diff --git "a/batch_s000039.csv" "b/batch_s000039.csv" new file mode 100644--- /dev/null +++ "b/batch_s000039.csv" @@ -0,0 +1,10354 @@ +source,target + Therefore. the simulated number of GCs stripped from NGC 1404 differs from the analytical estimation only by 3%.," Therefore, the simulated number of GCs stripped from NGC 1404 differs from the analytical estimation only by 3." +.. The probable reason for the larger number of the stripped GCs in the simulation is that the NGC 1404 system becomes less strongly self-eravitating (thus more susceptible to tidal stripping) alter stripping of dark matter ancl stellar components curing its dynamical evolution., The probable reason for the larger number of the stripped GCs in the simulation is that the NGC 1404 system becomes less strongly self-gravitating (thus more susceptible to tidal stripping) after stripping of dark matter and stellar components during its dynamical evolution. + The possibility of the present models overestimation of the number of stripped. CC's (clue to numerical relaxation effects) is discussed in the Appendix D. Fie., The possibility of the present model's overestimation of the number of stripped GCs (due to numerical relaxation effects) is discussed in the Appendix B. Fig. + 3 shows that as NCC 1404 orbits the centre of the Fornax cluster. the radial distribution of GCs in NGC 1404 becomes steeper and the radial Sx distribution becomes Hatter.," 3 shows that as NGC 1404 orbits the centre of the Fornax cluster, the radial distribution of GCs in NGC 1404 becomes steeper and the radial $S_{N}$ distribution becomes flatter." + This is essentially because GC's initially outside the galaxy are more likely to be tically stripped., This is essentially because GCs initially outside the galaxy are more likely to be tidally stripped. + Phe ον within 5H. is changed from 2.83 to 1.64 (a factor of 1.73 smaller) at P= 142 Garver whereas the Sx within 1072. is change from 5 to LSS (a factor of 2.66 smaller)., The $S_{N}$ within $R_{\rm e}$ is changed from 2.83 to 1.64 (a factor of 1.73 smaller) at $T$ = 1.42 Gyr whereas the $S_{N}$ within $R_{\rm e}$ is changed from 5 to 1.88 (a factor of 2.66 smaller). + These results sugeest that tidal stripping of GC's causes the steepening of racial distributions of GC's., These results suggest that tidal stripping of GCs causes the steepening of radial distributions of GCs. + Furthermore. they imply that if a cluster elliptical galaxy with lower Sx has a typical 9x estimated for its halo region within a few times Z2. and a significantly smaller Sx within 5 10 #.. the lower Sx of his elliptical can be caused by the strong cluster tidal field.," Furthermore, they imply that if a cluster elliptical galaxy with lower $S_{N}$ has a typical $S_{N}$ estimated for its halo region within a few times $R_{\rm e}$ and a significantly smaller $S_{N}$ within 5 $-$ 10 $R_{\rm e}$, the lower $S_{N}$ of this elliptical can be caused by the strong cluster tidal field." + Thus. we suggest that the ratio of the inner Sy and the outer Sv in a cluster elliptical is one observable test for the idal stripping of GC's in cluster elliptical galaxies.," Thus, we suggest that the ratio of the inner $S_{N}$ and the outer $S_{N}$ in a cluster elliptical is one observable test for the tidal stripping of GCs in cluster elliptical galaxies." + The derived: radial density profile with the. slope of ~ —2.6 for 0 RR. < 10 ds steeper yan the observed value of 1.3. (Forbes et al., The derived radial density profile with the power-law slope of $\sim$ $-2.6$ for 0 $\le$ $R/R_{\rm e}$ $\le$ 10 is steeper than the observed value of $-1.3$ (Forbes et al. + 1997)., 1997). + This clisagreemento between the present simulations and the observation is due partly to the adopted: initially steep slope 1.9). whieh is chosen such that the value is similar to the typical value of the power-law slope of elobular cluster systems in elliptical galaxies.," This disagreement between the present simulations and the observation is due partly to the adopted initially steep slope $-1.9$ ), which is chosen such that the value is similar to the typical value of the power-law slope of globular cluster systems in elliptical galaxies." + As the simulations emonstrate. the density. profile of the GC system. of an liptical in a cluster is more likely to become steeper as i orbits the cluster because of the more ellicient tidal stripping in the outer part of the galaxy.," As the simulations demonstrate, the density profile of the GC system of an elliptical in a cluster is more likely to become steeper as it orbits the cluster because of the more efficient tidal stripping in the outer part of the galaxy." + We therefore suggest tha if the origin of the observed low Spx of NGC 1404 is due to tidal stripping. the power-law slope of the GCs radia density profile should have been initially Uatter (1.0. before interaction with Fornax cluster).," We therefore suggest that if the origin of the observed low $S_{\rm N}$ of NGC 1404 is due to tidal stripping, the power-law slope of the GCs radial density profile should have been initially flatter (i.e. before interaction with Fornax cluster)." + The radial number density. profile of the GCS aroun GC. 1404 can be inlluenced. by [ater tical disruption. of GC's by NGC 1404., The radial number density profile of the GCS around NGC 1404 can be influenced by later tidal disruption of GCs by NGC 1404. + We can roughly estimate the effect of idal disruption of GC's on the number density. profile bv using carly numerical results by Aguilar et al. (, We can roughly estimate the effect of tidal disruption of GCs on the number density profile by using early numerical results by Aguilar et al. ( +1988).,1988). + They demonstrated that if the Galactic GCs are within ~ 2 kpe rom the Galactic centre. the GC's can be destroved by the strong tidal field. of the bulge.," They demonstrated that if the Galactic GCs are within $\sim$ 2 kpc from the Galactic centre, the GCs can be destroyed by the strong tidal field of the bulge." + Phe radius within which GCs can be destroved is referred to as fo. from now on or convenience (Rac. 2 kpe for the Galactic bulge)., The radius within which GCs can be destroyed is referred to as $R_{\rm des}$ from now on for convenience $R_{\rm des}$ $\sim$ 2 kpc for the Galactic bulge). +" By assuming that Z2, is simply scaled to Alia7 for a galaxy. (where Aa is the total Luminous mass of the galaxy). Rae. or NGC 1404 can be estimated to be 3.3 kpe (or 1.3 £.)."," By assuming that $R_{\rm des}$ is simply scaled to ${M_{\rm gal}}^{1/3}$ for a galaxy, (where $M_{\rm gal}$ is the total luminous mass of the galaxy), $R_{\rm des}$ for NGC 1404 can be estimated to be 3.3 kpc (or 1.3 $R_{\rm e}$ )." + In, In +of Dlazars interpreted dn terms of cliscoutimuitics i a Povuting flux jet.,of Blazars interpreted in terms of discontinuities in a Poynting flux jet. + We analyze ciffereut theoretical aud observational aspects connected wit1i such outbursts., We analyze different theoretical and observational aspects connected with such outbursts. + Accreting mater in a disk around a black hole carries with it an ordered aud a chaotic uaenetic field., Accreting matter in a disk around a black hole carries with it an ordered and a chaotic magnetic field. + When he matter reaches the black hole. :uall magnetic loops reconnect and the feld. aunibilates.," When the matter reaches the black hole, small magnetic loops reconnect and the field annihilates." + The more ordered COMMPONCIL of the field. which can have open field lines. eau © drageed iuto the black hole while remaining counected ο lore distant plasma in the corona of the disk ( Figure 1)," The more ordered component of the field, which can have open field lines, can be dragged into the black hole while remaining connected to more distant plasma in the corona of the disk ( Figure 1)." + Thus. the black hole may have a sigificant magnetic field passing throug Lit supported by external currents iu he disk aud corona (Blaudford Zuajek 1977: Macdonald Thorne 1982).," Thus, the black hole may have a significant magnetic field passing through it supported by external currents in the disk and corona (Blandford Znajek 1977; Macdonald Thorne 1982)." + Tje magnetic field of he iuner regions of the disk is likely to be comparable te| the field in the dack hole (Alaccouald Thorue 1982: Livio e al., The magnetic field of the inner regions of the disk is likely to be comparable to the field in the black hole (Macdonald Thorne 1982; Livio et al. + 1998)., 1998). + The area of the iuier region of the dis sas much larecr han the area of tle| black hole. so that the magnetic fiux and the Povutiug ewrev outflow rate of he inner regions of the disk is larger than that of the black hole (Livio ct al.," The area of the inner region of the disk is much larger than the area of the black hole, so that the magnetic flux and the Poynting energy outflow rate of the inner regions of the disk is larger than that of the black hole (Livio et al." + 1998: Lovelace et al., 1998; Lovelace et al. + 1987)., 1987). + The magnetic feld near the immer edge of fre disk is deduced to be of the order of B—(1010)G (Lovelace 1976)., The magnetic field near the inner edge of the disk is deduced to be of the order of $B\sim (10^3-10^4)~{\rm G}$ (Lovelace 1976). + Senüempirical models of gammarav flares based on iuverse Conipton and/or SSC mechanisnis. predict approximate values of the maeguetic field in different Dlazirs in the reeious of origin of the radiation (c.e@.. Sambruna. Maraschi Ur 1996: Sambruna et al.," Semi–empirical models of gamma–ray flares based on inverse Compton and/or SSC mechanisms, predict approximate values of the magnetic field in different Blazars in the regions of origin of the radiation (e.g., Sambruna, Maraschi Urry 1996; Sambruna et al." + 1997)., 1997). + Back extrapolated to the inner disk using D—l/r) ον} is the jet radius). gives a uaenetic field B=(102.101)G.," Back extrapolated to the inner disk using $B \sim 1/r_j$ $r_j(z)$ is the jet radius), gives a magnetic field $B=(10^2-10^4)~{\rm G}$." + The rotating disk aud black hole threaded by au ordered uaenetic Ποια eeucrate Povuting flux outflows. or jets in which the enerev density of the electromagnetic feld is uuch larger than the matter cucrey deusitv (see Lovelace. hese Proceediuez).," The rotating disk and black hole threaded by an ordered magnetic field generate Poynting flux outflows, or jets in which the energy density of the electromagnetic field is much larger than the matter energy density (see Lovelace, these Proceedings)." + Povuting fux winds were first discussed by Coldreich and Julian (1968) for pulsars. aud later Povutiug fax jets were proposed to explain extragalactic jets by Lovelace (1976) and DBlaudford (1976).," Poynting flux winds were first discussed by Goldreich and Julian (1968) for pulsars, and later Poynting flux jets were proposed to explain extragalactic jets by Lovelace (1976) and Blandford (1976)." + Solutions for Poviutine fiux outflows frou a disk around a massive black hole were investigated by Lovelace et al. (, Solutions for Poynting flux outflows from a disk around a massive black hole were investigated by Lovelace et al. ( +1987).,1987). + A Povuting flux jet is selfcollimated. with cucrey. imonientun. aud angular momentum transported mainly bv the electromagnetic field (Lovelace et al.," A Poynting flux jet is self–collimated, with energy, momentum, and angular momentum transported mainly by the electromagnetic field (Lovelace et al." + 1957)., 1987). + The collimation is due to the toroidal component of maguetic field., The collimation is due to the toroidal component of magnetic field. +" A steady Povuting flux jet is characterized in the lab faune by its asviuptotic ( 5>>ry ) magnetic field B,,= aud clectric field ΕΠ. ", A steady Poynting flux jet is characterized in the lab frame by its asymptotic ( $ z >> r_o $ ) magnetic field $B_\phi = - B_0 [r_0/r_j(z)]$ and electric field $E_r = - (v_j/c) B_0 [r_0/r_j(z)]$ +or beating interactions between these.,or beating interactions between these. +" Therefore 51.47 days is considered to be a real, physical periodicity in the XTE J1739—302 system."," Therefore 51.47 days is considered to be a real, physical periodicity in the XTE $-$ 302 system." + On the contrary no indication of the ~8 dday period predicted by Blayetal.(2008) is found in the analysis., On the contrary no indication of the $\sim$ day period predicted by \citet{Blay2008} is found in the analysis. + A Monte-Carlo based test was also used to estimate the uncertainty on the period found within the data., A Monte-Carlo based test was also used to estimate the uncertainty on the period found within the data. +" Flux values are randomised within their lo error bars and a Lomb-Scargle test performed, the period with highest power in the region around the initial period is recorded."," Flux values are randomised within their $\sigma$ error bars and a Lomb-Scargle test performed, the period with highest power in the region around the initial period is recorded." +" T'his process is repeated 200,000 times and the resulting distribution fit with a Gaussian, the width of which is taken as the 1o error on the identified period."," This process is repeated 200,000 times and the resulting distribution fit with a Gaussian, the width of which is taken as the $\sigma$ error on the identified period." + An error of + ddays was found for the dday period of XTE J1739—302., An error of $\pm$ days was found for the day period of XTE $-$ 302. + Figure 2 shows the phase-folded lightcurve of the XTE J1739—302 system using the identified period., Figure \ref{fig2} shows the phase-folded lightcurve of the XTE $-$ 302 system using the identified period. +" The ephemeris of 552698.2 is used, defining the initial zero phase at the first observation of XTE J1739—302 with INTEGRAL//IBIS."," The ephemeris of 52698.2 is used, defining the initial zero phase at the first observation of XTE $-$ 302 with /IBIS." + The phase-folded lightcurve shows a shape that is dominated by enhancement of emission at what appears to be three points in the orbit., The phase-folded lightcurve shows a shape that is dominated by enhancement of emission at what appears to be three points in the orbit. +" 'The supposed periastron, phase 0.4 to 0.6, also has two nearly symmetric side-peaks at phases of 0.25 to 0.35 and 0.65 to 0.75."," The supposed periastron, phase 0.4 to 0.6, also has two nearly symmetric side-peaks at phases of 0.25 to 0.35 and 0.65 to 0.75." + A more detailed discussion of this profile is given in Section 4., A more detailed discussion of this profile is given in Section 4. +" The public access RXTE//ASM and Swift//BAT lightcurves were also searched for periodic signals using the Lomb-Scargle method, however in these cases no significant signals were detected at any period."," The public access /ASM and /BAT lightcurves were also searched for periodic signals using the Lomb-Scargle method, however in these cases no significant signals were detected at any period." + While this is unusual it is not the first time that periods have been seen with one instrument and not others (Clarketal.2009).., While this is unusual it is not the first time that periods have been seen with one instrument and not others \citep{DaveJ17544}. + In conjunction with periodicity analysis the IBIS/ISGRI lightcurve was also searched for outbursts by a significance test., In conjunction with periodicity analysis the IBIS/ISGRI lightcurve was also searched for outbursts by a significance test. + The lightcurve is searched with windows of increasing size in all positions along its length and the significance across the entire data window calculated., The lightcurve is searched with windows of increasing size in all positions along its length and the significance across the entire data window calculated. + The data window with the maximum significance is then recorded and those ScWs removed from the lightcurve., The data window with the maximum significance is then recorded and those ScWs removed from the lightcurve. + This process is repeated until all regions with a significance greater than 4c have been identified., This process is repeated until all regions with a significance greater than $\sigma$ have been identified. + Statistical tests were performed to estimate how many detections could result from a combination of random noise in the data and the number of trials performed., Statistical tests were performed to estimate how many detections could result from a combination of random noise in the data and the number of trials performed. + A synthetic random lightcurve was created with the same statistical properties as the real data (RMS and number of data points) and run through the burst finding procedure., A synthetic random lightcurve was created with the same statistical properties as the real data (RMS and number of data points) and run through the burst finding procedure. +" This resulted in five ‘detections’ above the 4o level, the largest being 4.410."," This resulted in five `detections' above the $\sigma$ level, the largest being $\sigma$." +" Consequently, the seven events below 4.50 were removed from the outburst history."," Consequently, the seven events below $\sigma$ were removed from the outburst history." + Finally higher time resolution lightcurves (100ss binning) were generated for each of the remaining events and checked manually to ensure outburst behaviour could be observed., Finally higher time resolution lightcurves s binning) were generated for each of the remaining events and checked manually to ensure outburst behaviour could be observed. +" It was seen that the majority of the remaining events showed distinct flaring features while the remainder showed lower level activity, possibly due to small flares with emission mostly below the sensitivity of IBIS/ISGRI but where the peak of the emission is detected."," It was seen that the majority of the remaining events showed distinct flaring features while the remainder showed lower level activity, possibly due to small flares with emission mostly below the sensitivity of IBIS/ISGRI but where the peak of the emission is detected." + As a result thirty five outburst events have been identified within the XTE J1739—302 IBIS/ISGRI lightcurve., As a result thirty five outburst events have been identified within the XTE $-$ 302 IBIS/ISGRI lightcurve. + The subset of all those outbursts, The subset of all those outbursts +magnitude at random from the distributions shown in black in Figure A3.,magnitude at random from the distributions shown in black in Figure A3. + We also select à NUV image exposure time at random. again based on the real distribution of exposure times for the GASS parent sample.," We also select a NUV image exposure time at random, again based on the real distribution of exposure times for the GASS parent sample." + The NUV and r band fluxes are always rescaled so that the total NUV—r colour is conserved., The NUV and $r$ band fluxes are always rescaled so that the total $NUV-r$ colour is conserved. + After rebinning in size. the NUV and r band images are convolved with the GALEX and SDSS PSFs and background and poisson noise are added.," After rebinning in size, the NUV and $r$ band images are convolved with the GALEX and SDSS PSFs and background and poisson noise are added." + Figures AS and A6 show two examples of the resulting simulated images., Figures \ref{fig:NGC5701} and \ref{fig:NGC4314} show two examples of the resulting simulated images. +" Figure AS. shows a typical galaxy. which is blue on the outside (with negative A,(NOUV— ry. while Figure AG shows a galaxy that is blue on the inside (with positive A,ΝΟΥ— rp."," Figure \ref{fig:NGC5701} shows a typical galaxy, which is blue on the outside (with negative $\Delta_{o-i}(NUV-r)$ ), while Figure \ref{fig:NGC4314} shows a galaxy that is blue on the inside (with positive $\Delta_{o-i}(NUV-r)$ )." + After creating our library of 60.000 simulated images. we measure photometric parameters following the same steps described in Section 3.1..," After creating our library of 60,000 simulated images, we measure photometric parameters following the same steps described in Section \ref{subsec:phot_tech}." + The distribution of output NUV-r colours. r-band apparent magnitudes. semi-minor axis size (554) and NUV-r colour gradient values are plotted as red histograms in Figure A3.," The distribution of output $r$ colours, $r$ -band apparent magnitudes, semi-minor axis size $b_{50}$ ) and $r$ colour gradient values are plotted as red histograms in Figure A3." + We can see that the output values do ditfer from the input values., We can see that the output values do differ from the input values. + To quantify this in more detail. the left panel of Figure AS shows how the ditlerence between output and input colour gradients change as a function of sy. for galaxies with high S/N UV images σον—r)< 0.1.," To quantify this in more detail, the left panel of Figure \ref{fig:dnuvr_criteria} shows how the difference between output and input colour gradients change as a function of $b_{50}$ , for galaxies with high $S/N$ UV images $\sigma(NUV-r)<0.1$ )." +" When ba;>4 pixels (which corresponds to 6 ""). the output A,;CNUV—r) is quite close to the input value (systematically high by «0.05 mag on average)."," When $b_{50}>4$ pixels (which corresponds to 6 $''$ ), the output $\Delta_{o-i}(NUV-r)$ is quite close to the input value (systematically high by $\sim$ 0.05 mag on average)." + The scatter in therecovered gradient is less than 0.2 mag., The scatter in therecovered gradient is less than 0.2 mag. +" When bs,«+ AS ", When $b_{50}<4$ \ref{fig:dnuvr_criteria} +This confirms the finding by that in the relevant layers thermohaline mixing has much higher diffusion coefficients than rotational and magnetic.,This confirms the finding by that in the relevant layers thermohaline mixing has much higher diffusion coefficients than rotational and magnetic. + It is also perfectly consistent with the results of who studied the impact of rotation-induced mixing on the RGB for low-mass stars and showed that it cannot (with the present assumptions) account for the abundance anomalies observed in bright giants., It is also perfectly consistent with the results of who studied the impact of rotation-induced mixing on the RGB for low-mass stars and showed that it cannot (with the present assumptions) account for the abundance anomalies observed in bright giants. +" These authors noted that assuming differential rotation (i.e., uniform specific angular momentum) instead of solid body rotation (i.e., uniform angular velocity) in the convective envelope along the RGB does lead to higher efficiency of the rotation-induced processes below the convective envelope."," These authors noted that assuming differential rotation (i.e., uniform specific angular momentum) instead of solid body rotation (i.e., uniform angular velocity) in the convective envelope along the RGB does lead to higher efficiency of the rotation-induced processes below the convective envelope." +" However, even in that case, Palacios and collaborators showed that the total transport coefficient associated to rotation does not rise above 10? cm? s! in the outer HBS, which is still much lower than the thermohaline diffusion coefficient."," However, even in that case, Palacios and collaborators showed that the total transport coefficient associated to rotation does not rise above $10^5$ $^2$ $^{-1}$ in the outer HBS, which is still much lower than the thermohaline diffusion coefficient." + Thermohaline mixing thus governs the surface abundance variations on the upper half of the RGB as already discussed by CZ07., Thermohaline mixing thus governs the surface abundance variations on the upper half of the RGB as already discussed by CZ07. + The corresponding predictions for the 1.25 Me model computed with an initial rotation velocity of 110 km.s~! can be seen in Fig., The corresponding predictions for the 1.25 $_{\odot}$ model computed with an initial rotation velocity of 110 $^{-1}$ can be seen in Fig. + 6 (right panels)., \ref{fig:surfaceabundances1p25} (right panels). +" The 1.25 Ms model with an initial rotation velocity of 110 km s! was computed until the end of the superwind phase (total stellar mass and mass of the envelope being respectively equal to 0.566 M; and 0.014 Mo), and has undergone four thermal pulses."," The 1.25 $_{\odot}$ model with an initial rotation velocity of 110 km $^{-1}$ was computed until the end of the superwind phase (total stellar mass and mass of the envelope being respectively equal to 0.566 $_{\odot}$ and 0.014 $_{\odot}$ ), and has undergone four thermal pulses." + During the TP-AGB the behaviour of the surface abundances is similar to that discussed in 3.1.2., During the TP-AGB the behaviour of the surface abundances is similar to that discussed in 3.1.2. +" In the present case, the maximum N(Li) value reached at the end of the TP-AGB is ~ 0.8 (instead of 0.9 in the 1.25 M non-rotating model discussed in 3.1; see also Table 3))."," In the present case, the maximum N(Li) value reached at the end of the TP-AGB is $\sim$ 0.8 (instead of 0.9 in the 1.25 $_{\odot}$ non-rotating model discussed in 3.1; see also Table \ref{tableNLiTPAGB}) )." +" Again, predictions for carbon at that phase must be taken with caution since the impact of parametric convectively induced extra-mixing is not taken into account."," Again, predictions for carbon at that phase must be taken with caution since the impact of parametric convectively induced extra-mixing is not taken into account." +" CZ07 performed computations for various values of the coefficient C, and discussed the uncertainties on the efficiency of the thermohaline mixing that are basically related to the size and shape of the thermohaline cells.", CZ07 performed computations for various values of the coefficient ${\rm C_ t}$ and discussed the uncertainties on the efficiency of the thermohaline mixing that are basically related to the size and shape of the thermohaline cells. + Their prefered value for the aspect ratio @=5 (see 2.2) also used in the present computations corresponds to “fingers” rather than “blobs”whose shorter mixing length would translate into smaller value (by a factor of ~ 50) for the coefficient Ci.," Their prefered value for the aspect ratio $\alpha$ =5 (see 2.2) also used in the present computations corresponds to “fingers"" rather than “blobs""whose shorter mixing length would translate into smaller value (by a factor of $\sim$ 50) for the coefficient $_{\rm t}$ ." + Crude as it may, Crude as it may +characteristics in excelleut agreement with those derived from the three data-sets of HIT 151.,characteristics in excellent agreement with those derived from the three data-sets of HH 154. + The model also predicts that the A-ray cutting plasuia of the diamoud shock cools down at larger distances from the driving source as inferred from the observations., The model also predicts that the X-ray emitting plasma of the diamond shock cools down at larger distances from the driving source as inferred from the observations. + In fact. from the Chandra data. we found that the AIPE increases toward the base of the jet.," In fact, from the Chandra data, we found that the MPE increases toward the base of the jet." + While we cannot rule out that this result is associated with variations in Nyy (Exidluudetal.2005. found an increasing absorption towards the dviving source along the jet axis). higher values of MPE can be indicative of higher temperatures.," While we cannot rule out that this result is associated with variations in $N_H$ \citealt{fld05} found an increasing absorption towards the driving source along the jet axis), higher values of MPE can be indicative of higher temperatures." + Such variations of plasma teniperature would be naturally explained by our model., Such variations of plasma temperature would be naturally explained by our model. + We conclude therefore that IIT 151 offers the first evidence of a standiug diamond shock at the base of the jet probably near the jet launching/collimation reelon., We conclude therefore that HH 154 offers the first evidence of a standing diamond shock at the base of the jet probably near the jet launching/collimation region. +" We can infera characteristic size. dy, of the N-ray cluitting source frou the spectral analysis. using the value of the Ελpip and πο the hycrocwuamic model results. using the maxima particle density value derived from the diamond shock moceled."," We can infera characteristic size, $l_{sh}$, of the X-ray emitting source from the spectral analysis, using the value of the $EM_{best-fit}$, and from the hydrodynamic model results, using the maximum particle density value derived from the diamond shock modeled." +" Iu particular. we find Jy,2VE?[10H cmn. where V is the vole derived from the EAL=0.807 (following Favataetal. 2002)) and napiy2103 °? (see the peak of density in Fig. 5))"," In particular, we find $l_{sh} > V^{1/3}=4\times10^{14}$ cm, where $V$ is the volume derived from the $EM = 0.8 n^{2} V$ (following \citealt{ffm02}) ) and $n_{MAX}\approx10^{4}$ $^{-3}$ (see the peak of density in Fig. \ref{mod_prof}) )" + at 110 pe., at $140$ pc. + This value is in good agreecimoenut with both the observed radius of HII 151. 7;z30 AU (see discussion on this parameter iu both models aud observations in Bouitoetal.2007 and Bonitoctal. 2008)). aud with the size of the diamond shock 1iodeled.," This value is in good agreement with both the observed radius of HH 154, $r_{j}\approx30$ AU (see discussion on this parameter in both models and observations in \citealt{bop07} and \citealt{bff08}) ), and with the size of the diamond shock modeled." + Therefore. although the spatial resolution of the ACTS data. iuaproved by sub-pixel techniques. is more than an order of magnitude lower than that achieved by our unuerical model. its diagnostic power allows us to infer detailed iuformation on plvsical scales comparable to iuuercal simulatious.," Therefore, although the spatial resolution of the ACIS data, improved by sub-pixel techniques, is more than an order of magnitude lower than that achieved by our numerical model, its diagnostic power allows us to infer detailed information on physical scales comparable to numerical simulations." + The data. after this analysis. clearly show the presence of an clongated structure ou the right side of the nain source.," The data, after this analysis, clearly show the presence of an elongated structure on the right side of the main source." + Concernins an eventual evolution of this clonegated structure the most couscrvative interpretation could be that it is steady and we cau hardly constrain its catures. due to the lanited photon statistics.," Concerning an eventual evolution of this elongated structure the most conservative interpretation could be that it is steady and we can hardly constrain its features, due to the limited photon statistics." + However. eiven the insight provided by the model aud the evidence hat stellar jets flows are inherently variable. another interpretation is that we are observing the diaunuond shock variability ancl possibly knots formation aud notion due to the changes of the jet flow (cf.," However, given the insight provided by the model and the evidence that stellar jets flows are inherently variable, another interpretation is that we are observing the diamond shock variability and possibly knots formation and motion due to the changes of the jet flow (cf." + Donitoetal.2010a.— for example of effects of variable jet flows)., \citealt{bom10} for example of effects of variable jet flows). +" The sequence of the sioothed images of HIT 151 with a spatial scale of 0.25"" shown iu Fig.", The sequence of the smoothed images of HH 154 with a spatial scale of $0.25''$ shown in Fig. + d. suggests the preseuce of subsequent knots with a detectable proper motion., \ref{mappa-X-bin} suggests the presence of subsequent knots with a detectable proper motion. + In particular. by comparing the 2001 and 2005 data-sets; we counfiiu the results of Favataetal.(2006) who found a detectable westward proper motion ofthe elongated component of the X-ray source. corresponding to z500 kms: we find a hint of clongation again westward in the 2009 observations away frou the jet driving source. but closer to the stationary source than in the 2005 observations.," In particular, by comparing the 2001 and 2005 data-sets, we confirm the results of \citet{fbm06} who found a detectable westward proper motion of the elongated component of the X-ray source, corresponding to $\approx 500$ km/s; we find a hint of elongation again westward in the 2009 observations away from the jet driving source, but closer to the stationary source than in the 2005 observations." + This evidence may suggest the presence of a newly formed knot propagating away roni the diauond shock., This evidence may suggest the presence of a newly formed knot propagating away from the diamond shock. + However note that. iu the 2009 observation. the PSF asvuuuetry is directed aliiost along he N-ray extension axis. aud therefore it could iuflueuce he X-ray source elongation up to an angular scale zz1”.," However note that, in the 2009 observation, the PSF asymmetry is directed almost along the X-ray extension axis, and therefore it could influence the X-ray source elongation up to an angular scale $\approx1''$." +" ""Therefore. both the evidence of a standing shock at the vase of the IIT 151 jet over a 8 yrs timebase and a moving snot in 2005 together with a hint of a new clongatiou in the 2009 zinoothed iaage. indicate the scenario of a jozzle. creating the standing shock. iu the preseuce of a oulsed jet. as described in Bonitoetal.(20103)... which nay account for the movine/clongated compouent."," Therefore, both the evidence of a standing shock at the base of the HH 154 jet over a $8$ yrs timebase and a moving knot in 2005 together with a hint of a new elongation in the 2009 smoothed image, indicate the scenario of a nozzle, creating the standing shock, in the presence of a pulsed jet, as described in \citet{bom10}, which may account for the moving/elongated component." + No uatter how one mterprets the observations. there is a clear need for future observations of ΠΠ 151.," No matter how one interprets the observations, there is a clear need for future observations of HH 154." + The physical origin of the nozzle could be related to ie dense gas in which the L1551 IRS55 protostar is ubedded and/or the intense stellar magnetic field at je jet lanuchine‘collimation region., The physical origin of the nozzle could be related to the dense gas in which the L1551 5 protostar is embedded and/or the intense stellar magnetic field at the jet launching/collimation region. + In the hypothesis lat a duaenetic nozzle causes the cdiamoucd shock observed in TT 151. the Chaudra observations and i6 conirparison with our mnodel offer the possibility o constrain the maenetic fold strength near the jet launching‘collimation region.," In the hypothesis that a magnetic nozzle causes the diamond shock observed in HH 154, the Chandra observations and the comparison with our model offer the possibility to constrain the magnetic field strength near the jet launching/collimation region." +" Iu fact. the ποσο] xovides the total plasima pressure (pa,|pa) n ie N-rav chutting diamond shock that reproduces the observations. where pj. pa, and 4.4 are the pressure. nass densitv aud velocity in the post-shock region close to the nozzle exit. respectively,"," In fact, the model provides the total plasma pressure $(p_{\rm sh}+\rho_{\rm sh}u_{\rm sh}^2)$ in the X-ray emitting diamond shock that reproduces the observations, where $p_{\rm sh}$, $\rho_{\rm sh}$ and $u_{\rm sh}$ are the pressure, mass density and velocity in the post-shock region close to the nozzle exit, respectively." + Then. assuiiug re phasuna —(pasdpast)(D2/sz)zm1. where D is the magnetic field streneth we derive Dzm5 uG iu the magnetic nozzle at the base of the jet.," Then, assuming the plasma $\beta = (p_{\rm sh}+\rho_{\rm +sh}u_{\rm sh}^2)/(B^2/8\pi) \approx 1$, where $B$ is the magnetic field strength, we derive $B\approx 5$ mG in the magnetic nozzle at the base of the jet." + luterestiuglhv. this value is consistent with that inferred w Ballyetal.(2003).. namely B=1.Linc. in the contest of shocks associated to jet collimation. aud by Schneideretal.(2011).. who fund B.z6 mC. which is a reasonable value at the jet basis near the driviug source. according to Hartiganctal. (2007)..," Interestingly, this value is consistent with that inferred by \cite{bfr03}, namely $B = 1-4$ mG, in the context of shocks associated to jet collimation, and by \citet{sgs11}, who find $B\approx6$ mG, which is a reasonable value at the jet basis near the driving source, according to \citet{hfv07}. ." + We sugeest therefore that the comparison between our niodel aud the N-rav observations of ΠΠ 151 may allow us to probe the launching/collimation region ucar the driving source. very dificult to be directly observed iu svstemis so obscured.," We suggest therefore that the comparison between our model and the X-ray observations of HH 154 may allow us to probe the launching/collimation region near the driving source, very difficult to be directly observed in systems so obscured." +function of the “cloud” region.,"function of the “cloud"" region." + The result is indicated by the solid line in the figure., The result is indicated by the solid line in the figure. + The mass function. within (he limits of uncertainty indicated in Figure 8.. is consistent with the relatively flat. distribution found previously in p Oph for masses in excess of a few hundredths of a solar mass (Conmeronetal.1993).. but departs significantly from this behavior for lower masses.," The mass function, within the limits of uncertainty indicated in Figure \ref{fig8}, is consistent with the relatively flat distribution found previously in $\rho$ Oph for masses in excess of a few hundredths of a solar mass \citep{com93}, but departs significantly from this behavior for lower masses." + Specilicallv. our resulls suggest an order of magnitude increase in (he number of objects at ~0.003M... with respect to that al 0.1M...," Specifically, our results suggest an order of magnitude increase in the number of objects at $\sim0.003\,M_\odot$ with respect to that at $\sim0.1\,M_\odot$." + The actual increase may be even larger (han this. however: since some parts of the cloud have νι in excess of 100 magnitudes (see Figure 7)). we may be missing some low-mass objects more deeply embedded in the cloud.," The actual increase may be even larger than this, however; since some parts of the cloud have $A_V$ in excess of 100 magnitudes (see Figure \ref{fig7}) ), we may be missing some low-mass objects more deeply embedded in the cloud." + Theapparent Παtening-out of the distribution below 0.002 AL. is probably due to (he sensitivity. cutoll of the observations. as suggested bv Figure 7..," Theapparent flattening-out of the distribution below 0.002 $M_\odot$ is probably due to the sensitivity cutoff of the observations, as suggested by Figure \ref{fig7}." + llowever. we cannot rule out the possibility of an actual cutoff in the mass distribution.," However, we cannot rule out the possibility of an actual cutoff in the mass distribution." + Our inferred mass function is consistent with that found [or σ Orionis (CaballeroDihainetal.2009) based on broad-band SED information using techniques somewhat similar to those used here.," Our inferred mass function is consistent with that found for $\sigma$ Orionis \citep{cab07,bih09} based on broad-band SED information using techniques somewhat similar to those used here." + Thev similarly [found an order-of-magnitude increase in the mass funetion between 0.1 and 0.006 M. : the Caballeroetal.(2007) resulis have been overplotted on our Figure 5. [or comparison., They similarly found an order-of-magnitude increase in the mass function between 0.1 and 0.006 $M_\odot$ ; the \citet{cab07} results have been overplotted on our Figure \ref{fig8} for comparison. + In addition (Bihainetal.2009) found a possible hint of a turnover al ~0.004. AZ.. also reminiscent of Figure &..," In addition \citep{bih09} + found a possible hint of a turnover at $\sim0.004$ $M_\odot$, also reminiscent of Figure \ref{fig8}." + We have cross checked our results against previous work by searching published lists of spectroscopically confirmed. brown dwarfs in the p Oph cloud core region. but could only find one such case within our field.," We have cross checked our results against previous work by searching published lists of spectroscopically confirmed brown dwarfs in the $\rho$ Oph cloud core region, but could only find one such case within our field." + This is GY 204. listed by Nattaetal.(2002). as an M6 brown dwarf with a temperature of 2700 Ix aud a mass of 4080 Mj.," This is GY 204, listed by \citet{nat02} as an M6 brown dwarf with a temperature of 2700 K and a mass of 40–80 $M_J$ ." + It coincides with object 4660 in Table 1 for which we had estimated Tuy=2888+340 Ixand a mass, It coincides with object 60 in Table 1 for which we had estimated $T_{\rm eff}=2888\pm340$ Kand a mass +our observing ruu. which cause problems with the data reduction. as flexure could lapven. iu both spatial aud spectral directions.,"our observing run, which caused problems with the data reduction, as flexure could happen in both spatial and spectral directions." + We shifted tje spectral images along he both directions manually based on sla 0enmussion ines and fiat-field images before we fed the data to the xpeline., We shifted the spectral images along the both directions manually based on sky emission lines and flat-field images before we fed the data to the pipeline. + The pipeline corrected for auv simall residual shifts., The pipeline corrected for any small residual shifts. + We extracted the spectra of our targets and flux-calibrated the spectra using aligumoent stars., We extracted the spectra of our targets and flux-calibrated the spectra using alignment stars. + There were vpically 15 bright (16<£78 17) alignment stars yer duask used to alien asks., There were typically 4–5 bright $166.," The strongest emission line $5.8 \times 10^{-17}$ erg $^{-1}$ $^{-2}$ ) in our sample is as bright as the strongest LAEs from large LAE surveys of \citet{ouc09}, \citet{hu10}, and \citet{kas11}, indicating that it represents the bright end of LAEs at $z>6$." + Table I also includes the star formation rates (SFRs) estimated from the Ihuninosities bv which is based on the relation between SER aud the Ihuninositv (I&enuicutt1998) aud the line eiiission ratio of tto in Case D recombination (Osterbocketal. 1989).., Table 1 also includes the star formation rates (SFRs) estimated from the luminosities by which is based on the relation between SFR and the luminosity \citep{ken98} and the line emission ratio of to in Case B recombination \citep{ost89}. . + The derived SFRs are less than LO Mvr| for all but one ealaxy., The derived SFRs are less than 10 $\rm M_{\sun}\ yr^{-1}$ for all but one galaxy. + We estimate the rest-frame equivalent widths (ENs) using the observed, We estimate the rest-frame equivalent widths (EWs) using the observed +Mathysetal.(1997) suggested a possible anticorrelation between the mean magnetic Geld modulus and stellar rotation period.,\citet{Mathys97} suggested a possible anticorrelation between the mean magnetic field modulus and stellar rotation period. + 550 from Mathysctal.(1997) cdillers [rom our refbsybecausciehavecincludedscveralstarswithverystrong fields!lad usmopbuliodds Dreso, 50 from \citet{Mathys97} differs from our \\ref{bs_p} because we have included several stars with very strong fields that were found subsequent to \citet{Mathys97}. +lsseda(Awan) squarctongiltudinalmagneticf icldaasafunctionofrotationgesiekiilb lestΑλ obsstqucs, The root-mean-square longitudinal magnetic fields as a function of rotation period were studied by \citet{hubrig07} on a wider sample of Ap stars. +bypomcoholdanovdibissS€DOOAOy- ermide rsem pleof Ay ‘Together with previous papers (Erevhamamerctal. 2008: Elkinctal. 2010a:: Elkin.Kurtz.&Alathys 2011)) we have found a total of 34 new magnetic stars with resolved ancl partly resolved Zeeman components using high resolution spectra from our FEROS survey of cool Ap stars., They showed that the stars with strongest longitudinal field generally show periods less than d. Together with previous papers \citealt{Freyhammer08}; \citealt{Elkin10a}; \citealt{Elkin11}) ) we have found a total of 34 new magnetic stars with resolved and partly resolved Zeeman components using high resolution spectra from our FEROS survey of cool Ap stars. + Among them we found several stars with a mean magnetic field modulus more than LOKKG. Considering the number of observed Ap stars in this survey we can estimate that cdbaqieaadnts p, Among them we found several stars with a mean magnetic field modulus more than kG. Considering the number of observed Ap stars in this survey we can estimate that the proportion of stars with resolved Zeeman components is slightly less than $10$ percent. + (OU 47 magnetic Ap/Bp stars with resolved Zeeman splitting., \citet{Mathys04} noted only 47 magnetic Ap/Bp stars with resolved Zeeman splitting. + Our discovery of 34 stars with clear Zeeman splitting found among cool Ap stars is a significant contribution for further study of this type of star., Our discovery of 34 stars with clear Zeeman splitting found among cool Ap stars is a significant contribution for further study of this type of star. + This comes from our survey of, This comes from our survey of +The orbit ellipGicily also influences (he similarity between the (wo cluster tails.,The orbit ellipticity also influences the similarity between the two cluster tails. + For the quasi-circular orbit. (hese structures are simmetric for the whole duration of (he simulation. being elongated. al a given time. for the same length.," For the quasi-circular orbit, these structures are simmetric for the whole duration of the simulation, being elongated, at a given time, for the same length." + For more eccentric orbits. the leading tail tends to be more elongated than the trailing one when going from the apocenter to the orbital pericenter and. viceversa. i( is less elongated than the trailing tail when the cluster moves towards the apocenter.," For more eccentric orbits, the leading tail tends to be more elongated than the trailing one when going from the apocenter to the orbital pericenter and, viceversa, it is less elongated than the trailing tail when the cluster moves towards the apocenter." + Di any case. (he tail that precedes the cluster extends always slightly below the orbit while the trailing one lies slighliv above this latter. in agreement with what observed for Palomar 5.," In any case, the tail that precedes the cluster extends always slightly below the orbit while the trailing one lies slighlty above this latter, in agreement with what observed for Palomar 5." + The shape ancl orientation of the tails can be easily understood in the case of a cluster moving on a circular orbit in an axvsimumetric external field. using a rotating frame of relerence with the origin in the baricentre of the cluster. will the X-axis pointing towards the galactic center. the Y-axis parallel to the direction of motion of the cluster and (he Z- orthogonal to the orbital plane.," The shape and orientation of the tails can be easily understood in the case of a cluster moving on a circular orbit in an axysimmetric external field, using a rotating frame of reference with the origin in the baricentre of the cluster, with the $X$ -axis pointing towards the galactic center, the $Y$ -axis parallel to the direction of motion of the cluster and the $Z$ -axis orthogonal to the orbital plane." + In this reference frame. (he galactic tidal fiekl tends {ο accelerate stars along the dX directions (Ilegegie&Hut2003).. making stars to escape from the svstem through the Lagrangian points £4 and Ly (which are the (wo equilibrium points located along the X-axis).," In this reference frame, the galactic tidal field tends to accelerate stars along the $\pm X$ directions \citep{hh03}, making stars to escape from the system through the Lagrangian points $L_1$ and $L_2$ (which are the two equilibrium points located along the $X$ -axis)." + But (he Coriolis acceleration tends (to align escaping stars along the direction of motion of the cluster around (he galaxy. this velding the peculiar S-shape just outside (he cluster. in the inner part of the In order to describe the tidal debris ancl to compare our findings with observations (Lehmann&Scholz1997;Testaetal.2000:LeonοἱSiegel2001: 2003).. we studied (he radial profile of the volume aud surface densities (azimutallvy averaged) as a function of the distance οι the cluster center.," But the Coriolis acceleration tends to align escaping stars along the direction of motion of the cluster around the galaxy, this yelding the peculiar $S$ -shape just outside the cluster, in the inner part of the In order to describe the tidal debris and to compare our findings with observations \citep{ls97,testa00,lmc00,sieg00,lee03,oden03}, we studied the radial profile of the volume and surface densities (azimutally averaged) as a function of the distance from the cluster center." + Obviously. this description does not take into account the fact that stars lost [rom (he cluster are not placed in a spherically svannietric structure. but it has the advantage lo provide a global study of both the cluster ancl the tails that can be easily compared with observational data.," Obviously, this description does not take into account the fact that stars lost from the cluster are not placed in a spherically symmetric structure, but it has the advantage to provide a global study of both the cluster and the tails that can be easily compared with observational data." + In Fig.19 and 20.. (he volume density of the svstem is shown at dilferent epochs. for the various orbits.," In \ref{voldens} and \ref{voldenstutte}, the volume density of the system is shown at different epochs, for the various orbits." + Once the tails have completely developed. outside the 5--shape distribution. density chimps appears.," Once the tails have completely developed, outside the -shape distribution, density clumps appears." + They are svnuuetrically located in the (vo (ails. as shown in Fig.21 for the cluster on quasi-creular orbit: in thiscase. the most prominent chunps are located at a distance from the cluster center between 0.25ry and 0.475.," They are symmetrically located in the two tails, as shown in \ref{supdens2} for the cluster on quasi-circular orbit: in thiscase, the most prominent clumps are located at a distance from the cluster center between $0.25r_b$ and $0.4r_b$ ." + The density profiles are very similar to (hat, The density profiles are very similar to that + , +In our analysis we restrict ourselves to objects where we can be sure that the higher Balmer lines (I5. Ho. ete.),"In our analysis we restrict ourselves to objects where we can be sure that the higher Balmer lines $\gamma$ , $\delta$, etc.)" + are not contaminated bv region emission. ie. we avoid objects with clear indication of nebular Hla emission or with a hint of nebular emission al 115 above or below the 2-D stellar spectrum.," are not contaminated by region emission, i.e. we avoid objects with clear indication of nebular $\alpha$ emission or with a hint of nebular emission at $\gamma$ above or below the 2-D stellar spectrum." + In addition. we select only spectral types within a narrow range between BS and A+. where we know from our recent work (Przvhillaetal.2001:Przvbilla 2002)) that our model atinosphere analvsis tools are very reliable. in particular will regard to the relative accuracy of a strictly differential studs.," In addition, we select only spectral types within a narrow range between B8 and A4, where we know from our recent work \citealt{przybilla01a,przybilla01b,przybilla02}) ) that our model atmosphere analysis tools are very reliable, in particular with regard to the relative accuracy of a strictly differential study." + For (he given spectral types we adopt effective temperatures according to Table 1 and determine graviües Irom the higher Balmer lines as displaved in Fig., For the given spectral types we adopt effective temperatures according to Table 1 and determine gravities from the higher Balmer lines as displayed in Fig. + 1., 1. + We then calculate intrinsic colours with our model atmosphere code to determine reddening and extinction and use the ealeulated bolometric correction and (he distance modulus to obtain bolometric magnitudes., We then calculate intrinsic colours with our model atmosphere code to determine reddening and extinction and use the calculated bolometric correction and the distance modulus to obtain bolometric magnitudes. + The data set lor NGC 300 is not the only one available to us., The data set for NGC 300 is not the only one available to us. + In a similar wav. have used FORSI at the VLT to study 17 objects in the spiral galaxy NGC 3621 αἱ a distance of 6.7 Mpe Ga—M=29.08. Freedmanetal. 