stars., Absolute photometric transformations were derived from the observations of Persson (1998) HST standard stars. + Each standard star was observed every night iu five separate array positious., Each standard star was observed every night in five separate array positions. + The observations of the staucard stars were reduced in a similar manuuer to the cluster data (see Oke 1998)., The observations of the standard stars were reduced in a similar manner to the cluster data (see Oke 1998). + An approximate limitingn maguituden ofa 4-f=20H fora a -—5o detectionn was reached in a staudard aperture of radits Dlt()., An approximate limiting magnitude of $K^{'} = 20$ for a $5 \sigma$ detection was reached in a standard aperture of radius $3\farcs{0}$. + We used SExtractor version 2.1.5 (Berin&Arnouts1996) to perform the source detection and photometry because this program is aje to detect objects in one image and analyze the corresponding pixels in a separate image., We used SExtractor version 2.1.5 \citep{bertin96} to perform the source detection and photometry because this program is able to detect objects in one image and analyze the corresponding pixels in a separate image. + A)dliecL uniformly to multi-baud image data (i.e. use the sale detection image for all measurement 1jages). this method will produce a matched aperture j»hotoietric catalog.," Applied uniformly to multi-band image data (i.e. use the same detection image for all measurement images), this method will produce a matched aperture photometric catalog." + We geuerated au optiial detection image from the nmages Using. a X7> process (Szalay‘csefal.1998)., We generated an optimal detection image from the images using a $\chi^2$ process \citep{szalay98}. +. Briefly. this process involves convolving each input image with a Gaussian kernel matche to the seeing.," Briefly, this process involves convolving each input image with a Gaussian kernel matched to the seeing." + The counvolved images were squared and ormalized so that they have zero mean aud ilit variance., The convolved images were squared and normalized so that they have zero mean and unit variance. + The four processed images (correspoudiug o the original nmmages) were coadded. lormune+. the X7> deteciol. Image.," The four processed images (corresponding to the original images) were coadded, forming the $\chi^2$ detection image." + In order to determiue the optimal threstold parameters for source detection. we compared a istogram of the pixel distribution in the 4? imageH withH a 47 Honfunctionη with. Hfour degrees ofm [reecom. ," In order to determine the optimal threshold parameters for source detection, we compared a histogram of the pixel distribution in the $\chi^2$ image with a $\chi^2$ function with four degrees of freedom. (" +is distribution theoretically corresponds o the background pixel distribution for our coaddec image.),This distribution theoretically corresponds to the background pixel distribution for our coadded $\chi^2$ image.) + By takiug the dillereuce between the two histograms (pixel miuus Itheory). we generatec histogram of pixel να]es which were due to tle objects that we weΘ {rving to detect.," By taking the difference between the two histograms (pixel minus theory), we generated the histogram of pixel values which were due to the objects that we were trying to detect." + We ined the Bayesian detectiou threshold as the intersection of the sky (or theoretical prediction object pixel distributious where the object Pixel flux becomes dominant)., We defined the Bayesian detection threshold as the intersection of the sky (or theoretical prediction) and object pixel distributions where the object pixel flux becomes dominant). + To convert this οσα threshold for use with SExtractor. we scaled the 4? threshold (whicl is a [lux per pixe 1e) iuto a surface brightess tlireshold (which is i Linaenituces per square aresecoud).," To convert this empirical threshold for use with SExtractor, we scaled the $\chi^2$ threshold (which is a flux per pixel value) into a surface brightness threshold (which is in magnitudes per square arcsecond)." + The iufrared images were cataoged separately die {ο their radically different fiekl-of-view au pixel scale., The infrared images were cataloged separately due to their radically different field-of-view and pixel scale. + The catalog was generated usiug SExtractor as before but iu sinele image mode the detection nage was also tlie meastwement image)., The catalog was generated using SExtractor as before but in single image mode the detection image was also the measurement image). + Iu «ler to maximize the number of detections. we utilized the exposure image geieratecd by DINSUM curing the data reduction (see 82.1.3) to provide a weight map iu order o properly determine oject parameters in an inage with varviug signal-to-noise (due to tlie diffe‘ent total integration tiijes in different. pixels).," In order to maximize the number of detections, we utilized the exposure image generated by DIMSUM during the data reduction (see 2.1.3) to provide a weight map in order to properly determine object parameters in an image with varying signal-to-noise (due to the different total integration times in different pixels)." + All of our restant analyses use the total inagnitiides calculated by SExtractor., All of our resultant analyses use the total magnitudes calculated by SExtractor. + The optical magnitudes were. by design. iiitchied: apertures whici reduces the scatter in any photometric redshiftip technique.," The optical magnitudes were, by design, matched apertures which reduces the scatter in any photometric redshift technique." +. Siucem the fy-f baud inages. were not co-registered. with. the optical. images.. the aperture cau be slightly. cdiffereit.," Since the $K^{'}$ band images were not co-registered with the optical images, the aperture can be slightly different." + However. since the total apertures were rather large in augular," However, since the total apertures were rather large in angular" +It has recently become evident that globular clusters. hitherto considered as simple stellar populations. are actually made of multiple stellar populations (see Gratton et al.,"It has recently become evident that globular clusters, hitherto considered as simple stellar populations, are actually made of multiple stellar populations (see Gratton et al." + 2001. 2004).," 2001, 2004)." + Evidence includes both photometry (Bedin et al., Evidence includes both photometry (Bedin et al. + 2004: Piotto et al., 2004; Piotto et al. + 2007) and spectroscopy (Gratton et al., 2007) and spectroscopy (Gratton et al. + 2001: Carretta et al., 2001; Carretta et al. + 2009a. 2009b. 20101).," 2009a, 2009b, 2010a)." + Most globular clusters host only a small number of stellar populations. differing in their content of light elements. typically described by anticorrelations among C and N. Na and O. Mg and AL and likely He (Bedin et al.," Most globular clusters host only a small number of stellar populations, differing in their content of light elements, typically described by anticorrelations among C and N, Na and O, Mg and Al, and likely He (Bedin et al." + 2004: Carretta et al., 2004; Carretta et al. + 2009a; Gratton et al., 2009a; Gratton et al. + 2010). while the abundances of Fe-peak elements do not show any spread (Carretta et al.," 2010), while the abundances of Fe-peak elements do not show any spread (Carretta et al." + 20006)., 2009c). + However in a few. generally massive globular clusters. different populations differ in the abundances of virtually all elements.," However in a few, generally massive globular clusters, different populations differ in the abundances of virtually all elements." + On many respect. these objects can be considered as intermediate between globular clusters and ultra compact dwarf galaxies (see e.g. Forbes Kroupa 2011 and Norris Kannappan 2011).," On many respect, these objects can be considered as intermediate between globular clusters and ultra compact dwarf galaxies (see e.g. Forbes Kroupa 2011 and Norris Kannappan 2011)." + Examples include M54 (Carretta et al., Examples include M54 (Carretta et al. + 2010b). M22 (Marino et al.," 2010b), M22 (Marino et al." + 2009). NGCI851 (Lee et al.," 2009), NGC1851 (Lee et al." + 2009; Carretta et al., 2009; Carretta et al. + 20104) and ω Cen., 2010d) and $\omega$ Cen. + This last. which is the brightest and most massive Milky Way cluster. represents the most extreme case of such variations.," This last, which is the brightest and most massive Milky Way cluster, represents the most extreme case of such variations." + The presence of multiple populations in w Centauri was discovered almost half à century ago by Woolley (1966)., The presence of multiple populations in $\omega$ Centauri was discovered almost half a century ago by Woolley (1966). + Various studies provided evidence for the large spread in metallicity within this cluster: among many others. we may cite Freeman Rodgers (1975). Butler et al. (," Various studies provided evidence for the large spread in metallicity within this cluster: among many others, we may cite Freeman Rodgers (1975), Butler et al. (" +1978). Cohen (1981). Norris Da Costa (1995a. 1995b). Suntzeff Kraft (1996). and Smith et al. (,"1978), Cohen (1981), Norris Da Costa (1995a, 1995b), Suntzeff Kraft (1996), and Smith et al. (" +2000).,2000). + All these studies found a predominance of metal-poor stars Fe/H|]« —1.5). with à tail up to rather high metallicities Fe/H|-.— 1).," All these studies found a predominance of metal-poor stars $<-1.5$ ), with a tail up to rather high metallicities $\sim -1$ )." + More recently. Pancino et al. (," More recently, Pancino et al. (" +2000) discussed the presence of a group of metal-rich stars on the red of the main red giant branch (RGB). which they called RGB-a (for anomalous). and have a metallicity [Fe/H]>—1.,"2000) discussed the presence of a group of metal-rich stars on the red of the main red giant branch (RGB), which they called RGB-a (for anomalous), and have a metallicity $>-1$." + Perhaps the most surprising discovery was however the splitting of the main sequence (Bedin et al., Perhaps the most surprising discovery was however the splitting of the main sequence (Bedin et al. + 2004) into at least two (and possibly more) separate sequences. and the fact that the red sequence is clearly more numerous than the blue one.," 2004) into at least two (and possibly more) separate sequences, and the fact that the red sequence is clearly more numerous than the blue one." + This lead to the suspicion that the blue sequence is much more He- (Norris 2004). a faet soon confirmed by the spectroscopic analysis by Piotto et al. (," This lead to the suspicion that the blue sequence is much more He-rich (Norris 2004), a fact soon confirmed by the spectroscopic analysis by Piotto et al. (" +2005) showing that the blue main sequence Is more metal-rich than the red one. just the opposite of what should be expected if the splitting were to be attributed simply to à metal abundance difference.,"2005) showing that the blue main sequence is more metal-rich than the red one, just the opposite of what should be expected if the splitting were to be attributed simply to a metal abundance difference." + Many different populations are clearly present in co Cen: multiple populations are found in the RGB (Sollima et al., Many different populations are clearly present in $\omega$ Cen: multiple populations are found in the RGB (Sollima et al. + 2005a). subgiant branch and main sequence (Bellini et al.," 2005a), subgiant branch and main sequence (Bellini et al." + 2010)., 2010). + Early attempts to reconstruct the history of these populations met severe problems., Early attempts to reconstruct the history of these populations met severe problems. + For instance. various authors proposed age-metallicity relations for ω Cen by combining photometric and spectroscopic observations of subgiant branch stars (see e.g. Sollima et al.," For instance, various authors proposed age-metallicity relations for $\omega$ Cen by combining photometric and spectroscopic observations of subgiant branch stars (see e.g. Sollima et al." + 2005b: Stanford et al., 2005b; Stanford et al. + 2006: Villanova et al., 2006; Villanova et al. + 2007): however results were contradictory with each other. likely because these studies neglected the large variations in He content that are present among different groups of stars.," 2007); however results were contradictory with each other, likely because these studies neglected the large variations in He content that are present among different groups of stars." + However. reconstructing early history of globular clusters from photometry alone is very difficult. because the long time elapsed since the cluster formation makes differences due to ages subtle. and easily masked by other effects (He and heavy element variations).," However, reconstructing early history of globular clusters from photometry alone is very difficult, because the long time elapsed since the cluster formation makes differences due to ages subtle, and easily masked by other effects (He and heavy element variations)." + Some clarification might then possibly come from the chemistry. exploiting the facet. that different elements are produced by stars in different mass ranges. and hence on different timescales.," Some clarification might then possibly come from the chemistry, exploiting the fact that different elements are produced by stars in different mass ranges, and hence on different timescales." + Thanks to the use of multi-fibre instruments. very extensive high resolution spectroscopic studies of several hundred red giants are now available (Johnson Pilachowski 2010; Marino et al.," Thanks to the use of multi-fibre instruments, very extensive high resolution spectroscopic studies of several hundred red giants are now available (Johnson Pilachowski 2010; Marino et al." + 2011)., 2011). + These studies provide several interesting observations., These studies provide several interesting observations. + For instance. while a clear Na-O anticorrelation is present among metal-poor stars. overabundances of both Na and O are obtained for the most metal-rich ones (those on the RGB-a of Paneino et al.," For instance, while a clear Na-O anticorrelation is present among metal-poor stars, overabundances of both Na and O are obtained for the most metal-rich ones (those on the RGB-a of Pancino et al." + 2000)., 2000). + In addition. the Na-O anticorrelation is present in stars over a large range in metallicity. possibly its extension increasing with metallicity.," In addition, the Na-O anticorrelation is present in stars over a large range in metallicity, possibly its extension increasing with metallicity." + This is not easy to be reconciled with the typically very narrow metal distribution of other clusters., This is not easy to be reconciled with the typically very narrow metal distribution of other clusters. + Finally. the abundances of the n-capture elements mainly produced by the s—process clearly rise with," Finally, the abundances of the $n-$ capture elements mainly produced by the $s-$ process clearly rise with" +Recently... cosmological models with coupling terms in the evolution equations for the dark matter and the dark energy density have attracted interest. because these couplings alleviate the coincidence problem in an elegant way (22222). ,"Recently, cosmological models with coupling terms in the evolution equations for the dark matter and the dark energy density have attracted interest, because these couplings alleviate the coincidence problem in an elegant way \citep{2003PhRvD..67h3513C, 2007arXiv0706.3860O, 2008arXiv0802.1086P, 2008arXiv0801.1565B, 2008arXiv0801.4233H}." +"Sachs-Wolfe TosGSW) ettectxr. (2222?09999 )... whichdark energy refers to the frequency change of cosmic microwave background (CMB) photons if they cross time evolving gravitational potentials. is a direct probe of dark energy because it vanishes incosmologies with €,=| (?)."," The integrated Sachs-Wolfe (iSW) effect \citep{1967ApJ...147...73S, rees_sciama_orig, 1994PhRvD..50..627H, 2002PhRvD..65h3518C, 2006MNRAS.369..425S}, which refers to the frequency change of cosmic microwave background (CMB) photons if they cross time evolving gravitational potentials, is a direct probe of dark energy because it vanishes incosmologies with $\Omega_m=1$ \citep{1996PhRvL..76..575C}." + By now. it has been detected with high significance with a number of different tracer objects (2222?).. ," By now, it has been detected with high significance with a number of different tracer objects \citep{2003AIPC..666...67B, 2003ApJ...597L..89F, 2006PhRvD..74f3520G, 2007MNRAS.377.1085R, 2008arXiv0801.4380G}." +In this paper. I would like to focus on the derivation of the integrated Sachs-Wolfe ettect for cosmological models with coupled dark matter and dark energy fluids and to show that iSW- acquires a dependence on the Hubble function. the matter density parameter. the growth rate and their derivatives.," In this paper, I would like to focus on the derivation of the integrated Sachs-Wolfe effect for cosmological models with coupled dark matter and dark energy fluids and to show that iSW-effect acquires a dependence on the Hubble function, the matter density parameter, the growth rate and their derivatives." +" In this respect. the iSW-etlect in coupled models is much richer than in models with non-interacting constituents. where the iSW-ettect simply measures the line of sight integrated derivative dD,/a)/da of the growth function D,(a."," In this respect, the iSW-effect in coupled models is much richer than in models with non-interacting constituents, where the iSW-effect simply measures the line of sight integrated derivative $\dd (D_+/a)/\dd a$ of the growth function $D_+(a)$." +" Physically. the changes in the formulae are due to the fact that the matter density p,, does not ⊽ «cin ⊻↽↴⋡↘models. and relationthe relation O,,,(a)/Q,,,¢ ""ELSο,=37MAuna3. couplednot."," Physically, the changes in the iSW-formulae are due to the fact that the matter density $\rho_m$ does not develop $\propto a^{-3}$ in coupled models, and the relation $\Omega_m(a)/\Omega_m=H_0^2/H^2(a)/a^3$ does not hold." +" A consequence .> te islee a ↝⊾↜ditterent ups""n /relationdoes betweenhold. the gravitational ofpotentialthis and the overdensity field: and it is not clear how mechanism was incorporated in the derivation presented by ?..", A consequence of this is a different (time-evolving) relation between the gravitational potential and the overdensity field; and it is not clear how mechanism was incorporated in the derivation presented by \citet{2008arXiv0801.4517O}. + After extending the iSW-formulaeto coupled cosmological models in Sect. ??..," After extending the iSW-formulaeto coupled cosmological models in Sect. \ref{sect_homogeneous}," + I compute the power spectrum of the iSW- in Sect., I compute the power spectrum of the iSW-effect in Sect. + ??. for a phenomenological model in. which dark matter decays into dark energy., \ref{sect_isw} for a phenomenological model in which dark matter decays into dark energy. + A summary of my results is compiled in Sect. ??.., A summary of my results is compiled in Sect. \ref{sect_summary}. + I consider spatially flat homogeneous cosmologies4. with: adiabatic. ∡∙∡initial conditions∡∡∙∡ ⋡in the. The integrated cold dark matter field., I consider spatially flat homogeneous dark energy cosmologies with adiabatic initial conditions in the cold dark matter field. +" Specitic parameter choices are Hy1005km/s/Mpe with =0.72. 0,=025. 0,=OS and n,=|."," Specific parameter choices are $H_0=100h \:\mathrm{km}/s/\mathrm{Mpc}$ with $h=0.72$, $\Omega_m=0.25$, $\sigma_8=0.8$ and $n_s=1$." +" As an example. I compute the iSW-spectra for the coupled model proposed by ?.. in which cold dark matter (CDM) decays into dark energy: The evolution of the dark matter density p, and the dark energy density p, (with an equation of state parameter w) is described by the systemof ditterential equations. with the cosmic time / as the time variable."," As an example, I compute the iSW-spectra for the coupled model proposed by \citet{2008arXiv0801.1565B}, in which cold dark matter (CDM) decays into dark energy: The evolution of the dark matter density $\rho_m$ and the dark energy density $\rho_\phi$ (with an equation of state parameter $w$ ) is described by the systemof differential equations, with the cosmic time $t$ as the time variable." + The Friedmann constraint is given by 37=py+ po., The Friedmann constraint is given by $3H^2=\rho_m+\rho_\phi$ . + The coupling constant T corresponds to the CDM decay rate in units of the Hubble- Hp., The coupling constant $\Gamma$ corresponds to the CDM decay rate in units of the Hubble-constant $H_0$ . + Models with stable CDM and hence uncoupled fluids are recovered by setting D= 0., Models with stable CDM and hence uncoupled fluids are recovered by setting $\Gamma=0$ . + I reformulate the time derivatives, I reformulate the time derivatives + Spectroscopic observations during the transit of an exoplanet across its host star can measure the sky-projected angle between the spins of the planetary orbit and the stellar rotation (the obliquity) through the Rossiter-MeLaughlin (RM) effect (Holt 1893:; Rossiter 1924:;; MeLaughlin 1924))., Spectroscopic observations during the transit of an exoplanet across its host star can measure the sky-projected angle between the spins of the planetary orbit and the stellar rotation (the obliquity) through the Rossiter-McLaughlin (RM) effect (Holt \cite{holt93}; Rossiter \cite{rossiter24}; ; McLaughlin \cite{mclaughlin24}) ). + The occultation of a rotating star by a planet distorts the apparent stellar line shape by removing the profile part emitted by the hidden portion of the star., The occultation of a rotating star by a planet distorts the apparent stellar line shape by removing the profile part emitted by the hidden portion of the star. + This induces anomalous stellar radial velocity variations during the transit. which constrain the sky-projected obliquity Ct) and thus indicate whether the orbit is prograde. retrograde. or polar.," This induces anomalous stellar radial velocity variations during the transit, which constrain the sky-projected obliquity $\lambda$ ) and thus indicate whether the orbit is prograde, retrograde, or polar." + Queloz et al. (2000)), Queloz et al. \cite{queloz00}) ) + reported the first detection of the RM anomaly for an extrasolar planet. 2209458b.," reported the first detection of the RM anomaly for an extrasolar planet, 209458b." + That planet shows an aligned. prograde orbit. as did all of the first seve planets for which the RM effect was measured (as reviewed 1 Hébbrard et al. 2008)).," That planet shows an aligned, prograde orbit, as did all of the first seven planets for which the RM effect was measured (as reviewed in Hébbrard et al. \cite{hebrard08}) )." + These early results were interpreted aan a validation of theories of planetary formation and evolutio where a single giant planet migrates in a proto-planetary disk perpendicular to the stellar spin axis (e.g. Lin et al. 1996))., These early results were interpreted as a validation of theories of planetary formation and evolution where a single giant planet migrates in a proto-planetary disk perpendicular to the stellar spin axis (e.g. Lin et al. \cite{lin96}) ). + That migration is expected to conserve the initial alignment betwee the angular momentums of the disk and of the planetary orbits., That migration is expected to conserve the initial alignment between the angular momentums of the disk and of the planetary orbits. + Hébbrard et al. (2008)), Hébbrard et al. \cite{hebrard08}) ) + however found a first case of spin- misalignment for the XO-3b planet. confirmed by Win et al. (2009a)).," however found a first case of spin-orbit misalignment for the XO-3b planet, confirmed by Winn et al. \cite{winn09a}) )." + Thereafter. Moutou et al. (2009))," Thereafter, Moutou et al. \cite{moutou09}) )" + reported a second case. 880606 (see also Pont et al. 20001:," reported a second case, 80606 (see also Pont et al. \cite{pont09};" + Winn et al. 2009b::, Winn et al. \cite{winn09b}; + Hébbrard et al. 2010))., Hébbrard et al. \cite{hebrard10}) ). +" A dozen misaligned systems have now been identified. including some with retrograde or nearly polar orbits (e.g. Winn et al. 2009¢:,"," A dozen misaligned systems have now been identified, including some with retrograde or nearly polar orbits (e.g. Winn et al. \cite{winn09c};" + Narita et al. 2010a::, Narita et al. \cite{narita10a}; + Triaud et al. 2010::, Triaud et al. \cite{triaud10}; + Simpson et al. 2010))., Simpson et al. \cite{simpson10}) ). + These unexpected results favor alternative scenarios where close-in massive planets have been brought in by planet-planet (or planet-star) scattering. Kozai migration. and/or tidal friction (e.g. Malmberg et al. 2007::," These unexpected results favor alternative scenarios where close-in massive planets have been brought in by planet-planet (or planet-star) scattering, Kozai migration, and/or tidal friction (e.g. Malmberg et al. \cite{malmberg07};" + Fabrycky Tremaine 2007:: Chatterjee et al. 2008::, Fabrycky Tremaine \cite{fabrycky07}; Chatterjee et al. \cite{chatterjee08}; + Nagasawa et al. 2008::, Nagasawa et al. \cite{nagasawa08}; + Guillochon et al. 2010))., Guillochon et al. \cite{guillochon10}) ). + Alternatively. it hàs been proposed that the orbit still reflects the orientation of the disk. with the stellar spin instead having moved away. either early-on through magnetosphere-disk interactions (Lai et al. 20105).," Alternatively, it has been proposed that the orbit still reflects the orientation of the disk, with the stellar spin instead having moved away, either early-on through magnetosphere-disk interactions (Lai et al. \cite{lai10}) )," + or later through elliptical tidal instability (Cébbron et al. 2011))., or later through elliptical tidal instability (Cébbron et al. \cite{cebron11}) ). + Distinguishing between these mechanisms needs additional obliquity measurements (e.g. Morton Johnson 2010))., Distinguishing between these mechanisms needs additional obliquity measurements (e.g. Morton Johnson \cite{morton10}) ). + Here we present spectroscopic observations of one transit of HAT-P-6b., Here we present spectroscopic observations of one transit of . +. This hot jupiter transits a bright F star (V=10.5) every 3.8 days and was discovered by Noyes et al. (2008.. ," This hot jupiter transits a bright F star $V=10.5$ ) every 3.8 days and was discovered by Noyes et al. \cite{noyes08}, ," +NOS)., N08). + Its mass is 1.06+0.12 παπά its radius 1.33+0.06Ryup., Its mass is $1.06 \pm 0.12$ and its radius $1.33 \pm 0.06$. +". The August 21!"" 2010 transit of wwas observed withSOPHIE.", The August $^{\mathrm{th}}$ 2010 transit of was observed with. +. This cross-dispersed. stabilized echelle spectrograph is dedicated to high-precision radial velocity measurements (Perruchot et al. 2008:;," This cross-dispersed, stabilized echelle spectrograph is dedicated to high-precision radial velocity measurements (Perruchot et al. \cite{perruchot08};" + Bouchy et al. 2009))., Bouchy et al. \cite{bouchy09}) ). + It is fed by two optical fibers mounted at the focus of the 1.93-m telescope of the Haute-Provence Observatory (OHP. France).," It is fed by two optical fibers mounted at the focus of the 1.93-m telescope of the Haute-Provence Observatory (OHP, France)." + iis bright enough for observation in. the high-resolution mode of the spectrograph CUAL= 75.000) andwith fast detector readout.," is bright enough for observation in the high-resolution mode of the spectrograph $\lambda/\Delta\lambda=75,000$ ) andwith fast detector readout." +The observations were carried out three days before full Moon.,The observations were carried out three days before full Moon. + This was anticipated not to adversely impact the radial velocity accuracies. however. thanksto the large radial velocity shift between," This was anticipated not to adversely impact the radial velocity accuracies, however, thanksto the large radial velocity shift between" +secondly. in the marked point bootstrap. it is the marks (hat are used to compute the bootstrap estimate.,"Secondly, in the marked point bootstrap, it is the marks that are used to compute the bootstrap estimate." + Thus the resamplecl points do not have to be arranged to lorm a new point pattern., Thus the resampled points do not have to be arranged to form a new point pattern. + This makes it a lot easier to bootstrap data that are observed in irregularly shaped regions that are common in astronomy., This makes it a lot easier to bootstrap data that are observed in irregularly shaped regions that are common in astronomy. + In Loh&Stein(2004) for example. bootstrap on an absorber catalog was done using slices as well as spheres. wilh similar results for both ivpes of resampling regions.," In \citet{loh02a} for example, bootstrap on an absorber catalog was done using slices as well as spheres, with similar results for both types of resampling regions." + Thirdly. (he marks used for resampling are part of the original estimate and are computed during the estimation step.," Thirdly, the marks used for resampling are part of the original estimate and are computed during the estimation step." + The only additional computation required by the marked point bootsirap involves selecting points (that is. testing whether each point lies in a resampling region or nol). aud keeping track of the number of times each point is resampled.," The only additional computation required by the marked point bootstrap involves selecting points (that is, testing whether each point lies in a resampling region or not), and keeping track of the number of times each point is resampled." + Unlike the block bootstrap. there is no need to re-compute from scratch the estimates for each bootstrap sample.," Unlike the block bootstrap, there is no need to re-compute from scratch the estimates for each bootstrap sample." + This difference in computation is even greater for hieher-orcler statistics., This difference in computation is even greater for higher-order statistics. + These properties of (he marked point bootstrap make it a computationally feasible tool for analvsis., These properties of the marked point bootstrap make it a computationally feasible tool for analysis. + Our study. here suggests that non-parametric bootstrap can viekd valid estimates of errors under a wide range of point patterns., Our study here suggests that non-parametric bootstrap can yield valid estimates of errors under a wide range of point patterns. + The lack of specific model assumptions means that the non-parametric bootstrap method. and in particular (he marked point bootstrap. can serve as an alternate and complementary method lor quantifving errors.," The lack of specific model assumptions means that the non-parametric bootstrap method, and in particular the marked point bootstrap, can serve as an alternate and complementary method for quantifying errors." + Having estimates of errors obtained using Poisson approximations. parametric and non-parametric bootstrap allows one to have a better sense of the size of errors involved in an analvsis.," Having estimates of errors obtained using Poisson approximations, parametric and non-parametric bootstrap allows one to have a better sense of the size of errors involved in an analysis." + The simulation study performed here shows that bootstrap confidence intervals do attain coverage close to the nominal level. even for the clustered. point patterns where Poisson errors are known {ο be inaccurate. when sample sizes are large.," The simulation study performed here shows that bootstrap confidence intervals do attain coverage close to the nominal level, even for the clustered point patterns where Poisson errors are known to be inaccurate, when sample sizes are large." + More specifically. bootstrap performance improves wilh increasing number density. and also with increasing observation region size relative (o the correlation length.," More specifically, bootstrap performance improves with increasing number density, and also with increasing observation region size relative to the correlation length." + Unfortunately. in astronomy. the correlation length may be of the same scale as the observation region.," Unfortunately, in astronomy, the correlation length may be of the same scale as the observation region." + If the values of r at which the correlation Function estimates are computed are small relative to the resampling blocks (and (he observation region). (hen although the bootstrap procedure would distort the dependence structive al the large scales. it would still be valid for these smaller values of r.," If the values of $r$ at which the correlation function estimates are computed are small relative to the resampling blocks (and the observation region), then although the bootstrap procedure would distort the dependence structure at the large scales, it would still be valid for these smaller values of $r$ ." + If. instead. £(r). sav. lor r close to the size of the observation region is of interest. then the bootstrap procedure would start to break down. in the sense Chat the empirical coverage of confidence may not be close to the nominal level. and the bootstrap errors not reflect the true errors.," If, instead, $\xi(r)$, say, for $r$ close to the size of the observation region is of interest, then the bootstrap procedure would start to break down, in the sense that the empirical coverage of confidence may not be close to the nominal level, and the bootstrap errors not reflect the true errors." + In this case. the amount of information contained in the data is smaller and the boundary. effects are magnified.," In this case, the amount of information contained in the data is smaller and the boundary effects are magnified." + With respect to the marked point bootstrap. larger blocks are needed to capture (he dependence structure al (his larger scale.," With respect to the marked point bootstrap, larger blocks are needed to capture the dependence structure at this larger scale." + For a fixed sample. this cannot be done without reducing the variability of the bootstrap samples.," For a fixed sample, this cannot be done without reducing the variability of the bootstrap samples." + Themethod that, Themethod that +"V,'s from gravitational stellar collapses [16]..",$\bar \nu_e$ 's from gravitational stellar collapses \cite{lvd}. + LVD plans to be a neutrino flux monitor of the CNGS beam., LVD plans to be a neutrino flux monitor of the CNGS beam. +" LVD has 3 identical “towers”, each containing 8 active modules; a module has 8 counters of 1x1.5m3, filled with 1.2 t of liquid scintillator."," LVD has 3 identical “towers”, each containing 8 active modules; a module has 8 counters of $1 \times 1 \times 1.5~ m^3$, filled with 1.2 t of liquid scintillator." +" CNGS v,,’s are observed through the detection of muons produced in neutrino CC interactions in the surrounding rock or in the detector and through the detection of the hadrons produced in neutrino NC/CC interactions inside the detector.", CNGS $\nm$ 's are observed through the detection of muons produced in neutrino CC interactions in the surrounding rock or in the detector and through the detection of the hadrons produced in neutrino NC/CC interactions inside the detector. + In the 2006 test run LVD counted 50-100 muons per day and recorded ~500 events [16].., In the 2006 test run LVD counted 50-100 muons per day and recorded $\sim$ 500 events \cite{lvd}. +" [15] is a hybrid-emulsion-electronic detector, designed to search for the v,,<—>v; oscillations in the parameter region indicated by the atmospheric neutrinos, confirmed by the K2K and MINOS experiments."," \cite{opera} is a hybrid-emulsion-electronic detector, designed to search for the $\nmnt$ oscillations in the parameter region indicated by the atmospheric neutrinos, confirmed by the K2K and MINOS experiments." +" The v, appearance will be made by direct detection of the 7 lepton, from v, CC interactions and the 7 lepton decay products."," The $\nt$ appearance will be made by direct detection of the $\tau$ lepton, from $\nt$ CC interactions and the $\tau$ lepton decay products." +" To observe the decays, a spatial resolution of ~1um is necessary; this is obtained in emulsion sheets interspersed with thin lead target plates (Emulsion Cloud Chamber (ECC))."," To observe the decays, a spatial resolution of $\sim 1~\mu$ m is necessary; this is obtained in emulsion sheets interspersed with thin lead target plates (Emulsion Cloud Chamber (ECC))." +" OPERA may also search for the subleading v,,<—>νε oscillations and make a variety of observations using its electronic detectors.", OPERA may also search for the subleading $\nmne$ oscillations and make a variety of observations using its electronic detectors. +" 'The OPERA detector, Fig. 6,,"," The OPERA detector, Fig. \ref{structure}," +" is made of two identical supermodules, each consisting of asection with 31 target planes of lead/emulsion-film modules (“bricks”), of a scintillator tracker detector and of a muon spectrometer."," is made of two identical supermodules, each consisting of a with 31 target planes of lead/emulsion-film modules (“bricks”), of a scintillator tracker detector and of a muon spectrometer." + The final target mass is 1.55 kt., The final target mass is 1.55 kt. +" The first electronic subdetector is anwall to separate µ events coming from interactions in OPERA from those in the material and rock before Thetracker is made of scintillator strips, each 7 m long and of 25x15 2 cross section."," The first electronic subdetector is an to separate $\mu$ events coming from interactions in OPERA from those in the material and rock before The is made of scintillator strips, each 7 m long and of $ \times $ 15 $^2$ cross section." + A wavelength shifting fibre of 1 mm diameter transmits the light signals to both ends., A wavelength shifting fibre of 1 mm diameter transmits the light signals to both ends. + The readout is done by 1000 64 channel Hamamatsu PMTs., The readout is done by 1000 64 channel Hamamatsu PMTs. + Thespectrometer consists of 2 iron magnets instrumented with (RPC) andtubes., The consists of 2 iron magnets instrumented with (RPC) and. + Each magnet is an 8x m? dipole with a field of 1.52 T in the upward direction on one side and in the downward direction on the other side., Each magnet is an $8 \times 8$ $^2$ dipole with a field of 1.52 T in the upward direction on one side and in the downward direction on the other side. +" A magnet consists of twelve 5 cm thick iron slabs, alternated with RPC Thetracker measures the muon track coordinates in the horizontal plane."," A magnet consists of twelve 5 cm thick iron slabs, alternated with RPC The measures the muon track coordinates in the horizontal plane." +" It is made of drift tube planes, placed in front and behind each magnet and between the 2 magnets."," It is made of drift tube planes, placed in front and behind each magnet and between the 2 magnets." + The muon spectrometer has a Ap/p<0.25 for muon momenta <25 GeV/c. Two 45? crossed planes of are installed in front of the Thesystem uses a Gigabit network of 1150 nodes., The muon spectrometer has a $\Delta p / p \le 0.25$ for muon momenta $< 25$ GeV/c. Two $45^{\circ}$ crossed planes of are installed in front of the The uses a Gigabit network of 1150 nodes. +" To match the data of the different subdetectors a “time stamp"" is delivered by a clock using the GPS.", To match the data of the different subdetectors a “time stamp” is delivered by a clock using the GPS. + Also the synchronization with the beam spill is done via GPS., Also the synchronization with the beam spill is done via GPS. + The commissioning of each electronic detector was made with CR muons and with the CNGS at reduced intensity., The commissioning of each electronic detector was made with CR muons and with the CNGS at reduced intensity. +" The basic target module is a“brick”, consisting of 56 lead plates (1 mm thick) and 57 emulsion layers."," The basic target module is a, consisting of 56 lead plates (1 mm thick) and 57 emulsion layers." +" A brick has a size of 10.2x12.7 cm?, a depth of 7.5 cm (10 radiation lengths) and a weight of 8.3 kg."," A brick has a size of $10.2 \times 12.7$ $^2$ , a depth of 7.5 cm (10 radiation lengths) and a weight of 8.3 kg." +" Two additional emulsion sheets, thesheets (CS), are glued on"," Two additional emulsion sheets, the (CS), are glued on" +CCDs. cach of them 2018. «1612 pixels large.,"CCDs, each of them 2048 $\times$ 4612 pixels large." + The pixel scale is 0.1857 which gives a total Seld of view of 0.96«0.91 deg?., The pixel scale is 0.185” which gives a total field of view of $0.96 \times 0.94$ $^{2}$. + The seeing of the observations used to construct the stacks is better than 1.17. which guarantees high quality data for the three different surveys.," The seeing of the observations used to construct the stacks is better than 1.1”, which guarantees high quality data for the three different surveys." +" We present iu this paper an analysis of three fields of the ""Deep? Survey. Dl. D2 aud D3 of the CFIITLS release TOO01."," We present in this paper an analysis of three fields of the “Deep” Survey, D1, D2 and D3 of the CFHTLS release T0001." + These data are stacks of many iuages., These data are stacks of many images. + Field coordinates aud the median seeiug iu // in cach field are eiven in Table L.., Field coordinates and the median seeing in $i'$ in each field are given in Table \ref{table}. + The stacks aud catalogues used in this paper were released ax part of the TERAPIX T0001 public release., The stacks and catalogues used in this paper were released as part of the TERAPIX T0001 public release. + A 1xief outline of how these stacks were prepared is as follows., A brief outline of how these stacks were prepared is as follows. + CFUTLS observations are carried out with MEGACAAL in queue survey mode., CFHTLS observations are carried out with MEGACAM in queue survey mode. + For release T0001. only observatious from June. Ist 2003 to July. 22. 2001 were used.," For release T0001, only observations from June, 1st 2003 to July, 22, 2004 were used." + Pre-vediucions were carried out at the CEITT using the pre-vreduction gvsteià at CFUT and then these pre-reduced naages were shipped to TERAPIN. via. the Canadian Astronomy Data Centre. in Victoria. Canada.," Pre-reductions were carried out at the CFHT using the pre-reduction system at CFHT and then these pre-reduced images were shipped to TERAPIX via the Canadian Astronomy Data Centre, in Victoria, Canada." + These pre-ceduced iÁuages were then injected iuto the TERAPIX pipeline for inspection aud quality control purposes., These pre-reduced images were then injected into the TERAPIX pipeline for inspection and quality control purposes. + The TERAPIX tool QualitvFITS was used to Inspect aud erade cach image. and also to produce weight-maps derived from the CFUT-provided imaster flats using the WeightWatcher tool.," The TERAPIX tool QualityFITS was used to inspect and grade each image, and also to produce weight-maps derived from the CFHT-provided master flats using the WeightWatcher tool." + The global astrometric and photomoetric solutions were computed using the WIFIX )ackage. an earlier generation of the TERAPIX astrometric software. as the production astrometric software package was still in testing phase at the time of the T0001 reCase.," The global astrometric and photometric solutions were computed using the WIFIX package, an earlier generation of the TERAPIX astrometric software, as the production astrometric software package was still in testing phase at the time of the T0001 release." + For inclusion iu the stacks. Inages must have a seeiug better than 11° (1.37 in 4) aud aivimass less than 1.5.," For inclusion in the stacks, images must have a seeing better than 1.1” (1.3” in $u^{*}$ ) and airmass less than 1.5." + From this point ou for he image reductions. we ollowed. esscutially the same procedure as outlined in MeCracken et. al. 20051).," From this point on for the image reductions, we followed essentially the same procedure as outlined in McCracken et al. \cite{McCracken2003}) )," + aid we refer to the interested reader to this paper for more details., and we refer to the interested reader to this paper for more details. + The two siguificaut differences are firstly that we use weight maps computed roni the image flat-fields themselves aud secondly we use he USNO-B as the astrometric reference catalogue (which iuereases the robustuess of the overall astrometric solution with respect to the solutions utilising the USNO-A)., The two significant differences are firstly that we use weight maps computed from the image flat-fields themselves and secondly we use the USNO-B as the astrometric reference catalogue (which increases the robustness of the overall astrometric solution with respect to the solutions utilising the USNO-A). + Full details of the properties of the final stacks. including depth in cach filter and the accuracy of the final astromietrie solution can be found ou the TERAPIN webband-to-].," Full details of the properties of the final stacks, including depth in each filter and the accuracy of the final astrometric solution can be found on the TERAPIX web." + The internal accuracy of the astrometric solution (xud) is better than one pixel ruis over the entire MEGACAM field. whereas the externa astrometric solution is around ~0.257 rnus.," The internal accuracy of the astrometric solution (band-to-band) is better than one pixel rms over the entire MEGACAM field, whereas the external astrometric solution is around $\sim 0.25""$ rms." + Photometric calibrations for each pre-reduced naage is provided by the ELINIR pipeline., Photometric calibrations for each pre-reduced image is provided by the ELIXIR pipeline. + ELIXIR also applies a CCD-to-CCD fux scaling derived from repeated observatious of deuse stellar fields which are shifted iiauvy tes around the MEGACAM feld of view (providing uaenitude measurcmeuts of the same star on different CCDs)., ELIXIR also applies a CCD-to-CCD flux scaling derived from repeated observations of dense stellar fields which are shifted many times around the MEGACAM field of view (providing magnitude measurements of the same star on different CCDs). + This procedure is necessary to correctly account or the “scattered light? effect aud eusures that the flux of auv given object is indepeudent of the position ou the uosaic.," This procedure is necessary to correctly account for the ""scattered light"" effect and ensures that the flux of any given object is independent of the position on the mosaic." + The residual ccd-to-ccd magnitude error following his procedure is around ~3, The residual ccd-to-ccd magnitude error following this procedure is around $\sim 3\%$. + Iu constructing the final stacks. we compare the maeuitudes of objects in overlapping poiutiugs aud in each band the photometric exposures are indeutified as those in which the objects jiwe the hiehest flux: other nuages are scaled to these observations.," In constructing the final stacks, we compare the magnitudes of objects in overlapping pointings and in each band the photometric exposures are indentified as those in which the objects have the highest flux: other images are scaled to these observations." + Based ou an examination of ealaxy counts and stellar colour-colour plots (see below). we estinate hat our absolute photometric solution in cach filter ΠΕΠΠ svsteniatic error of ~0.05 magnitudes.," Based on an examination of galaxy counts and stellar colour-colour plots (see below), we estimate that our absolute photometric solution in each filter has a maximum systematic error of $\sim0.05$ magnitudes." + Catalogues were extracted using SExtractor iu dual-image uode. with detections carried out musing a chiesquared Hae (Szalav ot al. 2003))," Catalogues were extracted using SExtractor in dual-image mode, with detections carried out using a chi-squared image (Szalay et al. \cite{Szalay2003}) )" + constructed from the gi inages., constructed from the $g'r'i'$ images. + Ixon-like total magnitudes were used throughout., Kron-like total magnitudes were used throughout. + Through this paper. our magnitudes are preseuted iu the MECACAAL instrumental AB system.," Through this paper, our magnitudes are presented in the MEGACAM instrumental AB system." +" We separated point-like sources from) exteudecl ones using SExtractors (Bertin Árnouts 1996)) ""fiux-radius"" parameter measured ou the /]-band nuage."," We separated point-like sources from extended ones using SExtractor's (Bertin Arnouts \cite{Bertin96}) ) ""flux-radius"" parameter measured on the $i'$ -band image." + This parameter measures the radius which eucloses of the object's flux: for point-like sources this is indepeuceut of imaenitude. aud depeuds oulv on the image FWIIM.," This parameter measures the radius which encloses of the object's flux: for point-like sources this is independent of magnitude, and depends only on the image FWHM." + The stars were selected by automatically locating the stellar branch in the flus-raciusanaguitude diagram iu a series of 10 arcnuninute cells distributed over cach MIEGACAAL ?-stack. which accounts for variation of FWIIM over MEGACAM field of view.," The stars were selected by automatically locating the stellar branch in the flux-radius-magnitude diagram in a series of 10 minute cells distributed over each MEGACAM $i'$ -stack, which accounts for variation of FWHM over MEGACAM field of view." + Figure 1 shows the compactness parameter against the magnitude for the three CFIUTLS fields DI. D2 and D».," Figure \ref{star-gal-separation} + shows the compactness parameter against the magnitude for the three CFHTLS fields D1, D2 and D3." + At magnitudes, At magnitudes +"and we noted in Eq.(15)) the multipoles thetaW: -σπ- Tn addition to the threc-poiut correlation ¢, of the convergence. it can be useful to consider the threc-point correlation of the cosunüe shear x.","and we noted in \ref{zeta-B}) ) the multipoles _1=, _2=, _3^2=. In addition to the three-point correlation $\zetakappa$ of the convergence, it can be useful to consider the three-point correlation of the cosmic shear ${\vec\gamma}$." +" Because the latter is a spin-2 quantity. oue is led to consider several threc-poiut shear correlations (or ""natural couponcuts”). depending ou the choice of the reference direction (or of the projection procedure of the cosnüc shear vectors). see κ"," Because the latter is a spin-2 quantity, one is led to consider several three-point shear correlations (or “natural components”), depending on the choice of the reference direction (or of the projection procedure of the cosmic shear vectors), see \citet{Schneider2003,Schneider2005}." + Towever. they can all be written as iutegrals over the converseace bispecrun. such as Eq.(15)). Or iutegrals over the convergence three-point correlation (9]) (23..," However, they can all be written as integrals over the convergence bispectrum, such as \ref{zeta-B}) ), or integrals over the convergence three-point correlation \ref{zeta-def}) ) \citep{Shi2011}." + Therefore. alt]rough we oily consider the couvergenuce three-point correlaion (93) in this paper. we cau expect a simular level of agreement between our analytical iiodol and simulations for these other threc-poiut correlatious (in⋅ addition⋅⋅ we also consider. the third-order. moment of the apertureauass. can be related to both the convergence aud the cosmic Whichshear).," Therefore, although we only consider the convergence three-point correlation \ref{zeta-def}) ) in this paper, we can expect a similar level of agreement between our analytical model and simulations for these other three-point correlations (in addition we also consider the third-order moment of the aperture-mass, which can be related to both the convergence and the cosmic shear)." + Tt is also comunion practice to study snoothed averages X. of the or shear field. defined by their filtering window convergencen2(0) through NxB (0)) IT57(0)).," It is also common practice to study smoothed averages $X_s$ of the convergence or shear field, defined by their filtering window $W^{X_s}_{\theta_s}(\vtheta)$ through X_s = ) )." +" For mstauce. the sinoothed. convergence ας is defined by a top-hat filtering. (psy 1 andotherwise. while the “apertuve-mass” μμ d8 defined bw a colmpcusated filter (27).. ucl as δὴ 3 ) ) and H3u7""(8)= 03£|0|> 0,."," For instance, the smoothed convergence $\kappa_s$ is defined by a top-hat filtering, ) = 1 _s, while the “aperture-mass” $\Map$ is defined by a compensated filter \citep{Schneider1996,VanWaerbeke2001}, such as ) = 3 ) ) _s, and $W^{\Map}_{\theta_s}(\vtheta) = 0$ if $|\vtheta|>\theta_s$ ." +" This also reads in Fourier space as X. RENIN: theta, with theta (Θ)", This also reads in Fourier space as X_s = ) _s) with _s) = ) . +) Tn particular. we lave theta jets ," In particular, we have _s) = 2, _s) = 24 ." +"We mainly focus here ou one-point moments of κ aud May. that is CX/2. aud we do not consider inulti-poiut statistics such as CX.(01:0,44..X.(0,:0,,)). associated with p windows ceutered on p different directions and with p different angular radii."," We mainly focus here on one-point moments of $\kappa_s$ and $\Map$, that is $\lag X_s^p \rag$, and we do not consider multi-point statistics such as $\lag X_s(\vtheta_1;\theta_{s1}) .. X_s(\vtheta_p;\theta_{sp})\rag$ associated with $p$ windows centered on $p$ different directions and with $p$ different angular radii." + However. we will check the validity of o1uw mocdoel for 1nulti-«cale statistics. that is. for windows of cifferent sizes centered on the same direction. in Sect. 5," However, we will check the validity of our model for multi-scale statistics, that is, for windows of different sizes centered on the same direction, in Sect. \ref{multi-scale}." +" Iu the simpler case of one-point mnonents AVIíXTpD the variance reads as P.((1)) 002 while the third-order moment roads as EDDIE: ell, 1. ell, −≖⋏ SB, ο alle ole where we used the svuumetrics of the bispectruii aud we noted fay, "," In the simpler case of one-point moments $\lag X_s^p \rag$ the variance reads as = ) _s)^2, while the third-order moment reads as = _1 _1 _2 _2 _3) _1 _s) _2 _s) _3 _s), where we used the symmetries of the bispectrum and we noted _3^2= _2^2 -." +In practice.. to avoid. the umucrous oscillations.. and ραyoy Ofsign brought by the Fouricr-space⋅ filters⋅ HW;τν. een in Eq.(23)). we found it convenieut to express the third-order monent (28))in termsof the real-space threc-poiut correlation (9)). although this vields a five- iutegral iustead of the three-dineusional integral: (28)). = thetaya a thetasa (," In practice, to avoid the numerous oscillations and changes of sign brought by the Fourier-space filters $\tW^{X_s}_{\theta_s}$ given in \ref{tW-kappa-Map}) ), we found it convenient to express the third-order moment \ref{Xs-skewness}) )in termsof the real-space three-point correlation \ref{zeta-def}) ), although this yields a five-dimensional integral instead of the three-dimensional integral \ref{Xs-skewness}) ), = _1 _1 _1) _2 _2 _2)" +In practice.. to avoid. the umucrous oscillations.. and ραyoy Ofsign brought by the Fouricr-space⋅ filters⋅ HW;τν. een in Eq.(23)). we found it convenieut to express the third-order monent (28))in termsof the real-space threc-poiut correlation (9)). although this vields a five- iutegral iustead of the three-dineusional integral: (28)). = thetaya a thetasa (0," In practice, to avoid the numerous oscillations and changes of sign brought by the Fourier-space filters $\tW^{X_s}_{\theta_s}$ given in \ref{tW-kappa-Map}) ), we found it convenient to express the third-order moment \ref{Xs-skewness}) )in termsof the real-space three-point correlation \ref{zeta-def}) ), although this yields a five-dimensional integral instead of the three-dimensional integral \ref{Xs-skewness}) ), = _1 _1 _1) _2 _2 _2)" +Lovelace 1991: Contopoulos 1995: Ostriker 1997).,Lovelace 1994; Contopoulos 1995; Ostriker 1997). + See also reviews bv Bisnovatvi-lsoean (1993) and Livio (1997)., See also reviews by Bisnovatyi-Kogan (1993) and Livio (1997). + From the theory. a necessary condition for magneticallyοσαισααν driven outflows is that the poloidal maguetic field at the disks surface be inclined away frou the svunuetry axis (2) at a sufficiently large anele.," From the theory, a necessary condition for magnetically/centrifugally driven outflows is that the poloidal magnetic field at the disk's surface be inclined away from the symmetry axis $z$ ) at a sufficiently large angle." + Iowever. the analytical theory makes drastic sinplificatious such as assuming self-similar depeudeuces on the radial distance (r in cevliudrical coordiuates). or by iuteerating over the cross-section of the outflow.," However, the analytical theory makes drastic simplifications such as assuming self-similar dependences on the radial distance $r$ in cylindrical coordinates), or by integrating over the cross-section of the outflow." + The ποαιία solutions have diverecuces at both small aud large r so that the influence of these regious is unknown., The self-similar solutions have divergences at both small and large $r$ so that the influence of these regions is unknown. + Numerical ΑΠΟ sHuaulations are essential το establish the existence and understand the nature. of magnetically/contrifieally driven outflows., Numerical MHD simulations are essential to establish the existence and understand the nature of magnetically/centrifugally driven outflows. + Stationary aud nou-stationary MIID flows were investigated by Ixudolh Shibata (1995. 1997a.b) in one-dimensional (1.5D) simulations.," Stationary and non-stationary MHD flows were investigated by Kudoh Shibata (1995, 1997a,b) in one-dimensional $1.5$ D) simulations." + These simulations allowed au investigation of outflows for a wide range of parameters., These simulations allowed an investigation of outflows for a wide range of parameters. + However. they supposed a fixed configuration of the poloidal magnetic field.," However, they supposed a fixed configuration of the poloidal magnetic field." + Two-dimensional (2.5D) simulations of outflows from accretion disks were performed by Uchida Shibata (1985). Shibata Uchida (1986). Stone Norma (1991). Matzuiioto et al. (," Two-dimensional $2.5$ D) simulations of outflows from accretion disks were performed by Uchida Shibata (1985), Shibata Uchida (1986), Stone Norman (1994), Matsumoto et al. (" +1996).,1996). + These simulations led to stronely ion-stationary accretion and outflows from the disk., These simulations led to strongly non-stationary accretion and outflows from the disk. + Iu nost of these studies. the uon-stationaritv of the solutions is due to the start up conditions with the disk rotating mit the corona of the disk not rotating.," In most of these studies, the non-stationarity of the solutions is due to the start up conditions with the disk rotating but the corona of the disk not rotating." + In other cases he non-stationaritv is due to the disk rotating at a sienificautly sub-IKepleriauu rate., In other cases the non-stationarity is due to the disk rotating at a significantly sub-Keplerian rate. + These smiulatious are valuable iu showing that temporary ΑΠΟ outflows are xossible. but the results depeud strongly on the assumed initial conditions.," These simulations are valuable in showing that temporary MHD outflows are possible, but the results depend strongly on the assumed initial conditions." + Iu order to avoid the strong dependence ou initial conditions and the problems associated with following he internal dvuamics of the accretion disk. we earlier xoposed treating the outer. surface lavers ofthe disk as a )mndary condition (Ustvugova et al.," In order to avoid the strong dependence on initial conditions and the problems associated with following the internal dynamics of the accretion disk, we earlier proposed treating the outer, surface layers of the disk as a boundary condition (Ustyugova et al." + 1995: IKoldoba et al., 1995; Koldoba et al. + 1996: Romanova et al., 1996; Romanova et al. + 1997: Romanova et al., 1997; Romanova et al. + 1998)., 1998). + This approach has been followed by others (Ouved Pudritz 1997: Ouved. Pudritz Stone 1997: Meier et al.," This approach has been followed by others (Ouyed Pudritz 1997; Ouyed, Pudritz Stone 1997; Meier et al." + 1997)., 1997). + Iu these simmlatious the “disk” represents au outer laver of the accretion disk., In these simulations the “disk” represents an outer layer of the accretion disk. + In actual situation. the outfowing uatter will affect the disk evolution. or at least to the evolution of the surface lavers of the disk.," In actual situation, the outflowing matter will affect the disk evolution, or at least to the evolution of the surface layers of the disk." + The augular uonmentun carried away by ΑΠ) outflows can give a disk accretion rate mich larger than the viscous accretion rate of sav an a-disk. but the accretion speeds are typically uuch smaller than the free-fall speed (Lovelace. Bomauova Newman 1991: Lovelace. Newman Romanova 1997).," The angular momentum carried away by MHD outflows can give a disk accretion rate much larger than the viscous accretion rate of say an $\alpha$ -disk, but the accretion speeds are typically much smaller than the free-fall speed (Lovelace, Romanova Newman 1994; Lovelace, Newman Romanova 1997)." + Thus. the disk can be treated as stationary during the ormation aud establishment of MITD outflows which takes ace on a free-fall time scale.," Thus, the disk can be treated as stationary during the formation and establishment of MHD outflows which takes place on a free-fall time scale." + However. the long-time sinulatious of outflows including the back reaction on the disk are clearly of iuterest for future research.," However, the long-time simulations of outflows including the back reaction on the disk are clearly of interest for future research." + Different initial iiagnetic field configurations have becu asstuned im earlier studies., Different initial magnetic field configurations have been assumed in earlier studies. + The initial Seld assmnued bv Ouved Pudrtz (1997) was the Cao Spruit (1991) ποια which decreases slowly with radial distance on the disks surface., The initial field assumed by Ouyed Pudritz (1997) was the Cao Spruit (1994) field which decreases slowly with radial distance on the disk's surface. + On the other hand. the initial magnetic field of Ustvugova et al. (," On the other hand, the initial magnetic field of Ustyugova et al. (" +1995) was the splitaonopole field (Sakurai 1978: 1985). which decreases rapidly with radial distance ou the disk surface.,"1995) was the split-monopole field (Sakurai 1978; 1985), which decreases rapidly with radial distance on the disk surface." + The temperature of matter outflowing from the disk of Ouved Pudritz (1997) was sinall. and the initial maeuetic field was weak.," The temperature of matter outflowing from the disk of Ouyed Pudritz (1997) was small, and the initial magnetic field was weak." + However. Ouved Pudzritz (1997) introduced a spectrum of turbulent Alfvén waves with a high pressure which is ndlar to having a high temperature corona.," However, Ouyed Pudritz (1997) introduced a spectrum of turbulent Alfvénn waves with a high pressure which is similar to having a high temperature corona." + Thus the approach of Ouved Pudvitz (1997) is similar to that of Ustvugova ot al. (, Thus the approach of Ouyed Pudritz (1997) is similar to that of Ustyugova et al. ( +1995) where the magnetic field is wea- and the coronal temperature is high.,1995) where the magnetic field is weak and the coronal temperature is high. + In both papers. tlic initial twist of the maguetie Ποια results from the cis- rotation because the corona is not rotating.," In both papers, the initial twist of the magnetic field results from the disk rotation because the corona is not rotating." + This twisting of the mmaenetic field eives the collimation observed iu both papers., This twisting of the magnetic field gives the collimation observed in both papers. + It is portant to eet stationary outflows usus time-dependent ATID cquations because the nou-stationary flows may be artifacts of the initial conditions., It is important to get stationary outflows using time-dependent MHD equations because the non-stationary flows may be artifacts of the initial conditions. +" Stationary magneto-ceutriftugally driven outflows for relatively low temperature of the ""disk inatter were obtained in the 2.5D suuulatious by Romanova oet al. (", Stationary magneto-centrifugally driven outflows for relatively low temperature of the “disk” matter were obtained in the $2.5$ D simulations by Romanova et al. ( +1997) for the case where the initial magnetic field was a “tapered” split monopole type field.,1997) for the case where the initial magnetic field was a “tapered” split monopole type field. + This work found that iu the stationary state the outflow was quasi-spherical with essentially no collimation within the simulation region., This work found that in the stationary state the outflow was quasi-spherical with essentially no collimation within the simulation region. + Close to the disk the outflow was driven by the ceutrifugal force while at larger distances the maguetic force was dominant., Close to the disk the outflow was driven by the centrifugal force while at larger distances the magnetic force was dominant. + Tn this work we investigate the case of a pure (that is. non-tapered) split-anonopole magnetic field bv axisvuuunetrie (2.5D) αποΊσα. simulations.," In this work we investigate the case of a pure (that is, non-tapered) split-monopole magnetic field by axisymmetric (2.5D) numerical simulations." + The luotivation was to study ΑΠΟ outiows from a relatively cold accretion disk where maguetic field lines are iuclined away from the syauiuetrv axis., The motivation was to study MHD outflows from a relatively cold accretion disk where magnetic field lines are inclined away from the symmetry axis. + To remove the influence of the region near the axis where magnetic field lies are not significantly inclined. we pushed hot matter frou the disk in the small area around the axis.," To remove the influence of the region near the axis where magnetic field lines are not significantly inclined, we pushed hot matter from the disk in the small area around the axis." + We compare our simulation results with the theory of stationary MIID flows., We compare our simulation results with the theory of stationary MHD flows. + Further. we use our stationary simulation flows to investigate the influence of outer boundary conditions.," Further, we use our stationary simulation flows to investigate the influence of outer boundary conditions." + Qur earlier study. (Romanova et al., Our earlier study (Romanova et al. + 1997) showed that sole simple outer boundary conditious ou the toroidal magnetic field can lead to artificial forces on the boundary which significantly influence the flow within the simulation region., 1997) showed that some simple outer boundary conditions on the toroidal magnetic field can lead to artificial forces on the boundary which significantly influence the flow within the simulation region. + Here. we consider in further detail the influence of outer boundary conditions ou the calculated flows.," Here, we consider in further detail the influence of outer boundary conditions on the calculated flows." + Iu 82 the theory of stationary ΑΠΟ flows ds briefly reviewed., In 2 the theory of stationary MHD flows is briefly reviewed. + hi 82 the munerical model is prescuted., In 3 the numerical model is presented. + The influence of the outer boundary condition on the toroidal magnetic field aud the shape of the computational region is analyzed in &1., The influence of the outer boundary condition on the toroidal magnetic field and the shape of the computational region is analyzed in 4. + In 85 we present results of simulations of stationary flows aud compare them with theory., In 5 we present results of simulations of stationary flows and compare them with theory. + In 86 conclusious of this work are stuutatrized., In 6 conclusions of this work are summarized. + The theory of stationary. axisviunietric. ideal ATID flows was developed by Chandrasckhar (1956). Woltjer (1959). Mestel (1961). ISulikovskvi Lyubimov (1962). and others.," The theory of stationary, axisymmetric, ideal MHD flows was developed by Chandrasekhar (1956), Woltjer (1959), Mestel (1961), Kulikovskyi Lyubimov (1962), and others." +" Under these couditious the MIID. equations can be reduced to a single equation for the ""fiux function” Wort) dn cevliudneal (roo.2) coordinates (Πασά Olbert 1975: Lovelace et al."," Under these conditions the MHD equations can be reduced to a single equation for the “flux function” $\Psi(r,z)$ in cylindrical $(r,\phi,z)$ coordinates (Heinemann Olbert 1978; Lovelace et al." + 1986)., 1986). + The fiux function V labels fiux surfaces so that Wor2} —coust represcuts the," The flux function $\Psi$ labels flux surfaces so that $\Psi(r,z)=$ const represents the" +photometry. leading to an estimated. range of Mg of -]19.4 to -22.8 for the Coma cluster ellipticals. ancl -19.8 to -22.5 for the field. and. cluster cllipticals discussed. by James and Mobasher (1999).,"photometry, leading to an estimated range of $_R$ of -19.4 to -22.8 for the Coma cluster ellipticals, and -19.8 to -22.5 for the field and cluster ellipticals discussed by James and Mobasher \shortcite{ja:99}." +.. We investigated whether the dilferences in COpy scatter shown in Fig., We investigated whether the differences in $_{EW}$ scatter shown in Fig. + 2 result. from these dillerences in luminosity range by regressing py on absolute magnitude. anc studying the distributions of COi residuals about the best-lit lines.," 2 result from these differences in luminosity range by regressing $_{EW}$ on absolute magnitude, and studying the distributions of $_{EW}$ residuals about the best-fit lines." + The distributions of these residuals are shown in Fig., The distributions of these residuals are shown in Fig. + 3., 3. + The dashed. ciagonally shaded: columns. represent. the residuals for the BCCs: the thick. dotted. columns are those for the Coma eluster galaxies: ancl the solid lines represent the residuals for the field. group and cluster galaxies from James ancl Mobasher (19099)..," The dashed, diagonally shaded columns represent the residuals for the BCGs; the thick, dotted columns are those for the Coma cluster galaxies; and the solid lines represent the residuals for the field, group and cluster galaxies from James and Mobasher \shortcite{ja:99}. ." + The standard deviations of the gi residuals are 0.133 noi for the BCGs. 0.221 nm for the Coma ellipticaLg and 0.419 nm for the cluster plus feld. ellipticals.," The standard deviations of the $_{EW}$ residuals are 0.133 nm for the BCGs, 0.221 nm for the Coma ellipticals, and 0.419 nm for the cluster plus field ellipticals." + This reinforces the conclusion [rom Fig., This reinforces the conclusion from Fig. + 2 that the BCCs have substantially more homogeneous CO strengths than the other elliptical galaxies studied. and this result. does. not appear to be a selection elfect caused by the small luminosity. range of the BCCs.," 2 that the BCGs have substantially more homogeneous CO strengths than the other elliptical galaxies studied, and this result does not appear to be a selection effect caused by the small luminosity range of the BCGs." + Vhis uniformity in gi values is the main result. o£ this paper. and it is important to consider what it implies in terms of dilferences between BCGs and other ellipticals.," This uniformity in $_{EW}$ values is the main result of this paper, and it is important to consider what it implies in terms of differences between BCGs and other ellipticals." + oth high metallicity ancl recency of star formation. are expected to increase py values., Both high metallicity and recency of star formation are expected to increase $_{EW}$ values. + The ellect of metallicity on COpgiw values can he estimated. for the galaxies. with measured Ales indices. using the following method.," The effect of metallicity on $_{EW}$ values can be estimated for the galaxies with measured $_2$ indices, using the following method." + From Fig., From Fig. + 37 of Worthey (1994).. a change in. Fe/1l] from -0.25 to 0.00 changes the Ales index [rom 0.216 to 0.258. and the change is approximately linear over the modelled range.," 37 of Worthey \shortcite{wo:94}, a change in [Fe/H] from -0.25 to 0.00 changes the $_2$ index from 0.216 to 0.258, and the change is approximately linear over the modelled range." + Thus we infer a relation of the form Dovon et al., Thus we infer a relation of the form Doyon et al. + (1994). lind a relation between: Fe/L] and their CO index ος. and from the definitions in. Puxley. et al.," \shortcite{do:94} find a relation between [Fe/H] and their CO index $_{sp}$, and from the definitions in Puxley et al." +" (1997) dt is straightforward to convert from the index CO., to COzgw.", \shortcite{pu:97} it is straightforward to convert from the index $_{sp}$ to $_{EW}$. + Then.the measured scatter in Me». index of 0.029. for he BCGs should. cause a scatter of 0.060 nm in CO. of the observed scatter.," Then,the measured scatter in $_2$ index of 0.029 for the BCGs should cause a scatter of 0.060 nm in $_{EW}$, of the observed scatter." + For Coma ellipticals. the nmieasured Ales scatter is 0.024. equivalent to a scatter of 1.049 nm in Όρη. of that observed. ancl for the ield ancl cluster sample. the Mg» scatter is 0.030. ancl the wedicted COk scatter 0.062 nm. of that observed.," For Coma ellipticals, the measured $_2$ scatter is 0.024, equivalent to a scatter of 0.049 nm in $_{EW}$, of that observed, and for the field and cluster sample, the $_2$ scatter is 0.030, and the predicted $_{EW}$ scatter 0.062 nm, of that observed." + ote also that the scatters in Ales values are very. similar in the three subsamples. whereas they have very. cillerent COR istributions.," Note also that the scatters in $_2$ values are very similar in the three subsamples, whereas they have very different $_{EW}$ distributions." + Thus. we conclude that metallicity dilferences have little ellect on the measured. ey values or the elliptical. galaxies studied here. and. propose that star formation history is the dominant [actor causing the arger scatter for non-BCC ellipticals.," Thus, we conclude that metallicity differences have little effect on the measured $_{EW}$ values for the elliptical galaxies studied here, and propose that star formation history is the dominant factor causing the larger scatter for non-BCG ellipticals." + Lf so. the differences in the distributions of (μη. shown in Fig.," If so, the differences in the distributions of $_{EW}$, shown in Fig." + 2 would be he result. of wider variations in star formation history [or general field and cluster ellipticals than for the Εςας., 2 would be the result of wider variations in star formation history for general field and cluster ellipticals than for the BCGs. + This indicates that Εςας formed their stars very carly: if there its been more recent star formation in these galaxies then he rate of star formation as a function of epoch must have en very uniform [rom galaxy to galaxy., This indicates that BCGs formed their stars very early; if there has been more recent star formation in these galaxies then the rate of star formation as a function of epoch must have been very uniform from galaxy to galaxy. + Given the narrow range in BCG CO values. it is unrealistic to expect very strong. correlations with other BCG parameters.," Given the narrow range in BCG $_{EW}$ values, it is unrealistic to expect very strong correlations with other BCG parameters." + Nevertheless. Fig.," Nevertheless, Fig." + 4 does show a good correlation with absoluteR-banc magnitude in a 10 kpe metric aperture. Mg. with a correlation coefficient. of 0.51 and a probability of that this represents a true," 4 does show a good correlation with absoluteR-band magnitude in a 10 kpc metric aperture, $_R$ with a correlation coefficient of 0.51 and a probability of that this represents a true" +the level outside of Dares. and three long HI observations between 12/95 and 7/96 show average of Ly = 15.4. 6.6. and 5.0.LO erg st.,"the level outside of flares, and three long HRI observations between 12/95 and 7/96 show average of $_{X}$ = 15.4, 6.6, and $5.0\times10^{28}$ erg $^{-1}$." + To investigate this further. we performed a statistical analysis of the complete X-ray light curve to determine the minimum fraction of counts due to Lares. and the minimunr raction of time spent in a Daring state.," To investigate this further, we performed a statistical analysis of the complete X-ray light curve to determine the minimum fraction of counts due to flares, and the minimum fraction of time spent in a flaring state." + We assumed a truly non-variable. quiescent background rate exists that can be described. by a Poisson distribution.," We assumed a truly non-variable, quiescent background rate exists that can be described by a Poisson distribution." + We then. determined he fraction of counts due to Lares by integrating the counts eft unexplained by a least squares fit of a Poisson function o the low end of the count rate clistribution (Saar Bookbinder 1998)., We then determined the fraction of counts due to flares by integrating the counts left unexplained by a least squares fit of a Poisson function to the low end of the count rate distribution (Saar Bookbinder 1998). + We averaged the results of fits using several reasonable count rate binning sizes., We averaged the results of fits using several reasonable count rate binning sizes. + This analysis vields the Traction of [lare counts. since [lares xdow the instrument sensitivity. and possible quiescent level changes cue to rotation and evolution of magnetic regions ave all included in the derived quiescent level.," This analysis yields the fraction of flare counts, since flares below the instrument sensitivity, and possible quiescent level changes due to rotation and evolution of magnetic regions are all included in the derived quiescent level." + We find that (at least) 68 E of the PSPC counts and 59 + of the LIRE counts are due to flares., We find that (at least) 68 $\pm$ of the PSPC counts and 59 $\pm$ of the HRI counts are due to flares. + Upper limits to the uiescent [ux level and the fraction of time that the star is uiescent are also derived from the analvsis., Upper limits to the quiescent flux level and the fraction of time that the star is quiescent are also derived from the analysis. + We find that the (Poisson) mean quiescent count level is 0.022 + 0.001 counts + forthe PSPC (Lxz4.6502107 erg s 1) and 0.0056 + 0.0006 counts + for the LRL (Lxà5-40.610 ere +).," We find that the (Poisson) mean quiescent count level is 0.022 $\pm$ 0.001 counts $^{-1}$ for the PSPC $L_X \approx 4.6\pm 0.2 \times 10^{28}$ erg $^{-1}$ ) and 0.0056 $\pm$ 0.0006 counts $^{-1}$ for the HRI $L_X \approx 5.4\pm 0.6 +\times 10^{28}$ erg $^{-1}$ )." + The minimum fraction of time with a detectable Hare contribution to the observed Hux is 47 + (PSPC) and 41 + (LIRD., The minimum fraction of time with a detectable flare contribution to the observed flux is 47 $\pm$ (PSPC) and 41 $\pm$ (HRI). + All of the PSPC data was taken between 1990 ancl 1993. while the LI data include a significant fraction from. 1995 and 1996. with an exposure time weighted time cdillerence of ~1200 d. Thus it is possible that 10 small (~15%)) difference in the PSPC and. ΕΙ quiescent Huxes may be explained by time evolution of the quiet emission. due to ce.g.. long-term evolution in the numbers of active regions.," All of the PSPC data was taken between 1990 and 1993, while the HRI data include a significant fraction from 1995 and 1996, with an exposure time weighted time difference of $\sim$ 1200 d. Thus it is possible that the small $\sim$ ) difference in the PSPC and HRI quiescent fluxes may be explained by time evolution of the quiet emission, due to e.g., long-term evolution in the numbers of active regions." + Unfortunately. there are relatively few quiescent counts in the 1995-96 LEE data. making a cirect test of time variation inconclusive.," Unfortunately, there are relatively few quiescent counts in the 1995-96 HRI data, making a direct test of time variation inconclusive." + Further data over a longer timescale would help decide the level of the star's quiescent. coronal variablilitsy., Further data over a longer timescale would help decide the level of the star's quiescent coronal variablility. + We find that the quicseent and bolometric luminosity agree with the linear correlation between these quantities. as noted. by previous studies of lare stars (Pallavicini et al.," We find that the quiescent and bolometric luminosity agree with the linear correlation between these quantities, as noted by previous studies of flare stars (Pallavicini et al.," + 1990: Aerawal et aL.," 1990; Agrawal et al.," + 1986)., 1986). + We estimate à bolometric luminosity of 10% erg +. using Ady=11.7 and the bolometric correction of Pettersen (1983).," We estimate a bolometric luminosity of $\times10^{31}$ erg $^{-1}$, using $M_V = 11.7$ and the bolometric correction of Pettersen (1983)." + We extracted spectra from the brightest quiescent and fare PSPC images., We extracted spectra from the brightest quiescent and flare PSPC images. + During the longest pointing of this field. the source ος 2206.6|3517 was in quiescence (rplO0588) and olf-axis.," During the longest pointing of this field, the source 2E 2206.6+4517 was in quiescence (rp100588) and off-axis." + The data set corresponding to a [lare event with the highest number of source counts was rpl10591. for which the source was nearly on-axis )).," The data set corresponding to a flare event with the highest number of source counts was rp110591, for which the source was nearly on-axis )." + For the quicseent X-ray emission. we found. that. no single-component thermal plasma (Ravoonc ancl Smith 1978) model could. adequately fit the data.," For the quiescent X-ray emission, we found that no single-component thermal plasma (Raymond and Smith 1978) model could adequately fit the data." + Unfortunately. the signal to noise of our spectrum. was not sullicicnt to uniquely constrain a two-component model.," Unfortunately, the signal to noise of our spectrum was not sufficient to uniquely constrain a two-component model." + However. we found that models that did not contain a Itavmond-Smith component of kL1.0 keV. could be rejected (L6. 1).," However, we found that models that did not contain a Raymond-Smith component of $kT \approx 1.0$ keV could be rejected (i.e. $>> 1$ )." + hesemodcelssigni ficantlynunderprediclemission fromapprorinalel yd LOMA correspondinglothe Pek shellblend.," These models significantly underpredict emission from approximately 0.85-1.0 keV, corresponding to the Fe L-shell blend." +" Llowever, withanappropriate” highlemperaliurethermealplasmar sstatistics much less than one. indicating that the mocels are not well constrained."," However, with an appropriate ""high"" temperature thermal plasma model, the remaining low temperature emission has statistics much less than one, indicating that the models are not well constrained." +" Despite the poorly constrained two component model. the spectral fit suggests the existence of a coronal plasma of ki21 keV. A comparison of the normalizations of the two models shows that the ""hot"" and “cool” components contribute nearly equal flux in the PSPC band (Table 43)."," Despite the poorly constrained two component model, the spectral fit suggests the existence of a coronal plasma of $kT \approx 1$ keV. A comparison of the normalizations of the two models shows that the “hot” and “cool” components contribute nearly equal flux in the PSPC band (Table \ref{spec_fit}) )." + Because of the fewer counts in the fare observation. a larger binning factor was necessary to provide a significant S/N for spectral fitting.," Because of the fewer counts in the flare observation, a larger binning factor was necessary to provide a significant S/N for spectral fitting." + Llowever. we could not Lit the resulting spectrum with any one or two component model.," However, we could not fit the resulting spectrum with any one or two component model." + The heavy binning broadens the elfect of uncertain calibration features. particularly the PSPC window carbon edge at 0.4 keV. To compare the quiescent and fare spectra. we must mitigate this elfect.," The heavy binning broadens the effect of uncertain calibration features, particularly the PSPC window carbon edge at 0.4 keV. To compare the quiescent and flare spectra, we must mitigate this effect." + The peaks and troughs in the spectra most allected by binning all occur below about. 1 keV. Using only the photons above 1 keV has the added advantage that the “hot” component dominates in this regime. so we may use a single temperature model.," The peaks and troughs in the spectra most affected by binning all occur below about 1 keV. Using only the photons above 1 keV has the added advantage that the ""hot"" component dominates in this regime, so we may use a single temperature model." + We fit both spectra in the energv range 1.0-1.5 keV with single temperature ΠανπιοηΗΕ mocel. using the value of {from the full quiescent spectrum.," We fit both spectra in the energy range 1.0-1.8 keV with single temperature Raymond-Smith model, using the value of from the full quiescent spectrum." + Ao direct comparison of the Hare ancl quiescent normalization shows an increase bv nearly a factor of 20 in emission measure., A direct comparison of the flare and quiescent normalization shows an increase by nearly a factor of 20 in emission measure. + In addition. though the temperatures are not very well constrained. their le errors just barely overlap. indicating that the increase in X-ray emission was Likely. accompanied by an increase in the plasma temperature.," In addition, though the temperatures are not very well constrained, their $1\sigma$ errors just barely overlap, indicating that the increase in X-ray emission was likely accompanied by an increase in the plasma temperature." + This is consistent with behavior seen during Dares in. late-tvpe active stars (οσο. Giampapa et al..," This is consistent with behavior seen during flares in late-type active stars ( e.g., Giampapa et al.," + 1996. Singh et al..," 1996, Singh et al.," + 1999)., 1999). + The small number of counts does. not allow a determination of a temperature variation during the are decay., The small number of counts does not allow a determination of a temperature variation during the flare decay. + To investigate the spectral evolution of the flare. we calculated hardness ratios (Figure 4).," To investigate the spectral evolution of the flare, we calculated hardness ratios (Figure 4)." + Phe count distribution appears to harden by about 40.—50% during the onset of the flare., The count distribution appears to harden by about $40-50\%$ during the onset of the flare. + A decrease of the hardness ratio during the decay is evident. without certainty due to limited count statistics., A decrease of the hardness ratio during the decay is evident without certainty due to limited count statistics. + Singh et al. (, Singh et al. ( +1999) found that Fe abundances for active chvart stars with loge (Lx/Li4)73.7 are strongly subsolar. whereas the Fe abundances in the [ess active stars are within a factor of 2 of the solar value.,"1999) found that Fe abundances for active dwarf stars with log $(L_X/L_{\rm bol})>-3.7$ are strongly subsolar, whereas the Fe abundances in the less active stars are within a factor of 2 of the solar value." + Since the quiescent luminosity ratio for δις 2206.6|4517 hovers near this value. low abuncances may. also alfect our N-ray. spectral fits.," Since the quiescent luminosity ratio for 2E 2206.6+4517 hovers near this value, low abundances may also affect our X-ray spectral fits." + On the other hand. Dare activity has been observed to increase the apparent elemental. abundances (Ottman Schmitt 1996).," On the other hand, flare activity has been observed to increase the apparent elemental abundances (Ottman Schmitt 1996)." +extended ciunission atÀx21yan (e.g. Figure 2)).,extended emission at$\lambda \le 24 ~\micron$ (e.g. Figure \ref{mapfig}) ). +" Tucreasing the ISRF improves the overall ft of all models. but does not change the best-fittiug euvelope parameters, because the SED peal depends primarily ou fixed parameters (AL... ISRE)."," Increasing the ISRF improves the overall fit of all models, but does not change the best-fitting envelope parameters, because the SED peak depends primarily on fixed parameters , ISRF)." +"Figure 1. show the probabilities of each Jovian planet being excited to an eccentricity greater than 0.1 as a function of M. and X, in a fully relaxed embedded cluster (i.e. ari —5/3 corresponding to o;=J/(GM.)/ R.).",Figure \ref{fig:Jovian} show the probabilities of each Jovian planet being excited to an eccentricity greater than 0.1 as a function of $M_{c}$ and $\Sigma_{c}$ in a fully relaxed embedded cluster (i.e. $\alpha_{vir}=$ 5/3 corresponding to $\sigma_{v}=\sqrt{(GM_{c})/R_{c}}$ ). +" We use a range of 1071-100? g cm-? for X, because this covers the range of embedded cluster properties complied by ?..", We use a range of $^{-1}$ $^{0.5}$ g $^{-2}$ for $\Sigma_{c}$ because this covers the range of embedded cluster properties complied by \citet{FallEtAl-2010}. +" Similarly, we use masses from 10?-10°Mo because this covers the range of cluster masses seen in nearby galaxies and in the Milky Way (???).."," Similarly, we use masses from $^{2}$ $^{6}$ $_{\odot}$ because this covers the range of cluster masses seen in nearby galaxies and in the Milky Way \citep{LadaLada-2003,FallEtAl-2009,ChandarEtAl-2010}." +" Looking at the four graphs, we see that the probability is very low for all four planets in almost all combinations of X. and M, within the plausible range of mass and surface density."," Looking at the four graphs, we see that the probability is very low for all four planets in almost all combinations of $\Sigma_{c}$ and $M_{c}$ within the plausible range of mass and surface density." + The probability is less than for all four Jovian planets when the mass of the cluster is greater than 104*Mo., The probability is less than for all four Jovian planets when the mass of the cluster is greater than $^{4}M_{\odot}$. +" Neptune, the furthest planet from the Sun and thus the most likely to be excited, has excitation probabilities «196 over most of parameter space, and reaches a high of at M,=10?Mo, X,=109? g επι”."," Neptune, the furthest planet from the Sun and thus the most likely to be excited, has excitation probabilities $<$ over most of parameter space, and reaches a high of at $M_{c}=10^2M_{\odot}$, $\Sigma_{c}=10^{0.5}$ g $^{-2}$." +" A curious feature of Jovian is that as the mass of the cluster increases, the reffig:probability of an event decreases."," A curious feature of \\ref{fig:Jovian} is that as the mass of the cluster increases, the probability of an event decreases." +" To understand this, we first must realize that the number of encounters is independent of M, at fixed Σ.."," To understand this, we first must realize that the number of encounters is independent of $M_{c}$ at fixed $\Sigma_{c}$." + This is because AοςReterossM.ox MO., This is because $\Lambda \propto \frac{n_{c}t_{cross}} {\sigma_{v}^{3}}M_{c} \propto M^{0}_{c}$ . +" Next, looking at equation (8)) we see that as M, increases, so does the velocity dispersion."," Next, looking at equation \ref{eq:VelocityDispersion}) ) we see that as $M_{c}$ increases, so does the velocity dispersion." + Figure 2 shows the velocity dependence of the cross section obtained though our simulation., Figure \ref{fig:JovImpact} shows the velocity dependence of the cross section obtained though our simulation. +" We see that, at low velocities around 1 the cross section is high, comparable to the values km/s,obtained by ?.."," We see that, at low velocities around 1 km/s, the cross section is high, comparable to the values obtained by \citet{AdamsLaughlin-2001}." +" However, at slightly higher velocities the cross section dramatically decreases, dropping under at around 3 km/s. Thus, at higher M, the velocity(200 AU)?dispersion increases yet the number of encounters does not."," However, at slightly higher velocities the cross section dramatically decreases, dropping under (200 $^{2}$ at around 3 km/s. Thus, at higher $M_{c}$ the velocity dispersion increases yet the number of encounters does not." +" This explains the result inreffig:Jovian: higher mass clusters are less likely to increase a Jovian planet’s eccentricity because they produce no more encounters (at fixed 3), but reduce the effective cross section per encounter."," This explains the result in: higher mass clusters are less likely to increase a Jovian planet's eccentricity because they produce no more encounters (at fixed $\Sigma_{c}$ ), but reduce the effective cross section per encounter." +" Recent observational and theoretical evidence indicates that young embedded clusters can be sub-virial (???) and thus we make the same calculations for a cluster with 8 virial parameter that is one fifth the value of a fully relaxed cluster, @yir =1/3."," Recent observational and theoretical evidence indicates that young embedded clusters can be sub-virial \citep{FureszEtAl2008,TobinEtAl-2009,OffnerEtAl-2009} and thus we make the same calculations for a cluster with a virial parameter that is one fifth the value of a fully relaxed cluster, $\alpha_{vir}=$ 1/3." + Figure 3 shows probability of exciting a Jovian planet to an eccentricity greater than 0.1 in a sub-virial cluster., Figure \ref{fig:JovianVir} shows probability of exciting a Jovian planet to an eccentricity greater than 0.1 in a sub-virial cluster. +" We see that the probability is higher than that of a relaxed cluster, which makes sense due to the lower velocity dispersions, but the overall probability is still small."," We see that the probability is higher than that of a relaxed cluster, which makes sense due to the lower velocity dispersions, but the overall probability is still small." +" Again, Neptune is the likeliest to be excited with ~15% probability at the high X, low M, extreme, but as in a relaxed cluster, a majority of parameter space produces probability below for all of the Jovian planets."," Again, Neptune is the likeliest to be excited with $\sim$ probability at the high $\Sigma_{c}$, low $M_{c}$ extreme, but as in a relaxed cluster, a majority of parameter space produces probability below for all of the Jovian planets." +" This agrees with ? who show that the interaction rate in a sub-virial cluster is greater than that in a virialized one, but not by much."," This agrees with \citet{ProszkowAdams-2009} who show that the interaction rate in a sub-virial cluster is greater than that in a virialized one, but not by much." + We next check if close encounters could truncate the Kuiper Belt or excite an object to a Sedna-like orbit., We next check if close encounters could truncate the Kuiper Belt or excite an object to a Sedna-like orbit. +" To determine if the a close encounter could truncate the Kuiper Belt, we compute the expected fraction of the KBOs in each of our eight initial distance bins (see Section 2.1 for derivation)."," To determine if the a close encounter could truncate the Kuiper Belt, we compute the expected fraction of the KBOs in each of our eight initial distance bins (see Section 2.1 for derivation)." +" The resulting expected fractions in the 35-80AU and 455-500AU bins, which represent the extremes of our initial Kuiper Belt, are show in for relaxed clusters and for sub-virial clusters."," The resulting expected fractions in the 35-80AU and 455-500AU bins, which represent the extremes of our initial Kuiper Belt, are show in \\ref{fig:KBOLost01CT} for relaxed clusters and \\ref{fig:KBOLostVir01CT} for sub-virial clusters." +" We find that the expected fraction of KBOs stripped in the 35- bin is less than for most of parameter space,"," We find that the expected fraction of KBOs stripped in the 35-80AU bin is less than for most of parameter space," +"using the relation Ay/.A, = 0.142 (Rieke Lebolskyv 1955).",using the relation $A_H/A_V$ = 0.142 (Rieke Lebofsky 1985). + Thus the estimated Ay values for HIP13855 and IIDI90067 were 0.023 and 0.01 magnitudes., Thus the estimated $A_H$ values for HIP13855 and HD190067 were 0.028 and 0.01 magnitudes. + Figures 1 2 show II and Ix images of WD1900G67 and 11IP138555 along with their faint companions respectively., Figures 1 2 show H and K images of HD190067 and HIP13855 along with their faint companions respectively. + 11D190067 is a disk star (Eggen 1987). and based on its velocity components in the disk it seems that its age could be anything between 0.5 Gvrs to a few Gvrs (Eggen 1937. Mihilas Binney 1931).," HD190067 is a disk star (Eggen 1987), and based on its velocity components in the disk it seems that its age could be anything between 0.5 Gyrs to a few Gyrs (Eggen 1987, Mihilas Binney 1981)." + 11D13855 is at a distance of 74 pe (Hipparcos catalogue) a foreground star towards the star forming cloud MDMI2. whose distance is estimated to be somewhere between 90 pe to 275 pc (Lulimman 2001).," HIP13855 is at a distance of 74 pc (Hipparcos catalogue) a foreground star towards the star forming cloud MBM12, whose distance is estimated to be somewhere between 90 pc to 275 pc (Luhman 2001)." + AIBA 12 cloud contain very voung stars wilh ages 10 to LOO Myrs (IIeartv et al., MBM 12 cloud contain very young stars with ages 10 to 100 Myrs (Hearty et al. + 2000b)., 2000b). + Some members of the MDMI?2 cluster. however. are much closer: [or example. ILD17332 is at a distance of 33 pe (1ipparcos catalogue).," Some members of the MBM12 cluster, however, are much closer; for example, HD17332 is at a distance of 33 pc (Hipparcos catalogue)." + ILID1T232 is à young GIV star. since lithium is detected in its spectrum (IIearty et al.," HD17332 is a young G1V star, since lithium is detected in its spectrum (Hearty et al." + 2000b)., 2000b). + We qualitatively argue on (he basis of its proximity (hat HIP13855 could be associated with the MDMI2 cluster: however. there is no record of lithium detection in its spectrum.," We qualitatively argue on the basis of its proximity that HIP13855 could be associated with the MBM12 cluster; however, there is no record of lithium detection in its spectrum." + So we assume a lower limit for the age of IHIP13855 could be LOO Myrs (Ilearty et al., So we assume a lower limit for the age of HIP13855 could be 100 Myrs (Hearty et al. + 2000b)., 2000b). + Burrows et al. (, Burrows et al. ( +1997) developed models for voung substellar dwarls of various ages that show a similar trend. of absolute magnitudes vs NIR. infrared. colors for voung substellar dwarls that are less than 1.0 Gvrs.,1997) developed models for young substellar dwarfs of various ages that show a similar trend of absolute magnitudes vs NIR infrared colors for young substellar dwarfs that are less than 1.0 Gyrs. + Similar models of evolution of brown dwarls aud low mass stars with a time scale [rom less (han 100 Mrs to LO Gyrs have shown that the hydrogen burning limit is somewhere between 0.072 (o 0.075312. and the corresponding spectral (wpe varies wilh age (M6.5 at LOO Myrs to L4 al LOGvis (Baralle οἱ al., Similar models of evolution of brown dwarfs and low mass stars with a time scale from less than 100 Myrs to 10 Gyrs have shown that the hydrogen burning limit is somewhere between 0.072 to $M_{\odot}$ and the corresponding spectral type varies with age (M6.5 at 100 Myrs to L4 at 10Gyrs (Baraffe et al. + 1998 and 2001. Ixirkpatrick 1999b. Dasri 2000).," 1998 and 2001, Kirkpatrick 1999b, Basri 2000)." + Figure 3 shows such evolution model curves from, Figure 3 shows such evolution model curves from +a candidate tvpe-2 QSO. although more observations. are required to confirm the redshift measurements and to search for broad emission line components.,"a candidate type-2 QSO, although more observations are required to confirm the redshift measurements and to search for broad emission line components." + More. details on the properties of this source are given in Appendix ??.., More details on the properties of this source are given in Appendix \ref{app1}. + Figure 1. plots /-bancl maenitude against 2-8kkeV. X-ray lux., Figure \ref{fig_fxfo} plots $R$ -band magnitude against keV X-ray flux. + The log(fxιν)=3El lines in this figure delincate, The $\log (f_X/f_{opt})=\pm1$ lines in this figure delineate +of the three iudividual observations. showing up only in the combined frame.,"of the three individual observations, showing up only in the combined frame." + It is a relatively weak source aud its position accordingly has an error of 175 both in right ascension and in declination., It is a relatively weak source and its position accordingly has an error of $1\farcs5$ both in right ascension and in declination. + The shift required to brine X119 in coincidence with TYC 222811 is eiven in refta.. and has been :yplied to all positions of the N-rav sources: the resultiug xositious are listed im το αν. (," The shift required to bring 19 in coincidence with TYC 1 is given in \\ref{ta}, and has been applied to all positions of the X-ray sources; the resulting positions are listed in \\ref{tabb}. (" +The romaine offset between X111 and 991235 is within the nonmünal error for the right ascension. and within 2-sigma for the declination: note hat the error is composed of the statistical uncertainties in the positions of th 119 and 111.),"The remaining offset between 11 and 94235 is within the nominal error for the right ascension, and within 2-sigma for the declination: note that the error is composed of the statistical uncertainties in the positions of both 19 and 11.)" +" The detection linut iu the total observation is about ""S2 . ∣⋅∣∖∩⊔↸∖↥⋅∶↴∙⊾↸⊳⋯−↴∖↴↓∙"," The detection limit in the total observation is about $0.7\times10^{-14}\,\ergcms$." +⊀≚∐⋜⋯∖⋜↧↖↖↽↕↑↕⊔⋅⋜⊔∐∏↴∖↴∟⋗∙∣⋅↱⊐↕∐↑∐↸∖ ⋅↽⊲⋅ ROSAT Deep Survey coutaius 25 sources brighter than lis limit: we thus expect to find 0.6 in the region within he half-imass radius of 66752. 7j~2’.," An area with radius $12\farcm5$ in the ROSAT Deep Survey contains 25 sources brighter than this limit; we thus expect to find 0.6 in the region within the half-mass radius of 6752, $r_h\simeq2'$." + The sources in he core thus probably beloug to the cluster. aud possibly he two sources 66/À and ILI/D as well.," The sources in the core thus probably belong to the cluster, and possibly the two sources 6/A and 14/D as well." + Analvsiug the central source with the method described in Sect.22. we find four significant sources (the merease in lu£ is 29 both for the third aud for he fourth source).," Analysing the central source with the method described in 2, we find four significant sources (the increase in $\ln L$ is 29 both for the third and for the fourth source)." + This adds two sources to the two already. described by Grindlay (1993)., This adds two sources to the two already described by Grindlay (1993). + The position aud fuxes of these sources are listed in Table 6:: reffienecc— shows the positions aud X-ray contours of the center of 66752. together with the positious of the two ciudidate cataclysimic variables found by. Bailvu et (1996).," The position and fluxes of these sources are listed in Table \ref{tabb}; \\ref{figngcc} shows the positions and X-ray contours of the center of 6752, together with the positions of the two candidate cataclysmic variables found by Bailyn et (1996)." +" The southern cataclysimic variable (star Uy is at ιδο οι N77a. aud therefore remains a possible counterpart (assuming au error of 1"" for the optical position. aud taking into account the 2” CITOY O: X119)."," The southern cataclysmic variable (`star 1') is at $3.8\pm2.3''$ from 7a, and therefore remains a possible counterpart (assuming an error of $''$ for the optical position, and taking into account the $''$ error of 19)." + We have analysed the separate observations. keepiug the position of the four central sources fixed. at those of the co-added image (as listed in reftabb)). but allowing their fluxes to vary.," We have analysed the separate observations, keeping the position of the four central sources fixed at those of the co-added image (as listed in \\ref{tabb}) ), but allowing their fluxes to vary." + We do not find significant evidence for variation: due to the Ilmüte statistics we cannot exclude variations by a factor two., We do not find significant evidence for variation; due to the limited statistics we cannot exclude variations by a factor two. + A countrate ofd ccorresponds to a huninosity between 15 and 2.5 keV of L6«1077 aat the distance of 66752 and. for an ASSTHLLLC( kkeV. brenisstralilung spectrum., A countrate of 1 corresponds to a luminosity between 0.5 and 2.5 keV of $4.6\times 10^{31}$ at the distance of 6752 and for an assumed keV bremsstrahlung spectrum. + Thus. 77a aud 77b have N-ray luuinosities of about 7.5«10?!Cres. and X221 aud X222 about a quarter of this.," Thus, 7a and 7b have X-ray luminosities of about $7.5\times10^{31}$, and 21 and 22 about a quarter of this." + 66 aud X1LI. the two sources outside the cluster core have luniuosities of L6«10°! ," 6 and 14, the two sources outside the cluster core have luminosities of $4.6\times 10^{31}$ " +are valid.,are valid. + As discussed in Sect., As discussed in Sect. + 41. the number of YSOs in 1€1396W. is likely to be around. LO or less., \ref{census} the number of YSOs in IC1396W is likely to be around 10 or less. + Assuming an average mass of ~0.5AJ. gives a total stellar mass of M. and a star forming clliciency SEI around.," Assuming an average mass of $\sim 0.5\,M_{\odot}$ gives a total stellar mass of $\,M_{\odot}$ and a star forming efficiency SFE around." +.. This can be compared with SEIS values. determined: for nearby star forming regions: According to ? star formation is significantly. more cllicient 3%)) in lll. Lupus. Perseus. Serpens. and. Ophiuchus.," This can be compared with SFE values determined for nearby star forming regions: According to \citet{2009ApJS..181..321E} star formation is significantly more efficient $\ge 3$ ) in II, Lupus, Perseus, Serpens, and Ophiuchus." + With the exception of LLL. these clouds are much more massive than 1C1396W. On the other hand. 101396W. is comparable in SEIS with cores without stellar clusters in Cepheus (2).. but exceeds all these regions in mass.," With the exception of II, these clouds are much more massive than IC1396W. On the other hand, IC1396W is comparable in SFE with cores without stellar clusters in Cepheus \citep{2009ApJS..185..198K}, but exceeds all these regions in mass." + Thus. our survey establishes LOL396W as an intermediate case of a relatively massive cloud with low star formation elliciency.," Thus, our survey establishes IC1396W as an intermediate case of a relatively massive cloud with low star formation efficiency." + The SEE is still about one order of magnitude higher than in the Pipe nebula (0.064.2).. which appears to be a cloud in the earliest. phases of star formation.," The SFE is still about one order of magnitude higher than in the Pipe nebula \citep[0.06\%,][]{2009ApJ...704..292F}, which appears to be a cloud in the earliest phases of star formation." + There ave indications that the radiation from the O6.5V star in the center of the HIE region 101396 has an impact on the star forming activity in the surrounding clouds (?).. ie. clouds at larger distances are bigger and less active.," There are indications that the radiation from the O6.5V star in the center of the HII region IC1396 has an impact on the star forming activity in the surrounding clouds \citep{2005A&A...432..575F}, i.e. clouds at larger distances are bigger and less active." + 1€C1396W is one of the more remote clouds in this region. the distance from the exciting bright star is around ppc.," IC1396W is one of the more remote clouds in this region, the distance from the exciting bright star is around pc." + This could explain why the star forming ellicieney in 101396NV is found to be low., This could explain why the star forming efficiency in IC1396W is found to be low. + While visually inspecting the lDighteurves. we noticed a number of obvious variable objects.," While visually inspecting the lightcurves, we noticed a number of obvious variable objects." + In the following we report on the most prominent examples. including two eclipsing binaries and 8 periodic variables.," In the following we report on the most prominent examples, including two eclipsing binaries and 8 periodic variables." + All these objects [ulfill the conditions for variable objects as outlined in Sect. J., All these objects fulfill the conditions for variable objects as outlined in Sect. \ref{var}. + For the eclipsing binaries we present. additional [ow-resolution spectra., For the eclipsing binaries we present additional low-resolution spectra. + Further analysis of these serencdipitouslv discovered objects is postponed for future studies., Further analysis of these serendipitously discovered objects is postponed for future studies. + In the field. of LOLB9GW there are two stars which show clear. deep eclipses in our lighteurves.," In the field of IC1396W there are two stars which show clear, deep eclipses in our lightcurves." + In. both cases we observe only one eclipse. i.e. we cannot constrain the period.," In both cases we observe only one eclipse, i.e. we cannot constrain the period." + Based on the symmetry. of the ellipses and the smooth ingress/egress. we interpret the sources as eclipsing binaries. although in principle other origins are conceivable (e.g... eclipses by circumstellar material).," Based on the symmetry of the ellipses and the smooth ingress/egress, we interpret the sources as eclipsing binaries, although in principle other origins are conceivable (e.g., eclipses by circumstellar material)." + The parameters of these systems are given in Table 2.. their lighteurves are plotted in lig. 5S..," The parameters of these systems are given in Table \ref{t3}, their lightcurves are plotted in Fig. \ref{f6}." + If these eclipsing binaries are associated with the voung population of 1€1396W. they are of particular interest. to constrain the fundamental properties of voung low-mass objects.," If these eclipsing binaries are associated with the young population of IC1396W, they are of particular interest to constrain the fundamental properties of young low-mass objects." + This motivated us to obtain follow-up. spectra to look for evidence of vouth., This motivated us to obtain follow-up spectra to look for evidence of youth. + Phe ISIS spectrograph at the William LHerschel Telescope was used to observe these objects with erisms RSs .pper pixel. mmin integration time. date 18/07/2008) and 11120011. «ρα pixel. 30nimin. 21/07/2007 and 13/10/2008).," The ISIS spectrograph at the William Herschel Telescope was used to observe these objects with grisms R158R per pixel, min integration time, date 18/07/2008) and R1200R per pixel, min, 21/07/2007 and 13/10/2008)." + ALL data was taken in Service Mode., All data was taken in Service Mode. + A spectroscopic standard reduction was carried. out for these spectra. including bias and Batfield correction and background. removal. by subtracting a onedimoensional fit along the spatial clirection.," A spectroscopic standard reduction was carried out for these spectra, including bias and flatfield correction and background removal by subtracting a onedimensional fit along the spatial direction." + The spectra are exetracted using within ΗΛΙΟ., The spectra are exctracted using within IRAF. + Wavelength calibration is done based on C'u-Xr are spectra., Wavelength calibration is done based on Cu-Ar arc spectra. + The low-resolution data is Εαν calibrated. based. on a spectrum for the standard star SP2157|261., The low-resolution data is flux calibrated based on a spectrum for the standard star SP2157+261. + Vhe results are shown in Fig. 9.., The results are shown in Fig. \ref{f8}. + Based on the spectra it is safe to sav that the eclipsing binaries are not associated. with the voung population in 1C1396N. Three arguments are important here: a) There is no evidence for Hla emission. tvpical lor YSOs. either due to accretion. or magnetic activity.," Based on the spectra it is safe to say that the eclipsing binaries are not associated with the young population in IC1396W. Three arguments are important here: a) There is no evidence for $\alpha$ emission typical for YSOs, either due to accretion or magnetic activity." + In. fact. Ho is observed as an unshifted absorption line which also excludes the interpretation as extragalactic objects.," In fact, $\alpha$ is observed as an unshifted absorption line which also excludes the interpretation as extragalactic objects." + b) The high-resolution spectra. albeit at low signal-to-noise ratio. do not show any evidence for the deep Lithium absorption feature at .wwhich is found in voung stars with equivalent. widths of 0.5 Ctep2008XpJ...689.1127 M..," b) The high-resolution spectra, albeit at low signal-to-noise ratio, do not show any evidence for the deep Lithium absorption feature at which is found in young stars with equivalent widths of $\sim 0.5$ \\citep{2008ApJ...689.1127M}." +. ο) AE the objects are at. the distance of 1€1396W. and have an age of MMyr they are expected to be M-type stars (7).. which is inconsistent. with the spectra (see Fig. 9)).," c) If the objects are at the distance of IC1396W and have an age of Myr they are expected to be M-type stars \citep{2003ApJ...593.1093L}, which is inconsistent with the spectra (see Fig. \ref{f8}) )." + In particular. the characteristic TiO banclheacl at .aand the Call absorption at .Aare absent and the slope is almost flat.," In particular, the characteristic TiO bandhead at and the CaH absorption at are absent and the slope is almost flat." + Additionallv. the two objects are >5 away [rom the LRAS source in the core of the cloud.," Additionally, the two objects are $>5'$ away from the IRAS source in the core of the cloud." + Their colours indicate little recdening and there is no significant colour variability., Their colours indicate little reddening and there is no significant colour variability. + All this argues against association with 1€1396N. We conclude that these are objects in the background. of the cloud., All this argues against association with IC1396W. We conclude that these are objects in the background of the cloud. + The spectra are well-approximated with be or C-type templates with little redcdening. as seen in Fig. 9..," The spectra are well-approximated with F- or G-type templates with little reddening, as seen in Fig. \ref{f8}. ." + This is also consistent with the near-infrared colours: For a CGU-tvpe star (luminosity class ILL or V) the intrinsic JfA is 0.05 (?).. which vields ££A=0.2 for chy=2 (E-2) and 0.35 for eAy= d4mmas (E-1).," This is also consistent with the near-infrared colours: For a G0-type star (luminosity class III or V) the intrinsic $H-K$ is 0.05 \citep{1988PASP..100.1134B}, which yields $H-K=0.2$ for $A_V=2$ (E-2) and 0.35 for $A_V=4$ mag (E-1)." + The same testease gives J44=0.6 for Adeo 2and 0.85 for chy=4., The same testcase gives $J-H=0.6$ for $A_V=2$ and 0.85 for $A_V=4$. + All this is in perfect agreement with our measurements., All this is in perfect agreement with our measurements. + From the colours ancl the low-resolution spectra we cannot definitely tell if these two are giants or dwarfs., From the colours and the low-resolution spectra we cannot definitely tell if these two are giants or dwarfs. + For a GO cbwarl the Ix-band. ux would indicate a distance of Lkkpe. for a giant about kkpe.," For a G0 dwarf the K-band flux would indicate a distance of $\sim 1$ kpc, for a giant about kpc." + The sharpness of the eclipses favours cwarls. as a giant is more likely to produce a slow ingress and ceress.," The sharpness of the eclipses favours dwarfs, as a giant is more likely to produce a slow ingress and egress." + Another argument for dwarls is he relatively low extinction. (, Another argument for dwarfs is the relatively low extinction. ( +With Ap~0.7 mmag/kpe we would expect Lfy20.5 for giants.),With $A_V \sim 0.7$ mag/kpc we would expect $H_K>0.5$ for giants.) + The lack of a Hat phase in eclipse. the depth of he eclipses. and the lack of colour change in eclipse argues for svstems with roughly equal size components.," The lack of a flat phase in eclipse, the depth of the eclipses, and the lack of colour change in eclipse argues for systems with roughly equal size components." + Due to their faintness we didnot attempt to. obtain radial velocity monitoring to constrain their fundamental xwanmeters., Due to their faintness we didnot attempt to obtain radial velocity monitoring to constrain their fundamental parameters. + Anybody interested in working on these objects is encouraged to get in touch with us., Anybody interested in working on these objects is encouraged to get in touch with us. +to.. dependiug ou the »articular GBB.,"to, depending on the particular GRB." + These differences betwee e k-correctecl energies tid the simple uncorrected energies are highliehtecd in figure 1 where the crosses depict the simple icorrected. energies., These differences between the $k$ -corrected energies and the simple uncorrected energies are highlighted in figure \ref{fig:en-v-z} where the crosses depict the simple uncorrected energies. + Though i many Cases the Wo energles are situilar. some the differences 'e quite large (particularly those GRBs whe‘e [Ttences were 1neasured ii mall baudpass euergy ange).," Though in many cases the two energies are similar, in some the differences are quite large (particularly those GRBs where fluences were measured in a small bandpass energy range)." + While most Á-correctio S are of orcde! uui re GRB energy di:ibution spaus 1early 3 ders of maguituce.," While most $k$ -corrections are of order unity, the GRB energy distribution spans nearly 3 orders of magnitude." + As such. te distri»utlor o 1‘ected οiergles is citatively simila‘to the stribution of A-corrected energles.," As such, the distribution of uncorrected energies is qualitatively similar to the distribution of $k$ -corrected energies." + —un tlie future. most CRB thelices w]ll bei jeasured in the eiergy rauges 10—700 keV (Bep209ΑN/CIRBM) a16 10-1000 keV (HETE-IL/FRECATE) αιd so it is of interest to know the cliaracteristie Ae for these instruuents.," In the future, most GRB fluences will be measured in the energy ranges 40–700 keV (BeppoSAX/GRBM) and 10–1000 keV (HETE-II/FREGATE) and so it is of interest to know the characteristic $k$ -correction for these instruments." + Iu figtre | We SILIOW he meclian &-correctiou for seve‘al observec baidpassa energv ranges as a fiction of burst redshift and fixe co-moving bandpass., In figure \ref{fig:avgcor} we show the median $k$ -correction for several observed bandpass energy ranges as a function of burst redshift and fixed co-moving bandpass. + Tjese mectiat k-cor‘ection curves. whic1 are iudepeucdeut of cosiology. were οeueratec using the leimplate spectra luehod. described. hereit.," These median $k$ -correction curves, which are independent of cosmology, were generated using the template spectral method described herein." + Iu the absence of a reported specTuli these curves tay be used it Conjuuction with equation £ to calculate the prompt isotropic-equvalent energy of a burst.," In the absence of a reported spectrum, these curves may be used in conjunction with equation \ref{eq:theken} to calculate the prompt isotropic-equivalent energy of a burst." + Figure κ)+) shows alistogram of the A-corrected energies of ||I? GRBs., Figure \ref{fig:hist-e} shows a histogram of the $k$ -corrected energies of 17 GRBs. +" For a costiology. witl Hy=65 kins ' 1. Q,,=0.3. Q4 = 0.7. the minimum bolometric CRB energy of hose GRBs with measured redshifts is (GARB 990712) and tle tnanximum bolometric energy is ere (GARB 990123)."," For a cosmology with $H_0 = 65$ km $^{-1}$ $^{-1}$, $\Omega_m = 0.3$, $\Omega_\Lambda$ = 0.7, the minimum bolometric GRB energy of those GRBs with measured redshifts is (GRB 990712) and the maximum bolometric energy is erg (GRB 990123)." + The median bolometric energy release is (CARB 900510) with an rus., The median bolometric energy release is (GRB 990510) with an r.m.s. + scatter of 0.50 dex., scatter of 0.80 dex. + We emphasize that tus analysis of the characteristic k-corrected energies applies only to theobserved distribution of GRBs with redshifts: several observational biases (for exaltiple. in burst detection aud redshift determination obscure the true uucerlyiug euergy cistributiol.," We emphasize that this analysis of the characteristic $k$ -corrected energies applies only to the distribution of GRBs with redshifts; several observational biases (for example, in burst detection and redshift determination) obscure the true underlying energy distribution." + Given that mauy GRBs. rou aualysis of alterglow. are now believed to be jetecd (e.g..Harrisou2000:Halpernetal. 2000).. the real elerey release of a given GRB may be sltbstautially less tla the isoropic-equivalent energies derives herein.," Given that many GRBs, from analysis of afterglow, are now believed to be jetted \citepeg{hbf+99,bsf+00,hum+00}, the real energy release of a given GRB may be substantially less than the isotropic-equivalent energies derived herein." + To fiud the real total prompt energy release oue requires at additional correction factor tha takes in to accourt the geometry of the explosion., To find the real total prompt energy release one requires an additional correction factor that takes in to account the geometry of the explosion. + Iucludiug geometric corrections. the distributio1 of GRB energies appears to tighten toa significantly uarrower distribution than without the georjetric corrections (such work will be presented elsewhere in Frailetal.(2001).," Including geometric corrections, the distribution of GRB energies appears to tighten to a significantly narrower distribution than without the geometric corrections (such work will be presented elsewhere in \citet{fra01}." +. TIis tight distribuion. which suggests that (Ες may be viable staudard cauclles. uuderscores the ever-increasing need for accurate spectral aud fluence nueastires as well as an accurate accouuting o “the orcder-of-uauity f-correctious.," This tight distribution, which suggests that GRBs may be viable standard candles, underscores the ever-increasing need for accurate spectral and fluence measures as well as an accurate accounting of the order-of-unity $k$ -corrections." + The authors thauk D. Baucl for providit& unpublished s»ectral ancl fluence Ineasurelments of two recent bursts., The authors thank D. Band for providing unpublished spectral and fluence measurements of two recent bursts. + We acknowledge helpful «iscussious with he members of the GRB Collaboration. especially with P. Price. S. Ixullzwu. and D. Reichart.," We acknowledge helpful discussions with the members of the Caltech-NRAO-CARA GRB Collaboration, especially with P. Price, S. Kulkarni, and D. Reichart." + We thank the anonvinous referee for helpful comments., We thank the anonymous referee for helpful comments. + JSB gratefully. acsuowledges the fellowship [rom the Fannie aud John Hertz Foundation., JSB gratefully acknowledges the fellowship from the Fannie and John Hertz Foundation. + The NRAO is a facility of the National Science Founcation operated under cooperative agreement by Associated Universities. Inc.," The NRAO is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc." +significant VO absorption at AAT334 and 7850 iindicates that the spectral twpe is later than M5. and a visual comparison with the Wirkpatrick ct al standard sequence leads to classification as between M7 and. ALS.,"significant VO absorption at $\lambda\lambda 7334$ and 7850 indicates that the spectral type is later than M5, and a visual comparison with the Kirkpatrick et al standard sequence leads to classification as between M7 and M8." + A spectrum. of the well-known ALS dwarf VBIO is plotted in fieure 2 for comparison., A spectrum of the well-known M8 dwarf VB10 is plotted in figure 2 for comparison. + Extrapolating the results derived by Leggett et al (1996). d04 is likely to have Tyr&26001Ix. VBs (GL 644€) is the best-calibratecl MT. standard in the Ixirkpatrick et al svstem.," Extrapolating the results derived by Leggett et al (1996), d04 is likely to have $_{eff} \approx 2600$ K. VB8 (Gl 644C) is the best-calibrated M7 standard in the Kirkpatrick et al system." + Allowing for the uncertainties in Hawkins et al photographie photometry. DO4 has an De colour (2.63 mag.)," Allowing for the uncertainties in Hawkins et al photographic photometry, D04 has an $_C$ colour (2.63 mag.)" + consistent with that of VBS (2.41 mag. -, consistent with that of VB8 (2.41 mag. - + Legeett. 1992). while the (1-19) colours of the two stars are nearly identical at 3.7 magnitudes.," Leggett, 1992), while the (I-K) colours of the two stars are nearly identical at 3.7 magnitudes." + However. VBS las an absolute magnitude at 2.2520 of Aly=9.76. while Llawkins et al deduce Aly=12.24 lor DOF.," However, VB8 has an absolute magnitude at $\mu m$ of $_K = 9.76$, while Hawkins et al deduce $_K = 12.24$ for D04." + Given the similarity in spectral types ancl optical/LR colours. as well as 1ο absence of evidence for any chemical peculiarities in DO. it is reasonable to assume that the two objects have similar ellective temperatures and similar bolometric corrections.," Given the similarity in spectral types and optical/IR colours, as well as the absence of evidence for any chemical peculiarities in D04, it is reasonable to assume that the two objects have similar effective temperatures and similar bolometric corrections." + In dl Case. That is. the dillerence in luminosity of 2.5 magnitudes inferred. by Hawkins ct al implies that DO4 has a raclius which is three times smaller than that of VDS.," In that case, That is, the difference in luminosity of 2.5 magnitudes inferred by Hawkins et al implies that D04 has a radius which is three times smaller than that of VB8." + Legeett ct al (1996). have combined. optical ancl infrared spectroscopy ancl photometry with improved mocel atmospheres to derive effective temperatures. Iuminositics and radii for a small number of M. dwarls.," Leggett et al (1996) have combined optical and infrared spectroscopy and photometry with improved model atmospheres to derive effective temperatures, luminosities and radii for a small number of M dwarfs." + The lowest uminosity (ancl lowest temperature) star in their saniple is GJ 1111. spectral type M6.5. Mig~9.46. for which they estimate a radius of 0.8100 metres.," The lowest luminosity (and lowest temperature) star in their sample is GJ 1111, spectral type M6.5, $_K \sim 9.46$, for which they estimate a radius of $0.8 \times 10^8$ metres." + this corresponds to VIL ιν or slightly less than the radius of Jupiter (0.119 t.).," this corresponds to 0.11 $_\odot$, or slightly less than the radius of Jupiter (0.119 $_\odot$ )." + Assuming a similar radius for the slightly later-tvpe VBs. the luminosity deduced by Hawkins et al for Dot eads us to infer a radius of ~0.0354.. or one-third that of Jupiter.," Assuming a similar radius for the slightly later-type VB8, the luminosity deduced by Hawkins et al for D04 leads us to infer a radius of $\sim 0.035 R_\odot$, or one-third that of Jupiter." + This result is clearly at odds with predictions based on interior mocels of low-mass stars ancl brown dwarfs., This result is clearly at odds with predictions based on interior models of low-mass stars and brown dwarfs. + As the mass decreases towards 0.1. M. theoretical models predict that the racius also decreases to close to 0.12 I5... (Burrows Liebert. 1993. figure. 1).," As the mass decreases towards 0.1 $_\odot$, theoretical models predict that the radius also decreases to close to 0.12 $_\odot$ (Burrows Liebert, 1993, figure 1)." + However. electron. degeneracy takes over as the main source of pressure support in lower-mass objects. and. as a result. the radius is predicted. to vary by no more than ~30% as the mass decreases to one Jupiter mass (Burrows ct al. 1997).," However, electron degeneracy takes over as the main source of pressure support in lower-mass objects, and, as a result, the radius is predicted to vary by no more than $\sim 30\%$ as the mass decreases to one Jupiter mass (Burrows et al, 1997)." + Moreover. substellar-mass objects (AL« 0.075.) are predicted to have radii that of Jupiter at elective temperatures of 200019. Given that there is no evidence for unusual atmospheric opacities in DOF. and that the deduced. radius is in strong contradiction with a basic premise of stellar structure. an alternative explanation must be found for the faint absolute magnitudes deduced by Hawkins et al.," Moreover, substellar-mass objects $M < 0.075 M_\odot$ ) are predicted to have radii that of Jupiter at effective temperatures of 2600K. Given that there is no evidence for unusual atmospheric opacities in D04, and that the deduced radius is in strong contradiction with a basic premise of stellar structure, an alternative explanation must be found for the faint absolute magnitudes deduced by Hawkins et al." + Phe simplest is that the trigonometric parallax derived. by. Hawkins et al for ab least DOL (and. possibly DOT and. DI12) overestimates the true. value., The simplest is that the trigonometric parallax derived by Hawkins et al for at least D04 (and possibly D07 and D12) overestimates the true value. + Each star was observed at only three epochs. leading to astrometric solutions which are poorly constrained against systematic errors (cl," Each star was observed at only three epochs, leading to astrometric solutions which are poorly constrained against systematic errors (cf." + Pinsonneault et als (1998) comments on the Lipparcos Pleiades astrometry)., Pinsonneault et al's (1998) comments on the Hipparcos Pleiades astrometry). + Moreover. there is significant dispersion amongst 1ο individual astrometric measurements at a ogiven epoch for each of the three faint (L519.4) candidate brown chwarls (Llawkins et al. figure. 6).," Moreover, there is significant dispersion amongst the individual astrometric measurements at a given epoch for each of the three faint $\sim 19.4$ ) candidate brown dwarfs (Hawkins et al, figure 6)." + Finally. Tinnev (priv.," Finally, Tinney (priv." + comm.), comm.) + points out that the differential chromatic refraction corrections are constrained poorly. raising the possibility. of systematic errors in the final astrometric solution.," points out that the differential chromatic refraction corrections are constrained poorly, raising the possibility of systematic errors in the final astrometric solution." + Further astrometry of these objects is clearly desirable. but for the present. we favour interpreting the current data in alternative manner to the solution espoused by. Hawkins et al.," Further astrometry of these objects is clearly desirable, but for the present, we favour interpreting the current data in alternative manner to the solution espoused by Hawkins et al." + We identify DO4. DOT anc DI2 as AI7/AIS main-sequence cisk cwarls. lving at distances of 150 parsees. rather than as highlv-unusual brown cwarfs at distances of ~DO peursecs.," We identify D04, D07 and D12 as M7/M8 main-sequence disk dwarfs, lying at distances of $\sim 150$ parsecs, rather than as highly-unusual brown dwarfs at distances of $\sim 50$ parsecs." + ] would like to thank Cuwee Wirth and Gary Puniwai [ου assistance with the observations., I would like to thank Greg Wirth and Gary Puniwai for assistance with the observations. + The Ixeck. Observatory is operated by the Californian Association for Research in Astronomy. ancl was made possible by generous grants [rom the Keck W. M. Foundation.," The Keck Observatory is operated by the Californian Association for Research in Astronomy, and was made possible by generous grants from the Keck W. M. Foundation." +concentrate on the stabilitv and radiative properties of the jet beau. rather than studving the propagation of the jet’s head as it is done in the quoted papers.,"concentrate on the stability and radiative properties of the jet beam, rather than studying the propagation of the jet's head as it is done in the quoted papers." + Our approach is thus also different from that of Jones et al. (, Our approach is thus also different from that of Jones et al. ( +1999) who solve a simplified version of ie electron transport equation to account for shock diffusive acceleration and svuchrotron aging in a time-dependent simulation of a radio lobe.,1999) who solve a simplified version of the electron transport equation to account for shock diffusive acceleration and synchrotron aging in a time-dependent simulation of a radio lobe. + Iu studyiue the instability evolution. we adopt the so-called ‘temporal’ approach (see Bodo ct al.," In studying the instability evolution, we adopt the so-called `temporal' approach (see Bodo et al." + 199D). in whic[um oue can follow the system evolution for longer times. ay. opposed to the “spatial analysis’ (see Hardee Norma 1988a.b aud Stone. Nu ILudee 1997). in. which one is Πίος w the transit time through the eril.," 1994), in which one can follow the system evolution for longer times, as opposed to the `spatial analysis' (see Hardee Norman 1988a,b and Stone, Xu Hardee 1997), in which one is limited by the transit time through the grid." + While the spatial approac[um allows for more direct comparison with observations. tli temporal analysis is preferred when studving the plivsicy. of the iustabilitv evolution over long time scales. with good spatial resolution and without exceedingly large conrputational domains.," While the spatial approach allows for more direct comparison with observations, the temporal analysis is preferred when studying the physics of the instability evolution over long time scales, with good spatial resolution and without exceedingly large computational domains." + The plan of the paper is the following: iu the next section (Section 2). we describe the plivsical model for the jet. the hain assuniptious and the integration method: iu Sectio- we deal with the treatiueut of the evolution equation for the relativistic electrous distribution aud of the shock acceleration: the siaunulatious results are discussed in Sections Land 5 where a comparison between our model aud observational data of extragalactic jets is presented. aud the conclusions are eiven in Section 6.," The plan of the paper is the following: in the next section (Section 2), we describe the physical model for the jet, the main assumptions and the integration method; in Section 3 we deal with the treatment of the evolution equation for the relativistic electrons distribution and of the shock acceleration; the simulations results are discussed in Sections 4 and 5 where a comparison between our model and observational data of extragalactic jets is presented, and the conclusions are given in Section 6." + We consider a nowrelativistic. fluid jet that propagates iu a uuiforni medium and is in pressure equilibrium with its environment.," We consider a non-relativistic, fluid jet that propagates in a uniform medium and is in pressure equilibrium with its environment." + This cuviromment is permeated by a maenetic field. that is advected by the fiuid and has no effect in the momentum conservation equation Jolasmia> x).," This environment is permeated by a magnetic field, that is advected by the fluid and has no effect in the momentum conservation equation $\beta_{\rm plasma} \rightarrow \infty$ )." + Under these coucitious. the relevant equations are the lydvodvuaiic equations of mass. Ποιοτὰ aud energy conservation: where. as usual. p represcuts the thermal pressure. p the density. v the fluid velocity. aud P stauds for the ratio of specific heats.," Under these conditions, the relevant equations are the hydrodynamic equations of mass, momentum and energy conservation: where, as usual, $p$ represents the thermal pressure, $\rho$ the density, ${\bf v}$ the fluid velocity, and $\Gamma$ stands for the ratio of specific heats." +" We then restrict our analysis to an infinite jet iu cexlindiical geometry Qu the coordinates à τί consistently with our assunptions. the equation system (1).(2).(3) can be complemented bv the equations for the passive magnetic field. in the form: where Asg(ni) is the only compoucut of the vector potential for B.. D, (ήν) is usually called ‘streams function). as appropriate for the chosen geometry. and Dr.s) is the toroidal field."," We then restrict our analysis to an infinite jet in cylindrical geometry (in the coordinates $r,z$ ); consistently with our assumptions, the equation system (1),(2),(3) can be complemented by the equations for the passive magnetic field, in the form: where $A_{\phi}(r,z)$ is the only component of the vector potential for $B_z$, $B_r$ $r A_{\phi}(r,z)$ is usually called `stream function'), as appropriate for the chosen geometry, and $B_{\phi}(r,z)$ is the toroidal field." + One can notice that Eqs. (, One can notice that Eqs. ( +"1.5) have in conmnon the standard form of a tracer equation: where 7=rA, in Eq. (1) ","4,5) have in common the standard form of a `tracer' equation: where ${\cal T} \equiv r A_{\phi}$ in Eq. \ref{bfield1}) )" +"aud 7=B,,/pr in Eq. (5))."," and ${\cal T} \equiv +B_{\phi} / \rho r$ in Eq. \ref{bfield2}) )." + As 1meutioned before. we consider ani axially sviuinetric. cvliudical jet.," As mentioned before, we consider an axially symmetric, cylindrical jet." + The flow velocity is initially uniforii along he + direction (1l~) and the jet is in pressure equilibria. with the ambieut medium., The flow velocity is initially uniform along the $z$ direction $V_z$ ) and the jet is in pressure equilibrium with the ambient medium. + The initial velocity anc clensity xofiles iu the r coordinate. aud the perturbation to the rausverse velocity V(r2) are the same as in Rossi et al. (," The initial velocity and density profiles in the $r$ coordinate, and the perturbation to the transverse velocity $V_r(r,z)$ are the same as in Rossi et al. (" +1997).,1997). + Iu the calculations we measure leugths in uuits of the jet initial radius e. time i units of the radius souud crossing time t.=efe (e is the isothermal sound speed internal to the jet}. and the magnetic field in units of the initial value By.," In the calculations we measure lengths in units of the jet initial radius $a$, time in units of the radius sound crossing time $t_{\rm c} \equiv a/c_{\rm si}$ $c_{\rm si}$ is the isothermal sound speed internal to the jet), and the magnetic field in units of the initial value $B_0$." + The initial coufiguration for the magnetic field is asstuned poloidal (loueitudinal) plus azimuthal: with i—8., The initial configuration for the magnetic field is assumed poloidal (longitudinal) plus azimuthal: with $m=8$. + The system: of equations (1).(2).(3) is solved numerical by means of a PPM (Piecewise Parabolic Method) lvdrocode (Colella Woodward 1981) over an integration domain of 512206 eid points. with the jet radius spamming over 60 erid ponts. for a total domain of Q<2< 1l0r.0<0¢<20.," The system of equations (1),(2),(3) is solved numerically by means of a PPM (Piecewise Parabolic Method) hydrocode (Colella Woodward 1984) over an integration domain of $512 \times 256$ grid points, with the jet radius spanning over 60 grid points, for a total domain of $0 \leq z \leq 10 \pi$, $0 \leq r \leq 20$." +" The axis of the jet is coincident with the bottom boundary of the domain (7= 0). where svununetric (for p. p. V. aud D, /(pr)) or autisyuunetric (for Vand rl) boundary conditions are given."," The axis of the jet is coincident with the bottom boundary of the domain $r=0$ ), where symmetric (for $p$, $\rho$, $V_z$ and $B_{\phi} / (\rho r)$ ) or antisymmetric (for $V_r$ and $r A_{\phi}$ ) boundary conditions are given." + At the :—0 and +=20 boundaries. cousisteuthy with the assumption of a infinite jet. we have set periodic conditions. aud at the upper boundary (= HR) we have chosen a free outflow condition. by imposing for cach variable null eradicut (dfdr— 0).," At the $z=0$ and $z=20$ boundaries, consistently with the assumption of a infinite jet, we have set periodic conditions, and at the upper boundary $r=R$ ) we have chosen a free outflow condition, by imposing for each variable null gradient $d/dr=0$ )." + The grid in the kc direction is non-uniforii. but expands with r to avoid the effects of partial reflections at the top boundary (see Bodo et al.," The grid in the $r$ direction is non-uniform, but expands with $r$ to avoid the effects of partial reflections at the top boundary (see Bodo et al." + 1991 and Rossi ct al., 1994 and Rossi et al. + 1991)., 1997). +"The new up-and-coming survevs such as PSI. the Palomar Trausicut Factory. aud Skvimapper are best represeuted by simulations D aud E. for which the FoM is iuproved by about a factor of 2,","The new up-and-coming surveys such as PS1, the Palomar Transient Factory, and Skymapper are best represented by simulations D and E, for which the FoM is improved by about a factor of 2." + Not au insiguificaut gain. to be sure. but one that could casily be washed out by svstematic uucertainties if they are not carefully controlled.," Not an insignificant gain, to be sure, but one that could easily be washed out by systematic uncertainties if they are not carefully controlled." + The next leap forward. to be realized in the next decade by Piu-STARRS I. JDEM aud LSST. will bring the SN sample size to 10.000 or more objects. as in smnulatious Ct aud II. Usine the DETF FoM as our principal barometer. our simulations sugeest that a spectroscopy-free analysis using SOFT should be sufficieut to capitalize on the very laree SN samples coming in the next decade.," The next leap forward, to be realized in the next decade by Pan-STARRS 4, JDEM and LSST, will bring the SN sample size to 10,000 or more objects, as in simulations G and H. Using the DETF FoM as our principal barometer, our simulations suggest that a spectroscopy-free analysis using SOFT should be sufficient to capitalize on the very large SN samples coming in the next decade." + With cach new ecucration of SN survers the sample size increases bv a factor of 1.5. and the SOFT-based FoM iucreases bv a factor of 23.," With each new generation of SN surveys the sample size increases by a factor of 4–5, and the SOFT-based FoM increases by a factor of 2–3." + A close look at the uncertainties ou wy and wy in Table 3 highlights the fact that systematic effects will quickly become a douminaut source of uncertaiutv., A close look at the uncertainties on $w_0$ and $w_a$ in Table \ref{tab:darkmcResults} highlights the fact that systematic effects will quickly become a dominant source of uncertainty. + For a sample size of 2.000 objects the statistical wucertaiuty ou wy from our Aloute Carlo smiulatious is around -0.2. which is already comparable to the expected level of svsteimatic uncertainty.," For a sample size of 2,000 objects the statistical uncertainty on $w_0$ from our Monte Carlo simulations is around $\pm 0.2$, which is already comparable to the expected level of systematic uncertainty." + Tow can these results inform our strategic choices for new and upcoming SN cosmnologv projects?, How can these results inform our strategic choices for new and upcoming SN cosmology projects? + We would argue that the new surveys can be successful relving on light-curve-based redshitts derived bx SOFT or similar programs. informed by host galaxy plioto-is when possible.," We would argue that the new surveys can be successful relying on light-curve-based redshifts derived by SOFT or similar programs, informed by host galaxy $z$ 's when possible." + For spectroscopic follow-up. iustead of tarecting the most likelyTNSNe.. cosmological analyses will be better served bv focusing resources on objects that are eiven an ambiguous classification evade by SOFT.," For spectroscopic follow-up, instead of targeting the most likely, cosmological analyses will be better served by focusing resources on objects that are given an ambiguous classification grade by SOFT." + Most of these objects will be SNe of type Ib/c or Ia. perhaps with uimsual colors or anonmalous huuiuosities that make them difficult to classify.," Most of these objects will be SNe of type Ib/c or Ia, perhaps with unusual colors or anomalous luminosities that make them difficult to classify." + To the extent that spectroscopic mcasurements are able to provide a more definitive classification. we can sharpen SOFT’s ability to discrininate such marginal cases aud help to reduce systematic errors from musclassifications.," To the extent that spectroscopic measurements are able to provide a more definitive classification, we can sharpen SOFT's ability to discriminate such marginal cases and help to reduce systematic errors from misclassifications." + Iu spite of the close connection to real data. the results of our bootstrap Monte Carlo approach are likely to be overly optimistic.," In spite of the close connection to real data, the results of our bootstrap Monte Carlo approach are likely to be overly optimistic." + We are necessarily overlooking the effects of sample selection aud SN classification. aud we have knowinely omitted systematic uncertainties from our analysis.," We are necessarily overlooking the effects of sample selection and SN classification, and we have knowingly omitted systematic uncertainties from our analysis." + In order to realizo these optimistic predictions. it will be necessary to make adjustineuts and improvements to the SOFT program itself that will improve its precision and reduce systeatic effects.," In order to realize these optimistic predictions, it will be necessary to make adjustments and improvements to the SOFT program itself that will improve its precision and reduce systematic effects." + In the following section we provide an outline for that future development., In the following section we provide an outline for that future development. + As discussed in Section 2.. our use of fixed shape ight curve templates mtroduces au inhercut bias iuto the parameter estimates that can be derived roni cach individual template.," As discussed in Section \ref{sec:ParameterEstimation}, our use of fixed shape light curve templates introduces an inherent bias into the parameter estimates that can be derived from each individual template." + In this work we rave addressed this problem bv usine the fuzzv intersection operator When combining nemboerslip uctions., In this work we have addressed this problem by using the fuzzy intersection operator when combining membership functions. + The fuzzy AND emphasizes. collective aerecluent from all contributing templates. and herefore generally causes the imdividual biases ο cancel out.," The fuzzy AND emphasizes collective agreement from all contributing templates, and therefore generally causes the individual biases to cancel out." + Iu this section we consider two separate approaches that might reduce the effects of individual template biases by detecting and pre-cluptively correcting for those location parameter offsets., In this section we consider two separate approaches that might reduce the effects of individual template biases by detecting and pre-emptively correcting for those location parameter offsets. + Figure 7 illustrates how one could use a SN with a known location to measure the size aud direction of template biases., Figure \ref{fig:biasDemo} illustrates how one could use a SN with a known location to measure the size and direction of template biases. + The redshift and distance for our supposed calibration SN is marked w the ' After a SOFT comparison of our calibration SN against the model M4 (based on SN 1999ce in Figure 7)). we can iieasure the peak ocation of the AL cloud as τανfei).," The redshift and distance for our supposed calibration SN is marked by the “x.” After a SOFT comparison of our calibration SN against the model $M_1$ (based on SN 1999ee in Figure \ref{fig:biasDemo}) ), we can measure the peak location of the $M_1$ cloud as $(z_1,\mu_{e,1})$." + wowing he true location of the SN. we can then measure he distance from the cloud to the true position of the SN as (Az.Agee}.," Knowing the true location of the SN, we can then measure the distance from the cloud to the true position of the SN as $(\Delta z_1,\Delta \mu_{e,1})$." + This inunediatcly gives us a bias correction vector 4=(AcusAqua) hat cau be used to translate the eutire probability cloud down to the true location of the peal.," This immediately gives us a bias correction vector $\beta_1 = (-\Delta +z_1,-\Delta \mu_{e,1})$ that can be used to translate the entire probability cloud down to the true location of the peak." + We can compute simular correction vectors for model A» (as shown in FieureOo 7)) aud all other moclels., We can compute similar correction vectors for model $M_2$ (as shown in Figure \ref{fig:biasDemo}) ) and all other models. + Uufortunatelv. once we derive a set of bias correction vectors using a particular calibration object. we can ouly apply them to other caudidatc SNe that are basically identical to the calibration object.," Unfortunately, once we derive a set of bias correction vectors using a particular calibration object, we can only apply them to other candidate SNe that are basically identical to the calibration object." + Tf we lave a candidate SN that is physically more simular to the model M4 than our calibrator. then the 4 vector shown in Figure 7 would be an over-correction.," If we have a candidate SN that is physically more similar to the model $M_1$ than our calibrator, then the $\beta_1$ vector shown in Figure \ref{fig:biasDemo} would be an over-correction." + To avoid excessive bias correction. we need to scale the 3 values separately for each," To avoid excessive bias correction, we need to scale the $\beta$ values separately for each" +The nuclear spectra of hieh + quasars preseuts weak or absent ΠΟΠ aud strong NV., The nuclear spectrum of high $z$ quasars presents weak or absent HeII and strong NV. + /IIcIT75 aud NV/CTV. presents a large diversity with values sometimes 75)., $>$ 5 and NV/CIV presents a large diversity with values sometimes $>$ 5). + Tel is generally narrower (when detected) than other les like CTV aud CTIT| (Foltz et al. 1988.. ," HeII is generally narrower (when detected) than other lines like CIV and CIII] (Foltz et al. \cite{foltz88}, ," +Beckman et al. 1991))., Heckman et al. \cite{heck91}) ). + This has been interpreted as the origiu of au importan Yaction of the ΠΟΠ eiuissiou (75054 )) iu a lower velocity extranuclear region. possibly the ISM of the host galaxy of he quasar.," This has been interpreted as the origin of an important fraction of the HeII emission $\sim$ ) in a lower velocity extranuclear region, possibly the ISM of the host galaxy of the quasar." +" This gas will have au important coutribution o the Lyo euission, but lines like NV. CTI and CTV wil v6 dominated by the broad liue region (BER)."," This gas will have an important contribution to the $\alpha$ emission, but lines like NV, CIII] and CIV will be dominated by the broad line region (BLR)." + A view of he BLR in Ll would explain the weakuess of Well au he streneth of NV., A view of the BLR in L1 would explain the weakness of HeII and the strength of NV. + However. Ll is not a quasar since the lines are too arrow 2500 km Lin quasars).," However, L1 is not a quasar since the lines are too narrow $>$ 2500 km $^{-1}$ in quasars)." + CTI] is broac (CEWIDBI-G6100 kan 1) but this could be due to the contamination by the SiTIT1895 doublet.," CIII] is broad $\sim$ 6100 km $^{-1}$ ), but this could be due to the contamination by the SiIII]1895 doublet." + It is possible that he lines could appear narrower and asvuunuetric as the result of absorption by eas aud/or dust. which could be very cfiicicut at queuching the resonau lines (CIV. NV. Ίνα).," It is possible that the lines could appear narrower and asymmetric as the result of absorption by gas and/or dust, which could be very efficient at quenching the resonant lines (CIV, NV, $\alpha$ )." + However. Πα |[NIT| presents also a narrow profile (1060 kin 13 (IV98).," However, $\alpha$ +[NII] presents also a narrow profile $\sim$ 1060 km $^{-1}$ ) (IV98)." + Therefore. the emission lines are much narrower than m quasars aud Li is not a normal quasar.," Therefore, the emission lines are much narrower than in quasars and L1 is not a normal quasar." + The spectral propertics of Ll rather sugeesteo that it is a narrow line active galaxv (a Sevfert 2 or narrow iue quasar)., The spectral properties of L1 rather suggest that it is a narrow line active galaxy (a Seyfert 2 or narrow line quasar). + Why does it lie on the sequence defined by quasars in the NV/IIGIT NV/CIV diaersun?, Why does it lie on the sequence defined by quasars in the NV/HeII NV/CIV diagram? + Why does it show like quasars weak ΠΟΠ iux stroug NV relative to he € lines?, Why does it show like quasars weak HeII and strong NV relative to the C lines? + Since the BLR is not visible the spectrm nust be dominated by the intermediate deusity narrow ine region (1104 9) and/or the low density narrow lue region {x00. usually named the exteuded emission line reeion. EELR).," Since the BLR is not visible the spectrum must be dominated by the intermediate density rrow line region $n\sim$ $^{4-6}$ ) and/or the low density narrow line region $n\leq$ 100, usually named the extended emission line region, EELR)." + We showed above that the standard EELR uodels fail to reproduce the observed dine ratios., We showed above that the standard EELR models fail to reproduce the observed line ratios. + We xeseut in Fie., We present in Fig. + 7 two sequences (n UJ of models simillar o the AGN sequence described above. but for deusities n—10* aud »=10%," \ref{Fig7} two sequences (in $U$ ) of models lar to the AGN sequence described above, but for densities $n=$ $^5$ and $n=$ $^6$." + The »=10° sequence solves the discrepancies between the models aud the observed line ratios., The $n=$ $^6$ sequence solves the discrepancies between the models and the observed line ratios. + Therefore. the weakness of ΠΟΠ can be explained if the intermediate deusitv narrow line reeionu5 doniünates he lune emission.," Therefore, the weakness of HeII can be explained if the intermediate density narrow line region dominates the line emission." + Towever. these models still fail to reproduce the line ratios involving NV.," However, these models still fail to reproduce the line ratios involving NV." + Fig., Fig. + 8. shows hat the 72108 uodels (only the higher ionization model is preseut) predict the NV line too weak., \ref{Fig8} shows that the $n=$ $^6$ models (only the higher ionization model is present) predict the NV line too weak. + Ou the other iud. our models show that such high densities would xoduce [OLEHeEASΤον1]OU . while the ratio measured by IV9s js xd.," On the other hand, our models show that such high densities would produce $\frac{[OIII]\lambda5007}{H\alpha +[NII]}\geq$ 4, while the ratio measured by IV98 is $\leq$ 1." + Oue possibility is that the magnification due to he eravitationa lens is not the same for all emissiou ines., One possibility is that the magnification due to the gravitational lens is not the same for all emission lines. + The magnification depends strougly on the source size (Trentham 19051) Deine higher for a smaller size of he source., The magnification depends strongly on the source size (Trentham \cite{tren95}) ) being higher for a smaller size of the source. + Those lines whose emission is doula Ina nore nucleated region will be more magnified than those ines prefercutially enuütted iu a more exteuded region., Those lines whose emission is dominant in a more nucleated region will be more magnified than those lines preferentially emitted in a more extended region. + Since the high density models predict stronger metal lines relative to ΠΟ compared to the EELR models (density <100 3) we expect CTV. CIII| and NV to be wore uucleated aud therefore more amplified.," Since the high density models predict stronger metal lines relative to HeII compared to the EELR models (density $\leq$ 100 $^{-3}$ ) we expect CIV, CIII] and NV to be more nucleated and therefore more amplified." + Tn this scenario. the region cutting NV should at the same time be more nucleated than the regions enüttius the C hues to explain the laree N/C ratios.," In this scenario, the region emitting NV should at the same time be more nucleated than the regions emitting the C lines to explain the large N/C ratios." + Differential magnification has been suggested by Lacy ct al. (1998)), Differential magnification has been suggested by Lacy et al. \cite{lacy98}) ) + to explain the spectroscopic properties of FSCT021111721., to explain the spectroscopic properties of FSC10214+4724. + An alteruative explanation is that N is overabuudaut., An alternative explanation is that N is overabundant. + NVΠΟ and NV/CIV have been used both in quasars (ILuuaun Ferland 1993)) aud UzRC (Fosburv ot al. 1L998.. 