2001)).," In a similar way, \citealt{bresolin01} have used FORS1 at the VLT to study 17 objects in the spiral galaxy NGC 3621 at a distance of 6.7 Mpc $m-M = 29.08$, \citealt{freedman01}) )." + Applving the same selection criteria as above we can add four more objects to the sample and apply the same spectral analvsis., Applying the same selection criteria as above we can add four more objects to the sample and apply the same spectral analysis. + The result of the test is displaved in Fig., The result of the test is displayed in Fig. + 2. which shows a surprisingly Gght correlation. as predicted by Eq.(1).," 2, which shows a surprisingly tight correlation, as predicted by Eq.(1)." + The linear regression coellicients are α=—3.85 and b=13.13. the standard deviation of the the residual bolometric magnitude from this regression being g=0.26 mag.," The linear regression coefficients are $a=-3.85$ and $b=13.73$, the standard deviation of the the residual bolometric magnitude from this regression being $\sigma = 0.26$ mag." + The objects in NGC 3621 seem (o indicate a somewhat smaller distance modulus (bx 0.2 mag) than adopted., The objects in NGC 3621 seem to indicate a somewhat smaller distance modulus (by 0.2 mag) than adopted. + ILowever. we prefer (ο wail for forthcoming stellar photometry of both NGC 300 and NGC 3621 with the Advanced Camera on board of LIST. helore we follow up on the relative distance of these (wo galaxies.," However, we prefer to wait for forthcoming stellar photometry of both NGC 300 and NGC 3621 with the Advanced Camera on board of HST, before we follow up on the relative distance of these two galaxies." + The small standard deviation obtained in Fig., The small standard deviation obtained in Fig. + 2 might be an artifact resulting from the relatively low number of objects studied., 2 might be an artifact resulting from the relatively low number of objects studied. + We. therefore. analvze additional high resolution spectra presently available to us of a larger sample of objects in the Milkv Was. the Magellanic Clouds. M31. M33 and NGC 6822.," We, therefore, analyze additional high resolution spectra presently available to us of a larger sample of objects in the Milky Way, the Magellanic Clouds, M31, M33 and NGC 6822." + We apply the same technique as before. except lor the three objects in the SAIC. NGC 6822 and M33. which are extremely metal poor.," We apply the same technique as before, except for the three objects in the SMC, NGC 6822 and M33, which are extremely metal poor." + For those (following Venn 1999)) we do not rely on the spectral type. but determine from the non-LTE ionization equilibrium of Mg 1/1 and N I/HI.," For those (following \citealt{venn99}) ) we do not rely on the spectral type, but determine from the non-LTE ionization equilibrium of Mg I/II and N I/II." + We note that the inclusion of the galactic objects is somewhat problematic. as their distancesare more uncertain (Ixuciritzkietal.1999:Przvbilla 2002)).," We note that the inclusion of the galactic objects is somewhat problematic, as their distancesare more uncertain \citealt{kud99,przybilla02}) )." + We also note that the strictly dillerential character, We also note that the strictly differential character +0.52Zsxun.. and: SBC, data. <1 Zsun."," As expected, the best fit metallicity is dependent on the near-IR data: the $_K$ data has a best fit metallicity around; SBH data, $>2$, and; $_J$ data, $<1$ ." +". The SDC, set ofdata 1s in agreement with solar ucigliborhood measurements of the metallicity which eive an average close to solar (Tlavwood20013.", The $_K$ set ofdata is in agreement with solar neighborhood measurements of the metallicity which give an average close to solar \citep{Haywood01}. +. The SBII data is in disaerecnuent with solar iuetallicitv at the confidence level., The SBH data is in disagreement with solar metallicity at the confidence level. + For the rest of the paper. we use an average estimate of the AK-baud huminosity corresponding to from Coleetal.(2001). aud I&ochauckctal.(200101.," For the rest of the paper, we use an average estimate of the $K$ -band luminosity corresponding to from \cite{cole01} and \cite{kochanek01}." + The macertainty was increased. aud the J-band was not included. so that the coustraimts on the IME were not dependent on the discrepancies noted above.," The uncertainty was increased, and the $J$ -band was not included, so that the constraints on the IMF were not dependent on the discrepancies noted above." + This lo rauge in the A-baud hunuimositv density is also similar to the range deteriuued by Belletal. (2003).., This $\sigma$ range in the $K$ -band luminosity density is also similar to the range determined by \cite{bell03}. . + The ietallicity- contoursfor this data set (compilation designated SBav) are also shown in Figure 7.., The metallicity-IMF contoursfor this data set (compilation designated SBav) are also shown in Figure \ref{fig:Z-imf+0}. . + The best fit INE slope. P=1.384 0.1. shows the tiehtuess of the constraint if," The best fit IMF slope, $\Gamma=1.3\pm0.1$ , shows the tightness of the constraint if" +~s107 would produce similar effects.,"$\Omega_{dust}^{igm} \sim 3 +\times 10^{-5}$ would produce similar effects." + QuThe amount of dispersion iuduced by the dust is very iuportant but cau be estimated oulv roughly., The amount of dispersion induced by the dust is very important but can be estimated only roughly. +" Απο that the dust is uniformly distributed in randomly placed spheres of radius Z? with uumuber density ». the dispersion A is given approximately by Αντι=0.5)2N7, where Nis the uuniber of spheres intersected by a typical path. aud cau be written No~uitR?D. where D=24007, Ape is the distauce to. =0.5 in an ο=0.2 universe,"," Assuming that the dust is uniformly distributed in randomly placed spheres of radius $R$ with number density $n$ , the dispersion $\Delta$ is given approximately by $\Delta/A_V(z=0.5) \approx N^{-1/2}$, where $N$ is the number of spheres intersected by a typical path, and can be written $N \simeq +n\pi R^2D$ , where $D\approx 2400h_{65}^{-1}\,$ Mpc is the distance to $z=0.5$ in an $\Omega=0.2$ universe." + Now consider galaxies with sΓΗ.DApe? (Lin et al.," Now consider galaxies with $n = 0.008h_{65}^3(1+z)^3\,{\rm + Mpc^{-3}}$ (Lin et al." + 1996)., 1996). + For N12zl this uuplies R>πι.ταν?ο” ," For $N^{1/2} \ga 1$ this implies $R +\ga 70h_{65}^{-1}[(1+z)/1.5]^{-3/2}\,{\rm kpc}$." +Escape velocities frou splvals are >250kins so the dispersion m integrated optical depth due to dust ejected by raciation pressure or winds aud traveling away from the disk for time Ty... ds Figure 5 shows the (small) difference in optical depth between the total dust distribution aud the dust which has existed for 2200 Myr aud >1 Gyr. demonstrating that the dispersion induced by erey dust created but uot vet sufficiently dispersed would be small.," Escape velocities from spirals are $\ga 250\,{\rm km\,s^{-1}}$, so the dispersion in integrated optical depth due to dust ejected by radiation pressure or winds and traveling away from the disk for time $\tau_{esc}$ is Figure \ref{fig-depth} shows the (small) difference in optical depth between the total dust distribution and the dust which has existed for $> 200$ Myr and $> 1$ Gyr, demonstrating that the dispersion induced by grey dust created but not yet sufficiently dispersed would be small." + Larec-scale correlations between galaxies are uulikelv to be iniportaut in this analvsis., Large-scale correlations between galaxies are unlikely to be important in this analysis. +" The dispersion iu deusity ou 5 Mpc scales js l. but ~300 such domains lie between here aud Do0,5. leading to A~02/300=0.01."," The dispersion in density on 8 Mpc scales is $\sim 1$, but $\sim 300$ such domains lie between here and $z\sim 0.5$, leading to $\Delta \sim +0.2/\sqrt{300} = 0.01$." + The best way to estimate dispersion (currently underway) would probably be to measure the optical depth through raudoni lines of sight piercing a high-resolution cosmology simulation which either tracks metals (Cen Ostriker 1999): Cuedin 1998) or allows some prescription relating gas deusity to dust density iu the IGM., The best way to estimate dispersion (currently underway) would probably be to measure the optical depth through random lines of sight piercing a high-resolution cosmology simulation which either tracks metals (Cen Ostriker 1999b; Gnedin 1998) or allows some prescription relating gas density to dust density in the IGM. + Short of this. I note that Ceu Ostrikers simulations show that à~100 is characteristic of the bulk of the iietal-ricli eas.," Short of this, I note that Cen Ostriker's simulations show that $\delta +\sim 100$ is characteristic of the bulk of the metal-rich gas." +" This corresponds to R=GT0h,2(0|:)+ kpe for the spheres considered above.", This corresponds to $R \ga 670h_{65}^{-1}(1+z)^{-1}$ kpc for the spheres considered above. + Fairly uniform regions of this size and umber deusity would eive little dispersion., Fairly uniform regions of this size and number density would give little dispersion. + Ti Ro 1$ supernovae are measured. + A large number of supernovae is important both because the dispersion is comparable to the effect being measured. aud," A large number of supernovae is important both because the dispersion is comparable to the effect being measured, and" +correctly represented by (he current assumption of a CSM described by a simple power law and smoothly continued by a uniform density AM.,correctly represented by the current assumption of a CSM described by a simple power law and smoothly continued by a uniform density AM. + LW current. models of pre-SNla binary evolution are correct. the early evolution of their SNR cannot be described by anv kind of similarity solution.," If current models of pre-SNIa binary evolution are correct, the early evolution of their SNR cannot be described by any kind of similarity solution." + On (he other hand. a few restrictions can also be put ou presupernova evolution.," On the other hand, a few restrictions can also be put on presupernova evolution." + None of the wind models explored here is compatible with the known properties of Tveho's SNR. whereas wind model A (characterized by a high velocity wind lasting for about 2xLO? vr. followed by a phase of conservative evolution) gives results consistent wilh several features of SNRLOOG.," None of the wind models explored here is compatible with the known properties of Tycho's SNR, whereas wind model A (characterized by a high velocity wind lasting for about $2\times +10^5$ yr, followed by a phase of conservative evolution) gives results consistent with several features of SNR1006." + It is clear that a more complete exploration of the space of parameters describing pre-supernova wind is of high interest., It is clear that a more complete exploration of the space of parameters describing pre-supernova wind is of high interest. + This work has been supported by the AICYT grants ESD93-1348 and AYA2000-1735. and by the DGES grant PD98-1183-CO03-02.," This work has been supported by the MCYT grants ESP98-1348 and AYA2000-1785, and by the DGES grant PB98-1183-C03-02." + CD is verv indebted for α CIRIT grant., CB is very indebted for a CIRIT grant. +"The orbital evolution of a pair of planets with masses of ii,= 10 Mis shown in the left panelof Figure 1..",The orbital evolution of a pair of planets with masses of $m_p=$ 10 $M_\oplus$ is shown in the left panelof Figure \ref{run1}. + At the beginning of the simulation. corotation torques cause the inner planet to remain trapped at the edge of the dise cavity (see Paper D) located at 7~1.2.," At the beginning of the simulation, corotation torques cause the inner planet to remain trapped at the edge of the disc cavity (see Paper I) located at $r \sim 1.2$." +" The outer planet. which initially evolves on a circular orbit with a,=2.5. undergoes the usual type | migration and drifts inward."," The outer planet, which initially evolves on a circular orbit with $a_o=2.5$, undergoes the usual type I migration and drifts inward." +" As it nigrates. its eccentricity ο, slowly inereases due to the influence of the binary (see bottom left panel of Figure 1))."," As it migrates, its eccentricity $e_o$ slowly increases due to the influence of the binary (see bottom left panel of Figure \ref{run1}) )." + Also. the distance between the two bodies becomes smaller and smaller which can potentially leads to the formation of mean motion resonances (Papaloizou Szuszkiewiez 2005).," Also, the distance between the two bodies becomes smaller and smaller which can potentially leads to the formation of mean motion resonances (Papaloizou Szuszkiewicz 2005)." + Here. we find that the two planets become captured into the 4:3 resonance at r~1.9x107 binary orbits.," Here, we find that the two planets become captured into the 4:3 resonance at $t\sim 1.9\times 10^4$ binary orbits." +" The top right panel of Figure 1. displays the evolution of both the apsidal angle Aw=w;—ων and the resonant angle ΨΞA,—3.2;θωι. where 2; GU) and w; (o,) are respectively the mean longitude and longitude of pericentre of the inner (outer) planet."," The top right panel of Figure \ref{run1} displays the evolution of both the apsidal angle $\Delta\omega=\omega_i-\omega_o$ and the resonant angle $\psi=4\lambda_o-3\lambda_i-3\omega_i$, where $\lambda_i$ $\lambda_o$ ) and $\omega_i$ $\omega_o$ ) are respectively the mean longitude and longitude of pericentre of the inner (outer) planet." + Once the resonance is established. the libration amplitude of v slightly increases with time until ες4x107 binary orbits. and ther remains almost unchanged. suggesting that the planets are stably locked into the resonance.," Once the resonance is established, the libration amplitude of $\psi$ slightly increases with time until $t \sim 4\times 10^4$ binary orbits, and then remains almost unchanged, suggesting that the planets are stably locked into the resonance." + From this time onward. the system is close to an equilibrium state with both planets having constant semimajor axes and eccentricities.," From this time onward, the system is close to an equilibrium state with both planets having constant semimajor axes and eccentricities." +" At the end of the simulation. the ratio of semimajor axes is dildo~0.85 and the ratio of eccentricities is ¢;/e,0.6."," At the end of the simulation, the ratio of semimajor axes is $a_i/a_0 \sim 0.85$ and the ratio of eccentricities is $e_i/e_o \sim 0.6$." + Such a configuration can be achieved because the torques exerted by the dise on each planet act in an opposite way and can eventually counterbalance each other., Such a configuration can be achieved because the torques exerted by the disc on each planet act in an opposite way and can eventually counterbalance each other. + From the time the resonance Is established the negative torques exerted by the dise on the outer planet make the two planets migrate inward together., From the time the resonance is established the negative torques exerted by the disc on the outer planet make the two planets migrate inward together. + However. as both planets migrate. the innermost planet experiences stronger positive corotation torques which tend to push the pair of planets outward.," However, as both planets migrate, the innermost planet experiences stronger positive corotation torques which tend to push the pair of planets outward." + The bottom right panel of Fig., The bottom right panel of Fig. + 1. shows the evolution of the torques exerted on each planet as well as the effective torques acting on the whole system., \ref{run1} shows the evolution of the torques exerted on each planet as well as the effective torques acting on the whole system. + We see that as the evolution proceeds. the torques exerted on the inner planet are able to exactly counterbalance the ones exerted on the outer body. which leads consequently to a zero net torque acting on the system.," We see that as the evolution proceeds, the torques exerted on the inner planet are able to exactly counterbalance the ones exerted on the outer body, which leads consequently to a zero net torque acting on the system." + This happens from r~2.1x 107. thereby stopping the joined migration of the planets.," This happens from $t\sim 2.1\times 10^4$ , thereby stopping the joined migration of the planets." + Stable resonant locking was also found in some of the calculations with g>|., Stable resonant locking was also found in some of the calculations with $q \ge 1$. + Fig., Fig. +" 2. shows the results for Run? in which planets have masses of i;=10 and i,=5 Ma.", \ref{run2} shows the results for Run2 in which planets have masses of $m_i=10$ and $m_o=5$ $\mearth$. + With respect to Runl. the outer planet migrates more slowly since its mass ts smaller.," With respect to Run1, the outer planet migrates more slowly since its mass is smaller." + However. the mode of evolution found in Run? ts very similar to the one obtained in Runt. leading ultimately to a stable configuration with the two planets trapped in the 4:3 resonance from r~5x107.," However, the mode of evolution found in Run2 is very similar to the one obtained in Run1, leading ultimately to a stable configuration with the two planets trapped in the 4:3 resonance from $t\sim 5\times 10^4$." +" At earlier times. the evolution of e, shows some peaks at f~1.9x107 and [3x107 which coincide with the planets being temporary captured in the 2:1 and 3:2 resonances."," At earlier times, the evolution of $e_o$ shows some peaks at $t\sim 1.9\times 10^4$ and $t \sim 3\times + 10^4$ which coincide with the planets being temporary captured in the 2:1 and 3:2 resonances." +" At the end of the simulation. e, is still slightly increasing whereas e; Is slightly decreasing. which indicates that the equilibrium configuration is not fully established."," At the end of the simulation, $e_o$ is still slightly increasing whereas $e_i$ is slightly decreasing, which indicates that the equilibrium configuration is not fully established." + Nonetheless. comparing Figs.," Nonetheless, comparing Figs." + | and 2.. we can see that the libration amplitude of the resonant angle is much smaller in Run2 than in Runl. suggesting that the 4:3 resonance Is more stable in this —n models with mw;=20M. the simulations resulted in different modes of evolution. depending on the mass of the outer planet 1.," \ref{run1} and \ref{run2}, we can see that the libration amplitude of the resonant angle is much smaller in Run2 than in Run1, suggesting that the 4:3 resonance is more stable in this In models with $m_i=20\;\mearth$, the simulations resulted in different modes of evolution, depending on the mass of the outer planet $m_o$." + Fig., Fig. + 3 and Fig., \ref{run3} and Fig. +" 4. display the results of calculations with mz,=10Ma and i,=5Ma respectively.", \ref{run4} display the results of calculations with $m_o=10\;\mearth$ and $m_o=5\;\mearth$ respectively. +" Comparing these two figures. we can see that the final state of the system is quite similar in both cases. with planets evolving on fixed orbits with o;~1.2 and a,~1.6."," Comparing these two figures, we can see that the final state of the system is quite similar in both cases, with planets evolving on fixed orbits with $a_i\sim 1.2$ and $a_o\sim 1.6$." +" In the run with m,=10Ms. a 3:2 resonance forms attr ~1.4x107."," In the run with $m_o=10\;\mearth$, a 3:2 resonance forms at $t\sim 1.4 \times 10^4$ ." +" In the simulation with Ξ5M., however. there is no evidence that the planets are in mean motion resonance. even though the system is close to the 3:2 commensurability."," In the simulation with $m_o=5\;\mearth$ however, there is no evidence that the planets are in mean motion resonance, even though the system is close to the 3:2 commensurability." + In this case. examination. of the torques exerted by the dise (see upper panel of Fig. 5))," In this case, examination of the torques exerted by the disc (see upper panel of Fig. \ref{run42}) )" + reveals that the migration of the system stalls because the torques acting on both planets cancel., reveals that the migration of the system stalls because the torques acting on both planets cancel. + Here. such an effect arises because the mass of theinner planet is high enough to make the onset of non-linear effects possible.," Here, such an effect arises because the mass of theinner planet is high enough to make the onset of non-linear effects possible." + These can significantly alter the surface density profile and widen the size of the inner cavity., These can significantly alter the surface density profile and widen the size of the inner cavity. + Indeed. we find that the edge of the inner cavity is located at p.~1.2 m simulations with m;=10Ma and m;=5Ma whereas the bottom panel of Fig.," Indeed, we find that the edge of the inner cavity is located at $r\sim 1.2$ in simulations with $m_i=10\;\mearth$ and $m_i=5\;\mearth$ whereas the bottom panel of Fig." + 5 shows that it is located at p~1.5 in Rund., \ref{run42} shows that it is located at $r\sim 1.5$ in Run4. + Consequently. the evolution of the system in Rund is such that the migration of the outermost planet is halted at the edge of the cavity formed by the binary plus inner planet system. therefore preventing capture in the 3:2 resonance (or in resonances of higher degree such às 4:3).," Consequently, the evolution of the system in Run4 is such that the migration of the outermost planet is halted at the edge of the cavity formed by the binary plus inner planet system, therefore preventing capture in the 3:2 resonance (or in resonances of higher degree such as 4:3)." + For simulations with g<|. the evolution of the system differed significantly from that just described in all but one case (Run6).," For simulations with $q < 1$, the evolution of the system differed significantly from that just described in all but one case (Run6)." + Fig., Fig. +" 6 shows the results of a simulation (RunS with g=0.5 in which planets have masses of ji;=5Μ., anc m,=10Ma.", \ref{run5} shows the results of a simulation (Run5) with $q=0.5$ in which planets have masses of $m_i=5\;\mearth$ and $m_o=10\;\mearth$. + Here. the outer planet passes through the 4:3 resonance at f~1.8x10 and then slips into the 6:5 resonance with the inner planet at ¢~2x10.," Here, the outer planet passes through the 4:3 resonance at $t\sim 1.8\times 10^4$ and then slips into the 6:5 resonance with the inner planet at $t \sim 2\times +10^4$." + The passage through these resonances Is clearly accompanied by an increase of the inner planet eccentricity ej;, The passage through these resonances is clearly accompanied by an increase of the inner planet eccentricity $e_i$. + At f~2.1x10%. the inner planet undergoes a close encounter with the outer one as a result of resonant trapping.," At $t\sim 2.1\times 10^4$, the inner planet undergoes a close encounter with the outer one as a result of resonant trapping." + This subsequently leads to the scattering of the inner planet further out in the dise. while the outer one is pushed inward by virtue of conservation of angularmomentum., This subsequently leads to the scattering of the inner planet further out in the disc while the outer one is pushed inward by virtue of conservation of angularmomentum. + Interestingly. such an orbital exchange leads to a configuration of the system similar to that of models with 451.," Interestingly, such an orbital exchange leads to a configuration of the system similar to that of models with $q\ge +1$ ." + good agreement with what we described in Section ??.. we find that the final state of the systemis indeed an," In good agreement with what we described in Section \ref{qge1}, , we find that the final state of the systemis indeed an" +The errors caused by the smoothing procedures are well within for (65 jim) and. (00. jim). for (140 p/m). and for (160. jm).,"The errors caused by the smoothing procedures are well within for $65~\mu$ m) and $90~\mu$ m), for $140~\mu$ m), and for $160~\mu$ m)." + These error levels are consistent to or somewhat larger than the background fluctuation mainly caused by a hit «Xf high energy ionizing particle. which implies that the background fluctuation is a major component in he errors.," These error levels are consistent to or somewhat larger than the background fluctuation mainly caused by a hit of high energy ionizing particle, which implies that the background fluctuation is a major component in the errors." + The above vaues are adopted for the errors. but we adopt larger errors for some galaxies which have larger background noises.," The above values are adopted for the errors, but we adopt larger errors for some galaxies which have larger background noises." + At (160 jim). some objects are not detected.," At (160 $\mu$ m), some objects are not detected." + For hem. we adopt 3 times he background uncertainty as an upper imit.," For them, we adopt 3 times the background uncertainty as an upper limit." + Since the sample BCDs are compact enough to be treated as »oint sources with the resolution of FIS. we follow the point-source johotometry described in Verdugoetal.(2007).," Since the sample BCDs are compact enough to be treated as point sources with the resolution of FIS, we follow the point-source photometry described in \citet{verdugo07}." + Finally or the (140 jim) fluxes: the colour correction factor was assumed to be 0.93 (the flux was divided by this factor)., Finally for the $140~\mu$ m) fluxes: the colour correction factor was assumed to be 0.93 (the flux was divided by this factor). + We did not apply colour correction to the (65 jim). (160 μπι). and (90 jim) fluxes. following HOS.," We did not apply colour correction to the (65 $\mu$ m), (160 $\mu$ m), and $90~\mu$ m) fluxes, following H08." + For these three bands. the uncertainty caused by not applying colour correction is smaller than the errors put in Table I..," For these three bands, the uncertainty caused by not applying colour correction is smaller than the errors put in Table \ref{tab:flux}." + The FIR colours are defined by the flux ratio between two bands (Section. 2.3)., The FIR colours are defined by the flux ratio between two bands (Section \ref{subsec:colour}) ). + HHSO7 investigated the FIR. colours. of the Milky Way and the Magellanic Clouds by using the Zodi-Subtracted Mission Average (ZSMA) taken by the Diffuse Infrared Background Experiment (DIRBE) of the (COBE))., HHS07 investigated the FIR colours of the Milky Way and the Magellanic Clouds by using the Zodi-Subtracted Mission Average (ZSMA) taken by the Diffuse Infrared Background Experiment (DIRBE) of the ). +" Details of the observational data analysis can be ‘ound in Hibietal.(2006)... who adopted DIRBE bands of 60 jim. OO yam. and. 140 yam and two colours. 60 j/im-100 jm colour. (60/100),4. and 140 j/m—-100 sem colour. (140/100)."," Details of the observational data analysis can be found in \citet{hibi06}, who adopted DIRBE bands of 60 $\mu$ m, 100 $\mu$ m, and 140 $\mu$ m and two colours, 60 $\mu$ m–100 $\mu$ m colour, $(60/100)_\mathrm{cl}$, and 140 $\mu$ m–100 $\mu$ m colour, $(140/100)_\mathrm{cl}$." + We can also take two colours for our BCD sample., We can also take two colours for our BCD sample. + However. he wavelengths of the FIS bands are slightly different from the DIRBE bands.," However, the wavelengths of the FIS bands are slightly different from the DIRBE bands." + Thus. we apply the following corrections.," Thus, we apply the following corrections." + First. we tit lyDia) Chis a constant and 2 is the emissivity index) to the 65 iim and 90 jim fluxes derive the dust temperature 7:4.," First, we fit $A\nu^\beta B_\nu (T_\mathrm{d})$ $A$ is a constant and $\beta$ is the emissivity index) to the 65 $\mu$ m and 90 $\mu$ m fluxes derive the dust temperature $T_\mathrm{d}$." + We denote he dust temperature obtained in this way as Z4((65/90)4. 2).," We denote the dust temperature obtained in this way as $T_\mathrm{d}((65/90)_\mathrm{cl},\,\beta )$ ." + We adopt .?l and 2., We adopt $\beta =1$ and 2. +" Then. we estimate the 60 jim flux by evaluating ον(1) at A=60 jim under the values of ;d and 146065/90),4.977) obtained above."," Then, we estimate the 60 $\mu$ m flux by evaluating $A\nu^\beta B_\nu (T_\mathrm{d})$ at $\lambda =60~\mu$ m under the values of $A$ and $T_\mathrm{d}((65/90)_\mathrm{cl},\,\beta )$ obtained above." + The same procedure is applied for the 140 jam and 90 jim fluxes to obtain the 100 jim flux., The same procedure is applied for the 140 $\mu$ m and 90 $\mu$ m fluxes to obtain the 100 $\mu$ m flux. +" In this way. we ean obtain (60/100),; and (140/1002.4 for the BCD sample."," In this way, we can obtain $(60/100)_\mathrm{cl}$ and $(140/100)_\mathrm{cl}$ for the BCD sample." + In reffig:elrdat.. we show the colourcolour relation for the sample.," In \\ref{fig:clrdat}, we show the colour–colour relation for the sample." + For comparison. we also show the data of Hibietal.(2006) for the Milky Way (the Galactic plane with Galactic latitudes of b«re 5) and the Magellanic Clouds in reftig:elrdat..," For comparison, we also show the data of \citet{hibi06} + for the Milky Way (the Galactic plane with Galactic latitudes of $|b|<5^\circ$ ) and the Magellanic Clouds in \\ref{fig:clrdat}." + Hibietal.(2006) found that more than of the data lie on a strong correlation called main correlation. which can be fitted as The main correlation also explains the FIR colours of Galactic ugh latitudes (|b] 5°). the LMC. and the SMC (Hibietal.2006:Hibi 2006:: HHS07).," \citet{hibi06} found that more than of the data lie on a strong correlation called main correlation, which can be fitted as The main correlation also explains the FIR colours of Galactic high latitudes $|b|>5^\circ$ ), the LMC, and the SMC \citealt{hibi06,hibiphd06}; HHS07)." + In the Galactic plane. there is another correlation sequence. called subcorrelation in Hibietal.(2006): The subcorrelation is not seen in the high Galactic latitudes (Hibi2006:: HHS07).," In the Galactic plane, there is another correlation sequence, called subcorrelation in \citet{hibi06}: The subcorrelation is not seen in the high Galactic latitudes \citealt{hibiphd06}; HHS07)." + This supports the idea of Hibietal.(2006) that the subcorrelation is produced by a contamination of ISRF regions. which tend to reside in the Galactic plane.," This supports the idea of \citet{hibi06} that the subcorrelation is produced by a contamination of high-ISRF regions, which tend to reside in the Galactic plane." + It is interesting that not only the LMC and the SMC but also the current BCD sample has consistent FIR colours to the main correlation or the subcorrelation reftig:elrdat))., It is interesting that not only the LMC and the SMC but also the current BCD sample has consistent FIR colours to the main correlation or the subcorrelation \\ref{fig:clrdat}) ). + This implies that the wavelength dependence of the FIR emissivity is not different among the BCDs. the LMC. the SMC. and the Milky Way.," This implies that the wavelength dependence of the FIR emissivity is not different among the BCDs, the LMC, the SMC, and the Milky Way." + In the following section. we examine if the FIR colours of BCDs can really be reproduced with the emission properties adopted by HHS07. who explained the FIR colours of the Milky Way. theLMC. and the SMC (Section ??)).," In the following section, we examine if the FIR colours of BCDs can really be reproduced with the emission properties adopted by HHS07, who explained the FIR colours of the Milky Way, theLMC, and the SMC (Section \ref{sec:model}) )." + We present the dependence of FIR colours on ISRF., We present the dependence of FIR colours on ISRF. + Here we adopt Bn0 to concentrate only on the effects of ISRF intensity., Here we adopt $A_V=0$ to concentrate only on the effects of ISRF intensity. + In, In +so py is apart from structural constants the density of hydrogen within the Bohr radius. e. of the nucleus.,"so $\rho_o$ is apart from structural constants the density of hydrogen within the Bohr radius, $a_o$, of the nucleus." + po depends ou / through αμ., $\rho_o$ depends on $\hbar$ through $a_o$. + This is the mass of the cold planet of Παππα radius., This is the mass of the cold planet of maximum radius. + As stated it is essentially the fine structure coustaut to the 2 power times the Chanudrascklar mass or alternatively the ratio of electrical to gravitational forces between two protons. raised to the three halves power. times the hydrogen atoms mass.," As stated it is essentially the fine structure constant to the ${\scriptstyle{3 \over 2}}$ power times the Chandrasekhar mass or alternatively the ratio of electrical to gravitational forces between two protons, raised to the three halves power, times the hydrogen atom's mass." + Our mass-raclius relationship is now defined except for the constant ο) that we inserted in (21)) to allow for the extreme crudcness of our estimate of the electrical potential enerev., Our mass-radius relationship is now defined except for the constant $\beta$ that we inserted in (21)) to allow for the extreme crudeness of our estimate of the electrical potential energy. + This we shall evaluate by fitting our foxiiula to the radius of Saturn., This we shall evaluate by fitting our formula to the radius of Saturn. + Away from the relativistic regime formula (32) takes the even simpler form Now- both o;1/53 aud yD7 are proportional. to so for. a planet of. known AL aud R we solve for. JJ using. Saturn] where in spite of appearances cach bracketed term is independent of Jj and p=M(isD). The same calculation for Jupiter gives —1.161 so 2=1.137 is à good compromise differing from each by ouly 2.1 per cout., Away from the relativistic regime formula (32) takes the even simpler form Now both $\rho^{1/3}_o$ and $y^{-2}$ are proportional to $\beta$ so for a planet of known $M$ and $R$ we solve for $\beta $ using Saturn where in spite of appearances each bracketed term is independent of $\beta$ and $\rho = M/\left ({4 \over 3} \pi R^3 \right ).$ The same calculation for Jupiter gives $\beta = 1.161 $ so $\beta = 1.137$ is a good compromise differing from each by only $2.1$ per cent. +" This value of J vields p,=0.£19g:0en? and AL,=6.2110gin."," This value of $\beta$ yields $\rho_o=0.419gm\ cm^{-3}$ and $M_p=6.24 \times +10^{30}gm$." + The deusity of Hydrogen at the relatively low pressure (conipared with plauctary iuteriors) of half a Megabar is close to 0.5L gineimi? (Alavi et aL.," The density of Hydrogen at the relatively low pressure (compared with planetary interiors) of half a Megabar is close to 0.54 $gm\ cm^{-3}$ (Alavi et al.," + 1995)., 1995). + At umech lower pressures solid Uvdrogen and liquid Welimu have densities of 0.07 and 0.12 ginein>.," At much lower pressures solid Hydrogen and liquid Helium have densities of 0.07 and 0.12 $gm\ +cm^{-3}$." +" For Torrestial planets } (aud hence pi and AG ""j takes higher values appropriate to their composition.", For Terrestial planets $\beta$ (and hence $\rho_o^{1/3}$ and $M_p^{2/3}$ ) takes higher values appropriate to their composition. + From (31) we see that the planet of mmaxiuuun radius has a density of δρυ., From (34) we see that the planet of maximum radius has a density of $8\rho_o$. +" Thus although M, is independent of P nevertheless Fas depends on 7.", Thus although $M_p$ is independent of $\hbar$ nevertheless $R_{\rm{max}}$ depends on $\hbar$. + To sunuuarise our basic result is that the radius Π of a cold body of mmass AL is given by where the surd and the curly bracketed expression reduce to 1 for nonaclativistie white dwarfs aud simall bodies., To summarise our basic result is that the radius $R$ of a cold body of mass $M$ is given by where the surd and the curly bracketed expression reduce to 1 for non-relativistic white dwarfs and small bodies. + According to (36) the cold Plauct of asim radius has a mass of 3.3 times Jupiter's and its radius is 8.65«TOÀcens as opposed to Jupiters radius of 7.0«10? (after correction at coustant vole for the eccentricity)., According to (36) the cold Planet of maximum radius has a mass of 3.3 times Jupiter's and its radius is $8.65 \times 10^9 {\rm cms}$ as opposed to Jupiter's radius of $7.0 \times 10^{9}$ (after correction at constant volume for the eccentricity). + Equation (36) eves 7.0«LO? for the radius of a body of mass M;=1.899«&Loe Iu the above we have not aimed to treat the mass radius relationship for neutron stars but with suitable modification the same principles apply to them.," Equation (36) gives $7.0 +\times 10^9$ for the radius of a body of mass $M_J=1.899 \times +10^{30} {\rm gm}$ In the above we have not aimed to treat the mass radius relationship for neutron stars but with suitable modification the same principles apply to them." +"From this analysis it appears that the 3346 data are not consistent with a steep dependence of M, on the stellar mass of the type reported by Muzerolle et al. (",From this analysis it appears that the 346 data are not consistent with a steep dependence of $\dot M_{\rm acc}$ on the stellar mass of the type reported by Muzerolle et al. ( +2003) and Calvet et al. (,2003) and Calvet et al. ( +2004) in nearby star forming regions.,2004) in nearby star forming regions. + However. the gentler decline of Mace with mass that we find here is fully compatible with that obtained in a study of about 900 PMS stars recently identified in the regions around DDor (Spezzi et al..," However, the gentler decline of $\dot +M_{\rm acc}$ with mass that we find here is fully compatible with that obtained in a study of about 900 PMS stars recently identified in the regions around Dor (Spezzi et al.," + in preparation. Paper HI) as well as with the preliminary results of a ground-based study of about 500 PMS objects in the Orion Nebula Cluster (Da Rio et al..," in preparation, Paper III) as well as with the preliminary results of a ground-based study of about 500 PMS objects in the Orion Nebula Cluster (Da Rio et al.," + in preparation)., in preparation). + In all these cases. values of a2—0.6 and b=| in refeq7 give a good fit to the data.," In all these cases, values of $a=-0.6$ and $b=1$ in \\ref{eq7} give a good fit to the data." +" This suggests that we could use the same functional form and parameter values to fit the observed evolution of M,.. for Galactic PMS stars and compare the result to the data in the Magellanic Clouds.", This suggests that we could use the same functional form and parameter values to fit the observed evolution of $\dot M_{\rm acc}$ for Galactic PMS stars and compare the result to the data in the Magellanic Clouds. +" We do so in reffig]1.. where we show the run of the mass accretion rate. defined as a?=M,../m. as a function of time for the PMS objects in 3346 (circles) and for Galactic stars in Taurus (crosses: from Calvet et al."," We do so in \\ref{fig11}, where we show the run of the mass accretion rate, defined as $\dot m_{\rm}=\dot M_{\rm +acc}/m$, as a function of time for the PMS objects in 346 (circles) and for Galactic stars in Taurus (crosses; from Calvet et al." + 2000) and Trumpler 37 (squares: from Sicilia-Aguilar et al., 2000) and Trumpler 37 (squares; from Sicilia-Aguilar et al. + 2006)., 2006). + The hatched band represents the best fit to the 3346 data. the shaded band is the fit to the PMS stars in the DDor region as derived in ILL. whereas the light-shaded band refers to Galactic stars (including also the Orion Nebula Cluster: Panagia et al.," The hatched band represents the best fit to the 346 data, the dark-shaded band is the fit to the PMS stars in the Dor region as derived in III, whereas the light-shaded band refers to Galactic stars (including also the Orion Nebula Cluster; Panagia et al." + in preparation)., in preparation). + The hatched and solid bands correspond to the clo scatter (1.5. the range from 17 to 83 percentile) and indicate that the SMC and LMC data are compatible with one another. but that the difference with Galactic PMS stars ts significant.," The hatched and solid bands correspond to the $\pm 1 \, +\sigma$ scatter (i.e. the range from 17 to 83 percentile) and indicate that the SMC and LMC data are compatible with one another, but that the difference with Galactic PMS stars is significant." + The logarithmic value of the specific mass aceretion rate at MMyr. 4=logmntlMyr) calculated using the best fitting line as given in refeq7.. can serve as a measure of this difference.," The logarithmic value of the specific mass accretion rate at Myr, $q=\log \dot m(1\,{\rm Myr})$ calculated using the best fitting line as given in \\ref{eq7}, , can serve as a measure of this difference." + q takes on the values of —6.9+0.2. -6.7+0.4 and —7.7+0.6 respectively for 3346. the 30DDor region and the Galaxy.," $q$ takes on the values of $-6.9 \pm 0.2$, $-6.7 \pm 0.4$ and $-7.7 \pm +0.6$ respectively for 346, the Dor region and the Galaxy." + As already pointed out in PaperIL. the higher Mw. values of PMS stars in the LMC compared to Galactic objects of the same age could result from the lower metallicity of the clouds.," As already pointed out in I, the higher $\dot M_{\rm acc}$ values of PMS stars in the LMC compared to Galactic objects of the same age could result from the lower metallicity of the clouds." + The radiation pressure of the forming star is expected to be less strong on lower-metallicity dise material and this will delay the dissipation of the disc. thereby keeping the accretion process active for a longer time.," The radiation pressure of the forming star is expected to be less strong on lower-metallicity disc material and this will delay the dissipation of the disc, thereby keeping the accretion process active for a longer time." + This scenario ts compatible with the PMS stars in the Galaxy having a smaller value of the specific mass accretion rate g than those in the Magellanic Clouds., This scenario is compatible with the PMS stars in the Galaxy having a smaller value of the specific mass accretion rate $q$ than those in the Magellanic Clouds. + A possibility would be that the shallower photometric depth of the LMC data may cause the L(A) detection threshold for PMS stars to be higher (see THI for more details) and thus could skew the median value of M., A possibility would be that the shallower photometric depth of the LMC data may cause the $L(H\alpha)$ detection threshold for PMS stars to be higher (see III for more details) and thus could skew the median value of $\dot M_{\rm acc}$. + We will address this possibility in detail through the analysis of recently obtained HST observations of the same region (De Marchi et al..," We will address this possibility in detail through the analysis of recently obtained HST observations of the same region (De Marchi et al.," + in preparation)., in preparation). + Alternatively. it is also possible that below a certain metallicity threshold the radiation pressure on the disc material no longer changes.," Alternatively, it is also possible that below a certain metallicity threshold the radiation pressure on the disc material no longer changes." + Investigating this possibility requires the analysis of larger and homogeneous data set of Mace Measurements in low-metallicity environments., Investigating this possibility requires the analysis of larger and homogeneous data set of $\dot M_{\rm acc}$ measurements in low-metallicity environments. + Finally. we would like to highlight an interesting corollary result stemming from the large mass accretion rate values that we find for the objects in 3346.," Finally, we would like to highlight an interesting corollary result stemming from the large mass accretion rate values that we find for the objects in 346." + Using the rates as expressed by refeq7 we can estimate the total mass accreted by a star over the time span from birth to the ZAMS.," Using the rates as expressed by \\ref{eq7} + we can estimate the total mass accreted by a star over the time span from birth to the ZAMS." + Already in 1993 Palla Stahler (1993) showed that the timescale to reach the ZAMS is astrong function of the stellar mass., Already in 1993 Palla Stahler (1993) showed that the timescale to reach the ZAMS is a strong function of the stellar mass. + Fitting the more modern evolutionary calculations (DegInnocenti et al 2008: Tognelli et al 2011) for metallicities .. and stellar masses in the range 0.6 up toMsolar.. to within as: refeq7 provides an analytical expression for the average mass accretion rate of the detected stars.," Fitting the more modern evolutionary calculations (Degl'Innocenti et al 2008; Tognelli et al 2011) for metallicities $_\odot$ and stellar masses in the range $0.6$ up to, to within as: \\ref{eq7} provides an analytical expression for the average mass accretion rate of the detected stars." + On the other hand. there must be an appreciable fraction of PMS objects that. at any given time. are not detectable as strong Ha emitters.," On the other hand, there must be an appreciable fraction of PMS objects that, at any given time, are not detectable as strong $\alpha$ emitters." + Therefore. in order to properly estimate the amount of accreted mass over the PMS phase we have to make allowance for the appropriate duty cycle.," Therefore, in order to properly estimate the amount of accreted mass over the PMS phase we have to make allowance for the appropriate duty cycle." + While doing this would require a detailed knowledge of the time evolution of the Ha emission for a large sample of PMS stars in this region. for the sake of simplicity we will assume that the evolution consists in a series of two-level transitions that recur in time.," While doing this would require a detailed knowledge of the time evolution of the $\alpha$ emission for a large sample of PMS stars in this region, for the sake of simplicity we will assume that the evolution consists in a series of two-level transitions that recur in time." + In this simplified model the high state value corresponds to the average value measured for the detected PMS stars and the low state of the Ha undetected stars is zero., In this simplified model the high state value corresponds to the average value measured for the detected PMS stars and the low state of the $\alpha$ undetected stars is zero. + Thus. the true mass accretion rate of any star of mass a at the time ¢ will simply be the average value measured for the detected PMS stars multiplied by an efficiency factor o that in principle is a function of the stellar mass. the time and the metallicity of the region.," Thus, the true mass accretion rate of any star of mass $m$ at the time $t$ will simply be the average value measured for the detected PMS stars multiplied by an efficiency factor $\phi$ that in principle is a function of the stellar mass, the time and the metallicity of the region." + An approximate value of this function is given by the ratio of the number of PMS stars with detected Ha emission and the total number of candidate PMS stars as defined by their location in the H-R diagram., An approximate value of this function is given by the ratio of the number of PMS stars with detected $\alpha$ emission and the total number of candidate PMS stars as defined by their location in the H–R diagram. + In a companion paper. De Marchi. Panagia Sabbi (2011) show that for 3346 such a ratio is essentially constant over time up to PMS ages of MMyr at a level of <0.28.," In a companion paper, De Marchi, Panagia Sabbi (2011) show that for 346 such a ratio is essentially constant over time up to PMS ages of Myr at a level of $<\phi> \simeq 0.28$." + Note that similar values have been found in the field of 11987A for PMS stars with median age of MMyr (o>0.32: Panagia et al 2000)., Note that similar values have been found in the field of 1987A for PMS stars with median age of Myr $<\phi> \simeq 0.32$; Panagia et al 2000). + Therefore. adopting a constant value of ο720.28 for PMS stars in 3346 allows us to integrate the accretion rate over time from 0 up to fvams in order to estimate the total amount of mass (in units) accreted by these objects during their PMSphase.," Therefore, adopting a constant value of $<\phi>=0.28$ for PMS stars in 346 allows us to integrate the accretion rate over time from 0 up to $t_{\rm ZAMS}$ in order to estimate the total amount of mass (in units) accreted by these objects during their PMSphase." + From and 8 we can express it in units of as follows: showing that the amount of accreted mass is. virtually insensitive to the stellar mass., From \\ref{eq7} and 8 we can express it in units of as follows: showing that the amount of accreted mass is virtually insensitive to the stellar mass. + In the range 0.4 , In the range $0.4$ +"lie al V4,,,2227. 