199001)," NV/HeII and NV/CIV have been used both in quasars (Hamann Ferland \cite{hamm93}) ) and HzRG (Fosbury et al. \cite{fos98}, \cite{fos99}) )" + as abundance indicators., as abundance indicators. + By studvine the NVΠΟ NW/CTV diagram ancl the ight correlation defined by high redshift quasars. the authors conclude that the BLR of quasars at high redshift (2 22) preseut N overabundance aud a large range in iietalliities typically 1] to —10 times the solar values.," By studying the NV/HeII NV/CIV diagram and the tight correlation defined by high redshift quasars, the authors conclude that the BLR of quasars at high redshift $z>$ 2) present N overabundance and a large range in metallicities typically $\sim$ 1 to $\sim$ 10 times the solar values." +" N/C is enhanced colpared to the solar values due to secondary production (N behaves in a different way than C aud ο, NxZ?, where Z is the metallicitv)."," N/C is enhanced compared to the solar values due to secondary production (N behaves in a different way than C and O. $N\propto Z^2$, where $Z$ is the metallicity)." + Fosbury et al., Fosbury et al. + proposed a sinilar explanation (but referred to the iouized eas outside the BLR) for the correlation defined by WzRC in this diagrau., proposed a similar explanation (but referred to the ionized gas outside the BLR) for the correlation defined by HzRG in this diagram. + The failure of the solar abundance (both low and high deusitv)models to explain the strength, The failure of the solar abundance (both low and high density)models to explain the strength +particle to be magnetized to local MEL within gvroradius scale only in turbulence depending on a reduced number of space coordinates.,particle to be magnetized to local MFL within gyroradius scale only in turbulence depending on a reduced number of space coordinates. + Anv three-climensional extension could depend on specilic geometry but. would not be justified in general. as our result shows.," Any three-dimensional extension could depend on specific geometry but would not be justified in general, as our result shows." + Comparison wilh previous munerical simulations (see. e.e.. Giacalone&Jokipii(1999))) requires the evaluation of the MELRW. lor isotropic turbulence.," Comparison with previous numerical simulations (see, e.g., \citet{gj99}) ) requires the evaluation of the MFLRW, for isotropic turbulence." + UsingEq. (25)).," UsingEq. \ref{dMFL2}) )," + we find for the average square displacement of MEL (same contribution along ο and y-axes) here (he term integrated over scales smaller than coherence scale πω (or f2bh) Is recast as and the term integrated over scales larger than coherence scale οπf (or f k_{min}$ ) is recast as and the term integrated over scales larger than coherence scale $2\pi/k_{min}$ (or $k < k_{min}$ ) is recast as Figure \ref{iso2} shows the diffusive behaviour of MFL for a magnetic turbulence with isotropic wave-number spectrum. + As for the slab case. scales larger (han coherence length (heκ Αμ) dominate over the turbulent contribution (see Fig. 4)).," As for the slab case, scales larger than coherence length $k2x. at fixed: (sinall) ratio. 0412/0.," As seen from \ref{DGam0}) ), this regime corresponds to very massive halos, $\delta_L/\sigma\rightarrow\infty$, at fixed (small) ratio $\sigma_{12}/\sigma$." + Nevertheless. in the regime where AT is small (ic. in the large separation limit.» 2€). which covers the cases of interest encountered at low redshift. we can expand the exponential in Eq.(115)).," Nevertheless, in the regime where $\Delta\Gam$ is small (i.e. in the large separation limit $x\rightarrow \infty$ ), which covers the cases of interest encountered at low redshift, we can expand the exponential in \ref{xiM1M2}) )." +" Then. at lowest order over the terms that vanish iu the large separation limit. we obtain for cqualiass halos AC, ESTNEwhoVence Sube Ex qqols) p JUIqqiiQS) =F yy?6s) m I2fiaais) Ileroafter we call the bias Cr) obtained from 131)) and Eq.(119)) as the “linearized” bias."," Then, at lowest order over the terms that vanish in the large separation limit, we obtain for equal-mass halos : _M(x) -, whence _M(x) (s) + (s) 2 (s) 3 (s) ] + (s) + 2 (s) 2 (s) 3 (s) ] Hereafter we call the bias $b^2_M(x)$ obtained from \ref{xiMlin}) ) and \ref{bias_sig}) ) as the “linearized” bias." +" We can note that. following the approach of Kaiser (1981). Matarrese Verde (2008) also computed the """" of local-tvpe nou-Cuussiauitv (13) ou the halo two-point correlation."," We can note that, following the approach of Kaiser (1984), Matarrese Verde (2008) also computed the effect of local-type non-Gaussianity \ref{fNLdef}) ) on the halo two-point correlation." + Drawing ou earlier work bv Matarrese ↸∖↑⋜↧↕∙∐, Drawing on earlier work by Matarrese et al. ( +"⋂≺∖∖⊓⋟∙↖↖⇁∐∪↸⊳∪∐∏⋯↑↸∖↑∐↸∖∣⊢↻∪↕∐↑∐⋜↧↕∪↸⊳∪↥⋅↥⋅↸∖↕⋜↕⊓∪∐↴∖↴ ↴⋝↖↽↸∖⊼≻⋜⋯≼∐∐∩↑∐∖↥⋅↸∖↕↸∖↖⇁⋜⋯↑≻⋜↧↑∐≓↕∐↑↸∖∩⊾↥⋅⋜↧↕↴∖↴⋜⋯≼↧∐↸∖↘↑ c» C» seriesm"" within a⋅⋅ large-distance and rare-⋅ . aA obtain expressions of the form rane (0) prefactor↽ (15 | ópaj).191 audG(131)).σιmi (στ 19:5)) in the first line. that arise from (121) this prefactor. the last terme fj dn the second and bracket.","1986), who compute the $n$ -point halo correlations by expanding the relevant path-integrals and next resumming the series within a large-distance and rare-event approximation, they obtain expressions of the form \ref{xiM1M2}) ), without the prefactor $(1+\delta_{LM})$, and \ref{xiMlin}) ), without the terms in the first line, that arise from this prefactor, and the last term $f_{1;11}$ in the second bracket." +" This term arises from the factor oy, iu the denominator of expression (123)). associated with A(125) the effect primordial nou-Caussiauitv ou the ouc-poiut Gand) (26) distribution "," This latter term arises from the factor $\sigma_{12}^2$ in the denominator of expression \ref{Gam1_12_q}) ), associated with the effect of primordial non-Gaussianity on the one-point distribution \ref{Gam1}) )." +"can be seen as a renorlalization ; . 2 σπα5 (07 0,)0;. qU- since.it>shows theyo ==of .3( ' through the function 77 (5)."," It can be seen as a renormalization of the Gaussian term $(\delta_L^2/\sigma_q^4) \sigma^2_{q,q}(s)$, since it shows the same scale dependence through the function $\sigma^2_{q,q}(s)$." + The:L 262as[g ara2 a term(στ was already. noticed in Slosar etστο)” σόι]αι al. (, The presence of such a term was already noticed in Slosar et al. ( +2008) Fourier space. and Desjacques et al. (,"2008) in Fourier space, and Desjacques et al. (" +2009) aa pointed out it needs to be included to obtain a good agrecinent with nunerical simulations.,2009) pointed out that it needs to be included to obtain a good agreement with numerical simulations. + This will give Ws hock tl last term in Eq.(132)) aud the second. term e can check (116))↽ below., This will give rise to the last term in \ref{PkM}) ) and the second term in \ref{bMk}) ) and \ref{bMk1}) ) below. +ed On theee other haud.‘ the nuxed quantities. στὸ. first liue: of Eq.(131)).4n associated: with: thetu Ie asi prefactor (lL ΓΣ are due to the mapping οι Lagrangian to Eulerian space. and the first bracket in Eq.(131)) expresses the (small) effect of primordial nou- on this mapping.," On the other hand, the terms in the first line of \ref{xiMlin}) ), associated with the prefactor $(1+\delta_{LM})$ in \ref{xiM1M2}) ), are due to the mapping from Lagrangian to Eulerian space, and the first bracket in \ref{xiMlin}) ) expresses the (small) effect of primordial non-Gaussianity on this mapping." + Another differeuce between s(115)) Eqs.(105}) :and (131: )) aud previous works is that (within sone approximation) we take mto account the difference between Lagraugian and Euleriau distances s aud c., Another difference between \ref{xiM1M2}) ) and \ref{xiMlin}) ) and previous works is that (within some approximation) we take into account the difference between Lagrangian and Eulerian distances $s$ and $x$. + This can play a non-uecelieible role as seen in Fie., This can play a non-negligible role as seen in Fig. + 5. below., \ref{figbiasM_z0_r50} below. + We show in Fie., We show in Fig. + 5 the halo bias bajGe). as a functiou of o(AL) at fixed distance +=505. Mypce aud redshitt 7=0. for fxp=£200 and fxy=0.," \ref{figbiasM_z0_r50} the halo bias $b_M(x)$, as a function of $\sigma(M)$ at fixed distance $x=50 h^{-1} $ Mpc and redshift $z=0$, for $\fNL=\pm 200$ and $\fNL=0$." + We display both the nonlinear result (solid line} of Eq.(115)) ancl the linear result (dot-dashed line) of Eq.(131))., We display both the nonlinear result (solid line) of \ref{xiM1M2}) ) and the linear result (dot-dashed line) of \ref{xiMlin}) ). + In addition. for the (απία case we also displav the bias obtained by setting s=or iu Eq.(115)).," In addition, for the Gaussian case we also display the bias obtained by setting $s=x$ in \ref{xiM1M2}) )." + As in Valageas (20091). for the Caussian case (fxp= 0) we obtain a good agreement with the fits to muuerical simulations of Sheth. Mo Tormen (2001) and Pillepich (2009).," As in Valageas (2009b), for the Gaussian case $\fNL=0$ ) we obtain a good agreement with the fits to numerical simulations of Sheth, Mo Tormen (2001) and Pillepich (2009)." + Moreover. we cau see tjat it isunportaut to take into account the displacement of: the halos through; 116 Eq.(116)). as the approximation1 s=oe significautl overestinates the bias.," Moreover, we can see that it isimportant to take into account the displacement of the halos through \ref{xs}) ), as the approximation $s=x$ significantly overestimates the bias." + We checked that using- the simpler- --- Eq.(117)) gives- a close result the oue obtained with Eq.(116)) aud also agrees with the sinulatious., We checked that using the simpler \ref{sx}) ) gives a close result to the one obtained with \ref{xs}) ) and also agrees with the simulations. +. Thus.: for. practical. purposes it⋅⋅is sufficient⋅⋅ to use Eq.(117)).," Thus, for practical purposes itis sufficient to use \ref{sx}) )." + We can see that for all cases shown in Fie., We can see that for all cases shown in Fig. + he linear bias from Eq.(131)) eives results that are very lose to the fully nonlinear expression (115))., \ref{figbiasM_z0_r50} the linear bias from \ref{xiMlin}) ) gives results that are very close to the fully nonlinear expression \ref{xiM1M2}) ). + This justifies +je use of such Luearized expressions in this regine., This justifies the use of such linearized expressions in this regime. + This will be especially useful in section L2.. where we consider +je bias of dark matter halos in Fourier space.," This will be especially useful in section \ref{Fourier-bias}, , where we consider the bias of dark matter halos in Fourier space." + Indeed. it," Indeed, it" +In (his paper we are interested in continuous solutions to hyperbolic svstems in dimension one.,In this paper we are interested in continuous solutions to hyperbolic systems in dimension one. + Our work will focus on solutions εἰ.)=QU(I.m)ω. where d is an integer. of hyperbolic svstems which are cliagonal. i.e.," Our work will focus on solutions $\d{u(t,x)=(u^i(t,x))_{i=1,\dots, d}}$, where $d$ is an integer, of hyperbolic systems which are diagonal, i.e." + AN ZA4(T) with - Asg2(P) mu,"order given by \cite{Boyd,Kapusta} + N^2 g^4(T), with N g^2(T) =." += The perturbative interaction measure thus does show the observed scaling im N—1 justB mentioned.B assuming. .NTg doeis kept constant.," The perturbative interaction measure thus does show the observed scaling in $N^2-1$ just mentioned, assuming $N~\!g^2$ is kept constant." + In ((2)).OV Ay definesH the latlice. scale. which in the mentioned 5U(3) lattice studies. |l] was found to be determined by 0.25.," In \ref{gpert}) ), $\Lambda_T$ defines the lattice scale, which in the mentioned $SU(3)$ lattice studies \cite{Boyd} was found to be determined by $T_c/\Lambda_T = 7.16 \pm 0.25$ ." +" In this case. we thus obtain 1ΠΠΡΟ. At T/T.=3. we have Ny,70.13. which isstill about a factor 3 below the (continuum exirapolated) lattice result Ay,»0.4."," In this case, we thus obtain g^4=. At $T/T_c = 3$, we have $\Delta_{pert} \simeq 0.13$, which isstill about a factor 3 below the (continuum extrapolated) lattice result $\Delta_{lat} \simeq 0.4$." + Hence at this temperature. leading order perturbation theory cannot vel reproduce the plasma interaction.," Hence at this temperature, leading order perturbation theory cannot yet reproduce the plasma interaction." +" Nevertheless. we have here c0.19 for the strong coupling ας. so that in principle perturbation theory seems to be applicable. and we could expect that at somewhat higher temperatures. above T/T,~5—10. the perturbative form might account for the latlice result."," Nevertheless, we have here $\alpha_s=g^2/4\pi \simeq 0.19$ for the strong coupling $\alpha_s$, so that in principle perturbation theory seems to be applicable, and we could expect that at somewhat higher temperatures, above $T/T_c \simeq 5-10$, the perturbative form might account for the lattice result." +Phe authors would like to thank the technical stall at the AAT for their helpful assistance during the acquisition of the spectroscopic data.,The authors would like to thank the technical staff at the AAT for their helpful assistance during the acquisition of the spectroscopic data. + Also to Dr John Ixielkopf. (UofL) for his expertise in developing the University of Louisville Telescope at MIXO and to Roger MeQueen in taking some of the photometric data., Also to Dr John Kielkopf (UofL) for his expertise in developing the University of Louisville Telescope at MKO and to Roger McQueen in taking some of the photometric data. + We thank the anonymous referee for their diligence ancl many helpful comments that have made substantial improvemoents to this paper., We thank the anonymous referee for their diligence and many helpful comments that have made substantial improvements to this paper. + This project is supported by the Commonwealth of Australia uncer the International Science. Linkages program., This project is supported by the Commonwealth of Australia under the International Science Linkages program. + This project used the facilities of SIAIBAD. LIPPARCOS and. LRA.," This project used the facilities of SIMBAD, HIPPARCOS and IRAF." + This research has macle use of NASA's Astrophysics Data System., This research has made use of NASA's Astrophysics Data System. +"K1, respectively.",", respectively." + The most striking fact shown by these plots is the marked evolution of component #33., The most striking fact shown by these plots is the marked evolution of component 3. +" For the specific case ofNar, in the pre-outburst epoch this component is almost completely saturated, while on day +1.5 its depth has decreased by about a factor 2."," For the specific case of, in the pre-outburst epoch this component is almost completely saturated, while on day +1.5 its depth has decreased by about a factor 2." +" The line appears to have weakened further on day +12.5, after which it does not show any significant evolution up to the last epoch covered by our data (+46.6)."," The line appears to have weakened further on day +12.5, after which it does not show any significant evolution up to the last epoch covered by our data (+46.6)." +" The column density retrieved from component #33 changes from logN ~12.9 on day —672 to ~12.1 on day +1.5, to finally reach ~11.3 on day 22.6, implying a variation of over a factor 30."," The column density retrieved from component 3 changes from $\log N\sim$ 12.9 on day $-$ 672 to $\sim$ 12.1 on day +1.5, to finally reach $\sim$ 11.3 on day +22.6, implying a variation of over a factor 30." +" The line width (b=FWHM/1.665) derived for this component ranges between 3 and 4 km s! during the post-outburst epochs, while for the pre-outburst epoch the best fit gives b ~8.5 km s!."," The line width $b$ =FWHM/1.665) derived for this component ranges between 3 and 4 km $^{-1}$ during the post-outburst epochs, while for the pre-outburst epoch the best fit gives $b\simeq$ 8.5 km $^{-1}$." +" This is a further indication that an additional component is present prior to outburst, most likely due to the M giant intrinsic absorption (see Sect. 4))."," This is a further indication that an additional component is present prior to outburst, most likely due to the M giant intrinsic absorption (see Sect. \ref{sec:giant}) )." +" In general, the behavior seen in H&KK is very similar to that ofNar D, with component #33 clearly decreasing in intensity, both between the pre-outburst (—672) and the first outburst (41.5) epochs, and between the first two outburst epochs (1.5, +12.5)."," In general, the behavior seen in K is very similar to that of D, with component 3 clearly decreasing in intensity, both between the pre-outburst $-$ 672) and the first outburst (+1.5) epochs, and between the first two outburst epochs (+1.5, +12.5)." +" Importantly, the pronounced evolution displayed during the first two weeks after the outburst clearly demonstrates that this cannot be attributed solely to the disappearance of the photospheric component."," Importantly, the pronounced evolution displayed during the first two weeks after the outburst clearly demonstrates that this cannot be attributed solely to the disappearance of the photospheric component." +" In fact, during these phases the overall luminosity of the system is ~100 times larger than that of the M giant, making its relative contribution to the total spectrum negligible."," In fact, during these phases the overall luminosity of the system is $\sim$ 100 times larger than that of the M giant, making its relative contribution to the total spectrum negligible." +" This is illustrated in Fig. 7,,"," This is illustrated in Fig. \ref{fig:ircana3}," +" where we plotted the comparison between the evolution of the near-IR 48662 and D, across several of the epochs covered by our observations.", where we plotted the comparison between the evolution of the near-IR $\lambda$ 8662 and $_1$ across several of the epochs covered by our observations. +" While during quiescence the complex profile of is clearly detected, this is completely missing during the outburst."," While during quiescence the complex profile of is clearly detected, this is completely missing during the outburst." +" On the contrary, barring the variation seen in component #33, the blue-shifted components are always visible, ot all epochs."," On the contrary, barring the variation seen in component 3, the blue-shifted components are always visible, ot all epochs." + The same is true for the H&KK features., The same is true for the K features. +" Therefore, absorption components #11, #22 and #33 certainly arise outside of the stellar atmosphere, and outside the nova ejecta."," Therefore, absorption components 1, 2 and 3 certainly arise outside of the stellar atmosphere, and outside the nova ejecta." +" In addition, the variation seen in component #33 tells us that at least that feature cannot be interstellar."," In addition, the variation seen in component 3 tells us that at least that feature cannot be interstellar." +" In this respect, an even more conclusive argument about the nature of all blue-shifted features comes from a closer inspection of Fig. 6.."," In this respect, an even more conclusive argument about the nature of all blue-shifted features comes from a closer inspection of Fig. \ref{fig:kievol}." +" At variance with what is seen for D and H&KK, the absorptions disappear almost completely during the outburst (component #22 is still visible on days +1.5 and +12.5."," At variance with what is seen for D and K, the absorptions disappear almost completely during the outburst (component 2 is still visible on days +1.5 and +12.5." + See also Sect. 6))., See also Sect. \ref{sec:disc}) ). + This definitely rules out an interstellar origin for these lines., This definitely rules out an interstellar origin for these lines. + A hint to the physical mechanism responsible for the observed line variations comes from the following consideration., A hint to the physical mechanism responsible for the observed line variations comes from the following consideration. +" The variations appear to be stronger for species with lower ionization potentials: the largest changes are seen for (4.3 eV), while the weakest ones are observed for (11.9 eV), withNar (5.1 eV) showing an intermediate behavior."," The variations appear to be stronger for species with lower ionization potentials: the largest changes are seen for (4.3 eV), while the weakest ones are observed for (11.9 eV), with (5.1 eV) showing an intermediate behavior." +" This suggests that the weakening of absorption features is related to a change in the ionization balance, induced by the radiation field produced by the nova and/or by the interaction between the nova ejecta and pre-existing, circumstellar material."," This suggests that the weakening of absorption features is related to a change in the ionization balance, induced by the radiation field produced by the nova and/or by the interaction between the nova ejecta and pre-existing, circumstellar material." +" At variance with the SN case, where the system is completely disrupted by the explosion, the recurrent nova case offers the possibility of studying the CS environment also after the outburst."," At variance with the SN case, where the system is completely disrupted by the explosion, the recurrent nova case offers the possibility of studying the CS environment also after the outburst." +" With the aid of the +742 epoch, obtained when the system is supposed to be back to the quiescence phase (Worters et al. 2007)),"," With the aid of the +742 epoch, obtained when the system is supposed to be back to the quiescence phase (Worters et al. \cite{worters}) )," + one can directly verify whether the outburst has modified the CSM in a sensible way., one can directly verify whether the outburst has modified the CSM in a sensible way. +" In this respect, the evolution shown in Figs. 4,, 5,,"," In this respect, the evolution shown in Figs. \ref{fig:caevol}, \ref{fig:naevol}, ," + and 6 is revealing., and \ref{fig:kievol} is revealing. +" Although the post-outburst epoch was obtained at a similar orbital phase of the pre-outburst epoch —672 (see Table 1)), the profile is markedly different, with an enhanced absorption in the blue."," Although the post-outburst epoch was obtained at a similar orbital phase of the pre-outburst epoch $-$ 672 (see Table \ref{tab:obs}) ), the profile is markedly different, with an enhanced absorption in the blue." +" This is common toCan,Nat, and Kr, pointing to a global modification of the circumstellar environment produced by the nova ejecta."," This is common to, and , pointing to a global modification of the circumstellar environment produced by the nova ejecta." + This conclusion is strengthened by the analysis of the Ha profile presented in Fig. 9.., This conclusion is strengthened by the analysis of the $\alpha$ profile presented in Fig. \ref{fig:hevol}. +" The post-outburst profile departs from that seen during the 3 pre-outburst epochs, in that the absorption extends far more into the blue, reaching a systemic velocity of about —60 km s~!."," The post-outburst profile departs from that seen during the 3 pre-outburst epochs, in that the absorption extends far more into the blue, reaching a systemic velocity of about $-$ 60 km $^{-1}$." +" Given the evolution shown in the pre-outburst phases, it is evident that the variation seen on day +742 cannot be explained in terms of the pure orbital motion of the M giant."," Given the evolution shown in the pre-outburst phases, it is evident that the variation seen on day +742 cannot be explained in terms of the pure orbital motion of the M giant." + The question as to whether this is a transient phenomenon or a more stable perturbation of the circumstellar configuration will have to await for follow-up high resolution spectroscopy., The question as to whether this is a transient phenomenon or a more stable perturbation of the circumstellar configuration will have to await for follow-up high resolution spectroscopy. + A very remarkable fact observed inconjunction with the weakening of component #33 is the disappearance of a narrow, A very remarkable fact observed inconjunction with the weakening of component 3 is the disappearance of a narrow +The fist stars du the universe may have contributed early cosmic reionization and may have also euriched the interealactic mediua with heavy clemeuts such as carbon. oxvecu and dion (see. e.g. Bronunctal.(2009)— for a review).,"The first stars in the universe may have contributed early cosmic reionization and may have also enriched the inter-galactic medium with heavy elements such as carbon, oxygen and iron (see, e.g. \citet{bromm09} for a review)." +" Future observatious of tho cdistaut ""universe will exploit large grouud-based aud space-borne telescopes such asTelescope audTelescope to answer the important questions of how and when the first stars were formed aud how they affected the subsequent evolution of the uuiverse.", Future observations of the distant universe will exploit large ground-based and space-borne telescopes such as and to answer the important questions of how and when the first stars were formed and how they affected the subsequent evolution of the universe. +emission follows that of stars.,emission follows that of stars. +" It was shown by Cowieetal. that nearby LAEs (z< 1.0) have a variety of (2011)morphologies, some are disky, while others are mostly compact galaxies."," It was shown by \citet{Cowie11} that nearby LAEs $z \lesssim 1.0$ ) have a variety of morphologies, some are disky, while others are mostly compact galaxies." +" Galaxy morphology is closely tied to galaxy formation and evolution, and it is related to the galaxy mass."," Galaxy morphology is closely tied to galaxy formation and evolution, and it is related to the galaxy mass." +" As demonstrated in Figure 5,, which shows a sample of four galaxies ofdifferent masses at z=0.2, the Lya morphology changes with galaxy mass."," As demonstrated in Figure \ref{fig:lyamulti}, which shows a sample of four galaxies ofdifferent masses at $z=0.2$, the $\lya$ morphology changes with galaxy mass." +" In galaxies with lower mass (Mi<10'! Mo), the Lya luminosity is low (LiyaSS10? ergs-!), the Lyo morphology is highly compact."," In galaxies with lower mass $\Mtot \lesssim 10^{11}~\Msun$ ), the $\lya$ luminosity is low $\La \lesssim 10^{42}~\ergs$ ), the $\lya$ morphology is highly compact." +" At higher mass (Mio,=10!! Mo), the Lya luminosity is high (Lryo=10%erg s~'), Lya morphology shows disky and spiral structures."," At higher mass $\Mtot \gtrsim 10^{11}~\Msun$ ), the $\lya$ luminosity is high $\La \gtrsim 10^{42}~\ergs$ ), $\lya$ morphology shows disky and spiral structures." + This plot suggests that the various morphologies observed in low-redshift LAEs may reflect a wide range of galaxy mass in the sample., This plot suggests that the various morphologies observed in low-redshift LAEs may reflect a wide range of galaxy mass in the sample. +" We note that in Figure 4,, the azimuthally averaged surface brightness at z=3 is somewhat fainter than the detection threshold ofrecent narrow-band surveys, c10718ergss!cm-?arcsec? (Ouchietal. 2008)."," We note that in Figure \ref{fig:uvdist}, the azimuthally averaged surface brightness at $z \gtrsim 3$ is somewhat fainter than the detection threshold ofrecent narrow-band surveys, $\sim 10^{-18} ~\rm ergs \; s^{-1} \; cm^{-2} \; arcsec^{-2}$ \citep{Ouchi08}." +". However, since the local Lya distribution is inhomogeneous and anisotropic, as shown in Figure 3,, so bright regions with flux above the threshold may be detectable by such surveys."," However, since the local $\lya$ distribution is inhomogeneous and anisotropic, as shown in Figure \ref{fig:img}, so bright regions with flux above the threshold may be detectable by such surveys." + 'The detectability of these galaxies depends strongly on the sensitivity of the surveys., The detectability of these galaxies depends strongly on the sensitivity of the surveys. +" In the present work, unless noted otherwise, the Lya luminosity is computed by collecting all escaped photons without a flux limit."," In the present work, unless noted otherwise, the $\lya$ luminosity is computed by collecting all escaped photons without a flux limit." +" If a detection limit of a given instrument is imposed, the luminosity of individual galaxies, in particular that of the faint ones, may be reduced significantly, as suggested by Zhengetal.(2010).."," If a detection limit of a given instrument is imposed, the luminosity of individual galaxies, in particular that of the faint ones, may be reduced significantly, as suggested by \citet{Zheng10}. ." + The corresponding multi-wavelength SEDs of the galaxy sample in Figure 3 are shown in Figure 6.., The corresponding multi-wavelength SEDs of the galaxy sample in Figure \ref{fig:img} are shown in Figure \ref{fig:sed}. +" The shape of the SED changes significantly from z—10.2 to z=0, as a result of changes in radiation source and environment, since the radiation from stars, absorption of ionizing photons by gas and dust, and re-emission by the dust evolve dynamically with time."," The shape of the SED changes significantly from $z = 10.2$ to $z = 0$, as a result of changes in radiation source and environment, since the radiation from stars, absorption of ionizing photons by gas and dust, and re-emission by the dust evolve dynamically with time." + The Lya line appears to be strong in all cases., The $\lya$ line appears to be strong in all cases. + The deep decline of Lyman continuum <912A) at high redshifts (z>7) is caused by strong(I absorption of ionizing photons by the dense gas., The deep decline of Lyman continuum $l \le 912~\A$ ) at high redshifts $z \gtrsim 7$ ) is caused by strong absorption of ionizing photons by the dense gas. +" Galaxies at lower redshift have a higher floor of continuum emission from stars and accreting BHs, a higher ionization fraction of the gas, and a higher infrared bump owing to increasing amount of dust and absorption."," Galaxies at lower redshift have a higher floor of continuum emission from stars and accreting BHs, a higher ionization fraction of the gas, and a higher infrared bump owing to increasing amount of dust and absorption." +" Moreover, due to the effect of negative k-correction, the flux at observed frame A500µπι stays close in different redshifts."," Moreover, due to the effect of negative k-correction, the flux at observed frame $\lambda \gtrsim 500~\rm \mu m$ stays close in different redshifts." +" Our calculations show that the main progenitor has a flux of f,=0.057mJy at z~6 and 0.02mJy at z~8.5 at 850um in observed frame.", Our calculations show that the main progenitor has a flux of $f_{\nu} = ~0.057~\rm mJy$ at $z \sim 6$ and $0.02~~\rm mJy$ at $z \sim 8.5$ at $850~\rm \mu m$ in observed frame. +" The new radio telescope, (ALMA) may be able to Millimeter/submillimeterdetect such galaxies at z~6 with ~2 hours integration, and at z~8.5 for ~20 hours with 16 antennas (Yajimaetal. 2011)."," The new radio telescope, (ALMA) may be able to detect such galaxies at $z \sim 6$ with $\sim 2$ hours integration, and at $z \sim 8.5$ for $\sim 20$ hours with 16 antennas \citep{Yajima11A}. ." +". The resulting Lyo properties of the 60 most massive progenitors fromselected snapshots, and their evolution with redshift are shown in Figure 7.."," The resulting $\lya$ properties of the 60 most massive progenitors fromselected snapshots, and their evolution with redshift are shown in Figure \ref{fig:La}." + The top panel shows the emergent Lya luminosity να., The top panel shows the emergent $\lya$ luminosity $\La$. +" The main progenitor has a luminosity of [γαc1043ergs! at zX2, then increases to να~1045erg slatz-2-— 6, owing to the increase of SFR."," The main progenitor has a luminosity of $\La \sim 10^{42}~\ergs$ at $z \lesssim 2$, then increases to $\La \sim 10^{43}~\ergs$ at $z = 2-6$, owing to the increase of SFR." +" At high redshift z>6, the Liyq decreases to ~107?ergs7! due to low escape fraction and absorption by dust."," At high redshift $z \gtrsim 6$, the $\La$ decreases to $\sim 10^{42}~\ergs$ due to low escape fraction and absorption by dust." +" At high redshift, the galaxy size is small and most of the stars form around the galaxy center."," At high redshift, the galaxy size is small and most of the stars form around the galaxy center." +" Hence, the dust compactly distributes around young stars, which effectively absorbs the ionizing photons."," Hence, the dust compactly distributes around young stars, which effectively absorbs the ionizing photons." +" As a result, the intrinsic Lya emissivity drops even though SFR is enhanced by the accretion of cold gas."," As a result, the intrinsic $\lya$ emissivity drops even though SFR is enhanced by the accretion of cold gas." +" However, most of other model galaxies show that the escape fraction of Lya and UV continuum photons monotonically increases with redshift because of lower dust content."," However, most of other model galaxies show that the escape fraction of $\lya$ and UV continuum photons monotonically increases with redshift because of lower dust content." + The escaping process of continuum photons will be discussed in detail in a forthcoming paper (Yajima et al., The escaping process of continuum photons will be discussed in detail in a forthcoming paper (Yajima et al. + in preparation)., in preparation). +" Most of the galaxies at z=3 in this simulation have a luminosity below 104?ergs! the lower limit of many current observations using narrow-band filters, so they may not be observable."," Most of the galaxies at $z \gtrsim 3$ in this simulation have a luminosity below $10^{42}~\ergs$, the lower limit of many current observations using narrow-band filters, so they may not be observable." +" However, the improved sensitivity of deep survey of Cassataetal.(2011) reaches [γα~109!ergs-! at z~2— 6.6, which may detect more faint galaxies as the ones in our sample."," However, the improved sensitivity of deep survey of \citet{Cassata11} reaches $\La \sim 10^{41}~\ergs$ at $z \sim 2 - 6.6$ , which may detect more faint galaxies as the ones in our sample." +" As mentionedin previous sections, the luminosity is calculated as the sum of all escaped photons."," As mentionedin previous sections, the luminosity is calculated as the sum of all escaped photons." +" If we consider only pixels brighter thanS=10-1?ergss!cm? arcsec~?, the detection threshold of high-redshift LAE surveys (e.g., 2010), the total flux of the main progenitor is reduced by a factor of a few, resulting in"," If we consider only pixels brighter than$S = 10^{-18} ~\rm ergs \; s^{-1} \; cm^{-2} \; arcsec^{-2}$ , the detection threshold of high-redshift LAE surveys \citep[e.g.,][]{Ouchi08, Ouchi10}, , the total flux of the main progenitor is reduced by a factor of a few, resulting in" +our group finding algorithm.,our group finding algorithm. + In doing the least squares fit. we seek to minimize 2x. which is defined as and where v is the number of degrees of freedom.," In doing the least squares fit, we seek to minimize $\chi^2$, which is defined as and where $\nu$ is the number of degrees of freedom." + We then use the concentration parameter. defined as Crs= Rizsfrs. to characterize the density profile.," We then use the concentration parameter, defined as $C_{178} = R_{178}/r_{\rm{s}}$ , to characterize the density profile." + In Figure 6 (Left column) we show the measured concentrations versus spin parameters binned by mass., In Figure \ref{Struct} (left column) we show the measured concentrations versus spin parameters binned by mass. + Phere is only a small trend with. spin. ...implying. that the density. structure has only a weak dependence on the angular momentum properties of the halo.," There is only a small trend with spin, implying that the density structure has only a weak dependence on the angular momentum properties of the halo." + In thebottom left. panel of Figure 6... we show," In thebottom left panel of Figure \ref{Struct}, , we show" +went object or its nucleus.,parent object or its nucleus. + Tf so. this would secu o imply that the nuclear mass is quautized with at least three acceptable levels.," If so, this would seem to imply that the nuclear mass is quantized with at least three acceptable levels." + Since the ejected objects all have similar masses initially aud appear o expel mass (or energev) with time from the central QSO into a surrounding host. the discrete ature of the paramcter Af may then suggest that lis mass is ejected in discrete packets.," Since the ejected objects all have similar masses initially and appear to expel mass (or energy) with time from the central QSO into a surrounding host, the discrete nature of the parameter $M$ may then suggest that this mass is ejected in discrete ""packets""." + As far as the formation of galaxies is concerned. hese results do uot change significantly the ricture discussed carlicr (Bell2002a.b)..," As far as the formation of galaxies is concerned, these results do not change significantly the picture discussed earlier \citep{bel02a,bel02b}." + Thev still ugeest that galaxies are created continously hroughout the lite of the Universe., They still suggest that galaxies are created continuously throughout the life of the Universe. + However. if the intrinsic compoucut is eravitationallv produced. it would secur less likely that the model of NarlikarandDas(1980). plays any role.," However, if the intrinsic component is gravitationally produced, it would seem less likely that the model of \citet{nar80} plays any role." + In Fig., In Fig. + & the Zvο intrinsic redshifts are plotted vs Aec on a logarithuuic scale., 8 the $_{N = 2}$ intrinsic redshifts are plotted vs Age on a logarithmic scale. + It is clear that these iutriusic components play a very short-lived part iu the lite of a Sgalaxy. lastingS only for the first 2 mullion years.," It is clear that these intrinsic components play a very short-lived part in the life of a galaxy, lasting only for the first 3 million years." + By removine all ejectionarelated Doppler compoucuts from the redshifts of the compact QSOs near NGC 1068 it has been shown that the remaining intrinsic components can be defined by the relation z; — 0(.062]10NΑΠ where No = 2. Afη|1/2] and » = 0.1.2.3.1.5.," By removing all ejection-related Doppler components from the redshifts of the compact QSOs near NGC 1068 it has been shown that the remaining intrinsic components can be defined by the relation $_{\rm i}$ = $0.062[10N - M]$ where $N$ = 2, $M = [n(n+1)/2]$ and $n$ = 0,1,2,3,4,5." + This is he first iustauce iu which it has been possible to separate out the intrinsic componcut., This is the first instance in which it has been possible to separate out the intrinsic component. + It is shown hat this same relation will it the results obtained w BurbidgeandEHewit(1900) for redshifts jetween Z = 0.06 and z = 0.6. if N = 1 aud Aj=ns where 56 = 0.1.2... 9.," It is shown that this same relation will fit the results obtained by \citet{bur90} for redshifts between z = 0.06 and z = 0.6, if $N$ = 1 and $M = n$, where $n$ = 0,1,2,... 9." +" The Af-valucs or the No = 3 state follow cdirectlv from these wo states and it is shown that together these τος states predict iutriusic redshifts that agree closely with those values found to be preferred iu Cluission-line redshift aualvses from z = 0.06 to z = 2,", The $M$ -values for the $N$ = 3 state follow directly from these two states and it is shown that together these three states predict intrinsic redshifts that agree closely with those values found to be preferred in emission-line redshift analyses from z = 0.06 to z = 2. + These results iudicate that the Az = 0.062 redshift iuterval may thus represent a fundamental redshift spacing that arises from the very nature of] the .iutriusic redshifts., These results indicate that the $\Delta$ z = 0.062 redshift interval may thus represent a fundamental redshift spacing that arises from the very nature of the intrinsic redshifts. +lp Because this relation imeludes a constant (Za = 0.62) which can be related to eravitational redshifts. the tutrinsic components may have a gravitational origin.," Because this relation includes a constant $_{\rm gmax}$ = 0.62) which can be related to gravitational redshifts, the intrinsic components may have a gravitational origin." + If so. this increieut may be evidence for some form of eravitational quantization.," If so, this increment may be evidence for some form of gravitational quantization." +al. (,al. ( +2001). if this wall of irradiated material were optic:uly thick then it would radiate as a black body at the loca temperature. namely that of dust destrucjon (accordlue to Pollack et al.,"2001), if this wall of irradiated material were optically thick then it would radiate as a black body at the local temperature, namely that of dust destruction (according to Pollack et al." + 1991. Τομ120001100 Ix).," 1994, $T_{\rm evap}\!\sim\!1200 - 1400$ K)." +" The position. £,4,. aud height. Lyin. o this inraclatec wall can be computed following the mehods described in Dulle1noud. et al. ("," The position, $R_{\rm rim}$, and height, $H_{\rm rim}$, of this irradiated wall can be computed following the methods described in Dullemond et al. (" +2001).,2001). + Also. Muzerolle et al. (," Also, Muzerolle et al. (" +20:3b) inve recently fitted the neamr-IR lump iu the SEDs of Classical T Tauri stars with a black body arising frOll a sinilar mode for a dust destruction wall.,2003b) have recently fitted the near-IR bump in the SEDs of Classical T Tauri stars with a black body arising from a similar model for a dust destruction wall. + These αιthors 8nd best-fit teuperatures for the wall ο]re around 1100 IK. The main difference with respect O he first miedel is that the dust is not treated as opticaIv thick but the yosition of the run is computed with the sale dust size distributions as in D'Alessio et al. (, These authors find best-fit temperatures for the wall to be around 1400 K. The main difference with respect to the first model is that the dust is not treated as optically thick but the position of the rim is computed with the same dust size distributions as in D'Alessio et al. ( +2001) aid the mehods used in Calvet et al. (,2001) and the methods used in Calvet et al. ( +1991. 1992).,"1991, 1992)." + The projected area. A. of the rim is computed as in appeudix D iu Dullemond et al. (," The projected area, $A$, of the rim is computed as in appendix B in Dullemond et al. (" +2001).,2001). + The solid angle SULtended by this area is Afd?. where d is the distance | the source.," The solid angle subtended by this area is $A/d^{2}$, where $d$ is the distance to the source." + The normalization coustaut needed to fit jack body to the near-IR photometry is proportional the solid angle 3bteuded dy the rim. SO after COuputiug the position of the wall. P4. we can estimate i6 corresponding height so that the enuüttiug area is sistent with the phoolnetry.," The normalization constant needed to fit a black body to the near-IR photometry is proportional to the solid angle subtended by the rim, so after computing the position of the wall, $R_{\rm rim}$, we can estimate the corresponding height so that the emitting area is consistent with the photometry." + Then. 1sine equatio1i (HD) in Dullemioud et al. (," Then, using equation (14) in Dullemond et al. (" +"2001) 1a nple iterative procedure. we get R4,=0.31 AU and hay,0.ο AU.","2001) in a simple iterative procedure, we get $R_{\rm rim}\!=\!0.31$ AU and $H_{\rm +rim}\!=\!0.06$ AU." +" Also. using the equation for Ri, 1 Muzerolle e al. ("," Also, using the equation for $R_{\rm rim}$ in Muzerolle et al. (" +"20035) similar results were obtained (umuelv fu,0.31. AU and Jha,=001 AU).","2003b) similar results were obtained (namely $R_{\rm +rim}\!=\!0.31$ AU and $H_{\rm rim}\!=\!0.04$ AU)." + This aerecimoent ix due to the fact that the different optical epth assume for the dust in Muzerolle et al. (, This agreement is due to the fact that the different optical depth assumed for the dust in Muzerolle et al. ( +2003) is σοιvensated by the autoimaciatiou correction introduced lyv Dulleinoud et al. (,2003) is compensated by the autoirradiation correction introduced by Dullemond et al. ( +2001).,2001). +" It is reniarsable that the wight obtained iu this wav i wilar to the height of the surface cisk, Component at Bay Choa=0.06 AU)."," It is remarkable that the height obtained in this way is similar to the height of the surface disk component at $R_{\rm rim}$ $H_{\rm +model}\!=\!0.06$ AU)." +" Πωπονο, we must. take into accouut that the height of a snele disk where the large oOoradis are in the mid-plane aud the s11all grains in upper l:wers mav be different tothis’."," However, we must take into account that the height of a single disk where the large grains are in the mid-plane and the small grains in upper layers may be different to." +. Eimer conclusions about these heights require a self-conusisteit deerhnunation of the vertical structure with settled dust. sveliicliis left for future work.," Firmer conclusions about these heights require a self-consistent determination of the vertical structure with settled dust, which is left for future work." + As quoted in Natta et al. (, As quoted in Natta et al. ( +"2001). the hypothesis of the radiated wall assumes a negligibleo opacity of the eas disk mside Ryn, so that the stellar radiation is abe to reach the inner wall.","2001), the hypothesis of the irradiated wall assumes a negligible opacity of the gas disk inside $R_{\rm rim}$ so that the stellar radiation is able to reach the inner wall." + The caleulaion of the actua eas oicltv inside the wall is ciffieult because of the imutiple omc aud molecular absorption lines preseut., The calculation of the actual gas opacity inside the wall is difficult because of the multiple atomic and molecular absorption lines present. + Muzerolle al. (, Muzerolle et al. ( +20035) studied the opacity of a gaseous disk inside je dust destruction radius usine an extended set of gas Qpacitics aud a detailed treatment of the heating of the ooOas due to accretion and stellar ealation.,2003b) studied the opacity of a gaseous disk inside the dust destruction radius using an extended set of gas opacities and a detailed treatment of the heating of the gas due to accretion and stellar irradiation. + They fornd twat for typical parameters of TAcBe stars the optical depth of the inner hole would be low enough to allow a substantial fraction of the stellar radiation to reach the dust sublimation wall.," They found that for typical parameters of HAeBe stars, the optical depth of the inner hole would be low enough to allow a substantial fraction of the stellar radiation to reach the dust sublimation wall." + The thin solid line in Fie., The thin solid line in Fig. + 9 ds the contribution of the radiated wall to the SED., \ref{hd34282fit} is the contribution of the irradiated wall to the SED. + The thick solid line is the addition of the Ixurucz model and the contributions to the TR excess of the wall aud the mid-plane and surface clisks., The thick solid line is the addition of the Kurucz model and the contributions to the IR excess of the wall and the mid-plane and surface disks. + Iu Table 5. a smuniuw of the iuput paramcters for the models is given., In Table \ref{DISKS} a summary of the input parameters for the models is given. + Also the values found for the height at 10 AU aud the disks nasses for cach component are given., Also the values found for the height at 10 AU and the disks' masses for each component are given. +The dust distribution function /Ge) used to calculate the halo model (see Equation CAS) aud Figure [)) assumes a lack of absorption/scattering iu the imiediate vicinity of the source.,The dust distribution function $f(x)$ used to calculate the halo model (see Equation (A8) and Figure \ref{rad}) ) assumes a lack of absorption/scattering in the immediate vicinity of the source. + Such dust. distribution is consistent with the lack of evideuce of significant intrinsic absorption in the ⊓⊔↕⋜⋃⋅⊽, Such dust distribution is consistent with the lack of evidence of significant intrinsic absorption in the binary. +"∖⊽⋅⊺∐≺↵⋃↥↽≻↥↽≻↩↓⋅∐∐⊔∩∐↕∐≺↵∐⋃⋅⋯⊳∖↓∢∙∢∙∩∐⋯∐⊔⇂≺↵∐⊳∖∐⊽∖⇁↥⊳∖⋜≹⊳∖↥∩∖∖↽⋜↕⊳∖−≻⋅↻≍∐⋗−↓∢∙∢∙⋯−↸↜↗⋝⋅⋅∖∖↽∐↥≺↵. . . . . op""I D> poe ⋅ ∐↩↕∩↕⋜↕↥⋜↕∣≻⊳∖≺∐⋅∣≻↕∐∑≟∢∙∩↥⊔∐∐≺⇂↩∐⊳∖↥⊽∖⇁∐↕≺↵⋜↕⊳∖⋯⋅≺↵≺⇂∐⋅∩⋯⇀∖≟−↕⋅⋜↕⊽∖⇁⊳∖↽≻≺↵∢∙⋃⋅⋜⊔∙∐⋜↕∐∑∸≺↵⊳∖∣≻⊽∖⇁∿↕↽∐≻↸⋰∣⋰⊒↙⋖∫⋅∙⋝∖∖↽⊔↕ ∐⋜↕↓⋅⊽∖⊽↥↽≻∐⋜↕⊳∖≺↵⋅∟∩∖∖↽↥∐⋃⋅↥∐⊳∖↕∢∙⋜≹∣≻⊳∖∩↓⋅↽≻↕∎∩∐∖∖↽∩⋃↥≺⇂∣≻↩≺↵⊸∖↥↽≻≺↵∢∙↕≺↵≼⊔∎⋯∩⊳∖↕∩↥∎⇀↖≟−↕⋅⋜↕⊽∖⇁⊳∖⋜↕"," The upper limit on the intrinsic column density is as low as $2.6\times10^{21}$ $^{-2}$ \citep{2007A&A...473..545B,2009ApJ...697..592T}, while the total absorbing column density measured from X-ray spectra changes by $\lesssim 10\%$ \citep{2009ApJ...697..592T} with binary phase." +↓⋅≺↵≺↵⋯↥↕≺↵≼⊔∎⋜↕↓⋅∐⋅∩∐ ∐≺↵≺⇂∩∐∩↕⋅⊳∖↕⋜⋃⋅⋅∖∖↽∐≺↵↓⋅≺↵∐⊳∖∖∖↽↥∐≺⊔⊳∖⊳∖⋃∐∎∐∙↥≺↲∐∐⊽∖⊽↕⋅⋜⋃⋅≺↵∐≺↵≺⋜↜≺↵⋅∑≟⋅⋅↗⋝ ∖↾∖⊽≺↵⊳∖∐⋯∐≺⇂⋜↕↥⊳∖∩↥↽≻∩↥∐↕∩⋯↕∐⋜↕⋅∎∐⋜↕≺⇂≼∐⋃∩∐↕∩↕↥≺↵≺⇂⋃⊳∖↕≺∎⊳∖⋃⋅∐≻⋯↥∩∐↥↽≻↓⋅∩↓∐≺↲⋅," Low intrinsic absorption would be expected if most of X-rays are emitted far from the donor star, where its wind is sufficiently rarefied (e.g. \citealt{2011MNRAS.411..193S}) )." +∐≺↲⋔⊳∖↕⊳∖∢∙⋜↕⊓≺↵↕⋅∐∑≟ ∐⋯⇂≺↵↥∖∖↽↩⋃⊳∖≺↵∐⋜↕⊳∖↕∖∖↽∩∐⋅≺↵≺↵↥↽≻⋜⋃⋅⋜↕⊔≺↵≺↵↕⋅⊳∖↸∫⊳↔⊽⋜↕∐≼⇂↭⋟∖∖↽↥∏∢∙∐∢∙⋜↕∐⋜↕⊓⋜↕↕∐∖⇁⋜↕∐∐↵⊳∖∖∖↽∎∐∐∐⋅⋜↕↕∐≺↲↥⋅∣∐⋅∩⋯⇂ ⋅⋜↕∐∑≟≺↵⊳∖⋅≺⇂≺↵↥↽≻↩∐≺∐∐∑≟∩∐↕∐≺↵⋜↕∢∙⋯⋜↕↥↽∐⋅∩↥↽≻↩↓⋅∏≺↵⊳∖∩↥∎↕∐≺↵≺⊳∖↕∑≟↥⋅⋜↕∎↕⊳∖⋅⊺∐≺↵↓⋅≺↵↥∎∩↕⋅≺↵⋅↕∐≺↵∐≺↵↕⋅≺↵∎⋜↕∢∙∏∐⋜↕↕⇂≺↵ ∐⋯⇂≺↵↥≺↽↓⋃⋜↕∐↕⋜↕⋃∖⇁," We should also point out that, in addition to the dust distribution profile, the dust scattering model we use has two free parameters $S$ and $\Theta$ ) which can attain values within rather broad ranges, depending on the actual properties of the dust grains." +↩↥⊽∖⇁↓∎∐⊳∖↕∐≺↵∩∣≻⊳∖≺↵↥⋅∖⇁↩≺∣∐⋅↥∑≟⇂∐∐↩⊳∖⊳∖≺∐⊳∖↕⋅∎∥⊔↥∩∐≺⇂∩≺↵⊳∖∐∩↕∑≟⋃⋜⋃⋅⋜↕∐↕≺↵≺↵∐↕⋜↕↕∐≺↵≺↵⊸∖↕≺↵∐⇂≺↵≺⇂ ≺↵∐∏⊳∖⊳∖↥∩∐↥⊳∖⋜⊓⇂⋃⊳∖↕∐⋜↕↥∩⋅↕↕↥∎⋜∥∙↕⋅↕↩∩∣≻⊳∖≺↵↥⋅∖⇁≺↵≺⇂⋜↕∠↥∐⋯⋜↕," Therefore, the mere fact that the model qualitatively fits the observed brightness distribution does not guarantee that the extended emission is a dust halo." +↥⋜↕⊳∖⊽∖⇁∐∐≺↵⋃⋅⊽∖⊽⋜↕∐≼⇂↕∐≺↵∐⋜≹⋅≼⇂⊳∖↥↽≻≺↵∢∙⋃⋅⋯∐∩∎∐≺↵ ∎∐∐≺↵↕⋅↩⊸∖↕≺↵∐≼⇂≺↵≺⇂↩∐∏⊳∖⊳∖↥∩⊔∖∖↽∩⋃⇂≺⇂∣≻≺↲ ∐∐∢∙⋃∐↕∩↩⊸∖↥↽≻↥⋜↕↕∐∣≻⊽∖⊽⋜⊔⇂⋃⊳∖↕∐⋜↕↥∩⋅∺↕∑≟∐∐↕∢∙⋜⋃∐⊳∖↽≻≺," In fact, the observed azimuthal asymmetry and the hard spectrum of the inner extended emission would be difficult to explain by a dust halo." +↵∢∙⋃⋅⋜↕↥⊳∖∩↥∎↕≺↲↥∏↕∑≟∎⊳∖ ≺↵⊸∖↥↽≻≺↵∢∙↕↩≺⊔∎↕⋅∩⋯∐⋜↕↥∩∐↕⋯⇂≺↵⊳∖⋅∺↥↽≻↩, Significant spectral softening is expected from halo models. +∢∙↕∎∢∙⋜↕∐⊽∖⊽⋅↥∎∩↓⋅↕∐↩⋔⇂⊳∖↕↕⋯⇂≺↵↥⋃⊳∖≺↵≺⇂⋅↕∐≺↲⊳∖↥↽≻⋜↕∏⋜↕∐⊽∖⊽↥⊔≺↵∑≟↓⋅⋜↕↕≺↲≺⇂⋖∫∣⋈↵↕∖∖↽≺↵≺↵∐ ∣↝∶⊇∪∣∣⋜↕∐≺⊔∃∩⊔⋝⊳∖↥↽≻↩∢∙⋃⋅⋃⊔↥⊳∖≺↵⊸∖↥↽≻≺↵∢∙↕↩≼⊔∩∐⋜≹∖⇁≺↵↕↴↓⋯↓⊓≃↕↴↓⋯↥⊔↿↲↱⊇≃∶⋝⋅⋅↴⋅∣≻≺↵∢∙⋜⋯⊳∖≺↵↕∐≺↵⊳∖∢∙⋜↕⊓≺↲↕⋅↥⊔∑⇁⋟∢∙⋅∩↜∖↠∖− ↠∖≺↵∢∙∏∩∐√⊼∖↸∫≿↴⋝↖≿↴⊋↸⋮⊳∖≺↵≺↵⇀−∖↥↽≻↥↽≻↩∐≺∎⊸∖⇀−⊔⋅↕∐⊳∖↕≺↵⋜∥⇂⋅," Specifically, for the dust model used, the spatially integrated (between $r=20''$ and $60''$ ) spectrum is expected to have $\Gamma_{\rm halo}\simeq \Gamma_{\rm point}+2\simeq3.5$, because the scattering cross-section $\sigma_s(E)\propto E^{-2}$ (see Appendix A)." +∖∖↽≺↵∎∐≺⇂⋜↕⊳∖↥∑≟∐∐↕∢∙⋜↕∐∐⊽∖⊽∐⋜⋯⇂≺↵↕⋅⊳∖↥↽≻≺↵∢∙⋃⋅⋯∐⋅↕↴≈↽⊔∫⋅ ⋃∐↕∐≺↵∩↕∐≺↵↕," Instead, we find a significantly harder spectrum, $\Gamma\approx1.9$." +⋅∐⋜↕∐≺⇂⋅↕∐≺↵∩⊔↩↓⋅≺↵⊸∖↕↩∐⇂↩≺⇂↩∐∐⊳∖⊳∖↕∩∐↥⊳∖↥∐≼≺↵≺↵≺⊔∐⋯∙∐⊳∖∩↥∎↕≺↵↕⋅⋜↕∐≼⊔∐∩∐↵⊳∖⊽∖⇁∐⊔∐≺↵⋃⋅↥∢∙⋅∐≺↵∐∢∙≺↲ could have some contribution from a halo.," On the other hand, the outer extended emission is indeed much softer and more symmetric, hence could have some contribution from a halo." + The nature of the compact object (BH or NS) in rremmaius subject of a debate. (, The nature of the compact object (BH or NS) in remains subject of a debate. ( +aud 303)) are quite different in their temporal aud spectral properties from other ~QSOs aud HMXBs. which show transitions between different states and large variations in luminosity.,"and ) are quite different in their temporal and spectral properties from other $\mu$ QSOs and HMXBs, which show transitions between different states and large variations in luminosity." + These two systems are also. to date. the only jQSOs whose VHE emission has been firmly.," These two systems are also, to date, the only $\mu$ QSOs whose VHE emission has been firmly." +ected?.. The X-ray light curve of5039... which shows remarkable long-term stability (???).. and »eculiar. varlable radio morphology (2?)? argue agaiust the accretion scenario.," The X-ray light curve of, which shows remarkable long-term stability \citep{2009ApJ...697L...1K,2009ApJ...697..592T,2009A&A...494L..37H}, and peculiar, variable radio morphology \citep{2008A&A...481...17R} argue against the accretion scenario." + It. despite the lack of the usual mauilestatious of accretion. the compact object in iis a BH accreting in an unusual regime (?).. it may still be possible that it produces relativistic yarticles. e.g.. via the Blandford-Znajek process (2) or in au MHD jet.," If, despite the lack of the usual manifestations of accretion, the compact object in is a BH accreting in an unusual regime \citep{2005MNRAS.364..899C}, it may still be possible that it produces relativistic particles, e.g., via the Blandford-Znajek process \citep{1977MNRAS.179..433B} or in an MHD jet." + Iu this case. au extended rebula could still be formed.," In this case, an extended nebula could still be formed." + For the case of a black hole. the majority of higl-euergy. emission is expected to be produced ina jet-type axial outflow (e.g.. 2)).," For the case of a black hole, the majority of high-energy emission is expected to be produced in a jet-type axial outflow (e.g., \citealt{2006A&A...451..259P}) )." + The possible observational manifestations of such outflows ancl a discussion of their energetics is cliscussed by ?/ aud their exteuded emissiou, The possible observational manifestations of such outflows and a discussion of their energetics is discussed by \citet{2010arXiv1001.1244R} and their extended emission +could be connected to differences in the irractiatect disks and secondaries between. V2672 Oph and U Sco.,could be connected to differences in the irradiated disks and secondaries between V2672 Oph and U Sco. + The mass of the white dwarf of U Sco is believed. to be very close to the ��Chandrasekhar limit (Ixato&Llachisu1989:Hlachisuetal.2000:Phorougheood 2001).. ancl thus. if net mass is being added over time to the white dwarf. it ds à prime candidate for explosion as a Evpe Ia supernova.," The mass of the white dwarf of U Sco is believed to be very close to the Chandrasekhar limit \citep{KH89,HKK00,TDL01}, and thus, if net mass is being added over time to the white dwarf, it is a prime candidate for explosion as a Type Ia supernova." + The great similarity of all observational parameters between U Sco and V2672 Oph leads us to infer an equally massive white ebwarf also in the latter. and an additional candidate for a Future Galactic SNIa.," The great similarity of all observational parameters between U Sco and V2672 Oph leads us to infer an equally massive white dwarf also in the latter, and an additional candidate for a future Galactic SNIa." + The progenitor of V2672 Oph hack no recorded. optical or infrared. counterpart in 2ALASS and SDSS surveys., The progenitor of V2672 Oph had no recorded optical or infrared counterpart in 2MASS and SDSS surveys. +" Lf the onor star is an ALO giant as in the recurrent nova RS Oph. ux 10 parent population of V2672 Oph is the Galactic disk. ren its observed. infrared magnitude and colour should be A.12.3and JAHL. or νι10.9 and JA.,—2.0 if the onor star is an AIS giant. as in the other recurrent nova T CB. ""here are only three PALASS sources within 13 arcsec of 10 astrometric position of V2672 Oph."," If the donor star is an M0 giant as in the recurrent nova RS Oph, and the parent population of V2672 Oph is the Galactic disk, then its observed infrared magnitude and colour should be $K_s$$\sim$ 12.3 and $J$$-$$K_s$=1.8, or $K_s$$\sim$ 10.3 and $J$$-$$K_s$ =2.0 if the donor star is an M5 giant as in the other recurrent nova T CrB. There are only three 2MASS sources within 13 arcsec of the astrometric position of V2672 Oph." +" 2ALASS 17382110-2644114. lies 5.6 aresee away and has AY=12.1 and JWy=1.67: 2M1LASS 17382076-2644079 is 5.5 aresee away with A,—10.3 and JAL =1.69: 24LASS 17382052-2644184 lios at a distance of 5.2 aresee and has A,—13.2 and Joνι.", 2MASS 17382110-2644114 lies 5.6 arcsec away and has $K_s$ =12.1 and $J$$-$$K_s$ =1.67; 2MASS 17382076-2644079 is 5.5 arcsec away with $K_s$ =10.3 and $J$$-$$K_s$ =1.69; 2MASS 17382052-2644184 lies at a distance of 5.2 arcsec and has $K_s$ =13.2 and $J$$-$$K_s$ =1.39. + While the third source appears too blue. the first. two could. broadly agree with an AL giant. at. the distance and reddening of V2672 Oph.," While the third source appears too blue, the first two could broadly agree with an M giant at the distance and reddening of V2672 Oph." + Their. positions. however. are not reconcilable with V2672 Oph.," Their positions, however, are not reconcilable with V2672 Oph." + Nakano.Ya-maoka.&Ixadota(2009). lists five independent and accurate measurements for the astrometric position of the nova.," \citet{nakano} + lists five independent and accurate measurements for the astrometric position of the nova." + If a is the res., If $\sigma$ is the r.m.s. + of these five measurements. then all these three PALASS sources are more distant than 106 from the mean astrometric position of the nova.," of these five measurements, then all these three 2MASS sources are more distant than $\sigma$ from the mean astrometric position of the nova." + Llanes(1985) derived a GOV spectral tvpe for the donor star in U Sco. shining in quiescence at W=16.45./ I—0.43.," \citet{H85} derived a G0V spectral type for the donor star in U Sco, shining in quiescence at $K$ =16.45, $J$$-$$K$ =0.43." + Closely similar values were later measured by the 24LASS survey., Closely similar values were later measured by the 2MASS survey. + Such a donor star for V2672 Oph would put it far below the detection thresholds of both 2ALASS ancl SDSS SULVONS., Such a donor star for V2672 Oph would put it far below the detection thresholds of both 2MASS and SDSS surveys. + We may thus conclude that the donor star in V2672 Oph is à cool giant as in RS Oph and T CrD. but much more likely a να as in recurrent novae of the U Sco type and in most classical novae.," We may thus conclude that the donor star in V2672 Oph is a cool giant as in RS Oph and T CrB, but much more likely a dwarf as in recurrent novae of the U Sco type and in most classical novae." + Hs orbital period should. therefore be of the order of davs. and not months or vears.," Its orbital period should therefore be of the order of days, and not months or years." + Only a few spectral lines are usually recognisable on spectra of novae characterized. by very. large expansion. velocities., Only a few spectral lines are usually recognisable on spectra of novae characterized by very large expansion velocities. + This is caused by the [arge blending of individual lines that wash them out into the underlving continuum energy distribution., This is caused by the large blending of individual lines that wash them out into the underlying continuum energy distribution. + V2672 Oph is no exception to this rule as illustrated: by its spectral evolution presented. in. Figure 3., V2672 Oph is no exception to this rule as illustrated by its spectral evolution presented in Figure 3. + Only La ancl OL 8446 sstand out prominently. while all other lines emerge only weakly from the underlving continuum.," Only $\alpha$ and OI 8446 stand out prominently, while all other lines emerge only weakly from the underlying continuum." + Table 3 reports the absolute fluxes for emission lines that we were able to recognise and measure with confidence., Table 3 reports the absolute fluxes for emission lines that we were able to recognise and measure with confidence. + The spectra of V2672 Oph classify it among Lle/N novae. às is usually the case for last novae.," The spectra of V2672 Oph classify it among He/N novae, as is usually the case for fast novae." + The. general appearance of the V2672 Oph spectra is very similar to those of U Sco. once the reddenings of the two objects are matched. as illustrated in Figures 3 and 4.," The general appearance of the V2672 Oph spectra is very similar to those of U Sco, once the reddenings of the two objects are matched, as illustrated in Figures 3 and 4." + The top panel of Figure 1 compares the evolution of the integrated Hux of Ho to the photometric one., The top panel of Figure 1 compares the evolution of the integrated flux of $\alpha$ to the photometric one. + The decline rate is identical to that of the Y -band. flux. while it is slower than for /c.," The decline rate is identical to that of the $V$ -band flux, while it is slower than for $I_{\rm C}$ ." + This agrees with the VZe evolution. which is directed. toward. bluer. Vfo colours.," This agrees with the $V$$-$$I_{\rm C}$ evolution, which is directed toward bluer $V$$-$$I_{\rm C}$ colours." + The. Lea contributes less than to the V-band [lux (as proved, The $\alpha$ contributes less than to the $V$ -band flux (as proved +“flat” in the cluitting region: and (11) density eradieuts have no effect ou the estimate of Aey aud the correspouding IT density.,“flat” in the emitting region; and (iii) density gradients have no effect on the estimate of $M_{\rm CD}$ and the corresponding $_2$ density. + Iu the following. we shall use these plivsical parameters to analyse the stability aud structure of the clumps.," In the following, we shall use these physical parameters to analyse the stability and structure of the clumps." +" From Table 9 one can see that the mean ratio between Mey aud Mug is ~3.041.7. being ~1 only in the cases of C19.61 and 220126,"," From Table \ref{mvir-mcd} one can see that the mean ratio between $M_{\rm CD}$ and $M_{\rm vir}$ is $\sim$ $\pm$ 1.7, being $\sim$ 1 only in the cases of G19.61 and 20126." + Although such a ratio is only mareiually 1. it is such for all of the sources but two of them: this result secs too systematic to be due only to random errors on the quantities of interest.," Although such a ratio is only marginally $>$ 1, it is such for all of the sources but two of them: this result seems too systematic to be due only to random errors on the quantities of interest." + The question is whether the ratio feyλέων can be reduced to unitv by any incans., The question is whether the ratio $M_{\rm CD}/M_{\rm vir}$ can be reduced to unity by any means. + Let us examine a few possibilities., Let us examine a few possibilities. + As already ciscussecd iu Sects., As already discussed in Sects. +" 3.L1. and 3. 1.3.. optical depth effects aud density eradieuts can ouly increase the ratio AMop/Mjg,. as thev make Mop bigger and My sunaller."," \ref{stau} and \ref{sdgr}, , optical depth effects and density gradients can only increase the ratio $M_{\rm CD}/M_{\rm vir}$, as they make $M_{\rm CD}$ bigger and $M_{\rm vir}$ smaller." + Another possibility is that the aabundance Is nuderestimateck. which woul Cause all overestimate of Mop.," Another possibility is that the abundance is underestimated, which would cause an overestimate of $M_{\rm CD}$." + Iu principle this cannot be excluded. eivon the large variatious of molecular abundauces in cüffereu objects (see e.g. Irvine et al.," In principle this cannot be excluded, given the large variations of molecular abundances in different objects (see e.g. Irvine et al." + 1987): however. our estimate of Noucou (see Sect. 3.3))," 1987); however, our estimate of $X_{\rm CH_3C_2H}$ (see Sect. \ref{smass}) )" + is “direct”. as it nmaakes use of the continu cussion from the regions of interest and it is hence less prone to errors which instead affect values based ou chemical models.," is “direct”, as it makes use of the continuum emission from the regions of interest and it is hence less prone to errors which instead affect values based on chemical models." + Further evideuce for Mop beiug greater than My comes from the stucies ofCesaroni et al. (, Further evidence for $M_{\rm CD}$ being greater than $M_{\rm vir}$ comes from the studies ofCesaroni et al. ( +1991) and ofuer et al. (,1991) and Hofner et al. ( +2000) who jiapped some of our chimps respectively in the C?!S aud C1 O lines:as one can see in Fig. 6.. ,"2000) who mapped some of our clumps respectively in the $^{34}$ S and $^{17}$ O lines:as one can see in Fig. \ref{fmhof}, ," +iu all sources tle ratio, in all sources the ratio +The geometry of the low-luminosity (“low-hard™) state of Galactic Black Hole Candidates (GBHC). in. which. the spectrum is dominated by a power law X-ray flux extending to high energies. has been an open question for several decades.,"The geometry of the low-luminosity (“low-hard”) state of Galactic Black Hole Candidates (GBHC), in which the spectrum is dominated by a power law X-ray flux extending to high energies, has been an open question for several decades." + While it is generally believed that the power law spectrum is formed by inverse Compton scattering. there is no consensus about the geometry of the flow. source of seed photons or energy distribution for the Comptonizing electrons.," While it is generally believed that the power law spectrum is formed by inverse Compton scattering, there is no consensus about the geometry of the flow, source of seed photons or energy distribution for the Comptonizing electrons." + Broadly speaking. there are two classes of model to explain the spectrum in the low-hard state.," Broadly speaking, there are two classes of model to explain the spectrum in the low-hard state." +" The first is the ""corona"" model. in which the disk remains untruncated. or nearly untruncated at luminosities Lyz107Liq4."," The first is the “corona” model, in which the disk remains untruncated or nearly untruncated at luminosities $L_{\rm{X}} \simeq 10^{-3} L_{\rm{Edd}}$." + The hard power law spectrum comes from a hot and patehy corona (perhaps powered by magnetic flares (222))) on top of the disk. while the surrounding region is bombarded with high energy photons. producing the observed reflectior and Fe-K fluorescence components.," The hard power law spectrum comes from a hot and patchy corona (perhaps powered by magnetic flares \citep{1998MNRAS.299L..15D, 1999ApJ...510L.123B, +2001MNRAS.321..549M}) ) on top of the disk, while the surrounding region is bombarded with high energy photons, producing the observed reflection and Fe-K fluorescence components." +" In the alternate. ""truncated disk” model the thin disk i5 truncated at some distance from the black hole and the inner region is filled with a hot. radiatively-inefficient. flow. which produces the hard spectrum."," In the alternate, “truncated disk” model the thin disk is truncated at some distance from the black hole and the inner region is filled with a hot, radiatively-inefficient flow, which produces the hard spectrum." + The reflection spectrum and Fe-K fluorescence is then produced by the interaction of the hard X-rays with the inner part of the truncated disk. or in some cool outflow moving away from the disk.," The reflection spectrum and Fe-K fluorescence is then produced by the interaction of the hard X-rays with the inner part of the truncated disk, or in some cool outflow moving away from the disk." + For a recent discussion of the low-hard state see sect., For a recent discussion of the low-hard state see sect. + 4 of ?.., 4 of \cite{2007A&ARv..15....1D}. + In theory. the presence or absence of a cool disk should be confirmable through direct detection of a soft X-ray blackbody component at low energies.," In theory, the presence or absence of a cool disk should be confirmable through direct detection of a soft X-ray blackbody component at low energies." + In practice however. this is made difficult by the fact that at low accretion rates the temperature of even an untruncated disk will drop from about 1-2keV in the high soft state to ~ 0.1-0.3keV. which puts it out of the range of most X-ray detectors.," In practice however, this is made difficult by the fact that at low accretion rates the temperature of even an untruncated disk will drop from about 1-2keV in the high soft state to $\sim$ 0.1-0.3keV, which puts it out of the range of most X-ray detectors." + Additionally. the effects of interstellar absorption become very strong at around O.IkeV. so that detecting a soft excess and accurately measuring its parameters will depend somewhat on how accurately the interstellar absorption can be determined.," Additionally, the effects of interstellar absorption become very strong at around 0.1keV, so that detecting a soft excess and accurately measuring its parameters will depend somewhat on how accurately the interstellar absorption can be determined." + Even with these challenges. a soft excess in the low-hard state has previously been reported in several sources.," Even with these challenges, a soft excess in the low-hard state has previously been reported in several sources." + The first was Cyg X-1 (??).. although its association with an aceretion disk is complicated by the fact that Cyg X-1 is a high mass binary acereting from a wind.," The first was Cyg X-1 \citep{1995A&A...302L...5B, 2001ApJ...547.1024D}, although its association with an accretion disk is complicated by the fact that Cyg X-1 is a high mass binary accreting from a wind." + This question was also the focus of two recent papers. ??.. 1n which the authors studied long-exposure spectra of two different GBHCs. SWIFT J1753.5-0127 and GX 339-4. at low luminosities (Lx/Lua~0.003— 0.05).," This question was also the focus of two recent papers, \cite{2006ApJ...652L.113M, +2006ApJ...653..525M}, in which the authors studied long-exposure spectra of two different GBHCs, SWIFT J1753.5-0127 and GX 339-4, at low luminosities $L_{\rm{X}}/L_{\rm{Edd}} \sim +0.003-0.05$ )." + Soft excesses at similar luminosities in these two sources have also been reported in ?. (J1753.5-0127) and ? (GX 339-4).," Soft excesses at similar luminosities in these two sources have also been reported in \cite{2007MNRAS.378..182R} + (J1753.5-0127) and \cite{2008arXiv0802.3357T} (GX 339-4)." + Since these two observations. there have also been observations of soft excesses in several other sources.," Since these two observations, there have also been observations of soft excesses in several other sources." + ? made several observations of the soft component of XTE J1817-330 with Swift during the outburst decline of that source down to a luminosity of ἐκγω~0.001. while a soft component in GRO J1655-40 has been reported by both ? anc ? using different telescopes.," \cite{2007ApJ...666.1129R} made several observations of the soft component of XTE J1817-330 with $Swift$ during the outburst decline of that source down to a luminosity of $L_{\rm{X}}/L_{\rm{Edd}} \sim 0.001$ , while a soft component in GRO J1655-40 has been reported by both \cite{2006MNRAS.365.1203B} and \cite{2008PASJ...60S..69T} using different telescopes." + To interpret the soft excesses in SWIFT J1753.5-0127 anc GX 339-4. 2? fit the data with a severalXSPEC models. trying various black-body disk models and simple hard X-ray components (both a power law and various Comptonizatior models).," To interpret the soft excesses in SWIFT J1753.5-0127 and GX 339-4, \cite{2006ApJ...652L.113M, 2006ApJ...653..525M} fit the data with a several models, trying various black-body disk models and simple hard X-ray components (both a power law and various Comptonization models)." + In GX 339-4 a broad Fe-K line was also observed and fit with a relativistically broadened reflection model., In GX 339-4 a broad Fe-K line was also observed and fit with a relativistically broadened reflection model. + Using blackbody models for a standard accreting disk. the authors found disks with maximum temperatures ofkT ~ 0.2-0.4 keV. and inner radii consistent with the innermost stable circular orbit of a black hole.," Using blackbody models for a standard accreting disk, the authors found disks with maximum temperatures of $\sim$ 0.2-0.4 keV, and inner radii consistent with the innermost stable circular orbit of a black hole." + At the inferred low accretion rates in the hard state. a disk extending to the last stable orbit would produce a soft X-ray component with peak close to the cutoff due to interstellar absorption.," At the inferred low accretion rates in the hard state, a disk extending to the last stable orbit would produce a soft X-ray component with peak close to the cutoff due to interstellar absorption." + Unless an accurate independent neasure of the interstellar absorption column 1s. available. spectral fitting procedures cannot reliably distinguish betwee! a thermal peak at AT=0.3 keV with one interstellar absorption column and a cooler component with a lower energy component cutoff by a slightly higher interstellar absorption column.," Unless an accurate independent measure of the interstellar absorption column is available, spectral fitting procedures cannot reliably distinguish between a thermal peak at $kT = 0.3$ keV with one interstellar absorption column and a cooler component with a lower energy component cutoff by a slightly higher interstellar absorption column." + For energetic reasons the hard X-ray component which dominates the Iuminosity in the hard state must originate near the black hole. the same region as the proposed cool disk.," For energetic reasons the hard X-ray component which dominates the luminosity in the hard state must originate near the black hole, the same region as the proposed cool disk." +" Some form of interaction of hard X-rays with the cool disk must take place. and this implies that the isolated cool disk models used as ""components! in fits to observed spectra are unrealistic."," Some form of interaction of hard X-rays with the cool disk must take place, and this implies that the isolated cool disk models used as `components' in fits to observed spectra are unrealistic." + In fact. most models for the hard X-ray component include some prescription for the reprocessing of hard into soft radiation. whether these be truncated disks or extended disk models.," In fact, most models for the hard X-ray component include some prescription for the reprocessing of hard into soft radiation, whether these be truncated disks or extended disk models." + As shown by Haardt andMaraschi (1991). such," As shown by Haardt andMaraschi (1991), such" +AMO CVn systeus are an extremely rare type of cataclvsniüc variable with ultrashort binary orbital lods of less tla rabout an hour.,AM CVn systems are an extremely rare type of cataclysmic variable with ultrashort binary orbital periods of less than about an hour. + The most confideut current members of this elite. subclass have orbital veriods in the ra1ος of —]0-65 nmnüuutes. though two nore coutroversial Cases even clisplay 5-10 minute uodulatious: AM CVn svsteus thus areuably euccpass he shortes orbial periods of anv known class of πα. (e.g.SCCLOVICWSbyWarner1995:Nele-nans 2005).," The most confident current members of this elite subclass have orbital periods in the range of $\sim$ 10-65 minutes, though two more controversial cases even display 5-10 minute modulations; AM CVn systems thus arguably encompass the shortest orbital periods of any known class of binaries \citep[e.g., see reviews +by][]{war95,nel05}." +.. These systems are so conipact that both ο colaoneuts are proably degenerate (or degenerate). likely with iass-trauster from ao ποιαrich donor onto a white dwiuf. driven by eravitational radiation.," These systems are so compact that both binary components are probably degenerate (or semi-degenerate), likely with mass-transfer from a helium-rich donor onto a white dwarf, driven by gravitational radiation." + Their optical specra are distinct from vpical cataclysinics: menibership iu the AM. CVa class requires a virtual absence of hwdrogeu lines iu their spectrum. and instead heliuni Hines are pronuünueutsoioetines 111 enission. sometimes im absorption.," Their optical spectra are distinct from typical cataclysmics: membership in the AM CVn class requires a virtual absence of hydrogen lines in their spectrum, and instead helium lines are prominent—sometimes in emission, sometimes in absorption." +" Ivdrogen is t1ouehit to be lost from the binary during a prior coWMOenvelope phase. before t16 object is seen as au AX οδη,"," Hydrogen is thought to be lost from the binary during a prior common-envelope phase, before the object is seen as an AM CVn." + The exotic nature of the prototvpe. AM CV (sci hal? 1uinute orbit). was realized in the mid-LOGO's (SinasLOOT:Paczvuski 1967).," The exotic nature of the prototype, AM CVn (with a 17 minute orbit), was realized in the mid-1960's \citep{sma67,pac67}." +. But t1c passage of another three and half decades has vieldec ouly about a dozen aclitional members of this class: for example. 1l confident plus 2 controversial cases are discussed iu the review bv Nelemaus(2005). aud aiother likely addition is reported in a very recent telegram by Rykoff(2005) aud(1995).," But the passage of another three and half decades has yielded only about a dozen additional members of this class; for example, 11 confident plus 2 controversial cases are discussed in the review by \citet{nel05}, and another likely addition is reported in a very recent telegram by \citet{ryk05} and." +.. Athough they have lius far remained chisive. AAT CVn systems have τςnetheless eiierged as objects of renewed interest for multiple reasons: they iav serve as sites im whici to study come1 envelope binary evolution aud waistal heliuni-dominated accretion disks: they are possible SNy Ta pryecnitors (e.g...Livio&Ricss 2003): and. intriguinely. rey are predicted to be one of the most commonlv detected objects iu upcoming eyavity wave exporinents likeELSA.," Although they have thus far remained elusive, AM CVn systems have nonetheless emerged as objects of renewed interest for multiple reasons: they may serve as sites in which to study common envelope binary evolution and unusual helium-dominated accretion disks; they are possible SN Ia progenitors \citep[e.g.,][]{liv03}; and, intriguingly, they are predicted to be one of the most commonly detected objects in upcoming gravity wave experiments like." + For exiuuple. receut estimates. based on Oriaion and evolutionary models. Sugeest that ~10! ANM ΟΥ binaries will plausibly be detected/resolved 1 graviv waves by (Nelemausetal.200 L).," For example, recent estimates, based on formation and evolutionary models, suggest that $\sim 10^4$ AM CVn binaries will plausibly be detected/resolved in gravity waves by \citep{nel04}." +. Although most AMI CVn systems were first recognized via ficr optical properties. thev may also cuit N-ravs durmg evolutionary phases of substantial mass transfer (οUlla1995).. and are also sometimes detected im he ultraviolet.," Although most AM CVn systems were first recognized via their optical properties, they may also emit X-rays during evolutionary phases of substantial mass transfer \citep[e.g.,][]{ull95}, and are also sometimes detected in the ultraviolet." + Indeed. wo. of tlic| shortest-period. but also uost controversial candidates were noticed first bv hei N-vav endsson (Motcehet:d.1996:Israel1999:Croppereal. 2001).," Indeed, two of the shortest-period, but also most controversial, candidates were noticed first by their X-ray emission \citep{mot96,isr99,cro04}." +. Tho coubination of wavelength data sets can allow for eslates of the mass-Transfer rates. and provie orbital )oriods aud even their one-term stabili Vin some cases.," The combination of multi-wavelength data sets can allow for estimates of the mass-transfer rates, and provide orbital periods and even their long-term stability in some cases." + Such follow-on studies lay an importaif role in establishiis the evolutionary staee of individual svstens. and d1 testing evolutionary nodels.," Such follow-on studies play an important role in establishing the evolutionary stage of individual systems, and in testing evolutionary models." + Hieh-qualitv folow-up XAALNewton spectra ive recently exteuded study of tιο AAT CV unusual- signatures out to hieh-lonization N-ray lines as well (c.e..Strolumaver2001:Rausavetal. 2005)..," High-quality follow-up XMM-Newton spectra have recently extended study of the AM CVn unusual-abundance signatures out to high-ionization X-ray lines as well \citep[e.g.,][]{str04,ram05}. ." + Among several theoretical fornation scenarios for, Among several theoretical formation scenarios for +paradigm of structure and formation.,paradigm of structure and galaxy formation. +" the present status of observational results galaxy another However,important success to the ACDM model which as we grantshowed in this work, is able to aspects of the variations of galaxy properties reproducewith the unexpectedenvironment."," However, the present status of observational results grant another important success to the $\Lambda$ CDM model which as we showed in this work, is able to reproduce unexpected aspects of the variations of galaxy properties with the environment." + We thank Michael Drinkwater for very useful comments which significantly improved this paper., We thank Michael Drinkwater for very useful comments which significantly improved this paper. +" This work was supported in the FONDAP “Centro de partsica"" byand Fundaciónn Andes."," This work was supported in part by the FONDAP “Centro de sica"" and Fundaciónn Andes." + NP was supported by a Proyecto Fondecyt Regular No., NP was supported by a Proyecto Fondecyt Regular No. + 1071006., 1071006. + observations with the (Advanced CCD Imaging Spectrometer (ACIS) were available from the archive for four of the galaxies: Abell 1664. Abell 1835. ZWCL 3146. and RXJ 2129+00.," observations with the (Advanced CCD Imaging Spectrometer (ACIS) were available from the archive for four of the galaxies; Abell 1664, Abell 1835, ZWCL 3146, and RXJ 2129+00." + Exposure times are 11. 22. 49. and 12 ks respectively.," Exposure times are 11, 22, 49, and 12 ks respectively." + The event files were binned to I’pixels and the resulting images smoothed with the adaptive smoothing routine using the algorithm by Ebelingetal.(2006)., The event files were binned to pixels and the resulting images smoothed with the adaptive smoothing routine using the algorithm by \citet{ebeling06}. +. Constant surface brightness X-ray contours are shown for these four galaxies in Figures 11..12.. 14. and 16. overlayed on the continuum subtracted Ένα images.," Constant surface brightness X-ray contours are shown for these four galaxies in Figures \ref{fig:A1664}, \ref{fig:A1835}, \ref{fig:Z3146} and \ref{fig:R2129} + overlayed on the continuum subtracted $\alpha$ images." + Where available. we selected high resolution VLA observations from the NRAO archive.," Where available, we selected high resolution VLA observations from the NRAO archive." + For some sources we chose an additional data set in order to obtain a complementary lower resolution image., For some sources we chose an additional data set in order to obtain a complementary lower resolution image. + The NRAO AIPS package was used for the calibration. imaging. self-calibration. and deconvolution.," The NRAO AIPS package was used for the calibration, imaging, self-calibration, and deconvolution." + The properties of the final images are given in Table 2.., The properties of the final images are given in Table \ref{tab:VLA}. + We detected a faint point source in all the BCGs., We detected a faint point source in all the BCGs. + The flux densities of the point sources are given in Table 4.., The flux densities of the point sources are given in Table \ref{tab:point}. + These high resolution observations are not sensitive to very diffuse emission., These high resolution observations are not sensitive to very diffuse emission. + Figures 1-7 have been centered at the location of the central radio sources as measured from VLA archival data at 5 or 8.5 GHz (with positions listed in Table 1))., Figures 1-7 have been centered at the location of the central radio sources as measured from VLA archival data at 5 or 8.5 GHz (with positions listed in Table \ref{tab:tab1}) ). + Coordinate errors measured fromHST.Telescope and ACIS observations are of order an aresecond.," Coordinate errors measured from, and ACIS observations are of order an arcsecond." + The FUV and Lyn images lack point sources that could be used to register the Images at sub-aresecond scales., The FUV and $\alpha$ images lack point sources that could be used to register the images at sub-arcsecond scales. + We find that all 7 galaxies observed display extended emission in both FUV continuum and Ένα emission., We find that all 7 galaxies observed display extended emission in both FUV continuum and $\alpha$ emission. + The FUV continuum ts patchy. as was true for Abell 1795 and Abell 2597 (0Deaetal.2004).," The FUV continuum is patchy, as was true for Abell 1795 and Abell 2597 \citep{odea04}." +. As discussed in that work. the FUV continuum is likely associated with young stars in star clusters.," As discussed in that work, the FUV continuum is likely associated with young stars in star clusters." + The Ενα morphology contains both clumps and a more diffuse or filamentary component., The $\alpha$ morphology contains both clumps and a more diffuse or filamentary component. + The diffuse component in seen in Ένα but not in the FUV continuum. e.g. ZWCL 8193 (Figure 17)).," The diffuse component in seen in $\alpha$ but not in the FUV continuum, e.g., ZWCL 8193 (Figure \ref{fig:diffuse}) )." + Diffuse or filamentary Ενα was also seen by O'Deaetal.(2004) in Abell 1795 and Abell 2597., Diffuse or filamentary $\alpha$ was also seen by \citet{odea04} in Abell 1795 and Abell 2597. + The association between the Lya and FUV continuum implies that the FUV continuum contributes to the ionization of the Lya emitting gas., The association between the $\alpha$ and FUV continuum implies that the FUV continuum contributes to the ionization of the $\alpha$ emitting gas. + All our BCGs display asymmetry in the FUV emission., All our BCGs display asymmetry in the FUV emission. + In Abell 11. the FUV continuum and Lye emission is arranged in an extended clump cospatial with the visible nucleus. with a more diffuse component about 2west of the nucleus (also seen in the optical image).," In Abell 11, the FUV continuum and $\alpha$ emission is arranged in an extended clump cospatial with the visible nucleus, with a more diffuse component about west of the nucleus (also seen in the optical image)." + The main clump of emission is slightly offset from the center of theSpitzer IRAC 3j/m isophotes (see Figure 10))., The main clump of emission is slightly offset from the center of the IRAC $\mu$ m isophotes (see Figure \ref{fig:A11}) ). + In Abell 1664. three large clumps of FUV and Lye trace the disturbed morphology of the host galaxy as observed in the optical.," In Abell 1664, three large clumps of FUV and $\alpha$ trace the disturbed morphology of the host galaxy as observed in the optical." + Additionally. there is a low surface brightness filament of Lya emission extending ~25 kpe to the south of the three bright clumps.," Additionally, there is a low surface brightness filament of $\alpha$ emission extending $\sim 25$ kpc to the south of the three bright clumps." + This filament is not associated with any optical counterpart in the WFPC? image or any FUV continuum emission., This filament is not associated with any optical counterpart in the WFPC2 image or any FUV continuum emission. + The 3jim peak. cospatial with the galaxy’s nucleus. ts also cospatial with the dust lanes in the optical image (see Figure 11)).," The $\mu$ m peak, cospatial with the galaxy's nucleus, is also cospatial with the dust lanes in the optical image (see Figure \ref{fig:A1664}) )." + Abell 1835 has also been observed by Bildfelletal.(2008) who measure a size for the blue star forming region of 19+2 kpe. which ts in good agreement with our measurement of ~17 kpe for the size of the Lya emission (Table 3)).," Abell 1835 has also been observed by \citet{bildfell08} who measure a size for the blue star forming region of $19 \pm 2$ kpc, which is in good agreement with our measurement of $\sim 17$ kpc for the size of the $\alpha$ emission (Table \ref{tab:Ly}) )." + In Abell 1835 the 3j/m contours are also not centered on the brightest regions seen the FUV. Lyo or visible band images (see Figure 12)).," In Abell 1835 the $\mu$ m contours are also not centered on the brightest regions seen the FUV, $\alpha$ or visible band images (see Figure \ref{fig:A1835}) )." + For ZWCL 348 the visible and 3j/m emission peaks are nearly centered and the FUV emission peaks on the center of the galaxy., For ZWCL 348 the visible and $\mu$ m emission peaks are nearly centered and the FUV emission peaks on the center of the galaxy. + However the visible band image shows that the galaxy is disturbed and the outer contours seen at 3j/m are not round (see Figure 13))., However the visible band image shows that the galaxy is disturbed and the outer contours seen at $\mu$ m are not round (see Figure \ref{fig:Z348}) ). + The Lyco emission extends eastwards from the nucleus much further than to the west., The $\alpha$ emission extends eastwards from the nucleus much further than to the west. + In ZWCL 3146 the FUV and Lya emission are centered on the 3j/m contours (see Figure 14))., In ZWCL 3146 the FUV and $\alpha$ emission are centered on the $\mu$ m contours (see Figure \ref{fig:Z3146}) ). + For ZWCL 8193 there is a nuclear bulge in the optical and 3ym images., For ZWCL 8193 there is a nuclear bulge in the optical and $\mu$ m images. + However FUV and Lya emission ts brighter north of the nucleus. and has a spiral shape suggesting that a smaller galaxy has been recently disrupted in the outskirts of the BCG (see Figure 15)).," However FUV and $\alpha$ emission is brighter north of the nucleus, and has a spiral shape suggesting that a smaller galaxy has been recently disrupted in the outskirts of the BCG (see Figure \ref{fig:Z8193}) )." + The host galaxy is an elliptical in a rich environment with several nearby dwarf satellites., The host galaxy is an elliptical in a rich environment with several nearby dwarf satellites. + The disturbed morphology of the host galaxy is suggestive of a recent or ongoing series of minor mergers., The disturbed morphology of the host galaxy is suggestive of a recent or ongoing series of minor mergers. + RXJ 2129+00 displays Lya emission which extends on only the north-eastern side of the galaxy., RXJ 2129+00 displays $\alpha$ emission which extends on only the north-eastern side of the galaxy. + The offset between radio and Lya peaks is small and so may be due to a registration error in theHST image (see Figure 16))., The offset between radio and $\alpha$ peaks is small and so may be due to a registration error in the image (see Figure \ref{fig:R2129}) ). + We find that most of these BCGs display strong asymmetries or uneven distributions in their star formation as seen from the FUV continuum images (see Fig. 18))., We find that most of these BCGs display strong asymmetries or uneven distributions in their star formation as seen from the FUV continuum images (see Fig. \ref{fig:fuv}) ). + For these galaxies. corresponds to 2-4 kpe (see Table 1)) thus these asymmetries are on a scale of order 10-50 kpe.," For these galaxies, corresponds to 2–4 kpc (see Table \ref{tab:tab1}) ) thus these asymmetries are on a scale of order 10-50 kpc." + On smaller, On smaller +Figure 5 shows that the lag increases with the low energy spectral index o of the rest frame spectrum of the pulse.,Figure \ref{lag_alpha} shows that the lag increases with the low energy spectral index $\alpha$ of the rest frame spectrum of the pulse. + A arecr à means more photons are concentrated around. the −∕⋅ ∕↴∕T M ⋅ ≻∢⊾⋜↧↥⊔⊾⊔∢⊾↓⋅⋏∙≟∙∖⇁∆↗∣∪⊓↓↥⋖⋅∕∕∫↴⊳∖↓≻, A larger $\alpha$ means more photons are concentrated around the peak energy $E_p'$ of the $\nu'F_{\nu}'$ spectrum. +⋖⋅≼⇍↿↓⋅⊔⊔↓⊳∐∐⋅⊔⊳⇂∪↓⋅⋜↧⊔⋜⊔⋅↓⋅∪∖∖⋎∢⊾↓⋅ Es»eetrum. the curvature effect will work more cllectively in oducing the spectral lags.," Then, for a narrower spectrum, the curvature effect will work more effectively in producing the spectral lags." + This conjecture is supported =vhen wealter the high-energy. spectral index 3., This conjecture is supported when wealter the high-energy spectral index $\beta$. + We found ju a steeper high-cnergy power-law spectrum. produces a arger lag. c.g. the Channel 1/4 [ag has a increase for ? changing from -2.4 to -3.0.," We found that a steeper high-energy power-law spectrum produces a larger lag, e.g., the Channel 1/4 lag has a increase for $\beta$ changing from -2.4 to -3.0." + Compared with the Channel 1/4 lag. the Channel 1/3 lag has à weaker dependence upon 92.," Compared with the Channel 1/4 lag, the Channel 1/3 lag has a weaker dependence upon $\beta$." +" The lag's dependence on the observed. break energy of )0 spectrum Ly, is shown in Figure 6..", The lag's dependence on the observed break energy of the spectrum $E_p$ is shown in Figure \ref{lag_ep}. +" The lag has its maximum when £, falls near the starting energy of the 'orresponding high-energy channel that is used in measuring 1e lag (ie. ~ 100 keV for Channel 3. — 300 keV for Channel 1)."," The lag has its maximum when $E_p$ falls near the starting energy of the corresponding high-energy channel that is used in measuring the lag (i.e., $\sim$ 100 keV for Channel 3, $\sim$ 300 keV for Channel 4)." + The above findings about the lag's dependences on re spectral parameters. are. qualitatively. consistent. with 1e tendeney observed in those lone-lag wider-pulse bursts » Norris et al. (, The above findings about the lag's dependences on the spectral parameters are qualitatively consistent with the tendency observed in those long-lag wider-pulse bursts by Norris et al. ( +2005).,2005). +" They found that their. lone-lag (measured for Channel 1/3) burst sample has. on average. ower £, (centered around ~110 IxeV). larger aIow- energy power law) and smaller <7(soffer high-encrey power aw). than the bright burst sample analvzed by Preece et al. ("," They found that their long-lag (measured for Channel 1/3) burst sample has, on average, lower $E_p$ (centered around $\sim 110$ KeV), larger $\alpha$ low-energy power law) and smaller $\beta$ high-energy power law), than the bright burst sample analyzed by Preece et al. (" +2000).,2000). +" Substituting the “Band” spectrum with an alternative one of a single power law plus an exponential high-energv cut-olf causes no changes to the Channel 1/3 lag. while the Channel 1/4 lag has à ~40% increase i£ the observed. cut-olf energy. £5, is below 300 keV: for ££,> 300 keV. the increase of Channel 1/4 lage is much smaller."," Substituting the “Band” spectrum with an alternative one of a single power law plus an exponential high-energy cut-off causes no changes to the Channel 1/3 lag, while the Channel 1/4 lag has a $\sim$ increase if the observed cut-off energy $E_p$ is below 300 keV; for $E_p >$ 300 keV, the increase of Channel 1/4 lag is much smaller." + We find that longer rest-frame duration (f/)) of emission will cause larger lags. as is shown in Figure 7..," We find that longer rest-frame duration $t_d'$ ) of emission will cause larger lags, as is shown in Figure \ref{lag_td'}." + This result may be associated with an observed tendency that wider pulses exhibit. longer lags (Norris ct al., This result may be associated with an observed tendency that wider pulses exhibit longer lags (Norris et al. + 1906:Norris. Scarele )onnell 2001: Norris et al.," 1996;Norris, Scargle Bonnell 2001; Norris et al." + 2005)., 2005). + The lagὃν appears to be independent on /?. the radius of the racliation surface (sce Figure 8)).," The lag appears to be independent on $R$ , the radius of the radiation surface (see Figure \ref{lag_R}) )." +" We know £2 determines the angular spreading time scale. Tan,2A (2070)."," We know $R$ determines the angular spreading time scale, $T_{ang} \approx R/(2 \Gamma^2 c)$ ." + This result, This result +transfer.,transfer. + For each core mass. then above a certain envelope mass the radius is roughly constant: below that envelope mass the envelope shrinks If the donor star in RS Oph is Roche-lobe filling. it has a core mass of zO.4M.. (see.e.g.Justhametal. 2009):: based on these calculations. if the donor's envelope mass were to fall below ~2«I07M... the envelope would contract in 7g.<1 yr.," For each core mass, then above a certain envelope mass the radius is roughly constant; below that envelope mass the envelope shrinks If the donor star in RS Oph is Roche-lobe filling, it has a core mass of $\approx 0.4 M_{\odot}$ \citep[see, e.g.~][]{Justham+09}; based on these calculations, if the donor's envelope mass were to fall below $\sim 2 \times 10^{-3} M_{\odot}$, the envelope would contract in $\tau_{\rm KH,env} < 1$ yr." + Once contraction. of the envelope is complete then the radius of the star is essentially. insignificant; taking a separation of ~IOOR and a core size of zO.IR.. gives a fractional cross-section ..of ~10~ for interaction between the supernova shock and the companion star., Once contraction of the envelope is complete then the radius of the star is essentially insignificant; taking a separation of $\approx 100R_{\odot}$ and a core size of $\approx 0.1 R_{\odot}$ gives a fractional cross-section of $\sim 10^{-6}$ for interaction between the supernova shock and the companion star. + In. addition. after contraction any remaining envelope will be tightly bound to the compact core.," In addition, after contraction any remaining envelope will be tightly bound to the compact core." + After the end of accretion. the explosion will happen only after the WD redistributes or loses sufficient angular momentum (for differential οἱ solid-body rotation. respectively).," After the end of accretion, the explosion will happen only after the WD redistributes or loses sufficient angular momentum (for differential or solid-body rotation, respectively)." + The timescale for this angular momentum— loss or redistribution is uncertain., The timescale for this angular momentum loss or redistribution is uncertain. + However. an upper limit to the angular momentum loss and redistribution timescales of 10° years has been claimed from mapping the central density at ignition to the expected nucleosynthesis (Yoon 2005).," However, an upper limit to the angular momentum loss and redistribution timescales of $~10^{6}$ years has been claimed from mapping the central density at ignition to the expected nucleosynthesis \citep{YoonLanger2005}." +. But even if this delay is negligible then the finite time that carbon burning takes to runaway should be long enough to allow the envelope to contract., But even if this delay is negligible then the finite time that carbon burning takes to runaway should be long enough to allow the envelope to contract. + After the energy generation rate from carbon. burning exceeds the rate at which neutrinos can cool the core then convection currents are believed to postpone the explosion until the heating timescale becomes too short compared to the convective turnover timescale (e.g.Amett1969;Lesaffreetal. 2006).," After the energy generation rate from carbon burning exceeds the rate at which neutrinos can cool the core then convection currents are believed to postpone the explosion until the heating timescale becomes too short compared to the convective turnover timescale \citep[e.g.\ ][]{Arnett1969, Lesaffre+2006}." + The likely ~10° year delay due to this “simmering” phase would allow time for exhausted RG envelopes to shrink. even without considering the time taken for redistribution or loss of angular momentum (see reffig:tkhcollapse)).," The likely $\sim 10^{3}$ year delay due to this `simmering' phase would allow time for exhausted RG envelopes to shrink, even without considering the time taken for redistribution or loss of angular momentum (see \\ref{fig:tkhcollapse}) )." + The above model naturally applies to SD progenitors of SN la with RG donor stars., The above model naturally applies to SD progenitors of SN Ia with RG donor stars. + Our proposed mechanism is significant even if it only applies to most such RG+WD SD systems., Our proposed mechanism is significant even if it only applies to most such RG+WD SD systems. + However. our scenario may also extend to at least some progenitors from the supersoft channel: such systems with late Case A or early Case B donors will evolve into systems with giant donors if there is enough mass remaining in the envelope. and if the WD does not explode first.," However, our scenario may also extend to at least some progenitors from the supersoft channel; such systems with late Case A or early Case B donors will evolve into systems with giant donors if there is enough mass remaining in the envelope, and if the WD does not explode first." +" If the envelope mass is already too small. then there is no problem to solve: the donor will shrink to become a WD or core-helium burning hot subdwarf in à wide binary (until. that ts. the explosion of the WD breaks up the A class of exceptions to our model might be systems containing donor stars which are able to reach helium ignition after growing their WDs to Me, whilst still posessing a substantial hydrogen envelope."," If the envelope mass is already too small, then there is no problem to solve: the donor will shrink to become a WD or core-helium burning hot subdwarf in a wide binary (until, that is, the explosion of the WD breaks up the A class of exceptions to our model might be systems containing donor stars which are able to reach helium ignition after growing their WDs to $M_{\rm Ch}$ whilst still posessing a substantial hydrogen envelope." + These donor stars would contract away from contact after igniting helium. allowing explosion to occur.," These donor stars would contract away from contact after igniting helium, allowing explosion to occur." + Even in this case the donor star would no longer be Roche-lobe filling (by an order of magnitude or more)., Even in this case the donor star would no longer be Roche-lobe filling (by an order of magnitude or more). + Despite the extended-accretion model for single degenerate progenitors described above. there exists a plausible explanation for why most SN Ia apparently explode within a narrow range of masses: the mass reservoir in the donor may usually be too small to allow significantly super-Chandrasekhar masses.," Despite the extended-accretion model for single degenerate progenitors described above, there exists a plausible explanation for why most SN Ia apparently explode within a narrow range of masses: the mass reservoir in the donor may usually be too small to allow significantly super-Chandrasekhar masses." + Below we suggest that most SN Ia might reasonably still explode with WD masses =L.5M.., Below we suggest that most SN Ia might reasonably still explode with WD masses $\lesssim 1.5 M_{\odot}$. + The WD mass distribution at explosion directly relates to the question. of what fraction of SD SN Ia are subject to our proposed mechanism., The WD mass distribution at explosion directly relates to the question of what fraction of SD SN Ia are subject to our proposed mechanism. +" The remaining donor mass at explosion depends on the donor mass at the start of the accretion phase (M,;). the initial and final accretor masses (Myyp; Myywp;) and the mean accretion efficiency tthe fraction of the mass lost by the donor that the WD manages to accrete and retain)."," The remaining donor mass at explosion depends on the donor mass at the start of the accretion phase $M_{d,i}$ ), the initial and final accretor masses $M_{WD,i}$ $M_{WD,f}$ ) and the mean accretion efficiency the fraction of the mass lost by the donor that the WD manages to accrete and retain)." + There is considerable uncertainty in the population distribution of these: any model that could know them would have largely solved the question of which systems produce SN Ia. However. we can apply some constraints.," There is considerable uncertainty in the population distribution of these: any model that could know them would have largely solved the question of which systems produce SN Ia. However, we can apply some constraints." + The canonical limit for dynamically stable mass transfer limits the mass of a giant donor to be &1.2 times the mass of the So for an initial COWD mass of = 1.0 M.. then for a RG donor any final core mass of 0.2 M.. or more would require a mean accretion efficiency above before the final mass of the accretor could exceed z 1.5 M.. (i.e. before we must appeal to strong differential rotation)., The canonical limit for dynamically stable mass transfer limits the mass of a giant donor to be $\lessapprox 1.2$ times the mass of the So for an initial COWD mass of $\lesssim$ 1.0 $M_{\odot}$ then for a RG donor any final core mass of 0.2 $M_{\odot}$ or more would require a mean accretion efficiency above before the final mass of the accretor could exceed $\approx$ 1.5 $M_{\odot}$ (i.e. before we must appeal to strong differential rotation). + Much lower — even negative — mass accretion efficiencies for such RG-WD recurrent novae are common in. the literature (see.e.g..Yaronetal. 2005)..," Much lower – even negative – mass accretion efficiencies for such RG+WD recurrent novae are common in the literature \citep[see, e.g.,][]{Yaron+2005}. ." + Furthermore Chen&L1(2009) find that rapidly rotating WDs can experience even lower accretion efficiencies than non-rotating WDs., Furthermore \citet{ChenLi2009} find that rapidly rotating WDs can experience even lower accretion efficiencies than non-rotating WDs. + For the supersoft channel. dynamical stability canonically restricts the mass of a radiative donor to be =3 times the mass of the aecretor. in which case overall accretion efficiencies S would allow our model to be widely applicable in the restrictive case of solid-body This seems challenging without a significant and inefficent recurrent-nova phase.," For the supersoft channel, dynamical stability canonically restricts the mass of a radiative donor to be $\lesssim 3$ times the mass of the accretor, in which case overall accretion efficiencies $\lessapprox$ would allow our model to be widely applicable in the restrictive case of solid-body This seems challenging without a significant and inefficent recurrent-nova phase." + Hachisuetal.(2008) have suggested that the limit for dynamical stability could be significantly higher than expected. which would make it very difficult for the mechanism presented here to apply to those SD systems.," \citet{HachisuKatoNomoto2008} have suggested that the limit for dynamical stability could be significantly higher than expected, which would make it very difficult for the mechanism presented here to apply to those SD systems." + For à population of RG donor stars. Meng&Yang(2010) caleulated remaining envelope masses at explosion. under the standard assumption that SN la occur at a CO WD mass of 1.378 M...," For a population of RG donor stars, \citet{MengYang2010} calculated remaining envelope masses at explosion under the standard assumption that SN Ia occur at a CO WD mass of 1.378 $M_{\odot}$." + Extrapolating from their results. then for accretion efficiencies =0.5. almost none of the systems in one of the two populations they synthesised would increase the WD mass by more than 0.1M.. before the donor's envelope contracted.," Extrapolating from their results, then for accretion efficiencies $\lessapprox 0.3$, almost none of the systems in one of the two populations they synthesised would increase the WD mass by more than $M_{\odot}$ before the donor's envelope contracted." +" For more general SD systems. Chen&Li(2009) to makesuper-Chandrasekhar SN Ia by considering accretion onto rotating WDs. but found ""in most cases the final masses of the white dwarfs are not significantly exceeding"," For more general SD systems, \citet{ChenLi2009} to makesuper-Chandrasekhar SN Ia by considering accretion onto rotating WDs, but found `in most cases the final masses of the white dwarfs are not significantly exceeding" +discrepancy between theory and observation is also caused by other element(s). whose surface distribution was not mapped by (1999).,"discrepancy between theory and observation is also caused by other element(s), whose surface distribution was not mapped by ." +. Both the optical and UV light curves provide strong constraints on the opacity caused by this as yet unidentified element. which might redistribute the flux from UV region of about 2000—2500A.. especially to the region of Strómmgren u.," Both the optical and UV light curves provide strong constraints on the opacity caused by this as yet unidentified element, which might redistribute the flux from UV region of about $2000-2500\,$, especially to the region of Strömmgren $u$." + We tested if either of the chemical elements currently included in the TLUSTY model atmospheres could cause these light variations., We tested if either of the chemical elements currently included in the TLUSTY model atmospheres could cause these light variations. + Excluding magnesium because of its low abundance previously. no other element included in TLUSTY (1.e.. C. N. O. Ne. Al. and S) is able to cause the remaining light variations observed inVir.," Excluding magnesium because of its low abundance previously, no other element included in TLUSTY (i.e., C, N, O, Ne, Al, and S) is able to cause the remaining light variations observed in." +. Consequently. it 1s likely that another element (especially the iron-peak ones) could be the cause.," Consequently, it is likely that another element (especially the iron-peak ones) could be the cause." + Very recent observations in a broad spectral range suggest that titanium and oxygen could also be contributors to inhomogeneous abundance structures on the surface ofVir., Very recent observations in a broad spectral range suggest that titanium and oxygen could also be contributors to inhomogeneous abundance structures on the surface of. + Especially titanium. (provided it is significantly overabundant) is one of the potential causes of the UV variations we cannot simulate so far., Especially titanium (provided it is significantly overabundant) is one of the potential causes of the UV variations we cannot simulate so far. + Vertical abundance stratification is observed in some CP stars2004)., Vertical abundance stratification is observed in some CP stars. + proposed that the vertical abundance stratification may influence the light variability., proposed that the vertical abundance stratification may influence the light variability. + Our test caleulations confirmed these expectations., Our test calculations confirmed these expectations. + The models with overabundant iron in the outer regions (for the Rosseland optical depth τω« 0.1) indeed show a larger magnitude difference in 4than in the v. 5. and v colours.," The models with overabundant iron in the outer regions (for the Rosseland optical depth $\tau_\text{Ross}<0.1$ ) indeed show a larger magnitude difference in $u$than in the $v$, $b$, and $y$ colours." + Consequently. vertical abundance stratification could possibly explain the difference between the phases of maxima in individual Strómmgren filters.," Consequently, vertical abundance stratification could possibly explain the difference between the phases of maxima in individual Strömmgren filters." + However. the influence of vertical abundance stratification on the UV region ts relatively low. consequently another process is needed to explain the difference between observation and theory in this region.," However, the influence of vertical abundance stratification on the UV region is relatively low, consequently another process is needed to explain the difference between observation and theory in this region." + Surface temperature differences and variable temperature gradients were also suggested as possible causes of the CP star light variability1978)., Surface temperature differences and variable temperature gradients were also suggested as possible causes of the CP star light variability. +. Hot stars may retain subsurface convection zones2010). which can generate local magnetic fields.," Hot stars may retain subsurface convection zones, which can generate local magnetic fields." + These magnetic fields may give rise to the surface temperature differences. and consequently cause the light variability.," These magnetic fields may give rise to the surface temperature differences, and consequently cause the light variability." + However. mild differences between the observed and predicted light curves do not indicate any (effective) temperature differences on the surface ofVir.," However, mild differences between the observed and predicted light curves do not indicate any (effective) temperature differences on the surface of." +". This is supported also by the fact that e. ο, the predicted mean of the flux distribution simulates the observed one fairly well. as depicted in Fig. 8.."," This is supported also by the fact that e. g. the predicted mean of the flux distribution simulates the observed one fairly well, as depicted in Fig. \ref{ptok}." + Moreover. a good agreement between the observed and predicted light curves in the far-UV region and the vy light curves in the visible region excludes the temperature differences as a main source of the light variability.," Moreover, a good agreement between the observed and predicted light curves in the far-UV region and the $vby$ light curves in the visible region excludes the temperature differences as a main source of the light variability." + In our study we assumed a generic value of the microturbulent velocity 2kms'.," In our study we assumed a generic value of the microturbulent velocity $2\,\text{km}\,\text{s}^{-1}$." + This parameter. which roughly accounts for atmospheric. velocity. fields. likely has a zero value in corresponding normal stars2009).," This parameter, which roughly accounts for atmospheric velocity fields, likely has a zero value in corresponding normal stars." +. We kept a nonzero value here as à very rough approximation of Zeeman line broadening., We kept a nonzero value here as a very rough approximation of Zeeman line broadening. + The adopted value of the microturbuler= velocity may. however. influence the emergent flux.," The adopted value of the microturbulent velocity may, however, influence the emergent flux." + At higher microturbulent velocities the line transitions are able to absorb radiation more effectively. increasing thus the temperature 1 the continuum forming regions.," At higher microturbulent velocities the line transitions are able to absorb radiation more effectively, increasing thus the temperature in the continuum forming regions." +" To estimate the magnitude of this effect. we calculated an additional model with higher microturbulent velocity 4kms7! and assuming enhanced abundance of heavier elements (2j.=—1.0. £4;2—2.25. ec,=—4.9. εις=—3.4)."," To estimate the magnitude of this effect, we calculated an additional model with higher microturbulent velocity $4\,\text{km}\,\text{s}^{-1}$ and assuming enhanced abundance of heavier elements $\varepsilon_\text{He}=-1.0$, $\varepsilon_\text{Si}=-2.25$, $\varepsilon_\text{Cr}=-4.9$ , $\varepsilon_\text{Fe}=-3.4$ )." + We compared the resulting flux distributioi with the model with the same chemical composition. but with a standard microturbulent velocity of 2kms!.," We compared the resulting flux distribution with the model with the same chemical composition, but with a standard microturbulent velocity of $2\,\text{km}\,\text{s}^{-1}$." + The calculated magnitude difference (Eq. 5)), The calculated magnitude difference (Eq. \ref{velik}) ) + between these models has its minimum —0.05mag in the near-UV region 3000—3800 aand a maximum about —0.10 mag in the region 2200—25580 A..," between these models has its minimum $-0.05\,$ mag in the near-UV region $3000-3800\,$ and a maximum about $-0.10\,$ mag in the region $2200-2550\,$ ." + These are the regions. where the most apparent differences. between observed and predicted light. variations occur., These are the regions where the most apparent differences between observed and predicted light variations occur. + Consequently. a higher value of the microturbulent velocity and/or surface microturbulent velocity distribution (see Sect. 7.8))," Consequently, a higher value of the microturbulent velocity and/or surface microturbulent velocity distribution (see Sect. \ref{slunik}) )" + cannot be ruled out as a possible cause of the remaining difference between theory and observation., cannot be ruled out as a possible cause of the remaining difference between theory and observation. + bbelongs to the fast rotators among CP stars., belongs to the fast rotators among CP stars. +" From Table | we can infer its rotational velocity v,2320kms!. indicating a rotational velocity close to the critical one."," From Table \ref{hvezda} we can infer its rotational velocity $v_\text{rot}=320\,\text{km}\,\text{s}^{-1}$, indicating a rotational velocity close to the critical one." + To quantify this. the stellar radius has to be known with sufficiently highprecision.," To quantify this, the stellar radius has to be known with sufficiently highprecision." + Using the stellar parameters derived from spectroscopy and photometry (e.. vjsinf. inclination. and period. see Table 1)). we can estimate the equatorial radius to be Ruy=3.340.6Rs.," Using the stellar parameters derived from spectroscopy and photometry (i.e., $v_\text{rot} \sin i$, inclination, and period, see Table \ref{hvezda}) ), we can estimate the equatorial radius to be $R_\text{eq}=3.3\pm0.6\,{R}_\odot$." +" This value agrees well with the stellar radius derived from the evolutionary tracks in the 7s,—logg plane of(1992).. which is R=3.2€0.5R« (the derived mass is M=38+ 02M)."," This value agrees well with the stellar radius derived from the evolutionary tracks in the $T_\text{eff}- +\log g$ plane of, which is $R=3.2\pm0.5\,{R}_\odot$ (the derived mass is $M=3.8\pm0.2\,{M}_\odot$ )." + Note. however. that this yields a significantly higher radius than that derived from the observed UV flux. which is R=1.9+0.1R« assuming a distance of 79+|pe2007)..," Note, however, that this yields a significantly higher radius than that derived from the observed UV flux, which is $R=1.9\pm0.1\,{R}_\odot$ assuming a distance of $79\pm1\,\text{pc}$." + This possibly points either to a problem with the absolute flux calibration. or to an inclination that is too low.," This possibly points either to a problem with the absolute flux calibration, or to an inclination that is too low." + The latter is supported by a lower radius of R=2.3€0.1R« derived from photometry and evolutionary tracks by(2006).," The latter is supported by a lower radius of $R=2.3\pm0.1\,{R}_\odot$ derived from photometry and evolutionary tracks by." +". To study the effect of fast rotation at its extremum. we assumed the equatorial radius R4,ST=3.3Rs. and M=3.8M... the polar radius is then Ry=Rey(1+valGM)"" 1963).."," To study the effect of fast rotation at its extremum, we assumed the equatorial radius $R_\text{eq}=3.3\,R_\odot$, and $M=3.8\,M_\odot$, the polar radius is then $R_\text{p} =R_\text{eq} \zav{1+v_\text{rot}^2R_\text{eq}/\zav{2GM}}^{-1} +=2.7\,R_\odot$ ." +" The ratio of the rotational velocity to the critical one ts then οι=vi/y2GM/3R, 0.75."," The ratio of the rotational velocity to the critical one is then $v_\text{rot}/v_\text{krit}= +v_\text{rot}/\sqrt{{2GM}/{3R_\text{p}}}= 0.75$ ." + If the star rotates this rapidly. the polar to equator difference in the effective surface gravity and effective temperature are," If the star rotates this rapidly, the polar to equator difference in the effective surface gravity and effective temperature are" +The accretion induced. collapse of a rapidly rotating white dwarf can result in the formation of a rapielly and differentially rotating compact object.,The accretion induced collapse of a rapidly rotating white dwarf can result in the formation of a rapidly and differentially rotating compact object. + It has been suggested that such rapidly. rotating objects could. emit a substantial amount of gravitational radiation (Thorne1995).. which might be observable by the gravitational wave observatories such as LIGO. VIRGO and GEO.," It has been suggested that such rapidly rotating objects could emit a substantial amount of gravitational radiation \cite{thorne95}, which might be observable by the gravitational wave observatories such as LIGO, VIRGO and GEO." + It has been demonstrated that if the collapse is axisvmmetric. the energy. emitted by &ravitational waves is rather small (Müller&Llillcbranelterger&Müller. 1997).," It has been demonstrated that if the collapse is axisymmetric, the energy emitted by gravitational waves is rather small \cite{muller81,finn90,monchmeyer91,zwerger97}." +".. However. if the collapsed: object rotates rapidly enough to develop a non-axisvmmetrie ""bar instability. the total energy released by gravitational waves could be 103 times greater than the axisvmimetric case (Llouser.Centrella&Smith1994:Houser1996:Smith.Houser&Centrella1996:Llouser 1998)."," However, if the collapsed object rotates rapidly enough to develop a non-axisymmetric `bar' instability, the total energy released by gravitational waves could be $10^4$ times greater than the axisymmetric case \cite{houser94,houser96,smith96,houser98}." +. Rotational instabilities of rotating stars arise [rom non-axisvmmoetric perturbations of the form. eS where 4 is the azimuthal angle.," Rotational instabilities of rotating stars arise from non-axisymmetric perturbations of the form $e^{im\varphi}$, where $\varphi$ is the azimuthal angle." + The m=2 mode is known as themode. which is often the fastest growing unstable mode.," The $m=2$ mode is known as the, which is often the fastest growing unstable mode." + There are two kinds of instabilities., There are two kinds of instabilities. + Aodynamical instability is driven by hvdrodynamics ancl gravity. and develops on a dynamical timescale. tthe time for sound waves to travel across the star.," A instability is driven by hydrodynamics and gravity, and develops on a dynamical timescale, the time for sound waves to travel across the star." + Asecular instability is driven by dissipative processes such as viscosity or gravitational radiation reaction. and the growth time is determined. by the. clissipative timescale.," A instability is driven by dissipative processes such as viscosity or gravitational radiation reaction, and the growth time is determined by the dissipative timescale." + These. secular imescales are usually much. longer than the dynamical imescale of the system., These secular timescales are usually much longer than the dynamical timescale of the system. + An interesting class of secular ancl dynamical. instabilities only occur in rapidly rotating stars., An interesting class of secular and dynamical instabilities only occur in rapidly rotating stars. + One convenient. measure of the rotation of a star is he parameter 3=Tha/[|W|. where Zi is the rotational kinetic energy and M is the gravitational potential energy.," One convenient measure of the rotation of a star is the parameter $\beta=T_{\rm rot}/|W|$, where $T_{\rm rot}$ is the rotational kinetic energy and $W$ is the gravitational potential energy." +" Dvnamical and secular instabilitiesset in when d exceeds the critical values 4 and 3, respectively.", Dynamical and secular instabilitiesset in when $\beta$ exceeds the critical values $\beta_d$ and $\beta_s$ respectively. +" Lt is well known that 2;7:0.27 and 3,70.14 for uniformly. rotating. constant ensity ancl incompressible stars. the Maclaurin. spheroids (Chancrasekhar1960)."," It is well known that $\beta_d \approx 0.27$ and $\beta_s\approx +0.14$ for uniformly rotating, constant density and incompressible stars, the Maclaurin spheroids \cite{chandrasekhar69}." +.. Numerous numerical simulations in Newtonian theory show that 3%) and ἐς have roughly. jese same values for dilferentially rotating polvtropes with le same specific angular momentum distribution as the Alaclaurin spheroids (Vohline.Durisen&MeCollough1985:Davis1996:Llouser1998:New.Centrella&Tobline 2000).," Numerous numerical simulations in Newtonian theory show that $\beta_d$ and $\beta_s$ have roughly these same values for differentially rotating polytropes with the same specific angular momentum distribution as the Maclaurin spheroids \cite{tohline85,durisen86,williams88,houser94,smith96,houser96,pickett96,houser98,new99}." +. However. the critical values of 7 are smaller for polvtropes with some other angular momentum distributions (Imamura 2000)..," However, the critical values of $\beta$ are smaller for polytropes with some other angular momentum distributions \cite{imamura95,pickett96,centrella00}. ." + And general relativistic simulations also suggest that the critical values o£; are smaller than the classical, And general relativistic simulations also suggest that the critical values of $\beta$ are smaller than the classical +larger scales. with a very small number o&oinge bevond .,"larger scales, with a very small number going beyond $l = 30\,h^{-1}$ Mpc." +ὃνl ∪⇂⊳∖⋜↧↓↿⊳∐∪∖∖⊽⋖⊾∖⇁∢⊾↓⋅⊳↿⇂⊔⊾↓⋅∢⊾↓⊳∖⋜↧⋏∙≟⋖⋅⊔⋖⋅↓⋅⋜↧↓⇂↓⋅∢⋅⊔∠⇂⇂∪↓⋅⊔↓∪↓⋅∢⊾⋖⋅⇀∖↿∢⊾⊔∠⇂⋖⋅∠⇂, In Figure \ref{shape_vs_length} we plot $e_2/e_1$ versus $l$ for the $b = 0.6$ sample. + ⋅ ⋅ ⋅∣⋡↓⋅⋜⋯≼⇍↓↥∢⋅≱∖↿∪∣⋡∢⋅⊔↓∪↓⋅∢⊾∐↓⋜⋯↓∢⊾⊔↿⋜⊔⋅∖⇁↦ clearly visible as horizontal stripes.," Below $l = 20\,h^{-1}$ Mpc the effect of the grid is clearly visible as horizontal stripes." +" There appears to be a tendeney for shorter branches to have a broader distribution in cs/60,.", There appears to be a tendency for shorter branches to have a broader distribution in $e_2/e_1$. + This trend is almost entirely caused by how the es are computed., This trend is almost entirely caused by how the $e$ 's are computed. + The shortest branches consist of only a few cells. and thus their shapes have to be taken with a >grain H .," The shortest branches consist of only a few cells, and thus their shapes have to be taken with a grain of salt." + ⋅ ⋅ ↓⊔↓⊲↓⋏∙≟⊔↓⋅⋖⋅↓∪∖∖⋎∢⊾↓≻↓∪↿↙↴⊐↙↴⊥∖⇁⋖⋅↓⋅≱∖⊔⊳∖∣⇂∪↓⋅↥⇂↥⋖⋅∣↗∶∪⋅↻," However, there is a general trend for more extended branches to be more ." +GMC mass but for simplicity we adopt everywhere {ως=I0* M. since the most massive known clusters have masses of the order of a few 10* M. (Walcher et al.,"GMC mass but for simplicity we adopt everywhere $M_{cl,max}=10^{8}$ $_{\odot}$ since the most massive known clusters have masses of the order of a few $10^{7}$ $_{\odot}$ (Walcher et al." + 2005. Portegies Zwart et al.," 2005, Portegies Zwart et al." + 2010)., 2010). + NGV4) is Che mass Function of protochister forming clumps which we take to be AN(Mj)—AyAL? in agreement with the results of Dib et al. (, $N (M_{cl})$ is the mass function of protocluster forming clumps which we take to be $N (M_{cl})=A_{cl} M_{cl}^{-2}$ in agreement with the results of Dib et al. ( +"2011) and Parmentier (2011). and vy is a normalisation coefficient given by 2d[eeMoe)N(ALjdM,=e. where O$ and $\left$ are, respectively, the characteristic SFE and the epoch at which gas is expelled from the protocluster region for the clump mass distribution associated with a given $\Sigma_{g}$ ." +" Writing (/,,,) in terms of the characteristic clump free-fall time (pp) pr). Eq."," Writing $\left$ in terms of the characteristic clump free-fall time $\left$ $n_{exp}=t_{exp}/t_{ff}$ ), Eq." + 2. becomes: In Eq. 6..," \ref{eq2} becomes: In Eq. \ref{eq6}," +" (f,jy) represents the characteristic star formation efliciency per Iree-fal] time of the clumpmass distribution in the leedback regulated star formation model."," $\left$ represents the characteristic star formation efficiency per free-fall time of the clumpmass distribution in the feedback regulated star formation model." +" In order to calculate (f,py) we use the results of Dib et al. ("," In order to calculate $\left< f_{\star,ff} \right>$ we use the results of Dib et al. (" +2011).,2011). + Fig., Fig. +" 1. displays the dependence of SFE, and lee, on clump mass and metallicity for a serie of models in which the 0.2.", \ref{fig1} displays the dependence of $SFE_{exp}$ and $t_{exp}$ on clump mass and metallicity for a serie of models in which the $CFE_{ff}=0.2$ . +" The 5Εν, depends stronly on metallicity butweakly on mass whereas /,,, displavs a clear dependence on both quantities.", The $SFE_{exp}$ depends stronly on metallicity butweakly on mass whereas $t_{exp}$ displays a clear dependence on both quantities. +" The quantity f,jj=5FEns is displaved in Fig."," The quantity $f_{\star,ff}=SFE_{exp}/n_{exp}$ is displayed in Fig." + as a [function of mass and metallicity (left panel)., \ref{eq2} as a function of mass and metallicity (left panel). + A fit to the fyy CUu.Z ) data points with a 2-variables second order polynomial vields (hefollowing relation (shown in Fig. 2.. ," A fit to the $f_{\star,ff}$ $M_{cl},Z^{'}$ ) data points with a 2-variables second order polynomial yields thefollowing relation (shown in Fig. \ref{fig2}, ," +right panel): Using Eq. 7.. ," right panel): Using Eq. \ref{eq7}, ," +it is then possible to caleulate (f. rp):," it is then possible to calculate $\left$ :" +The study of supernovae at high redshifts offers the possibility of seeing evolutionary effects in action.,The study of supernovae at high redshifts offers the possibility of seeing evolutionary effects in action. + SNAP will exploit this feature extensively to decouple svstematies from the true cosmological signal using ils 2<1.7 sample., SNAP will exploit this feature extensively to decouple systematics from the true cosmological signal using its $z<1.7$ sample. + Given the relative insensitivity οἱ Inmiinosity distance to dark energv for z>1.7 (see relsec:dark)). deviations in the IIubble diagram could potentially be useful as a means {ο reveal astvoplivsical svstematics (Riess&Livio2006).," Given the relative insensitivity of luminosity distance to dark energy for $z>1.7$ (see \\ref{sec:dark}) ), deviations in the Hubble diagram could potentially be useful as a means to reveal astrophysical systematics \citep{riess06}." +. The value of such higher reclshilt SNe la for probing svstematics that could. affect. cosmological measurements thus hinges on whether or not some property of SNe Ia is especiallv-well probed or constrained in this redshift interval., The value of such higher redshift SNe Ia for probing systematics that could affect cosmological measurements thus hinges on whether or not some property of SNe Ia is especially-well probed or constrained in this redshift interval. + Such circumstances might include extraorcdinarilv low metallicity or extension of the lookback lime early enough such that the upper limit set by (the age of the universe meaningfullv constrains (he timescales lor SN Ia progenitor models., Such circumstances might include extraordinarily low metallicity or extension of the lookback time early enough such that the upper limit set by the age of the universe meaningfully constrains the timescales for SN Ia progenitor models. + In reality. extending the study of SNe Ia [rom z=1.7 (o z=3 increases the lookback time by a mere 1.7 Gyr.," In reality, extending the study of SNe Ia from $z=1.7$ to $z=3$ increases the lookback time by a mere 1.7 Gyr." +" Since the age lor à O,,=0.3. flat. ACD. universe al z=3 is 2.2 Gyr. the first generations of stus in (he canonical 38 AL. mass range expected. [or C/O white dwarl progenitors (Iben&Renzini1983) will have evolved and begun producing oNe Ia via the various channels currently in contention (Belezvuskietal.2005)."," Since the age for a $\om=0.3$, flat $\Lambda$ CDM universe at $z=3$ is 2.2 Gyr, the first generations of stars in the canonical 3–8 $M_\odot$ mass range expected for C/O white dwarf progenitors \citep{iben83} will have evolved and begun producing SNe Ia via the various channels currently in contention \citep{belczynski05}." +. Therefore. it will remain difficult to directly. probe systematic effects due to the progenitor mass.," Therefore, it will remain difficult to directly probe systematic effects due to the progenitor mass." + Even proposed channels with long delav times of 24 Gyr (Stroleeretal.2004:ScannapiecoBildsten2005) would be operative over the 1.7«z3 vedshill range.," Even proposed channels with long delay times of 2–4 Gyr \citep{strolger04,scannapieco05b} would be operative over the $1.719,000 K (dependent on initial conditions) as the “hot ionized medium” (hereafter HIM)."," We refer to the transient regime with $T>19,000$ K (dependent on initial conditions) as the “hot ionized medium” (hereafter HIM)." +" The mass fractions of the thermal phases (fr, fc. and fy) in a relaxed state mostly depend on the mean gas density in the box po."," The mass fractions of the thermal phases $f_F$, $f_G$, and $f_H$ ) in a relaxed state mostly depend on the mean gas density in the box $\rho_0$." +" If po is low enough, both the unstable and cold phases are transient, and evolution ends up with a single warm gas phase once the turbulence generated during the violent relaxation to thermal equilibrium decays."," If $\rho_0$ is low enough, both the unstable and cold phases are transient, and evolution ends up with a single warm gas phase once the turbulence generated during the violent relaxation to thermal equilibrium decays." +" If po is higher than Pmin, Corresponding to the local pressure minimum on the bistable thermal equilibrium curve, the evolution ends up with a single cold phase."," If $\rho_0$ is higher than $\rho_{min}$, corresponding to the local pressure minimum on the bistable thermal equilibrium curve, the evolution ends up with a single cold phase." +" For intermediate mean gas densities, the system evolves to a multiphase state with an asymptotic fy/fr ratio dependent solely on the value of p.! The mass fraction of thermally unstable gas can be 250% during the violent relaxation stage (including the cases with transient cold phase), but decreases to < later, when it also strongly correlates with the rms Mach number (fgοςΜΑ, where B~ 5)."," For intermediate mean gas densities, the system evolves to a multiphase state with an asymptotic $f_H/f_F$ ratio dependent solely on the value of $\rho_0$ The mass fraction of thermally unstable gas can be $\gsim50$ during the violent relaxation stage (including the cases with transient cold phase), but decreases to $\lsim$ later, when it also strongly correlates with the rms Mach number $f_G\propto{\mathcal M}^{\beta}$, where $\beta\sim{2\over3}$ )." +" Time variations in the heating rate Τ translate the location of the thermal equilibrium curve £(p,T)=0 in the phase plane (p,P) along an isotherm (leaving the shape of the curve unchanged if Τ= const)."," Time variations in the heating rate $\Gamma$ translate the location of the thermal equilibrium curve ${\mathcal L}(\rho,T)=0$ in the phase plane $(\rho, P)$ along an isotherm (leaving the shape of the curve unchanged if $\Gamma=const$ )." +" For a given radiative cooling efficiency, the higher the heating rate, the higher the equilibrium pressure and density, in particular, p,,j,cxI."," For a given radiative cooling efficiency, the higher the heating rate, the higher the equilibrium pressure and density, in particular, $\rho_{min}\propto\Gamma$." +" Thus, global I variations in a medium with constant mean density on a sufficiently short timescale will necessarily entail some phase adjustment."," Thus, global $\Gamma$ variations in a medium with constant mean density on a sufficiently short timescale will necessarily entail some phase adjustment." + Oscillations of the gas pressure and redistribution of mass between the thermal phases generate gas flows that gain their kinetic energy at the expense of the thermal energy supplied by the heating source., Oscillations of the gas pressure and redistribution of mass between the thermal phases generate gas flows that gain their kinetic energy at the expense of the thermal energy supplied by the heating source. + Phase restructuring in response to variations of I' involves a broad range of length scales and produces highly irregular flows since the density distribution in a multiphase medium itself is irregular., Phase restructuring in response to variations of $\Gamma$ involves a broad range of length scales and produces highly irregular flows since the density distribution in a multiphase medium itself is irregular. +" Therefore, to a certain extent, turbulence can be sustained by time-dependent heating if substantial variations occur on a timescale that is not too long compared with the turbulence decay timescale."," Therefore, to a certain extent, turbulence can be sustained by time-dependent heating if substantial variations occur on a timescale that is not too long compared with the turbulence decay timescale." +" Otherwise, during long periods of quiescence, the turbulence would get fossilized."," Otherwise, during long periods of quiescence, the turbulence would get fossilized." +" In the following, we present results for two models: (1) a low-po case in which the cold phase gets fully dissolved into the warm phase during the high heating state and in which the medium hovers between single- and two-phase states as I' varies, and (2) an intermediate-oo case with varying phase content in a two-phase medium."," In the following, we present results for two models: (1) a $\rho_0$ case in which the cold phase gets fully dissolved into the warm phase during the high heating state and in which the medium hovers between single- and two-phase states as $\Gamma$ varies, and (2) an $\rho_0$ case with varying phase content in a two-phase medium." +" For our low-density run, we take initial conditions from the fiducial model of at t=2 Myr (Fig. 1a)."," For our low-density run, we take initial conditions from the fiducial model of at $t=2$ Myr (Fig. \ref{fig1}{ )." +" By this time, the gas has partially relaxed to a bistable thermal equilibrium after violent radiative cooling from a temperature of 2x10° K. However, the gas pressure variations still remain substantial (AP/P~3, see Fig."," By this time, the gas has partially relaxed to a bistable thermal equilibrium after violent radiative cooling from a temperature of $2\times10^6$ K. However, the gas pressure variations still remain substantial $\Delta P/P\sim3$, see Fig." + in KNO2 for a phase diagram) and M is slightly above one., in KN02 for a phase diagram) and $\mathcal{M}$ is slightly above one. +" For average conditions at t=2 Myr in the thermally unstable regime, the cooling scale is A,~4 pc and the conductive (Field) scale is \,,~0.4 pc (see KN02 for definitions)."," For average conditions at $t=2$ Myr in the thermally unstable regime, the cooling scale is $\lambda_p\sim4$ pc and the conductive (Field) scale is $\lambda_{\kappa}\sim 0.4$ pc (see KN02 for definitions)." +" Thus, on our low resolution grid, the cooling scale is marginally resolved, and the conductive scale falls below the resolution limit."," Thus, on our low resolution grid, the cooling scale is marginally resolved, and the conductive scale falls below the resolution limit." +" The higher resolution model (256?) of KN02 at t=2 Myr returns a slightly higher value for fj and slightly lower value for fg, while fr is roughly the same as in the low- model(the relative differences are 0.16, 0.16, and 0.005, respectively)."," The higher resolution model $256^3$ ) of KN02 at $t=2$ Myr returns a slightly higher value for $f_H$ and slightly lower value for $f_G$, while $f_F$ is roughly the same as in the low-resolution model(the relative differences are 0.16, 0.16, and 0.005, respectively)." + The relative difference in generated kinetic energy for the high- and low-resolution models at t=2 Myr is 0.013., The relative difference in generated kinetic energy for the high- and low-resolution models at $t=2$ Myr is 0.013. +" At later times, as relaxation becomes less violent, the deviations get smaller."," At later times, as relaxation becomes less violent, the deviations get smaller." + We consider the above values to, We consider the above values to +These are based on the (V.Ay colour as well as on logg and Fe/H].,These are based on the $(V-K)_0$ colour as well as on $\log g$ and $Fe/H$ ]. + Phe V. and A band. were taken [rom theSZALDA and catalogues. respectively.," The $V$ and $K$ band were taken from the and catalogues, respectively." + For logg we use the valueD from our spectroscopy., For $\log g$ we use the value from our spectroscopy. + For the metallicity. following Brunttetal.