28.",lie at $_{nuc}$$\simeq$ 27–28. + None were identified as variable abovethe 30 threshold in our survey., None were identified as variable abovethe $\sigma$ threshold in our survey. + The average nuclear magnitude of this sample is 1 magnitude brighter than the Jarvis MacAlIpine QSOs., The average nuclear magnitude of this sample is $\sim$ 1 magnitude brighter than the Jarvis MacAlpine QSOs. + If these are variable QSOs/AGN-dominated galaxies. we would again expect an average magnitude change of ~0.1 0.2.," If these are variable QSOs/AGN-dominated galaxies, we would again expect an average magnitude change of $\sim$ 0.1–0.2." + The average change in magnitude for the Conti sample over the5 vear interval is 20.03 magnitudes. with all sources vine well below the 26 significance limit.," The average change in magnitude for the Conti sample over the5 year interval is $\sim$ 0.03 magnitudes, with all sources lying well below the $\sigma$ significance limit." + The extensive redshift surveys of the HDF from Cohen (1996: 2000). Phillips (1997) and Barger (2002) have revealed only two broad-Iinne AGNs (BLAGNs) in (he IDF proper.," The extensive redshift surveys of the HDF from Cohen (1996; 2000), Phillips (1997) and Barger (2002) have revealed only two broad-line AGNs (BLAGNs) in the HDF proper." + These are2-251.0 (z=0.96 variable galaxy and. X-ray source discussed above) and4-852.1:2 (220.949. X-ray source)., These are (z=0.96 variable galaxy and X-ray source discussed above) and (z=0.943 X-ray source). + The measured variability signilicance of 633.1218 0.350., The measured variability significance of is $\sigma$. + It is possible that this source is variable but has been observed at (wo points inits light curve that are close to the same magnitude., It is possible that this source is variable but has been observed at two points in its light curve that are close to the same magnitude. + Further monitoring of the IIDE would be necessary to rule out optical variability for this DLAGN., Further monitoring of the HDF would be necessary to rule out optical variability for this BLAGN. +" We have studied (he available spectra For all of the galaxies hosting variable nuclei to determine if anv of the sources show specific emission lines or line flux ratios indicative of Type 2 AGN,", We have studied the available spectra for all of the galaxies hosting variable nuclei to determine if any of the sources show specific emission lines or line flux ratios indicative of Type 2 AGN. + Of the 16 variables. optical spectra exist lor 13.," Of the 16 variables, optical spectra exist for 13." + One of these is the BLAGN 2-251.0 already. discussed. which shows broad MegllI (A2800) emission ancl absorption in its spectrum.," One of these is the BLAGN already discussed, which shows broad MgII $\lambda$ 2800) emission and absorption in its spectrum." + Almost all of the remaining 12 show emission lines in their spectra., Almost all of the remaining 12 show emission lines in their spectra. + Nine out of 11 show OILA2727) when in range. wilh several sources also displaving IL? and. OIIL(A5007 ).," Nine out of 11 show $\lambda$3727) when in range, with several sources also displaying $\beta$ and $\lambda$ 5007)." + The X-rav and strong radio FRI galaxy.752.1. displays only strong absorption lines in ils specirum.," The X-ray and strong radio FRII galaxy, displays only strong absorption lines in its spectrum." + Only one source.4-254.0. shows weak NeV(A3426) emission. a line indicative ol the presence of an AGN (Hall 2000).," Only one source, shows weak $\lambda$ 3426) emission, a line indicative of the presence of an AGN (Hall 2000)." + NeIII(A3369). also stronger in AGN than in starforming galaxies (lola 1991). is seen weakly in 2 sources.2-42.0 aud111111.," $\lambda$ 3869), also stronger in AGN than in starforming galaxies (Rola 1997), is seen weakly in 2 sources, and." + These galaxies also show ΟΠ and Ie. but with [lux ratios consistent with star formation rather than AGN activity (Veilleux Osterbrock 1997).," These galaxies also show OIII and $\beta$, but with flux ratios consistent with star formation rather than AGN activity (Veilleux Osterbrock 1997)." + Onlv the spiral galaxy is low enough redshift to reveal strong Ila. SII(AGT132-61231) and. AG300) emission in the optical spectrum.," Only the spiral galaxy is low enough redshift to reveal strong $\alpha$ , $\lambda$ 6713+6731) and $\lambda$ 6300) emission in the optical spectrum." + The line flux ratios of OIIL/IL2. SII/IIo. and OlI/IIo all indicate that this source is near the border that divides starforming galaxies and AGN (Veilleux Osterbrock 1997).," The line flux ratios of $\beta$, $\alpha$ and $\alpha$ all indicate that this source is near the border that divides starforming galaxies and AGN (Veilleux Osterbrock 1997)." + Therefore. based on the optical spectra alone. objects 2251.0 (BLAGN). possibly (LINER/Sevlert 2). andpossibly 4-254.0 (through the weak presence of NeV) show evidence ofAGN.," Therefore, based on the optical spectra alone, objects (BLAGN), possibly (LINER/Seyfert 2), andpossibly (through the weak presence of NeV) show evidence ofAGN." +"The expressions for D, up to n=6 are given below.",The expressions for $D_n$ up to $n=6$ are given below. +" For convenience, we write s=ag (skewness) and k=o4—3 (excess kurtosis)."," For convenience, we write $\sfs=\alpha_3$ (skewness) and $\sfk=\alpha_4-3$ (excess kurtosis)." +" D3 =k—-—s 2+? Dy = sfsr-24--s Ds = Dg = Note that for the Gaussian distribution (s=k 0), these D,,’s are all positive as expected."," D_3 = ^2+2, D_4 = ^4 D_5 = D_6 = Note that for the Gaussian distribution $\sfs=\sfk=0$ ), these $D_n$ 's are all positive as expected." +" The condition D,,>0 always describes a closed region in the (s,k) plane containing the origin and bounded by the curve D,= 0."," The condition $D_n\geq0$ always describes a closed region in the $(\sfs,\sfk)$ plane containing the origin and bounded by the curve $D_n=0$ ." + Figure shows these regions for n—5 (outermost ellipse) to n—10 (innermost ellipse)., Figure shows these regions for $n=5$ (outermost ellipse) to $n=10$ (innermost ellipse). +" To make a connection with later sections, we have labelled the axes as (0.53,02.54), where oS3=S,, Sick. as can be easily shown using relation avoid cluttering we sometimes write c to mean og)."," To make a connection with later sections, we have labelled the axes as $(\sigma S_3, \sigma^2 S_4)$, where S_3 = ^2 S_4 = as can be easily shown using relation (to avoid cluttering we sometimes write $\sigma$ to mean $\sigma_R$ )." +" As n increases, the region corresponding to D;,>0 becomes(27)- (29)smaller."," As $n$ increases, the region corresponding to $D_n\geq0$ becomes smaller." +"(to Interestingly, the regions for any two consecutive values of n are nested and co-tangential."," Interestingly, the regions for any two consecutive values of $n$ are nested and co-tangential." +" One can continue inductively this way to find that as n—oo, the ellipses converge to the origin, implying that there is no room for any deviation from Gaussianity."," One can continue inductively this way to find that as $n\rightarrow\infty$, the ellipses converge to the origin, implying that there is no room for any deviation from Gaussianity." + We conclude that deviations in the skewness and kurtosis alone cannot consistently parametrize a non-Gaussian pdf., We conclude that deviations in the skewness and kurtosis alone cannot consistently parametrize a non-Gaussian pdf. +" The upshot of all this is that fwr, and gwr, by themselves cannot completely describe a non-Gaussian pdf.", The upshot of all this is that $\fnl$ and $\gnl$ by themselves cannot completely describe a non-Gaussian pdf. + Information on higher-order correlation must be available for the pdf to be well defined., Information on higher-order correlation must be available for the pdf to be well defined. +" As described in the Introduction, the Edgeworth expansion is a convenient way to express a weakly non-Gaussian pdf as a series comprising its cumulants."," As described in the Introduction, the Edgeworth expansion is a convenient way to express a weakly non-Gaussian pdf as a series comprising its cumulants." +" Suppose that we only have estimates on fwi, and gwr, and no higher-order non-Gaussianity."," Suppose that we only have estimates on $\fnl$ and $\gnl$, and no higher-order non-Gaussianity." + The result of the previous section shows that the resulting pdf cannot be non-negative., The result of the previous section shows that the resulting pdf cannot be non-negative. +" Nevertheless, this result only holds if we use an infinite number of cumulants in the reconstruction of the pdf."," Nevertheless, this result only holds if we use an infinite number of cumulants in the reconstruction of the pdf." + This is equivalent to having aninfinite number terms in the Edgeworth expansion., This is equivalent to having aninfinite number terms in the Edgeworth expansion. +" In numerical implementations, however,"," In numerical implementations, however," +the long-term spin evolution presented in the previous section we ean put coustraints on |P|<107!Iles?.,"the long-term spin evolution presented in the previous section we can put constraints on $|\ddot{\nu}|\lesssim10^{-24}\rm\,Hz\,s^{-2}$." + We couclude that the enhanced ablation scenario is not supported by the observatious., We conclude that the enhanced ablation scenario is not supported by the observations. + A dynamically induced period derivative in the eravitational potential well of a third body cau also be excluded., A dynamically induced period derivative in the gravitational potential well of a third body can also be excluded. + The effect of a potential well is identical ou the orbital and spin frequencies aud derivatives: where Ελ is the u-th time derivative of the orbital or spin frequency. a is the acceleration due to the third body. fh is a uuit vector along the line of sight aud ο the speed of light.," The effect of a potential well is identical on the orbital and spin frequencies and derivatives: where $f^{(n)}$ is the n-th time derivative of the orbital or spin frequency, $\mathbf{a}$ is the acceleration due to the third body, $\mathbf{\hat{n}}$ is a unit vector along the line of sight and $c$ the speed of light." +" To explain the observed B, we need à-10P—Mans? aud ||~10.Πεν|. which is not observed."," To explain the observed $\ddot{P}_b$ we need $\dot{\mathbf{a}}\sim10^{-15}-10^{-16}\rm\,m\,s^{-3}$ and $|\ddot{\nu}|\sim10^{-21}\hzs$, which is not observed." + If the measured orbital robaron. is a short-term eveut. then one explanation canbe found with the donor spin-orbit coupling model.," If the measured orbital evolution is a short-term event, then one explanation can be found with the donor spin-orbit coupling model." + A coupling between the pulsar rotational cuerey loss (in form of winds or fields) aud the orbital augular momentum (Damour&Tavlor1991) is ruled out by the sinall magnitude of the effect produced by the tiny E of, A coupling between the pulsar rotational energy loss (in form of winds or fields) and the orbital angular momentum \citep{dam91} is ruled out by the small magnitude of the effect produced by the tiny $\dot{E}$ of. + A qnass quadrupole variation of the donor star is a more promising possibility., A mass quadrupole variation of the donor star is a more promising possibility. +" A change AQ iu the mass quadrupole leads to a chaneein orbital period tersonL 1987): where M aud HR are the douor mass and radius. AL, isa thin shell of 1iass ecucrating the quadrupole. aud © the angular velocity of the star."," A change $\Delta Q$ in the mass quadrupole leads to a change in orbital period \citep{ric94, app94, app87}: where $M$ and $R$ are the donor mass and radius, $M_s$ is a thin shell of mass generating the quadrupole, and $\Omega$ the angular velocity of the star." + If we assume that the aneular velocity of the donor is almost svuchrouous witli the orbital angular velocity. then the variation 0.00Ls observed in the last 13 vears gives: The observed orbital period variations m the eclipsing mullisecond pulsar PSR J2051-0827 aud PSR BLlOS7|20 are likely to be caused by changes in the quadrupole moment of the companion (Arzomnuanianetal.1991:Dorosheukoetal.2001:Lazaridis 2011).," If we assume that the angular velocity of the donor is almost synchronous with the orbital angular velocity, then the variation $\Delta P_b\simeq 0.004\rm\,s$ observed in the last 13 years gives: The observed orbital period variations in the eclipsing millisecond pulsar PSR J2051-0827 and PSR B1957+20 are likely to be caused by changes in the quadrupole moment of the companion \citep{arz94,dor01,laz11}." +. Applegate(1992) proposed a magnetic activity evele that leads to a deformation of the star at the origin of this behavior., \citet{app92} proposed a magnetic activity cycle that leads to a deformation of the star at the origin of this behavior. + The donor star of lis also iu Roche lobe contact. whereas binary uillisecoucd mulsars are detached systems.," The donor star of is also in Roche lobe contact, whereas binary millisecond pulsars are detached systems." + Tf the orbital period of thas decreasedlL iu the past for some tine. then the Roche lobe has moved across the outer euvelope of the xowu dwarf euliauciug the mass transfer rate.," If the orbital period of has decreased in the past for some time, then the Roche lobe has moved across the outer envelope of the brown dwarf enhancing the mass transfer rate." + A detailed discussion of this effect is bevoud the scope of this letter. mut we can speculate that thas gone through periodic episodes (cach lasting 7.10 vr) of cuhanced accretion in the past.," A detailed discussion of this effect is beyond the scope of this letter, but we can speculate that has gone through periodic episodes (each lasting $\tau_{acc}\sim10$ yr) of enhanced accretion in the past." + This effect is opposite during the accelerated orbital expansion. witli he mass trausfer being less than in the non-accelerated case.," This effect is opposite during the accelerated orbital expansion, with the mass transfer being less than in the non-accelerated case." + The quadrupolar moment change has also the effect of heating the star. providing an explanation for the large eutropv coutent of the donor (Delovectal.2008)..," The quadrupolar moment change has also the effect of heating the star, providing an explanation for the large entropy content of the donor \citep{del08}. ." +Spectral οσο effects are ignored here.,Spectral edge effects are ignored here. + Eq., Eq. + BLO agai refers to the pure power-law spectra case., \ref{eq:alphanu2} again refers to the pure power-law spectra case. + We define the optical depth of the source by τν)Παν.," We define the optical depth of the source by $\tau(\nu) = R\, \alpha_\nu$." +" The svuchrotronu surface brightuess Sis the integrated cluissivity along the line of sight through the ποτος, corrected for the svuchrotron sclfabsorption."," The synchrotron surface brightness $S_\sync$ is the integrated emissivity along the line of sight through the source, corrected for the synchrotron self-absorption." +" For a line-ofsight passing the source ceuter at distance kr. this is: From this the total svuchrotron source luminosity can be obtained via siuace integration: The svuchrotron photon uuuber density as a function of position and frequency is best calculated with the help of the radiative (ους fiction in a homogenuecously absorbing οςπα, which is The svuchrotron photon density within the source (for ro AR) is given by an inteeration over the spherical enission voluue V where Eit:) denotes the exponcutial integral."," For a line-of-sight passing the source center at distance $r$, this is: From this the total synchrotron source luminosity can be obtained via surface integration: The synchrotron photon number density as a function of position and frequency is best calculated with the help of the radiative Greens function in a homogeneously absorbing medium, which is The synchrotron photon density within the source (for $r0 and Tox,"," The volume and central line-of-sight integrated number densities can be approximated by These approximations have an accuracy of $10\%$ and they are asymptotically correct for $\tau = \tau(\nu) \rightarrow 0$ and $\tau +\rightarrow \infty$." + A photon with frequency v is on average shifted to the frequency iu an IC collision with a relativistic electrons with moment p., A photon with frequency $\nu$ is on average shifted to the frequency in an IC collision with a relativistic electrons with momentum $p$. + This relation is assumed to hold exactly in the monochromatic approximation., This relation is assumed to hold exactly in the monochromatic approximation. + The IC photon production spectrum is therefore where vr} is the tarect photon spectral density.," The IC photon production spectrum is therefore where $n(\nu,r)$ is the target photon spectral density." + We write for the target photon frequency vy. Which is required in order to produce a scattered photon with » bv an clectrou with momentum p.," We write for the target photon frequency $\nu_0$, which is required in order to produce a scattered photon with $\nu$ by an electron with momentum $p$." + A volue inteeration of the IC emissivitv qic(7(c) gives the total IC ux: Tere Α(vj is the total target photon spectrum within the source region.," A volume integration of the IC emissivity $q_\ic(\nu,r)$ gives the total IC flux: Here $N(\nu)$ is the total target photon spectrum within the source region." + Similarly. the central surface brigltuess 1s Given by where δη) is the central line-of-sight integrated photon spectru.," Similarly, the central surface brightness is given by where $\Sigma(\nu)$ is the central line-of-sight integrated photon spectrum." + Some care has to be taken iu the case of siguificaut overlap of the target photon spectrum aux the spectral range of interest. as it is the case for the CMD-IC process.," Some care has to be taken in the case of significant overlap of the target photon spectrum and the spectral range of interest, as it is the case for the CMB-IC process." + The up-scattered CMD photons are nüssing at CXMB frequencies., The up-scattered CMB photons are missing at CMB frequencies. + Therefore a negative brieltucss cau be superimposed ou the CMD duc to IC scatteriug., Therefore a negative brightness can be superimposed on the CMB due to IC scattering. + Iu order to take this into account. we use inthe case of the CMD-IC process aud where my=nir. p).," In order to take this into account, we use in the case of the CMB-IC process and where $\nu_0 = \nu_0(\nu,p)$ ." +where I have detined the dimensionless potential ο rescaled with the square of the Hubble distance for convenience.,"where I have defined the dimensionless potential $\varphi\equiv\Delta^{-1}\delta/d_H^2$ , rescaled with the square of the Hubble distance $d_H=c/H_0$ for convenience." + The weighting functions can be identitied. which allow the expressions for the iSW- spectrum Ον. the iSW-cross spectrum Cz) and the galaxy spectrum C. to be written in a compact notation. applying a Limber-projection (2) in the flat-skv approximation. for simplicity: with the cross-spectrum Pk).=PAGO/GlykY. and the spectrum Poth)=ΒΚ) of the potential q.," The weighting functions can be identified, which allow the expressions for the iSW-auto spectrum $C_{\tau\tau}(\ell)$, the iSW-cross spectrum $C_{\tau\gamma}(\ell)$ and the galaxy spectrum $C_{\gamma\gamma(\ell)}$ to be written in a compact notation, applying a Limber-projection \citep{1954ApJ...119..655L} in the flat-sky approximation, for simplicity: with the cross-spectrum $P_{\varphi\delta}(k) = P_{\delta\delta}(k) / (d_H k)^2$ and the spectrum $P_{\varphi\varphi}(k) = P_{\delta\delta}(k) / (d_H k)^4$ of the potential $\varphi$." + For the CDM power spectrum I make the ansatz T7. with the transfer function (?).. where the wave vector g is given in units of the shape parameter ή.," For the CDM power spectrum I make the ansatz $P(k)\propto k^{n_s} T^2(k)$ , with the transfer function \citep{1986ApJ...304...15B}, where the wave vector $q$ is given in units of the shape parameter $\Omega_m h$." + Pk) is normalised to the value c on the scale R-8Mpc/h. with a Fourier-transformed spherical top-hat Wt)=3jjGo/x as the filter function.," $P(k)$ is normalised to the value $\sigma_8$ on the scale $R=8~\mathrm{Mpc}/h$ , with a Fourier-transformed spherical top-hat $W(x)=3j_1(x)/x$ as the filter function." + 7;(9 denotes the spherical Bessel function of the first kind of order £ (2).., $j_\ell(x)$ denotes the spherical Bessel function of the first kind of order $\ell$ \citep{1972hmf..book.....A}. +" The contribution of nonlinear structure formation to the power spectrum PCA) was described with the mode proposed by ?.. yielding the power spectrum P4,(GO. where the parameterisation of the nonlinear contribution to the fluctuation amplitude with ©,,(a@) as the time variable is suited for coupled models."," The contribution of nonlinear structure formation to the power spectrum $P(k)$ was described with the model proposed by \citet{2003MNRAS.341.1311S}, yielding the power spectrum $P_{\delta\delta}(k)$, where the parameterisation of the nonlinear contribution to the fluctuation amplitude with $\Omega_m(a)$ as the time variable is suited for coupled models." + I use the redshift distribution of the main galaxy sample of the Dark UNiverse (2).. which will observe half of the sky out to redshifts of unity and which will be of particular use for iSW-observations (2111 with 5=3/2 and zy=0.64. which results in a median redshift Of zi=0.9.," I use the redshift distribution of the main galaxy sample of the Dark UNiverse \citep{2008arXiv0802.2522R}, which will observe half of the sky out to redshifts of unity and which will be of particular use for iSW-observations \citep{2008arXiv0802.0983D}: with $\beta=3/2$ and $z_0=0.64$, which results in a median redshift of $z_\mathrm{med}=0.9$." + For simplicity. the bias 5 is assumed to be and equal to unity.," For simplicity, the bias $b$ is assumed to be non-evolving and equal to unity." +" The angular spectra Ομ and ο, are shown in Figs.", The angular spectra $C_{\tau\tau}(\ell)$ and $C_{\tau\gamma}(\ell)$ are shown in Figs. + 3 and x. respectively. for the decaying CDM cosmology outlined in Sect. ??..," \ref{fig_isw_auto} and \ref{fig_isw_cross}, respectively, for the decaying CDM cosmology outlined in Sect. \ref{sect_homogeneous}." +" Ditferences between the cosmologies considered are not strongly scale dependent as expected for changes on the homogeneous level and observing linear structure formation. and amount to half an order of magnitude in the auto spectrum C,.(0)."," Differences between the cosmologies considered are not strongly scale dependent as expected for changes on the homogeneous level and observing linear structure formation, and amount to half an order of magnitude in the auto spectrum $C_{\tau\tau}(\ell)$." + The cross spectrum C..(£) exhibits ditferences up to a factor of two., The cross spectrum $C_{\tau\gamma}(\ell)$ exhibits differences up to a factor of two. + Both spectra seem to be equally sensitiveto the dark energy equation of state as well as to the coupling term I. and these two parameters are naturally degenerate with the fluctuation amplitude oy of the density field.," Both spectra seem to be equally sensitiveto the dark energy equation of state as well as to the coupling term $\Gamma$, and these two parameters are naturally degenerate with the fluctuation amplitude $\sigma_8$ of the density field." + For the chosen redshift distribution. most of the cross signal originates at a redshift of z=1.0 (a=0.5. c.f.," For the chosen redshift distribution, most of the cross signal originates at a redshift of $z\simeq1.0$ $a=0.5$, c.f." + Fig. 2).," Fig. \ref{fig_qval}) )," + where the source function dQ/da is significantly stronger in models with either evolving dark energy or CDM decay. compared to ACDM.," where the source function $\dd Q/\dd a$ is significantly stronger in models with either evolving dark energy or CDM decay, compared to $\Lambda$ CDM." + The spectra show degeneracies between wu. T and oy. such that a precision measurement will have to rely on a good prior on oy in order to unlock the sensitivity of the ISW-etfect on w and T.," The spectra show degeneracies between $w$, $\Gamma$ and $\sigma_8$, such that a precision measurement will have to rely on a good prior on $\sigma_8$ in order to unlock the sensitivity of the iSW-effect on $w$ and $\Gamma$ ." + In this mammarypaper. I extend the expressions for the iSW-etfect to cosmological models with couplingsbetween the dark matter and dark energy densities. and compute the auto and cross correlation," In this paper, I extend the expressions for the iSW-effect to cosmological models with couplingsbetween the dark matter and dark energy densities, and compute the auto and cross correlation" +without irraclialon effects included.,without irradiation effects included. + We first recall that evaporation effects do not affect the evolution. and thus he mnass-racius relatiouship of the plauet as long as this atter is not in t16 evaporation ruuaway phase (see Baraffe et al.," We first recall that evaporation effects do not affect the evolution, and thus the mass-radius relationship of the planet as long as this latter is not in the evaporation runaway phase (see Baraffe et al." + 2001)., 2004). + T1ο values of radii given in Table ο are lus also characeristic of radii obtained for evolutionary sequences inclucΠιο evaporation for same lass aud age (if they are no in the runaway phase), The values of radii given in Table \ref{neptune} are thus also characteristic of radii obtained for evolutionary sequences including evaporation for same mass and age (if they are not in the runaway phase). +" As seen iu the able (case 1 vs case 2). an increase of heavy element youn Z,70.1 ο Ζω vields a ~ decrease of he radius of au nvracdiaed Neptune mass planet at 5 Cr while. for a given metal earichement Zea. =O.lL. irradiatio- effects Increase he radius by ~ at a given age."," As seen in the table (case 1 vs case 2), an increase of heavy element from $\zenv$ =0.1 to $\zenv$ =0.4 yields a $\sim$ decrease of the radius of an irradiated Neptune mass planet at 5 Gyr while, for a given metal enrichement $\zenv$ =0.4, irradiation effects increase the radius by $\sim$ at a given age." + Table 3 aso shows that radii as large as 0.8 Ry after a few Cir can |)o reached for an envelope ictal fraction Zou =0.1 in the iradiated case., Table \ref{neptune} also shows that radii as large as 0.8 $\rjup$ after a few Gyr can be reached for an envelope metal fraction $\zenv$ =0.1 in the irradiated case. + This envelope metallicity js predictec by our fornation model if the initial plauct Lass ds 150 M. (~ 0.6 AZ)., This envelope metallicity is predicted by our formation model if the initial planet mass is $>$ 150 $\mearth$ $\sim$ 0.6 $\mjup$ ). + In order for such a lig[um progenitor lass to reach a Neptune mass plauet within a fow eigavears. high escape rates are required (see 81.1 and Fie. 2)).," In order for such a high progenitor mass to reach a Neptune mass planet within a few gigayears, high escape rates are required (see 4.1 and Fig. \ref{fig2}) )." + TUs analysis shows that the aforementioned ~ 0.6 Ry lower limit for the radius of hot Neptunes stems esseutiallv frou the effect of nradiation on a planet which retains a sibstantial gaseous (IT. Πο) envelope.," This analysis shows that the aforementioned $\sim$ 0.6 $\rjup$ lower limit for the radius of hot Neptunes stems essentially from the effect of irradiation on a planet which retains a substantial gaseous (H, He) envelope." + Iu contrast. fog Aradike planets are hot cores with simall saseous envelope. as suggested bv Druniui Cionco (2005). their radius should be siguificautlv sunaller. closer to the Neptune planet radius (~ 0.35 Ry).," In contrast, if $\mu$ -Ara-like planets are hot cores with small gaseous envelope, as suggested by Brunini Cionco (2005), their radius should be significantly smaller, closer to the Neptune planet radius $\sim$ 0.35 $\rjup$ )." + Radius determinations of lot-Neptunes could. thus distinguish between different ormation scenarios., Radius determinations of hot-Neptunes could thus distinguish between different formation scenarios. + They nay also provide information about the efficiency of the evaporation process. xóHaco lucasurements of radii larecr han ~ 0.5 Ry. for vlanets older than a few Cyr. would nmicate hieli initial xogenitor mass aud tli1s high escape rates. as above nenjoned.," They may also provide information about the efficiency of the evaporation process, since measurements of radii larger than $\sim$ 0.8 $\rjup$, for planets older than a few Gyr, would indicate high initial progenitor mass and thus high escape rates, as above mentioned." +" Evaporation raes also affect he| fie spent in fhe mass range 10-20 Mj, (0.03-0.06 AL ).", Evaporation rates also affect the time spent in the mass range 10-20 $\mearth$ (0.03-0.06 $\mjup$ ). + Evolution of auets at the maximal evaporation rate proceeds rapiv and the correspoucine detection Duybability while the planet lies within this mass ranec Is uuch smaller tha1 for significantly reduced rates., Evolution of planets at the maximal evaporation rate proceeds rapidly and the corresponding detection probability while the planet lies within this mass range is much smaller than for significantly reduced rates. + The internal couposition also strongv affects the evolution of the planet., The internal composition also strongly affects the evolution of the planet. + The sequence witi initial niass, The sequence with initial mass +" Mp. σ,. ἀέυμ-σ, LO°A/.. ~3<109ML. 1/5;. the mass of the dark matter halo is linked to BH mass. by comparing maximum rotation velocities. Ένας. of disk galaxies with their corrected central velocity dispersion and finding a good correlation."," $M_{BH}$ $\sigma_c$ $M_{BH}$ $\sigma_c$ $10^5 M_{\odot}$ $\sim 3 \times 10^{9} M_{\odot}$ $M_{BH}$ the mass of the dark matter halo is linked to BH mass, by comparing maximum rotation velocities, $V_{\rm max}$, of disk galaxies with their corrected central velocity dispersion and finding a good correlation." + Generally. it can be stated that galaxies with larger bulges tend to be found in more massive dark matter halos. but this relationship. while being a good correlationaverage. has a lot of scatter (see. e.g.. Ho 2007).," Generally, it can be stated that galaxies with larger bulges tend to be found in more massive dark matter halos, but this relationship, while being a good correlation, has a lot of scatter (see, e.g., Ho 2007)." + Since spiral arm pitch angle also depends on mass concentration. once again this may point to a relation between spiral arm pitch angle and BH mass.," Since spiral arm pitch angle also depends on mass concentration, once again this may point to a relation between spiral arm pitch angle and BH mass." + Such a relation may be important. as it could possibly be an indirect means of determining the masses of supermassive BHs in distant disk galaxies. and hence the growth of BHs in spirals as a funetion of look back time.," Such a relation may be important, as it could possibly be an indirect means of determining the masses of supermassive BHs in distant disk galaxies, and hence the growth of BHs in spirals as a function of look back time." + The range of supermassive BHs in spirals is less than the entire observed range of masses for all galaxy types., The range of supermassive BHs in spirals is less than the entire observed range of masses for all galaxy types. + For spirals. BH masses typically range from ~10A£.. (similar to the Milky Way galaxy: Ghez et 22005; Genzel et 2000) to ~105AZ.. (for more massive spiral galaxies like M31: e.g.. Bender et 22005).," For spirals, BH masses typically range from $\sim10^6 M_{\odot}$ (similar to the Milky Way galaxy; Ghez et 2005; Genzel et 2000) to $\sim10^8 M_{\odot}$ (for more massive spiral galaxies like M31; e.g., Bender et 2005)." + In this letter we show that a correlation exists between supermassive BH mass and spiral arm pitch angle (à measure of the tightness or looseness of spiral arms in disk galaxies)., In this letter we show that a correlation exists between supermassive BH mass and spiral arm pitch angle (a measure of the tightness or looseness of spiral arms in disk galaxies). + Our sample consists of a total of 27 spiral galaxies with BH masses that have been determined using several different methods., Our sample consists of a total of 27 spiral galaxies with BH masses that have been determined using several different methods. + The first 12 galaxies have estimates of their supermassive BHs using direct determinations., The first 12 galaxies have estimates of their supermassive BHs using direct determinations. +" The next 11 galaxies were selected from the sample of Ferrarese (2002) and the BH masses have been determined using the central velocity dispersion of the bulge. 7,.. and converting to BH mass using the relation from Ferrarese (2002)."," The next 11 galaxies were selected from the sample of Ferrarese (2002) and the BH masses have been determined using the central velocity dispersion of the bulge, $\sigma_c$, and converting to BH mass using the relation from Ferrarese (2002)." + The last 4 galaxies have lower limits for the BH masses based upon the Eddington limit and have been taken from the sample of Satyapal et (2007. 2008).," The last 4 galaxies have lower limits for the BH masses based upon the Eddington limit and have been taken from the sample of Satyapal et (2007, 2008)." + It should be noted that these lower limits are order of magnitude estimates at best., It should be noted that these lower limits are order of magnitude estimates at best. + Our galaxies consist of those galaxies with known BH masses. with Hubble types ranging from Sa to Sm. for which it is possible to measure spiral arm pitch angle.," Our galaxies consist of those galaxies with known BH masses, with Hubble types ranging from Sa to Sm, for which it is possible to measure spiral arm pitch angle." + The sourceof theBHmass or velocity dispersion of the, The sourceof theBHmass or velocity dispersion of the +"110"" to 110” where it intersects the CND at the same velocity.",$''$ to $''$ where it intersects the CND at the same velocity. + SEL is also connected to tle CND by emission at 50 kun s4| in Πο.) anc (2.2).," SE1 is also connected to the CND by emission at 50 km $^{-1}$ in (1,1) and (2,2)." + The connection is narrow and weaker than enmuüssiou from either SEL or the CND., The connection is narrow and weaker than emission from either SE1 or the CND. + It mav be weak due to the intrinsic chuupiness of the clouds. or it also may have been disrupted by an interaction with another cloud.," It may be weak due to the intrinsic clumpiness of the clouds, or it also may have been disrupted by an interaction with another cloud." + Tineiatic evidence from HC'N (1-0) indicates that the northern half of the CND may be on a different orbit than the rest of the rug (Wrightetal.2001)., Kinematic evidence from HCN (1-0) indicates that the northern half of the CND may be on a different orbit than the rest of the ring \citep{wri00}. +. The independence of this feature from the rest of the CND would also account for the different iuclinatiou angles observed for tle two halves of the CND., The independence of this feature from the rest of the CND would also account for the different inclination angles observed for the two halves of the CND. + Civen the stroug connection between the CND aud SEL. it appears that some of the eas in the northern lobe originated ia SEL aud is not part of a coherent rotating rine.," Given the strong connection between the CND and SE1, it appears that some of the gas in the northern lobe originated in SE1 and is not part of a coherent rotating ring." + Position velocity cut οἱ in Figure LL shows a strikine velocity gradient of Lkanstaresee + along the eutire 150” (6pc) leneth of the western streamer., Position velocity cut $d$ in Figure \ref{pv} shows a striking velocity gradientof 1 km $^{-1}$ $^{-1}$ along the entire $''$ (6pc) length of the western streamer. +" The southern eud of the streamer at 60” lias a velocity of T0 lans3| while the northern cud has high velocity cussion at |90 knis + at 220"".The sae velocity eradieut is observed in NIT3((1.1) and (2.2) in position-velocity diagrams L2dend13d."," The southern end of the streamer at $''$ has a velocity of –70 km $^{-1}$ while the northern end has high velocity emission at +90 km $^{-1}$ at $''$.The same velocity gradient is observed in (1,1) and (2,2) in position-velocity diagrams \ref{11pv}$ $d$ and \ref{22pv}$ $d$." + The large velocity eradieut aloug the leneth of the cloud could be due to intrinsic rotation or the cloud could be orbiting the uucleus., The large velocity gradient along the length of the cloud could be due to intrinsic rotation or the cloud could be orbiting the nucleus. + If we assume a circular orbit for the western streamer at a distance of 2 (L6 pc) the observed velocity eradieut is consisteut with a Xkepleriui orbit around a ecutral mass of 10* M. (Gucluding Ser A* aud the stellar population. see Talleretal. (1996))) inclined. by ~30° to the line of sight.," If we assume a circular orbit for the western streamer at a distance of $'$ (4.6 pc) the observed velocity gradient is consistent with a keplerian orbit around a central mass of $^7$ $_\odot$ (including Sgr A* and the stellar population, see \citet{hal96}) ) inclined by $\sim30^\circ$ to the line of sight." + Additionally. the inypact of Ser A East could cuhance the eradieut along this streamer.," Additionally, the impact of Sgr A East could enhance the gradient along this streamer." + The westeru streamer is uot seen iu 1.2 nuu dust cluission (see Fiewre 91)., The western streamer is not seen in 1.2 mm dust emission (see Figure \ref{pbcor}) ). + The dust may have been destroved by photous from the uucleus or by iuteractious with Ser A East., The dust may have been destroyed by photons from the nucleus or by interactions with Sgr A East. + As seen in Figure 10.. the curve of the western streamer follows the edee of Ser A East.," As seen in Figure \ref{sgeast.fig}, the curve of the western streamer follows the edge of Sgr A East." + It is possible that this gas originated closer to the nucleus aud was pushed outward., It is possible that this gas originated closer to the nucleus and was pushed outward. + Iu this scenario. auv dust that was in the gas was removed when it was close to the nucleus.," In this scenario, any dust that was in the gas was removed when it was close to the nucleus." + Three narrow flunenuts appear to connect the western streamer to the CND in the velocity iuteerated maps., Three narrow filaments appear to connect the western streamer to the CND in the velocity integrated maps. +" The southernmost projected connection. at 1715 365.5. 29°02/00"". is visible in position-velocity cut d at 20"" with a velocity of 0 kun |."," The southern-most projected connection, at $17\h45\m36\s.5$ , $-29\dg02'00''$, is visible in position-velocity cut $d$ at $''$ with a velocity of 0 km $^{-1}$." + This cloud is the same exteusion of the 20 lan | cloud towards the soutliwesteru lobe of the CND that was seen bv Coil&Πο(1999.2000) in Πο1) aud (2.2).," This cloud is the same extension of the 20 km $^{-1}$ cloud towards the southwestern lobe of the CND that was seen by \citet{coi99,coi00} + in (1,1) and (2,2)." + Ninematically. it is associated with the 20 kins 1 cloud and not the western streamer.," Kinematically, it is associated with the 20 km $^{-1}$ cloud and not the western streamer." + Although the extension is spatially connected to the CND in NIT4(CC.2). HCN(1-0) and dust cunission (see Figures G and 9)). there is no kinematic evidence for a plivsical connection between the 20 kan 1: cloud aud this soutb-western part of the CND which has typical velocitics of 110 kunrs+.," Although the extension is spatially connected to the CND in (3,3), HCN(1-0) and dust emission (see Figures \ref{hcn.fig} and \ref{pbcor}) ), there is no kinematic evidence for a physical connection between the 20 km $^{-1}$ cloud and this south-western part of the CND which has typical velocities of –110 km $^{-1}$." + The use of CLEANecd data for the positiou-velocity diagrams makes it difficult to see faint. extended connections between features.," The use of CLEANed data for the position-velocity diagrams makes it difficult to see faint, extended connections between features." + It is possible that features which show morphological connections but no obvious kinematic associations with the CND are connected to the CND by faint aud extended gas., It is possible that features which show morphological connections but no obvious kinematic associations with the CND are connected to the CND by faint and extended gas. +" The second possible connection between the western streamer aud the southwest lobe of the CND is at 17?ιοστο, —29?00/55""."," The second possible connection between the western streamer and the southwest lobe of the CND is at $17\h45\m36\s.5$, $-29\dg00'55''$." + In position velocity cut llothebrightelumpat207 .ccuteredat δη +. is the western streamer.," In position velocity cut \ref{pv}$ $e$ the bright clump at $''$, centered at -20 km $^{-1}$, is the western streamer." +" Eiission from the CND is is seen from SO"" to 180"".", Emission from the CND is is seen from $''$ to $''$. + In the western-iost part of the CND. there is bright cinissiou at the same velocity as the western streamer (807). but amv connection is tenuous.," In the western-most part of the CND, there is bright emission at the same velocity as the western streamer $''$ ), but any connection is tenuous." + The line widths are extremely high iu this region (FWIAL up to 50 hans +) indicating turbulence. G, The line widths are extremely high in this region (FWHM up to 50 km $^{-1}$ ) indicating turbulence. ( +T.1) aud (2.2) slow the same kinematics.,"1,1) and (2,2) show the same kinematics." + Iu NID3((3.3). the southwestern lobe of the CND at 100” shows two brielt chumps centered at ~SO laus. 1 and ~[Os Iu ," In (3,3), the southwestern lobe of the CND at $''$ shows two bright clumps centered at $\sim80$ km $^{-1}$ and $\sim-10$ km $^{-1}$ ." +"NIISGIA) there is pronunent eniüssion ~lOO dans + at 110% which is either part of the ""uceative velocity lobe” of theCND observed in TICN(1-0) or high velocity gas at the nucleus."," In (1,1) there is prominent emission at $\sim-100$ km $^{-1}$ at $''$ which is either part of the “negative velocity lobe” of theCND observed in HCN(1-0) or high velocity gas at the nucleus." + The features at10 id |SO kan + are more prominent i aud do not fit a rotation pattern., The features at–10 and +80 km $^{-1}$ are more prominent in and do not fit a rotation pattern. + In particular. the feature at) 10 Ian sthas a high line width which exteuds over GO kan especially in NIT3((2.2).," In particular, the feature at –10 km $^{-1}$ has a high line width which extends over 60 km $^{-1}$, especially in (2,2)." +" Positiou-velocity cut f follows ο possible connection to the CND at 1715""375.. 2970000""."," Position-velocity cut $f$ follows northern-most possible connection to the CND at $17\h45\m37\s$, $-29\dg00'00''$." +" The western streamer is at a velocity of 30 lan s| at position of 10"".", The western streamer is at a velocity of 30 km $^{-1}$ at position of $''$. + There is no obvious connection to the CND which κατ knns ft and has a velocity eradicut gomme to 30 kin s+ towards the cast., There is no obvious connection to the CND which is at 70 km $^{-1}$ and has a velocity gradient going to 30 km $^{-1}$ towards the east. + The two northern projected comnections between the CND and the western streamer are seen as fllamcuts m 6 cui coutinmun ciission., The two northern projected connections between the CND and the western streamer are seen as filaments in 6 cm continuum emission. + The filamentary structures in the continuni cussion are intriguins and mav be the result of superhova remuiauts or expansion of Ser A East through the CND., The filamentary structures in the continuum emission are intriguing and may be the result of supernova remnants or expansion of Sgr A East through the CND. +" Overall. we detect three plivsical connections to the ΝΕΟ,"," Overall, we detect three physical connections to the CND." + We confirm the presence of the southern streamer which connects the 20 lau | cloud to the CND., We confirm the presence of the southern streamer which connects the 20 km $^{-1}$ cloud to the CND. +" The northern ridge is also connected to the CND with a velocity eradient of 0.6 lau s| | spanning 110"" (1 pe).", The northern ridge is also connected to the CND with a velocity gradient of 0.6 km $^{-1}$ $^{-1}$ spanning $''$ (4 pc). + SELextends northwiuds aud kinematically connects to the eastern lobe of the CND., SE1extends northwards and kinematically connects to the eastern lobe of the CND. +" The western streamer slows a velocity eradicnt of L lau | | alone a leugth of 150"" (G6pc). but we do not see auv definite physical connections to the CND."," The western streamer shows a velocity gradient of 1 km $^{-1}$ $^{-1}$ along a length of $''$ (6pc), but we do not see any definite physical connections to the CND." +" There is significant absorption in Πο} aud (2.2) where cut e passes close to Ser À* at 120""."," There is significant absorption in (1,1) and (2,2) where cut $e$ passes close to Sgr A* at $''$." +" The NIT3((3.3) lagrain. however. has little absorption iud instead shows cCluission with a coliereut velocity eradicut frou, |80 kii pA lat 95"" toO kus tat 115""."," The (3,3) diagram, however, has little absorption and instead shows emission with a coherent velocity gradient from +80 km $^{-1}$ at $''$ to 0 km $^{-1}$ at $''$ ." + This feature is within 2 pe in projected distance frou Ser A*., This feature is within 2 pc in projected distance from Sgr A*. +" The positive velocity obe of the CND is seen at 170"" aud is not a continmation X the eradicut.", The positive velocity lobe of the CND is seen at $''$ and is not a continuation of the gradient. + A similar eracdicut is seen as cut f passes rough the interior of the CND (70-1307)., A similar gradient is seen as cut $f$ passes through the interior of the CND $''$ ). + Unlike cut €. je velocity eradieut of gas near Ser A* in cut f is not coustant.," Unlike cut $e$ , the velocity gradient of gas near Sgr A* in cut $f$ is not constant." +" The velocitydecreases frou 75 kins | at 75” to 5ülauns Lat 907 aud thou is approsimatcly coustaut at 35 aus +from 100-115"".", The velocitydecreases from 75 km $^{-1}$ at $''$ to 50 km $^{-1}$ at $''$ and then is approximately constant at 35 km $^{-1}$from $''$ . +" At 125"". there is cunission from 50 aus το | 40s +."," At $''$ , there is emission from –50 km $^{-1}$ to +40 km $^{-1}$ ." + Although not shown iu this paper. je salue feature is seen over a range ofposition angles youn 60-1007. The feature must contribute to Πο.) cluission seen close to Ser A* in the velocity iutegrated," Although not shown in this paper, the same feature is seen over a range ofposition angles from $\dg$ The feature must contribute to (3,3) emission seen close to Sgr A* in the velocity integrated" + their inflated radii., their inflated radii. + In thisLetter. we build on our previous work on magnetic drag (Perna et al.," In this, we build on our previous work on magnetic drag (Perna et al." + 2010: hereafter PMR10) to investigate the magnitude of ohmic dissipation in. the atmospheres of hot Jupiters. and its consequences for the dynamies and the thermal evolution of these planets.," 2010; hereafter PMR10) to investigate the magnitude of ohmic dissipation in the atmospheres of hot Jupiters, and its consequences for the dynamics and the thermal evolution of these planets." + We use specific three-dimensional atmospheric circulation models of the planet HD 209458b., We use specific three-dimensional atmospheric circulation models of the planet HD 209458b. + We compare the amount of Ohmic heating expected for typical magnetic field strengths with the extra heat required in the deep atmosphere to slow down contraction according to planetary evolutionary models (Guillot Showman 2002)., We compare the amount of Ohmic heating expected for typical magnetic field strengths with the extra heat required in the deep atmosphere to slow down contraction according to planetary evolutionary models (Guillot Showman 2002). + While our calculations are specific to the case of HD 209458b. our overall results are expected to hold more generally for hot Jupiters with similar gravity. irradiation strength. and magnetic field.," While our calculations are specific to the case of HD 209458b, our overall results are expected to hold more generally for hot Jupiters with similar gravity, irradiation strength, and magnetic field." + The fiducial atmospheric circulation model used here was computed by Rauscher Menou (2010) for HD 209458b. under the assumption of no significant dragflow.," The fiducial atmospheric circulation model used here was computed by Rauscher Menou (2010) for HD 209458b, under the assumption of no significant drag." + The model describes the atmospheric flow in à frame that is rotating with the bulk planetary interior., The model describes the atmospheric flow in a frame that is rotating with the bulk planetary interior. + The meridional and zonal wind speeds in the atmosphere. as well as its thermodynamie variables. are returned at each erid location in. the three-dimensional model atmosphere.," The meridional and zonal wind speeds in the atmosphere, as well as its thermodynamic variables, are returned at each grid location in the three-dimensional model atmosphere." + Location is identified by the angular spherical coordinates (60.0) and pressure. p. for the vertical coordinate. The model bottom is located at 220 bar while the top level is set at a pressure of | mbar.," Location is identified by the angular spherical coordinates $(\theta,\phi)$ and pressure, $p$, for the vertical coordinate, The model bottom is located at 220 bar while the top level is set at a pressure of 1 mbar." + In addition to this drag-free model. we also perform some of our calculations for the model with strongest drag described in PMRIO.," In addition to this drag-free model, we also perform some of our calculations for the model with strongest drag described in PMR10." + Since. apart from wind drag. these two models are identical. this allows us to evaluate the consequences for ohmic dissipation of an. atmospheric flow with significantly dragged winds.," Since, apart from wind drag, these two models are identical, this allows us to evaluate the consequences for ohmic dissipation of an atmospheric flow with significantly dragged winds." + In our circulation models. the local heating/cooling rate (energy per unit mass) is modeled as Newtonian (linear) relaxation. οἱ=(p.00)1τρ). where Trad represents the radiative timescale on which the local temperature 7 relaxesto the prescribed equilibrium profile Τμ. eye," In our circulation models, the local heating/cooling rate (energy per unit mass) is modeled as Newtonian (linear) relaxation, $Q_T = +({T_{\rm eq}(p,\theta,\phi) - T})/{\tau_{\rm rad}(p)}$, where $\tau_{\rm rad}$ represents the radiative timescale on which the local temperature $T$ relaxesto the prescribed equilibrium profile $T_{\rm +eq}$ ." +3elore removing the stars from further. consideration in this paper. we use them for an accurate [lux calibration of the ELAIS. Z5O0-data.,"Before removing the stars from further consideration in this paper, we use them for an accurate flux calibration of the ELAIS -data." +. We mateh observed. near-LH3i. and micd-LH1t. colours to corresponding model colours of infrared stanclard stars. and are able to derive the tux calibration for he ELAIS ISOCAAL data with better accuracy than done eviouslv.," We match observed near-IR and mid-IR colours to corresponding model colours of infrared standard stars, and are able to derive the flux calibration for the ELAIS ISOCAM data with better accuracy than done previously." + “Phe derivation is performed in the Appendix A: we adopt values of 1.23 and 1.05 ADU/gain/s/mJv. for he LW? ancl LAWS filters. respectively. the catalogue v1.3. values for LW? and LW3 have to be multiplied o» these [actors to have Uuxes in my.," The derivation is performed in the Appendix A: we adopt values of 1.23 and 1.05 ADU/gain/s/mJy for the LW2 and LW3 filters, respectively, the catalogue v.1.3 values for LW2 and LW3 have to be multiplied by these factors to have fluxes in mJy." + Note that. the actors were not included in Figs., Note that the factors were not included in Figs. + 2. and 3 above. (, \ref{relstar_matches1} and \ref{relstar_matches2} above. ( +Phe LAWS calibration is in disagreement with the one,The LW3 calibration is in disagreement with the one + (c.c.T) (e.g...7?7?j..," \citep[e.g.,][]{Mateo98} \citep[e.g.,][]{Mateo98,Lokas09,Walker_etal09}." + (e.g...7) (e.e..2). ο7)..," \citep[e.g.,][]{Grcevich_Putman09} \citep[e.g.,][]{Mateo98} \citep[e.g.,][]{Grebel00}." + (e.g.?77?77?777) (?).. inodel(?) Tn," \citep[e.g.,][]{Einasto_etal74,Faber_Lin83,Mayer_etal01,Kravtsov_etal04, + Mayer_etal06,Mayer_etal07,Klimentowski_etal09,Kazantzidis_etal11} + \citep{D'Onghia_etal09}." + the