(2008).. we adopted. Fe/H]=02+ ," For the metallicity, following \citet{bruntt08}, we adopted $[Fe/H]=-0.2 \pm 0.2$ ." +This arbitrary value has only a small impact on the results because varving Fe/1] by 2e gives an error of only OWI in Liu.," This arbitrary value has only a small impact on the results because varying $[Fe/H]$ by $2\sigma$ gives an error of only K in $T_{\rm +eff}$ ." + Vo de-redden the observed (VoA) colours we adopted the reddening reported in reftabl.. using the relation (VA)2BSLgy) (Cardellietal.1989). [or the stars with Strómmgren photometry. arn BVN)—2.E(B.V) for the other stars.," To de-redden the observed $(V-K)$ colours we adopted the reddening reported in \\ref{tab1}, using the relation $E(V-K) = 3.8\,E(b-y)$ \citep[][]{cardelli89} for the stars with Strömmgren photometry, and $E(V-K) = 2.8\,E(B-V)$ for the other stars." + Vhe resulting Tig and the relative errors are reported in reftab2 (column 5)., The resulting $T_{\rm eff}$ and the relative errors are reported in \\ref{tab2} (column 5). + In. general. there is good agreemen between the photometric and spectroscopic values," In general, there is good agreement between the photometric and spectroscopic values." + Near infrared photometry from 2NLASS. complement w the one in the optical. can be used to derive an alternative estimate of Zi by means of the Infrared. Flax Metho (IREM. Blackwell Shallis 1977).," Near infrared photometry from 2MASS, complemented by the one in the optical, can be used to derive an alternative estimate of $T_{\rm eff}$ by means of the Infrared Flux Method (IRFM, Blackwell Shallis 1977)." + In. particular. broaci-uiid photometry (this work. plus λος I-mag. NOALAD Vnmag. ΟΔΙΕ r. mag and 2MASS photometry) was use ο estimate the total observed. bolometric Dux. (fi).," In particular, broad-band photometry (this work, plus TASS4 I-mag, NOMAD R-mag, CMC14 r' mag and 2MASS photometry) was used to estimate the total observed bolometric flux $f_{\rm tot}$ )." + Phe ;Whotometrv was converted. to [uxes and the best-fitting Ixurucz(1993b) model [ux distribution. was found. ane integrated to determine fi..., The photometry was converted to fluxes and the best-fitting \citet{kur93b} model flux distribution was found and integrated to determine $f_{\rm tot}$. + The Infrared. Flax Methoc (Blackwell&Shallis1977) was then used with 2PALASS fluxes o determine the Tr reported in Table 2. (column 7)., The Infrared Flux Method \citep{black77} was then used with 2MASS fluxes to determine the $_{\rm eff}$ reported in Table \ref{tab2} (column 7). +" Finally. we inspected. theορίο Input Catalogue(κο, Lathametal. (2005)))) where additional estimates for Yap and logy based mainly on ng.rCos are present."," Finally, we inspected the Input Catalogue, \citet{latham05}) ) where additional estimates for $T_{\rm eff}$ and $\log g$ based mainly on $u^{'},g^{'},r^{'},i^{'},z^{'}$ are present." + These value are reported. in columns (5) and (11) of Table 2., These value are reported in columns (8) and (11) of Table \ref{tab2}. + Lt is worth noticing that the WIC catalogue was mainly aimed at separating dwarfs from giants. therefore the Zi and logg are not expected. to be very precise.," It is worth noticing that the KIC catalogue was mainly aimed at separating dwarfs from giants, therefore the $T_{\rm eff}$ and $\log g$ are not expected to be very precise." + Since no errors are p in the WIC catalogue. we assumed. uncertainties of250 Ix. and. 0.3 dex in Lap and logg. respectively.," Since no errors are present in the KIC catalogue, we assumed uncertainties of 250 K and 0.3 dex in $T_{\rm eff}$ and $\log g$, respectively." + We determined {μι and logg of the stars by minimizing the difference between the observed and. the synthetic 1L3 profiles., We determined $T_{\rm eff}$ and $\log g$ of the stars by minimizing the difference between the observed and the synthetic $\beta$ profiles. +" For the goodness-of-Iit. paramicter we used X7 defined niLy(5sDENNA) where UN ds the total number of points. fon. and din are the intensities of the observed. anc computed: profiles. respectively. and 344, is the photon noise."," For the goodness-of-fit parameter we used $\chi^2$ defined $\displaystyle \chi^2 = \frac{1}{N} \sum \bigg(\frac{I_{\rm obs} - I_{\rm +th}}{\delta I_{\rm obs}}\bigg)^2$ where $N$ is the total number of points, $I_{\rm obs}$ and $I_{\rm th}$ are the intensities of the observed and computed profiles, respectively, and $\delta +I_{\rm obs}$ is the photon noise." + The. errors have been estimated fromthe variation in the parameters, The errors have been estimated fromthe variation in the parameters +hence a much steeper spectrum).,hence a much steeper spectrum). + This may simply be because dust-correlated emission is more significant in the 15GHz data., This may simply be because dust-correlated emission is more significant in the 15GHz data. + Similarily since the Haslam -correlated emission is more signiticant at 10 GHz. the joint correlation method gives a lower value of à for the dust-correlated component and a correspondingly higher value for the synchrotron-correlated. component.," Similarily since the Haslam -correlated emission is more significant at 10 GHz, the joint correlation method gives a lower value of $\hat{a}$ for the dust-correlated component and a correspondingly higher value for the synchrotron-correlated component." + Being able to correct for this effect might therefore sort the systematic discrepancy., Being able to correct for this effect might therefore sort the systematic discrepancy. + However. since we see this discrepancy with the synchrotron spectral index we should be wary of the dust template correlation as well.," However, since we see this discrepancy with the synchrotron spectral index we should be wary of the dust template correlation as well." + If we now consider the DIRBE template to be an exact oredietor for either spinning dust or free-free emission (so that all he features present in this template are present in the Tenerife data: as We are assuming when performing the correlation analysis) then he level of ‘contamination’ «& will be independent of the region ested., If we now consider the DIRBE template to be an exact predictor for either spinning dust or free-free emission (so that all the features present in this template are present in the Tenerife data; as we are assuming when performing the correlation analysis) then the level of `contamination' $a$ will be independent of the region tested. + This means that each value of α in Table | should be the same for the 10 and 15GHz data respectively., This means that each value of $a$ in Table 1 should be the same for the 10 and 15GHz data respectively. + We can therefore ake the variance of a across the different regions analysed as a measure of the error in this method. and find that weighted mean and rms at 10 GHz and 15 GHz are 157 (20) and 122 (10) uk / (MIy sr!) respectively.," We can therefore take the variance of $a$ across the different regions analysed as a measure of the error in this method, and find that weighted mean and rms at 10 GHz and 15 GHz are 157 (20) and 122 (10) $\mu$ K / (MJy $^{-1}$ ) respectively." + This would correspond to a spectral index of 0.6Qi., This would correspond to a spectral index of $-0.6^{+0.5}_{-0.5}$. + We now divide the data into halves in RA. which gives two regions. one towards the Galactic centre and one towards the Galactic anticentre. at each declination.," We now divide the data into halves in RA, which gives two regions, one towards the Galactic centre and one towards the Galactic anticentre, at each declination." + Repeating our analysis on these data we quantify the visual impression from Figure 2., Repeating our analysis on these data we quantify the visual impression from Figure 2. + Although the rise of the Galactic plane signal is equally strong in both regions of the dust template. we only tind a significant correlation with the 10 and 15GHz data in the Galactic centre region. in spite of the fact that the noise errors in both regions are comparable.," Although the rise of the Galactic plane signal is equally strong in both regions of the dust template, we only find a significant correlation with the 10 and 15GHz data in the Galactic centre region, in spite of the fact that the noise errors in both regions are comparable." + The results of this analysis are listed in table 4., The results of this analysis are listed in table 4. + It is seen that of the tive declination stripes in the centre region only the three at higher declination are significantly correlated., It is seen that of the five declination stripes in the centre region only the three at higher declination are significantly correlated. + The anticentre regions are found to be uncorrelated or even significantly anticorrelated in two stripes. which again demonstrates that the structure is not correlated rather han that our sensitivity is reduced when dividing the data.," The anticentre regions are found to be uncorrelated or even significantly anticorrelated in two stripes, which again demonstrates that the structure is not correlated rather than that our sensitivity is reduced when dividing the data." + Again if we take the weighted mean and rms in the value of « between declinations. we get 197 (66) and 157 (91) uK / (MIy sr!) for he centre regions at IO and 15 GHz respectively. giving a spectral index of 0.6ii," Again if we take the weighted mean and rms in the value of $a$ between declinations, we get 197 (66) and 157 (91) $\mu$ K / (MJy $^{-1}$ ) for the centre regions at 10 and 15 GHz respectively, giving a spectral index of $-0.6^{+2.2}_{-2.8}$." + The variation between declinations is high and he spectral index thus obtained is consistent with both free-free and spinning dust models., The variation between declinations is high and the spectral index thus obtained is consistent with both free-free and spinning dust models. + We perform vet another split of the data in an attempt to identify the region where the correlation mainly comes from., We perform yet another split of the data in an attempt to identify the region where the correlation mainly comes from. + It was found that the 20 pixels at lowest Galactic latitude of all declinations taken together (100 pixels) gave significant correlations. while the remaining pixels (750) gave no correlation (see table 5).," It was found that the 20 pixels at lowest Galactic latitude of all declinations taken together (100 pixels) gave significant correlations, while the remaining pixels (750) gave no correlation (see table 5)." + Again the spectral index for dust-correlated emission is small and negative. while that for emission correlated to the Haslam map is steeper than expected.," Again the spectral index for dust-correlated emission is small and negative, while that for emission correlated to the Haslam map is steeper than expected." + Since it is clear that the different declinations correlate differently. correlating them together is incorrect.," Since it is clear that the different declinations correlate differently, correlating them together is incorrect." + Hence. shown also in table 5 are the values obtained for the same analysis on the 20 pixels at lowest Galactic latitude of each declination.," Hence, shown also in table 5 are the values obtained for the same analysis on the 20 pixels at lowest Galactic latitude of each declination." + Even though the signal to noise is much lower here. it is clear that the Galactic plane signal correlates with a free-free like spectral index while the rest of the pixels shows a significant anti-correlation with dust at 10 GHz for some declinations.," Even though the signal to noise is much lower here, it is clear that the Galactic plane signal correlates with a free-free like spectral index while the rest of the pixels shows a significant anti-correlation with dust at 10 GHz for some declinations." + The Galaxy correlates positively while the remaining regions correlate negatively or insignificantly., The Galaxy correlates positively while the remaining regions correlate negatively or insignificantly. + It is clear from analysing such splits that the correlation coefficients obtained when taking all declinations together as in tables | 2 (520 ) and in table 5. and which seem to indicate an almost flat or less negative spectral index between 10 and 15 GHz. are composed of regions that correlate with a negative spectral index and regions that do not correlate significantly at all.," It is clear from analysing such splits that the correlation coefficients obtained when taking all declinations together as in tables 1 2 $b>20\deg$ ) and in table 4 5, and which seem to indicate an almost flat or less negative spectral index between 10 and 15 GHz, are composed of regions that correlate with a negative spectral index and regions that do not correlate significantly at all." + The anti-correlation. which occurs mostly in the IOGHz data. lowers the combined best fit & value at that frequency. and hence raises the spectral index of dust-correlated emission.," The anti-correlation, which occurs mostly in the 10GHz data, lowers the combined best fit $a$ value at that frequency, and hence raises the spectral index of dust-correlated emission." + Note here that the high values of a obtained need not to be in contradiction to the level of free-free allowed by Hy as the detections are all close to the Galactic plane. where the level of free-free is expected to be high.," Note here that the high values of 'a' obtained need not to be in contradiction to the level of free-free allowed by $_\alpha$ as the detections are all close to the Galactic plane, where the level of free-free is expected to be high." + We still see a large variance between the three declinations which correlate signiticantly., We still see a large variance between the three declinations which correlate significantly. + If we take the weighted mean and rms of the highest three declinations as indicative of a composite correlation. we get 313 (172) and 219 (83) uK / (MIy sr. oat 10 GHz and 15 GHz respectively. giving a spectral index of 0.9tote85». again. consistent. with. both free-free. and spinning dust.," If we take the weighted mean and rms of the highest three declinations as indicative of a composite correlation, we get 313 (172) and 219 (83) $\mu$ K / (MJy $^{-1}$ ) at 10 GHz and 15 GHz respectively, giving a spectral index of $-0.9^{+2.8}_{-2.2}$, again consistent with both free-free and spinning dust." + Note that this value was obtained from the weighted average of three pairs of numbers shown in table 5. where each pair indicated a negative spectral index.," Note that this value was obtained from the weighted average of three pairs of numbers shown in table 5, where each pair indicated a negative spectral index." + The spectral index obtained simultaneously for the component correlated to the Haslam map is consistent within | 6 with the synchrotron spectral index., The spectral index obtained simultaneously for the component correlated to the Haslam map is consistent within 1 $\sigma$ with the synchrotron spectral index. + Given that the dust templates correlate with the data only in a small part of the Tenerife patch above b=20. we further test. how physically meaningful the detection is.," Given that the dust templates correlate with the data only in a small part of the Tenerife patch above $b = 20\deg$ we further test, how physically meaningful the detection is." + This is important because the spectral index of a component in this method is inferred by assuming that the difference in the correlation amplitude between the frequencies is solely due to the change of emissivity of a single physical component and is not due to a spurious change in the strength of the correlation., This is important because the spectral index of a component in this method is inferred by assuming that the difference in the correlation amplitude between the frequencies is solely due to the change of emissivity of a single physical component and is not due to a spurious change in the strength of the correlation. + Another way to test for systematic errors in the method is to take random samples from the Galactic templates themselves as “Monte Carlo” simulations.," Another way to test for systematic errors in the method is to take random samples from the Galactic templates themselves as ""Monte Carlo"" simulations." + The advantage is that we can test against chance correlations with typical structure in the templates without having to understand the templates to a degree that would allow us to model this structure., The advantage is that we can test against chance correlations with typical structure in the templates without having to understand the templates to a degree that would allow us to model this structure. + Since the rise of the signal towards the Galactic plane clearly is a strong feature in the data and high Galactic latitude correlations are at best weak. we correlate to rotated / flipped maps in the northern and southern hemispheres. which all have the same orientation relative to the Galactic plane.," Since the rise of the signal towards the Galactic plane clearly is a strong feature in the data and high Galactic latitude correlations are at best weak, we correlate to rotated / flipped maps in the northern and southern hemispheres, which all have the same orientation relative to the Galactic plane." + Figure 3 shows à and its significance for IO and 15 GHz. for the b= Galactic cut. the Galactic centre region of all declination strips taken together. and the spectral indices derived from these values.," Figure 3 shows $\hat{a}$ and its significance for 10 and 15 GHz, for the $b = 20\deg$ Galactic cut, the Galactic centre region of all declination strips taken together, and the spectral indices derived from these values." + We find that the real pateh does not correlate most significantly at either frequency., We find that the real patch does not correlate most significantly at either frequency. + Given the number of patches that correlate more significantly we conclude that the real correlation is at most typical and only due to the Galactic plane signal., Given the number of patches that correlate more significantly we conclude that the real correlation is at most typical and only due to the Galactic plane signal. + Further we see that the 15 GHz real correlation although less significant than the, Further we see that the 15 GHz real correlation although less significant than the + ? established an observationallv-based. Lramework whereby planetary. nebulae (DN) with dillerent morphologies were mapped to the shaping mechanism that could produce ihem., \citet{Soker1997} established an observationally-based framework whereby planetary nebulae (PN) with different morphologies were mapped to the shaping mechanism that could produce them. + These mechanisms ranged [rom single stars to a multitude of binary interactions with stellar aud substellar (brown dwarf and planetary) companions., These mechanisms ranged from single stars to a multitude of binary interactions with stellar and substellar (brown dwarf and planetary) companions. + Many discoveries. both observational and theoretical have been made in the last ten vears that have thickened the debate of what shapes PN.," Many discoveries, both observational and theoretical have been made in the last ten years that have thickened the debate of what shapes PN." + Kev to the debate have been the theoretical work of ? ancl ?./— (but see previous work by 2)). who described the difficulty wilh which single asvmptotie giant branch (AGB) stars can sustain rotation and global magnetic fields for long enough to affect the geometry of the mass-loss aud (he shape of the subsequent PN.," Key to the debate have been the theoretical work of \citet{Soker2006} and \citet{Nordhaus2007} (but see previous work by \citet{Soker2002b}) ), who described the difficulty with which single asymptotic giant branch (AGB) stars can sustain rotation and global magnetic fields for long enough to affect the geometry of the mass-loss and the shape of the subsequent PN." + In the case ofstars. rotation and elobal magnetic fields. have been the leading mechanism suggested for the shaping of non-spherical PN (e.g..?)..," In the case of, rotation and global magnetic fields, have been the leading mechanism suggested for the shaping of non-spherical PN \citep[e.g.,][]{GarciaSegura2005}." + Lacking a [ull understanding of how single AGB stars can produce winds that greatly diverge [rom a spherical distribution. several authors started looking more favourably (o binary origin explanations (for a review see ?)). where the companion is either à AGB wind shaping agent (i.e.. via gravity). or il induces primary envelope rotation aud magnetic fields.," Lacking a full understanding of how single AGB stars can produce winds that greatly diverge from a spherical distribution, several authors started looking more favourably to binary origin explanations (for a review see \citealt{DeMarco2009b}) ), where the companion is either a AGB wind shaping agent (i.e., via gravity), or it induces primary envelope rotation and magnetic fields." + Irrespective of what camp of the debate each researcher favours. the scheme of ? has been used as a basis against which (o test various hypotheses (e.g..2??)..," Irrespective of what camp of the debate each researcher favours, the scheme of \citet{Soker1997} has been used as a basis against which to test various hypotheses \citep[e.g.,][]{GarciaSegura1999,Parker2006,Lu2009}." + Dherelore. in lieht of the last decade of observational ancl theoretical results. (here is scope for a revision of that framework.," Therefore, in light of the last decade of observational and theoretical results, there is scope for a revision of that framework." + In particular. the role of planets in shaping PN was already discussed in the late 90s. but could not be observationally quantified at that tme.," In particular, the role of planets in shaping PN was already discussed in the late 90s, but could not be observationally quantified at that time." + Today. we know more on the statistics of planetary systems. and. alühbough many questions still remain. (his is enough to update our estimate of the role of planets in shaping PN.," Today, we know more on the statistics of planetary systems, and, although many questions still remain, this is enough to update our estimate of the role of planets in shaping PN." + Finally. new planetary discoveries are changing our understanding of stars.," Finally, new planetary discoveries are changing our understanding of stars." + New questions are being asked as to the influence planets have on stellar evolution. ancl. conversely. how stars affect planet evolution and survival (see for instance the proceedings of the conference," New questions are being asked as to the influence planets have on stellar evolution, and, conversely, how stars affect planet evolution and survival (see for instance the proceedings of the conference" +The standard notation for the divisibility is as follows: The concept of divisibility applies to the polynomials as well. we treat such situations in the subsequent paragraphs.,"The standard notation for the divisibility is as follows: The concept of divisibility applies to the polynomials as well, we treat such situations in the subsequent paragraphs." +" Now consider two given integers 2, and z». with at least one of them being a non-zero number."," Now consider two given integers $z_1$ and $z_2$, with at least one of them being a non-zero number." +" The “greatest common divisor tor the ""greatest common factor’ or the ""highest common factor’) of σι and z». denoted by ged(z4.22). is the positive integer +=. which satisfies: In other words. the greatest common divisorged(z;.22) of two non zero integers τι and z» is the largest possible integer that divides both the integers without leaving any remainder."," The `greatest common divisor' (or the `greatest common factor' or the `highest common factor') of $z_1$ and $z_2$, denoted by $gcd(z_1,z_2)$ , is the positive integer $z_d{\in}{\mathbb Z}$, which satisfies: In other words, the greatest common divisor$gcd(z_1,z_2)$ of two non zero integers $z_1$ and $z_2$ is the largest possible integer that divides both the integers without leaving any remainder." +" Two numbers z, and z» are called co-prime] (alternatively. ‘relatively prime’). if: The idea of a greatest common divisor can be generalized by detining the greater common divisor of a non empty set of integers."," Two numbers $z_1$ and $z_2$ are called `co-prime] (alternatively, `relatively prime'), if: The idea of a greatest common divisor can be generalized by defining the greater common divisor of a non empty set of integers." +" If S is a non-empty set of integers. then the greatest common divisor of S. is a positive integer 2, such that: then we denote z,,=gced(S-)."," If ${\cal S_{\mathbb Z}}$ is a non-empty set of integers, then the greatest common divisor of ${\cal S_{\mathbb Z}}$ is a positive integer $z_d$ such that: then we denote $z_d=gcd({\cal S_{\mathbb Z}})$." + Euclidean algorithm (first described in detail in Euclid’s “Elements” in 300 BC. and is still in use. making it the oldest available numerical algorithm still in common use) provides an efficient procedure for computing the greatest common divisor of two integers.," Euclidean algorithm (first described in detail in Euclid's `Elements' in 300 BC, and is still in use, making it the oldest available numerical algorithm still in common use) provides an efficient procedure for computing the greatest common divisor of two integers." +" Following Stark1978). below we provide a simplitied illustration of the Euclidean algorithm for two integers: Let us first set à ""counter ¢ for counting the steps of the algorithm. with initial step corresponding to 7=0."," Following Stark, below we provide a simplified illustration of the Euclidean algorithm for two integers: Let us first set a `counter' $i$ for counting the steps of the algorithm, with initial step corresponding to $i=0$." +" Let any ith step of the algorithm begins with two non-negative remainders 7;, and r;2 with the requirement that;4,«r;2. owing to the fact that the fundamental aim of the algorithm is to reduce the remainder in successive steps. to finally bring it down to the zero in the ultimate step which terminates the algorithm."," Let any $i$ th step of the algorithm begins with two non-negative remainders $r_{i-1}$ and $r_{i-2}$ with the requirement that $r_{i-1} 0."," In this paper we study the following generalization of the original Cardassian model: We call this model “Modified Polytropic Cardassian” (MP \citep{gondolo}, where $G=1/m_{pl}^2$ is Newton's universal gravitation constant, $\rho_{\rm Card}$ is a characteristic constant energy density, and where we take $n<2/3$ and $q>0$." +Theoriginal power law Cardassian model corresponds to g = 1., The original power law Cardassian model corresponds to $q=1$. + For comparison. we remind the reader of the original power law Cardassian model that was proposed in Freese&Lewis(2002). which had the following specific form of g(paj): This is equivalent to wriling The first term inside the bracket of Eq.(2)) and Eq.(4)) dominates initially. so that ordinary Friecanann Robertson Walker (FRW) behavior takes place thiroughout the early universe.," For comparison, we remind the reader of the original power law Cardassian model that was proposed in \cite{freeselewis}, which had the following specific form of $g(\rhom)$: This is equivalent to writing The first term inside the bracket of \ref{eq:FRW}) ) and \ref{eq:friedcard}) ) dominates initially, so that ordinary Friedmann Robertson Walker (FRW) behavior takes place throughout the early universe." + At a redshilt 2644~1. the two terms inside the bracket become ecual. and henceforth the second term. dominates.," At a redshift $\zcard \sim 1$, the two terms inside the bracket become equal, and henceforth the second term dominates." + Once the second term dominates. it. drives the universe (0 accelerate.," Once the second term dominates, it drives the universe to accelerate." + The energy density at which the two terms become equal is zea)’. where py isthe matter density today.," The energy density at which the two terms become equal is $\rhocard=\rho_0 (1+\zcard)^3$ , where $\rho_0$ isthe matter density today." + The MP Cardassian model of Eq.(2)) depends on three parameters: the numbers » and q and (he density pou., The MP Cardassian model of \ref{eq:FRW}) ) depends on three parameters: the numbers $n$ and $q$ and the density $\rhocard$. + The latter can be traded for the observed matter mass density Q (see Eq. |1]], The latter can be traded for the observed matter mass density $\Omega_m^{obs}$ (see Eq. \ref{eq:rhocard}] ] + below)., below). +" The original power law Cardassian model gave the same cdistance-redshift relation as a quintessence model with constant equation of state parameter ie,=1— 1."," The original power law Cardassian model gave the same distance-redshift relation as a quintessence model with constant equation of state parameter $w_q +=n-1$ ." + Generalized Cardassian models. on the other hand. give predictions for the cdistance-redshilt. relation," Generalized Cardassian models, on the other hand, give predictions for the distance-redshift relation" +estimated based on either SDSS or USNO-B1 photometry for bright stars in the field.,estimated based on either SDSS or USNO-B1 photometry for bright stars in the field. + The pipeline then optimizes the of each epoch to minimize the median photometric variability of all the remaining sources., The pipeline then optimizes the of each epoch to minimize the median photometric variability of all the remaining sources. + This first optimization the to below typicallythe percent improveslevel., This first optimization typically improves the long-term photometric stability to below the percent level. +" The long-termpipeline then filters photometricthe stabilitygenerated light curves, searching for epochs that produce anomalous photometry for a large fraction of the sources; those epochs are usually those affected clouds, moonlight or some other effect that varies across bythe images."," The pipeline then filters the generated light curves, searching for epochs that produce anomalous photometry for a large fraction of the sources; those epochs are usually those affected by clouds, moonlight or some other effect that varies across the images." +" Typically of epochs are flagged by this process, and are removed from further consideration."," Typically of epochs are flagged by this process, and are removed from further consideration." + A second iteration of variable-source removal and zeropoint optimization is then performed., A second iteration of variable-source removal and zeropoint optimization is then performed. +" The final zeropoints are applied to each light curve, along with flags for poor conditions, nearby sources that could cause confusion, bad pixels, and other problems that could affect the photometry."," The final zeropoints are applied to each light curve, along with flags for poor conditions, nearby sources that could cause confusion, bad pixels, and other problems that could affect the photometry." + Running on a 2.5 GHz quad-core desktop computer the pipeline processes a 300-epoch set of 11 chips (54 GB of image data) in less than 24 hours., Running on a 2.5 GHz quad-core desktop computer the pipeline processes a 300-epoch set of 11 chips (54 GB of image data) in less than 24 hours. + The achieves a photometric stability of 3-5 pipelinemillimags over typicallyperiods of months (figure 2))., The pipeline typically achieves a photometric stability of 3-5 millimags over periods of months (figure \ref{fig:phot_perf}) ). +" The photometric precision is photon-limited for all sources fainter than mR ~16, except in regions of crowding or nebulosity."," The photometric precision is photon-limited for all sources fainter than mR $\approx$ 16, except in regions of crowding or nebulosity." + The has been used for several PTF projects such as the open pipelineclusterrotation project (?).., The pipeline has been used for several PTF projects such as the open clusterrotation project \citep{Agueros2011}. . +smmearing.,mearing. + , +thus lower mass-to-light ratios. m our sample galaxies (Paper D.,"thus lower mass-to-light ratios, in our sample galaxies (Paper I)." +" In order to investigate the magnitude of this uncertaiutv. we estimate dyvnanücal masses Aqua, for a subset of our sample. as described below."," In order to investigate the magnitude of this uncertainty, we estimate dynamical masses $M_{\rm{dyn}}$ for a subset of our sample, as described below." + Dynamical mass should be a good approximation of the stellar mass of the bulee Aic. since In general stars should dominate the eravitational potential ou the scale of the bulge.," Dynamical mass should be a good approximation of the stellar mass of the bulge $M_{\rm{bulge}}$, since in general stars should dominate the gravitational potential on the scale of the bulge." + Dynamical masses for the bulges are estimated as Maa=Dra?(CG. where ας is the effective radius and σ is the velocity dispersion of the bulge (Paper D.," Dynamical masses for the bulges are estimated as $M_{\rm{dyn}}=5 +r_e\sigma^2/G$, where $r_e$ is the effective radius and $\sigma$ is the velocity dispersion of the bulge (Paper I)." + Were we use a prefactor of 5 to be cousisteut with aud(2011)., Here we use a prefactor of $5$ to be consistent with and. +. Dynamical masses for the siuuple of Ciüllteliu et al., Dynamical masses for the sample of Gülltekin et al. + ave from(2001)., are from. + For the pseudobulges from (2011).. we use effective radii from(2011).," For the pseudobulges from , we use effective radii from." +. We also include 6 additional pseudobulges identified by|Sanictal2011., We also include $6$ additional pseudobulges identified by. + For the galaxies with stellar velocity dispersion ineasuremenuts. the average difference between the predicted BIT imasses Chased— on the best fitting relation of (πο et al," For the galaxies with stellar velocity dispersion measurements, the average difference between the predicted BH masses (based on the best fitting relation of Gülltekin et al." +s sample and estimated dynamical masses) and observed values is CoeAονο=0.79+0.09.,"'s sample and estimated dynamical masses) and observed values is $\langle \log(M_{\text{predict}}/ \mbh) +\rangle=0.79\pm0.09$." + This offset is significantly larger than any reasonable formal uncertaintv in the virial BIT masses (0.10.15 dex)., This offset is significantly larger than any reasonable formal uncertainty in the virial BH masses $0.4-0.48$ dex). + Furthermore. even after correcting for stellar populations. our sample follows a steeper relation between AMpg aud Apc than the inactive./ ellipticals taken aloue (Table 1)).," Furthermore, even after correcting for stellar populations, our sample follows a steeper relation between $M_{\rm BH}$ and $M_{\rm bulge}$ than the inactive ellipticals taken alone (Table \ref{fittingrelation}) )." + This is cousisteut with our observed. Faber-Jackson relation iu Paper I (Figure 9). in that at a fixed bulee magnitude. pesudobulges have sanaller stellar velocity dispersions.," This is consistent with our observed Faber-Jackson relation in Paper I (Figure 9), in that at a fixed bulge magnitude, pesudobulges have smaller stellar velocity dispersions." + When a dark matter halo is included. the prefactor in the formula for ανασα. mass decreases by ~12%2006)..," When a dark matter halo is included, the prefactor in the formula for dynamical mass decreases by $\sim12\%$." +. Furthermore. show that the normalization of ανασα. mass formmla for bulges with Sérrsic iudex η=2 (as is the case for our sample of predominantly pseudobulges) is be larger bv ~1015€.," Furthermore, show that the normalization of dynamical mass formula for bulges with Sérrsic index $n=2$ (as is the case for our sample of predominantly pseudobulges) is be larger by $\sim40\%$." + Combining the above two effects would increase our estimated dviuauical mass by ~284., Combining the above two effects would increase our estimated dynamical mass by $\sim28\%$. + Considering the large uncertainty in the virial BIT masses (a factor of 3). this is unlikely to change our results.," Considering the large uncertainty in the virial BH masses (a factor of 3), this is unlikely to change our results." + Fiathermore. if we were to boost the clymamucal masses ofthe galaxies in our sample. the differcuce between our saluple and Cülltekin et al.," Furthermore, if we were to boost the dynamical masses of the galaxies in our sample, the difference between our sample and Gülltekin et al." +’s sample would be larger.,'s sample would be larger. + Tuterestinely. the galaxies without extended disks show the largest offset (red triangles in Figure 11).," Interestingly, the galaxies without extended disks show the largest offset (red triangles in Figure \ref{MBH}) )." + They are also the largest outlicrs in the Faber-Jacksou relation in Paper 1. Rather than scaling like pseudobulges. these ealaxies scale like spheroidals in the fuucinenutal plane.," They are also the largest outliers in the Faber-Jackson relation in Paper I. Rather than scaling like pseudobulges, these galaxies scale like spheroidals in the fundamental plane." + We have no complete explanation for why these galaxies are the largest outliers. but it isintriguing’.," We have no complete explanation for why these galaxies are the largest outliers, but it is." +".. Finally, we look at pseudobulees (both active and inactive) and use the [Eeudalls 7 rank correlation cocfücient tfo test whether pseudobulge huuünositv correlates with BIT mass."," Finally, we look at pseudobulges (both active and inactive) and use the Kendall's $\tau$ rank correlation coefficient to test whether pseudobulge luminosity correlates with BH mass." + The salple of pseudobulees taken alone has 7=0.11L aud P—0d., The sample of pseudobulges taken alone has $\tau=0.44$ and $P=0.1$. + There is no significant ccorrelation amoug these galaxies., There is no significant correlation among these galaxies. + Πιο—ποας our sample vields 7=0.13 and P=0.03., Including our sample yields $\tau=0.13$ and $P=0.03$. + In this case there is mareial evidence for a very weak correlation., In this case there is marginal evidence for a very weak correlation. + Thus we support the conclusion of that pseudobulees show no correlation between BIT mass aud bulee nass., Thus we support the conclusion of that pseudobulges show no correlation between BH mass and bulge mass. + We investigate the aand rrelatious focused on 1071.1 at the confidence level.," The best-fit indicates an edge energy in the range (0.36–0.47) keV with a best-fit value of 0.44 keV. This value is consistent with the mean expected energy of the C and the C edge (at 0.391 keV and 0.487 keV, respectively) which is 0.439 keV. The derived energy range indicates an ionization state to be somewhere between C and C. The optical depth is ${\rm +\tau_{\rm C}}>1.1$ at the confidence level." +" In this model the blackbody temperature is found to be Ls76 eV. The oof C0.—5.0)102"" TIatomscla PAis inH agreeimeut with- the foreground. colui.", In this model the blackbody temperature is found to be 48–76 eV. The of ${\rm (3.0-5.0)\ 10^{20}}$ ${\rm H-atoms~cm^{-2}}$ is in agreement with the foreground column. + We applied the F-test statistics aud find a probability of ~70% that a fit iucludiug a C- is more likely than a fit without an edge (leaving the blackbody temperature in the ft as a free parameter}., We applied the F-test statistics and find a probability of $\sim$ that a fit including a C-edge is more likely than a fit without an edge (leaving the blackbody temperature in the fit as a free parameter). + As before. the edge energies were next fixed at the values appropriate to C and € edees in the spectral fit.," As before, the edge energies were next fixed at the values appropriate to C and C edges in the spectral fit." + The fit is acceptable with a \? of 35 for 56 dof., The fit is acceptable with a $\chi^2$ of 35 for 56 dof. + The best-fit optical depths are το y= 0.92.6 and το 471.1 at confidence. Tey<2.9 at confidence.," The best-fit optical depths are ${\rm \tau_{\rm C~V}}$ = 0.9–2.6 and ${\rm \tau_{\rm C~VI}}$ =1.1--7.5 at confidence, ${\rm \tau_{\rm +C~V}}<2.9$ at confidence." + The blackbody kT is in the rauge 5081 eV. Using the Saha equation we may coustrain the electron density (cf., The blackbody kT is in the range 50–81 eV. Using the Saha equation we may constrain the electron density (cf. + Sect., Sect. + 5.1)., 5.1). + The oof (3.15.1)102? ITatomscni Is ye.1 agreement. with. the galactic foreground column.," The of ${\rm (3.1-5.1)\ 10^{20}}$ ${\rm H-atoms\ +cm^{-2}}$ is in agreement with the galactic foreground column." +"source photons receive the same high probability weights as pulsed photons but are distributed uniformly in phase, decreasing the effective S/N. However, for modest ratios of pulsed to unpulsed flux, the performance of the weighted test is not unduly diminished.","source photons receive the same high probability weights as pulsed photons but are distributed uniformly in phase, decreasing the effective S/N. However, for modest ratios of pulsed to unpulsed flux, the performance of the weighted test is not unduly diminished." +" In Figure 7,, we have examined the flux threshold for a single-peaked light curve with equal contributions of pulsed and unpulsed emission."," In Figure \ref{ch5_plot13}, we have examined the flux threshold for a single-peaked light curve with equal contributions of pulsed and unpulsed emission." +" As expected, we see an overall increased flux threshold of about 2 over the fully-pulsed source "," As expected, we see an overall increased flux threshold of about 2 over the fully-pulsed source (c.f." +Figure , Figure \ref{ch5_plot4}) ). +"Despite a slight increase in the ratio of (c.f.weighted-to-unweighted4)). thresholds, the weighted statistics still offer appreciably improved sensitivity."," Despite a slight increase in the ratio of weighted-to-unweighted thresholds, the weighted statistics still offer appreciably improved sensitivity." +" From these demonstrations, it is clear that the probability-weighted statistics have, on average, a factor of 1.5 to 2 improved sensitivity relative to the unweighted versions."," From these demonstrations, it is clear that the probability-weighted statistics have, on average, a factor of $1.5$ to $2$ improved sensitivity relative to the unweighted versions." +" One potential objection is that we have used the known spectra in determining the photon weights, whereas with real data, of course, we must first estimate the spectra of source and background."," One potential objection is that we have used the known spectra in determining the photon weights, whereas with real data, of course, we must first estimate the spectra of source and background." +" To assess the impact of using estimated parameters with concomitant uncertainty, we calculate the weights based on parameters estimated via maximum likelihood spectral analysis with the tool "," To assess the impact of using estimated parameters with concomitant uncertainty, we calculate the weights based on parameters estimated via maximum likelihood spectral analysis with the tool \citep{my_thesis}." +"For this test, we simulated 20 realizations(?).. of the Vela-like point source."," For this test, we simulated 20 realizations of the Vela-like point source." +" From Figure 4,, we see that the detection threshold is about z8x10-?ph "," From Figure \ref{ch5_plot4}, we see that the detection threshold is about $\approx8\times10^{-9}$ " +the halo profile.,the halo profile. + The mass of a homogeneous sphere with 200 times the critical density of the Universe is also shown., The mass of a homogeneous sphere with 200 times the critical density of the Universe is also shown. + The crossing of a mass distribution with this line defines the total Galactic mass and the virial radius for this density distribution which is 210 kpc for a Galactic mass of 10? Mo. The mass distributions of the NFW and the BE profile are quite similar since these profiles differ only in the region around the GC where the influence of DM is small., The crossing of a mass distribution with this line defines the total Galactic mass and the virial radius for this density distribution which is 210 kpc for a Galactic mass of $^{12}$ $_\odot$ The mass distributions of the NFW and the BE profile are quite similar since these profiles differ only in the region around the GC where the influence of DM is small. + The 240 profile yields the smallest mass while the mass distribution of the PISO profile shows a linear increase with radius., The 240 profile yields the smallest mass while the mass distribution of the PISO profile shows a linear increase with radius. + The reason is the quadratic decrease (ος r?) of the PISO profile., The reason is the quadratic decrease $\propto$ $^{-2}$ ) of the PISO profile. +" Consequently, the integral of such a profile leads to a linear increase of the Galactic mass."," Consequently, the integral of such a profile leads to a linear increase of the Galactic mass." +" By going from spherical to elliptical profiles the mass can be changed significantly, as will be discussed later."," By going from spherical to elliptical profiles the mass can be changed significantly, as will be discussed later." +" Each object, which is bound to the MW, is orbiting around the GC."," Each object, which is bound to the MW, is orbiting around the GC." +" Most of the stars and the interstellar medium (gas, dust, etc.)"," Most of the stars and the interstellar medium (gas, dust, etc.)" + are rotating with a velocity distribution v(r)., are rotating with a velocity distribution v(r). + This velocity distribution is called the (RC) of the For a circular rotation of the objects within the Galactic disc the rotation velocity is given by the equality of the centripetal and the gravitational force where v is the rotation velocity at the Galactocentric distance r. The gravitational potential Φ is given by the Poisson equation where G is the gravitational constant and p(r) is the matter density distribution model., This velocity distribution is called the (RC) of the For a circular rotation of the objects within the Galactic disc the rotation velocity is given by the equality of the centripetal and the gravitational force where v is the rotation velocity at the Galactocentric distance r. The gravitational potential $\Phi$ is given by the Poisson equation where G is the gravitational constant and $\rho (\mathrm{r})$ is the matter density distribution model. + For a given DM density profile the gravittational potential and therefore the rotation curve can be calculated and a comparison with experimental data is an important check for the DM density profile., For a given DM density profile the tational potential and therefore the rotation curve can be calculated and a comparison with experimental data is an important check for the DM density profile. +" The rotation curve can be most easily measured from the Doppler shifts, like the 21 cm from neutral hydrogen or the rotational transition lines of carbon monoxide (CO) in the millimeter wave range."," The rotation curve can be most easily measured from the Doppler shifts, like the 21 cm from neutral hydrogen or the rotational transition lines of carbon monoxide (CO) in the millimeter wave range." + A review of the various methods was given by ?.., A review of the various methods was given by \citet{Sofue:2000jx}. +" A recent summary of all data on the rotation curve of the Milky Way can be found in the publication by ?,, where the numerical values can be found on the author’s webpage."," A recent summary of all data on the rotation curve of the Milky Way can be found in the publication by \citet{Sofue:2008wt}, where the numerical values can be found on the author's webpage." +" For radii inside the solar radius the distances do not need to be determined, since the maximum Doppler shift observed in a given direction is in the tangential direction of the circle, so the longitude of that direction determines the distance from the center."," For radii inside the solar radius the distances do not need to be determined, since the maximum Doppler shift observed in a given direction is in the tangential direction of the circle, so the longitude of that direction determines the distance from the center." +" For radii larger than the solar radius the distances to the tracers have to be determined independently, usually by the angular thickness of the HI layer, as first proposed by ?.."," For radii larger than the solar radius the distances to the tracers have to be determined independently, usually by the angular thickness of the HI layer, as first proposed by \citet{Merrifield:1992nb}." + These independent distance determinations lead to larger errors in the outer rotation curve., These independent distance determinations lead to larger errors in the outer rotation curve. +" The most precise determination and with it the normalization of the rotation curve is obtained from the Oort constants, which can be determined from the precise distances and velocities of nearby stars, as discussed in most textbooks, e.g. (???).."," The most precise determination and with it the normalization of the rotation curve is obtained from the Oort constants, which can be determined from the precise distances and velocities of nearby stars, as discussed in most textbooks, e.g. \citep{Binney,Sparke,Zeilik}." + These constants are defined as: where the experimental values have been taken from ?.., These constants are defined as: where the experimental values have been taken from \citet{Kerr:1986hz}. +" One observes that A-B =νο/το defines the local normalization of the rotation curve, while A+B defines the slope at the solar position."," One observes that A-B $= {\mathrm{v}_\odot}/{\mathrm{r}_\odot}$ defines the local normalization of the rotation curve, while A+B defines the slope at the solar position." + The combination A-B can be more precisely determined than the individual constants., The combination A-B can be more precisely determined than the individual constants. + ? found A-B=Vo/ro 27+ 2.5 km s! kpc!.., \citet{Kerr:1986hz} found $\mathrm{A-B} = \mathrm{v}_\odot/\mathrm{r}_\odot =$ $\pm$ 2.5 km $^{-1}$ $^{-1}$. +" Using the proper motion of the black hole in the Galactic centre (Sgr A*) ? found in excellent agreement with recent measurements of parallaxes using the Very Large Baseline Interferometry (VLBI) (?), which yield A-B Ξνο/ο= 30.3 + 0.9 km s kpc!."," Using the proper motion of the black hole in the Galactic centre (Sgr A*) \citet{Reid:2004rd} found in excellent agreement with recent measurements of parallaxes using the Very Large Baseline Interferometry (VLBI) \citep{Reid:2009nj}, which yield A-B $= $ $_\odot$ $_\odot =$ 30.3 $\pm$ 0.9 km $^{-1}$ $^{-1}$." + A further interesting property of the RC is its slope at the position of the Sun., A further interesting property of the RC is its slope at the position of the Sun. + This value is strongly connected to the, This value is strongly connected to the +the next two higher overtones respectively.,the next two higher overtones respectively. + The present data clo not show such clearly separated sequences except perhaps between the Miras and the others., The present data do not show such clearly separated sequences except perhaps between the Miras and the others. + Phe ellect may be blurred in the Galactic Centre relative to the Large. Magellanic Cloud by the depth in the line of sight of the Bulge., The effect may be blurred in the Galactic Centre relative to the Large Magellanic Cloud by the depth in the line of sight of the Bulge. + For example. the scatter of theaveraged 4v mags of Miras about the P-L relation is 0.35 mag for the latter as compared to 0.13 for the LMC (Class et al.," For example, the scatter of the $K$ mags of Miras about the P-L relation is 0.35 mag for the latter as compared to 0.13 for the LMC (Glass et al." + 1987)., 1987). + Included. in the diagram is a P-L sequence for the Llipparcos (nearby) SRVs from Bedding and Zijlstra (1998)., Included in the diagram is a P-L sequence for the Hipparcos (nearby) SRVs from Bedding and Zijlstra (1998). + Similar lines. which cross the loci of the various pulsation modes. were predicted by Vassiliadis Wood. (1993) as evolutionary sequences. their absolute Luminosity depending on initial mass and metallicity.," Similar lines, which cross the loci of the various pulsation modes, were predicted by Vassiliadis Wood (1993) as evolutionary sequences, their absolute luminosity depending on initial mass and metallicity." + Phe position of the line suggests that there is little dillerence between the Bulge and local samples., The position of the line suggests that there is little difference between the Bulge and local samples. + The spectra of Mira variables in the Bulge can also be matched well by local Miras (LAV)., The spectra of Mira variables in the Bulge can also be matched well by local Miras (LW). + In the Baade’s Windows As. Jdy diagram> the most luminous stars are the Miras and SRVs.," In the Baade's Windows $K_S$, $J-K$ diagram the most luminous stars are the Miras and SRVs." + The SRWs with significant mass-Ioss are generally more luminous than those without., The SRVs with significant mass-loss are generally more luminous than those without. + The average 4.J. JH. LEN and JIx colours of the SRMVs increase with period but the elfect is much Less pronounced if the mass-Iosing stars are omitted.," The average $I-J$, $J-H$, $H-K$ and $J-K$ colours of the SRVs increase with period but the effect is much less pronounced if the mass-losing stars are omitted." + The scatter in the colours of SIltVs is greatest ind JJ., The scatter in the colours of SRVs is greatest in $I-J$. + Hn all the colours considered here. scatter increases with period.," In all the colours considered here, scatter increases with period." + The average JH colours of the shorter-period Bulge AMiras ( 200d) are much bluer than the average of the SRVs with similar periods., The average $J-H$ colours of the shorter-period Bulge Miras $\sim$ 200d) are much bluer than the average of the SRVs with similar periods. + A similar but. less conspicuous cliscontinuity occurs in the ffdv and Jdy colours., A similar but less conspicuous discontinuity occurs in the $H-K$ and $J-K$ colours. + This ellect is attributed to the onset of L2O absorption. which allects 44 and A more than J.," This effect is attributed to the onset of $_2$ O absorption, which affects $H$ and $K$ more than $J$." + In cach of JH. hol and JA. the average Mira colours show steeper rates of increase with period than the SRMs.," In each of $J-H$, $H-K$ and $J-K$, the average Mira colours show steeper rates of increase with period than the SRVs." + The colours of solar neighbourhood SRWs ancl AMliras. derived for the DENIS and 2ALASS systems from the LAL spectrophotometry. agree with those of the Bulge.," The colours of solar neighbourhood SRVs and Miras, derived for the DENIS and 2MASS systems from the LM spectrophotometry, agree with those of the Bulge." + In addition. the locations in the A. PdiagramoflheS RVs. whichshouldbesensitiveltoangdi ferencesininilic ," In addition, the locations in the $K$, $P$ diagram of the SRVs, which should be sensitive to any differences in initial mass and metallicity, are in good agreement." +We thank A. Lancoon for her help in calculating the svnthetic near-H15— colours of stars from the spectrophotometry of LW and AL Omont for his helpful comments., We thank A. Lançoon for her help in calculating the synthetic near-IR colours of stars from the spectrophotometry of LW and A. Omont for his helpful comments. + We also thank EF. Ixerschbaum Lor access to unpublished. photometry., We also thank F. Kerschbaum for access to unpublished photometry. + MS thanks SAAQO and ISG thanks the LAP for heir hospitality during visits financed. through the CNRS (France)/NRE (South Africa) agreement., MS thanks SAAO and ISG thanks the IAP for their hospitality during visits financed through the CNRS (France)/NRF (South Africa) agreement. + AIS is supported. by the Fonds zur. οσα der wissenschaltlichen Forschung (ENE). Austria. under the xoject number JLOTI-PILY.," MS is supported by the Fonds zur Förrderung der wissenschaftlichen Forschung (FWF), Austria, under the project number J1971-PHY." + The DENIS project is supported. in France bw he Institut National des Sciences de [PUnivers. the Ecuecation Ministrv and the Centre National de [a techerche Scientifique. in Germany by the State of Daden-Würtemberg. in Spain bv the DGICYT. in Haly by he Consiglio Nazionale delle Ricerche. in Austria by the Fonds zur Forrderung der wissenschaltlichen Forschung und Dundesministerium ftir Wissenschaft und Forschung This publication makes use of cata products from the Two Micron All Sky Survey. which is a joint prodect of the University of Massachusetts and the Enfrared Processing ancl Analysis Center/California Institute of Technology. [πάσα by the National Acronautics and Space Aciministration and the National Science Foundation.," The DENIS project is supported, in France by the Institut National des Sciences de l'Univers, the Education Ministry and the Centre National de la Recherche Scientifique, in Germany by the State of Baden-W\""urrtemberg, in Spain by the DGICYT, in Italy by the Consiglio Nazionale delle Ricerche, in Austria by the Fonds zur Förrderung der wissenschaftlichen Forschung und Bundesministerium fürr Wissenschaft und Forschung This publication makes use of data products from the Two Micron All Sky Survey, which is a joint prodect of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation." +where we considered a single population defined by the same density threshold 87..,where we considered a single population defined by the same density threshold $\deltaLs$. +" Neglecting the width of thedistribution Pr(V5454). whence of PzGr). aud in the liuut of large separation. s>X. where 02μιCOwe can iuvert Eq.(18)) as SOLT ο... ση] where oi, is also evaluated at distance 2."," Neglecting the width of thedistribution $\cP_L(\Psi_{L12\parallel})$, whence of $\cP_L(x)$, and in the limit of large separation, $s\rightarrow \infty$, where $\sigma^2_{q_1,q_2,s}\rightarrow 0$, we can invert \ref{x-s}) ) as s(M_1,M_2;x) x ], where $\sigma^2_{12}$ is also evaluated at distance $x$." + It is interesting to note that the expression (19)) is very close to the oue obtained in? from a spherical collapse model., It is interesting to note that the expression \ref{s-x}) ) is very close to the one obtained in \citet{Valageas2009d} from a spherical collapse model. +" The main difference is that this uew result involves he quantity: 672, defiwed in Eq.(17)). which: contaius ↕∐∖↑↕∐⋅↸∖↸∖↖↖⇁↕∐≺∐≻↖↖↰∖↴⊓⊽≺∕≍⋮↙∣ )AV (he). aad Wi(es). whereas he foruer result oulv involved quantities sucli 5 qU2 ⋜↧↴∖↴∪∣−∣⊳∙∖⋅⋜⊔≼↧∪≺⇀∖∶⋟↑∐⋜↧↑∪∐↕⋅↖⇁↸⊳∪∐⋜⊔∐↑↖↖↽∪↖↖⇁∐∐↧∪↖↖↽↴∖↴∙↽∕∏∐∖ ⋅"," The main difference is that this new result involves the quantity $\sigma^2_{q_1,q_2,s}$ defined in \ref{sigq1q2s}) ), which contains the three windows $\tW(kq_1), \tW(kq_2)$ , and $\tW(ks)$, whereas the former result only involved quantities such as $\sigma^2_{q,s}$ and $\sigma^2_{q,0}(s)$ that only contain two windows." + ⋅ ↴ ↥⋅↸∖⋜↧↴∖↴∪∐↕↴∖↴ that the model used in ? treated cach halo as a est particle within the spherical gravitational field. built x the other halo. whereas in the derivation of Eq.(19)) above we did not need to make this approximation aud we smauultaueotsly fake iuto account the effect of both alos on the nmiial eravitational field.," The reason is that the model used in \citet{Valageas2009d} treated each halo as a test particle within the spherical gravitational field built by the other halo, whereas in the derivation of \ref{s-x}) ) above we did not need to make this approximation and we simultaneously take into account the effect of both halos on the initial gravitational field." + Nevertheless. itis reassuring that both models eive simular results. as could vc expected from qualitative aremucents (for rare and wellseparated halos).," Nevertheless, itis reassuring that both models give similar results, as could be expected from qualitative arguments (for rare and well-separated halos)." +" Equation (19)) gives the ""tvpical Lagraugian-space distance s between two halos that are observed iu the ionlinear deusitv feld at the Eulerian distance c.", Equation \ref{s-x})) gives the “typical” Lagrangian-space distance $s$ between two halos that are observed in the nonlinear density field at the Eulerian distance $x$. + This akes care of the first effect 1) associated with halo notions., This takes care of the first effect i) associated with halo motions. + As noticed above. the secoud effect ii) of laQ displacements is to change volumes so that dxzds.," As noticed above, the second effect ii) of halo displacements is to change volumes so that $\dd\vx\neq\dd\vs$." + Then. * conservation of the ummber of pairs. the Lagraueianu- and Euleriau-space correlations at distances s and x are related by Eqs.(11)} aud (19)) to estimate he factor |ds/dx|.," Then, by conservation of the number of pairs, the Lagrangian-space and Eulerian-space correlations at distances $\vs$ and $\vx$ are related by ) and \ref{s-x}) ) to estimate the factor $|\dd\vs/\dd\vx|$ ." +" However. for rare massive halos. of Lagrangian radius q. this is a subdominant ctffect. since from Eq.(19)) we have |As/Arl~δεσονση. whereas the argument of the exponcutial (5)) behaves as OF""mOT/71q"," However, for rare massive halos, of Lagrangian radius $q$, this is a subdominant effect, since from \ref{s-x}) ) we have $|\Delta s / \Delta x| \sim \deltaLs \sigma^2_{q,q,s}/\sigma_q^2$, whereas the argument of the exponential \ref{xiL-s}) ) behaves as $\deltaLs^2 \sigma^2_{12}/\sigma_q^4$." + T:mis. the latter is. larger than the former bv a facOr OL2σι. which is much ereater than unity (and this is Πατier amplified for very rare halos by the exponential).," Thus, the latter is larger than the former by a factor $\deltaLs/\sigma_q^2$, which is much greater than unity (and this is further amplified for very rare halos by the exponential)." + Therefore. to avoid introducing unuecessary approxinatious and to make the model as simple as possible. we neelectoO this volume effect aud we ouly keep the exponential behavior of the two-poimt correlation of rare halos.," Therefore, to avoid introducing unnecessary approximations and to make the model as simple as possible, we neglect this volume effect and we only keep the exponential behavior of the two-point correlation of rare halos." +" This gives for equalinass halos. with AL)MoA and qq=qoq. (AL) whereas the Lagrangian distance reads frou, Eq.(19)) as SOM.X) Sh)."," This gives for equal-mass halos, with $M_1=M_2=M$ and $q_1=q_2=q$, (M,x), whereas the Lagrangian distance reads from \ref {s-x}) ) as s(M,x) = x ( )." + Then. since at large distance the dark matter two-point correlation function is within the linear regime and reads as £Ce)2egD4G0). we obtain. for+ the bias+ of. halos of. iss A.," Then, since at large distance the dark matter two-point correlation function is within the linear regime and reads as $\xi(x) \simeq \sigma^2_{0,0}(x)$, we obtain for the bias of halos of mass $M$, (M,x) = = -1 ]." + Tere the subscript “re., Here the subscript “r.e.” +" stands for the ""Yrareeveut? lit to recall that the results obtained so far have been derived for very massive and rare halos. and do not apply to small objects."," stands for the “rare-event” limit to recall that the results obtained so far have been derived for very massive and rare halos, and do not apply to small objects." + It is very difficult to derive ana )proxinate noccl for the as. aid even the mass functio1. of snall halos.," It is very difficult to derive an approximate model for the bias, and even the mass function, of small halos." + Iudecd. such objects associated with typical deusitv fiuctuations wave been stronely distorted by tidal effects and lave ofteu undergone various mereiig evens.," Indeed, such objects associated with typical density fluctuations have been strongly distorted by tidal effects and have often undergone various merging events." + Then. it is not possible o identify iu a simple manner the precursors of these halos oei the initial linear deislitv field.," Then, it is not possible to identify in a simple manner the precursors of these halos in the initial linear density field." +" Iu this article we propose io folowing simple prescriptioi fo bypass this problem: we ad to the asviuptotic restIt (21)) a consant terni with respect to the haο Dass, fyGe). which we obtain from 16 normalization of the bias,"," In this article we propose the following simple prescription to bypass this problem: we add to the asymptotic result \ref{b2-def}) ) a constant term with respect to the halo mass, $b_0(x)$, which we obtain from the normalization of the bias." + \ore precisely. iialiug the approximation that the das factorizes (which however is rot exact. even in the larec-miass reeime. see Eq.(21)) aud Fie.," More precisely, making the approximation that the bias factorizes (which however is not exact, even in the large-mass regime, see \ref{b2-def}) ) and Fig." + 12 in ?)). as 111.M WAL).4] δήMo.SU n we model the bias bCMe) as b(NEX) — Ow) Ite).," 12 in \citet{Valageas2009d}) ), as b^2(M_1,M_2;x) b(M_1,x) b(M_2,x) , we model the bias $b(M,x)$ as b(M,x) = (M,x) +b_0(x) ." +" Here by.(Ar) ds eiven by Eq(21))(taking the square-root of this positive quantitv). while dye) is set by the normalization (at fixed distance ο) 1, whence 1o OM.) fon) &."," Here $b_{\rm r.e.}(M,x)$ is given by \ref{b2-def}) )(taking the square-root of this positive quantity), while $b_0(x)$ is set by the normalization (at fixed distance $x$ ) b(M,x) ) = 1 , whence b_0(x) = 1 - (M,x) ) ," +because the shock emerges at points with ϐρ>0 after it does at the point with 09=0.,because the shock emerges at points with $\theta_0>0$ after it does at the point with $\theta_0=0$. +" Therefore, the duration of the emission is roughly estimated as 7/2)."," Therefore, the duration of the emission is roughly estimated as $R/c+T(\alpha,\pi/2)$." +" Furthermore, since the total energy of theR/c+T(a, burst is same for all models, the average luminosity is small for models with large a."," Furthermore, since the total energy of the burst is same for all models, the average luminosity is small for models with large $\alpha$." + Figure 5 shows light curves for a fixed viewing angle O(=90°) and various a., Figure \ref{f5} shows light curves for a fixed viewing angle $\Theta(=90\degr)$ and various $\alpha$. +" In this case, the duration of the emission takes a similar value for all models."," In this case, the duration of the emission takes a similar value for all models." +" For models with a large a, the feature claimed above, i.e., the sudden rise and the subsequent gradual decrease of the luminosity, is prominent."," For models with a large $\alpha$, the feature claimed above, i.e., the sudden rise and the subsequent gradual decrease of the luminosity, is prominent." +" In this letter, we investigate effects of an aspherical explosion on the light curves during the supernova shock breakout."," In this letter, we investigate effects of an aspherical explosion on the light curves during the supernova shock breakout." +" To obtain the emergence time distribution we performed a series of two-dimensional T(o,0),hydrodynamical calculations of aspherical supernova explosions."," To obtain the emergence time distribution $T(\alpha,\theta)$, we performed a series of two-dimensional hydrodynamical calculations of aspherical supernova explosions." + We establish an approximate way to calculate light curves during the shock breakout using results of the simulations and confirm that resultant light curves successfully reproduce some features of the emission from the supernova shock breakout., We establish an approximate way to calculate light curves during the shock breakout using results of the simulations and confirm that resultant light curves successfully reproduce some features of the emission from the supernova shock breakout. + We find that the light curves strongly depend on the viewing angle and the degree of asphericity of an explosion., We find that the light curves strongly depend on the viewing angle and the degree of asphericity of an explosion. +" For small viewing angles from the symmetry axis, the luminosity gradually increases and then reaches the peak value."," For small viewing angles from the symmetry axis, the luminosity gradually increases and then reaches the peak value." +" On the contrary, for large viewing angles, the luminosity suddenly reaches the peak value and then gradually decreases."," On the contrary, for large viewing angles, the luminosity suddenly reaches the peak value and then gradually decreases." +" For a larger degree of asphericity, the light curve can be distinguished from that of a spherical symmetric explosion irrespective of the viewing angle."," For a larger degree of asphericity, the light curve can be distinguished from that of a spherical symmetric explosion irrespective of the viewing angle." + These features allow us to use light curves during the supernova shock breakout as a probe for the explosion geometry of CCSNe., These features allow us to use light curves during the supernova shock breakout as a probe for the explosion geometry of CCSNe. +" It is noteworthy that the light curve of the shock breakout of SN 2008D (Soderbergetal.2008) is similar to that of models with large viewing angles, e.g., the model with a=0.5 and O=90, except for the duration."," It is noteworthy that the light curve of the shock breakout of SN 2008D \citep{s08} is similar to that of models with large viewing angles, e.g., the model with $\alpha=0.5$ and $\Theta=90$, except for the duration." +" The nebular phase observations of SN 2008D (Tanakaetal.2009) revealed that SN 2008D was a side-viewed bipolar explosion, which also prefers large viewing angle models."," The nebular phase observations of SN 2008D \citep{t09} revealed that SN 2008D was a side-viewed bipolar explosion, which also prefers large viewing angle models." +" In this study, we only calculate the supernova shock breakout from the progenitor of SN 1987A, i.e., a blue supergiant, in order to confirm the validity of our approximate way to calculate light curves by comparing results of other studies that adopt more sophisticated ways."," In this study, we only calculate the supernova shock breakout from the progenitor of SN 1987A, i.e., a blue supergiant, in order to confirm the validity of our approximate way to calculate light curves by comparing results of other studies that adopt more sophisticated ways." +" However, since the duration of the shock breakout from red supergiant progenitors, whose radii are typically of the order of 1015 cm, is expected to be longer than those from blue supergiant progenitors (Matzner&Mc-Kee1999),, the shock breakout from a red supergiant progenitor is likely to be observed by future observations."," However, since the duration of the shock breakout from red supergiant progenitors, whose radii are typically of the order of $10^{13}$ cm, is expected to be longer than those from blue supergiant progenitors \citep{mm99}, the shock breakout from a red supergiant progenitor is likely to be observed by future observations." +" In the forthcoming paper (Suzuki&Shigeyama2010b),, we will present results of the calculations for other progenitor models as well as the description of details of the hydrodynamical simulations."," In the forthcoming paper \citep{ss10b}, we will present results of the calculations for other progenitor models as well as the description of details of the hydrodynamical simulations." +" This work has been partly supported by Grant-in-Aid for JSPS Fellows (21-1726) and Scientific Research on Priority Areas (21018004) of the Ministry of Education, Culture, Sports, Science, and Technology in Japan."," This work has been partly supported by Grant-in-Aid for JSPS Fellows $\cdot$ 1726) and Scientific Research on Priority Areas (21018004) of the Ministry of Education, Culture, Sports, Science, and Technology in Japan." +Cousidering their widespread use in college aciuissious. the predictive power (validity) of tests such as the SAT aud. ACT is a surprisingly controversial topic.,"Considering their widespread use in college admissions, the predictive power (validity) of tests such as the SAT and ACT is a surprisingly controversial topic." + On the negative side. one often reads Claims that the correlation of SAT with freslunan GPA is as low as 0.25 to 0.35 (Sackett 2008).," On the negative side, one often reads claims that the correlation of SAT with freshman GPA is as low as 0.25 to 0.35 (Sackett 2008)." + On the positive side. oue cannot help but be impressed by a measure of cognitive ability that requires only a few hours of testing. is [falrly stable (see results below) aud has roughly as," On the positive side, one cannot help but be impressed by a measure of cognitive ability that requires only a few hours of testing, is fairly stable (see results below) and has roughly as" +The standard theory of the origin of the large-scale structure of the universe involves the assumption that the structure we see today grew by gravitational instability [rom initial small Iluetuations in the density field.,The standard theory of the origin of the large-scale structure of the universe involves the assumption that the structure we see today grew by gravitational instability from initial small fluctuations in the density field. + In most popular variants of this model. particularly those involving cosmic inllation. the initial Ductuations are of a particularly simple. form known as a Gaussian random field.," In most popular variants of this model, particularly those involving cosmic inflation, the initial fluctuations are of a particularly simple form known as a Gaussian random field." + Gaussian random fields are useful because many properties of Caussian random clensity fields can be caleulatecl analytically (e.g. Bardeen et al., Gaussian random fields are useful because many properties of Gaussian random density fields can be calculated analytically (e.g. Bardeen et al. + 1986)., 1986). +" Some direct motivation for such an assumption emerges from inflationary models. wherein the Iuctuations are generated by quantum oscillations of the scalar. field driving inflation (the inllation"")."," Some direct motivation for such an assumption emerges from inflationary models, wherein the fluctuations are generated by quantum oscillations of the scalar field driving inflation (the “inflation”)." + Even if inllation. turns out to be incorrect. however. the Central Limit Theorem tends to produce Ciaussian Uuetuations in any Linear process. so that they are the most generic form for small initial conditions and a natural default assumption.," Even if inflation turns out to be incorrect, however, the Central Limit Theorem tends to produce Gaussian fluctuations in any linear process, so that they are the most generic form for small initial conditions and a natural default assumption." +" One particularly interesting property of Gaussian random fields is that the requirement for the density contrast (κ)=qux)pu]/po to be a Gaussian. random feld. is equivalent to that the real and imaginary. parts of its Fourier components 9,. where are independently distributed."," One particularly interesting property of Gaussian random fields is that the requirement for the density contrast $\delta({\bf x})=[\rho({\bf x})-\rho_{0}]/\rho_{0}$ to be a Gaussian random field is equivalent to that the real and imaginary parts of its Fourier components $\tilde{\delta}_k$, where are independently distributed." + In. other words. the Fouricr modes ο). possess phases óx which are independently distributed and uniformly random on the interval 0.25].," In other words, the Fourier modes $\tilde{\delta}({\bf k})$ , possess phases $\phi_{\bf k}$ which are independently distributed and uniformly random on the interval $[0,2\pi]$." + As the density Ποια is simply a sum over a large number of Fourier moces and if the phases of cach of Fourier. modes. are. random. the Central Limit Fheorem guarantees that the resulting superposition of the one-point probability distribution (5) is close to Gaussian. and that all of the fields. joint probability. distributions are multivariate Ciaussians.," As the density field is simply a sum over a large number of Fourier modes and if the phases of each of Fourier modes are random, the Central Limit Theorem guarantees that the resulting superposition of the one-point probability distribution ${\cal P}(\delta)$ is close to Gaussian and that all of the field's joint probability distributions are multivariate Gaussians." + The statistical properties of an isotropic Gaussian random field are then completely specified by its second-order statistical quantity: the covariance function. or alternatively. its power spectrum (E)=07(fe).," The statistical properties of an isotropic Gaussian random field are then completely specified by its second-order statistical quantity: the covariance function, or alternatively, its power spectrum $P(k)=\langle\tilde{\delta}^2(k)\rangle$." + In the framework of gravitational instability. the growth of Dluctuations can be understood. analytically when the density [üctuation amplitucle is small compared to the mean density: the linear. perturbation theory. tells us that. each Fouricr mode grows with the same rate independent of wavenumber and the statistical distribution of à. remains constant except its variance.," In the framework of gravitational instability, the growth of fluctuations can be understood analytically when the density fluctuation amplitude is small compared to the mean density; the linear perturbation theory tells us that each Fourier mode grows with the same rate independent of wavenumber and the statistical distribution of $\delta$ remains constant except its variance." + The linear theory breaks down when 197? is comparable with unity or bevond. and. diferent Fourier modes: start coupling.," The linear theory breaks down when $\langle\delta^2\rangle$ is comparable with unity or beyond, and different Fourier modes start coupling." + One wav to look at the mode coupling is that 9 is always constrained to value 0=1., One way to look at the mode coupling is that $\delta$ is always constrained to value $\delta \geq -1$. + When the perturbation is small. the tail of 7P(8) in the part of91.2, and with Hio—[3.6]=2 is less problematic at fainter magnitudes."," However, at face value, it would appear that contamination from such sources with $J_{125}-H_{160}>1.2$, and with $H_{160}-[3.6]\gtrsim2$ is less problematic at fainter magnitudes." +" We note, however, that contamination from similar galaxies with less extreme colors may be more abundant also at Higo>26 mag) may (whichstill be non-negligible due to photometric scatter (see also §3.5))."," We note, however, that contamination from similar galaxies with less extreme colors (which may be more abundant also at $H_{160}>26$ mag) may still be non-negligible due to photometric scatter (see also \ref{sec:additionalcontamin}) )." +" Furthermore, it is interesting to note that it is very difficult to construct clean z~10 galaxy samples purely based on HST data alone."," Furthermore, it is interesting to note that it is very difficult to construct clean $z\sim10$ galaxy samples purely based on HST data alone." +" Even if we were to increase the color criteria to J155—Heo>2.0, there would still be two contaminating galaxies in the sample together with our only viable z~10 candidate."," Even if we were to increase the color criteria to $J_{125}-H_{160}>2.0$, there would still be two contaminating galaxies in the sample together with our only viable $z\sim10$ candidate." +" Thus, also for future constraints on the bright end of the z~10 LF, it will be important to perform additional follow-up studies to validate the candidates, e.g. with Spitzer."," Thus, also for future constraints on the bright end of the $z\sim10$ LF, it will be important to perform additional follow-up studies to validate the candidates, e.g. with Spitzer." +" This will be less of a concern for future z~9 galaxy samples, which can be obtained, e.g., based on new F140W filter data."," This will be less of a concern for future $z\sim9$ galaxy samples, which can be obtained, e.g., based on new F140W filter data." + In such a data set intrinsically red galaxies can be sorted out by requiring a blue continuum across F140W and F160., In such a data set intrinsically red galaxies can be sorted out by requiring a blue continuum across F140W and $H_{160}$. +" Here, we only give a brief summary of the possible sample contamination."," Here, we only give a brief summary of the possible sample contamination." + For a thorough discussion we refer the reader to Bouwensetal.(2011a)., For a thorough discussion we refer the reader to \citet{Bouwens11}. +". Essentially, the only probable chance for contamination is due to photometric scatter of a red lower redshift source."," Essentially, the only probable chance for contamination is due to photometric scatter of a red lower redshift source." +" We estimate this to be a chance based on our photometric scatter experiments described in section 3.2,, including the x2,, cuts."," We estimate this to be a chance based on our photometric scatter experiments described in section \ref{sec:candsel}, including the $\chi^2_{opt}$ cuts." +" Other typical contaminants to LBG selections such as very cool dwarf stars and supernovae can essentially be excluded based on the relatively blue Ji25—Hieo 1.1) colors of stellar SEDs, on the fact that the source(< is detected in both the first and the second year of the HUDF09 WFC3/IR data, and due to the fact that the candidate shows clear signs of an extended morphology."," Other typical contaminants to LBG selections such as very cool dwarf stars and supernovae can essentially be excluded based on the relatively blue $J_{125}-H_{160}$ $<1.1$ ) colors of stellar SEDs, on the fact that the source is detected in both the first and the second year of the HUDF09 WFC3/IR data, and due to the fact that the candidate shows clear signs of an extended morphology." +" Additionally, it is very unlikely that this source is spurious, since the flux distribution in circular apertures randomly distributed over empty regions of the HUDF Hi6o image are nearly exactly Gaussian, and the source is well detected at 6.30."," Additionally, it is very unlikely that this source is spurious, since the flux distribution in circular apertures randomly distributed over empty regions of the HUDF $H_{160}$ image are nearly exactly Gaussian, and the source is well detected at $6.3\sigma$." +" In this section we compute the expected abundance of z~10 galaxies in our dataset, and derive constraints on the z10 LF based on our data."," In this section we compute the expected abundance of $z\sim10$ galaxies in our dataset, and derive constraints on the $z\sim10$ LF based on our data." +" In order to estimate the number of sources we expect in our data from a given LF, we have to estimate the completeness as a function of magnitude C(m) and selection function as a function of redshift and magnitude S(z,m)."," In order to estimate the number of sources we expect in our data from a given LF, we have to estimate the completeness as a function of magnitude $C(m)$ and selection function as a function of redshift and magnitude $S(z,m)$." +" Following Oeschetal.2009),, this is done by inserting artificial galaxies in(2007, the observational data and rerunning the source detection with the exact same setup as for the original catalogs."," Following \citet{Oesch07,Oesch09}, this is done by inserting artificial galaxies in the observational data and rerunning the source detection with the exact same setup as for the original catalogs." + This is done for each of our fields individually., This is done for each of our fields individually. + Two sets of simulations were run., Two sets of simulations were run. +" In the first set, we follow Bouwensetal.(2003),, where the artificial galaxies are ‘cloned’ from the z~4 dropout sample of the GOODS and HUDF fields."," In the first set, we follow \citet{Bouwens03}, where the artificial galaxies are `cloned' from the $z\sim4$ dropout sample of the GOODS and HUDF fields." +" The images of these sources are adjusted for surface brightness dimming, the difference in angular diameter distance, as well as a size scaling of (1+ as observed for the Lyman Break galaxy population z)-!across z~3—7 (seee.g.Fergusonetal.2004;Bouwensetal.Oesch 2010a)."," The images of these sources are adjusted for surface brightness dimming, the difference in angular diameter distance, as well as a size scaling of $(1+z)^{-1}$ as observed for the Lyman Break galaxy population across $z\sim3-7$ \citep[see e.g.][]{Ferguson04,Bouwens04a,Oesch10b}." +. These are then inserted in the observed images with galaxy colors as expected for star-forming galaxies between z=8 and z=12., These are then inserted in the observed images with galaxy colors as expected for star-forming galaxies between $z=8$ and $z=12$. +" When computing the galaxy colors we assume a distribution of UV continuum slopes with 8=—2.5+0.4 (seee.g.Bouwensetal.2009,2010b;Finkelstein2010;Stanwayetal. 2005)."," When computing the galaxy colors we assume a distribution of UV continuum slopes with $\beta=-2.5\pm0.4$ \citep[see e.g.][]{Bouwens09b,Bouwens10b,Finkelstein10,Stanway05}." +". From these simulations, we compute the completeness as a function of observed Hi¢go,4g magnitude for each field, taking into account the scatter and offsets between input and output magnitudes."," From these simulations, we compute the completeness as a function of observed $H_{160,AB}$ magnitude for each field, taking into account the scatter and offsets between input and output magnitudes." +" Additionally, we compute the selection probabilities as a function of redshift and magnitude by measuring the fraction of sources that meet our selection criteria."," Additionally, we compute the selection probabilities as a function of redshift and magnitude by measuring the fraction of sources that meet our selection criteria." +" By construction, galaxies are selected at >50% at redshifts z>9.5."," By construction, galaxies are selected at $>50\%$ at redshifts $z\gtrsim9.5$." +" In the second set of simulations, we repeat the above procedure."," In the second set of simulations, we repeat the above procedure." +" However, instead of using observed galaxy images, we use theoretical galaxy profiles from a mix of exponential (Sersic τι= 1) and de Vaucouleur (Sersic n= 4) profiles."," However, instead of using observed galaxy images, we use theoretical galaxy profiles from a mix of exponential (Sersic $n=1$ ) and de Vaucouleur (Sersic $n=4$ ) profiles." + The size distribution is chosen to be log- again with the same size scaling as a function of redshift.," The size distribution is chosen to be log-normal, again with the same size scaling as a function of redshift." + The completeness and selection functions of our two procedures are in excellent agreement., The completeness and selection functions of our two procedures are in excellent agreement. +" This demonstrates the reliability of our approach, which"," This demonstrates the reliability of our approach, which" +the applications prescuted im this paper is the collection of L«1000 sky signal spectrmm samples.,the applications presented in this paper is the collection of $4\times 1000$ sky signal spectrum samples. + These form the basis of the BlackwellRao estimator. and may be used for parameter estimation as clemoustrated in this paper.," These form the basis of the Blackwell-Rao estimator, and may be used for parameter estimation as demonstrated in this paper." + A corresponding Fortran 90 module is also provided., A corresponding Fortran 90 module is also provided. + Second. a set of 1000 ensemble averaged spectruni samples are presented.," Second, a set of 4000 ensemble averaged spectrum samples are presented." + These may be| used for visualization purposes of the power spectrum., These may be used for visualization purposes of the power spectrum. + Third. a set of sky map samples are provided for ες50.," Third, a set of sky map samples are provided for $\ell \le 50$." +" These may be used for analyses that require phase information. for instance studies of non-Caussianity,"," These may be used for analyses that require phase information, for instance studies of non-Gaussianity." + Thus. we conclude that although fast methods such as MASTER are very useful in the early stages of analyzing a new experiueut. when fast turn around times are essential the extensions to Cübbs sample (as described in the Appendices) have now reudered au exact method quite tractable with currently available conrputiug resources.," Thus, we conclude that although fast methods such as MASTER are very useful in the early stages of analyzing a new experiment, when fast turn around times are essential, the extensions to Gibbs sampling (as described in the Appendices) have now rendered an exact method quite tractable with currently available computing resources." + Based upon our experience with these methods. we believe that Cibbs sampling can aud will play a significant role in the future analysis of Plauck data.," Based upon our experience with these methods, we believe that Gibbs sampling can and will play a significant role in the future analysis of Planck data." + Low-( likelihood. evaluation from high-resolution data has received considerable attention in the last few vears (Efstathiou2001:Slosaretal.πιαct2006).," $\ell$ likelihood evaluation from high-resolution data has received considerable attention in the last few years \citep{efstathiou:2004, slosar:2004, hinshaw:2006}." +.. The reason is simply that while the currently popular pseudo-spectruui power spectrm estimators (Ilivouetal.2002) work very well on intermediate aud small angular scales. they are clearly sub-optinial ou large scales.," The reason is simply that while the currently popular pseudo-spectrum power spectrum estimators \citep{hivon:2002} work very well on intermediate and small angular scales, they are clearly sub-optimal on large scales." + The log-likelihood for a pixelized Gaussian random field d. with vanishing mean aud covariance matrix C. is given by up toa normalization constant.," The log-likelihood for a pixelized Gaussian random field $\mathbf{d}$, with vanishing mean and covariance matrix $\mathbf{C}$, is given by up to a normalization constant." + Evaluation of this expression requires inversion of the pixel-pixel covariance matrix. and therefore scales as OUNS.L).," Evaluation of this expression requires inversion of the pixel-pixel covariance matrix, and therefore scales as $\mathcal{O}(N_{\textrm{pix}}^3)$." + Consequently. direct likehhood analvsis of 1iega-pixel maps is not. currently feasible.," Consequently, direct likelihood analysis of mega-pixel maps is not currently feasible." +" The covariance matrix consists of a series of terms depeuding ou the data model. but at the very least oue needs a signal terii S. which for au assed isotropic CMD is eiven by the augular power spectrum C. Tere 5, is the Legeudre trausforiu of the (circularly svuunetrüc) experinieutal beam. £606) are the Leecudre polvuoimials 0;j is the angle between pixels / aud j. aud fijas is a sufficicutly large multipole."," The covariance matrix consists of a series of terms depending on the data model, but at the very least one needs a signal term $\mathbf{S}$, which for an assumed isotropic CMB is given by the angular power spectrum $C_{\ell}$, Here $b_{\ell}$ is the Legendre transform of the (circularly symmetric) experimental beam, $P_{\ell}(x)$ are the Legendre polynomials, $\theta_{ij}$ is the angle between pixels $i$ and $j$, and $\ell_{\textrm{max}}$ is a sufficiently large multipole." + The exact definition of ~suffiicicutly huge will be made explicit shortly., The exact definition of “sufficiently large” will be made explicit shortly. + Next. in most real-world applications there is also a term describing instrumental noise. N.," Next, in most real-world applications there is also a term describing instrumental noise, $\mathbf{N}$." + Often. this is modeled as independent between pixels (white). aud given by an overall noise level per observation ay aud a total umuber of observations por pixel Noi). such that Vy;=σιVYNon);j.," Often, this is modeled as independent between pixels (white), and given by an overall noise level per observation $\sigma_0$ and a total number of observations per pixel $N_{\textrm{obs}}(i)$, such that $N_{ij} = \sigma_0 / +\sqrt{N_{\textrm{obs}}(i)} \delta_{ij}$." + For current CAIB experiments. such asWALAP.. this is stronely sub-domunant to the signal term on large auegular scales. aud may in principle be omitted without significant loss of accuracy.," For current CMB experiments, such as, this is strongly sub-dominant to the signal term on large angular scales, and may in principle be omitted without significant loss of accuracy." + However. this is not eutirelv true. since it can (and should) play an inportaut role in reeularizing the COVALTALCO nintrix.," However, this is not entirely true, since it can (and should) play an important role in regularizing the covariance matrix." + Finally. it is useful to include a iunuber of template terms over which amplitudes oue wishes to mareialize 0.," Finally, it is useful to include a number of template terms over which amplitudes one wishes to marginalize \citep{bond:1998, +slosar:2004}." + Consider for instance a eiven foreground template £ whose spatial structure is known. but overall amplitude is unknown.," Consider for instance a given foreground template $\mathbf{f}$ whose spatial structure is known, but overall amplitude is unknown." +" Then the correspoudiug covariance matrix is eiveu by the outer product F=££"". and by assigning a sufficicutly: large uncertainty to this structure the corresponding mode is projected out from the data."," Then the corresponding covariance matrix is given by the outer product $\mathbf{F} = \mathbf{f}\,\mathbf{f}^{t}$, and by assigning a sufficiently large uncertainty to this structure the corresponding mode is projected out from the data." + In total. the covariance matrix nay be written as where A; are nuniericallv sufficiently large coustauts.," In total, the covariance matrix may be written as where $\lambda_i$ are numerically sufficiently large constants." + Conceptually speaking. the above description completely defines the likelibood problem.," Conceptually speaking, the above description completely defines the likelihood problem." + However. for the particular problem of low-resolution analysis with high signal-to-noise data there is oue particular issue that iust be considered in greater detail in order to produce robust results. aud that is the relatiouship between a finite pixclization. bauchwidth Iunitation. and covariance matrix regularization.," However, for the particular problem of low-resolution analysis with high signal-to-noise data there is one particular issue that must be considered in greater detail in order to produce robust results, and that is the relationship between a finite pixelization, bandwidth limitation, and covariance matrix regularization." + For the expausion in equation À2 to be valid. (ya. must be chosen sufficiently larec such that there is neelieible power bevond this multipole.," For the expansion in equation \ref{eq:signal_mat} to be valid, $\ell_{\textrm{max}}$ must be chosen sufficiently large such that there is negligible power beyond this multipole." + At the same time it must be smaller than the corresponding Nyquist fequeney of the chosen, At the same time it must be smaller than the corresponding Nyquist frequency of the chosen +the cell in comoving coordinates.,the cell in comoving coordinates. +" The cell center is also easily obtained from αρ, 21 and x9."," The cell center is also easily obtained from $x_0$ , $x_1$ and $x_2$." +" Hence, we can define a spherical polygon that represents the footprint of the cell on the sky in a manner similar to what we have used for onthe case off 2D cellscells."," Hence, we can define a spherical polygon that represents the footprint of the cell on the sky in a manner similar to what we have used for the case of 2D cells." +" o get the positions of galaxies⋅⋅ in redshift⋅ space, we apply the transformation in equation(18)."," To get the positions of galaxies in redshift space, we apply the transformation in equation." +. Then a galaxy is a member of a cell if the distance between the galaxy and cell center is⋅ less than r., Then a galaxy is a member of a cell if the distance between the galaxy and cell center is less than $r$. +" Since the two-point correlation function is a well-studied description of clustering, we first compute the two-point correlation functions £o(r) from the counts-in-cells distribution using equation and compare our results with earlier works."," Since the two-point correlation function is a well-studied description of clustering, we first compute the two-point correlation functions $\xi_2(r)$ from the counts-in-cells distribution using equation and compare our results with earlier works." + This allows us to check the validity of our data and method by comparing our results to results from previous studies., This allows us to check the validity of our data and method by comparing our results to results from previous studies. + For this stud» we focus on the Ppower law approximation of the two-point correlation function since we are dealing with small scales.," For this study, we focus on the power law approximation of the two-point correlation function since we are dealing with small scales." + The power law approximation of the two-point correlation function at small scales is (e.g. [Totsuji&Kiharal1969)) for 3D cells and for 2D cells., The power law approximation of the two-point correlation function at small scales is (e.g. \citealt{1969PASJ...21..221T}) ) for 3D cells and for 2D cells. + We obtain the parameters rg and às fitting a linear relation and , We obtain the parameters $r_0$ and $\gamma$ by fitting a linear relation between $\log(\xi_2(r))$ and $\log(r)$. +"Since previous studies M ShownaHawkinsae:etαἱ.two-pointlog(r2003[Connollyetal] UA that the correlation function 2002))deviates from a power law at large scales, we use datapoints from scales smaller than 10.0h-! Mpc for 3D cells or scales smaller than 1.25? for 2D cells to determine a power law fit."," Since previous studies (e.g. \citealt{2003MNRAS.346...78H,2002ApJ...579...42C}) ) have shown that the two-point correlation function deviates from a power law at large scales, we use datapoints from scales smaller than $10.0 h^{-1}$ Mpc for 3D cells or scales smaller than $1.25^{\circ}$ for 2D cells to determine a power law fit." +" Because £(r) depends on the gradient of V&,(r), we use a 5-point moving average of V&,(r) to obtain the overall shape of for our analysis."," Because $\xi_2(r)$ depends on the gradient of $V\overline{\xi}_2(r)$, we use a 5-point moving average of $V\overline{\xi}_2(r)$ to obtain the overall shape of $V\overline{\xi}_2(r)$ for our analysis." +" We summarize our results in tables Vé,(r)and Bl.", We summarize our results in tables \ref{tres-2dcorr} and \ref{tres-3dcorr}. +" We find2] that the value of y for the 3D two-point correlation function is about 1.5~1.6 and &,3p(r) begins to deviate from a power law at scales of r=11~12h-! Mpc, in agreement with earlier work such as Hawkinsetal.|(2005)..."," We find that the value of $\gamma$ for the 3D two-point correlation function is about $1.5\sim1.6$ and $\xi_{2,3D}(r)$ begins to deviate from a power law at scales of $r = 11\sim12 h^{-1}$ Mpc, in agreement with earlier work such as \citet{2003MNRAS.346...78H}." + The value of for the 2D two- correlation: function Eis about 1.7~1.8 and is: close to the value obtained by [Connollyetal], The value of $\gamma$ for the 2D two-point correlation function is about $1.7\sim1.8$ and is close to the value obtained by \citet{2002ApJ...579...42C}. +" We note that έοορ(θ) shows a break from the power (2002)..law fit at 0=1.75?ο for the 1a and 2b samples, and 0~z2.4?on2.6ο for the 1b samples."," We note that $\xi_{2,2D}(\theta)$ shows a break from the power law fit at $\theta \approx 1.75^\circ$ for the 1a and 2b samples, and $\theta \approx 2.4^\circ \sim 2.6^\circ$ for the 1b samples." +" To compareP the 2D and 3D samples,p'es, we first note that the 2D samples measure the projected correlation function while the 3D samples measure the redshift space correlation function."," To compare the 2D and 3D samples, we first note that the 2D samples measure the projected correlation function while the 3D samples measure the redshift space correlation function." +" The 3D samples are affected by distortions in redshift space causedby peculiar velocities while the 2D samples, which ignore the detailed distance information, are not affected by redshift space distortions."," The 3D samples are affected by distortions in redshift space causedby peculiar velocities while the 2D samples, which ignore the detailed distance information, are not affected by redshift space distortions." + Therefore the comparison between 2D and 3D samples can help quantify the effect of these distortions., Therefore the comparison between 2D and 3D samples can help quantify the effect of these distortions. +Lunit line).,"Limit"" line)." + In this case the wind contribution to the column density becomes large near orbital phase 0.25. when the line-of-sight passes near the companions surface. and the X3 for the column clensity fit becomes large.," In this case the wind contribution to the column density becomes large near orbital phase 0.25, when the line-of-sight passes near the companion's surface, and the $\chi_N^2$ for the column density fit becomes large." + An example of this is the (4842..757) case in Table l., An example of this is the $R_{\odot}$ $^\circ$ ) case in Table 1. + Finally. we have calculated the mass-loss rate in the stream and added (his as column 10 in Table 1.," Finally, we have calculated the mass-loss rate in the stream and added this as column 10 in Table 1." + It is seen that the stream mass-loss rate is about a [actor of 2 (o 2.5 times higher than the mass-loss rate in the wind., It is seen that the stream mass-loss rate is about a factor of 2 to 2.5 times higher than the mass-loss rate in the wind. + This is a dramatic confirmation of the importance of {he stream in the total mass-loss rate from WRAY 977., This is a dramatic confirmation of the importance of the stream in the total mass-loss rate from WRAY 977. + It is also consistent with WRAY 977 being close to filling its Roche lobe., It is also consistent with WRAY 977 being close to filling its Roche lobe. +" Since this can only occur at lower inclinations without having WRAY 977 too close to eclipsing. this is another indicator that the svstem inclination is near (he low end of the allow range (near ~55°),"," Since this can only occur at lower inclinations without having WRAY 977 too close to eclipsing, this is another indicator that the system inclination is near the low end of the allow range (near $\sim55^\circ$ )." + Long term (10-vear) monitoring of GX301-2 with the RNTE/ASM has revealed some new properties of this hieh-mass X-rav binary., Long term (10-year) monitoring of GX301-2 with the RXTE/ASM has revealed some new properties of this high-mass X-ray binary. + Secular changes in Bux (Fig., Secular changes in flux (Fig. + 2) are also accompanied bv flux oscillations wilh a period of four 41.5-day binary orbits., 2) are also accompanied by flux oscillations with a period of four 41.5-day binary orbits. + The orbital light curve is seen to be significantly different between bright. medium and dim flux levels (Fig.3).," The orbital light curve is seen to be significantly different between bright, medium and dim flux levels (Fig.3)." + We have constructed an improved stellar wind ancl stream model for the GX301-2/ WRAY 977 binary svstem. extending the work of L02.," We have constructed an improved stellar wind and stream model for the GX301-2/ WRAY 977 binary system, extending the work of L02." + The model is compared to long term lighteurve observations from the RANTE/ASA and to colunn densities derived [rom the RNTE/ASM 3-5 keV to 5-12 keV softness ratios., The model is compared to long term lightcurve observations from the RXTE/ASM and to column densities derived from the RXTE/ASM 3-5 keV to 5-12 keV softness ratios. + We have validated the necessity of including a stream in the mass flow from WRAY 977 in addition to a spherically svmimetric wind in order (ο explain the observed light curves ancl column densiües., We have validated the necessity of including a stream in the mass flow from WRAY 977 in addition to a spherically symmetric wind in order to explain the observed light curves and column densities. + The imines and amplitudes of the (wo peaks in the lighteurve. near orbital phases 0.92 and 0.5 are naturally explained by accretion onto the neutron star [from an Archimedes spiral-Qvpe stream.," The timings and amplitudes of the two peaks in the lightcurve, near orbital phases 0.92 and 0.5 are naturally explained by accretion onto the neutron star from an Archimedes spiral-type stream." + The quality of the column density. data ds low due to statistical uncertainties., The quality of the column density data is low due to statistical uncertainties. + Yet the column density data provides (he primary constraint on the stellar wind mass loss rate., Yet the column density data provides the primary constraint on the stellar wind mass loss rate. + We have [ound best [it parameters for a range of radii lor WRAY 977 and a rauge of svstem inclinations which are consistent with the physical constraints such as no eclipse and maxinum mean radius not exceeding the mean Roche radius (see Fig., We have found best fit parameters for a range of radii for WRAY 977 and a range of system inclinations which are consistent with the physical constraints such as no eclipse and maximum mean radius not exceeding the mean Roche radius (see Fig. + 5)., 5). + From the model fits. we find the change between bright aud medium intensity levels is primarily due to decreased mass loss in the stellar wind. but the change between medium and dim intensity levels is primarily due to decreased stream density.," From the model fits, we find the change between bright and medium intensity levels is primarily due to decreased mass loss in the stellar wind, but the change between medium and dim intensity levels is primarily due to decreased stream density." + For any. intensity level. the total mass-loss rate in the stream exceeds (hat in the wind by a factor of ~2.5. indicating the crucial role of the stream in this," For any intensity level, the total mass-loss rate in the stream exceeds that in the wind by a factor of $\sim$ 2.5, indicating the crucial role of the stream in this" +the sky inG«8! strips.,"the sky in$6^{\circ }\times +8^{\prime }$ strips." +" Coadded images. with 7.8-« total integration. are produced frou six dithered frames. after rebinuiugto 1"" pixels."," Coadded images, with 7.8-s total integration, are produced from six dithered frames, after rebinningto $^{\prime \prime }$ pixels." + The 2\LASS Production Processing Syste provides final Atlas Buages and source extractions with precise photometric calibration and astrometricpositions. with 10σ sensitivities of15.8 mag atJ. 15.1 atJT. aud 11.3 at A.," The 2MASS Production Processing System provides final Atlas Images and source extractions with precise photometric calibration and astrometricpositions, with $\sigma $ sensitivities of15.8 mag at$J$, 15.1 at$H$, and 14.3 at $K_{s}$." + The LAIC was observed as part of routine mightly southern operations iu L998 000., The LMC was observed as part of routine nightly southern operations in 1998 – 2000. + Production processing resulted i nearly 7.1 nülliou source extractions for the LMC in a working point source database. which also includes image artifacts. such as filter eliuts aud diffraction spikes from bright stars. as well as coufused objects. detection upper hits. and multiple source apparitious due to scan overlaps.," Production processing resulted in nearly 7.1 million source extractions for the LMC in a working point source database, which also includes image artifacts, such as filter glints and diffraction spikes from bright stars, as well as confused objects, detection upper limits, and multiple source apparitions due to scan overlaps." + Nikolaev Weinberg (2000) discuss the results of analysis ou the working point source atabase for the LAIC., Nikolaev Weinberg (2000) discuss the results of analysis on the working point source database for the LMC. + Subsequently. artifacts. which cau )o welb-cliaracterized and identified. were climinated. aiu uplicate sources were removed. as part of the catalog ecucration process for the 2\TASS Second Tacremenuta Data Release (2IDR)in 2000 March.," Subsequently, artifacts, which can be well-characterized and identified, were eliminated, and duplicate sources were removed, as part of the catalog generation process for the 2MASS Second Incremental Data Release (2IDR)in 2000 March." + The ΠΟΠ coutains IT of the sky. including most of the observed field. of the LAIC. which is comprised of 1.399.637 point sources and 12311 extended sources.," The 2IDR contains $\sim $ of the sky, including most of the observed field of the LMC, which is comprised of 1,399,637 point sources and 12311 extended sources." +" Two relatively simall sections of the galaxy (15.6 aac LLS square degrees. respectively) were not part of the 2IDR.Thefirst section.spanningapproximately right ascension a=""39"" to L’28"" and declination 6=72° tto((J2000).coincidentally,had the highest source censity."," Two relatively small sections of the galaxy (15.6 and 14.8 square degrees, respectively) were not part of the 2IDR.Thefirst section,spanningapproximately right ascension $\alpha=4^h39^m$ to $4^h28^m$ and declination $% +\delta=-7 to$-$(J2000),coincidentally,had the highest source density." + The second. covering e=1/00 to 105 and à=ορ” tto. (152000). is somewhat less deuse.," The second, covering $\alpha=4^h00^m$ to $4^h05^m$ and $% +\delta=-6 to $-$ (J2000), is somewhat less dense." + Data for these sectious were drawn from the working point source database. and therefore may be coutaminated by artifacts audconfused. aud duplicate sources.," Data for these sections were drawn from the working point source database, and therefore may be contaminated by artifacts andconfused and duplicate sources." + The combined released and unreleased datasets form the basis of our uear-IR/uid-IR point source cross-correlation and subsequent analysis., The combined released and unreleased datasets form the basis of our near-IR/mid-IR point source cross-correlation and subsequent analysis. + We have also cross-correlated the MSN. PSC with the 2ATASS exteuded source catalog (NSC). drawn from both the 21DR audthe working database for the two strips of uureleased data.," We have also cross-correlated the MSX PSC with the 2MASS extended source catalog (XSC), drawn from both the 2IDR andthe working database for the two strips of unreleased data." + TheAISN aud 2MASS catalogs Lavebeen cross-referenced using a simple positional correlation. requiring the positioneye error gooducss-offitto statistic.H DX7. to be less than18.1. where For a two-dimensional uormalerror distribution. we expect 99.99 of the source matches to be found within this 4? limit.," TheMSX and 2MASS catalogs havebeen cross-referenced using a simple positional correlation, requiring the position error goodness-of-fit statistic, $\chi ^{2}$, to be less than$18.4$, where For a two-dimensional normalerror distribution, we expect 99.99 of the source matches to be found within this $\chi ^{2}$ limit." + Figure 2 shows the distribution of V7 valuesfor matches between the MSN catalog aud the 2IDR., Figure 2 shows the distribution of $\chi ^{2}$ valuesfor matches between the MSX catalog and the 2IDR. + The figure also shows theciunulative fractionof source niatelies asa function of 7.which for a traly normal distribution of errors would viek of sources with 47«32.3. with 4?«6.17. aud 99.73 with 4?<11.18.," The figure also shows thecumulative fractionof source matches asa function of $\chi ^{2}$,which for a truly normal distribution of errors would yield of sources with $\chi ^{2}<2.3$, with $\chi +^{2}<6.17$, and 99.73 with $\chi ^{2}<11.18$." + The distribution of the 4? statistic found. for this dataset is quite close tothis. eiviug us confidencethat mostof the position matches are true.," The distribution of the $\chi +^{2}$ statistic found for this dataset is quite close tothis, giving us confidencethat mostof the position matches are true." + The driving uncertainty in these matches is that of the AISN position. which is of order 175 in both nme-scan (6) aud cross-scan (a) directions. (," The driving uncertainty in these matches is that of the MSX position, which is of order $% +1{\farcs} 5 in both in-scan $\delta )$ and cross-scan $\alpha $ ) directions. (" +This is somewhat better than the quoted uncertainties in the MSN PSC Version 1.2 [Egan et al.,This is somewhat better than the quoted uncertainties in the MSX PSC Version 1.2 [Egan et al. + 1999]. since the subsequent LAIC pointing refinement used 2MASS and MISN IR. Astrometric Catalog [Egan Price 1996] stars. Which vielded morepointing update stars per square degree for the LMC refinement the Calactic Plane boresight poiutiug refinement.aud reduced the MSX LAC positional ΠΠ," 1999], since the subsequent LMC pointing refinement used 2MASS and MSX IR Astrometric Catalog [Egan Price 1996] stars, which yielded morepointing update stars per square degree for the LMC refinement the Galactic Plane boresight pointing refinement,and reduced the MSX LMC positional uncertainties.)" + ΡΕ positional 072. 4?«18.," 2MASS positional $0{\farcs}2$ $% +\chi ^{2}<18." +3. lo J9Ivy) ox2 (>>6. 02003(10/5). J. HT. We (J H.Jty. JOA. TlNu. IH A.N.OA). N-dimenusional ," $% +\sigma $J-K_{s}$ $\chi ^{2}<18.4$ $\chi ^{2}<2$ $\chi ^{2}>6$ $0{\fdg}003$$10{\farcs}8$ $J$ $H$ $K_{s}$ $J-H$ $J-K_{s}$ $J-{\rm A}$ $H-K_{s}$ $H-{\rm A}$ $K_{s}-{\rm A}$ $N$ " +ARBs have been shown to have M>23.4... and these objects are all excellent DII candidates (MeClintock Remillard 2004).,XRBs have been shown to have $M>3M_\odot$ and these objects are all excellent BH candidates (McClintock Remillard 2004). + However. the mass estimates are reliable only if 7 (and lo a lesser extent AM.) is well determined. which is not always the case.," However, the mass estimates are reliable only if $i$ (and to a lesser extent $M_c$ ) is well determined, which is not always the case." +" Fortunately. an inspection of equation (3) shows that the mass function. /(M). which depends only on the two accurately measured cuantities A, and 2,4, is a strict lower bound on M."," Fortunately, an inspection of equation (3) shows that the mass function $f(M)$, which depends only on the two accurately measured quantities $K_c$ and $P_{\rm +orb}$, is a strict lower bound on $M$ ." + Most of the 20 ARBs have f(A) itself greater than or of order 3A.., Most of the 20 XRBs have $f(M)$ itself greater than or of order $3M_\odot$. + Therefore. these svstems are excellent DII candidates. regardless of uncertainties in their inclinations and companion star masses.," Therefore, these systems are excellent BH candidates, regardless of uncertainties in their inclinations and companion star masses." + In the center of our Milkv. Way. Galaxy is a dark massive object whose existence has been inferred. for a munber of vears [rom its effect on the motions of stars and gas in its vicinitv., In the center of our Milky Way Galaxy is a dark massive object whose existence has been inferred for a number of years from its effect on the motions of stars and gas in its vicinity. + Recently. high resolution infrared observations have enabled (wo independent groups to follow the orbits of individual stars around this object (Schóddel et al.," Recently, high resolution infrared observations have enabled two independent groups to follow the orbits of individual stars around this object (Schöddel et al." + 2002: Eisenhaner et al., 2002; Eisenhauer et al. + 2003: Ghez et al., 2003; Ghez et al. + 2003. 2004).," 2003, 2004)." + Moviel and Movie2 show (iime-elapsed images of the Galactic Center region revealing the (eccentric) orbits of several stars., Movie1 and Movie2 show time-elapsed images of the Galactic Center region revealing the (eccentric) orbits of several stars. + By modeling the orbits with Newtonian dvnanmics essentially using the generalization of equation (2) Lor elliptical orbits ihe mass of the dark object has been estimated to be 3.7£0.2xLOYAL...," By modeling the orbits with Newtonian dynamics — essentially using the generalization of equation (2) for elliptical orbits — the mass of the dark object has been estimated to be $3.7\pm 0.2\times10^6 +M_\odot$." + The mass must lie within about 2xLOM m (the distance of closest approach of the observed stars). strongly suggesting that the object is à BIL," The mass must lie within about $2\times10^{13}$ m (the distance of closest approach of the observed stars), strongly suggesting that the object is a BH." + If the object is not a DII. then the only reasonable hypothesis is (hat it is a dense cluster of dark compact stars.," If the object is not a BH, then the only reasonable hypothesis is that it is a dense cluster of dark compact stars." + However. such a cluster would be short-lived and would become a DII in much less time than the age of the Galaxy (Maoz 1998). so this is not a very likely scenario.," However, such a cluster would be short-lived and would become a BH in much less time than the age of the Galaxy (Maoz 1998), so this is not a very likely scenario." + A famous radio source called Sagittarius À* (Ser À*) is located very close to the position of the dark mass described above: it has for long been suspected to be the supermassive DII., A famous radio source called Sagittarius A* (Sgr A*) is located very close to the position of the dark mass described above; it has for long been suspected to be the supermassive BH. + Reid Drunthaler (2004) have followed the motion of Ser A* over a period of eight νους using radio interferometry ancl have shown that the component of its velocity perpendicular to the plane of the Galaxy is —0.4220.9kms|. consistent with zero.," Reid Brunthaler (2004) have followed the motion of Sgr A* over a period of eight years using radio interferometry and have shown that the component of its velocity perpendicular to the plane of the Galaxy is $-0.4\pm0.9 ~{\rm +km\,s^{-1}}$, consistent with zero." + Since Ser Α should experience Drownian motion as a result of gravitational interactions with stars in its vicinity. ils lack of apparent motion implies that it has a large mass.," Since Sgr A* should experience Brownian motion as a result of gravitational interactions with stars in its vicinity, its lack of apparent motion implies that it has a large mass." + Depending on the statistical nethod that one emplovs and the confidence level that one seeks. one infers that Ser A* must dave a miass of al least 107...: in fact. Ser A* most likely encompasses the entire dark mass in (he Galactic Center.," Depending on the statistical method that one employs and the confidence level that one seeks, one infers that Sgr A* must have a mass of at least $10^5 M_\odot$; in fact, Sgr A* most likely encompasses the entire dark mass in the Galactic Center." + The image of Ser A* as measured in millimeter radio waves indicates an angular size of about 240 micro-aresecond (Bower et al., The image of Sgr A* as measured in millimeter radio waves indicates an angular size of about 240 micro-arcsecond (Bower et al. + 2004). which corresponds to 2745 or a DII mass of 3.7x10M. and a distance of 8 Κρο," 2004), which corresponds to $27 R_S$ for a BH mass of $3.7\times10^6M_\odot$ and a distance of 8 kpc." + Thus. Ser Α has both a large mass and a very smallradius.," Thus, Sgr A* has both a large mass and a very smallradius." + Surely it must be a BIL!, Surely it must be a BH! +"various steps of this procedure, and are specified in Table 1..","various steps of this procedure, and are specified in Table \ref{tab:samps}." + One final filtering step is necessary due to imperfections in the SDSS photometric pipeline., One final filtering step is necessary due to imperfections in the SDSS photometric pipeline. +" For nearby bright galaxies (a significant portion of our primary sample), individual HII regions in a star forming disk are sometimes classified as in the SDSS pipeline, as shown in the lower separatepanel of objectsFigure 1."," For nearby bright galaxies (a significant portion of our primary sample), individual HII regions in a star forming disk are sometimes classified as separate objects in the SDSS pipeline, as shown in the lower panel of Figure \ref{fig:hiiex}." +". Because these HII regions are extended sources and have redshifts matching the host, they are included in all secondary samples, including the clean sample."," Because these HII regions are extended sources and have redshifts matching the host, they are included in all secondary samples, including the clean sample." +" Fortunately, this effect is only significant out to separations of ~10 kpc, so there are a small enough number of possible such pairs (~ 50) that they can be removed by visual examination."," Fortunately, this effect is only significant out to separations of $\sim 10$ kpc, so there are a small enough number of possible such pairs $\sim50$ ) that they can be removed by visual examination." + All samples below have been cleaned of these HII regions., All samples below have been cleaned of these HII regions. +" This process is not ideal, as it may remove faint satellites that truly are present, but are superimposed over a disk and thus appear indistinguishable from an HII "," This process is not ideal, as it may remove faint satellites that truly are present, but are superimposed over a disk and thus appear indistinguishable from an HII region." +"some secondaries be hidden from view region.by being Alternatively,behind the primary."," Alternatively, some secondaries may be hidden from view by being behind the primary." +" Thus, mayremoving apparent HII regions may result in under-counting satellites at small projected separations."," Thus, removing apparent HII regions may result in under-counting satellites at small projected separations." +" Fortunately, this is only of consequence for dproj<10 only ~0.3% of a typical primary's dark kpc,matter halo representingvolume."," Fortunately, this is only of consequence for $d_{\rm proj} \lesssim 10$ kpc, representing only $\sim 0.3 \%$ of a typical primary's dark matter halo volume." +" Hence, these under-counting effects are not significant relative to Poisson errors in the discussion below."," Hence, these under-counting effects are not significant relative to Poisson errors in the discussion below." +" The clean selection criteria define a sample of galaxy pairs that are isolated from other luminous galaxies, and composed of a ~L, primary with a nearest satellite with I~ Lyumc."," The clean selection criteria define a sample of galaxy pairs that are isolated from other luminous galaxies, and composed of a $\sim L_*$ primary with a nearest satellite with $L \sim L_{\rm LMC}$ ." +" We show the g—r, M, color-magnitude diagram (CMD) as Figure 2,, with the clean sample represented by the red (primary) and white (secondary) points plotted over all isolated primaries (above the black line) and all galaxies with magnitudes (below) in the volume-limited sample."," We show the $g-r$, $M_r$ color-magnitude diagram (CMD) as Figure \ref{fig:matchcmd}, with the clean sample represented by the red (primary) and white (secondary) points plotted over all isolated primaries (above the black line) and all galaxies with secondary-like magnitudes (below) in the volume-limited sample." +" We secondary-likenote here that because the luminosity function climbs sharply for fainter galaxies, the typical luminosity of the clean sample is close to the faintcutoff for these samples: for the isolated the median absolute magnitude is M,=--21.9 (very primaries,close to ΛΜ. from ?)), while for the secondaries, it is M,=—19.3."," We note here that because the luminosity function climbs sharply for fainter galaxies, the typical luminosity of the clean sample is close to the faintcutoff for these samples: for the isolated primaries, the median absolute magnitude is $M_r=\medpri$ (very close to $M_*$ from \citealt{blanton03lf}) ), while for the secondaries, it is $M_r=\medsec$." + It is important to also note that the secondary sample is not complete because the SDSS spectroscopic survey is not complete., It is important to also note that the secondary sample is not complete because the SDSS spectroscopic survey is not complete. + The two main sources of systematic incompleteness are due to two fiber collision effects., The two main sources of systematic incompleteness are due to two fiber collision effects. +" The first is collision between the primary and secondary, but this does not significantly bias our sample because the typical primary-secondary separation is larger than the on-sky fiber diameter for most of our objects."," The first is collision between the primary and secondary, but this does not significantly bias our sample because the typical primary-secondary separation is larger than the on-sky fiber diameter for most of our objects." +" The second effect concerns the case where a potential satellite is near a bright background cluster, and hence is not available to be for a spectrum in the SDSS sample."," The second effect concerns the case where a potential satellite is near a bright background cluster, and hence is not available to be targeted for a spectrum in the SDSS sample." + This effect is discussed targetedfurther in §4.., This effect is discussed further in \ref{sec:sampanl}. . + 10000 The selection criteria discussedabove define a sample, 10000 The selection criteria discussedabove define a sample +(?).,. +". Here j numbers the resonance, j:(j—1)."," Here $j$ numbers the resonance, $j:(j-1)$." +" In the limit of large j, adjacent resonances are separated by a distance Equating these two distances gives the outermost resonance where overlap occurs as Since a—ap:=2/(37) for large j, the chaotic zone width is thus given by This scaling is successfully reproduced by numerical iterations of the encounter mapbelow)."," In the limit of large $j$, adjacent resonances are separated by a distance Equating these two distances gives the outermost resonance where overlap occurs as Since $a-a_\mathrm{pl}= 2/(3j)$ for large $j$, the chaotic zone width is thus given by This scaling is successfully reproduced by numerical iterations of the encounter map." +" However, the resonance width grows with particle eccentricity, as can be seen in panel of Figure 1.."," However, the resonance width grows with particle eccentricity, as can be seen in panel of Figure \ref{fig:chaoticzone}." +" This means that resonances that do not overlap at low eccentricities may overlap at higher eccentricities, and cause the chaotic zone to be wider."," This means that resonances that do not overlap at low eccentricities may overlap at higher eccentricities, and cause the chaotic zone to be wider." +" When eccentricities are not small, the width of the resonance can be found by considering the width of the resonant libration region after the resonant separatrix forms, which is given by δι)=4(4J)V interms of the canonical momentum J."," When eccentricities are not small, the width of the resonance can be found by considering the width of the resonant libration region after the resonant separatrix forms, which is given by $\delta J =4(4 J)^{1/4}$ interms of the canonical momentum $J$." +" Now J is related to e by where kj~(33m/2ma)?/?/2 in the limit of largej(2?),, and so Using the relationship between eccentricity change and major axis change in a resonance da=2jaede(?),, we then have for the maximum libration width in semi-major axis."," Now $J$ is related to $e$ by where $k_j\sim(3jm_\odot/2m_\oplus)^{2/3}/2$ in the limit of large $j$, and so Using the relationship between eccentricity change and semi-major axis change in a resonance $\delta a = 2jae\delta e$, we then have for the maximum libration width in semi-major axis." + Equating this to the resonance separation and redoing the previous derivation then gives as the width of the chaotic zone at higher eccentricities., Equating this to the resonance separation and redoing the previous derivation then gives as the width of the chaotic zone at higher eccentricities. +" Note the two implications of this equation:first, the chaotic zone width grows weakly with eccentricity."," Note the two implications of this equation:first, the chaotic zone width grows weakly with eccentricity." + The dependence is shown in Figure 1 as solid red lines., The dependence is shown in Figure \ref{fig:chaoticzone} as solid red lines. + The agreement with the results from the encounter map is striking., The agreement with the results from the encounter map is striking. +" We also show the dependence on Figure 2,, where we can see many unstable particles above the solid red line."," We also show the dependence on Figure \ref{fig:nbody}, where we can see many unstable particles above the solid red line." +" Second, the 7/7 dependence of the chaotic zone width on planet mass, valid in the low-eccentricity regime, is replaced with a ul? dependence."," Second, the $\mu^{2/7}$ dependence of the chaotic zone width on planet mass, valid in the low-eccentricity regime, is replaced with a $\mu^{1/5}$ dependence." +" To verify this, in Figure 3 we plot the width of the chaotic zone at an eccentricity of e=0.01 as a function of p."," To verify this, in Figure \ref{fig:width e=0.01} we plot the width of the chaotic zone at an eccentricity of $e=0.01$ as a function of $\mu$." + The width was determined by finding the innermost cell where all trajectories were regular from the grids presented in Figure 1.., The width was determined by finding the innermost cell where all trajectories were regular from the grids presented in Figure \ref{fig:chaoticzone}. +" The regression line through these points gives a dependence (óa/a)emaos=0.86,,:205. in excellent agreement with the analytical result from Equation 10.."," The regression line through these points gives a dependence $(\delta a/a)_\mathrm{chaos}=0.86\mu^{0.208}$, in excellent agreement with the analytical result from Equation \ref{eq:eccentric chaotic zone}." +" Thus, for higher eccentricities, the chaotic zone width is given by a ul? scaling, not the more familiar j/?/7."," Thus, for higher eccentricities, the chaotic zone width is given by a $\mu^{1/5}$ scaling, not the more familiar $\mu^{2/7}$." +" For comparison, the width of the chaotic zone at e=0 as a function of µ is shown on the same Figure."," For comparison, the width of the chaotic zone at $e=0$ as a function of $\mu$ is shown on the same Figure." +" The regression line here gives (óa/a)cnaos=1.359278, in excellent agreement with Wisdom’s original result."," The regression line here gives $(\delta a/a)_\mathrm{chaos}=1.35\mu^{0.278}$, in excellent agreement with Wisdom's original result." + Equation 10 also allows the critical eccentricity separating the two regimes to be estimated., Equation \ref{eq:eccentric chaotic zone} also allows the critical eccentricity separating the two regimes to be estimated. +" Equating (da/a)chaos obtained from Equation 10,, for eccentric particles, with the value from Equation 6., for low-eccentricity particles, gives growing with ju, as is seen in Figure 1.."," Equating $(\delta a / a)_\mathrm{chaos}$ obtained from Equation \ref{eq:eccentric chaotic zone}, for eccentric particles, with the value from Equation \ref{eq:circular chaotic zone}, for low-eccentricity particles, gives growing with $\mu$, as is seen in Figure \ref{fig:chaoticzone}." +" Note that e=0.01 is the critical eccentricity for jj=10”3, and indeed the widths of the classical and extended zones coincide at this point (Figure 3))."," Note that $e=0.01$ is the critical eccentricity for $\mu=10^{-3},$ and indeed the widths of the classical and extended zones coincide at this point (Figure \ref{fig:width e=0.01}) )." + Note that there is a maximum eccentricity for which this derivation of the extended chaotic zone is valid., Note that there is a maximum eccentricity for which this derivation of the extended chaotic zone is valid. + This occurs where the solid red line in Figure 1 marking the boundary of the extended chaotic zone intersects the dashed black line denoting the region of planet-crossing orbits., This occurs where the solid red line in Figure \ref{fig:chaoticzone} marking the boundary of the extended chaotic zone intersects the dashed black line denoting the region of planet-crossing orbits. +" At eccentricities above this, particles will be removed directly by close encounters rather than via chaotic diffusion."," At eccentricities above this, particles will be removed directly by close encounters rather than via chaotic diffusion." + The maximum eccentricity is given by and in this regime particles are unstable if In the next Section we adopt the slightly more conservative condition that particles are also unstable if they approach within one Hill's radius of the planet., The maximum eccentricity is given by and in this regime particles are unstable if In the next Section we adopt the slightly more conservative condition that particles are also unstable if they approach within one Hill's radius of the planet. + This result has important implications for the interactions of planets and debris discs., This result has important implications for the interactions of planets and debris discs. + Discs showing inner clearings are commonly explained by the existence of a planet removing particles from its chaotic zone e., Discs showing inner clearings are commonly explained by the existence of a planet removing particles from its chaotic zone . +"g.,)mainBodyCitationEnd2222][]QuillenFom06. The mass and semi-major axis of the planet determine both the location and the sharpness of the inner edge (???)..", The mass and semi-major axis of the planet determine both the location and the sharpness of the inner edge . + Since our investigations above have revealed that the extent of the chaotic, Since our investigations above have revealed that the extent of the chaotic +Powerful radio galaxies at high redshift (222: Ηλ hereinafter) continue to. play an. important role in cosmological investigations.,Powerful radio galaxies at high redshift $\ga$ 2: HzRG hereinafter) continue to play an important role in cosmological investigations. + “Phey provide a means to identify and study the most massive galaxies in the early universe (e.g. Rotttgering et al., They provide a means to identify and study the most massive galaxies in the early universe (e.g. Rötttgering et al. + 1994: Sevmour et al., 1994; Seymour et al. + 2007). and represent. an opportunity to. examine the possible svmbiosis between the nuclear activity and the host galaxy (e.g. Nesvadba et al.," 2007), and represent an opportunity to examine the possible symbiosis between the nuclear activity and the host galaxy (e.g. Nesvadba et al." + 2006)., 2006). + Vhe Ελ MIRC 0406-244 (z—2.44: AleCarthy et al., The HzRG MRC 0406-244 (z=2.44: McCarthy et al. + 1901) has been the subject of observations in various wavebands., 1991) has been the subject of observations in various wavebands. + Raclio images obtained at ~5 and ~S Cillz (~16 and 28 Cllz in the rest-frame) show a triple radio source which has a relatively small projected. cliameter (82 kpc). and which shows a significant rotation measure (Rush οἱ al.," Radio images obtained at $\sim$ 5 and $\sim$ 8 GHz $\sim$ 16 and 28 GHz in the rest-frame) show a triple radio source which has a relatively small projected diameter (82 kpc), and which shows a significant rotation measure (Rush et al." + 1997: Carilli et al., 1997; Carilli et al. + 1997)., 1997). + Ehe presence of warm ionized sas. with a spatial extent of at. least 66. kpc. has been revealed through spectroscopy and narrow-bancl imaging (AleCarthy ct al.," The presence of warm ionized gas, with a spatial extent of at least 66 kpc, has been revealed through spectroscopy and narrow-band imaging (McCarthy et al." + 1991: Eales Rawlings L998: Rush ct al., 1991; Eales Rawlings 1993; Rush et al. + 1997: Pentericci οἱ al., 1997; Pentericci et al. + 2001: Taniguchi et al., 2001; Taniguchi et al. + 2001: απο et al., 2001; Iwamuro et al. + 2003: Nesvadba ct al., 2003; Nesvadba et al. + 2008)., 2008). + The spatially integrated Iluxes of the UV-optical emission lines are collectively well explained. by photoionization by the active nucleus. with roughly solar metallicity. ancl an internal extinction A.<0.5 mag (IIumphrey ct al.," The spatially integrated fluxes of the UV-optical emission lines are collectively well explained by photoionization by the active nucleus, with roughly solar metallicity, and an internal extinction $_{v}<0.5$ mag (Humphrey et al." + 2008a)., 2008a). + In addition. a spatially extended: absorption feature has been detected in the two-dimensional spectrum of Ενα (Pentericci ct al.," In addition, a spatially extended absorption feature has been detected in the two-dimensional spectrum of $\alpha$ (Pentericci et al." + 2001)., 2001). + The two-dimensional spectrum of the CIV. AT1549 line is also consistent with having been absorbed (Laniguchi et al., The two-dimensional spectrum of the CIV $\lambda$ 1549 line is also consistent with having been absorbed (Taniguchi et al. + 2001)., 2001). + UsingSpizer photometrey. Sevmour et al. (," Using photometrey, Seymour et al. (" +2007) have estimated the stellar mass of AIRC 0406-244 to be [oilο(HST,2007) have estimated the stellar mass of MRC 0406-244 to be $10^{11.36\pm0.13}$. + hereinafter) images obtained by Rush et al. (, hereinafter) images obtained by Rush et al. ( +1997) and Pentericci et al. (,1997) and Pentericci et al. ( +2001) show spatially resolved emission. with a complex figure-of-cight morphology aligned with the axis of the radio emission.,"2001) show spatially resolved emission, with a complex figure-of-eight morphology aligned with the axis of the radio emission." + A likely scenario is that this fieure-ol-cight structure is a pair of ‘superbubbles” resulting from. ambient. interstellar meclia being swept up by a superwind (AleCarthy et al., A likely scenario is that this figure-of-eight structure is a pair of `superbubbles' resulting from ambient interstellar media being swept up by a superwind (McCarthy et al. + 1999: ‘Taniguchi et al., 1999; Taniguchi et al. + 2001) or by the radio source (Nesvadba οἱ al., 2001) or by the radio source (Nesvadba et al. + 2008)., 2008). + LE indeed. this is the case. then AIRC 0406-244 represents an excellent opportunity to study superwinds and fecclback related phenomena.," If indeed this is the case, then MRC 0406-244 represents an excellent opportunity to study superwinds and feedback related phenomena." + In this letter. we investigate the nature of the superbubbles. using lone-slit spectroscopy of the rest-frame optical emission of MIC! 0406-244.," In this letter, we investigate the nature of the superbubbles, using long-slit spectroscopy of the rest-frame optical emission of MRC 0406-244." + We also revisit the, We also revisit the + We also revisit the , We also revisit the + We also revisit the ο, We also revisit the + We also revisit the ο), We also revisit the +he GAB pointing error.,the GRB pointing error. + The energy threshold. £i is either 100 MeV. or 1: GeV. These conditions select. photons with energies larger than fy that arrived within 1500 s after the rust from the region of interest (ROL)., The energy threshold $E_0$ is either 100 MeV or 1 GeV. These conditions select photons with energies larger than $E_0$ that arrived within 1500 s after the burst from the region of interest (ROI). + The latter is a circle with the energv-dependent: radius determined by the two contributions: the error of the photon arrival direction and he error of the GRB position., The latter is a circle with the energy-dependent radius determined by the two contributions: the error of the photon arrival direction and the error of the GRB position. + Usually the first contribution dominates., Usually the first contribution dominates. + Phe error of the GRB position was taken to ro equal to. 1 in the case of GBAL bursts and 0.57. in he case of bursts detected by Swift., The error of the GRB position was taken to be equal to $^{\circ}$ in the case of GBM bursts and $^{\circ}$ in the case of bursts detected by Swift. + Errors for all other »ursts were determined individually from the GCN website., Errors for all other bursts were determined individually from the GCN website. + The observed. pre-burst photons are selected. by an obvious moclilication of the conditions (2))., The observed pre-burst photons are selected by an obvious modification of the conditions \ref{cndA}) ). + Next. we calculate the expected background. corresponding to the energy fo£s.," Next, we calculate the expected background $B$ corresponding to the energy $E>E_0$." + Since GRBs are exceptional events. for the backgroun calculation we may use the photons from the same spatial region for the entire duration of the mission.," Since GRBs are exceptional events, for the background calculation we may use the photons from the same spatial region for the entire duration of the mission." + Thus. the background is given by the total number of photons observed from the ROL during the whole mission. multiplied by the ratio of the exposure corresponding to 1500 s after the burst to the total exposure of ROL.," Thus, the background is given by the total number of photons observed from the ROI during the whole mission, multiplied by the ratio of the exposure corresponding to 1500 s after the burst to the total exposure of ROI." + The caleulation which takes into account the energy dependence of ROL is presented in the Appendix A.., The calculation which takes into account the energy dependence of ROI is presented in the Appendix \ref{app:bgnd}. +" Finally, having calculated. the observed number. of photons n and the expected background D. the probability p tor the GRB in question is calculated. from. the Poisson distribution. where Z(B.n) is the probability to. observe n or more events at D expected."," Finally, having calculated the observed number of photons $n$ and the expected background $B$, the probability $p$ for the GRB in question is calculated from the Poisson distribution, where $\mathcal P(B,n)$ is the probability to observe $n$ or more events at $B$ expected." + I this probability satisfies the condition (1)) lor at least one of the two energy regions of interest. we have a detection and include the corresponding GID in the detection list. Fable 1..," If this probability satisfies the condition \ref{condition}) ) for at least one of the two energy regions of interest, we have a detection and include the corresponding GRB in the detection list, Table \ref{candlist}." + Applving the method. of Sect., Applying the method of Sect. + 3. to 581. GRB we have achieved 19 detections of the post-burst HIE. emission. of which 4 (namely. CRB 081009. GRB 090720D. GRB 100728A and GRB 100911) were previously unreported.," \ref{sec:method} to 581 GRB we have achieved 19 detections of the post-burst HE emission, of which 4 (namely, GRB 081009, GRB 090720B, GRB 100728A and GRB 100911) were previously unreported." + All detections correspond to GBs present in the Fermi-GDM part of the GRB list., All detections correspond to GRBs present in the Fermi-GBM part of the GRB list. + No pre-burst LIE emission was found., No pre-burst HE emission was found. + Of the new detections. CRB LOOT2SA demonstrated particularly bright and lone LUE afterglow: 4 photons with," Of the new detections, GRB 100728A demonstrated particularly bright and long HE afterglow: 4 photons with" +well as the pressure play an important role in the stability analysis of our accompanying paper.,well as the pressure play an important role in the stability analysis of our accompanying paper. + The pressure shows a ring structure., The pressure shows a ring structure. +" By increasing the parameter g, we show below that one can create a double-layered prominence."," By increasing the parameter $g$, we show below that one can create a double-layered prominence." + The safety factor q and the radial derivative of the Shafranov shift are plotted in Fig. 10.., The safety factor $q$ and the radial derivative of the Shafranov shift are plotted in Fig. \ref{fig:constantT_smallg_safetyfactor}. . +" For small g, the safety factor q has two flat regions that correspond to the ring-like cavity of low pressure."," For small $g$ , the safety factor $q$ has two flat regions that correspond to the ring-like cavity of low pressure." +" Furthermore, note that the q—1 and q—3/2 surfaces both exist for this equilibrium."," Furthermore, note that the $q=1$ and $q=3/2$ surfaces both exist for this equilibrium." +" As for cool prominences,thiswill mean that"," As for cool prominences,thiswill mean that" +liue component which is closely related to the outburst and is decaving with tine.,line component which is closely related to the outburst and is decaying with time. +" In? we reported on ou-gonmg crystallization of silicate erains curving the outburst. and our monitoring of the crystalline silicate features showed evidence for a fast radial transport of silicate crystals ον,"," In \citet{abraham2009} we reported on on-going crystallization of silicate grains during the outburst, and our monitoring of the crystalline silicate features showed evidence for a fast radial transport of silicate crystals \citep{juhasz2010}." + Tn Juhdssz et al., In Juhássz et al. + we also modeled the whole optical-to-uum spectral energy distribution of LLup in outburst aud fouud that most of the accretion Inuuinositv is chuitted as a sinele temperature blackbody of II. Iu this paper we present the medium resolution uear-infrared spectra of our campaign. and use the observed Cluission Hines to analyze the location. kinematics. aud cherectics of wari atomic and molecular eas present iu the inner few tenths of AUs in the LLup syste.," we also modeled the whole optical-to-mm spectral energy distribution of Lup in outburst and found that most of the accretion luminosity is emitted as a single temperature blackbody of K. In this paper we present the medium resolution near-infrared spectra of our campaign, and use the observed emission lines to analyze the location, kinematics, and energetics of warm atomic and molecular gas present in the inner few tenths of AUs in the Lup system." + We observed LLup with SINFONT. an adaptive optics CAO) assisted integral field spectrograph installed ou the ULL telescope of the VET (27)..," We observed Lup with SINFONI, an adaptive optics (AO) assisted integral field spectrograph installed on the UT4 telescope of the VLT \citep{eisenhauer2003, bonnet2004}." + Measurements were taken iu service mode at three different epochs. ou the uights 21/25. 28/29. aud 230/31 July 2008. as part of the project 281.C-5031 (PI: AL. Coto).," Measurements were taken in service mode at three different epochs, on the nights 24/25, 28/29, and 30/31 July 2008, as part of the project 281.C-5031 (PI: M. Goto)." + Three dimensional spectra were taken with the J. IT aud Is eratines using a Tawa 2RC detector.," Three dimensional spectra were taken with the J, H and K gratings using a Hawaii 2RG detector." + The dispersion of the selected mode was num/pixel in the J baud gan). nuni/pixel in the IE band 1.55;uu). aud 1mn/pixel in the K baud 2.]54nu).," The dispersion of the selected mode was nm/pixel in the J band $\,\mu$ m), nm/pixel in the H band $\,\mu$ m), and nm/pixel in the K band $\,\mu$ m)." + The spectral resolution was A/AA5 2100. 1100. and E100 im the J. IT. and I& band. respectively.," The spectral resolution was $\lambda / +\Delta\lambda\,\approx$ 2400, 4100, and 4400 in the J, H, and K band, respectively." + Spectra were obtained by rotating the iustruuenut by 07 1807. 