cureut ealaxy formation paradienà (ee.?).. the quiescent cooling of gas within a virialized DM halo results in the formation of a rotationally-supported disk of stars.," \citep{Mayer_etal01} In the current galaxy formation paradigm \citep[e.g.,][]{White_Rees78}, the quiescent cooling of gas within a virialized DM halo results in the formation of a rotationally-supported disk of stars." + Thus. any scenario for dSph formation must incorporate plivsieal processes for transforming initially rotationallv-supported stellar svstenis to ones dominated by raüudonm motions.," Thus, any scenario for dSph formation must incorporate physical processes for transforming initially rotationally-supported stellar systems to ones dominated by random motions." + Iuteractions aud mergers between galaxies ma constitute such a mechianisui., Interactions and mergers between galaxies may constitute such a mechanism. + ludeed. ou larger scales. the tidal heating aud violeut relaxation associated with iuergers of massive. disk ealaxies effectively destrov the stellar disks creating a kinematically hot. pressure-supported spheroid that resenibles an elliptical galaxy (6:9...2).," Indeed, on larger scales, the tidal heating and violent relaxation associated with mergers of massive, disk galaxies effectively destroy the stellar disks creating a kinematically hot, pressure-supported spheroid that resembles an elliptical galaxy \citep[e.g.,][]{Barnes92}." +. It has also been demonstrated that encounters between dwarf halos cau lead to their very strong evolution (e.g..22).," It has also been demonstrated that encounters between dwarf halos can lead to their very strong evolution \citep[e.g.,][]{Knebe_etal06,Klimentowski_etal10}." + ?. reported in their constrained DM cosimological simulation of the LG that a few percent of all surviviug subhalos had nudergone a substantial eucounter with another chwart halo iu the past., \citet{Klimentowski_etal10} reported in their constrained DM cosmological simulation of the LG that a few percent of all surviving subhalos had undergone a substantial encounter with another dwarf halo in the past. + Most of these eveuts occurred carly in the LG history and before the dwarf halos were accreted and became satellites of either the MW. or AD., Most of these events occurred early in the LG history and before the dwarf halos were accreted and became satellites of either the MW or M31. + Therefore. although the great majority of LG dut ealaxies should not lave participated im mersers with other dwarfs in the past. at least some of then may lave experienced such interactions.," Therefore, although the great majority of LG dwarf galaxies should not have participated in mergers with other dwarfs in the past, at least some of them may have experienced such interactions." + Motivated by these findines. we selected «σι morecr events from the same LC sinulatiou aud re-simulated them at higher resolution. enmibeddius stellar disks inside the dwarf DAL halos.," Motivated by these findings, we selected eight merger events from the same LG simulation and re-simulated them at higher resolution, embedding stellar disks inside the dwarf DM halos." + Our goal is to deteriuue whether mergers of initially rotatioually-supported dwarfs can produce systemswith kincmatic and structural properties akinto those of the classic LG dSplis., Our goal is to determine whether mergers of initially rotationally-supported dwarfs can produce systemswith kinematic and structural properties akinto those of the classic LG dSphs. +line is only detectable down to [Fe/H]~—1 with the present means.,line is only detectable down to $\left[\mathrm{Fe}/\mathrm{H}\right] \sim -1$ with the present means. + Our results from the [S1] line favor a flat trend for [S/Fe] as a function of [Fe/H] for halo stars (see Fig., Our results from the $[\ion{S}{i}] $ line favor a flat trend for $\left[\mathrm{S}/\mathrm{Fe}\right]$ as a function of $\left[\mathrm{Fe}/\mathrm{H}\right]$ for halo stars (see Fig. + [6] and [7/))., \ref{fig:evo} and \ref{fig:Si_evo}) ). + Fitting a line to the gives [S/Fe]=—0.021-[Fe/H]+0.39 and the simple measurementq?]mean gives [S/Fe]=0.43 with a standard deviation of σ=0.11., Fitting a line to the gives $\left[\mathrm{S}/\mathrm{Fe}\right]=-0.021 \cdot \left[\mathrm{Fe}/\mathrm{H}\right] +0.39$ and the simple mean gives $\left[\mathrm{S}/\mathrm{Fe}\right]=0.43$ with a standard deviation of $\sigma = 0.11$. +" Since the [S1] line is not believed to be affected by non-LTE effects, and 3D effects are smaller, we consider these measurements more robust than the measurements using the 1045 nm triplet."," Since the $[\ion{S}{i}] $ line is not believed to be affected by non-LTE effects, and 3D effects are smaller, we consider these measurements more robust than the measurements using the 1045 nm triplet." + By just comparing the two leftmost panels in Fig., By just comparing the two leftmost panels in Fig. +" ifi it seems that the non-LTE corrected sulphur abundances from the 1045 nm triplet are similar, but perhaps somewhat lower, than the abundances from the 1082 nm i] line."," \ref{fig:Si_evo} it seems that the non-LTE corrected sulphur abundances from the 1045 nm triplet are similar, but perhaps somewhat lower, than the abundances from the 1082 nm ] line." + We have conducted a Kolmogorov-Smirnov checking the probability for all our non-LTE corrected [S/Fe] 1045 nm triplet measurements to come from the [S/Fe] distribution as described by our [S1] line measurements., We have conducted a Kolmogorov-Smirnov checking the probability for all our non-LTE corrected $\left[\mathrm{S}/\mathrm{Fe}\right]$ 1045 nm triplet measurements to come from the $\left[\mathrm{S}/\mathrm{Fe}\right]$ distribution as described by our $[\ion{S}{i}]$ line measurements. +" The Kolmogorov-Smirnov statistic for these two distributions is 0.40 and p-value for this isJ, meaning that formally the two distributions are similar to a low degree and therefore pointing toward a possible problem with the non- corrections applied to the 1045 nm triplet."," The Kolmogorov-Smirnov statistic for these two distributions is 0.40 and p-value for this is, meaning that formally the two distributions are similar to a low degree and therefore pointing toward a possible problem with the non-LTE corrections applied to the 1045 nm triplet." + When instead comparing the sulphur abundance distribution from the [S 1]-line with the sulphur abundance distribution from the triplet the Kolmogorov-Smirnov statistic is as expected larger; 0.50 and the p-value 0.11., When instead comparing the sulphur abundance distribution from the $[\ion{S}{i}]$ -line with the sulphur abundance distribution from the triplet the Kolmogorov-Smirnov statistic is as expected larger; 0.50 and the p-value 0.11. + Thus the non-LTE corrections of ? at least adjust the LTE distribution of sulphur abundances from, Thus the non-LTE corrections of \cite{Takeda2005} at least adjust the LTE distribution of sulphur abundances from +iuner-auost stable orbit the accretion flow would be supersonic and viscous contact impossible.,inner-most stable orbit the accretion flow would be supersonic and viscous contact impossible. + Black-hole candidates would be dimer because unable to lose their rotational cucrey., Black-hole candidates would be dimmer because unable to lose their rotational energy. +" Finally, we note that objects with a surface would be dinner than less conrpact objects. suplv because of redshift and light benudiug."," Finally, we note that objects with a surface would be dimmer than less compact objects, simply because of redshift and light bending." + If the surface is below the photon orbit. the fraction of “outward moving photons which escape to infinity is iu the Selisviuzschild metric For the lowest possible value for a causality-liuit equation of state RiRs=9/8. this factor aud the redshift squared vield a luminosity at iufinity which is equal to ouly 0.010 of the luminosity at the source.," If the surface is below the photon orbit, the fraction of “outward moving” photons which escape to infinity is in the Schwarzschild metric For the lowest possible value for a causality-limit equation of state $R/R_S=9/8$, this factor and the redshift squared yield a luminosity at infinity which is equal to only 0.040 of the luminosity at the source." + Three of the SNTs show uullisecond pulsations. and two of them are N-ray bursters.," Three of the SXTs show millisecond pulsations, and two of them are X-ray bursters." + They all have very short orbital periods. 2 hr in the case of SAN JLso0s8.[-3658 (Wijniuids aud van der Iklis 1998: Chakrabarty aud. Morgan 1998)). 15.6 min for NTE J1751-305 (Markwiuxlt et al. 2002)).," They all have very short orbital periods, 2 hr in the case of SAX J1808.4-3658 (Wijnands and van der Klis \cite{wvdk}; Chakrabarty and Morgan \cite{cm98}) ), 43.6 min for XTE J1751-305 (Markwardt et al. \cite{marketal}) )," + aud 142 miu for NTE 0929-311 (Calloway et al. 2002))., and 42 min for XTE J0929-314 (Galloway et al. \cite{galetal}) ). + Tt is perfectly well uuderstood that occurrence of colerent pulsations or of type I ταν bursts is incompatible with the presence of an event horizon. so none of these sources can be found on the list of black hole caucidates. even though their masses are unknown.," It is perfectly well understood that occurrence of coherent pulsations or of type I X-ray bursts is incompatible with the presence of an event horizon, so none of these sources can be found on the list of black hole candidates, even though their masses are unknown." +" However. it is true. as pointed out by Naravan Ilevl (2002)). that none of the longer (binary) period SNTs. with a 1ieasured mass function ereater than 3M, is a type I burster."," However, it is true, as pointed out by Narayan Heyl \cite{nh02}) ), that none of the longer (binary) period SXTs, with a measured mass function greater than $3M_\odot$ is a type I burster." + Naravan Πο (2002)) compute instability. of accretion onto a hvpothetical LOAL.. star with a surface of radius between (00/8)R4 and 348. aud report that for a range of accretion rates compatible with observations of N-rav novae. the star is expected to eive rise to an N-vav burst if the accreted column deusity is .l0e/cu?534105 οu. this quautity is very stall. The power of any radiation enuütte bv the surface of a gravastar ds groatlv reduced because onlv the radiation-. within. the solidB angle 2727x-vd1 arouud the normal to the surface escapes to infinity.," To see this, let us denote the surface redshift by For astrophysically interesting gravastars, with mass greater than $M_{\odot}$, i.e., $R_S > 3\times 10^{5}$ cm, this quantity is very small, The power of any radiation emitted by the surface of a gravastar is greatly reduced because only the radiation within the solid angle $27\varepsilon^2/4$ around the normal to the surface escapes to infinity." +" Further. because of eravitational redshift. the power of radiation received. by a distaut. observer is. only z ""nof what was emitted. at the eravastars surface."," Further, because of gravitational redshift, the power of radiation received by a distant observer is only $\varepsilon^2$ of what was emitted at the gravastar's surface." + Therefore. the power emitted from the surface is reduced by by the time it reaches a distant observer.," Therefore, the power emitted from the surface is reduced by by the time it reaches a distant observer." + Oneshould conclude that a gravastar with mass ercater than AL.. is to a distaut observer as blackas a black hole., Oneshould conclude that a gravastar with mass greater than $M_{\odot}$ is to a distant observer as blackas a black hole. + , +"while (he Maxwell equation (24) reduces to the following algebraic relation: In these equations. the following dimensionless notation is used for the constants: Ry,= AEQ. Ro= oC, A)= κο). RO)=Κ.Ο). e=(uu) bor (C./CAY. NF=(NyyΟν)”.","while the Maxwell equation (24) reduces to the following algebraic relation: In these equations, the following dimensionless notation is used for the constants: $R_y \equiv A_y/k_xC_A$ , $R_z \equiv A_z/k_xC_A$ , ${\cal K}_y(0) \equiv k_y(0)/k_x$ , ${\cal K}_z(0) \equiv +k_z(0)/k_x$, $\varepsilon \equiv (k_z z_0)^{-1}$, $\sigma^2 \equiv +(C_s/C_A)^2$ , $N^2 \equiv (N_{BV}/C_Ak_x)^2$." +" The dimensionless variables appearing in the above set of equations are defined as: e;2u;/C4. 5;—ib;/Dy. d=iofpy. P=ip/pyC2.e =—h,sf/(0.sy). THh,Cyl. KT)KO)— Rr. K.(7)=K.(0)—ΙΤ."," The dimensionless variables appearing in the above set of equations are defined as: $v_j \equiv {\hat u}_j/C_A$, $b_j \equiv i{\hat b}_j/B_0$, $d +\equiv i{\hat \varrho}/\rho_0$, ${\cal P} \equiv i{\hat +p}/\rho_0C_s^2$, $e \equiv -k_x {\hat s}/(\partial_zs_0)$, $\tau +\equiv k_xC_At$, ${\cal K}_y(\tau) \equiv {\cal K}_y(0) - {\cal +R}\tau$ , ${\cal K}_z(\tau) \equiv {\cal K}_z(0) - R\tau$." + Nolice that (his svstem is closed. because we have only equations lor variables (v.b.d.e. P).," Notice that this system is closed, because we have only equations for variables ${\bf v}, {\bf b}, +d, e, \cal P$ )." + The closure of the set of equations is ensured by the thermodynamic relation that follows from Eq. (, The closure of the set of equations is ensured by the thermodynamic relation that follows from Eq. ( +14) [a= κος]: This svstem of equations describes the temporal evolution of Gravito-MIID waves moclilied bv (the presence of a velocity shear in the (wo planes transversal to the flow direction.,"14) $\alpha +\equiv g/k_xC_s^2$ ]: This system of equations describes the temporal evolution of Gravito-MHD waves modified by the presence of a velocity shear in the two planes transversal to the flow direction." + The full analvsis of this set of equations is bevond the scope of the present paper., The full analysis of this set of equations is beyond the scope of the present paper. + Instead. in the next sections. we focus our study on (he relatively simple 2D and incompressible case.," Instead, in the next sections, we focus our study on the relatively simple 2D and incompressible case." + We will see that even in (his simplifiedcase thepresence of the velocity shear brings a considerable novelty in thedynamics ofperturbations., We will see that even in this simplifiedcase thepresence of the velocity shear brings a considerable novelty in thedynamics ofperturbations. + ARIILT5S8« ~ , $\sim$ +This point is a significant (30) outlier. which contradicts a F606 measurement. taken al almost exactly the same (ime.,"This point is a significant $3\,\sigma$ ) outlier, which contradicts a F606 measurement taken at almost exactly the same time." +" Our fit vields (he following parameter estimates: relative parallax z4—1.78040.185 mas: relative proper molion fire,=21.381+0.022masvrI proper motion components feta17.547x0.0209masvr. fy and praixoan=—12.217£0.022masvr.I: and. position angle 12485X 07.08."," Our fit yields the following parameter estimates: relative parallax $\pi_\rel = 1.780\pm 0.185\,$ mas; relative proper motion $\mu_\rel = 21.381\pm 0.022\,\rm mas\, yr^{-1}$; proper motion components $\mu_{\rm rel,East} =17.547\pm 0.029\,\rm mas\, yr^{-1}$ ; and $\mu_{\rm rel,North} = -12.217\pm 0.022\,\rm mas\, yr^{-1}$; and position angle $\phi=124^\circ\hskip-2pt .85 \pm 0^\circ\hskip-2pt .08$ ." + As noted by Drakeetal.(2004).. the residuals for the ΑΕΡΟΣ point are quite small compared to their reported errors. with Ay?=0.11 for 2 degrees of freedom (cof).," As noted by \citet{drake}, the residuals for the WFPC2 point are quite small compared to their reported errors, with $\Delta\chi^2=0.11$ for 2 degrees of freedom (dof)." + This mav imply that the errors were overestimated by Alcocketal.(2001)., This may imply that the errors were overestimated by \citet{alcock01}. +. However. since there is a probability of having such low residuals by chance. no definite conclusions can be drawn regarding a possible overestimation of the error bars.," However, since there is a probability of having such low residuals by chance, no definite conclusions can be drawn regarding a possible overestimation of the error bars." + In this paper. we will draw together [four sources of data to measure the mass of ALACIIO-LMC-5.," In this paper, we will draw together four sources of data to measure the mass of MACHO-LMC-5." +. We first summarize these sources. then cliscuss a series of tests that we have carried out to determine whether (μον are consistent with each other.," We first summarize these sources, then discuss a series of tests that we have carried out to determine whether they are consistent with each other." + Onlv alter these tests are successfully concluded do we combine the data., Only after these tests are successfully concluded do we combine the data. + The primary data set is the original MACIIO SoDoPIIOT pipeline photometry of the event. which occurred. in 1993.," The primary data set is the original MACHO SoDoPHOT pipeline photometry of the event, which occurred in 1993." + These data have already been analvzed by and Gould(2004)., These data have already been analyzed by \citet{alcock01} and \citet{gould04}. +. They consist of 352 points in the non-standard MACIIO red filter (hereafter /23;) ancl 265 points in the non-standard NACIIO blue filter (hereafter V3; )., They consist of 352 points in the non-standard MACHO red filter (hereafter $R_M$ ) and 265 points in the non-standard MACHO blue filter (hereafter $V_M$ ). + We slightly deviate from previous authors by recursively removing outliers ancl renormalizing the errors so as to enforce 47 per degree of freedom (dof) equal to unitv in each bandpass separately., We slightly deviate from previous authors by recursively removing outliers and renormalizing the errors so as to enforce $\chi^2$ per degree of freedom (dof) equal to unity in each bandpass separately. + We repeat (his procedure until all 3.50 outliers are removed.," We repeat this procedure until all $3.5\,\sigma$ outliers are removed." + This removes three Ra; points and one V3; point. all greater (han 3.95.," This removes three $R_M$ points and one $V_M$ point, all greater than $3.9\,\sigma$." + The next largest deviation is al 30. bul with more than GOO points. such a deviation is consistent with Gaussian statistics and so cannot be considered an outlier.," The next largest deviation is at $3\,\sigma$, but with more than 600 points, such a deviation is consistent with Gaussian statistics and so cannot be considered an outlier." + The error renormalization [actors are 0.79 in Ly; and 0.51 in V., The error renormalization factors are 0.79 in $R_M$ and 0.81 in $V_M$. + Gould(2004) had argued against blindly applving this renormalization procedure because the mass determination is dominated by the relatively small number of points during the event. while V7 /dof is dominated bv the much larger nunber of baseline points taken over," \citet{gould04} had argued against blindly applying this renormalization procedure because the mass determination is dominated by the relatively small number of points during the event, while $\chi^2$ /dof is dominated by the much larger number of baseline points taken over" +and the currently available observational results pertaining to PMS star accretion rate. are consistent with the model of spherically symmetric fractal accretion.,"and the currently available observational results pertaining to PMS star accretion rate, are consistent with the model of spherically symmetric fractal accretion." + It has also been argued by Roy(2007) that the accretion rate is scaled as iiAL?+ where D(«3) is the mass dimension of the surrounding ISM.," It has also been argued by \citet{roy07} that the accretion rate is scaled as $\dot{m} \sim M^{D-1}$ , where $D(<3)$ is the mass dimension of the surrounding ISM." + So. if the proposed global model for accretion onto PMS stars — spherically symmetric accretion at large distances from the star and dise accretion close to it — is correct. then in the steady state. going by equation (413). one will have 2A{)1«2.," So, if the proposed global model for accretion onto PMS stars — spherically symmetric accretion at large distances from the star and disc accretion close to it — is correct, then in the steady state, going by equation \ref{flowratescal}) ), one will have $2\Delta=D-1<2$." + This will imply that the dise will also have a fractal structure. if the surrounding medium. from which the large scale accretion takes place. is fractal in nature.," This will imply that the disc will also have a fractal structure, if the surrounding medium, from which the large scale accretion takes place, is fractal in nature." + The fractal nature of the accreting matter acts against multitransonicity., The fractal nature of the accreting matter acts against multitransonicity. + Nevertheless. this does not preclude transonicity itself.," Nevertheless, this does not preclude transonicity itself." + If anything. he static flow shows that prominent fractal features will certainly bring about the existence of one saddle-type critical point in the phase xortrait of the flow.," If anything, the static flow shows that prominent fractal features will certainly bring about the existence of one saddle-type critical point in the phase portrait of the flow." + The overall appearance of a conspicuously sub-Keplerian fractal flow will. therefore. be like that of a monotransonic spherically symmetric Bondi(1952) flow.," The overall appearance of a conspicuously sub-Keplerian fractal flow will, therefore, be like that of a monotransonic spherically symmetric \citet{bon52} flow." + This is fortunate in many respects. because the Bondi(1952) solution has by now become quite a well-understood and a regularly-invoked paradigm in accretion studies. and any close convergence between it and the fractal dise flow. will yave the way for making insightful comparisons.," This is fortunate in many respects, because the \citet{bon52} solution has by now become quite a well-understood and a regularly-invoked paradigm in accretion studies, and any close convergence between it and the fractal disc flow, will pave the way for making insightful comparisons." + The most significant of these is that there will at least be one continuous solution which will connect the outer boundary of the flow to he event horizon of the black hole aecretor. in a process that will make black hole accretion realisable in its expected fashion.," The most significant of these is that there will at least be one continuous solution which will connect the outer boundary of the flow to the event horizon of the black hole accretor, in a process that will make black hole accretion realisable in its expected fashion." + The steady state conditions will imply that this solution will pass through a saddle point. which is known to be unstable (Jordan&Smith1999).," The steady state conditions will imply that this solution will pass through a saddle point, which is known to be unstable \citep{js99}." +. Any solution passing through this point will suffer from the problem of fine tuning the outer boundary condition with infinite precision 2002)., Any solution passing through this point will suffer from the problem of fine tuning the outer boundary condition with infinite precision \citep{rb02}. +. These difficulties can be avoided through the dynamics. and indeed in the case of fractal spherically symmetric accretion. it has been shown (Roy&Ray2007) that the stronger is the fractal nature of the flow. the more successful is the time-evolutionary drive towards the Bondi(1952). solution.," These difficulties can be avoided through the dynamics, and indeed in the case of fractal spherically symmetric accretion, it has been shown \citep{rnr07} that the stronger is the fractal nature of the flow, the more successful is the time-evolutionary drive towards the \citet{bon52} solution." + This happens simply because a fractal medium translates equivalently as a continuum with an effective lesser density. ie. a fractal flow can be construed as a more dilute continuum.," This happens simply because a fractal medium translates equivalently as a continuum with an effective lesser density, i.e. a fractal flow can be construed as a more dilute continuum." + Since a sizeable resistance against gravity-driven transonicity happens due to the pressure build-up in the flow (which. through the polytropic relation. is connected to the local flow density). any dilution in the flowing medium will detract from the opposition against transonicity.," Since a sizeable resistance against gravity-driven transonicity happens due to the pressure build-up in the flow (which, through the polytropic relation, is connected to the local flow density), any dilution in the flowing medium will detract from the opposition against transonicity." + Hence. this entire effect will enable an accreting solution to cross the sonic horizon smoothly. premised on the condition that this solution will also correspond to a minimum possible energy configuration. and. concomitantly. to the maximum possible inflow rate 2007)..," Hence, this entire effect will enable an accreting solution to cross the sonic horizon smoothly, premised on the condition that this solution will also correspond to a minimum possible energy configuration, and, concomitantly, to the maximum possible inflow rate \citep{bon52,gar79,rb02,rnr07}." + This line of reasoning can be carried over fully to the case of inviscid axisymmetric accretion., This line of reasoning can be carried over fully to the case of inviscid axisymmetric accretion. + As a matter of fact. in the context of inviscid thin-dise flows. Ray&Bhattacharjee(2007) have already argued that transonicity is determined and governed by the same dynamic and non-perturbative criteria. as they are for the Bondi(1952). flow.," As a matter of fact, in the context of inviscid thin-disc flows, \citet{rbcqg} have already argued that transonicity is determined and governed by the same dynamic and non-perturbative criteria, as they are for the \citet{bon52} flow." + The analogy with the Bondi(1952) solution will be more so true for sub-Keplerian solutions with low angular momentum (having feeble centrifugal effects pitted against gravity)., The analogy with the \citet{bon52} solution will be more so true for sub-Keplerian solutions with low angular momentum (having feeble centrifugal effects pitted against gravity). + Fractal features in this kind of dise contiguration will only serve to facilitate transonicity even further., Fractal features in this kind of disc configuration will only serve to facilitate transonicity even further. + As opposed to a completely non-perturbative approach to the question of time-dependence in the fractal dise flow tall of which will require the mathematics of partial differential equations). it would also be worthwhile to study the properties of the background stationary flow under the influence of < linearised time-dependent perturbative effect.," As opposed to a completely non-perturbative approach to the question of time-dependence in the fractal disc flow (all of which will require the mathematics of partial differential equations), it would also be worthwhile to study the properties of the background stationary flow under the influence of a linearised time-dependent perturbative effect." + This will yield much information on the global stability of the flow solutions., This will yield much information on the global stability of the flow solutions. +" In order to achieve that. it will first be necessary to define a new physical variable. co=p.170i7, closely following a perturbative procedure prescribed by Pettersonetal.(1980). and Theuns&David(1992). for spherically symmetric flows. and applied successfully later to thin dise flows (Ray2003:Chaudhuryetal.2006:Ray&Bhattacharjee2007)."," In order to achieve that, it will first be necessary to define a new physical variable, $\psi =\rho^{(\gamma +1)/2} v r^{\sigma}$, closely following a perturbative procedure prescribed by \citet{pso80} and \citet{td92} + for spherically symmetric flows, and applied successfully later to thin disc flows \citep{ray03,crd06,rbcqg}." +. It is quite obvious from the form of equations (7)) and (14)). that the stationary value of c will be a global constant. co. which can be closely identified with the matter flux rate. within a constant geometrical factor.," It is quite obvious from the form of equations \ref{rhocon}) ) and \ref{con}) ), that the stationary value of $\psi$ will be a global constant, $\psi_0$, which can be closely identified with the matter flux rate, within a constant geometrical factor." + A perturbation prescription of the form e(1./)=eu(r)|eGP) and οί.)=patr)|p.d). will give. on linearising in the primed quantities. with o being a linearised time-dependent perturbation about the constant matter inflow rate. cy.," A perturbation prescription of the form $v(r,t) = v_0(r) + v^{\prime}(r,t)$ and $\rho (r,t) = \rho_0 (r) + \rho^{\prime}(r,t)$, will give, on linearising in the primed quantities, with $\psi^{\prime}$ being a linearised time-dependent perturbation about the constant matter inflow rate, $\psi_0$ ." + It is significant that the foregoing expression for c is free of the explicit presence of e., It is significant that the foregoing expression for $\psi^{\prime}$ is free of the explicit presence of $\sigma$. + Linearising in p and ( about po and e. respectively. in both equations (7)) and (134). and expressing p and ο separately in terms of £ only. will ultimately lead to a linearised equation for the perturbation as which is an expression that is exactly the same as what can derived upon perturbing the stationary solutions of conserved axisymmetric inflows (Ray2003:Chaudhuryetal.2006).," Linearising in $\rho^{\prime}$ and $v^{\prime}$ about $\rho_0$ and $v_0$, respectively, in both equations \ref{rhocon}) ) and \ref{fulleuler}) ), and expressing $\rho^{\prime}$ and $v^{\prime}$ separately in terms of $\psi^{\prime}$ only, will ultimately lead to a linearised equation for the perturbation as which is an expression that is exactly the same as what can derived upon perturbing the stationary solutions of conserved axisymmetric inflows \citep{ray03,crd06}." +.. Another aspect of equation (43)) is that its form has no explicit dependence on the potential that is driving the flow., Another aspect of equation \ref{tpert}) ) is that its form has no explicit dependence on the potential that is driving the flow. + This is entirely to be expected. because the potential. being independent of time. will appear only in the stationary background flow.," This is entirely to be expected, because the potential, being independent of time, will appear only in the stationary background flow." + Arguments regarding stability will. therefore. be more dependent on the boundary conditions of the steady flow.," Arguments regarding stability will, therefore, be more dependent on the boundary conditions of the steady flow." + As the form ofthe equation of motion for the linearised perturbation remains unchanged even for a flow in a fractal medium. and as the physicalboundary conditions are also not altered in this case. the general conclusions reached earlier regarding non-fractal axisymmetric flows," As the form ofthe equation of motion for the linearised perturbation remains unchanged even for a flow in a fractal medium, and as the physicalboundary conditions are also not altered in this case, the general conclusions reached earlier regarding non-fractal axisymmetric flows" +steepening can also contribute to erroneous Hubble constant values if isothermality is assumed (Dobke.King&Fellhauer2007).,steepening can also contribute to erroneous Hubble constant values if isothermality is assumed \citep{dobkeb}. + Outside the group environment. line-of sight structures can also orovide contributions to the lens potential (Momchevaetal.2006).," Outside the group environment, line-of sight structures can also provide contributions to the lens potential \citep{momc}." +. These effects can result in either an over or underestimate of the Hubble constant by virtue of a contributed increase or decrease in he density profile slope., These effects can result in either an over or underestimate of the Hubble constant by virtue of a contributed increase or decrease in the density profile slope. + The intrinsic shape of the lensing galaxy has also been suspected to have a direct bearing on Hubble constant derivation., The intrinsic shape of the lensing galaxy has also been suspected to have a direct bearing on Hubble constant derivation. + Oguri(2007). recently demonstrated the importance of substructures and external perturbations in. galaxy lensing: urthermore. in an investigation with models of 35 galaxy enses Saha&Williams(2006) proposed that shape-modelling degeneracies (e.g. caused by triaxiality) could also contribute to changes in the time delays and hence the derived Hubble constant values.," \cite{ogurc} recently demonstrated the importance of substructures and external perturbations in galaxy lensing; furthermore, in an investigation with models of 35 galaxy lenses \citet{sahab} proposed that shape-modelling degeneracies (e.g. caused by triaxiality) could also contribute to changes in the time delays and hence the derived Hubble constant values." + Triaxiality is of particular interest because the dark matter halos of ACDM are predicted to be fully triaxial with axis ratios in the mass distribution as low as 0.4 (e.g. Bettetal.2007:: Maccioetal. 20073). a prediction which observations have loosely contirmed (e.g. Bak&Statler 20007).," Triaxiality is of particular interest because the dark matter halos of $\Lambda$ CDM are predicted to be fully triaxial with axis ratios in the mass distribution as low as 0.4 (e.g. \citealt{bett}; \citealt{maccio}) ), a prediction which observations have loosely confirmed (e.g. \citealt{bak}) )." + Moreover. it has been shown that the triaxiality of CDM halos can effect the overall lensing probabilities and relative number of different image configurations (double. quadruple. naked cusp lenses) (Oguri&Keeton2004:: Rozoetal. 2007)).," Moreover, it has been shown that the triaxiality of CDM halos can effect the overall lensing probabilities and relative number of different image configurations (double, quadruple, naked cusp lenses) \citealt{ogurb}; \citealt{rozo}) )." + Triaxial studies in galaxy cluster weak lensing have further revealed that neglecting halo shape can result in significant over and underestimates of cluster concentration and mass (Corless 2007)., Triaxial studies in galaxy cluster weak lensing have further revealed that neglecting halo shape can result in significant over and underestimates of cluster concentration and mass \citep{corl}. +. It seems apparent then that triaxiality can affect a numberof critical observables and derived quantities in both strong and weak lensing and as such cannot be ignored., It seems apparent then that triaxiality can affect a number of critical observables and derived quantities in both strong and weak lensing and as such cannot be ignored. + However. due to the small number of constraints available in galaxy lensing analyses. halo shape is typically addressed only via an elliptical perturbation to the projected spherical lensing potential. ignoring altogether halo structure along the line-of-sight.," However, due to the small number of constraints available in galaxy lensing analyses, halo shape is typically addressed only via an elliptical perturbation to the projected spherical lensing potential, ignoring altogether halo structure along the line-of-sight." + In this paper we investigate what errors this often necessary neglect of triaxiality in galaxy lensing analyses introduces in best fit Hubble parameter values., In this paper we investigate what errors this often necessary neglect of triaxiality in galaxy lensing analyses introduces in best fit Hubble parameter values. + We fit an elliptical isothermal mass model to lensing systems of highly (as predicted in simulations) triaxial isothermal galaxy lenses to investigate the maximum discrepancies that can arise from fitting a simplified model to data that in fact originates from a fully triaxial lens., We fit an elliptical isothermal mass model to lensing systems of highly (as predicted in simulations) triaxial isothermal galaxy lenses to investigate the maximum discrepancies that can arise from fitting a simplified model to data that in fact originates from a fully triaxial lens. + We ask: to what extent can galaxy triaxiality explain the discrepancies between some lensing-derived values for the Hubble constant and those of other methods?, We ask: to what extent can galaxy triaxiality explain the discrepancies between some lensing-derived values for the Hubble constant and those of other methods? + The outline of the paper is as follows: in 322 we introduce the softened triaxial isothermal model and its lensing properties. $33 goes on to present our analysis method and key results. and S44 draws some conclusions based upon our findings.," The outline of the paper is as follows: in 2 we introduce the softened triaxial isothermal model and its lensing properties, 3 goes on to present our analysis method and key results, and 4 draws some conclusions based upon our findings." +" A standard ACDM cosmology with //,=72 km/s/Mpc. 0.3. Ὃν=0.7 is employed throughout."," A standard $\Lambda$ CDM cosmology with $H_0 = 72$ km/s/Mpc, $\Omega_m = 0.3$ , $\Omega_{\Lambda}=0.7$ is employed throughout." + To generate a full parameterisation for a softened) triaxial isothermal halo we follow the procedure given first in Suto(2002). and implemented for weak lensing in Corless&King(2007) for a triaxial NFW., To generate a full parameterisation for a softened triaxial isothermal halo we follow the procedure given first in \cite{jing} and implemented for weak lensing in \cite{corl} for a triaxial NFW. +" We first generalise the spherical softened isothermal profile to obtain a density profile where Ge is an effective Einstein radius. 5 a triaxial core radius. £2 a triaxial radius afe and b/e the minorimajor and. intermediate:major axis ratios. respectively. and {2 the angular diameter distance between the lens and source and 2, that between the observer and source."," We first generalise the spherical softened isothermal profile to obtain a density profile where $\theta_E$ is an effective Einstein radius, $S$ a triaxial core radius, $R$ a triaxial radius $a/c$ and $b/c$ the minor:major and intermediate:major axis ratios, respectively, and $D_{ls}$ the angular diameter distance between the lens and source and $D_s$ that between the observer and source." + The mass contained within radius /? is The virial mass is defined as that mass contained within an ellipsoid containing a mean density 200 times the critical density pez) at the redshift of the halo.Mog)=BRDRSaup(2): combining that definition with (3)) gives an expression for θε as a function of the virial radius 2590: The full derivation of the lensing properties of a triaxial halo is given by Oguri.Lee.&Suto(2003). and we summarise some of that work here.," The mass contained within radius $R$ is The virial mass is defined as that mass contained within an ellipsoid containing a mean density 200 times the critical density $\rho_c(z)$ at the redshift of the halo,$M_{200} = \frac{800\pi}{3}ab R_{200}^3\rho_c(z)$; combining that definition with \ref{eq:MinR}) ) gives an expression for $\theta_E$ as a function of the virial radius $R_{200}$: The full derivation of the lensing properties of a triaxial halo is given by \cite{ogur}, and we summarise some of that work here." + The triaxial halo is projected onto the plane of the sky to find its projected elliptical isodensity contours as a function of the halo's axis ratios and orientation angles (6. 6) with respect to the the observer's line-of-sight.," The triaxial halo is projected onto the plane of the sky to find its projected elliptical isodensity contours as a function of the halo's axis ratios and orientation angles $\theta$, $\phi$ ) with respect to the the observer's line-of-sight." + The axis ratio q of the elliptical density contours is given by the elliptical radius by and the orientation angle © on the sky by here where and General expressions for the lensing potential of a softened elliptical isothermal halo are given in Keeton (2001):: we modify them to incorporate the geometry of the halo projection to establish, The axis ratio $q$ of the elliptical density contours is given by the elliptical radius by and the orientation angle $\Omega$ on the sky by here where and General expressions for the lensing potential of a softened elliptical isothermal halo are given in \cite{keeta}; ; we modify them to incorporate the geometry of the halo projection to establish +preseut.,present. + The [St A6731 line has a higrer critical deusity of ~Lx10? ? than he A6716 line (cls«lO0 7j aud hence is less-affected by collisional de-excitation 1- lieh-deusitv regious.," The [S ] $\lambda6731$ line has a higher critical density of $\sim4\times10^3$ $^{-3}$ than the $\lambda6716$ line $\sim1\times10^3$ $^{-3}$ ), and hence is less-affected by collisional de-excitation in high-density regions." +" For a deusity tiat decreases aud increases outwards. the ο AG?31 line is then strouger in low- and high-veocity regions. respecively,"," For a density that decreases and increases outwards, the [S ] $\lambda6731$ line is then stronger in low- and high-velocity regions, respectively." + As s1OWll in Figs., As shown in Figs. +" | aud 5.. he profile discrepa vos particularly remarkable when tli (SI | AAGT3L.6716 lires add the [5 ui] ALOTG hne are conrLCE because the later has a nuch lugher critical density 210 8], "," \ref{n_neg} and \ref{n_pos}, the profile discrepancy is particularly remarkable when the [S ] $\lambda\lambda6731,6716$ lines and the [S ] $\lambda4076$ line are compared because the latter has a much higher critical density $\sim10^6$ $^{-3}$ )." +Dowever. we note that temperature fitctua10119 nav continite partialv to the profile discrepaicy between fjese deusity diagnostic lines.," However, we note that temperature fluctuations may contribute partially to the profile discrepancy between these density diagnostic lines." + Apart from for the deusitv clistribition. thiο basic assunrptious are idetical ii each nodel.," Apart from for the density distribution, the basic assumptions are identical in each model." + Figure 5 shows a larecr separation etween f1e two Cluission peaks than in Fie. L., Figure \ref{n_pos} shows a larger separation between the two emission peaks than in Fig. \ref{n_neg}. + This is because d it1ο case of outwardly-lncreaslie density distributio1. cluissiou lines weieli the lugh-velocity regions more highly.," This is because in the case of outwardly-increasing density distribution, emission lines weight the high-velocity regions more highly." + The analysis nucthods are applied o other (Gesity diagnostics. such as [O n] ÀA31206.3129. |C] I AADSLT.5537. aud |ο uj AALTIL.1710.," The analysis methods are applied to other density diagnostics, such as [O ] $\lambda\lambda3726,3729$, [Cl ] $\lambda\lambda5517,5537$, and [O ] $\lambda\lambda4711,4740$." + As an exiunple. Fie.," As an example, Fig." + 6 shows the profiles of the [Ar v] AAMT:.ArLO üσαies for higl-excitatiou. PNe wit lastelax teniperature of II uuder the assuniptioi of ouwardly decreasing aud increasing density «listribitious.," \ref{ar} shows the profiles of the [Ar ] $\lambda\lambda4711,4740$ lines for high-excitation PNe with a stellar temperature of K under the assumption of outwardly decreasing and increasing density distributions." + Iu the two xts of density structures. the reatious between he two nσα16 profiles are completely the opposite.," In the two sorts of density structures, the relations between the two line profiles are completely the opposite." + The |Ar 1v] AL711 li1ο has a lower critical deusitv hau the [Ar ΑΙΤΙΟ Tσαje. and thus weights lower-deusity regions more highly.," The [Ar ] $\lambda4711$ line has a lower critical density than the [Ar ] $\lambda4740$ line, and thus weights lower-density regions more highly." + Hence. if the nebula has a uceative density eradicut. the [Ày 1v] AITIL liue wcights the ouer regions more. where the expansion velocity is larger. wuch produces a broader," Hence, if the nebula has a negative density gradient, the [Ar ] $\lambda4711$ line weights the outer regions more, where the expansion velocity is larger, which produces a broader" +aabsorbers with redshifts 0.412.<20.84 by Nestoretal.(2006)..,absorbers with redshifts $0.42 < z < 0.84$ by \citet{2006astro.ph.10760N}. +" The principal result is the detection. in essentially all cases. of a galaxy. which. if physically associated with the absorber. lies projected within kkpe of the quasar and has luminosity O.3L""."," The principal result is the detection, in essentially all cases, of a galaxy, which, if physically associated with the absorber, lies projected within kpc of the quasar and has luminosity $L \ga 0.3L^*$ ." +" Seven of the sample are absorbers. and six of these possess a galaxy within kKpe with luminosities 0.3L 2.0L""."," Seven of the sample are absorbers, and six of these possess a galaxy within kpc with luminosities $0.3L^* +\la L \la 2.0L^*$ ." + Allowing for the chance projection of one or two galaxies. the results are entirely consistent with the findings presented in this paper.," Allowing for the chance projection of one or two galaxies, the results are entirely consistent with the findings presented in this paper." + The second result of the Nestor et al., The second result of the Nestor et al. + study is the detection of an excess of apparently bright galaxies. which. if physically associated with the absorber. have projected separations extending to — ΚΚΡο and extremely high luminosities. 4°=Lx1913.," study is the detection of an excess of apparently bright galaxies, which, if physically associated with the absorber, have projected separations extending to $\sim$ kpc and extremely high luminosities, $4L^* \la L \la +13L^*$." + We can perform a similar analysis using our dataset by comparing the observed number of galaxies brighter than 4L.(2) if placed üt tap. In each of our absorber field images (which extend to c kkpe from the quasars) to the predictions from the K20-survey number-magnitude distribution., We can perform a similar analysis using our dataset by comparing the observed number of galaxies brighter than $4L_K^*(z)$ if placed at $z_{abs}$ in each of our absorber field images (which extend to $\simeq$ kpc from the quasars) to the predictions from the K20-survey number-magnitude distribution. + Eight field galaxies are predicted. whereas we find a total of |] such galaxies around eight quasars.," Eight field galaxies are predicted, whereas we find a total of 11 such galaxies around eight quasars." + Thus. we find no evidence in our sample for any such excess.," Thus, we find no evidence in our sample for any such excess." + Nestor et al., Nestor et al. + discuss an interpretation for the observed excess in terms of elevated levels of star-formation in the galaxies., discuss an interpretation for the observed excess in terms of elevated levels of star-formation in the galaxies. + At the rest-frame wavelengths of ~4000 pprobed by their observations. they are certainly far more affected by the presence of ongoing and recent star-formation than the ~ wwavelengths probed by our A -band observations.," At the rest-frame wavelengths of $\sim$ probed by their observations, they are certainly far more affected by the presence of ongoing and recent star-formation than the $\sim$ wavelengths probed by our $K$ -band observations." + However. we note that the photometric redshifts from the SDSS DRS tAdelman-MeCarthy et al.," However, we note that the photometric redshifts from the SDSS DR5 (Adelman-McCarthy et al." + 2007) for all of their galaxies with LxL are consistent with their lying at considerably lower redshifts than the absorbers. supporting their identification as more typical objects at lowerredshifts”.," 2007) for all of their galaxies with $L \ge 4L^*$ are consistent with their lying at considerably lower redshifts than the absorbers, supporting their identification as more typical objects at lower." + Finally. a powerful constraint on the luminosities of galaxies associated with absorbers comes from the stacking analysis of SDSS images in the regions around absorbers by Zibettietal. (2006)..," Finally, a powerful constraint on the luminosities of galaxies associated with absorbers comes from the stacking analysis of SDSS images in the regions around absorbers by \citet{2006astro.ph..9760Z}." + The mean integrated rest-frame luminosity within 100 ΚΚΡο of their sample of absorbers with redshifts 0.76:2 101 Λες)= 22.4(AB system)., The mean integrated rest-frame luminosity within $100$ kpc of their sample of absorbers with redshifts $0.76 \le z \le 1.0$ is $M_i(z)=-22.4$ (AB system). +" The absolute magniude corresponds to ~AL""0.5. or AZ (220)."," The absolute magnitude corresponds to $\simeq$$M^*-0.5$, or $M^*$ $z$ =0)." + At lower redshifts. wlere the signal is strong enough for division of the sample. Zibettietal.(2006) find only a small difference between the mean absolute magnitudes of galaxies associated with all the absorbers and those associated with the strongest absorbers.," At lower redshifts, where the signal is strong enough for division of the sample, \citet{2006astro.ph..9760Z} find only a small difference between the mean absolute magnitudes of galaxies associated with all the absorbers and those associated with the strongest absorbers." + Assuming the same holds for the 0.76<2:1.0 absorber sample. and noing that approximately half the luminosity within kkpe lies wihin the smaller aperture of SOKKpe. produces an average absoute magnitude of 2-A/*(:20)40.75.," Assuming the same holds for the $0.76 \le z \le 1.0$ absorber sample, and noting that approximately half the luminosity within kpc lies within the smaller aperture of kpc, produces an average absolute magnitude of $\simeq$$M^*$ $z$ =0)+0.75." + The KKde aperture corresponds closely to the spatial scale of our observed excess of galaxies and the average absolute magnitude of galaxies associated with al 30 absorbers is. 2M (220H40.2540.2., The kpc aperture corresponds closely to the spatial scale of our observed excess of galaxies and the average absolute magnitude of galaxies associated with all 30 absorbers is $\simeq$$M^*$ $z$ $\pm$ 0.2. + The estimate is insensitive to whether the galaxies associated with the nine absorbers without detected galaxies are excluded or included (even, The estimate is insensitive to whether the galaxies associated with the nine absorbers without detected galaxies are excluded or included (even +"In order to update the effects caused by X-rays on the temperature of the gas, we ported an X-ray dominated region chemical code (XDR code) created by ? into FLASH.","In order to update the effects caused by X-rays on the temperature of the gas, we ported an X-ray dominated region chemical code (XDR code) created by \cite{2005A&A...436..397M} into FLASH." +" This code incorporates all of the heating (photo-ionization, yielding non-thermal electrons) and cooling processes from atomic (fine-structure, semi-forbidden) and molecular transitions (CO, H2, H2O)."," This code incorporates all of the heating (photo-ionization, yielding non-thermal electrons) and cooling processes from atomic (fine-structure, semi-forbidden) and molecular transitions (CO, $_{2}$, $_{2}$ O)." +" Effects from internal UV, cosmic rays, and dust-gas coupling are treated as well."," Effects from internal UV, cosmic rays, and dust-gas coupling are treated as well." +" Given an X-ray flux, gas density, and column density along the line of sight to the source, the XDR code calculates the temperature and the chemical abundances."," Given an X-ray flux, gas density, and column density along the line of sight to the source, the XDR code calculates the temperature and the chemical abundances." + This output is fed into the simulation at every iteration., This output is fed into the simulation at every iteration. + Most of the computation is spent finding the column densities for every cell., Most of the computation is spent finding the column densities for every cell. +" A ray-tracing algorithm, specifically created for this purpose, searches the grid and sums up the column densities of each cell lying along the line of sight from the source, the accreting black hole, to the target cell."," A ray-tracing algorithm, specifically created for this purpose, searches the grid and sums up the column densities of each cell lying along the line of sight from the source, the accreting black hole, to the target cell." +" The flux is an E? power law between 1 and 100 keV. X-ray scattering is not very important, but is nonetheless treated in the XDR-code."," The X-ray flux is an $^{-0.9}$ power law between 1 and 100 keV. X-ray scattering is not very important, but is nonetheless treated in the XDR-code." +" A uniform background of cosmic rays prevents the temperature from dropping below 10 K. For this, a cosmic ray ionization rate typical for the Milky Way Z25x107""s!, is assumed (?) We create a spherical gas cloud with solar abundances at a distance of 10 parsec from a 10’Mo black hole."," A uniform background of cosmic rays prevents the temperature from dropping below 10 K. For this, a cosmic ray ionization rate typical for the Milky Way $\rm \zeta=5\times10^{-17} ~s^{-1}$, is assumed \citep{2005ApJ...626..644S} + We create a spherical gas cloud with solar abundances at a distance of 10 parsec from a $^7 \rm M_{\odot}$ black hole." + We run two separate simulations and name them simulation A and B. Simulation A represents a molecular cloud near an active black hole under the impact of X-rays., We run two separate simulations and name them simulation A and B. Simulation A represents a molecular cloud near an active black hole under the impact of X-rays. +" Simulation B has a cloud near an inactive black hole and has isothermal conditions, with an equation of state of the form P«p."," Simulation B has a cloud near an inactive black hole and has isothermal conditions, with an equation of state of the form $\rm P \propto \rho$." + The XDR code that updates the thermodynamics is only linked with simulation A where we do have X-rays., The XDR code that updates the thermodynamics is only linked with simulation A where we do have X-rays. +" The 107Mg black hole, at of Eddington, yields a flux of 160 ergs!cm? with some extinction (?).."," The $^7 \rm M_{\odot}$ black hole, at of Eddington, yields a flux of 160 $\rm erg ~s^{-1} ~cm^{-2}$ with some extinction \citep{2007A&A...461..793M}." +" ? show that column densities of 10??5cm? can typically exist in the central R~10pc of an AGN, leading to a 1 keV optical depth of 2-3."," \cite{2009ApJ...702...63W} show that column densities of $\rm 10^{22.5} cm^{-2}$ can typically exist in the central $\rm R \simeq 10 ~pc$ of an AGN, leading to a 1 keV optical depth of 2-3." +" Furthermore, ? show that column densities as large as 1074cm""? occur and persist in a statistical sense in the dynamically active inner 20 pc."," Furthermore, \cite{2009ApJ...702...63W} show that column densities as large as $^{24} \rm ~cm^{-2}$ occur and persist in a statistical sense in the dynamically active inner 20 pc." +" A gaseous cloud can thus be shielded by this clumpy medium around the AGN and remain cold, while the temperature rises rapidly once the cloud is exposed to the radiation."," A gaseous cloud can thus be shielded by this clumpy medium around the AGN and remain cold, while the temperature rises rapidly once the cloud is exposed to the radiation." +" Both our simulations start with the same initial conditions, but we expose simulation A to an X-ray source once the simulation starts."," Both our simulations start with the same initial conditions, but we expose simulation A to an X-ray source once the simulation starts." +" In this, heating is nearly immediate, since the timescale for heating is much shorter than the collapse time, thear1tg, with tg=4/32/32Gp and 10° throughout this work."," This process keeps the turbulence strong to large dynamical times, i.e., $\rm >1 ~t_{ff}$, with $\rm t_{ff} = \sqrt{ 3\pi / \rm 32G\rho}$ and $^{5}$ throughout this work." +" The shearing time, tshear=Detoud/AVshear, 18 almost 3 times larger than the cloud free-fall time and gravitationally bound (roughly) spherical clouds are likely to exist at densities of 10?cm."," The shearing time, $\rm t_{shear}=D_{cloud}/\triangle \rm v_{shear}$, is almost 3 times larger than the cloud free-fall time and gravitationally bound (roughly) spherical clouds are likely to exist at densities of $\sim$ $^{5} \rm ~cm^{-3}$." + The molecular cloud starts with a uniform number density of 10°cm? and has a size of 0.33 pc in radius., The molecular cloud starts with a uniform number density of $10^{5} \rm ~cm^{-3}$ and has a size of 0.33 pc in radius. +" With a mean molecular weight of µ = 2.3, the total mass of the cloud amounts to 800 solar masses."," With a mean molecular weight of $\mu$ = 2.3, the total mass of the cloud amounts to 800 solar masses." + The rest of the medium is filled with gas that has a uniform density of 100 cm., The rest of the medium is filled with gas that has a uniform density of 100 $\rm cm^{-3}$. +" The simulation box, a cube of size 24 pc, has outflow boundaries and is isolated in terms of gravity."," The simulation box, a cube of size 24 pc, has outflow boundaries and is isolated in terms of gravity." + We increase the resolution where needed according to a self-developed Jeans criterion., We increase the resolution where needed according to a self-developed Jeans criterion. +" The algorithm calculates the Jeans length at every grid cell, compares it against the Truelove criterion, and adds resolution when this is about to be violated."," The algorithm calculates the Jeans length at every grid cell, compares it against the Truelove criterion, and adds resolution when this is about to be violated." + The maximum grid resolution that we allow for any simulation is 8192? cells., The maximum grid resolution that we allow for any simulation is $^{3}$ cells. +" With the box size of 24 pc, the maximum spatial resolution becomes"," With the box size of 24 pc, the maximum spatial resolution becomes" +This section reviews the dynamical model and (he numerical action procedure.,This section reviews the dynamical model and the numerical action procedure. + The details of the new method of solution are described in the Appendix., The details of the new method of solution are described in the Appendix. + The starting idea is to reduce the evolution of the mass distribution to an N-body problem in which a single particle represents the mass concentrated around a galaxy or a tightly bound svstem of galaxies., The starting idea is to reduce the evolution of the mass distribution to an N-body problem in which a single particle represents the mass concentrated around a galaxy or a tightly bound system of galaxies. + This is thought to be a good approximation at low redshift because the galaxies in our neighborhood by and large are well separated relative to stancard estimates of the sizes of their dark matter halos., This is thought to be a good approximation at low redshift because the galaxies in our neighborhood by and large are well separated relative to standard estimates of the sizes of their dark matter halos. + The approximation need not be vitiated by meregimeg. because a particle may (race the effective mass center and momentum of the two svslenis before the merger as well as in the merged svstem.," The approximation need not be vitiated by merging, because a particle may trace the effective mass center and momentum of the two systems before the merger as well as in the merged system." + Further details of this line of argument mav be traced back through P09., Further details of this line of argument may be traced back through P09. + In (his analysis of the N-body problem the ire cosmologv is taken to be spatially flat with constant dark energy density., In this analysis of the N-body problem the tre cosmology is taken to be spatially flat with constant dark energy density. + The expansion parameter a(/) satisfies ;-o + - 0)NM with present value αν=1.," The expansion parameter $a(t)$ satisfies = + (1 - )H_o^2, with present value $a_o=1$." + Hubbles constant is ο. O is the density parameter. ancl nmalter pressure is ignored.," Hubble's constant is $H_o$, $\Omega$ is the density parameter, and matter pressure is ignored." + The action e + » |. summed over particles /. with fixed present positions and the initial condition," The action + + _i H_o^2 ], summed over particles $i$, with fixed present positions and the initial condition" +eficiency of the photoclectric heating.,efficiency of the photoelectric heating. + The average radiation field. y. was estimated to be above the local interstellar radiation field (ISRE). y—L.6yo. where \y refers to the sumi of the II cosmic backeround aud the spectrum given by al.(1982) and Mathisetal.(1983).," The average radiation field, $\chi$, was estimated to be above the local interstellar radiation field (ISRF), $\chi \sim 1.6 +\chi_0$ , where $\chi_0$ refers to the sum of the K cosmic background and the spectrum given by \citet{mezger82} and \citet{mathis83}." +. Tu the present work we follow the same approach as in Inealls ot al. (, In the present work we follow the same approach as in Ingalls et al. ( +2002). in the seuse of deriving theoretical relations between the FUV. absorption and the FIR euission aud then using the empirical relation between [CTI] aud FIR intensities to estimate the average efficiency of the plhotoclectric heating.,"2002), in the sense of deriving theoretical relations between the FUV absorption and the FIR emission and then using the empirical relation between [CII] and FIR intensities to estimate the average efficiency of the photoelectric heating." + Towever. our models of the FUV absorption and FIR enuüsson is significantly more detailed and realistic than in Inealls ct al. (," However, our models of the FUV absorption and FIR emission is significantly more detailed and realistic than in Ingalls et al. (" +2002).,2002). + We compute the radiative transfer on cloud models based on three dimensional ununuerical simulations of compressible maeguetoπάτοςαπαλή turbulence., We compute the radiative transfer on cloud models based on three dimensional numerical simulations of compressible magneto–hydrodynamic turbulence. + The density distribution of these turbulent flows provides a realistic model for the density iuhomogencity of iuterstellar clouds (Padoanetal.19972.b.1998.1999:Pacdoau&Nordluud 1999)..," The density distribution of these turbulent flows provides a realistic model for the density inhomogeneity of interstellar clouds \citep{pjn97,pnj97,padoan98,padoan99,Padoan+Nordlund99MHD}." + The penetration of FUV radiation iuto the cloud depends on the cloud. structure., The penetration of FUV radiation into the cloud depends on the cloud structure. + Inside au inhomogencous cloud ie dutensitv of short wavelength radiation is üiegher than inside a homogenous cloud., Inside an inhomogeneous cloud the intensity of short wavelength radiation is higher than inside a homogenous cloud. + Furthermore. density variations generate a significant scatter in 1ο relation between he local FUV. absorption and FIR enmuüsson.," Furthermore, density variations generate a significant scatter in the relation between the local FUV absorption and FIR emission." + Our model cau herefore he used to estimate what fraction of the observed scatter can be attributed to the imbomoecucous nature of he density field., Our model can therefore be used to estimate what fraction of the observed scatter can be attributed to the inhomogeneous nature of the density field. + Other Actors that could also contribute to the observed scatter. such as anisotropy du the radiation field or abundance variations. are not considered.," Other factors that could also contribute to the observed scatter, such as anisotropy in the radiation field or abundance variations, are not considered." + Other iuprovenients of our work. compared with Iugalls et al. (," Other improvements of our work, compared with Ingalls et al. (" +2002). are related to the euploved dust model.,"2002), are related to the employed dust model." + We use the three component model of Li&Draine (2001).., We use the three component model of \citet{li01}. . + The FIR iuteusities are calculated using the method of Juvelaetal.(2003) and the Cluission from trausicutly heated dust erains is included., The FIR intensities are calculated using the method of \citet{juvela03} and the emission from transiently heated dust grains is included. + The density distributions of the models are the result of three dimensional simulations of superAlfvéónuic. compressible. magnetobydrodvuamic (AMID) turbulence.," The density distributions of the models are the result of three dimensional simulations of super--Alfv\'{e}nnic, compressible, magneto–hydrodynamic (MHD) turbulence." + Three models are used. from three simulations with different values of the rimis sonic Mach umber of the flow. Ag=0.6. 2.5 ancl 10.0 in model A.B. aud C. respectively.," Three models are used, from three simulations with different values of the rms sonic Mach number of the flow, $M_{\rm S}=0.6$, 2.5 and 10.0 in model $A$ $B$ , and $C$, respectively." + The simulations are carried out on a stagecred exkl of 250° computational cells. with periodic )oundarv conditions.," The simulations are carried out on a staggered grid of $^{3}$ computational cells, with periodic boundary conditions." + Turbuleuce is set up as an initial large scale random aud solenoidal velocity field (generated in Fourier space with power oulv in the range of wavenunibers doO agalust an association.," 1986), arguing against an association." + For coniparison. the optical ho spots studied by Làhlteenmakki Vataoja (1999) have linear sizes beween 1 aud 7 kpe.," For comparison, the optical hot spots studied by Lähhteenmäkki Valtaoja (1999) have linear sizes between 1 and 7 kpc." + Alternativelv. this klot may be an H ΠΠ region. elher caused by tle interaction or iuducec wv the jyessure of the Jet impacting the interstellar medium.," Alternatively, this knot may be an H II region, either caused by the interaction or induced by the pressure of the jet impacting the interstellar medium." + Eviclence or such jet-iuduced star Oruatic31 has been fouid iu a number of systems (e.g. ¢e Young 1981: va1 Breugel οἱ al.," Evidence for such jet-induced star formation has been found in a number of systems (e.g., de Young 1981; van Breugel et al." + 1985: vat Bruegel Dey 1993: Ctaliam 1993)., 1985; van Bruegel Dey 1993; Graham 1998). + This optical knot. |Owever. was IOt cetected in our Παν I hap. giving Lyra < 3.5 x 107 erg |.," This optical knot, however, was not detected in our $\alpha$ +[N II] map, giving $_{H\alpha}$ $\le$ 3.5 $\times$ $^{38}$ erg $^{-1}$." + This is lower than the luminosities of the H II regions it he tails of the Anteniie galaxy (Mirabel. Dottori. Lutz 1992) and the Mice pair (Hibbar van Gorkom 1996). aud lower thau the luninosity of Minkowski's object.," This is lower than the luminosities of the H II regions in the tails of the Antennae galaxy (Mirabel, Dottori, Lutz 1992) and the Mice pair (Hibbard van Gorkom 1996), and lower than the luminosity of Minkowski's object." + However. this upp ]nit ls consistent witl the Ha luminosities of the H IL regious in the tails of NGC 2782 (Sini et al.," However, this upper limit is consistent with the $\alpha$ luminosities of the H II regions in the tails of NGC 2782 (Smith et al." + 1999). Arp 295. NCC 520. and NCC 3621 (Hibbard van Corkom 1996). as well as tle yossible jet-incuced H LU regious in Cen A studied by Graham (1998).," 1999), Arp 295, NGC 520, and NGC 3621 (Hibbard van Gorkom 1996), as well as the possible jet-induced H II regions in Cen A studied by Graham (1998)." + Thus. the lack of observec Ha emission associated with the northern knot in the NGC [110 tail does not rule out ou-goi18," Thus, the lack of observed $\alpha$ emission associated with the northern knot in the NGC 4410 tail does not rule out on-going" + Thus. the lack of observec Ha emission associated with the northern knot in the NGC [110 tail does not rule out ou-goi18o," Thus, the lack of observed $\alpha$ emission associated with the northern knot in the NGC 4410 tail does not rule out on-going" + Thus. the lack of observec Ha emission associated with the northern knot in the NGC [110 tail does not rule out ou-goi18oO," Thus, the lack of observed $\alpha$ emission associated with the northern knot in the NGC 4410 tail does not rule out on-going" +the lensing equation now reads To calculate spatial angular element 924x05s we use the Jaccobian equation Given Eq. A4.,"the lensing equation now reads To calculate spatial angular element $\delta\beta_{1} \times \delta\beta_{2}$ we use the Jaccobian equation Given Eq. \ref{b:x}," + we get: where function G is defined as and, we get: where function $G$ is defined as and +suppressed by a factor expA/T) whereas color-paired vd-coutributious remain to be suppressed.,suppressed by a factor $\mbox{exp}(-\Delta /T)$ whereas color-paired $ud$ -contributions remain to be suppressed. + With these findiugs we calculate the cooling history of QNS and QS., With these findings we calculate the cooling history of QCNS and QS. + The results are presented in Fie., The results are presented in Fig. + 5 for 3;=10 p=δρυ (thick lines). aud y=0. p=Spo (thin lines).," 5 for $Y_e =10^{-5}$ , $\rho =3\rho_0$ (thick lines), and $Y_e =0$, $\rho =5\rho_0$ (thin lines)." + We see that ini both cases the cooling history of QCNS aud also of QS with a tiny crust (Z5;=5-10 ?T) nicely agrees with the X-raw data., We see that in both cases the cooling history of QCNS and also of QS with a tiny crust $T_s =5\cdot 10^{-2}T$ ) nicely agrees with the X-ray data. + The cooling of QS with ueslieible crust does not agree with the data., The cooling of QS with negligible crust does not agree with the data. + We have estimated the contributions of various quark processes to the enissivitv., We have estimated the contributions of various quark processes to the emissivity. + Amoueg thei. he new decay process of the massive maxed xXhoton-eluou excitation is operating at the carly stage of the cooling and QDU. QMU aud. QB o0rocesses on red quarks determine the cooling of he 25C phase.," Among them, the new decay process of the massive mixed photon-gluon excitation is operating at the early stage of the cooling and QDU, QMU and QB processes on red quarks determine the cooling of the 2SC phase." +" We discussed the cooling history of QS and QCNS taking into account differcut yosstbilitics: 35.> Vand Y,x the normal quark phase. and various color superconducting ghases as the ""eds-pliase - 11all gaps” suggested x BailinandLove(198 1).. the CFL phase. aud he 28C phase. as sueeested im recent works (Alfordetal.1998:RappSchaferAlfordetal.1999:Rapp 1999)."," We discussed the cooling history of QS and QCNS taking into account different possibilities: $Y_e >Y_{ec}$ and $Y_e 0.5."," One may understand this result by noting that if we sum two sine waves, with phases $\phi_1 ~\rm{and}~ \phi_2$, the peak will be found in the range $\phi_1~ \rm{to}~ \phi_2$ if $|\phi_1-\phi_2|<0.5$ , and outside that range if $|\phi_1-\phi_2|>0.5$ ." + Expressed in the formu: iu which it would be measured experimentally. this foriila becomes Hn which A is the amplitude of the variation. and & is the phase of the peak.," Expressed in the form in which it would be measured experimentally, this formula becomes in which $K$ is the amplitude of the variation, and $\kappa$ is the phase of the peak." + By comparing Eqs., By comparing Eqs. + | and 5. aud separating out cocfiicicuts ofcos(250) and sin(270). we fiud that ffrom which we fiud that theasviuuetry coefficient ο is related to & by This cocticicut is shown as a function of phase iu Figure 1..," \ref{eq4} and \ref{eq5} and separating out coefficients of$\cos\left(2\pi\phi\right)$ and $\sin\left(2\pi\phi\right)$, we find that from which we find that theasymmetry coefficient $A$ is related to $\kappa$ by This coefficient is shown as a function of phase in Figure \ref{fig1}." + The cocficient is negative for &=θ to o4 aud positive for &—o4|0.5 tol., The coefficient is negative for $\kappa=0$ to $\phi_A$ and positive for $\kappa=\phi_A+0.5$ to 1. +" I£&=o,. the cocficicut Is zero. as we would expect."," If$\kappa=\phi_o$, the coefficient is zero, as we would expect." + Ife=oy. the coefficient is infinite. again as we would expect.," If $\kappa=\phi_A$, the coefficient is infinite, again as we would expect." + We also &ud from Eq., We also find from Eq. + 6 that the coupling cocfiicicut Tis eiven bx where the “coupling factor” G(r) is given by This factor is shownasa function of phase in Figure 2. , \ref{eq6} that the coupling coefficient $\Gamma$ is given by where the “coupling factor” $G\left(\kappa\right)$ is given by This factor is shownasa function of phase in Figure \ref{fig2}. . +"I£ &= o,. the factor is uuitv."," If $\kappa=\phi_o$ , the factor is unity." + Ife=oy or o4| 0.5. the factor is zero.," If $\kappa=\phi_A$ or $\phi_A+0.5$ , the factor is zero." +parameters of the lower-frequency g-modes.,parameters of the lower-frequency $g$ -modes. + In total we detected 20 periodicities with 24., In total we detected 20 periodicities with $\geq$ 4. + All pre-whitened frequencies are listed in Table 3.., All pre-whitened frequencies are listed in Table \ref{freq_7668647}. + The bottom panel of Fig., The bottom panel of Fig. + 6. still contains peaks with significant amplitude., \ref{ft_7668647} still contains peaks with significant amplitude. + However. all those peaks lie close to already—removed periodicities.," However, all those peaks lie close to already–removed periodicities." + This may indicate amplitude/phase variation of the periodicities. or that thereare a number of nearly—degenerate oscillation modes that remain unresolved in this 30-day observation.," This may indicate amplitude/phase variation of the periodicities, or that thereare a number of nearly--degenerate oscillation modes that remain unresolved in this 30-day observation." + We did not attempt to pre-whiten those residual peaks., We did not attempt to pre-whiten those residual peaks. + The mean noise level in the tinal residual amplitude spectrum is mmma., The mean noise level in the final residual amplitude spectrum is mma. + As in the case of he previous object. the amplitude spectrum of 110001893. presented in the top panel of Fig. 7..," As in the case of the previous object, the amplitude spectrum of 10001893, presented in the top panel of Fig. \ref{ft_10001893}," + is also dominated by a number of peaks in the low frequency region., is also dominated by a number of peaks in the low frequency region. + Two harmonies of the LC artefact (7! and 8! appear in the high frequency range., Two harmonics of the LC artefact $^{\rm th}$ and $^{\rm th}$ ) appear in the high frequency range. + Three remaining igh-frequency peaks lie slightly above the detection threshold., Three remaining high-frequency peaks lie slightly above the detection threshold. +" Two of them are found in a ""transition region"" and one in the p-mode region."," Two of them are found in a ""transition region"" and one in the $p$ -mode region." + The latter. if real. might be a signature of hybridity.," The latter, if real, might be a signature of hybridity." + In the low frequeney region we detected 24 peaks., In the low frequency region we detected 24 peaks. + The frequencies and amplitudes tof order of mmm) suggest that these peaks are associated with g-modes. so it is another HHer star.," The frequencies and amplitudes (of order of mma) suggest that these peaks are associated with $g$ -modes, so it is another Her star." + The list of detected peaks is given in Table 4.., The list of detected peaks is given in Table \ref{freq_10001893}. + The bottom panel of Fig., The bottom panel of Fig. + 7 displays the final residual amplitude spectrum with all 27 detected peaks removed., \ref{ft_10001893} displays the final residual amplitude spectrum with all 27 detected peaks removed. + The Yorizontal line represents a detection threshold of 4 times the mean noise level. which for this star is mmma.," The horizontal line represents a detection threshold of 4 times the mean noise level, which for this star is mma." + As is clearly seen. no peaks are left in the residuals at this level or above.," As is clearly seen, no peaks are left in the residuals at this level or above." + This denotes hat all peaks were resolved and no amplitude/phase variations on ime scale of the run duration are present in this star., This denotes that all peaks were resolved and no amplitude/phase variations on time scale of the run duration are present in this star. + This star has the smallest number of peaks in he amplitude spectrum (Fig.8}) in this sample., This star has the smallest number of peaks in the amplitude spectrum \ref{ft_8302197}) ) in this sample. + We found only 7 peaks in the low frequency region. shown in the middle panel of Fig.8.. and one at high frequency with an amplitude above the detection threshold.," We found only 7 peaks in the low frequency region, shown in the middle panel of \ref{ft_8302197}, and one at high frequency with an amplitude above the detection threshold." + All peaks are listed inTable 5.., All peaks are listed inTable \ref{freq_8302197}. . + We can easily, We can easily +al.,al. + 1998)., 1998). + Llowever. it is clear that the source was not at its highest possible luminosity demonstrating that verv-high state behaviour can also occur at low luminosities. similar o what has been found in other BIICS (e.g. Homan et al.," However, it is clear that the source was not at its highest possible luminosity demonstrating that very-high state behaviour can also occur at low luminosities, similar to what has been found in other BHCs (e.g., Homan et al." + 2001)., 2001). + We showed that only during the second: part of he observation the 5 Hz QPO and its first overtone were prominently present., We showed that only during the second part of the observation the 5 Hz QPO and its first overtone were prominently present. + During the first part only a broad noise component was present for energies below LO keV and a xoad ΟΡΟ near 3 Lz for energies above that., During the first part only a broad noise component was present for energies below 10 keV and a broad QPO near 3 Hz for energies above that. + ALL the QPOs considerably increased. in strength. with increasing photon energies. and the phase laes for all the QPOs demonstrate hat the hard. photons preceded the soft ones by as much as 1.52.5 radian.," All the QPOs considerably increased in strength with increasing photon energies, and the phase lags for all the QPOs demonstrate that the hard photons preceded the soft ones by as much as 1.5–2.5 radian." + The similarities between the 3 Hz QPO and the 5 Lz QPO (see Tab. 2)), The similarities between the 3 Hz QPO and the 5 Hz QPO (see Tab. \ref{tab:diff}) ) + strongly suggests that they are directly related to cach other., strongly suggests that they are directly related to each other. + Most. likely. the 3 Lz QPO evolved in the 5 Hz QPO. during which the frequency of the Q?O increased. the energy. dependence of the QPO became less depended on energy. and the soft phase lag dropped. from 2.5 raclian to 1 radian (between the energy ranges 2.88.7 keV and 8.7GO keV).," Most likely, the 3 Hz QPO evolved in the 5 Hz QPO, during which the frequency of the QPO increased, the energy dependence of the QPO became less depended on energy, and the soft phase lag dropped from 2.5 radian to $\sim$ 1 radian (between the energy ranges 2.8–8.7 keV and 8.7–60 keV)." + Unfortunately. this evolution occurred during an Earth occultation of the source and. a passage of the satellite through the SAA. so a detail study of this oocess could not be made.," Unfortunately, this evolution occurred during an Earth occultation of the source and a passage of the satellite through the SAA, so a detail study of this process could not be made." + From the X-ray colours. and he LUWDs and CD. it is clear that a small but. significant spectral difference is present between the two parts of the observation. with the part containing the 5 Hz QPO slightly iarder than the part with the 3 Lz QPO.," From the X-ray colours and the HIDs and CD, it is clear that a small but significant spectral difference is present between the two parts of the observation, with the part containing the 5 Hz QPO slightly harder than the part with the 3 Hz QPO." + This shows that a very slight change of the X-ray spectrum is accompanied by a significant change in the rapid X-ray variability., This shows that a very slight change of the X-ray spectrum is accompanied by a significant change in the rapid X-ray variability. + Whatever rigecred this change. it only minorlv elected. the X-ray spectrum.," Whatever triggered this change, it only minorly effected the X-ray spectrum." + This significant difference between the two parts of the observation also makes it clear that curing the VLIS of GRS 1739278. the accretion processes involved: are [ar rom stable but they are very dynamic on a time scale of ess than an hour.," This significant difference between the two parts of the observation also makes it clear that during the VHS of GRS 1739–278, the accretion processes involved are far from stable but they are very dynamic on a time scale of less than an hour." + The difference between the first. part and. seconc xwt of the observation was not reported. by. Borozdin ‘Trudolvuboy (2000). most. likely because they combinec roth parts together in their analysis without performing any ime selections.," The difference between the first part and second part of the observation was not reported by Borozdin Trudolyubov (2000), most likely because they combined both parts together in their analysis without performing any time selections." + The 5 Lz QPO parameters quoted by then are therefore contaminated by the inclusion of the first par of the data which does not contain this feature., The 5 Hz QPO parameters quoted by them are therefore contaminated by the inclusion of the first part of the data which does not contain this feature. + Therefore. we report a significantly larger strength for the 5 Llz QPO and its first overtone then Borozdin Trudolvubov (2000).," Therefore, we report a significantly larger strength for the 5 Hz QPO and its first overtone then Borozdin Trudolyubov (2000)." + ltecentlv. the phase lags of the low-frequency QPOs in BUC have received a considerable amount of attention in the literature.," Recently, the phase lags of the low-frequency QPOs in BHC have received a considerable amount of attention in the literature." + However. so [ar the phenomenology of these QPOs anc their phase lags in particular are far from understood.," However, so far the phenomenology of these QPOs and their phase lags in particular are far from understood." + The lags have now been studied. for 120 Lz QPOs in GS 1124683 Clakizawa ct al., The lags have now been studied for 1–20 Hz QPOs in GS 1124–683 (Takizawa et al. + 1997). NPL J1550564 (Wijnands. Homan. van der Wlis 1999: Cui et al.," 1997), XTE J1550--564 (Wijnands, Homan, van der Klis 1999; Cui et al." + 2000: Remillard ct al., 2000; Remillard et al. + 2001). GS. 1915|105 (1tcig et al.," 2001), GRS 1915+105 (Reig et al." + 2000: Lin et al., 2000; Lin et al. + 2000: Tomsick Ixaaret. 2001). NTE 11859|226 (Cui et al.," 2000; Tomsick Kaaret 2001), XTE J1859+226 (Cui et al." + 2000). ancl GRS 1739278 (this study).," 2000), and GRS 1739–278 (this study)." + The phase lags show a large variety of behaviour., The phase lags show a large variety of behaviour. +" The cillerent xwmonics can have all the same sign for the lags (e.g.. Cis 1124683: GRS 17392758: although the sign can be both »ositive or negative) or can have dillerent signs (the so-called. ""alternating phase lags’: c.g. NTE J1550564: GRS 1915|105)."," The different harmonics can have all the same sign for the lags (e.g., GS 1124–683; GRS 1739–278; although the sign can be both positive or negative) or can have different signs (the so-called 'alternating phase lags'; e.g., XTE J1550–564; GRS 1915+105)." + Ehe situation is made even more complex by the very complex evolution of the phase lags in several sources (οσι ATE J1550-564: CIUS 1915|105).," The situation is made even more complex by the very complex evolution of the phase lags in several sources (e.g., XTE J1550-564; GRS 1915+105)." + Several theoretical studies have tried. to. address the complicated phase lags behaviour of the low-frequency QPOs in BUCs (e.g. Nobili et al.," Several theoretical studies have tried to address the complicated phase lags behaviour of the low-frequency QPOs in BHCs (e.g., Nobili et al." + 2000: Bottteher Liang2000: Bottteher 2001). but those studies have focussed on the QPOs in CIUS 1915|105.," 2000; Bötttcher Liang; Bötttcher 2001), but those studies have focussed on the QPOs in GRS 1915+105." + Lt is unclear to what extent the overall very complex behaviour of this source is influencing its QPO behaviour., It is unclear to what extent the overall very complex behaviour of this source is influencing its QPO behaviour. + Extrapolation from models. for the behaviour (Le. the QPOs and their phase lag behaviour) of GRS 1915|105 to other DIICS might turn out to be clillicult and subject to errors.," Extrapolation from models for the behaviour (i.e., the QPOs and their phase lag behaviour) of GRS 1915+105 to other BHCs might turn out to be difficult and subject to errors." + At the moment. there is no model available which can explain the observed phase lags of the QPOs. the evolution ofthose lags for the individual sources. and the dillerences between QPO behaviour in the dillerent BCs.," At the moment, there is no model available which can explain the observed phase lags of the QPOs, the evolution of those lags for the individual sources, and the differences between QPO behaviour in the different BHCs." + However. it is clear that a Comptonizing medium around the black-hole (thought to produce the power-law tail in the spectrum) cannot explain the lags observed. for the QPOs around 6 Hz. either due to Compton up- or down-scattering.," However, it is clear that a Comptonizing medium around the black-hole (thought to produce the power-law tail in the spectrum) cannot explain the lags observed for the QPOs around 6 Hz, either due to Compton up- or down-scattering." + ltecently. in several BUC transicnts QPOs above 100 llz were found (ο... Remillard et al.," Recently, in several BHC transients QPOs above 100 Hz were found (e.g., Remillard et al." + 19992.b: Cui ct al.," 1999a,b; Cui et al." + 2000: LLoman et al., 2000; Homan et al. + 2001: Strohmaver 2001)., 2001; Strohmayer 2001). + Often. although not always. these QPOs are founcl simultaneously with low-[requeney QPOs («10 Lz). with similar characteristics as the 5 Uz ΟΡΟ in GRS 1739278.," Often, although not always, these QPOs are found simultaneously with low-frequency QPOs $<$ 10 Hz), with similar characteristics as the 5 Hz QPO in GRS 1739–278." + Therefore. similar high-frequency QPOs might also be present in CRS 1739278.," Therefore, similar high-frequency QPOs might also be present in GRS 1739--278." + However. a search for such QPOs did not result in a," However, a search for such QPOs did not result in a" +and p. the radial Quid displacement and Eulerian pressure perturbation. respectively. may then be written in the form (2) where fo—cos@ is the normalized. latitucinal distance from the equatorial plane. w is the pulsation frecqucney in the co-rotating reference frame. ancl Qj(jp) is a Lough function (7:2)..,"and $p'$, the radial fluid displacement and Eulerian pressure perturbation, respectively, may then be written in the form \cite{LeeSai1997} + where $\mu \equiv \cos \theta$ is the normalized latitudinal distance from the equatorial plane, $\omega$ is the pulsation frequency in the co-rotating reference frame, and $\hough(\mu;\nu)$ is a Hough function \cite{Bil1996,LeeSai1997}." + These Lough functions are the ceigensolutions of Laplace's tidal equation (?).. and form a one-paramoeter family in pj=20/w. where Q=[0] is the angular frequency of rotation.," These Hough functions are the eigensolutions of Laplace's tidal equation \cite{Lon1968}, , and form a one-parameter family in $\nu \equiv 2\Omega/\omega$, where $\Omega +\equiv |\bOmega|$ is the angular frequency of rotation." +" The integer indices / and m. with /z0 and [m]xf. correspond to the harmonic degree and azimuthal order. respectively. of the associated Legendre polynomials 27""G4) (7) to which. the Lough functions reduce in the non-rotating limit. so that ΟΕ(0)=PI""(qn)."," The integer indices $l$ and $m$, with $l\ge0$ and $|m|\le l$, correspond to the harmonic degree and azimuthal order, respectively, of the associated Legendre polynomials $\legen(\mu)$ \cite{AbrSte1964} to which the Hough functions reduce in the non-rotating limit, so that $\hough(\mu; +0) \equiv \legen(\mu)$." + This indexing scheme. based on the one adopted by Lee Saio (2).. is less general than that of Lee Salo (2). in that it does not encompass the Hough functions corresponding to Rossby and oscillatory convective modes (which do not have non-rotating counterparts): however. such modes. are not considered herein. and the current scheme is sullicient.," This indexing scheme, based on the one adopted by Lee Saio \shortcite{LeeSai1990}, is less general than that of Lee Saio \shortcite{LeeSai1997}, in that it does not encompass the Hough functions corresponding to Rossby and oscillatory convective modes (which do not have non-rotating counterparts); however, such modes are not considered herein, and the current scheme is sufficient." +" Note that o is considered to be positive throughout the following iscussion. and. therefore. prograde and. retrograde modes ""orrespond to negative and positive values of m. respectively."," Note that $\omega$ is considered to be positive throughout the following discussion, and, therefore, prograde and retrograde modes correspond to negative and positive values of $m$, respectively." +" The radial dependence of the solutions (1- 2)) is escribed by the eigenfunctions. £,(r) and pr). which are governed by a pair of coupled. first-order differential equations."," The radial dependence of the solutions \ref{eqn:solution1}- \ref{eqn:solution2}) ) is described by the eigenfunctions $\xi_r(r)$ and $p'(r)$, which are governed by a pair of coupled first-order differential equations." + In order to facilitate subsequent manipulation. it is useful to write these equations in the form and where p. c. g and N are the local equilibrium values of the density. acliabatic sound. speed. gravitational acceleration and [frequeney. respectively.," In order to facilitate subsequent manipulation, it is useful to write these equations in the form and where $\rho$, $\sound$, $g$ and $\brunt$ are the local equilibrium values of the density, adiabatic sound speed, gravitational acceleration and frequency, respectively." + Note that € and p are now taken to be functions of r alone in both these ancl subsequent equations. unless explicitly stated.," Note that $\xi_{r}$ and $p'$ are now taken to be functions of $r$ alone in both these and subsequent equations, unless explicitly stated." +" The quantity Ap, appearing in equation (3)). which arises as separation constant when solutions of the form are sought. is the eigenvalue of Laplaces tidal equation corresponding to the appropriate Hough function Oy""nn(ji9)"," The quantity $\llm$ appearing in equation \ref{eqn:pulsation1}) ), which arises as separation constant when solutions of the form are sought, is the eigenvalue of Laplace's tidal equation corresponding to the appropriate Hough function $\hough(\mu;\nu)$." + In the limit 7=0. this eigenvalue is equal to fff|. 1). and equations (3-. 4)) are then identical to those appropriate for a non-rotating star(c.g... Unno 11989. $115.1).," In the limit $\nu = 0$, this eigenvalue is equal to $l(l+1)$ , and equations \ref{eqn:pulsation1}- \ref{eqn:pulsation2}) ) are then identical to those appropriate for a non-rotating star, Unno 1989, 15.1)." + The utility of the traditional approximation thus lies in the fact that much of the formalism of the non- case nav also be applied to rotating stars with the simple replacement of /(/|1) by Ap. a result first found by Lee Sato (?)..," The utility of the traditional approximation thus lies in the fact that much of the formalism of the non-rotating case may also be applied to rotating stars with the simple replacement of $l(l+1)$ by $\llm$, a result first found by Lee Saio \shortcite{LeeSai1987a}." + Global solution of cquations (3- 4)) must typically be approached. numerically: however. an cxamination of the local character of the solutions sullices in the present qualitative context.," Global solution of equations \ref{eqn:pulsation1}- \ref{eqn:pulsation2}) ) must typically be approached numerically; however, an examination of the local character of the solutions suffices in the present qualitative context." + This character is governed by the dispersion relation applicable to the equations. discussed in the following section.," This character is governed by the dispersion relation applicable to the equations, discussed in the following section." + Jo derive a local dispersion. relation for the pulsation equations (3- 4)). it is useful first to place the equations in a canonical form similar to that introduced. by Osaki (?) for thenon-rotating case.," To derive a local dispersion relation for the pulsation equations \ref{eqn:pulsation1}- \ref{eqn:pulsation2}) ), it is useful first to place the equations in a canonical form similar to that introduced by Osaki \shortcite{Osa1975} for thenon-rotating case." +" By defining the two new clecnfunetions. the left-hand sides of both pulsation equations may be written as a single derivative. and the canonical form is found as where Note that f(r) is always positive. so that the original cigenfunctions £, and p everywhere share the same sign as € and. 7g. respectively."," By defining the two new eigenfunctions, the left-hand sides of both pulsation equations may be written as a single derivative, and the canonical form is found as where Note that $h(r)$ is always positive, so that the original eigenfunctions $\xi_{r}$ and $p'$ everywhere share the same sign as $\tilde{\xi}$ and $\tilde{\eta}$, respectively." + Qualitative solution of these canonical equations is accomplished using the same method as Osaki (2).. namely. bv assuming that the cocllicients on the right-hand. sides are independent. of r.," Qualitative solution of these canonical equations is accomplished using the same method as Osaki \shortcite{Osa1975}, namely, by assuming that the coefficients on the right-hand sides are independent of $r$." + Such an assumption will be valid. if the characteristic variationscale of the solutions is much smaller than that of the coellicients., Such an assumption will be valid if the characteristic variationscale of the solutions is much smaller than that of the coefficients. + Then. local solutions of the form lead to a dispersion relation for the radial wavenumber Ay. ὃν introducing the ellective transverse wavenumber Ay). defined by Bilelsten as the dispersion relation may be re-written in themore useful form," Then, local solutions of the form lead to a dispersion relation for the radial wavenumber $k_{r}$ , By introducing the effective transverse wavenumber $\ktr$, defined by Bildsten \\shortcite{Bil1996} as the dispersion relation may be re-written in themore useful form" +with much better spatial resolution (about 1-2 aresec) by Ikastuer et al. (,with much better spatial resolution (about 1-2 arcsec) by Kastner et al. ( +1991) and Latter et al. (,1994) and Latter et al. ( +01995).,1995). + The excitation iiechauisumi of the vibrationally excited Hines in this. ax iu other Όλοι is still uncertain.," The excitation mechanism of the vibrationally excited lines in this, as in other PNe, is still uncertain." +" Zuckerman Gatley (1988) discuss the possibility tha they form, iu a shock driven by the fast wind emütted bv the ceutral star.", Zuckerman Gatley (1988) discuss the possibility that they form in a shock driven by the fast wind emitted by the central star. + Iastuer et al. (, Kastner et al. ( +1991) surveyed. a sample of bipolar planetary nebulae Gucliding NGC 2316): they conclude that the cecluission very likely originates in thoernallv excited (possibly shocked) molecular gas.,1994) surveyed a sample of bipolar planetary nebulae (including NGC 2346); they conclude that the emission very likely originates in thermally excited (possibly shocked) molecular gas. + Receuth. Natta Ilolleubach (1998: hereafter NII98) have computed theoretical models of the evolution of PN shells aud predicted. alone others. the iutensitv of the most οπου] observed vvibrationallv excited lines (aamely. the 1-08(1) at 2.12 aud the 2-18(1) at 2.25;00)).," Recently, Natta Hollenbach (1998; hereafter NH98) have computed theoretical models of the evolution of PN shells and predicted, among others, the intensity of the most commonly observed vibrationally excited lines (namely, the 1-0S(1) at 2.12 and the 2-1S(1) at )." + They cousider the emission of the photodissociation region (PDR) formed by the UV. photons ciuitted by the ceutral star iupiueiue on the shell. including in the calculations time-dependent cchemuistry aud the effects of the soft N-rav radiation Clittec bv the central star. which are important iu1 SOTIECOS ike NGC 2316 where 210° K. NII98 compute also the cluission of the shocked gas at the interface )otwoeen the shell and the wind ejected bv the ceutral star in its previous red eint phase.," They consider the emission of the photodissociation region (PDR) formed by the UV photons emitted by the central star impinging on the shell, including in the calculations time-dependent chemistry and the effects of the soft X-ray radiation emitted by the central star, which are important in sources like NGC 2346 where $\simgreat 10^5$ K. NH98 compute also the emission of the shocked gas at the interface between the shell and the wind ejected by the central star in its previous red giant phase." +" They poiut out hat yoth anechanisius (PDR and shocks) can produce lunes of simular intensity. with reasonable values of the model araleters,"," They point out that both mechanisms (PDR and shocks) can produce lines of similar intensity, with reasonable values of the model parameters." + The PN properties that determine the intensity of the lines are very differeut in the two cases., The PN properties that determine the intensity of the lines are very different in the two cases. + As discussed iu NII9S. if the cussion is produced in the wari. neutral PDR eas. the line inteusitv epends mostly on the stellar radiation feld which reaches the shell aud. to a lower degree. on the deuxitv of the neutral gas itself.," As discussed in NH98, if the emission is produced in the warm, neutral PDR gas, the line intensity depends mostly on the stellar radiation field which reaches the shell and, to a lower degree, on the density of the neutral gas itself." + If the cCluission is produced iu the shocked eas. then the line intensity does not depend directly ou the properties of the central star or of the PN shell. but oulv on the shock velocity and ou the rate of umass-loss of the precursor red-ejut.," If the emission is produced in the shocked gas, then the line intensity does not depend directly on the properties of the central star or of the PN shell, but only on the shock velocity and on the rate of mass-loss of the precursor red-giant." + It is therefore clear hat. before attributing any diagnostic capability to the lines. we need to understand which of the possible excitation mechanisms dominate the PN emission.," It is therefore clear that, before attributing any diagnostic capability to the lines, we need to understand which of the possible excitation mechanisms dominate the PN emission." + This paper is a first attempt to understaud the ecluission of a welbstudied PN in a quantitative way. ic. by comparing the observations to detailed models of PDR and shock enmüssiou. such as those discussed. in NII9S.," This paper is a first attempt to understand the emission of a well-studied PN in a quantitative way, i.e., by comparing the observations to detailed models of PDR and shock emission, such as those discussed in NH98." + To this purpose. we have collected uew ucar-IR broad aud narrow-band tages of NGC 2316 as well as Iv band spectra with resolution 1000.," To this purpose, we have collected new near-IR broad and narrow-band images of NGC 2346 as well as K band spectra with resolution $\sim$ 1000." + These observations are described in 82., These observations are described in 2. + The results are described iu 823 aud compared to the predictions of PDR and shock models iu Sl., The results are described in 3 and compared to the predictions of PDR and shock models in 4. + A discussion of the results follows in 85: 86 sunuuarizes the main conchisions of the paper., A discussion of the results follows in 5; 6 summarizes the main conclusions of the paper. + NGC 2316 was observed during two observing ruus iu Jaunary 1996 using ARNICAÀ (ARcetri New Tatrared CAmera) mounted on the L5 telescope., NGC 2346 was observed during two observing runs in January 1996 using ARNICA (ARcetri Near Infrared CAmera) mounted on the 1.5m telescope. + ARNICA is equipped with a 256x256 NICAIOS3 array. the pixel size with the optics used at TIRGO is 0.96”: for a colplete description of iustrmucut performances. see Lisi ct al. (1996))," ARNICA is equipped with a 256x256 NICMOS3 array, the pixel size with the optics used at TIRGO is $0.96^{\prime\prime}$; for a complete description of instrument performances, see Lisi et al. \cite{Lea96}) )" + aud IIunt ct al. (1996))., and Hunt et al. \cite{Hea96}) ). + Buages were obtained iu the IX broad-band filter (centered at 2.2 μιά)} aud in a narrow-band filter ceutered on the 2.12 11-081) line (AASA~1 Vauzi ct al.," Images were obtained in the K broad-band filter (centered at 2.2 ) and in a narrow-band filter centered on the 2.12 1-0S(1) line $\Delta\lambda/\lambda\sim 1\%$, Vanzi et al." + 199s).," \cite{VGCT97} + )." + The seeing was approximately αμα the observed field was ~2<2) covering all the nebula.," The seeing was approximately and the observed field was $\sim 2^\prime\times 2^\prime$, covering all the nebula." + Data reduction was carried out usine the aud ARNICA (unt ct al., Data reduction was carried out using the and ARNICA (Hunt et al. + 1991) software packages., 1994) software packages. + Photometric calibration in the I& baud was performed by observing the photometric standards of the FSLI group from the list of Wut et al. (1997))., Photometric calibration in the K band was performed by observing the photometric standards of the FS14 group from the list of Hunt et al. \cite{Hea97}) ). + The quality of the night was rather poor. and the calibration accuracy is estimated to be ~I5.," The quality of the night was rather poor, and the calibration accuracy is estimated to be $\sim 15\%$." + The image in the LL-OS(1) line has been calibrated using the 5 brightest (unsaturated) stairs in the ARNICA images. under the asstuuption that for cach star the fiux density measured in the line filter was equal to the flux density nieasured iu the Ix band.," The image in the 1-0S(1) line has been calibrated using the 5 brightest (unsaturated) stars in the ARNICA images, under the assumption that for each star the flux density measured in the line filter was equal to the flux density measured in the K band." + Iuteerated line fluxes ou the nebula were then obtained multiplving the fiux density by the baudwith of the narrowband filter (Vanzi et al., Integrated line fluxes on the nebula were then obtained multiplying the flux density by the bandwith of the narrowband filter (Vanzi et al. + 1998)., 1998). + The accuracy ds I5.., The accuracy is $\sim$. + IK (2.2 gnu) baud spectra of NCC 2316 were «tained using the LouCGSp (Loneslit Cornererat Spectrometer) spectrometer mounted. at the Casscerain focus on the TIRGO telescope., K (2.2 ) band spectra of NGC 2346 were obtained using the LonGSp (Longslit Gornergrat Spectrometer) spectrometer mounted at the Cassegrain focus on the TIRGO telescope. + The spectrometer is equipped with cooled reflective optics and erating in Littrow configuration., The spectrometer is equipped with cooled reflective optics and grating in Littrow configuration. + The detector is a 2564256 cneinecring evade NICAMOS3 array (for detector performances see Vauzi ct al. 1995))., The detector is a $\times$ 256 engineering grade NICMOS3 array (for detector performances see Vanzi et al. \cite{VMG95}) ). +" The pixel sizes are 11.5 (Ust order) aud W773 iun the dispersion and «lit directions. respectively,"," The pixel sizes are 11.5 (first order) and 73 in the dispersion and slit directions, respectively." + LONGSP operates in the range 0.9-2.5 aachieving a spectral resolution at first order of, LONGSP operates in the range 0.9-2.5 achieving a spectral resolution at first order of +(2010).,. +. However. by combining it with a_ statistically rigorous bootstrapping method and the high cadence observations afforded by STEREO//EUVI we can minimise the errors typically encountered with the analysis of CBFs.," However, by combining it with a statistically rigorous bootstrapping method and the high cadence observations afforded by /EUVI we can minimise the errors typically encountered with the analysis of CBFs." + The similarity in. derived velocity between this work and previous investigations Is interesting given that most previous works have used point-and-click techniques applied to running-difference images., The similarity in derived velocity between this work and previous investigations is interesting given that most previous works have used point-and-click techniques applied to running-difference images. + These studies identify the forward edge of the CBF at a given time. which ts then used to determine the kinematics of the disturbance as a whole.," These studies identify the forward edge of the CBF at a given time, which is then used to determine the kinematics of the disturbance as a whole." + The analyses performed using such techniques have mainly returned kinematics that suggest a zero acceleration (1.e.. constant velocity) interpretation of the CBF phenomenon.," The analyses performed using such techniques have mainly returned kinematics that suggest a zero acceleration (i.e., constant velocity) interpretation of the CBF phenomenon." + In, In +period to a negligible value.,period to a negligible value. + Also. as cliscussed by HRHC. some of the data in SMALV were outside the dyuamical boundaries of the ONC. possibly inclucing stars of dillerent ages than the ONC.," Also, as discussed by HRHC, some of the data in SMMV were outside the dynamical boundaries of the ONC, possibly including stars of different ages than the ONC." + The HRHC observations were mace contiunuotsly within each observiug seasou (weather permitting). which permits the reliable detection of periods louger thar 8 days.," The HRHC observations were made continuously within each observing season (weather permitting), which permits the reliable detection of periods longer than 8 days." + At periods below this value. there is significant overlap between tliese «ata aud SMALV.," At periods below this value, there is significant overlap between these data and SMMV." + In the overlap. there is good agreement between the two sets of data.," In the overlap, there is good agreement between the two sets of data." + For comparison. we also corsidered several analytic initial period cistributious: a flat distribution from 1 to 12 days. a delta fuiction at 8 days. aud a Gaussian curve centered on 8 days with a standard deviation of E days. truucated at 1 aud 15 days.," For comparison, we also considered several analytic initial period distributions: a flat distribution from 1 to 12 days, a delta function at 8 days, and a Gaussian curve centered on 8 days with a standard deviation of 4 days, truncated at 1 and 15 days." + Masses aud ages for the HRHC stars were obtained rom Hillenbrand (1997). which were interpolated fromm tie stellar evolutionary racks of D'Antoia& Mazzitelli (1991).," Masses and ages for the HRHC stars were obtained from Hillenbrand (1997), which were interpolated from the stellar evolutionary tracks of D'Antona Mazzitelli (1994)." + This gave us a sample of 81 stars 1 (he mass ange., This gave us a sample of 81 stars in the mass range. +. For stars wiere ages were not available. the mean age of the cluster. 