907. and 2707. in order to be able to better remove iustrunenutal effects.," Spectra were obtained by rotating the instrument by $^{\circ}$, $^{\circ}$, $^{\circ}$, and $^{\circ}$, in order to be able to better remove instrumental effects." + Exposure time was 1iuninu for cach rotator auele. ceiving a total exposure tine of [nuuin per baud per epoch.," Exposure time was min for each rotator angle, giving a total exposure time of min per band per epoch." + Beside LLup. calibration sources of spectral type G2V were also observed in order to enable proper tellavic correction: 993685 and 779161 were observed in the J baud on 25 July. 580982 was observed in all three bands ou Jul 29. and 778652 was observed also in all three bauds ou Jul 31.," Beside Lup, calibration sources of spectral type G2V were also observed in order to enable proper telluric correction: 93685 and 79464 were observed in the J band on 25 July, 80982 was observed in all three bands on Jul 29, and 78652 was observed also in all three bands on Jul 31." + We started the data reduction with product files xovided by the SINFONI pipeline as part of the service mode data delivery: product code SCDJ (full. coadded science product cubes) for the science arect. and PCST (full. coadded standard star cube) or the telhuic standard.," We started the data reduction with product files provided by the SINFONI pipeline as part of the service mode data delivery: product code SCDJ (full, coadded science product cubes) for the science target, and PCST (full, coadded standard star cube) for the telluric standard." + These fles contain dark curenut-ubtracted. flattield-corrected. ska-subtractecl. waveleneth-calibrated. co-acdded data products iu the orm of « 61ppixel imaecs for cach waveleusth. with a spatial scale of 1uunas/pixel aud a feld of view of 078 « O08.," These files contain dark current-subtracted, flatfield-corrected, sky-subtracted, wavelength-calibrated, co-added data products in the form of $\,{\times}\,$ pixel images for each wavelength, with a spatial scale of mas/pixel and a field of view of $\farcs$ $\,{\times}\,$ $\farcs$ 8." + Further data reduction was done using custoniwiitten IDL scripts., Further data reduction was done using custom-written IDL scripts. + For both the science target and the telluric calibration stars. we first calculated the centroid for cach tage in the data cubes.," For both the science target and the telluric calibration stars, we first calculated the centroid for each image in the data cubes." + Then we extracted spectra by using an aperture with a radius of 10 pixel and a sky aunulus between 20 aud 25 pixel to calculate the fux of the star at each waveleneth., Then we extracted spectra by using an aperture with a radius of 10 pixel and a sky annulus between 20 and 25 pixel to calculate the flux of the star at each wavelength. + The spectrin of the telluric standard star contained not 6ilv the tellure absorption lines. but intrinsic stellar photospheric lues.," The spectrum of the telluric standard star contained not only the telluric absorption lines, but intrinsic stellar photospheric lines." + To correct for the latter. we used the normalized solar spectruu available at the SINFONIwebpage’.," To correct for the latter, we used the normalized solar spectrum available at the SINFONI." +.. We nuniltiplied it by a blackbody. convolved it o the spectral resolution of SINFONT aud scaled it.," We multiplied it by a blackbody, convolved it to the spectral resolution of SINFONI and scaled it." + By changing the temperature of the blackbodsy. the width of he Caussian convolution kernel. aud the scaling factor. it was possible to remove any intrinsic stellar features frou he tellure correction spectra.," By changing the temperature of the blackbody, the width of the Gaussian convolution kernel, and the scaling factor, it was possible to remove any intrinsic stellar features from the telluric correction spectra." + The obtained correction curves characterize the transmission of the atmosphere as a function of wavelength (Fig. 1))., The obtained correction curves characterize the transmission of the atmosphere as a function of wavelength (Fig. \ref{fig:calib}) ). + Since for the first night 10 IE and I calibration observations were available. we used the average of the curves obtained on the two other üghts.," Since for the first night no H and K calibration observations were available, we used the average of the curves obtained on the two other nights." + Finally. the spectra of LLup were divided by hese correction curves. and the results were normalizec x fitting a third degree polvuouial to the continua.," Finally, the spectra of Lup were divided by these correction curves, and the results were normalized by fitting a third degree polynomial to the continuum." + Comparison of the spectra taken ou the three differeut iehts revealed insiguificaut differences. thus we average ini to increase the signal-to-noise ratio (S:N).," Comparison of the spectra taken on the three different nights revealed insignificant differences, thus we averaged them to increase the signal-to-noise ratio (S:N)." +" For uost of the following analysis. we used these average spectra, which are plotted iu Fies. 2.. 3.."," For most of the following analysis, we used these averaged spectra, which are plotted in Figs. \ref{fig:specj}, \ref{fig:spech}," + and. νι, and \ref{fig:speck}. + SiN is NO160 in the muddle of the atmospheric windows ar zw from strong tellurie bands (e.g. at gan. or at μι). LOsO where there are strong telluric absorption (e.g. around ju). aud 20.10 at the edges of the atinospherie windows (c.g. above 1.3140 in the J baud or above 2.10422 in the Is baud).," S:N is 80–160 in the middle of the atmospheric windows and far from strong telluric bands (e.g. at $\,\mu$ m, or at $\,\mu$ m), 40–80 where there are strong telluric absorption (e.g. around $\,\mu$ m), and 20–40 at the edges of the atmospheric windows (e.g. above $\,\mu$ m in the J band or above $\,\mu$ m in the K band)." + We dave acquired ÁAO-asssted near-infrared polariuectiic/ observations —of LLup in visitor mode using the NACO iustruneut mounted on the UTI telescope of the VET on 10/11 April 2008. as part of the project 381.C-02 (PT: A. Kosspall).," We have acquired AO-assisted near-infrared polarimetric observations of Lup in visitor mode using the NACO instrument mounted on the UT4 telescope of the VLT on 10/11 April 2008, as part of the project 381.C-0241 (PI: Á.. Kósspáll)." + NACO consists of the Nasuivth Adaptive11 Optics System aud the CONICA near-ufrared camera (??)..," NACO consists of the Nasmyth Adaptive Optics System and the CONICA near-infrared camera \citep{lenzen1998,rousset2003}." + The observations were made using the differential polarimetric imaging techuique (DPI:seee.g.?)..," The observations were made using the differential polarimetric imaging technique \citep[DPI; see + e.g.][]{kuhn2001}." + The basic idea of the DPT is to take the difference of two orthogonally polarized. simultaneously acquired tages of the same object in order to remove all non-polarized light.," The basic idea of the DPI is to take the difference of two orthogonally polarized, simultaneously acquired images of the same object in order to remove all non-polarized light." + As the non-polarized light mainly comes from the central star. after subtraction oulv the polarized light. such as the scattered lelt frou the circumstellar material. remains.," As the non-polarized light mainly comes from the central star, after subtraction only the polarized light, such as the scattered light from the circumstellar material, remains." + We obtained polarimetric images with NAC'O through the II filter. using a Wollastou priu with a 2” Wollaston mask to exclude overlapping beams of orthogonal polarization.," We obtained polarimetric images with NACO through the H filter, using a Wollaston prism with a $''$ Wollaston mask to exclude overlapping beams of orthogonal polarization," +"for the photometry, about of the host flux was included.","for the photometry, about of the host flux was included." + We adopted the host galaxy flux densities given by 2mainBodyCitationEnd1523]rai09; these authors also discussed that the host contribution can be considered negligible in the UV., We adopted the host galaxy flux densities given by ; these authors also discussed that the host contribution can be considered negligible in the UV. +" The comparison between the UVOT u, b, and v data and the U, B, and V data taken by the GASP observers reveals that an Offset is present between the space light curves and the ground-based ones."," The comparison between the UVOT $u$ , $b$ , and $v$ data and the $U$, $B$, and $V$ data taken by the GASP observers reveals that an offset is present between the space light curves and the ground-based ones." +" We estimated mean offsets U—u=0.2, B—b=0.1, and V—v=—0.05."," We estimated mean offsets $U-u=0.2$, $B-b=0.1$, and $V-v=-0.05$." + The UVOT light curves shown in refuvir have been shifted accordingly., The UVOT light curves shown in \\ref{uvir} have been shifted accordingly. +" Taking into account that the average UVOT colour indices of BL Lacertae are u—b~—0.4 and b—v~0.8, the above offsets disagree with those derived by for the objects on which they based their photometric calibration of UVOT, PPickles stars and GRB models."," Taking into account that the average UVOT colour indices of BL Lacertae are $u-b \sim -0.4$ and $b-v \sim 0.8$, the above offsets disagree with those derived by for the objects on which they based their photometric calibration of UVOT, Pickles stars and GRB models." +" Indeed, these objects have a different spectral shape, so that the calibrations may not hold for BL Lacertae."," Indeed, these objects have a different spectral shape, so that the calibrations may not hold for BL Lacertae." +" The UVOT data confirm the variability trend traced bythe ground-based ones, extending it to UV frequencies."," The UVOT data confirm the variability trend traced bythe ground-based ones, extending it to UV frequencies." +" This indicates that the variability mechanism affecting the near-IR-optical emission, which is dominated by beamed synchrotron radiation, can also produce flux changes in the UV, where a contribution from the synchrotron emission is thus expected, besides a possible contribution from thermal disc radiation."," This indicates that the variability mechanism affecting the near-IR--optical emission, which is dominated by beamed synchrotron radiation, can also produce flux changes in the UV, where a contribution from the synchrotron emission is thus expected, besides a possible contribution from thermal disc radiation." +" The derivation of the source intrinsic flux densities for further analysis (see refsec,,odel))requiressomeattention.", The derivation of the source intrinsic flux densities for further analysis (see \\ref{sec_model}) ) requires some attention. +"Intheir paperonthephotometriccalib forthev,b,u, uvw1, uvm2, anduvw2 filters, respectively, butwarnthatth of the UV filters will be longer for very red spectra."," In their paper on the photometric calibration of UVOT, give effective wavelengths of 5402, 4329, 3501, 2634, 2231, and 2030 for the $v$, $b$, $u$, $uvw1$, $uvm2$, and $uvw2$ filters, respectively, but warn that the $\lambda_{\rm eff}$ of the UV filters will be longer for very red spectra." +" Moreover, they provide count-rate-to-flux conversion factors forbothPickles stars and GRB models, but in the UV bands their validity range is limited to b—v=0.1 and b—v= 0.03, respectively, while BL Lacertae has b—v~ 0.8."," Moreover, they provide count-rate-to-flux conversion factors forbothPickles stars and GRB models, but in the UV bands their validity range is limited to $b-v=0.1$ and $b-v=0.03$ , respectively, while BL Lacertae has $b-v \sim 0.8$ ." +1988).,. +. For reviews. see Cowan.Thielemann.&Truran(1991): (1997).," For reviews, see \cite{ctt91,wal97}." +. The requisiteconditions for r— process nuceosvnthesis in explosive scenarios wilh material freezing oul Irom nuclear statistical equilibriun (NSE) have been derived with the general understanding that particular combinations of {hree parameters. (he entropy. electron fraction (Y.). and expansion timescale. eive rise to specilic leatures of the solar r—-abundance pattern (Qian&Woosley1996).," The requisiteconditions for $r-$ process nucleosynthesis in explosive scenarios with material freezing out from nuclear statistical equilibrium (NSE) have been derived with the general understanding that particular combinations of three parameters, the entropy, electron fraction $Y_e$ ), and expansion timescale, give rise to specific features of the solar $r-$ abundance pattern \citep{qw96}." +. As the wind evolves these parameters must sweep out a range of conditions that produce (he many features of the solar r—process abundances. particularly the relative heights of the 2nd 3rd peaks (Wooslevοἱal.1994).," As the wind evolves these parameters must sweep out a range of conditions that produce the many features of the solar $r-$ process abundances, particularly the relative heights of the 2nd 3rd peaks \citep{woo94}." +. Recent models of core collapse still fall short of the necessary conditions to explain all the abundance features of the solar r—process. especially the high mass C1>130) component Qian LOOT).," Recent models of core collapse still fall short of the necessary conditions to explain all the abundance features of the solar $r-$ process, especially the high mass $A\ge 130$ ) component \citep{hof97}." + A site that has received recent interest involves explosions of O-Ne-Mg cores in 8—1011. supernovae., A site that has received recent interest involves explosions of O-Ne-Mg cores in $8-10 \Msun$ supernovae. + Successful SN explosions from such svstemis have been (he subject of nuch debate (Wheeler.Cowan.&Hillebrandt|1993).. some efforts Found prompt explosions Nomoto.&Wolff.19894:Nomoto 1984).. others did not (Burrows&Lattimer1985:Baron.Cooperstein.&Lahana 1987).. with the former now being completely ruled out with the advent of modern treatments of neutrino transport.," Successful SN explosions from such systems have been the subject of much debate \citep{wch98}, some efforts found prompt explosions \citep{hnw84, nom84}, others did not \citep{bl85,bck87}, with the former now being completely ruled out with the advent of modern treatments of neutrino transport." + Appeals to late-time neutrino heating have also been suggested (Alavle&WilsonLOSS)., Appeals to late-time neutrino heating have also been suggested \citep{mw88}. + li should be noted that nearly every altempt has used a common progenitor model (Nomoto|1984)., It should be noted that nearly every attempt has used a common progenitor model \citep{nom84}. +. Recent efforts to revive the idea of a low-Y.. low-entropy. scenario lor r—processing have included detailed nucleosvnthesis calculations (Wanajoet.al.2005;2Mever 2007).," Recent efforts to revive the idea of a $Y_e$, low-entropy scenario for $r-$ processing have included detailed nucleosynthesis calculations \citep{wan05,nqm07}." +". In the former case. an unmodified SN model (computed without. neutrino transport) provides a very low explosion energv (Ler,c0.02 D). with modestlv neutron rich conditions (35.,,5,= 0.45) and no r—process."," In the former case, an unmodified SN model (computed without neutrino transport) provides a very low explosion energy $E_{exp}\sim 0.02$ B), with modestly neutron rich conditions $Y_{e,min} = 0.45$ ) and no $r-$ process." + To obtain it (μον artificially increased the shock heating term to obtain Luger explosions (o1 D) and lower electron fractions (0.14 130 are prelerentially associated, appeal to this scenario to help bolster observational suggestions that $r-$ process nuclei with A $\geq$ 130 are preferentially associated +appears that the actual pixelisation process is a major source of additional noise in the source-parameter determination.,appears that the actual pixelisation process is a major source of additional noise in the source-parameter determination. +" For the final test runs, on the effects of ellipticity on the"," For the final test runs, on the effects of ellipticity on the" +sterner test than that advocated by νο et al. (,sterner test than that advocated by Klein et al. ( +1999).,1999). + Lf one accepts the notion of opacity-linited fragmentation. then in nature the Jeans mass should not fall below ~10%AL..," If one accepts the notion of opacity-limited fragmentation, then in nature the Jeans mass should not fall below $\sim +10^{-3} M_\odot$." + Therefore this limited sense — we are also subjecting our code to a sterner test than that set hy nature., Therefore – in this limited sense – we are also subjecting our code to a sterner test than that set by nature. + In the standard simulation there are 600.000. particles from the outset. sullicient to satisfy the Jeans condition without Particle Splitting.," In the standard simulation there are 600,000 particles from the outset, sufficient to satisfy the Jeans condition without Particle Splitting." + In the other two simulations there are only 45.000. particles at the outset. anc the Jeans condition is accommodated by implementing particle splitting. first Nested. Particle Splitting ancl then On-The-Fly Particle Splitting.," In the other two simulations there are only 45,000 particles at the outset, and the Jeans condition is accommodated by implementing particle splitting, first Nested Particle Splitting and then On-The-Fly Particle Splitting." + “Phe Nest« Particle Splitting simulation ends up with 320.000 particles. and the On-The-Fly Particle Splitting simulation ends up with ~ 140.000 particles.," The Nested Particle Splitting simulation ends up with $\sim$ 320,000 particles, and the On-The-Fly Particle Splitting simulation ends up with $\sim$ 140,000 particles." + We follow the suggestion of Truelove ct al. (, We follow the suggestion of Truelove et al. ( +1997. 1998) that numerical results should be compared. not at. precisely the same elapsed time. but instead when the peak density in the computational domain. peakρου. reaches the same value.,"1997, 1998) that numerical results should be compared, not at precisely the same elapsed time, but instead when the peak density in the computational domain, $\rho\pea$, reaches the same value." +" In particular we present results when Ppeak=Perit—5101 ecm and when ppeak2225.LOD ""gem 37. ""Ph"," In particular we present results when $\rho\pea \simeq \rho\cri += 5 \times 10^{-12}$ g $^{-3}$, and when $\rho\pea \simeq 2 \times 10^{-9}$ g $^{-3}$." +eThe reasonpes foror this is that the evolution of a simulation appears to progress slightly more rapidly if the resolution is higher., The reason for this is that the evolution of a simulation appears to progress slightly more rapidly if the resolution is higher. + Phe same ellect was reported bv Truelove et al. (, The same effect was reported by Truelove et al. ( +1997. 1998) for their AAIR. simulations.,"1997, 1998) for their AMR simulations." + The plots are all grev-seale column-density images wough the central. 0.004. pc O.004 pe (SOO AL ον SOO AU) of the computational domain. viewed down the rotation axis.," The plots are all grey-scale column-density images through the central 0.004 pc $\times$ 0.004 pc (800 AU by 800 AU) of the computational domain, viewed down the rotation axis." + Phe calibration of the grev-scale is given in the figure captions., The calibration of the grey-scale is given in the figure captions. + Times are given in terms of the initial freefall time {νι&0.03 Myr., Times are given in terms of the initial freefall time $t\FF \simeq 0.03$ Myr. + 1n Figure 1 we show the results of a simulation of the BB79 test with ος=51077 ο em7. performed using our standard ΟΙ] code with 600.000 constant-mass xuwticles.," In Figure 1 we show the results of a simulation of the BB79 test with $\rho\cri = 5 \times 10^{-12}$ g $^{-3}$, performed using our standard SPH code with 600,000 constant-mass particles." +" This simulation has sullicient. particles to satisfy he Jeans condition throughout the simulation without ""article Splitting.", This simulation has sufficient particles to satisfy the Jeans condition throughout the simulation without Particle Splitting. + We note that our SPII code has been developed: entirely independently of that used by Date Burkert (1997) and differs from that code in several major regards. in particular the integration scheme and the gravity solver.," We note that our SPH code has been developed entirely independently of that used by Bate Burkert (1997) and differs from that code in several major regards, in particular the integration scheme and the gravity solver." + Figuree la shows a Cgrev-scale coblumn-densitv imageoO of the centre of the computational domain at the moment the density in the binary components Pyeak passes Perit. L6. at?=L231/pp.," Figure 1a shows a grey-scale column-density image of the centre of the computational domain at the moment the density in the binary components $\rho\pea$ passes $\rho\cri$, i.e. at $t = 1.237 t\FF$." + Both the binary components and the bar connecting them approximate to filamentary singularities. and there is no sign of bar fragmentation.," Both the binary components and the bar connecting them approximate to filamentary singularities, and there is no sign of bar fragmentation." +" Figure lh shows the same region at the end of the simulation. /=1.245/,í."," Figure 1b shows the same region at the end of the simulation, $t = 1.245 t\FF$." + By this stage the gas in the densest parts. Le. the binary components. has become aciabatie and heated up.," By this stage the gas in the densest parts, i.e. the binary components, has become adiabatic and heated up." + As à result the binary components are approximately circular in. projection., As a result the binary components are approximately circular in projection. + Llowever. the interconnecting bar is still isothermal: it continues to approximate to a filamentary singularity and shows no sign of fragmenting.," However, the interconnecting bar is still isothermal; it continues to approximate to a filamentary singularity and shows no sign of fragmenting." +" Me re-iterate that this simulation extends the isothermal evolution to Pes,=51017 g em7. which is two orders of magnitude higher than the critical density used by IxIein et al. ("," We re-iterate that this simulation extends the isothermal evolution to $\rho\cri = 5 \times 10^{-12}$ g $^{-3}$, which is two orders of magnitude higher than the critical density used by Klein et al. (" +1999).,1999). + Therefore it constitutes a very stern test of the code's validity., Therefore it constitutes a very stern test of the code's validity. + Figure 2 shows the result of a simulation of the DD79 test. again with fest=510P g 7. but now performed with only 45.000 equal-mass particles at the outset.," Figure 2 shows the result of a simulation of the BB79 test, again with $\rho\cri = 5 \times 10^{-12}$ g $^{-3}$, but now performed with only 45,000 equal-mass particles at the outset." +" Nested ""article Splitting is applied after (ya=1244/5. within a evlindrical sub-domain of radius 0.003 pe (600 AU) and wight 0.003 pe (600 AUD."," Nested Particle Splitting is applied after $t_{\rm split} = 1.244 t\FF$, within a cylindrical sub-domain of radius 0.003 pc (600 AU) and height 0.003 pc (600 AU)." + Phe svmmetry axis of the exlinder is aligned. with the rotation axis of the cloud., The symmetry axis of the cylinder is aligned with the rotation axis of the cloud. + Its size is chosen so as to contain all regions which become so dense hat without Particle Splitting they would eventually violate he Jeans Condition. i.e. the final binary components. which jwe an orbit of radius 0.002 pe (400 AL).," Its size is chosen so as to contain all regions which become so dense that without Particle Splitting they would eventually violate the Jeans Condition, i.e. the final binary components, which have an orbit of radius 0.002 pc (400 AU)." + Figures 2a and 2b correspond to times /=1258/44 (when ppeakX Perit) and /—126584 (the encL of 1c simulation. at 72=100 ecm 37).," Figures 2a and 2b correspond to times $t = 1.258 t\FF$ (when $\rho\pea \simeq \rho\cri$ ) and $t = 1.265 t\FF$ (the end of the simulation at $\rho\pea \simeq +2 \times 10^{-9}$ g $^{-3}$ )." + By comparing.: Figs., By comparing Figs. +" 1. and 2.Ppeal we see that the simulation with Nested! ""article Splitting reproduces the crucial features of. the evolution found in the standard high-resolution simulation described in Section S.T."," 1 and 2, we see that the simulation with Nested Particle Splitting reproduces the crucial features of the evolution found in the standard high-resolution simulation described in Section 8.1." + As before. a binary system formis with a bar between the components. and as long as the eas remains isothermal the binary components and the bar evolve towards filaunentary singularities. with no tendency or additional [ragments to condense out of the bar.," As before, a binary system forms with a bar between the components, and as long as the gas remains isothermal the binary components and the bar evolve towards filamentary singularities, with no tendency for additional fragments to condense out of the bar." + There is à small density peak at the centre of the bar in the first rame (28: Peak= Perit): but this quickly disperses. and herefore we do not consider it to be critical.," There is a small density peak at the centre of the bar in the first frame (2a; $\rho\pea \simeq +\rho\cri$ ), but this quickly disperses, and therefore we do not consider it to be critical." + ὃν the end. approximately half the particles have »en split. so there are 320.000 particles in total.," By the end, approximately half the particles have been split, so there are $\sim$ 320,000 particles in total." + The simulation with Nested. Particle Splitting therefore requires ess than half the memory and. approximately of he CPU usec by the standard simulation (with 600.000 xwticles. 88.1).," The simulation with Nested Particle Splitting therefore requires less than half the memory and approximately of the CPU used by the standard simulation (with 600,000 particles, 8.1)." + Finally Fig., Finally Fig. + 3 shows the result of a simulation of the BB79 test. again with peg=5107 ο and again performed. using only 45.000. ccual-mass particles at. the outset. but now with Particle Splitting applied On-The-bly. in response to imminent violation of the Jeans Condition.," 3 shows the result of a simulation of the BB79 test, again with $\rho\cri = 5 \times 10^{-12}$ g $^{-3}$, and again performed using only 45,000 equal-mass particles at the outset, but now with Particle Splitting applied On-The-Fly, in response to imminent violation of the Jeans Condition." + Fies., Figs. +" 3a and 3b correspond to times /—1.259/94 (οι Ppeak= Peri) and |=127054. (he end of the simulation A Peak=3.10 °e em"" a slightly: higher final density than in the other two simulations. sce below)."," 3a and 3b correspond to times $t = 1.259 t\FF$ (when $\rho\pea \simeq \rho\cri$ ) and $t = 1.270 t\FF$ (the end of the simulation at $\rho\pea = 3 \times 10^{-9}$ g $^{-3}$; a slightly higher final density than in the other two simulations, see below)." + Again the simulation reprocluces all the critical features reported by ‘Truclove et al. (, Again the simulation reproduces all the critical features reported by Truelove et al. ( +1998) ancl Wlein et al. (,1998) and Klein et al. ( +1999). in particular no tencdeney for additional [fragments to condense out of the,"1999), in particular no tendency for additional fragments to condense out of the" + zz (Mummaetal.1993)., $\approx$ \citep{Mea93}. +IID 1391323b.,HD 189733b. + Thus. revising the radius of Bakosetal.(2006b) of 1.154 Γης. our new estimate for this value is Rytanct=1.1920.08 A045.," Thus, revising the radius of \citet{2006ApJ...650.1160B} of 1.154 $R_{\rm Jup}$, our new estimate for this value is $R_{\rm planet} = 1.19 \pm 0.08$ $R_{\rm Jup}$." + Furthermore. adopting the value of for the mass of the planet of 1.15 Mj. we derive a new estimate for the density of HID 189733b to be p=0.91£0.18 g .," Furthermore, adopting the value of \citet{2005A&A...444L..15B} for the mass of the planet of 1.15 $M_{\rm Jup}$, we derive a new estimate for the density of HD 189733b to be $\rho = 0.91 \pm 0.18$ g $^{-3}$." + These values are in good agreement with (2007).. who used transit photometry to constrain the stellar ancl planetary radii.," These values are in good agreement with \citet{winn2007}, who used transit photometry to constrain the stellar and planetary radii." + The values ο PIpjaec: 200. Potaner ave all consistent with the modest collection of these parameters presently available for àransiting exoplanet svstemis and support the conclusion that IID 189733 is not among the few hot Jupiters (hat present extraordinarilv large radii for their masses.," The values of $M_{\rm planet}$, $R_{\rm planet}$, and $\rho_{\rm planet}$ are all consistent with the modest collection of these parameters presently available for transiting exoplanet systems and support the conclusion that HD 189733 is not among the few hot Jupiters that present extraordinarily large radii for their masses." + Given the higher resolution of interferometric arrays. a possible close-separation tertiary companion max affect our measures of WD 189733s visibility. and thereby. complicate our interpretation.," Given the higher resolution of interferometric arrays, a possible close-separation tertiary companion may affect our measures of HD 189733's visibility and thereby complicate our interpretation." + As such. it was prudent [or us (to also observe WD 189733 with the Palomar Testbed Interferometer (PTI) (Colavitaetal.1999).. an instrument with intermediate baselines on a variely of skv projections. suitable for exploration of possible unseen nearby luminous (stellar) companions.," As such, it was prudent for us to also observe HD 189733 with the Palomar Testbed Interferometer (PTI) \citep{1999ApJ...510..505C}, an instrument with intermediate baselines on a variety of sky projections, suitable for exploration of possible unseen nearby luminous (stellar) companions." + PTI has been demonstrated to be sensitive to nearby companions with AA«4.0 (Bodenetal.1993).. whieh for a IX2-3. V. primary star rules out any M-ciwarf companions (Bessell&Brett1933)..," PTI has been demonstrated to be sensitive to nearby companions with $\Delta K < 4.0$ \citep{1998ApJ...504L..39B}, which for a K2-3 V primary star rules out any M-dwarf companions \citep{1988PASP..100.1134B}." + PTI observed IID 139733 in the A-band on the nights of 2006 June 10-12. 2006 June 24. and 2006 July 8-10.," PTI observed HD 189733 in the $K$ -band on the nights of 2006 June 10-12, 2006 June 24, and 2006 July 8-10." + Four of those nights used PTUs 85-m NW baseline configuration. two used the 110-m NS baseline. and one night was a 85-m SW baseline night.," Four of those nights used PTI's 85-m NW baseline configuration, two used the 110-m NS baseline, and one night was a 85-m SW baseline night." + For all of these niehts. ILD 189732's normalized V. cata points were indisünguishable from unit visibility. which corresponds (ο a completely unresolved. point source. as would be expected [for a single ~0.37 mas star being observed by PTI at 2.2 jan. Our results for the radii of (he host star and planet in the IID 189733 exoplanet system are lormally in good agreement with existing measurements of these parameters as well as with (he estimate for the density of the planet and have the additional and significant merit (hat (hev represent direc! measurements of stellar aud planetary diameters (hat cdo nol rely upon inferences about stellar atmospheres.," For all of these nights, HD 189733's normalized $V$ data points were indistinguishable from unit visibility, which corresponds to a completely unresolved point source, as would be expected for a single $\sim 0.37$ mas star being observed by PTI at 2.2 $\mu$ m. Our results for the radii of the host star and planet in the HD 189733 exoplanet system are formally in good agreement with existing measurements of these parameters as well as with the estimate for the density of the planet and have the additional and significant merit that they represent $direct$ measurements of stellar and planetary diameters that do not rely upon inferences about stellar atmospheres." + While (he diameter measurements are currently at a level of accuracy. we expect to improve this considerably as we implement," While the diameter measurements are currently at a level of accuracy, we expect to improve this considerably as we implement" +"radius rsoo to calculate L599, while we use the gas particles inside the projected radius rsoo to obtain Tso9.","radius $r_{500}$ to calculate $L_{500}$, while we use the gas particles inside the projected radius $r_{500}$ to obtain $T_{500}$." + Also note that we exclude very cold high-density gas particles with T«3x10K and densities above 500 times the mean baryon density as well as multiphase particles to avoid spurious contributions from the multiphase model for the star-forming gas., Also note that we exclude very cold high-density gas particles with $T \! < 3 \!\times\! 10^4 \rm K$ and densities above 500 times the mean baryon density as well as multiphase particles to avoid spurious contributions from the multiphase model for the star-forming gas. + We focus in this work on how AGN feedback affects the Lx—T relation and the gas mass fractions in clusters., We focus in this work on how AGN feedback affects the $L_{\rm X}-T$ relation and the gas mass fractions in clusters. +" Additional cluster properties and simulations where the feedback energy in the ""radio mode"" is not injected thermally but in the form of cosmic rays etal.2008) will be discussed in a forthcoming companion(Sijacki paper.", Additional cluster properties and simulations where the feedback energy in the “radio mode” is not injected thermally but in the form of cosmic rays \citep{Sijacki2008} will be discussed in a forthcoming companion paper. +" In Figure 1,, we show the ratio of gas mass to total mass inside the radius rsoo as a function of halo X-ray temperature."," In Figure \ref{fig:gas_fractions}, we show the ratio of gas mass to total mass inside the radius $r_{500}$ as a function of halo X–ray temperature." +" For each simulated halo, arrows connect the results obtained without and with AGN heating."," For each simulated halo, arrows connect the results obtained without and with AGN heating." +" For comparison, we show constraints on halo gas fractions obtained from X-ray observations (Vikhlininetal.2006;Sun2008)."," For comparison, we show constraints on halo gas fractions obtained from X–ray observations \citep{Vikhlinin2006,Sun2008}." +. Also shown are gas fractions we computed from the gas density and temperature profile parameters given in Sandersonet (2003).., Also shown are gas fractions we computed from the gas density and temperature profile parameters given in \cite{Sanderson2003}. + The most obvious effect of the AGN feedback is the significantly reduced gas fraction at the low temperature end of our i.e. in clusters and groups.," The most obvious effect of the AGN feedback is the significantly reduced gas fraction at the low temperature end of our sample, i.e. in poor clusters and groups." +" There the AGN heating sample,drives a substantialpoor fraction of the gas to radii outside of rsoo.", There the AGN heating drives a substantial fraction of the gas to radii outside of $r_{500}$. + This lowers halo gas fractions in spite of the reduced fraction of gas that is converted into stars in the runs with AGN., This lowers halo gas fractions in spite of the reduced fraction of gas that is converted into stars in the runs with AGN. +" The potential wells of massive clusters are, on the other hand, too deep for AGN heating to efficiently remove gas from them."," The potential wells of massive clusters are, on the other hand, too deep for AGN heating to efficiently remove gas from them." + Thus the effect of the suppressed star formation becomes more important or even dominant towards more massive systems., Thus the effect of the suppressed star formation becomes more important or even dominant towards more massive systems. +" While the gas fraction in the very inner regions of massive clusters is somewhat reduced by the AGN, we find it unchanged or slightly increased within rso."," While the gas fraction in the very inner regions of massive clusters is somewhat reduced by the AGN, we find it unchanged or slightly increased within $r_{500}$." +" Given that AGN heating removes gas from the centers of poor clusters and groups, it is no surprise that it also suppresses their X-ray luminosities and affects the Lx—T relation."," Given that AGN heating removes gas from the centers of poor clusters and groups, it is no surprise that it also suppresses their X–ray luminosities and affects the $L_{\rm X}-T$ relation." +" In Figure 2,, we plot the X-ray luminosities Lsoo against the spectroscopic temperatures 7599, for all halos of our sample."," In Figure \ref{fig:L_X-T_relation}, we plot the X–ray luminosities $L_{500}$ against the spectroscopic temperatures $T_{500}$, for all halos of our sample." + The arrows indicate the change due to the AGN feedback for each halo., The arrows indicate the change due to the AGN feedback for each halo. + Data from a number of observational X-ray studies is shown for comparison 1998)..," Data from a number of observational X–ray studies is shown for comparison \citep{Horner2001, Helsdon2000, Osmond2004, Arnaud1999, Markevitch1998}. ." +(Majorana) or g=6 (Dirac).,(Majorana) or $g = 6$ (Dirac). + Recent underground experiments have shown that (he mass differences among three species of neutrinos are smaller than 0.05 eV (Shirai2005)., Recent underground experiments have shown that the mass differences among three species of neutrinos are smaller than $0.05$ eV \citep{shirai}. +. Lu order for massive neutrinos {ο have masses greater than 1 eV. (μον must have similar masses (degenerate in mass).," In order for massive neutrinos to have masses greater than 1 eV, they must have similar masses (degenerate in mass)." + The mean number density of relic neutrinos is cosmologically fixed and there is the well known relation for the contribution of the relie neutrinos to ο. where /=1~3 for Majorana neutrinos and ;=1~6 for Dirac neutrinos.," The mean number density of relic neutrinos is cosmologically fixed and there is the well known relation for the contribution of the relic neutrinos to $\Omega$, where $i=1\sim3$ for Majorana neutrinos and $i=1\sim6$ for Dirac neutrinos." +" The maximum allowed neutrino mass can be estimated by setting Q,=0.3 and f=0.7. to be 4.7 or 2.3 eV respectively for Majorana or Dirac neutrinos."," The maximum allowed neutrino mass can be estimated by setting $\Omega_\nu = 0.3$ and $h=0.7$, to be 4.7 or 2.3 eV respectively for Majorana or Dirac neutrinos." + The former gives /=0 or the degenerate mass of LOMA. in 100 kpc. and the latter gives {=2 or that of 5x10!!M. in 300 kpe.," The former gives $f=0$ or the degenerate mass of $10^{14}M_\odot$ in 100 kpc, and the latter gives $f=2$ or that of $5\times10^{14}M_\odot$ in 300 kpc." + These are rather comlortable numbers for this cluster profile., These are rather comfortable numbers for this cluster profile. + If we question the CDM cosmology based on the possible inconsistency of the hieh concentration of the observed mass profile with the CDM predictions mentioned above. we might as well revive massive neutrinos (hot dark matter) as the candidate for the dominant dark matter.," If we question the CDM cosmology based on the possible inconsistency of the high concentration of the observed mass profile with the CDM predictions mentioned above, we might as well revive massive neutrinos (hot dark matter) as the candidate for the dominant dark matter." + In (he previous section. we have studied a possibility Chat fully degenerate fermions forms a huge mass concentration al the center of a cluster of galaxies and we mainly examined the case for massive neutrinos.," In the previous section, we have studied a possibility that fully degenerate fermions forms a huge mass concentration at the center of a cluster of galaxies and we mainly examined the case for massive neutrinos." + Is this possibility really true?, Is this possibility really true? + In order to answer this question. we foeus on the universality and the scalability of FEDES.," In order to answer this question, we focus on the universality and the scalability of FDFS." + We (ry to extend this idea of FDFS to other neutrinos and fermions with different masses., We try to extend this idea of FDFS to other neutrinos and fermions with different masses. + As we have already seen in Eq.(1..31)). {he rest mass of the fermion mostly determines the characteristic mass scale of the structure: more massive fermions form lighter structures.," As we have already seen in \ref{Mfermi}, \ref{Mmax}) ), the rest mass of the fermion mostly determines the characteristic mass scale of the structure; more massive fermions form lighter structures." + The most extreme condensed. structure is a black hole., The most extreme condensed structure is a black hole. + We have already known that (here exist many black holes of several species in (he Universe (Gebhardtetal.2002).., We have already known that there exist many black holes of several species in the Universe \citep{variousBH}. +" Thev are the most familiar stellar mass black holes (M. ). giant black holes al the center of a galaxy (2.10*ΛΙ, ). and the intermediate mass black holes (zz10. )."," They are the most familiar stellar mass black holes $\approx M_{\odot}$ ), giant black holes at the center of a galaxy $\approx 10^{7}M_{\odot }$ ), and the intermediate mass black holes $\approx 10^{3}M_{\odot }$ )." + Although these massive black holes are actively studied. based ou the bottom-up scenarios that they. are formed bv the coalescence of the stellar sized black holes. we (rv to propose vet. another scenario based on (he context of FDES.," Although these massive black holes are actively studied based on the bottom-up scenarios that they are formed by the coalescence of the stellar sized black holes, we try to propose yet another scenario based on the context of FDFS." + The most prominent property of those black holes are that they appear to have a hierarchy in mass range., The most prominent property of those black holes are that they appear to have a hierarchy in mass range. + Most of the black holes are classified in the above three (vpes and (hose in other mass ranges is rare., Most of the black holes are classified in the above three types and those in other mass ranges is rare. + Therelore it would be natural to suspect any definite mechanism to construct such hierarchy from the fundamental level., Therefore it would be natural to suspect any definite mechanism to construct such hierarchy from the fundamental level. +We consider two different cases of photochemical eunchimenut.,We consider two different cases of photochemical enrichment. +" Iu the first case. the CIT, escape from the upper atinosphere of Titan is neglected."," In the first case, the $_4$ escape from the upper atmosphere of Titan is neglected." +" In the second. this escape aud a consequent additional fractionation between CIT;D and CIT, are inehidect."," In the second, this escape and a consequent additional fractionation between $_3$ D and $_4$ are included." + Fiewe 20 sununarizes the results for ceuterimu eunchiment via photodissociation calculated with Eq., Figure \ref{logR_q} summarizes the results for deuterium enrichment via photodissociation calculated with Eq. + 3 assundue that $ = 0. aud shows the initial methane reservoir A (normalized to the present one] against q.," \ref{new_R} assuming that $\Phi$ = 0, and shows the initial methane reservoir $R$ (normalized to the present one) against $q$." +" Three cases of prescut-day οσοπα eurchniueut iu the atinospheric methane of Titan are represented: the solid curve corresponds to the nominal value reported bv Dézzurd (2007) (f = 5.6) aud the dashed curves to the extreme values (f = 157.2) obtained when ""uncertainties are taken iuto account.", Three cases of present-day deuterium enrichment in the atmospheric methane of Titan are represented: the solid curve corresponds to the nominal value reported by Bézzard (2007) $f$ = 5.6) and the dashed curves to the extreme values $f$ = 4.5–7.2) obtained when uncertainties are taken into account. + We assiuune in all our calculations that the D/II ratio iu the methane initially acquired by Titan cing its accretion is protosolar., We assume in all our calculations that the D/H ratio in the methane initially acquired by Titan during its accretion is protosolar. + Note that a smaller value of gq viclds ereater fractionation for a given amount of methane photolysis. because it correspouds to deuterium being more tightly bound (Lunine 1999).," Note that a smaller value of $q$ yields greater fractionation for a given amount of methane photolysis, because it corresponds to deuterium being more tightly bound (Lunine 1999)." + Therefore. for a given deutermuu enrichment. simaller values of 4 allow the initial methane reservoir of Titan to be smaller than in the case required for higher values of 4.," Therefore, for a given deuterium enrichment, smaller values of $q$ allow the initial methane reservoir of Titan to be smaller than in the case required for higher values of $q$." + The two horizontal lines represent values that would be acquired bv R df the actual methane reservoir were to exist since 0.6 or L5 Car ago. respectively (see Eq. 5)).," The two horizontal lines represent values that would be acquired by $R$ if the actual methane reservoir were to exist since 0.6 or 4.5 Gyr ago, respectively (see Eq. \ref{eq_R_2}) )." + Figure 2. shows that the initial reservoir of Titan's atmospheric ucthane was 16 times more massive thui the current one if it was formed 0.6 Car ago. provided that F remained fixed to its current value throughout the existence of this reservoir.," Figure \ref{logR_q} shows that the initial reservoir of Titan's atmospheric methane was $\sim$ 16 times more massive than the current one if it was formed 0.6 Gyr ago, provided that $F$ remained fixed to its current value throughout the existence of this reservoir." + If methane were present in the atmosphere of Titan since 1.5 ανν ago. the initial reservoir Was ~ 126 times more massive than the current one.," If methane were present in the atmosphere of Titan since 4.5 Gyr ago, the initial reservoir was $\sim$ 126 times more massive than the current one." + Table 1 sunuuarizes the deuteriuni eurichineuts via photolysis iu the atmospheric methane caleulated for the adopted lits on plausible values of 4 aud the two different values of r. in the case $ = 0.," Table \ref{res} summarizes the deuterium enrichments via photolysis in the atmospheric methane calculated for the adopted limits on plausible values of $q$ and the two different values of $\tau$, in the case $\Phi$ = 0." + This table shows that. asstuing a protosolar D/II iu the methane originally released into the surfacc-atiuiosphere system. the photochemical curichiment is not efficient enough to allow the atmosphere D/II to reach the observed chrichment. even if the reservoir is postulated o have existed since L5 Cyr.," This table shows that, assuming a protosolar D/H in the methane originally released into the surface-atmosphere system, the photochemical enrichment is not efficient enough to allow the atmospheric D/H to reach the observed enrichment, even if the reservoir is postulated to have existed since 4.5 Gyr." + A hieher D/II ratio hau the protosolar value must be advocated iu the uecthaue of Titan prior its outgassiug. in order to explain he observed curichiment.," A higher D/H ratio than the protosolar value must be advocated in the methane of Titan prior its outgassing, in order to explain the observed enrichment." + Depending ou the adopted value for q. the range of initial deuterimm eurichineuts fo ueceded by the initial methane reservoir to allow xhotolvsis to reach the uominal value of Bézzard (2007) as between 3.2 aud LO for 7 = 0.6 Corr. and vetween 2.2 and 3.2 for 7 = L5 Cor.," Depending on the adopted value for $q$, the range of initial deuterium enrichments $f_{0}$ needed by the initial methane reservoir to allow photolysis to reach the nominal value of Bézzard (2007) is between 3.2 and 4.0 for $\tau$ = 0.6 Gyr, and between 2.2 and 3.2 for $\tau$ = 4.5 Gyr." + Figure 3 shows the results for deuterium curichmicut via photocdissociation calculated with Eq., Figure \ref{logR_q2} shows the results for deuterium enrichment via photodissociation calculated with Eq. + 3 assuming hat @=2:8.1077 7. ὃν and shows R agaist q.," \ref{new_R} assuming that $\Phi = 2.8 \times 10^{13}$ $^{-2}$ $^{-1}$, and shows $R$ against $q$ ." + The two upper left curves have heen determined for f = 5.6 in Eq. 3..," The two upper left curves have been determined for $f$ = 5.6 in Eq. \ref{new_R}," + namely the nominal value reported by Béezzard (2007)., namely the nominal value reported by Bézzard (2007). +" The solid. curve corresponds to he case where uo fractionation occurs between CIL;D and CTL, duriug methane escape. while the dot-dot-dashed curve asstunes there is fractionation."," The solid curve corresponds to the case where no fractionation occurs between $_3$ D and $_4$ during methane escape, while the dot-dot-dashed curve assumes there is fractionation." + A word of caution must be eiven here., A word of caution must be given here. +" We have arbitrarily set the escape rate equal to the CIT, /CIT;D molar ratio { = 16/17) in order to quantify the iufluence of a possible fractionation between these two species.", We have arbitrarily set the escape rate equal to the $_4$ $_3$ D molar ratio $l$ = 16/17) in order to quantify the influence of a possible fractionation between these two species. + This is an order-ofmaguitude estimate because the escape mechanism of iiethaue remains unelear (Yelle 2008)., This is an order-of-magnitude estimate because the escape mechanism of methane remains unclear (Yelle 2008). + As a result. the fractionation may behave dittereuth.," As a result, the fractionation may behave differently." + Figure 3 shows that. despite the higher values of R obtainedwith the methane loss in the upper atinosphere of Titan (Rc 2 for 7 = 0.6 Cir and R ~ 166 for 7 =," Figure \ref{logR_q2} shows that, despite the higher values of $R$ obtainedwith the methane loss in the upper atmosphere of Titan $R$ $\simeq$ 22 for $\tau$ = 0.6 Gyr and $R$ $\simeq$ 166 for $\tau$ =" +communication).,",." +..scale..sources..channel.. Fields A and B were calibrated. with. three. phase-only iterations because the total flux in these fields was too low for amplitude self calibration., Fields A and B were calibrated with three phase-only iterations because the total flux in these fields was too low for amplitude self calibration. + The remaining fields were calibrated with two phase-only iterations and one amplitude/phase iteration., The remaining fields were calibrated with two phase-only iterations and one amplitude/phase iteration. + Each 10 MHz band was self calibrated with a single Jones matrix per All fields were imaged and deconvolved separately., Each 10 MHz band was self calibrated with a single Jones matrix per All fields were imaged and deconvolved separately. + The point spread functions (PSFs) and dirty channel images in all Stokes parameters were created using AIPS++., The point spread functions (PSFs) and dirty channel images in all Stokes parameters were created using AIPS++. + The uv-plane was uniformly weighted., The uv-plane was uniformly weighted. + Because of a fractional bandwidth. of15%.," Because of a fractional bandwidth of,." +.taper.. All maps are in north celestial pole (NCP) projection with the projection centre at (J2000: a=3 19n481601. 6=+41°30'42 106).," All maps are in north celestial pole (NCP) projection with the projection centre at (J2000: $\alpha=3^\mathrm{h}19^\mathrm{m}48\fs1601$ , $\delta= +41\degr30\arcmin42\farcs106$ )." +" The dirty maps have 2048x2048 pixels of 30”x30"" each.reached..baselines.. 84.", The dirty maps have $\times$ 2048 pixels of $30\arcsec\times30\arcsec$ each. +. The size of the mosaic is 45 in declination by 7° in right ascension., The size of the mosaic is $4\fdg5$ in declination by $7\degr$ in right ascension. + Figure 2. shows a full resolution Stokes 7 map of the area., Figure \ref{brentjens_perseusmosaic_fig:imap} shows a full resolution Stokes $I$ map of the area. + It is the average of 143 channels with an average frequency of 351 MHz., It is the average of 143 channels with an average frequency of 351 MHz. + The peak flux is 19.97 Jy beam! at the location of84., The peak flux is 19.97 Jy $^{-1}$ at the location of. +. The actual RMS noise level of the total intensity map rangesfrom 1.5 mJy beam™! in the most western, The actual RMS noise level of the total intensity map rangesfrom 1.5 mJy $^{-1}$ in the most western +where Cáaqgy is the CMB cucrev deusity in the jet frame. modified by the deviation froii the beamed Cluission power from that computed for an isotropic seed photon field.,"where $U'_{\rm CMB}$ is the CMB energy density in the jet frame, modified by the deviation from the beamed emission power from that computed for an isotropic seed photon field." + Equating the two expressions for R (Eqs., Equating the two expressions for R (Eqs. + A21. and À22)). Thus with 1 parameters which depend on the observable data (a. z. D(1). aud R(1)) we can solve eq.," \ref{eq:robs} and \ref{eq:rexp}) ), Thus with 4 parameters which depend on the observable data $\alpha$, z, B(1), and R(1)) we can solve eq." + Πιοσαν by finding the range of j/ó aud D pairs which satisfv the equation., \ref{eq:result} numerically by finding the range of $\mu'$ and $\Gamma$ pairs which satisfy the equation. + If we ignore the second P. term aud replace BY with eq. AT...," If we ignore the second $\Gamma$ term and replace $^{\prime}$ with eq. \ref{eq:b1}," + we obtain an approximate expression for the beanung parameters in terms of the observables (see fig. L)):, we obtain an approximate expression for the beaming parameters in terms of the observables (see fig. \ref{fig:results}) ): + Once we have the allowed values of @;.6. aud P. we need to determine where the eiissiou. bauds occur and which segments of the electron euergy spectruii are responsible for the observed radiation.," Once we have the allowed values of $\theta_{\rm j}, \delta,$ and $\Gamma$, we need to determine where the emission bands occur and which segments of the electron energy spectrum are responsible for the observed radiation." + To determine the IC cussion frequency of olectrous responsible for à particular svuchrotrou frequency: aud the reverse: To find the electron euerev responsible for a particular svuchrotron frequency. we use eqs A3.. AT.. and A20: Foror the electronelect euergve respousibleble ffor au IC frequency| we use eqs| AS aud ALO: For the halflives. we use the normal expression: (4Edt)«7=E/2.," To determine the IC emission frequency of electrons responsible for a particular synchrotron frequency: and the reverse: To find the electron energy responsible for a particular synchrotron frequency, we use eqs \ref{eq:shiftf}, \ref{eq:b1}, , and \ref{eq:fsy}: For the electron energy responsible for an IC frequency we use eqs \ref{eq:shiftf} and \ref{eq:fic}: For the halflives, we use the normal expression: $(dE/dt) \times \tau = E/2$." + This results in: where D is in μα and 7! is in years., This results in: where $B'$ is in $\mu$ G and $\tau'$ is in years. + Making the usual approximations for quantities close to one. aud since time intervals in the jet frame are observed at theEarth as:," Making the usual approximations for quantities close to one, and since time intervals in the jet frame are observed at theEarth as:" +The 21 cm emission line from the hyperfine (ransiüon of neutral hydrogen offers a complementary probe of ionized region topology.,The 21 cm emission line from the hyperfine transition of neutral hydrogen offers a complementary probe of ionized region topology. + Sullicientiv sensitive 21 cm line maps would allow much smaller ionized bubbles to be measured. [for (wo reasons.," Sufficiently sensitive 21 cm line maps would allow much smaller ionized bubbles to be measured, for two reasons." + First. there is no clisereteness in the HII emission. unlike the eenitters. aud so there is no corresponding requirement that an identifiable bubble be large enough to contain multiple sources.," First, there is no discreteness in the HI emission, unlike the emitters, and so there is no corresponding requirement that an identifiable bubble be large enough to contain multiple sources." + Second. (the typical velocity resolution of radio telescopes is a dew kms+.," Second, the typical velocity resolution of radio telescopes is a few $\kms$." + Bubbles whose expansion velocity ΓΗ] is larger than this should be visible to sullidentlv sensitive 21 cm mapping., Bubbles whose expansion velocity $r H$ is larger than this should be visible to sufficiently sensitive 21 cm mapping. + This is much smaller (han (he minimum bubble expansion velocity scale for the (test. which may be estimated as 1.2MpcZ4/z1000[(L+ys]“kms| (see section 3)).," This is much smaller than the minimum bubble expansion velocity scale for the test, which may be estimated as $\sim 1.2\Mpc H \approx 1000 [(1+z)/8]^{3/2} \kms$ (see section \ref{lya_req}) )." + A more fundamental limit to the resolution of 21 em mapping along (he line of sight is set bv the peculiar motions of the IGM., A more fundamental limit to the resolution of 21 cm mapping along the line of sight is set by the peculiar motions of the IGM. + The velocities within ionized gas bubbles are nol relevant. of course. since the emission comes only [rom the neutral regions.," The velocities within ionized gas bubbles are not relevant, of course, since the emission comes only from the neutral regions." + The velocity in the neutral regions is unlikely to be affected by nongravitational phivsies al any level much ereater than ~50kms.|. which is the velocity corresponding to the ionization potential ol hydrogen.," The velocity in the neutral regions is unlikely to be affected by nongravitational physics at any level much greater than $\sim 50 +\kms$, which is the velocity corresponding to the ionization potential of hydrogen." + Gravilationally driven velocities are similarly unlikely to much exeeed tens of kms! outside virialized halos. which coneititute a verv small fraction of barvons at the epoch of reionization.," Gravitationally driven velocities are similarly unlikely to much exceed tens of $\kms$ outside virialized halos, which consititute a very small fraction of baryons at the epoch of reionization." + Thus. 21 em mapping αςld identify bubbles down to at least »50kpc proper size (~0.5Mpec comoving). and probabyv smaller. provided sensitivity aud foreground contamination issues can be overcome.," Thus, 21 cm mapping could identify bubbles down to at least $\sim 50 \kpc$ proper size $\sim 0.5 \Mpc$ comoving), and probably smaller, provided sensitivity and foreground contamination issues can be overcome." + The primary concern in 21 enm reionizalio1 tesis is contamination from foreground radio sources and from [ree-Iree emission in the ionized bubbles al the epoch of reionization., The primary concern in 21 cm reionization tests is contamination from foreground radio sources and from free-free emission in the ionized bubbles at the epoch of reionization. + The best strategy for removing both foregrounds may be mapping in frequency space. because the contaminaling signals vary as featureless power laws on velocity scales up to several thousand lans4.," The best strategy for removing both foregrounds may be mapping in frequency space, because the contaminating signals vary as featureless power laws on velocity scales up to several thousand $\kms$." + Still. the foregrounds are dramatically brighter than the reionization signals. and exquisite foreground subtraction is needed.," Still, the foregrounds are dramatically brighter than the reionization signals, and exquisite foreground subtraction is needed." + Current 216m experiments (e.g.. LOFAR |Falcke et al 2006]. the Mileura. Widelfield. Array |[MWA: Morales et al 2006]. and the Primeval Structure Telescope [PAST: Peterson. Pen. Wu 2005]) ave all aiming first [or statistical detections of the 21em reionizatüion signature. with bubble mapping a possible future step onlv if radio interference and astronomical loregrounds prove sufficiently tractable.," Current 21cm experiments (e.g., LOFAR [Falcke et al 2006], the Mileura Widefield Array [MWA; Morales et al 2006], and the Primeval Structure Telescope [PAST; Peterson, Pen, Wu 2005]) are all aiming first for statistical detections of the 21cm reionization signature, with bubble mapping a possible future step only if radio interference and astronomical foregrounds prove sufficiently tractable." + The overlap phase of reionization can be defined topologically and sought using a, The overlap phase of reionization can be defined topologically and sought using a +are Indeed still not well settled.,are indeed still not well settled. + We therefore model the VHE emission assuming the afterglow could be described in the context of the standard afterglow model (Piran1999;Zhang 2007).," We therefore model the VHE emission assuming the afterglow could be described in the context of the standard afterglow model \citep{Pir99,Zha07}." + Finally. we comment possible modifications induced by additional phenomena which in general can even increase the expected VHE flux.," Finally, we comment possible modifications induced by additional phenomena which in general can even increase the expected VHE flux." +" In order to characterize the afterglow spectrum we must compute the synchrotron injection. v4. and cooling. νο, frequency values."," In order to characterize the afterglow spectrum we must compute the synchrotron injection, $\nu_{\rm m}$ , and cooling, $\nu_{\rm c}$, frequency values." + The injection frequency is where most of the synchrotron emission occurs and the cooling frequency identifies where electrons cool effectively., The injection frequency is where most of the synchrotron emission occurs and the cooling frequency identifies where electrons cool effectively. +" In case of constant circumburst medium (Yostetal.2003:Fan&Piran2006) we have: and wherez is the redshift of the source. 7 the medium particle density. £j the kinetic energy of the outflow. f the time delay after the GRB and C,=13(p-2)/[3(p-D]."," In case of constant circumburst medium \citep{Yos03,FaPi06} we have: and where $z$ is the redshift of the source, $n$ the medium particle density, $E_{\rm k}$ the kinetic energy of the outflow, $t$ the time delay after the GRB and $C_p = 13(p-2)/\left[3(p-1)\right]$." + We will assume for the micro-physical parameters €. the fraction of total energy going to electrons. and ep. the fraction of total energy going to magnetic fields. the values of 0.1 and 0.01. respectively.," We will assume for the micro-physical parameters $\epsilon_{\rm e}$, the fraction of total energy going to electrons, and $\epsilon_{\rm B}$, the fraction of total energy going to magnetic fields, the values of $0.1$ and $0.01$, respectively." + These figures are typical values measured during late-time afterglows (seee.g.Panaitescu&Kumar2002:Yostetal.2003) and in agreement with the results of the analysis of 0080430.," These figures are typical values measured during late-time afterglows \citep[see e.g.][]{PaKu02,Yos03} and in agreement with the results of the analysis of 080430." + The relation for the cooling frequency is approximate since we are neglecting the possible role played by additional inverse Compton (IC) cooling., The relation for the cooling frequency is approximate since we are neglecting the possible role played by additional inverse Compton (IC) cooling. + We will consider this issue again in refsec:ssc.., We will consider this issue again in \\ref{sec:ssc}. + The total energy can be derived from the burst isotropic energy Ei; with some assumptions about the spectrum and by correcting it for the fireball radiative efficiency 7., The total energy can be derived from the burst isotropic energy $_{\rm iso}$ with some assumptions about the spectrum and by correcting it for the fireball radiative efficiency $\eta$. +" We estimate E;,, as the integral of the burst spectral model (Stamatikosetal.2008) in the 1—107 kkeV band (Amatietal.2002).. the energy range covering most of the prompt emission of GRBs."," We estimate $_{\rm iso}$ as the integral of the burst spectral model \citep{Stam08} in the $1 - 10^4$ keV band \citep{Ama02}, the energy range covering most of the prompt emission of GRBs." + In this energy band the spectrum of a burst is typically described by a Band function (Bandetal.1993): In ordeir to calculate the integral we need to know the two power-law photon indices a and fg and the peak energy Εως=(2+ a)£Ey., In this energy band the spectrum of a burst is typically described by a Band function \citep{Band93}: In order to calculate the integral we need to know the two power-law photon indices $\alpha$ and $\beta$ and the peak energy $_{\rm peak} = (2+\alpha)E_0$ . + Unfortunately. the Siwiff--BAT energy range is often too narrow for a direct Έρις measurement.," Unfortunately, the -BAT energy range is often too narrow for a direct $_{\rm peak}$ measurement." +" We therefore run a set of integrations by varying Έρις and derive the corresponding E;,, using the 15—150 kkeV BAT fluence to normalize the spectrum.", We therefore run a set of integrations by varying $_{\rm peak}$ and derive the corresponding $_{\rm iso}$ using the $15 - 150$ keV BAT fluence to normalize the spectrum. + In each integration. depending on the value of Έρως. we identify the observed photon index with one of the two indices of the Band function. fixing the other one to a canonical value (1 and 2.3 for the low- and the high- power-laws. respectively).," In each integration, depending on the value of $_{\rm peak}$, we identify the observed photon index with one of the two indices of the Band function, fixing the other one to a canonical value (1 and 2.3 for the low- and the high-energy power-laws, respectively)." +" The chosen values of Eja, and Ej. are those satisfying the Amati relation (Amatietal. 2002).", The chosen values of $_{\rm peak}$ and $_{\rm iso}$ are those satisfying the Amati relation \citep{Ama02}. +". According to this method. we estimate Ej;4,=39 kkeV. and Ei,=3»IO?! eerg."," According to this method, we estimate $_{\rm peak} = 39$ keV, and $_{\rm iso} = 3 \times 10^{51}$ erg." + The errors are estimated to be about for both quantities mainly due to the lack of observational data better constraining the prompt emission spectrum., The errors are estimated to be about for both quantities mainly due to the lack of observational data better constraining the prompt emission spectrum. + Peak energies for GRBs can also be estimated following a correlation between peak energy and spectral parameters as measured by Swifr--BAT instrument (Sakamotoetal.2009) yielding. consistent results with our analysis., Peak energies for GRBs can also be estimated following a correlation between peak energy and spectral parameters as measured by -BAT instrument \citep{Sak09} yielding consistent results with our analysis. + The derived total energy is typical for cosmological GRBs. although it is common to observe events substantially more energetic (Sakamotoetal.2008).," The derived total energy is typical for cosmological GRBs, although it is common to observe events substantially more energetic \citep{Sak08}." +. The relatively low estimated peak energy can allow one to classify this event as X-Ray Flash or X-Ray Rich (Zhang2007.andreferencestherein).., The relatively low estimated peak energy can allow one to classify this event as X-Ray Flash or X-Ray Rich \citep[][and references therein]{Zha07}. +" If we then assume a radiative efficiency 77 of10%.. we find the total kinetic energy going to the outflow Eji,=3»I0 eerg."," If we then assume a radiative efficiency $\eta$ of, we find the total kinetic energy going to the outflow $_{\rm k, iso} = 3 \times 10^{52}$ erg." + The radiative efficiency during the prompt emission phase can vary among individual bursts (Zhangetal...2007)., The radiative efficiency during the prompt emission phase can vary among individual bursts \citep{Zhaet07}. +.. A satisfactory treatment of the prompt emission phase emission process is still lacking., A satisfactory treatment of the prompt emission phase emission process is still lacking. + We choose as a conservative limit recalling it can be higher for events characterized by a shallow decay phase (Nouseketal.2006) in the X-rays as it might be the case for 0080430., We choose as a conservative limit recalling it can be higher for events characterized by a shallow decay phase \citep{Nou06} in the X-rays as it might be the case for 080430. +" Summing up. for modeling the high energy emission of the afterglow. we have applied these parameters: energy Eyicox10* eerg. e.~0.1. eg0.01. p-2.1. the circumburst medium density profile 2~1 cem""? and the redshift z~0.76."," Summing up, for modeling the high energy emission of the afterglow, we have applied these parameters: energy $_{\rm k, iso} \sim 3 \times 10^{52}$ erg, $\epsilon_{\rm e} \sim 0.1$, $\epsilon_{\rm B} \sim 0.01$, $p \sim 2.1$, the circumburst medium density profile $n \sim 1$ $^{-3}$ and the redshift $z \sim 0.76$." + Our observation was at ¢~8 kksec after the burst onset., Our observation was at $t \sim 8$ ksec after the burst onset. +" At this epoch we have vy,2.1«10""? HHz and v,~8.8x10 HHz.", At this epoch we have $\nu_{\rm m} \sim 2.1 \times 10^{12}$ Hz and $\nu_{\rm c} \sim 8.8 \times 10^{15}$ Hz. +" The afterglow synchrotron emission is in the so called ""slow-cooling"" regime (1.8. the synchrotron cooling frequency is above the synchrotron injection frequency) as confirmed by the modeling of the Spectral Energy Distribution (SED) from optical to X-rays (DEUGIO) and usually expected at the epoch of the observations for typical afterglows (Zhang&Mészáros 2004)."," The afterglow synchrotron emission is in the so called ""slow-cooling"" regime (i.e. the synchrotron cooling frequency is above the synchrotron injection frequency) as confirmed by the modeling of the Spectral Energy Distribution (SED) from optical to X-rays (DEUG10) and usually expected at the epoch of the observations for typical afterglows \citep{ZhMe04}." + The analysis of the high-energy emission from the various phases of a GRB has been considered by many authors as a powerful diagnostic tool of GRB physics (Dermer&FryerXueetal.2009:Gilmore2009b:Murase 2009).," The analysis of the high-energy emission from the various phases of a GRB has been considered by many authors as a powerful diagnostic tool of GRB physics \citep{DeFr08,GaPi08,FaPi08,Pan08,Aha08,Falc08,Cov09,LeDe09,KuBD09,Fan09,Xue09,Gilm09,Mur09}." + In the present case. the most important emission process to consider is essentially the Synchrotron-Self Compton (SSC)," In the present case, the most important emission process to consider is essentially the Synchrotron-Self Compton (SSC)." + Due to the long delay between the MAGIC observations anc the GRB onset (about two hours) any residual prompt emisstor can be ruled out., Due to the long delay between the MAGIC observations and the GRB onset (about two hours) any residual prompt emission can be ruled out. + Superposed to the SSC component. External InverseCompton (EIC) processes could also play a role anc will be briefly mentioned later.," Superposed to the SSC component, External InverseCompton (EIC) processes could also play a role and will be briefly mentioned later." + We do not consider here hadronicmodels (Bóttceher&Dermer1998;Pe'erWaxmar in our discussion.," We do not consider here hadronicmodels \citep{BoDe98,PeWa05} in our discussion." + They could. however. be of special interest if GRBs are important sources of cosmic-rays.," They could, however, be of special interest if GRBs are important sources of cosmic-rays." +" Once the parameters of the lower-energy synchrotror emission are known. it is possible to predict the SSC component with good reliability,"," Once the parameters of the lower-energy synchrotron emission are known, it is possible to predict the SSC component with good reliability." + Among the many possible, Among the many possible + lauy edge-on disk gaaxies show integral-sigu warps. where the majority of the disk is planar but where the outer regio1 of the disk lies above the plane on oue side of the galaxy. aud. below the ylane ou the other (e.e. Binney 1992).,"t} Many edge-on disk galaxies show integral-sign warps, where the majority of the disk is planar but where the outer region of the disk lies above the plane on one side of the galaxy and below the plane on the other (e.g. Binney 1992)." + Most exteuded HI disks appear war;»ed (e.g. Briggs 1990) aud hall of all disk gaaxies have optical warps (Reshetuikov Combes 1905)., Most extended HI disks appear warped (e.g. Briggs 1990) and half of all disk galaxies have optical warps (Reshetnikov Combes 1998). + Various imetlods lave been pro2056 for creating and imalntaiuin:e warps. such as normal jendiug modes (e.g. Sparke Caserauo 1985) aud disks askew in flatteled dark matter ha (Tootwe 1983: Dekel Shlosinan 1983).," Various methods have been proposed for creating and maintaining warps, such as normal bending modes (e.g. Sparke Casertano 1988) and disks askew in flattened dark matter halos (Toomre 1983; Dekel Shlosman 1983)." + Motivated by the idea that iualliug material will al he «lirection of the aeular momentiu of a galaxy. (C)uinu& Diuney 1902). Ost‘iker Biuney (1989) studied the reaction of massive ‘ines to a slewing cli: yoleLtial.," Motivated by the idea that infalling material will alter the direction of the angular momentum of a galaxy (Quinn Binney 1992), Ostriker Binney (1989) studied the reaction of massive rings to a slewing disk potential." + They [oui that warps occrrec in regions o low surface densiy., They found that warps occurred in regions of low surface density. + Also motivated by the costc iufall of anguar monendum. Debattista Selwood (1999) [ound that when tlie augu nonmelntao ‘a halo aid disk are misaligued. dsyuamical friction between tjem can produce a warp," Also motivated by the cosmic infall of angular momentum, Debattista Sellwood (1999) found that when the angular momenta of a halo and disk are misaligned, dynamical friction between them can produce a warp." + h a cosmological setting. a galacic disk is expected to continuously experience tidal torees roni a variety of sotrces. the three more important j)eing the distribuion of mass in the local envioinuent of a gal:xy. substclive in the dark matter halo such as dwarf satellites aud bieh velocity clouds (HVCs). aud a uisalienuent between he disk angular momentum aud the figure axes of the dark matter halo.," In a cosmological setting, a galactic disk is expected to continuously experience tidal torques from a variety of sources, the three more important being the distribution of mass in the local environment of a galaxy, substructure in the dark matter halo such as dwarf satellites and high velocity clouds (HVCs), and a misalignment between the disk angular momentum and the figure axes of the dark matter halo." + h thisS paper. we Use ¢'osmological N-body simulatious to deduce what graviational tidal torques a typical galaxy expejeuces froin these tliree sources. aud study whether these torques provide a yossible origin for warped clisks.," In this paper, we use cosmological N-body simulations to deduce what gravitational tidal torques a typical galaxy experiences from these three sources, and study whether these torques provide a possible origin for warped disks." +Returning to our development of (5). for these axisvnunietric fields we will consider here. it is convenient to decompose D into toroidal ancl poloidal components Equation (5) then vields where We note then that if the field is initially purely toroical it will remain so. whereas if it is initially purely poloicdal it will immediately induce a toroidal part as well. and once both components are present cach will act back on the other.,"Returning to our development of (5), for these axisymmetric fields we will consider here, it is convenient to decompose $\bf B$ into toroidal and poloidal components Equation (5) then yields where We note then that if the field is initially purely toroidal it will remain so, whereas if it is initially purely poloidal it will immediately induce a toroidal part as well, and once both components are present each will act back on the other." + ‘Taking the region exterior to the star to be a source-Lree vacuum. the outer boundary. conditions are simply where / is the spherical. harmonic. degree.," Taking the region exterior to the star to be a source-free vacuum, the outer boundary conditions are simply where $l$ is the spherical harmonic degree." + Since the numerical solution already involves decomposition of st and D into Legendre functions. implementing this /-dependent boundary condition presents no dilliculties.," Since the numerical solution already involves decomposition of $A$ and $B$ into Legendre functions, implementing this $l$ -dependent boundary condition presents no difficulties." + The inner boundary conditions are not quite so straightforward. and depend very much on what assumptions we make about the interior of the star. about which little is known for certain.," The inner boundary conditions are not quite so straightforward, and depend very much on what assumptions we make about the interior of the star, about which little is known for certain." + However. one common assumption BBhattacharva Datta 1996: Ixonenkov Geppert 2001) is that it is superconducting. in which case the magnetic field will be expelled. from it.," However, one common assumption Bhattacharya Datta 1996; Konenkov Geppert 2001) is that it is superconducting, in which case the magnetic field will be expelled from it." + The boundary conditions are then that the normal component of the magnetic field and the tangential components of the associated. electric field must. vanish., The boundary conditions are then that the normal component of the magnetic field and the tangential components of the associated electric field must vanish. +" D,=0 immediately vields 44=0. but £,=0 is a little more complicated. ancl requires a little algebra before vielding Such a nonlinear boundary condition is unfortunately very dillieult. to. implement."," $B_r=0$ immediately yields $A=0$, but $E_t=0$ is a little more complicated, and requires a little algebra before yielding Such a nonlinear boundary condition is unfortunately very difficult to implement." + We would therefore. like to simplify it in some wav., We would therefore like to simplify it in some way. + We do so bv noting that in the relevant Ry1 limit the second term ought to be negligible (assuming OB/Or does not increase with fy. that is. assuming that no boundary. lavers develop). in. which case we are left. with just £2=0.," We do so by noting that in the relevant $R_B\gg1$ limit the second term ought to be negligible (assuming $\partial B/\partial r$ does not increase with $R_B$, that is, assuming that no boundary layers develop), in which case we are left with just $B=0$." +" For our inner boundary conditions we therefore take The radi at which we will apply these boundary conditions are r;=0.75 and r,=1.", For our inner boundary conditions we therefore take The radii at which we will apply these boundary conditions are $r_i=0.75$ and $r_o=1$. +" Although this is still not quite as thin as neutron star crusts are believec to be (ri£r,80.9 would be more appropriate). it shoul be enough to capture most of the geometrical cllects of having a thin shell. but without. experiencing. numerica clilficulties due to too extreme a disparity between the raclia and [atitudinal lengthscales."," Although this is still not quite as thin as neutron star crusts are believed to be $r_i/r_o \approx 0.9$ would be more appropriate), it should be enough to capture most of the geometrical effects of having a thin shell, but without experiencing numerical difficulties due to too extreme a disparity between the radial and latitudinal lengthscales." + Finally. a few runs were also done with insulating boundaries inside as well as outside.," Finally, a few runs were also done with insulating boundaries inside as well as outside." + This is obviously no realistic. but allows one to assess the extent to which the solutions are allected by dillering boundary. conditions.," This is obviously not realistic, but allows one to assess the extent to which the solutions are affected by differing boundary conditions." + | turned out that while this certainly altered the quantitative details. the general features remained the same.," It turned out that while this certainly altered the quantitative details, the general features remained the same." + In many problems the specific initial conditions are largely irrelevant. as one is only interested in the final. equilibrated solutions.," In many problems the specific initial conditions are largely irrelevant, as one is only interested in the final, equilibrated solutions." +" In this case though. the only ""equilibrated solution is B=0. since (as noted above. and as we will show below). all solutions of (5) necessarily decay in time."," In this case though, the only `equilibrated' solution is ${\bf B}=0$, since (as noted above, and as we will show below), all solutions of (5) necessarily decay in time." + So. what we are interested in instead is to start with some xwiicular initial condition. and study the precise manner of the decay. whether it is significantly faster than just Ohmic decay. whether higher harmonies are excited in the »ocess. ete.," So, what we are interested in instead is to start with some particular initial condition, and study the precise manner of the decay, whether it is significantly faster than just Ohmic decay, whether higher harmonics are excited in the process, etc." + In this problem therefore we need to give careful consideration to our choice of initial conditions., In this problem therefore we need to give careful consideration to our choice of initial conditions. + Η we temporarily neglect the Hall terms in equations (12) and (13). we can solve for the individual free decay modes.," If we temporarily neglect the Hall terms in equations (12) and (13), we can solve for the individual free decay modes." + Figure 1 shows the lowest /=1 and /=2poloidal modes. and also the lowest /=2 toroidal mode.," Figure 1 shows the lowest $l=1$ and $l=2$poloidal modes, and also the lowest $l=2$ toroidal mode." +" The free decay rates for these three modes are 4041.. 6Ry. and 16642,."," The free decay rates for these three modes are $49R_B^{-1}$, $61R_B^{-1}$, and $166R_B^{-1}$." +" We label them B,.. D,». and Bye. and normalize them so that 2.0.0)=1 for the poloidal modes. and Das=1 for the toroidal mode."," We label them ${\bf B}_{p1}$, ${\bf B}_{p2}$, and ${\bf B}_{t2}$, and normalize them so that $B_r(r_o,0)=1$ for the poloidal modes, and $B_{\rm max}=1$ for the toroidal mode." + Our initial conditions will then consist of either these modes in isolation. or else simple linear combinations of them.," Our initial conditions will then consist of either these modes in isolation, or else simple linear combinations of them." + At this point it is worthwhile also to briefly consider some of thesvmmetries associated with (12) and (13). to avoid doing clleetively duplicate runs.," At this point it is worthwhile also to briefly consider some of thesymmetries associated with (12) and (13), to avoid doing effectively duplicate runs." + For example. (5) is clearly not invariant under B DB. so do we need to consider Ίο.," For example, (5) is clearly not invariant under ${\bf B}\rightarrow-{\bf B}$ , so do we need to consider $\pm{\bf B}_{p1}$ ," +star forming clouds and the remaining 464 clouds as non-massive star forming clouds.,star forming clouds and the remaining 464 clouds as non-massive star forming clouds. +" In reffig:cloud, ropertieswepresentnormalisedhistogramsandcumulativedi stribution -function( massivestar formingclouds(grey).", In \\ref{fig:cloud_properties} we present normalised histograms and cumulative distribution function (CDF) plots for a number of physical parameters for both the massive star forming clouds (red) and the non-massive star forming clouds (grey). +T hesehistogramsandC DFplotsclearlyillukgrat the signifi , These histograms and CDF plots clearly illustrate the significant differences between the two samples of clouds. +We used Kolmorgorov-Smirnov (K-S) tests to evaluate the significance of the parametric differences between the two cloud samples., We used Kolmorgorov-Smirnov (K-S) tests to evaluate the significance of the parametric differences between the two cloud samples. + We are able to reject the null hypothesis that the two population are drawn from the same parent population with confidence values above 3c for all of the parameters mentioned in the previous paragraph., We are able to reject the null hypothesis that the two population are drawn from the same parent population with confidence values above $\sigma$ for all of the parameters mentioned in the previous paragraph. + The only parameter that is not significantly different between the two cloud samples is the optical depth (7)., The only parameter that is not significantly different between the two cloud samples is the optical depth $\tau$ ). +" In Table ?? we present a summary of the averages, minimum and maximum values and the result of Kolmorgorov-Smirnov (K-S) tests comparing the massive star forming and non-massive star forming clouds."," In Table \ref{tbl:cloud_comparions} we present a summary of the averages, minimum and maximum values and the result of Kolmorgorov-Smirnov (K-S) tests comparing the massive star forming and non-massive star forming clouds." +" The clouds associated with massive star formations are in generally larger, more massive and, perhaps not suprisingly, are found to have significantly higher column densities."," The clouds associated with massive star formations are in generally larger, more massive and, perhaps not suprisingly, are found to have significantly higher column densities." +" Furthermore, the massive star forming clouds are warmer and more turbulent as indicated by the higher excitation temperatures and larger velocity dispersion than found towards the non-massive star forming clouds."," Furthermore, the massive star forming clouds are warmer and more turbulent as indicated by the higher excitation temperatures and larger velocity dispersion than found towards the non-massive star forming clouds." + The only parameter that is not significantly different between the two cloud samples is the optical depth (7)., The only parameter that is not significantly different between the two cloud samples is the optical depth $\tau$ ). + In this section we will use the distance and luminosity results obtained previously to investigate the spatial distribution of massive stars in the Galaxy., In this section we will use the distance and luminosity results obtained previously to investigate the spatial distribution of massive stars in the Galaxy. + Regions of massive star formation are almost exclusively found to be associated with the spiral arms where molecular clouds are thought to form (?))., Regions of massive star formation are almost exclusively found to be associated with the spiral arms where molecular clouds are thought to form \citealt{kennicutt2005}) ). +" The Galactic distribution of massive young stars is, therefore, an important probe of Galactic structure."," The Galactic distribution of massive young stars is, therefore, an important probe of Galactic structure." + In reffig:galjistwepresenttwoplotsshowingtheGalacticdistributiono f fythan eadingvedper, In \\ref{fig:gal_dist} we present two plots showing the Galactic distribution of our complete sample of young massive stars. +" off f RMS sources(Lgo, 104 Isun)) are indicated by filled red circles, the sizes of which provides an indication of their bolometric luminosities."," In both plots the positions of the RMS sources $L_{\rm{Bol.}}\geq$ $^4$ ) are indicated by filled red circles, the sizes of which provides an indication of their bolometric luminosities." + For RMS sources that have been associated with a molecular cloud we have assumed the RMS source distance is the same as its host cloud., For RMS sources that have been associated with a molecular cloud we have assumed the RMS source distance is the same as its host cloud. + Using the systemic velocity of the cloud smooths out localised velocity perturbations that might lead to larger scatter in the distances., Using the systemic velocity of the cloud smooths out localised velocity perturbations that might lead to larger scatter in the distances. +" Distances for the high latitude sources (i.e., |b]> 1°) have been taken from ?.."," Distances for the high latitude sources (i.e., $|b|> 1\degr$ ) have been taken from \cite{urquhart_13co_north}." + The left panel of this figure simply presents the positions of the sample without the addition of Galactic features to lead the eye., The left panel of this figure simply presents the positions of the sample without the addition of Galactic features to lead the eye. +" Examining the distribution shown in this plot there are no immediately obvious structures, however, one can begin to see structures that suggest the presence of spiral arms between the locus of tangent points and the solar circle."," Examining the distribution shown in this plot there are no immediately obvious structures, however, one can begin to see structures that suggest the presence of spiral arms between the locus of tangent points and the solar circle." +" In the right panel of reffig:gal,istweplotthe positionso f theRMS sourcesoveranimageo lak ftheGatuasgmodstaeslabéunkwor eG riihim plitationwithRobertBe Whitewater).", In the right panel of \\ref{fig:gal_dist} we plot the positions of the RMS sources over an image of the Galaxy produced by Robert Hurt of the Spitzer Science Center in consultation with Robert Benjamin (University of Wisconsin-Whitewater). +"T hisimageattemptstosynthesiseallthathasbeenlearntaboutGAdariycseygalgréuver hgynfirdüt a3.1 kkpcGalacticBaratanangleof wwithrespecttotheGalacticCentre— sunaxis(???)), asecondnon axisymmetricstructureref erredtoasthe* LongBar"" (?))withaGalacticradithwFadg-Barkkpe at an angle of +10° citepbenjamin2005,, the Near and Far 3-kpc arms, and the four principle arms: Norma, Sagittarius, Perseus and Scutum-Centaurus."," This image attempts to synthesise all that has been learnt about Galactic structure over the past fifty years including: a kpc Galactic Bar at an angle of with respect to the Galactic Centre-sun axis \citealt{binney1991,blitz1991,dwek1995}) ), a second non-axisymmetric structure referred to as the “Long Bar” \citealt{hammersley2000}) ) with a Galactic radius of $4.4\pm0.5$ kpc at an angle of $\pm 10$ \\citep{benjamin2005}, the Near and Far 3-kpc arms, and the four principle arms: Norma, Sagittarius, Perseus and Scutum-Centaurus." +" The position of the arms is based on the ? model which has been modified to incorporate Very Long Baseline Array maser parallax measurements (e.g., ?)) and refined directions for the spiral arm tangents from ?.."," The position of the arms is based on the \citet{georgelin1976} model which has been modified to incorporate Very Long Baseline Array maser parallax measurements (e.g., \citealt{xu2006}) ) and refined directions for the spiral arm tangents from \citet{dame2001}." + The Perseus and Scutum-Centaurus arms have been emphasised in this image to reflect the overdensities seen in the old stellar disk population towards their expected Galactic longitudes tangent positions (??)..," The Perseus and Scutum-Centaurus arms have been emphasised in this image to reflect the overdensities seen in the old stellar disk population towards their expected Galactic longitudes tangent positions \citep{benjamin2008,churchwell2009}." +" Comparing the distribution of our sample of young massive stars with the arms shown in the right panel of reffig:gal,istrevealsthemtobestronglycorrelated.", Comparing the distribution of our sample of young massive stars with the arms shown in the right panel of \\ref{fig:gal_dist} reveals them to be strongly correlated. +T hehighestdensityo fmassivestarsis Centaurusarm., The highest density of massive stars is coincident with the end of the Galactic bar and the proposed location of the start of the Scutum-Centaurus arm. +T hehighconcentrationo f youngmassivestarstoward stheendo fthebara luminosity; see ? for more details)., The high concentration of young massive stars towards the end of the bar also correlates with the strongest peak in the gas mass distribution (as traced by the $^{13}$ CO luminosity; see \citealt{roman2009} for more details). +" Both distributions peak ourcorappeoxsmajelo tiboothor] tdiinsposit&teeyl te the direction of rotation, and tailing off behind the bar."," Both distributions peak approximately at the leading edge of the bar, falling off steeply in the direction of rotation, and tailing off behind the bar." + This high density of massive stars is also coincident with the co-rotation radius (~4.5 kkpc)., This high density of massive stars is also coincident with the co-rotation radius $\sim$ kpc). + It is therefore unclear whether the high density of massive stars is the result of dynamical interaction between the bar and the spiral arms or co-rotation., It is therefore unclear whether the high density of massive stars is the result of dynamical interaction between the bar and the spiral arms or co-rotation. +" We also note the correlation between the massive young stars and the Sagittarius and Perseus arms, this is particularly strong towards the Perseus arm."," We also note the correlation between the massive young stars and the Sagittarius and Perseus arms, this is particularly strong towards the Perseus arm." +" We note that the correlation of RMS sources with the far section of the Sagittarius arm is not as strong as seen towards the near section, with a number of sources lying between the Sagittarius and Perseus arms in the model."," We note that the correlation of RMS sources with the far section of the Sagittarius arm is not as strong as seen towards the near section, with a number of sources lying between the Sagittarius and Perseus arms in the model." + This may suggest that the model needs small adjustments or that we have a small systematic error in these sources., This may suggest that the model needs small adjustments or that we have a small systematic error in these sources. +" Comparing the position of the tangent-circle sources and the far kkpc arm we see correlation between them, which suggests they are associated."," Comparing the position of the tangent-circle sources and the far kpc arm we see correlation between them, which suggests they are associated." +" In reffig:gal,gcgistweshowthesourcedensityperkpc? of young pith&Sabitter’s", In \\ref{fig:gal_rgc_dist} we show the source density per $^{-2}$ of young massive stars as a function of Galactocentric radius. +"inelppliagimatelyntewc 4, 6 and kkpc."," This plot clearly reveals three significant peaks at approximately 4, 6 and kpc." +" Inspection of the spatial poaksdistribution plot 9) shows that the strongest peak at kkpc coincides with the intersection of the Scutum-Centaurus arm, and that the second and third peaks are at the Galactocentric radii of the Sagittarius and Perseus arms, respectively."," Inspection of the spatial distribution plot 9) shows that the strongest peak at kpc coincides with the intersection of the Long Bar and the Scutum-Centaurus arm, and that the second and third peaks are at the Galactocentric radii of the Sagittarius and Perseus arms, respectively." + The distribution with Galactocentric radius is only dependent on the Galactic rotation curve and not on the solution of near-far ambiguity., The distribution with Galactocentric radius is only dependent on the Galactic rotation curve and not on the solution of near-far ambiguity. +" Therefore, the correlation"," Therefore, the correlation" +probing overdense structures for which the gas temperature has little dependence on redshift or distance from the source.,probing overdense structures for which the gas temperature has little dependence on redshift or distance from the source. + The evolution in the ccolumn density and. Doppler parameter joint distribution is shown in Figure 9. for model IID4.5 over the redshift range 4.6>2o4.0., The evolution in the column density and Doppler parameter joint distribution is shown in Figure \ref{fig:NHI-b} for model HD4.5 over the redshift range $4.6>z>4.0$. + Phe onset of rreionization bas two ellects., The onset of reionization has two effects. + It increases the median Doppler parameter. while narrowing the width of the ccolumn density distribution as the recombination rate is reduced. due to the increase in the gas temperature.," It increases the median Doppler parameter, while narrowing the width of the column density distribution as the recombination rate is reduced due to the increase in the gas temperature." + ‘This enhances the reduction in the number density of hieh column density systems along a line of sight due to the decrease in the absolute density of the gas as a result. of cosmological expansion (7)..., This enhances the reduction in the number density of high column density systems along a line of sight due to the decrease in the absolute density of the gas as a result of cosmological expansion \citep{ZMAN98}. + A clear envelope of minimum Doppler parameters. increasing with Nyy. is) produced both before and after full helium reionization.," A clear envelope of minimum Doppler parameters, increasing with $N_{\rm HI}$, is produced both before and after full helium reionization." +" For svstenis with Nutl014cm2τι the envelope is ⋠⋅found to rise""E from Onin©kn to by&1015kms following rreionizalion. consistent with the increase in gas toniperatures."," For systems with $N_{\rm HI}>10^{14}\,{\rm + cm^{-2}}$, the envelope is found to rise from $b_{\rm + min}\approx7\kms$ to $b_{\rm min}\approx10-15\kms$ following reionization, consistent with the increase in gas temperatures." + Aluch of the temperature structure of the ΕΛΛ after helium reionization may be accounted for by the hardening of the raciation field as filtered through the LGAL curing rreionization., Much of the temperature structure of the IGM after helium reionization may be accounted for by the hardening of the radiation field as filtered through the IGM during reionization. +" Approximating the spectrum of the radiation field. locally as a power law J,=ημοι)"". where Jou is the angle-averaged intensity at the pphotoclectric threshold frequceney vou. the ionization and heating rates per lion are. respectively. and where the photoclectric eross-section for ionising iis approximated as σημHel)* ancl Dp is the Planck constant."," Approximating the spectrum of the radiation field locally as a power law $J_{\nu}=J_{\rm + HeII}(\nu/\nu_{\rm HeII})^{-\alpha}$, where $J_{\rm HeII}$ is the angle-averaged intensity at the photoelectric threshold frequency $\nu_{\rm HeII}$, the ionization and heating rates per ion are, respectively, and where the photoelectric cross-section for ionising is approximated as $\sigma_{\rm HeII}(\nu/\nu_{\rm HeII})^{-3}$, and $h_{\rm P}$ is the Planck constant." + This then gives for the expected energy. injected into the gas per ionization Deviations from this will occur due to spectral structure within the ionization front. especially as the mean free path of high energy photons is long compared with that of photons just above the photoelectric threshold. resulting in à hardening of the spectrum through the Lfront.," This then gives for the expected energy injected into the gas per ionization Deviations from this will occur due to spectral structure within the ionization front, especially as the mean free path of high energy photons is long compared with that of photons just above the photoelectric threshold, resulting in a hardening of the spectrum through the I-front." + The relation serves to provide an approximate estimate for the expected amount of energy. injection ancl the sensitivity to the hardness of the elfective spectral index within the ionization front. which max even achieve negative values (a« 0) in regions for which more high energy. photons are able to penetrate than low.," The relation serves to provide an approximate estimate for the expected amount of energy injection and the sensitivity to the hardness of the effective spectral index within the ionization front, which may even achieve negative values $\alpha<0$ ) in regions for which more high energy photons are able to penetrate than low." + The evolution of the energy. per ionization is shown in Figure 10..., The evolution of the energy per ionization is shown in Figure \ref{fig:energy-per-ionization}. . + At early times after the source just turns on (the panels for >=4.4 and >=4.0). heating rates per ionization more than an order of magnitude greater than Eq. (4))," At early times after the source just turns on (the panels for $z=4.4$ and $z=4.0$ ), heating rates per ionization more than an order of magnitude greater than Eq. \ref{eq:E-per-ion}) )" + for a—0.5 (the source spectral index) ave found., for $\alpha=0.5$ (the source spectral index) are found. + The helium in these regions is still largely in the form ofHer. with the rregion just beginning to emerge [rom the source at z=4.4. ancl not quite reaching the edge of the polar grid bv z=4.00. as shown in Figure 11..," The helium in these regions is still largely in the form of, with the region just beginning to emerge from the source at $z=4.4$, and not quite reaching the edge of the polar grid by $z=4.00$, as shown in Figure \ref{fig:HeIII-ionization}." + Whilst the üionization fraction rg. evolves rapidly within the ionization front. it is found that the heating rate per ionization is nearly constant for à given value of (gau.," Whilst the ionization fraction $x_{\rm HeII}$ evolves rapidly within the ionization front, it is found that the heating rate per ionization is nearly constant for a given value of $x_{\rm HeII}$." + This is illustrated in Figure 12.., This is illustrated in Figure \ref{fig:E_per_ion_parametrised_contour}. + Phe energy. per ionization is well-described by where /—org|2xcga., The energy per ionization is well-described by where $t = x_{\rm HeII} + 2 x_{\rm HeI}$. + Phe right region corresponds to gas that is ionising from oLeu. whilst the left region shows the level of as the helium becomes fully ionized.," The right region corresponds to gas that is ionising from to, whilst the left region shows the level of as the helium becomes fully ionized." + The bridge between 10 regions indicates the rapid depletion of vis it is converted intoLeu., The bridge between the regions indicates the rapid depletion of as it is converted into. +.. As the lis ionizecl intoHeinr. the energy per ionization rapidly eclines as the effective ionising spectrum softens towards 1¢ intrinsic spectral shape of the source.," As the is ionized into, the energy per ionization rapidly declines as the effective ionising spectrum softens towards the intrinsic spectral shape of the source." + The expected boost in the gas temperature. allowing for the injected energy to be shared by all the species present. is where Ay is the Boltzmann constant.," The expected boost in the gas temperature, allowing for the injected energy to be shared by all the species present, is where $k_{\rm B}$ is the Boltzmann constant." + Comparison with Figure 10. shows that the rises in the median temperature in Figure 3. following full helium. ionization are of the magnitudes expected. although the actual local increase may »: much Larger. depending on the evolution of the iionization fraction argo within the ionization front.," Comparison with Figure \ref{fig:energy-per-ionization} shows that the rises in the median temperature in Figure \ref{fig:los-temperature} following full helium ionization are of the magnitudes expected, although the actual local increase may be much larger, depending on the evolution of the ionization fraction $x_{\rm HeII}$ within the ionization front." + The eas will also rapidly cool in dense regions due to radiative osses. and in underdense regions due to adiabatic expansion cooling.," The gas will also rapidly cool in dense regions due to radiative losses, and in underdense regions due to adiabatic expansion cooling." + By z=4.00. the highest heating rates are confined o the periphery of the polar grid (Figure 10)). where pockets of Toy Continue to survive in shadows cast. by overdense clumps blocking the source. as shown by à comparison oween Figures Ll and 2..," By $z=4.00$, the highest heating rates are confined to the periphery of the polar grid (Figure \ref{fig:energy-per-ionization}) ), where pockets of $x_{\HeII}$ continue to survive in shadows cast by overdense clumps blocking the source, as shown by a comparison between Figures \ref{fig:HeIII-ionization} and \ref{fig:overdensity}." + In the inner regions. where he helium is fully ionized. the gas is able to cool through radiative losses and the temperature lowers. leaving the »vipheral regions at relatively higher temperatures.," In the inner regions, where the helium is fully ionized, the gas is able to cool through radiative losses and the temperature lowers, leaving the peripheral regions at relatively higher temperatures." + This is the origin. of the trend. of increasing temperature. with impact parameter shown in Figure 3.., This is the origin of the trend of increasing temperature with impact parameter shown in Figure \ref{fig:los-temperature}. + High heating rates are found to persist down to z=3.60 even after most of the helium is Cully ionized. ancl indeed increase by ο=3.20 as dense clumps continue to gather near the centrally. placed source further filtering theradiation field. demonstrating that raciative transfer. effects may continue to allect the temperature of the gas in distant. regions even well after helium reionization has completed.," High heating rates are found to persist down to $z=3.60$ even after most of the helium is fully ionized, and indeed increase by $z=3.20$ as dense clumps continue to gather near the centrally placed source further filtering theradiation field, demonstrating that radiative transfer effects may continue to affect the temperature of the gas in distant regions even well after helium reionization has completed." +probed along the spectra]viel2002..,"probed along the \\citep[see][for a discussion in the case of power +spectra]{viel2002}." + All the lines falling in the (forest have. been fitted with a Voigt prolile via A7 minimization., All the lines falling in the forest have been fitted with a Voigt profile via $\chi^{2}$ minimization. + The lines with an equivalent width (EW) lower than three times the related EW uncertainty have been removed. from the list of fitted lines., The lines with an equivalent width (EW) lower than three times the related EW uncertainty have been removed from the list of fitted lines. + Phe metal lines have been identified first looking for the most common cdoublets (e.g.Iv.Silv.OVL. and Mg).," The metal lines have been identified first looking for the most common doublets (e.g., and )." + Then. we have searched for other common transitions (e.g.SIIIL.Sill.Cll. Fei)) at the redshift ofthe previously determined systems.," Then, we have searched for other common transitions (e.g., ) at the redshift of the previously determined systems." + Our sample provides 21 QSO pairs with angular separations uniformlv clistributec between ~1 and 14 arcmin. corresponding to comoving spatial separations between ~L4 and 21.6 Mpe.," Our sample provides 21 QSO pairs with angular separations uniformly distributed between $\sim 1$ and 14 arcmin, corresponding to comoving spatial separations between $\sim 1.4$ and 21.6 $^{-1}$ Mpc." + The median redshift of the [forest is z Ls. , The median redshift of the forest is $z \sim 1.8$ . +This is the largest sample of high-resolution spectra of QSO pairs ever collected. unique both for the number density - we have six QSOs in a region of 0.04 deg - and the variety of sseparations investigated.," This is the largest sample of high-resolution spectra of QSO pairs ever collected, unique both for the number density - we have six QSOs in a region of $\sim 0.04$ $^{2}$ - and the variety of separations investigated." + 1n order to both assess the nature of the [forest inferred. from. simulations and to constrain the cosmological scenario of the same simulations. we compared the results obtained for our sample of observed QSO spectra with analogous results for a sample of mock [Torests.," In order to both assess the nature of the forest inferred from simulations and to constrain the cosmological scenario of the same simulations, we compared the results obtained for our sample of observed QSO spectra with analogous results for a sample of mock forests." + The details of the adopted. simulations can be found in Paper bL here we provide only the basic. information.," The details of the adopted simulations can be found in Paper I, here we provide only the basic information." + We used simulations run with the parallel hyvero-dynamical ClrecSPLII) code2005)., We used simulations run with the parallel hydro-dynamical (TreeSPH) code. +". ""Phe simulations were performed with. periodic x»indary. conditions with an equal number of dark matter ancl gas particles and used. the conservative ormulation® of SPII proposed. by Springel&Lerneuist (2002).", The simulations were performed with periodic boundary conditions with an equal number of dark matter and gas particles and used the conservative `entropy-formulation' of SPH proposed by \citet{springel2002}. +. hadiative cooling and heating processes were ollowed for a primordial mix of hydrogen ancl helium., Radiative cooling and heating processes were followed for a primordial mix of hydrogen and helium. + We assumed a mean UV background: produced by quasars aud ealaxies as given by Llaarcdt&Alacau(1996) with helium wating rates multiplied by a factor 3.3 in order to. Lit observational constraints on the temperature evolution of he IGM.," We assumed a mean UV background produced by quasars and galaxies as given by \citet{hm96} + with helium heating rates multiplied by a factor 3.3 in order to fit observational constraints on the temperature evolution of the IGM." + More details can be found in Vieletal.(2004)., More details can be found in \citet{viel2004}. +". The cosmological model corresponds to a ""fiducia ACDAL universe with parameters Qo=0.26.Qu,174.Qu,=0.0063 and My=τὸ km + + (the D2 series of Vieletal. 2004))."," The cosmological model corresponds to a `fiducial' $\Lambda$ CDM universe with parameters $\Omega_{0\rm{m}}=0.26,\ +\Omega_{0\Lambda}=0.74,\ \Omega_{0\rm{b}}=0.0463$ and $H_0 = 72$ km $^{-1}$ $^{-1}$ (the B2 series of \citealt{viel2004}) )." + We have used 2400° dark matter and gas particles in à 1205.+ comoving Alpe ox., We have used $2\times 400^3$ dark matter and gas particles in a $120\ h^{-1}$ comoving Mpc box. + The gravitational softening was set to 5 f+ kpe in comoving units for all particles., The gravitational softening was set to 5 $h^{-1}$ kpc in comoving units for all particles. + We note that the parameters chosen here. including the thermal history of the IGM. are in xrfect agreement. with observational constraints including recent results on the CMD and other results obtained by the forest community (e.g.Spergelοἱal.2008:Vielet2004:Seljaketal. 2005).," We note that the parameters chosen here, including the thermal history of the IGM, are in perfect agreement with observational constraints including recent results on the CMB and other results obtained by the forest community \citep[e.g. ][]{spergel03,viel2004,seljak05}." +. The 2=LS output of the simulated. box was pierced » three in order to obtain 50 triplets of spectra. carefully reproducing the observed. τρίο mutual separations and spectral properties., The $z=1.8$ output of the simulated box was pierced by three in order to obtain 50 triplets of spectra carefully reproducing the observed Triplet mutual separations and spectral properties. + The same was done for 50 sextets of rreproducing the observed. Sextet and 50. pairs. of aat the same angular separation as Pair U. 50. cillerent realizations of Pair A spectra and of Pair Q were obtained from the output box atredshift z= 2.4., The same was done for 50 sextets of reproducing the observed Sextet and 50 pairs of at the same angular separation as Pair U. 50 different realizations of Pair A spectra and of Pair Q were obtained from the output box atredshift $z=2.4$ . + Finally. we added το the simulated spectra. both," Finally, we added to the simulated spectra both" + , +in which the trausits of 1Γρle objects can be seen in the first quarter of plitometric data (a 33.5-dav data seement from Mav 13 to June 15 UT. 2009) frou the spacοσαΕξ.,"in which the transits of multiple objects can be seen in the first quarter of photometric data (a 33.5-day data segment from May 13 to June 15 UT, 2009) from the spacecraft." + While not confirmed plajet. discoveries. hese systems have assed several iniportant tests hat eliminate false-)osifivo sienas.," While not confirmed planet discoveries, these systems have passed several important tests that eliminate false-positive signals." +" Tf all were τιtimatevo shown to )e planets. then these svstenis would coutai1 four anets with radi simaller than three Earth racii (the smallest being two Earth radi). at least two xürs of planets in or very near a low-order wealnotion resonaree (ADAIR. axd oue system with at east three disΠιο transiting planets,"," If all were ultimately shown to be planets, then these systems would contain four planets with radii smaller than three Earth radii (the smallest being two Earth radii), at least two pairs of planets in or very near a low-order mean-motion resonance (MMR), and one system with at least three distinct transiting planets." + For simplicity. we will refer to these objects as “planets” throughout this paper. recognizing hat their coufiriiation as such is vet Incomplete aud that some of these trausit signals may be due to other astroplivsies.," For simplicity, we will refer to these objects as “planets” throughout this paper, recognizing that their confirmation as such is yet incomplete and that some of these transit signals may be due to other astrophysics." + The stellar references hat we will use throughout tjs paper are Objects of Interest (IKOI) |52. 101. 209. S77. and S896 with the transiting panets denoted by “OTT οον ete.," The stellar references that we will use throughout this paper are Objects of Interest (KOI) 152, 191, 209, 877, and 896 with the transiting planets denoted by “.01”, “.02”, etc." + beginning in tjc order that they were identified wit ithe transit detection software from the pixliue., beginning in the order that they were identified with the transit detection software from the pipeline. +" Thus. he planet nuuber designation does not necessarily"" reflect the order of the plajets within each system."," Thus, the planet number designation does not necessarily reflect the order of the planets within each system." + We do not use letter designations. which Ww convention are reserved for confirmed plaucts.," We do not use letter designations, which by convention are reserved for confirmed planets." + This paoer will proceed as follows., This paper will proceed as follows. + First. we eive the known propertics of the host stius (82)).," First, we give the known properties of the host stars \ref{secStar}) )." + Tn 83 we discuss the photmuctric reduction and the aleorithin used to identify the mutiple candidates within cach svstem., In \ref{falsepositive} we discuss the photometric reduction and the algorithm used to identify the multiple candidates within each system. + \Ve also outline the tests we have conducted to clininate false-positive systems., We also outline the tests we have conducted to eliminate false-positive systems. + We present estimates of the orbita aud physical properies of these objects should they prove to be planets 1) , We present estimates of the orbital and physical properties of these objects should they prove to be planets \ref{properties}) ). +Iu 85 we discuss the possible fuure detection of transit timing variatious based upon a Moute Carlo sinulatiou of these canclidae systems., In \ref{TTV} we discuss the possible future detection of transit timing variations based upon a Monte Carlo simulation of these candidate systems. + Finally. we discuss the inplications of these results in rofsecDiscuss..," Finally, we discuss the implications of these results in \\ref{secDiscuss}." + For each of the five stars. we obtained high resolution echelle spectroscopy from the McDonald Observatory 2.71n telescope Tull C'oudé spectrometer with resolving power B260.000.," For each of the five stars, we obtained high resolution echelle spectroscopy from the McDonald Observatory 2.7m telescope Tull Coudé spectrometer with resolving power R=60,000." + We also obtained one spectrum of IKOI 155 with the FIES spectrograph Ol the Nordic Optical Telescope and one spectruui of KOI 191. KOT 209. KOI s77. and KOT 596 with the itt Peak National Observatory dau telescope.," We also obtained one spectrum of KOI 155 with the FIES spectrograph on the Nordic Optical Telescope and one spectrum of KOI 191, KOI 209, KOI 877, and KOI 896 with the Kitt Peak National Observatory 4-m telescope." + These spectra were obtained for t1C purpose of coustraiine effective temperature Lig. surface eravity logg. projected rotational velocity for the star esin/. aud ietallicity |U/HJ.," These spectra were obtained for the purpose of constraining effective temperature $T_{\text{eff}}$, surface gravity $\log g$, projected rotational velocity for the star $v\sin i$, and metallicity $[M/H]$." + T1C MeDonald spectra were reduced and extracted using the IRAF echelle packageο, The McDonald spectra were reduced and extracted using the IRAF echelle package. +"ν, Iu all cases. the spectroscopic aualvsis was done by natching the observed spectra to a library SNhetic spectra."," In all cases, the spectroscopic analysis was done by matching the observed spectra to a library of synthetic spectra." + The svuthetic spectra cover t waveleugth region ((ceuntered roughly on the Me b ines)., The synthetic spectra cover the wavelength region (centered roughly on the Mg b lines). + The eric has coarseness of 250 I& in Zig. 1-1 kis in ÜUyorcecsin/. and 0.5 dex in logg and |M/IT]. inplviug uucertaintes ohalf those values;," The grid has coarseness of 250 K in $T_{\text{eff}}$, 1-4 km/s in $v_{\text{rot}} \simeq v \sin i$, and 0.5 dex in $\log g$ and $[M/H]$, implying uncertaintes of half those values." + For the LOS stars with low SNR spectra. we performed a diagrostic using the Ix color to verify that their com)ositious are consistent with solar netallicity. it he values we report are sinply from template-natching with [A/77] fixed at 0.," For the host stars with low SNR spectra, we performed a diagnostic using the $-$ K color to verify that their compositions are consistent with solar metallicity, but the values we report are simply from template-matching with $[M/H]$ fixed at 0." + Table l lists the resutine stellar paraicters for all five sars as well as the iustruments used in the observations., Table \ref{starproperties} lists the resulting stellar parameters for all five stars as well as the instruments used in the observations. + All five stars appareutlv reside near or on the main sequence., All five stars apparently reside near or on the main sequence. + Laci of these systems was found using the Transiting Planet Search Pipeline (TPS) which identifies siguifican trausit-like features. or Threshold Crossing Eveuts CECE). in the light curves (JenkinsIscfal20)0).," Each of these systems was found using the Transiting Planet Search Pipeline (TPS) which identifies significant transit-like features, or Threshold Crossing Events (TCE), in the light curves \citep{jenk2010}." +". Data showing TCEs are then passed to the Data Validation (DV) pipcline (Wuοἱal,2010).", Data showing TCEs are then passed to the Data Validation (DV) pipeline \citep{wu2010}. +. The purpose of the DV pipeπιο is twofold: 1) to fl a transiting planet iode το the data. roniove it from the light curve. and to return the resit to TPS in au effort to find additional trausit catures and 2) to complete a suite of statistica tests that are applied to the data after all TCEs are ideutified in an effort to assess the likeihood of false-positives.," The purpose of the DV pipeline is twofold: 1) to fit a transiting planet model to the data, remove it from the light curve, and to return the result to TPS in an effort to find additional transit features and 2) to complete a suite of statistical tests that are applied to the data after all TCEs are identified in an effort to assess the likelihood of false-positives." + The binarv discriniuaion statistics aud the motion detection statistic. in particular. speak to the," The binary discrimination statistics and the motion detection statistic, in particular, speak to the" +further cools and isobarically compresses to p(t). theu the shock velocity in the frame of the eas will be further reduced by a factor of ~py f/plt). or ροκCintall~ρυριρα)(rrm]~ipu p(t). auc thus the length of the post shock region is (ignoring nunierical factors order ity). where Gury=tay(CALSRyyh?~D3ALLl|2)Lol!?]ins4 fhe virial (or infall) velocity.,"further cools and isobarically compresses to $\rho(t)$, then the shock velocity in the frame of the gas will be further reduced by a factor of $\sim \rho_1/\rho(t)$ , or $v_{\rm shock}/v_{\rm infall}\sim \rho_0\rho_1/[\rho(t)(\rho_1-\rho_0)]\sim \frac{4}{3}\rho_0/\rho(t)$ , and thus the length of the post shock region is (ignoring numerical factors order unity), where $v_{\text{infall}} = v_{\text{vir}} = (GM/R_{\rm vir})^{1/2}\simeq 23\, M_8^{1/3} [(1+z)/10]^{1/2}\,\text{km s}^{-1}$ the virial (or infall) velocity." +" Isobaric cooling requires τοι>f£. While eravitational (Jeaus) instability and the onset of fragmentation requires f,> fg."," Isobaric cooling requires $t_{\rm cool} > t_{\rm s}$, while gravitational (Jeans) instability and the onset of fragmentation requires $t_{\rm s} > t_{\text{ff}}$ ." + lt is possible that eravitational instability does not set iu before the gas cools to the CAMB temperature., It is possible that gravitational instability does not set in before the gas cools to the CMB temperature. + Iu this case. isobaricity is euarauteed aud the fragmentation lnass scale is entirelv set by the CAIB temperature and the initial conditions of the accretion flow.," In this case, isobaricity is guaranteed and the fragmentation mass scale is entirely set by the CMB temperature and the initial conditions of the accretion flow." + We asstune that following the initial eravitational instability. the eas fragments into chuups with masses eiven by the local Dounor-Ebert (BE) mass. assumndue isoharic deusity evolutiou with T;=Ti1.1410:K and 5;=LOSTem7.," We assume that following the initial gravitational instability, the gas fragments into clumps with masses given by the local Bonnor-Ebert (BE) mass, assuming isobaric density evolution with $T_{i} = T_{\text{vir}} = 1.1\times10^{4}\,\text{K}$ and $n_{i} = 4.0\times10^{3}\,\text{cm}^{-3}$." + The resulting chup size sets an upper limit to the masses of the star im the aftermath of the fraginentation., The resulting clump size sets an upper limit to the masses of the star in the aftermath of the fragmentation. +" Due to subtle processes affecting post-fragiucutation accretion. the final stellar masses could be a fraction of the fragmentation scale: AM,~aMpg. where a<0.5 in star formation in the local universe (Mcl&oe&Tan2002)."," Due to subtle processes affecting post-fragmentation accretion, the final stellar masses could be a fraction of the fragmentation scale: $M_\star \simeq \alpha M_{\text{BE}}$, where $\alpha < 0.5$ in star formation in the local universe \citep{MT02}." +". For our case studies. we consider a high aud low netallicity case (LO2 and 10 Zo). a lugh and low IW radiation fields (J,=10.10°. aud 104). and source cmperatures ofT,=101 and 103K."," For our case studies, we consider a high and low metallicity case $10^{-2}$ and $10^{-6}\, Z_{\odot}$ ), a high and low LW radiation fields $J_{21} = 10, 10^{3}$, and $10^{4}$ ), and source temperatures of $T_{\ast} = 10^{4}$ and $10^{5}\,\text{K}$." + We do not present a run with hieh metallicity aud cfiicient molecular cooling. mt we do conuneut on the outcome of such a run at he eud of this section.," We do not present a run with high metallicity and efficient molecular cooling, but we do comment on the outcome of such a run at the end of this section." + In Table 2. we provide the xuanmeters of our four representative ruus., In Table \ref{tab:parameters} we provide the parameters of our four representative runs. + We preseut he results for cach case iu succession., We present the results for each case in succession. + See Figures 1|- 7 for the temperature history. cooling rate. IT? fraction. audionization deerce (defined such that ionizationHoοςPHplanyfora) Yespectively. for cach run. Run A represents a relatively high inetallicity euvironnient with aio stroug LW backeround that photodissociates I». reudering metals the precdominaut coolant at TP5.," The discrepancy between the merger tree predictions and the EPS predictions for the mass function of halo progenitors grows toward higher redshifts, and exceeds a factor of $2$ at $z>5$." + Likewise. ie halo mereer rates obtained from the tree aeree with ιο EPS rates to within a factor of two for 0= 0.05) does not significantly affect ie lmerecr rate predictions: the discrepancy between trees aath A:=0.01 aud A:=0.05 is largest (~ 254%) at.=h 5nd reduces to nearly zero at +=0., A convergence test shows that the redshift step used for the calculations $\Delta z=0.05$ ) does not significantly affect the merger rate predictions: the discrepancy between trees with $\Delta z=0.01$ and $\Delta z=0.05$ is largest $\sim 25 \%$ ) at $z=5$ and reduces to nearly zero at $z=0$. + These tests guarantee iat the mass fictions aud merger rates produced by the uereer tree are accurate to a factor of two or better in ie redshift range of interest (2 <5)., These tests guarantee that the mass functions and merger rates produced by the merger tree are accurate to a factor of two or better in the redshift range of interest $z\leq 5$ ). + We chose not to sxtend our results bevond :=5. where the accuracy of ie dnerecr tree degrades rapidly.," We chose not to extend our results beyond $z=5$, where the accuracy of the merger tree degrades rapidly." + Further details aud tests of the implementation of the merecr tree will be eiven iu a separate publication (Tainan. Menuou Naravanan 2001. in preparation).," Further details and tests of the implementation of the merger tree will be given in a separate publication (Haiman, Menou Narayanan 2001, in preparation)." + The merger tree we use describes 104 halos picked frou he PS inass function at 2=0. which are subsequently woken up iuto zWS«10! halos by :=5.," The merger tree we use describes $10^{4}$ halos picked from the PS mass function at $z=0$, which are subsequently broken up into $\approx +8.8 \times 10^{4}$ halos by $z=5$." + Because of nunierical constraints. the οσο. tree tracks the ucreer historv of halos over a finite range iu halos mass. which varies with redshift.," Because of numerical constraints, the merger tree tracks the merger history of halos over a finite range in halos mass, which varies with redshift." + The ιακανα mass at any redslift corresponds to the most massive halo amoung he initial LO! halos drawn from a PS distribution at >=0 (corresponding to Aagcmδεν10172ML.)., The maximum mass at any redshift corresponds to the most massive halo among the initial $10^{4}$ halos drawn from a PS distribution at $z=0$ (corresponding to $M_{\rm max} \approx 8.4 \times 10^{12} {\rm M_\odot}$ ). +" For he mimi mass. we adopt the redshitt-dependent value (οι, Navarro. Freuk White 1997) corresponding to a virial temperature of the halo of Ta,105 K. This value represents the mininnun halo mass below which. in a metal-free gas; barvons cannot cool cficicntly within the age of the universe at that redshift. and therefore cannot form a SMDIT."," For the minimum mass, we adopt the redshift-dependent value (e.g. Navarro, Frenk White 1997) corresponding to a virial temperature of the halo of $T_{\rm vir}=10^4$ K. This value represents the minimum halo mass below which, in a metal-free gas, baryons cannot cool efficiently within the age of the universe at that redshift, and therefore cannot form a SMBH." +. Although this is a reasonable clioice. the precise value of the limiting cooling lnass is uncertaiu (t depends on the metallicity aud II chemistry: see. c.g. Taian. Abel Rees 2000).," Although this is a reasonable choice, the precise value of the limiting cooling mass is uncertain (it depends on the metallicity and ${\rm H_2}$ chemistry; see, e.g. Haiman, Abel Rees 2000)." + Ounce a realization of the merger tree has been generated. it can be used backwards (ne. fom high + to low +) to follow the meregcr history of dark matter halos which potentially contain black holes.," Once a realization of the merger tree has been generated, it can be used backwards (i.e., from high $z$ to low $z$ ) to follow the merger history of dark matter halos which potentially contain black holes." + We estimate the statistical errors on the various quantities calculated below from the dispersion iu the correspouding quantities among ten independent realizations of the merger tree with the sale paraueters., We estimate the statistical errors on the various quantities calculated below from the dispersion in the corresponding quantities among ten independent realizations of the merger tree with the same parameters. + We fud that the statistical uncertainties are geuerallv sinall aud are belowthe expected level of systematic errors in the mergertree method.," We find that the statistical uncertainties are generally small, and are belowthe expected level of systematic errors in the merger–tree method." + The merger tree predictions can be translated iuto plivsical wuits using the equivalent comoving volume that contains the initial 104 halos described by the mereer tree., The merger tree predictions can be translated into physical units using the equivalent comoving volume that contains the initial $10^{4}$ halos described by the merger tree. + The PS mass function predicts 0.579 halos per Mpe? at 2=0. in the appropriate mass ranee AM0) Mag.," The PS mass function predicts $0.579$ halos per $^3$ at $z=0$, in the appropriate mass range $M_{\rm min} (z=0)$ $M_{\rm max}$." + Thus. we infer that our merger tree sinulates a fixed comoving volume of AV=101/0.579L.73«104 Ape?.," Thus, we infer that our merger tree simulates a fixed comoving volume of $\Delta V=10^4/0.579 =1.73 \times +10^{4}$ $^3$." + The various models that have been proposed so far for the formation of SMDIIs in individual galactic uuclci (Rees 1981 and references therein: Quinlan Shapiro 1990: Eiseusteiu Loeb 1995: Silk Rees 1998: Schwood Moore 1999: Ostriker 2000) eenerallv lack à robust xedietion regarding the preseuce or absence of a SMDITI in a galaxy., The various models that have been proposed so far for the formation of SMBHs in individual galactic nuclei (Rees 1984 and references therein; Quinlan Shapiro 1990; Eisenstein Loeb 1995; Silk Rees 1998; Selwood Moore 1999; Ostriker 2000) generally lack a robust prediction regarding the presence or absence of a SMBH in a galaxy. + Here. we explore the predictions for two differeut illustrative models. im which SMDIIS are assumed to be oxeseut in only a small fraction of all the halos that can xteutiallv harbor a SMDIT at high redshift (2= 5. the initialredshift iu the merger tree).," Here, we explore the predictions for two different illustrative models, in which SMBHs are assumed to be present in only a small fraction of all the halos that can potentially harbor a SMBH at high redshift $z=5$ the initialredshift in the merger tree)." + We demonstrate that: (a) these two widely different models can nonetheless be consistent with the near ubiquity of ceutral SMDIIS in 1unuinous galaxies at 5= 0. aud (b) the detection of low- eravitational waves expected from the merger of," We demonstrate that: (a) these two widely different models can nonetheless be consistent with the near ubiquity of central SMBHs in luminous galaxies at $z=0$ , and (b) the detection of low-frequency gravitational waves expected from the merger of" +older.,older. + In summary. we conclude that the exceeclinely hieh spectroscopic ages found [ον 47 Tuc in previous works was due to: 1) the use of theoretical isochrones (hat neglect important effects such as IHe-diffusion ancl a-enhancement. as shown by Vazdekis et al. (," In summary, we conclude that the exceedingly high spectroscopic ages found for 47 Tuc in previous works was due to: 1) the use of theoretical isochrones that neglect important effects such as He-diffusion and $\alpha$ -enhancement, as shown by Vazdekis et al. (" +2001). and 2) the underestimate of the number of giant stars above the horizontal branch. whieh was partly due to the omission of AGB stars [rom the isochrones. and partly to a gennine apparent shortfall in the predicted numbers of AGB stars and. most likely. [irst-ascent giants as well.,"2001), and 2) the underestimate of the number of giant stars above the horizontal branch, which was partly due to the omission of AGB stars from the isochrones, and partly to a genuine apparent shortfall in the predicted numbers of AGB stars and, most likely, first-ascent giants as well." + Another requirement. which is cliseussecl in Paper L is on the iron abundance of the cluster.," Another requirement, which is discussed in Paper I, is on the iron abundance of the cluster." + Models provide a good match if/Fe/I// is 0.05 dex lower than found by Carretta Gratton (1997)., Models provide a good match if is 0.05 dex lower than found by Carretta Gratton (1997). + Such a shift in./Pe/H/ is well within the errorbars of Carrettà Gratton's analysis and the uncertainties in the scale of our stellar library., Such a shift in is well within the errorbars of Carretta Gratton's analysis and the uncertainties in the -scale of our stellar library. + With regard to our long term goal of constructing metal-rich stellar population models for elliptical galaxies. we have made considerable progress.," With regard to our long term goal of constructing metal-rich stellar population models for elliptical galaxies, we have made considerable progress." + First. the ages [from {419 and {σσων agree. alter the latter is corrected [or the effect of C.N abundance variations (see Paper I).," First, the ages from $H\beta$ and $H\gamma_{\sigma<130}$ agree, after the latter is corrected for the effect of C,N abundance variations (see Paper I)." + Second. all metal lines are correctly predicted for the same ages obtained from Balmer lines.," Second, all metal lines are correctly predicted for the same ages obtained from Balmer lines." + Third. the giant temperature scale of the Salaris models looks to be generally correct.," Third, the giant temperature scale of the Salaris models looks to be generally correct." + On the other hand. £05 is shown to be a problematic feature. embedded as it is in a forest of CN lines.," On the other hand, $H\delta_F$ is shown to be a problematic feature, embedded as it is in a forest of CN lines." + This problem is likely to be further exacerbated in elliptical galaxies. which have notoriouslv strong CN [eatures.," This problem is likely to be further exacerbated in elliptical galaxies, which have notoriously strong CN features." + Moreover. the present models do not include varlalions in Tvpe Ia vs. Type II supernovae element ratios (Trager et al.," Moreover, the present models do not include variations in Type Ia vs. Type II supernovae element ratios (Trager et al." + 1998). nor do they probe the high-metallicity regime needed for ellipticals.," 1998), nor do they probe the high-metallicity regime needed for ellipticals." + Finally. we have identifiecl an error in (he upper eiant. branch Iuminositv. function of current evolutionary models. which underestimate the aggregate number of luminous red giants in 47 Tuc by roughly a factor of 2.," Finally, we have identified an error in the upper giant branch luminosity function of current evolutionary models, which underestimate the aggregate number of luminous red giants in 47 Tuc by roughly a factor of 2." + We have furthermore shown that an accurate LE for these stars is needed for accurate spectroscopic age determination., We have furthermore shown that an accurate LF for these stars is needed for accurate spectroscopic age determination. + A major unknown is whether the red-giant excess of 47 Tue extends to all metal-rich old populations. anc what its magnitude might be.," A major unknown is whether the red-giant excess of 47 Tuc extends to all metal-rich old populations, and what its magnitude might be." + Testing the luminosity function in old metalrich populations has emerged as an important prerequisite for stellar population studies., Testing the luminosity function in old metal-rich populations has emerged as an important prerequisite for stellar population studies. + These and further improvements are left for future works., These and further improvements are left for future works. + We would like to thank Maurizio Salaris lor making his isochrones available., We would like to thank Maurizio Salaris for making his isochrones available. + Stefano Covino is thanked for the red integrated spectrum of 47 Tuc., Stefano Covino is thanked for the red integrated spectrum of 47 Tuc. + We would also like to thank Alexandre Vazdekis. Maurizio Salaris. Manuela. Zoceali. Achim Weiss ancl Mike. Bolte for helpful discussions.," We would also like to thank Alexandre Vazdekis, Maurizio Salaris, Manuela Zoccali, Achim Weiss and Mike Bolte for helpful discussions." + The referee. Drad Gibson. is thanked for valuable suggestions (hiat greatly improved (his paper.," The referee, Brad Gibson, is thanked for valuable suggestions that greatly improved this paper." + R.P.5. thanks (the hospitality of the Physics Dept., R.P.S. thanks the hospitality of the Physics Dept. + of the University ol North Carolina. Chapel Will. where part of this work was developed.," of the University of North Carolina, Chapel Hill, where part of this work was developed." + Likewise. J.A.R. thanks the Astronomy Department al UC. Santa Cruz for hospitality during a visit in which part of this work was developed.," Likewise, J.A.R. thanks the Astronomy Department at UC, Santa Cruz for hospitality during a visit in which part of this work was developed." + This work has made extensive use of the Simbad database., This work has made extensive use of the Simbad database. +recently determined the spectral type of the donor in CCve to be KO. but with a radius 1.6 times larger than a main sequence star.,"recently determined the spectral type of the donor in Cyg to be K0, but with a radius 1.6 times larger than a main sequence star." + [uterestingly. suspected that CCve has recently cone through a classical uova explosion. however. their Mages of the svstem do not uuiuubieuouslv reveal sigus of a nova shell.," Interestingly, suspected that Cyg has recently gone through a classical nova explosion, however, their images of the system do not unambiguously reveal signs of a nova shell." + The spectral type of the donor star in Col is only poorly coustrained. aud nothing is known about the donor in CCun.," The spectral type of the donor star in Col is only poorly constrained, and nothing is known about the donor in Cam." + sugeest that a large fraction. up o one third. of the CW population might be descended roni supersoft X-ray binaries.," suggest that a large fraction, up to one third, of the CV population might be descended from supersoft X-ray binaries." + Tle sample of CVs analyzed o» contained data for 20 svsteuis. of which two CCam and ΑΔ} display παν areeiv. line ratios.," The sample of CVs analyzed by contained data for 20 systems, of which two Cam and Aqr) display unusually large line ratios." + At the time of writing. we wave obtained ZLST//STIS snapshot spectra of 31 CVs with strong cussion lines. and found four svstcms with extremely cuhanced ratios.," At the time of writing, we have obtained /STIS snapshot spectra of 31 CVs with strong emission lines, and found four systems with extremely enhanced ratios." + While the xesenutly available sample is still too simall for any definite conclusion. it sugeests that the fraction of CVs that lave eone through a phase of thermal time-scale mass transfer and that display large abundance anomalies could well be of the order of 1015 While reffanomalous ay sueeest that the occurence of “anomalous” CVs is higher among maenetic svstenis. we stress that such a conclusion has to be treated with ereat care because of the involved selection effects.," While the presently available sample is still too small for any definite conclusion, it suggests that the fraction of CVs that have gone through a phase of thermal time-scale mass transfer and that display large abundance anomalies could well be of the order of $10-15$ While \\ref{f-anomalous} may suggest that the occurence of “anomalous” CVs is higher among magnetic systems, we stress that such a conclusion has to be treated with great care because of the involved selection effects." + The study of coutains 7 maguetic CVs in a total saluple of 20 systems. which suggestsOO that the fraction of magnetic CVs with sufücieutlv good. observatious is larecr than that of non-magnetic CVs.," The study of contains 7 magnetic CVs in a total sample of 20 systems, which suggests that the fraction of magnetic CVs with sufficiently good observations is larger than that of non-magnetic CVs." + Our STIS sample contains 5 magnetic CVs out of 31 emissiou-Ime systeuis. and all svstems displaving huge line flux ratios within this sample are non-maeuctic.," Our STIS sample contains 5 magnetic CVs out of 31 emission-line systems, and all systems displaying large line flux ratios within this sample are non-magnetic." + As a final note. we recall that evidence for carbou-depletion aud nitrogeun-culhauceimeut has also been fouud in FUV observations of the accreting white dwiufs in several dwarf novae (c.g.Y GGomi: aud III: 20013). aud have so far been discussed primarily in the coutext of the aftermath of a (recent) nova explosion.," As a final note, we recall that evidence for carbon-depletion and nitrogen-enhancement has also been found in FUV observations of the accreting white dwarfs in several dwarf novae (e.g. Gem: and Hyi: ), and have so far been discussed primarily in the context of the aftermath of a (recent) nova explosion." + Our ΤΙΣ suapshot spectra of JJ2329. CE3L5. BZUUAa. and CCre reveal extremely large andΑΙ line fux ratios. similar to those observed in AAgr.," Our /STIS snapshot spectra of J2329, CE315, UMa, and Cyg reveal extremely large and line flux ratios, similar to those observed in Aqr." +ΑΟ Such anomalous line flux ratios are expected in CVs that went through a phase of thermal timescale mass transfer and now accrete CNO processed material fou a companion stripped of its external lavers., Such anomalous line flux ratios are expected in CVs that went through a phase of thermal timescale mass transfer and now accrete CNO processed material from a companion stripped of its external layers. + A full understanding of the possible links between the observed anomalous line ratios and the evolution of CVs requires a significautly larecr sample of svsteus for which high-quality ultraviolet spectroscopy is available., A full understanding of the possible links between the observed anomalous line ratios and the evolution of CVs requires a significantly larger sample of systems for which high-quality ultraviolet spectroscopy is available. + Our 111 snapshot program and its approved continuation in 112 will eventually provide such a data base., Our 11 snapshot program and its approved continuation in 12 will eventually provide such a data base. +5—-8mss !.,$5-8$ $^{-1}$. + As we are looking for radial velocity variations of order 10 to 100 ss'. this is adequate and hence no attempt has been made to reach the 3 mss' accuracy which is in principle possible with this setup (2)..," As we are looking for radial velocity variations of order 10 to 100 $^{-1}$, this is adequate and hence no attempt has been made to reach the 3 $^{-1}$ accuracy which is in principle possible with this setup \citep{butler1996}." + For the determination of the radial velocities the pipeline described by ? is used., For the determination of the radial velocities the pipeline described by \citet{butler1996} is used. + In this pipeline. a template todine spectrum and a template spectrum of the target star obtained without an iodine cell in the lightpath are used to model the stellar observations with à superposed iodine spectrum.," In this pipeline, a template iodine spectrum and a template spectrum of the target star obtained without an iodine cell in the lightpath are used to model the stellar observations with a superposed iodine spectrum." + The Doppler shift is a free parameter in this model., The Doppler shift is a free parameter in this model. + Note that with this method the absolute radial velocity is not measured. but the radial velocity relative to the stellar template is obtained.," Note that with this method the absolute radial velocity is not measured, but the radial velocity relative to the stellar template is obtained." + All 179 stars are subjected to a period search., All 179 stars are subjected to a period search. + The periodicity of the radial velocity variations is determined first of all from a classical Lomb-Seargle (LS) periodogram (?).., The periodicity of the radial velocity variations is determined first of all from a classical Lomb-Scargle (LS) periodogram \citep{scargle1982}. . + The significance threshold is set to 6c. where the noise level is determined from the average power of the residual Scargle periodogram for frequencies between 0 and 0.03 cycles per day (c/d) (0.35 μΗΖ) and a frequency step of 0.00001 c/d (0.12 - 107 Hz).," The significance threshold is set to $\sigma$, where the noise level is determined from the average power of the residual Scargle periodogram for frequencies between 0 and 0.03 cycles per day (c/d) (0.35 $\mu$ Hz) and a frequency step of 0.00001 c/d (0.12 $\cdot$ $^{-3}$ $\mu$ Hz)." + We adopted the conventional method of iterative sinewave fitting (‘prewhitening’) to search for subsequent frequencies (2).., We adopted the conventional method of iterative sinewave fitting (`prewhitening') to search for subsequent frequencies \citep{kuschnig1997}. + In Figs 1. and 2.. the radial velocity variation as a function of phase is shown for two stars.," In Figs \ref{vradphase1} and \ref{vradphase2}, the radial velocity variation as a function of phase is shown for two stars." + The period of the star in Fig., The period of the star in Fig. + 1. is highly significant. while the one in Fig.," \ref{vradphase1} is highly significant, while the one in Fig." + 2. is close to the significance threshold., \ref{vradphase2} is close to the significance threshold. + Periodograms are shown in the bottom panels of these figures., Periodograms are shown in the bottom panels of these figures. + As properly emphasized by ?.. such a classical period search may not be appropriate for unevenly spaced sparse data. even though we set the significance level at a conservatively high level.," As properly emphasized by \citet{cumming1999}, such a classical period search may not be appropriate for unevenly spaced sparse data, even though we set the significance level at a conservatively high level." + In order to check this. we have done an additional LS analysis after prewhitening the original data by a linear polynomial.," In order to check this, we have done an additional LS analysis after prewhitening the original data by a linear polynomial." + This led almost always to the same frequencies., This led almost always to the same frequencies. + We only accepted a frequency when it was found to meet the significance criterion for both these analyses., We only accepted a frequency when it was found to meet the significance criterion for both these analyses. + The significant frequencies are listed in Table 1.., The significant frequencies are listed in Table \ref{freqs}. + ? already investigated the origin of the observed. radial velocities in K giant stars., \citet{hatzes1998} already investigated the origin of the observed radial velocities in K giant stars. + Although their sample contained only 9 stars. they suggested that the amplitude of the radial velocity increases with decreasing surface gravity (log g).," Although their sample contained only 9 stars, they suggested that the amplitude of the radial velocity increases with decreasing surface gravity $\log g$ )." + In lower surface gravity it takes longer to decrease the velocity of a moving parcel which results in larger amplitudes and the relation suggested by ? would therefore be evidence for pulsations or rotational modulation as the mechanism for these long period radial velocity variations., In lower surface gravity it takes longer to decrease the velocity of a moving parcel which results in larger amplitudes and the relation suggested by \citet{hatzes1998} would therefore be evidence for pulsations or rotational modulation as the mechanism for these long period radial velocity variations. + For the present sample. logg values were determined spectroscopically by ?.. by imposing excitation and tonisation equilibrium of iron lines through stellar models.," For the present sample, $\log g$ values were determined spectroscopically by \citet{hekker2007}, by imposing excitation and ionisation equilibrium of iron lines through stellar models." + The equivalent widthof about two dozen carefully selected tron lines were used for a spectroscopic LTE analysis based on the 2002, The equivalent widthof about two dozen carefully selected iron lines were used for a spectroscopic LTE analysis based on the 2002 +Extrasolar planets (ESPs) have an unexpected distribution of orbital radii around (heir host stars (Udryetal.2009) - ranging from about 0.02 to 70 astronomical units In parücular. ESPs are observed to obev a mass-period (M-P) relation wherein lower mass planets end up in short period orbits around their host stars (Udrv&Santos2007).,"Extrasolar planets (ESPs) have an unexpected distribution of orbital radii around their host stars \citep{ufq07} - ranging from about 0.02 to 70 astronomical units In particular, ESPs are observed to obey a mass-period (M-P) relation wherein lower mass planets end up in short period orbits around their host stars \citep{us07}." +. The predominance of very short period planets is generally thought to arise as a consequence οἱ planetary migration., The predominance of very short period planets is generally thought to arise as a consequence of planetary migration. + As an example. the tidal interaction of a planet with its surrounding gaseous disk excites density waves in the disk at so-called. Lindblad resonances.," As an example, the tidal interaction of a planet with its surrounding gaseous disk excites density waves in the disk at so-called Lindblad resonances." + These waves exert a torque back on the planet which results in a net angular momentum (ransler between them (Goldreich&Tremaine1980)., These waves exert a torque back on the planet which results in a net angular momentum transfer between them \citep{gt80}. +. Planets may also exchange angular momentum with (he eas inside of their horseshoe region (Ward1991)., Planets may also exchange angular momentum with the gas inside of their horseshoe region \citep{ward91}. +. For locally isothermal protoplanetary disks with smoothly declining distributions of disk column density aud temperature will radius. (he net torque generally leaves a planet spiraling inwards through the disk 2002).. i.e. the torque exerted by (he outer wake is mareinally stronger than that of the inner wake (Ward1997).," For locally isothermal protoplanetary disks with smoothly declining distributions of disk column density and temperature with radius, the net torque generally leaves a planet spiraling inwards through the disk \citep{ttw02}, i.e. the torque exerted by the outer wake is marginally stronger than that of the inner wake \citep{ward97}." +. Many caleulations and simulations show that the migration timescale of planets in such standard disk models is very short - roughly two orders of magnitude smaller than (he disk lifetime (one to ten million νους (Myr)) (Ward1997:Tanakaetal.2002:D'Angelo 2003).," Many calculations and simulations show that the migration timescale of planets in such ""standard"" disk models is very short - roughly two orders of magnitude smaller than the disk lifetime (one to ten million years (Myr)) \citep{ward97,npmk00,ttw02,dkh03}." +. Why are there anv planetary svslenis at all?, Why are there any planetary systems at all? + The kev to understanding the M-P relation ancl (he survival of planetary svstenis is in how the dynamics of planetary motion is coupled to the properties and structure of, The key to understanding the M-P relation and the survival of planetary systems is in how the dynamics of planetary motion is coupled to the properties and structure of +IMF can be different from nearby stars. too (Omulaüetal.2005).,"IMF can be different from nearby stars, too \citep{Omukai05}." +. Existence of the low mass EXP survivors iu the Galactic halo proves that some low mass EXIP stars can be formed. but typical mass of the EAIP population stars can be ore massive than Population I stars.," Existence of the low mass EMP survivors in the Galactic halo proves that some low mass EMP stars can be formed, but typical mass of the EMP population stars can be more massive than Population I stars." + TNomivaetal.