1 Myr. was used.," For stars where ages were not available, the mean age of the cluster, 1 Myr, was used." + Our calculaious are not seusitive to the minor age spread iu the ONC. aud runuiug our models with all stars aving an age of 1 Myr did not siguificantly change the results.," Our calculations are not sensitive to the minor age spread in the ONC, and running our models with all stars having an age of 1 Myr did not significantly change the results." + To investigate he effect o£ disk-lockii& with our mocels. we used a variety of values [or 74.4 aud for the distributi Jes. frugis).," To investigate the effect of disk-locking with our models, we used a variety of values for $\tau_{disk}$ and for the distribution of of disk lifetimes, $f(\tau_{disk})$." + First. we used a model in wlich there were no disks. aud models in w ss with the same τικ.," First, we used a model in which there were no disks, and models in which all stars had disks with the same $\tau_{disk}$." + Then we unplemeuted a model for Frais) motivated by 'ecent. Obseryis of young clusters., Then we implemented a model for $f(\tau_{disk})$ motivated by recent observations of young clusters. + Haisch. Lada Laca (2001) reported results of JHIXL photouetry of cl eine ni mean age 'om 0.5-5 Myr.," Haisch, Lada Lada (2001) reported results of JHKL photometry of clusters ranging in mean age from $\sim$ 0.5–5 Myr." + They exaimiued the fraction of stars in eacl1 cluster witl Tared excess iudiceative of cicrumstella: disks., They examined the fraction of stars in each cluster with the infrared excess indicative of cicrumstellar disks. +" The initial disk fraction is very hie decreases linearly with age to au extrayolated maximum disk lifetime of 7,4, 6 Myr.", The initial disk fraction is very high $\ge$ ) and decreases linearly with age to an extrapolated maximum disk lifetime of $\tau_{max} \sim$ 6 Myr. + Their 'esults imply that a] stars are born wih accretion disks around them and that t 1 of disk lifetimes is flat in this range of 0-6 lvr., Their results imply that all stars are born with accretion disks around them and that the spectrum of disk lifetimes is flat in this range of 0–6 Myr. + With the initial conditions of mass. age. and initial perio. the rotation of an observed star can be computed at any futi Or a given aid qj;," With the initial conditions of mass, age, and initial period, the rotation of an observed star can be computed at any future time for a given and $\tau_{disk}$." + At the age of the Pleiades. the projected period o “the ONC star ls Converted to an equatorial rotation velocity aud then multiplied by alaudour sini. generated by p'oduciug a raudon number 0«p<1 and ¢alculating UL? ," At the age of the Pleiades, the projected period of the ONC star is converted to an equatorial rotation velocity and then multiplied by a random $\sin i$ , generated by producing a random number $00.274, the core is dynamically unstable to the growth of non-axisymmetric structure (?????????)..","If the first core is rotating rapidly enough that its own value of $\beta > 0.274$, the core is dynamically unstable to the growth of non-axisymmetric structure \citep{Bate1998,Machidaetal2005,SaiTom2006,SaiTomMat2008,Bate2010, MacInuMat2010,Tomidaetal2010b,SaiTom2011, MacMat2011}." +" For the particular initial conditions used here, this occurs for the G=0.001—0.01 cases (see Figs."," For the particular initial conditions used here, this occurs for the $\beta=0.001-0.01$ cases (see Figs." + 2 and 3)), \ref{images_D_barotropic} and \ref{images_xyD}) ). +" The torus that forms in the 6=0.04 calculations is also dynamically unstable, but this case is somewhat different and will be discussed further below."," The torus that forms in the $\beta=0.04$ calculations is also dynamically unstable, but this case is somewhat different and will be discussed further below." +" In each of the 6=0.001—0.005 cases, the first core begins as an axisymmetric flattened pre-stellar disc, but after several rotations it develops a bar-mode (e.g. the second panel of the third row in each of Figures 2 and 3))."," In each of the $\beta=0.001-0.005$ cases, the first core begins as an axisymmetric flattened pre-stellar disc, but after several rotations it develops a bar-mode (e.g. the second panel of the third row in each of Figures \ref{images_D_barotropic} and \ref{images_xyD}) )." + The ends of the bar subsequently lag behind and the bar winds up to produce a spiral structure., The ends of the bar subsequently lag behind and the bar winds up to produce a spiral structure. +" Spiral structure removes angular momentum from the inner parts of the first core via gravitational torques (?),, the effect of which can be seen in the evolution of density and temperature in Fig. 5.."," Spiral structure removes angular momentum from the inner parts of the first core via gravitational torques \citep{Bate1998}, the effect of which can be seen in the evolution of density and temperature in Fig. \ref{first_core_time}." +" For example, in the 9=0.005 case, the slow increases in central density and temperature after first core formation suddenly accelerate with the onset of the spiral structure."," For example, in the $\beta=0.005$ case, the slow increases in central density and temperature after first core formation suddenly accelerate with the onset of the spiral structure." + This occurs at about 1300 yrs before stellar core formation for the radiation hydrodynamical calculation with 86=0.005 and about 600 yrs before stellarcore formation for the barotropic calculation., This occurs at about 1300 yrs before stellar core formation for the radiation hydrodynamical calculation with $\beta=0.005$ and about 600 yrs before stellarcore formation for the barotropic calculation. + Similar accelerations are seen for both the 6=0.01 cases and also for the barotropic 6=0.001 case., Similar accelerations are seen for both the $\beta=0.01$ cases and also for the barotropic $\beta=0.001$ case. +" Thus, the removal of angular momentum from the central regions of the core substantially accelerates the evolution of the first core towards the second collapse, which would take much longer to reach without the angular momentum redistribution ddue to accretion and radiative cooling alone)."," Thus, the removal of angular momentum from the central regions of the core substantially accelerates the evolution of the first core towards the second collapse, which would take much longer to reach without the angular momentum redistribution due to accretion and radiative cooling alone)." + In Figs., In Figs. +" 2 and 3,, the development of the spiral structure and the subsequent concentration of material towards the centre of the core due to the redistribution of angular momentum is clearly visible for the barotropic cases with —0.001—0.01 and the radiation hydrodynamical cases with 6=0.005—0.01."," \ref{images_D_barotropic} and \ref{images_xyD}, the development of the spiral structure and the subsequent concentration of material towards the centre of the core due to the redistribution of angular momentum is clearly visible for the barotropic cases with $\beta=0.001-0.01$ and the radiation hydrodynamical cases with $\beta=0.005-0.01$." + In Fig., In Fig. +" 8 we also provide the density-weighted temperature, for comparison with the column density in Fig. 3.."," \ref{images_xyT} we also provide the density-weighted temperature, for comparison with the column density in Fig. \ref{images_xyD}." + As gas is concentrated to the centre of the cores its temperature greatly increases., As gas is concentrated to the centre of the cores its temperature greatly increases. + It is also apparent that the spiral shocks in the discs are hotter than the rest of the discs., It is also apparent that the spiral shocks in the discs are hotter than the rest of the discs. +" The barotropic and radiation hydrodynamical evolutions are qualitatively similar in that both display the progression from an axisymmetric core, to bar instability, to a torus as the initial rotation rate of the molecular cloud core is increased."," The barotropic and radiation hydrodynamical evolutions are qualitatively similar in that both display the progression from an axisymmetric core, to bar instability, to a torus as the initial rotation rate of the molecular cloud core is increased." +" However, radiation hydrodynamical calculations are more resistant to the bar instability than the barotropic calculations."," However, radiation hydrodynamical calculations are more resistant to the bar instability than the barotropic calculations." + This is directly attributable to the difference in the thermal evolution of the gas that was discussed above., This is directly attributable to the difference in the thermal evolution of the gas that was discussed above. +" Since the gas is somewhat hotter in the radiation hydrodynamical calculations, the first core is larger (more ‘puffy’) and has a lower value of £ for a given 8 value of the initial molecular cloud core."," Since the gas is somewhat hotter in the radiation hydrodynamical calculations, the first core is larger (more `puffy') and has a lower value of $\beta$ for a given $\beta$ value of the initial molecular cloud core." + ? also noticed that the first cores in their radiation magnetohydrodynamical calculations had higher entropies and larger sizes than when they used a barotropic equation of state., \cite{Tomidaetal2010a} also noticed that the first cores in their radiation magnetohydrodynamical calculations had higher entropies and larger sizes than when they used a barotropic equation of state. +" It should be noted, however, that with radiation hydrodynamics there is no one-to-one relation between temperature and density (seealso???).."," It should be noted, however, that with radiation hydrodynamics there is no one-to-one relation between temperature and density \citep[see also][]{Bossetal2000,WhiBat2006,Tomidaetal2010a}." +" This is illustrated in Fig. 7,,"," This is illustrated in Fig. \ref{temp_vs_density_snapshot}, ," + where we plot temperature versus density from various snapshots from the 8=0.005 calculation and compare this to both the run, where we plot temperature versus density from various snapshots from the $\beta=0.005$ calculation and compare this to both the run +With the addition of the NLTE corrections. we see in Table that there is. for the most part. an increase in Τω from the LTE Ts of ?.. for both cases of Sy.,"With the addition of the NLTE corrections, we see in Table \ref{Table2} that there is, for the most part, an increase in $T_{\rm eff}$ from the LTE $T_{\rm eff}$ 's of \citet{Hosfordetal2009}, , for both cases of $\rm S_{H}$." + The only exception is CD-33°1173 in the Sy = 0 case. for which there is a 93 K decrease.," The only exception is $-$ $^{\circ}$ 1173 in the $\rm S_{H}$ = 0 case, for which there is a 93 K decrease." + We return. to this star below., We return to this star below. + The 74r corrections we have derived average 59 K for Sy = 0 and 73 K for Su = | (treating LP815—43 as one datum. not two).," The $T_{\rm eff}$ corrections we have derived average 59 K for $\rm S_{H}$ = 0 and 73 K for $\rm S_{H}$ = 1 (treating $-$ 43 as one datum, not two)." + For Sy = 0 the temperature corrections tend to merease at cooler temperatures. whilst the tendency is weaker or opposite for Sy =]. re. corrections increase at higher temperatures (obviously the gravity and metallicity of the stars also affects their NLTE corrections. but nevertheless we find it intsructive to consider temperature as one useful discriminating variable).," For $\rm S_{H}$ = 0 the temperature corrections tend to increase at cooler temperatures, whilst the tendency is weaker or opposite for $\rm S_{H}$ =1, i.e. corrections increase at higher temperatures (obviously the gravity and metallicity of the stars also affects their NLTE corrections, but nevertheless we find it intsructive to consider temperature as one useful discriminating variable)." +" This gives rise to a change in the difference ATyys,-0—ATars,i with temperature. with this quantity being negative for the two hottest stars. CD-3371173 and LP815—43."," This gives rise to a change in the difference $\Delta T_{\rm eff, S_{H} = 0} - \Delta T_{\rm eff, S_{H} = 1}$ with temperature, with this quantity being negative for the two hottest stars, $-$ $^{\circ}$ 1173 and $-$ 43." + The switch over from Sy = 0 having the larger correction to Sy = 1 having the larger correction is at aroud τω= 6200 K. Further testing has shown that this is not a random error and is clearly something to investigate further in the future., The switch over from $\rm S_{H}$ = 0 having the larger correction to $\rm S_{H}$ = 1 having the larger correction is at around $T_{\rm eff} \approx$ 6200 K. Further testing has shown that this is not a random error and is clearly something to investigate further in the future. + This 1s further shown by Fig., This is further shown by Fig. + 8 where the abundance correction versus y for the stars CD-33°1173 and LP815—43 (SGB) are plotted., \ref{Fig:CD/LP-chiAbund} where the abundance correction versus $\chi$ for the stars $-$ $^{\circ}$ 1173 and $-$ 43 (SGB) are plotted. + It is seen that for 15-43 (SGB). increasing Sy has a larger effect on the lower excitation lines thai for higher ones.," It is seen that for $-$ 43 (SGB), increasing $\rm S_{H}$ has a larger effect on the lower excitation lines than for higher ones." + This has induced a trend of abundance with y larger than that of the Sy = 0 case., This has induced a trend of abundance with $\chi$ larger than that of the $\rm S_{H}$ = 0 case. + This iu turn leads to a larger temperature correction for Sy = | than for Sy = 0., This in turn leads to a larger temperature correction for $\rm S_{H}$ = 1 than for $\rm S_{H}$ = 0. + The reason for this effect is still uncertain., The reason for this effect is still uncertain. + To investigate this behaviour further. the test of Increasing the Sy value of the upper levels. as done on HD140283 in Sect 4..," To investigate this behaviour further, the test of increasing the $\rm S_{H}$ value of the upper levels, as done on HD140283 in Sect 4.," + has also been performed on LP815—43 for the MS and SGB parameters., has also been performed on $-$ 43 for the MS and SGB parameters. + This has shown that the effect of collisions with neutral H are indeed larger for the lower levels of the atom. and that this effect is larger for LP815—43 (MS). which is the hottest star.," This has shown that the effect of collisions with neutral H are indeed larger for the lower levels of the atom, and that this effect is larger for $-$ 43 (MS), which is the hottest star." +" This indicates that there is a temperature dependence. ie. the difference between the mean difference (AA(Fe)s,422 — AA(Fe)s,_)) (where Sy=1+2 indicates the scenario of having Sy=2 for the top 0.5 eV worth of levels) for the levels with -2 eV and those with »>2 eV is greater for the hotter star. LP815—43 (MS)."," This indicates that there is a temperature dependence, i.e. the difference between the mean difference $\Delta A(\rm Fe)_{S_H=1+2}$ – $\Delta A(\rm Fe)_{S_{H}=1}$ ) (where $\rm S_{H}=1+2$ indicates the scenario of having $\rm S_{H} = 2$ for the top 0.5 eV worth of levels) for the levels with $\chi < 2$ eV and those with $\chi > 2$ eV is greater for the hotter star, $-$ 43 (MS)." + However. when performing this test on LP815—43 (SGB). which has a similar log e to HDI40283 whilst still being hotter. the effect is not as great as for HD140283.," However, when performing this test on $-$ 43 (SGB), which has a similar log $g$ to HD140283 whilst still being hotter, the effect is not as great as for HD140283." + This shows that there ts some gravity dependence on the neutral H collisions along with the temperature dependence re. the gravity indirectly affects the collisional rates. by impacting on the number density of hydrogen atoms at a given optical depth.," This shows that there is some gravity dependence on the neutral H collisions along with the temperature dependence i.e. the gravity indirectly affects the collisional rates, by impacting on the number density of hydrogen atoms at a given optical depth." + Fig. 8..," Fig. \ref{Fig:CD/LP-chiAbund}," + along with Fig. 5..," along with Fig. \ref{Fig:abnd-chi/ew-HD140283}," + clearly show that NLTE has varying star to star effects. i.e. from the similar effects at different Sy values in HD140283 (Fig. 5)).," clearly show that NLTE has varying star to star effects, i.e. from the similar effects at different $\rm S_{H}$ values in HD140283 (Fig. \ref{Fig:abnd-chi/ew-HD140283}) )," + to the differing effects in CD—33*1173 and LP815—43 (SGB) (Fig. 8))., to the differing effects in $-$ $^{\circ}$ 1173 and $-$ 43 (SGB) (Fig. \ref{Fig:CD/LP-chiAbund}) ). +" The range of ATs, values. and the negative value for CD-331173. shows the intricacies of the NLTE process. and that generalisations are not easily made when identifying the effects of NLTE on temperatures determined by the excitation. energy. method."," The range of $\Delta T_{\rm eff}$ values, and the negative value for $-$ $^{\circ}$ 1173, shows the intricacies of the NLTE process, and that generalisations are not easily made when identifying the effects of NLTE on temperatures determined by the excitation energy method." + For the purposes of this paper. which is concerned with the effective temperatures in the context of the available NLTE model. it is appropriate to acknowledge these NLTE effects and to move ahead to use them in the study of the Li problem. whilst still recognising that much work remains before we approach a complete description of the Fe atom.," For the purposes of this paper, which is concerned with the effective temperatures in the context of the available NLTE model, it is appropriate to acknowledge these NLTE effects and to move ahead to use them in the study of the Li problem, whilst still recognising that much work remains before we approach a complete description of the Fe atom." + Although we discussed the possibility that the extreme (negative) ATay correction for CD-33*1173 is due to corrrections being temperature-dependent. this unusual case may be in part due to the fact that only a subset of the original lines measured is available through the NLTE atomic model.," Although we discussed the possibility that the extreme (negative) $\Delta T_{\rm eff}$ correction for $-$ $^{\circ}$ 1173 is due to corrrections being temperature-dependent, this unusual case may be in part due to the fact that only a subset of the original lines measured is available through the NLTE atomic model." + The atomic model does not contain every level of the Fe atom and therefore some transitions are not present in the calculations., The atomic model does not contain every level of the Fe atom and therefore some transitions are not present in the calculations. + This means that not every line measured for a given star is present in the calculations and leads to a trend being introduced in the y-abundance plot prior to the trend induced by the NLTE corrections., This means that not every line measured for a given star is present in the calculations and leads to a trend being introduced in the $\chi$ -abundance plot prior to the trend induced by the NLTE corrections. + This ts because the original nulling of the y-abundance plot was achieved with a greater number of points., This is because the original nulling of the $\chi$ -abundance plot was achieved with a greater number of points. +" CD-33°1173 has the least lines available from the atomic model used withMULTI. however. there ts no distinct trend between AT, and the number of lines available for each star. and after testing we found that the effect of the subset. i.e. the measured lines that are available with our atomic model. is to increase the LTE temperature."," $-$ $^{\circ}$ 1173 has the least lines available from the atomic model used with, however, there is no distinct trend between $\Delta T_{\rm eff}$ and the number of lines available for each star, and after testing we found that the effect of the subset, i.e. the measured lines that are available with our atomic model, is to increase the LTE temperature." + This implies that the decrease in 7. for this star is most likely due to NLTE effects., This implies that the decrease in $T_{\rm eff}$ for this star is most likely due to NLTE effects. + Although there is no obvious correlation between the number of lines available and the temperature correction. this emphasises the need for a complete atomic model.," Although there is no obvious correlation between the number of lines available and the temperature correction, this emphasises the need for a complete atomic model." + This is especially true when considering the abundance of individual lines. as in the excitation technique used in this work.," This is especially true when considering the abundance of individual lines, as in the excitation technique used in this work." + Asin Paper I. we have compared our 7. values with those of ?.. 2.. and ?..," As in Paper I, we have compared our $T_{\rm eff}$ values with those of \citet{Ryanetal1999}, \citet{MelendezRamirez2004}, and \citet{Asplundetal2006}." + Fig., Fig. + 9. presents these comparisons., \ref{Fig:TempComp} presents these comparisons. +" Comparing against the photometric temperatures of ? for five stars in common. we see that our new 7, scale is hotter by an average of 132 K. with a minimum and maximum of 43 K and 211 K respectively for an Sy = 0."," Comparing against the photometric temperatures of \citet{Ryanetal1999} for five stars in common, we see that our new $T_{\rm eff}$ scale is hotter by an average of 132 K, with a minimum and maximum of 43 K and 211 K respectively for an $\rm S_{H}$ = 0." + Recall that Sy = 0 corresponds to the maximal NLTE effect. i.e. no collisions with the hydrogen. for the model atom we have adopted.," Recall that $\rm S_{H}$ = 0 corresponds to the maximal NLTE effect, i.e. no collisions with the hydrogen, for the model atom we have adopted." + For Sy = I. our scale is hotter by an average of 162 K. with a minimum and maximum of 101 K and 267 K respectively.," For $\rm S_{H}$ = 1, our scale is hotter by an average of 162 K, with a minimum and maximum of 101 K and 267 K respectively." + We have three stars in common with ?.., We have three stars in common with \citet{MelendezRamirez2004}. + Their temperatures are hotter than the ones we derived here by 196 K on average for Sy = 0 with a minimum and maximum difference of 27 K and 381 K respectively. and by 193 K on average for Sy = ]. with a minimum and maximum difference of 84 K and 247 K respectively.," Their temperatures are hotter than the ones we derived here by 196 K on average for $\rm S_{H}$ = 0 with a minimum and maximum difference of 27 K and 381 K respectively, and by 193 K on average for $\rm S_{H}$ = 1, with a minimum and maximum difference of 84 K and 247 K respectively." + Therefore. even with NLTE corrections we stillcannot achieve the high Τω of the ? study.," Therefore, even with NLTE corrections we stillcannot achieve the high $T_{\rm eff}$ of the \citet{MelendezRamirez2004} study." + It has however been noted (Meléndez 2009 - private communication) that the ? temperatures suffer from systematic. errors due a imperfect calibration of the bolometric correction for the choice of photometric bands used., It has however been noted $\rm \acute{e}$ ndez 2009 - private communication) that the \citet{MelendezRamirez2004} temperatures suffer from systematic errors due a imperfect calibration of the bolometric correction for the choice of photometric bands used. + This led to an inaccurate zero point and hotter Z4js than most other studies., This led to an inaccurate zero point and hotter $T_{\rm eff}$ 's than most other studies. + The revision of their temperature scale is not yet available and comparisons to their new Τομς is not possible at this time., The revision of their temperature scale is not yet available and comparisons to their new $T_{\rm eff}$ 's is not possible at this time. +On the other hand a value i<1500 Ixm/s would not allow for acceleration of electrons up to high enough energy. to explain the observed. X-ray emission.,On the other hand a value $u_0< 1500$ Km/s would not allow for acceleration of electrons up to high enough energy to explain the observed X-ray emission. + Here we adopt à value ol wy=4300 Ixm/s necessary to fit the cutoll in the N-ray spectrum as detected by Suzaku., Here we adopt a value of $u_0=4300$ Km/s necessary to fit the cutoff in the X-ray spectrum as detected by Suzaku. + A lower value of about~3000 Ixm/s would be needed to fit the ASCA data. but we do not discuss this case any further here. given the superior quality of the Suzaku data.," A lower value of $\sim 3000$ Km/s would be needed to fit the ASCA data, but we do not discuss this case any further here, given the superior quality of the Suzaku data." + The model parameters are further constrained by. the [act that the magnetic field in the downstream plasma. D». is an output of our calculations. for given Do. as it is the result of cosmic rav induced: magnetic field amplification and further enhancement by compression in the precursor and at the subshock.," The model parameters are further constrained by the fact that the magnetic field in the downstream plasma, $B_2$, is an output of our calculations, for given $B_0$, as it is the result of cosmic ray induced magnetic field amplification and further enhancement by compression in the precursor and at the subshock." + The correct. solution of the problem is found. by not only. requiring that the Duxes of observed raciations are fit. but also requiring that D» corresponds to the value inferred from the measured thickness of the X-ray rim.," The correct solution of the problem is found by not only requiring that the fluxes of observed radiations are fit, but also requiring that $B_2$ corresponds to the value inferred from the measured thickness of the X-ray rim." + For SNIUIUN J1713.7-3946. we use the data presented in Lazendicetal.(2004) where the authors use à CLIANDRA observation at 5 keV. to infer the rim thickness in the northwestern region of the SNR.," For SNR RX J1713.7-3946, we use the data presented in \cite{laz04} + where the authors use a CHANDRA observation at 5 keV to infer the rim thickness in the northwestern region of the SNR." + The procedure. leads. to AR.&O02Rex (see their Pig.," The procedure leads to $\Delta +R_{\rm obs} \simeq 0.02 R_{\rm SNR}$ (see their Fig." + 9)., 9). + Clearly this thickness oes not lead to an estimate of D» if due to damping of the magnetic field (as proposed. by Pohletal.(2005))) rather jun to particles’ energy losses., Clearly this thickness does not lead to an estimate of $B_2$ if due to damping of the magnetic field (as proposed by \cite{pohl05}) ) rather than to particles' energy losses. + Below. we first assume that 1e downstream magnetic field can indeed be derived [rom rw extent of the X-ray filaments and then we investigate 10 consequences of relaxing this constraint.," Below, we first assume that the downstream magnetic field can indeed be derived from the extent of the X-ray filaments and then we investigate the consequences of relaxing this constraint." + A first indication of the origin of the observed racliations can be obtained by looking at the eutolf frequencies in the different bands., A first indication of the origin of the observed radiations can be obtained by looking at the cutoff frequencies in the different bands. + In the upper panel of Fie., In the upper panel of Fig. + 1 we show the cutollenergies for svnchrotron emission (dotted line. in units of keV). a decay (solid line. in TeV) and LOS (cdash-dotted line for LCS on the infrared light and dashed line for LCS on the CAIB) as given byEqs. (8)). (9))," \ref{fig:f1} we show the cutoff energies for synchrotron emission (dotted line, in units of keV), $\pi^0$ decay (solid line, in TeV) and ICS (dash-dotted line for ICS on the infrared light and dashed line for ICS on the CMB) as given byEqs. \ref{eq:cutgamma}) ), \ref{eq:cutsyn}) )" + and (112)., and \ref{eq:cutics}) ). + Ehe plot is obtained for fixed €=3.7 and varvine By between 0.1 and. LOG: (upper .r-axis). while the lower .-axis shows the corresponding value of D».," The plot is obtained for fixed $\xi=3.7$ and varying $B_0$ between $0.1$ and $10\,\mu{\rm G}$ (upper $x$ -axis), while the lower $x$ -axis shows the corresponding value of $B_2$." + The vertical thick solid line shows the solution that. provides the central value of the measured rim thickness (corresponding to D»=100540) while the dashed vertical lines bound the allowed region corresponding to T410 TeV provided Byz(0.3. μέ which interestingly enough is also the region where D» is consistent with the thickness of the X-ray rims. if these are interpreted as the result of severe svnchrotron losses downstream.," The cutoff energy for gamma rays produced by $\pi^0$ decay is $>10$ TeV provided $B_0>(0.3-1)\,\mu$ G, which interestingly enough is also the region where $B_2$ is consistent with the thickness of the X-ray rims, if these are interpreted as the result of severe synchrotron losses downstream." + The cutoll energy. of svnchrotron. emitted. photons. which. assuming Bohm cillusion. in linear theory would not depend on the value of the magnetic field. now acquires a weak dependence on Dy. and. varies between ~ 1 and 2 keV for the considered. range of magnetic field. values. e&ranted that Boz 204€. Things change drastically when D» is lower than this threshold and the maximum electron energy," The cutoff energy of synchrotron emitted photons, which, assuming Bohm diffusion, in linear theory would not depend on the value of the magnetic field, now acquires a weak dependence on $B_0$ , and varies between $\sim$ 1 and 2 keV for the considered range of magnetic field values, granted that $B_2 \gtrsim 20\,\mu$ G. Things change drastically when $B_2$ is lower than this threshold and the maximum electron energy" +"From Figure 1 we can see that the radiative generation of UPE is much greater than the generation of APE, although we know from Table 1 that it will integrate to a smaller global rate.","From Figure \ref{fig:eq} we can see that the radiative generation of UPE is much greater than the generation of APE, although we know from Table 1 that it will integrate to a smaller global rate." +" This is a reflection of the fact that the radiative heating on hot Jupiters is intense and a large amount of energy will be stored in UPE, but by its very nature this will have a small net effect on the atmospheric flow."," This is a reflection of the fact that the radiative heating on hot Jupiters is intense and a large amount of energy will be stored in UPE, but by its very nature this will have a small net effect on the atmospheric flow." +" According to the left panel of Figure 1,, most of the UPE is generated on the day side and most of the APE is generated on the night side (with opposite behavior for the loss)."," According to the left panel of Figure \ref{fig:eq}, most of the UPE is generated on the day side and most of the APE is generated on the night side (with opposite behavior for the loss)." + This is simple to explain by comparing the signs of the local efficiency factor (T;/T) and the radiative heating/cooling (qra4)., This is simple to explain by comparing the signs of the local efficiency factor $T_r/T$ ) and the radiative heating/cooling $q_{\mathrm{rad}}$ ). +" The calculation of the reference temperature, T;., is a mass-weighted integral over the atmosphere (Equation 13)) and the deepest layers, which contain the most mass, are generally hotter than the upper layers (see Figure 5 of Rauscher Menou 2010 for a plot of"," The calculation of the reference temperature, $T_r$, is a mass-weighted integral over the atmosphere (Equation \ref{eq:Tr}) ) and the deepest layers, which contain the most mass, are generally hotter than the upper layers (see Figure 5 of Rauscher Menou 2010 for a plot of" +supporting the validity of the method and our assumptions.,supporting the validity of the method and our assumptions. + In particular. this provides direct evidence that the observed component speeds in the VLBI jet. represent. the actual physical speeds of these components. rather than the pattern speed of a shock.," In particular, this provides direct evidence that the observed component speeds in the VLBI jet represent the actual physical speeds of these components, rather than the pattern speed of a shock." + This technique should also be checked using more sources. which we plan to do in a future stuck.," This technique should also be checked using more sources, which we plan to do in a future study." + We have used. our method. to derive Ay values. for 3€ 345., We have used our method to derive $k_r$ values for 3C 345. + We find clear evidence lor variability of A). with the measured. values ranging [rom 0.4 to 1.9.," We find clear evidence for variability of $k_r$, with the measured values ranging from 0.4 to 1.9." +" We find evidence that A, increases with the core Dux level. reaching saturation at a value of &L8 above core κος of about 6 Jv."," We find evidence that $k_r$ increases with the core flux level, reaching saturation at a value of $\simeq 1.8$ above core fluxes of about 6 Jy." +" In. principle. time evolution of A, could come about due to changes in the core spectral index. magnetic-ield clistribution. or electron. number-density. distribution. since kh, depends on o. m. and n (see formula 5))."," In principle, time evolution of $k_{r}$ could come about due to changes in the core spectral index, magnetic-field distribution, or electron number-density distribution, since $k_{r}$ depends on $\alpha$, $m$, and $n$ (see formula \ref{k_r}) )." +" There is no obvious relationship between the value of A, ancl the core spectral index (Lable 12).", There is no obvious relationship between the value of $k_r$ and the core spectral index (Table \ref{3c345_flares}) ). + Unfortunately. we cannot directly separate the m anc values from the fy equation (the only exception is if Ay is close to unity. ie. close to equipartition. in which case it is reasonable to infer m=1 and η= 2).," Unfortunately, we cannot directly separate the $m$ and $n$ values from the $k_r$ equation (the only exception is if $k_r$ is close to unity, i.e., close to equipartition, in which case it is reasonable to infer $m = 1$ and $n=2$ )." + Therefore. we cannot unambiguously prove that Ay variations are due. for example. purely to variations in o. m or no dt ds likely that all three parameters contribute to time variability of Ay.," Therefore, we cannot unambiguously prove that $k_{r}$ variations are due, for example, purely to variations in $\alpha$, $m$ or $n$; it is likely that all three parameters contribute to time variability of $k_{r}$." +" Using our &, values we can estimate the distance. of the radio core from the base of the jet. the equipartition magnetic field at 1 pe distance. and the equipartition magnetic field in the core (Lobanov(1998). and. LHirotani (2005)))."," Using our $k_r$ values we can estimate the distance of the radio core from the base of the jet, the equipartition magnetic field at 1 pc distance, and the equipartition magnetic field in the core \citet{Lobanov_1998} and \citet{Hirotani_2005}) )." + Since not all outbursts are in the equipartition regime as was shown in the previous sections. we have selected for magnetic fields caleulations one outburst Lf with Ay value [rom a ‘Table 1. closest to unity (and therefore to equipartition regime).," Since not all outbursts are in the equipartition regime as was shown in the previous sections, we have selected for magnetic fields calculations one outburst $H$ with $k_{r}$ value from a Table \ref{3c345_flares} closest to unity (and therefore to equipartition regime)." +" We have usec intrinsic jet hall-opening angle &=0.57 (Jorstadetal.2005)... jet viewing angle yo=2.577 (Jorstadetal.2005).. Doppler. factor 0=7S (lovattactal.2009)... and. luminosity distance D,=3473 Mpc."," We have used intrinsic jet half-opening angle $\theta=0.5^\circ$ \citep{Jorstad_2005}, jet viewing angle $\varphi = 2.7^\circ$ \citep{Jorstad_2005}, Doppler factor $\delta = +7.8$ \citep{Hovatta_2009}, and luminosity distance $D_L = 3473$ Mpc." + Table 3. shows calculated: frequency- core shifts. distances between the radio core and the base of the jet. magnetic field at 1 pe. and magnetic field in the core for individual pairs of frequencies.," Table \ref{table_mfield} shows calculated frequency-dependent core shifts, distances between the radio core and the base of the jet, magnetic field at 1 pc, and magnetic field in the core for individual pairs of frequencies." + We have not used S Cllz data in the analysis. since the frequencydependent time lag for the 8/37 Gllz pair of frequencies is not very reliable.," We have not used 8 GHz data in the analysis, since the frequency-dependent time lag for the 8/37 GHz pair of frequencies is not very reliable." + In error analysis we took into account only the errors in time lags measurements and apparent speeds of jet components., In error analysis we took into account only the errors in time lags measurements and apparent speeds of jet components. +" The averaged magnetic field in the core of 3€ 345 is D,=0.07£0.02 G and magnetic field. at lpeis D,—0.45£0.09 Ci. ὃν caleulating the frequencev-dependent core. shifts from the frequenev-dependent. time delays: measured: for integrated light curves. we can study the long-term evolution of the core shifts and. calculate. the core shifts for any particular time when long-term radio lieht-curves are available."," The averaged magnetic field in the core of 3C 345 is $B_{core} = 0.07\pm0.02$ G and magnetic field at 1 pc is $B_{1pc} = 0.45\pm0.09$ G. By calculating the frequency-dependent core shifts from the frequency-dependent time delays measured for integrated light curves, we can study the long-term evolution of the core shifts and calculate the core shifts for any particular time when long-term radio light-curves are available." + Since the total Uus-cdensity light. curves covering more than 30 vears are available for dozens of radio sources. this makes it possible. in principle. to calculate the core-shift evolution over more than 30 vears without constructing ancl aligning VLBI maps at multiple frequencies.," Since the total flux-density light curves covering more than 30 years are available for dozens of radio sources, this makes it possible, in principle, to calculate the core-shift evolution over more than 30 years without constructing and aligning VLBI maps at multiple frequencies." + The only input needed [rom direct VLBI observations is the apparent speeds of jet components (which can be measured from a series of observations at a single frequency), The only input needed from direct VLBI observations is the apparent speeds of jet components (which can be measured from a series of observations at a single frequency). + Ν.Α. Ixudirvavtseva was supported for this research through a stipend from the International Max. Planck Research School (LAIPRS) for adio and Infrared Astronomy at the Universities of Bonn and Cologne., N. A. Kudryavtseva was supported for this research through a stipend from the International Max Planck Research School (IMPRS) for Radio and Infrared Astronomy at the Universities of Bonn and Cologne. + We would like to thank Shane O'Sullivan lor useful discussions., We would like to thank Shane O'Sullivan for useful discussions. + This publication has cmanated from research. conducted: with the financial support of Science Foundation. Ireland., This publication has emanated from research conducted with the financial support of Science Foundation Ireland. + Phe UMICXO has been supported from the series of grants from the NSE and NASA and from the University of Michigan., The UMRAO has been supported from the series of grants from the NSF and NASA and from the University of Michigan. +survival rate (Lo. whether the mass distribution of the actual data points may be allectec significantly by simall-number statistics rather than physical effects). we have run simulations starting from 60 clusters (i.0.. the approximate number of clusters expected to have been formed initially in this scenario)) randomly drawn from the Gaussian. initial CME.,"survival rate (i.e., whether the mass distribution of the actual data points may be affected significantly by small-number statistics rather than physical effects), we have run simulations starting from 60 clusters (i.e., the approximate number of clusters expected to have been formed initially in this scenario), randomly drawn from the Gaussian initial CMF." + The results are shown in Fig., The results are shown in Fig. +" 4. for case 4]. where we assume the disruption time-scale predicted: by AN-body simulations (£A,c0.8 Cyr)."," \ref{lognormal_N60.fig} for case [4], where we assume the disruption time-scale predicted by $N$ -body simulations $t_{\rm dis}^4 \simeq +0.8$ Gyr)." + For various random seeds. the predicted: cluster mass distributions mateh the observed CME satisfactorily. showing that the elfects owing to small-number statistics are minimal. ancl unimportant with respect to our overall conclusions.," For various random seeds, the predicted cluster mass distributions match the observed CMF satisfactorily, showing that the effects owing to small-number statistics are minimal, and unimportant with respect to our overall conclusions." +" lt appears. therefore. that on the grounds of both our observational data and the theoretical arguments presented in the previous sections. the initial mass distribution of the AIS2 B clusters surviving past the ""infant mortality epoch (i.c. the first few Myr in which unbound low-mass clusters are dispersed: c.g. Boily Ixroupa 2003: Vesperini Zepf 2003: Whitmore 2004: Bastian et al."," It appears, therefore, that on the grounds of both our observational data and the theoretical arguments presented in the previous sections, the initial mass distribution of the M82 B clusters surviving past the “infant mortality” epoch (i.e., the first few Myr in which unbound low-mass clusters are dispersed; e.g., Boily Kroupa 2003; Vesperini Zepf 2003; Whitmore 2004; Bastian et al." + 2005: Mengel et al., 2005; Mengel et al. + 2005: see also Tremonti et al., 2005; see also Tremonti et al. + 2001) must have been closely matched by a log-normal distribution., 2001) must have been closely matched by a log-normal distribution. + In fact. the presence of a large excess (up to TO90 per cent: Whitmore 2004: Mengel et al.," In fact, the presence of a large excess (up to 70–90 per cent; Whitmore 2004; Mengel et al." + 2005) of presumably unbound clusters at ages below ~I0 Myr in the Antennae system (Whitmore 2004. his fig.," 2005) of presumably unbound clusters at ages below $\sim 10$ Myr in the Antennae system (Whitmore 2004, his fig." + 2: Mengel et al., 2; Mengel et al. + 2005. their ig.," 2005, their fig." + I0) and. M51 (Bastian et al., 10) and M51 (Bastian et al. + 2005. their fig.," 2005, their fig." + 10) could. in principle. provide further limits on the initial CME of οί the bound. ancl unbouncl clusters.," 10) could, in principle, provide further limits on the initial CMF of both the bound and unbound clusters." + A seven to. nine-old increase. of unbound clusters at. very early times. as implied. by these observational studies. although of low mass in general. would boost initial stellar density levels to ruly unphysical numbers if the bound. longer-lived clusters were formed following a power-law mass-number scaling.," A seven to nine-fold increase of unbound clusters at very early times, as implied by these observational studies, although of low mass in general, would boost initial stellar density levels to truly unphysical numbers if the bound, longer-lived clusters were formed following a power-law mass-number scaling." + For he initial log-normal CME scenario. the resulting initial densities could. be used to place limits on the total mass (ancl possibly the number. if the mass distribution. were known) in unbound star clusters.," For the initial log-normal CMF scenario, the resulting initial densities could be used to place limits on the total mass (and possibly the number, if the mass distribution were known) in unbound star clusters." + Llowever. at this point the observational cata are statistically insullicienthy robust. in erms of excess cluster numbers (similar data are needed for arecr numbers of cluster populations). while the masses of hese voung unbound cluster populations are as vet. poorly determined. so that any (statistical) extrapolations to other ealaxies are as vet. umwvarrantecd.," However, at this point the observational data are statistically insufficiently robust in terms of excess cluster numbers (similar data are needed for larger numbers of cluster populations), while the masses of these young unbound cluster populations are as yet poorly determined, so that any (statistical) extrapolations to other galaxies are as yet unwarranted." + In this paper. we start from the robust detection of de Curis et al. (," In this paper, we start from the robust detection of de Grijs et al. (" +2003a.b) of an approximately log-normal CME for the 1 Gvr-old. intermediate-age star cluster svstem in MS2 D. and explore whether we can constrain the shape of theinilial distribution of cluster masses.,"2003a,b) of an approximately log-normal CMF for the 1 Gyr-old, intermediate-age star cluster system in M82 B, and explore whether we can constrain the shape of the distribution of cluster masses." + In particular. we investigate whether the most. likely initial CME was more similar to either a log-normal or a power-law distribution. bv taking into account the dominant evolutionary processes (including stellar. evolution. and internal and external gravitational effects). allecting the mass distributions of star cluster svstenis over time-scales of up to ~1 vr in the presence of a realistic underlving eravitational potential.," In particular, we investigate whether the most likely initial CMF was more similar to either a log-normal or a power-law distribution, by taking into account the dominant evolutionary processes (including stellar evolution, and internal and external gravitational effects) affecting the mass distributions of star cluster systems over time-scales of up to $\sim 1$ Gyr in the presence of a realistic underlying gravitational potential." + The MS2 D cluster. population represents an ideal sample to test these evolutionary scenarios for. since it is a roughly coeval intermecdiate-age population in a spatially confined region.," The M82 B cluster population represents an ideal sample to test these evolutionary scenarios for, since it is a roughly coeval intermediate-age population in a spatially confined region." + For such à coeval population. the observational selection elfects are very well unclerstoocl (de Crijs et al.," For such a coeval population, the observational selection effects are very well understood (de Grijs et al." + 2003a.b). while the dynamical cluster disruption elfects. are very similar for this entire »opulation.," 2003a,b), while the dynamical cluster disruption effects are very similar for this entire population." + After considering the gravitational elfects and geometry of ALS? itself. its starburst region. D. ancl its position in he MSI/MS2/NGC 3077 group of interacting galaxics. we conclude that we can approximate the gravitational x»ential felt by ALs2 B. in a time-independent fashion. dominated by the mass of MS2 inside the radius of M82 D. In such a static gravitational potential. Vesperini (1998) shows conclusively that there exists a particular CAL of which the initial mean mass. width and radial dependence remain unaltered during the entire evolution over a IIubble time.," After considering the gravitational effects and geometry of M82 itself, its starburst region B, and its position in the M81/M82/NGC 3077 group of interacting galaxies, we conclude that we can approximate the gravitational potential felt by M82 B in a time-independent fashion, dominated by the mass of M82 inside the radius of M82 B. In such a static gravitational potential, Vesperini (1998) shows conclusively that there exists a particular CMF of which the initial mean mass, width and radial dependence remain unaltered during the entire evolution over a Hubble time." +" In fact. the mean mass and width ofany initial log-normal ""NIE tends to evolve towards the values for this equilibrium ""NIE."," In fact, the mean mass and width of initial log-normal CMF tends to evolve towards the values for this equilibrium CMF." + Thus. the fact that for MS2. Bowe observe log(Ad.fAl.