(2007.2009a) eive constraints on the IME of EMDP stars from statistics of observed EXP survivors.," \citet{Komiya07, Komiya09} give constraints on the IMF of EMP stars from statistics of observed EMP survivors." + It is known that lhwee fraction (~20%) of the EMP survivors Colprise carbon eulhauced stars referred to as Carbou Enhanced Moetal-Poor (CEMP) stars., It is known that large fraction $\sim 20\%$ ) of the EMP survivors comprise carbon enhanced stars referred to as Carbon Enhanced Metal-Poor (CEMP) stars. + More thaw half of thei show large s-process clement culancement., More than half of them show large -process element enhancement. + Abundance anomalies of the s-process clement cuhanced CEMP stars sstars) are due to binary mass transfer., Abundance anomalies of the -process element enhanced CEMP stars stars) are due to binary mass transfer. + Tutermediate massive EMP stars with 08S—9A... svuthesize carbou and s-process elements in the asviuptotiec giaut brauch (AGB) phase. and pollute their companions to male them sstars.," Intermediate massive EMP stars with $0.8-3 \msun$ synthesize carbon and -process elements in the asymptotic giant branch (AGB) phase, and pollute their companions to make them stars." + We propose that CEAIP stars without s-process chhancement sstars) are also formed through binary mass transfer but frou more massive priuaries with |GOAL..., We propose that CEMP stars without -process enhancement stars) are also formed through binary mass transfer but from more massive primaries with $4-6\msun$. + From observational statistics of the aud sstars. we give constraints ono lass gistribution of primary stars of EXIP binaries aud conclude that typical mass of EMP stars is large (vomivaetal.2007).," From observational statistics of the and stars, we give constraints on mass distribution of primary stars of EMP binaries and conclude that typical mass of EMP stars is large \citep{Komiya07}." +. I&onivaetal.(2009a). discuss the constraints of the IAIF from CENP stars again in detail aud give an additional constraint from the total number of EXIP survivors., \citet{Komiya09} discuss the constraints of the IMF from CEMP stars again in detail and give an additional constraint from the total number of EMP survivors. + The unuuber of EMP. survivors in the Calactic halo is very sanall aud it indicates that the fraction of low lass survivors amoung the EMDP population is small., The number of EMP survivors in the Galactic halo is very small and it indicates that the fraction of low mass survivors among the EMP population is small. + As a result. a lognormal IME with medium mass. μαc LOAL... and clispersion. Aq~0.1. can satisfy all the constraiuts.," As a result, a lognormal IMF with medium mass, $\mmd \sim 10\msun$ , and dispersion, $\dm \sim 0.4$, can satisfy all the constraints." + Lucatelloetal.(2005) also eive a conustraiut ou the IAIF of EXP stars from statistics of sstars and arene that the typical mass of EXIP stars is shehtly higher than more metal rich stars., \citet{Lucatello05} also give a constraint on the IMF of EMP stars from statistics of stars and argue that the typical mass of EMP stars is slightly higher than more metal rich stars. + However. because they do not take account of sstars aud assiuae a stellar evolution model ciffereut from ours. they conclude lower typical mass. M4=0.79AL...," However, because they do not take account of stars and assume a stellar evolution model different from ours, they conclude lower typical mass, $\mmd=0.79\msun$." + Tn paper L we build a ierecr tree of the Calaxy and computethe enrichment history of mon abundance along the tree.," In paper I, we build a merger tree of the Galaxy and computethe enrichment history of iron abundance along the tree." + The high mass IME with M4=10M. (Ikoiiyvactal.2007) as adopted in the computations., The high mass IMF with $\mmd=10\msun$ \citep{Komiya07} is adopted in the computations. + We also discussed. origin of IIMP. stars considering the effect of surface pollution by accretion of metal enriched interstellar matter., We also discussed origin of HMP stars considering the effect of surface pollution by accretion of metal enriched interstellar matter. + In this paper. we investigate chemical evolution of several elemieuts with detailed theoretical nucleosvuthetic vields of metal deficicut massive stars.," In this paper, we investigate chemical evolution of several elements with detailed theoretical nucleosynthetic yields of metal deficient massive stars." + Model results with liagh aud low mass IMIFs are compared with compiled observational data., Model results with high and low mass IMFs are compared with compiled observational data. + To deal with individual characteristics of the EXP stars. all the individual EXIP population stars are registered im our conrputations.," To deal with individual characteristics of the EMP stars, all the individual EMP population stars are registered in our computations." + We discuss not oulv averaged abundances nmt also dispersion of thou., We discuss not only averaged abundances but also dispersion of them. +" ""Tuuuliusou(2006) preseuts a senianalvtic hierarchical nodel for the Calactic halo.", \citet{Tumlinson06} presents a semianalytic hierarchical model for the Galactic halo. + Salvadorietal.(2006) also calculate a hierarchical model with sas blowout roni halos by bursty star formation taken iuto account. mt they do not deal with iudividual stars aud do uot investigate diversity of the clement abuudauces.," \citet{Salvadori06} also calculate a hierarchical model with gas blowout from halos by bursty star formation taken into account, but they do not deal with individual stars and do not investigate diversity of the element abundances." + These xevious studies assiune the Salpeter IME for EXP stars., These previous studies assume the Salpeter IMF for EMP stars. + Additionally. these previous studies with hierarchical models investigate only iron abundance.," Additionally, these previous studies with hierarchical models investigate only iron abundance." + We calculate formation aud evolution of stellar halo with different IMEs aud compare the predicted mctallicity distribution functions (AIDFs) aud. abundance ratio distributions., We calculate formation and evolution of stellar halo with different IMFs and compare the predicted metallicity distribution functions (MDFs) and abundance ratio distributions. + We use four different sets of core-collapse SN. vields calculated for metal-poor stars., We use four different sets of core-collapse SN yields calculated for metal-poor stars. + Areastetal.(2000) aud INarlsson(2005) investigate clement abuudances of EMP stars usine inhomogeneous chemical evolution models., \citet{Argast00} and \citet{Karlsson05} investigate element abundances of EMP stars using inhomogeneous chemical evolution models. + However. they do not take account of the mereie history of the Calasy aud stars are assunied to be formed randomly iu space.," However, they do not take account of the merging history of the Galaxy and stars are assumed to be formed randomly in space." + They also do not investigate the IME dependence., They also do not investigate the IMF dependence. + This paper ids organized as follows., This paper is organized as follows. + Computation method and assuniptious appear in the next section., Computation method and assumptions appear in the next section. + Especially. asstuuptions about IMES and SN vields are described iu Sections ?? and ??.. respectively.," Especially, assumptions about IMFs and SN yields are described in Sections \ref{IMFS} and \ref{yieldS}, , respectively." + Iu Section ?7.. observational sample for comparison is deseribed.," In Section \ref{obsS}, observational sample for comparison is described." + We eive results in Section ?? and conclude the paper in Section ??.., We give results in Section \ref{resultS} and conclude the paper in Section \ref{concS}. + A hierarchical chemical evolution model for EMP stars is developed in Paper L We built a ποσο tree analytically using the method of Somerville&Ixolatt(1999) based on the extended Press-Schechter formialisi (Lacey&Cole1993)., A hierarchical chemical evolution model for EMP stars is developed in Paper I. We built a merger tree semi-analytically using the method of \citet{SK99} based on the extended Press-Schechter formalism \citep{LC93}. +. Alone the inerger tree. chemical eurichiueut and formation history of EMDP stars are calculated.," Along the merger tree, chemical enrichment and formation history of EMP stars are calculated." + In this paper. abuudauces of O. Na. Me. Cr. Fe. and Zu are computed aud compared to observations of metal poor stars.," In this paper, abundances of O, Na, Mg, Si, Cr, Fe, and Zn are computed and compared to observations of metal poor stars." + Stars are assumed to be formed in halos with virial temperature. Zi. higher than LOK. Star formation efficiency assunued to be constant and determined to sive |[Fo/H|=0 at: =0 (214«410HM/—11«10.8/vy for the following computations).," Stars are assumed to be formed in halos with virial temperature, $\Tv$, higher than $10^3$ K. Star formation efficiency assumed to be constant and determined to give $\feoh=0$ at $z=0$ $2.1\times 10^{-11} - 1.1\times 10^{-10}/{\rm yr}$ for the following computations)." + To investigate diversity of element abundances. all the iudividual EMP population stars are registered in our computations.," To investigate diversity of element abundances, all the individual EMP population stars are registered in our computations." + Mass of cach EMP staris specified randomly according to the statistical weight with the IME., Mass of each EMP staris specified randomly according to the statistical weight with the IMF. + ITalf of the all stellar systems are taken to be binaries and a flat mass ratio distribution is assumed., Half of the all stellar systems are taken to be binaries and a flat mass ratio distribution is assumed. + Adopted IMEs iare described iu Section 2? iu detail., Adopted IMFs are described in Section \ref{IMFS} in detail. + We set uucleosvuthesis vields of cach mmassive star as a fiction of it’s initial nass aud metallicity., We set nucleosynthesis yields of each massive star as a function of it's initial mass and metallicity. + Asstuuptions about vields are described in Section ??.., Assumptions about yields are described in Section \ref{yieldS}. + Each ninilialo is assumed to be chemically homogeneous., Each minihalo is assumed to be chemically homogeneous. + We use the same asstuptious as Model P in Paper I about radiative and cdvuamical feedback frou. massive stars., We use the same assumptions as Model P in Paper I about radiative and dynamical feedback from massive stars. + Massive stars ionize the ambient matter., Massive stars ionize the ambient matter. + At 2κ20. Lyinan-Werner backeround radiation inhibits star formation in nuini-halos those are not pre-donized.," At $z<20$, Lyman-Werner background radiation inhibits star formation in mini-halos those are not pre-ionized." + Encrectic SN. explosious blowout gas iu their lostninihalos when their effective kinetic cucrev. e£. ds lavecr than biudiug euergv. £j. of the eas of their host halos.," Energetic SN explosions blowout gas in their hostminihalos when their effective kinetic energy, $\epsilon E_{\rm k}$ , is larger than binding energy, $E_{\rm bin}$ , of the gas of their host halos." + Gas and metal ejected from iminihalos are nüxed muuediatelv and homogencously throughout the intergalactic imediun UCAD)., Gas and metal ejected from minihalos are mixed immediately and homogeneously throughout the intergalactic medium (IGM). + ΕΕ explosion enereies. Ly. of SNe are described iu Sec. ??..," Assumed explosion energies, $E_k$ , of SNe are described in Sec. \ref{yieldS}. ." + Fromlarger halos. a little fraction. εςEy. of metalejected by SNe is assumed to eo to IGAL where € is the fraction of supernovae explosion energy converted iuto kinetic," Fromlarger halos, a little fraction, $\eta\epsilon E_k/E_{\rm bin}$, of metalejected by SNe is assumed to go to IGM, where $\epsilon$ is the fraction of supernovae explosion energy converted into kinetic" +"og( FAL} 11) systems show a systematic and Lgignificant deviation. of up to AloeRh,~0.1 dex. from the xtrapolation of such a straight line.","$\log$ ) $\gtrsim 11$ ) systems show a systematic and significant deviation, of up to $\Delta \log R_e\sim 0.1$ dex, from the extrapolation of such a straight line." + Analogously. Fig.," Analogously, Fig." + 1c garows that the same subsample of old and massive galaxies. also show a significant departure of Ioge~0.05 dex above logC ffl.) 11 from the straight. long-dashed line of gaope 0.29. derived from fitting the rrelation calibrated on vounger galaxies only.," 1c shows that the same subsample of old and massive galaxies, also show a significant departure of $\Delta \log \sigma\sim 0.05$ dex above $\log$ ) $\gtrsim 11$ from the straight, long-dashed line of slope $\sim 0.29$, derived from fitting the relation calibrated on younger galaxies only." + In the overall. lis curvature is similar to that found for Εςέως. for which it is even more evident 2..," In the overall, this curvature is similar to that found for BCGs, for which it is even more evident \citet{Bernardi09}." + We stress here that this gradual steepening and corresponding Iattening in the relations. are present in galaxies ofa fixed age. thus mirroring a clear break in the homology when moving from lower to more massive svstcHis.," We stress here that this gradual steepening and corresponding flattening in the relations, are present in galaxies of a fixed age, thus mirroring a clear break in the homology when moving from lower to more massive systems." +The procedure described above provides a correlation function model at the redshifts where the simulation outputs were saved.,The procedure described above provides a correlation function model at the redshifts where the simulation outputs were saved. + The AGNs span a wide redshift range and we have to bin the data into several redshift intervals to achieve an acceptable level of accuracy for the correlation function measurements., The AGNs span a wide redshift range and we have to bin the data into several redshift intervals to achieve an acceptable level of accuracy for the correlation function measurements. +" Therefore, we need to account for any z-dependent trends of the correlation function models."," Therefore, we need to account for any $z$ -dependent trends of the correlation function models." +" Fortunately, for our choice of observables, ry and the &,(1)/Ep(rp) ratio, the redshift trends are very weak."," Fortunately, for our choice of observables, $r_{0}$ and the $\xip/\xir$ ratio, the redshift trends are very weak." + This is illustrated in 10.., This is illustrated in Fig. \ref{fig:z-trend}. +" The left shows ro as a function of Vmin for a populationFig. model with panelf=1 (all objects are at the centers of distinct halos) for the simulation outputs at z=0.5, 1, 2, and 3."," The left panel shows $r_{0}$ as a function of $\Vmin$ for a population model with $\fcen=1$ (all objects are at the centers of distinct halos) for the simulation outputs at $z=0.5$, 1, 2, and 3." +" Obviously, there is almost no change in ro for a fixed Vai, at z« 3."," Obviously, there is almost no change in $r_{0}$ for a fixed $\Vmin$ at $z<3$ ." + Any changes are much smaller than the uncertainties of our ry measurement even for thefull sample., Any changes are much smaller than the uncertainties of our $r_{0}$ measurement even for thefull sample. +" Therefore, we conclude that the model 7p as a function of Vinin does not evolve over our redshift range of The ratio also shows little, if any, evolution with redshift."," Therefore, we conclude that the model $r_{0}$ as a function of $\Vmin$ does not evolve over our redshift range of The ratio $\xip/\xir$ also shows little, if any, evolution with redshift." + The right ἔπ(π)/ἐρ(ηρ), The right panel in Fig. +" panelin Fig. 10 shows the results for the population model with V,=310 and f=0.5 of objects are in the satellite subhaloskm of Vmax>310km halos)."," \ref{fig:z-trend} shows the results for the population model with $\Vmin=310\,$ and $\fcen=0.5$ of objects are in the satellite subhalos of $\vmax>310\,$ halos)." + Any difference between the simulation outputs is within the uncertainties (estimated from analyzing three different projections for each simulation output)., Any difference between the simulation outputs is within the uncertainties (estimated from analyzing three different projections for each simulation output). +" The lack of evolution in the model over our redshift interval (and also the lack of clusteringdetectable evolution of ro with z, see refsec:res:vmin-z below) indicates that we can safely combine the data over the entire redshift range in the sample."," The lack of evolution in the clustering model over our redshift interval (and also the lack of detectable evolution of $r_{0}$ with $z$, see \\ref{sec:res:vmin-z} below) indicates that we can safely combine the data over the entire redshift range in the sample." +" Furthermore, there is no need to weight the models with the redshift distribution — one simply can use the results for the simulation output at z=1."," Furthermore, there is no need to weight the models with the redshift distribution — one simply can use the results for the simulation output at $z=1$." +" We take this approach in fitting the parameters of the population model, Vii, and f 5.1))."," We take this approach in fitting the parameters of the population model, $\Vmin$ and $\fcen$ \ref{sec:res:vmin-f}) )." +" In addition, we constrain the evolution of Vinin with z(§ 5.2)) under the assumption that the fraction of AGNs in the subhalos does not evolve (i.e., using a fixed f derived from the analysis of the entire sample)."," In addition, we constrain the evolution of $\Vmin$ with $z$ \ref{sec:res:vmin-z}) ) under the assumption that the fraction of AGNs in the subhalos does not evolve (i.e., using a fixed $\fcen$ derived from the analysis of the entire sample)." +" Finally, we note that the numerical simulations we use were run assuming a high value of the power spectrum normalization, σε=0.9 at z=0."," Finally, we note that the numerical simulations we use were run assuming a high value of the power spectrum normalization, $\sigma_{8}=0.9$ at $z=0$." +" This results in an incorrect prediction of the correlation amplitude for halos of a given mass, and thus slightly biases the derived parameters of the AGN population model, in particular, Vinin."," This results in an incorrect prediction of the correlation amplitude for halos of a given mass, and thus slightly biases the derived parameters of the AGN population model, in particular, $\Vmin$." +" Obviously, it would be best to use the simulations performed for the currently favored cosmological model with og«0.8 but in general, these were unavailable at the time of this investigation."," Obviously, it would be best to use the simulations performed for the currently favored cosmological model with $\sigma_{8}\approx0.8$ but in general, these were unavailable at the time of this investigation." +" In Appendix A,, we describe a procedure which can be used to scale the results from the comparison with the simulation to any desired cosmology."," In Appendix \ref{sec:cosm-depend-scal}, we describe a procedure which can be used to scale the results from the comparison with the simulation to any desired cosmology." +" In particular, if we usethe best-fit flat ACDM cosmological model derived from the joint analysis of the galaxy cluster mass function and other cosmological datasets, σε=0.786 and Qy=0.268(?),, the masses reported below should be scaled by a factor of 0.69, the Vinin’s decreased by10%,, and the number density of objectsincreased by 20%."," In particular, if we usethe best-fit flat $\Lambda$ CDM cosmological model derived from the joint analysis of the galaxy cluster mass function and other cosmological datasets, $\sigma_{8}=0.786$ and $\Omega_{M}=0.268$, the masses reported below should be scaled by a factor of $0.69$ , the $\Vmin$ 's decreased by, and the number density of objectsincreased by ." +". Figure 11 shows the combined constraints on the population model parameters, Vmin and f, obtained from fitting the full sample of AGNs."," Figure \ref{fig:Vmin-f} shows the combined constraints on the population model parameters, $\Vmin$ and$\fcen$ , obtained from fitting the full sample of AGNs." + The best-fit velocity threshold is Vinin=320+20km CL ," The best-fit velocity threshold is $\Vmin=320\pm20\,$ CL one-parameter uncertainty)." +"At z= 1, this toΜαρ= Mo, or uncertainty).2.4x10?AT!Μο after correspondscorrecting for the lower-orgcosmology (see 4.4.0 and Appendix A))'®.."," At $z=1$ , this corresponds to$\M200=4.1\times10^{12}\,h^{-1}\,M_{\odot}$ , or $2.4\times10^{12}\,h^{-1}\,M_{\odot}$ after correcting for the $\sigma_{8}$cosmology (see \ref{sec:sigma8:corr} and Appendix \ref{sec:cosm-depend-scal}) ." + where 2. is the effective radius of a cluster. elliptical ealaxv.,", where $R_{\rm +e}$ is the effective radius of a cluster elliptical galaxy." +" From now on. we refer to this Spx ratio as ra, just for convenience."," From now on, we refer to this $S_{\rm N}$ ratio as $r_{\rm sn}$ just for convenience." + As our simulations have demonstrated. the outer GC's are much more elficientIy stripped than the inner GC's in an elliptical galaxy.," As our simulations have demonstrated, the outer GCs are much more efficiently stripped than the inner GCs in an elliptical galaxy." + As a natural result. of this. for example. the ratio of Sx within 2. to that within 10 72. in NGC 1404 is changed from 0.18 into 0.49 during 2 Gyr of dvnamical evolution (for an orbital eccentricity of 0.76).," As a natural result of this, for example, the ratio of $S_{\rm N}$ within $R_{\rm e}$ to that within 10 $R_{\rm e}$ in NGC 1404 is changed from 0.18 into 0.49 during 2 Gyr of dynamical evolution (for an orbital eccentricity of 0.76)." + We can therefore distinguish the tidal stripping scenario of low Spx E formation from that in which NGC 1404 has initially a small Sp of ~ 2. because only the former scenario predicts a larger ry (2 0.2).," We can therefore distinguish the tidal stripping scenario of low $S_{\rm N}$ E formation from that in which NGC 1404 has initially a small $S_{\rm N}$ of $\sim$ 2, because only the former scenario predicts a larger $r_{\rm +sn}$ $>$ 0.2)." + NGC 1404 has a local Sx of 0.5 at 2 = |A. and 2.0 at /2 — OF. and thus a larecr ry of 0.25. which implies that tical stripping can be responsible for the observed low Sx of 2 in NGC 1404.," NGC 1404 has a local $S_{\rm N}$ of 0.5 at $R$ = $1R_{\rm e}$ and 2.0 at $R$ = $9R_{\rm e}$ and thus a larger $r_{\rm +sn}$ of 0.25, which implies that tidal stripping can be responsible for the observed low $S_{\rm N}$ of 2 in NGC 1404." + The second observable characteristic of the tidal stripping scenario is the formation of an elongated. or Iattened distribution (or “tidal stream) ofLOGCs along the orbit of their previous host. galaxy., The second observable characteristic of the tidal stripping scenario is the formation of an elongated or flattened distribution (or “tidal stream”) of ICGCs along the orbit of their previous host galaxy. + We do. however. point out that it is formidable task to determine which cluster member ealaxy previously hosted. cach “LCGC stream”.," We do, however, point out that it is formidable task to determine which cluster member galaxy previously hosted each “ICGC stream”." + Ixinematic and metallicity information of ICCGCSs may help up to identify each individual stream. only i£ the ICCGCs have not been alfected by scattering and dynamical relaxation via interaction between these ICGCSs and other cluster member galaxies since they were stripped from their host galaxies.," Kinematic and metallicity information of ICGCs may help up to identify each individual stream, only if the ICGCs have not been affected by scattering and dynamical relaxation via interaction between these ICGCs and other cluster member galaxies since they were stripped from their host galaxies." + The central region of a cluster is a place where many galaxies mutually interact with one another. and much Larger number of metal-poor GC's could be stripped from numerous dwarf galaxies surrounding the central cluster ¢D. which hampers the identification of the possible LOCC streams formed. by GC stripping from cluster ellipticals.," The central region of a cluster is a place where many galaxies mutually interact with one another, and much larger number of metal-poor GCs could be stripped from numerous dwarf galaxies surrounding the central cluster cD, which hampers the identification of the possible ICGC streams formed by GC stripping from cluster ellipticals." + Phus we conclude that it is very hard to demonstrate that the process of GC stripping is taking place from the projected. distributions alone., Thus we conclude that it is very hard to demonstrate that the process of GC stripping is taking place from the projected distributions alone. + The third is the statistical correlation between the distance of an elliptical galaxy from the centre of a cluster and the Sp of the galaxy., The third is the statistical correlation between the distance of an elliptical galaxy from the centre of a cluster and the $S_{\rm N}$ of the galaxy. + Ehe present numerical results weciet that if the orbital eccentricities of galaxies docs not depend on the location of these with respect to the centre of a cluster. Sy ofa galaxy can correlate with the distance from he cluster centre such that Sx is smaller for à galaxy. close o the cluster core.," The present numerical results predict that if the orbital eccentricities of galaxies does not depend on the location of these with respect to the centre of a cluster, $S_{\rm N}$ of a galaxy can correlate with the distance from the cluster centre such that $S_{\rm N}$ is smaller for a galaxy close to the cluster core." + Some evidence of this trend can be seen in the Fornax eluster., Some evidence of this trend can be seen in the Fornax cluster. + We expect the proposed. correlation o be more obvious in the more dvnamicallv relaxedfolder galaxy clusters. because elliptical galaxies in these clusters jwe already. experienced. pericenter passages several times and lost their GC's by tidal stripping.," We expect the proposed correlation to be more obvious in the more dynamically relaxed/older galaxy clusters, because elliptical galaxies in these clusters have already experienced pericenter passages several times and lost their GCs by tidal stripping." + In our future work we will gencralise our simulations to more galaxies within a cluster. and to clusters of varving properties.," In our future work we will generalise our simulations to more galaxies within a cluster, and to clusters of varying properties." + Various cilferent physical mechanisms are considered to play a role in ealaxy evolution in clusters: c.g.. Itam. pressure stripping (Ciunn Cott 1972). tidal encounters (Iche 1985: Aloore et al.," Various different physical mechanisms are considered to play a role in galaxy evolution in clusters: e.g., Ram pressure stripping (Gunn Gott 1972), tidal encounters (Iche 1985; Moore et al." + 1996). tidal compression by the gravitational field ofa cluster (Byrd Valtonen 1990). minor or uncqual-mass mergers (DBekki 1998).," 1996), tidal compression by the gravitational field of a cluster (Byrd Valtonen 1990), minor or unequal-mass mergers (Bekki 1998)." + One of the most. important parameters which determine the elfectiveness of the each physical mechanism: is suggested. to be. the. pericenter distance of the orbit of a galaxy., One of the most important parameters which determine the effectiveness of the each physical mechanism is suggested to be the pericenter distance of the orbit of a galaxy. + For example. ram pressure stripping is ellicient. only when a gas-rich. cluster galaxy can pass through the cluster core where there is plenty of rot gas (e.g. Abadi et al.," For example, ram pressure stripping is efficient only when a gas-rich cluster galaxy can pass through the cluster core where there is plenty of hot gas (e.g., Abadi et al." + 1999)., 1999). + Equally. morphological ransformation via a cluster tidal field can be significant only when the pericenter of a cluster galaxy is small enough o approach the core radius (it should be noted here that the adest hieh-resolution simulations on dynamical evolution of galaxies in hierarchically forming clusters by Cinedin (2003) demonstrate that the tidal effects can be important hroughout the cluster).," Equally, morphological transformation via a cluster tidal field can be significant only when the pericenter of a cluster galaxy is small enough to approach the core radius (it should be noted here that the latest high-resolution simulations on dynamical evolution of galaxies in hierarchically forming clusters by Gnedin (2003) demonstrate that the tidal effects can be important throughout the cluster)." + Therefore it is important to give some observational constraints on the orbital properties (c.g... mean eecentricity of galaxy orbits ancl its dispersion) of galaxies in clusters.," Therefore it is important to give some observational constraints on the orbital properties (e.g., mean eccentricity of galaxy orbits and its dispersion) of galaxies in clusters." + Jased on the present numerical results. we propose hat thegaleries.," Based on the present numerical results, we propose that the." + Figs., Figs. + δ and 9 illustrate which kinematical properties can be useful for this purpose., 8 and 9 illustrate which kinematical properties can be useful for this purpose. + In these two figures. we first choose GCs that are outside LO 72. of NGC 1404 in each model and then investigated kinematical properties of these stripped. CC's that are regarded as as LOGCs drifting Fornax cluster.," In these two figures, we first choose GCs that are outside 10 $R_{\rm e}$ of NGC 1404 in each model and then investigated kinematical properties of these stripped GCs that are regarded as as ICGCs drifting Fornax cluster." + The upper panel of Fig., The upper panel of Fig. + S shows that the distribution of ICCGCSs, 8 shows that the distribution of ICGCs +"Depending on the details of the coefficients. the FP can be understood im terms of a systematic relation between huninosity+. aud a dimeusional.B mass such as Afgan,—C2) of the form £κ (e.g.Faberetal.1987:a7(R,Bender1992:CiottiAL,al. 1996).","Depending on the details of the coefficients, the FP can be understood in terms of a systematic relation between luminosity and a dimensional mass such as $M_{\mathrm{dim}} \equiv G^{-1} \sigma_{e2}^2 (R_e / 2)$ of the form $L \propto M_{\mathrm{dim}}^{\eta}$ \citep[e.g.,][]{faber_87, bbf_92, clr_fp_96}." +. Such a relation leads to FP coefficieuts i Equation 2 given bya=η yyandhb=α1)., Such a relation leads to FP coefficients in Equation \ref{fpform} given by $a = 2 \eta / (2 - \eta)$ and $b = -1 / (2 - \eta)$. +" This may be conceptualized as a systematic variation of a “dimensional mass-to-light ratio” Yon,=Afgan/£ with Aan.", This may be conceptualized as a systematic variation of a “dimensional mass-to-light ratio” $\Upsilon_{\mathrm{dim}} \equiv M_{\mathrm{dim}} / L$ with $M_{\mathrm{dim}}$ . + It is. however. maportaut to keep iu imiud that Youu is linerly. proportional to the ht ratio Y oulv if the FP tilt is due to a systematic mass-to-lelt ratio treud. rather than to a trend in mass-dynamical structure.," It is, however, important to keep in mind that $\Upsilon_{\mathrm{dim}}$ is linearly proportional to the mass-to-light ratio $\Upsilon$ only if the FP tilt is due to a systematic mass-to-light ratio trend, rather than to a trend in mass-dynamical structure." +" The availability of stroug-leusiug aperture masses in addition to the traditional FP observables allows us to directly test the alternative hypotheses for the ""tilt of the FP. because in addition to Mg. we measure the aperture mass M44 from strong lensing."," The availability of strong-lensing aperture masses in addition to the traditional FP observables allows us to directly test the alternative hypotheses for the “tilt” of the FP, because in addition to $M_{\mathrm{dim}}$, we measure the aperture mass $M_{\mathrm{lens}}$ from strong lensing." + Consider the following two relations: Consider also the following two alternative hypotheses: (1) on average. earlv-tvpe galaxies have a universal lnass-dvnamucal structure. aud the tilt of the FP is due to a systematic trend in total mass-to-light ratio with mass: or (2) on average. early-type galaxies lave a universal mass-to-lieht ratio. aud the tilt of the FP is due to a systematic trend dm ΤΝπα structure.," Consider the following two relations: Consider also the following two alternative hypotheses: (1) on average, early-type galaxies have a universal mass-dynamical structure, and the tilt of the FP is due to a systematic trend in total mass-to-light ratio with mass; or (2) on average, early-type galaxies have a universal mass-to-light ratio, and the tilt of the FP is due to a systematic trend in mass-dynamical structure." + If hypothesis (1) is correct. then we should find 9~ l. whereas if hypothesisρα (2) is correct. we should fiud &zmy ," If hypothesis (1) is correct, then we should find $\delta \simeq 1$ , whereas if hypothesis (2) is correct, we should find $\delta \simeq \eta$." +Of course. we may also find that y«6<1. since iu principle both explanations could contribute to the tilt of theFP.," Of course, we may also find that $\eta < \delta < 1$, since in principle both explanations could contribute to the tilt of the." +". Roughly speaking. lawpothesis (1) represeuts “homology” aud hypothesis (2) represents ""non-honmologv."," Roughly speaking, hypothesis (1) represents “homology” and hypothesis (2) represents “non-homology”." + Before proceeding. we uote that nunerous works ive explored the possible role of a systematically varving Sérysic iudex s in causing the tilt of the FP (e.g.Tjorth&Aladsen1995:GrahamColless1997:etal.2002:Trujillo 2001).. and thus we uust not disregard this possibility in our own analysis.," Before proceeding, we note that numerous works have explored the possible role of a systematically varying Sérrsic index $n$ in causing the tilt of the FP \citep[e.g.,][]{hjorth_madsen, graham_colless_97, bcdp_02, tbb_fp}, and thus we must not disregard this possibility in our own analysis." + We compute » for all SLACS lenses by continuing he de Vaucouleurs model optimizations after frecing he iudex from its fixed 5»=αι value., We compute $n$ for all SLACS lenses by continuing the de Vaucouleurs model optimizations after freeing the index from its fixed $n = 1/4$ value. + We find hat » is courpletely uncorrelated with leusiug lass. dynamical mass dDundnositv. and velocity. dispersion within the sample. and therefore the inclusion of the Sérrsic index as a significant factor i our analysis is not motivated by the data.," We find that $n$ is completely uncorrelated with lensing mass, dynamical mass, luminosity, and velocity dispersion within the sample, and therefore the inclusion of the Sérrsic index as a significant factor in our analysis is not motivated by the data." + This lack of correlation between n and other quantitiesis iu fact cousisteut with other studies. since the SLACS sample is confined to rclatively lighanass/ligh-luminosity carly-type galaxies. aud does uot extend over a sufücieut ranee to define the » L correlation significantly eiveu the level of intrinsic scatter (ee.Caonetal.1993:D'Onofrio199Caiman2003:Ferrareseetal.," This lack of correlation between $n$ and other quantitiesis in fact consistent with other studies, since the SLACS sample is confined to relatively high-mass/high-luminosity early-type galaxies, and does not extend over a sufficient range to define the $n$ $L$ correlation significantly given the level of intrinsic scatter \citep[e.g.,][]{caon_93, donofrio_94, graham_guzman, ferrarese_06}." + 2006).. Table 3 shows the results of fits for the nonualizations and expoueuts of the relations defined in Equations and 6. as well as for the relation between πιοντν and lensing mass.," Table \ref{mlcoeffs} shows the results of fits for the normalizations and exponents of the relations defined in Equations \ref{mlformone} and \ref{mlformtwo}, as well as for the relation between luminosity and lensing mass." + Within the uncertainties. the clear result is that à~1 wlüle jg<1: thus. we conclude based upon our smuple of leuses that the tilt of the FP.as defined bv iassive cllipticalsis due to a systematic trend ia iass-to-lieht ratio aud not to a trend nimassdensmundeal structure.," Within the uncertainties, the clear result is that $\delta \simeq 1$ while $\eta < 1$: thus, we conclude based upon our sample of lenses that the tilt of the FP—as defined by massive ellipticals—is due to a systematic trend in mass-to-light ratio and not to a trend inmass-dynamical structure." +" These relations are shown eraphically iu Figure 3.. where we cau see by eve that the logarithmic slope of the Mj-versus- Moin relation is significautlv less shallow than those of the Ly-versus-Mqg, and Ly-versus- Mya; relations."," These relations are shown graphically in Figure \ref{m_vs_l}, , where we can see by eye that the logarithmic slope of the $M_{\mathrm{lens}}$ $M_{\mathrm{dim}}$ relation is significantly less shallow than those of the $L_V$ $M_{\mathrm{dim}}$ and $L_V$ $M_{\mathrm{lens}}$ relations." +"with e=AT;/m, and the factor of i;bn. would be isn5 lor n;5©1.","with $c_s^2 = kT_{ism}/m_p$ and the factor of $n_{ism,5}^{3/2}$ would be $n_{ism,5}$ for $n_{ism,5} > 1$." +" The coellicient. F. is a function of the ambient medium. but independent of Mj; (except for the implicit dependence through 7;,5)."," The coefficient, $F$, is a function of the ambient medium, but independent of $M_{BH}$ (except for the implicit dependence through $T_{in,5}$ )." +" The solution to Equation 19 is thus: where Mp4 is the initial mass of the black hole and /,4. is the time when the black hole began to accrete."," The solution to Equation \ref{mdot2} is thus: where $M_{BH,0}$ is the initial mass of the black hole and $t_{acc}$ is the time when the black hole began to accrete." +" For a black hole born at time /; lor which accretion was delaved by a lime /;,4,,. (hen lace=ly+lactay."," For a black hole born at time $t_b$ for which accretion was delayed by a time $t_{delay}$, then $t_{acc} = t_b + t_{delay}$." + Figure 1 gives à schematic diagram of the growth of a black hole seed in this framework and Figure 2 gives the black hole mass as a function of lime for various choices of the interstellar densitv. with other parameters held coustant.," Figure 1 gives a schematic diagram of the growth of a black hole seed in this framework and Figure 2 gives the black hole mass as a function of time for various choices of the interstellar density, with other parameters held constant." +" The timescale for a seed black hole to grow to infinite mass is given (for nj,«1) bv: Note that this (ime scale increases verv steeply with the velocity of the black hole."," The timescale for a seed black hole to grow to infinite mass is given (for $n_{ism,5} < 1$ ) by: Note that this time scale increases very steeply with the velocity of the black hole." + ⇁−∙ − 23..− ⋅ 9EE2∙∙ − ⋅⋅ ∖∖↕⋅↕⊔∐↖≺↽↔↴⊔∐↲∖⇁≼↲↥∪≺∢∐∡∖↽≺∢∪↕⋅↕⋅≼↲≺∢⊔∪∐↓⋯∢↥∪↕⋅≀↧↪∖⊽∙∕≳⇁∶≼⋡∣⇁−⊹∣↽⇀∶∣⋝∕∕∕∣↽⇀∶≀↧↴∐≼⇂≺∢∪∐↕∣↽≻∐∐∐≸≟⊏≺⇂∏≀↧↴⊔∪∐⋟∖⊽−≻−≻≀↕↴∐≼⇂ we can write: Aly for fichicial temperature parameters. and [or joy<1.," Writing the velocity correction factor as $f_v = (v^2 + c_{s}^2)/c_{s}^2$ and combining Equations \ref{MBH1} and \ref{growtime}, we can write: for fiducial temperature parameters, and for $n_{ism,5} < 1$." + In our model. (he most massive black holes will be those that began growing Irom seeds at a time. {ων alter the first stellar mass black holes began to form at fo. or lee.=fo+fugi.," In our model, the most massive black holes will be those that began growing from seeds at a time, $t_{delay}$ after the first stellar mass black holes began to form at $t_0$, or $t_{acc} = t_0 + t_{delay}$." + With seed black holes of mass Alps=AL... the most massive black hole will have a mass of about 22 Gv (at z.— 3) after (he [ist stellar mass black holes lormec and about. aat 3Gv.," With seed black holes of mass $M_{BH,0} = 10$, the most massive black hole will have a mass of about 2 Gy (at z 3) after the first stellar mass black holes formed and about at 3Gy." + The mass would formally become infinite at 7.2 Gv for the chosen parameters. bul conditions. especially Γρ. would have changed by then and (the accretion might be limited bv the Edclington limit.," The mass would formally become infinite at 7.2 Gy for the chosen parameters, but conditions, especially $n_{ism}$ , would have changed by then and the accretion might be limited by the Eddington limit." + For the timescales of interest here and nj;<1. this extreme growth is not of interest.," For the timescales of interest here and $n_{ism,5} < 1$, this extreme growth is not of interest." + We retium in relEddington to discuss the possible effect of growth to accretion at the Ecldineton limit., We return in \\ref{Eddington} to discuss the possible effect of growth to accretion at the Eddington limit. + We can now evaluate (he number of black holes that will have lormed by a certain epoch. their luminosity al Chat epoch. ancl the energy they. will have emitted by that epoch.," We can now evaluate the number of black holes that will have formed by a certain epoch, their luminosity at that epoch, and the energy they will have emitted by that epoch." + The number of black holes of a specilic mass. Mgj(/) al a Gime. (t. will depend on the rate at which the seed black holes were bornand their accretion history.," The number of black holes of a specific mass, $M_{BH}(t)$ at a time, t, will depend on the rate at which the seed black holes were bornand their accretion history." + Equation 22. can, Equation \ref{MBH1} can +and Therefore. (he partition function is given bv where Ziwist The integral in equation (107)) is taken over all possible paths of w(s).,"and Therefore, the partition function is given by where and The integral in equation \ref{app3-Ztw}) ) is taken over all possible paths of $\omega (s)$." + The average end-to-end extension of DNA ean be ealeulated from equation (56))., The average end-to-end extension of DNA can be calculated from equation \ref{z2}) ). + Since Zi44 does not depend on f. one can write It is clear from equations (102)) and (103))that one needs to calculate onlv Zj.," Since $Z_{\mathrm{twist}}$ does not depend on $f$, one can write It is clear from equations \ref{app3-ER}) ) and \ref{app3-EI}) )that one needs to calculate only $Z_I$ ." +" Ζ can be calculated simply by replacing 4A with -- in the expression obtained for Z,.", $Z_R$ can be calculated simply by replacing $\hat{A}$ with $-\hat{A}$ in the expression obtained for $Z_I$ . + From equation (103)) we have where and, From equation\ref{app3-EI}) ) we have where and +The companion itself might produce x-ray Luminosity of 107*.77ergst. unless it is extremely magnetically active (Stelzer et al.,"The companion itself might produce x-ray luminosity of $10^{27-28} \erg~s^{-1}$, unless it is extremely magnetically active (Stelzer et al." + 2005)., 2005). +" Berehdller Wencdker (2000) analvzed. ROSAT LR observations of P Cyeni and clerivec an upper limit for the lux which translates tol,«XNd10""mergs+ for⋅⋠ dts x-ray luminosity.. adopting the more recent distance estimate of 1.7kpc (Najarro et al."," Berghöffer Wendker (2000) analyzed ROSAT HRI observations of P Cygni and derived an upper limit for the flux which translates to $L_x \leq 8.4 \times 10^{30} \erg~s^{-1}$ for its x-ray luminosity, adopting the more recent distance estimate of $1.7\kpc$ (Najarro et al." + 1997a)., 1997a). + Therclore the x-ray Luminosity expected from the presence of the companion does not contracict observations., Therefore the x-ray luminosity expected from the presence of the companion does not contradict observations. + more sensitive observations might indeed detect the x-ray luminositw of 107ergs. that my model predicts., A more sensitive observations might indeed detect the x-ray luminosity of $L_x \sim 10^{29} \erg~s^{-1}$ that my model predicts. + The spectra of P Cvgni in the optical ancl near-L1 show that the emission lines typically have broadening of ~200kms+ (Najarro et al., The spectra of P Cygni in the optical and near-IR show that the emission lines typically have broadening of $\sim 200~\rm{km~s^{-1}}$ (Najarro et al. + 1997b)., 1997b). + It is expected in mx moclel. that radial velocity shift in spectral lines due to orbital motion would not be detected.," It is expected in my model, that radial velocity shift in spectral lines due to orbital motion would not be detected." + Most of the spectral lines that are observed: are. emitted from the LBV. as it is much more luminous than the companion.," Most of the spectral lines that are observed are emitted from the LBV, as it is much more luminous than the companion." + For the orbital parameters and stellar masses that Lsugeest in this paper. the radial velocity of the LBY relative to the center of mass at periastron iseTOkms+.," For the orbital parameters and stellar masses that I suggest in this paper, the radial velocity of the LBV relative to the center of mass at periastron is $\simeq 70~\rm{km~s^{-1}}$." + Γης maximal racial velocity is smaller than the broadening of the lines due to the LDV wind., This maximal radial velocity is smaller than the broadening of the lines due to the LBV wind. + In addition. the binary svstem. might. be inclined. to our line of sight. so this velocity might be further reduced.," In addition, the binary system might be inclined to our line of sight, so this velocity might be further reduced." + According to the model. presently the LBY reaches that velocity. only once every ~Yves. or possibly slightly less. as there is mass transfer in the last peak. and therefore the final orbital period should be somewhat shorter than the interval between. last two peeks.," According to the model, presently the LBV reaches that velocity only once every $\sim 7 \yrs$, or possibly slightly less, as there is mass transfer in the last peak, and therefore the final orbital period should be somewhat shorter than the interval between last two peeks." + Thus. every ~7ves it should be possible to detect radial velocity changes due to orbital motion in spectral lines. if the inclination angle is large enough.," Thus, every $\sim7 \yrs$ it should be possible to detect radial velocity changes due to orbital motion in spectral lines, if the inclination angle is large enough." + L therefore predict. that. a continuous 7 vear long observation of pronounced lines may reveal a small doppler shift variation. close to the periastron passage.," I therefore predict that a continuous 7 year long observation of pronounced lines may reveal a small doppler shift variation, close to the periastron passage." + Lt is impossible at the moment to predict the exact imes of periastron passages., It is impossible at the moment to predict the exact times of periastron passages. + The astrometric wobble should be casily detected v future telescopes., The astrometric wobble should be easily detected by future telescopes. +" For example. if PP Cveni is to be one of the ~10"" galactic stars observed T0 times by the Global Astrometric Laterferometer for Astrophysics (GALA) during its planned 5 vear mission. there are avorable chances of detecting the companion."," For example, if P Cygni is to be one of the $\sim 10^9$ galactic stars observed 70 times by the Global Astrometric Interferometer for Astrophysics (GAIA) during its planned 5 year mission, there are favorable chances of detecting the companion." + Also. if the Space Laterferometry Mission. (SIM) is to be unched and targeted to PP Cyeni every ~0.5ves. it should detect the companion.," Also, if the Space Interferometry Mission (SIM) is to be lunched and targeted to P Cygni every $\sim 0.5 \yrs$, it should detect the companion." + LE strongly encourage to include P Cvgni in the list of observed objects for these wo future missions., I strongly encourage to include P Cygni in the list of observed objects for these two future missions. + In Washi Soker (2009) we suggested that major LBV eruptions are triggered.oo by binary. interaction., In Kashi Soker (2009) we suggested that major LBV eruptions are triggered by binary interaction. + The possible most problematic example to be considered against our claim was P C€vgni. as it was believed to be à single star which underwent such an eruption.," The possible most problematic example to be considered against our claim was P Cygni, as it was believed to be a single star which underwent such an eruption." + In this paper E show that even the eruption of P Cvgni presents evidence of binary interaction. and by that ] strengthen the conjecture that. probably all major LBY eruptions are trigecrecl by interaction of a stellar companion.," In this paper I show that even the eruption of P Cygni presents evidence of binary interaction, and by that I strengthen the conjecture that probably all major LBV eruptions are triggered by interaction of a stellar companion." + From the calculation in section 3 it is evident that the circularization time for LBV systems is long. and for that it is probable that many LDVs have binary companion in an eccentric orbit.," From the calculation in section \ref{subsec:discussion:dragtidal}, it is evident that the circularization time for LBV systems is long, and for that it is probable that many LBVs have binary companion in an eccentric orbit." + The parameter space of the companion stellar and orbital parameters is large. ancl therefore it. is expected that LBVs would have varving types of major eruptions.," The parameter space of the companion stellar and orbital parameters is large, and therefore it is expected that LBVs would have varying types of major eruptions." + However. Lsuggest that in most cases there will be a common characteristic. a change in the orbital period as a result of mass transfer. that can be expressed in the light curve.," However, I suggest that in most cases there will be a common characteristic, a change in the orbital period as a result of mass transfer, that can be expressed in the light curve." + As the companion responsible for triggering the LBY eruptions. which are mass loss episodes. it has avery important role in the evolution of the massive LBY.," As the companion responsible for triggering the LBV eruptions, which are mass loss episodes, it has a very important role in the evolution of the massive LBV." + The process by which companions enhance the mass loss from LBV stars during major eruptions accelerates the evolution. of LBV stars to the WR hase., The process by which companions enhance the mass loss from LBV stars during major eruptions accelerates the evolution of LBV stars to the WR phase. + The differences between dillerent. LBVs might »e a result of dillerences in the binary. properties. such as orbital period. cecentricity and. companion: nass and wind momentum.," The differences between different LBVs might be a result of differences in the binary properties, such as orbital period, eccentricity and companion mass and wind momentum." + Particularly. the companion avs a major role in determining the destiny of the LBY and the binary system.," Particularly, the companion plays a major role in determining the destiny of the LBV and the binary system." + For example. the presence of massive cireumbinary nebula might lead to a very sight supernova.," For example, the presence of massive circumbinary nebula might lead to a very bright supernova." + “Vhis process ancl its observational imprints have been theoretically studied by Kotak Vink (2006). anc might have been observed in SN 2006gv (Smith et al.," This process and its observational imprints have been theoretically studied by Kotak Vink (2006), and might have been observed in SN 2006gy (Smith et al." + 2007)., 2007). + Ll thank my advisor Noam Soker for advising me in writing this paper. and the referee John J. Eledriclec [or comments that helped to improve the paper.," I thank my advisor Noam Soker for advising me in writing this paper, and the referee John J. Eldridge for comments that helped to improve the paper." + This research: was supported by the Asher Fund for Space ltesearch at the Technion. and the [Esrael Science Founcation.," This research was supported by the Asher Fund for Space Research at the Technion, and the Israel Science Foundation." +spectra such as those obtained with FUSE. which extend down (to the Lyman limit where in some cases a disk and photosphere present disünguishable signatures.,"spectra such as those obtained with FUSE, which extend down to the Lyman limit where in some cases a disk and photosphere present distinguishable signatures." + The slope of the continuum in V751 Cveni is relatively flat even alter the large de-reddening while the Lya absorplion is narrow., The slope of the continuum in V751 Cygni is relatively flat even after the large de-reddening while the $\alpha$ absorption is narrow. +" We were unable to find any optically Chick. steady state accretion disk model that woiuld yield a satifactory fit to the STIS spectrum of V?51 (νο,"," We were unable to find any optically thick, steady state accretion disk model that woiuld yield a satifactory fit to the STIS spectrum of V751 Cygni." + Therefore. we could not determine a reliable accretion rate for this svstem.," Therefore, we could not determine a reliable accretion rate for this system." +" As stated earlier, Vr51 Cvgni could turn out to be an SW Sextantis subclass of nova-like variables."," As stated earlier, V751 Cygni could turn out to be an SW Sextantis subclass of nova-like variables." + Many. such svstems reveal reclelish UV-optical spectral energy distributions ancl (hus cannot be fit with standard disk moclels., Many such systems reveal reddish UV-optical spectral energy distributions and thus cannot be fit with standard disk models. + For V380 Oph. a definite SW Sextantis nova-like svstem. the FUV spectrum is dominated by broad emission features. a relatively [at continuum ancl a narrow Lyo absorption feature.," For V380 Oph, a definite SW Sextantis nova-like system, the FUV spectrum is dominated by broad emission features, a relatively flat continuum and a narrow $\alpha$ absorption feature." + Even with a reddening of E(D-V)— 0.2 and hieher. our svnthetic spectral analvsis using standard accretion disk models was unable to derive a reliable accretion rate for V380 Oph.," Even with a reddening of E(B-V)= 0.2 and higher, our synthetic spectral analysis using standard accretion disk models was unable to derive a reliable accretion rate for V380 Oph." + This is another example of an SW Sex star wilh a reddish UV-optical spectral energy distribution that cannot be fit successlully with standard disk models., This is another example of an SW Sex star with a reddish UV-optical spectral energy distribution that cannot be fit successfully with standard disk models. + On the other hand. as shown in Figures 6 and 7. there are some definite SW Sex svstems can be fit sucessfully with standard: disk models.," On the other hand, as shown in Figures 6 and 7, there are some definite SW Sex systems can be fit sucessfully with standard disk models." + Like V751 Cvgni. we can saw little about the white dwarl in V380 Oph during it high state without FUV spectra which extend down to the Lyman Limit.," Like V751 Cygni, we can say little about the white dwarf in V380 Oph during it high state without FUV spectra which extend down to the Lyman Limit." + Further determinations of accretion rates and. whenever possible. white dwail temperatures are required. to elucidate the role of SW Sex stars and other nova-like variables in CV evolution.," Further determinations of accretion rates and, whenever possible, white dwarf temperatures are required to elucidate the role of SW Sex stars and other nova-like variables in CV evolution." + This work was supported by HST grant snapshot grants GO-090357.02A. GO-0724.02A NSF erant ASTOSO0T392. NASA erant NNGOIGETSG and by summer undergraduate research support from the NASA-Delaware Space Grant Consortium.," This work was supported by HST grant snapshot grants GO-09357.02A, GO-9724.02A NSF grant AST0807892, NASA grant NNG04GE78G and by summer undergraduate research support from the NASA-Delaware Space Grant Consortium." + The ISM model used in this work was generated bx Paul E. Barrett (USNO) for the analvsis of theFUSE spectra of DNs and NLs related (o a different project (PI Godon)., The ISM model used in this work was generated by Paul E. Barrett (USNO) for the analysis of the spectra of DNs and NLs related to a different project (PI Godon). + PG wishes to thank Mario Livio for his kind hospitality as the Space Telescope Science Institute. where part of this work was carried out.," PG wishes to thank Mario Livio for his kind hospitality as the Space Telescope Science Institute, where part of this work was carried out." + Some or all of the data presented in this paper were obtained from the Alultimission Archive αἱ the Space Telescope Science Institute (AIAST)., Some or all of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST). + STSel is operated bv the Association of Universities for Research in Astronomy. Inc.. under NASA contract NAS5-26555.," STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555." + Support for NLAST for non-IIST data is provided bv the NASA Office of Space Science via grant. NÀG5-7584 and by other grants and contracts., Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NAG5-7584 and by other grants and contracts. +to model the easdyvunamical friction between plivsically extended protostars durius close encounters.,to model the gasdynamical friction between physically extended protostars during close encounters. + In an attempt to maximize this effect. we have implemented adhesive sink particles iu addition to a more staudard ornmulation of sink particles.," In an attempt to maximize this effect, we have implemented adhesive sink particles in addition to a more standard formulation of sink particles." + This leads to am increased uereer rate. so that fewer protostars survive.," This leads to an increased merger rate, so that fewer protostars survive." + However. even this extreme assunuption docs uot prevent the orlmation of a relatively rich cluster of protostars.," However, even this extreme assumption does not prevent the formation of a relatively rich cluster of protostars." + A final caveat is that we do not selfcousistenthy model he interaction of the protostars with the surounudius eas., A final caveat is that we do not self-consistently model the interaction of the protostars with the surrounding gas. + It is unclear how important the resulting ucelect of easdvuaiical friction and torques is. siace simulations hat model the protostellar surface as well as the pareut eas cloud are not vet feasible.," It is unclear how important the resulting neglect of gasdynamical friction and torques is, since simulations that model the protostellar surface as well as the parent gas cloud are not yet feasible." + Towever. it appears uulikely that this caveat will qualitatively affect our conchisions. since fragmentation typically occurs ou scales larger than the minima resolution leneth.," However, it appears unlikely that this caveat will qualitatively affect our conclusions, since fragmentation typically occurs on scales larger than the minimum resolution length." + Modulo the uncertainties mentioned above. the siuulatious presented here portray ai very different picture of primordial star formation than is commonly asstumed.," Modulo the uncertainties mentioned above, the simulations presented here portray a very different picture of primordial star formation than is commonly assumed." + Bustead of foruuug a single object. the eas in nünihalos fraenieuts vigorously iuto a nuniber of protostars with a range of asses.," Instead of forming a single object, the gas in minihalos fragments vigorously into a number of protostars with a range of masses." + It is an open question as to how this carly iuass function will be mapped into the final mass funetion of Pop ΠΠ. after accretion. fraeiieutation aud mereiue have finally stopped.," It is an open question as to how this early mass function will be mapped into the final mass function of Pop III, after accretion, fragmentation and merging have finally stopped." + However. it is interesting to speculate how this nonlinear mapping will plav out.," However, it is interesting to speculate how this nonlinear mapping will play out." + If a flat. broad mass function persists. a number of lower-mass Pop UT stars will have formed which could survive to the preseut dav if their mass remains below ~OAL...," If a flat, broad mass function persists, a number of lower-mass Pop III stars will have formed which could survive to the present day if their mass remains below $\sim 0.8\,M_\odot$." + Although this possibility is speculative because of the above uncertainties and the fact that we follow the protostellar accretion ouly for thefirst 1000 out of 10° or 10933. it is worth looking for such Pop III fossils iu ougoiug and plaunued large surveys of metal-poor stars in the Alilkv Way (Beers&Cliaistlich2005)..," Although this possibility is speculative because of the above uncertainties and the fact that we follow the protostellar accretion only for thefirst $1000$ out of $10^5$ or $10^6\,{\rm yr}$, it is worth looking for such Pop III fossils in ongoing and planned large surveys of metal-poor stars in the Milky Way \citep{bc05}." + Specifically. such survevs should be focused ou the Galactic bulee. where the Pop III survivors should prefercutially reside due to the biasiug of the nuünibhalo formation sites (Diocniaudetal.2005:Ciao2010).," Specifically, such surveys should be focused on the Galactic bulge, where the Pop III survivors should preferentially reside due to the biasing of the minihalo formation sites \citep{dmm05,gao10}." +.. The planned Apache Point Observatory Calactic Evolution Experiment (APOGEE) with its near-IR capability may be well suited for this search (Alajewskietal.20103., The planned Apache Point Observatory Galactic Evolution Experiment (APOGEE) with its near-IR capability may be well suited for this search \citep{majewski10}. +.. Because of interstellar pollution. even true Pop TT fossils would appear as extreme Pop II stars. but upper duuits would be sienificautly lower than the currently probed values (Frebeletal.2009).," Because of interstellar pollution, even true Pop III fossils would appear as extreme Pop II stars, but upper limits would be significantly lower than the currently probed values \citep{fjb09}." +. Furthermore. the preseuce aud mutual competition of uultiple accretors iu a given nünibhalo will act to Lait he growth of the most massive objects," Furthermore, the presence and mutual competition of multiple accretors in a given minihalo will act to limit the growth of the most massive objects." + Pop III stars are therefore less likely to reach masses mi excess of ~110 M... the threshold for triggering extremely energetic xir-ustabilitv supernovac (PISNe) curving stellar death (Ποσο&Woosley2002).," Pop III stars are therefore less likely to reach masses in excess of $\sim 140\,{\rm M}_\odot$ , the threshold for triggering extremely energetic pair-instability supernovae (PISNe) during stellar death \citep{hw02}." +. A reduced PISN rate is more casily compatible with the absence of them distinct micleosvuthetic signatures m auy of the extremely uctal-2001 halo stars observed so far Chwaiotoetal.2005)., A reduced PISN rate is more easily compatible with the absence of their distinct nucleosynthetic signatures in any of the extremely metal-poor halo stars observed so far \citep{iwamoto05}. +. Pop III stars could still have given rise to numerous extremielv huuinous supernova explosious. if they had nasses of a few 10ML. and if they were rapid rotators. as sugecsted by recent studies (Stacyctal. 2011)..," Pop III stars could still have given rise to numerous extremely luminous supernova explosions, if they had masses of a few $10\,{\rm M}_\odot$ and if they were rapid rotators, as suggested by recent studies \citep{sbl11}. ." + They would then have exploded as core-collapse hivperuovac. with explosion energies that are similar to PISNe (Vineda&Nomoto 2002).," They would then have exploded as core-collapse hypernovae, with explosion energies that are similar to PISNe \citep{un02}." +. Finally. our results may challeuge models of so-called cdark stars’. which are Pop UI stars powered by DAL selfaunililatiou heating (Freeseetal.2008:Tocco 2008).," Finally, our results may challenge models of so-called `dark stars', which are Pop III stars powered by DM self-annihilation heating \citep{freese08,iocco08}." +. These models iuvoke au increased DM interaction rate at the center of the Pop III star which itself les at rest at the center of its miuilalo., These models invoke an increased DM interaction rate at the center of the Pop III star which itself lies at rest at the center of its minihalo. + On top of recent claims that the initial collapse is not substantially delaved by DAL anuililatious (Ripamouti 2010).. the complex dynamics of a protostellar cluster at the ceuter of the munihalo may further precludecfhcieut DAL capture aud heating.," On top of recent claims that the initial collapse is not substantially delayed by DM annihilations \citep{ripamonti10}, , the complex dynamics of a protostellar cluster at the center of the minihalo may further precludeefficient DM capture and heating." +contributions from the layers with negative anisotropy.,contributions from the layers with negative anisotropy. + The behavior of the anisotropy for the CN blend at 3869.1 is in principle similar to that 1n. the bandhead. although the emitted radiation at this wavelength forms lower in the atmosphere. where the temperature gradient d7/d/ is larger.," The behavior of the anisotropy for the CN blend at 3869.1 is in principle similar to that in the bandhead, although the emitted radiation at this wavelength forms lower in the atmosphere, where the temperature gradient $dT/dh$ is larger." + Also. the gradient in the optical depth scale dT/dr is even higher. because of the smaller opacity at this wavelength.," Also, the gradient in the optical depth scale $dT/d \tau$ is even higher, because of the smaller opacity at this wavelength." + It is this gradient that defines the limb-darkening law and. therefore. important for the anisotropy.," It is this gradient that defines the limb-darkening law and, therefore, important for the anisotropy." + Hence. the anisotropy at 3869.9 is always greater than that at the bandhead and never becomes negative.," Hence, the anisotropy at 3869.9 is always greater than that at the bandhead and never becomes negative." + The continuum radiation forms much lower in the atmosphere. where the temperature gradient is very high so that the surface effect becomes negligible.," The continuum radiation forms much lower in the atmosphere, where the temperature gradient is very high so that the surface effect becomes negligible." + Therefore. the behavior of the continuum anisotropy is simpler than in the previous cases. and it monotonically inereases with height.," Therefore, the behavior of the continuum anisotropy is simpler than in the previous cases, and it monotonically increases with height." + We considered a number of additional known models such as PALA. FALC. FALF and FALP of Fontenlaetal. (1993). FALX of Avrett(1995) and colder models like model 2 of Anderson(1989). and AYCOOL of Ayresetal.(1986) and Solankietal.(1994).," We considered a number of additional known models such as FALA, FALC, FALF and FALP of \citet{fontenlaetal1993}, FALX of \citet{avrett1995} and colder models like model 2 of \citet{anderson1989} and AYCOOL of \citet{ayresetal1986} and \citet{solankietal1994}." +. Only the model AYCOOL which has a strong temperature drop in the highest layers is able to produce relatively well the overall level of polarization. but it gives an incorrect polarization ratio 1n the bandhead compared to lines 0.5-1 away from it.," Only the model AYCOOL which has a strong temperature drop in the highest layers is able to produce relatively well the overall level of polarization, but it gives an incorrect polarization ratio in the bandhead compared to lines 0.5–1 away from it." + This model gives also completely wrong intensity profiles., This model gives also completely wrong intensity profiles. + The main conclusion from the above discussion is that the anisotropy of the radiation field driven by the temperature gradient in the FALC model is too low to explain the observed polarization., The main conclusion from the above discussion is that the anisotropy of the radiation field driven by the temperature gradient in the FALC model is too low to explain the observed polarization. + On the other hand. increasing the temperature gradient. for example. by lowering the temperature in. the chromosphere. fails to reproduce the observed center-to-limb variations in the intensity.," On the other hand, increasing the temperature gradient, for example, by lowering the temperature in the chromosphere, fails to reproduce the observed center-to-limb variations in the intensity." +" Therefore. it appears that one-component modeling can reproduce either 7/7, or Q/I signals depending on the choice of the temperature gradient. but not both simultaneously."," Therefore, it appears that one-component modeling can reproduce either $I/I_{\rm c}$ or $Q/I$ signals depending on the choice of the temperature gradient, but not both simultaneously." + Next we try to fit the observations with a multi-component atmosphere model., Next we try to fit the observations with a multi-component atmosphere model. + There have been many theoretical. and observational evidences for a temperature bifurcation in the upper photosphere and lower chromosphere., There have been many theoretical and observational evidences for a temperature bifurcation in the upper photosphere and lower chromosphere. + One comes from observations of CO fundamental vibration-rotation transitions in the near infrared (Noyes&Hall1972:Uitenbroek2000.andreferences therein)...," One comes from observations of CO fundamental vibration-rotation transitions in the near infrared \citep[][and references therein]{noyeshall1972, uitenbroek2000}." + Also. to explain the difference between field strengths deduced from Hanle effect analysis of the 4607 and C» lines. TrujilloBuenoetal.(2004). suggested that the observed polarization in these lines 1s formed in regions with different temperature and anisotropy (seealso2007.andreferences therein)..," Also, to explain the difference between field strengths deduced from Hanle effect analysis of the 4607 and ${\rm C}_2$ lines, \citet{trujilloetal2004} suggested that the observed polarization in these lines is formed in regions with different temperature and anisotropy \citep[see also][and references therein]{asensiotrujillo2005, trujilloshchukina2007}." + Further. Holzreuteretal.(2006) showed that a temperature bifurcation is necessary for the explanation of the linearly polarized K profile.," Further, \citet{holzreuteretal2006} showed that a temperature bifurcation is necessary for the explanation of the linearly polarized K profile." + We tried also to construct new two-component atmosphere models., We tried also to construct new two-component atmosphere models. + We found that it is possible to construct a model which can fit reasonably well all five Q// curves but at the same time fails to fit 7/7. curves., We found that it is possible to construct a model which can fit reasonably well all five $Q/I$ curves but at the same time fails to fit $I/I_{\rm c}$ curves. + We found another model which can fit simultaneously 7/7. and Q// curves for one particular µ- value. but fails to fit observations for other p-values.," We found another model which can fit simultaneously $I/I_{\rm c}$ and $Q/I$ curves for one particular $\mu$ -value, but fails to fit observations for other $\mu$ -values." + So. we can conclude that although some compromises can be found. it is impossible to fit simultaneously the whole set of the observed data by combining two models.," So, we can conclude that although some compromises can be found, it is impossible to fit simultaneously the whole set of the observed data by combining two models." +" The failure to fit simultaneously 7/7, and Q// signals with the considered combinations of atmosphere models for the broad range of p-values is not surprising.", The failure to fit simultaneously $I/I_{\rm c}$ and $Q/I$ signals with the considered combinations of atmosphere models for the broad range of $\mu$ -values is not surprising. + To reproduce the polarization signal the temperature gradient in one of the atmosphere components has to be larger than in FALC (see Sect. ?2))., To reproduce the polarization signal the temperature gradient in one of the atmosphere components has to be larger than in FALC (see Sect. \ref{subsec:one}) ). + However. such a large gradient will result in wrong intensity center-to-limb variations.so the temperature gradient in the second atmosphere component has to be lower than," However, such a large gradient will result in wrong intensity center-to-limb variations,so the temperature gradient in the second atmosphere component has to be lower than" +(Dasvra et al.,(Dasyra et al. + 2006b) we obtain Lj;5xI0L.. a value that is positioned just above the typical SB luminosity in local ULIBRGs.," 2006b) we obtain $L_{limit} \sim 5 \times 10^{12} L_\odot$, a value that is positioned just above the typical SB luminosity in local ULIRGs." + ILowever. (he interplay aud mutual feedback between ihe AGN and SB components during a merger process are still debated (e.g. Springel et al.," However, the interplay and mutual feedback between the AGN and SB components during a merger process are still debated (e.g. Springel et al." + 2005: Johansson. Naab. Burkert 2009).," 2005; Johansson, Naab, Burkert 2009)." +" All the optical and near-IR. imaging survevs reveal a tight connection between extreme IR huninosity and large-scale gravitational disturbance: above Ly,>LOL. virtually all the svslelus appear to be involved in a different stage of an interaction or merger process (Ixim et al.", All the optical and near-IR imaging surveys reveal a tight connection between extreme IR luminosity and large-scale gravitational disturbance: above $L_\mathit{IR}>10^{12} L_\odot$ virtually all the systems appear to be involved in a different stage of an interaction or merger process (Kim et al. + 2002. and references therein).," 2002, and references therein)." + As briefly mentioned above. numerical studies have been very useful to shed light on the dynamics of these major encounters: the huge gas and dust content observed in (he central regions of ULIBGs has been funneled via angular momentum dissipation. and act as both a reservoir aid an absorbing screen for black hole accretion aud star formation.," As briefly mentioned above, numerical studies have been very useful to shed light on the dynamics of these major encounters: the huge gas and dust content observed in the central regions of ULIRGs has been funneled via angular momentum dissipation, and act as both a reservoir and an absorbing screen for black hole accretion and star formation." + There is an obvious link to the AGN/SD feedback., There is an obvious link to the AGN/SB feedback. + It was early suggested that ULIRGs could represent the transition stage between cooler svstems and optically bright quasars (Sanders οἱ al., It was early suggested that ULIRGs could represent the transition stage between cooler systems and optically bright quasars (Sanders et al. + 1988)., 1988). + According to this scenario. the radiation pressure. the violent stellar winds and the supernova-clriven shocks pervading (he nuclear environment eventually expel the gas and the dust from the line of sieht to the active nucleus. as the SD starts to fade.," According to this scenario, the radiation pressure, the violent stellar winds and the supernova-driven shocks pervading the nuclear environment eventually expel the gas and the dust from the line of sight to the active nucleus, as the SB starts to fade." + When the bulk of the dust lavers responsible lor the reprocessing are swept away. optical and UV photons are able to escape. unveiling the quasar (Llopkins et al.," When the bulk of the dust layers responsible for the reprocessing are swept away, optical and UV photons are able to escape, unveiling the quasar (Hopkins et al." + 2006. and references therein).," 2006, and references therein)." + Some recent works. however. seem (o exclude the possibility that the ULIRG population as a whole evolve into powerful optical quasars.," Some recent works, however, seem to exclude the possibility that the ULIRG population as a whole evolve into powerful optical quasars." + The properties of the massive merger remnants look similar to those of quiescent elliptical galaxies. aud the masses inferred. for the ULIRG black holes lie in the Sevfert range.," The properties of the massive merger remnants look similar to those of quiescent elliptical galaxies, and the masses inferred for the ULIRG black holes lie in the Seyfert range." + The luminosity of ULIRGSs is suggested to be quasar-like only because of the Iuelling mechanism. (hat allows both star formation and accretion to Ταζαἱο at near-Ecddington efficiencies (Tacconi et al.," The luminosity of ULIRGs is suggested to be quasar-like only because of the fuelling mechanism, that allows both star formation and accretion to radiate at near-Eddington efficiencies (Tacconi et al." + 2002: \lurray et al., 2002; Murray et al. + 2005: Dasvra et al., 2005; Dasyra et al. + 200Gb)., 2006b). + This latter explanation is still in part controversial. due to (he large discrepancies amone the different methods adopted to determine the black hole mass.," This latter explanation is still in part controversial, due to the large discrepancies among the different methods adopted to determine the black hole mass." + There is opposite evidence of a tight overlap between radio-quiet. PG. quasars and highlv-evolved ULIRGs in terms of both black hole mass and accretion rate (Veilleux οἱ al., There is opposite evidence of a tight overlap between radio-quiet PG quasars and highly-evolved ULIRGs in terms of both black hole mass and accretion rate (Veilleux et al. + 2006: Veilleux οἱ al., 2006; Veilleux et al. + 2009b)., 2009b). + ILowever. such a similarity could be due also to the lack of a," However, such a similarity could be due also to the lack of a" +densities.,densities. + In the case of the USSco nebular spectra. it is possible to compute the [Ne/O] abundance from the flux ratio of the lines 19569 and 15007. in both the March and April spectra.," In the case of the Sco nebular spectra, it is possible to compute the [Ne/O] abundance from the flux ratio of the lines $\lambda$ 3869 and $\lambda$ 5007, in both the March and April spectra." + In the high-density limit (e.g. Dopita 2001) the line flux can be written as where / and j are the two levels of the transition. N; is the density of level 7. £;; is the energy of the transition. Aj; is the transition. probability. ETve; and SJg; are the statistical weights of thestates. & is the Boltzmann constant. and Τ the gas temperature.," In the high-density limit (e.g. Dopita 2001) the line flux can be written as where $i$ and $j$ are the two levels of the transition, $N_i$ is the density of level $i$, $E_{ij}$ is the energy of the transition, $A_{ij}$ is the transition probability, $g_i$ and $g_j$ are the statistical weights of thestates, $k$ is the Boltzmann constant, and $T$ the gas temperature." +" Adopting T,~ KK. as derived from the above considerations and Fig.22. one obtains the relative abundances of |Ne/O|=1.97 (March) and [Ne/O]=1.69 (April). as reported in I]."," Adopting $_e\sim$ K, as derived from the above considerations and 2, one obtains the relative abundances of [Ne/O]=1.97 (March) and [Ne/O]=1.69 (April), as reported in 1." + Kingdom and Williams (1997) established that the ][13869/[Om15007 pair is a good indicator of the [Ne/O] abundance for gas densities « 10°cem™. while SSco ejecta have densities that are about one order of magnitude higher.," Kingdom and Williams (1997) established that the $\lambda$ $\lambda$ 5007 pair is a good indicator of the [Ne/O] abundance for gas densities $<10^6$ $^{-3}$, while Sco ejecta have densities that are about one order of magnitude higher." + To quantify the uncertainty associated to the method in this case. IL applied it to Vel (Della Valle et al.," To quantify the uncertainty associated to the method in this case, I applied it to Vel (Della Valle et al." + 2002. their 33). a very fast nova. which developed strong [Nett] optical emission lines in a high-density ejecta (=107 eem™). similarly to SSco.," 2002, their 3), a very fast nova, which developed strong ] optical emission lines in a high-density ejecta $\simeq 10^7$ $^{-3}$ ), similarly to Sco." +" Comparing VVel [Ne/O] abundance derived from the ,4138569/15007 flux ratio. with that obtained via photo-ionization modeling (Shore et al."," Comparing Vel [Ne/O] abundance derived from the $\lambda$ $\lambda$ 5007 flux ratio, with that obtained via photo-ionization modeling (Shore et al." + 2003). one obtains relative errors in the range5t.. depending on the epoch.," 2003), one obtains relative errors in the range, depending on the epoch." + Hence. the SSco [Ne/O] abundances could be as low as 0.99 and 0.857044 for the March and April spectra. respectively.," Hence, the Sco [Ne/O] abundances could be as low as $^{+0.01}_{-0.10}$ and $^{+0.01}_{-0.06}$ for the March and April spectra, respectively." + 2This would not change the conclusion derived in the next section., This would not change the conclusion derived in the next section. + The general consensus about SNIIa progenitors is that they originate. from CO WDs acereting. matter up to the Chandrasekhar limit either via stellar merging (double degenerate scenario where two CO WDs coalesce) or via mass transfer from a less evolved companion (single degenerate scenario)., The general consensus about Ia progenitors is that they originate from CO WDs accreting matter up to the Chandrasekhar limit either via stellar merging (double degenerate scenario where two CO WDs coalesce) or via mass transfer from a less evolved companion (single degenerate scenario). + Within the single degenerate scenario the accreting WD ought to be massive (re. close to the Chandrasekhar limit). and accreting at a high rate ( 2107-1077 MM. yyr. Nomoto et al.," Within the single degenerate scenario the accreting WD ought to be massive (i.e. close to the Chandrasekhar limit), and accreting at a high rate ( $\geq$ $^{-8}$ $^{-7}$ $_\odot$ $^{-1}$, Nomoto et al." + 2007 and reference therein. see also. Yaron et al.," 2007 and reference therein, see also Yaron et al." + 2005)., 2005). + Hence. RNe whose frequent outbursts are explained by massive WDs and high mass-transfer rates (e.g. Truran et al.," Hence, RNe whose frequent outbursts are explained by massive WDs and high mass-transfer rates (e.g. Truran et al." + 1988) remain viable candidates. contrary to what is suggested by the population synthesis simulations (Di Stefano 2010 and reference therein) and their census (Della Valle and Livio 1996).," 1988) remain viable candidates, contrary to what is suggested by the population synthesis simulations (Di Stefano 2010 and reference therein) and their census (Della Valle and Livio 1996)." + USSco. having a WD »1.37M. (Hachisu et al.," Sco, having a WD $>$ $_\odot$ (Hachisu et al." + 2000; Thoroughgood et al., 2000; Thoroughgood et al. + 2001) and aecreting at a rate >ΙΟ MM. yyr! (Hachisu et al., 2001) and accreting at a rate $>10^{-7}$ $_\odot$ $^{-1}$ (Hachisu et al. + 2000: Matsumoto et al., 2000; Matsumoto et al. + 2003). seems very likely to explode as a Ia. However. it is also general consensus that an accreting ONeMg WD cannot lead to a Ha explosion but. eventually. to a core collapse and the formation of a neutron star or a millisecond pulsar (e.g. Nomoto and Kondo 1991).," 2003), seems very likely to explode as a Ia. However, it is also general consensus that an accreting ONeMg WD cannot lead to a Ia explosion but, eventually, to a core collapse and the formation of a neutron star or a millisecond pulsar (e.g. Nomoto and Kondo 1991)." + The high SSco [Ne/O] abundance (when compared to the solar values of —0.76) is intriguing both because it points to dredged-up material and a possibly eroded WD. and because it provides information about the composition/nature of the underlying WD.," The high Sco [Ne/O] abundance (when compared to the solar values of $-$ 0.76) is intriguing both because it points to dredged-up material and a possibly eroded WD, and because it provides information about the composition/nature of the underlying WD." + Dredged-up material is typically associated with an eroded WD because. according to thermo-nuclear (TNR) computations (e.g. Prialnik and Livio 1995). anything that is mixed within the H-layer where the TNR ignites 15 ejected into the circumbinary space.," Dredged-up material is typically associated with an eroded WD because, according to thermo-nuclear (TNR) computations (e.g. Prialnik and Livio 1995), anything that is mixed within the H-layer where the TNR ignites is ejected into the circumbinary space." + If at any outburst the mass of the ejecta matches or exceeds the acereted mass. then the WD (independent of its composition) cannot increase in mass and reach the Chandrasekhar limit.," If at any outburst the mass of the ejecta matches or exceeds the accreted mass, then the WD (independent of its composition) cannot increase in mass and reach the Chandrasekhar limit." + On the other hand. if the primary star is an ONeMg WD. it will never explode as a Ila even in case of mass gain up to the Chandrasekhar limit of 14M...," On the other hand, if the primary star is an ONeMg WD, it will never explode as a Ia even in case of mass gain up to the Chandrasekhar limit of $_\odot$." + Hence. it has become critical to establish the composition of the accreting primary for USSco because despite its WD mass. high accretion rate and small ejecta mass (a few 1077 MM... lijima 1999; Anupama and Dewangan 2000. but see also Diaz et al.," Hence, it has become critical to establish the composition of the accreting primary for Sco because despite its WD mass, high accretion rate and small ejecta mass (a few $10^{-7}$ $_\odot$ , Iijima 1999; Anupama and Dewangan 2000, but see also Diaz et al." + 2010). it might not explode as a IIa but undergo core collapse at the very most.," 2010), it might not explode as a Ia but undergo core collapse at the very most." + (WallRichardsetal.2006a) (e.g.Giavaliscoetal.,"\citep{magorrian98} \citep{wall05,richards06} \citep[e.g.][]{sfrh_goods}." +2004).. high-z (e.g.WillottReulandοἱal.2003:Deelenet2006) (IIutchingsetal.2006:Hopkins2006).. 2005).," $z$ \citep[e.g.][]{willott02,dusty_radio,beelen06} \citep{hutchings06,role_mergers}. \citep{tadhunter05}." +. z (Nesvacdbaetal.2006).. (e.g.Canalizo&Stockton2001).. (e.g.Martfne," $z$$\sim$ \citep{outflows_rl}. \citep[e.g.][]{cs01}. \citep[e.g.][]{alejo05,donley05}." +z-Sansigreetal.2005;Donlev2," $z$ $\sim$ \citep{yan07,sajina07}." +"005).. z ~ (Yanetal.2007;Sajina2007).. ACDAM £4, Q.2 //, kms.!MpeB ", $\Lambda$ $\Omega_{\rm{M}}$ $\Omega_{\Lambda}$ $H_0$ $\rm{km}\rm{s}^{-1}\rm{Mpc}^{-1}$ +high background. periods (filtered for the extraction of the spectra) are comparable to the source Hix and are not easily subtracted [rom the lighteurve.,high background periods (filtered for the extraction of the spectra) are comparable to the source flux and are not easily subtracted from the lightcurve. + We have searched for an optical counterpart of INO 30 in the Digitized Sky Survey. but we did not find any possible companion neither in the POSS-LL Red nor in the Blue plate. so implying that the source is fainter than Rox21 and Dj z22.5.," We have searched for an optical counterpart of IXO 30 in the Digitized Sky Survey, but we did not find any possible companion neither in the POSS-II Red nor in the Blue plate, so implying that the source is fainter than R $\simeq21$ and Bj $\simeq22.5$." + lt is rerefore quite dillieult to. guess its real nature., It is therefore quite difficult to guess its real nature. + A possible interpretation is in terms of an AGN. which must be a background object. otherwise its Iuminosity would be too low.," A possible interpretation is in terms of an AGN, which must be a background object, otherwise its luminosity would be too low." + In any case. the presence of an iron line allows us to put an upper limit on the redshift of the source. assuming that the line comes from LHx-like iron: this limit. being approximately z«0.1. implics that the 2-10. keV luminosity of the source cannot be larger than c2.107 erg 5. quite low for an AGN.," In any case, the presence of an iron line allows us to put an upper limit on the redshift of the source, assuming that the line comes from H-like iron: this limit, being approximately $z<0.1$, implies that the 2-10 keV luminosity of the source cannot be larger than $\simeq2\times10^{42}$ erg $^{-1}$, quite low for an AGN." + Moreover. the EW of the iron line. though determined with large uncertainty. would be tvpical of a Compton-thick object. but this would be at odds with the observed. photon index.," Moreover, the EW of the iron line, though determined with large uncertainty, would be typical of a Compton-thick object, but this would be at odds with the observed photon index." + On the other hand. if associated with the Mrk 3 galaxy. its luminosity is comparable with that usually found for Ultra Luminous X-ray sources (ULXs) often detected in the vicinity of an GIN. ancl possibly. related: to. Intermecdiate-Alass Black Lloles (seee.g.?)..," On the other hand, if associated with the Mrk 3 galaxy, its luminosity is comparable with that usually found for Ultra Luminous X-ray sources (ULXs) often detected in the vicinity of an AGN and possibly related to Intermediate-Mass Black Holes \citep[see e.g.][]{cm04}." + If the latter interpretation is correct. at least a mass of &300 AL. is required. if the source is emitting near the Eddington limit.," If the latter interpretation is correct, at least a mass of $\simeq300$ $_\odot$ is required, if the source is emitting near the Eddington limit." + Llowever. the origin of the huge iron line remains obscure. even if at least another ULX was recently found in M82. showing a similar feature (2)..," However, the origin of the huge iron line remains obscure, even if at least another ULX was recently found in M82, showing a similar feature \citep{sm03}." + Furthermore. a separation of 1.6 arcmin at the redshift of Mrk 3 would imply a large clistance of the source from the nucleus. being z25 kpe. which is very. close to the optical Dos diameter of the host galaxy (2)... so that the probability. of contamination from. hackeround/foreground objects is significant. (sece.g.?7)..," Furthermore, a separation of 1.6 arcmin at the redshift of Mrk 3 would imply a large distance of the source from the nucleus, being $\simeq25$ kpc, which is very close to the optical $D_{25}$ diameter of the host galaxy \citep{devau91}, so that the probability of contamination from background/foreground objects is significant \citep[see e.g.][]{pc04}." + Finally. it is possible an interpretation in terms of a Galactic source. like ai Cataclysmic Variable (CV).," Finally, it is possible an interpretation in terms of a Galactic source, like a Cataclysmic Variable (CV)." +" This scenario is favoured by the spectral analysis. since a bremsstrahlung component and a huge iron line are generally the main ingredients to model these objects e.g. οι,"," This scenario is favoured by the spectral analysis, since a bremsstrahlung component and a huge iron line are generally the main ingredients to model these objects \citep[see e.g.][]{ms93}." +" At a distance of =500 pe from the Earth. a 2-10 keV luminosity of &210"" erg 4 would make IXO 30 a weak CV. but still in the observed range (seee.g.2).."," At a distance of $\simeq500$ pc from the Earth, a 2-10 keV luminosity of $\simeq2\times10^{30}$ erg $^{-1}$ would make IXO 30 a weak CV, but still in the observed range \citep[see e.g.][]{ms93}." + On the other hand. if we assume. as it is generally found. that the secondary of this system. is a typical AL red να we can ect a lower limit on the distance of the CV. based on the upper limit we have on its apparent Ro magnitude.," On the other hand, if we assume, as it is generally found, that the secondary of this system is a typical M red dwarf, we can get a lower limit on the distance of the CV, based on the upper limit we have on its apparent R magnitude." + Phe resulting distance. approximately do>4 kpc. is in agreement with an origin of the source in the Galactic disc. taking also into account its Galactic coordinates.," The resulting distance, approximately $d>4$ kpc, is in agreement with an origin of the source in the Galactic disc, taking also into account its Galactic coordinates." + This would imply a 10 keV luminosity larger than 1077 erg JL. which is within the observed range in CVs.," This would imply a 2-10 keV luminosity larger than $10^{32}$ erg $^{-1}$, which is within the observed range in CVs." + We have analysed. the first spectrum. of Alek 3., We have analysed the first spectrum of Mrk 3. + The analvsis confirm. previous results. showing a spectrum. composed by three main components: a strongly absorbed. powerlaw. a pure Compton reflection with the same photon index associated to an iron Wea line. both produced as rellection from a Compton-thick torus. and an unabsorbed powerlaw. againwith the same photon index of the primary continuum. associated to a large number of emission lines. likely produced as reflection from a thin. photoionised material.," The analysis confirm previous results, showing a spectrum composed by three main components: a strongly absorbed powerlaw, a pure Compton reflection with the same photon index associated to an iron $\alpha$ line, both produced as reflection from a Compton-thick torus, and an unabsorbed powerlaw, againwith the same photon index of the primary continuum, associated to a large number of emission lines, likely produced as reflection from a Compton-thin, photoionised material." + The iron [xo line EW with respect. to the Compton rellection component. being only 610EU eV. is consistent with a low inclination angle and an iron underabundance of a factor 2: 0.82. properties indipendentIy derived for the torus. via the amount of Compton rellection and the depth," The iron $\alpha$ line EW with respect to the Compton reflection component, being only $610^{+30}_{-50}$ eV, is consistent with a low inclination angle and an iron underabundance of a factor $\simeq0.82$ , properties indipendently derived for the torus, via the amount of Compton reflection and the depth" +for any combination and may be over 1000 times the probability of a scattered disk origin.,for any combination and may be over 1000 times the probability of a scattered disk origin. + From these results we believe that 2006 SQsr. is the most distant LPC discovered to date., From these results we believe that 2006 $_{372}$ is the most distant LPC discovered to date. + If 2006 SQac is from the Oort Cloud. even more intriguing is that it almost certainly resided in the inner. unobserved regions of the Oort Cloud rather than the outer parts where all LPCs observed near Earth are thought to originate.," If 2006 $_{372}$ is from the Oort Cloud, even more intriguing is that it almost certainly resided in the inner, unobserved regions of the Oort Cloud rather than the outer parts where all LPCs observed near Earth are thought to originate." + The clvnamical reasoning is as follows., The dynamical reasoning is as follows. +" Planetary perturbations must have been responsible for lowering the seminajor axis of this orbit to 10 AU, vet this raudom-walk process proceeds at a very slow pace."," Planetary perturbations must have been responsible for lowering the semimajor axis of this orbit to $\sim$ $^{3}$ AU, yet this random-walk process proceeds at a very slow pace." +" From ?.. it can be shown that andl where D is the average energv kick per perilelion passage. ey is the original senminajor axis. ay is the final senmünajor axis. aud fp is the time required for the semiünmajor axis to diffuse down to a, frou ay via planetary kicks."," From \citet{dun87}, it can be shown that and where $D$ is the average energy kick per perihelion passage, $a_0$ is the original semimajor axis, $a_f$ is the final semimajor axis, and $t_D$ is the time required for the semimajor axis to diffuse down to $a_f$ from $a_0$ via planetary kicks." + Setting a¢ to S00 AU and. D(25 AU) to te ΕΦ) we can then plot £p as a fiction of initial seuiniajor axis iu the Oort Cloud in Figure 3.," Setting $a_f$ to 800 AU and $D$ (25 AU) to $^{-4.7}$ $^{-1}$ \citep{dun87, fernbrun00} , we can then plot $t_D$ as a function of initial semimajor axis in the Oort Cloud in Figure 3." + As can be seen in this plot. fp is 130 Mivrs for «=10! AU and increases for larger ay.," As can be seen in this plot, $t_D$ is 130 Myrs for $a=10^4$ AU and increases for larger $a_0$." + Left uuchecked. the planets would be able to draw down the scmimajor axes of any Oort Cloud comet within a couple hundred million years.," Left unchecked, the planets would be able to draw down the semimajor axes of any Oort Cloud comet within a couple hundred million years." + Before chough time cau clapse for this to happen. however. most comets have their peribelia lifted back out of the plauctary region again by the galactic tide.," Before enough time can elapse for this to happen, however, most comets have their perihelia lifted back out of the planetary region again by the galactic tide." + Ifa comoets perihelion is moved outward by ~10 AU from 25 AU to 35 AU. the plaucts cease to have a large effect on the dynamics. aud the randoniswalk of seimiüniajor axis stops.," If a comet's perihelion is moved outward by $\sim$ 10 AU from 25 AU to 35 AU, the planets cease to have a large effect on the dynamics, and the random-walk of semimajor axis stops." +" The timescale for this to occur is given in 7. as Asstuuing a porihelion of 25 AU. f, is also plotted in Figure 3."," The timescale for this to occur is given in \citet{dun87} as Assuming a perihelion of 25 AU, $t_q$ is also plotted in Figure 3." + To produce SQsr.-like orbits from the Oort Cloud. fp aust be shorter than fj. otherwise a=I AU will never be reached.," To produce $_{372}$ -like orbits from the Oort Cloud, $t_D$ must be shorter than $t_q$, otherwise $a=10^3$ AU will never be reached." + As can be secu in this plot. this is only the case for a subset of Oort Cloud bodies.," As can be seen in this plot, this is only the case for a subset of Oort Cloud bodies." + Onulv for initial semuinajor axes below ~5000 AU cau the semimajor axis be drawn down to 10° AU before the perihelion is lifted out of the planetary region., Only for initial semimajor axes below $\sim$ 5000 AU can the semimajor axis be drawn down to $^{3}$ AU before the perihelion is lifted out of the planetary region. + This process is verified when we examine the distribution of initial Oort Cloud semimajor axes for all of the $012 SQuz- orbits we eencrate. which is also shown in Figure 3.," This process is verified when we examine the distribution of initial Oort Cloud semimajor axes for all of the $_{372}$ -like orbits we generate, which is also shown in Figure 3." + It cau be seen in this figure that the distribution falls off quickly for &2 10 AU., It can be seen in this figure that the distribution falls off quickly for $a \gtrsim$ $^4$ AU. + Therefore. we cau couclude frou," Therefore, we can conclude from" +the probability P(|Zij|dfg/dfy(a/m0), i.e. an increase in mass loss would allow more energy loss for a/m=0.99 case."," By direct comparison of these figures, we note that rotation of a black hole $a$ is also effective such that $d f_E / d f_{\dot{M}}(a/m=0.99) > d +f_E / d f_{\dot{M}}(a/m=0)$, i.e. an increase in mass loss would allow more energy loss for $a/m=0.99$ case." +" Therefore, more energetic outflows can be expected from a shock around a rotating black hole."," Therefore, more energetic outflows can be expected from a shock around a rotating black hole." +" The upstream flow energy E, also affects the mass loss fraction.", The upstream flow energy $E_1$ also affects the mass loss fraction. + It is noted that the energy-dependence of f; is strong; higher energy E can lead to larger mass outflow fraction for a given angular momentum A and a shock location Τε., It is noted that the energy-dependence of $f_{\dot{M}}$ is strong; higher energy $E_1$ can lead to larger mass outflow fraction for a given angular momentum $\lambda$ and a shock location $r_{\rm sh}$ . +" For instance, with A=3.5 for a/m=0 case (in Fig. 4)),"," For instance, with $\lambda = 3.5$ for $a/m=0$ case (in Fig. \ref{fig:E-a0}) )," +" fy,«20% when Ej=1.003, 20—30% when E,=1.004 and as large as ~40% when E;=1.005."," $f_{\dot{M}} < 20\%$ when $E_1=1.003$, $20-30 +\%$ when $E_1=1.004$ and as large as $\sim 40\%$ when $E_1=1.005$." +" With A=2.16 for a/m=0.99 (in Fig. 5)),"," With $\lambda=2.16$ for $a/m=0.99$ (in Fig. \ref{fig:E-a099}) )," +" fy;20—85% when E;=1.003, 40—85% when E,=1.004, and it is as high as 60—85% when E,=1.005."," $f_{\dot{M}} \sim 20-85 \%$ when $E_1=1.003$, $40-85\%$ when $E_1=1.004$, and it is as high as $60-85\%$ when $E_1=1.005$." +" As a reference, we also examine the energy-dependence of the shock strength in Figure 6 where the (local) compression ratio n2/n, is plotted against ra, for different energies: E,=1.003,1.004 and 1.005 as used before."," As a reference, we also examine the energy-dependence of the shock strength in Figure \ref{fig:n12} where the (local) compression ratio $n_2/n_1$ is plotted against $r_{\rm sh}$ for different energies: $E_1=1.003,~1.004$ and $1.005$ as used before." + Angular momentum A is fixed in each case to see energy-dependence alone (although different values of A fordifferent spin a must be chosen to obtain the solutions)., Angular momentum $\lambda$ is fixed in each case to see energy-dependence alone (although different values of $\lambda$ fordifferent spin $a$ must be chosen to obtain the solutions). + We find that our dissipative shocks (coupled to, We find that our dissipative shocks (coupled to +47 Tue (NGC 104) is among the most massive globular clusters in the Galaxy andl is thus one of the most powerhu laboratories to investigate the finer details of elobular cluster formation and evolution.,47 Tuc (NGC 104) is among the most massive globular clusters in the Galaxy and is thus one of the most powerful laboratories to investigate the finer details of globular cluster formation and evolution. + As the large stellar population renders any potential statistic more accessible. it is interesting that 47 Tue is not among those globular clusters with more clearly delineated evidence for multiple populations (Berebusch&Stetson2009)..," As the large stellar population renders any potential statistic more accessible, it is interesting that 47 Tuc is not among those globular clusters with more clearly delineated evidence for multiple populations \citep{2009AJ....138.1455B}." + llowever. it has been known lor several decades that the stars in the inner part of the elobular cluster have stronger CN absorption (Norris&Freeman1979:Palloglou 1990)..," However, it has been known for several decades that the stars in the inner part of the globular cluster have stronger CN absorption \citep{1979ApJ...230L.179N,1990BAAS...22.1289P}. ." + Recently. diCriseienzoetal.(2010). have argued that this chemical gradient is due to the presence of multiple generations of stus. with later generations being helium and CN enhanced by the ejecta of first-generation asvmptotie giant branch (AGB) stars.," Recently, \citet{2010MNRAS.408..999D} have argued that this chemical gradient is due to the presence of multiple generations of stars, with later generations being helium and CN enhanced by the ejecta of first-generation asymptotic giant branch (AGB) stars." + Thev found strong evidence of a helium-spread in the morphology of the subgiant branch. (8GD) and horizontal branch (HD) stars., They found strong evidence of a helium-spread in the morphology of the subgiant branch (SGB) and horizontal branch (HB) stars. + Their work followed an investigation bv Andersonοἱal.(2009).. who usedT) data to measured the color widths of the cluster main sequence. which they argued could be explained by à spread of AY~0.027.," Their work followed an investigation by \citet{2009ApJ...697L..58A}, who used data to measured the color widths of the cluster main sequence, which they argued could be explained by a spread of ${\Delta}Y \sim 0.027$." + If the is due to a second generation. and if the second. generation is indeed more centrally concentrated. as suggested bv the CN band strengths ancl dvnamical arguments (1)Ercoleetal.2008).. one should expect a higher helium abundance in (hie center.," If the helium-enhancement is due to a second generation, and if the second generation is indeed more centrally concentrated, as suggested by the CN band strengths and dynamical arguments \citep{2008MNRAS.391..825D}, one should expect a higher helium abundance in the center." + It has recently been posited that the presence of multiple generations differing in properties such as initial helium abundance and the relative abundances of sodium and oxveen are in fact a ubiquitous property of globular clusters (Coarrettaοἱal.2010).., It has recently been posited that the presence of multiple generations differing in properties such as initial helium abundance and the relative abundances of sodium and oxygen are in fact a ubiquitous property of globular clusters \citep{2010A&A...516A..55C}. + In (his paper we test the hypothesis of a helium gradient in 47 Tue using four methods that are rooted in (he properties of (wo censely-populated phases of post main-sequence stellar evolution. (he red giant branch bump (RGDD) aud the WB.," In this paper we test the hypothesis of a helium gradient in 47 Tuc using four methods that are rooted in the properties of two densely-populated phases of post main-sequence stellar evolution, the red giant branch bump (RGBB) and the HB." + The RGDD phase occurs during the first ascent of the red eiant branch., The RGBB phase occurs during the first ascent of the red giant branch. + As the hydrogen burning shell expands. it eventually comes into contact with the convective envelope (Cassis&Salaris1997).," As the hydrogen burning shell expands, it eventually comes into contact with the convective envelope \citep{1997MNRAS.285..593C}." +. This increase in [uel causes the star to become Inter as (he [uel is used up belore becoming brighter again. effectively crossing the same huninosity three limes. leading to a “bump” in (he luminosity function.," This increase in fuel causes the star to become fainter as the fuel is used up before becoming brighter again, effectively crossing the same luminosity three times, leading to a “bump” in the luminosity function." + This bump is most populated aud (hus more measurable in clusters such as 47 Tue (Zocealietal.1999:Bono2001:Rielloal.2010:Cassisiet 2011)..," This bump is most populated and thus more measurable in metal-rich clusters such as 47 Tuc \citep{1999ApJ...518L..49Z,2001ApJ...546L.109B,2003A&A...410..553R,2010ApJ...712..527D,2011A&A...527A..59C}." + stellar evolution predicts the RGDD lifetime to be sienilicantly shortened for increased initial helium abundance (Bonoetal.2001:DiCecco2010:Natal2010)..," Stellar evolution predicts the RGBB lifetime to be significantly shortened for increased initial helium abundance \citep{2001ApJ...546L.109B,2010ApJ...712..527D,2010arXiv1011.4293N}." + If this stellar theory. prediction is correct. and (he hypothesis of a centrallv-concentrated. enhanced population in 47 Tuc is correct as well. (hen RGBB stus should be less prominent relative {ο the remainingRG stars closer to the eluster center.," If this stellar theory prediction is correct, and the hypothesis of a centrally-concentrated, helium-enhanced population in 47 Tuc is correct as well, then RGBB stars should be less prominent relative to the remainingRG stars closer to the cluster center." + We detect a variation in the, We detect a variation in the +other haud. the isotopic ratio is ercatly culauced with respect to the primordial abuudauce [D/I]] =bs10. due to fractionation effects.,"other hand, the isotopic ratio is greatly enhanced with respect to the primordial abundance [D/H] $=4\times 10^{-5}$, due to fractionation effects." + According to the results shown in Fie., According to the results shown in Fig. + Ll the main nolecular species containing helimu is ell!. formed by he radiative association of Πο and IE!.," 4, the main molecular species containing helium is $^+$, formed by the radiative association of He and $^+$." + As cuplasized x Lepp Shull (1981). this reaction is slower than the usual formation mode via association of He! aud IL but since the abundance of He! is quite sumall. reaction (Hes) akes over.," As emphasized by Lepp Shull (1984), this reaction is slower than the usual formation mode via association of $^+$ and H, but since the abundance of $^+$ is quite small, reaction (He8) takes over." + The | ious are removed by CBR photons 2S250 also w collisions with II atoms to reform IT] (reaction Tell)., The $^+$ ions are removed by CBR photons and at $z\la 250$ also by collisions with H atoms to reform $_2^+$ (reaction He11). + This explains the abrupt chauge iu he slope ofthe curve of shown in Fig., This explains the abrupt change in the slope of the curve of $^+$ shown in Fig. + I., 4. + The final abundance is suiall. M] ~6ς0 Pats =.," The final abundance is small, $^+$ /H] $\sim 6\times +10^{-13}$ at $z=1$." + Finally. the chemistry of ithiuni is complicated. but he molecular abuudauces are iucdecd very siuall.," Finally, the chemistry of lithium is complicated, but the molecular abundances are indeed very small." + The more abundant couples is whose formation is controlled w the radiative association of Li! and Π (see Dalearuo Lopp 1987)., The more abundant complex is $^+$ whose formation is controlled by the radiative association of $^+$ and H (see Dalgarno Lepp 1987). + As shown in Fie., As shown in Fig. + L lithium remains more ionized at low redshifts aud this explains why Lill is less abuudant than Lill!.," 4, lithium remains more ionized at low redshifts and this explains why LiH is less abundant than $^+$." + The final abundance of Lill! is 10 at ial.," The final abundance of $^+$ is $\simeq +10^{-17}$ at $z=1$." + The final values of the molecular abundances depend ou the choice of the cosmological parameters., The final values of the molecular abundances depend on the choice of the cosmological parameters. + Each model is in fact specified by three parameters iy. Qy and Ph.," Each model is in fact specified by three parameters $\eta_{10}$, $\Omega_0$ and $h$." + The observational (aud theoretical) uucertainties associated with cach of them are still rather large., The observational (and theoretical) uncertainties associated with each of them are still rather large. + We have selected as standard model that that better fits the constraints nuposed bv the observations of the abundances of the light clemeuts., We have selected as standard model that that better fits the constraints imposed by the observations of the abundances of the light elements. + To gauge the effects that a change of igo induces ou the chemistry network. we have run a model with jgg—8.0. the maxinnun value still compatible with the constraints on standard big bane uucleosvuthlesis eiveu by observations of lithiun iun- Pop-II stars (Douifacio Molaro 1997).," To gauge the effects that a change of $\eta_{10}$ induces on the chemistry network, we have run a model with $\eta_{10}$ =8.0, the maximum value still compatible with the constraints on standard big bang nucleosynthesis given by observations of lithium in Pop-II stars (Bonifacio Molaro 1997)." + The results are Ooeiven in Table 6 for a direct comparison with the standard case., The results are given in Table 6 for a direct comparison with the standard case. + Note that the abundance of IT» is the same in the two models. makine this molecule a poor diagnostic of cosmological models.," Note that the abundance of $_2$ is the same in the two models, making this molecule a poor diagnostic of cosmological models." + Lithium molecules are quite sensitive to iy. showing au increase of a actor of3.1.," Lithium molecules are quite sensitive to $\eta_{10}$, showing an increase of a factor of 3–4." + For the other species. however. a higher value of iy nÓuplies a lower final abundance as a result of the lower initial value of cach clement predicted by the staudard big bane nucleosvuthesis which colmpensates for the higher total baryon density.," For the other species, however, a higher value of $\eta_{10}$ implies a lower final abundance as a result of the lower initial value of each element predicted by the standard big bang nucleosynthesis which compensates for the higher total baryon density." + As shown by Palla et al. (, As shown by Palla et al. ( +1995). larger variations of the molecular abundances than those shown in Table 6 can be expected for more drastic variations of the other cosmological paraueters: both Lill aud WD can vary by 2 or 3 orders of magnitudes by allowing changes to Ορ aud Ph of a factor of 5 and 2. respectively.,"1995), larger variations of the molecular abundances than those shown in Table 6 can be expected for more drastic variations of the other cosmological parameters: both LiH and HD can vary by 2 or 3 orders of magnitudes by allowing changes to $\Omega_0$ and $h$ of a factor of 5 and 2, respectively." +" Wowever. current observations indicate that a ligh value of the IDubble constant is unlikely, aud that a universe with 9,«1. as in the case of a nonzero value of the cosimnological constant. is less favored by theoretical models."," However, current observations indicate that a high value of the Hubble constant is unlikely, and that a universe with $\Omega_0<1$, as in the case of a nonzero value of the cosmological constant, is less favored by theoretical models." + The chemical network discussed im Sect., The chemical network discussed in Sect. + 2 consists of 87 reactions. 69 collisional and Is radiative.," 2 consists of 87 reactions, 69 collisional and 18 radiative." + Although the integration of such system does not prescut particular difficulties (apart for the iutriusic stiffuess of the rate equations) or require exceedingly long computer times. for a better understanding of the chemistry of the primordial eas it is more convenient to reduce the reactions to ouly those that are esseutial to accurately nodel the formation/destruction of cach molecular species.," Although the integration of such system does not present particular difficulties (apart for the intrinsic stiffness of the rate equations) or require exceedingly long computer times, for a better understanding of the chemistry of the primordial gas it is more convenient to reduce the reactions to only those that are essential to accurately model the formation/destruction of each molecular species." + Such a reduced system has been called them, Such a reduced system has been called the. +odel Xbel et al. (, Abel et al. ( +1997) have devised a reduced network in their discussion of the uon-equilibrimim effects and clemical dynamics of the primordial gas.,1997) have devised a reduced network in their discussion of the non-equilibrium effects and chemical dynamics of the primordial gas. + However. their application ciffers from ours. since they are mainly interested iu the formation of IT iu the post-shock laver of a cosmological pancake auc cousider ouly collisional processes.," However, their application differs from ours, since they are mainly interested in the formation of $_2$ in the post-shock layer of a cosmological pancake and consider only collisional processes." + Our muita niodel consists of the 33 reactions indicated in the diagram shown in Fig., Our minimum model consists of the 33 reactions indicated in the diagram shown in Fig. + 6., 6. + The main reactions are listed in bold face in Tables 1 to |., The main reactions are listed in bold face in Tables 1 to 4. + Notice that in order to describe fully the Πο chemistry oulv ll reactious out of 22 are needed., Notice that in order to describe fully the $_2$ chemistry only 11 reactions out of 22 are needed. + The formation of IL. involves two reaction sequences with aud IT] ious Whose abundance is restricted byphotodestruction processes., The formation of $_2$ involves two reaction sequences with $^-$ and $_2^+$ ions whose abundance is restricted byphotodestruction processes. + Tlowever. for a competing destruction channel is the unitual ueutralization with IT! ious which contributes ~20 to the total rate at redshifts 2S100.," However, for $^-$ a competing destruction channel is the mutual neutralization with $^+$ ions which contributes $\sim 20$ to the total rate at redshifts $z\la 100$." +" The IL, system would be closed if not for the external source of IT] ious comuimeg from the destruction of Tell! by IL atoms (reaction Holl) at redshifts :x250.", The $_2$ system would be closed if not for the external source of $_2^+$ ions coming from the destruction of $^+$ by H atoms (reaction He11) at redshifts $z\la 250$ . + It is nuportaut to consider this path since it modifies substantially the evolution of IT] (see Fig., It is important to consider this path since it modifies substantially the evolution of $_2^+$ (see Fig. + 1). although it does iot affect the final abuudauce of IT» molecules.," 4), although it does not affect the final abundance of $_2$ molecules." + As we have already joted. in the absence of this channel the final abundance of IL} would be of the same order as that of I.. vecamse of the importance of reaction (IT19).," As we have already noted, in the absence of this channel the final abundance of $_2^+$ would be of the same order as that of $_3^+$, because of the importance of reaction (H19)." + The chemistry of deuterium is rather simple aud ouly G reactions out of 21 need to be considered., The chemistry of deuterium is rather simple and only 6 reactions out of 24 need to be considered. + The molecule TD is ormed rapidly by reaction (D8) which involves ionized deuterium., The molecule HD is formed rapidly by reaction (D8) which involves ionized deuterium. + Thus. if is important to consider all the reactions that determine the ionization balance.," Thus, it is important to consider all the reactions that determine the ionization balance." + The main destruction route is by reaction (DLO). while other reactions involving I. (DII) and IE (D9) are πιο] less nuportaut.," The main destruction route is by reaction (D10), while other reactions involving $_3^+$ (D11) and H (D9) are much less important." + Finally. the chemistry of Li is more complex than the rest and even the reduced network contains a large uunnboer of reactions (11 out of 26).," Finally, the chemistry of Li is more complex than the rest and even the reduced network contains a large number of reactions (14 out of 26)." + This is mainly due to the fact that Πα remains partly ionized and the routes to the formation of Lill aud Lill! couipete effectively with cach other., This is mainly due to the fact that lithium remains partly ionized and the routes to the formation of LiH and $^+$ compete effectively with each other. + Note also that at redshifts zzx 100. the main route to Lillformation is from associative detachinent of ," Note also that at redshifts $z\la 100$ , the main route to LiHformation is from associative detachment of $^-$ " +"The escape probability 2,4 is defined using the Sobolev escape probability as where /,, is the oscillator strength of the line between excited level n and the ground state.",The escape probability $\beta_{n1}$ is defined using the Sobolev escape probability as where $f_{n1}$ is the oscillator strength of the line between excited level n and the ground state. +" 2, and », are the number densities of the ground state and the excited state referred by index n. respectively."," $n_{1}$ and $n_{n}$ are the number densities of the ground state and the excited state referred by index n, respectively." + A4 is (he wavelength of the line. / is the time since explosion in seconds.," $\lambda_{n1}$ is the wavelength of the line, $t$ is the time since explosion in seconds." +" g,, is the degeneracy of level n and Pρω- (?).", $g_{n}$ is the degeneracy of level n and $\frac{g_{1}}{g_{2}} \sim \frac{1}{n^{2}}$ \citep{mihalas78sa}. +In 3J) we discuss our approach to quantify the photo-ionization rate. the escape probability. and the collisional de-exeitation rate.," In \ref{sec:modelatoms} we discuss our approach to quantify the photo-ionization rate, the escape probability, and the collisional de-excitation rate." + To set up the physical structure of each svstem we use the density. profile and luminosity from a full NLTE caleulation of a model atmosphere in. homologous expansion. with a power-law density profile poxe.*. 20 days after explosion. which is a reasonable fit to observed spectra of SN 1999em at that epoch.," To set up the physical structure of each system we use the density profile and luminosity from a full NLTE calculation of a model atmosphere in homologous expansion, with a power-law density profile $\rho \propto v^{-7}$, 20 days after explosion, which is a reasonable fit to observed spectra of SN 1999em at that epoch." + This uuderlyviug densitv profile aud the total bolometric Iuminositv in the observers [rame are chosen to be representative of the condiGons in SNe IP near maximum light., This underlying density profile and the total bolometric luminosity in the observer's frame are chosen to be representative of the conditions in SNe IIP near maximum light. + Give (his structure we use our general purpose model atmosphere code 1D to solve for ihe new temperature structive and level populations under the new conditions (such as (he hydrogen model atom and the presence of other metals)., Give this structure we use our general purpose model atmosphere code 1D to solve for the new temperature structure and level populations under the new conditions (such as the hydrogen model atom and the presence of other metals). + The initial model of SN 1999em at 20 davs after explosion was generated using a 31 level hvdrogen model atom and solar metals were included., The initial model of SN 1999em at 20 days after explosion was generated using a 31 level hydrogen model atom and solar metals were included. + We call this starting model our base moclel., We call this starting model our base model. + Our base model was generated treating hvdrogen and other elements in NLTE., Our base model was generated treating hydrogen and other elements in NLTE. + The, The +"The iuteerated hard X-ray Iuuinosity in May 2003 was L,(üds GÜkeV)—Ls107 erefs. LQ(GU—120keV)24.10? cre/s (asume the 5 kpe distauce to which is about of the soft N-rav jet luuinosity.","The integrated hard X-ray luminosity in May 2003 was $L_x(18-60 \hbox{keV})\sim 4\times 10^{35}$ erg/s, $L_x(60-120 \hbox{keV})\sim 2\times 10^{35}$ erg/s (assuming the 5 kpc distance to SS433), which is about of the soft X-ray jet luminosity." + Using the OSA-3 software. we could uot significantly detect the source in the JEM-X data.," Using the OSA-3 software, we could not significantly detect the source in the JEM-X data." + Instead. we made use of the more detailedRATE observations of SS133 performed simultaucouslv with in March 2001 to obtain the broadband 2-100 keW spectrum of SS133.," Instead, we made use of the more detailed observations of SS433 performed simultaneously with in March 2004 to obtain the broadband 2-100 keV spectrum of SS433." + The source Was observed a few davs after the disk maxiumn opening uiase., The source was observed a few days after the disk maximum opening phase. + The OSA-3 software also did not allow us to sienificautly detect the source at euergies above TO keV. so we used the IRI software to obtain the SS133 spectrum up to 100 keV. This software has proven its quality aud efficiency in processing observations of the Galactic ceuter (Revnivtsey ot al.," The OSA-3 software also did not allow us to significantly detect the source at energies above 70 keV, so we used the IKI software to obtain the SS433 spectrum up to 100 keV. This software has proven its quality and efficiency in processing observations of the Galactic center (Revnivtsev et al." + 2001)., 2004b). + The resulting broadband X-ray. spectrum of $5133 in March 2001 is shown in Fig. 2.., The resulting broadband X-ray spectrum of SS433 in March 2004 is shown in Fig. \ref{fig:RXTEIBIS_sp}. + It can he adequately fitted bv the bremisstralluug cussion from optically thin thermal plasina with AD—30 keV ( model “bremss” from NSPEC )ickage was used: sce Table J )).," It can be adequately fitted by the bremsstrahlung emission from optically thin thermal plasma with $kT\sim 30$ keV ( model ""bremss"" from XSPEC package was used; see Table \ref{sp_param}) )." + The reduced chi-square value for 50 dof is ~0.8. which correspouds to a uull hypothesis probability of ~0.9.," The reduced chi-square value for $50$ dof is $\sim 0.8$, which corresponds to a null hypothesis probability of $\sim 0.9$." + D. The IBIS/ISCRI count rates of SS133 in May. 2003 are presented in Fie. 3.., B. The IBIS/ISGRI count rates of SS433 in May 2003 are presented in Fig. \ref{fig:IBIS_lc}. + The X-ray eclipse at lard euergies is observed to be sliehtlv narrower than the optical onc. slightly broader than in the 16-27 keV euergy range and displavs extended wines (Fig. 6)).," The X-ray eclipse at hard energies is observed to be slightly narrower than the optical one, slightly broader than in the 4.6-27 keV energy range and displays extended wings (Fig. \ref{fig:eclips_Xop}) )." + This is opposite to what is found in ordinary eclipsing X-ray binaries (like Cen N-3. Vela N-1 ete.).," This is opposite to what is found in ordinary eclipsing X-ray binaries (like Cen X-3, Vela X-1 etc.)," + iu which the ταν eclipse duration decreases with cucrey., in which the X-ray eclipse duration decreases with energy. + C. The eclipse depth is observed to be at least 1- iard X-rays compared to ~504 in the 16-27 keV banca (Fig. l--6))., C. The eclipse depth is observed to be at least in hard X-rays compared to $\sim 50\%$ in the 4.6-27 keV band (Fig. \ref{fig:prec}- \ref{fig:eclips_Xop}) ). + D. The 25-50 keV N-rav flux increases from ~5 to ~20 uCrab caving Marchi-May 2003 schien the source precessed roni the crossover (T2) phase to the maxima opening disk phase (T3)., D. The 25-50 keV X-ray flux increases from $\sim 5$ to $\sim 20$ mCrab during March-May 2003 when the source precessed from the crossover (T2) phase to the maximum opening disk phase (T3). + This modulation is ~2 times larger than Observer in the 2-10 keV energy baud (see Fie. 5))., This modulation is $\sim 2$ times larger than observed in the 2-10 keV energy band (see Fig. \ref{fig:prec_ampl}) ). + Thus. )oth precessional aud eclipsing hard N-vav variahilities in SS133 exceed by ~2 times those in the standard X-rav band (Fig. 5)).," Thus, both precessional and eclipsing hard X-ray variabilities in SS433 exceed by $\sim 2$ times those in the standard X-ray band (Fig. \ref{fig:prec_ampl}) )." + This suggests a more compact vertical structure of the hard N-ray. ciuitting region iu the ceutral parts of the accretion disk., This suggests a more compact vertical structure of the hard X-ray emitting region in the central parts of the accretion disk. +" As incutioned above. the 25-50 keV flux of SS133 varies fom Fn~5 mCrab to E,,.~20 μιςτα, with Pj, aud ρω Corresponding to precession yhases of the disk seen edge-ou (moment T2) and at maxima open (moment T3). respectively. viclding the ratio 44,—PinardPin l1."," As mentioned above, the 25-50 keV flux of SS433 varies from $F_{min}\sim 5$ mCrab to $F_{max}\sim 20$ mCrab, with $F_{min}$ and $F_{max}$ corresponding to precession phases of the disk seen edge-on (moment T2) and at maximum open (moment T3), respectively, yielding the ratio $A_{pr}\equiv F_{max}/F_{min}\sim 4$ ." + Iu Fig., In Fig. + bo we present all our available observations of $$133., \ref{fig:prec} we present all our available observations of SS433. + The left panel shows the 2003 data orbits 19. 51. 53. 56. 58. 60. 67-70).," The left panel shows the 2003 data orbits 49, 51, 53, 56, 58, 60, 67-70)." + The right panel shows the 2001 data (March 21- orbits 176 and 177).," The right panel shows the 2004 data (March 24-25, orbits 176 and 177)." + The uneclipsed flax of 58133 in 2001 (when the source was observed ucar the T3 phase), The uneclipsed flux of SS433 in 2004 (when the source was observed near the T3 phase) +"As was previously. mentioned.B 3> becomes inlinitelyBH large at ir—7, i£(tom >&.","As was previously mentioned, $M^{2}$ becomes infinitely large at $x=x_{\rm c}$ if $\xi>\xi_{\rm c}$." +à For highly. relativistic outflows this critical radius is approximately given by A possible conliguration of a field line given by the parameter £ lareer than € would be asvimiptotically evlindrical. because il can be confined within a radius smaller than 7 even in the limit Z—x.," For highly relativistic outflows this critical radius is approximately given by A possible configuration of a field line given by the parameter $\xi$ larger than $\xi_{\rm c}$ would be asymptotically cylindrical, because it can be confined within a radius smaller than $x_{\rm c}$ even in the limit $Z\rightarrow\infty$." + Unless € is verv close to unity. the value of c is of order of unitv. and sucha evlindrical jet becomes very narrow.," Unless $\xi$ is very close to unity, the value of $x_{\rm c}$ is of order of unity, and sucha cylindrical jet becomes very narrow." + In the limit #—ur... the energy ratio AP is estimaled to be The narrow jet corresponding to £. of order of unity can be kinetic-enerey dominated only if the asymptotic radius oz dis very close tore. Le. 1—(r/r;)=O(L/E?).," In the limit $x\rightarrow x_{\rm c}$, the energy ratio $\mm^{2}$ is estimated to be The narrow jet corresponding to $\xi_{\rm c}$ of order of unity can be kinetic-energy dominated only if the asymptotic radius $x$ is very close to $x_{\rm c}$, i.e., $1-(x/x_{\rm c})=O(1/E^{2})$." + This is the line-tuning problem recquired for the evlindrical field to realize highly relativistic acceleration ol bulk motion., This is the fine-tuning problem required for the cylindrical field to realize highly relativistic acceleration of bulk motion. +" On the other hand for a cevlindrieal field line with the value of £ such that i£?=οE?) the maximum radius 7 may become of order of E7. and from equation (30)) we find (hat at least a rough equipartition Ly~£,, will be realized at the scale of x9E without. (he fine-tuning. of. «—c."," On the other hand for a cylindrical field line with the value of $\xi$ such that $|\xi^{2}-1|=O(1/E^{2})$ the maximum radius $x$ may become of order of $E^{2}$, and from equation \ref{largex}) ) we find that at least a rough equipartition $E_{k}\sim E_{m}$ will be realized at the scale of $x\sim E$ without the fine-tuning of $x\rightarrow x_{\rm c}$." + In particular.. if ∙⊳⊳↽£x⊳↽€.. namely. €&xr)x1—(1/£7).> the field line may be extendinge to an infinite radius .—o. where M? becomes equal to (EV1—&?-—1)1," In particular, if $\xi\leq \xi_{\rm c}$, namely, $\xi^{2}\leq 1-(1/E^{2})$, the field line may be extending to an infinite radius $x\rightarrow\infty$, where $\mm^{2}$ becomes equal to $(E\sqrt{1-\xi^{2}}-1)^{-1}$." +" Such a field line configuration may be asvmptotically. paraboloidal or conical. and the efficient οποιονe. conversion into the state E;Á>E,m becomes possible at v>E tor field lines with 1—S€&=O(I/↜∕E72)."," Such a field line configuration may be asymptotically paraboloidal or conical, and the efficient energy conversion into the state $E_{k}\geq E_{m}$ becomes possible at $x\geq E$ for field lines with $1-\xi^{2}=O(1/E^{2})$." + This is another fine-tuning problem required for the poloidal electric and toroidal magnetic field amplitudes., This is another fine-tuning problem required for the poloidal electric and toroidal magnetic field amplitudes. +" The precise fine-tuning of €=[-—(1/E?) means that the magnetic enerev E,, can be completely transported into the kinetic enerev 7j as outflows propagate to an infinite radius.", The precise fine-tuning of $\xi^{2}=1-(1/E^{2})$ means that the magnetic energy $E_{m}$ can be completely transported into the kinetic energy $E_{k}$ as outflows propagate to an infinite radius. + To claim that the kinetic energv can asvinplotically become larger (han the magnetic energv for injection of magnetic-energv dominated outflows with very large £. we must solve the fine-tuning problem such that 1—Gr./c)=O(1/27) or |£?—1|=O(1/E?) as a result of MIID interaction described by the Gracd-Shalranoy equation.," To claim that the kinetic energy can asymptotically become larger than the magnetic energy for injection of magnetic-energy dominated outflows with very large $E$, we must solve the fine-tuning problem such that $1-(x_{\rm c}/x)=O(1/E^{2})$ or $|\xi^{2}-1|=O(1/E^{2})$ as a result of MHD interaction described by the Grad-Shafranov equation." + In (his paper we consider a jel ejection with a verv small opening angle such that HR/Zx 1/E. and we study the spatial variation of£ to show the dynamical fine-tuning of€ in jet flows.," In this paper we consider a jet ejection with a very small opening angle such that $R/Z\leq 1/E$ , and we study the spatial variation of $\xi$ to show the dynamical fine-tuning of $\xi$ in jet flows." + The asvinplolic analvsis of relativisüc outflows has been developed in previous works, The asymptotic analysis of relativistic outflows has been developed in previous works +with this small shear are steady-state radial and azimuthal magnetic fields. which we plot in Figure 2..,"with this small shear are steady-state radial and azimuthal magnetic fields, which we plot in Figure \ref{fig:bfields}." +" This confirms that B,/B,,«1. which is expected. because the toroidal field growth is driven by shearing."," This confirms that $B_r/B_\phi\ll1$, which is expected because the toroidal field growth is driven by shearing." +" The convection associated with the simmering phase (as studied in $3)) may destroy this magnetic field for M,=1M... but the field within the convectively stable region will remain."," The convection associated with the simmering phase (as studied in \ref{sec:convection}) ) may destroy this magnetic field for $M_r\lesssim1\ M_\odot$, but the field within the convectively stable region will remain." + Whether or not these fields are important for the later flame propagation when the WD is incinerated or for observations of the SNe Ia is an interesting question., Whether or not these fields are important for the later flame propagation when the WD is incinerated or for observations of the SNe Ia is an interesting question. + According to Piro&Bildsten(20072) both B..BoxM'!* for the Tayler-Spruit dynamo.," According to \citet{pb07a} both $B_r,B\phi\propto\dot{M}^{1/2}$ for the Tayler-Spruit dynamo." + Thus any process or observational diagnostic that 15 sensitive to the magnetic field strength would reveal something about M. an important diseriminant between progenitor models.," Thus any process or observational diagnostic that is sensitive to the magnetic field strength would reveal something about $\dot{M}$, an important discriminant between progenitor models." + There 1s uncertainty in applying the Tayler-Spruit formulae to the case of an accreting WD., There is uncertainty in applying the Tayler-Spruit formulae to the case of an accreting WD. + In the analysis presented by Spruit(2002)... 1t is assumed that N>Owa. where wa=B/\(4zp)'7r] is the Alfvénn frequency.," In the analysis presented by \citet{spr02}, it is assumed that $N>\Omega>\omega_{\rm A}$, where $\omega_{\rm A}=B/[(4\pi\rho)^{1/2}r]$ is the Alfvénn frequency." + Such inequalities are appropriate for the radiative interior of the sun (for which this work was originally motivated)., Such inequalities are appropriate for the radiative interior of the sun (for which this work was originally motivated). + In the WD interior it is possible that O2N since the Brunt-Váiisállá frequency is decreased by degeneracy effects (eq. [18]]). Denissenko, In the WD interior it is possible that $\Omega\gtrsim N$ since the Brunt-Väiisällä frequency is decreased by degeneracy effects (eq. \ref{eq:brunt}] ]). +v&Pinsonneault(2007) consider the effects of a large spin and find the effective viscosity of the dynamo is significantly reduced by a factor of (K/72N)*(O/N)Sa/0y7«1., \citet{dp07} consider the effects of a large spin and find the effective viscosity of the dynamo is significantly reduced by a factor of $(K/r^2N)^{1/6}(\Omega/N)^{1/6}(\sigma/\Omega)^{2/3}\ll1$. + We hesitate from implementing their prescriptions because their results are based on purely heuristic arguments without the rigorous analysis of an appropriate dispersion relation (aswasprovidedinSpruit 2006)., We hesitate from implementing their prescriptions because their results are based on purely heuristic arguments without the rigorous analysis of an appropriate dispersion relation \citep[as was provided in][]{spr06}. +. Since the baroclinic instability still contributes a large viscosity. our conclusion of solid body rotation is unchanged.," Since the baroclinic instability still contributes a large viscosity, our conclusion of solid body rotation is unchanged." + An interesting possibility is that in the limit of large spin. a different instability other than Tayler instability is responsible for turbulently creating poloidal magnetic field components as is necessary for closing the dynamo loop.," An interesting possibility is that in the limit of large spin, a different instability other than Tayler instability is responsible for turbulently creating poloidal magnetic field components as is necessary for closing the dynamo loop." + The magnetorotational instability (Velikhov1959;Chandrasekhar1992;Balbus1995) cannot provide closure to the dynamo since it requires dO/dr«0. which ts opposite to what is found in the WD interior.," The magnetorotational instability \citep{vel59,cha60,fri69,ach78,bh91,bh92,bal95} cannot provide closure to the dynamo since it requires $d\Omega/dr<0$, which is opposite to what is found in the WD interior." + For similar reasons magnetic shear inabilities are also ruled out (Acheson1978)., For similar reasons magnetic shear inabilities are also ruled out \citep{ach78}. +. Since the magnetic fields plotted in Figure 2. decrease with radius near the outer parts of the WD. it 1s possible that the magnetic buoyancy instability occurs.," Since the magnetic fields plotted in Figure \ref{fig:bfields} decrease with radius near the outer parts of the WD, it is possible that the magnetic buoyancy instability occurs." + Using the results from Acheson(1978).. Spruit(1999) shows in the limit of σ/οδι. we conclude that the Tayler instability limits magnetic field growth and not the buoyancy instability.," Since $B_{\rm buoy}\gg B_\phi$, we conclude that the Tayler instability limits magnetic field growth and not the buoyancy instability." + Apparently even when O>N Tayler instability is the correct magnetohydrodynamie instability for closing the shear-driven dynamo in the core of accreting WDs., Apparently even when $\Omega>N$ Tayler instability is the correct magnetohydrodynamic instability for closing the shear-driven dynamo in the core of accreting WDs. + These WD models provide the local viscous timescale for angular momentum transport. fie=min|H7.R7|v. and the heating provided by viscous dissipation.," These WD models provide the local viscous timescale for angular momentum transport, $\tvisc={\rm min}[H^2,R^2]/\nu$, and the heating provided by viscous dissipation." +" In the top/ panel of Figure 3. we plot {μις for the baroclinic instability and the Tayler-Spruit dynamo,", In the top panel of Figure \ref{fig:time} we plot $\tvisc$ for the baroclinic instability and the Tayler-Spruit dynamo. + Both are significantly smaller than the accretion timescale. thus our approximations presented at the beginning of 82. are justified.," Both are significantly smaller than the accretion timescale, thus our approximations presented at the beginning of \ref{sec:accretion} are justified." + Compositional discontinuities present a possible barrier to angular momentum transport which we have ignored since we are focused on the WD core., Compositional discontinuities present a possible barrier to angular momentum transport which we have ignored since we are focused on the WD core. + Piro&Bildsten(2007a) show in the case of accreting neutron stars that such compositional changes can inhibit turbulent mixing. but do not alter angular momentum transport any more than introducing a slight spin. discontinuity.," \citet{pb07a} show in the case of accreting neutron stars that such compositional changes can inhibit turbulent mixing, but do not alter angular momentum transport any more than introducing a slight spin discontinuity." + Our assumption of steady-state transport in the core is therefore not affected., Our assumption of steady-state transport in the core is therefore not affected. + Figure 3 shows that there is a clear hierarchy of timescales., Figure \ref{fig:time} shows that there is a clear hierarchy of timescales. + If both mechanisms were acting. the Tayler-Spruit dynamo acts sufficiently rapid that it limits the shear before the baroclinicinstability becomes important.," If both mechanisms were acting, the Tayler-Spruit dynamo acts sufficiently rapid that it limits the shear before the baroclinicinstability becomes important." + The viscous heating per unit mass is sigma so that the total luminosity ts," The viscous heating per unit mass is = ^2, so that the total luminosity is" +elliptical masses. but instead we determine the equivaleut mass of a spherical NFW halo.,"elliptical masses, but instead we determine the equivalent mass of a spherical NFW halo." +" With the ? best-fit scale convergence ας and scale radius 74. we estimate the cluster nass within radius ra as where s—rfr. aud Mog is the critical surface mass density. defined as which depends ou the augular diameter distances Dj,4. from the observer to the lens. to the source. aud from the leus to the source. respectively."," With the \cite{CO06.1} best-fit scale convergence $\kappa_\mathrm{s}$ and scale radius $r_\mathrm{s}$, we estimate the cluster mass within radius $r_\Delta$ as where $x \equiv r_\Delta/r_\mathrm{s}$ and $\Sigma_\mathrm{crit}$ is the critical surface mass density, defined as which depends on the angular diameter distances $D_{\rm l,s,ls}$ from the observer to the lens, to the source, and from the lens to the source, respectively." + We estimate the errors in mass by propagating the errors in the best-fit NEW parameters., We estimate the errors in mass by propagating the errors in the best-fit NFW parameters. + As detailed iu ? these errors are quite s12all but are realistic. because the reproduced lensed image is scusitive to slight variations In a parameters value.," As detailed in \cite{CO06.1} these errors are quite small but are realistic, because the reproduced lensed image is sensitive to slight variations in a parameter's value." +" Ποπονο, we note that these errors are relevant only to the choice of lens model and data and do not represent a elobal systematic uncertainty."," However, we note that these errors are relevant only to the choice of lens model and data and do not represent a global systematic uncertainty." + We use the iethod described here to measure the lensing cluster masses im Table 1.. as well as the cluster masses Afogy aud. Mosoo in Table 2..," We use the method described here to measure the lensing cluster masses in Table \ref{tbl:mass}, as well as the cluster masses $M_{200}$ and $M_{2500}$ in Table \ref{tbl:props}." + Since one of our alms is fo iueasure the imass-telperature relation for relaxed leusiug clusters. we nist deteriuuue which of the cight clusters im our sample are dynamically relaxed.," Since one of our aims is to measure the mass-temperature relation for relaxed lensing clusters, we must determine which of the eight clusters in our sample are dynamically relaxed." + N-ray cluster mass estimates are based ou the assunptiou that the cluster is iu wdrostatic equilibrium. and if a cbluster is relaxed it is also in hwdrostatie equilibrium.," X-ray cluster mass estimates are based on the assumption that the cluster is in hydrostatic equilibrium, and if a cluster is relaxed it is also in hydrostatic equilibrium." + Therefore. X-ray mass ucasureineuts for relaxed clusters should be accurate and consistent with leusime mass nieasurenmients.," Therefore, X-ray mass measurements for relaxed clusters should be accurate and consistent with lensing mass measurements." + We use X-ray nass estimates from the literature. where he N-rav masses are measured for cach cluster at two or hee different radii.," We use X-ray mass estimates from the literature, where the X-ray masses are measured for each cluster at two or three different radii." + For cach cluster. Table 1. eives the Cusine nass and X-ray mass mueasured within the two or three different cluster radi," For each cluster, Table \ref{tbl:mass} gives the lensing mass and X-ray mass measured within the two or three different cluster radii." + Table d. also shows the ensine mass to N-ray mass ratio and the reduced 4? of the comparison of leusimg aud X-ray masses., Table \ref{tbl:mass} also shows the lensing mass to X-ray mass ratio and the reduced $\chi^2$ of the comparison of lensing and X-ray masses. +" For six clusters, at all radii at which masses were measured. the ratio of lensing mass to X-ray mass is consistent with unity and the reduced. 4? is <1. suggesting that these six clusters could be relaxed."," For six clusters, at all radii at which masses were measured, the ratio of lensing mass to X-ray mass is consistent with unity and the reduced $\chi^2$ is $\lesssim 1$, suggesting that these six clusters could be relaxed." + Additional observational evidence in 3.2.0 and 3.2.0 shows that four of these six clusters are relaxed. while the remaining two clusters are uurelaxed.," Additional observational evidence in \ref{relaxed} and \ref{unrelaxed} shows that four of these six clusters are relaxed, while the remaining two clusters are unrelaxed." + For at least one of the radii cousidered. the two clusters MS 23 aud C1 | 1713 cach exhibit lensing to A-rayv πας ratios that are inconsistent with unitv and reduced 4? that are ercater than unity. which is evidence that the clusters axe wnrelaxed.," For at least one of the radii considered, the two clusters MS $-$ 23 and Cl $+$ 4713 each exhibit lensing to X-ray mass ratios that are inconsistent with unity and reduced $\chi^2$ that are greater than unity, which is evidence that the clusters are unrelaxed." + We measure masses for MS 2157. 23 within three different radii. aud within one of these radii the mass ratio is inconsistent with unitv and the reduced. \? is ereater than unity.," We measure masses for MS $-$ 23 within three different radii, and within one of these radii the mass ratio is inconsistent with unity and the reduced $\chi^2$ is greater than unity." + However there is opposing evidence. given iu 3.2.0.. that characterizes MS 2137 23 as a relaxed cluster.," However there is opposing evidence, given in \ref{relaxed}, , that characterizes MS $-$ 23 as a relaxed cluster." + For Cl 0939 L713. the mass ratios measured at both radii considered| are inconsistent with unitv aud both reduced 4? are much ercater than unity. suggesting C] | 1713 may be an unurelaxed cluster.," For Cl $+$ 4713, the mass ratios measured at both radii considered are inconsistent with unity and both reduced $\chi^2$ are much greater than unity, suggesting Cl $+$ 4713 may be an unrelaxed cluster." + In 3.2.0. we preseut more evidence in support of this conclusion., In \ref{unrelaxed} we present more evidence in support of this conclusion. + Additional information about the cwuamical state of a cluster can be found in ifs X-ray emission map., Additional information about the dynamical state of a cluster can be found in its X-ray emission map. + For exanple. the position of the BCG relative to the peak iu the clusters X-ray profile may be evidence of a clusters ανασα. state: if the two are coincident the cluster is likely relaxed. otherwise it is likely uurelaxed.," For example, the position of the BCG relative to the peak in the cluster's X-ray profile may be evidence of a cluster's dynamical state: if the two are coincident the cluster is likely relaxed, otherwise it is likely unrelaxed." + The ceutroid shift is one means of quautifviug this positional differeuce (e.g.. ?2)).," The centroid shift is one means of quantifying this positional difference (e.g., \citealt{MO93.1, JE08.1}) )." + Additionally a smooth distribution of N-rav gas indicates the cluster is likely iu a relaxed state.," Additionally, a smooth distribution of X-ray gas indicates the cluster is likely in a relaxed state." +" Towever. if the ταν gas is distributed nreeularly or shows evidence of shocks or substructure. the cluster is likely unrelaxed and undergoing a Ποσο,"," However, if the X-ray gas is distributed irregularly or shows evidence of shocks or substructure, the cluster is likely unrelaxed and undergoing a merger." + Below we examine evicence for the dvuamical state of cach cluster individually aud label cach cluster as relaxed or uurelaxed (these labels are also given inTable 1))., Below we examine evidence for the dynamical state of each cluster individually and label each cluster as relaxed or unrelaxed (these labels are also given inTable \ref{tbl:mass}) ). + We first discuss the four relaxed clusters. then the four nurelaxed clusters.," We first discuss the four relaxed clusters, then the four unrelaxed clusters." +The dispersion in the residtials abott the 1jean relation S 0.1.) uiag.,The dispersion in the residuals about the mean relation is $\pm 0.13$ mag. +" If we extrapolate the relation to an assumed solar color of B—V = 0.652. AL, becunes 1.560. only slightly fainter than our adopted value of Ady = LAL"," If we extrapolate the relation to an assumed solar color of $B-V$ = 0.652, $M_V$ becomes 4.86, only slightly fainter than our adopted value of $M_{V_{\odot}}$ = 4.84." + Give1 the age of the Sun. oie niet expect a larger clifferential compared to the unevolved inaiu sequeice.," Given the age of the Sun, one might expect a larger differential compared to the unevolved main sequence." + We will return to his isstte in Sec., We will return to this issue in Sec. + 1., 4. + Τje linear Lit is shown as a solid liue in Fig., The linear fit is shown as a solid line in Fig. + 2., 5. + To derive the unevolved main seqteuce relation [or a raige ol [Fe/H]. our iuitial sample of 1982 stars with reliable abundances aud parallax measures was restricted to single. non-variable stars with [Fe/H between —0.50 aud 4-E0.50. AL fainter han +1.5. B—V bluer than 1.30. and B-—V redder than B—V=(.2[Fe/H]+0.72. cutting he clataset to 533 stars.," To derive the unevolved main sequence relation for a range of [Fe/H], our initial sample of 1982 stars with reliable abundances and parallax measures was restricted to single, non-variable stars with [Fe/H] between $-0.50$ and +0.50, $M_V$ fainter than +4.5, $B-V$ bluer than 1.30, and $B-V$ redder than $B-V = 0.2{\rm [Fe/H]} + 0.72$, cutting the dataset to 533 stars." + Bluarles were tagged [rom the ueh-cispersion spectra obtained to derive the abundances in eaci study included iu the composite catalog. wlile significant variaiity was checked throwh the Tye10 catalog.," Binaries were tagged from the high-dispersion spectra obtained to derive the abundances in each study included in the composite catalog, while significant variability was checked through the Tycho catalog." + After a preliminary polynomial fit to the data. inclunο tests of up to cubic terms in B—V. quadratic terms in [Fe/H]. aud multipe Cross-leri combilatious. Ony the linean terms in B—V and [Fe/H] survived. the former result beiug cousistent wiil what was found Lo‘the solar sample.," After a preliminary polynomial fit to the data, including tests of up to cubic terms in $B-V$, quadratic terms in [Fe/H], and multiple cross-term combinations, only the linear terms in $B-V$ and [Fe/H] survived, the former result being consistent with what was found for the solar sample." +" All stars with residuals in AA greate ""than 0.35 mae we'e excluded and the firal calibration repeated.", All stars with residuals in $M_V$ greater than 0.35 mag were excluded and the final calibration repeated. + The final sample consisted of 50!| stars with a stana«d deviation amoung he residuals in Ady) of 0.135 mae., The final sample consisted of 501 stars with a standard deviation among the residuals in $M_V$ of 0.135 mag. +" The derived polyuori"" Auction is: For solar metallicity stars. the slope of the uuevolved mai secuence based upon the derived relation is somewhat steeper than [fouud previously. leacing to stars that are 0.03 mag brighter at B—V =0.75. but 0.09 nae fainte at B—V = 1.25."," The derived polynomial function is: For solar metallicity stars, the slope of the unevolved main sequence based upon the derived relation is somewhat steeper than found previously, leading to stars that are 0.03 mag brighter at $B-V$ = 0.75, but 0.09 mag fainter at $B-V$ = 1.25." + HE we dema ultiat the main sequence relation have the same slope at solar metalicity as derived from the solar sample. the relation becomes The standard deviation among the 502 residuals increases slightly to 0.137.," If we demand that the main sequence relation have the same slope at solar metallicity as derived from the solar sample, the relation becomes The standard deviation among the 502 residuals increases slightly to 0.137." + For reasons that will be discussed iu Sec., For reasons that will be discussed in Sec. + L it is probable that even the slope of LT is too steep for the true. unevolved main sequence.," 4, it is probable that even the slope of 4.77 is too steep for the true, unevolved main sequence." + As stated iu Sec., As stated in Sec. + 1. α primary goal of this investigation is to test the sensitivity of the absolute iaguitude of unevolved cooler main sequence stars as B—V aud [Fe/H] are varied.," 1, a primary goal of this investigation is to test the sensitivity of the absolute magnitude of unevolved cooler main sequence stars as $B-V$ and [Fe/H] are varied." + Qualitatively. our data relatious confirm that. within the current uncertainties. there is uo statistically significant evidence for a variation in the ratio. AAA) /A[Fe/H]. with B—Vor [Fe/H] between +0.5 and —0.5 for truly unevolved stars.," Qualitatively, our data relations confirm that, within the current uncertainties, there is no statistically significant evidence for a variation in the ratio, $\Delta M_V/\Delta$ [Fe/H], with $B-V$or [Fe/H] between +0.5 and $-0.5$ for truly unevolved stars." + The coustaut ratio is cousistent with the work of Percivaletal. (2003," The constant ratio is consistent with the work of \citet{pe03}, ," + The coustaut ratio is cousistent with the work of Percivaletal. (2003)," The constant ratio is consistent with the work of \citet{pe03}, ," + The coustaut ratio is cousistent with the work of Percivaletal. (2003).," The constant ratio is consistent with the work of \citet{pe03}, ," +and o; the error in the observed QPO frequency difference for the binary labeled 7.,and $\sigma_i$ the error in the observed QPO frequency difference for the binary labeled $i$. + We use the Ly-norm but other choices are possible like the Ls-norm. although the latter being less robust.," We use the $L_1$ -norm but other choices are possible like the $L_2$ -norm, although the latter being less robust." + We found no significant changes when applying the second choice., We found no significant changes when applying the second choice. + In any case. the best fil corresponds to a minimum of the figure-of-merit fiction JF.," In any case, the best fit corresponds to a minimum of the figure-of-merit function $\mathcal{F}$." + Moreover. we tried other merit functions with no difference in the best fit parameters.," Moreover, we tried other merit functions with no difference in the best fit parameters." + Finally. some words about the mass-clependence on stellar rotation.," Finally, some words about the mass-dependence on stellar rotation." + Assuming the same mass as well as the same moment of inertia lor all the set of neutron star binaries is a crude first guess., Assuming the same mass as well as the same moment of inertia for all the set of neutron star binaries is a crude first guess. + A detailed deseription of the inner structure of rapidly rotating neutron stars is a difficult caleulation only numerically treatable (Shapiro&Teukolskv. 200T)..," A detailed description of the inner structure of rapidly rotating neutron stars is a difficult calculation only numerically treatable \citep{1983bhwd.book.....S, 2007coaw.book.....C}." + For uniform rotation. the mass increase is expected to be less than20%.," For uniform rotation, the mass increase is expected to be less than." +. However. Lyfordetal.(2003). computed equilibrium configurations with differential rotation aud found an increase up toGOW... even for moderate spin rate.," However, \cite{2003ApJ...583..410L} computed equilibrium configurations with differential rotation and found an increase up to, even for moderate spin rate." + The salient feature to keep in mind from all these studies is an increase of the gravitational mass with rotation., The salient feature to keep in mind from all these studies is an increase of the gravitational mass with rotation. + Thus. to better adjust the observations without handling all these complicated computations. we can however release the constant mass hypothese and use a neutron star spin dependent mass based on the following heuristic argument (Ghosh2007)..," Thus, to better adjust the observations without handling all these complicated computations, we can however release the constant mass hypothese and use a neutron star spin dependent mass based on the following heuristic argument \citep{2007rapp.book......}." +" The rotation ol the neutron star. containing a fixed munber of N nucleons. increases its gravitational mass MCN.O,40) compared to the non rotating limit AZ(N.O,=0)."," The rotation of the neutron star, containing a fixed number of $N$ nucleons, increases its gravitational mass $M(N,\Omega_*\neq0)$ compared to the non rotating limit $M(N,\Omega_*=0)$." +" Because kinetic energv is equivalent to mass and therefore induces gravitation. a simple relation between both gravitational masses is suchthat For the remainder of the paper. we use lighter notations. setting AM=ΜΗΝ.0) for the mass of a non-rotating neutron star and AZ,=AL(N.Q,) for that of the same neutron star (Le. equal number of baryons V) but rotating al an angular speed ©..."," Because kinetic energy is equivalent to mass and therefore induces gravitation, a simple relation between both gravitational masses is suchthat For the remainder of the paper, we use lighter notations, setting $M +\equiv M(N,0)$ for the mass of a non-rotating neutron star and $M_* +\equiv M(N,\Omega_*)$ for that of the same neutron star (i.e. equal number of baryons $N$ ) but rotating at an angular speed $\Omega_*$." + Eq. (9)), Eq. \ref{eq:RelationSpinMasse}) ) + shows the quadratic dependence on spin O7. the same functional dependence as the one [rom the," shows the quadratic dependence on spin $\Omega_*^2$ , the same functional dependence as the one from the" +laver as the main path of accretion onto the star. a model often invoked for OOvrionis-type outbursts (?).. especially since the innerost parts of a boundary laver is ub-I&eplerian.,"layer as the main path of accretion onto the star, a model often invoked for Orionis-type outbursts \citep{hk96}, especially since the innermost parts of a boundary layer is sub-Keplerian." + Although the boundary laver. or strong turbulence could explain the single-peaked line profile. they cannot reproduce the ligh-velocity high-amplitude spectro-astrometiic signal.," Although the boundary layer, or strong turbulence could explain the single-peaked line profile, they cannot reproduce the high-velocity high-amplitude spectro-astrometric signal." + Qur results suggest that hydrogen eas is orbiting the central star but its velocity profile is not Keplerian. iu a sense that there is lagh-velocity eas farther frou the star.," Our results suggest that hydrogen gas is orbiting the central star but its velocity profile is not Keplerian, in a sense that there is high-velocity gas farther from the star." + This poiuts to a funnel flow or disk wind origin. where the material is launched from the iuncr disk along the magnetic field lines with hieh velocities.," This points to a funnel flow or disk wind origin, where the material is launched from the inner disk along the magnetic field lines with high velocities." + This max also help to explain why the hydrogen gas is hotter than the CO., This may also help to explain why the hydrogen gas is hotter than the CO. + The wind scenario is supported by the CCveui profiles observed in several optical lines by ?.., The wind scenario is supported by the Cygni profiles observed in several optical lines by \citet{aspin2010}. + Supposing that the disk wind scenario is true for LLup. it should be optically thin. otherwise the excitation diagram m Fie.," Supposing that the disk wind scenario is true for Lup, it should be optically thin, otherwise the excitation diagram in Fig." + 5 would show flatter line ratios (?).., \ref{fig:caseB} would show flatter line ratios \citep{lorenzetti2009}. + Tn this paper we performed a near-infrared spectroscopic aud spectro-astrometric study of LLiup during its most extreme outburst in 2008., In this paper we performed a near-infrared spectroscopic and spectro-astrometric study of Lup during its most extreme outburst in 2008. + Our main conchisions are the following: Based on our findings. we can attempt to reconstruct the ecometrical and kinematic structure of the circustellar material within the iuner few tenths of AU iu the LLup svstem during the outburst.," Our main conclusions are the following: Based on our findings, we can attempt to reconstruct the geometrical and kinematic structure of the circumstellar material within the inner few tenths of AU in the Lup system during the outburst." + The dust disk has an iuner radius of AAU (??)..," The dust disk has an inner radius of AU \citep{sipos2009,juhasz2010}." + Within this area. there is an optically thin eas disk. whose temperature is a few thousand Ix. as imdicated by the CO and neutral metal cussion lines.," Within this area, there is an optically thin gas disk, whose temperature is a few thousand K, as indicated by the CO and neutral metal emission lines." + This arca certainty also contains hydrogen gas. but this component is uot visible in the spectro-astrometric signal due to its low velocity.," This area certainly also contains hydrogen gas, but this component is not visible in the spectro-astrometric signal due to its low velocity." + We see evidence for high temperature (2:10 IKIS). Ligh velocity (100 1 lydroecu eas in the system. which is not located iu the equatorial plane.," We see evidence for high temperature $\approx$ K), high velocity $\approx$ $^{-1}$ ) hydrogen gas in the system, which is not located in the equatorial plane." + Part of this lydroecu probably falls outo the stellar surface along magnetic fuuncl flows., Part of this hydrogen probably falls onto the stellar surface along magnetic funnel flows. + DIudoeed. based ou X-rav and UV data. ?— reported on the presence of acerction shocks and accretion hot spots on the stellar surface of LLup.," Indeed, based on X-ray and UV data, \citet{grosso2010} reported on the presence of accretion shocks and accretion hot spots on the stellar surface of Lup." + Some of the UV. photons hus generated must reach the disk surface aud produce he fluorescent cussion we observe iu certam sodiuni. nagnesit and oxvgen ues.," Some of the UV photons thus generated must reach the disk surface and produce the fluorescent emission we observe in certain sodium, magnesium and oxygen lines." + The UV radiation may also trigger chemical changes in the disk., The UV radiation may also trigger chemical changes in the disk. + Part of the ivdrogen gas docs not fall onto the stellar surface mt leaves the system in the form of a hot wind. as evidenced by the CCvenui profile of the optical hydrogen ines.," Part of the hydrogen gas does not fall onto the stellar surface but leaves the system in the form of a hot wind, as evidenced by the Cygni profile of the optical hydrogen lines." + Considering all these argunmieuts. the cuereiue Xeture is broadly consistent with that of the standard uaenetosphneric accretion model usually assunued for rormally accreting TTauri stars (e.g. 7)).," Considering all these arguments, the emerging picture is broadly consistent with that of the standard magnetospheric accretion model usually assumed for normally accreting Tauri stars (e.g. \citealt{bouvier2007}) )." + Several models are described in the literature to explain the increased accretion iu voung eruptive stars., Several models are described in the literature to explain the increased accretion in young eruptive stars. + Our results mav place constraints on the applicability of these models for the case of LLup., Our results may place constraints on the applicability of these models for the case of Lup. + Our results do not indicate the preseuce of a fully ionized rius of uateriil during the eruption of LLup. which seems ο coutradict the thermal iustabilitv model of 2? aud 7..," Our results do not indicate the presence of a fully ionized ring of material during the eruption of Lup, which seems to contradict the thermal instability model of \citet{hk96} and \citet{bell1994}." + No stellar or planetary companions to LLup have con found so far (?.audreferencestherein).. neither do our spectro-astrometric analysis suggests the presence of ouc.," No stellar or planetary companions to Lup have been found so far \citep[][and references therein]{sipos2009}, neither do our spectro-astrometric analysis suggests the presence of one." + This makes outburst mocels involving perturbation wea close companion unlikelv (7).., This makes outburst models involving perturbation by a close companion unlikely \citep{bonnell1992}. + The model of ? involves gravitational instability and fragmentation in he outer disk. and the iufall of these fragments onto he star.," The model of \citet{vorobyov2010} + involves gravitational instability and fragmentation in the outer disk, and the infall of these fragments onto the star." + The modest disk mass. and the fact that our spectro-astrometric observations indicate an azinuthliallv svuuuetre mass distribution in the immer disk reasons against this model.," The modest disk mass, and the fact that our spectro-astrometric observations indicate an azimuthally symmetric mass distribution in the inner disk reasons against this model." + Recently. ? proposed that accretion outo a strongly magnetic protostar is iuherentlv episodic if the disk is truncated close to the corotation radius.," Recently, \citet{dangelo2010} proposed that accretion onto a strongly magnetic protostar is inherently episodic if the disk is truncated close to the corotation radius." + In their model. the magnetic field initially truncates the disk outside the corotation radius. thus accretion onto the star is inhibited.," In their model, the magnetic field initially truncates the disk outside the corotation radius, thus accretion onto the star is inhibited." + As gas in the inner regions of the disk piles up. luaterial is pushed inside the corotation radius. and the accinulated material is accreted onto the star until the reservoir is depleted. aud the immer radius of the disk is again outside the corotation radius.," As gas in the inner regions of the disk piles up, material is pushed inside the corotation radius, and the accumulated material is accreted onto the star until the reservoir is depleted, and the inner radius of the disk is again outside the corotation radius." + ? reported a csini of Ll+t2kkinss ! for LLup. which translates iuto a rotation period of about 13 davs (ising an inclination of 15? aud stellar radius of ..). and a corotation radius of about AAT (ising a stellar mass of NINE...," \citet{sipos2009} reported a $v \sin i$ of $\,{\pm}\,$ $^{-1}$ for Lup, which translates into a rotation period of about 13 days (using an inclination of $^{\circ}$ and stellar radius of $_{\odot}$ ), and a corotation radius of about AU (using a stellar mass of $_{\odot}$ )." + This value is close to the radius of the dust-freezone., This value is close to the radius of the dust-freezone. + Our results show that during outburst. eas is present m this area. potentially channeled along magnetic fuunel flows.," Our results show that during outburst, gas is present in this area, potentially channeled along magnetic funnel flows." + Thus. the model of ? may be applicable for LLup.," Thus, the model of \citet{dangelo2010} + may be applicable for Lup." + The results published in this paper are based on data collected at the Enropean Southern Observatory in the rane of the programs 281.C-5031 and διςΟδ13., The results published in this paper are based on data collected at the European Southern Observatory in the frame of the programs 281.C-5031 and 381.C-0243. + We hank the referee.Colin Aspin. whose sugeestions helped o imupove this paper.," We thank the referee,Colin Aspin, whose suggestions helped to impove this paper." + A.. KX. would like to thank Uma Corti and Arjan Bik for useful discussious about ucar-infrared spectroscopy., Á.. K. would like to thank Uma Gorti and Arjan Bik for useful discussions about near-infrared spectroscopy. + The research of A. Kis supported w the Nederlands Orgauizatiou for Scieutic Research., The research of Á.. K. is supported by the Nederlands Organization for Scientific Research. + Zs., Zs. +" R. has been supported im part by the DAAD-PPP nobility eraut. P-MODD/811/ and by the ""Leudüllet Youne Researcher Program of the Wnuearian Academy of Scicuces. (SINFONT).. (NACO)..", R. has been supported in part by the DAAD-PPP mobility grant P-MÖBB/841/ and by the “Lendüllet” Young Researcher Program of the Hungarian Academy of Sciences. . +0.4.,$\Upsilon_{\ast}^H=1.0\pm 0.4$. +" Observations for 11 galaxies were not included in our photometric study either because the galaxy remained invisible in the final mosaics despite our faint H-band surface brightness limit of 24—26 mmag arcsec™?, or the galaxy was detected but foreground stars interfered with the analysis."," Observations for 11 galaxies were not included in our photometric study either because the galaxy remained invisible in the final mosaics despite our faint $H$ -band surface brightness limit of $24-26$ mag ${}^{-2}$, or the galaxy was detected but foreground stars interfered with the analysis." +" In this section, we discuss the four galaxies labelled as “no galaxy detected"" in Table AM0717-571, KK2000-04, KK2000-06 and NGC2784 [I]:DW1."," In this section, we discuss the four galaxies labelled as “no galaxy detected"" in Table \ref{badgals}: AM0717-571, KK2000-04, KK2000-06 and NGC2784 DW1." +" While they remain as candidates for galaxies with a pure young stellar component, we show it is unlikely that this is the case."," While they remain as candidates for galaxies with a pure young stellar component, we show it is unlikely that this is the case." +" We also include KK2000-03 which had a marginal detection, and the galaxy pair HIZOAJ1616-55 and SJK98 J1616-55 which were not detected but we note that the images had serious foreground contamination."," We also include KK2000-03 which had a marginal detection, and the galaxy pair HIZOAJ1616-55 and SJK98 J1616-55 which were not detected but we note that the images had serious foreground contamination." +As shown in Figure L.. most |j values in the three targets are less than 1.,"As shown in Figure \ref{fig_betamap}, most $\beta$ values in the three targets are less than 1." + For a convenient comparison. the sale erav scales have been adopted for all three maps.," For a convenient comparison, the same gray scales have been adopted for all three maps." + The actual ranges of ο) values are in Table 5. with the averages., The actual ranges of $\beta$ values are in Table \ref{tab_beta} with the averages. + As listed in the table. the λαπα values are larger than1.0.," As listed in the table, the maximum values are larger than1.0." + However. those large 3 values appear only ou a few pixels of source boundaries. which may be due to contamination frou ambient clouds.," However, those large $\beta$ values appear only on a few pixels of source boundaries, which may be due to contamination from ambient clouds." + (j| and its averages in most reeions of the three sources are similar to or less than 1., $\beta$ and its averages in most regions of the three sources are similar to or less than 1. + Iu the case of LILis IRS 3. in which three Class 0 sources (3A. 3D. and 3€) exist. 3 values orrespouding to the three sources are separately listed in Table 3..," In the case of L1448 IRS 3, in which three Class 0 sources (3A, 3B, and 3C) exist, $\beta$ values corresponding to the three sources are separately listed in Table \ref{tab_beta}." + Like the other targets. these three sources of Lllls IRS 3 have ο) around or less than 1.," Like the other targets, these three sources of L1448 IRS 3 have $\beta$ around or less than 1." + The L1118 TRS 3A and 3B fiuxes are obtaiuedsimply by cutting 1e protuberance in Figure 1.., The L1448 IRS 3A and 3B fluxes are obtainedsimply by cutting the protuberance in Figure \ref{fig_betamap}. + Table 3. also has > values ybtained from the total fluxes at the two waveleneths. which have been estimated m source reeious limited by 1ο three SNR threshold at both wavelengths.," Table \ref{tab_beta} also has $\beta$ values obtained from the total fluxes at the two wavelengths, which have been estimated in source regions limited by the three SNR threshold at both wavelengths." + All sources except LILis IRS 3B have 3 values comparable to the uean values of the Jj maps., All sources except L1448 IRS 3B have $\beta$ values comparable to the mean values of the $\beta$ maps. + Another feature to note is that there are ο) eradicuts with radius iu all sources., Another feature to note is that there are $\beta$ gradients with radius in all sources. + L1157 has a smaller |j iu he northeast-to-soutlnvest direction. roughly cousisteut with the aan 2.7 nuu results of ?..," L1157 has a smaller $\beta$ in the northeast-to-southwest direction, roughly consistent with the and 2.7 mm results of \citet{beltran2004}." + However. it is noteworthy hat they restored their two nuages with an identical cau size without auv weielting schemes. which could cause a biased result due to differentwe coverage of the wo waveleusth data.," However, it is noteworthy that they restored their two images with an identical beam size without any weighting schemes, which could cause a biased result due to different coverage of the two wavelength data." +" The radial depeudeuce of ο) is etter shown iu retsec,.on pandisdiscussedindetail forthe LULSTRS3 Ισ οΠΡ 7s, We have also examined ο) values in space. which is the Fourier transformed space of an image."," The radial dependence of $\beta$ is better shown in \\ref{sec_vis_comp} and is discussed in detail for the L1448 IRS 3B case via modeling in \\ref{sec_discussion} + We have also examined $\beta$ values in space, which is the Fourier transformed space of an image." + Data of interferometric observations are obtained inve space and calledwe visibilities or just visibilitics., Data of interferometric observations are obtained in space and called visibilities or just visibilities. +" To obtain a sky intensity distribution. inverse Fourier transformation and deconvolution (ο, CLEANING algorithin) are cluploved (0.9...2).."," To obtain a sky intensity distribution, inverse Fourier transformation and deconvolution (e.g., CLEANING algorithm) are employed \citep[e.g.,][]{isra2001}." +" However. limitedwe coverage causes cüffieulties. Ίο, the decouvolution introduces systematic biases. especially for nou-poiut. extended sources."," However, limited coverage causes difficulties, i.e., the deconvolution introduces systematic biases, especially for non-point, extended sources." + One of the best wavs to overcome this difficulty is to investigate the visibility data inwe space instead., One of the best ways to overcome this difficulty is to investigate the visibility data in space instead. + The results of 9 caleulated iuwe space are displayed iu Figure 2.., The results of $\beta$ calculated in space are displayed in Figure \ref{fig_uvamp}. . + Visibilities have been vector-averaged in annmuli., Visibilities have been vector-averaged in annuli. + Since the euvelope structures frou our observations are spherical. the annulus averaging is valid.," Since the envelope structures from our observations are spherical, the annulus averaging is valid." + The annulus biu sizes aye 3.1 cexcept when the SNR is too low. usually at the relatively longer baschues.," The annulus bin sizes are $\sim 3.1$ except when the SNR is too low, usually at the relatively longer baselines." + This is most noticeable iu L1157 atnun., This is most noticeable in L1157 at. + Although the«e coverage is comparable at both wavelengths. the lower SNR at rrequires larger bins.," Although the coverage is comparable at both wavelengths, the lower SNR at requires larger bins." + The 3 values are calculated at the bbius with vvisubilities linearly iuterpolated using the nearest biu values., The $\beta$ values are calculated at the bins with visibilities linearly interpolated using the nearest bin values. + When the Dbin ceuter is bevoud last bbiu center (extrapolation case). then the nearest biu value for lix used.," When the bin center is beyond last bin center (extrapolation case), then the nearest bin value for is used." + Tu the case of LLLIS IRS 3. oulv 3D is considered for the } caleulation imue space.," In the case of L1448 IRS 3, only 3B is considered for the $\beta$ calculation in space." +" The other two objects. 2À aud 3C, are too παπα} aud weak to carry out the calculation."," The other two objects, 3A and 3C, are too small and weak to carry out the calculation." + Ou the other hand. 3A aud 3C should be removed fous the visibilities to obtain the 3B data.," On the other hand, 3A and 3C should be removed from the visibilities to obtain the 3B data." + Using the MIRIAD task UVAIODEL auc image models excluding the two coniponeuts; we subtracted the 3A aud 3€ visibilitics at both aand sseparatelv.," Using the MIRIAD task UVMODEL and image models excluding the two components, we subtracted the 3A and 3C visibilities at both and separately." + In addition. since the ddata set has been taken with two pointings offset from the center. we compensated the primary beam seusitivitv loss using à UVAIODEL inultiplication.," In addition, since the data set has been taken with two pointings offset from the center, we compensated the primary beam sensitivity loss using a UVMODEL multiplication." + Iun Figure 2.. the upper panels show amplitudes of ((opeu squares) and ceases (open triangles).," In Figure \ref{fig_uvamp}, the upper panels show amplitudes of (open squares) and cases (open triangles)." + The error bars represent the statistical standard errors in each bin., The error bars represent the statistical standard errors in each bin. +" The solid aud dashed nes preseut the best fit iiodoels described iu retsec,,odelingandFiqure3..", The solid and dashed lines present the best fit models described in \\ref{sec_modeling} and Figure \ref{fig_likelihood}. + Thelowerpanelsshow 3 values with distance. calculated by equation (3)).," The lower panels show $\beta$ values with distance, calculated by equation \ref{eq_beta}) )." + The open circles indicate ο) values calculated from the visibilitics shown on the upper panels., The open circles indicate $\beta$ values calculated from the visibilities shown on the upper panels. + The error bars with caps on the open circles represcut 2 value rauges corresponding to the statistical amplitude errors of the upper paucls., The error bars with caps on the open circles represent $\beta$ value ranges corresponding to the statistical amplitude errors of the upper panels. + The filled circles auc error bars without caps show the effect that the absolute flux calibration uncertainty has on the calculation of 3., The filled circles and error bars without caps show the effect that the absolute flux calibration uncertainty has on the calculation of $\beta$ . + We adopt flux calibrationuncertainties for ΙΟ delata. as discussed in τοκος bs.," We adopt flux calibrationuncertainties for data and for data, as discussed in \\ref{sec_obs}." + P helarger.? poiuts iudicate the case in which hieher fluxes at and lower fluxes at aare considered and vise verse for the lower | points., The larger $\beta$ points indicate the case in which higher fluxes at and lower fluxes at are considered and vise verse for the lower $\beta$ points. + The ./ ranges are around m0.35. as log(1.15/0.90)οσοfy)zz0.35 where ηνcm2 (refer to eq. 3)).," The $\beta$ ranges are around $\pm +0.35$, as $\textrm{log}(1.15/0.90)/\textrm{log}(\nu_1/\nu_0) \approx +0.35$ where $\nu_1/\nu_0 \approx 2$ (refer to eq. \ref{eq_beta}) )." + Two lain features should be noted in Figure 2.., Two main features should be noted in Figure \ref{fig_uvamp}. + One point is that the 3 values are around 1 or less than lin all three objects., One point is that the $\beta$ values are around 1 or less than 1 in all three objects. + It is arguablv true even when considering the absolute fiux calibration uncertainties., It is arguably true even when considering the absolute flux calibration uncertainties. +" The other point is the radial dependences of ο,", The other point is the radial dependences of $\beta$. + Iu Litts TRS 2 and L1157. JJ arguably decreases ou sinaller scales (larger ve distances).," In L1448 IRS 2 and L1157, $\beta$ arguably decreases on smaller scales (larger distances)." + L1EIS IRS 3D. however. distinctly prescutsa radial dependence.," L1448 IRS 3B, however, distinctly presentsa radial dependence." + The 3} variation is fit with the logarithimuic function of (0)=L00.57loe(c). where ¢ is the distance in units of kA.," The $\beta$ variation is fit with the logarithmic function of $\beta(\zeta) = 1.0 - 0.57~\textrm{log}(\zeta)$, where $\zeta$ is the distance in units of $\lambda$." +" When assuming power-law distributions of deusitv and temperature of euvelopes as discussed in refscc,odcling..thedistributionsoftheintensituintegratedalongliin sightaswellastheradialintensity followa lawundertheopticallythinassaimptionand Rayleigh Jeaunsapprocimation(2).."," When assuming power-law distributions of density and temperature of envelopes as discussed in \\ref{sec_modeling}, the distributions of the intensity integrated along line-of-sight as well as the radial intensity follow a power-law under the optically thin assumption and Rayleigh-Jeans approximation \citep{adams1991}. ." +H henignoringprimargbeaincf fectsof iuf lawle.g. 27). ," When ignoring primary beam effects of interferometers and assuming infinite size envelopes,the visibilities are also in a power-law \citep[e.g.][]{harvey2003,looney2003}. ." +5.3 is obtained from equation (3)). here. we assume a logarithmic function of J(Q).," As $\beta$ is obtained from equation \ref{eq_beta}) ) here, we assume a logarithmic function of $\beta(\zeta)$ ." +" There are a few possible interpretations to explain this radial dependence of οὐ, ", There are a few possible interpretations to explain this radial dependence of$\beta$ . +It could be caused by increasing the fraction of optically thick cussion on smaller scales, It could be caused by increasing the fraction of optically thick emission on smaller scales +2002).,. +. We found no significant signal in the Fourier traisform at the precession period of ~3.6 d. Iu Figure 23. we show the results of the O-C analvsis for the Q2 data., We found no significant signal in the Fourier transform at the precession period of $\sim$ 3.6 d. In Figure \ref{fig: negshomc} we show the results of the O-C analysis for the Q2 data. + To create the Figure. we fit 5-cvcle sine curves of period 2.05 hr to the residual liebt curve. shifting the data bv one cvele between fits.," To create the Figure, we fit 5-cycle sine curves of period 2.05 hr to the residual light curve, shifting the data by one cycle between fits." + The shape of the O-C diagram is concave up until the peak of ie first outburst at day —28 indicating that the period of the signal is lenethcuime curing this time span., The shape of the O-C diagram is concave up until the peak of the first outburst at day $\sim$ 28 indicating that the period of the signal is lengthening during this time span. + The uaenitude of the negative superhunp period deficit is oewersely related to the retrograde precession period of ie tilted disk a shorter precession period vields a arecr period deficit., The magnitude of the negative superhump period deficit is inversely related to the retrograde precession period of the tilted disk – a shorter precession period yields a larger period deficit. += A disk that was not precessiug at Ul would show a negative superhuup period equal to ie orbital period., A disk that was not precessing at all would show a negative superhump period equal to the orbital period. + The observation that the uegative superhunup period iu V311 Lyr is leustheniug during davs —2 to 27 indicates that the precession period of ie tilted disk is increasing (i.c.. the rate of precession is decreasing).," The observation that the negative superhump period in V344 Lyr is lengthening during days $\sim$ 2 to 27 indicates that the precession period of the tilted disk is increasing (i.e., the rate of precession is decreasing)." +" Coincident with the first DN outburst outburst 1) in Q2. there is a cusp in the O-C diagrai. ""midicating a juup to shorter period (faster retrograde precession rate)."," Coincident with the first DN outburst (outburst 1) in Q2, there is a cusp in the O-C diagram, indicating a jump to shorter period (faster retrograde precession rate)." + The amplitude of the signal begius to ecline significantly following outburst 1. aud the signal is effectively quenched by outburst 2.," The amplitude of the signal begins to decline significantly following outburst 1, and the signal is effectively quenched by outburst 2." + Note that between avs 28 and 35 the O-C diagram is again concave up. Uthough with less curvature than before outburst 1.," Note that between days $\sim$ 28 and 35 the O-C diagram is again concave up, although with less curvature than before outburst 1." + We show the 2D DFT of the pre-superoutburst O2 ata in Figure 2L., We show the 2D DFT of the pre-superoutburst Q2 data in Figure \ref{fig: 2dDFTq2}. + Here we used a window width of 2 davs that was shifted 1/8 dav between transforms., Here we used a window width of 2 days that was shifted 1/8 day between transforms. + We plot the amplitude in counts per cadence., We plot the amplitude in counts per cadence. + It is evident that outburst 1 shifts the oscillation frequency. as well quenching the amplitude of the sigual.," It is evident that outburst 1 shifts the oscillation frequency, as well quenching the amplitude of the signal." +" Outhurst 2 triggers a short-lived signal with a period of roughly 11.9 cfd (2.02 hr). aud outburst 3 appears to generate sicnals near the frequencies of the negative and positive superhunps that rapidly evolve to higher aud lower frequencies. respectively, onlv to. fade to to noise backeround by the end of the outburst."," Outburst 2 triggers a short-lived signal with a period of roughly 11.9 c/d (2.02 hr), and outburst 3 appears to generate signals near the frequencies of the negative and positive superhumps that rapidly evolve to higher and lower frequencies, respectively, only to fade to to noise background by the end of the outburst." + Outburst 3 has a somewhat slower rise to muaxinun than most of the outbursts in the time series aud is the last outburst before the first superoutburst. but is otherwise unremarkable.," Outburst 3 has a somewhat slower rise to maximum than most of the outbursts in the time series and is the last outburst before the first superoutburst, but is otherwise unremarkable." + This is the only time we see this behavior in the 3 quarters of data we present. so it is unclear what the nuderlving plivsical mechanisin is.," This is the only time we see this behavior in the 3 quarters of data we present, so it is unclear what the underlying physical mechanism is." + Although much of the Q3 lieht curve is dominated by the negative superhunp signal. the amplitude is mich lower than carly in Q2. and in addition there is contanination from the orbital aud positive superlinup sienals.," Although much of the Q3 light curve is dominated by the negative superhump signal, the amplitude is much lower than early in Q2, and in addition there is contamination from the orbital and positive superhump signals." + In Figure 25 we show the 2D DFT for the Q3 data between davs 93 aud 162. again showing he amplitude iu counts per cadence versus time and requeney.," In Figure \ref{fig: 2dDFTq3} we show the 2D DFT for the Q3 data between days 93 and 162, again showing the amplitude in counts per cadence versus time and frequency." + We used a window width of 2 davs that was shifted 1/8 dav between transforms., We used a window width of 2 days that was shifted 1/8 day between transforms. + Iu Figure 26 we show the O-C phase diagram obtained x fitting a D-cvele sine curve of period 2.06 hr to data spanning davs 93.2 to 110.0., In Figure \ref{fig: negshomc2} we show the O-C phase diagram obtained by fitting a 5-cycle sine curve of period 2.06 hr to data spanning days 93.2 to 140.0. + The amplitude during this ime is considerably sinaller than was the case for the O2 reeative superhumps., The amplitude during this time is considerably smaller than was the case for the Q2 negative superhumps. + Before dav 106. there appears to )e Contamination from periodicitics near the superlinp requency of 10.9 c/d that are evident in Figure 25.. iid after day 126 the signal fades dramatically.," Before day 106, there appears to be contamination from periodicities near the superhump frequency of 10.9 c/d that are evident in Figure \ref{fig: 2dDFTq3}, and after day 126 the signal fades dramatically." + It was oulv during davs 106.5 to 123.2 that the aisplituce of the negative superhuup signal was lavee enough. stable enough. and uncontaminated to vield a clean O-C phase diagram.," It was only during days 106.5 to 123.2 that the amplitude of the negative superhump signal was large enough, stable enough, and uncontaminated to yield a clean O-C phase diagram." + These data lic between outbursts 8 and 9. and comprise the longest quiesceut streteh in Q2.," These data lie between outbursts 8 and 9, and comprise the longest quiescent stretch in Q3." + It can be seen that the O-C curve is again concave upward indicating a positive rate of period change as calculated above. and the bottom panel indicates that the amplitude of the signal is increasing during this time span.," It can be seen that the O-C curve is again concave upward indicating a positive rate of period change as calculated above, and the bottom panel indicates that the amplitude of the signal is increasing during this time span." + The retrograde precession rate of a tilted accretion disk is a direct function of the effective (mass weighted) radius of the disk., The retrograde precession rate of a tilted accretion disk is a direct function of the effective (mass weighted) radius of the disk. + Several groups have studied the precession properties of tilteddisks (Papaloizou&wood&Papaloizou1997:Lai," Several groups have studied the precession properties of tilteddisks \citep{papterq95,larwood96,larwood98,lp97,lai99}." +" 1999).. Papaloizouctal.(1997) derived the following expression for the induced precession frequency iy of a tilted accretion disk. where is the leading-order terii of the induced precession w,frequency for a differcutially rotating fluid disk. calculated using linear perturbation theory. Str) is the axisvnunetric surface deusitv profile aud (x) the unperturbed Keplerian angular velocity profile. « is the orbital separation. Mo is the mass of the secondary. aud à is the tilt of the disk with respect to the orbital plane."," \citet{papaloizou97} derived the following expression for the induced precession frequency $\omega_p$ of a tilted accretion disk, where $\omega_p$ is the leading-order term of the induced precession frequency for a differentially rotating fluid disk, calculated using linear perturbation theory, $\Sigma(r)$ is the axisymmetric surface density profile and $\Omega(r)$ the unperturbed Keplerian angular velocity profile, $a$ is the orbital separation, $M_2$ is the mass of the secondary, and $\delta$ is the tilt of the disk with respect to the orbital plane." + The integrals are to be taken between the inner aud outer radi of the disk., The integrals are to be taken between the inner and outer radii of the disk. + Tn a later study of the precession of tilted accretion disks. Larwood(1997.andsee(190951). derived the expression for the precession frequency of a disk witli constant surface denusitv X aud polvtropic equation of state with ratio of specific heats equal to 5/3: where here Qy is the IKeplerian angular velocity of the outer disk of radius Ry. aud 4 is the mass ratio.," In a later study of the precession of tilted accretion disks, \citet[][and see Larwood (1998)]{larwood97} derived the expression for the precession frequency of a disk with constant surface density $\Sigma$ and polytropic equation of state with ratio of specific heats equal to 5/3: where here $\Omega_0$ is the Keplerian angular velocity of the outer disk of radius $R_0$ , and $q$ is the mass ratio." + The physical interpretation of Equations 5 and 6 is that tilted accretion disks weighted to larger radii will," The physical interpretation of Equations \ref{eq: pt95} and \ref{eq: +larwood} is that tilted accretion disks weighted to larger radii will" +Or already been shock-processed. or some steady-state between the two.,"or already been shock-processed, or some steady-state between the two." + Specifically. there is evideuce for the fonination of large egraius iu novae (Shore ct al.," Specifically, there is evidence for the formation of large grains in novae (Shore et al." + 1991). alc possibly iu supernovae (see Wooden 1997 aud Pun ct al.," 1994), and possibly in supernovae (see Wooden 1997 and Pun et al." + 1995). aud erains are presumably huger in molecular clotids where hieh values of Π are measured.," 1995), and grains are presumably larger in molecular clouds where high values of $R_V$ are measured." + It 1nav be. thej that pre-shock graius teud to be somewhat larecr. alc the MBN distribution is more characteristic of eraius afteY seuificaut shattering has occurred.," It may be, then, that pre-shock grains tend to be somewhat larger, and the MRN distribution is more characteristic of grains after significant shattering has occurred." + The assunaptiou of lis paper is that dust leaving its progenitor galaxv wil have an grain size distribution characteristic of dust inthe ISM., The assumption of this paper is that dust leaving its progenitor galaxy will have an grain size distribution characteristic of dust in the ISM. + Tn the absence of significant shattering. this is probably conservative. since a sigenificaut fraction of dust is contained m ¢euse clouds with lieh Ay (0.9. Ii. Martiu IIeudry 1991).," In the absence of significant shattering, this is probably conservative, since a significant fraction of dust is contained in dense clouds with high $R_V$ (e.g. Kim, Martin Hendry 1994)." + Rather little is kown about the destruction of dust in the ICAL, Rather little is known about the destruction of dust in the IGM. + Schuidt (1971) estimates that soft cosmic ravs would provide the nost efficient. destruction. but caunot determine whetler or not the destruction fine would exceed the Itubble nue: moreaver. Draine Salpeter (19790) find that cosmic rays are uuiniportaut dust destrovers iu he Galaxy (where they should he at least as effective as in the IGMD.," Schmidt (1974) estimates that soft cosmic rays would provide the most efficient destruction, but cannot determine whether or not the destruction time would exceed the Hubble time; moreover, Draine Salpeter (1979b) find that cosmic rays are unimportant dust destroyers in the Galaxy (where they should be at least as effective as in the IGM)." +" The hot gas component of the IGAL. however. could sputter eraius effectively, even at low density."," The hot gas component of the IGM, however, could sputter grains effectively, even at low density." +" Usiis again Draine Salpeter's (19794). the lifetime cau be written where O,,, signifies the hot eas density in critical mits and à is a cluXue factor."," Using again Draine Salpeter's (1979a), the lifetime can be written where $\Omega_{gas}$ signifies the hot gas density in critical units and $\delta$ is a clumping factor." + The ITubble time (for O= 1) is ΠΠιτ)=1.6<ορ|i)8Ayr. suggestingoo the efficient destrucion of grains for which The chuupiug factor (ie. the overensitv felt bv a ‘typical’ erain] is quite uncertain. but the simnulatious of Cen Ostriker (1999b). which muuericallv track the distribution of netallicity. tudicate tha at 2~0.5. the ean universal moetallicitv. approaches he metallicity of à~100 regions.," The Hubble time (for $\Omega=1$ ) is $H^{-1}(z) = 1.6 \times 10^{10}h_{65}^{-1}(1+z)^{-3/2}\,{\rm yr}$, suggesting the efficient destruction of grains for which The clumping factor (i.e. the overdensity felt by a `typical' grain) is quite uncertain, but the simulations of Cen Ostriker (1999b), which numerically track the distribution of metallicity, indicate that at $z\sim 0.5$, the mean universal metallicity approaches the metallicity of $\delta \sim 100$ regions." + Reejons of much higher overdensity do uot have much higher metallicity aud hence cannot contain most of the metals for example. à~1000 regions lave ouly about twice the uctallicity. so dense ‘subregions’ can contain ouly about of the metals in 6~100 reeions.," Regions of much higher overdensity do not have much higher metallicity and hence cannot contain most of the metals – for example, $\delta \sim 1000$ regions have only about twice the metallicity, so dense `subregions' can contain only about of the metals in $\delta \sim 100$ regions." + If a tvpical erain experiences à~100. then Q~26 for 0:01jan grains and Q~2.6 for 0.1yam erains.," If a `typical' grain experiences $\delta \sim 100$, then $Q \sim 26$ for $0.01 \mic$ grains and $Q \sim 2.6$ for $0.1\mic $ grains." + This is xugeestive (but sugeestive)OO that sputtering by lot iuterealactic gas nüght provide vet another moechliauisii by which grains of àx0.1an night be selectively destroved., This is suggestive (but suggestive) that sputtering by hot intergalactic gas might provide yet another mechanism by which grains of $a \la 0.1\mic$ might be selectively destroyed. + Finally. note that the low mean dust deusitv iu the ICAL and in extended galaxy halos would strougly suppress the erain-erain collisious thought to shatter large eraijs info stall ones in the since dus formation is also incfficieut in the IGAL there is probabv ono source ofnow snall eraius outsle of galaxies.," Finally, note that the low mean dust density in the IGM and in extended galaxy halos would strongly suppress the grain-grain collisions thought to shatter large grains into small ones in the; since dust formation is also inefficient in the IGM there is probably no source of small grains outside of galaxies." + The efficiency. of dust destruclol ¢epends in a rather complicated wav cπι the euvironment: moreover the type aud details of the dondnuut neciuisu of metal ejection for galaxies are 1ncertain., The efficiency of dust destruction depends in a rather complicated way on the environment; moreover the type and details of the dominant mechanism of metal ejection for galaxies are uncertain. + Thus the arguments of this section are intered merely to nake plausible the chief of this paper. whicLois hat C»erains of size ax0.050.1jn are removed (eiher by destruction or by failure to escape tlei progenitor ealaxies) frou t10 eralu-size distribution ccharacterizing ust outside of ealaxies. whereas larger grains are not.," Thus the arguments of this section are intended merely to make plausible the chief of this paper, which is that grains of size $a \la +0.05-0.1 \mic$ are removed (either by destruction or by failure to escape their progenitor galaxies) from the grain-size distribution characterizing dust outside of galaxies, whereas larger grains are not." + The estimate of the deusitv of iuntergalactie dust in section did not take into account dust destruclon Or he preferential expulsion of dust., The estimate of the density of intergalactic dust in section \\ref{sec-metals} did not take into account dust destruction or the preferential expulsion of dust. + Lets us assume that a luass fraction (1fos) of dust is destroved as it leaves the diss and/or traverses the halo. aud that a further fractio (1Fig) is destroved in the IGM after the dust escape:-LLsXxc the halos but before 2~0.5.," Lets us assume that a mass fraction $(1-f_{esc})$ of dust is destroyed as it leaves the disk and/or traverses the halo, and that a further fraction $(1-f_{igm})$ is destroyed in the IGM after the dust escapes the halos but before $z +\sim 0.5$." + There are three genera acejuios indicated by the dust ejection and destructio mechauisunis outline above: Assmnuius that 0.5↽ 1.","when $\theta_e < 1$, and when $\theta_e > 1$ ." +" Hove. r9e,μηο ""is the classical. electron radius and j—exp(3g)=0.5616."," Here, $r_{e}=e^{2}/m_{e}c^{2}$ is the classical electron radius and $\eta=\exp(-\gamma_{E})=0.5616$." + The emissivitv per frequency is eiveu by where / is the Planck coustaut aud C is the Gaunt factor which is written (Rybicki & Lightman 1979) as The above cited formule contain a few minor defects., The emissivity per frequency is given by where $h$ is the Planck constant and $\bar{G}$ is the Gaunt factor which is written (Rybicki $\&$ Lightman 1979) as The above cited formule contain a few minor defects. + For exaniple. the non-clativistie But calculated for electron-ion process from equations (16)) aud (20)) differs by about from the standard formula (Rvbicki Lightman 1979).," For example, the non-relativistic limit calculated for electron-ion process from equations \ref{eqn:Bei}) ) and \ref{eqn:G}) ) differs by about from the standard formula (Rybicki Lightman 1979)." + Equation (20)) assuues the same values of the Gaunt factor for both clectrou-clectrou aud electrou-iou processes., Equation \ref{eqn:G}) ) assumes the same values of the Gaunt factor for both electron-electron and electron-ion processes. + In spite of these defects. we adopt the above formmle according to Naravau Y1 (1995b) aud A\Lammoto et al. (," In spite of these defects, we adopt the above formule according to Narayan Yi (1995b) and Manmoto et al. (" +1997). considering that these are the best ones we can eniplov at preseut throughout the euergv rage of our interest.,"1997), considering that these are the best ones we can employ at present throughout the energy rage of our interest." + The adoption of the same formule as in the previous calculations is also suitable for the purpose of comparison of the predictions of differeut models. such as the viscous aud resistive ones.," The adoption of the same formule as in the previous calculations is also suitable for the purpose of comparison of the predictions of different models, such as the viscous and resistive ones." + Svuchrotrou emission is au essential process to produce the radio wave-leneth part of the spectra from optically thin ADAFs in ACNs., Synchrotron emission is an essential process to produce the radio wave-length part of the spectra from optically thin ADAFs in AGNs. + Especially in the resistive ADAF model. some iuformation about the streneth of the anbicut maguetic field may be obtained from the process of spectral fitting.," Especially in the resistive ADAF model, some information about the strength of the ambient magnetic field may be obtained from the process of spectral fitting." + The optically-thin svuchrotron emissivitv by relativistic Maxwellian electrons is calculated from the formula (Naravan Yi 1995b: ATahaclevan. Naravan Yi 1996). where eds the clemeutary charee aud Tu equation(21)). the areuimenutOo of 7/ is specified as where B is the local value of magnetic field for which we substitute b...," The optically-thin synchrotron emissivity by relativistic Maxwellian electrons is calculated from the formula (Narayan Yi 1995b; Mahadevan, Narayan Yi 1996), where $e$ is the elementary charge and In \ref{eqn:synChi}) ), the argument of $I^{\prime}$ is specified as where $B$ is the local value of magnetic field for which we substitute $b_{\varphi}$." + The soft photous whose flux is eiven by equation (10)) are Compton scattered by the relativistic electrous in the flow., The soft photons whose flux is given by equation \ref{eqn:Fnu}) ) are Compton scattered by the relativistic electrons in the flow. + We adopt the rate equation of Coppi Blaudford (1990) as the basis of our consideratious., We adopt the rate equation of Coppi Blandford (1990) as the basis of our considerations. + This equation applies to homogeneous. isotropic distributions.," This equation applies to homogeneous, isotropic distributions." + The first term on the right-hand side of their equation describes the rate of decrease in the photou's uuuber deusity with a eiven enerev owine to the scattering iuto other cucreies. while the secoud term does the increase owing to the scattering iuto this cnerey from other cucreics.," The first term on the right-hand side of their equation describes the rate of decrease in the photon's number density with a given energy owing to the scattering into other energies, while the second term does the increase owing to the scattering into this energy from other energies." + Tn the situations of our interest. we can neglect the first term because the umber density of Conmptouized photons are small compared with that of the seed photons.," In the situations of our interest, we can neglect the first term because the number density of Comptonized photons are small compared with that of the seed photons." + Tusteack. we use the secoud term. iteratively to calculate the effects of multiple scattering.," Instead, we use the second term iteratively to calculate the effects of multiple scattering." + The scattering occurs ou the average when the condition cop.dt=Lis satisfied. where fis time and ο is the παπα: density of clectrous.," The scattering occurs on the average when the condition $c\sigma_{\rm T}n_edt=1$ is satisfied, where $t$ is time and $n_e$ is the number density of electrons." +" The probability that such a condition is satisfied. j-times before the photous come out of the surface may be given by the Poisson formula. Then. the production rate for the photons with a normalizedB euergy e=Phifinco is eivenB by where ο is the clectrou mass and ny, is the uuniber density of seed plotous."," The probability that such a condition is satisfied $j$ -times before the photons come out of the surface may be given by the Poisson formula, Then, the production rate for the photons with a normalized energy $\epsilon\equiv h\nu/m_e c^2$ is given by where $m_e$ is the electron mass and $n_{\rm in}$ is the number density of seed photons." + The nou-dimensional scattering rate 766.5) including Wleiu-Nishina cross section σεν is written explicitly (Coppi & Blandford 1990) as Scattered-photon distribution is denoted by Pere.2) and. in the present calculation. approximated by a ó- (LightmanZdziarski 1987. Fabian ct al.," The non-dimensional scattering rate $R(\epsilon,\gamma)$ including Klein-Nishina cross section $\sigma_{\rm KN}$ is written explicitly (Coppi $\&$ Blandford 1990) as Scattered-photon distribution is denoted by $P(\epsilon;\epsilon^{\prime},\gamma)$ and, in the present calculation, approximated by a $\delta$ -function (LightmanZdziarski 1987, Fabian et al." + 1986): This is merely for simplicity and a more exact expression has been derived by Jones (1968) aud corrected afterwards by Coppi Blaucdtord (1990)., 1986): This is merely for simplicity and a more exact expression has been derived by Jones (1968) and corrected afterwards by Coppi Blandford (1990). +independent of the LOS of the envelope.,independent of the EOS of the envelope. + However. the niiximunmn) compactness. Maas00.3404. vields for the sequence corresponding to the Py=2 envelope models.," However, the maximum compactness, $u_{\max} \simeq 0.3404$, yields for the sequence corresponding to the $\Gamma_1 = 2$ envelope models." +" While for the the same value of transition density 4,=2710 em at the core-envelope boundary. this upper boundl on NS mass found to be fully consistent with those of the models formulated with the advance. nuclear theory (Ixalogera Baym 1996). the Py=2 envelope model indicates the appropriateness of the (average) value of Py for the entire envelope."," While for the the same value of transition density $E_b = 2.7 \times 10^{14}$ $^{-3}$ at the core-envelope boundary, this upper bound on NS mass found to be fully consistent with those of the models formulated with the advance nuclear theory (Kalogera Baym 1996), the $\Gamma_1 = 2$ envelope model indicates the appropriateness of the (average) value of $\Gamma_1$ for the entire envelope." +" Joside its fundamental feature. this stucy also uneerlines the importance of the applicability οἱ ""compatibility criterion το the conventional models of NSs."," Beside its fundamental feature, this study also underlines the importance of the applicability of `compatibility criterion' to the conventional models of NSs." +" Since. we find that when the ccompatibility— criterion is not satisfied (for the case of the. models corresponding to an envelope with Py=5/3 and 2. if the ratio of pressure to energv-densitvy ab the core-envelope boundary. εν. ds ‘arbitrarily’ assigned to be about 1.064510 7) or not ""appropriately? satisfied. (for. the case of the models corresponding to an envelope with p,—43. PLE,o1.064510 2) by the sequences. the corresponding range of the eliteh. healing parameter turns out to be 0.558«xϱx0.948."," Since, we find that when the `compatibility criterion' is not satisfied (for the case of the models corresponding to an envelope with $\Gamma_1 = 5/3$ and 2, if the ratio of pressure to energy-density at the core-envelope boundary, $P_b/E_b$, is `arbitrarily' assigned to be about $1.0645 \times 10^{-2}$ ) or not `appropriately' satisfied (for the case of the models corresponding to an envelope with $\Gamma_1 = 4/3$, if $P_b/E_b \simeq 1.0645 \times 10^{-2}$ ) by the sequences, the corresponding range of the glitch healing parameter turns out to be $0.558 \leq Q \leq 0.948$." + This feature is consistent with the other conventional NS models. discussed. in. the literature and can explain only the higher values of Q on the basis of starquake model of eliteh generation for the Crab-like pulsars., This feature is consistent with the other conventional NS models discussed in the literature and can explain only the higher values of $Q$ on the basis of starquake model of glitch generation for the Crab-like pulsars. +" For the minimum weighted mean value of Q= 0.7. our models (corresponding to an envelope with Py=2.5/3 and 4/3 respectively) vield the minimum masses Ad,στL44M..z1.6M. and AL,z2.0341. for the Crab pulsar."," For the minimum weighted mean value of $Q\simeq 0.7$ , our models (corresponding to an envelope with $\Gamma_1 = 2, 5/3$ and 4/3 respectively) yield the minimum masses $M_c \simeq 1.44M_\odot,\,M_b \simeq 1.6M_\odot$ and $M_a\simeq 2.03M_\odot$ for the Crab pulsar." + Among these values. the first two values are comparable with those of the minimum values 1.35. and 1.6544. obtained by Crawford ancl Demiatisski (2003) bv using the GAVAL (CGlendenning. Weber. Moszkowski 1992) and WNP (LHlaensel. Ixutschera. Proszenski 1981) LOss.," Among these values, the first two values are comparable with those of the minimum values $1.35M_\odot$ and $1.65M_\odot$ obtained by Crawford and Demiańsski (2003) by using the GWM (Glendenning, Weber, Moszkowski 1992) and HKP (Haensel, Kutschera, Proszynski 1981) EOSs." + Whereas. corresponding to (Q20.7. the other five IEOSs of the dense nuclear matter considered. by Crawford and Demiaásski (2003) vield the minimum mass Af«LM. [or the Crab pulsar (see. c.g. Crawford. and Demiasski 2003: and references therein).," Whereas, corresponding to $Q \simeq 0.7$, the other five EOSs of the dense nuclear matter considered by Crawford and Demiańsski (2003) yield the minimum mass $M < 1M_\odot$ for the Crab pulsar (see, e.g. Crawford and Demiańsski 2003; and references therein)." + However for the maximum. weighted mean value of Q20.2 corresponding to the Vela pulsar. our models also vield the unrealistically small mass values for the Vela pulsar together with the other mocels cdiscussed in the literature (Crawford and Deniuaisski 2003).," However for the maximum weighted mean value of $Q \simeq 0.2$ corresponding to the Vela pulsar, our models also yield the unrealistically small mass values for the Vela pulsar together with the other models discussed in the literature (Crawford and Demiańsski 2003)." +" On the other hand. as soon as the ‘compatibility criterion"" is “appropriately” satisfied. by all the models corresponding to an envelope with Py=4/3.5/3 and 2 respectively (that is. if the ratio of pressure to energy-density at the core-envelope boundary. P,/εν is set. (and not ‘arbitrarily’ assigned) to be about 4.60410? for all the sequences) the corresponding range of the elitch healing parameter turns out to be 0.016Q<0.779."," On the other hand, as soon as the `compatibility criterion' is `appropriately' satisfied by all the models corresponding to an envelope with $\Gamma_1 = 4/3, 5/3$ and 2 respectively (that is, if the ratio of pressure to energy-density at the core-envelope boundary, $P_b/E_b$, is set (and not `arbitrarily' assigned) to be about $4.694 \times 10^{-2}$ for all the sequences), the corresponding range of the glitch healing parameter turns out to be $0.016 \leq Q \leq 0.779$." + This range. however. can explain both (the higher as well as lower) values of Q on the basis of starquake model of eliteh generation. for the Crab. as well as for the Vela-like pulsars.," This range, however, can explain both (the higher as well as lower) values of $Q$ on the basis of starquake model of glitch generation for the Crab, as well as for the Vela-like pulsars." +" “Phe sequences corresponding to an envelope with DL,=5/3 and 2 vield the maximum masses AL,c2.06A/7..AL.=LS5SAL. for the Vela (ῷ= 0.2) and the minimum masses Ad,o41A..AL3.98AL. for the Crab ((22 0.7) pulsar respectively."," The sequences corresponding to an envelope with $\Gamma_1 = 5/3$ and 2 yield the maximum masses $M_b \simeq 2.06M_\odot,\, M_c \simeq 1.85M_\odot$ for the Vela $Q \simeq 0.2$ ) and the minimum masses $M_b \simeq 4.1M_\odot,\,M_c\simeq 3.98M_\odot$ for the Crab $Q \simeq 0.7$ ) pulsar respectively." +" The sequence corresponding toan envelope with Py=4/3. however. vields the maximum mass AL,22.67M. for the Vela pulsar (Q2 0.2) but it does not provide the minimum stable mass for the Crab pulsar as soon as the constraint of (970.7 is imposed."," The sequence corresponding to an envelope with $\Gamma_1 = 4/3$, however, yields the maximum mass $M_a \simeq 2.67M_\odot$ for the Vela pulsar $Q \simeq 0.2$ ) but it does not provide the minimum stable mass for the Crab pulsar as soon as the constraint of $Q \geq 0.7$ is imposed." + The higher mass values mentioned in the last paragraph [or the Crab pulsar seem to be unlikely. since none of the observational and/or the theoretical study predict such higher mass values for the Crab pulsar.," The higher mass values mentioned in the last paragraph for the Crab pulsar seem to be unlikely, since none of the observational and/or the theoretical study predict such higher mass values for the Crab pulsar." +" Fhus. unlike the results of steps 2 - 3 (section. 3) which deal with the study of NS models without implementing the ""appropriate fulfillment of ""compatibility criterion’. the implementation of the ""appropriate fulfillment. of ""compatibility: criterion’ also reveals that in order to construct a ‘realistic’ NS sequence composed of NS masses comparable with those of the observations. we have to mocdifv the value of matching density at. the. core-envelope boundary."," Thus, unlike the results of steps 2 - 3 (section 3) which deal with the study of NS models without implementing the `appropriate' fulfillment of `compatibility criterion', the implementation of the `appropriate' fulfillment of `compatibility criterion' also reveals that in order to construct a `realistic' NS sequence composed of NS masses comparable with those of the observations, we have to modify the value of matching density at the core-envelope boundary." +" In. view of the modern EO5s of dense nuclear matter. the upper bound on NS mass compatible with causality and ciynamical stability can reach up to a value as large as 2.2M.. since among the variety of modern. EOSs discussed. in. the [iterature only the following EOSs vield the maximum mass of NS model in excess of 24.: SLY (Douchin IHaensel 2001) EOS. Minas=2.05.M.: DGNI (Dalberg Gal 1997) EOS. Alva,=2.ISAL.: and APR (Akmal et."," In view of the modern EOSs of dense nuclear matter, the upper bound on NS mass compatible with causality and dynamical stability can reach up to a value as large as $2.2M_\odot$, since among the variety of modern EOSs discussed in the literature only the following EOSs yield the maximum mass of NS model in excess of $M_\odot$: SLy (Douchin Haensel 2001) EOS, $M_{\rm max} = 2.05M_\odot$; BGN1 (Balberg Gal 1997) EOS, $M_{\rm max} = 2.18M_\odot$; and APR (Akmal et." + al., al. + 1998) EOS. Als=22M. (see. eg Haensel et al 2006).," 1998) EOS, $M_{\rm max} = 2.21M_\odot$ (see, e.g. Haensel et al 2006)." + Llowever. on the basis of other modern. EOSs for NS matter. fitted to experimental. nucleon-nucleon scattering data and the properties of light. nuclei. Kalogera Baym (1996: and references therein) have also shown that the lowest possible upper bound on NS mass. compatible with causality and dynamical stability. corresponds to the value of 22M. which can exceed up to a value as large as 2.9M..," However, on the basis of other modern EOSs for NS matter, fitted to experimental nucleon-nucleon scattering data and the properties of light nuclei, Kalogera Baym (1996; and references therein) have also shown that the lowest possible upper bound on NS mass, compatible with causality and dynamical stability, corresponds to the value of $2.2 M_\odot$ which can exceed up to a value as large as $2.9 M_\odot$." +" Considering thei mean ~2.6M. as the most Likely recent. value to the upper bound on NS masses and substituting this value as an upper bound to our miocels mentioned in step 4 of section 3. we obtain the ‘appropriate’ value of matching density 45,=7.0704«Lotte at the core-cnvelope boundary."," Considering their mean $\sim 2.6M_\odot$ as the most likely recent value to the upper bound on NS masses and substituting this value as an upper bound to our models mentioned in step 4 of section 3, we obtain the `appropriate' value of matching density $E_b = 7.0794 \times 10^{14}$ $^{-3}$ at the core-envelope boundary." +" On the basis of this density. our re-constructecl sequences (corresponding to an envelope with Py=5/3 ancl 2 respectively) vield the maximum. masses Af,&1.28M..M,=1.1ΛΙ. for the Vela (Q= 0.2) and the minimuni masses AL,2.53A1..ALc2.45.M. [or the Crab (Q=0.7) pulsar as shown in Fig.6."," On the basis of this density, our re-constructed sequences (corresponding to an envelope with $\Gamma_1 = 5/3$ and 2 respectively) yield the maximum masses $M_b \simeq 1.28M_\odot,\, M_c \simeq 1.14M_\odot$ for the Vela $Q \simeq 0.2$ ) and the minimum masses $M_b \simeq 2.53M_\odot,\,M_c\simeq 2.45M_\odot$ for the Crab $Q \simeq 0.7)$ pulsar as shown in Fig.6." +" The sequence corresponding to an envelope with Py=4/3. however. vields the maximum: mass A,c1.66M. for the Vela pulsar (Q= 0.2) but as shown in Fig.6. the minimum mass of the Crab pulsar (AL,= 2.46M.) belongs to the unstable branch of the sequence as soon as the constraint of €20.7 is imposed."," The sequence corresponding to an envelope with $\Gamma_1 = 4/3$, however, yields the maximum mass $M_a \simeq 1.66M_\odot$ for the Vela pulsar $Q \simeq 0.2$ ) but as shown in Fig.6, the minimum mass of the Crab pulsar $M_a \approx 2.46M_\odot$ ) belongs to the unstable branch of the sequence as soon as the constraint of $Q \geq 0.7$ is imposed." +" Obviously. the other conclusions of the present study. drawn on the basis of assigning the fiduciary. density L,=2.5.10 atthe boundary will reniain unalterecd."," Obviously, the other conclusions of the present study, drawn on the basis of assigning the fiduciary density $E_b = 2.7\times 10^{14}$ $^{-3}$ atthe boundary will remain unaltered." + The author gratefully acknowledges Prof. M. €. Durgapal [or his valuable advice and discussion and. the referee [or his helpful comments ancl suggestion. that improved the manuscript., The author gratefully acknowledges Prof. M. C. Durgapal for his valuable advice and discussion and the referee for his helpful comments and suggestion that improved the manuscript. + Phe Arvabhatta Rescarch Institute of Observational Sciences. (ARIES). Nainital ds. gratefully acknowledged: for providing library and computer-centre [acilities.," The Aryabhatta Research Institute of Observational Sciences (ARIES), Nainital is gratefully acknowledged for providing library and computer-centre facilities." +observed Os abundance in the U-star by a special Z7 eveut contanunating the ΕΛΙΤ would require either extremely large fluctuations in the process production bv au Lf eveut or wide variatious iu the amount of ISM that dilutes the rprocess ejecta.,observed Os abundance in the U-star by a special $H$ event contaminating the ISM would require either extremely large fluctuations in the $r$ -process production by an $H$ event or wide variations in the amount of ISM that dilutes the $r$ -process ejecta. + It follows that the abundances iu the U-star do not represent a sample of the ISAL with enornous enhancement in r-clemeuts., It follows that the abundances in the U-star do not represent a sample of the ISM with enormous enhancement in $r$ -elements. + We propose that the U-star was once a binary companion fo a massive (~10 60 AZ.) star.," We propose that the U-star was once a binary companion to a massive $\sim 10$ $60\,M_\odot$ ) star." + The massive star exploded as an SNII fF event aud contaminated the U-star. providing a high Chhancement im its surface abundances of +-elements.," The massive star exploded as an SNII $H$ event and contaminated the U-star, providing a high enhancement in its surface abundances of $r$ -elements." + If the process material received from the SNIT is iixect with ~107AL. of hydrogen in the surface laver of the U-star. then only a fraction ~Lilla2/3«10!)z5«107 of the r-process ejecta from an Z7 event is needed to eive the observed enhancement of ¢-clemenuts in this star.," If the $r$ -process material received from the SNII is mixed with $\sim 10^{-2}\,M_\odot$ of hydrogen in the surface layer of the U-star, then only a fraction $\sim 141(10^{-2}/3\times 10^4)\approx 5\times 10^{-5}$ of the $r$ -process ejecta from an $H$ event is needed to give the observed enhancement of $r$ -elements in this star." + If the proposed binary survived the SNII explosion. the U-star should now lave a compact companion. most Likely a stellaznuass black hole.," If the proposed binary survived the SNII explosion, the U-star should now have a compact companion, most likely a stellar-mass black hole." + We were iufoxiued. that the U-star has a rather hieh proper motion for its distance., We were informed that the U-star has a rather high proper motion for its distance. + Lone-term observations of its radial velocity should provide a definitive test of whether it is in a binary., Long-term observations of its radial velocity should provide a definitive test of whether it is in a binary. + We note that laree overabundance of O. Mg. Si; aud S associated with SNID explosions has heen observed in the linary companion to a possible black hole (sraclian et al.," We note that a large overabundance of O, Mg, Si, and S associated with SNII explosions has been observed in the binary companion to a possible black hole (Israelian et al." + 1999)., 1999). + We have ignored the possibility that ueutron star mergers (NSMs) could be responsible for the heavy r-elemoeuts., We have ignored the possibility that neutron star mergers (NSMs) could be responsible for the heavy $r$ -elements. +" I£ NSAIs were the source for such elements in the sun. the average enrichment resulting from au NSM would be ~3<10° times that for au SNIT {1 event (Qian 2000),"," If NSMs were the source for such elements in the sun, the average enrichment resulting from an NSM would be $\sim 3\times 10^3$ times that for an SNII $H$ event (Qian 2000)." + To explain the observed Os abundance in the U-star aud the range of Os abundances in other UMP stars [a scatter in loge(Os) of1.79 dex]by NSMs would then require erosslv variable 2amounts of ISM to mix with the ejecta., To explain the observed Os abundance in the U-star and the range of Os abundances in other UMP stars [a scatter in $\log\epsilon({\rm Os})$ of $>1.79$ dex] by NSMs would then require grossly variable amounts of ISM to mix with the ejecta. + As NSAIs play essentially no role in Fe enrichment. the large scatter in abundances of heavy +-clements should persist at [Fe/T]| 3 if NSAIs were the sources for these elements (Qian 2000).," As NSMs play essentially no role in Fe enrichment, the large scatter in abundances of heavy $r$ -elements should persist at [Fe/H] $>-3$ if NSMs were the sources for these elements (Qian 2000)." + Tlowever. the extensive data of Burris ct al. (," However, the extensive data of Burris et al. (" +2000) on the heavy i-clemieut. En show that the scatter iuloge(Eu) is z1 dex at |Fo/II]| =2.5 and decreases at higher |Fe/TI].,2000) on the heavy $r$ -element Eu show that the scatter in $\log\epsilon({\rm Eu})$ is $\approx 1$ dex at [Fe/H] $\approx -2.5$ and decreases at higher [Fe/H]. + Thus we do uot consider that NSMs are the sources for the heavy +-clemeuts. nor can they explain the observed r-abundances in the U-star.," Thus we do not consider that NSMs are the sources for the heavy $r$ -elements, nor can they explain the observed $r$ -abundances in the U-star." +" Abundances of ?9""Th aud ?U in the U-star have been used dote the age of this star (Cavrel et al.", Abundances of $^{232}$ Th and $^{238}$ U in the U-star have been used to determine the age of this star (Cayrel et al. + 2001)., 2001). +" If thefo 2°2Th aud rnine 2°SU observed in a star are the result of a single SNIT 77 eveut. the age equation for the star is where Yosu/Yo3» is the relative vield of 2°°U to 2°°Th for the LF eveut. τους=6.15 Civr and 7559=20.3 Cir are the lifetimes of the two nuclei. aud fa, Is the time interval between the event aud observation."," If the $^{232}$ Th and $^{238}$ U observed in a star are the result of a single SNII $H$ event, the age equation for the star is where $Y_{238}/Y_{232}$ is the relative yield of $^{238}$ U to $^{232}$ Th for the $H$ event, $\bar\tau_{238}=6.45$ Gyr and $\bar\tau_{232}=20.3$ Gyr are the lifetimes of the two nuclei, and $t_{\rm star}$ is the time interval between the event and observation." + As euipliasized by Cowan ct al. (, As emphasized by Cowan et al. ( +1999) and Coricly Clerbaux (1999). the calculated age depends critically ou the relative viclds that are very difficult to determine frominitio r-process models.,"1999) and Goriely Clerbaux (1999), the calculated age depends critically on the relative yields that are very difficult to determine from $r$ -process models." + The solar inventory of ruuclei at the time of solar system formation (SSF: 1.55 Cyr before the prescut time) is the result of previous Galactic nucleosyuthliesis., The solar inventory of $r$ -nuclei at the time of solar system formation (SSF; 4.55 Gyr before the present time) is the result of previous Galactic nucleosynthesis. + Asstuuing that the rate of SNIT production per hydrogen atom in the ISM is constant. we have where Typ is the total time of uniform process production prior to SSF.," Assuming that the rate of SNII production per hydrogen atom in the ISM is constant, we have where $T_{\rm UP}$ is the total time of uniform $r$ -process production prior to SSF." + The ratio (PU/2227T]jyF=0.131 CAnders Crevesse 1989) has au uucertaintv of <10%.," The ratio $(^{238}{\rm U}/^{232}{\rm Th})_{\odot}^{\rm SSF} +=0.431$ (Anders Grevesse 1989) has an uncertainty of $<10\%$." + The tenu iu square brackets inm equation (2)) ranges frou 1. (for Tipp=0) to 0.518 (Tip=x)., The term in square brackets in equation \ref{sun}) ) ranges from 1 (for $T_{\rm UP}=0$ ) to 0.318 $T_{\rm UP}=\infty$ ). + Thus there is only an extremely restricted range m Yosu/353» for a wide range in Zypb., Thus there is only an extremely restricted range in $Y_{238}/Y_{232}$ for a wide range in $T_{\rm UP}$. + The relationship between timescales aud loue-lved aud short-lived απο] has beeu discussed extensively by Schramun Wasserbure (1970)., The relationship between timescales and long-lived and short-lived $r$ -nuclei has been discussed extensively by Schramm Wasserburg (1970). + Aucstimate of Yo54/Y1542 was first made by Burbidec ct al. (, An estimate of $Y_{238}/Y_{232}$ was first made by Burbidge et al. ( +1957) aud later bv Fowler IIovle (1960) based on the nuuber of progenitors for 7°°Th and 7U. The estimated value of 3534/35545%0.61£0.06 with euesstiiated crrors its not been substantially iniproved upon over the past LO vears (cf.,1957) and later by Fowler Hoyle (1960) based on the number of progenitors for $^{232}$ Th and $^{238}$ U. The estimated value of $Y_{238}/Y_{232}\approx 0.61\pm 0.06$ with guesstimated errors has not been substantially improved upon over the past 40 years (cf. + Cowan et al., Cowan et al. + 1999: Conelv Clerbaux 1999)., 1999; Goriely Clerbaux 1999). + For hese values of 3554/355523 we obtain Tipz7.542.5 Cr which corresponds to a time of z12+42 Cyr since he ouset of Galactic process uucleosvuthesis., For these values of $Y_{238}/Y_{232}$ we obtain $T_{\rm UP}\approx 7.5\pm 2.5$ Gyr which corresponds to a time of $\approx 12\pm 2.5$ Gyr since the onset of Galactic $r$ -process nucleosynthesis. + The age of 12.543 Cer for the U-star obtained bv Cavrel ct al. (, The age of $12.5\pm 3$ Gyr for the U-star obtained by Cayrel et al. ( +2001) is for a sinele event.,2001) is for a single event. + The value ουκνου~ corresponds to an age of z11.L Cyr for this star., The value $Y_{238}/Y_{232}\approx 0.61$ corresponds to an age of $\approx 11.4$ Gyr for this star. + The estimated ages of the U-star. the values of Tip calculated from the solar system data for uniforii r-process xoduetion rates. and the timescale calculated by Fowler IIovle (1960) for au exponential model are iu seeucral accord.," The estimated ages of the U-star, the values of $T_{\rm UP}$ calculated from the solar system data for uniform $r$ -process production rates, and the timescale calculated by Fowler Hoyle (1960) for an exponential model are in general accord." + The values of Tip are also consistent with the uniform production period assumed above to calculate the umber of SNIT 77 eveuts coutributing to the solar inventory., The values of $T_{\rm UP}$ are also consistent with the uniform production period assumed above to calculate the number of SNII $H$ events contributing to the solar inventory. + The IH-xield of ??? Th can be calculated from where frpzm(10*vr)| is the frequency of Lf events., The $H$ -yield of $^{232}$ Th can be calculated from where $f_H\approx(10^7\ {\rm yr})^{-1}$ is the frequency of $H$ events. + For Trpz10 Gyr we obtain loge(C7Th)z ," For $T_{\rm UP}\approx 10$ Gyr we obtain $\log\epsilon_H(^{232}{\rm Th}) +\approx -2.72$." +A value of logegy(7U)&2.89 is in��kuly obtained., A value of $\log\epsilon_H(^{238}{\rm U})\approx -2.89$ is similarly obtained. + These viclds are consistent with the observed Th aud U abuudances iu he U-star for an age of 11.5 Cyr (see Figure 1)., These yields are consistent with the observed Th and U abundances in the U-star for an age of 14.5 Gyr (see Figure 1). + A deeper question is the relationship of ages obtaiue roni r-process chrononmeters to the age of the universe., A deeper question is the relationship of ages obtained from $r$ -process chronometers to the age of the universe. + It has been argued above that onset of process imcleosvuthnesis was represented by rapid occurrence of IT eveuts at Το = , It has been argued above that onset of $r$ -process nucleosynthesis was represented by rapid occurrence of $H$ events at [Fe/H] $\approx -3$. +These eveuts were precede κ nucleosvuthesis iu the first very massive stars that sienificantly produced ouly clemeuts up to Zr., These events were preceded by nucleosynthesis in the first very massive stars that significantly produced only elements up to Zr. + The iuescale over which agerceation of matter proceededunti a metallicity correspoudiug to [Fe/II]z3 was achieve permit formation of uormal stars is not established., The timescale over which aggregation of matter proceeded until a metallicity corresponding to [Fe/H] $\approx -3$ was achieved to permit formation of normal stars is not established. + lu addition. assenüibly. disasseniblv. aud reassembly of xuvonie Inatter at various stages in earlier epochs of the universe possibly leave a large time interval prior to onse of SNIL," In addition, assembly, disassembly, and reassembly of baryonic matter at various stages in earlier epochs of the universe possibly leave a large time interval prior to onset of SNII." + From consideration of [Fe/II| in damped Lye systems. it has been argued that there is a long interval (~ 15 Car) between Bie Bane aud onset of normal star," From consideration of [Fe/H] in damped $\alpha$ systems, it has been argued that there is a long interval $\sim 1$ –5 Gyr) between Big Bang and onset of normal star" +drops by about 0.15 dex.,drops by about 0.15 dex. + This later Ba abundances are adopted throught this The abundance derivation of the heavier s- and r-process elements (eg., This later Ba abundances are adopted throught this The abundance derivation of the heavier s- and r-process elements (eg. + Nd. Eu) were attempted by spectral svuthesis," Nd, Eu) were attempted by spectral synthesis." + Although spectral svuthesis allows for abundance derivation frou some bleuded lines. the spectral regious of these lines were far too bleuded with many other unidentified lines also present.," Although spectral synthesis allows for abundance derivation from some blended lines, the spectral regions of these lines were far too blended with many other unidentified lines also present." + Our svuthetic input line list was primarily composed of spectral line data as provided bv the VALD database., Our synthetic input line list was primarily composed of spectral line data as provided by the VALD database. + All known clement line data within the specific wavelength regiou of our lines of interest were extracted from the VALD database to suit the stellar parameters., All known element line data within the specific wavelength region of our lines of interest were extracted from the VALD database to suit the stellar parameters. + However fits to the observed. spectra were poor. likely due to inaccurate and incomplete atomic line list.," However fits to the observed spectra were poor, likely due to inaccurate and incomplete atomic line list." + As a result. we were unable to derive accurate abundances for the heavier s- and r-process elements.," As a result, we were unable to derive accurate abundances for the heavier s- and r-process elements." + We note that C05 also did. not obtain abundances for elements heavier than Da., We note that C05 also did not obtain abundances for elements heavier than Ba. + Since our aim is to determine the level of homogeucity within the cluster. we derive abundances with refercuce to the cluster star 2307. as it has an effective temperature in the muddle of the range for our sample stars.," Since our aim is to determine the level of homogeneity within the cluster, we derive abundances with reference to the cluster star 2307, as it has an effective temperature in the middle of the range for our sample stars." +" The final differcutial abundances (ALN/ΠΙΑ, were derived by subtracting the absolute abundance of cach individual lue of the refercuce star from the same lie of the saluple stars and taking the mean for each element."," The final differential abundances $\Delta$ [X/H]), were derived by subtracting the absolute abundance of each individual line of the reference star from the same line of the sample stars and taking the mean for each element." + The advantage of such relative abundances is that the nucertaity due to systematic errors (eg., The advantage of such relative abundances is that the uncertainty due to systematic errors (eg. + errors in gf values) are much reduced., errors in $gf$ values) are much reduced. + Our differential abundauces are plotted iu Figure 1 for Fe. and Figure 2 for clemeuts πο Na to Da.," Our differential abundances are plotted in Figure \ref{cr261fe} for Fe, and Figure \ref{cr261light} for elements from Na to Ba." + We present our absolute abundances iu log e form: in Table {.., We present our absolute abundances in log $\epsilon$ form in Table \ref{ab_table}. + The abundances for star 2311 are higher iu all elements and deviate significantly from the other cluster member abuudances., The abundances for star 2311 are higher in all elements and deviate significantly from the other cluster member abundances. + This star is represented by au open circle iu Figures d. and 2.., This star is represented by an open circle in Figures \ref{cr261fe} and \ref{cr261light}. + A radial velocity analysis performed at a later stage shows that this star is à ΠΟΠΠΟΙΟΣ., A radial velocity analysis performed at a later stage shows that this star is a non-member. + We will further discuss this iu Section [.., We will further discuss this in Section \ref{ch6:rv}. + The main sources of errors are the error associated with EW measurements. continu placement ancl stellar parameters. as well as the nuniber of lines used to calculate the final abundance.," The main sources of errors are the error associated with EW measurements, continuum placement and stellar parameters, as well as the number of lines used to calculate the final abundance." + Errors in the atomic line data and model atmospheres are least likely to affect the estimated levels of chemical homogencity as we are cluploving a differeutial abundance analysis relative to a cluster member., Errors in the atomic line data and model atmospheres are least likely to affect the estimated levels of chemical homogeneity as we are employing a differential abundance analysis relative to a cluster member. + Abundance dependencies ou the stellar parameters and EW nmeasurenaentss as well as the typical values of the total estimated uncertaünutv for cach clement are elven in Table 7..," Abundance dependencies on the stellar parameters and EW measurements, as well as the typical values of the total estimated uncertainty for each element are given in Table \ref{tab:error}." + The error in EWs estimated by repeated measurements of each line. is between tto depending on the strength of the lines," The error in EWs estimated by repeated measurements of each line, is between to depending on the strength of the lines." + The typical error in the stellar parameters are around οτε = 50 Ix. dlog = 0.1 ? and ὃς =+," The typical error in the stellar parameters are around $\delta T_{eff}$ = 50 K, $\delta$ log = 0.1 $^{-2}$ and $\delta \xi$ =." +", Our analysis is based on IKurucz models.", Our analysis is based on Kurucz models. +" Iowever due to the cooler Ty¢y¢ for some of the sunple stars. we tested our results using NARCS models for three stars (2285. 323255, 3709) which cover the full temperature range."," However due to the cooler $_{eff}$ for some of the sample stars, we tested our results using MARCS models for three stars (2285, 2288, 3709) which cover the full temperature range." + For the hotter star 2285 the change in abundance was niünmual for all clements with a mean difference of + 0.01 dex., For the hotter star 2285 the change in abundance was minimal for all elements with a mean difference of $\pm$ 0.01 dex. + For star 2288. differences of 0.07 and 0.1 or Si and Ni were fouud.," For star 2288, differences of 0.07 and 0.1 for Si and Ni were found." + For the coolest star 3709. arecr differences of 0.15 dex for Na and Ca. aud 0.35 ex for Zr were found.," For the coolest star 3709, larger differences of 0.15 dex for Na and Ca, and 0.35 dex for Zr were found." + Table 5— sunuuarizes these Mfereuces., Table \ref{models1} summarizes these differences. + These results were based ou the same stellar xusnueters derived παν with Γιο models., These results were based on the same stellar parameters derived initially with Kurucz models. + To enable a better comparison. the stellar iucroturbuleuce was then adjusted by 0.2 to fit the MARCS models.," To enable a better comparison, the stellar microturbulence was then adjusted by 0.2 to fit the MARCS models." + This resulted iu a better agreement with our initial results. with a 1ucau differeuce of about + 0.03 dex.," This resulted in a better agreement with our initial results, with a mean difference of about $\pm$ 0.03 dex." + A suuunuarv of the latter results are presented in Table 6.., A summary of the latter results are presented in Table \ref{models2}. + We calculated the radial velocities of the sample stars to check for iiv possible non-members., We calculated the radial velocities of the sample stars to check for any possible non-members. + The RVs were determined by Fourier transform: cross correlation of template spectra with observed spectra. makiug use of the IRAF packages RVSAO/NCSAO (αν&Miuk1998:Ikurtzetal. 1992).," The RVs were determined by Fourier transform cross correlation of template spectra with observed spectra, making use of the IRAF packages RVSAO/XCSAO \citep{rvsao,xcsao}." +. From the available spectra and template waveleneth range. RVs were estimated using the blue region from 1200 - 1100A.," From the available spectra and template wavelength range, RVs were estimated using the blue region from 4200 - 4400." +. Template spectra frou Zwitteretal.(2001) were obtained via private conunununication from M. Williams., Template spectra from \citet{zwitter} were obtained via private communication from M. Williams. + Since the stellar parameters were already established: from our earlier spectroscopic studies. templates matching closest to the sample parameters were selected for the cross correlation.," Since the stellar parameters were already established from our earlier spectroscopic studies, templates matching closest to the sample parameters were selected for the cross correlation." + Our errors are within 2|., Our errors are within 2. + Table 8. shows our derived heliocentrie RVs. as well as those obtained by Fricletal.(2002).," Table \ref{cr261rv} shows our derived heliocentric RVs, as well as those obtained by \citet{friel02}." + Our results are on average higher than Frieletal.(2002) by 5ts: larecr differences are seen for the two stars 2311 aud 3029., Our results are on average higher than \citet{friel02} by 5; larger differences are seen for the two stars 2311 and 3029. + Fricletal.(2002). find stay 2311 to have a RV of -30 ssinular to their derived cluster mean value., \citet{friel02} find star 2311 to have a RV of -30 similar to their derived cluster mean value. + This ds inconsistent with our result of -I8τν our velocity indicates that star 2311 as likely to be a non-member of the cluster., This is inconsistent with our result of -18; our velocity indicates that star 2311 is likely to be a non-member of the cluster. + Couverselv. Fricletal.(2002). πια the star 3029 to have a RV of -16+. although they did not class if a uou-member.," Conversely, \citet{friel02} find the star 3029 to have a RV of -16, although they did not class it a non-member." + Our results show that 3029 has a RV of-21. which places it well within the cluster RV Om results based on a lareer sample of stars are comparable to the mean abundances found carlicr by C05. although differences. are prescut in the iudividual stars.," Our results show that 3029 has a RV of -24, which places it well within the cluster RV Our results based on a larger sample of stars are comparable to the mean abundances found earlier by C05, although differences are present in the individual stars." + Five out of six of their stars are in common with our study. and in Figure 3. we compare the abundances of these five individual stars.," Five out of six of their stars are in common with our study, and in Figure \ref{cr261comp} we compare the abundances of these five individual stars." + The largest difference seeu for the coolest star 3709. which is at the tip of the red eiut brauch. is interesting.," The largest difference seen for the coolest star 3709, which is at the tip of the red giant branch, is interesting." + The adopted stellar paramcters are vorv similar in both studies; aud are therefore unlikely to be the reason," The adopted stellar parameters are very similar in both studies, and are therefore unlikely to be the reason" +"account, all epochs require dust extinction.","account, all epochs require dust extinction." + The SMC and type extinction curves provide a good fit to the data at all the three analyzed epochs (Fig.2)., The SMC and SN-type extinction curves provide a good fit to the data at all the three analyzed epochs (Fig.2). +" At T+0.47 days and at T+1.25 days the obtained extinction values are systematically higher and lower, respectively, than those obtained at T+3.4 days."," At $T+0.47$ days and at $T+1.25$ days the obtained extinction values are systematically higher and lower, respectively, than those obtained at $T+3.4$ days." +" Since such an evolution with time has no physical explanation, we interpret these discrepancies as the result of the systematics affecting the optical data reduction (see Zafar et al."," Since such an evolution with time has no physical explanation, we interpret these discrepancies as the result of the systematics affecting the optical data reduction (see Zafar et al." + 2010)., 2010). +" By averaging the results obtained assuming the SMC and the SN-type extinction curve over all epochs, the amount of dust absorption at νου=3000 lis at a level of «A3000>=0.25+0.07 mag where the uncertainty takes our ignorance on the true extinction curve into account."," By averaging the results obtained assuming the SMC and the SN-type extinction curve over all epochs, the amount of dust absorption at $\lambda_{rest}=3000$ is at a level of $=0.25\pm0.07$ mag where the uncertainty takes our ignorance on the true extinction curve into account." +" The average best-fit optical to X-ray spectral index, independent of its initial fixed range (Tables 2, 3 and 4), is «βχορι>=1.13+0.22, which is nicely consistent with the range of values expected from past broad band modeling of this burst, which is p/2 with the electron spectral index in the "," The average best-fit optical to X-ray spectral index, independent of its initial fixed range (Tables 2, 3 and 4), is $<\beta_{X,opt}>=1.13\pm0.22$, which is nicely consistent with the range of values expected from past broad band modeling of this burst, which is $p/2$ with the electron spectral index in the range $p\sim2.1-2.5$ \citep{Frail2006,Gou2007,Zou2006,Chandra2010}." +We find that the average properties of X-ray flares (???) provide convincing indications that flare activity is strongly damped or has ceased at late times for GRB 050904.," We find that the average properties of X-ray flares \citep{Margutti2011,Bernardini2011,Chincarini2010} provide convincing indications that flare activity is strongly damped or has ceased at late times for GRB 050904." +" We estimate the transition from flare-dominated to afterglow-dominated X-ray flux at about T+0.5 day, where the expected average flare peak intensity starts to overpredicts the observed fluxes and when an abrupt hard-to-soft spectral transition is observed (Fig.1)."," We estimate the transition from flare-dominated to afterglow-dominated X-ray flux at about $T+0.5$ day, where the expected average flare peak intensity starts to overpredicts the observed fluxes and when an abrupt hard-to-soft spectral transition is observed (Fig.1)." +" The X-ray flux measure at T+3.254 days is more than one order of magnitude lower than the expected flare intensity, therefore likely representative of the"," The X-ray flux measure at T+3.254 days is more than one order of magnitude lower than the expected flare intensity, therefore likely representative of the" +In some sense we have been breaking into an open door.,In some sense we have been breaking into an open door. + Even without considering the non-transitivitv of the theories. they are plagued by severe. problems.," Even without considering the non-transitivity of the theories, they are plagued by severe problems." + There exist. two equally plausible wavs of. cliseretising phase-space. one with equal volume elements and one with equa mass elements. which vield two clilferent results.," There exist two equally plausible ways of discretising phase-space, one with equal volume elements and one with equal mass elements, which yield two different results." + More importantly. the ability of the theories to predict the fina outcome of a violent-relaxation process is very lDimited.," More importantly, the ability of the theories to predict the final outcome of a violent-relaxation process is very limited." + ]ndeed. as was mentioned in2.. the most importan reason for this is that. violent-relaxation is almost never complete: the [uetuations of the gravitational potential clic much faster for the system to settle in the most. probable state.," Indeed, as was mentioned in, the most important reason for this is that violent-relaxation is almost never complete; the fluctuations of the gravitational potential die much faster for the system to settle in the most probable state." + Nevertheless. we believe. that these clilliculties and ambiguities in exactly how to do the statistical mechanics of the collisionless Boltzmann equation teach us an important lesson.," Nevertheless, we believe that these difficulties and ambiguities in exactly how to do the statistical mechanics of the collisionless Boltzmann equation teach us an important lesson." + The non-transitivity that we have shown is a sign that a kinetic cleseription of violent relaxation is probably incomplete. as the equilibrium is dependent on the evolutionary path of the system.," The non-transitivity that we have shown is a sign that a kinetic description of violent relaxation is probably incomplete, as the equilibrium is dependent on the evolutionary path of the system." + Instead. what is probably needed is a dvnamical approach to the problem.," Instead, what is probably needed is a dynamical approach to the problem." + Indeed most of the above cillicultics are circumvented if instead of aiming to derive a universal most. probable state. we recluce our aim to that of finding an appropriate and useful evolution equation for the coarse-grainecl f.," Indeed most of the above difficulties are circumvented if instead of aiming to derive a universal most probable state, we reduce our aim to that of finding an appropriate and useful evolution equation for the coarse-grained $\bar{f}$." + An interesting attempt to find such equation was taken bv Chavanis—(1998).. who used the maximal entropy-production principle (MISPP) to obtain a close equation [or f.," An interesting attempt to find such equation was taken by \citet{ref:Cha98b}, who used the maximal entropy-production principle (MEPP) to obtain a close equation for $\bar{f}$." + llis analysis. however. uses the initial line-grained T(g) to define the (Lvnden-Dell) entropy. rather than the instantaneous. coarse-grained τη). which according to the above discussion. is more correct.," His analysis, however, uses the initial fine-grained $\tau(\eta)$ to define the (Lynden-Bell) entropy rather than the instantaneous, coarse-grained $\tau(\bar{\eta})$, which according to the above discussion is more correct." + Derivation of a useful dynamical equation for f thus remains a challenging open problem., Derivation of a useful dynamical equation for $\bar{f}$ thus remains a challenging open problem. + We thank Peter Johansson for his help with the manuscript., We thank Peter Johansson for his help with the manuscript. +" This work was supported by a Marie-C'urie. Individual Fellowship of the European Community No. HPME-C""IE-", This work was supported by a Marie-Curie Individual Fellowship of the European Community No. HPMF-CT-2002-01997. +crucial experiments.,crucial experiments. + “Pherefore. every alternative method of restricting cosmological parameters is desired.," Therefore, every alternative method of restricting cosmological parameters is desired." + In this spirit a number of combined analyses involving lensing statistics (Silva Bertolami 2003). CMDIL measurements (Spergel et al.," In this spirit a number of combined analyses involving lensing statistics (Silva Bertolami 2003), CMBR measurements (Spergel et al." + 2003. Llinshaw et al.," 2003, Hinshaw et al." + 2009). age-redshift relation (Alcaniz. Jain Dey 2003) x-ray luminosities of galaxy clusters (Allen et al.," 2009), age-redshift relation (Alcaniz, Jain Dev 2003), x-ray luminosities of galaxy clusters (Allen et al." + 2008) or the large scale structure considerations (Kisenstein et al., 2008) or the large scale structure considerations (Eisenstein et al. + 2005) have been performed in the literature (references above being far from complete)., 2005) have been performed in the literature (references above being far from complete). + In this paper we use stroneglv gravitationally lensed systems for providing additional constraints on clark energy models., In this paper we use strongly gravitationally lensed systems for providing additional constraints on dark energy models. + The idea of using such systems for measuring the cosmic equation of state was discussed in. Biesiaca (2006) and also in more recent paper by Cirillo et al. (, The idea of using such systems for measuring the cosmic equation of state was discussed in Biesiada (2006) and also in more recent paper by Grillo et al. ( +2008).,2008). + The first (to ow knowledge) formulations of this approach can be traced back to Futamase Yoshida (2001)., The first (to our knowledge) formulations of this approach can be traced back to Futamase Yoshida (2001). + Next sections outline the method. the sample used anc cosmological scenarios tested.," Next sections outline the method, the sample used and cosmological scenarios tested." + The last section presents the results and conclusions., The last section presents the results and conclusions. + Strong gravitational lensing occurs whenever the source. the ens and observer are so well aligned. that. the observersource direction lies inside the so called Einstein ring of the ens.," Strong gravitational lensing occurs whenever the source, the lens and observer are so well aligned that the observer--source direction lies inside the so called Einstein ring of the lens." + In cosmological context the source is usually a (quasar with a galaxy acting as the lens., In cosmological context the source is usually a quasar with a galaxy acting as the lens. + Although strong lensing ov clusters is known and number of such cases increases. we will be concerned with galaxies acting as lenses.," Although strong lensing by clusters is known and number of such cases increases, we will be concerned with galaxies acting as lenses." + For detailec heory of gravitational lensing see e.g. Schneider. Ehlers Faleo (1992).," For detailed theory of gravitational lensing see e.g. Schneider, Ehlers Falco (1992)." + Strong lensing reveals itself as multiple images of the source., Strong lensing reveals itself as multiple images of the source. + The image separations in the system depen on angular-ciamoeter distances to the lens and to the source. which in turn are determined by background. cosmology.," The image separations in the system depend on angular-diameter distances to the lens and to the source, which in turn are determined by background cosmology." + This opens a possibility to constraining the cosmologica model provided that we have goock knowledge of the lens model., This opens a possibility to constraining the cosmological model provided that we have good knowledge of the lens model. + Since the discovery of the first gravitational lens the number of strongly lensed systems increased to à hundred (in the CASTLES database 7)) and. is steadily increasing Following the new surveys like SLACS (Sloan Lens ACS Survey “y, Since the discovery of the first gravitational lens the number of strongly lensed systems increased to a hundred (in the CASTLES database ) and is steadily increasing following the new surveys like SLACS (Sloan Lens ACS Survey ). +y dt turns out that in vast majority of cases the lens is a late twpe LE/SO galaxy., It turns out that in vast majority of cases the lens is a late type E/SO galaxy. + This could be understood since ellipticals being a latecomers in hierarchical structure formation are created in mergers of low-mass spiral galaxies., This could be understood since ellipticals being a latecomers in hierarchical structure formation are created in mergers of low-mass spiral galaxies. + llence they are more massive than spirals and. because the Einstein ring radius scales with mass. the probability of their acting as lenses is higher.," Hence they are more massive than spirals and because the Einstein ring radius scales with mass, the probability of their acting as lenses is higher." + Despite they lack bright kincmatic tracers at large radii (e.g. like LID in clisk galaxies) and thus their kinematics is more dillieult to measure. there exists an increasing evidence that their mass density. profile can well be approximated by singular isothernial sphere OSES) model (or à variant thereof called. singular isothermal ellipsoid SLE).," Despite they lack bright kinematic tracers at large radii (e.g. like HI in disk galaxies) and thus their kinematics is more difficult to measure, there exists an increasing evidence that their mass density profile can well be approximated by singular isothermal sphere (SIS) model (or a variant thereof called singular isothermal ellipsoid – SIE)." + Now. the idea is that formula for the Einstein radius in a SIS lens (or its SIE equivalent) depends on the cosmological model through the ratio of (angular-diameter) distances between lens ancl source and between observer and lens.," Now, the idea is that formula for the Einstein radius in a SIS lens (or its SIE equivalent) depends on the cosmological model through the ratio of (angular-diameter) distances between lens and source and between observer and lens." + The angular diameter distance in Hat Friedmann-lItobertson-Malker cosmology reads: where dfy is the present value of the Hubble: function and h(z:p) is a cimensionless expansion rate dependent on redshift z and cosmological model parameters p., The angular diameter distance in flat Friedmann-Robertson-Walker cosmology reads: where $H_0$ is the present value of the Hubble function and $h(z;{\mathbf p})$ is a dimensionless expansion rate dependent on redshift $z$ and cosmological model parameters ${\mathbf p}$. +" For example in Hat ACDAL model h(z:p)=VIS!Pay|OY we have ον=1OQ, hence p={Q,,} in this case."," For example in flat $\Lambda$ CDM model $h(z;{\mathbf p}) = \sqrt{\Omega_m (1+z)^3 + \Omega_{\Lambda}}$ we have $\Omega_{\Lambda} = 1 - \Omega_m$ hence ${\mathbf p} = \{ +\Omega_m \}$ in this case." + Expansion rates in other cosmological scenarios are given in Section 4., Expansion rates in other cosmological scenarios are given in Section 4. +" From now on we will assume spatial Hatness of the Universe since it is strongly supported by independent. ancl precise experiments. e.g. a combined WALAPS. BAO and supernova data analysis gives ο=1.0050ΟΕooo,ΟΙ (Llinshaw et al."," From now on we will assume spatial flatness of the Universe since it is strongly supported by independent and precise experiments, e.g. a combined WMAP5, BAO and supernova data analysis gives $\Omega_{tot} = +1.0050^{+0.0060}_{-0.0061}$ (Hinshaw et al." + 2009)., 2009). + “Phe sample upon which we work is small. and aclelition of (otherwise well constrained) curvature parameter would only clistort the results.," The sample upon which we work is small, and addition of (otherwise well constrained) curvature parameter would only distort the results." + Provided one has reliable knowledge about the lensing systenn Le. the Einstein radius 6& (from image astrometry) and stellar velocity. dispersion as;s (form central velocity dispersion συ obtained [rom spectroscopy) one can use it to test the background cosmology., Provided one has reliable knowledge about the lensing system: i.e. the Einstein radius $\theta_E$ (from image astrometry) and stellar velocity dispersion $\sigma_{SIS}$ (form central velocity dispersion $\sigma_0$ obtained from spectroscopy) one can use it to test the background cosmology. + Fhis method is independent on the Llubble constant value (which gets cancelled in the distance ratio) and is not allected by dust. absorption or source evolutionary elfects., This method is independent on the Hubble constant value (which gets cancelled in the distance ratio) and is not affected by dust absorption or source evolutionary effects. +. Lt depends. however. on. the reliability. of lens modelling (c.g. SIS or SLE assumption) and measurements of ay.," It depends, however, on the reliability of lens modelling (e.g. SIS or SIE assumption) and measurements of $\sigma_0$." + Hopefully. starting with the Lens Structure and Dynamics (LSL)) survey and the more recent SLACS survey spectroscopic data for central parts of lens ealaxies became available allowing to assess their central velocity clispersions.," Hopefully, starting with the Lens Structure and Dynamics (LSD) survey and the more recent SLACS survey spectroscopic data for central parts of lens galaxies became available allowing to assess their central velocity dispersions." + In. practice central velocity dispersion συ is estimated from the velocity dispersion within £2./S where A. is optical elfective radius., In practice central velocity dispersion $\sigma_0$ is estimated from the velocity dispersion within $R_e / 8$ where $R_e$ is optical effective radius. + Phorough discussion of these issues can be found in (Lreu et al., Thorough discussion of these issues can be found in (Treu et al. + 2006. Cirillo st al.," 2006, Grillo st al." + 2008) where the arguments in favor of using συ as representative (o asys are presented., 2008) where the arguments in favor of using $\sigma_0$ as representative to $\sigma_{SIS}$ are presented. + Moreover. there is a growing evidence for homologous structure of late type galaxies Clreu et al.," Moreover, there is a growing evidence for homologous structure of late type galaxies (Treu et al." + 2006. Ixoopmans et al.2006.. 2009) supporting reliability of. SIS/SIIS assumption.," 2006, Koopmans et al.2006, 2009) supporting reliability of SIS/SIE assumption." + In particular it was shown in (lxoopmans et al., In particular it was shown in (Koopmans et al. + 2009) that inside one ellective radius massive elliptical galaxies are kinematically incistinguishable from an isothermal ellipsoid., 2009) that inside one effective radius massive elliptical galaxies are kinematically indistinguishable from an isothermal ellipsoid. + In the method. used in this paper cosmological moclel enters not through a distance measure directly. but rather through a distance ratio," In the method used in this paper cosmological model enters not through a distance measure directly, but rather through a distance ratio" + where ez>—5f P/pis. the loca sound speed. aud > is he ratio of specilic heats.,"the terminal rise velocity of buoyant plumes with a diameter $\sim h_{\rm p}$ (Layzer 1955): where $v_{\rm s}^2 = \gamma P/\rho$ is the local sound speed, and $\gamma$ is the ratio of specific heats." + For the purpose of classifyiug turbulent buruiug regünes. we are interested mainly in the amplitude of turbulent velocity £licluations at the scale o‘the combustious fronts width (Niemeyer ]|xerstein. 1997).," For the purpose of classifying turbulent burning regimes, we are interested mainly in the amplitude of turbulent velocity fluctuations at the scale of the combustions front's width (Niemeyer Kerstein 1997)." + Assuming tiat the couvectively driven. large scale. fluctuations estallish a turbulent cascade with the expoient n. we cau write The value of (» for buoyaucy-driveu turbulent. cascades is not unambiguously agreed upon.," Assuming that the convectively driven, large scale, fluctuations establish a turbulent cascade with the exponent $n$, we can write The value of $n$ for buoyancy-driven turbulent cascades is not unambiguously agreed upon." + It appears reasonable at present to use either =1/3 for Ixolimogorov scaling. or η=3/5 for Bolgiano- scaling (Niemever Ixerstein 19907).," It appears reasonable at present to use either $n = 1/3$ for Kolmogorov scaling, or $n = 3/5$ for Bolgiano-Obukhov scaling (Niemeyer Kerstein 1997)." + We will assume »=1/3 Ixolmogorov scaling for the remaiucder of this paper., We will assume $n=1/3$ Kolmogorov scaling for the remainder of this paper. + Dellagratious under astrophysical conditious are caracterized by the thermal cdiffusivity α comitating over all other microscopic trausport coelficiei s.sueh as viscosity 7 and mass diffISLVILY D.," Deflagrations under astrophysical conditions are characterized by the thermal diffusivity $\kappa$ dominating over all other microscopic transport coefficients, such as viscosity $\nu$ and mass diffusivity $D$." + In terms of the dimeusionless uuumbers representiug he transport properties of the fluid. the Prandtl number P?rvir is very small. aud the Lewis number Le=&/D is very large.," In terms of the dimensionless numbers representing the transport properties of the fluid, the Prandtl number $Pr = \nu/\kappa$ is very small, and the Lewis number $Le = \kappa/D$ is very large." + Asa result of this dispa‘ity between the Praudtl ancl Lewis umbers the conventional classificajon of ΟΙeut burning regimes (e.g.. Bradley 1993). which is sed exclusively ou time scale criteria. is inappropriate (Nietjever Ixerstein 1997).," As a result of this disparity between the Prandtl and Lewis numbers the conventional classification of turbulent burning regimes (e.g., Bradley 1993), which is based exclusively on time scale criteria, is inappropriate (Niemeyer Kerstein 1997)." + It is more app'opriate in suchli astrophysical coucitlous to combine the lengtli scales and time scales. and compare a turbulent diffusivity Diund)~tieU)xd with the thermal ci[Pusivity &.," It is more appropriate in such astrophysical conditions to combine the length scales and time scales, and compare a turbulent diffusivity $D_{\rm turb}(l) \sim +v_{\rm turb}(l) \times l$ with the thermal diffusivity $\kappa$." + Note the turhtlent cliffusivity is a function of he length scale beiug exaulned., Note the turbulent diffusivity is a function of the length scale being examined. + Since Diy is a growing fur1Ctioi of length scale for most turuleut cascades. ios sullicient for our purposes to cousider tte largest scale relevant for the flame structure. the fame widhi à.," Since $D_{\rm turb}$ is a growing function of length scale for most turbulent cascades, it is sufficient for our purposes to consider the largest scale relevant for the flame structure, the flame width $\delta$." + One may expect that a change «Xx bu‘ing regimes occurs when DuyQ9 RO equivalently. wen Ciugp(0)»Sp.," One may expect that a change of burning regimes occurs when $D_{\rm turb} \sim \kappa$ or, equivalently, when $v_{\rm +turb}(\delta) \sim S_{\rm L}$." + It must be stressed hat these dimensional relationships may lave potentially la‘ee dimeusionless coelficieuts that cai ouly be determined by experiumietr| or direct nuajerical simulation., It must be stressed that these dimensional relationships may have potentially large dimensionless coefficients that can only be determined by experiment or direct numerical simulation. +" The regime where μμὅ)«S,.," Bayes's theorem provides the posterior distribution for $\gamma$, that is the probability of the model given the data: where $P(\gamma )$ is the prior distribution for $\gamma$ (the distribution assigned to $\gamma$ in the absence of the data), and $P(D)$ is a term which does not depend on the model parameter $\gamma$." + For the purposes of parameter estimation (JD) is determined by normalisation. bby requiring that the integral of the posterior over all possible values of 5 is unity.," For the purposes of parameter estimation $P(D)$ is determined by normalisation, by requiring that the integral of the posterior over all possible values of $\gamma$ is unity." + In the following we use a uniform prior: (A2)) (A5)) eive the posterior distribution for >: 0040-20)? the normalization constant. which for a uniform prior is 5» — (ÀY)) Pa.) denotes the incomplete Gamma function: ⊾ 1 T(a) is the Gannna (factorial) finetion (Abramowilz Stegun 1964).," In the following we use a uniform prior: Equations \ref{eq:pl_likelihood}) \ref{eq:pl_prior}) ) give the posterior distribution for $\gamma$ : where $C$ is the normalization constant, which for a uniform prior is In equation \ref{eq:norm_pl}) ) $P (a,x)$ denotes the incomplete Gamma function: and is the Gamma (factorial) function (Abramowitz Stegun 1964)." +N/O is roughly constant below | loe(O/TI)~a. L. and proportional to O/II above this value.,"N/O is roughly constant below $+$ $\sim$ 8.4, and proportional to O/H above this value." +" This iuplies that larger values of /|Ou]] lead. to higher metallicities. but this calibration does not take iuto account. the depeudence of Ποπ on the variation of the N/O ratio at a given O/T. According to PAICO9, large. values of the N/O ratio can enhance the ii]| ratio even in the low metallicity regime."," This implies that larger values of ] lead to higher metallicities, but this calibration does not take into account the dependence of ] on the variation of the N/O ratio at a given O/H. According to PMC09, large values of the N/O ratio can enhance the ] ratio even in the low metallicity regime." +" Iu Figure 3.. we studied the stellar mass metallicity relation (AL, Z. and the relation between N/O aud the stellar mass (AM, N/O: PMCO9) for the CPs. LBAs. aud SDSS SFCs."," In Figure \ref{fig3}, we studied the stellar $-$ metallicity relation \citep[$M_{\star}- -Z, and the relation between N/O and the stellar mass $M_{\star}-$ N/O; PMC09) for the GPs, LBAs, and SDSS SFGs." +" Estimates of M, for the three ealaxy salples have been taken from C09 (CPs). Overzieretal.(2009.LBAs).. and the ΠΠ: Calog (SFCs)."," Estimates of $M_{\star}$ for the three galaxy samples have been taken from C09 (GPs), \citet[][LBAs]{Overzier09a}, and the $-$ JHU catalog (SFGs)." + They were derived using spectral enerev distribution fitting aud SDSS photometry., They were derived using spectral energy distribution fitting and SDSS photometry. + Thus. stellar 1iasses are expected to to be consisteut within a typical dispersion of ~ 0.20 dex (ce.e..Droryetal.2001:vanderWel 2006).," Thus, stellar masses are expected to to be consistent within a typical dispersion of $\sim$ 0.20 dex \citep[e.g.,][]{Drory,vanderwel06}." +.. This value. is lower than the expected uncertainties of 0.3 dex quoted for GPs aud LBAs as due to uncertainties in their star formation history Overzieretal.," This value, is lower than the expected uncertainties of 0.3 dex quoted for GPs and LBAs as due to uncertainties in their star formation history \citep[C09;][]{Overzier09a}." +" 2009).. Iu the M, Z plane. SDSS SFCs show a clear positive trend which flattens toward higher masses and showa relatively linge scatter at lower masses. πι aerecinent with previous findines for local ealaxies οιοTremontietal.2001).."," In the $M_{\star}-$ Z plane, SDSS SFGs show a clear positive trend which flattens toward higher masses and showa relatively large scatter at lower masses, in agreement with previous findings for local galaxies \citep[e.g.,][]{Tremonti}." +" Similarly. GPs aud LBAs increase their metallicity with increasing niasses,"," Similarly, GPs and LBAs increase their metallicity with increasing masses." +" Nevertheless. GPs lie more than a factor of 2 (2 0.3 dex) below the AIZR of SDSS SEC. Lo.SECs, A simular shift iu the AIZR has been observed for the less nassive M.)= 10) LBAs (IHoopesetal.2007:Overzieretal.2010.this svork)."," Nevertheless, GPs lie more than a factor of 2 $\ga$ 0.3 dex) below the MZR of SDSS SFGs, i.e. A similar shift in the MZR has been observed for the less massive $_{\star}) \la 10$ ) LBAs \citep[][this + work]{Hoopes07,Overzier09b}." +. Iu terms of stellar mass. the observed offset (as large as 1 dex) larecly exceeds the typical uncertainty quoted for the GP masses.," In terms of stellar mass, the observed offset (as large as 1 dex) largely exceeds the typical uncertainty quoted for the GP masses." +" Ou the other haud. the SDSS SFCs display a correlation between N/O aud M,. with higher N/O ratios at higher stellar masses. in agreement with PAICO9 for a differcut sample of local SFCs."," On the other hand, the SDSS SFGs display a correlation between N/O and $M_{\star}$, with higher N/O ratios at higher stellar masses, in agreement with PMC09 for a different sample of local SFGs." +" The existence of the AZ, N/O relation reflects tle fact that the most massive galaxies evolve more quickly aud. heuce. they should have on average higher metallicities and N/O ratios."," The existence of the $M_{\star}-$ N/O relation reflects the fact that the most massive galaxies evolve more quickly and, hence, they should have on average higher metallicities and N/O ratios." +" Though the scatter inthe AL, N/O relation is lee. most GPs and low-mass LBAs are roughly consistent with the treud of SDSS SFCs. aud no svstematic offset is observed."," Though the scatter in the $M_{\star}-$ N/O relation is large, most GPs and low-mass LBAs are roughly consistent with the trend of SDSS SFGs, and no systematic offset is observed." + The shape of the MIZR in galaxies has Όσσα ound to depend on several key processes du ealaxv evolution. inchiding the cfiicicney of star ormationu (c.e..Lequeuxetal.1979:Moll&Diaz2005:Brooksetal.2007:Calura 2009).. the action of ποτάΊο selective outflows aud imetal-ooor gas inflows (e.g...Larson1971:Garnett2002:Tremontietal.2001:Finlator&Davé 2008).. aud he possible viiatious in the iitial mass fiction (Isoppenetal.2007).," The shape of the MZR in galaxies has been found to depend on several key processes in galaxy evolution, including the efficiency of star formation \citep[e.g.,][]{Lequeux79,MollaDiaz05,Brooks07,Calura09}, the action of metal-rich selective outflows and metal-poor gas inflows \citep[e.g.,][]{Larson74,Garnett02,Tremonti,Finlator08}, and the possible variations in the initial mass function \citep{Koppen07}." +. Moreover. different a1iounts of dark matter can also assist iu some of these uechauisius (Dekel&Silk1986).," Moreover, different amounts of dark matter can also assist in some of these mechanisms \citep{Dekel86}." +. The GPs follow a relation between lass and imetalliitv that parallels the AIZR defined o the SDSS SFCs. but is offset 20.3 dex to ower ietalliities.," The GPs follow a relation between mass and metallicity that parallels the MZR defined by the SDSS SFGs, but is offset $\ga$ 0.3 dex to lower metallicities." +" Interestingly, we find some remarkable simuübudties between the GPs aud the »o»pulation of 1|-sclected galaxies of similar ""uumositv in the + ranec 0.290.12 recently fouud w Salzeretal.(2009)."," Interestingly, we find some remarkable similarities between the GPs and the population of ]-selected galaxies of similar luminosity in the $z$ range 0.29–0.42 recently found by \citet{Salzer09}." +. These galaxies follow a iuetallicitv relation that parallels the oue defined by SFCs. but is offset by a factor of more than 10 to lower abundances.," These galaxies follow a $-$ metallicity relation that parallels the one defined by SFGs, but is offset by a factor of more than 10 to lower abundances." + Ou the other haud. since GPs aud low-mass LBAs lie in a sinülar offset position in the MZR relative to normal SFCs. their mentioned similarities appear even greater.," On the other hand, since GPs and low-mass LBAs lie in a similar offset position in the MZR relative to normal SFGs, their mentioned similarities appear even greater." + One possibility to explain their offset position in the MZR is that these galaxies could be still converting a large amount of their cold eas reservoirs into stars., One possibility to explain their offset position in the MZR is that these galaxies could be still converting a large amount of their cold gas reservoirs into stars. + In that case. their low abundances could be due to their relatively voung ages compared to normal SECs.," In that case, their low abundances could be due to their relatively young ages compared to normal SFGs." +" Iu the same range of masses, both GPs aud LBAs have much vigher SSFR (typically 210 ?vy 3) compared o other SFCs of similar mass (C09)."," In the same range of masses, both GPs and LBAs have much higher SSFR (typically $>$ $^{-9}$ $^{-1}$ ) compared to other SFGs of similar mass (C09)." + Receut studies show that galaxies with higher SSFRs or arecr halfleht radi for their stellar mass lave systematically lower metallicities (6.9...Tremouti 2008)..," Recent studies show that galaxies with higher SSFRs or larger half-light radii for their stellar mass have systematically lower metallicities \citep[e.g.,][]{Tremonti, + Ellison08}. ." + ILowever. we rave found even greater under-abunudances in the GPs. which have high SSERs but are extremely," However, we have found even greater under-abundances in the GPs, which have high SSFRs but are extremely" +We measured the bar pattern speed for cach sample galaxy by applying the TW method as done in Paper I. To compute the mean position of stars. .V. along the slits. we generally. extracted: profilesfrom { and. V-band surface photometry along the positions of the slits.,"We measured the bar pattern speed for each sample galaxy by applying the TW method as done in Paper I. To compute the mean position of stars, $\pin$, along the slits, we generally extracted profilesfrom $I$ and $V$ -band surface photometry along the positions of the slits." + In the case of NGC 1440. because of the radial colour gradient. we preferred to use the intensity. [rom the slit. spectra themselves. although they are somewhat noisier.," In the case of NGC 1440, because of the radial colour gradient, we preferred to use the intensity from the slit spectra themselves, although they are somewhat noisier." + For the remaining galaxies. the /-band profiles match very well the profiles obtained by collapsing the spectra along the wavelength direction. confirming that the slits were placed as intended.," For the remaining galaxies, the $I$ -band profiles match very well the profiles obtained by collapsing the spectra along the wavelength direction, confirming that the slits were placed as intended." + We used the broad. band. profiles to compute .X because these are less noisy than the spectral profiles. particularly at large racii.," We used the broad band profiles to compute $\pin$ because these are less noisy than the spectral profiles, particularly at large radii." + We computed the value of .V at each slit position by Monte Carlo simulation. with photon. reac-out and sky noise to compute the errors.," We computed the value of $\pin$ at each slit position by Monte Carlo simulation, with photon, read-out and sky noise to compute the errors." + Formally. the integrals in PW equation are over ooSONX ox but can be limited to NyeSNEUNSuus νε has reached the axisvmmetrie part of the disc: still larger values o£ γω add noise only.," Formally, the integrals in TW equation are over $-\infty \leq X \leq \infty$ , but can be limited to $-X_{max} \leq X \leq X_{max}$ if $X_{max}$ has reached the axisymmetric part of the disc; still larger values of $X_{max}$ add noise only." + Phe .V values thus obtained are given in Tab. 7.., The $\pin$ values thus obtained are given in Tab. \ref{tab:TW_values}. + ‘To measure the Iuminositv-weighted Iine-of-sight stellar velocity. V. for cach slit. position. we collapsed: cach two-dimensional spectrum along its spatial direction to obtain a one-dimensional spectrum.," To measure the luminosity-weighted line-of-sight stellar velocity, $\kin$, for each slit position, we collapsed each two-dimensional spectrum along its spatial direction to obtain a one-dimensional spectrum." + The resulting spectra have been analvsed with the FCQ method. using the same template star adopted in Sect., The resulting spectra have been analysed with the FCQ method using the same template star adopted in Sect. + 6.1. to derive the stellar kinematics of the galaxy: Y is then the radial velocity derived. [rom the LOSVD of the one-dimensional spectra., \ref{sec:kinematics} to derive the stellar kinematics of the galaxy; $\kin$ is then the radial velocity derived from the LOSVD of the one-dimensional spectra. + For cach slit position. the uncertainty on Y was estimated by. means of Monte. Carlo simulations as done for b in measuring the stellar kinematics.," For each slit position, the uncertainty on $\kin$ was estimated by means of Monte Carlo simulations as done for $v$ in measuring the stellar kinematics." + Phe Y values we derived. along cach slit and the adopted wavelength: (always including the Mg triplet) and. radial ranges (limited hy the noise. ancl after removing the contribution of foreground. stars by. linear interpolation) are given in Tab. 7..," The $\kin$ values we derived along each slit and the adopted wavelength (always including the Mg triplet) and radial ranges (limited by the noise, and after removing the contribution of foreground stars by linear interpolation) are given in Tab. \ref{tab:TW_values}. ." +" For each galaxy. we derived Q,sin? by fitting a straight line to the values GV.Y) obtained from the available slit positions (Fig. 11))."," For each galaxy, we derived $\om \sin i$ by fitting a straight line to the values $(\pin,\kin)$ obtained from the available slit positions (Fig. \ref{fig:corotations}) )." +" Finally the value of O, (Lable 8)) was derived. from the adopted: galaxy inclination. as given in ‘Table 3.."," Finally the value of $\om$ (Table \ref{tab:bar_kinematics}) ) was derived from the adopted galaxy inclination, as given in Table \ref{tab:measured_pa}." +" ‘To measure the svstemic velocity of the galaxies. we fit interpolating splines to the measured: velocities ancl fitted ""Uülted. vines”. of fixed. 7 and. P (as obtained. from the photometry). tothe inner parts of the galaxies."," To measure the systemic velocity of the galaxies, we fit interpolating splines to the measured velocities and fitted “tilted rings”, of fixed $i$ and PA (as obtained from the photometry), tothe inner parts of the galaxies." + In the case of NGC 1308. our data were not of sullicient S/N to permit such fits. in which case we used Y on the major axis: for the other four galaxies. comparision of Tables 7. and 8. shows that the major-axis V is à very good approximation to Va.," In the case of NGC 1308, our data were not of sufficient S/N to permit such fits, in which case we used $\kin$ on the major axis; for the other four galaxies, comparision of Tables \ref{tab:TW_values} and \ref{tab:bar_kinematics} shows that the major-axis $\kin$ is a very good approximation to $V_{\rm sys}$ ." + In ‘Table S.. we compare our measurements of Voss with those in RCS.," In Table \ref{tab:bar_kinematics}, we compare our measurements of $V_{\rm + sys}$ with those in RC3." + In all cases we find excellent. agreement., In all cases we find excellent agreement. + Once Viv. is measured. we obtain the stellar. mean streaming velocities. Ἐν. by subtracting Va. then folding about the origin the major-axis data.," Once $V_{\rm sys}$ is measured, we obtain the stellar mean streaming velocities, $V_*$, by subtracting $V_{\rm sys}$, then folding about the origin the major-axis data." + Figure I0. shows that our folded spectra have no substantial asvmmetries on the two sides.," Figure \ref{fig:asym_drift_corr} + shows that our folded spectra have no substantial asymmetries on the two sides." +" Aleasurement of O, with the PW. method. requires. no modeling.", Measurement of $\om$ with the TW method requires no modeling. + However. in the absence of gas velocities at large radii. measurement of A requires some modeling to recover the rotation curve from the observed. stellar streaming velocities.," However, in the absence of gas velocities at large radii, measurement of $\vpd$ requires some modeling to recover the rotation curve from the observed stellar streaming velocities." + This asvmmetric drift correction can be fairly large in earlv-tyvpe dise galaxies. where the velocity dispersions are large.," This asymmetric drift correction can be fairly large in early-type disc galaxies, where the velocity dispersions are large." + We start [rom the asvmimetrie drift equation BBinney Tremaine 1987] Eqn., We start from the asymmetric drift equation Binney Tremaine [1987] Eqn. +" 4-33) where V; is the circular velocity. p is the disks volume density. and σι, and op are the tangential and radial velocity dispersions in the evlindrical coordinates of the galaxys intrinsic plane."," 4-33) where $V_c$ is the circular velocity, $\rho$ is the disk's volume density, and $\sigma_\phi$ and $\sigma_R$ are the tangential and radial velocity dispersions in the cylindrical coordinates of the galaxy's intrinsic plane." + We then make the following assumptions: With these assumptions. the asymmetric drift equation becomes We apply this correction to all velocity. data points (including those not on the major-axis) outside the bar racius and within 30° of the major-axis.," We then make the following assumptions: With these assumptions, the asymmetric drift equation becomes We apply this correction to all velocity data points (including those not on the major-axis) outside the bar radius and within $30\degrees$ of the major-axis." + We average over all these points to obtain Viana with an additional error [rom the scatter of the points addedin quadrature.," We average over all these points to obtain $V_{\rm + c,flat}$, with an additional error from the scatter of the points addedin quadrature." + We report our lindings of Voi in Table S.. and in Fig. 10..," We report our findings of $V_{\rm c,flat}$ in Table \ref{tab:bar_kinematics}, and in Fig. \ref{fig:asym_drift_corr}. ." + In Paper Lo the high surface brightnessof NGC 1023 allowed us to drop the assumption that σιση= i and insteac we used the velocitydispersion data from all slits to obtain Via=270431 ((having assumed 0.00.5 are predominantly giants.," 2, stars with J-K $\leq 0.35$ are almost exclusively dwarfs, while those with J-K $\geq 0.5$ are predominantly giants." + The hatched area. containing only of all stars. shows those stars with radii less than 1.3 R.. ie. those for which a central (ransil by a fairly large planet would have ὁ>.01.," The hatched area, containing only of all stars, shows those stars with radii less than 1.3 $R_\sun$, i.e., those for which a central transit by a fairly large planet would have $\delta \geq .01$." + Thus. even amone main-sequence stars. only about a third of the stars in the sample will have radii small enough for transits to be observed in a routine wav.," Thus, even among main-sequence stars, only about a third of the stars in the sample will have radii small enough for transits to be observed in a routine way." + Moreover. any failines in photometric precision cause a disproportionate decrease in the planet catch.," Moreover, any failings in photometric precision cause a disproportionate decrease in the planet catch." + Figure :3 shows the expected distribution of 6 for (ransils by planets. bv main-sequence binaries. aud by diluted binary and triple svstenis.," Figure 3 shows the expected distribution of $\delta$ for transits by planets, by main-sequence binaries, and by diluted binary and triple systems." + Onlv about a third of all planetary transits should have 9 as large as .01. and the fraction drops rapidly as the 9 threshold is raised.," Only about a third of all planetary transits should have $\delta$ as large as .01, and the fraction drops rapidly as the $\delta$ threshold is raised." + The most common source of false alarms is main-sequence binaries (wpe MSU)., The most common source of false alarms is main-sequence binaries (type MSU). + These should occur at a rate of several per LO! target stars. and should tvpicallv show relatively large depths and short periods.," These should occur at a rate of several per $10^4$ target stars, and should typically show relatively large depths and short periods." + Diluted main-sequence transits account for the rest of the false alarms. about equally distributed between types AISDF and MSDT.," Diluted main-sequence transits account for the rest of the false alarms, about equally distributed between types MSDF and MSDT." + Although {μον are intvinsically rare. the triple svstenis appear fairly commonly in transit searches because (heir 9 distribution peaks near .01. the canonical value for transits by Jovian planets.," Although they are intrinsically rare, the triple systems appear fairly commonly in transit searches because their $\delta$ distribution peaks near .01, the canonical value for transits by Jovian planets." + Integrating over the full ranges in all of the parameters 77). IH. 0. d shows that about of all stars observed should reveal (hemselves as eclipsing binaries (ignoring window [unction elfects).," Integrating over the full ranges in all of the parameters $m_0$, $\Pi$, $\delta$, $d$ shows that about of all stars observed should reveal themselves as eclipsing binaries (ignoring window function effects)." + Although detailed comparisons with these predictions have not vet been made. these false alarm and eclipsing-binary rates seem to agree with experience from the STARE and Vulcan survevs. αἱ least within a [actor of 2.," Although detailed comparisons with these predictions have not yet been made, these false alarm and eclipsing-binary rates seem to agree with experience from the STARE and Vulcan surveys, at least within a factor of 2." +Vhe theory of inflation (Guth (1981)... Albrecht&Stein-harclt (1982).. Linde (1982))) provides attractive solutions to a number of cosmological problems. including the large-scale homogeneity and. [latness of the universe.,"The theory of inflation \citet{gut81}, , \citet{alb82}, \citet{lin82}) ) provides attractive solutions to a number of cosmological problems, including the large-scale homogeneity and flatness of the universe." + Lt has garnered strong support from the and observations of the cosmic microwave background. radiation. (Smootetal (1992).. Spergeletal (2007).. Hinshawetal (2009).. ]xomatsuetal (20112).," It has garnered strong support from the and observations of the cosmic microwave background radiation \citet{smo92}, \citet{spe07}, \citet{hin09}, \citet{kom11}) )." + Quantum fluctuations in a scalar inflaton field can explain the origin and near scale-invariant power spectrum. of the primordial density. perturbations. although getting the amplitude right requires fine tuning. as is establishing the preconditions for inflation.," Quantum fluctuations in a scalar inflaton field can explain the origin and near scale-invariant power spectrum of the primordial density perturbations, although getting the amplitude right requires fine tuning, as is establishing the preconditions for inflation." + Early versions of the theory envisaged a pre-intlationary Fricchmann-Robertson-Walker (PI). stage., Early versions of the theory envisaged a pre-inflationary Friedmann-Robertson-Walker (FRW) stage. +" One of the claimed. advantages of the theory was that. the. rapid expansion effectively erased: all traces of that earlier phase. although it was realized before (Frieman&""Turner (1984))) that that is not strictly true: what it. does is not to eliminate. perturbations but. to. stretch them to unobservable scales."," One of the claimed advantages of the theory was that the rapid expansion effectively erased all traces of that earlier phase, although it was realized before \citet{fri84}) ) that that is not strictly true; what it does is not to eliminate perturbations but to stretch them to unobservable scales." + This leaves open the question of whether there could. be perturbations on very tiny scales that are stretched. to observable size., This leaves open the question of whether there could be perturbations on very tiny scales that are stretched to observable size. + H0 has been shown (Magueijo&Singh (2007))) that without. clrastic modifications such perturbations could. not explain the observed power spectrum of density perturbations., It has been shown \citet{mag07}) ) that without drastic modifications such perturbations could not explain the observed power spectrum of density perturbations. + llere we wish to go much further than Magueijo&Singh (2007).. to argue that under rather general conditions the initial small scale perturbations would indeed. be and. besides having the wrong power spectrum would be far too large in amplitude to be consistent with the use of linear. perturbation theory.," Here we wish to go much further than \citet{mag07}, to argue that under rather general conditions the initial small scale perturbations would indeed be and besides having the wrong power spectrum would be far too large in amplitude to be consistent with the use of linear perturbation theory." + This is because thermal radiation has Large fluctuations on scales comparable with the thermal wavelength. and such scales have been stretched to cosmological size today.," This is because thermal radiation has large fluctuations on scales comparable with the thermal wavelength, and such scales have been stretched to cosmological size today." + Under these circumstances. it is not possible to say what the outcome would be.," Under these circumstances, it is not possible to say what the outcome would be." + It. should be emphasized that there is a key dillerence between this paper ancl previous ones on the topies of “warm inflation’ and ‘thermal inflation’., It should be emphasized that there is a key difference between this paper and previous ones on the topics of `warm inflation' and `thermal inflation'. + Phese latter rely on either a mild to strong coupling between the inllaton and some other field to maintain a thermal medium even during the slow roll phase (Berera (1995a.b))). or an extension of standard. model to include anaddifionad period of inflation with a significant thermal component (Barreiroetal (1996))).," These latter rely on either a mild to strong coupling between the inflaton and some other field to maintain a thermal medium even during the slow roll phase \citet{arj96a,arj96b}) ), or an extension of standard model to include an period of inflation with a significant thermal component \citet{bar96}) )." + Phe question we are asking. on the other hand. is what happens if there was a pre-inllationary raciation dominated. universe?," The question we are asking, on the other hand, is `what happens if there was a pre-inflationary radiation dominated universe'?" +" This phase can certainlv exist.independently of warm! or ""thermal inflation.", This phase can certainly exist of `warm' or `thermal' inflation. + Lt is an especially pertinent question because the cosmologically relevant scales today could very easily. have originated from scales well beneath one wavelength of such a radiation component., It is an especially pertinent question because the cosmologically relevant scales today could very easily have originated from scales well beneath one wavelength of such a radiation component. + None of the three papers. cited above. nor papers related to them. addressed the extremely «quantum phenomenon of Fluctuations on the wavelength and sub-wavelength scales.," None of the three papers cited above, nor papers related to them, addressed the extremely quantum phenomenon of fluctuations on the wavelength and sub-wavelength scales." + That is the purpose of ourwork., That is the purpose of ourwork. + lt has also been previously argued, It has also been previously argued +conrposifional class is of ereat interest.,compositional class is of great interest. + This class includes objects with extreme Co and NI depletions that are related to CoIIo aud NIT; depletions iun nuclear ices., This class includes objects with extreme $_2$ and $_2$ depletions that are related to $_2$ $_2$ and $_3$ depletions in nuclear ices. + We would expect a low IENC'/IICN ratio in these objects as well., We would expect a low HNC/HCN ratio in these objects as well. + So far. very few members of this class have been ideutified (Fink&Wicks1996).," So far, very few members of this class have been identified \citep{fink96}." +. The upper Πιτ for the IENC/IICN ratio iu. Cüacobini-Ziuner obtained during its 1998 apparition (<114.. Diveretal. 