})=5.1£01 and σc0.5. at an age of ~1 Gyr. implies that the AIS2 B initial CME have had a mean mass very close to that of the equilibrium CME.," Thus, the fact that for M82 B we observe $\langle \log( M_{\rm cl} / +{\rm M}_\odot )\rangle = 5.1 \pm 0.1 $ and $\sigma \simeq 0.5$, at an age of $\sim 1$ Gyr, implies that the M82 B initial CMF have had a mean mass very close to that of the equilibrium CMF." + If the presently. observed. MS82 B. CALF is to remain unchanged for a Hubble time. so that we are currently probing thefat CAIP. then theniial CME must have been characterized by a mean mass that was only slightly larger than the present mean mass.," If the presently observed M82 B CMF is to remain unchanged for a Hubble time, so that we are currently probing the CMF, then the CMF must have been characterized by a mean mass that was only slightly larger than the present mean mass." + This is a robust result. ancl holds for gravitational potentials associated with host ealaxies spanning the entire observational range of masses and ellective radii.," This is a robust result, and holds for gravitational potentials associated with host galaxies spanning the entire observational range of masses and effective radii." + From our detailed. analysis of the expected evolution of CMES starting from initial log-normal and initial power-law clistributions. we conclude that our observations of the ΔΙΣ D CALF are inconsistent with a scenario in. which the 1 Civr-old. cluster population originated from an initial power-law mass distribution.," From our detailed analysis of the expected evolution of CMFs starting from initial log-normal and initial power-law distributions, we conclude that our observations of the M82 B CMF are inconsistent with a scenario in which the 1 Gyr-old cluster population originated from an initial power-law mass distribution." + TFhis applies to a range of characteristic disruption time-scales. from (ij.~30 Myr to the ~16305 longer time-seale resulting from Baumearelt Makino's (2003) N-bocly simulations.," This applies to a range of characteristic disruption time-scales, from $t_{\rm dis}^4 \sim 30$ Myr to the $\sim 16-30 \times$ longer time-scale resulting from Baumgardt Makino's (2003) $N$ -body simulations." + Our conclusion is supported by arguments related. to the initial density. in AIS2 DB. which would be unphysically high. if the present," Our conclusion is supported by arguments related to the initial density in M82 B, which would be unphysically high if the present" +The localization of Gamma-Ray Bursts (GRBs) to within a few are-minutes by the Italian-Dutch satellite BeppoSAX. the Interplanetary Network. and the Rossi—-ray Transient Explorer have enabled us to carry out ground-based follow-up searches for afterglow emission.,"The localization of Gamma-Ray Bursts (GRBs) to within a few arc-minutes by the Italian–Dutch satellite BeppoSAX, the Interplanetary Network, and the $X$ -ray Transient Explorer have enabled us to carry out ground-based follow-up searches for afterglow emission." + The current. database of multrwavelength (radio. millimeter. optical. and V-ray) observations allows us to begin a statistical study of the physical properties of GRB afterglows.," The current database of multiwavelength (radio, millimeter, optical, and $X$ -ray) observations allows us to begin a statistical study of the physical properties of GRB afterglows." + This is à third in a series of papers modelling the broadband emission of GRB afterglows. with the aim of determining the total energy in the relativistic ejecta. the Jet opening angle. the density and profile of the medium in the immediate vicinity C101? em) of the burst. and the microphysical shock parameters.," This is a third in a series of papers modelling the broadband emission of GRB afterglows, with the aim of determining the total energy in the relativistic ejecta, the jet opening angle, the density and profile of the medium in the immediate vicinity $\siml 10^{18}$ cm) of the burst, and the microphysical shock parameters." + The first paper (PKOI) has presented the modelling of the afterglows 990123. 990510. and 991216 while the second (Panaitescu 2001) analyzed the peculiar afterglow 000301c. whose emission fall-off exhibited a sharp break.," The first paper (PK01) has presented the modelling of the afterglows 990123, 990510, and 991216 while the second (Panaitescu 2001) analyzed the peculiar afterglow 000301c, whose emission fall-off exhibited a sharp break." + Here we present our results for the afterglows 970508. 980519. 991208. 000926. 000418. and 010222.," Here we present our results for the afterglows 970508, 980519, 991208, 000926, 000418, and 010222." +" With the exception of 000418. after 1 day the decay of their optical emission is steep or exhibits à steepening. as expected if the GRB ejecta are well collimated (Rhoads 1999), thus their modelling allows the determination of the jet aperture and energy."," With the exception of 000418, after 1 day the decay of their optical emission is steep or exhibits a steepening, as expected if the GRB ejecta are well collimated (Rhoads 1999), thus their modelling allows the determination of the jet aperture and energy." + Section refmodel outlines the model used to fit the broadband emission of these afterglows., Section \\ref{model} outlines the model used to fit the broadband emission of these afterglows. + The jet properties inferred for individual afterglows are presented in refnumeric. and the results for the entire set are analyzed in reffeatures.., The jet properties inferred for individual afterglows are presented in \\ref{numeric} and the results for the entire set are analyzed in \\ref{features}. + The calculation of the afterglow emission is carried out in the standard framework of relativistic ejecta decelerated by an external medium (Mésszárros Rees 1997). with allowance for the effects due to collimation (Rhoads 1999).," The calculation of the afterglow emission is carried out in the standard framework of relativistic ejecta decelerated by an external medium (Mésszárros Rees 1997), with allowance for the effects due to collimation (Rhoads 1999)." + The equations governing the dynamics of jet-medium interaction and those for the calculation of the synchrotron and inverse Compton emission are presented in KPOO. PKOO and ΡΚΟΙ.," The equations governing the dynamics of jet–medium interaction and those for the calculation of the synchrotron and inverse Compton emission are presented in KP00, PK00 and PK01." +" Similar analytical treatments of jet dynamics and/or emission of radiation can be found in Waxman (1997). Granot. Piran Sari (1999), Gruzinov Waxman (1999). Wijers Galama (1999). Chevalier Li (2000). and Sari Esin (2001)."," Similar analytical treatments of jet dynamics and/or emission of radiation can be found in Waxman (1997), Granot, Piran Sari (1999), Gruzinov Waxman (1999), Wijers Galama (1999), Chevalier Li (2000), and Sari Esin (2001)." + The effect of interstellar scintillation on the radio afterglow emission (Goodman 1997) is taken into account following the treatment of Walker (1998)., The effect of interstellar scintillation on the radio afterglow emission (Goodman 1997) is taken into account following the treatment of Walker (1998). + In our treatment. the afterglow modelling has the following features: 1) the jet is considered uniform. with an energy per solic angle independent of direction within the jet: 2) the shocked gas internal energy density is assumed uniform: 3) the jet dynamics is calculated by following the evolutior of its energy (which decreases due to radiative losses). mass (increasing. as the jet sweeps-up the surrounding medium). and aperture (which increases due to jet expansion in the comoving frame).," In our treatment, the afterglow modelling has the following features: $1)$ the jet is considered uniform, with an energy per solid angle independent of direction within the jet; $2)$ the shocked gas internal energy density is assumed uniform; $3)$ the jet dynamics is calculated by following the evolution of its energy (which decreases due to radiative losses), mass (increasing, as the jet sweeps-up the surrounding medium), and aperture (which increases due to jet expansion in the comoving frame)." + The equations employed are accurate in any relativistic, The equations employed are accurate in any relativistic +for e-like and p-likesub-GeV andmulti-GeV events are shown in Fig.,for $e$ -like and $\mu$ -like and events are shown in Fig. + 3 left., 3 left. + The MC problem described before exists also in SK [10]:: the e-like events were in agreement with the HKKM95 MC predictions for they are higher than the HKKMO01 non oscillated MC., The MC problem described before exists also in SK \cite{skam}: the e-like events were in agreement with the HKKM95 MC predictions for no-oscillations; they are higher than the HKKM01 non oscillated MC. +" For pi-like events, the new MC predictions are low: to reduce these problems the normalization is a free The ratios e-like events/MC do not depend from L/E, while p-like events/MC show a dependence on L/E, consistent with an oscillation hypothesis, Fig."," For $\mu$ -like events, the new MC predictions are low: to reduce these problems the normalization is a free The ratios $e$ -like events/MC do not depend from $L/E_\nu$ while $\mu$ -like events/MC show a dependence on $L/E_\nu$ consistent with an oscillation hypothesis, Fig." + 3 right., 3 right. + The overall best fit of SK data corresponds to maximal mixing and Am?=2.5-107? ον”., The overall best fit of SK data corresponds to maximal mixing and $\Delta m^2 = 2.5 \cdot 10^{-3}$ $^2$. + MACRO and SuperK data were used to search for sub-dominant oscillations due to Lorentz invariance violation (or violation of the equivalence principle)., MACRO and SuperK data were used to search for sub-dominant oscillations due to Lorentz invariance violation (or violation of the equivalence principle). + In the first case there could be mixing between flavor and velocity eigenstates., In the first case there could be mixing between flavor and velocity eigenstates. + 9096 c.l., $\%$ c.l. +" limits were placed in the Lorentz invariance violation parameters |Av|<6-10:34 at sin? 20,—0 and |Av|<4-10776 at sin?20,= +1 [22]..decay", limits were placed in the Lorentz invariance violation parameters $\left|\Delta v\right|<6\cdot10^{-24}$ at ${\stheta}_v$ =0 and $\left|\Delta v\right|<4\cdot10^{-26}$ at ${\stheta}_v=\pm$ 1 \cite{lorentz}. + could be another exotic explanation for neutrino disappearence; no radiative decay was observed [23].., could be another exotic explanation for neutrino disappearence; no radiative decay was observed \cite{notte}. + Neutrino physics has opened new windows into phenomena beyond the Standard Model of particle physics., Neutrino physics has opened new windows into phenomena beyond the Standard Model of particle physics. + Long baseline neutrino experiments may allow further insight into v physics., Long baseline neutrino experiments may allow further insight into $\nu$ physics. +" The first long baseline v beam was the KEK to Kamioka (K2K) beam, the 274 was the Fermilab to the Soudan mine beam (NuMi)."," The first long baseline $\nu$ beam was the KEK to Kamioka (K2K) beam, the $^{nd}$ was the Fermilab to the Soudan mine beam (NuMi)." + CNGS [24] was commissioned in 2006 and started sending neutrinos to the GS Lab., CNGS \cite{CNGS} was commissioned in 2006 and started sending neutrinos to the GS Lab. + Thebeam., The. + Fig., Fig. +" 4 left shows the main components of the v,, beam at CERN [24]..", 4 left shows the main components of the $\nm$ beam at CERN \cite{CNGS}. + A 400 GeV beam is extracted from the SPS and is transported to the target., A 400 GeV beam is extracted from the SPS and is transported to the target. +" Secondary pions and kaons are focused into a parallel beam by 2 magnetic lenses, called horn and reflector."," Secondary pions and kaons are focused into a parallel beam by 2 magnetic lenses, called horn and reflector." +" Pions and kaons decay into v,, and µ in", Pions and kaons decay into $\nu_{\mu}$ and $\mu$ in +an uncertainty in their staus as black holes.,an uncertainty in their status as black holes. + One possible way to constrain the mass of these lenses is to look for X-rays from accretion., One possible way to constrain the mass of these lenses is to look for X-rays from accretion. + Figure 6 shows the flux as a function of distance for NLACTIO 96-BLG-5. ALACTLIO 98-BLG-6. and (Mao et al.," Figure 6 shows the flux as a function of distance for MACHO 96-BLG-5, MACHO 98-BLG-6, and OGLE-1999-BUL-32 (Mao et al." + 2001) or a number density of 1 cm with the total velociMESE 3/2 times the observed sky velocity projected on to the lens pane (ignoring the unknown projected source velociv) and subtracted from the Galactic rotation velocity (220 km L ) and an X-rayB elicienev of e=10.7., 2001) for a number density of 1 $^{-3}$ with the total velocity set to $\sqrt{3/2}$ times the observed sky velocity projected on to the lens plane (ignoring the unknown projected source velocity) and subtracted from the Galactic rotation velocity (220 km $^{-1}$ ) and an X-ray efficiency of $\epsilon_{\rm ion}=10^{-3}$. + We note that if t1ο sky velocity of the source is significant. then the inferred lens velocity will be ciülfernt. typically smaller. which will increas! the Iuminosity.," We note that if the sky velocity of the source is significant, then the inferred lens velocity will be different, typically smaller, which will increase the luminosity." + The Dux scales as £xen for small distances since tjc mass dej»nds on the inverse of the distance anc the Lux decreases as the inverse of distance squared., The flux scales as $F\propto \epsilon n D^{-4}$ for small distances since the mass depends on the inverse of the distance and the flux decreases as the inverse of distance squared. + Οἱserving in the X-ray woul be advantageous to avoid confusion wi1 the background microlensed star., Observing in the X-ray would be advantageous to avoid confusion with the background microlensed star. + In the soft X-ray. a 10 keV flux of ~10n Cre gm2 hi+ can be detected with a 400 ksec exposure with or 200 ksec withXALAM-Newlon.," In the soft X-ray, a 1–10 keV flux of $\sim 10^{-15}$ erg $^{-2}$ $^{-1}$ can be detected with a $\sim$ 400 ksec exposure with or $\sim$ 200 ksec with." +" X detection of a black-hole candidate at such a Lux level will zοον an upper limit on the distance of ~1.3J kpe to be paced. assuming they aceree from the cdilfuse ISAT with n»«Pix=lem ""and assuming an X-ray cllicicney less than eas=107""."," A detection of a black-hole candidate at such a flux level will allow an upper limit on the distance of $\sim 1-3$ kpc to be placed, assuming they accrete from the diffuse ISM with $n < n_{\rm max} =1$ $^{-3}$ and assuming an X-ray efficiency less than $\epsilon_{\rm max} =10^{-3}$." + AX decrease in clliciency will [σας to a decrease in ux. and jus à decrease in the distance upper limit.," A decrease in efficiency will lead to a decrease in flux, and thus a decrease in the distance upper limit." + An upper limit on distance converts into a lower limit on mass. since MxD7. which may confirm the black-hole hypothesis.," An upper limit on distance converts into a lower limit on mass, since $M \propto D^{-1}$, which may confirm the black-hole hypothesis." + The mass lower limit is proportional to MiiX(Custansαν}1log weak de»endence on our assumed. parameters.," The mass lower limit is proportional to $M_{\rm min} \propto (\epsilon_{\rm max} +n_{\rm max}/F)^{-1/4}$, a weak dependence on our assumed parameters." + A eloud or companion could. increase the accretion rate. resulting in a higher luminosity. thus a lareer distance for the same Εαν: however. clouds occupy. less than 5 per cent of the volume near the Galactie plane and can be searched for in HE 21 em or CO absorption or emission (the ALACLILO fields are toward Baace’s window. thus unlikely to contain a high molecular column densitv). while companions should be detectable with LIST.," A cloud or companion could increase the accretion rate, resulting in a higher luminosity, thus a larger distance for the same flux; however, clouds occupy less than 5 per cent of the volume near the Galactic plane and can be searched for in HI 21 cm or CO absorption or emission (the MACHO fields are toward Baade's window, thus unlikely to contain a high molecular column density), while companions should be detectable with HST." + 2mm We have estimated the number of isolated black holes that might be revealed by their X-ray emission. from accretion of interstellar gas., 2mm We have estimated the number of isolated black holes that might be revealed by their X-ray emission from accretion of interstellar gas. + We have improved upon previous calculations by taking into account the density distrixition of the interstellar medium. as well as using the known properties of black-hole X-ray binaries and ALACIIO blac.hole candidates to constrain the phase space and accretion ellieiency of isolated accreting black holes.," We have improved upon previous calculations by taking into account the density distribution of the interstellar medium, as well as using the known properties of black-hole X-ray binaries and MACHO black-hole candidates to constrain the phase space and accretion efficiency of isolated accreting black holes." +" We conclude that persistent isolated black holes may be competitive with neutron stars in creating detectable X-ray Εαν if their elliciencies diller bv egg~O""evsCNBaINN)UN"," We conclude that persistent isolated black holes may be competitive with neutron stars in creating detectable X-ray flux if their efficiencies differ by $\epsilon_{BH} \sim 10^{-4} \epsilon_{NS} +(N_{BH}/N_{NS})^{0.8}$." + The ROSAXE survey did not have the sensitivity to detecteither isolated. accreting neutron sars or black holes: an all-sky survey with two orders of magnitude more sensitivitv. 10ll erg cni 1. may be able to detect ~LO?Noet=» accreting black holes.," The ROSAT survey did not have the sensitivity to detecteither isolated accreting neutron stars or black holes; an all-sky survey with two orders of magnitude more sensitivity, $\sim 10^{-14}$ erg $^{-2}$ $^{-1}$ ${-1}$, may be able to detect $\sim 10^3N_9\epsilon_{-5}^{1.2}$ accreting black holes." + Phe X-ray observatories and may be able to detect this population with pointed observations: however. they sulfer from having small fields of view.," The X-ray observatories and may be able to detect this population with pointed observations; however, they suffer from having small fields of view." + Despite this limitation. Galacic plane surveys being carried out with these telescopes may. be able to detect tens per vear for e.5= 1.," Despite this limitation, Galactic plane surveys being carried out with these telescopes may be able to detect tens per year for $\epsilon_{-5}=1$ ." +" HE the accreting sources with M10, est ", If the accreting sources with $\dot M > 10^{15}$ g $^{-1}$ +" e IL,7. ο d. IL, (Freediamanetal.2001) IL,=72£8 IMpe. t. (Arp2002:2002d:Russell2002) Freedauanctal.(2001) IL, (£8 + !) Vearp IL;-value Freeciuanetal."," $v$ $_{\rm o}d$ $v$ $d$ $_{\rm o}$ \citep{fre01} $_{\rm o} = 72 \pm 8$ $^{-1}$ $^{-1}$ \citep{arp02,bel02d,rus02} \citet{fre01} $_{\rm o}$ $\pm8$ $^{-1}$ $^{-1}$ $_{CMB}$ $_{\rm o}$ \citet{fre01}." +"(2001).. IL,~71 IMpe lofoy. and d) Type II superuovae.", $_{\rm o} \sim71$ $^{-1}$ $^{-1}$ and d) Type II supernovae. +" However. a much ueher value of IL, = 52 lin IxMDpe + was found or fundamental plane (EP)clusters."," However, a much higher value of $_{\rm o}$ = 82 km $^{-1}$ $^{-1}$ was found for fundamental plane (FP)clusters." + Iu Fig., In Fig. + l. Vesp velocities for the FP clusters isted in Table 9 of Freedmanetal.(2001). are otted vs distance iu Mpc.," 1, $_{\rm CMB}$ velocities for the FP clusters listed in Table 9 of \citet{fre01} are plotted vs distance in Mpc." +" The liue has a slope of I, = 88.15 lau + 1 aud represents the slope of a line through zero velocity aud distance hat elves a minium near 165 ki s in the RAIS deviation in Veappy velocities.", The line has a slope of $_{\rm o}$ = 88.15 km $^{-1}$ $^{-1}$ and represents the slope of a line through zero velocity and distance that gives a minimum near 465 km $^{-1}$ in the RMS deviation in $_{\rm CMB}$ velocities. +This τάται is shown in Fie.,This minimum is shown in Fig. + 2 which is a plot of the RAIS deviation in velocity as a function of Πω., 2 which is a plot of the RMS deviation in velocity as a function of $_{\rm o}$. +" The slope found here. 88.15. is significantly higher than the value IL, = 82 reported by Freedmanetal.(2007 for the FP clusters."," The slope found here, 88.15, is significantly higher than the value $_{\rm o}$ = 82 reported by \citet{fre01} for the FP clusters." + A linear rceression calculation using the data in Fig., A linear regression calculation using the data in Fig. + 1 gave a slope of 81.6 with a standard error of L7 kn + + and a distance velocity intercept of 293 km s1, 1 gave a slope of 84.6 with a standard error of 4.7 km $^{-1}$ $^{-1}$ and a zero-distance velocity intercept of 293 km $^{-1}$. + The τή RAUS deviation in the velocities in Fig., The minimum RMS deviation in the velocities in Fig. + 2 is in excess of IGO Ian !. even hough all peculiar velocitics are assumed to rave been removed.," 2 is in excess of 460 km $^{-1}$, even though all peculiar velocities are assumed to have been removed." + This value seeunis high. since all prinordial turbulence is expected to have 2001 dauped out by adiabatic expansion (I&raau-Ikortewee 1986)..," This value seems high, since all primordial turbulence is expected to have been damped out by adiabatic expansion \citep{kra86}. ." + Why is the zero-distance velocity intercept⋅ (293 kins Ly so high?, Why is the zero-distance velocity intercept (293 km $^{-1}$ ) so high? +" Previously. oeculiar velocities have been used to explain such aree velocities (Jorgensenetal.1996).. but this interpretation can be questioned since these larec ""peculiar velocities tend to be mostly redshifts with very few blueshifts (Russell2002)."," Previously, peculiar velocities have been used to explain such large velocities \citep{jor96}, but this interpretation can be questioned since these large ""peculiar velocities"" tend to be mostly redshifts with very few blueshifts \citep{rus02}." +. Thus the possibility that intrinsic redshifts may plav a role seenis to be indicated., Thus the possibility that intrinsic redshifts may play a role seems to be indicated. + This sueecstion is lighly controversial but it may no longer be possible to ignorethispossibilityiu lightof recent evidence (πια1996.1997:Bell 2002d)..," This suggestion is highly controversial but it may no longer be possible to ignorethispossibilityin lightof recent evidence \citep{tif96,tif97,bel02d}. ." + Astudy ofthecompact objectsnearNCC LOGS(Bell 2002a.b.c).. aud earlier work (Burbidgeaud 1990). sugeested that quasar redshifts may contain an Παάθλο component that is harmonicallyrelated to O.G2+0.01.," Astudy ofthecompact objectsnearNGC 1068\citep{bel02a,bel02b,bel02c}, , and earlier work \citep{bur90}, , suggested that quasar redshifts may contain an intrinsic component that is harmonicallyrelated to $\pm0.01$ ." + Also. Tutt was able to define several families of," Also, \citet{tif97} was able to define several families of" +nourclativistic perfect eas. it is well known that It is clearly not possible to determine any two of these three quantities T..X.Z. from e aud yp. since if the p variatious are ignored. we always have δυο=dp/p. axd these constraiuts are not independent.,"nonrelativistic perfect gas, it is well known that It is clearly not possible to determine any two of these three quantities $T,X,Z$, from $c$ and $p$, since if the $\rho$ variations are ignored, we always have $2\delta c/c=\delta p/p$, and these constraints are not independent." + Thus. we need to check if the actial ccuation of state used iu solar model conrputations allows hese quantities to be independent.," Thus, we need to check if the actual equation of state used in solar model computations allows these quantities to be independent." + Another basic problem iu trvius to determine Z usi Eqs. (, Another basic problem in trying to determine $Z$ using Eqs. ( +231) is that in general we would expect |[9Z|.<< X|. while the «erivaIves warf.,"3–4) is that in general we would expect $|\delta Z|<<|\delta X|$ , while the derivatives w.r.t." + Z are sinaller than those wit., $Z$ are smaller than those w.r.t. + X and heico we would expect he ó9Z tec to be uuch siualler than the à.X terii makine it difficult determine Z using these equations.," $X$ and hence we would expect the $\delta Z$ term to be much smaller than the $\delta X$ term, making it difficult to determine $Z$ using these equations." + Thus we cau only hope o use these equatious to deteruiιο Poaud X. while Z can be determined from equations oftretinal ecquilibr hrough the opacity. which depeucds scusitively on Z.," Thus we can only hope to use these equations to determine $T$ and $X$, while $Z$ can be determined from equations of thermal equilibrium through the opacity, which depends sensitively on $Z$." + Fie., Fig. + E shows the ratio of partialderivatives for e aud p. asa function of rin a solar nocdel and it is clear that these derivatives are alinost equa.," 4 shows the ratio of partial derivatives for $c^2$ and $p$, as a function of $r$ in a solar model and it is clear that these derivatives are almost equal." + The wigeOOes in the curve are probably due to errors in estimating these derivatives aud it is clear that the departure of the ratio from uuitv is conrparable to these errors. waticularly. for the derivatives with respect to (X.," The wiggles in the curve are probably due to errors in estimating these derivatives and it is clear that the departure of the ratio from unity is comparable to these errors, particularly, for the derivatives with respect to $X$." + Thus. for the solu case these two constraints are uot indoepexdeut aid it is demonstrably not possible to get auv additional information by using the pressure profile.," Thus, for the solar case these two constraints are not independent and it is demonstrably not possible to get any additional information by using the pressure profile." + Αν attempt to do so will ouly vicld arbitrary results maenifvine the errors arising from those in the equation of state aud primary inversions., Any attempt to do so will only yield arbitrary results magnifying the errors arising from those in the equation of state and primary inversions. + Iu order to estimate the extent of error maeuification we can try to compute the ratio and simular ratios between derivatives with respect to (T.Z) or CX.Z).," In order to estimate the extent of error magnification we can try to compute the ratio and similar ratios between derivatives with respect to $(T,Z)$ or $(X,Z)$." + It turus out that al these quautities are greater than 200 over the eutire solar model., It turns out that all these quantities are greater than 200 over the entire solar model. + Thus all errors will be maguted by a factor of at least 200. if we attempt to determine the Z profile. i1 addition to T..X profiles.," Thus all errors will be magnified by a factor of at least 200, if we attempt to determine the $Z$ profile, in addition to $T,X$ profiles." + Even if we do not impose the additional constraint arising frou pressure. we can calculate the pressure profile using t16 OPAL equation of state from the inferred T.p.IX. and assunied Z profiles.," Even if we do not impose the additional constraint arising from pressure, we can calculate the pressure profile using the OPAL equation of state from the inferred $T,\rho,X$ and assumed $Z$ profiles." + As imnenutioned earlier. we also apply the relativistic corrections (Elliot IXosovichev 1998]) to the equation of state.," As mentioned earlier, we also apply the relativistic corrections (Elliot Kosovichev \cite{ell98}) ) to the equation of state." + This p-profile can he conipared with that inferred from primary luverslons using the equation of hydrostatic equilibriua and Fie., This $p$ -profile can be compared with that inferred from primary inversions using the equation of hydrostatic equilibrium and Fig. + 5 shows the results., 5 shows the results. +" It is clear hat even without applying jo adiitional coustraiut ron p(T.p..X.Z) the resulting xofile Comes ou to he ταν οose to the ""iudependently oeterre profile. well wihin the 1o error hinüts."," It is clear that even without applying the additional constraint from $p(T,\rho,X,Z)$ the resulting profile comes out to be very close to the “independently” inferred profile, well within the $1\sigma$ error limits." + Moreover. ie inferred profile is rather insensitive to Z aud hence ffectiugc» a changeC» in Z is unlikely to produce the profiles vat will match the primary iuversion exactly.," Moreover, the inferred profile is rather insensitive to $Z$ and hence effecting a change in $Z$ is unlikely to produce the profiles that will match the primary inversion exactly." + It is. ierefore. evideit tha he pressure profile does not xovide an iude)onden constraint.," It is, therefore, evident that the pressure profile does not provide an independent constraint." + There are only two oeadependent constraints (0.8.. ον p) that can be calculated youn the priuary inversious and it becomes well nigh oeupossible to decrnuue Z profile iu additiou to the 7. xofiles.," There are only two independent constraints (e.g., $c,\rho$ ) that can be calculated from the primary inversions and it becomes well nigh impossible to determine $Z$ profile in addition to the $T,X$ profiles." + We have stressed earlicr that if is not feasible to determine both .X aud Z profiles. in addition to the teiiperature. four equations of thermal equilibrium axd primary iuversious.," We have stressed earlier that it is not feasible to determine both $X$ and $Z$ profiles, in addition to the temperature, from equations of thermal equilibrium and primary inversions." + Towever. we cau reverse the process and determine the Z profile instead of the V xofile. usingi these equations.," However, we can reverse the process and determine the $Z$ profile instead of the $X$ profile, using these equations." + We. therefore. prescribe au (X profile YOUL some solar model aud seek to determine the Z profile using the equations described earlier.," We, therefore, prescribe an $X$ profile from some solar model and seek to determine the $Z$ profile using the equations described earlier." + In this case the equatiou of state e=c(T.p..X.Z) issed to determine { aud then uxue Eqs. (," In this case the equation of state $c=c(T,\rho,X,Z)$ is used to determine $T$ and then using Eqs. (" +"12) we can deerniue L, and B.",1–2) we can determine $L_r$ and $\kappa$. + From the opacity & woe can determine the required vali eof Z usi1ο the OPAL opacity tables., From the opacity $\kappa$ we can determine the required value of $Z$ using the OPAL opacity tables. + Tius dno this process we wolId also ect an estimate of opacity variations required to make the solar model cousisteut with helioseisiuic data., Thus in this process we would also get an estimate of opacity variations required to make the solar model consistent with helioseismic data. + This is «λα to what has. indeed. been done by Tripathy (1998)) except for the fact that," This is similar to what has, indeed, been done by Tripathy \cite{tri98}) ) except for the fact that" +than 907 for WATS. based largely on tailed sources at smaller redshifts than our sources.,"than $\sim$ $^\circ$ for WATs, based largely on tailed sources at smaller redshifts than our sources." + Although it would be relevant to examine the ellects of resolution and surface brightness sensitivity as one finds more tailed sources at moderate ancl high redshifts. the opening anele of 1159 is close to that of a WAT.," Although it would be relevant to examine the effects of resolution and surface brightness sensitivity as one finds more tailed sources at moderate and high redshifts, the opening angle of S1189 is close to that of a WAT." + Although WATS do tend to be associates with the dominant aegalaxv. it could be associated with a bright.C agalaxy close to the brightest galaxy in a cluster or group (seeRucinick&Owen1977:Blanonetal.2001).," Although WATs do tend to be associated with the dominant galaxy, it could be associated with a bright galaxy close to the brightest galaxy in a cluster or group \citep[see][]{Rudnick77, +Blanton01}." +. The associated galaxy Of SLISO is the 1jext brightest galaxy. only 0.75 mage fainter than the cD galaxy.," The associated galaxy of S1189 is the next brightest galaxy, only 0.75 mag fainter than the cD galaxy." + Ruclnick&Owen(LOTT) also suggested tha WATS tend to have larger sizes than the narrow-anele! tadled sources., \citet{Rudnick77} also suggested that WATs tend to have larger sizes than the narrow-angle tailed sources. + With a total size of over a MIpe. it woud be more consistent with the sizes of WATS.," With a total size of over a Mpc, it would be more consistent with the sizes of WATs." + Considering all the aspects. we presently classify it as a WAT.," Considering all the aspects, we presently classify it as a WAT." + We discuss the results of our AXOmega observations and the environment of this source in Section ??.., We discuss the results of our AAOmega observations and the environment of this source in Section \ref{S1189}. + S1192 is similar to S132 in both shape ancl extent. but the two tails in S1192 are more symmetric in brightness.," S1192 is similar to S132 in both shape and extent, but the two tails in S1192 are more symmetric in brightness." + Both the DSS red. and 3.6-pmi. images show a number of galaxies forming a lilamentary-like structure alone with the host galaxy of the WAT., Both the DSS red and $\mu$ m images show a number of galaxies forming a filamentary-like structure along with the host galaxy of the WAT. + The photometric redshifts (Itowan-ltobinsonctal.2008) within a racius of 2 arcmin. which corresponds to ~500 kpe at z=0.3690. show a concentration of ealaxies at about the redshift of 81192. (Pie. 5)).," The photometric redshifts \citep{Rowan-Robinson08} within a radius of 2 arcmin, which corresponds to $\sim$ 500 kpc at z=0.3690, show a concentration of galaxies at about the redshift of S1192 (Fig. \ref{S1192photz}) )." + This overdensity is largely due to the galaxies in the filamentary-like structure., This overdensity is largely due to the galaxies in the filamentary-like structure. + Although S031. exhibits. distinct gaps of emission between the radio core and the two tails of emission. the identification process described. by Norris.etal.(2006) unambiguouslv classifies these three components as a triple radio source.," Although S031 exhibits distinct gaps of emission between the radio core and the two tails of emission, the identification process described by \citet{Norris06} unambiguously classifies these three components as a triple radio source." + The peaks of emission in the tails are towards the radio core as, The peaks of emission in the tails are towards the radio core as +spacing.,spacing. + This lens array is glued on the back side of the KID sample., This lens array is glued on the back side of the KID sample. + The misalignment between the lens and the twin slot antenna is less than 10 pm. ensuring good coupling efficiency.," The misalignment between the lens and the twin slot antenna is less than 10 $\mu$ m, ensuring good coupling efficiency." + The general principles of frequency-multiplexed KID readout have been described in. detail elsewhere (Swensonetal. 2009.. Yatesetal.2009.. Monfardinietal. 2010)).," The general principles of frequency-multiplexed KID readout have been described in detail elsewhere \cite{swenson:84}, , \cite{yates:042504}, \cite{Monfardini:29}) )." + The current digital electronics used for the NIKA readout were developed in the context of an international collaboration known as the Open Source Readout (OSR) (Duanο”etal. 2010))., The current digital electronics used for the NIKA readout were developed in the context of an international collaboration known as the Open Source Readout (OSR) \cite{duan:7741}) ). + This system was based on a digital platform known as ROACH. itself having been developed in the context of another collaboration known as Center for Astronomy Signal Processing and Electronics Research (CASPER) (Parsonsetal. 2006).," This system was based on a digital platform known as ROACH, itself having been developed in the context of another collaboration known as Center for Astronomy Signal Processing and Electronics Research (CASPER) \cite{Parsons2006}) )." + The ROACH hardware provides powerful signal processing capabilities by integrating a field-programmable gate array. an on-board power pe. and a variety of high-speed communication interfaces.," The ROACH hardware provides powerful signal processing capabilities by integrating a field-programmable gate array, an on-board power pc, and a variety of high-speed communication interfaces." + Building on this. the OSR developed new high-speed. dual-input analog-to-digital and dual-output digital-to-analog interface cards.," Building on this, the OSR developed new high-speed, dual-input analog-to-digital and dual-output digital-to-analog interface cards." + For NIKA. both of these cards were clocked by the same rubidium-referenced external clock generator.," For NIKA, both of these cards were clocked by the same rubidium-referenced external clock generator." + Operating at 466 megasamples per second. the resulting useful IF measurement bandwidth of the NIKA readout was 233 MHz.," Operating at 466 megasamples per second, the resulting useful IF measurement bandwidth of the NIKA readout was 233 MHz." + In order to drive the individual pixels and subsequently read out their state. the NIKA collaboration developed customized software to use with the OSR hardware.," In order to drive the individual pixels and subsequently read out their state, the NIKA collaboration developed customized software to use with the OSR hardware." + Similar to standard lock-in techniques. the implemented algorithm allowed 112 separate measurement tones to be generated and simultaneously monitored within the IF measurement bandwidth.," Similar to standard lock-in techniques, the implemented algorithm allowed 112 separate measurement tones to be generated and simultaneously monitored within the IF measurement bandwidth." + The NIKA readout uses a standard up-down converter configuration based on two [IQ mixers per board to transpose the generated IF frequency comb to the resonator operating frequencies., The NIKA readout uses a standard up-down converter configuration based on two IQ mixers per board to transpose the generated IF frequency comb to the resonator operating frequencies. + One ROACH board and a set of IQ mixers was used for each array., One ROACH board and a set of IQ mixers was used for each array. + Currently. the LEKID array operates in the frequency range 1.27-1.45 GHz.," Currently, the LEKID array operates in the frequency range 1.27-1.45 GHz." + Within this bandwidth. 104 pixels and 8 off-resonance blind tones could be used for measurement.," Within this bandwidth, 104 pixels and 8 off-resonance blind tones could be used for measurement." + The antenna-coupled KID array has a central pixel core operating at 5-5.2 GHz., The antenna-coupled KID array has a central pixel core operating at 5-5.2 GHz. + Due to the larger inter-resonator frequency spacing of this array. only 72 core pixels could be simultaneously measured out of the total 256 pixels in the array.," Due to the larger inter-resonator frequency spacing of this array, only 72 core pixels could be simultaneously measured out of the total 256 pixels in the array." + The response of every pixel imn an array Is measured simultaneously and broadeast via UDP packets by the ROACH electronics to the control computers at a rate of 22 Hz., The response of every pixel in an array is measured simultaneously and broadcast via UDP packets by the ROACH electronics to the control computers at a rate of 22 Hz. + The individual pixel responses are composed of a pair of in-phase (1) and quadrature (Q) values which result from the final stage of digital mixing and low-pass filtering., The individual pixel responses are composed of a pair of in-phase $I$ ) and quadrature $Q$ ) values which result from the final stage of digital mixing and low-pass filtering. + Theses values can be translated into the traditional transmission phase and amplitude using the identities € = aretan(Q//) and amplitudes = P + Q., Theses values can be translated into the traditional transmission phase and amplitude using the identities $\theta$ = $\arctan(Q/I)$ and $^2$ = $I^2$ + $Q^2$. + An alternative approach is to plot these values in the complex plane., An alternative approach is to plot these values in the complex plane. + An example of a standard frequency sweep around a resonance is provided in 4((a)., An example of a standard frequency sweep around a resonance is provided in (a). + Small changes in illumination result primarily in motion around this curve and thus it is convenient to define a new angle 6 about the center of curvature (7...O..): where $0ση] rotates the plane such that the curve intersects the X axis at the resonance frequency fo.," Small changes in illumination result primarily in motion around this curve and thus it is convenient to define a new angle $\phi$ about the center of curvature $(I_c, Q_c)$ : where $\phi_0$ rotates the plane such that the curve intersects the x axis at the resonance frequency $f_0$." + We have observed that the KID response to radiation depends critically on the driving power and frequency of the readout electronics., We have observed that the KID response to radiation depends critically on the driving power and frequency of the readout electronics. + While still not fully understood. it is reasonable to conjecture that this dependence could be causedby: non-linear thinfilm effects. quasiparticle generation," While still not fully understood, it is reasonable to conjecture that this dependence could be causedby: non-linear thinfilm effects, quasiparticle generation" +boundary.,boundary. + The mass-averaged CNO abundance in the envelope reached ~ 0.206 at the end of this simulation. close to the value found for model A. These results confirm that 800 km is an appropriate choice for the width of the computational domain. stressing that above a threshold value the course of the TNR is insensitive to the adopted width. in agreement with the sensitivity study performed by Glasner et al. (," The mass-averaged CNO abundance in the envelope reached $\sim$ 0.206 at the end of this simulation, close to the value found for model A. These results confirm that 800 km is an appropriate choice for the width of the computational domain, stressing that above a threshold value the course of the TNR is insensitive to the adopted width, in agreement with the sensitivity study performed by Glasner et al. (" +2007).,2007). +" The specific length adopted along the vertical direction (see model G). while unimportant for the time of appearance of the instabilities (around 155 s after the start of the simulation. as in model A), affects the time required to reach the outer boundary. located 200 km above the value adopted for model A. Moreover. the larger extension of the computational domain along the radial (vertical). direction allows the convective eddies to pump additional metal-rich core material into the envelope compared with all the simulations reported previously in this paper."," The specific length adopted along the vertical direction (see model G), while unimportant for the time of appearance of the instabilities (around 155 s after the start of the simulation, as in model A), affects the time required to reach the outer boundary, located 200 km above the value adopted for model A. Moreover, the larger extension of the computational domain along the radial (vertical) direction allows the convective eddies to pump additional metal-rich core material into the envelope compared with all the simulations reported previously in this paper." + Indeed. the mean. mass-averaged metallicity in model G achieves the largest value of all the simulations reported. ~0.291.," Indeed, the mean, mass-averaged metallicity in model G achieves the largest value of all the simulations reported, $\sim 0.291$." + This result suggests that the likely mean mass-averaged metallicity driven by Kelvin-Helmholtz instabilities should be Z=0.3.," This result suggests that the likely mean mass-averaged metallicity driven by Kelvin-Helmholtz instabilities should be $Z +\approx 0.3$." + In summary. we conclude that the size of the computational domain. above a certain threshold value. has little influence on the physical quantities that are more directly related with the mixing process at the core-envelope interface.," In summary, we conclude that the size of the computational domain, above a certain threshold value, has little influence on the physical quantities that are more directly related with the mixing process at the core-envelope interface." + All simulations discussed so far (e.g.. models A to G) were performed with a resolution of 1.56x km. a value similar to the minimum resolutions adopted in Glasner et al. (," All simulations discussed so far (e.g., models A to G) were performed with a resolution of $1.56 \times 1.56$ km, a value similar to the minimum resolutions adopted in Glasner et al. (" +2007) which is roughly ~1.4»ΤΕ km. and in Kercek et al. (,"2007) which is roughly $\sim 1.4 \times 1.4$ km, and in Kercek et al. (" +1998). 