1999: Fie.," The upper limit for the HNC/HCN ratio in Giacobini-Zinner obtained during its 1998 apparition $<$, \citealt{biver99}; Fig." + 3) is uot sensitive enough to draw definitive conchisions., 3) is not sensitive enough to draw definitive conclusions. + Comet 21P/CGiacobiniZiuner will make a favorable apparition in 2018 (at 0.1 AU from the Earth). during which scusitive measurcunents will be possible using the Atacama Laree Millimeter/Subinillimeter Array (ALMA).," Comet 21P/Giacobini-Zinner will make a favorable apparition in 2018 (at 0.4 AU from the Earth), during which sensitive measurements will be possible using the Atacama Large Millimeter/Submillimeter Array (ALMA)." + Observations of livdrogen isocvanide du cometary atmospheres carried out to date indicate that the TING production has to be efficient iu the immer coma. just as the material leaves the nucleus.," Observations of hydrogen isocyanide in cometary atmospheres carried out to date indicate that the HNC production has to be efficient in the inner coma, just as the material leaves the nucleus." + The process has to be temperature dependent to explain the observed variation iu the IINC/TIICN ratio with the heliocentric distance., The process has to be temperature dependent to explain the observed variation in the HNC/HCN ratio with the heliocentric distance. + Thermal degradation of macromolecules or polviucrs produced frou anuuonia and carbon compounds. sich as acetylene. methane. or ethaue appears consistent with all existing data. iucludiug the very low INC/TICNratio in comet το)/Sclavassinann-Wachimann reported here.," Thermal degradation of macromolecules or polymers produced from ammonia and carbon compounds, such as acetylene, methane, or ethane appears consistent with all existing data, including the very low HNC/HCN ratio in comet 73P/Schwassmann-Wachmann reported here." +" Such polviners have beeu invoked previously to explain anomalous HN/I?N ratios measured iu cometary CN,", Such polymers have been invoked previously to explain anomalous $^{14}$ $^{15}$ N ratios measured in cometary CN. + Additional interferometric observations of IENC' in colts are needed to provide constraints on the spatial distribution of this molecule in the cometary comac., Additional interferometric observations of HNC in comets are needed to provide constraints on the spatial distribution of this molecule in the cometary comae. + Such observations will soon be possible iu moderately productive comets with (sub)nilimeter iuterferoimeters (e.g. e-SATA).," Such observations will soon be possible in moderately productive comets with (sub)millimeter interferometers (e.g., e-SMA)." + Aleasurements of the WeNCALING isotopic ratio would be iustrumental in determining whether the IICN polviners similar to those invoked to explain the euliauced LN abundance in CN may also be a source of cometary INC., Measurements of the $^{15}$ $^{14}$ NC isotopic ratio would be instrumental in determining whether the HCN polymers similar to those invoked to explain the enhanced $^{15}$ N abundance in CN may also be a source of cometary HNC. + Towever. such measurements will have to await the comunissioning of ALMA.," However, such measurements will have to await the commissioning of ALMA." + This research has been supported by NSF erat AS'T-05loss? to the Caltech Subinillinmeter Observatory., This research has been supported by NSF grant AST-0540882 to the Caltech Submillimeter Observatory. + D.C.L. acknowledges support from the Observatoire de Paris during his stav in Meudon., D.C.L. acknowledges support from the Observatoire de Paris during his stay in Meudon. + S.D.C. acknowledges support from NASAs Planetary Atinosphlieres Program., S.B.C. acknowledges support from NASA's Planetary Atmospheres Program. + We thank N. Fray for useful discussions aud the referce. AL DiSauti. for a thorough aud helpful review of the nanuseript.," We thank N. Fray for useful discussions and the referee, M. DiSanti, for a thorough and helpful review of the manuscript." +For a uniform spatial distribution of deliveries. oue expects the number of arrivals to vary as the cosine of the latitude due to the sinaller surface area at higher latitudes.,"For a uniform spatial distribution of deliveries, one expects the number of arrivals to vary as the cosine of the latitude due to the smaller surface area at higher latitudes." + Figure 6 shows tliat to an excellent approximation. the Earth is uniformly struck by impactors (in latitude).," Figure \ref{fig:elat} shows that to an excellent approximation, the Earth is uniformly struck by impactors (in latitude)." + To account for the area in each latitude biu. divide by: where the co-latitucles 04>05 are measured uorth (rom the south pole.," To account for the area in each latitude bin, divide by: where the co-latitudes $\theta_1 > \theta_2$ are measured north from the south pole." +We have shown that the degeneracy between dust temperature and redshift severcly limits the use of the far-IR dust peak alone as a redshift indicator.,We have shown that the degeneracy between dust temperature and redshift severely limits the use of the far-IR dust peak alone as a redshift indicator. + The color selection of Ssyy2Sassy (and Ssyy2Sosy) cau be used to identify suuples of caudidate hieh redshift ealaxies., The color selection of $S_{500}>S_{350}$ (and $S_{500}>S_{250}$ ) can be used to identify samples of candidate high redshift galaxies. + Iu order to further constrain the redshift of individual sources requires prior kuowledge of the dust temperature or additional nuiutinwavelcueth data. particularly in the radio or at gin. We present 8 candidate 500 pau 7peakers from the BLAST ECDFS survev with Ssyy> 151iuJw: a fraction of which we expect to be at z>1 depending on the distribution of dust temperatures.," In order to further constrain the redshift of individual sources requires prior knowledge of the dust temperature or additional multi-wavelength data, particularly in the radio or at $\mu$ m. We present 8 candidate $\,\mu$ m `peakers' from the BLAST ECDFS survey with $_{500}>45\,$ mJy; a fraction of which we expect to be at $z>4$ depending on the distribution of dust temperatures." + The nuuber deusitv of these high redshift candidates is <17 7 aud is consistent with the το densities of the brightest pauesclected galaxies.," The number density of these high redshift candidates is $<17$ $^{-2}$ and is consistent with the number densities of the brightest $\,\mu$ m-selected galaxies." + The correspouding fraction of pan-selected galaxies in the BLAST survey which could be at z2 Lis <35%.," The corresponding fraction of $\,\mu$ m-selected galaxies in the BLAST survey which could be at $z>4$ is $<35\%$." + Tn order to further constrain the space density of the most distant SMCs will require deep. wide area surveys with MHerschel/SPIRE in addition to sufficieutlv deep inultiavaveleusth data to weed out the eecmuine high redshift candidates οι pau peakers that are lower redshift salaxies with cooler than average dust temperatures.," In order to further constrain the space density of the most distant SMGs will require deep, wide area surveys with /SPIRE in addition to sufficiently deep multi-wavelength data to weed out the genuine high redshift candidates from $\,\mu$ m `peakers' that are lower redshift galaxies with cooler than average dust temperatures." + Reeardless. our upper limits on the ΠΠΟΥ density of: 2f Iuuinous dusty galaxies suggests a strong decline in their number density frou +~2.," Regardless, our upper limits on the number density of $z>4$ luminous dusty galaxies suggests a strong decline in their number density from $z\sim2$." + We thauk the referee for constructive coments which nuproved the prescutation of this work., We thank the referee for constructive comments which improved the presentation of this work. + We thank the BLAST team for making thei data public., We thank the BLAST team for making their data public. + AP acknowledges support provided by NASA through the Fellowship. Program. through a contract issued by the Jet Propulsion Laboratory. California Institute of Technology under a coutract with NASA.," AP acknowledges support provided by NASA through the Fellowship Program, through a contract issued by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA." +Lossless compression of a discrete information source to its entropy rate H is a well studied topic.,Lossless compression of a discrete information source to its entropy rate $\m{H}$ is a well studied topic. + A possibly lesser known approach to this problem is one based on svinbolic dvnamical svstems. where the information generating mechanism is modeled by a randomly initialized iterative mapping of the unit interval to itselL. aud (he emitted source sequence is a quantized observation of that process.," A possibly lesser known approach to this problem is one based on symbolic dynamical systems, where the information generating mechanism is modeled by a randomly initialized iterative mapping of the unit interval to itself, and the emitted source sequence is a quantized observation of that process." + For well behaved mappings (lie source sequence constitutes an of the initial point. ie.. corresponds to a unique such point.," For well behaved mappings the source sequence constitutes an of the initial point, i.e., corresponds to a unique such point." +" Furthermore. the prefixes of this expansion describe the initial point with (exponentially) increasing resolution. and the unit interval can be uniformly partitioned into zz2"" subintervals so (hat with high probability. (he subinterval containing (he initial point will wave all its points acdimitting the same leneth-n expansion."," Furthermore, the prefixes of this expansion describe the initial point with (exponentially) increasing resolution, and the unit interval can be uniformly partitioned into $\approx 2^{n\m{H}}$ subintervals so that with high probability, the subinterval containing the initial point will have all its points admitting the same $n$ expansion." + This leads (o a conceptually simple and optimal compression scheme: A linite source sequence is mapped to a representing subinterval by computing the corresponding reverse trajectory of the clvnamical svstem. and is reconstructed by following the trajectory of an arbitrary point in (hat.," This leads to a conceptually simple and optimal compression scheme: A finite source sequence is mapped to a representing subinterval by computing the corresponding reverse trajectory of the dynamical system, and is reconstructed by following the trajectory of an arbitrary point in that." +terval!.. A comprehensive study of the svanbolic dynamics framework for information sources can be found in|1]., A comprehensive study of the symbolic dynamics framework for information sources can be found in. +. Some of the ideas can be traced back to Rénnyi. see and references therein.," Some of the ideas can be traced back to Rénnyi, see and references therein." +concentrations seen Is ~+20%..,concentrations seen is $\sim \pm$. + Regarding the modeling of the scatter in the concentration. it is natural to examine this in the context of different assembly histories for halos with the same mass (Wechsleretal.2002: (See also. Cohn&White2005..)," Regarding the modeling of the scatter in the concentration, it is natural to examine this in the context of different assembly histories for halos with the same mass \citep{wechsler01, zhao03} (See also, \citealt{cohn05}. .)" + However. in their MS analysis. etal.(2007) find that the concentration scatter cannot be accountedNeto for by differences in the time of formation alone.," However, in their MS analysis, \cite{neto07} find that the concentration scatter cannot be accounted for by differences in the time of formation alone." + Additional consequences of environmental effects (Wechsleretal.2006) appear to be important primarily for low-mass halos., Additional consequences of environmental effects \citep{wechsler05} appear to be important primarily for low-mass halos. + Therefore one is driven to the general conclusion that there is still no replacement for large-scale simulations 1f reliable predictions for halo concentrations and the distribution of concentrations are required., Therefore one is driven to the general conclusion that there is still no replacement for large-scale simulations if reliable predictions for halo concentrations and the distribution of concentrations are required. + In this section. we compare our simulation results with some of the recent observations of the concentration-mass relation for clusters.," In this section, we compare our simulation results with some of the recent observations of the concentration-mass relation for clusters." + The observational results span a variety of techniques. including strong and weak lensing (e.g.. Comerford&Natara-jan 2007:: Broadhurstetal. 2008:; Mandelbaumetal. 2008:: Okabeetal. 2010:: Ogurietal... 2011)) X-ray observations of relaxed clusters (e.g.. Buoteetal.2007:: Vikhlininetal. 2006: Schmidt&Allen. 2007:; Vikhlininetal. 2009)) and relaxed and unrelaxed clusters (Ettorietal.2011)... and cluster kinematies (e.g.. Rines&Diaferio2006) Wojtak 2010).," The observational results span a variety of techniques, including strong and weak lensing (e.g., \citealt{comerford07}; \citealt{broadhurst08}; \citealt{mandelbaum08}; ; \citealt{okabe09}; ; \citealt{oguri11}) ) X-ray observations of relaxed clusters (e.g., \citealt{buote06}; \citealt{vikhlinin05}; \citealt{schmidt06}; \citealt{vikhlinin09}) ) and relaxed and unrelaxed clusters \citep{ettori11}, and cluster kinematics (e.g., \citealt{rines06}; \citealt{wojtak10}) )." + Our aim is to provide a set of figures that enables the reader to judge by eye the current status of how well the theoretical predictions match against observations., Our aim is to provide a set of figures that enables the reader to judge by eye the current status of how well the theoretical predictions match against observations. + Because there are significant observational systematics that are unclear and the observational statistics are still limited. we do not believe that a more complete statistical analysis 1s necessary. or even particularly useful.," Because there are significant observational systematics that are unclear and the observational statistics are still limited, we do not believe that a more complete statistical analysis is necessary, or even particularly useful." + The strategy we follow is to take the ratio of each measured concentration to the theoretically predicted concentration at the object’s observed mass and redshift., The strategy we follow is to take the ratio of each measured concentration to the theoretically predicted concentration at the object's observed mass and redshift. + We then bin in mass to show a relatively limited number of comparison points in each figure., We then bin in mass to show a relatively limited number of comparison points in each figure. + Thus each point in the observation plots represents an average over ~5 data points. (, Thus each point in the observation plots represents an average over$\sim$ 5 data points. ( +The corresponding Poisson error bars use the improved formula 7+=VN)+14+1/2 as given by Heinrich2003.. which asymptotes to /N; at large Ny.),"The corresponding Poisson error bars use the improved formula $\sigma_{\pm}=\sqrt{N_h+1/4}\pm 1/2$ as given by \citealt{heinrich03},, which asymptotes to $\sqrt{N_h}$ at large $N_h$ .)" + We begin our comparison using results from X-ray observations of relaxed clusters as shown in Fig. 7.., We begin our comparison using results from X-ray observations of relaxed clusters as shown in Fig. \ref{fig:xrayrel}. + Schmidt&Allen(2007) have measured the concentration of 34 dynamically relaxed clusters (0.06—z« 0.69) from observations (left panel).," \cite{schmidt06} + have measured the concentration of 34 dynamically relaxed clusters $0.064«10""7M. with minor tension at lower masses."," The theoretical predictions are in good agreement for masses $M_{vir} > +4\times 10^{14} \mau$, with minor tension at lower masses." + The data presented by Buoteetal.(2007) are a compilation of analyses of relaxed systems from andXMM-Newton: we show only the higher mass range. represented by results taken from Pointecouteau.Arnaud.&Pratt(2005).. etal. (2006).. Zappacostaetal. (2006).. and Gastaldelloetal. (2007).. spanning a redshift range of 0.016«z0.23.," The data presented by \cite{buote06} are a compilation of analyses of relaxed systems from and; we show only the higher mass range, represented by results taken from \cite{point05}, \cite{vikhlinin05}, \cite{zappacosta06}, and \cite{gastaldello07}, spanning a redshift range of $0.0164«10""47!M..."," As with the \cite{schmidt06} + comparison, we find that the simulation results are in good agreement with these observations for $M_{200} > 4\times 10^{14} \mau$ ." + As the authors themselves note. a slope cannot be fitted to their data because of the narrow mass range of the observations relative to their errors.," As the authors themselves note, a slope cannot be fitted to their data because of the narrow mass range of the observations relative to their errors." + Thus. we regard the current level of agreement as being quite satisfactory.," Thus, we regard the current level of agreement as being quite satisfactory." + We now consider lensing measurements of cluster profiles using weak and strong lensing and combinations thereof., We now consider lensing measurements of cluster profiles using weak and strong lensing and combinations thereof. + Figure shows the comparison of the theoretical predictions. against the results of LocUss. a weak lensing study of 30 clusters with Subaru/Suprime-Cam imaging data (Okabeetal.2010) and a combined strong and weak lensing analysis of 28 clusters from the Sloan Giant Ares Survey (Ogurietal.2011).," Figure \ref{fig:lens} + shows the comparison of the theoretical predictions against the results of LocUss, a weak lensing study of 30 clusters with Subaru/Suprime-Cam imaging data \citep{okabe09} and a combined strong and weak lensing analysis of 28 clusters from the Sloan Giant Arcs Survey \citep{oguri11}." +. The left panel of Fig., The left panel of Fig. + 9 shows theweak lensing results displayed in the same manner as for the X-ray datasets., \ref{fig:lens} shows theweak lensing results displayed in the same manner as for the X-ray datasets. + The results from Okabeetal.(2010) are in excellent agreement with our predictions. completely consistent with the corresponding measurements from relaxed clusters.," The results from \cite{okabe09} are in excellent agreement with our predictions, completely consistent with the corresponding measurements from relaxed clusters." +" The results of Ogurietal.(2011) are consistent with our predictions for M,>4«I0!7M... but at lower masses. there appears to be a significant discrepancy. with a much steeper c—M dependence."," The results of \cite{oguri11} are consistent with our predictions for $M_{vir} > 4\times 10^{14} \mau$, but at lower masses, there appears to be a significant discrepancy, with a much steeper $c-M$ dependence." + Although baryon cooling may play a role at smaller masses. there is no convincing reason for such a large effect — for which there is no signal in the X- data (nor in the simulations of Duffyetal...2010)).," Although baryon cooling may play a role at smaller masses, there is no convincing reason for such a large effect – for which there is no signal in the X-ray data (nor in the simulations of \citealt{duffy10}) )." + Note that the target selection in the two surveys is quite different. that of Okabeetal.(2010) being essentially volume-limited. while any strong-lensing selected sample such as that of Ogurietal.(2011) must have a significant amount of selection and projection bias (Rozoetal.2008:: Meneghettietal.2010)).," Note that the target selection in the two surveys is quite different, that of \cite{okabe09} being essentially volume-limited, while any strong-lensing selected sample such as that of \cite{oguri11} must have a significant amount of selection and projection bias \citealt{rozo08}; \citealt{meneghetti10}) )." + Note also that an analysis based on mock weak lensing observations in the MS (Bahéetal.2011) has shown that there is bias in weak lensing measurements of concentration as well. tending to depress the measured concentration by à small amount from the predicted value.," Note also that an analysis based on mock weak lensing observations in the MS \citep{bahe11} has shown that there is bias in weak lensing measurements of concentration as well, tending to depress the measured concentration by a small amount from the predicted value." + The right panel of Fig., The right panel of Fig. + 9. shows the combined strong plus weak lensing analysis including a model for lensing bias (Ogurietal. 2011)., \ref{fig:lens} shows the combined strong plus weak lensing analysis including a model for lensing bias \citep{oguri11}. +". Processing the results through the lensing bias model (by enhaneing the theoretical prediction) brings down the discrepancy significantly but there is still evident tension for masses Mj,«41047!M..."," Processing the results through the lensing bias model (by enhancing the theoretical prediction) brings down the discrepancy significantly but there is still evident tension for masses $M_{vir} < +4\times 10^{14} \mau$." + Nevertheless. we note that there is à clear trend of lensing concentrations reducing over time and becoming more consistent with the theoretical predictions.," Nevertheless, we note that there is a clear trend of lensing concentrations reducing over time and becoming more consistent with the theoretical predictions." + Other data our results appear to be in agreement with can be found in Comerford&Natarajan(2007) (strong lensing) and Coeetal.(2012) (strong and weak lensing).," Other data our results appear to be in agreement with can be found in \cite{comerford07} + (strong lensing) and \cite{coe12} (strong and weak lensing)." + A cautionary note regarding weak lensing concentration measurements of clusters is provided in Figure 6 of Comerford&Natarajan(2007) regarding Abell 1689 and in the results given in (2011) as part of the400d weak lensing survey., A cautionary note regarding weak lensing concentration measurements of clusters is provided in Figure 6 of \cite{comerford07} regarding Abell 1689 and in the results given in \cite{israel11} as part of the weak lensing survey. + Instead of using individual objects. a stacked statistical analysis can be applied to clusters. as carried out using the Sloan Digital Sky Survey by Mandelbaumetal. (2008).. to a cluster mass range of ος10447!M ...," Instead of using individual objects, a stacked statistical analysis can be applied to clusters, as carried out using the Sloan Digital Sky Survey by \cite{mandelbaum08}, , to a cluster mass range of $\sim +6\times 10^{14} \mau$ ." +" This analysis sees no evidence for a major boost in concentration at lower masses and the final result — οσο,~4.60.7 at (zj=0.22 at amass of Moos~ is 20-40% less than our prediction of esos~6.5 at the correspondingM mass.", This analysis sees no evidence for a major boost in concentration at lower masses and the final result – $c_{200b} \sim 4.6 \pm 0.7$ at $\left < z \right> =0.22$ at amass of $M_{200b} \sim 10^{14} \mau$ is $20-40\%$ less than our prediction of $c_{200b}\sim 6.5$ at the corresponding mass. + The mild c—M dependence they observe is however in good agreement with our predictions — ~0.09 compared to the observedslope of 0.13 4-0.07.Finally. we consider the estimates of the concentration using galaxy kinematics in clusters.," The mild $c-M$ dependence they observe is however in good agreement with our predictions – $\sim 0.09$ compared to the observedslope of $0.13 \pm +0.07$ .Finally, we consider the estimates of the concentration using galaxy kinematics in clusters." + Rines&Diaferto(2006) matched, \cite{rines06} matched +are eiven in Table 1.. aud the parameters for the Atacama Large Millimeter Array aro given in) Table 2..,"are given in Table \ref{vla}, and the parameters for the Atacama Large Millimeter Array are given in Table \ref{alma}." + We model the svuthetic observation using au effective Gaussian beam rather than doing a full-fledged simulation of aperture svutlesis., We model the synthetic observation using an effective Gaussian beam rather than doing a full-fledged simulation of aperture synthesis. + For the wavelengths with Ax:θσι observable by ALMA. in addition to the free-free eiuissiou we nist also ake iuto account continuuu cussion bv dust particles.," For the wavelengths with $\lambda \leq 0.3\,$ cm observable by ALMA, in addition to the free-free emission we must also take into account continuum emission by dust particles." + We use to generate dust emission maps as well as maps of combined frec-free aud dust ciission roni the simulation data., We use to generate dust emission maps as well as maps of combined free-free and dust emission from the simulation data. + RADMC-3D is an AAR-based radiative transfer xickage for continua aud line rachative trauster., RADMC-3D is an AMR-based radiative transfer package for continuum and line radiative transfer. + It las au interface for PARAMESII (MacNeiceetal.2000).. he AMR evid library of FLASIT.," It has an interface for PARAMESH \citep{macneiceetal00}, the AMR grid library of FLASH." + We use RADAIC-3D or two tasks., We use RADMC-3D for two tasks. + First. to compute the dust temperature selt-cousistently. using the staudard Monte Carlo method of Bjorlkanan&Wood(2001).. combined with Lucy's uecthod of treating optically thin regions (Lucy1999).," First, to compute the dust temperature self-consistently, using the standard Monte Carlo method of \citet{bjorkmanwood01}, combined with Lucy's method of treating optically thin regions \citep{lucy99}." +.. Second. to compute the images of the free-free and dust continui cussion by using it as a volume-rencderine rav-tracer tool.," Second, to compute the images of the free-free and dust continuum emission by using it as a volume-rendering ray-tracer tool." + RADMC-3D is the successor of the RADAIC code (Dulleiiond&Dominik2001). which las been used in nuuerous papers., RADMC-3D is the successor of the RADMC code \citep{dullemdom04} which has been used in numerous papers. + RADMC-3D has been tested against the eulier 2D version of RADAIC for various ID aud 2D test cases., RADMC-3D has been tested against the earlier 2D version of RADMC for various 1D and 2D test cases. +" A detailed discussion of RADMC-3D will be published separately, but since this is the first scientific use of the code. we show the results of a simple test case here."," A detailed discussion of RADMC-3D will be published separately, but since this is the first scientific use of the code, we show the results of a simple test case here." + It involves a simiple 1D spherically saunietric cuvelope around a star., It involves a simple 1D spherically symmetric envelope around a star. + The density of the envelope is pauaír)pPoLr/LAU) ?. where py takes the values 101? ecce for test case Land LO[| Ὁ for test case 2.," The density of the envelope is $\rho_{\mathrm{dust}}(r)=\rho_0(r/1\mathrm{AU})^{-2}$ , where $\rho_0$ takes the values $10^{-15}$ $^{-3}$ for test case 1 and $10^{-14}$ $^{-3}$ for test case 2." + The iuner radius lies at 5 AU. the outer radius at 100 AU.," The inner radius lies at 5 AU, the outer radius at 100 AU." + The star has solar parameters. but we treat the stellar spectrmm as a blackbody of T=5780 Ix. For the opacity we use silicate dust spheres of 0.1 jan. using optical constants of olivine from the Jonadatabase’... but. we artificially set the scattering opacity to zero in order to be able to compare our results to the results from a shuple 1D variable eddiugton factor dust radiative trausfer code calledTRANSPIIERE??.," The star has solar parameters, but we treat the stellar spectrum as a blackbody of $T=5780$ K. For the opacity we use silicate dust spheres of 0.1 $\mu$ m, using optical constants of olivine from the Jena, but we artificially set the scattering opacity to zero in order to be able to compare our results to the results from a simple 1D variable eddington factor dust radiative transfer code called." +", With RADAIC-3D we now compute the cust temperature using the Moute Carlo method.", With RADMC-3D we now compute the dust temperature using the Monte Carlo method. + We do this in two wavs., We do this in two ways. + First. we use a spherical 1D erid. similar to what we use for TRANSPIIERE.," First, we use a spherical 1D grid, similar to what we use for TRANSPHERE." + Secoudh. we use a 3D Cartesian AMR-vefined evid. where the refuciment is doue with the criterion that the cells with centers having radii kr>5 AU from the star should have a size Av>O.2r.," Secondly, we use a 3D Cartesian AMR-refined grid, where the refinement is done with the criterion that the cells with centers having radii $r > 5$ AU from the star should have a size $\Delta x \geq 0.2 r$." + This is a relatively coarse resolution. neant to test the effect of low resolution on the results.," This is a relatively coarse resolution, meant to test the effect of low resolution on the results." + The outcome of this comparison is displaved in Figure L.. showing the excellent aereeimmeut between the temperature profiles.," The outcome of this comparison is displayed in Figure \ref{radmctests}, showing the excellent agreement between the temperature profiles." + Our simulations follow the gravitational collapse of the initial massive clump and lead to the formation of hniehauass stars., Our simulations follow the gravitational collapse of the initial massive clump and lead to the formation of high-mass stars. + The collapse leads to the forination of a iassive rotationally flattened structure. which is eravitationally unstable aud fragments.," The collapse leads to the formation of a massive rotationally flattened structure, which is gravitationally unstable and fragments." + Onlv a single star is allowed to form in run A. It accretes T2AL.. in 115 kvr.," Only a single star is allowed to form in run A. It accretes $72 M_\odot$ in $145\,$ kyr." +" In ται D. three highauass stars with Af>10M, form within το kvr. aud become the dominant source of ioniziug radiation within the star cluster."," In run B, three high-mass stars with $M \geq 10 M_\odot$ form within $70\,$ kyr, and become the dominant source of ionizing radiation within the star cluster." + The interaction of the ionizing radiation with the iufalliug accretion flow leads to imultiple effects observable in both spatial aud spectral diagnostics., The interaction of the ionizing radiation with the infalling accretion flow leads to multiple effects observable in both spatial and spectral diagnostics. + The most striking property of the resulting iregious is thei extremely high variability in time and shape., The most striking property of the resulting regions is their extremely high variability in time and shape. + In the online material of Paper I we presented movies of radio continuum maps from cdiffercut viewpoints., In the online material of Paper I we presented movies of radio continuum maps from different viewpoints. + The radio maps were generated for VLA paralucters at a waveleneth of A= 2cm. using a beam with full width at half masini of 0711 and a noise level of 10. Jy.," The radio maps were generated for VLA parameters at a wavelength of $\lambda = 2\,$ cm, using a beam with full width at half maximum of $0\farcs14$ and a noise level of $10^{-3}$ Jy." + The asstuned distance was 2.65 kpc.," The assumed distance was $2.65\,$ kpc." + All the movies show the continuous build-up aud destruction of rreeious., All the movies show the continuous build-up and destruction of regions. + The timescale for changes of more than 5000 AU in size cau be as short as LOOvr.," The timescale for changes of more than $5000$ AU in size can be as short as $100\,$ yr." + This flickering is caused by the accretion flow in which the sources are enibedded., This flickering is caused by the accretion flow in which the sources are embedded. + When the protostar passes through deuse. gravitationally unstable filaments in the accretion flow. they absorb its ionizing radiation. so that," When the protostar passes through dense, gravitationally unstable filaments in the accretion flow, they absorb its ionizing radiation, so that" +ks light travel time-scales.,ks light travel time-scales. + More realistically. the time required for the ADAF to respond to a change in i will depend on the sound speed. which approaches 0.25e (stationary blackhole) or 0.5e (rotatingblackhole} at small radi (Jaroszvuski&Isarpiewski 1997)). resulting in a time-scale ou the order of ~620 kx.," More realistically, the time required for the ADAF to respond to a change in $\dot{m}$ will depend on the sound speed, which approaches $0.25c$ (stationary blackhole) or $0.5c$ (rotating blackhole) at small radii \cite{JK97}) ), resulting in a time-scale on the order of $\sim 6-20$ ks." + It is evident that a Werr metric should result ia a more variable ADAE. while ADAF outo a blackhole at least as massive as ~10*AL. should not be variable on time-scales less than several to tens of ks.," It is evident that a Kerr metric should result in a more variable ADAF, while ADAF onto a blackhole at least as massive as $\sim 10^7 \rm \ M_{\odot}$ should not be variable on time-scales less than several to tens of ks." + The time-scales probed by the observation are ou this order., The time-scales probed by the observation are on this order. + This analysis is based ou the assumption that the any variability would be caused by rapid changes in mand that the ADAF will remain stable uuder these changes., This analysis is based on the assumption that the any variability would be caused by rapid changes in $\dot{m}$ and that the ADAF will remain stable under these changes. + However. detailed modeling by Mammotooti.(1996) and Takeuchi&Mineshiee(1997). showee that instabilities produced by rapid chanees in i are —LBikelv to produce “shots” in the X-ray hnunünositv of an ADAE with time-scales on the order of severa hnuudred ο fas observed iu the low state of Cyeuus X-1). suggestingoo that tle time-scales assume above are very conservative.," However, detailed modeling by \cite{Man96} and \cite{Tak97} showed that instabilities produced by rapid changes in $\dot{m}$ are likely to produce “shots” in the X-ray luminosity of an ADAF with time-scales on the order of several hundred $R_{Schw}/c$ (as observed in the low state of Cygnus X-1), suggesting that the time-scales assumed above are very conservative." + It may be simply that the accretion rate itself is more steady in LLACN than it is in Sevtert galaxies., It may be simply that the accretion rate itself is more steady in LLAGN than it is in Seyfert galaxies. + Note that this also woul hen iudicate a break with Sevterts. assunüug that changes in accretion rate are ultimately responsible or variability in Sevterts.," Note that this also would then indicate a break with Seyferts, assuming that changes in accretion rate are ultimately responsible for variability in Seyferts." + If occultation events are he cause of variability in Sevferts. then the accretion Hows in LLAGN lack material subteudiug a sufficieut solid angle to produce the same type of variability. again sugeestive of a larger region responsible for the xoduction of N-ravs.," If occultation events are the cause of variability in Seyferts, then the accretion flows in LLAGN lack material subtending a sufficient solid angle to produce the same type of variability, again suggestive of a larger region responsible for the production of X-rays." + Note also that if variability ou short time-scales is observed in à LLAGN believed o have au ADAF is due to either an occultation event or an instability (where the N-ray fiux would be dominated by shocks rather thau the steady ADAF How emission). then detectable spectral variability is ikelv to accompany the event.," Note also that if variability on short time-scales is observed in a LLAGN believed to have an ADAF is due to either an occultation event or an instability (where the X-ray flux would be dominated by shocks rather than the steady ADAF flow emission), then detectable spectral variability is likely to accompany the event." + Note that many of the arguimeuts in this letter apply equally well to other wavelengths. although with the exception of radio. the nuclear compoucut of the cussion frou a typical galaxy is absorbed. difficult to segregate from extra-nuclear euission. or both.," Note that many of the arguments in this letter apply equally well to other wavelengths, although with the exception of radio, the nuclear component of the emission from a typical galaxy is absorbed, difficult to segregate from extra-nuclear emission, or both." + However. since ADAF models predict that the contribution of svuchrotrou cooling (douinatiug the radio) aud Compton aud bremsstralluug cooliug (dominating πι N-ravs) fo the ADAE Lunimosties varies onlv slightly as a function of radius. monitoring of the radio and XN-rav hunuiuositv of au ADAF should be further test of ADAF models.," However, since ADAF models predict that the contribution of synchrotron cooling (dominating the radio) and Compton and bremsstrahlung cooling (dominating in X-rays) to the ADAF luminosities varies only slightly as a function of radius, monitoring of the radio and X-ray luminosity of an ADAF should be further test of ADAF models." + M81 was observed to vary in the radio on time-scales of weeks (Dieteubolz&Bartel1998.. Ποetal.1998)) and large-scale (ΔΙΙΓ~1.7) Nav variability with a time-scale of months and variability with time-scale of ~1 day was observed by (Ushisakietal.1996.. Serlemitsos.Ptak&Yaqoob1996)).," M81 was observed to vary in the radio on time-scales of weeks \cite{biet98}, \cite{Ho98}) ) and large-scale $\Delta I/I \sim 1.7$ ) X-ray variability with a time-scale of months and variability with time-scale of $\sim 1$ day was observed by \cite{ishi96}, \cite{S96}) )." + Accordingly. the ADAF model predicts not only a specific broadband spectral shape but also that the racio aud X-aay flix from galaxies such as M81 would be correlated over long periods of time (.c.. on time-scales sufficient for the ADAF to be in equilibrimm).," Accordingly, the ADAF model predicts not only a specific broadband spectral shape but also that the radio and X-ray flux from galaxies such as M81 would be correlated over long periods of time (i.e., on time-scales sufficient for the ADAF to be in equilibrium)." +" Finally. uote that as the accretion rate increases, the transition ταςτις where the acerction flow changes from au ADAF to a thin-disk flow would decrease (see Esin.MeCliu-ock.&Naravan 1997)). possibly resulting iu short-erm variability as observed in Sevtert 1 galaxies."," Finally, note that as the accretion rate increases, the transition radius where the accretion flow changes from an ADAF to a thin-disk flow would decrease (see \cite{Esin97}) ), possibly resulting in short-term variability as observed in Seyfert 1 galaxies." + Iu the case of lard N-rav cussion. this «ουτσι variability should be accompanied by the spectral catures associated with a-disks (1.60... Fe-I&. cussion and the Compton reflection “lap) which should rot be present in ACN dominated by ADAFs.," In the case of hard X-ray emission, this short-term variability should be accompanied by the spectral features associated with $\alpha$ -disks (i.e., Fe-K emission and the Compton reflection “hump”) which should not be present in AGN dominated by ADAFs." + The authors would like to thauk Luis Πο for carefully reading an early version of this manuscript and an auonviuous referee for useful commuciuts., The authors would like to thank Luis Ho for carefully reading an early version of this manuscript and an anonymous referee for useful comments. +"Equation (2)) is exact if f,=1 Knox 1995) and is approximately correct at multipoles {κ(a0 corresponding to angular scales small compared to the dimensions 27/1 of an incomplete sky map.",Equation \ref{eq:Dcell}) ) is exact if $f_{sky} = 1$ Knox 1995) and is approximately correct at multipoles $\ell \gta \ell_{cut}$ corresponding to angular scales small compared to the dimensions $2\pi /\ell_{cut}$ of an incomplete sky map. + The accuracy of cosmological parameter. estimation via the covariance matrix approach depends on: (1) the validity. of the Gaussian approximation to the likelihood function: (2) the number ancl choice. of the parameters s defining the theoretical. model: (3) the parameters. s- of the target. model: (4) thenumerical accuracy of the derivatives of Cy: (5) the inclusion of prior constraints on the parameters (6) systematic errors in estimates of C; caused by Galactic and extragalactic foregrounds., The accuracy of cosmological parameter estimation via the covariance matrix approach depends on: (1) the validity of the Gaussian approximation to the likelihood function; (2) the number and choice of the parameters ${\bf s}$ defining the theoretical model; (3) the parameters ${\bf s_\circ}$ of the target model; (4) thenumerical accuracy of the derivatives of ${\rm C}_\ell$; (5) the inclusion of prior constraints on the parameters${\bf s}$; (6) systematic errors in estimates of ${\rm C}_\ell$ caused by Galactic and extragalactic foregrounds. + For high resolution experiments which tightly constrain many of the cosmological parameters. a Ciaussian approximation about the maximum likelihood should be quite good. (Ixnox. 1995. Spergel private communication). although positivity and other constraints can truncate general excursions in the likelihood space.," For high resolution experiments which tightly constrain many of the cosmological parameters, a Gaussian approximation about the maximum likelihood should be quite good (Knox 1995, Spergel private communication), although positivity and other constraints can truncate general excursions in the likelihood space." + We ignore systematic errors. caused by foreground. subtraction. since over much of the sky. these are very likely to be much smaller than the variance of equation (2)) (sce Tegmark anc Efstathiou 1996 for a discussion of foreground removal from CALB maps).," We ignore systematic errors caused by foreground subtraction, since over much of the sky these are very likely to be much smaller than the variance of equation \ref{eq:Dcell}) ) (see Tegmark and Efstathiou 1996 for a discussion of foreground removal from CMB maps)." + Here we consider the remaining four points., Here we consider the remaining four points. + Parameters describing the theoretical angular power spectra include those for initial conditions and those characterizing 1 transport of radiation through photon decoupling to re present., Parameters describing the theoretical angular power spectra include those for initial conditions and those characterizing the transport of radiation through photon decoupling to the present. + LE we were to allow all possible variations. rw count of parameters could. easily exceed. 20: in our nalvsis. we use 1l variables.," If we were to allow all possible variations, the count of parameters could easily exceed $20$; in our analysis, we use $\le 11$ variables." + We characterize the initia luctuation spectra by an amplitude and a spectral index ilt) for the scalar ancl tensor components. 74/7q1/2(hy) au na pi/2Peay(hy) and i.," We characterize the initial fluctuation spectra by an amplitude and a spectral index (tilt) for the scalar and tensor components, ${\cal +P}_{\Phi}^{1/2}(k_n) $ and $n_s$, ${\cal P}_{GW}^{1/2}(k_n) $ and $n_t$ ." + MPhe primordial. amplitude. parameters ⋅or the gravitational⋠⋠ potential. [luctuations.. pi/273(τω). aux we gravity. wave [uctuations.. pliPeay(hs). are chosen here o be normalized. at a wavenumber corresponding to the rorizon scale.," The primordial amplitude parameters for the gravitational potential fluctuations, ${\cal P}_{\Phi}^{1/2}(k_n) $, and the gravity wave fluctuations, ${\cal P}_{GW}^{1/2}(k_n) $, are chosen here to be normalized at a wavenumber corresponding to the horizon scale." + “Lhe fluctuations arising from inflation coul » much more complicated. requiring. for example. the »vrameterization of variations of the spectral indices with waventunber &. inclusion of isocurvature as well as acliahatic components in the scalar perturbations. and possibly of non-Caussian features.," The fluctuations arising from inflation could be much more complicated, requiring, for example, the parameterization of variations of the spectral indices with wavenumber $k$, inclusion of isocurvature as well as adiabatic components in the scalar perturbations, and possibly of non-Gaussian features." + At the time of decoupling. the key parameters determining the temperature. power spectrum are. the densities of various twpesof matter. the expansion rate. the sound. speed. and the damping rate: all of these depend only on the density parameters. wy;Oih. where j=b.cdim.παπιοον velers to barvons. cold dark matter. hot dark matter. and the various relativistic particles present then. such as photons and relativistic neutrinos.," At the time of decoupling, the key parameters determining the temperature power spectrum are the densities of various typesof matter, the expansion rate, the sound speed, and the damping rate; all of these depend only on the density parameters $\omega_j \equiv +\Omega_j {\rm h}^2$, where $j=b, cdm, hdm, \gamma , er\nu$ refers to baryons, cold dark matter, hot dark matter, and the various relativistic particles present then, such as photons and relativistic neutrinos." + The Hubble parameter at that time only depends upon OL the massive neutrinos were nonrelativistic then?)) and ay=wedue," The Hubble parameter at that time only depends upon (if the massive neutrinos were nonrelativistic ) and $\omega_{er}= +\omega_{\gamma}+\omega_{er\nu}$." + ‘The transport to an angular structure of scale (6| now from the post-decoupling spatial pattern of. temperature Iuctuations of comoving scale & depends on. the cosmological angle-distance relation. £~WR. where for an open universe Bond Efstathiou 1984).," The transport to an angular structure of scale $\ell^{-1}$ now from the post-decoupling spatial pattern of temperature fluctuations of comoving scale $k^{-1}$ depends on the cosmological angle-distance relation, $\ell \sim k {\cal R}$, where for an open universe Bond Efstathiou 1984)." +" lere wy=Ον parameterizes the energy density associated with a cosmological constant A (OQ=Af(315) and wy,=(1.OQ)b = (1.€,OA)h parameterizes the energy associated with the mean curvature of the universe."," Here $\omega_{\Lambda} \equiv +\Omega_{\Lambda} {\rm h}^2$ parameterizes the energy density associated with a cosmological constant $\Lambda$ $\Omega_{\Lambda}=\Lambda +/(3H_0^2)$ ) and $\omega_k \equiv (1-\Omega_0){\rm h}^2$ = $(1-\Omega_m-\Omega_\Lambda){\rm h}^2$ parameterizes the energy associated with the mean curvature of the universe." +" This results in a degencracy along elTR)=0 lines. which leads to a linear relation between δω ane de, for fixed z,,. with cocllicients that depend: upon the explicit target model."," This results in a degeneracy along ${\delta (\omega_{m}^{1/2} {\cal R})} = 0$ lines, which leads to a linear relation between $\delta +\omega_k$ and $\delta \omega_{\Lambda}$ for fixed $\omega_{m}$, with coefficients that depend upon the explicit target model." + The angular pattern we observe also depends upon the change of the gravitational metric in time between post-cecoupling ancl the present. which breaks this degeneracy.," The angular pattern we observe also depends upon the change of the gravitational metric in time between post-decoupling and the present, which breaks this degeneracy." + However. this late-time integrated. Sachs-Wolfe. οσοι influences only low multipoles which have a large cosmic variance.," However, this late-time integrated Sachs-Wolfe effect influences only low multipoles which have a large cosmic variance." + Thus. there exists one combination of variables which cannot be determined accurately from CMD observations alone. even with a high precision experiment such as the Planck Survevor. as the lower right. panel of Fig.," Thus, there exists one combination of variables which cannot be determined accurately from CMB observations alone, even with a high precision experiment such as the Planck Surveyor, as the lower right panel of Fig." + 1 illustrates., \ref{fig:CLpower} illustrates. + Some parameters are tightly constrained by measurements other than CMD anisotropies., Some parameters are tightly constrained by measurements other than CMB anisotropies. +" For cxample. ie epends on the temperature Z5. of the CMD. iss depends as well on the number of massless neutrino types: the C;'s also depend. on the helium. abundance. parameterized by Yg,."," For example, $\omega_\gamma$ depends on the temperature $T_0$ of the CMB, $\omega_{er\nu}$ depends as well on the number of massless neutrino types; the ${\rm C}_\ell$ 's also depend on the helium abundance, parameterized by $Y_{He}$." + Rather than allow such parameters complete freedom. we use the prior probabilities to restrict their allowed: variations. (," Rather than allow such parameters complete freedom, we use the prior probabilities to restrict their allowed variations. (" +Since the experimental errors on Yg.. do and ΑΝ are small.. they have a weak ellect on other cosmological parameters ancl hence we include only Y4. in our analvsis to illustrate the methodology.),"Since the experimental errors on $Y_{He}$, $T_0$ and $N_\nu$ are small, they have a weak effect on other cosmological parameters and hence we include only $Y_{He}$ in our analysis to illustrate the methodology.)" + There also could. be many parameters needed to characterize the ionization history of the Universe: here we use the Compton optical depth τε from the present to the redshift of reheating. assuming Full ionization.," There also could be many parameters needed to characterize the ionization history of the Universe; here we use the Compton optical depth $\tau_C$ from the present to the redshift of reheating, assuming full ionization." +" We therefore analyse a maximum of 11. parameters in this paper: Ya... Τε. 4 initial condition paranicters and 5 density. parameters w,."," We therefore analyse a maximum of 11 parameters in this paper: $Y_{He}$ , $\tau_C$ , 4 initial condition parameters and 5 density parameters$\omega_j$ ." + For a given model. the amplitudes. of the scalar ancl tensor power spectra are uniquely related. to. the observed. amplitude of the CMD. power spectrum ancl that of the present cay mass [uctuations (characterised. for," For a given model, the amplitudes of the scalar and tensor power spectra are uniquely related to the observed amplitude of the CMB power spectrum and that of the present day mass fluctuations (characterised, for" +"Therefore one way of describing the temperature anisotropies, ATg,4, is to extract the corresponding spherical harmonic coefficients (az): where |a;;,| and 9,5, are the amplitudes and phases of the spherical harmonic coefficients, and Y,,, are the spherical harmonics which are defined here as: where Py, is the associated Legendre Polynomial.","Therefore one way of describing the temperature anisotropies, $\Delta \Tp$, is to extract the corresponding spherical harmonic coefficients $\alm$ ): where $ |\alm|$ and $\plm$ are the amplitudes and phases of the spherical harmonic coefficients, and $\ylm$ are the spherical harmonics which are defined here as: where $P_{\lm}$ is the associated Legendre Polynomial." +" Note that this definition of spherical harmonics includes a phase factor of (—1)™, also known as the Condon-Shortley phase."," Note that this definition of spherical harmonics includes a phase factor of $(-1)^{m}$, also known as the Condon-Shortley phase." +" In the standard cosmological model, the temperature fluctuation field is produced by stochastic fluctuations which are Gaussian and statistically stationary over the celestial sphere."," In the standard cosmological model, the temperature fluctuation field is produced by stochastic fluctuations which are Gaussian and statistically stationary over the celestial sphere." +" In this case the phases ®¢,, of each spherical harmonic mode Gem are independent and uniformly random on the interval [0,27] (Colesetal.2004)."," In this case the phases $\plm$ of each spherical harmonic mode $\alm$ are independent and uniformly random on the interval $[0,2\pi]$ \citep{Coles2004}." +. If instead the temperature pattern on the sky is produced by a Bianchi geometry then the aem are no longer stochastically generated but can be directly calculated from parameters of the model., If instead the temperature pattern on the sky is produced by a Bianchi geometry then the $\alm$ are no longer stochastically generated but can be directly calculated from parameters of the model. +" Analytical forms for the temperature pattern can be used to obtain the spherical harmonic phases (McEwenetal.2006;Bridges2008),, but it is clumsy to transform these between different coordinate systems (Colesetal.2004).."," Analytical forms for the temperature pattern can be used to obtain the spherical harmonic phases \citep{McEwen1,McEwen2}, but it is clumsy to transform these between different coordinate systems \citep{Coles2004}." +" In the following we therefore obtain distributions of ®g,, from Bianchi maps generated using the method described by Sung&Coles(2010).", In the following we therefore obtain distributions of $\plm$ from Bianchi maps generated using the method described by \cite{Sung2010}. +". To visualize the information held in the phases, ®¢,,, of the spherical harmonic coefficients, az;4,, we plotted them over all £ and m."," To visualize the information held in the phases, $\plm$, of the spherical harmonic coefficients, $\alm$, we plotted them over all $\l$ and $m$." +" Rather than using a 3D plot, colour has been used to represent the $,,, following Coles&Chiang(2000)."," Rather than using a 3D plot, colour has been used to represent the $\plm$ following \cite{cc2000}." +". The colours equate to the angle on a colour wheel: red (9;,,— 0), green (®¢m= 7/2), cyan (95,— 1), and purple (95,= 37/2)."," The colours equate to the angle on a colour wheel: red $\plm = 0$ ), green $\plm =\pi/2$ ), cyan $\plm =\pi$ ), and purple $\plm=3\pi/2$ )." +" 'To understand these plots, first consider what we would expect to see in the case of an isotropic and homogeneous universe as predicted by the concordance model."," To understand these plots, first consider what we would expect to see in the case of an isotropic and homogeneous universe as predicted by the concordance model." +" This would be a uniform map (as we are not at this point considering fluctuations) but in spherical harmonics this only has power in one mode (£=m 0), so there is no phase for the other modes."," This would be a uniform map (as we are not at this point considering fluctuations) but in spherical harmonics this only has power in one mode $\l=m=0$ ), so there is no phase for the other modes." + Better to consider a map with Gaussian fluctuations as later in the section we will move on to add noise to the Bianchi maps., Better to consider a map with Gaussian fluctuations as later in the section we will move on to add noise to the Bianchi maps. +" Figure shows the phases (®g,,) for a homogeneous and isotropic map with Gaussian fluctuations.", Figure \ref{figRandom} shows the phases $\plm$ ) for a homogeneous and isotropic map with Gaussian fluctuations. + The phases are random over the space i.e. there are no visible patterns in the distribution of colours in the plot., The phases are random over the space i.e. there are no visible patterns in the distribution of colours in the plot. +" Note that for all the maps, ®;,, = 0 or π for"," Note that for all the maps, $\plm$ = 0 or $\pi$ for" +4 Massive scalar fields (his sectionwe willbriellv show thatthe quantum interest inequalities (14)) ancl(22)) and henceallthe res,"field is non- zero (e.g. in the Casimir effect) we may still expect quantum interest to hold, but then “negative” energy would refer to energies less than that of the ground An important consequence of quantum interest is what it tells us about the nature of negative energies in free fields." +ults from (he previous section also applyto the massive scalar , A local pulse of negative energy is not an entity that can be manipulated or interacted with independently of the accompanying positive energy that must be near by. +"field in 4dimensional Minkowski spacetime. Fewster and Eveson [14] obtained the following expression for (p,,5,)in 4D Minkowski spacetime fora scalar fieldof mass"," Even if there are states where the positive and negative energies are separated by a sizeable distance (as suggested by \ref{x_max_ie}) ) when the amount of negative energy is very small), one could still only interact with the pulse pair as a single entity." +" m: a[ 4do (Pirin) — dij, w;[te n— 1n.. IPTE205 bu yf? . (31) is a g! 2(s) isE!the 5Fourier tran"," For example, absorbing, reflecting or scattering only the positive part of the flux would create an isolated negative pulse, violating the quantum inequalities." +sformof g ?(/).ancl whereone integrates the offieldmodes aΗ mode (pu)wilh(m) frequencydenotes theως). minimum," Furthermore, this implies that one cannot subject a hot body to a net flux of negative energy that otherwise might have lowered its entropy in violation of the $2^{nd}$ law of thermodynamics." + negative bound. forfield, I would like to thank Werner Israel for many stimulating discussions. +Using (145) the perturbation in position is given by where o is the unperturbed azimuthal angle.,Using\ref{eq:rhoperturb}) ) the perturbation in position is given by where $\phi_{0}$ is the unperturbed azimuthal angle. + For calculations using οo>0.5 this is no longer a good approximation an we instead apply the perturbation by changing particle masses appropriately., For calculations using $A>0.5$ this is no longer a good approximation an we instead apply the perturbation by changing particle masses appropriately. + The results of the binary star formation calculations with the initial magnetic field aligned with the rotation axis are shown in Figure 6.. where as previously we have computed a series of runs of increasing magnetic field strength. corresponding to flux ratios in units of the critical value of (from top to bottom) x (that is. hydrodynamics). 20.10.7.5.5 and 4.," The results of the binary star formation calculations with the initial magnetic field aligned with the rotation axis are shown in Figure \ref{fig:binarycoldens}, where as previously we have computed a series of runs of increasing magnetic field strength, corresponding to mass-to-flux ratios in units of the critical value of (from top to bottom) $\infty$ (that is, hydrodynamics), $20, 10, 7.5, 5$ and $4$ ." + Given the initial, Given the initial +"in galaxies (Gao Solomon 2004). extending “down” to individual GAICs aud spanning 7-8 orders of magnitude in Ly, (Wu et al.","in galaxies (Gao Solomon 2004), extending “down” to individual GMCs and spanning 7-8 orders of magnitude in $\rm L_{IR}$ (Wu et al." + 2005)., 2005). + It also provides (he basis lor our aforementioned CO-IICN line ratio diagnostic and its abilitv to. “weec-out” dust-affected CO SLEDs from genuinely low-excitation ones., It also provides the basis for our aforementioned CO-HCN line ratio diagnostic and its ability to “weed-out” dust-affected CO SLEDs from genuinely low-excitation ones. +" In the few cases where multi-J dense gas (racers (e.g. IICN. CS) and dust SEDs are available to constrain the state of the dense gas in LIRGs. it is always found in the warm and sell-gravitating ""corner of the available parameter space. tvpical of star-Iorming eas (Mao οἱ al."," In the few cases where multi-J dense gas tracers (e.g. HCN, CS) and dust SEDs are available to constrain the state of the dense gas in LIRGs, it is always found in the warm and self-gravitating “corner” of the available parameter space, typical of star-forming gas (Mao et al." + 2000: Papaclopoulos et al., 2000; Papadopoulos et al. + 2007; Greve et al., 2007; Greve et al. + 2009). ancl where Ts2z0.45.," 2009), and where $\rm R_{65/32}$$\ga $ 0.45." + Moreover for the lowest possible temperature of Ty~1LOIIN in dense starless cores deep in GMCSs (regulated by cosmic ravs rather than photons). a minimum is expected for the optically thick CO emission (shown also in Figure 4 as a dotted line).," Moreover for the lowest possible temperature of $\rm T_{k}$$\sim $ K in dense starless cores deep in GMCs (regulated by cosmic rays rather than photons), a minimum is expected for the optically thick CO emission (shown also in Figure 4 as a dotted line)." +" Thus even for the unlikely easeof a high Ryexsco ratio due to a massive and dense but otherwise SF-idle cold gas phase. this is the lowest 45,4» value possible."," Thus even for the unlikely caseof a high $\rm +R_{HCN/CO}$ ratio due to a massive and dense but otherwise SF-idle cold gas phase, this is the lowest $\rm R_{65/32}$ value possible." + Values of BR5;4550.3 would then imply either a dominant gas phase (hat necessarily has (n(IS))£10! * (and (hus also low Ryex co). or dust-suppression of the CO J=65 line luminosity.," Values of $\rm R_{65/32}$$\la $ 0.3 would then imply either a dominant gas phase that necessarily has $\rm \langle n(H_2)\rangle +$$\la $ $^4$ $^{-3}$ (and thus also low $\rm R_{HCN/CO}$ ), or dust-suppression of the CO J=6–5 line luminosity." + In the second case such dust-allected LIRGs would then populate the area marked by προς and Ruexco 20.15. shown in Figure 11 to be containing several objects.," In the second case such dust-affected LIRGs would then populate the area marked by $\rm +R_{65/32}$$\la$ 0.3 $\rm R_{HCN/CO}$$\ga $ 0.15, shown in Figure 11 to be containing several objects." + The brightest CO J=65 lines in our sample are measured in the hosts of two powerful AGNs. the optically luminous QSO 11119—-120 and the FRI radio galaxy 2293 known for a particularly powerful jet (Flove et al.," The brightest CO J=6–5 lines in our sample are measured in the hosts of two powerful AGNs, the optically luminous QSO 1119+120 and the II radio galaxy 293 known for a particularly powerful jet (Floyd et al." + 2006)., 2006). + These are also the only (wo objects where I5;45271. possible only lor CO line emission that is optically thinand remains up to J=65. which requires verv warm and dense molecular gas.," These are also the only two objects where $\rm +R_{65/32}$$>$ 1, possible only for CO line emission that is optically thin remains well-excited up to J=6–5, which requires very warm and dense molecular gas." + This becomes apparent from its maximum value. achieved in the LTE optically thin limit. where J(r.Ty)=(hr/ky)fexp(hv/kpTi)—1)! (the CMD has been omitted lor simplicity).," This becomes apparent from its maximum value, achieved in the LTE optically thin limit, where $\rm J(\nu, +T_k)=(h\nu/k_B)\left[exp\left(h\nu/k_BT_k\right)-1\right]^{-1}$ (the CMB has been omitted for simplicity)." +" For 11119120 even R5;45»—2 (i.e. (the measured 0) vields T,=96 IX. which is rather high for the bulk of its molecular gas."," For 1119+120 even $\rm +R_{65/32}$ =2 (i.e. $\sim $ (the measured $\sigma$ ) yields $\rm +T_k=96\,K$ , which is rather high for the bulk of its molecular gas." + S9ubmm interferometric imaging has recently, Submm interferometric imaging has recently +Salpeter form (a=2.35).,Salpeter form $\alpha =2.35$ ). + The lower mass cutoff was set at 0.LAZ. and the upper mass cutoff al 120 M..., The lower mass cutoff was set at $M_{\odot }$ and the upper mass cutoff at 120 $M_{\odot }$. + For the purpose of the models presented here. the actual form of the assumed IMF is relatively unimportant in determining the final results. since the strength of the EUV field aud the metallicity of the gas prove to be more important than the shape of the ionizing spectrum in determining the EUV absorption bv dust.," For the purpose of the models presented here, the actual form of the assumed IMF is relatively unimportant in determining the final results, since the strength of the EUV field and the metallicity of the gas prove to be more important than the shape of the ionizing spectrum in determining the EUV absorption by dust." + Table 1 gives the abundance set used in (he models. and our assumed. gas-phase depletion factors.," Table 1 gives the abundance set used in the models, and our assumed gas-phase depletion factors." + These differ shehtly [rom the Dopita kewlev (2000) models because we have adopted the revised solar abundances for QO. C. Si and Fe (Asplund2000;Asplundetal.2000:AllendePrieto2001.2002).," These differ slightly from the Dopita Kewley (2000) models because we have adopted the revised solar abundances for O, C, Si and Fe \citep{Asplund00a, Asplund00b, Allende01, +Allende02}." +. In order to investigate tlie effects of ionization parameter. 4. aud the chemical abundanuces (which. effectively determines the gas-to-clust ratio). we ran three sets of models [or the abundances Z=0.4.1.0 and 2.0Z.. and covering a range of initial dimensionless ionization parameter from 4=0.000 up to 4—0.0066.," In order to investigate the effects of ionization parameter, ${\cal U}$, and the chemical abundances (which effectively determines the gas-to-dust ratio), we ran three sets of models for the abundances $Z=0.4, 1.0$ and $2.0Z_{\odot}$, and covering a range of initial dimensionless ionization parameter from ${\cal U} = 0.000$ up to ${\cal U} = 0.0066$." + This encompasses the full range that is normally encountered in range of ionization parameters encountered in bright rreelons (see Dopita Ixewlev. 2000).," This encompasses the full range that is normally encountered in range of ionization parameters encountered in bright regions (see Dopita Kewley, 2000)." + Each model had the chemical abundances of the central cluster set the same as for the gas in the rreeion., Each model had the chemical abundances of the central cluster set the same as for the gas in the region. + Ii spherical rreeion models. the spherical divergence of the radiation field ensures (hat the mean ionization parameter is not well defined when the rreeion becomes thick in comparison to its radius.," In spherical region models, the spherical divergence of the radiation field ensures that the mean ionization parameter is not well defined when the region becomes thick in comparison to its radius." + We have therefore ensured that the models remain geometrically thin with a well-defined 4 by raising the assumed hydrogen density from η—10 up to n=100 * for the models with the highest ionization parameter., We have therefore ensured that the models remain geometrically thin with a well-defined ${\cal U}$ by raising the assumed hydrogen density from $n = 10$ $^{-3}$ up to $n = 100$ $^{-3}$ for the models with the highest ionization parameter. + The absorption of the PAL molecules is very important in determining the EUV extinction. since (hev have a very. large absorption cross-section per carbon atom above 13.6 eV. Since we have no wav of directly determining whether such molecules survive in the rregion itself. we have run (wo sets of models. one which did not include PAIL-Iike molecules. and another in which we have set the abundance of PAIL molecules equivalent to of the total carbon atoms.," The absorption of the PAH molecules is very important in determining the EUV extinction, since they have a very large absorption cross-section per carbon atom above 13.6 eV. Since we have no way of directly determining whether such molecules survive in the region itself, we have run two sets of models, one which did not include PAH-like molecules, and another in which we have set the abundance of PAH molecules equivalent to of the total carbon atoms." + This is probably an overestimate of their (rue abundance. since only a maximum of of interstellar carbon is locked. up in carbonaceous grains (Duley&Seahra1999).. and studies of PAIL emission suggests that perhaps only about ol the interstellar carbon is actually locked up in PAL-like molecules (Li&Draine2002).," This is probably an overestimate of their true abundance, since only a maximum of of interstellar carbon is locked up in carbonaceous grains \citep{Duley99}, and studies of PAH emission suggests that perhaps only about of the interstellar carbon is actually locked up in PAH-like molecules \citep{ Li02}." +. For most models. we have also run a comparison dust-free rreeion model with (he same gas-phase abundances as in our dusty models in order both to check the absolute value of the dust-Iree IL5 recombination line flux. ancl to ensure that this is independent of (he ionization parameter for a eiven input spectrunm. as required by theory.," For most models, we have also run a comparison dust-free region model with the same gas-phase abundances as in our dusty models in order both to check the absolute value of the dust-free $\beta$ recombination line flux, and to ensure that this is independent of the ionization parameter for a given input spectrum, as required by theory." + We [find that. over the metallicity range covered by these models. the EUV blanketing of the central star cluster has very little effect on the number of Lyman continuum photons," We find that, over the metallicity range covered by these models, the EUV blanketing of the central star cluster has very little effect on the number of Lyman continuum photons" +data are important since it allows the reflection component an its strength to be properly fit. assessing its contribution lothe continuum and Wis region (e.g. Reeves et al.,"data are important since it allows the reflection component and its strength to be properly fit, assessing its contribution to the continuum and K region (e.g. Reeves et al." + 2007)., 2007). + Fiting features such as the Compton hump at 30 kkeV allows. for example. the ionization state of the rellecting maerial to be determined (Ross Fabian 2005).," Fitting features such as the Compton hump at $\sim30$ keV allows, for example, the ionization state of the reflecting material to be determined (Ross Fabian 2005)." + With the aim of measuring properties of the accretion disc and. the central black hole itself. broad-band data allows us to start making constraints on parameters in these regions based upon the shape of the kis line profile.," With the aim of measuring properties of the accretion disc and the central black hole itself, broad-band data allows us to start making constraints on parameters in these regions based upon the shape of the K line profile." + Previous studies of iron lines have been. mace using data from over the kkeV. (Nancdra et al., Previous studies of iron lines have been made using data from over the keV (Nandra et al. + 2007) and kkeV. energv. ranges (Brenneman Revnolds 2009). finding complex emission in the Why band in the majority of Type 1 Sevfert ACN over and above narrow line components originating from distant. material.," 2007) and keV energy ranges (Brenneman Reynolds 2009), finding complex emission in the K band in the majority of Type 1 Seyfert AGN over and above narrow line components originating from distant material." + In a sample of 26 objects Nandra et. al. (, In a sample of 26 objects Nandra et al. ( +2007). found that narrow kkeV. emission is ubiquitous amongst AGN and broad. Feds lines feature in ~40 of ΔΝ and ionized emission due to and is relatively rare amongst AGN.,2007) found that narrow keV emission is ubiquitous amongst AGN and broad K lines feature in $\sim$ of AGN and ionized emission due to and is relatively rare amongst AGN. + Brenneman Itevnolds (2009) found that 4/8. AGN were best fit bv à model consisting of relativistically blurred. reflection from the inner regions of the accretion disc wit1 2/8 objects suggesting non-zero spin. however noting that he kkeV. eutol with the EPIC-pn camera limis their findings of the reflection continum.," Brenneman Reynolds (2009) found that 4/8 AGN were best fit by a model consisting of relativistically blurred reflection from the inner regions of the accretion disc with 2/8 objects suggesting non-zero spin, however noting that the keV cutoff with the EPIC-pn camera limits their findings of the reflection continuum." + This small sample features predominantly bare Sevferts i.c. with a very weak warm absorber., This small sample features predominantly bare Seyferts i.e. with a very weak warm absorber. + This is in an attempt to simplify the modelling of the broad-band spectrum. and therefore. provide a basic understanding of the properties of the FelxIx region and any accompanying broad. rec-wing without the need for debate over differing interpretations of the origin of various absorption components in the spectrum. (Turner Miller. 2009)., This is in an attempt to simplify the modelling of the broad-band spectrum and therefore provide a basic understanding of the properties of the K region and any accompanying broad red-wing without the need for debate over differing interpretations of the origin of various absorption components in the spectrum (Turner Miller 2009). + Using data [roms. δις (Ixovama et al., Using data from XIS (Koyama et al. + 2007) and LIND (Takahashi ct al., 2007) and HXD (Takahashi et al. + 2007) detectors spanning kkeV. anc BAP cata (from the 22 month all sky survey. Tueller et al.," 2007) detectors spanning keV and BAT data (from the 22 month all sky survey, Tueller et al." + 2010) over LOOLOkkeV. provides the broad.band spectra necessary for detailed. modelling and measurement of the Felxlx region and the associated. Compton reflection hump., 2010) over keV provides the broad–band spectra necessary for detailed modelling and measurement of the K region and the associated Compton reflection hump. + This, This +Ixobavashi.S. Piran.T Sari. 1999. ApJ. 513. Ixobavashi.S Sari.R. 2000. ApJ. 542. Lamb.D. et al.,"Kobayashi,S, Piran,T Sari,R. 1999, ApJ, 513, Kobayashi,S Sari,R. 2000, ApJ, 542, Lamb,D. et al." + 2002. GCN Lazzali.D.. Rossi.E..Covino.s..Ghisellini.G Malesani.D. 2002. AA in press. Alalesani.D. et al.," 2002, GCN Lazzati,D., Rossi,E.,Covino,S.,Ghisellini,G Malesani,D. 2002, A in press, Malesani,D. et al." + 2002a. GCN Alalesani.D. et al.," 2002a, GCN Malesani,D. et al." + 2002b. GCN Matheson.T et al.," 2002b, GCN Matheson,T et al." + 2002. submitted to ApJL. Alasetti.N. et al.," 2002, submitted to ApJL, Masetti,N. et al." + 2002. GCN Alatsumoto. Yanmaoka.lI. 2002a. GCN AMatstumotosy. Ixasvai.N. 2002b. GCN Mésszárros.D. Rees.ALJ. 1997. ApJ. 476. IxXemp.J. 2002a. 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Aho,M. 2002, GCN During,D. 2002, GCN" +"τεςd,fe~ 107s in the CBM rest frame. and particles caught in the wake reach Lorentz factors upward of 7,~30.","$\tau_b \sim \delta_e/c \sim 10^{-4}$ s in the CBM rest frame, and particles caught in the wake reach Lorentz factors upward of $\gamma_e \sim 30$." +" Forwardly accelerated plasma — above the yellow line in — relaxes to |p-,|-Ec in a pace proportional to the burst duration. in order to counter-act the bulk backwards flow (the ""dip) initiated by the photons."," Forwardly accelerated plasma – above the yellow line in – relaxes to $\left|p_{z,e}\right| \sim +\pm m_ec$ in a pace proportional to the burst duration, in order to counter-act the bulk backwards flow (the 'dip') initiated by the photons." + The plasma undergoes violent accelerations. to maintain charge-neutrality.," The plasma undergoes violent accelerations, to maintain charge-neutrality." +". Burst photons keep the electron population ‘inflated’ as long as photon free energy and anisotropy is available in the plasma: far downstream the ""inflated"" non-thermal population lasts through the duration of our simulations.", Burst photons keep the electron population 'inflated' as long as photon free energy and anisotropy is available in the plasma; far downstream the 'inflated' non-thermal population lasts through the duration of our simulations. + The violent electrostatic acceleration of plasma electrons. due to the sharp gradient in photon pressure. will produce bremsstrahlung and synchrotron. photons.," The violent electrostatic acceleration of plasma electrons, due to the sharp gradient in photon pressure, will produce bremsstrahlung and synchrotron photons." + In. subsequent upscattering these photons will eventually also affect the spectrum. (Barbiellintet.al...2006)., In subsequent upscattering these photons will eventually also affect the spectrum \citep{bib:Barbiellini2006}. +.. More. importantly. millisecond variability could — in our assumed environment — arise directly from the enhanced density variations. scattering and possibly pair production (leading to higher densities and more scattering).," More importantly, millisecond variability could – in our assumed environment – arise directly from the enhanced density variations, scattering and possibly pair production (leading to higher densities and more scattering)." + Such a variability. which is comparable to the plasma frequency in a medium with density 25~10 cm — 10°em™. could therefore be self-feeding and grow in strength and duration.," Such a variability, which is comparable to the plasma frequency in a medium with density $n_0 \sim 10^{-1}$ cm $^{-3} - 10^0$ $^{-3}$, could therefore be self-feeding and grow in strength and duration." + We may be observing a weak seed to such spike in the spectrum at high energy. marked by the two pink arrows in3.," We may be observing a weak seed to such spike in the spectrum at high energy, marked by the two pink arrows in." +. Such photons spikes could facilitate pair production. and modify the GRB spectrum as the burst traverses the CBM.," Such photons spikes could facilitate pair production, and modify the GRB spectrum as the burst traverses the CBM." + Most intriguingly. we observe growth of a strong. large-scale magnetic field in the downstream wakefield gradient region.," Most intriguingly, we observe growth of a strong, large-scale magnetic field in the downstream wakefield gradient region." + The scenario is captured in4., The scenario is captured in. +".. A cross section of the 3D volume is shown for electrons. photons. ions and the transverse magnetic field. B, (top-to-bottom). for the 3D run described in Section 2."," A cross section of the 3D volume is shown for electrons, photons, ions and the transverse magnetic field, $B_\perp$ (top-to-bottom), for the 3D run described in Section 2." +" Barely visible in the electron population is the same electrostatic spiky structure that shows in2.. but somewhat weaker due comparatively higher density and lower resolution,"," Barely visible in the electron population is the same electrostatic spiky structure that shows in, but somewhat weaker due comparatively higher density and lower resolution." + From the ion density and electron density panels it is seen that both species undergo instability to form confluent filaments m the plasma (although the inertia difference plays a role)., From the ion density and electron density panels it is seen that both species undergo instability to form confluent filaments in the plasma (although the inertia difference plays a role). + The filamentation build-up is initiated by fluctuating EM fields in CBM plasma ahead of the burst., The filamentation build-up is initiated by fluctuating EM fields in CBM plasma ahead of the burst. + As described in Section ??.. the plasma forms a two-stream anisotropy in reaction to the burst forcing.," As described in Section \ref{subsect:wake-effects}, the plasma forms a two-stream anisotropy in reaction to the burst forcing." + The fastest growing instability in this case Is the two-stream filamentation mode — tantamount to the Weibel instability (Weibel1959) — which produces quasi-static magnetic fields., The fastest growing instability in this case is the two-stream filamentation mode – tantamount to the Weibel instability \citep{bib:Weibel1959} – which produces quasi-static magnetic fields. + The effect is self-sustaining as long as the photon momentum anisotropy Is sufficiently high., The effect is self-sustaining as long as the photon momentum anisotropy is sufficiently high. +" Furthermore. ponderomotive particle forcing. F,x-qiuurVE. is likely to be active in the strongly oscillatory wakefield plasma."," Furthermore, ponderomotive particle forcing, ${\bf F}_p \propto -{q_e^2} {(m\omega)}^{-1} \nabla{\bf E}^2$, is likely to be active in the strongly oscillatory wakefield plasma." + This drift force is independent of the charge sign: both electrons and ions drift in the same manner., This drift force is independent of the charge sign; both electrons and ions drift in the same manner. + Such effects has been reported by other authors (Hoshino2008;Liang&Noguchi2007) to being responsible for the acceleration of particles due to forcing by Poynting flux pulses.," Such effects has been reported by other authors \citep{bib:Hoshino2008,bib:Liang2007} to being responsible for the acceleration of particles due to forcing by Poynting flux pulses." + The nature of the plasma forcing by these authors. contrasts our foreing.," The nature of the plasma forcing by these authors, contrasts our forcing." + Determining how the magnetic field will decay is a challenge yet to be met: modeling a larger plasma volume is necessary to determine the ultimate temporal and spatial development., Determining how the magnetic field will decay is a challenge yet to be met; modeling a larger plasma volume is necessary to determine the ultimate temporal and spatial development. + Resorting to lower-dimensional models will not solve the problem: the instability is inherently 3D in nature and cannot develop realistically in lower dimensions (cf.Frederiksenetal.2004)., Resorting to lower-dimensional models will not solve the problem; the instability is inherently 3D in nature and cannot develop realistically in lower dimensions \citep[cf.][]{bib:Frederiksen2004}. +. We also observe in that filaments. current structures and field scales are limited by the computational volume -- 1.e. they are “boxed-in’.," We also observe in that filaments, current structures and field scales are limited by the computational volume – i.e. they are 'boxed-in'." + Nonetheless.," Nonetheless," +As a result. (he partition function can be written as where By inserting Cpants) from equation (43)) into equation (40)). one can see (hat CI(8) satisfies (he following differential equations for p=0. and [or p>0. The value of [V(0)) is determined by anchoring the DNA hence independent ol A.,"As a result, the partition function can be written as where By inserting $C_{n,k,m}(s)$ from equation \ref{Cexpand}) ) into equation \ref{difeq2}) ), one can see that $C^{\,(p)}_{n,0,0}(s)$ satisfies the following differential equations for $p=0$, and for $p>0$ The value of $|\Psi (0)\rangle$ is determined by anchoring the DNA hence independent of $\lambda$." +" Thus the corresponding initial conditions are It can be seen from. equation. (46))NN that Co,-(0) is. constant Therefore. (he partition function to the zeroth order of A is given by where Z! is the partition [unction of an isotropic DNA with bending constant cl. "," Thus the corresponding initial conditions are It can be seen from equation \ref{Cdot0}) ) that $C^{\,(0)}_{n,\,k,\,m}$ is constant Therefore, the partition function to the zeroth order of $\lambda$ is given by where $Z^{(\,0)}$ is the partition function of an isotropic DNA with bending constant $A$ " +Variable stars in globular clusters (particularly binaries) play an important role in understanding cluster dvnamical evolution.,Variable stars in globular clusters (particularly binaries) play an important role in understanding cluster dynamical evolution. + Despite this. such clusters have seldom been the (targets of detailed study for the presence of variables. mainlv due (o the difficulty in obtaining accurate photometry from the ground of faint stars in very. crowded fields.," Despite this, such clusters have seldom been the targets of detailed study for the presence of variables, mainly due to the difficulty in obtaining accurate photometry from the ground of faint stars in very crowded fields." + Due to technological advances in recent vears. however. the number of clusters studied and the list of variable stars discovered has increased dramatically.," Due to technological advances in recent years, however, the number of clusters studied and the list of variable stars discovered has increased dramatically." + As a general overview ol the field. those major clusters investigated recently include Omega Centauri al.1996.1997:Ilaggardet 2003).. M5 (Yan&Reid1996).. MIT] (Yan&Mateo 1994).. M4 (Ialuzuy.Thompson.&Ixrzeminski 1997).. NGC6397 (Ixaluznv.1997)... M22 (Pietrukowiez&Kaluzny 2003).. NGC6946 (Guldenschuh.Lavden.Weleh.&Webb 2003).. AI69 (Gregorsok.Lavden.Weleh.&Webb2003).. M15 (Zheleznvak&Kravisov 2003).. MI3 (Ixopacki.IXolaczkowski.&Pigulski2003) ancl M23 (Strader.Everitt.&Danford2002).," As a general overview of the field, those major clusters investigated recently include Omega Centauri \citep{Kal96,Kal97,Hag03}, , M5 \citep{YR96}, M71 \citep{YM94}, M4 \citep{KTK97}, , NGC6397 \citep{K97}, M22 \citep{Piet03}, , NGC6946 \citep{Guld03}, , M69 \citep{Gregorsok03}, M15 \citep{Zhel03}, , M13 \citep{Kopacki03} and M3 \citep{Strader02}." +. Yan&Cohen(1996). discovered six spectroscopic binaries in NGC5053., \citet{YC96} discovered six spectroscopic binaries in NGC5053. + Clement(2001) and Int(1996) review recent and more historical studies into globular variables., \citet{Clement01} and \citet{H96} review recent and more historical studies into globular variables. + A [ew previous survevs have searched for variable stars in 47 Tuc., A few previous surveys have searched for variable stars in 47 Tuc. + SawyerΠοσο(1973) discovered (wo variables., \citet{Hogg73} discovered two variables. + Edmondsetal.(1996):Eclimonds&Gilliland(1996) used a LIST dataset to detect 75 variable stars. including Eclipsing Binaries and variability among ]x-giants.," \citet{Edmonds96a,Edmonds96b} used a HST dataset to detect 75 variable stars, including Eclipsing Binaries and variability among K-giants." + Albrowοἱal.(2001) uncovered 107 variable stars. the largest number to date. and derived an overall binaryfrequency of 1476235476using the sameIST datasetas Gilliland to search for Hot Jupiter planetsin the cluster.," \citet{Alb01} uncovered 107 variable stars, the largest number to date, and derived an overall binaryfrequency of $\%\pm$ $\%$using the sameHST datasetas \citet{Gil2000} to search for Hot Jupiter planetsin the cluster." + Naluzuyetal.(1993). performed, \citet{Kal98} performed +Iu the framework of hierarchical clustering. the Universe is believed to be iade of galaxies distributed iu sheets encircliug voids or flaments. at the intersection of which clusters of galaxies are located.,"In the framework of hierarchical clustering, the Universe is believed to be made of galaxies distributed in sheets encircling voids or filaments, at the intersection of which clusters of galaxies are located." + Such models can be tested through the aualvsis of clusters. which are likely to keep a “inemory” of their formation.," Such models can be tested through the analysis of clusters, which are likely to keep a “memory” of their formation." + This is suggested for example bv the alignment effects observed in sole clusters. such as for example Abell 3558 (Dautas ct al.," This is suggested for example by the alignment effects observed in some clusters, such as for example Abell 3558 (Dantas et al." + 1997) or Abell 85 (Durret et al., 1997) or Abell 85 (Durret et al. + 1998). where the ¢D. tle brightest galaxies. the X-ray enutting eas aud possibly even larger scale structures (n the case of Abell 85) all appear alieued along the same direction.," 1998), where the cD, the brightest galaxies, the X-ray emitting gas and possibly even larger scale structures (in the case of Abell 85) all appear aligned along the same direction." + Multi-vaveleusth studies of clusters of galaxies also allow us to draw a elobal and coherent portrait of these objects. which we can then use to address other questions of interest. such as the influence of merecrs and environmental effects at various scales on the properties of both ealaxics aud N-rax eas.," Multi-wavelength studies of clusters of galaxies also allow us to draw a global and coherent portrait of these objects, which we can then use to address other questions of interest, such as the influence of mergers and environmental effects at various scales on the properties of both galaxies and X-ray gas." + Large scale (1.0. cluster size) niergers are quite ofte- observed from) substructures detected im the X-raw eas: smaller scale mergers (1e. group size) such as the iufall of dwarf galaxies onto groups surrounding bright ealaxies cau be derived frou various methods such as those of Serna Cerbal (1996) or ανα Mazure (1998). which require optical velocity aud magnitude catalogues: the existence of subclustering also has an influence on the shape of the ealaxy luminosity function. which iu sole cases appears to show a deficit of faint salaxies often interpreted as due to accretion of dwarf galaxies outo larger galaxies or groups (e.g. iu Coma. Lobo et al.," Large scale (i.e. cluster size) mergers are quite often observed from substructures detected in the X-ray gas; smaller scale mergers (i.e. group size) such as the infall of dwarf galaxies onto groups surrounding bright galaxies can be derived from various methods such as those of Serna Gerbal (1996) or Gurzadyan Mazure (1998), which require optical velocity and magnitude catalogues; the existence of subclustering also has an influence on the shape of the galaxy luminosity function, which in some cases appears to show a deficit of faint galaxies often interpreted as due to accretion of dwarf galaxies onto larger galaxies or groups (e.g. in Coma, Lobo et al." + 1997. Adaini ct al.," 1997, Adami et al." + 2000)., 2000). + It therefore appears importaut to analyze cluster properties in detail before using them in other studies., It therefore appears important to analyze cluster properties in detail before using them in other studies. + Note iu particulary that the existence, Note in particular that the existence +the maximum value of agwgA increases with (EWHA).,the maximum value of $\sigma_{EWHA}$ increases with $\langle$ $\rangle$. +" As noted above, the absolute equivalent width values depend on spectral type due to the changing continuum flux near Ho, with earlier type stars having relatively smaller equivalent width due to their higher continuum flux."," As noted above, the absolute equivalent width values depend on spectral type due to the changing continuum flux near $\alpha$, with earlier type stars having relatively smaller equivalent width due to their higher continuum flux." + We illustrate this effect in Figure 5bb using the fractional variability metric ogwgA/(EWHA)., We illustrate this effect in Figure \ref{sigmaewha}b b using the fractional variability metric $\sigma_{EWHA}/\langle$ $\rangle$. +" The skewed nature of the o distributions at a given evident in Figure 5aa (and analogous to the (EWHA),skewed distributions in Rew shown in Figure 4)), again leads us to use the median value to characterize eEWHA/(EWHA) for each (EWHA) bin."," The skewed nature of the $\sigma$ distributions at a given $\langle$ $\rangle$, evident in Figure \ref{sigmaewha}a a (and analogous to the skewed distributions in $R_{EW}$ shown in Figure \ref{maxmin}) ), again leads us to use the median value to characterize $\sigma_{EWHA}/\langle$ $\rangle$ for each $\langle$ $\rangle$ bin." +" The spectral type dependence of is clearly indicated by the separation of the early (EWHA)(M0-M32, green squares), mid (M3-M5, purple diamonds) and late (M6—M9, red crosses) types for the SDSS sample."," The spectral type dependence of $\langle$ $\rangle$ is clearly indicated by the separation of the early (M0–M2, green squares), mid (M3–M5, purple diamonds) and late (M6--M9, red crosses) types for the SDSS sample." + The median values for all spectral types are shown as black ogw#a/(EWHA)asterisks (SDSS) and blue filled circles (Hydra)., The median $\sigma_{EWHA}/\langle$ $\rangle$ values for all spectral types are shown as black asterisks (SDSS) and blue filled circles (Hydra). + The variability metric decreases with increasing (EWHA) from ~0.2 for stars with low EWHA to ~0.14 for stars with (EWHA)> 5À.., The variability metric decreases with increasing $\langle$ $\rangle$ from $\sim$ 0.2 for stars with low EWHA to $\sim$ 0.14 for stars with $\langle$ $\rangle>5$ . + A better measure of magnetic activity strength that accounts for the continuum dependence on spectral type is Lua/Loo., A better measure of magnetic activity strength that accounts for the continuum dependence on spectral type is $_{\rm{H}\alpha}$ $_{bol}$ . +" Figure 6 illustrates the same fractional variability metric ogwaa/(EWHA) as in Figure 5bb, versus activity strength."," Figure \ref{lhalbol} illustrates the same fractional variability metric $\sigma_{EWHA}/\langle$ $\rangle$ as in Figure \ref{sigmaewha}b b, versus activity strength." +" The spectral types are no longer separated; in fact the three spectral type groups from Figure 5bb, have shifted horizontally so that they now overlap and form a smooth distribution."," The spectral types are no longer separated; in fact the three spectral type groups from Figure \ref{sigmaewha}b b, have shifted horizontally so that they now overlap and form a smooth distribution." + It is clear that the underlying variability relationship is not a function of spectral type but rather of activity strength., It is clear that the underlying variability relationship is not a function of spectral type but rather of activity strength. +" However, the median fractional variability (black asterisks)decreases with increasing activity from ~0.3 at log(Lua/Lso) —4.5 to ~0.1 at log(Luo/L»o) —3.5."," However, the median fractional variability (black asterisks) with increasing activity from $\sim$ 0.3 at $_{\rm{H}\alpha}$ $_{bol})\sim-4.5$ to $\sim$ 0.1 at $\log($ $_{\rm{H}\alpha}$ $_{bol}) +\sim-3.5$." +" The median value for the variability metric across the entire sample is 0.16, shown as the dashed line on the Figure."," The median value for the variability metric across the entire sample is 0.16, shown as the dashed line on the Figure." +" The Hydra data filled circles) in Figures 5bb and 6 show relatively flat (bluedistributions that are influenced by small numbers, uneven spectral type sampling, and a bias toward very active stars especially at early spectral types (due to the Ha—R color selection of the targets)."," The Hydra data (blue filled circles) in Figures \ref{sigmaewha}b b and \ref{lhalbol} show relatively flat distributions that are influenced by small numbers, uneven spectral type sampling, and a bias toward very active stars especially at early spectral types (due to the $\alpha-R$ color selection of the targets)." +" 'Therefore, they are not as useful as the SDSS data for understanding the behavior of the variability metric with activity strength."," Therefore, they are not as useful as the SDSS data for understanding the behavior of the variability metric with activity strength." + The picture we have developed is that highly active stars of all spectral types are relatively less variable than low activity stars., The picture we have developed is that highly active stars of all spectral types are relatively less variable than low activity stars. +" This only becomes evident when the well-known underlying relationship between activity strength and spectral type is removed, as in Figure 6.."," This only becomes evident when the well-known underlying relationship between activity strength and spectral type is removed, as in Figure \ref{lhalbol}." +" Physically, the strong level of persistent emission in the high activity stars may be due to a large surface coverage of active regions, while the low activity stars may have relatively smaller filling factor."," Physically, the strong level of persistent emission in the high activity stars may be due to a large surface coverage of active regions, while the low activity stars may have a relatively smaller filling factor." +" An increase in Ha emission,a for example due to a new active region appearing on the surface, or a magnetic heating episode or microflare in one of the existing active regions, will then manifest as barely visible in the more active star, while it willcontributesignificant new emission in the"," An increase in $\alpha$ emission, for example due to a new active region appearing on the surface, or a magnetic heating episode or microflare in one of the existing active regions, will then manifest as barely visible in the more active star, while it willcontributesignificant new emission in the" +along the radial direction of /;. ant its densitv is fy larger (han the ambient wind density fw=Alyο ,"along the radial direction of $l_b$, ant its density is $k_b$ larger than the ambient wind density $\rho_w=\dot M_w/4 \pi r^2 v_w$." +"The gravitational force on the blob is where AZ, is the mass of the central star.", The gravitational force on the blob is where $M_\ast$ is the mass of the central star. + I assume that the blob is dense and large enough such that most of the radiation is absorbed by the dusty blob. such that the force due to radiation pressure is The condition for the blob to fall back is Fy>Fraa.," I assume that the blob is dense and large enough such that most of the radiation is absorbed by the dusty blob, such that the force due to radiation pressure is The condition for the blob to fall back is $F_g > F_{\rm rad}$." + Scaling the expression Lor the forces gives the fall back condition in the form Models that assume clumps exist in the literature., Scaling the expression for the forces gives the fall back condition in the form Models that assume clumps exist in the literature. + Lopez et al. (, Lopez et al. ( +"1997). for example. considered a model where dusty clumps denser by a factor of ~LOO than their environment exist al 50AU from Mira A. They didn't consider the dynamical evolution of the elumps. but rather assume their existence to explain the IR emission of Mira. A. Mira A has a mass loss rate of M,cfewxLOTAL.vro (Ryde Schéiier 2001). much lower than the scaling value used here.","1997), for example, considered a model where dusty clumps denser by a factor of $\sim 100$ than their environment exist at $50 \AU$ from Mira A. They didn't consider the dynamical evolution of the clumps, but rather assume their existence to explain the IR emission of Mira A. Mira A has a mass loss rate of $\dot M_w \simeq {\rm few} \times 10^{-7} M_\odot \yr^{-1}$ (Ryde Schöiier 2001), much lower than the scaling value used here." + Still. the extended region above Mira. A has clumps and it is turbulence (e.g.. Rvede Schoiier 2001). as discussed in section 1.," Still, the extended region above Mira A has clumps and it is turbulence (e.g., Ryde Schöiier 2001), as discussed in section 1." +" Therefore. it is quite possible that {he elfervescent model proposed here applies also to strongly pulsating AGB stars even when their mass loss rate is M,<10PAL,vr|."," Therefore, it is quite possible that the effervescent model proposed here applies also to strongly pulsating AGB stars even when their mass loss rate is $ \dot M_w \ll 10^{-5} M_\odot \yr^{-1}$." +" For example. if 0,75kms.| and hy~100 in Mira A. Dense clumps have larger pressure (han (heir environment. and thev expand."," For example, if $v_w \sim 5 \km \s^{-1}$ and $k_B \sim 100$ in Mira A. Dense clumps have larger pressure than their environment, and they expand." + Therefore. very clense clump are losing mass aud become smaller.," Therefore, very dense clump are losing mass and become smaller." + When the wind mass loss rate is very high and the wind is slow. then for the blob to fall back it is sufficient. [or it to be only slightly denser (han the environment.," When the wind mass loss rate is very high and the wind is slow, then for the blob to fall back it is sufficient for it to be only slightly denser than the environment." + In any case. the effervescent zone will be extended to a radius of fi[ewxR(r=1). where R(r=1) is the radius where the optical depth is T=1 according to equation 2.," In any case, the effervescent zone will be extended to a radius of $R_{e} \sim {\rm few} \times R({\tau=1})$, where $R({\tau=1})$ is the radius where the optical depth is $\tau=1$ according to equation $\ref{tau1}$." + In cases of strong magnetic activity. e.g.. as proposed for Mira A. the elfervescent zone might exist even for optically thin wind. because magnetic activity. e.&.. [lares and cool magnetic spots. might also eject material from the AGB star.," In cases of strong magnetic activity, e.g., as proposed for Mira A, the effervescent zone might exist even for optically thin wind, because magnetic activity, e.g., flares and cool magnetic spots, might also eject material from the AGB star." +"accreting neutron stars in N-rav binaries when one looks at pulse period. pulsed fraction aud pulse duty evcle (ο,ος, Norton Watson 1989). the pulsed. fraction of IPs. if nieasured. always increases to lower photon energies.","accreting neutron stars in X-ray binaries when one looks at pulse period, pulsed fraction and pulse duty cycle (e.g., Norton Watson 1989), the pulsed fraction of IPs, if measured, always increases to lower photon energies." + This is opposite to what we see in1515., This is opposite to what we see in. +". Secoud. the Galactic latitude of lis snadl which is consistent with, ne distribution of IIMXND mulsars along the plane. iu contrast with IPs which are distributed homogeneously across the sky beiue relatively ucarby)."," Second, the Galactic latitude of is small which is consistent with the distribution of HMXB pulsars along the plane, in contrast with IPs which are distributed homogeneously across the sky (being relatively nearby)." + If bbelougs to the TAINB pulsar eroup. its trausicut nature places it in the subgroup of IIMNDs with Oc or Be cColmpalion stars.," If belongs to the HMXB pulsar group, its transient nature places it in the subgroup of HMXBs with Oe or Be companion stars." + A voung object like au carly D type star is ucarly always fouud close to its birthplace., A young object like an early B type star is nearly always found close to its birthplace. + Iu the liue of sieht of tthree potential places of recent star formation are within our ealaxy: 16 OB association (νο OBT at approximately TOO pe (Dame Thaddeus 1985). the Perseus aru at i»proxinatelv [pe (e.g.. Vost Moffat 1975. Ceoreclin Coorecliu 1976) aud the III Cveuus arn at about 1l kpe (νι. Blitz Iciles 1982).," In the line of sight of three potential places of recent star formation are within our galaxy: the OB association Cyg OB7 at approximately 700 pc (Dame Thaddeus 1985), the Perseus arm at approximately 4 kpc (e.g., Vogt Moffat 1975, Georgelin Georgelin 1976) and the HI Cygnus arm at about 11 kpc (Kulkarni, Blitz Heiles 1982)." +" A peal. flux of SNIO Mere ὃν + implies respecive Iuiiinosities of DOM, L8s1079 and 1.3&LO ere st for these three locations."," A peak flux of $8.8\times10^{-10}$ erg $^{-2}$ $^{-1}$ implies respective luminosities of $5\times10^{34}$, $1.7\times10^{36}$ and $1.3\times10^{37}$ erg $^{-1}$ for these three locations." + All of these values are consistent with the Be Xoaay binary interpretation ofΓΙ., All of these values are consistent with the Be X-ray binary interpretation of. +.. Au optical identification is suggestedOO |x the appareut proxiuitv to ΠΟ 200709., An optical identification is suggested by the apparent proximity to HD 200709. + For a main sequence Ba star. the absolute visual magnitude AA is 0.0 (Allen 1973).," For a main sequence B8 star, the absolute visual magnitude $M_{\rm V}$ is 0.0 (Allen 1973)." + Reeardless of extinction. au apparent visual magnitude of mx=9.21 iuplies au upper huit to the distance of «107 pe.," Regardless of extinction, an apparent visual magnitude of $m_{\rm V}=9.21$ implies an upper limit to the distance of $7\times10^2$ pc." + This distance appears to be consistent. with a imembership of WD 200709 to Cve OB7 although it las uot been recognize as such vet., This distance appears to be consistent with a membership of HD 200709 to Cyg OB7 although it has not been recognized as such yet. +" TD 200709 is not a very eood calidate coiiterpart for two reasons: tle positional coincidence is mareinal and it is not recognized as au Cluission type star as ds conuuon for transient Πλ», although it should be noted that the spectral classification appears to be based on iuultibaud photometry only (Douiet 1959)."," HD 200709 is not a very good candidate counterpart for two reasons: the positional coincidence is marginal and it is not recognized as an emission type star as is common for transient HMXBs, although it should be noted that the spectral classification appears to be based on multiband photometry only (Bouigue 1959)." + Corl (1986) discovered a relationship for Be X-ray binaries between pulse period and orbital period., Corbet (1986) discovered a relationship for Be X-ray binaries between pulse period and orbital period. + For a pulse period of 358.61 s this προς au orbita period of ~190 d. No evidence was found for a modulation iu the A-rav cluission with this period iu the WFC data., For a pulse period of $358.61$ s this implies an orbital period of $\sim$ 190 d. No evidence was found for a modulation in the X-ray emission with this period in the WFC data. + The pulse period gives a lower limi to the uuinositv hrough the propeller effect (c.g Tlavionoy Suuvaev 1975).," The pulse period gives a lower limit to the luminosity through the propeller effect (e.g., Illarionov Sunyaev 1975)." + Tf the Αντόν radius is lareer than the co-rotation radius (this is the location where the ERKepleriau oxdod is equal to that of the neutron star). iufalliug uatter is prevented from euteriug the magnetosphere vecatise of centrifugal forces. and accretion through the naguctosplere onto the neutron star poles is impossible.," If the Alfvénn radius is larger than the co-rotation radius (this is the location where the Keplerian period is equal to that of the neutron star), infalling matter is prevented from entering the magnetosphere because of centrifugal forces, and accretion through the magnetosphere onto the neutron star poles is impossible." +" Tn the case of spherical accretion the lower limit to the ""nnumositv becomes: LynLx--lovDLPaonUS ore 1 (Campana ct al.", In the case of spherical accretion the lower limit to the luminosity becomes: $L_{\rm min}=4\times 10^{37} B_{12}^2 P^{-7/3}$ erg $^{-1}$ (Campana et al. + 1998) where P is the spin period iu s and Z4» the neutron star magnetic feld in units of 1012 C. Standard neutron star values ire asned here for radius (10° cmi) aud mass (1.1 M)., 1998) where $P$ is the spin period in s and $B_{12}$ the neutron star magnetic field in units of $10^{12}$ G. Standard neutron star values are assumed here for radius $10^6$ cm) and mass (1.4 $_\odot$ ). + For a magnetic field of B—10h C aud a period of 358.61 s this gives Lu=5107 cre period.1., For a magnetic field of $B=10^{12}$ G and a period of 358.61 s this gives $L_{\rm min}=5\times 10^{31}$ erg $^{-1}$. + This is not very constraimiue. due to the loug pulse ," This is not very constraining, due to the long pulse period." +To determine whether the measured upper huit on the pulse period derivative is mecauineful. we calculated what maximuun derivative is expected when the accreted matter deposits all of its angular momentiun at the magnetospheric boundary aud the magnetic field lues transport this momentum to the neutron star.," To determine whether the measured upper limit on the pulse period derivative is meaningful, we calculated what maximum derivative is expected when the accreted matter deposits all of its angular momentum at the magnetospheric boundary and the magnetic field lines transport this momentum to the neutron star." + Using the expression for the Alfvéóun radius by Chosh Lamb (1991) for spherical accretion ancl assuniüug standard values for the neutron star magnetic Ποια. Πο ΕΜ of inertia (107 οe cn?) and radius. the spin period derivative is given by dP/dt—Li«10ILUP?," Using the expression for the Alfvénn radius by Ghosh Lamb (1991) for spherical accretion and assuming standard values for the neutron star magnetic field, mass, moment of inertia $^{45}$ g $^2$ ), and radius, the spin period derivative is given by ${\rm d}P/{\rm d}t=4.1\times10^{-44}L^{6/7}P^2$." + For the three huninosities given above. this derivative indicates a period clhauge over 23 days of |AP|=0.006. 0.1 and (8s. The last possibility is excluded by our observations which means that either the source is not at that distance or the change of augular uonieuntuni is not as hieh.," For the three luminosities given above, this derivative indicates a period change over 23 days of $|\Delta P|=0.006$, 0.1 and 0.8 s. The last possibility is excluded by our observations which means that either the source is not at that distance or the change of angular momentum is not as high." + We conclude that our upper Iit for the period derivative is iot constrainieg., We conclude that our upper limit for the period derivative is not constraining. +There is a growing interest in trying to identify the mechanisms driving galaxy evolution in different kinds of environments. [rom cluster cores to their outskirts and bevond. i.e. in what is commonly called the “field” (LewisGomezetal. 2003).,"There is a growing interest in trying to identify the mechanisms driving galaxy evolution in different kinds of environments, from cluster cores to their outskirts and beyond, i.e. in what is commonly called the “field"" \citep{lew02,bal03,gom03}." +. Dynamical analysis and n-body simulations (Barnes1990:Bocleetal.1994:Mooreal.1998:Dubinski1993:Mihos1999) predict Chat galaxies closer Chan a few hall-leht radii. whether in a group or a rich cluster of galaxies. are likely to merge within short timescales.," Dynamical analysis and -body simulations \citep{bar90,bod94,moo98,dub98,Mihos99} predict that galaxies closer than a few half-light radii, whether in a group or a rich cluster of galaxies, are likely to merge within short timescales." + Simulations also predict a merger remnant to display a rl! profile: NGC 1132. an isolated elliptical with extended X.ray diffuse emission (Mulehaey&Zabludoff1999).. could actually represent (he prototypical example of the final evolution of all smallscale dense svstems (Wikhlininetal.1999:Jones2003:Stocke2003).," Simulations also predict a merger remnant to display a $r^{1/4}$ profile: NGC 1132, an isolated elliptical with extended X–ray diffuse emission \citep{mul99}, could actually represent the prototypical example of the final evolution of all small–scale dense systems \citep{vik99,jon03,sto03}." +. Several arguments indicate however that the chemical. dynamical and photometrical parameters of massive ellipticals are nol compatible with their formation being the result of several major merging events diluted along the IInbble time (Mezaοἱal.2003:Thomaset2004).," Several arguments indicate however that the chemical, dynamical and photometrical parameters of massive ellipticals are not compatible with their formation being the result of several major merging events diluted along the Hubble time \citep{mez03,tho04}." +. On the observational side. (here is surely good evidence of mergers at low redshift. but spectacular svstems such," On the observational side, there is surely good evidence of mergers at low redshift, but spectacular systems such" +Otherwise. some photon trajectories may pass through both sides of a slat. but not the top or bottom faces. which the advanced formula docs not describe.,"Otherwise, some photon trajectories may pass through both sides of a slat, but not the top or bottom faces, which the advanced formula does not describe." + Sinularly. if we define a parameter f(f) as the time-dependent cistance from the outermost edge of one slat shadow to the next (see Fig. 5)).," Similarly, if we define a parameter $b'(t)$ as the time-dependent distance from the outermost edge of one slat shadow to the next (see Fig. \ref{fig:advanced}) )," + then we must also cusure that τή{δή20: else. Uluuination of the detector may never be achieved.," then we must also ensure that $\mbox{min}\{b'(t)\} \ge 0$; else, illumination of the detector may never be achieved." + These two requirements provide a constraimt on the ecolmetry of tle mask subject to the FOV. θεον.. of the instrument: We perform Monte Carlo simulations with various instrument ecometrics aud compare the results with the profiles derived frou. the advanced aud. where suitable. the standard count rate formulae.," These two requirements provide a constraint on the geometry of the mask subject to the FOV, $\theta_{FOV}$, of the instrument: We perform Monte Carlo simulations with various instrument geometries and compare the results with the profiles derived from the advanced and, where suitable, the standard count rate formulae." + For the results described below (uuless otherwise indicated). a lead mask (p=11.31 e/cm?) is suspended L=1 ii above the detection plane.," For the results described below (unless otherwise indicated), a lead mask $\rho = 11.34$ $^3$ ) is suspended $L = 1$ m above the detection plane." + Monoenergetie 662 keV photons have a total mass attenuation of c=0.108 cu? /e., Monoenergetic 662 keV photons have a total mass attenuation of $\sigma = 0.103$ $^2$ /g. + Results are computed for various colmbinations of e. b. aud c.," Results are computed for various combinations of $a$, $b$, and $c$." + Dackground is assuned to be zero. aud onlv photopeak eveuts are included in the aualvsis.," Background is assumed to be zero, and only photopeak events are included in the analysis." + Additional mask ecometry and source paralcters are selected for cach scenario individually to demonstrate a particular advantage of the advanced formula., Additional mask geometry and source parameters are selected for each scenario individually to demonstrate a particular advantage of the advanced formula. + For a direct. comparison of the computational expcusc for the advanced versus the standard formula. iustruncutl response functions are calculated using both solutions for an RM with a L7 ΕΟΝ divided iuto 12’ field bius (1900 elements) aud. count profiles broken up iuto 560 time bius.," For a direct comparison of the computational expense for the advanced versus the standard formula, instrument response functions are calculated using both solutions for an RM with a $^{\circ}$ FOV divided into $'$ field bins (4900 elements) and count profiles broken up into 560 time bins." + The caleulatious are performed using IDL 6.3 on a Windows machine., The calculations are performed using IDL 6.3 on a Windows machine. + The standard formula computes the mstrineut response (one profile per sky bin) iu 0.5 s for cach detector., The standard formula computes the instrument response (one profile per sky bin) in 0.8 s for each detector. +" The advanced formmla. ignoring the Gy tenu. takes 2.6 s, while inclusion of the approximated Gy term increases the time to 5.1 s. The processing time is still many orders of magnitude shorter than that required to determine the instrument response using a Monte Carlo simulation."," The advanced formula, ignoring the $G_1$ term, takes 2.6 s, while inclusion of the approximated $\widetilde{G_1}$ term increases the time to 5.4 s. The processing time is still many orders of magnitude shorter than that required to determine the instrument response using a Monte Carlo simulation." + If we require a signal-to-noise ratio of 10 per time bin to derive a Monte Carlo profile that is suitable for the purposes of image reconstruction. the intrument response for a single detector would take almost 1.3 davs to compute.," If we require a signal-to-noise ratio of 10 per time bin to derive a Monte Carlo profile that is suitable for the purposes of image reconstruction, the intrument response for a single detector would take almost 1.3 days to compute." +in our sample.,in our sample. + There are the ones with normal (round) bulges and the ones that look like they are undergoing some heavy evolution with blue rings and bars., There are the ones with normal (round) bulges and the ones that look like they are undergoing some heavy evolution with blue rings and bars. + But besides appearance no systematic differences show up in the rest of their investigated properties., But besides appearance no systematic differences show up in the rest of their investigated properties. + It remains unclear whether the bulge formed before or after the disk., It remains unclear whether the bulge formed before or after the disk. + More observations are needed to resolve this issue., More observations are needed to resolve this issue. + We did not find any systematic differences in structural parameters or colors of the bulges between LSB and HSB galaxies., We did not find any systematic differences in structural parameters or colors of the bulges between LSB and HSB galaxies. +" To unravel the evolutionary history of bulge dominated LSB galaxies we need additional information on content and distribution, and chemical abundance information."," To unravel the evolutionary history of bulge dominated LSB galaxies we need additional information on content and distribution, and chemical abundance information." + Our sample has extended the fact that LSB galaxies cover a wide range in color. luminosity. size and morphology.," Our sample has extended the fact that LSB galaxies cover a wide range in color, luminosity, size and morphology." + The bulge dominated LSB galaxies fit in with the general trends defined by their HSB counterparts., The bulge dominated LSB galaxies fit in with the general trends defined by their HSB counterparts. +"for calculating (he reverse rate coelficient from the forward rate coefficient: for T in kelvins. and where n, and n, are the nunbers of products and reactants. respectively. in the forward reaction.","for calculating the reverse rate coefficient from the forward rate coefficient: for $T$ in kelvins, and where $n_{p}$ and $n_{r}$ are the numbers of products and reactants, respectively, in the forward reaction." +" Note (hat in cases where (he number of products equals (he number of reactantsοι, when ny—n,=0). the pressure-correction term becomes unity and hp=Negg/l as in equation (6))."," Note that in cases where the number of products equals the number of reactants, when $n_{p}-n_{r}=0$ ), the pressure-correction term becomes unity and $K_{P}=K_{eq}=k_{f}/k_{r}$, as in equation \ref{eq:reversibility}) )." +" For three-body (termolecular) reactions. the forward rate coelficient used in equation (12)) can be obtained fom experimental or theoretical data at appropriate temperatures and pressures. and A, can then be determined from the above procedure at each point along the atmospheric grid."," For three-body (termolecular) reactions, the forward rate coefficient $k_{f}$ used in equation \ref{eq:reversal}) ) can be obtained from experimental or theoretical data at appropriate temperatures and pressures, and $k_r$ can then be determined from the above procedure at each temperature-pressure point along the atmospheric grid." + 1 7; has not been measured at each P-T. point along the grid. as is often the case. approximate expressions can be used.," If $k_f$ has not been measured at each $P$ $T$ point along the grid, as is often the case, approximate expressions can be used." +" For example. the rale coefficient at (Che low-pressure limit (Ay in units of em"" 1) and high-pressure limit (A, in units of cm’? !)1 have often been determined at a [unction of temperature."," For example, the rate coefficient at the low-pressure limit $k_0$ in units of $^{6}$ $^{-1}$ ) and high-pressure limit $k_{\infty}$ in units of $^{3}$ $^{-1}$ ) have often been determined at a function of temperature." + At intermediate pressures. Ay can be calculated from the expression where Jj is given by and £.ids the center broadening factor (e.g..seeDaulehetal.2005).," At intermediate pressures, $k_{f}$ can be calculated from the expression where $\beta$ is given by and $F_{c}$ is the center broadening factor \citep[e.g., see][]{baulch2005}." +". As in our previous studies (Visscheretal.2010:Moses2010).. we calculate hy for every pressure and temperature along (he atmospheric grid. ancl (then use equation (12)) to determine A, for the reverse of every reaction al each atmospheric level using (hie appropriate temperature- and pressure-dependent values for A; and C."," As in our previous studies \citep{visscher2010icarus,moses2010}, we calculate $k_f$ for every pressure and temperature along the atmospheric grid, and then use equation \ref{eq:reversal}) ) to determine $k_{r}$ for the reverse of every reaction at each atmospheric level using the appropriate temperature- and pressure-dependent values for $k_{f}$ and $\Delta_{r}G^{\circ}$." + The outcome of this approach is a rate coellicient list of 2800 forward reactions and 75800 corresponding reverse reactions involving H-C-N-O species. for each atmospheric profile.," The outcome of this approach is a rate coefficient list of $\sim$ 800 forward reactions and $\sim$ 800 corresponding reverse reactions involving H-C-N-O species, for each atmospheric profile." + As a result when not including photochenmistry. and atmospheric transport. and given enough time to achieve steady state our fullv-reversed. kinetics model vields results indistinguishable from those given by thermochenmical-equilibrium calculations.," As a result — when not including photochemistry and atmospheric transport, and given enough time to achieve steady state — our fully-reversed kinetics model yields results indistinguishable from those given by thermochemical-equilibrium calculations." + Further description of the model can be found in Visscherοἱal.(2010) and Mosesetal.(2010. 2011)..," Further description of the model can be found in \citet{visscher2010icarus} and \citet{moses2010,moses2011}. ." +it does have a strong 6 dependence: only ~ο of Lenses are dark when 6=mN but ~50% when 0=15'.,it does have a strong $\theta$ dependence; only $\sim 5$ of lenses are dark when $\theta= 3'$ but $\sim 50$ when $\theta= 15'$. + In ligure 12 we plot the number of virialized and clark Lenses as a function of 6 for the ACDAL model., In Figure 12 we plot the number of virialized and dark lenses as a function of $\theta$ for the $\Lambda$ CDM model. + As @ increases rom 3 to 15’ the sky density of dark lenses. increases rom zero to 5 per square degree while the sky. density of virialized lenses peaks at @=5% and gradually: declines or larger aperture sizes., As $\theta$ increases from $'$ to $'$ the sky density of dark lenses increases from zero to 5 per square degree while the sky density of virialized lenses peaks at $\theta = 5'$ and gradually declines for larger aperture sizes. + Figure 13 explains this trend., Figure 13 explains this trend. +" For an overdensity of mass Al=5LOYAL. we plot. as a 'unction of redshift. 65. the projected. angular size of the virialization raclius. and 64,4. the projected angular size of he maximum radius that produces a detectable lens (i.e. Gruss=ual)Dials) where Is=XMAx Aut)."," For an overdensity of mass $M = 5 \times 10^{14} M_{\odot}$ we plot, as a function of redshift, $\theta_{\rm{vir}}$, the projected angular size of the virialization radius, and $\theta_{\rm{max}}$, the projected angular size of the maximum radius that produces a detectable lens (i.e., $\theta_{\rm{max}}=R_{\rm{max}}(z)/D_{\rm{d}}(z)$ where $R_{\rm{max}}^3=3M / 4 \pi \Delta_{\rm{min}}(z)$ )." +" For xfi, an overdensity can be non-virialized: anc still produce a detectable lensing signal (i.c.. a dark lens)."," For $\theta_{\rm{max}} > \theta_{\rm{vir}}$ an overdensity can be non-virialized and still produce a detectable lensing signal (i.e., a dark lens)." + Llowever. since @ defines the maximum observable angular scale. for sulliciently small @ there is no range in redshif such that 6>@yay μι overdensities cannot. produce a detectable lens.," However, since $\theta$ defines the maximum observable angular scale, for sufficiently small $\theta$ there is no range in redshift such that $\theta > \theta_{\rm{max}} > \theta_{\rm{vir}}$, in which case non-virialized overdensities cannot produce a detectable lens." + In. genera we find that the minimum aperture size needed. to. detec dark lenses is 3., In general we find that the minimum aperture size needed to detect dark lenses is $\sim 3'$. +" For larger ϐ. the area below 0,4 ane above 64 has a substantial relative increase while the area below 6, has just a mild relative increase."," For larger $\theta$, the area below $\theta_{\rm{max}}$ and above $\theta_{\rm{vir}}$ has a substantial relative increase while the area below $\theta_{\rm{vir}}$ has just a mild relative increase." + After taking into account the fact that the aperture mass Al.)(9) decreases with increased 8. this translates to an increase in the sky clensity of dark lenses ancl a decrease in the sky density of virialized. lenses for @>5’.," After taking into account the fact that the aperture mass $M_{\rm{ap}} (\theta)$ decreases with increased $\theta$, this translates to an increase in the sky density of dark lenses and a decrease in the sky density of virialized lenses for $\theta > 5'$." + The fraction of lenses that are dark therefore increases with aperture size., The fraction of lenses that are dark therefore increases with aperture size. + We have examined the possibility. of using the measured abundance of weak gravitational lenses to constrain a principal property of the dark energy. its equation-of-state parameter dw.," We have examined the possibility of using the measured abundance of weak gravitational lenses to constrain a principal property of the dark energy, its equation-of-state parameter $w$." + Since dark energy. modifies both the background. cosmology of the universe and the growth of structure it will necessarily have an ellect on the elliciency of weak lensing., Since dark energy modifies both the background cosmology of the universe and the growth of structure it will necessarily have an effect on the efficiency of weak lensing. + Phe goal of this paper was to determine the nature and strength of the ellect., The goal of this paper was to determine the nature and strength of the effect. + The change in the background cosmology with w inlluences the predicted weak lens abundance in essentially hree ways., The change in the background cosmology with $w$ influences the predicted weak lens abundance in essentially three ways. + First. the size of comoving volume elements shrink with increasing dw.," First, the size of comoving volume elements shrink with increasing $w$." +" Second. the cdistance-recdshift relation is mocdified. thereby shifting the location of the ensine-kernel maximum (Lo. where the combination of angular ciameter distances 4,I4/D. peaks)."," Second, the distance-redshift relation is modified, thereby shifting the location of the lensing-kernel maximum (i.e., where the combination of angular diameter distances $D_{\rm{ds}} D_{\rm{d}}/ D_{\rm{s}}$ peaks)." + Third. since 16 evolution of the background matter density is mocified the dark energy. the density ofa given halo relative to the xickeround density changes with e.," Third, since the evolution of the background matter density is modified by the dark energy, the density of a given halo relative to the background density changes with $w$." + Phis. in turn. alfects the μαrength of a halo's lensing signal: the larger the overdensity 1e stronger the signal.," This, in turn, affects the strength of a halo's lensing signal; the larger the overdensity the stronger the signal." + While the volume term is explicitly actorecd into the expression for the weak-lens sky. density equation. (22)]. the latter two ellects are incorporated into 16 signal-to-noise estimator for whieh we use the mass technique introduced by Schneider (1996).," While the volume term is explicitly factored into the expression for the weak-lens sky density [equation (22)], the latter two effects are incorporated into the signal-to-noise estimator for which we use the aperture-mass technique introduced by Schneider (1996)." + The changeὃν in the ogrowth of structure with d is somewhat more subtle., The change in the growth of structure with $w$ is somewhat more subtle. + Phe dark energy. modifies both the rate of structure growth and the amplitude of the matter power spectrum., The dark energy modifies both the rate of structure growth and the amplitude of the matter power spectrum. + To determine the former we solved. the spherical-collapse model with dark energy included., To determine the former we solved the spherical-collapse model with dark energy included. + Though, Though +D182124. the giant pulse radio emission is co-Iocated with high energv emission in the outer magnetosphere. where strong power law. X-ray components indicate sites of dense pair production.,"B1821–24, the giant pulse radio emission is co-located with high energy emission in the outer magnetosphere, where strong power law X-ray components indicate sites of dense pair production." + Vela and PSR DITO6-44. are also 5-ràv emitters: in the outer magnetosphere picture. this high energy emission comes from the pole opposite to that viewed in the radio., Vela and PSR B1706-44 are also $\gamma$ -ray emitters; in the outer magnetosphere picture this high energy emission comes from the pole opposite to that viewed in the radio. + They do not show strong X-ray. pulses ancl so itis perhaps not surprising that we have not found. giant pulse emission coincident with the *5-ravs in these objects. as the Earth line-of-sight evidently does not sample regions of dense pair production.," They do not show strong X-ray pulses and so it is perhaps not surprising that we have not found giant pulse emission coincident with the $\gamma$ -rays in these objects, as the Earth line-of-sight evidently does not sample regions of dense pair production." + Nevertheless. there may be a high enerev connection to the giant micro-pulse emission if the outer magnetosphere above the radio pole is also actively »oducing pairs.," Nevertheless, there may be a high energy connection to the giant micro-pulse emission if the outer magnetosphere above the radio pole is also actively producing pairs." + Phe high energy emission from bevond the null charge surface would not be visible (rom this pole. but some pairs [from the gap would be expected to Low inward vast the null charge surface.," The high energy emission from beyond the null charge surface would not be visible from this pole, but some pairs from the gap would be expected to flow inward past the null charge surface." + We can speculate vat this jxasma mirrors in the converging field lines above the racio vole and that this mirrored. counter-streaming population would sulfer instability growth and produce the giant micro-»ulse components.," We can speculate that this plasma mirrors in the converging field lines above the radio pole and that this mirrored, counter-streaming population would suffer instability growth and produce the giant micro-pulse components." + A final question concerns the asymmetry. of the giant micro-pulse component., A final question concerns the asymmetry of the giant micro-pulse component. + Why oes it [ead in the case of Vela. but lag for PSR 44?," Why does it lead in the case of Vela, but lag for PSR $-$ 44?" + For Vela. the radio pulse las a steep rise and slow fall suggesting the leading edge of a cone: the giant micro-pulse component is at. higher altitudes on the same side.," For Vela, the radio pulse has a steep rise and slow fall suggesting the leading edge of a cone; the giant micro-pulse component is at higher altitudes on the same side." + For PSR 44. one would hen infer that the main radio pulse is the trailing edge of a cone. although this is morphologically less clear.," For PSR $-$ 44, one would then infer that the main radio pulse is the trailing edge of a cone, although this is morphologically less clear." + Lf there is a high energy connection. then it is intruiging to note hat the leading οταν pulse is stronger for Vela. while for SR BITOG 44. the trailing component is stronger at most jiegh energies.," If there is a high energy connection, then it is intruiging to note that the leading $\gamma$ -ray pulse is stronger for Vela, while for PSR $-$ 44, the trailing component is stronger at most high energies." + More examples are clearly. needed to see if the dominance of leading versus trailing giant micro-pulses has a deterministic connection with other pulsar emission and if some elobal asymmetry in the magnetosphere geometry controls this choice., More examples are clearly needed to see if the dominance of leading versus trailing giant micro-pulses has a deterministic connection with other pulsar emission and if some global asymmetry in the magnetosphere geometry controls this choice. + We have found evidence for giant micro-pulses in PSR D1TOG44 which are very similar to those seen in the Vela pulsar., We have found evidence for giant micro-pulses in PSR B1706–44 which are very similar to those seen in the Vela pulsar. + They. are located in a small window. of pulse phase. have a duration of 1 ms and significant phase jitter.," They are located in a small window of pulse phase, have a duration of $\sim$ 1 ms and significant phase jitter." + Their amplitude: distribution is power-law and so may extend into true giant pulses’ if observed. for long enough., Their amplitude distribution is power-law and so may extend into true `giant pulses' if observed for long enough. +" Ht is unclear whether the giant micro-pulses are just another manifestation of pulsar ""weather! associated: with the standard radio emission from pulsars or whether they are more closely related to high-energy phenomena and the classical giant pulses.", It is unclear whether the giant micro-pulses are just another manifestation of pulsar `weather' associated with the standard radio emission from pulsars or whether they are more closely related to high-energy phenomena and the classical giant pulses. + No giant pulses or any other giant micro-pulses. were detected: within our sensitivity limits in any of the other 5 pulsars in our survey., No giant pulses or any other giant micro-pulses were detected within our sensitivity limits in any of the other 5 pulsars in our survey. + Where it was possible to measure amplitude cistributions. these were generally loe-normal as surmised by Cairns ct al. (," Where it was possible to measure amplitude distributions, these were generally log-normal as surmised by Cairns et al. (" +2001).,2001). + The Parkes telescope is funded. by the Commonwealth: of Australia for operation as à National Facility managed by CSIRO., The Parkes telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. + The 512 channel filterbank system used. in. the observations was designed. and. built at the Jodrell Bank Observatory. University of Manchester.," The 512 channel filterbank system used in the observations was designed and built at the Jodrell Bank Observatory, University of Manchester." + Observing software was provided by the Pulsar Multibeam Survey group., Observing software was provided by the Pulsar Multibeam Survey group. +very long exposure limes (o achieve the necessary signal-noise ratio.,very long exposure times to achieve the necessary signal-noise ratio. + The search for emission-Ine galaxies using a given narrow-band filter is open to different lines at different. redshifts., The search for emission-line galaxies using a given narrow-band filter is open to different lines at different redshifts. + Lines whose redshilted wavelength fall inside the narrow-band filler range could be detected., Lines whose redshifted wavelength fall inside the narrow-band filter range could be detected. + When the emission-line is bright enough the galaxy. will be selected., When the emission-line is bright enough the galaxy will be selected. + The more prominent lines that can be detected in the and atmospheric windows are (at redshift z20.24 and z20.4). (2790.6 and 2 O08). (z01.2 and zc1.5) and (2©5.7 and z26.5).," The more prominent lines that can be detected in the and atmospheric windows are (at redshift $z\simeq0.24$ and $z\simeq0.4$ ), $z\simeq0.6$ and $z\simeq0.8$ ), $z\simeq1.2$ and $z\simeq1.5$ ) and $z\simeq5.7$ and $z\simeq6.5$ )." + The line is an excellent tracer of (he Star Formation Rate (SER...22).. provided that the ionizing flux comes [rom voung stars and not from non-thermal activity.," The line is an excellent tracer of the Star Formation Rate \citep[SFR, ][]{1998ARA&A..36..189K, 2001MNRAS.323..887C}, provided that the ionizing flux comes from young stars and not from non-thermal activity." + Other commonly used SFR tracers are the lar infrared (FII) and the UV., Other commonly used SFR tracers are the far infrared (FIR) and the UV. + The (three tracers share sensitivity to the parameters of the Initial Mass Function., The three tracers share sensitivity to the parameters of the Initial Mass Function. + SER is affected by obscuration but is not very sensitive to metallicity., SFR is affected by obscuration but is not very sensitive to metallicity. + The FIR is not affected by obscuration. but there is uncertainty in how the total (8-1000j/mi) luminosity is computed. [from monochromatic measurements (e.g. Spitzers 24jmi) and the contribution of different non-SFR related components (cirrus. hot dust) to the FIR.," The FIR is not affected by obscuration, but there is uncertainty in how the total $\mu$ m) luminosity is computed from monochromatic measurements (e.g. Spitzer's $\mu$ m) and the contribution of different non-SFR related components (cirrus, hot dust) to the FIR." + Finally the UV is heavily alfected by obscuration., Finally the UV is heavily affected by obscuration. + As shown by ?.. ohseuration corrected is consistent. to a [actor of 2. with the SFRs estimated using UV and FIR(8-L000;a).," As shown by \citet{2003apj...586..794b}, obscuration corrected is consistent, to a factor of 2, with the SFRs estimated using UV and $\mu$ m)." + Consequently. observations of galaxy samples with UV and FIR. data provides an invaluable (ool to understand the evolution of the SER. and the role of obscuration in the determination of global SFR lor galaxies.," Consequently, observations of galaxy samples with UV and FIR data provides an invaluable tool to understand the evolution of the SFR and the role of obscuration in the determination of global SFR for galaxies." + Some works have used narrow-band imaging to select candidates in the window: ??? ancl ?..," Some works have used narrow-band imaging to select candidates in the window: \citet{2001A&A...379..798P, +2003ApJ...586L.115F, 2004ApJ...601..805U} and \citet{2006PASJ...58..113A}." + Given (hat small amounts of dust reddening can completely extinetish Lya--emission. is the strongest emission line in many starburst galaxies.," Given that small amounts of dust reddening can completely extinguish -emission, is the strongest emission line in many starburst galaxies." + The doublet is in many cases the other strongest emission line., The doublet is in many cases the other strongest emission line. + In fact. the ratio is 0.6 in local star-forming galaxies (2)..," In fact, the ratio is 0.6 in local star-forming galaxies \citep{2005MNRAS.362.1143M}." + This line is not used to trace the star formation but (o trace the power of AGN (see.forexample?)..," This line is not used to trace the star formation but to trace the power of AGN \citep[see, for example][]{2003MNRAS.346.1055K}." + Thus. emitters can be a tool to unveil AGN at different. redshilts.," Thus, emitters can be a tool to unveil AGN at different redshifts." + is also intense when compared withHa.. with a ratio = 0.45 (?)..," is also intense when compared with, with a ratio = 0.45 \citep{1992ApJ...388..310K}." + However. the ratio depends on Iuminositv ancl metallicity (7). and varies from sample to sample.," However, the ratio depends on luminosity and metallicity \citep{2001ApJ...551..825J} and varies from sample to sample." + This line is used as a star-Iormation indicator at redshifts where is outside the visible range (which happens at 2> 0.4)., This line is used as a star-formation indicator at redshifts where is outside the visible range (which happens at $z > 0.4$ ). + SFR based on comes from the fact that there is a good correlation between emission and emission., SFR based on comes from the fact that there is a good correlation between emission and emission. + is used as a proxy for theemission., is used as a proxy for theemission. + Different calibrations of SER. based on are used (see.e.g.2???) but. in general. the correlation between SFR," Different calibrations of SFR based on are used \citep[see, +e.g. ][]{1989AJ.....97..700G,1998ARA&A..36..189K,2002MNRAS.332..283R,2004AJ....127.2002K} + but, in general, the correlation between SFR" +reduction in brightness close to component B comes fron the 15-CGllz VLA map shown in Biges et al. (,reduction in brightness close to component B comes from the 15-GHz VLA map shown in Biggs et al. ( +1999).,1999). + “Phe radio jet can be seen emerging from the southern edee of the Einstein ring as the two protrusions at the bottom., The radio jet can be seen emerging from the southern edge of the Einstein ring as the two protrusions at the bottom. + These correspond. well to similar features in the VLA 15-GlLIz radio map of Biges et al. (, These correspond well to similar features in the VLA 15-GHz radio map of Biggs et al. ( +1999).,1999). + Another interesting area of the map is the bright spot he third brightest component in the map) that Lies outside 10 Einstein ring. ~150 mas to the north of component A. This has not been identified. before and is noticeable bv its absence in the MEERLIN 5 CGllz map of Patnaik et al. (," Another interesting area of the map is the bright spot (the third brightest component in the map) that lies outside the Einstein ring, $\sim$ 150 mas to the north of component A. This has not been identified before and is noticeable by its absence in the MERLIN 5 GHz map of Patnaik et al. (" +1998).,1993). + Hecently though. a feature. at. the same position and with similar brightness has been seen in a combined ALERLIN/European VLBI Network (EWN) image at 1.7 Cllz (A. 1t. Patnaik. private communication)," Recently though, a feature at the same position and with similar brightness has been seen in a combined MERLIN/European VLBI Network (EVN) image at 1.7 GHz (A. R. Patnaik, private communication)." + In addition to this. four-telescope VLBI cata (Vermeulen et al.," In addition to this, four-telescope VLBI data (Vermeulen et al.," + in preparation) shows LL absorption associated with the lensing galaxy against three components A. D and a third component located. close ancl to the north-east: of A. For the purposes of this discussion we shall refer to this as Component C. What this third component might be is currently. undetermined. but given that its position is so close to component A it is unlikely that it is not a lensed image.," in preparation) shows HI absorption associated with the lensing galaxy against three components — A, B and a third component located close and to the north-east of A. For the purposes of this discussion we shall refer to this as component C. What this third component might be is currently undetermined, but given that its position is so close to component A it is unlikely that it is not a lensed image." + Its counterpart (component D sav) is most likely to be located close to component D. but if we assume that the relative magnification between € anc D is similar to that between A and. D. component D will be dillicult to detect.," Its counterpart (component D say) is most likely to be located close to component B, but if we assume that the relative magnification between C and D is similar to that between A and B, component D will be difficult to detect." + This is because it will be weakened by about a third compared to € and closer to component D than € is to A by a similar factor., This is because it will be weakened by about a third compared to C and closer to component B than C is to A by a similar factor. + lt is the lensed emission in the Einstein ring tha interests us most as it is this which will enable us to constrain the lens model., It is the lensed emission in the Einstein ring that interests us most as it is this which will enable us to constrain the lens model. + One wav of doing this is to identify Lensec images of the same surface brightness as these are likely to be images of the same background source (às gravitationa lensing preserves surface brightness)., One way of doing this is to identify lensed images of the same surface brightness as these are likely to be images of the same background source (as gravitational lensing preserves surface brightness). + This is the basis of the lting Cvele algorithm (Ixochaneketal.1989). that attempts to optimise the mass model so that. when back-projectec into the source plane. the surface brightness. dispersion within individual pixels is minimised.," This is the basis of the Ring Cycle algorithm \cite{kochanek89} that attempts to optimise the mass model so that, when back-projected into the source plane, the surface brightness dispersion within individual pixels is minimised." + A natural consequence of this process is a reconstruction of the unlensed: source., A natural consequence of this process is a reconstruction of the unlensed source. + However. it is clear from Fig.," However, it is clear from Fig." + 4. that the two ares of the Einstein ring contain substructure with different surface iehtnesses., \ref{mervla} that the two arcs of the Einstein ring contain substructure with different surface brightnesses. + This is almost certainly due to the fact that he finite beam of the combined observations is not sullicient o resolve Lully the brightness variations in the Einstein ring., This is almost certainly due to the fact that the finite beam of the combined observations is not sufficient to resolve fully the brightness variations in the Einstein ring. + In this case the appropriate action is to use the LensClean (Ixochanek&Naravan1992). algorithm., In this case the appropriate action is to use the LensClean \cite{kochanek92} algorithm. + This represents a considerable improvement on the IHing ονο]ο ancl uses the CLEAN algorithm familiar to racio astronomers to allow or resolution clleets like those present in the combined ALERLIN/VLA map of DO218|357., This represents a considerable improvement on the Ring cycle and uses the CLEAN algorithm familiar to radio astronomers to allow for resolution effects like those present in the combined MERLIN/VLA map of B0218+357. + Xs with the Ring evcle. LensClean simultaneously finds the best-fit lens model and oocduces a map of the unlensed source structure.," As with the Ring cycle, LensClean simultaneously finds the best-fit lens model and produces a map of the unlensed source structure." + This work is currently underway. and will feature in a future paper (Wucknitz et al..," This work is currently underway and will feature in a future paper (Wucknitz et al.," + in preparation)., in preparation). + In this paper we have presented a new image of the eravitational lens svstem D0218|357 at a mean frequency close to 5 CGllz., In this paper we have presented a new image of the gravitational lens system B0218+357 at a mean frequency close to 5 GHz. + This has combined data from both the VLA and. MISILIN. the latter in multi-frequeney mode observing ab three separate frequencies.," This has combined data from both the VLA and MERLIN, the latter in multi-frequency mode observing at three separate frequencies." + The resulting data set. has excellent (oe) coverage and sensitivity. as well as resolution veh enough (~50 mas) to easily resolve the Einstein ring.," The resulting data set has excellent $(u,v)$ coverage and sensitivity, as well as resolution high enough $\sim50$ mas) to easily resolve the Einstein ring." + The new map is the best made of this svstem., The new map is the best made of this system. + The motivation for making this map was to improve the ens model for this svstem and hence to improve the estimate of Hy., The motivation for making this map was to improve the lens model for this system and hence to improve the estimate of $H_0$. + ‘This currently stands at I * Alpe+ siegesοἱal.LO99).. but there are only limited. constraints on the mass mocel available from the VLBI substructure of he compact images and the centre of the lensing galaxy. is »xoorlv determined.," This currently stands at $^{+13}_{-19}$ $^{-1}\,$ $^{-1}$ \cite{biggs99}, but there are only limited constraints on the mass model available from the VLBI substructure of the compact images and the centre of the lensing galaxy is poorly determined." + The next stage will be to exploit the new image for lensing constraints., The next stage will be to exploit the new image for lensing constraints. + The results of applying the Lens Clean algorithm will allow us to improve substantially he estimate of dfy from the time delay., The results of applying the Lens Clean algorithm will allow us to improve substantially the estimate of $H_0$ from the time delay. + ADB acknowledges the receipt of a PPABC studentship., ADB acknowledges the receipt of a PPARC studentship. + We thank Olaf Wueknitz for fruitful discussions and the anonvmous referee for several sugeestions that significantly improved this paper., We thank Olaf Wucknitz for fruitful discussions and the anonymous referee for several suggestions that significantly improved this paper. +" This research was supported in part by the European C'ommission. TMBB Programme. Research Network Contract ERBEARACT96-0034 ""CERES."," This research was supported in part by the European Commission TMR Programme, Research Network Contract ERBFMRXCT96-0034 `CERES'." + MEBRLIN is run by the University of Manchester as a National Facility on behalf of PPARC., MERLIN is run by the University of Manchester as a National Facility on behalf of PPARC. + The VLA is operated by the National Radio Astronomy Observatory which is a facility of the National Science Foundation operated under cooperative agreement by Associated: Universities. Inc.," The VLA is operated by the National Radio Astronomy Observatory which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc." +be treated: equivocallv.,be treated equivocally. + In. fact. predictions. are average values over the entire galaxy and over the timestep. whereas observations look at more central regions (sce below) and wvield an instantaneous SER value.," In fact, predictions are average values over the entire galaxy and over the timestep, whereas observations look at more central regions (see below) and yield an instantaneous SFR value." + We can thus eain more insight from the comparison of the relative dillerences ancl evolution. in the predicted. and observed SERs than their numerical values., We can thus gain more insight from the comparison of the relative differences and evolution in the predicted and observed SFRs than their numerical values. + Indeed. our. predicted SERs (see Fig.," Indeed, our predicted SFRs (see Fig." + 7 below) are quite lower than those observed bv ? who find an average SER of 100A. vr.+ but are consistent with those from ? who find a median value of ~30M ve* although we do not reproduce some of their extreme cases (with SERs ~300AL. +).," \ref{fig:srf} below) are quite lower than those observed by \citet{amaze} who find an average SFR of $\sim$ $M_\odot$ $^{-1}$ but are consistent with those from \citet{erb2} who find a median value of $\sim30M_\odot$ $^{-1}$, although we do not reproduce some of their extreme cases (with SFRs $\sim300M_\odot$ $^{-1}$ )." + While a (small) fraction of the disagreement can be explained by a small dilference in the adopted upper mass limit for the IME between our model and the value adopted by the observational works. we believe that this is a general problem of semi-analvtie mocels (see.forexample.?.andreferences therein)..," While a (small) fraction of the disagreement can be explained by a small difference in the adopted upper mass limit for the IMF between our model and the value adopted by the observational works, we believe that this is a general problem of semi-analytic models \citep[see, for example,][and references therein]{khoch}." + For instance. if the gas acerction ancl cooling are uneven over a timestep. the SER may. present spikes that are in better agreement with the values reported o» both ? and ?..," For instance, if the gas accretion and cooling are uneven over a timestep, the SFR may present spikes that are in better agreement with the values reported by both \citet{amaze} and \citet{erb06}." + Phe dynamics of these high. redshift ealaxies are not always consistent with a smooth star orming dise. instead they are hiehly turbulent (see.forexample.7). and a large fraction do not seem to rotate (forexample.thoseobservedby.2)..," The dynamics of these high redshift galaxies are not always consistent with a smooth star forming disc, instead they are highly turbulent \citep[see, for example,][]{genz} and a large fraction do not seem to rotate \citep[for example, those observed by][]{Law}." + A similar discussion of he dvnamies of the AMAZIZ galaxies is given in ?.., A similar discussion of the dynamics of the AMAZE galaxies is given in \citet{gner}. + This star forming mode is not vet accounted for in. and. perhaps. the high value for 7 that we obtain should » interpreted. as a warning: the treatment of the star ormation must be improved. possibly taking into account eas supplies that are enhanced. by cold. streams.," This star forming mode is not yet accounted for in and, perhaps, the high value for $\beta$ that we obtain should be interpreted as a warning: the treatment of the star formation must be improved, possibly taking into account gas supplies that are enhanced by cold streams." + Namely he required. boosting in the SER is not only given by an increase in the elliciency. but also by augmenting the eas supply.," Namely the required boosting in the SFR is not only given by an increase in the efficiency, but also by augmenting the gas supply." + This has to preferentially happen in more massive ealaxies. where the disagreement with observations occur and. as can be inferred. [rom the results. presented. in. the orevious sections. a much better fit could. be obtained. by cilferentiallv increasing a and 23 at the high mass end with respect to their fiducial values. namely those that correctly it the low mass end.," This has to preferentially happen in more massive galaxies, where the disagreement with observations occur and, as can be inferred from the results presented in the previous sections, a much better fit could be obtained by differentially increasing $\alpha$ and $\beta$ at the high mass end with respect to their fiducial values, namely those that correctly fit the low mass end." + On the other hand ? have observed he SER as a function of log(M./ÀA.) for another sample of galaxies at 23 and have found. on average. a lower SER han in the AMLAZIS sample. while at the same time the O abundances are similar to those we are using in this work.," On the other hand \citet{Mann} have observed the SFR as a function of $\log\left(M_*/M_\odot\right)$ for another sample of galaxies at $z\sim3$ and have found, on average, a lower SFR than in the AMAZE sample, while at the same time the O abundances are similar to those we are using in this work." +" In particular. in the mass range 9.5I7kpe are included in each sample (K3-64. K3-70. and M1-9. K3-66. respectively). all four PNe having medioerily determined O abundances (quoted errors from 0.2 to 0.5 dex) and distances.," In fact, in the most recent works, those by \cite{henry10} and \cite{stanghellini10}, only two PNe with $D_{GC}> 17 kpc$ are included in each sample (K3-64, K3-70, and M1-9, K3-66, respectively), all four PNe having mediocrily determined O abundances (quoted errors from 0.2 to 0.5 dex) and distances." + However. these distant nebulae are obviously critical for the gradient determination.," However, these distant nebulae are obviously critical for the gradient determination." + In this context. LACPN provides a valuable data point located at the outer reaches of the Galaxy. and its well-constrained O abundance do support nodels with a flatter gradient toward the external disk.," In this context, IACPN provides a valuable data point located at the outer reaches of the Galaxy, and its well-constrained O abundance do support models with a flatter gradient toward the external disk." + An intriguing possibility is that [ACPN and perhaps also the other four PNe with Doc >17 kpe might even have an extragalactic origin. if indeed the Monoceros Ring proposed to be located at these radii (eg.?) is attributable to a satellite accretion event.," An intriguing possibility is that IACPN and perhaps also the other four PNe with $_{GC}$ $>$ 17 kpc might even have an extragalactic origin, if indeed the Monoceros Ring proposed to be located at these radii \citep[eg.][]{conn08} is attributable to a satellite accretion event." + À consensus on this has not yet been reached (eg.?).., A consensus on this has not yet been reached \citep[eg.][]{hammersley10}. + But either way it is clear that the properties of the outer Galactic dise are still in need of much better observational definition., But either way it is clear that the properties of the outer Galactic disc are still in need of much better observational definition. + We are exploring the new IPHAS planetary nebula candidates (?) towards the Galactic Anticentre in order to better sample the Galactic abundance gradient at large galactocentric distances., We are exploring the new IPHAS planetary nebula candidates \citep{viironen09b} towards the Galactic Anticentre in order to better sample the Galactic abundance gradient at large galactocentric distances. + In this paper. the discovery of a new PN located at only 4+ degrees from the Galactic Anticentre. IPHASX J052531.19+281945.1. is presented. its physical and chemical properties are studied and its distance determined.," In this paper, the discovery of a new PN located at only 4 degrees from the Galactic Anticentre, IPHASX J052531.19+281945.1, is presented, its physical and chemical properties are studied and its distance determined." + The object turned out to be a low-density. distant. and aged PN.," The object turned out to be a low-density, distant, and aged PN." + It is the Galactic PN with the largest galactocentric distance (20.843.8 kpe) where the chemical abundances have been measured. and this. combined with its relatively high oxygen abundance. 12 + log(O/H) = 8.3620.03. points to a flattening of the Galactic abundance gradient towards the outer Galaxy rather than to a linearly decreasing oxygen abundance (e.g.?.andreferences therein).," It is the Galactic PN with the largest galactocentric distance $\pm$ 3.8 kpc) where the chemical abundances have been measured, and this, combined with its relatively high oxygen abundance, 12 + log(O/H) = $\pm$ 0.03, points to a flattening of the Galactic abundance gradient towards the outer Galaxy rather than to a linearly decreasing oxygen abundance \citep[e.g.][and references therein]{maciel09}." + To properly study the behaviour of the abundance gradient at the outer Galaxy. reasonably accurate abundance measurements on a sample of objects at large galactocentric distances are needed.," To properly study the behaviour of the abundance gradient at the outer Galaxy, reasonably accurate abundance measurements on a sample of objects at large galactocentric distances are needed." + We have recently discovered in theIPHAS images about 180 new faint PN candidates located in a 30°x10° region around the Anticentre (?).., We have recently discovered in theIPHAS images about 180 new faint PN candidates located in a $30^{\circ} \times 10^{\circ}$ region around the Anticentre \citep{viironen09b}. . + Further abundance measurements of confirmed candidates inthis region would help to build a robust chemical gradient determination and reach firmer conclusions concerning its flattening., Further abundance measurements of confirmed candidates inthis region would help to build a robust chemical gradient determination and reach firmer conclusions concerning its flattening. + , +- in ees 7 1) adopted from IHunuterctal.1986.. for a Salpeter IMFE (Salpeter 1955)) between 0.1-100.,"$L_{FIR}$ in ergs $^{-2}$ $^{-1}$ ), adopted from \cite{hunter86}, for a Salpeter IMF \cite{salpeter55}) ) between 0.1-100." +AZ... Althoueh IR huninous galaxies seen to require a larger IME Riekeetal.1980. 1993)). this is more colmplicated to assess than iu the case of ποσα] ealaxies. because of the heavy obscuration iu those systenis aud the hielilv time-variable SFRs.," Although IR luminous galaxies seem to require a larger IMF \cite{rieke80,rieke93}) ), this is more complicated to assess than in the case of normal galaxies, because of the heavy obscuration in those systems and the highly time-variable SFRs." + The conventional IME chosen here is sufficicut to make an inter-comparisou of our smuuples., The conventional IMF chosen here is sufficient to make an inter-comparison of our samples. + Tn Figure 15. we plot the histograms of yy for our three subsamples aud their median values as vertical bars., In Figure \ref{f8} we plot the histograms of $_{IR}$ for our three subsamples and their median values as vertical bars. + All samples spau a laree rauge of SERs. iu particular the Cold sample (9-380 +) which has a larger median 71.5 |! than the Warm siuuple.," All samples span a large range of SFRs, in particular the Cold sample (9-380 $^{-1}$ ) which has a larger median 71.5 $^{-1}$ than the Warm sample." + The Sevfert 1 and Sevfert 2 subsamples span simular ranges (75-150) with medians 21.9 aud 38.6 | respectively. excluding the four highly IR luminous (Loy 10H) Sevfert 2sthat have SER5; 7150 +.," The Seyfert 1 and Seyfert 2 subsamples span similar ranges $\sim$ 5-150) with medians 24.9 and 38.6 $^{-1}$ respectively, excluding the four highly IR luminous $L_{60}\geq$ $^{11}$ ) Seyfert 2s that have $_{IR}\geq$ 150 $^{-1}$." + When the four ultraluuinous (UL) objects are imcluded the two samples have siguificautly different variances and means (significance O.0001 and 0.02. respectively).," When the four ultraluminous (UL) objects are included the two samples have significantly different variances and means (significance 0.0001 and 0.02, respectively)." + We should be cautious when interpreting the FIR Iuiuinosities as reliable indicator of the star formation activity in galaxies., We should be cautious when interpreting the FIR luminosities as reliable indicator of the star formation activity in galaxies. + It is iiportaut to compare samples for which the (precursor) galaxy dust properties are known aud similar., It is important to compare samples for which the (precursor) galaxy dust properties are known and similar. + For mstauce. there is very likely an intrinsic difference in the dust couteut of galaxies selected at GO µια. compared to galaxies selected optically.," For instance, there is very likely an intrinsic difference in the dust content of galaxies selected at 60 $\mu$ m, compared to galaxies selected optically." + Also. bigecr galaxies reradiate more enerev at all waveleneths (ideally oue should normalize £eyye by the galaxy size).," Also, bigger galaxies reradiate more energy at all wavelengths (ideally one should normalize $L_{FIR}$ by the galaxy size)." + Moreover. Ley is due to different dust componcuts. oulv the wiuiner component being associated with star formation.," Moreover, $L_{FIR}$ is due to different dust components, only the warmer component being associated with star formation." + Ihowever. iu dusty star forming regious with large optical depth. the stellar radiation field is dominated by τος stellar populations aud thus Leyyy effectively nieasires the Lys of the starburst.," However, in dusty star forming regions with large optical depth, the stellar radiation field is dominated by young stellar populations and thus $L_{FIR}$ effectively measures the $L_{bol}$ of the starburst." +" Moreover. iu Paper IT we have shown that the Lpg;g for our samples is related to the disk component. thus it is less depeudent on the AGN,"," Moreover, in Paper II we have shown that the $L_{FIR}$ for our samples is related to the disk component, thus it is less dependent on the AGN." + Consequently. the assmuption of Lp; being au accurate star formation indicator seenis to be a goo approximation for the objects in our (IB-selected) saluples.," Consequently, the assumption of $L_{FIR}$ being an accurate star formation indicator seems to be a good approximation for the objects in our (IR-selected) samples." + Reepiug iu müud the limitations outline above. if is iustructive to compare our results with those of some other characteristic galaxy samples.," Keeping in mind the limitations outlined above, it is instructive to compare our results with those of some other characteristic galaxy samples." + Using the equivalent widths of Πα ciiission. IKeunicut1983 found a SER (extinction corrected) as high as 20 b du giaut Se eulaxies aud suggeste hat in late-type spirals. current SFRs are simular to vast SFRs averaged over the age of the disk.," Using the equivalent widths of $\alpha$ emission, \cite{kennicutt83} found a SFR (extinction corrected) as high as 20 $^{-1}$ in giant Sc galaxies and suggested that in late-type spirals, current SFRs are similar to past SFRs averaged over the age of the disk." + SFRs obtained from IR data are usually larger than those Youn optical ciuission: Armasetal.1990/ argued that a factor of ~3 difference between the two values is within the uncertainties attached to the models used or the calculation of SFRs aud to the poorly known zinount of extinction that affects the Πα emission., SFRs obtained from IR data are usually larger than those from optical emission; \cite{armus90} argued that a factor of $\sim$ 3 difference between the two values is within the uncertainties attached to the models used for the calculation of SFRs and to the poorly known amount of extinction that affects the $\alpha$ emission. + For a sample of isolated galaxies. drawn from the colmplete IRAS bright galaxy sample (ith fiy25.21 Jv) the mean SERjj is 9.9 p (Soiferetal.L989)).," For a sample of isolated galaxies, drawn from the complete IRAS bright galaxy sample (with $f_{60}\geq$ 5.24 Jy) the mean $_{IR}$ is 9.9 $^{-1}$ \cite{soifer89}) )." +" A salple of Markarian on-eoiug and advanced merge svstenis (nost of them starbursts aud some Sevferts) shows median SER;,,—6.8 band Ες 1 (Alazzarclla19913).", A sample of Markarian on-going and advanced merging systems (most of them starbursts and some Seyferts) shows median $_{H\alpha}$ =6.8 $^{-1}$ and $_{IR}$ =12.5 $^{-1}$ \cite{mazzarella91}) ). + Iu these iiultiple-uucleus svstenis. vari dust is concentrated in the nuclear regions aud is heated by active star formation. producing the bulk of far-IR cunission and thei wari far-IR colours.," In these multiple-nucleus systems, warm dust is concentrated in the nuclear regions and is heated by active star formation, producing the bulk of far-IR emission and their warm far-IR colours." + It is clear that our [R-warin Seyfert samples show larger values than their Markarian (UV-selected) counterparts., It is clear that our IR-warm Seyfert samples show larger values than their Markarian (UV-selected) counterparts. +" A far-IR warm (colow-selected) sample of powerful FIR ealasies (Avisetal. 1990)) shows mean ;,, 210 band SER;42117 +.", A far-IR warm (colour-selected) sample of powerful FIR galaxies \cite{armus90}) ) shows mean $_{H\alpha}$ =40 $^{-1}$ and $_{IR}$ =117 $^{-1}$. + These objects ave suspected to be receut mergers uuereolus strong circunmnuclear bursts of star formation that ionize the interstellar medimn throughout the ealaxy., These objects are suspected to be recent mergers undergoing strong circumnuclear bursts of star formation that ionize the interstellar medium throughout the galaxy. + Our Cold sauple was not selected according to far-IR warluness as the Arms sample. but it is directly conrparable to it in terms of Ley aud jos.oy).," Our Cold sample was not selected according to far-IR warmness as the Armus sample, but it is directly comparable to it in terms of $L_{FIR}$ and $\alpha_{(25,60)}$." +" The ULFIRG sample (Lgjg 210 LE.) shows an even lavecr mneau SER; 4,2313 vr.", The ULFIRG sample $L_{FIR}\geq$ $^{12}$ ) shows an even larger mean $_{IR}$ =313 $^{-1}$. +| This isa suuple of extremely bright. strongly interacting svstenis. their far-IR cinission being associated with large scale star formation. triggered by the interaction.," This is a sample of extremely bright, strongly interacting systems, their far-IR emission being associated with large scale star formation, triggered by the interaction." + Mazzarcllaetal.1001. argued that the differences in IR. properties (aud SFRs) between these samples can be convincingly explained by invoking differing relative fractious aud temperatures of the wari dust. increasing from and T;210 K for the Markarian sample to and Ty=h0 K for the ULFIRGs sample.," \cite{mazzarella91} argued that the differences in IR properties (and SFRs) between these samples can be convincingly explained by invoking differing relative fractions and temperatures of the warm dust, increasing from and $_{d}$ =40 K for the Markarian sample to and $_{d}$ =50 K for the ULFIRGs sample." + They suggested that there are possible correlations betweenstrony encounters and increased far-IR cmission. euliauced star formation and/or nuclear activity.," They suggested that there are possible correlations between encounters and increased far-IR emission, enhanced star formation and/or nuclear activity." + This agrees with the conclusions that we reached earlier from our colour eracdient data (see previous section) and is also consistent with the SFRs that we find for our sample objects: the Cold galaxies (ostly strouely interacting svstenis) show larger values by factors 2- compared to the Wii Sevtert sample., This agrees with the conclusions that we reached earlier from our colour gradient data (see previous section) and is also consistent with the SFRs that we find for our sample objects: the Cold galaxies (mostly strongly interacting systems) show larger values by factors 2-3 compared to the Warm Seyfert sample. + The four, The four +UMa-II and both are substantially brighter than Coma.,UMa-II and both are substantially brighter than Coma. +" However, at 20 arcmin the surface brightness of Coma exceeds that of M31 by a factor of 4 and that of UMa-II by about a factor of 6."," However, at 20 arcmin the surface brightness of Coma exceeds that of M31 by a factor of 4 and that of UMa-II by about a factor of 6." +" Beyond about 70 arcmins, M31 is again the brightest object."," Beyond about 70 arcmins, M31 is again the brightest object." +" For y-ray telescopes like the Fermi Large Area Telescope (LAT), the detectability of extended objects depends on their contrast relative to the diffuse background."," For $\gamma$ -ray telescopes like the Fermi Large Area Telescope (LAT), the detectability of extended objects depends on their contrast relative to the diffuse background." +" As a simple indicator of signal-to-noise (S/N), in the right panel of Figure 3 we estimate the signal within circular aperture from the enclosed luminosity, and the noise as thea square root of the background counts, assumed to beBxAxt, where B is the background count rate per unit area, A is the area of the aperture in square arc minutes, and { is the exposure time. ("," As a simple indicator of signal-to-noise $S/N$ ), in the right panel of Figure 3 we estimate the signal within a circular aperture from the enclosed luminosity, and the noise as the square root of the background counts, assumed to be$B\times A \times t$, where $B$ is the background count rate per unit area, $A$ is the area of the aperture in square arc minutes, and $t$ is the exposure time. (" +"This assumes that the background is uniform and larger than the signal, which may not be the case for the smallest apertures.)","This assumes that the background is uniform and larger than the signal, which may not be the case for the smallest apertures.)" +" For the dwarf galaxy UMa-II, the effective S/N is almost independent of aperture for radii less than 10 arcmin, but drops dramatically at larger radii."," For the dwarf galaxy UMa-II, the effective $S/N$ is almost independent of aperture for radii less than 10 arcmin, but drops dramatically at larger radii." +" In contrast, the S/N for Coma rises steeply with increasing aperture to a peak at a radius of about 30 arcmin, significantly larger than the few arcmin resolution of the Fermi-LAT at energies ~10 GeV. For M31, the effective S/N has a minimum on this scale and has maxima on scales of one and 300 arcmin."," In contrast, the $S/N$ for Coma rises steeply with increasing aperture to a peak at a radius of about 30 arcmin, significantly larger than the few arcmin resolution of the Fermi-LAT at energies $\sim 10$ GeV. For M31, the effective $S/N$ has a minimum on this scale and has maxima on scales of one and 300 arcmin." + In this simple set-up the maximum achievable S/N ratios for Coma and M31 exceed that for UMa-II by about a factor of 3., In this simple set-up the maximum achievable $S/N$ ratios for Coma and M31 exceed that for UMa-II by about a factor of 3. +" In practice, realistic experiments will find it difficult to achieve these theoretical S/N values for very large apertures."," In practice, realistic experiments will find it difficult to achieve these theoretical $S/N$ values for very large apertures." + Systematic effects due to variable backgrounds and difficulties in masking bright sources make background correction significantly easier for small apertures., Systematic effects due to variable backgrounds and difficulties in masking bright sources make background correction significantly easier for small apertures. +" M31 is a particularly difficult case because of its very large angular size, its low galactic latitude, and confusion from other y-ray sources in its inner regions."," M31 is a particularly difficult case because of its very large angular size, its low galactic latitude, and confusion from other $\gamma$ -ray sources in its inner regions." + The Coma cluster is significantly more promising because it lies close to the North Galactic Pole and appears 10 times smaller on the sky., The Coma cluster is significantly more promising because it lies close to the North Galactic Pole and appears 10 times smaller on the sky. +" On the other hand, an overly small aperture, corresponding for example to the few arcmin resolution of the Fermi LAT instrument at about 10GeV, would miss a large fraction of the signal in Coma and other nearby galaxy clusters."," On the other hand, an overly small aperture, corresponding for example to the few arcmin resolution of the Fermi LAT instrument at about $10\,{\rm + GeV}$, would miss a large fraction of the signal in Coma and other nearby galaxy clusters." +" For a uniform background, the optimal filter has a shape similar to the predicted profile (?) shown in Figure 3 and represented by equation (2)."," For a uniform background, the optimal filter has a shape similar to the predicted profile \citep{sp08a} + shown in Figure 3 and represented by equation (2)." + In Table 1 we summarise properties of some nearby astronomical objects which are relevant for the detectability of their dark matter annihilation signal., In Table \ref{TabObes} we summarise properties of some nearby astronomical objects which are relevant for the detectability of their dark matter annihilation signal. +" We consider six galaxy clusters which were already analyzed by the Fermi collaboration (?),, thirteen of the known dwarf satellites of our Galaxy, and the nearest giantgalaxy, M31."," We consider six galaxy clusters which were already analyzed by the Fermi collaboration \citep{ackermann10}, thirteen of the known dwarf satellites of our Galaxy, and the nearest giantgalaxy, M31." +" For the galaxy clusters, distances were taken from the NASA/IPAC Extragalactic Database!,, and virial masses, M299 (based on X-ray data), from ?.."," For the galaxy clusters, distances were taken from the NASA/IPAC Extragalactic , and virial masses, ${\rm M_{200}}$ (based on X-ray data), from \cite{reiprich02}. ." + Values for Vinax and rmax were, Values for $V_{\rm max}$ and $r_{\rm max}$ were +"mass per field of zzντο. 8 10"" MM...","mass per field of $\approx +f_{z>\rm 5}\times$ $\rightarrow$ 2.8 $\times 10^9$ $_{\odot}$." + In this case it is valid to include the quasar contribution. regardless of whether their submm luminosity is powered by starburst or AGN.," In this case it is valid to include the quasar contribution, regardless of whether their submm luminosity is powered by starburst or AGN." +" The result is ~1.9 23.3 10"" . Y.", The result is $\sim$ $\rightarrow$ 3.3 $\times 10^9$ $_{\odot}$ ). + If the dust-to-gas ratio in these objects is similar to that of the Milky Way. their total gas mass is (Sons/mJv)10 MM..," If the dust-to-gas ratio in these objects is similar to that of the Milky Way, their total gas mass is $\sim(S_{\rm 850\mu m}/{\rm mJy})\times +10^{10}$ $_{\odot}$." + Finally. we consider the possibility that some of the submm companions are powered by buried AGN rather than obscured star formation.," Finally, we consider the possibility that some of the submm companions are powered by buried AGN rather than obscured star formation." + This is not implausible given evolutionary scenarios for SMGs involving co-evolution between black holes and massive spheroids., This is not implausible given evolutionary scenarios for SMGs involving co-evolution between black holes and massive spheroids. + Assuming. in the most extreme case. that Lyin represents the bolometric luminosity of the AGN. and assuming Eddington-limited accretion. the brightest SMGs (10 mmly) would have black holes of mass =4.107 MM...," Assuming, in the most extreme case, that $L_{\rm FIR}$ represents the bolometric luminosity of the AGN, and assuming Eddington-limited accretion, the brightest SMGs $\approx$ mJy) would have black holes of mass $\approx 4\times 10^8$ $_{\odot}$." +" Their hard X-ray fluxes (2-lOkkeV) would be zz4.10."""" ?ss. |."," Their hard X-ray fluxes keV) would be $\approx 4\times +10^{-15}$ $^{-2}$ $^{-1}$." + For the general SMG population. or at least the radio-identitied subset. deep X-ray observations (e.g.2) show that their AGN are weak compared with their bolometric luminosity.," For the general SMG population, or at least the radio-identified subset, deep X-ray observations \citep[e.g.][]{alexander05} show that their AGN are weak compared with their bolometric luminosity." + We have no reason to believe the SMGs in our high-redshift quasar tields should be any different: indeed. their SMBHs are likely somewhat less developed than those explored by ? at 2—2.2.," We have no reason to believe the SMGs in our high-redshift quasar fields should be any different; indeed, their SMBHs are likely somewhat less developed than those explored by \citeauthor{alexander05} at $z\sim\rm 2.2$." + To measure source sizes requires knowledge of the PSF. determined to be [3.4 aresec and near-cireular by fitting a 2-dimensional (2-D) Gaussian to a beam map of 3345.," To measure source sizes requires knowledge of the PSF, determined to be 13.4 arcsec and near-circular by fitting a 2-dimensional (2-D) Gaussian to a beam map of 345." + We have used these parameters to determine the size of the most significant (> 67) sources. again using 2-D Gaussian fits within the software environment.," We have used these parameters to determine the size of the most significant $>6\sigma$ ) sources, again using 2-D Gaussian fits within the software environment." + SDSS 0756-4104 appears to be resolved along an axis with PA 69°., SDSS J0756+4104 appears to be resolved along an axis with PA $^{\circ}$. + Along the orthogonal axis. the quasar's submim emission is point-like.," Along the orthogonal axis, the quasar's submm emission is point-like." + Deconvolving the beam from the best-bet 2-D Gaussian fit suggests an emission region of size (16.043:1.5) aaresee (0.01.5) aaresec. though the apparent morphology could be mimicked by two or more well-separated. compact sources.," Deconvolving the beam from the best-bet 2-D Gaussian fit suggests an emission region of size $\rm (16.0\pm 1.5)$ arcsec $\times$ $\rm (0.0\pm 1.5)$ arcsec, though the apparent morphology could be mimicked by two or more well-separated, compact sources." + At first sight SDSS 10 0125 also appears resolved. albeit with less certainty than for the ~l4o detection of SDSS JO75644104.," At first sight SDSS $-$ 0125 also appears resolved, albeit with less certainty than for the $\sim$ $\sigma$ detection of SDSS J0756+4104." + However. the best-fit 2-D Gaussian has dimensions similar to those of the beam: (14.4+2.5) aaresec 2.5) aaresee at PA 1257. so we conclude that there is no compelling evidence that the emission from SDSS 0125 has been resolved.," However, the best-fit 2-D Gaussian has dimensions similar to those of the beam: $\rm (14.4\pm 2.5)$ arcsec $\times$ $\rm +(12.5\pm 2.5)$ arcsec at PA $^{\circ}$, so we conclude that there is no compelling evidence that the emission from SDSS $-$ 0125 has been resolved." + The angular scale is zz6 tats ~5/—6. so the physical scale of the emission from SDSS J07564-4104 corresponds to z kkpe on the plane of the sky.," The angular scale is $\approx$ $^{-1}$ at $z\sim\rm 5-6$, so the physical scale of the emission from SDSS J0756+4104 corresponds to $\approx$ kpc on the plane of the sky." + This suggests. perhaps. that we ure witnessinga colossal merger.," This suggests, perhaps, that we are witnessinga colossal merger." + Lensing might provide an alternative explanation. though there is scant evidence for this from optical images.," Lensing might provide an alternative explanation, though there is scant evidence for this from optical images." + Evidence of source structure deviating from that of a point source has been noted in previous submm observations of high-redshift galaxies (e.g.22)...," Evidence of source structure deviating from that of a point source has been noted in previous submm observations of high-redshift galaxies \citep[e.g.][]{ivison00, stevens03}." +" The mm continuum and CO line emission from the ;=4.7 quasar, BR 0725. was clearly separated into two components by ?.. albeit with a smaller angular separation aaresec) than single-dish submm imaging is capable of resolving."," The mm continuum and CO line emission from the $z=\rm 4.7$ quasar, BR $-$ 0725, was clearly separated into two components by \citet{omont96}, albeit with a smaller angular separation arcsec) than single-dish submm imaging is capable of resolving." + Several high-redshift radio galaxies have also been resolved in CO line emission (22) on aresee scales using the IRAM Plateau de Bure interferometer (PdBD.," Several high-redshift radio galaxies have also been resolved in CO line emission \citep{pppp00, debreuck05} on arcsec scales using the IRAM Plateau de Bure interferometer (PdBI)." + The linear Press-Sehechter approximation can be used to demonstrate analytically the concept of bias in a hierarchical cosmology (e.g.2)., The linear Press–Schechter approximation can be used to demonstrate analytically the concept of bias in a hierarchical cosmology \citep[e.g.][]{mo+white02}. +" However. numerical simulations of the evolution of CDM. which can track the collapse of fluctuations on large scales into the non-linear regime. reveal a more complex picture. the dark matter exhibiting a rich spatial structure (filaments. clusters: the so-called “cosmic web"")."," However, numerical simulations of the evolution of CDM, which can track the collapse of fluctuations on large scales into the non-linear regime, reveal a more complex picture, the dark matter exhibiting a rich spatial structure (filaments, clusters: the so-called “cosmic web”)." +" In the ""Millenium Simulation"". ?. specitically identify +=6 quasars. Selecting them as the objects with the most massive dark matter haloes and/or the largest stellar mass."," In the “Millenium Simulation”, \citet{springel05} specifically identify $z=\rm 6$ quasars, selecting them as the objects with the most massive dark matter haloes and/or the largest stellar mass." +" These objects have halo masses ~104°"" MM.. SFRs of several ΙΟΟΜΜ. yyr and evolve into the central dominant galaxies of rich clusters at >=0."," These objects have halo masses $\sim10^{12.5}$ $_{\odot}$, SFRs of several $_{\odot}$ $^{-1}$ and evolve into the central dominant galaxies of rich clusters at $z=\rm 0$." + At >=6 they are surrounded by numerous star-forming galaxies and lie on prominent dark matter tilaments (Fig., At $z=\rm 6$ they are surrounded by numerous star-forming galaxies and lie on prominent dark matter filaments (Fig. + 3 of 2))., 3 of \citealt{springel05}) ). + The knots strung out on these filaments are reminiscent of the submm companions to z>>5 quasars — especially. for example. the neighbouring pair in the SDSS JO75644104 image (Fig. 19).," The knots strung out on these filaments are reminiscent of the submm companions to $z>\rm 5$ quasars – especially, for example, the neighbouring pair in the SDSS J0756+4104 image (Fig. \ref{scuba}) )," + and the possible binarity of the quasar host itself., and the possible binarity of the quasar host itself. + However. such claims are premature: the angular scale over which one would confidently expect to see large-scale structure is somewhat greater than that enclosed within the field-of-view of SCUBA.," However, such claims are premature: the angular scale over which one would confidently expect to see large-scale structure is somewhat greater than that enclosed within the field-of-view of SCUBA." + The present images correspond only to the innermost | MMpe of such structures., The present images correspond only to the innermost $\sim$ Mpc of such structures. +" A tentative evolutionary scheme in which to interpret our observations is the ""anti-hierarchical"" model of ??.."," A tentative evolutionary scheme in which to interpret our observations is the “anti-hierarchical” model of \citet{granato04, granato06}." + This scheme not only incorporates the effects of feedback. from the AGN on star formation. but explicitly takes account of dust.," This scheme not only incorporates the effects of feedback from the AGN on star formation, but explicitly takes account of dust." + A counter-intuitive feature of this model is that the evolution progresses more rapidly for the most massive objects., A counter-intuitive feature of this model is that the evolution progresses more rapidly for the most massive objects. + SMGs are envisaged as massive spheroids undergoing a major episode of dust-enshrouded star formation. containing small (but. gradually accreting) black holes in their cores.," SMGs are envisaged as massive spheroids undergoing a major episode of dust-enshrouded star formation, containing small (but gradually accreting) black holes in their cores." + Eventually the black hole becomes sufficiently massive to power a quasar. thereby terminating star formation via jets in radio-loud systems or via aceretion-driven winds in radio- objects.," Eventually the black hole becomes sufficiently massive to power a quasar, thereby terminating star formation via jets in radio-loud systems or via accretion-driven winds in radio-quiet objects." + The system then evolves passively as a massive elliptical galaxy to the present day., The system then evolves passively as a massive elliptical galaxy to the present day. + Submm-luminous high-redshift quasars presumably correspond to the late stages of this transition between SMG and QSO ¢??)..," Submm-luminous high-redshift quasars presumably correspond to the late stages of this transition between SMG and QSO \citep{page04, stevens05}. ." + If the QSO represents the most massive collapsed object in its field (by design we have selected, If the QSO represents the most massive collapsed object in its field (by design we have selected +Alagnetic cataclysmic variables (polars or AAI Ler stars) are binary svstems where a magnetised (5~101 €) white chvarl accretes from a low mass companion (see e.g. the review by Cropper 1990).,Magnetic cataclysmic variables (polars or AM Her stars) are binary systems where a magnetised $B\sim 10^7$ G) white dwarf accretes from a low mass companion (see e.g. the review by Cropper 1990). + Such magnetic fields are strong enough to disrupt disk formation., Such magnetic fields are strong enough to disrupt disk formation. + Instead. the accreting stream is entrained by the magnetic field and Falls freely through the eravitational potential until it hits the white dwarf surface.," Instead, the accreting stream is entrained by the magnetic field and falls freely through the gravitational potential until it hits the white dwarf surface." + The resultant. strong shock has a typical temperature of tens of keV for optically thin material. giving rise to an Ν΄ταν criittine plasma.," The resultant strong shock has a typical temperature of tens of keV for optically thin material, giving rise to an X–ray emitting plasma." + Normally such systems are locked into svnchronous rotation by the magnetic field. so that (to zeroth order) the stream impacts onto the same part of the magnetosphere.," Normally such systems are locked into synchronous rotation by the magnetic field, so that (to zeroth order) the stream impacts onto the same part of the magnetosphere." + However. there are now three svstenis known where the orbital period and white dwarf spin period ave slightly cillerent. BY Cam. V1500 Cvg and WA 1940.2-1025 (e.g. Watson et al 1995). so that the aceretion geometry changes continuously.," However, there are now three systems known where the orbital period and white dwarf spin period are slightly different, BY Cam, V1500 Cyg and RXJ 1940.2-1025 (e.g. Watson et al 1995), so that the accretion geometry changes continuously." + Recent progress in understanding the detailed. shape of the Xray emission has concentrated on the ellects of reprocessing of the hard. Xrav. emission., Recent progress in understanding the detailed shape of the X–ray emission has concentrated on the effects of reprocessing of the hard X–ray emission. + Inclusion. of the effect. of Compton reflection from. the white. dwarf surface complex absorption from the accreting materiaand the multitemperature shock structure are. necessary ingredients in the spectral model., Inclusion of the effect of Compton reflection from the white dwarf surface complex absorption from the accreting material the multi–temperature shock structure are necessary ingredients in the spectral model. + While the importance of any one or two of these individual ellects have long been recognised (c.g. Imamura Durisen 1983.— absorption anc shock structure: Swank. Fabian Ross 1984: Deardmore et al 1995 absorption and. reflection) all three are," While the importance of any one or two of these individual effects have long been recognised (e.g. Imamura Durisen 1983 – absorption and shock structure; Swank, Fabian Ross 1984; Beardmore et al 1995 – absorption and reflection) all three are" +from Lvyman-limit ancl damped Lyman-a systems.,from Lyman-limit and damped $\alpha$ systems. + “Phis absorption is generally not. included. in simulations of the Ένα forest. and it arises from dense. self-shielding svstenmis that are not captured: properly. in almost. all cosmological simulations anyway (2?) ," This absorption is generally not included in simulations of the $\alpha$ forest, and it arises from dense, self-shielding systems that are not captured properly in almost all cosmological simulations anyway \citep{katz96, mcquinn11}." +"""These svstems could alter the of-ight power at the 1054 level at &(2:0.1Alpe t (7). and at the 10054 [evel at &,=0.01 ! (Appendix DJ). Appendix D. discusses a simple mocel for the power in these systems that qualitatively reproduces the numerical estimates for the ellect of damping wings in ? and that allows us to estimate their impact for 3D analyses."," These systems could alter the line-of-sight power at the $10\%$ level at $k_\parallel \approx 0.1~$ $^{-1}$ \citep{mcdonald05}, and at the $100\%$ level at $k_\parallel = 0.01~$ $^{-1}$ (Appendix \ref{ap:DLAs}) Appendix \ref{ap:DLAs} discusses a simple model for the power in these systems that qualitatively reproduces the numerical estimates for the effect of damping wings in \citet{mcdonald05} and that allows us to estimate their impact for $3$ D analyses." + We show that much of the line-of-sight power from. damping wings arises [rom the uncorrelat (shot) component oftheir power., We show that much of the line-of-sight power from damping wings arises from the uncorrelated (shot) component of their power. + The shot contribution toed the 3D flux. power from damping wings is much smaller than in the linc-of-sight (ux power spectrum. and. thus. the role of damping wings as a contaminant is reduced. (Appendix DJ).," The shot contribution to the $3$ D flux power from damping wings is much smaller than in the line-of-sight flux power spectrum, and, thus, the role of damping wings as a contaminant is reduced (Appendix \ref{ap:DLAs}) )." + However. we show that they still are likely to add power to £4 at the tens of percent level.," However, we show that they still are likely to add power to $P_{\rm F}$ at the tens of percent level." + This paper studied issues relevant to upcoming 3D. Lya forest’ surveys., This paper studied issues relevant to upcoming $3$ D $\alpha$ forest surveys. + We derived. asimple. formula. for how to optimally weight sightlines with varving S/N levels., We derived asimple formula for how to optimally weight sightlines with varying $S/N$ levels. +" We found that simply weighting sightline bv (1|an;umo21 where e$; and 77, are respectively the variance of the noise and of the Lye forest normalized lux in a 10 Alpe region or ereater. performs nearly as well as the weights specified. by the minimum variance quadratic estimator."," We found that simply weighting sightline $i$ by $(1 +\sigma_{{\rm N}, i}^2/\sigma_{\rm los}^2)^{-1}$, where $\sigma_{{\rm N}, i}^2$ and $\sigma_{\rm los}^2$ are respectively the variance of the noise and of the $\alpha$ forest normalized flux in a $10~$ Mpc region or greater, performs nearly as well as the weights specified by the minimum variance quadratic estimator." + These weights should be simple to apply to data even in the presence of real-world complications., These weights should be simple to apply to data even in the presence of real-world complications. + We derived an expansion. (which involves only. matrix multiplications) that converges to the minimum variance quadratic estimator and for which our suggested. weights are the lowest order contribution., We derived an expansion (which involves only matrix multiplications) that converges to the minimum variance quadratic estimator and for which our suggested weights are the lowest order contribution. + We showed that the next term in this expansion has the intuitive behavior of suppressing the contribution from quasars that have an overabundance within riKL., We showed that the next term in this expansion has the intuitive behavior of suppressing the contribution from quasars that have an overabundance within $r_{\perp} \lesssim k_\perp^{-1}$. + We showed that the sensitivity of a spectroscopic survey to the Lya forest flux power spectrum can be quantified bv just a single number. ma à number densitv of sources on the sky so that noisc-weightedvar(κ)=20M|Dal {ην ," We showed that the sensitivity of a spectroscopic survey to the $\alpha$ forest flux power spectrum can be quantified by just a single number, $\bar{n}_{\rm eff}$ – a noise-weighted number density of sources on the sky – so that ${\rm var}[\widehat{P}_{\rm F}(\bfk)] = 2 \, (P_{\rm F} + \bar{n}_{\rm eff}^{-1} \,P_{\rm los})^2$ ." +While this number technically depends on the Ay of the wavevector in. question. in. practice this dependence is extremely weak at Ay«0.5 I because D is almost constant over these waveveectors.," While this number technically depends on the $k_\parallel$ of the wavevector in question, in practice this dependence is extremely weak at $k_\parallel < 0.5~$ $^{-1}$ because $P_{\rm los}$ is almost constant over these wavevectors." + These. are he same wavevectors at which 3D Lya surveys have the potential to derive competitive constraints on Cosmological xuwameters (7). and that are the most. interesting Lor studying astrophysical sources of Iluctuations in the Lya forest (?).., These are the same wavevectors at which $3$ D $\alpha$ surveys have the potential to derive competitive constraints on cosmological parameters \citep{mcdonald07} and that are the most interesting for studying astrophysical sources of fluctuations in the $\alpha$ forest \citep{mcquinn10}. + We calculated nar as a function of survey specifications or both quasar and galaxy surveys at clillerent: redshifts., We calculated $\bar{n}_{\rm eff}$ as a function of survey specifications for both quasar and galaxy surveys at different redshifts. + For quasar surveys. it is dillieult to achieve significantly vigher sar than =34«10 (or =30 per 2 ἄοστ) at any redshift owing to the shallowness of the faint end of the quasar luminosity function.," For quasar surveys, it is difficult to achieve significantly higher $\bar{n}_{\rm eff}$ than $\approx 3 \times 10^{-3}~$ $^{-2}$ (or $\approx 30$ per $^{2}$ ) at any redshift owing to the shallowness of the faint end of the quasar luminosity function." + A survey. with mar=3.10 >? js aliasing noise-limited at &0.1 1, A survey with $\bar{n}_{\rm eff} = 3\times10^{-3}~$ $^{-2}$ is aliasing noise-limited at $k > 0.1~$ $^{-1}$. +n this limit. the S/N on Py scales linearlywith nor.," In this limit, the $S/N$ on $P_{\rm F}$ scales linearlywith $\bar{n}_{\rm eff}$." + This paper also discussed: survey strategy tradcolls., This paper also discussed survey strategy tradeoffs. + The previous results allowed for a simpler characterization of these tradeolfs than in. prior studies., The previous results allowed for a simpler characterization of these tradeoffs than in prior studies. + We showed that a surveys sensitivity to the flux correlation function. is maximized with the strategy of integrating on cach field just ong enough to achieve S/N=2 in à lA »pixel for an ἐν quasar.," We showed that a survey's sensitivity to the flux correlation function is maximized with the strategy of integrating on each field just long enough to achieve $S/N\approx 2$ in a $1\,$ pixel for an $L_*$ quasar." + Llowever. we found that a shallower strateey but covering a wider field Llormally obtains a comparable sensitivity to £p at OL ⋅ ⊀ −⋜⋯∠⇂⋏∙≟⋜↧∖⇁⋖⊾⋜⋯⋯⇂⋖⊾⊏↥⊔⋜⋯⋅↓∐∖∖⊽∐↓↕∖−∶↻−≽⊔⊰⇂∪↓⋅⋅↱≻⇀⊰2 ⋅−⋅⋅ ⋅ egrees of freedom., Fitting the spectrum (Figure \ref{fig_spec}) ) with the absorbed power-law resulted in a photon index $\Gamma$ of 2.17 $\pm$ 0.13 and a hydrogen column density$N_\mathrm{H}$ of (8.1 $\pm$ 0.1) $\times$ $^{21}$ $^{-2}$ and gave an adequate fit with $\chi^2$ = 62.3 for 53 degrees of freedom. + The quoted uncertainties are at the, The quoted uncertainties are at the + , + , +In case none of the eigenvalues fulfill the criterium (to be expected in extremely noisy spectra). we have chosen to reconstruct using only the first eigenvector.,"In case none of the eigenvalues fulfill the criterium (to be expected in extremely noisy spectra), we have chosen to reconstruct using only the first eigenvector." + The upper and bottom left panels of Fig., The upper and bottom left panels of Fig. + 2. show. for the cases discussed in the next section. the ratio between the eigenvalues of the cross-product matrix obtained from the synthetic data plus noise and the eigenvalues of the pure noise cross-product matrix.," \ref{autoval_ratio} show, for the cases discussed in the next section, the ratio between the eigenvalues of the cross-product matrix obtained from the synthetic data plus noise and the eigenvalues of the pure noise cross-product matrix." + The horizontal dashed line indicates the threshold that we choose to select the eigenvectors., The horizontal dashed line indicates the threshold that we choose to select the eigenvectors. + The bottom right panel of the figure shows the first four selected eigenvectors for the less noisy case that we analyze in this paper., The bottom right panel of the figure shows the first four selected eigenvectors for the less noisy case that we analyze in this paper. + We present in this section the behavior of the PCA denoising in several S/N regimes., We present in this section the behavior of the PCA denoising in several $S/N$ regimes. + We range from very noisy profiles in which the signal is completely masked by the noie to less noisy profiles in which the PCA technique can be used to improve even more the quality of the data for the analysis of individual spectral lines., We range from very noisy profiles in which the signal is completely masked by the noise to less noisy profiles in which the PCA technique can be used to improve even more the quality of the data for the analysis of individual spectral lines. + For the sake of simplicity. all the figures showing individual line profiles present results for Stokes V. although similar results (for similar values of the S/N) are obtained for Stokes Q and U.," For the sake of simplicity, all the figures showing individual line profiles present results for Stokes $V$, although similar results (for similar values of the $S/N$ ) are obtained for Stokes $Q$ and $U$." + However. the general denoising trends are presented both for circular and linear polarisation states.," However, the general denoising trends are presented both for circular and linear polarisation states." + As representative. of an intermediate. S/N. we present the results obtained when the S/N in the 630.2 nm line is 3.358.," As representative of an intermediate $S/N$, we present the results obtained when the $S/N$ in the 630.2 nm line is 3.358." + As can be seen in Fig., As can be seen in Fig. + 3. amplitudes like the one of the 630.2 nm are not very common in the spectrum., \ref{ampl_v} amplitudes like the one of the $630.2$ nm are not very common in the spectrum. + This means that most of the spectral lines would have S/N values at least 5 to 10 times smaller., This means that most of the spectral lines would have S/N values at least 5 to 10 times smaller. + Then. we are dealing with a an example that can be representative of a typical observational case in stellar polarised spectra.," Then, we are dealing with a an example that can be representative of a typical observational case in stellar polarised spectra." + Although the real signal is still below the noise level for most of the lines. the number of selected eigenvectors 1s 4 according to the eriterium of Sec. 3.4..," Although the real signal is still below the noise level for most of the lines, the number of selected eigenvectors is 4 according to the criterium of Sec. \ref{sec:procedure}." + The left panels of Fig., The left panels of Fig. + 4 show the comparison between the original synthetic profile without noise and the profile recovered after PCA denoising starting from the noisy profiles., \ref{sn3360} show the comparison between the original synthetic profile without noise and the profile recovered after PCA denoising starting from the noisy profiles. + The right panels of Fig., The right panels of Fig. + 4 show the comparison between the noisy and the PCA-filtered signals of three individual spectral lines and a line widely known in solar physies., \ref{sn3360} show the comparison between the noisy and the PCA-filtered signals of three individual spectral lines and a line widely known in solar physics. + In these conditions. the shape of all the spectral lines is roughly reproduced and the S/N of the filtered data is good enough for a reliable study of these individual spectral lines.," In these conditions, the shape of all the spectral lines is roughly reproduced and the $S/N$ of the filtered data is good enough for a reliable study of these individual spectral lines." + The results presented so far have been obtained, The results presented so far have been obtained +of the visibility changes accordingly. tthe curvature of V indicates the changing slope of the spatial intensity distribution.,"of the visibility changes accordingly, the curvature of V indicates the changing slope of the spatial intensity distribution." + Thus. the visibility constrains the grain radii not only via its slope. but also via its curvature.," Thus, the visibility constrains the grain radii not only via its slope, but also via its curvature." + The observed visibility τηε declines in almost a straight line to values below ~0.10 at q=13.5aresoc.| with onlya slight curvature., The observed visibility $V_{\rm obs}$ declines in almost a straight line to values below $\sim 0.40$ at $q=13.5{\rm arcsec^{-1}}$ with onlya slight curvature. + Έρις 1s fairly well matched by the model with a.=0.16μια. although the curvature of the model visibility is a little too strong.," $V_{\rm obs}$ is fairly well matched by the model with $a_{\rm gr}=0.16\,{\rm\mu m}$, although the curvature of the model visibility is a little too strong." +" Since the visibilities for models with a,=0.15;an and μι=0.17jan already fall outside the error bars of the observation. at least for certain spatial frequencies. the grain radius is determined by τς with an uncertainty <0.01jan GGroenewegen 1997))."," Since the visibilities for models with $a_{\rm gr}=0.15\,{\rm\mu m}$ and $a_{\rm gr}=0.17\,{\rm\mu m}$ already fall outside the error bars of the observation, at least for certain spatial frequencies, the grain radius is determined by $V_{\rm obs}$ with an uncertainty $<0.01\,{\rm\mu m}$ Groenewegen \cite{Groe97}) )." + However. the SED for the model with νι=0.16gan. shows a deficit of flux below A=μια.," However, the SED for the model with $a_{\rm gr}=0.16\,{\rm\mu m}$, shows a deficit of flux below $\lambda = 3\,{\rm\mu m}$." + This deficit cannot be removed by a change of Tj or Tig., This deficit cannot be removed by a change of $T_{1}$ or $T_{\rm eff}$. + Although lowering T4 increases the flux at Àx3μι it also decreases the flux at longer wavelengths.," Although lowering $T_{1}$ increases the flux at $\lambda \la 3\,{\rm\mu m}$ it also decreases the flux at longer wavelengths." + Furthermore. the inner boundary of the dust shell is moved outwards which deforms the resulting visibility in a way that destroys the fit.," Furthermore, the inner boundary of the dust shell is moved outwards which deforms the resulting visibility in a way that destroys the fit." + Increasing Ty yields a similiar behaviour., Increasing $T_{\rm eff}$ yields a similiar behaviour. + The deficit of the short wavelength model flux could have several causes. but the clear evidence for a non-spherical dust distribution around from our speckle masking observations favors the explanation that the deficiency of flux in the model is due to the assumption of a spherically symmetric circumstellar dust shell.," The deficit of the short wavelength model flux could have several causes, but the clear evidence for a non-spherical dust distribution around from our speckle masking observations favors the explanation that the deficiency of flux in the model is due to the assumption of a spherically symmetric circumstellar dust shell." +" A more general assumption would be that the CDS has an axisymmetric. ""disk-like structure."," A more general assumption would be that the CDS has an axisymmetric, `disk–like' structure." + Theoretical investigations show that the variation of the effective optical depth with the inclinatior of a disk-like dust distribution affects the shape of the SED up to far infrared wavelengths. as well as the monochromatic intensity distributions and the corresponding visibilities EEfstathiou Rowan-Robinson 1990:: Collison Fix 1991:: Lopez et cite_LML95S:: Men’shchikov Henning 1997)).," Theoretical investigations show that the variation of the effective optical depth with the inclination of a disk–like dust distribution affects the shape of the SED up to far infrared wavelengths, as well as the monochromatic intensity distributions and the corresponding visibilities Efstathiou Rowan–Robinson \cite{EfRo90}; Collison Fix \cite{CoFi91}; Lopez et \\cite{LML95}; Men'shchikov Henning \cite{MeHe97}) )." + If the disk- dust distribution is viewed at an intermediate inclination one expects more flux at visual wavelengths than in the case of a spherically symmetric dust distribution. due to scattered light escaping from the optically thinner polar region located either above or below the equatorial plane.," If the disk--like dust distribution is viewed at an intermediate inclination one expects more flux at visual wavelengths than in the case of a spherically symmetric dust distribution, due to scattered light escaping from the optically thinner polar region located either above or below the equatorial plane." + In other words. we expect a deficiency of the model flux at short wavelengths if we model the SED of an aspherical dust distribution assuming a spherically symmetric dust distribution.," In other words, we expect a deficiency of the model flux at short wavelengths if we model the SED of an aspherical dust distribution assuming a spherically symmetric dust distribution." + We have presented the first diffraction-Iimited 2.11ju speckle masking observations of the circumstellar dust shell around the highly obscured type II OH/IR star 2290.," We have presented the first diffraction–limited $2.11\,{\rm\mu m}$ speckle masking observations of the circumstellar dust shell around the highly obscured type II OH/IR star ." +. The resolution achieved with the SAO 6 m telescope is 75 mas. which is sufficient to partially resolve the circumstellar dust," The resolution achieved with the SAO 6 m telescope is 75 mas, which is sufficient to partially resolve the circumstellar dust" +The lack of recent star formation activity in the LCs indicates that the Mglll absorbing gas is likely due to infalling clouds instead. of starburst driven outllows.,The lack of recent star formation activity in the LRGs indicates that the II absorbing gas is likely due to infalling clouds instead of starburst driven outflows. + Uncer the infall scenario. different theoretical models have been studied to explain the presence of cool halo gas.," Under the infall scenario, different theoretical models have been studied to explain the presence of cool halo gas." + οσο include cold Lows citealtfaucher-giguere2011a)). cool clouds condensed out of the hot halos due to thermal instabilities (Mo Aliralela-Escudé 1996: Maller Bullock 2004. hereafter MDBOA). anc stripped material from satellite galaxies citealtwangl003a.agertz2009a)).," These include cold flows \\citealt{faucher-giguere2011a}) ), cool clouds condensed out of the hot halos due to thermal instabilities (Mo Miralda-Escud\'e 1996; Maller Bullock 2004, hereafter MB04), and stripped material from satellite galaxies \\citealt{wang1993a,agertz2009a}) )." + Irrespective of the physica mechanism that produces the observed HL absorbers near the LRGs. the cool clouds are expected to fall and fue star formation at the center of the halo.," Irrespective of the physical mechanism that produces the observed II absorbers near the LRGs, the cool clouds are expected to fall and fuel star formation at the center of the halo." + At the same time. the galaxies are found to be quiescent for at least the pas 1 Gar. implving that these Mglll clouds do not survive the infall through the hot halo.," At the same time, the galaxies are found to be quiescent for at least the past 1 Gyr, implying that these II clouds do not survive the infall through the hot halo." + Whether or not cool clouds can reach the center of the halo depends. on the infall time scale relative to the disruption time scale., Whether or not cool clouds can reach the center of the halo depends on the infall time scale relative to the disruption time scale. + Under hydrostatie equilibrium. the infall time scale. is determined: primarily by the ram pressure drag. while the cliscruption time scale is driven predominantly by heat conduction.," Under hydrostatic equilibrium, the infall time scale is determined primarily by the ram pressure drag, while the discruption time scale is driven predominantly by heat conduction." + Lf the evaporation time scale. Tae is shorter than the time scale needed. for ram pressure drag to sap the energy. the clouds will likely evaporate before reaching the center of the halo.," If the evaporation time scale, $\tau_{\rm evap}$, is shorter than the time scale needed for ram pressure drag to sap the energy, the clouds will likely evaporate before reaching the center of the halo." + This allows us το constrain the physical properties of the cool clouds MMaller Bullock 2004), This allows us to constrain the physical properties of the cool clouds Maller Bullock 2004). +" Lor this particular model, Τον~ where gno ds the cloud mass in units of LO? A7.. 45= ΙΙΙ is the halo gas temperature. A. and fs=F/(SGyr) are the cooling parameter anc halo formation time scale(see equation 35 and Appendix D in MDO4)."," For this particular model, $\tau_{\rm evap} \simeq +16\,m_6^{2/3}T_6^{-3/2}(\Lambda_z t_8)^{-1/3}~\rm{Gyr}$ where $m_6$ is the cloud mass in units of $10^6$ $M_{\odot}$, $T_6 = T/10^6$ K is the halo gas temperature, $\Lambda_z$ and $t_8=t/(8~\rm{Gyr})$ are the cooling parameter and halo formation time scale (see equation 35 and Appendix B in MB04)." +" Assuming that the hot gas is isothermal with Z—6«LO? Wh. fs is the age of the universe at z0.5. and the metallicity of the gas is 0.1 solar. we found that. za,c1.1m;Gyr."," Assuming that the hot gas is isothermal with $T +\sim 6 \times 10^6$ K, $t_8$ is the age of the universe at $z \sim +0.5$, and the metallicity of the gas is 0.1 solar, we found that $\tau_{\rm evap} \simeq 1.1\,m_6^{2/3}~\rm{Gyr}$." + The parameter Teva Constitutes the typical time scale over which clouds will be disrupted due to heat conduction., The parameter $\tau_{\rm evap}$ constitutes the typical time scale over which clouds will be disrupted due to heat conduction. + To calculate the infall time scale. we first adopted the maximum rotation velocity of the halo to estimate the ram pressure drag force.," To calculate the infall time scale, we first adopted the maximum rotation velocity of the halo to estimate the ram pressure drag force." + The time scale over which ram pressure drag force is then elven by Tuyoc2.6mlqMeCNOE?Car (scc equation 43 in ALBOL," The time scale over which ram pressure drag force is then given by $\tau_{\rm{rp}} \simeq 2.6\,m_6^{1/3} T_6^{-1/2} (\Lambda_z +t_8)^{1/3}~\rm{Gyr}$ (see equation 43 in MB04)." +" We found n—Lime""Gyr."," We found $\tau_{\rm{rp}} \simeq 1.1\,m_6^{1/3}~\rm{Gyr}$." + Because the cool naare expected. to be disrupted. before. reaching the center of the halo. zipXTp.," Because the cool clouds are expected to be disrrupted before reaching the center of the halo, $\tau_{\rm evap} \la \tau_{\rm rp}$." +" Fhis led to à mass limit of im10"" MM...", This led to a mass limit of $m \la 10^6$ $_{\odot}$. + We note a main caveat in this calculation., We note a main caveat in this calculation. + If the hot halo is oul of equilibrium either due to supernova driven wind or AGN outllows. then the structure of halo gas distribution is expected to be different before hydrostatie equilibrim can be restored BBrighenti Alathews 2003).," If the hot halo is out of equilibrium either due to supernova driven wind or AGN outflows, then the structure of halo gas distribution is expected to be different before hydrostatic equilibrim can be restored Brighenti Mathews 2003)." + The estimated mass limit is therefore very uncertain. depending on the thermal state of the halo.," The estimated mass limit is therefore very uncertain, depending on the thermal state of the halo." + For example. outflows/wines are expected to increase the ram pressure. prolonging the infall time. ancl thereby increasing the mass limit.," For example, outflows/winds are expected to increase the ram pressure, prolonging the infall time, and thereby increasing the mass limit." + Lt is also possible that the observed: LLL absorbers originate in the ISAL of a satellite galaxy. clirectly intercepting the QSO sightline.," It is also possible that the observed II absorbers originate in the ISM of a satellite galaxy, directly intercepting the QSO sightline." + However. we find this an unlikely scenario.," However, we find this an unlikely scenario." + Gauthier.etal.(2010). have shown based on an analytic calculation that if the eas content of satellite galaxies remains intact as they orbit. around. the primary galaxy. then satellite galaxies could be a dominant contributor to the gas cross-section only at small distances (p«100 )).," \citet{gauthier2010a} have shown based on an analytic calculation that if the gas content of satellite galaxies remains intact as they orbit around the primary galaxy, then satellite galaxies could be a dominant contributor to the gas cross-section only at small distances $\rho < +100$ )." + Given that ram pressure and. tical stripping is effective in removing gas in satellite. ealaxies citealtehvnoweth2008a)). we consider this a conservative upper limit to possible satellite contributions to the observed Alellb absorption features.," Given that ram pressure and tidal stripping is effective in removing gas in satellite galaxies \\citealt{chynoweth2008a}) ), we consider this a conservative upper limit to possible satellite contributions to the observed II absorption features." + We expect that empirical knowledge of the satellite environment of the LRGs and gas kinematics of the absorbers will provide further insights into the physical origin of the observed. extended. eas in LAG halos., We expect that empirical knowledge of the satellite environment of the LRGs and gas kinematics of the absorbers will provide further insights into the physical origin of the observed extended gas in LRG halos. + We thank Andrey Ixravtsov. Mariska Ixriek. Michael Rauch. and Vivien Wild. for illuminating discussions.," We thank Andrey Kravtsov, Mariska Kriek, Michael Rauch, and Vivien Wild for illuminating discussions." + We also thank Don York for helpful comments on an earlier. draft of the paper., We also thank Don York for helpful comments on an earlier draft of the paper. + We would. like to thank the anonymous referee for their insightful comments that improved the draft significantly., We would like to thank the anonymous referee for their insightful comments that improved the draft significantly. + JRG acknowledges support from the Brinson Predoctoral Fellowship and by a Crant-Ln-Aicl of Research from the National Academy of Sciences. administered. by Sigma Xi. The Scientific Research Society.," JRG acknowledges support from the Brinson Predoctoral Fellowship and by a Grant-In-Aid of Research from the National Academy of Sciences, administered by Sigma Xi, The Scientific Research Society." +over a wide range of parameter values (hat are plausible for the sun.,over a wide range of parameter values that are plausible for the sun. + But at the same lime we must recognize that this 3-Iaver model is much simpler (han the real sun. and much simpler than 2D flux (transport dynamos in spherical shells.," But at the same time we must recognize that this 3-layer model is much simpler than the real sun, and much simpler than 2D flux transport dynamos in spherical shells." +" Solutions of equation (44) in the limit of small 2, are of particular interest. since we expect the bottom laver to have (he lowest magnetic diffusivitv."," Solutions of equation (44) in the limit of small $P_{\eta L}$ are of particular interest, since we expect the bottom layer to have the lowest magnetic diffusivity." +" Ia that limit the two roots are à,=0.8D,/12."," In that limit the two roots are $\alpha_L=0,sD_L/12$." + In that case. (here is resonance even if the a-effect is zero in the bottom laver.," In that case, there is resonance even if the $\alpha$ -effect is zero in the bottom layer." + lere we answer (he question of where in the parameter space we will find resonance occurring., Here we answer the question of where in the parameter space we will find resonance occurring. + In organizing the results it is helpful to differentiate roles plaved by the various parameters in (he real sun. including how thev might vary with either time or space.," In organizing the results it is helpful to differentiate roles played by the various parameters in the real sun, including how they might vary with either time or space." + For example. while we do not know with precision the thickness of the bottom laver of the convection zone where we expect (he magnetic diffusivity to be small. this thickness should nol vary much with time. or probably with latitude.," For example, while we do not know with precision the thickness of the bottom layer of the convection zone where we expect the magnetic diffusivity to be small, this thickness should not vary much with time, or probably with latitude." + Therefore we can think of the thickness as an externally specified parameter., Therefore we can think of the thickness as an externally specified parameter. + So we would like to know where in the range of other parameters resonance should occur. for a selection of assumed bottom laver thicknesses.," So we would like to know where in the range of other parameters resonance should occur, for a selection of assumed bottom layer thicknesses." + Sinularly. the solar differential rotation does not appear to vary much with lime in the sun (the well-known torsional oscillations in rotation are about one-half of one percent of the equatorial rotation). so we can treat il in the same way.," Similarly, the solar differential rotation does not appear to vary much with time in the sun (the well-known torsional oscillations in rotation are about one-half of one percent of the equatorial rotation), so we can treat it in the same way." + The meridional flow. varies more with time. but because of the density. increase with depth. we expect the flow in the lower laver always to be much less than that of the upper laver and in the opposite direction.," The meridional flow varies more with time, but because of the density increase with depth, we expect the flow in the lower layer always to be much less than that of the upper layer and in the opposite direction." +" Somewhat arbitrarily we lake the ratio of the two. D,=--θ.1."," Somewhat arbitrarily we take the ratio of the two, $P_{v_L}=-0.1$." + We also take the meridional flow of the middle laver to equal that of the upper laver. for simplicity and with some guidance from observations. e.g. Gizon and Renipel (2008). that do not show a reversal in meridional flow at mid-depth in the solar convection Zone.," We also take the meridional flow of the middle layer to equal that of the upper layer, for simplicity and with some guidance from observations, e.g. Gizon and Rempel (2008), that do not show a reversal in meridional flow at mid-depth in the solar convection zone." + (Frou (theoretical considerations. we also do not expect the magnetic diffusivitv. in the bottom laver to vary with (ime. since i( represenis an average over many (urbulent fluctuations: we do expect it to vary. with depth. and (his we have taken into account within the limitations of a 2 or 3 laver model.," >From theoretical considerations, we also do not expect the magnetic diffusivity in the bottom layer to vary with time, since it represents an average over many turbulent fluctuations; we do expect it to vary with depth, and this we have taken into account within the limitations of a 2 or 3 layer model." + By contrast. the a-elleet in the bottom laver may come [rom the action of a relatively small number of global events. such as global. MIID instabilitv. so it mieht fIuctuate ereally with time. perhaps even changing sign.," By contrast, the $\alpha$ -effect in the bottom layer may come from the action of a relatively small number of global events, such as global MHD instability, so it might fluctuate greatly with time, perhaps even changing sign." + Therefore, Therefore +rreeions in M33 and NGC 6946 are similar to the ccomplexes in the Milky Way which has a similar star formation rate.,regions in M33 and NGC 6946 are similar to the complexes in the Milky Way which has a similar star formation rate. + NGC 253. by contrast. has a much higher star formation rate based on its FIR. luminosity. alühough high. visual extinctions make the //o. luminosities very uncertain.," NGC 253, by contrast, has a much higher star formation rate based on its FIR luminosity, although high visual extinctions make the $H\alpha$ luminosities very uncertain." + It certainly contains a more intense starburst. which is also in accord with the more massive regions it hosts.," It certainly contains a more intense starburst, which is also in accord with the more massive regions it hosts." + It seems Likely that the traction of time a super star cluster spends in the pphase is a small fraction of the massive star lifetime. perhapsLO-15%.. in accord with the estimated lifetimes of individual regions based on the number of rreeions compared wilh the number of optically visible O stars in the Galaxy L989hb).," It seems likely that the fraction of time a super star cluster spends in the phase is a small fraction of the massive star lifetime, perhaps, in accord with the estimated lifetimes of individual regions based on the number of regions compared with the number of optically visible O stars in the Galaxy \citep[e.g.,][]{wood89b}." +. Indeed. rreeion lifetimes have been a topic of much discussion since Wood&Churchwell(1959a) introduced the liletime problem”: in short. if rreelons are significantly overpressured with respect to the surrounding ISM. they should expand and dissipate on (ime scales zz107 vears.," Indeed, region lifetimes have been a topic of much discussion since \citet{wood89a} introduced the “lifetime problem”; in short, if regions are significantly overpressured with respect to the surrounding ISM, they should expand and dissipate on time scales $\approx 10^4$ years." + However. the number of regions observed is greater than is allowed for by (his (me scale.," However, the number of regions observed is greater than is allowed for by this time scale." + Several mechanisms have been proposed (ο address (this issue. most of which are likely to also be applicable to Ls. Wood&Churchwell(L989a) proposed that infalling matter or bow shocks might act to increase (he external pressure. thus extending the pphase.," Several mechanisms have been proposed to address this issue, most of which are likely to also be applicable to s. \citet{wood89a} proposed that infalling matter or bow shocks might act to increase the external pressure, thus extending the phase." + It is also possible that the ambient pressure is (vpicallv sienificantly higher than the value used by Wood&Churchwell(L989a) as proposed by (1995)., It is also possible that the ambient pressure is typically significantly higher than the value used by \citet{wood89a} as proposed by \citet{depree95}. +. The lifetimes of rreeions could also be extended if thev. are replenished by material photoevaporated from the surrounding ceireiumstellar disks (e.g..Hollenbachetal.1994).," The lifetimes of regions could also be extended if they are replenished by material photoevaporated from the surrounding circumstellar disks \citep[e.g.,][]{hollenbach94}." +. The first argument for the extreme vouth of rreeions is simply by analogy to rreeions in (he Galaxy., The first argument for the extreme youth of regions is simply by analogy to regions in the Galaxy. + If UDILIIs are composed of individual rreeions. we should expect them to have similar lifetimes provided that star lormation is relatively instantaneous over the massive star cluster.," If s are composed of individual regions, we should expect them to have similar lifetimes provided that star formation is relatively instantaneous over the massive star cluster." + As is the case for rreeions. the densities in UDILIIs are extremely. hieh. aud the implied pressures constitute an over-pressure compared (o ἐνρίσα ISM pressures.," As is the case for regions, the densities in s are extremely high, and the implied pressures constitute an over-pressure compared to typical ISM pressures." + To first order. such over-pressed regions must expand and disperse on (ime scales comparable (o the sound-crossing time scale which is a x10? vr (see Ikobulnickv Johnson 1999 for more complete details).," To first order, such over-pressed regions must expand and disperse on time scales comparable to the sound-crossing time scale which is a $\times10^5$ yr (see Kobulnicky Johnson 1999 for more complete details)." + ILowever. as discussed above for," However, as discussed above for" +Photometric calibration of the HAWK-I images was achieved via bootstrapping from aperture photometry measured in the HAWK-I images for the star 2MASS J10442989-5933170: this star is about 10” to the south-west of the disk object. appears well isolated. and has 2MASS magnitudes of J = 14.272 + 0.04. H=13.376x0.04. Ky=13.015+0.05.,"Photometric calibration of the HAWK-I images was achieved via bootstrapping from aperture photometry measured in the HAWK-I images for the star 2MASS J10442989-5933170; this star is about $10''$ to the south-west of the disk object, appears well isolated, and has 2MASS magnitudes of $J$ = 14.272 $\pm$ 0.04, $H = 13.376 \pm 0.04$, $K_s = 13.015 \pm 0.05$." +" For the bright near the disk object we determined magnitudes of /=15.3. H=14.6. and K,= 14.7."," For the bright near the disk object we determined magnitudes of $J \approx 15.3$, $H \approx 14.6$, and $K_s \approx 14.7$ ." +" The rather bluish color of this star (H—K,= —O.1) suggests a very low level of extinction and may imply that this object is located in front of the dark cloud.", The rather bluish color of this star $H-K_s = -0.1$ ) suggests a very low level of extinction and may imply that this object is located in front of the dark cloud. + It also implies that its contribution to the mid- and far-infrared fluxes for the disk object will most likely be very small and can be neglected., It also implies that its contribution to the mid- and far-infrared fluxes for the disk object will most likely be very small and can be neglected. +" For the disk object. we determined the following measurements: The peak surface brightness in the //ssouthern lobes is 17.85//116.97 mag/sqaresee in. the J-band. 115.01 mag/sqaresee in the H-band. and 12.44//113.13 mag/sqaresee in the K,-band."," For the disk object, we determined the following measurements: The peak surface brightness in the southern lobes is 16.97 mag/sqarcsec in the $J$ -band, 15.01 mag/sqarcsec in the $H$ -band, and 13.13 mag/sqarcsec in the $K_s$ -band." +" The ratio of the integrated fluxes of the northern and southern lobes ts 11 in the 7-band. 11 in the H-band. and 11 in the K,-band."," The ratio of the integrated fluxes of the northern and southern lobes is 1 in the $J$ -band, 1 in the $H$ -band, and 1 in the $K_s$ -band." +" The magnitudes of the central source in the H- and the A,-band (measured in circular apertures with 2.5-pixel radii from which the average of the fluxes measured in two equally large apertures placed just to the east and west of the center in the dust lane was subtracted to account for the local background) are found to be Κι~16.1. H~19.6. J>21.8: note that the errors of these measurements are substantial due to the complicated background."," The magnitudes of the central source in the $H$ - and the $K_s$ -band (measured in circular apertures with 2.5-pixel radii from which the average of the fluxes measured in two equally large apertures placed just to the east and west of the center in the dust lane was subtracted to account for the local background) are found to be $K_s \sim 16.1$, $H \sim 19.6$, $J > 21.8$; note that the errors of these measurements are substantial due to the complicated background." +" If we assume that the observed emission ts actually the central young stellar object. the observed color H—K,«3.5 and the assumption that the intrinsic color of the central star should be (H—Kyjox0.1 lead to an extinction estimate of Ay>54 mag."," If we assume that the observed emission is actually the central young stellar object, the observed color $H-K_s \approx 3.5$ and the assumption that the intrinsic color of the central star should be $(H-K_s)_0 \leq 0.1$ lead to an extinction estimate of $A_V > 54$ mag." + However. we note that the central pateh in the images may also just be reflected light from the innermost parts of the circumstellar disk: in that case. the true extinction and optical depth to the central source would be much higher.," However, we note that the central patch in the images may also just be reflected light from the innermost parts of the circumstellar disk; in that case, the true extinction and optical depth to the central source would be much higher." + In all optical HST images. is clearly visible. but the disk object cannot be seen.," In all optical HST images, is clearly visible, but the disk object cannot be seen." + Only the “tail” at the south-western edge of the disk object is visible in the F555W and F850LP image. suggesting that it may represent reflected light from a cloud that is unrelated to the disk object.," Only the “tail” at the south-western edge of the disk object is visible in the F555W and F850LP image, suggesting that it may represent reflected light from a cloud that is unrelated to the disk object." + In Fig., In Fig. + 5. we compare the Spitzer IRAC images to our HAWK-I near-infrared images and the HST F555W image., \ref{disk-mw-fig} we compare the Spitzer IRAC images to our HAWK-I near-infrared images and the HST F555W image. + Although the IRAC images do not have enough angular resolution to show the structure of the disk object. it can be seen that the optically invisible disk object strongly brightens with increasing wavelength.," Although the IRAC images do not have enough angular resolution to show the structure of the disk object, it can be seen that the optically invisible disk object strongly brightens with increasing wavelength." + The same is true for32., The same is true for. +2-/4.. We assembled the spectral energy distribution of the disk object from the images and literature data discussed above., We assembled the spectral energy distribution of the disk object from the images and literature data discussed above. + For our HAWK-I data we performed aperture photometry using an aperture diameter of about 5”. excluding31.," For our HAWK-I data we performed aperture photometry using an aperture diameter of about $5''$, excluding." +3-77.. For the Spitzer IRAC data an aperture diameter of 7” was used., For the Spitzer IRAC data an aperture diameter of $7''$ was used. + Due to the lower angular resolution of the IRAC data. the disk object and cannot be separated.," Due to the lower angular resolution of the IRAC data, the disk object and cannot be separated." +" However. as the K,-band flux of is only 8.8x1077 Jy. ie. 40 times lower than that of the disk object and since shows quite blue colors. we are confident that its contribution to the emission in the IRAC bands can safely be neglected."," However, as the $K_s$ -band flux of is only $8.8 \times 10^{-4}$ Jy, i.e. 40 times lower than that of the disk object and since shows quite blue colors, we are confident that its contribution to the emission in the IRAC bands can safely be neglected." + The second embedded source is clearly separated from the disk object in the IRAC images (see Fig. 5)), The second embedded source is clearly separated from the disk object in the IRAC images (see Fig. \ref{disk-mw-fig}) ) + and does not contaminate our photometry., and does not contaminate our photometry. + Although the Spitzer MIPS maps also have sufficient angular resolution to clearly separate the disk object from32.2-14.. both objects are heavily saturated and therefore no quantitative photometric analysis is possible.," Although the Spitzer MIPS maps also have sufficient angular resolution to clearly separate the disk object from, both objects are heavily saturated and therefore no quantitative photometric analysis is possible." + In. order to check the reliability of the mid- to far-infrared fluxes determined by Rathborneetal.(2002) from the MSX data. we analyzed and compared the Spitzer MIPS 24 jim image and the MSX E-band (21.3 μι) image.," In order to check the reliability of the mid- to far-infrared fluxes determined by \citet{Rathborne02} from the MSX data, we analyzed and compared the Spitzer MIPS $24\,\mu$ m image and the MSX E-band $21.3\,\mu$ m) image." + The MIPS image shows a bright. roughly circular nebulosity with a diameter of about 50” with three embedded compact. point-like sources.," The MIPS image shows a bright, roughly circular nebulosity with a diameter of about $50''$ with three embedded compact, point-like sources." + The brightest of these point-like sources is the disk object. the second brightest isYSO32.2-/4.. and the third one is the 2MASS source 10443341-5933189 (the bright object near the lower left corner of Fig.," The brightest of these point-like sources is the disk object, the second brightest is, and the third one is the 2MASS source 10443341-5933189 (the bright object near the lower left corner of Fig." + 3)., 3). + In order to determine the 24m flux of the nebula. we used an aperture with diameter 54” and excluded cireular regions with diameters of 11 centered on each of the three point-like sources.," In order to determine the $24\,\mu$ m flux of the nebula, we used an aperture with diameter $54''$ and excluded circular regions with diameters of $11''$ centered on each of the three point-like sources." + Subtracting the large-scale background level estimated from several nearby regions. we found a flux of =46 Jy for the nebula.," Subtracting the large-scale background level estimated from several nearby regions, we found a flux of $\approx 46$ Jy for the nebula." + In the MSX image. the cloud is also clearly visible.but the point- sources are not resolved.," In the MSX E-band image, the cloud is also clearly visible,but the point-like sources are not resolved." + The total flux. measured again ina 54” diameter aperture. is =95 Jy; this is the sum of the emission from the cloud and the embedded point-like sources.," The total flux, measured again in a $54''$ diameter aperture, is $\approx 95$ Jy; this is the sum of the emission from the cloud and the embedded point-like sources." +population (Reid. Sahu Hawley 2001: Torres et al.,"population (Reid, Sahu Hawley 2001; Torres et al." + 2002)., 2002). + After all. and as pointed out by Gyuk Gates (1999). the thick disk population presents a reasonable alternative to a halo population of lenses.," After all, and as pointed out by Gyuk Gates (1999), the thick disk population presents a reasonable alternative to a halo population of lenses." + Several observational (Oppenheimer et al., Several observational (Oppenheimer et al. + 2001: Kilic et al., 2001; Kilic et al. + 2006: Harris et al., 2006; Harris et al. + 2006; Vidrih et al., 2006; Vidrih et al. + 2007) works have addressed this question. but this is still a controversial issue. and a definitive answer still requires more theoretical and observational efforts.," 2007) works have addressed this question, but this is still a controversial issue, and a definitive answer still requires more theoretical and observational efforts." + In this paper we extend our previous studies of the populations of halo red and white dwarfs., In this paper we extend our previous studies of the populations of halo red and white dwarfs. + In particular. we include the contribution of non-DA halo white dwarfs to the microlensing event rate and we analyze the role played by the thick-disk populations of these stars.," In particular, we include the contribution of non-DA halo white dwarfs to the microlensing event rate and we analyze the role played by the thick-disk populations of these stars." + Special emphasis has been put on the analysis of the simulated microlensing events as afunction of the range of colors susceptible to be detected by surveys like EROS and to compare our results with those of the MACHO team., Special emphasis has been put on the analysis of the simulated microlensing events as a function of the range of colors susceptible to be detected by surveys like EROS and to compare our results with those of the MACHO team. + The paper ts organized as follows., The paper is organized as follows. + In Sect., In Sect. + 2 we summarize the main ingredients of our Monte Carlo code and other basic assumptions and procedures necessary to evaluate the microlensing optical depth towards the LMC., 2 we summarize the main ingredients of our Monte Carlo code and other basic assumptions and procedures necessary to evaluate the microlensing optical depth towards the LMC. + In this section we also deseribe in depth our thick disk model., In this section we also describe in depth our thick disk model. + Section 3 is devoted to the discussion of our main results. including the contribution of red dwarfs and DA and non-DA white dwarfs to the microlensing optical depth towards the LMC. and to compare our results with those of the EROS team.," Section 3 is devoted to the discussion of our main results, including the contribution of red dwarfs and DA and non-DA white dwarfs to the microlensing optical depth towards the LMC, and to compare our results with those of the EROS team." + In this section we also estimate the probability that a microlensing event could be assigned to the thick disk or the halo. and we discuss the contribution of red and white dwarfs to the baryonic content of the Galaxy.," In this section we also estimate the probability that a microlensing event could be assigned to the thick disk or the halo, and we discuss the contribution of red and white dwarfs to the baryonic content of the Galaxy." + Finally. in Sect.," Finally, in Sect." + 4 our major findings are summarized and we draw our conclusions., 4 our major findings are summarized and we draw our conclusions. + A detailed description of our Monte Carlo simulator has been already presented in Garefaa-Berro et al. (, A detailed description of our Monte Carlo simulator has been already presented in a-Berro et al. ( +1999). Garefaa-Berro et al. (,"1999), a-Berro et al. (" +2004). Camacho et al. (,"2004), Camacho et al. (" +2007) and Torres et al. (,2007) and Torres et al. ( +2002).,2002). + Consequently. we will only summarize the most important inputs here.," Consequently, we will only summarize the most important inputs here." + At the core of any Monte Carlo simulator there is a pseudo-random number generator algorithm. for which we have used that of James (1990).," At the core of any Monte Carlo simulator there is a pseudo-random number generator algorithm, for which we have used that of James (1990)." + It belongs to the linear congruential generator family., It belongs to the linear congruential generator family. + It provides excellent statistical properties and ensures a repetition period of 210'. which is virtually infinite for our purposes.," It provides excellent statistical properties and ensures a repetition period of $\ga +10^{18}$, which is virtually infinite for our purposes." + Each one of the Monte Carlo simulations presented here consists of an ensemble of ~5x10! independent realizations of the synthetic star population. for which the average of any observational quantity and its corresponding standard. deviation were computed.," Each one of the Monte Carlo simulations presented here consists of an ensemble of $\sim5\times10^4$ independent realizations of the synthetic star population, for which the average of any observational quantity and its corresponding standard deviation were computed." + Here the standard deviation means the ensemble mean of the sample dispersions for a typical sample., Here the standard deviation means the ensemble mean of the sample dispersions for a typical sample. + The main sequence mass is obtained by drawing a pseudo-random number according to an initial mass function., The main sequence mass is obtained by drawing a pseudo-random number according to an initial mass function. + We have adopted the standard initial mass function of Scalo (1998)., We have adopted the standard initial mass function of Scalo (1998). + Other biased non-conventional initial mass functions (Adams Laughlin 1996: Chabrier et al., Other biased non-conventional initial mass functions (Adams Laughlin 1996; Chabrier et al. + 1996) have been disregarded since these mass functions are incompatible with the observed properties of the halo white dwarf population (Isern et al., 1996) have been disregarded since these mass functions are incompatible with the observed properties of the halo white dwarf population (Isern et al. + 1998; Garcíaa-Berro. et al., 1998; a–Berro et al. + 2004). with the contribution of thermonuclear supernovae to the metallicity of the Galactic halo (Canal et al.," 2004), with the contribution of thermonuclear supernovae to the metallicity of the Galactic halo (Canal et al." + 1997). and with the observations of galactic halos in deep galaxy surveys (Charlot Silk 1995).," 1997), and with the observations of galactic halos in deep galaxy surveys (Charlot Silk 1995)." + Once the mass of the star is chosen. its main-squence lifetime 15 derived (Iben Laughlin 1989). and we are able to determine which stars have evolved into white dwarfs or remain in the main-squence as red dwarfs.," Once the mass of the star is chosen, its main-squence lifetime is derived (Iben Laughlin 1989), and we are able to determine which stars have evolved into white dwarfs or remain in the main-squence as red dwarfs." + We considered red dwarfs to have masses in the range of 0.08«M/Ma1., We considered red dwarfs to have masses in the range of $0.08>7) and calculate yi.," For example, if we want to see the constraints imposed by $n$ samples of standard candles, we actually generate $N$ mock samples with $N \gg n$ and calculate $\chi_N^2$." + Then y; is given by Throughout this paper. we choose N=1.0E5.," Then $\chi_n^2$ is given by Throughout this paper, we choose $N = 1.0\mathrm{E}5$." +" The fiducial cosmological model we used to generate mock data is the flat ACDM model with ©,,=0.279 and Ho= (see ?))."," The fiducial cosmological model we used to generate mock data is the flat $\Lambda$ CDM model with $\Omega_m = 0.279$ and $H_0 = 70.1 +\mathrm{km/s/Mpc}$ (see \citet{Komatsu:2008hk}) )." + For SNe la. we approximate the intrinsic noise m distance moduli as a Gaussian scatter with," For SNe Ia, we approximate the intrinsic noise in distance moduli as a Gaussian scatter with" +were also constructed for the content of the former regions.,were also constructed for the content of the former regions. + Automatic photometry was carried out with SEXtractor (Bertin and Arnouts 1996) in the different error boxes reported for GRB 970111., Automatic photometry was carried out with SEXtractor (Bertin and Arnouts 1996) in the different error boxes reported for GRB 970111. + We compared the images taken at CAHA on January 12 with the ones obtained on February 10 and ΕΙ., We compared the images taken at CAHA on January 12 with the ones obtained on February 10 and 11. + Variable sources have neither been found within the X-ray error boxes of ISAX J1528.8++1944 and ISAX J1528.8++1937. nor in the whole 16 diameter field.," Variable sources have neither been found within the X-ray error boxes of 1SAX +1944 and 1SAX +1937, nor in the whole $^{\prime}$ diameter field." + Fig., Fig. + 3 shows the magnitude differences in the B and R filters for objects inside the error boxes of GRB 970111 when the frames taken in CAHA 19 hours after the burst and ~ | month later are compared., \ref{dif} shows the magnitude differences in the B and R filters for objects inside the error boxes of GRB 970111 when the frames taken in CAHA 19 hours after the burst and $\sim$ 1 month later are compared. + If a suspected variable. object is found. it is compared to the images taken at Loiano and La Silla.," If a suspected variable object is found, it is compared to the images taken at Loiano and La Silla." + As it is shown there is no object varying by more than 1c neither in the R nor in the B filter observations. as reported elsewhere (Castro-Tirado et al.," As it is shown there is no object varying by more than $ 1 \sigma$ neither in the R nor in the B filter observations, as reported elsewhere (Castro-Tirado et al." + 1997)., 1997). + Furthermore. none of the objects within the different GRB 970111 error box has changed in brightness in the images taken at Lotano and La Silla.," Furthermore, none of the objects within the different GRB 970111 error box has changed in brightness in the images taken at Loiano and La Silla." + The fields of both X-ray sources. ISAX J1528.84--1944 and ISAX J1528.8++1937 were observed at Loiano and CAHA using B and R filters., The fields of both X-ray sources 1SAX +1944 and 1SAX +1937 were observed at Loiano and CAHA using B and R filters. + No variations in brightness were found for any of the objects within the two X-ray sources error boxes., No variations in brightness were found for any of the objects within the two X-ray sources error boxes. + Fig., Fig. + 4. shows the field of both sources in the B-band., \ref{figure2} shows the field of both sources in the B-band. + B and R magnitudes for the objects inside the X-ray error boxes of ISAX J1528.8--1944 and ISAX J1528.8--1937 are shown in Tables 6 and 7..," B and R magnitudes for the objects inside the X-ray error boxes of 1SAX +1944 and 1SAX +1937 are shown in Tables \ref{table6} + and \ref{table7}." + For objects with magnitudes fainter than 23.5 m B and 22.5 in R. the errors introduced by the photometry do not allow to get reliable values of the B-R colour index.," For objects with magnitudes fainter than 23.5 in B and 22.5 in R, the errors introduced by the photometry do not allow to get reliable values of the B-R colour index." +"time-series aud a model curve combining both effects: we added stellar distortion with an amplitude of 1.5 πας and relativistic beaming with au amplitude of 2.2 ας, vanW",time-series and a model curve combining both effects: we added stellar distortion with an amplitude of 1.5 mmag and relativistic beaming with an amplitude of 2.2 mmag. +evlawwijketal.(2010) and Shporeretal.(2010) discuss the beaming effect iu close binaries: because the primary outshines the secondary. the amplitude of the effect can be written simply as dzaeία1)νο). where eds the speed of light. A (=288 liups)) the velocity semui-uuplitude. aud a=fafhDigg where vis the frequency of the photometric bandpass aud Jig is the stellar effective temperature.," \citet{van2010} and \citet{shp2010} discuss the beaming effect in close binaries; because the primary outshines the secondary, the amplitude of the effect can be written simply as $A\approx \alpha\,{\rm e}^\alpha/({\rm e}^\alpha-1)\times(K/c)$, where $c$ is the speed of light, $K$ $=288$ ) the velocity semi-amplitude, and $\alpha = h\nu/kT_{\rm eff}$ where $\nu$ is the frequency of the photometric bandpass and $T_{\rm eff}$ is the stellar effective temperature." + In the V. band. the amplitude of the effect in GALEN JL717|6757 is expected to be A=2.3 nunag.," In the $V$ band, the amplitude of the effect in GALEX J1717+6757 is expected to be $A=2.3$ mmag." + This is the second star in which relativistic beamine was detected from the erouud after NLTT 11718 (Shporeretal. 2010).., This is the second star in which relativistic beaming was detected from the ground after NLTT 11748 \citep{shp2010}. . +" Adopting for the primary and secondary A,50.150νι, Rp=OLR. ((Section 3.1) aud Ao=O.9AL.... Ro—0008R citep|usiug—mass-radiusrelations—— of]]bon1999.. respectively. the secondary eclipse would last τη to 100 s at ;=90° with a depth of 7 munae assumune an identical surface flux for the primary and secondary stars."," Adopting for the primary and secondary $M_1=0.185$, $R_1=0.1$ (Section 3.1) and $M_2=0.9$, $R_2=0.008$ \\citep[using mass-radius relations of][]{ben1999}, respectively, the secondary eclipse would last up to 400 s at $i=90^\circ$ with a depth of 7 mmag assuming an identical surface flux for the primary and secondary stars." +" Emploving ouly the June data Gvhite helt) we observed four secondarv eclipses at T(ILID2155000|)=715.5252.716.5098.717.1911. and 720.1476. aud lasting ou average ο0-150 s G=86.75 £0.05"") with a depth of 5 munae."," Employing only the June data (white light) we observed four secondary eclipses at $T({\rm HJD~2455000+}) = +715.5252,\ 716.5098,\ 717.4944$, and $720.4476$ , and lasting on average 80-150 s $i = 86.75\pm0.05^\circ$ ) with a depth of 8 mmag." + The eclipse times are consistent with phase =0 with au offset of only 0.0030.001. and sueeest ouly a small adjustinent to the orbital period of 00000055 d. ie.. within quoted errors.," The eclipse times are consistent with phase $=0$ with an offset of only $-0.003\pm0.004$, and suggest only a small adjustment to the orbital period of $-0.0000025$ d, i.e., within quoted errors." + Figure 3. shows the white-lelt time series phased with the adjusted period., Figure \ref{fig3} shows the white-light time series phased with the adjusted period. + The primary eclipse. ie. the transit of the secondary. is uot clearly detected with a maxima depth of ~| nunag.," The primary eclipse, i.e., the transit of the secondary, is not clearly detected with a maximum depth of $\approx 4$ mmag." + The primary eclipse is partially compcusatecd by eravitational deflection by the massive white dw., The primary eclipse is partially compensated by gravitational deflection by the massive white dwarf. + With the adopted parameters and a binary separation ofLYR.. the Eiusteiu radius of the secoudary is Re=04036..," With the adopted parameters and a binary separation of, the Einstein radius of the secondary is $R_E=0.0036$." +". The totaltransit depth imcliding the lensing effect may be written as (Alarsh2001) Am(RS/RUP2Re/Ry)? where ""17 designates the ELM primary. aud 727 the massive unseen conipanion."," The totaltransit depth including the lensing effect may be written as \citep{mar2001} $\Delta m \approx (R_2/R_1)^2-2(R_E/R_1)^2$, where “1” designates the ELM primary, and “2” the massive unseen companion." + Consequeutlv. the predicted transit is Ao»z:l1 uae. consistent with the deepest feature fouud at phase 0.5.," Consequently, the predicted transit is $\Delta m \approx 4$ mmag, consistent with the deepest feature found at phase 0.5." + This lensing effect has been observed in NLTT 11718 (Steinfadtctal.2010)., This lensing effect has been observed in NLTT 11748 \citep{ste2010}. +.. The ELM GALEN Ji71716757 constitutes au interesting test of evolutionary models., The ELM GALEX J1717+6757 constitutes an interesting test of evolutionary models. + Following low-metallicitv evolutionary tracks. the white dwarf has a cooling age of ! Alvr. but it is not possible to derive an age using the solaranetallicitvbi tracks duc to alarec eap in properties above 0," Following low-metallicity evolutionary tracks, the white dwarf has a cooling age of $^{+40}_{-30}$ Myr, but it is not possible to derive an age using the solar-metallicity tracks due to alarge gap in properties above ." +.16937... Figure b compares the evolutionary models to samples of ELM whitedwarts., Figure \ref{fig4} compares the evolutionary models to samples of ELM whitedwarfs. +refsec:cosm-neon-abund)).,). +" The neon abundance predicted by WR evolutionary models is Ne/He=6.6x 10-?, or over 17 times the cosmic value."," The neon abundance predicted by WR evolutionary models is $\nehe=6.6\times +10^{-3}$ , or over 17 times the cosmic value." +" This result, first described by ?,, has remained valid despite recent model updates to accomodate rotational mixing and the turbulent diffusion of core material into the wind it drives (?).."," This result, first described by \citet{Maeder1983}, has remained valid despite recent model updates to accomodate rotational mixing and the turbulent diffusion of core material into the wind it drives \citep{Maeder2000}." +" We will give background on the detection of neon in WR winds in describe the observations in refsec:observations,, outline the abundance calculation and inputs in refsec:abund-calc-—5,, and present the results in refsec:results.."," We will give background on the detection of neon in WR winds in \\ref{sec:background}, describe the observations in \\ref{sec:observations}, , outline the abundance calculation and inputs in \\ref{sec:abund-calc}- \ref{sec:targets--inputs}, and present the results in \\ref{sec:results}." +" Despite lingering uncertainties concerning the true structure of WR. winds, broad agreement between the surface abundances predicted by core evolution models was obtained early on for almost all abundant elements, both for WN (e.g.?) and WC (e.g.?) stars."," Despite lingering uncertainties concerning the true structure of WR winds, broad agreement between the surface abundances predicted by core evolution models was obtained early on for almost all abundant elements, both for WN \citep*[e.g.][]{Crowther1995} and WC \citep[e.g.][]{Maeder1994a} stars." +" However, a long standing discrepancy concerning| the model-sensitive neon abundance predictions centered on 7? Velorum (WC8), the nearby, optically-brightest WR star."," However, a long standing discrepancy concerning the model-sensitive neon abundance predictions centered on $\gamma^2$ Velorum (WC8), the nearby, optically-brightest WR star." +" While the ? abundances were well-confirmed for all other elements, the measured neon abundances of 4? Vel remained quite low, near or just above the cosmic value."," While the \citeauthor{Maeder1983} abundances were well-confirmed for all other elements, the measured neon abundances of $\gamma^2$ Vel remained quite low, near or just above the cosmic value." +" In one of the earliest mid-infrared (MIR) measurements ofa WR star, ? ccalculated Ne* and S?* abundances in 4? Vel from ground-based spectra. ?"," In one of the earliest mid-infrared (MIR) measurements ofa WR star, \citet*{Aitken1982} calculated $^{+}$ and $^{3+}$ abundances in $\gamma^{2}$ Vel from ground-based spectra. \citet{vanderHucht1985}" +" found a similarly elevated neon abundance for 4? Vel using IRAS LWS spectra, seemingly confirming its predicted over-abundance with respect to cosmic levels."," found a similarly elevated neon abundance for $\gamma^{2}$ Vel using IRAS LWS spectra, seemingly confirming its predicted over-abundance with respect to cosmic levels." +" Both of these results, however, were later significantly corrected by ?,, who discovered flaws in the calculations and in the atomic inputs, and found a revised neon abundance again quite close to cosmic values. ?"," Both of these results, however, were later significantly corrected by \citet{Barlow1988}, , who discovered flaws in the calculations and in the atomic inputs, and found a revised neon abundance again quite close to cosmic values. \citet{Dessart2000}" +" adjusted 4? Velorum's neon abundance yet again, using ISO data and an improved distance value along with more modern, clumping-corrected mass loss rates to derive a value coincidentally quite close to the original determination of ?,, and in good agreement with theory."," adjusted $\gamma^{2}$ Velorum's neon abundance yet again, using ISO data and an improved distance value along with more modern, clumping-corrected mass loss rates to derive a value coincidentally quite close to the original determination of \citeauthor{Aitken1982}, and in good agreement with theory." +" ? found an elevated neon abundance in the ISO SWS spectrum of WR.1146 and in total, four ISO WC stars (77) and one WN (WC5),star (?) have yielded neon abundances."," \citet{Willis1997} found an elevated neon abundance in the ISO SWS spectrum of 146 (WC5), and in total, four ISO WC stars \citep{Willis1997,Dessart2000} and one WN star \citep{Morris2000} have yielded neon abundances." +" ? used early Spitzer IRS spectra to measure the neon abundance of WN4 star WR6, and found values consistent with no enhancement."," \citet{Morris2004} + used early Spitzer IRS spectra to measure the neon abundance of WN4 star WR6, and found values consistent with no enhancement." + ? (hereafter ?)) present a flux-calibrated sspectral survey of a large sample of northern Galactic WR stars representing all sub-types., \citet{2001AJ....121.2115S} (hereafter \citetalias{2001AJ....121.2115S}) ) present a flux-calibrated spectral survey of a large sample of northern Galactic WR stars representing all sub-types. +" Among the sample, four stars exhibited broad, non-nebular lline emission."," Among the sample, four stars exhibited broad, non-nebular line emission." +" These are listed in Table 1,, along with spectral types, photometric or cluster distances and reddening, visual magnitudes and mid-infrared fluxes."," These are listed in Table \ref{tab:targets}, along with spectral types, photometric or cluster distances and reddening, visual magnitudes and mid-infrared fluxes." +" 'The spectra were obtained with a citep1998SPIE.3354..7985,1998PASP..110.1479V,,prototype instrument for the short wavelength, high resolution module of Spitzer’s IRS spectrograph (7),, operated at the Palomar5m!."," The spectra were obtained with \\citep{1998SPIE.3354..798S,1998PASP..110.1479V}, a prototype instrument for the short wavelength, high resolution module of Spitzer's IRS spectrograph \citep{Houck2004}, operated at the Palomar." +. Standard beam-switched 5Hz chopping and nodding were used to remove the sky signal., Standard beam-switched 5Hz chopping and nodding were used to remove the sky signal. + The chop amplitude was chosen to be small enough so that the object fell within SCORE’ss ddiameter slit-viewer field when the slit was on adjacent sky., The chop amplitude was chosen to be small enough so that the object fell within s diameter slit-viewer field when the slit was on adjacent sky. +" Two equal amplitude source images in the slit-viewer’s ssilicate filter were thus obtained simultaneously with the spectra, and used to correct the absolute flux calibration for the changing slit throughput function, which is affected by seeing, pointing accuracy, and object acquisition."," Two equal amplitude source images in the slit-viewer's silicate filter were thus obtained simultaneously with the spectra, and used to correct the absolute flux calibration for the changing slit throughput function, which is affected by seeing, pointing accuracy, and object acquisition." +" This calibration, and a general description of the spectral reduction process, are described in more detail by ?.."," This calibration, and a general description of the spectral reduction process, are described in more detail by \citetalias{2001AJ....121.2115S}." + Initial flux-calibration was performed using same-airmass observations of ? infrared standard stars., Initial flux-calibration was performed using same-airmass observations of \citet{Cohen1995} infrared standard stars. + Line strengths were computed using a polynomial fit to the nearby continuum., Line strengths were computed using a polynomial fit to the nearby continuum. + Fig., Fig. + 1 shows the MMIR spectra of one of the WN and the single WC program stars.," \ref{fig:wrspec} + shows the MIR spectra of one of the WN and the single WC program stars." +" The WN star exhibits lines of helium and neon, while the WC star exhibits only [Nerr]."," The WN star exhibits lines of helium and neon, while the WC star exhibits only ." +. Onedistinct differencebetween the ddata used here and ISO SWS spectra used to compute previous neon abundances is worth mentioning., Onedistinct differencebetween the data used here and ISO SWS spectra used to compute previous neon abundances is worth mentioning. + The entirety of ISO’s SWS spectral beam (~20”x 35”) is mapped onto the spectrograph’s large detector elements, The entirety of ISO's SWS spectral beam $\sim20\arcsec\times35\arcsec$ ) is mapped onto the spectrograph's large detector elements +(Ménardetal.2011).,\citep{Menard_etal_2011}. +". Using composite spectra, VandenBerketal.(2008) showed that AAL quasars on average have dust extinction almost twice that observed in quasars with intervening absorbers (e.g.Yorketal.2006), and the associated absorbers have a higher ionization state than intervening absorbers."," Using composite spectra, \citet{Vanden_Berk_etal_2008} showed that AAL quasars on average have dust extinction almost twice that observed in quasars with intervening absorbers \citep[e.g.,][]{York_etal_2006}, and the associated absorbers have a higher ionization state than intervening absorbers." +" To some extent, this supports the idea that AALs are physically associated with the quasar (or at least affected by the radiation field of the quasar), but a direct link between AALs and the quasar is still elusive (cf.,Wildetal.2008)."," To some extent, this supports the idea that AALs are physically associated with the quasar (or at least affected by the radiation field of the quasar), but a direct link between AALs and the quasar is still elusive \citep[cf.,][]{Wild_etal_2008}." +". ~1800 with associated aabsorbersUsing from the quasarsSDSS, we will show Mgthat there is a link between AALs and eemission from the quasar host, suggesting that a substantial fraction of AALs are intrinsic to the and its host."," Using $\sim 1800$ quasars with associated absorbers from the SDSS, we will show that there is a link between AALs and emission from the quasar host, suggesting that a substantial fraction of AALs are intrinsic to the quasar and its host." +" We further argue that the properties of AAL quasarquasars are in favor of them being the transitional population in the Sanders Mirabel picture, with signatures of feedback."," We further argue that the properties of AAL quasars are in favor of them being the transitional population in the Sanders Mirabel picture, with signatures of feedback." + We describe our sample in and present our main results in refsec:composite.., We describe our sample in \\ref{sec:data} and present our main results in \\ref{sec:composite}. + In refsec:disc we present an evolutionary picture to interpret our results and discuss its implications., In \\ref{sec:disc} we present an evolutionary picture to interpret our results and discuss its implications. + We search all the DR7 quasars (Schneideretal.2010) with ccoverage (~85 kk quasars) for associated aabsorption., We search all the DR7 quasars \citep{Schneider_etal_2010} with coverage $\sim 85$ k quasars) for associated absorption. + This restricts our sample to 0.4Sz2 (z 1.2). which extends to lower redshift than the sample in VandenBerketal. (2008).," This restricts our sample to $0.4\la z\la 2$ $\bar{z}\sim 1.2$ ), which extends to lower redshift than the sample in \citet{Vanden_Berk_etal_2008}." +. The unabsorbed continuum plus emission line flux is modeled with a y fit with rejections of absorption troughs (Shenetal.2011)., The unabsorbed continuum plus emission line flux is modeled with a $\chi^2$ fit with rejections of absorption troughs \citep{Shen_etal_2011}. +. We refer the reader to that paper on the details of our fitting procedure., We refer the reader to that paper on the details of our fitting procedure. +" In short, we fit the restframe with a power-law continuum plus an iron template, and a rregionset of Gaussians for the lline."," In short, we fit the restframe region with a power-law continuum plus an iron template, and a set of Gaussians for the line." +" During the fitting, we mask out 3c pixel outliers below the 20 pixel boxcar-smoothed spectrum to minimize the"," During the fitting, we mask out $\sigma$ pixel outliers below the 20 pixel boxcar-smoothed spectrum to minimize the" +((2006) give VCR=7.8kpe)233.6kms!.,(2006) give $\Vc(R=7.8\;\textrm{kpc}) = 233.6\;\kms$. + This is difficult to reconcile with 8.0kpe)=219kms.+ (Reid 11999) with purely circular motion in any (wpe of model., This is difficult to reconcile with $\Theta_0(R_0=8.0\;\textrm{kpc}) = 219\;\kms$ (Reid 1999) with purely circular motion in any type of model. + Variations of this sort are al least conceivable in MOND (Fig. 11)).," Variations of this sort are at least conceivable in MOND (Fig. \ref{MW_empirical}) )," + but probably reflect a real difference between the first and fourth quadrants., but probably reflect a real difference between the first and fourth quadrants. + Hence I have made no attempt to force a fit to the solar value., Hence I have made no attempt to force a fit to the solar value. + The Oort constants of this model are fairly reasonable: A=15.9kms!kpe| and B=-13.0kms!kpe|.," The Oort constants of this model are fairly reasonable: $\textrm{A} = 15.9\;\kms\,\textrm{kpc}^{-1}$ and $\textrm{B} = -13.0\;\kms\,\textrm{kpc}^{-1}$." + The value of A may seem a bit high. but note that since the rotation velocity is inferred to be higher than the solar value. A-—B must also be higher.," The value of A may seem a bit high, but note that since the rotation velocity is inferred to be higher than the solar value, $-$ B must also be higher." + This is in the data., This is in the data. + The model fits the detailed terminal velocity curve as lar as il is reported (up lo R=7.8 kpc). so these are in effect the measured values of the Oort constants in the fourth quadrant.," The model fits the detailed terminal velocity curve as far as it is reported (up to $R = 7.8$ kpc), so these are in effect the measured values of the Oort constants in the fourth quadrant." + There is only a modest model dependent extrapolation to the solar radius., There is only a modest model dependent extrapolation to the solar radius. + Barring svstematic errors in the data or sharp features in the rotation curve near (he solar radius. the uncertainty in these estimates is &1kms!kpe.|.," Barring systematic errors in the data or sharp features in the rotation curve near the solar radius, the uncertainty in these estimates is $< 1\;\kms\,\textrm{kpc}^{-1}$." + Indeed. it is instructive that (his exercise can be successfully done at all.," Indeed, it is instructive that this exercise can be successfully done at all." + The inferred surface densitv has the sorts of bumps ancl wigeles conunontly observed in the azimuthially averaged surface brightness profiles of spiral galaxies., The inferred surface density has the sorts of bumps and wiggles commonly observed in the azimuthally averaged surface brightness profiles of spiral galaxies. + These correspond to the bumps and wieeles in the rotation curve. as thev must in MOND. and as they. are observed to do in eeneral (Renzo's rule).," These correspond to the bumps and wiggles in the rotation curve, as they must in MOND, and as they are observed to do in general (Renzo's rule)." + This correspondence follows in the dark matter picture only if disks are cdvnamicallvy important., This correspondence follows in the dark matter picture only if disks are dynamically important. + This is hard to arrange with the cuspy halos obtained in CDM simulations (e.g.. Navarro. Frenk. White 1997) as these place too nmch dark mass at small radii.," This is hard to arrange with the cuspy halos obtained in CDM simulations (e.g., Navarro, Frenk, White 1997) as these place too much dark mass at small radii." + Low surface brightness disks ean not have dynamically significant mass in the dark malter picture (de Blok MeGaugh 1997). vet still obey (he correspondence of bumps ancl wigeles encapsulated by Renzo’s rule (e.g.. Broeils 1992).," Low surface brightness disks can not have dynamically significant mass in the dark matter picture (de Blok McGaugh 1997), yet still obey the correspondence of bumps and wiggles encapsulated by Renzo's rule (e.g., Broeils 1992)." + This occurs naturally in MOND. the predictions of which (Milgrom 1983b) are realized in LSB ealaxies (Milgrom Braun 1938: MeGaugh de Blok 1998).," This occurs naturally in MOND, the predictions of which (Milgrom 1983b) are realized in LSB galaxies (Milgrom Braun 1988; McGaugh de Blok 1998)." + The specific pattern of bumps auc wiggles seen in Fig., The specific pattern of bumps and wiggles seen in Fig. + ll. is in principle testable bv star count analyses.," \ref{MW_empirical} + is in principle testable by star count analyses." + In. particular. il is tempting (o associate the dip in surface density αἱ e»5 kpe and (he subsequent shelf with a ring or spiral arms. perhaps emanating from the end of the long (~4.5 kpc) bar (Cabrera-Lavers 22007) amorpholoev [requentIy seen in other galaxies and naturally reproduced in MOND simulations (Tiret Combes 2007).," In particular, it is tempting to associate the dip in surface density at $\sim 5$ kpc and the subsequent shelf with a ring or spiral arms, perhaps emanating from the end of the long $\sim 4.5$ kpc) bar (Cabrera-Lavers 2007) — a morphology frequently seen in other galaxies and naturally reproduced in MOND simulations (Tiret Combes 2007)." + Again however. the details of star counts will depend on the choice of interpolation function and the level of non-circular motions.," Again however, the details of star counts will depend on the choice of interpolation function and the level of non-circular motions." + Indeed. even for a given interpolation function and purely circular motion. the result at this level of detail depends on whether we use the modified gravity of Bekenstein Milgrom (1984: equation 2)) or modified inertia (equaion 1)).," Indeed, even for a given interpolation function and purely circular motion, the result at this level of detail depends on whether we use the modified gravity of Bekenstein Milgrom (1984; equation \ref{AQUAL}) ) or modified inertia (equaion \ref{mondeqn}) )." + I have implicitly assumed the latter here., I have implicitly assumed the latter here. + Another intriguinge thinge to note is that a fit to the surface densities in Table 3. exgives, Another intriguing thing to note is that a fit to the surface densities in Table \ref{MWSD_emp} gives +absolute accuracy 1s 200yis in this mode (Saito 11997).,"absolute accuracy is $200 \ +\mu\rm{s}$ in this mode (Saito 1997)." + The PCA data were collected using the Good Xenon mode with 0.9ys timing resolution.," The PCA data were collected using the Good Xenon mode with $0.9 +\mu$ s timing resolution." + For the current analysis. the absolute timing uncertainty is ~1005 (Rots 11998).," For the current analysis, the absolute timing uncertainty is $\sim 100 \mu$ s (Rots 1998)." + Photons collected by the MECS are time tagged with 15 ys resolution., Photons collected by the MECS are time tagged with 15 $\mu$ s resolution. + We do not include data from ASCA's Solid-state Imaging Spectrometers (SIS). as the pulsar fell just off the edge of its FOV.," We do not include data from 's Solid-state Imaging Spectrometers (SIS), as the pulsar fell just off the edge of its FOV." + Nor do we include data from SAYX's other instruments as the observing time is insufficient for these instruments to measure the pulsar periodicity reltably. as a part of the observation was interrupted prematurely.," Nor do we include data from 's other instruments as the observing time is insufficient for these instruments to measure the pulsar periodicity reliably, as a part of the observation was interrupted prematurely." + Each data set was processed through its standard pipeline reduction for that mission and edited to exclude times of high background contamination using the standard screening criteria., Each data set was processed through its standard pipeline reduction for that mission and edited to exclude times of high background contamination using the standard screening criteria. + This rejects time intervals of South Atlantic Anomaly passages. Earth occultations. bright Earth limb in the FOV aand oonly). and other periods of high particle activity.," This rejects time intervals of South Atlantic Anomaly passages, Earth occultations, bright Earth limb in the FOV and only), and other periods of high particle activity." + The resulting effective observation times are summarized in Table |., The resulting effective observation times are summarized in Table 1. + For each observation. event data from all detectors were co-added and the arrival times of each event were corrected to the solar system barycenter using the softwareCIMECONV (ASCA)).NNV (SAX)). or (XTE)).," For each observation, event data from all detectors were co-added and the arrival times of each event were corrected to the solar system barycenter using the software ), ), or )." + The X-ray images obtained with both aand aabove 3 keV reveal AXS J161730-505505 4 outside the SNR shell (see figure là and 1b of Gotthelf 11997; Gotthelf. Petre. Vasisht 1999).," The X-ray images obtained with both and above 3 keV reveal AXS J161730–505505 $4'$ outside the SNR shell (see figure 1a and 1b of Gotthelf 1997; Gotthelf, Petre, Vasisht 1999)." + To increase the signal-to-noise ratio for detecting pulsations from the pulsar. we extracted photons from an 8’ diameter aperture centered on the pulsar. restricting the energy range of extracted photons to 3—[0 keV for GIS and 3—12 keV for the other instruments.," To increase the signal-to-noise ratio for detecting pulsations from the pulsar, we extracted photons from an $'$ diameter aperture centered on the pulsar, restricting the energy range of extracted photons to $3-10$ keV for GIS and $3-12$ keV for the other instruments." + For the PCA data. in this energy band. we further restrict our search to Layer | data only. which provides the best sensitivity for a Crab-like spectrum: For the higher energy analysis afforded by the PCA. above ~12 keV. we used data from all three PCA layers.," For the PCA data, in this energy band, we further restrict our search to Layer 1 data only, which provides the best sensitivity for a Crab-like spectrum; For the higher energy analysis afforded by the PCA, above $\sim 12$ keV, we used data from all three PCA layers." + We searched each data set for the expected 69 ms period predicted from the initial period and period derivative measurement (Tori 11998)., We searched each data set for the expected 69 ms period predicted from the initial period and period derivative measurement (Torii 1998). + A periodgram was constructed using the X statistic to test against a null hypothesis., A periodgram was constructed using the $\chi^2$ statistic to test against a null hypothesis. + For each trial period. we folded the data into 10 bins and computed the X of the resultant profile.," For each trial period, we folded the data into 10 bins and computed the $\chi^2$ of the resultant profile." + We search a narrow range of periods centered on the expected period 4-0. ms. sampled in increments of 0.1«7/T. where Τ is the observation1 duration. and P is the test period.," We search a narrow range of periods centered on the expected period $\pm 0.1$ ms, sampled in increments of $0.1 \times P^2/T$, where $T$ is the observation duration, and $P$ is the test period." + A highly significant signal was detected from each of our data sets., A highly significant signal was detected from each of our data sets. + As well as the newly obtained data. we have re-analyzed the previous aand ddata (Aoki 11992; Torti 11998) in a uniform way and revised the period and its error by using the method of Leahy (1987).," As well as the newly obtained data, we have re-analyzed the previous and data (Aoki 1992; Torii 1998) in a uniform way and revised the period and its error by using the method of Leahy (1987)." +" Our X-ray timing results derived from these 13 measurements are listed in. table 1. along with an updated radio ephemeris (Kasp1 1999, Private communication)."," Our X-ray timing results derived from these 13 measurements are listed in table 1, along with an updated radio ephemeris (Kaspi 1999, Private communication)." + We search for spectral dependence of the pulse profile by comparing the folded light curves in several energy bands., We search for spectral dependence of the pulse profile by comparing the folded light curves in several energy bands. + No strong energy dependence is evident in the energy resolved light curves., No strong energy dependence is evident in the energy resolved light curves. + Furthermore. the pulse amplitude and pulse profile remained unchanged between observational epochs.," Furthermore, the pulse amplitude and pulse profile remained unchanged between observational epochs." + We examined the aand ddata on Που any long term changes in its energy spectrum or flux., We examined the and data on for any long term changes in its energy spectrum or flux. + As for the timing analysis. we restrict our comparison to the energy range above 3 keV and extract photons from an 8 diameter aperture centered on the source.," As for the timing analysis, we restrict our comparison to the energy range above $3$ keV and extract photons from an $8'$ diameter aperture centered on the source." + We fitted the spectrum with a power law function modified by interstellar absorption., We fitted the spectrum with a power law function modified by interstellar absorption. + The absorption was fixed at 6.8«107em™ (Torii 11998).," The absorption was fixed at $6.8\times 10^{22} \ {\rm +cm^{-2}}$ (Torii 1998)." + Spectra from each observation. were found to be consistent with each other., Spectra from each observation were found to be consistent with each other. + Combining the 7 oobservations. we obtain the pulse phase averaged photon index. D=1.43:0.2. and the observed flux of (3.640.2)<107eress7!em confidence errors) in the 3-10 keV range. which is consistent with the previous measurement (Torti 11998).," Combining the 7 observations, we obtain the pulse phase averaged photon index, $\Gamma = 1.4\pm0.2$ , and the observed flux of $(3.6\pm 0.2)\times 10^{-12}\, {\rm ergs\,s^{-1}\,cm^{-2}}$ confidence errors) in the 3-10 keV range, which is consistent with the previous measurement (Torii 1998)." + A X fit to the all I4 data points as summarized in table | gives the mean spin-down rate of P=1.361101)«107 sis and P=0.069347150(1) at MJD 50.000.0 (Figure 1).," A $\chi ^2$ fit to the all 14 data points as summarized in table 1 gives the mean spin-down rate of $\dot{P}= 1.3611(1) \times 10^{-13}$ s/s and $P=0.069347150(1)$ at MJD 50,000.0 (Figure 1)." + However. the quality of the fit is bad. with \7/d.o.f.24808/12.," However, the quality of the fit is bad, with $\chi ^2/d.o.f. = 4808/12$." + The residual of the fit shows a jump of AP~—1.2«1077 s between the observations of 1993 August (MJD 49.217.6) and 1997 September (MJD 50.696.0) (Figure 2. top panel).," The residual of the fit shows a jump of $\Delta P \simeq -1.2\times 10^{-7}$ s between the observations of 1993 August (MJD 49,217.6) and 1997 September (MJD 50,696.0) (Figure 2, top panel)." + Within the observation span of 10 years. the residual is neither periodic nor smooth.," Within the observation span of 10 years, the residual is neither periodic nor smooth." + A sudden change in the period between MJD 49.217.6 and MJD 50.696.0 is suggested.," A sudden change in the period between MJD 49,217.6 and MJD 50,696.0 is suggested." + We consider the most likely explanation for these residuals is due to a glitch. similar to those observed in several voung rotation-powered pulsars.," We consider the most likely explanation for these residuals is due to a glitch, similar to those observed in several young rotation-powered pulsars." + Given the clear evidence of glitch activity. we next attempted to model the spin-down data with a single glitch followed by an exponential recovery.," Given the clear evidence of glitch activity, we next attempted to model the spin-down data with a single glitch followed by an exponential recovery." + The data coverage is limited and we simply assumed the following relation for the spin-down., The data coverage is limited and we simply assumed the following relation for the spin-down. + where AP=0 for rfo. the closure phase distribution changes and the resulting closure phases concentrate around zero. creating the effect of a source that is completely indistinguishable from a real one using any test.," That is, if selfcal generates a spurious source from noise and the visibilities are averaged in time bins of $t$ seconds, with $t>t_0$, the closure phase distribution changes and the resulting closure phases concentrate around zero, creating the effect of a source that is completely indistinguishable from a real one using any test." + For very small values of the flux density F. this test is not às good as the first one.," For very small values of the flux density $F$, this test is not as good as the first one." + As we can see in Fig. 2..," As we can see in Fig. \ref{RelaTeo}," + the closure phases do not dramatically change their distribution for flux densities in the range between 0 and ~ of the rms of the visibility amplitudes., the closure phases do not dramatically change their distribution for flux densities in the range between 0 and $\sim$ of the rms of the visibility amplitudes. + For tentative detections under critical circumstances in that range. this test could lead us to the wrong conclusion about the reliability of à source detection.," For tentative detections under critical circumstances in that range, this test could lead us to the wrong conclusion about the reliability of a source detection." + Looking at it from a different viewpoint. Fig.," Looking at it from a different viewpoint, Fig." + 2 provides an interesting lesson:noise-like., \ref{RelaTeo} provides an interesting lesson:. + Thus. a conclusion on the reliability of a source detectior based only on the closure phase distribution being extremely noisy. is not definitive.," Thus, a conclusion on the reliability of a source detection based only on the closure phase distribution being extremely noisy, is not definitive." + Another thing worth-noticing ts that this test assumes the same sensitivity for all the antennas and a source compact enough for generating closure phases close to zero even for the longest baselines (which may not be the case. specially for sources with à very low flux density per unit beam).," Another thing worth-noticing is that this test assumes the same sensitivity for all the antennas and a source compact enough for generating closure phases close to zero even for the longest baselines (which may not be the case, specially for sources with a very low flux density per unit beam)." + These assumptions impose limitations to the use of this test., These assumptions impose limitations to the use of this test. + However. it could still be applied by restricting its use to the shortest baselines with similar antennas.," However, it could still be applied by restricting its use to the shortest baselines with similar antennas." + For an array with a large antenna. the closure phases in which that antenna appears could still be used (for sensitivity optimization in the closure phase distribution). but then the flux density estimated from the amplitude rms might have a bias produced by the very different rms in different baselines.," For an array with a large antenna, the closure phases in which that antenna appears could still be used (for sensitivity optimization in the closure phase distribution), but then the flux density estimated from the amplitude rms might have a bias produced by the very different rms in different baselines." + We must also note that in cases of high SNR. the rms of the visibility amplitudes is no longer related only to the thermal noise of the baselines (the flux density of the source affects the value of the rms). and the fraction F/p shown in Fig.," We must also note that in cases of high SNR, the rms of the visibility amplitudes is no longer related only to the thermal noise of the baselines (the flux density of the source affects the value of the rms), and the fraction $F/\rho$ shown in Fig." + 2 should be accordingly corrected., \ref{RelaTeo} should be accordingly corrected. + For cases of high SNR. the quantity that will substitute p in the fraction F/p shown in Fig.," For cases of high SNR, the quantity that will substitute $\rho$ in the fraction $F/\rho$ shown in Fig." + 2. is, \ref{RelaTeo} is $\sqrt{\rho^2-F^2}$. + Real data do not obey the simplifying assumptions that we have used in the earlier sections., Real data do not obey the simplifying assumptions that we have used in the earlier sections. + The baselines of a real interferometer have different sensitivities. which also vary in time.," The baselines of a real interferometer have different sensitivities, which also vary in time." + Thus. in order to check the reliability of a source detection from real data we must search a subset of observations in which the sensitivity of the antennas Is approximately constant.," Thus, in order to check the reliability of a source detection from real data we must search a subset of observations in which the sensitivity of the antennas is approximately constant." + Moreover. we must only work with the subset of most sensitive antennas of the interferometer.," Moreover, we must only work with the subset of most sensitive antennas of the interferometer." + If there is one antenna in our nterferometer that is clearly more sensitive than the others. we should compute only the average of the closure phases 1 which this more sensitive antenna appears. in order to nsure the possible signature of the source in the closure phase distribution.," If there is one antenna in our interferometer that is clearly more sensitive than the others, we should compute only the average of the closure phases in which this more sensitive antenna appears, in order to insure the possible signature of the source in the closure phase distribution." + In what follows. we apply our reliability criteria to real data corresponding to the radio supernova 22004et Aarti-Vidal et al. 20071).," In what follows, we apply our reliability criteria to real data corresponding to the radio supernova 2004et (Martí–Vidal et al. \cite{MartiVidal2007}) )." + We observed this supernova on 20 February 2005., We observed this supernova on 20 February 2005. + From all data reported in Martí-Vidal et al. (20071).," From all data reported in Martí–Vidal et al. \cite{MartiVidal2007}) )," + we have chosen the following subset of antennas: Brewster. Fort Davis. Green Bank. Hancock. Kitt Peak. and Owens Valley.," we have chosen the following subset of antennas: Brewster, Fort Davis, Green Bank, Hancock, Kitt Peak, and Owens Valley." + We have only computed the closure phases in which the antenna Green Bank appears. and we have used data only from hhr to 20hhr (UT).," We have only computed the closure phases in which the antenna Green Bank appears, and we have used data only from hr to hr (UT)." + These choices are based on the quality of the data for our purposes (1.e.. the stability of the antenna sensitivities. which We assume proportional to the system temperatures registered for each station).," These choices are based on the quality of the data for our purposes (i.e., the stability of the antenna sensitivities, which we assume proportional to the system temperatures registered for each station)." + First test: we self-calibrated the 22004et data using different averaging times. ranging from 2 to sseconds (roughly. the duration of one scan).," First test: we self-calibrated the 2004et data using different averaging times, ranging from 2 to seconds (roughly, the duration of one scan)." +" The fit of the flux densities recovered from the 22004et data as a function of the averaging time of the selfcal solutions. equation 8.. results ina value of F,,,,20.90+0.13 mmJy."," The fit of the flux densities recovered from the 2004et data as a function of the averaging time of the selfcal solutions, equation \ref{SelfcalTime}, results in a value of $F_{real} = 0.90\pm0.13$ mJy." + This value is clearly higher than zero. indicating that there is a real signal in the data.," This value is clearly higher than zero, indicating that there is a real signal in the data." + This value is also close to the flux density of 22004et reported by Martí-Vidal et al..," This value is also close to the flux density of 2004et reported by Martí–Vidal et al.," + 0.87+0.03 mmJy. recovered from phase referenced data with a deconvolution using CLEAN.," $0.87\pm0.03$ mJy, recovered from phase referenced data with a deconvolution using CLEAN." + Second test: even though we know that it is not quite appropriate. we have also performed this test on the 22004et data.," Second test: even though we know that it is not quite appropriate, we have also performed this test on the 2004et data."