1x2 km.,"1998), $1 \times 2$ km." + To quantitatively assess the possible effect of the resolution. two additional test cases were computed with exactly the same input parameters as in model A but with two different resolutions: |x1 km (model H) and 0.39x km (modelή.," To quantitatively assess the possible effect of the resolution, two additional test cases were computed with exactly the same input parameters as in model A but with two different resolutions: $1 \times +1$ km (model H) and $0.39 \times 0.39$ km (model." + As shown in Table |. the increase in resolution produces a delay in the time required for the first instabilities to develop. {κη.," As shown in Table 1, the increase in resolution produces a delay in the time required for the first instabilities to develop, $t_{\rm +KH}$." + This seems to be a numerical artifact., This seems to be a numerical artifact. + In models with à coarser resolution. the larger size of the blocks artificially generates a larger numerical diffusion compared to models with a finer resolution (a similar resolution dependence ts clearly seen as well in the Kercek et al.," In models with a coarser resolution, the larger size of the blocks artificially generates a larger numerical diffusion compared to models with a finer resolution (a similar resolution dependence is clearly seen as well in the Kercek et al." + 1998 simulations)., 1998 simulations). + Actually. the ratio of differences in. the initial build up times (1.e.. (model I-model A)/(model H-model A)) scales approximately as the zone size dimensions to the power of two.," Actually, the ratio of differences in the initial build up times (i.e., (model I-model A)/(model H-model A)) scales approximately as the zone size dimensions to the power of two." + This is a purely numerical perturbation that forces the development of instabilities., This is a purely numerical perturbation that forces the development of instabilities. + To test this hypothesis. we computed an additional test case (not included in Table 1l). identical to model A but without any initial perturbation.," To test this hypothesis, we computed an additional test case (not included in Table 1), identical to model A but without any initial perturbation." + The onset of the instabilities in such an extremely low numerical diffusion. regime is substantially delayed., The onset of the instabilities in such an extremely low numerical diffusion regime is substantially delayed. + The simulations reported by Glasner et al. (, The simulations reported by Glasner et al. ( +1997) also show the early appearance of instabilities 1n à model with substantial numerical noise:p,1997) also show the early appearance of instabilities in a model with substantial numerical noise:. +"erturbations, A similar behavior is also found for the time required for the convective front to reach the outer boundary. ty. and for the history of the nuclear energy generation rate (Fig."," A similar behavior is also found for the time required for the convective front to reach the outer boundary, $t_Y$, and for the history of the nuclear energy generation rate (Fig." + 4)., 4). + As expected. filamentary structures and convective cells are better resolved in the finer resolution model I. compared to those computed with somewhat coarser grids (models A and H: see Fig.," As expected, filamentary structures and convective cells are better resolved in the finer resolution model I, compared to those computed with somewhat coarser grids (models A and H; see Fig." + 5)., 5). + These minor differences do not. however. show significant variations in the final. mean CNO abundances achieved in the envelope: while Z~0.224 in model A. models H and I yield 0.201 and 0.205. by mass. respectively.," These minor differences do not, however, show significant variations in the final, mean CNO abundances achieved in the envelope: while $Z\sim 0.224$ in model A, models H and I yield 0.201 and 0.205, by mass, respectively." + Similar agreement is found in the peak temperatures achieved and in the overall nuclear energy generation rates (Fig., Similar agreement is found in the peak temperatures achieved and in the overall nuclear energy generation rates (Fig. + 4)., 4). + Thus. the adopted resolution has not a critical effect for the mixi£z models presented in this work.," Thus, the adopted resolution has not a critical effect for the mixing models presented in this work." + The variation in the final mean CNO abundance in the envelope. under the range of resolutions adopted. is only about (when comparing results for models A. H. and D. a quite reasonable value.," The variation in the final mean CNO abundance in the envelope, under the range of resolutions adopted, is only about (when comparing results for models A, H, and I), a quite reasonable value." + In this paper we have reported results for à series of nine 2-D numerical simulations that test the influence of the initial perturbation (duration. strength. location. and size). the resolution of the grid. and the size of the computational domain on the results.," In this paper we have reported results for a series of nine 2-D numerical simulations that test the influence of the initial perturbation (duration, strength, location, and size), the resolution of the grid, and the size of the computational domain on the results." + We have shown that mixing at the core-envelope interface proceeds almost independently of the specific choice of such initial parameters. above threshold values.," We have shown that mixing at the core-envelope interface proceeds almost independently of the specific choice of such initial parameters, above threshold values." + The study confirms that the metallicity enhancement inferred from observations of the ejecta of classical novae can be explained by Kelvin-Helmholtz instabilities. powered by an effective shearing resulting from the initial buoyancy.," The study confirms that the metallicity enhancement inferred from observations of the ejecta of classical novae can be explained by Kelvin-Helmholtz instabilities, powered by an effective shearing resulting from the initial buoyancy." + Fresh core material is efficiently transported from the outermost layers of the white dwarf core and mixed with the approximately solar composition material of the accreted envelope., Fresh core material is efficiently transported from the outermost layers of the white dwarf core and mixed with the approximately solar composition material of the accreted envelope. +" As soon as ""C and ΙΟ are dredged up. convection sets in and small convective cells appear. accompanied by an increased nuclear energy generation rate."," As soon as $^{12}$ C and $^{16}$ O are dredged up, convection sets in and small convective cells appear, accompanied by an increased nuclear energy generation rate." + The size of these convective cells increases in time., The size of these convective cells increases in time. + Eventually. these cells merge into large convective eddies with a size comparable to the envelope height.," Eventually, these cells merge into large convective eddies with a size comparable to the envelope height." + The range of mean mass-averaged envelope metallicities obtained in our simulations at the time when the convective front hits the outer boundary. 0.21—0.29. matches the values obtained for classical novae hosting CO. white dwarfs.," The range of mean mass-averaged envelope metallicities obtained in our simulations at the time when the convective front hits the outer boundary, $0.21 - 0.29$, matches the values obtained for classical novae hosting CO white dwarfs." + It is. however. worth noting that the convective pattern is actually produced by the adopted geometry (e.g.. 2-D). forcing the fluid motion to behave very differently than 3-D convection (Shore 2007: Meakin Arnett 2007).," It is, however, worth noting that the convective pattern is actually produced by the adopted geometry (e.g., 2-D), forcing the fluid motion to behave very differently than 3-D convection (Shore 2007; Meakin Arnett 2007)." + Nevertheless. the levels of metallicity enhancement found in our 2-D simulations will," Nevertheless, the levels of metallicity enhancement found in our 2-D simulations will" +intermeciate-miass X-ray. binaries where it is assumed. that the neutron star was formed. by core. collapse (CC) of a massive (AL SM.) star. and is subsequently. spun up to millisecond. periods during an accretion disc. phase (Bhattacharya van den Heuvel 1991: Bisnovatvi-Ixogan Ixomberg 1974).,"intermediate-mass X-ray binaries where it is assumed that the neutron star was formed by core collapse (CC) of a massive $M> +8\Msun$ ) star, and is subsequently spun up to millisecond periods during an accretion disc phase (Bhattacharya van den Heuvel 1991; Bisnovatyi-Kogan Komberg 1974)." +" We shall refer to this class of objects as the 7""Core-C'ollapsed. LAXDs. ancl IMXDs or. more xiellv. the LAINBs(CCO/INMNDs(CC)."," We shall refer to this class of objects as the “Core-Collapsed LMXBs and IMXBs” or, more briefly, the LMXBs(CC)/IMXBs(CC)." + AXecretion. induced ield. decay is an integral part of this model which appears ralausible from. a theoretical view-point. particularly if he fields in neutron stars are of crustal origin (Ixonar Bhattacharya 1997. but see. Rucerman 2006 for an alternative. model).," Accretion induced field decay is an integral part of this model which appears plausible from a theoretical view-point, particularly if the fields in neutron stars are of crustal origin (Konar Bhattacharya 1997, but see Ruderman 2006 for an alternative model)." + Reeardless of the origin of the low ields in the MSPs. a long standing problem with the LAINB/LAINB scenario has been the difficulty in reconciling heir semi-empirical birth rates with those of the radio MSPs (e.g. Lorimer 1995: Cordes Chernoll 1997).," Regardless of the origin of the low fields in the MSPs, a long standing problem with the LMXB/IMXB scenario has been the difficulty in reconciling their semi-empirical birth rates with those of the radio MSPs (e.g. Lorimer 1995; Cordes Chernoff 1997)." + The oblem with the birth rates has been confirmed. by recent population svnthesis calculations which have also uighlighted the cillicultics in explaining the observed orbital »eriod distribution of AISPs on the LAINB(CC)/LAINBICC) scenario (Pfhal et al., The problem with the birth rates has been confirmed by recent population synthesis calculations which have also highlighted the difficulties in explaining the observed orbital period distribution of MSPs on the LMXB(CC)/IMXB(CC) scenario (Pfhal et al. + 2003)., 2003). + Another often discussed. channel for the production of AISPs involves the ALC of an ONeMG white dwarf (Michel 1987)., Another often discussed channel for the production of MSPs involves the AIC of an ONeMG white dwarf (Michel 1987). + Hlere. during the course of mass transfer. a white dwarf reaches the Chandrasekhar limit. and. collapses to form a neutron star (Bhattacharva Van den Heuvel 1991).," Here, during the course of mass transfer, a white dwarf reaches the Chandrasekhar limit, and collapses to form a neutron star (Bhattacharya Van den Heuvel 1991)." + In the AIC scenario. we may expect the magnetic field distribution of the AISPs to reflect in some way the magnetic field distribution of their progenitor white cwarfs obviating the need Lor field decay.," In the AIC scenario, we may expect the magnetic field distribution of the MSPs to reflect in some way the magnetic field distribution of their progenitor white dwarfs obviating the need for field decay." + A low-mass or intermediate-niass X-rav binary phase may follow the collapse of the white dwarf ancl we shall refer to this class of objects as the “Accretion Induced: Collapse LAINBs and. LAINBs” or. more. briellv. as the LMNDsCAICO/ININDsCAIC).," A low-mass or intermediate-mass X-ray binary phase may follow the collapse of the white dwarf and we shall refer to this class of objects as the “Accretion Induced Collapse LMXBs and IMXBs” or, more briefly, as the LMXBs(AIC)/IMXBs(AIC)." + Population. synthesis calculations indicate that the expected birth rates from the AIC channel may be significantly higher than those from the LMXDB(CCO/INMXD(CC) route (Lurley et al., Population synthesis calculations indicate that the expected birth rates from the AIC channel may be significantly higher than those from the LMXB(CC)/IMXB(CC) route (Hurley et al. + 2002: Tout οἱ al 2007: Llurley 2006. private communication)," 2002; Tout et al 2007; Hurley 2006, private communication)." + In this paper. we present an analysis of the 1.5 kpc sample of MSPs which is considered. to. be. sulficientIv sampled out (Lyne et al.," In this paper, we present an analysis of the 1.5 kpc sample of MSPs which is considered to be sufficiently sampled out (Lyne et al." + 1998: IxXramer et al., 1998; Kramer et al. + 1998). with the aim of establishing. the MSP birth. properties. anc constraining the cdillerent. models that have been. proposec for their origin., 1998) with the aim of establishing the MSP birth properties and constraining the different models that have been proposed for their origin. + Our estimate of the Galactic birth rate of the AISPs is at the upper end. of previous estimates (c.g. Cordes Chernol! 1997) anc again brings into question the LAINB(CO)/LAINB(CC) scenario as being the dominan route for the origin of the MSPs., Our estimate of the Galactic birth rate of the MSPs is at the upper end of previous estimates (e.g. Cordes Chernoff 1997) and again brings into question the LMXB(CC)/IMXB(CC) scenario as being the dominant route for the origin of the MSPs. + The paper is arrange as Lollows., The paper is arranged as follows. + In section. 2 we cescribe the clata set ane our mocel, In section 2 we describe the data set and our model. + Our results are. presented: anc discussed. in section 3 where we also present the case for and. agains LAINBICO)AAINB(CO) progenitors anc ALC progenitors [or the AISPs., Our results are presented and discussed in section 3 where we also present the case for and against LMXB(CC)/IMXB(CC) progenitors and AIC progenitors for the MSPs. + Our conclusions are presented in section 4., Our conclusions are presented in section 4. + In 1998. Ixramer et al.," In 1998, Kramer et al." + conducted a very. detailed: study ainied. at comparing the radio emission properties of MISPs to those of normal pulsars., conducted a very detailed study aimed at comparing the radio emission properties of MSPs to those of normal pulsars. + In their work. they restricted their comparative studies to objects within 1.5 kpe. on the grounds that the. population of all. raclio-pulsars is sulliciently sampled out up to this distance. as first pointed out bx Lyne et al. (," In their work, they restricted their comparative studies to objects within 1.5 kpc, on the grounds that the population of all radio-pulsars is sufficiently sampled out up to this distance, as first pointed out by Lyne et al. (" +1998).,1998). + Itecently. this assumption has eained Further strength through the hieh-latituce survey of jurgav et al. (," Recently, this assumption has gained further strength through the high-latitude survey of Burgay et al. (" +2006) in the region of the sky limited. by 2207«/260 and Jb]κ60 conducted with the 20-cm multi-beam receiver on the Parkes racdio-telescopoe.,2006) in the region of the sky limited by $220\gradi0.1 are statistically significant(?)."," We note that in the UV luminosity range of PG 1126-041 there is a $\sigma$ dispersion in the expected $\alpha_{\rm{ox}}(\ell_{2500\AA})$ of about 0.1, so that only values of $|\Delta\alpha_{\rm{ox}}|>0.1$ are statistically significant." +". We also computed the £277,2keV luminosity densities corrected for intrinsic X-ray absorption, and the corresponding o5?""Ox and Aoc""."," We also computed the $\ell_{2\,keV}^{corr}$ luminosity densities corrected for intrinsic X-ray absorption, and the corresponding $\alpha_{\rm{ox}}^{\rm{corr}}$ and $\Delta\alpha_{\rm{ox}}^{\rm{corr}}$." + In Table 6 we report the Optical/X-ray photometry results., In Table \ref{tabAOX} we report the Optical/X-ray photometry results. + There are variations in the observed luminosity density of PG 1126-041 both at UV and at X-ray wavelength., There are variations in the observed luminosity density of PG 1126-041 both at UV and at X-ray wavelength. +" While the observed 2500 A flux density steadily increases from 2004 to 2009, and is varying by about30%,, the observed 2 keV flux density increases from 2004 to 2008, and then decreases again in 2009, with variations as high as a factor of ~4—5 between the Dec. 2008 and the 2009 Long Look observations."," While the observed 2500 $\AA$ flux density steadily increases from 2004 to 2009, and is varying by about, the observed 2 keV flux density increases from 2004 to 2008, and then decreases again in 2009, with variations as high as a factor of $\sim 4-5$ between the Dec. 2008 and the 2009 Long Look observations." +" As a result, the observed o, is variable between the different epochs, spanning from values typical of radio quiet type 1 AGN (i.e., αοχ~—1.7 in the Dec. 2008 observation) to values typical of Soft X-ray Weak AGN (i.e., @x~—2 in the 2009 Long Look observation)."," As a result, the observed $\alpha_{\rm{ox}}$ is variable between the different epochs, spanning from values typical of radio quiet type 1 AGN (i.e., $\alpha_{\rm{ox}}\sim -1.7$ in the Dec. 2008 observation) to values typical of Soft X-ray Weak AGN (i.e., $\alpha_{\rm{ox}}\sim -2$ in the 2009 Long Look observation)." +" However, compared to the expected dox(y5994), the source is found to be “EX-ray weak"" in all the epochs, with AQox—0.3—0.6."," However, compared to the expected $\alpha_{\rm{ox}}(\ell_{2500\AA})$, the source is found to be “ÊX-ray weak” in all the epochs, with $\Delta\alpha_{\rm{ox}}\sim -0.3-0.6$." +" Once the effect of intrinsic X-ray absorption is taken into account, the maximum observed variations in the 2 keV flux density between the different epochs decrease to about a factor of two."," Once the effect of intrinsic X-ray absorption is taken into account, the maximum observed variations in the 2 keV flux density between the different epochs decrease to about a factor of two." +" Consequently, also the Aa, decreases to Aa”~0.1—0.3."," Consequently, also the $\Delta\alpha_{\rm{ox}}$ decreases to $\Delta\alpha_{\rm{ox}}^{\rm{corr}}\sim 0.1-0.3$." +" It is worth noting that there could be intrinsic UV absorption at the redshift of the source, e.g. by dust in the AGN host galaxy; the amount of intrinsic UV absorption is unknown so we do not try to model it, but we keep in mind that this effect might make the actual (intrinsic) o, flatter than QoxCOIT-"," It is worth noting that there could be intrinsic UV absorption at the redshift of the source, e.g. by dust in the AGN host galaxy; the amount of intrinsic UV absorption is unknown so we do not try to model it, but we keep in mind that this effect might make the actual (intrinsic) $\alpha_{\rm{ox}}$ flatter than $\alpha_{\rm{ox}}^{\rm{corr}}$." + PG 1126-041 is observed to be highly variable in X-rays on time scales of both months and kiloseconds., PG 1126-041 is observed to be highly variable in X-rays on time scales of both months and kiloseconds. + The variability on time scales of months (observed to be as high as 4x in flux) is dominated by a spectral component emerging at E< 6 keV (Fig. 1))., The variability on time scales of months (observed to be as high as $\times$ in flux) is dominated by a spectral component emerging at $E\lesssim$ 6 keV (Fig. \ref{FIG1}) ). +" On the other hand, the RMS variability analysis performed on the 2009 Long Look pn observation (92 ks of contiguous good exposure time) revealed the presence of a spectral component emerging only at Ez1.5 keV, which dominates the variability on time scales of kiloseconds (up to variations in flux, Fig. 2))."," On the other hand, the RMS variability analysis performed on the 2009 Long Look pn observation (92 ks of contiguous good exposure time) revealed the presence of a spectral component emerging only at $E\gtrsim 1.5$ keV, which dominates the variability on time scales of kiloseconds (up to variations in flux, Fig. \ref{FIG2}) )." + A wealth of information has been obtained both on the intrinsic X-ray continuum emission of PG 1126-041 and on the reprocessing media that happen to be in the inner regions of this AGN., A wealth of information has been obtained both on the intrinsic X-ray continuum emission of PG 1126-041 and on the reprocessing media that happen to be in the inner regions of this AGN. +" We discuss our results starting from the inner regions around the SMBH (i.e., the shortest time scales) and moving farther out (i.e., the longest time scales)."," We discuss our results starting from the inner regions around the SMBH (i.e., the shortest time scales) and moving farther out (i.e., the longest time scales)." + We adopt the SMBH mass estimate of Mgy=1.2x108Mo as given by?.," We adopt the SMBH mass estimate of $M_{BH}= 1.2 +\times 10^{8}\,M_{\odot}$ as given by." +. The Mg estimated by through scaling relations is a factor of 2.4 lower., The $M_{BH}$ estimated by through scaling relations is a factor of 2.4 lower. + Adopting the bolometric luminosity [νο=10!?Lo and assuming an accretion efficiency 7=0.1 gives an accretion rate needed to power PG 1126-041 of M~0.7 Mo/yr and an Eddington ratio A=Lpoi/Leaa0.26.," Adopting the bolometric luminosity $L_{bol}=10^{12}\,L_{\odot}$ and assuming an accretion efficiency $\eta=0.1$ gives an accretion rate needed to power PG 1126-041 of $\dot{M}\sim 0.7\,M_{\odot}/$ yr and an Eddington ratio $\lambda\equiv L_{bol}/L_{Edd}\sim 0.26$." +" The gravitational radius is rg~1.8xX1019 cm and the corresponding light travel time is { 6005. Two absorbers are detected in the X-ray spectra of PG 1126-041, a moderately ionized (log£""~1.5 erg cm s!) and a highly ionized (log""~3.5 erg cm s!) one."," The gravitational radius is $r_g\sim 1.8\times 10^{13}$ cm and the corresponding light travel time is $t_L\sim 600$ s. Two absorbers are detected in the X-ray spectra of PG 1126-041, a moderately ionized $\log\xi^{m.i.}\sim 1.5$ erg cm $^{-1}$ ) and a highly ionized $\log\xi^{h.i.}\sim 3.5$ erg cm $^{-1}$ ) one." + Strong variations in both the intrinsic continuum and of the highly ionized outflowing absorber are responsible of the observed kilosecond time scale variability., Strong variations in both the intrinsic continuum and of the highly ionized outflowing absorber are responsible of the observed kilosecond time scale variability. +" The power-law photon index I~2 is found not to vary on kilosecond time scales, while the intensity of the intrinsic power-law spectrum ifollows the pattern of the 1.5-10 keV count rate over the whole observation (see the middle bottom panel of Fig."," The power-law photon index $\Gamma\sim 2$ is found not to vary on kilosecond time scales, while the intensity of the intrinsic power-law spectrum ifollows the pattern of the 1.5-10 keV count rate over the whole observation (see the middle bottom panel of Fig." +" 2 and Table 4)), and doubles in a time interval A: lasting about 8 ks (the seventh interval)."," \ref{FIG2} and Table \ref{tabletimre}) ), and doubles in a time interval $\Delta t$ lasting about 8 ks (the seventh interval)." + The variability time scale of the intrinsic continuum can set a constraint on the geometrical size D of the X-ray, The variability time scale of the intrinsic continuum can set a constraint on the geometrical size $D$ of the X-ray +he optical light from the rest of the system (van Paraclijs 1983. van Paraclijs AleClintock 1995)) particularly. in he outburst phase. and the companion itself may only να. evident at a very faint level when the system is in quiescence.,"the optical light from the rest of the system (van Paradijs 1983, van Paradijs McClintock 1995), particularly in the outburst phase, and the companion itself may only be evident at a very faint level when the system is in quiescence." + Various approximately linear. relationships rclween the orbit. period. outburst amplitude. absolute magnitude ancl distance have been derived. for LAINB ransients by Shahbaz Ixuulkers (1098).," Various approximately linear relationships between the orbit period, outburst amplitude, absolute magnitude and distance have been derived for LMXB transients by Shahbaz Kuulkers (1998)." + Although it is unclear if these relationships can be applied to such a low mass and short period system we obtain a pre-outburst magnitude of 128.75 lor SAX. JISOS.43658., Although it is unclear if these relationships can be applied to such a low mass and short period system we obtain a pre-outburst magnitude of =28.75 for SAX J1808.4–3658. + These relationships also give a quiescence absolute magnitude of ΔΙΣ) = 13.3 for the companion ancl M(cisc) = 4.65., These relationships also give a quiescence absolute magnitude of M(2) = 13.3 for the companion and M(disc) = 4.65. + The companion peak apparent magnitude of 16.7 implies a distance of «2.5 kpc., The companion peak apparent magnitude of $\la$ 16.7 implies a distance of $<$ 2.5 kpc. + Given the uncertainties in the Shahbaz Ixuulkers (1998). relationships. this distance is not inconsistent with that deduced from the observation of wo Tvpe E X-ray. bursts during the 1996 outburst which indicate a distance of 4 kpe (in 1 Zand οἱ al.," Given the uncertainties in the Shahbaz Kuulkers (1998) relationships, this distance is not inconsistent with that deduced from the observation of two Type I X-ray bursts during the 1996 outburst which indicate a distance of 4 kpc (in 't Zand et al." + 1998)., 1998). + The optical decline appears to precede the X-ray decline w 3+1 days., The optical decline appears to precede the X-ray decline by $3\pm1$ days. + This delay could be interpreted as the time aken to clear out the accretion disc round the neutron star after a sharp drop in the mass flow rate. by roche [obe overllow or stellar wind. from the companion.," This delay could be interpreted as the time taken to clear out the accretion disc round the neutron star after a sharp drop in the mass flow rate, by roche lobe overflow or stellar wind, from the companion." + The delay hen represents a flow transit time from the outer to the inner cdge of the disc., The delay then represents a flow transit time from the outer to the inner edge of the disc. + Vhis explanation also suggests that he disc hot spot might decrease in intensity as the general accretion rate diminishes following the main transient event., This explanation also suggests that the disc hot spot might decrease in intensity as the general accretion rate diminishes following the main transient event. + Our observations show that both the optical intensity and its modulation amplitude at the binary period decrease., Our observations show that both the optical intensity and its modulation amplitude at the binary period decrease. + The sudden and rapid X-ray decline then follows since the disc is now mostly depleted. with little remaining material available to spiral in towards the neutron star. and a low external accretion rate to replenish it.," The sudden and rapid X-ray decline then follows since the disc is now mostly depleted, with little remaining material available to spiral in towards the neutron star, and a low external accretion rate to replenish it." + Phe sharp X-ray decline is conventionally expected. for LAINB transients. and can be explained in terms of the closure of a centrifugal barrier at low accretion rates as the magnetosphere of a neutron star reaches its corotation radius (Campana et al.," The sharp X-ray decline is conventionally expected for LMXB transients, and can be explained in terms of the closure of a centrifugal barrier at low accretion rates as the magnetosphere of a neutron star reaches its corotation radius (Campana et al." + 1998)., 1998). + In the case of SAX JISOS.E3658 we then see a plateau in the optical flux lasting 22 weeks but there are no simultaneous X-ray observations., In the case of SAX J1808.4–3658 we then see a plateau in the optical flux lasting $\ga$ 2 weeks but there are no simultaneous X-ray observations. + A final optical decline over the [ew weeks after this plateau is not constrained by our observations., A final optical decline over the few weeks after this plateau is not constrained by our observations. + Our observations have established bevonc doubt that the candidate proposed by Roche et al (1998) as the optical counterpart for the A-ray transient SAN JISOS43658 is correct., Our observations have established beyond doubt that the candidate proposed by Roche et al (1998) as the optical counterpart for the X-ray transient SAX J1808.4–3658 is correct. + This has been demonstrated. by the following kev points as the proposed object: Since this source was seen in an earlier. transient outburst. during September 1996 (in t Zand et al., This has been demonstrated by the following key points as the proposed object: Since this source was seen in an earlier transient outburst during September 1996 (in 't Zand et al. + 1998) it has most probably burst before and will do so again., 1998) it has most probably burst before and will do so again. +" The optical flux of SAN JISOS.43658 is expected to brighten on all these occasions so further observations. particularly, spectroscopy while in its brightest state. are highly desirable. We thank Ike Bolton. D. Phythian and B. Wilson. of the Physics Department technical support group for their invaluable work on the CCL) camera svstem."," The optical flux of SAX J1808.4–3658 is expected to brighten on all these occasions so further observations, particularly spectroscopy while in its brightest state, are highly desirable, We thank K. Bolton, D. Phythian and B. Wilson of the Physics Department technical support group for their invaluable work on the CCD camera system." + DP. Cieslik kindlv obtained some measurements between PLANET observations., P. Cieslik kindly obtained some measurements between PLANET observations. + We also thank T. Strohmayer of the PCA team for timely information on the occurrence of the transient., We also thank T. Strohmayer of the PCA team for timely information on the occurrence of the transient. +"date, the mean travel times vary with the azimuthal angle. with a magnitude of approximately 0.2 minutes relative to the average value inside penumbra.","date, the mean travel times vary with the azimuthal angle, with a magnitude of approximately 0.2 minutes relative to the average value inside penumbra." +" Additionally, the angular dependence of the variations of the mean travel times 1s different for different dates, which implies that such variations are not caused by the properties of the sunspot itself, but by some systematic effects in the helioseismie measurements."," Additionally, the angular dependence of the variations of the mean travel times is different for different dates, which implies that such variations are not caused by the properties of the sunspot itself, but by some systematic effects in the helioseismic measurements." +" More examinations of different sunspots confirmed that such variations are systematic measurement effects that are related to the projection effect, rather than caused by the real variations in solar structures or dynamics."," More examinations of different sunspots confirmed that such variations are systematic measurement effects that are related to the projection effect, rather than caused by the real variations in solar structures or dynamics." + Comparing Figure | with Figure 2," Comparing Figure \ref{fg1} + with Figure 2" +ihe OVI A1032 line.,the OVI $\lambda$ 1032 line. + There is emission from the CHI A977 line at a flux of x10. !! eig ? FL error). with a line width of 1.00.1 and a line center of 982.87 ((at the svstemic redshift. it woulcl have been al 982.61 A).," There is emission from the CIII $\lambda$ 977 line at a flux of $\times$ $^{-14}$ erg $^{-2}$ $^{-1}$ error), with a line width of $\pm$ 0.1 and a line center of 982.87 (at the systemic redshift, it would have been at 982.61 )." +" 1C 1459: This galaxy has among (he lowest Galactic HI column in (he sample and very little reddening (1.19x LO?"" 7). although it has the usual Galactic atomic absorption lines that can be seen on the stellar continuum (Figure 24)."," IC 1459: This galaxy has among the lowest Galactic HI column in the sample and very little reddening $\times$ $^{20}$ $^{-2}$ ), although it has the usual Galactic atomic absorption lines that can be seen on the stellar continuum (Figure 24)." + The airglow lines are strong during the daytime observing. so although only of the observing time was at night (only 2.5 ksec). the night-time data are better for the analvsis of the OVI region. while the total data set is better [or analvsis in the CIII region.," The airglow lines are strong during the daytime observing, so although only of the observing time was at night (only 2.5 ksec), the night-time data are better for the analysis of the OVI region, while the total data set is better for analysis in the CIII region." + There is a broad emission line coincident with the strong redshifted OVI line. which is relatively uncontaminated by Galactic absorption features (also present in the Lil2b channel).," There is a broad emission line coincident with the strong redshifted OVI line, which is relatively uncontaminated by Galactic absorption features (also present in the Lif2b channel)." + The weaker OVI line is not detected al a statistically significant level. but as it is half the strength of the OVI AI032 line. this is not inconsistent with a detection of the OVI A1032 line.," The weaker OVI line is not detected at a statistically significant level, but as it is half the strength of the OVI $\lambda$ 1032 line, this is not inconsistent with a detection of the OVI $\lambda$ 1032 line." + The CII A977 line is also detected. with a flux that is poorly determined because it is unclear where to mark the boundaries of the line., The CIII $\lambda$ 977 line is also detected with a flux that is poorly determined because it is unclear where to mark the boundaries of the line. + If we use (he single peak. to the blue of line center. the line width is 0.3 ((line flux of 1.3x10 11 ere em7 1) and a line center al 982.0 ((expected to be αἱ 982.5 A).," If we use the single peak, to the blue of line center, the line width is 0.8 (line flux of $\times$ $^{-14}$ erg $^{-2}$ $^{-1}$ ) and a line center at 982.0 (expected to be at 982.5 )." + If we use the weaker red part of the line as well. (he line center is exactly that expected lor the recession velocity. the line width becomes 2.1 ((at a line flux o£ 2.1x10. !! erg 7 1).," If we use the weaker red part of the line as well, the line center is exactly that expected for the recession velocity, the line width becomes 2.1 (at a line flux of $\times$ $^{-14}$ erg $^{-2}$ $^{-1}$ )." + Given the uncertainties associated with each of the lines. it is difficult to compare the OVI and CII] lines.," Given the uncertainties associated with each of the lines, it is difficult to compare the OVI and CIII lines." + This galaxy has à strong radio source and is known to be a LINER., This galaxy has a strong radio source and is known to be a LINER. + An important goal of the program is to test whether the X-ray cooling rate is a good predictor of the true cooling rate. which would be reflected in the OVI line Iuminosity. presumed (to be a better measure of the net cooling rate.," An important goal of the program is to test whether the X-ray cooling rate is a good predictor of the true cooling rate, which would be reflected in the OVI line luminosity, presumed to be a better measure of the net cooling rate." + There certainly is not a one-to-one relationship between the X-ray value of M (ALy) and the OVI value of AY (Mog). such as for the galaxies NGC 1399 and NGC 1404. (vo of the most X-ray luminous sources but with no detectable OVI emission.," There certainly is not a one-to-one relationship between the X-ray value of ${\dot{M}}$ ${\dot{M}}_X$ ) and the OVI value of ${\dot{M}}$ ${\dot{M}}_{OVI}$ ), such as for the galaxies NGC 1399 and NGC 1404, two of the most X-ray luminous sources but with no detectable OVI emission." + Llowever. there are statistical correlations between the X-ray and OVI cooling rates.," However, there are statistical correlations between the X-ray and OVI cooling rates." + For the analvsis of our sample. we have summarized the results in Table 3. where we eive a varietv of X-ray and optical properties. along with the OVI results.," For the analysis of our sample, we have summarized the results in Table 3, where we give a variety of X-ray and optical properties, along with the OVI results." + The measure of a detection is given by either upper limits. detections. or possible detections.," The measure of a detection is given by either upper limits, detections, or possible detections." + The detections are lines whose strength exceeds 360. and where the signal appears clearly on the spectrum., The detections are lines whose strength exceeds $\sigma$ and where the signal appears clearly on the spectrum. +13d in Barazzaetal. 2008)).,13d in \citealt{barazza08}) ). + The g—r color of our galaxies spans from ~0.2 to ~1.0 as shown in Figure 17.., The $g-r$ color of our late-type galaxies spans from $\sim$ 0.2to $\sim1.0$ as shown in Figure \ref{gr_bf}. +" This figure is very similar to Figure 3 in Masterset(2011),, but we distinguish weak bars from strong bars and display the fraction of the two types."," This figure is very similar to Figure 3 in \citet{masters11}, but we distinguish weak bars from strong bars and display the fraction of the two types." +" The excess of fspe2 at blue end becomes more noticeable compared to that in Figure 7aa. We find that fgpo decreases as g—r increases, which is similar to the result in Barazzaetal. (2008)."," The excess of $\bfrsbw$ at blue end becomes more noticeable compared to that in Figure \ref{params_bf}a a. We find that $\bfrsbw$ decreases as $g-r$ increases, which is similar to the result in \citet{barazza08}." +". Interestingly, at g—r«0.5, fgpi also shows a similar trend."," Interestingly, at $g-r<0.5$, $\bfrsbo$ also shows a similar trend." +" Therefore, it becomes obvious that their color dependence is only for blue disk galaxies."," Therefore, it becomes obvious that their color dependence is only for blue disk galaxies." +" Our result shows a low peak of fj, (SB1+SB2) at g—r~0.35, which is also seen in Figure 1d of Nair& From (2010b)."," Our result shows a low peak of $\bfr$ (SB1+SB2) at $g-r\simeq0.35$, which is also seen in Figure 1d of \citet{nair10b}." +".the fact that fgpi is higher in redder galaxies, we suggest two possibilities."," From the fact that $\bfrsbo$ is higher in redder galaxies, we suggest two possibilities." +" First, bars could have an important role in the formation of red late-type galaxies."," First, bars could have an important role in the formation of red late-type galaxies." + Mastersetal. also suggested an idea that transition from blue (2011)spirals to red spirals may be due to turning off star formation by bars., \citet{masters11} also suggested an idea that transition from blue spirals to red spirals may be due to turning off star formation by bars. + This idea is supported by an argument that strong bars drive gas into central part of galaxies more efficiently compared with weak bars (Menéndez, This idea is supported by an argument that strong bars drive gas into central part of galaxies more efficiently compared with weak bars \citep{del07}. +"-Delmestreetal.2007).. In Figure 8bb, we find that there are SB1 galaxies with higher SFR or with very low SFR."," In Figure \ref{ur_rabsmag_lineHa}b b, we find that there are SB1 galaxies with higher SFR or with very low SFR." +" In terms of secular evolution, SB1 galaxies with very low SFR are considered to be at the later stages where cold gas in disk had been used up by strong bars."," In terms of secular evolution, SB1 galaxies with very low SFR are considered to be at the later stages where cold gas in disk had been used up by strong bars." + Interestingly it shows a gap at W(Ha)~5 A where SB1 galaxies are relatively rare., Interestingly it shows a gap at $W(\ha)\simeq5$ ${\rm \AA}$ where SB1 galaxies are relatively rare. + This gap may suggest an observational evidence that the color transition by a bar occurs quickly., This gap may suggest an observational evidence that the color transition by a bar occurs quickly. +" Second, red late-type galaxies are likely to provide better conditions for hosting a bar."," Second, red late-type galaxies are likely to provide better conditions for hosting a bar." + In general red late-type galaxies have earlier-type morphologies than blue late-type galaxies., In general red late-type galaxies have earlier-type morphologies than blue late-type galaxies. +" We already checked that fsgi shows a peak at small c;,, corresponding to early-type spirals."," We already checked that $\bfrsbo$ shows a peak at small $c_{in}$, corresponding to early-type spirals." + Some numerical simulations (Athanassoula&Misiriotis suggested that bars in early-type spiral galaxies could be stronger and have longer life than those in late-type spirals.," Some numerical simulations \citep{am02,ath2002,ath2003,ath2005} + suggested that bars in early-type spiral galaxies could be stronger and have a longer life than those in late-type spirals." +" This expectationa has a logical connection with our results that red late-type galaxies have a large fgpi, that blue late-type galaxies are likely to have a weak bar."," This expectation has a logical connection with our results that red late-type galaxies have a large $\bfrsbo$, that blue late-type galaxies are likely to have a weak bar." +" Also, the excess of fap; in red galaxies implies that strong bars occur more frequently in the systems undergoing long passive evolution, which is also supported by the result that fspgi drops when galaxies suffer from strong tidal interactions (as shown in Figure 11bb, 1288 and 14))."," Also, the excess of $\bfrsbo$ in red galaxies implies that strong bars occur more frequently in the systems undergoing long passive evolution, which is also supported by the result that $\bfrsbo$ drops when galaxies suffer from strong tidal interactions (as shown in Figure \ref{envir_bf}b b, \ref{locden_distnei}a a and \ref{distnei_4params_sb1}) )." +" In galactic dynamics, the central velocity dispersion reflects the mass of a galaxy including dark halo."," In galactic dynamics, the central velocity dispersion reflects the mass of a galaxy including dark halo." + The fact that fgpi reaches a maximum value at intermediate velocity dispersions shows that occurrence of bars is most probable in intermediate mass systems., The fact that $\bfrsbo$ reaches a maximum value at intermediate velocity dispersions shows that occurrence of bars is most probable in intermediate mass systems. +" Cameronetal.(2010) also found that [να- for the 0.2«z<0.6 galaxies in the COSMOS field is higher in intermediate stellar mass systems, which is consistent with our result."," \citet{cameron10} also found that $\bfr$ for the $0.2300 keV).," In the range 0.1 keV – 1 MeV, the generic spectrumof a stellar-mass BH candidate is characterized by three components, even if their relative intensities vary with the object and, for a given object, with time: $i)$ a soft X-ray component (energies $< 10$ keV), $ii)$ a hard power law X-ray component with an exponential cutoff (energies in the range $10-200$ keV, photon spectral index in the range $1-2.5$ ), and $iii)$ a $\gamma$ -ray component (energies $> 300$ keV)." + For a review. see e.g. Liaic(1998)..," For a review, see e.g. \citet{liang}." + The soft N-rav component is conunonly interpreted as the thermal spectra of a thin disk. while the exact oriein of the other two componenuts is not so clear.," The soft X-ray component is commonly interpreted as the thermal spectrum of a thin disk, while the exact origin of the other two components is not so clear." + Ceometrically thin and optically thick accretion disks can be described bv the Novikov-Thorue model 1973).., Geometrically thin and optically thick accretion disks can be described by the Novikov-Thorne model \citep{n-t}. + Trev are expected when the accretion flow is radiativele cfiicient. which requires a luuinosity LS03 Lea. where Lr is the Eddinetou linit.," They are expected when the accretion flow is radiatively efficient, which requires a luminosity $L \lesssim 0.3$ $L_{Edd}$ , where $L_{Edd}$ is the Eddington limit." + The ciission is Dblackbody-like., The emission is blackbody-like. +" Assuming that the inner edge of he disk is at the inerinost stade circular orbiMISCO). the disk huninosity of a Ier BID is deteriiued only by its nass, AM. the mass aceretion rae. M. aud the spin parameter. e= J/AM?."," Assuming that the inner edge of the disk is at the innermost stable circular orbit, the disk luminosity of a Kerr BH is determined only by its mass, $M$, the mass accretion rate, $\dot{M}$ , and the spin parameter, $a=J/M^2$ ." + This fact can thus be exploited to estimate he spin ofstellax-1nass DII candidates (Zhangetal. 1997)., This fact can thus be exploited to estimate the spin ofstellar-mass BH candidates \citep{zhang}. . +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocke, This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocket, This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocketa, This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocketal, This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocketal., This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocketal.2, This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocketal.20, This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocketal.201, This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocketal.2010, This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +. This is the continua fitting method and at preseut has con used to estimate the spin xuiueter of a ew stellaax-1iass BIT candidates (MeClintocketal.2010), This is the continuum fitting method and at present has been used to estimate the spin parameter of a few stellar-mass BH candidates \citep{mcclintock} +in clusters.,in clusters. + However. not all powerful radio galaxies reside in kuown clusters of galaxies.," However, not all powerful radio galaxies reside in known clusters of galaxies." + How cau stich sources be explained?, How can such sources be explained? + One possible explauatio Lis that such radio galaxies ¢ο. in fact. reside in clusters of galaxies but that these clusters are siiiply too poor to have been iucuced iu Classical catalogs.," One possible explanation is that such radio galaxies do, in fact, reside in clusters of galaxies but that these clusters are simply too poor to have been included in classical catalogs." + For example. the lowest richuess clusters ist the Abell catalog (Abell1958:Abell.Corwin.&Olowin1989) must contain at least 325 galaxies in the interval described by ve clusters third brightest galaxy to a ealaxy two magnitudes [αἱnter thai this galaxy.," For example, the lowest richness clusters in the Abell catalog \citep{abel1958,abel1989} must contain at least 35 galaxies in the interval described by the cluster's third brightest galaxy to a galaxy two magnitudes fainter than this galaxy." + This arbirary cutoll implies that systems which 'epresen meaninelul associtious of galaxies cotld easily ye inissecl. despite having environments lear entical to those of the poo‘er clusters of the cataOg.," This arbitrary cutoff implies that systems which represent meaningful associations of galaxies could easily be missed, despite having environments nearly identical to those of the poorer clusters of the catalog." + itionalls. the couec‘ion between poweTul radio galaxies aud real galaxy overdensities uight be exploited to ideuily samples of clusters aud grouys.," Additionally, the connection between powerful radio galaxies and real galaxy overdensities might be exploited to identify samples of clusters and groups." + The powerful radio galaxies would be early vkideal siguposts. as tev Du οσοservable out o very high redshifts zu are nearly always [oun| in the ceitermost regious of clusters (Ledlow&€)wen1995).," The powerful radio galaxies would be nearly ideal signposts, as they are observable out to very high redshifts and are nearly always found in the centermost regions of clusters \citep{ledl1995}." +. Iu fact.studies iucludiug eal.(1993). have akel advantage of this technique.," In fact,studies including \citet{alli1993} have taken advantage of this technique." + However. tje. picture is likely more complica)ed.," However, the picture is likely more complicated." + Specifically. there is θν]ςence that ciffereut types of powerul radio sources inhabit cffe‘elt euvironiments.," Specifically, there is evidence that different types of powerful radio sources inhabit different environments." + For exauple. radio galaxies are often separated based on radio IumiuosiM7 aud iLOLshology (audopticalηςdle:seeOwen&White1991:Ledow1996 ito FR I alle FR II sources (FanarcAF&Rilev1971).," For example, radio galaxies are often separated based on radio luminosity and morphology \citep[and optical magnitude; see][]{owen1991,ledo1996} into FR I and FR II sources \citep{fana1974}." +". The FR I sources appear to be more f“equentM7 ASSOC]ated witl cluster envirotneils hau FR II sources t. 1999).. altheyey this may οἱuly be t""ue at lower redshift as at higher redshift their envi‘OL1iets typear more siuilar (e.g..Presage&Peacock1988)."," The FR I sources appear to be more frequently associated with cluster environments than FR II sources \citep[e.g.,][]{long1979,mill1999}, although this may only be true at lower redshift as at higher redshift their environments appear more similar \citep[e.g.,][]{pres1988}." +. There may also be environmental cliferences ΠΟΙΟ the more powerful radio gaaxies (generally FR ID). with some being fairly normal opticalVv luinuous ellipticals whereas οhers are clearly clistured aud apparent galaxy-galaxy merger systelus (Heckimaueta.1956).," There may also be environmental differences among the more powerful radio galaxies (generally FR II), with some being fairly normal optically luminous ellipticals whereas others are clearly disturbed and apparent galaxy-galaxy merger systems \citep{heck1986}." +. Co1secueltly. in order to τιse radio galaxies to identify samples oclt sters txl groups it appears to beiuportaut to cousider he naure of the radio source.," Consequently, in order to use radio galaxies to identify samples of clusters and groups it appears to be important to consider the nature of the radio source." + In Milleretal.(1999.le'eafterPaper1) we explored tlese themes using a sample of nearby powerful radio galaxies whicl were not members o| Abel clusters., In \citet[][hereafter Paper 1]{mill1999} we explored these themes using a sample of nearby powerful radio galaxies which were not members of Abell clusters. + The local euvirouments of the radio galaxies were exami1ec via analysis of X-ray data frou the Rosat All-Sky Survey (RASS: All statistical measures of ¢uste‘ne rou optical images., The local environments of the radio galaxies were examined via analysis of X-ray data from the Rosat All-Sky Survey \citep[RASS; see][]{voge1993} and statistical measures of clustering from optical images. + The X-ray. data confirmed. that the majoJjv of the radio sources were associated with X-ray emission., The X-ray data confirmed that the majority of the radio sources were associated with X-ray emission. + We also noted a probable difference between FR I and FR ILeivironinents. with the FR I sources more frequently associated witl extended X-ray. emission and optical overdeusities of galaxies.," We also noted a probable difference between FR I and FR II environments, with the FR I sources more frequently associated with extended X-ray emission and optical overdensities of galaxies." + Thus. the FR I sources clid appear to be associated with poor clisters while the FR II sources were more isolatect.," Thus, the FR I sources did appear to be associated with poor clusters while the FR II sources were more isolated." + In this paper. we report on the use of inultiiber spectroscopy to further investigate the environments ο ‘powerful uearby radio galaxies which a‘e not members of classical Abell clusters.," In this paper, we report on the use of multifiber spectroscopy to further investigate the environments of powerful nearby radio galaxies which are not members of classical Abell clusters." + The optical analysis ὀμιρίονος in Paper 1 iucluded no velocity information. aud was instead based on the two-poitt spatial correlation function. B gu.," The optical analysis employed in Paper 1 included no velocity information, and was instead based on the two-point spatial correlation function, $B_{gg}$ ." + Velocity measurements are therefore necessary, Velocity measurements are therefore necessary +they are only detected im the infrared because of heavy obscuration by sas and dust (Lada&Lada.2003).,they are only detected in the infrared because of heavy obscuration by gas and dust \citep{Lada03}. +. The recent development of infrared array detectors has provided au iiportaut impulse to our knowledge of these objects., The recent development of infrared array detectors has provided an important impulse to our knowledge of these objects. + Iun the present work we investigate the nature of 50 stellar overdeusities from the catalogue of Froebrich.Scholz&Raftery(2007) towards the Calactic auticeutre. in the sector (1607(< 2007). Classified Jy them as probable OC aud labcHed with quality flags 2 and 3 (Table 11.," In the present work we investigate the nature of 50 stellar overdensities from the catalogue of \citet{Froebrich07} towards the Galactic anticentre, in the sector $160^\circ\,\leq\,\ell\,\leq 200^\circ$ ), classified by them as probable OC and labelled with quality flags 2 and 3 (Table \ref{tab1}) )." + This paper is organised as follows., This paper is organised as follows. + Iu Sect., In Sect. + 2. we present the OC. candidates., \ref{sec:2} we present the OC candidates. + Iu Sect., In Sect. + 3 Wwe present the 2ATASS photometry aud discuss the methods and tools cluploved in the CMD analyses. expecially the field star decontamination algorithia.," \ref{sec:3} we present the 2MASS photometry and discuss the methods and tools employed in the CMD analyses, especially the field star decontamination algorithm." + Section [ is dedicated to the discussion of the methods aud tools used for the analysis of cluster structure., Section \ref{sec:4} is dedicated to the discussion of the methods and tools used for the analysis of cluster structure. + In Sect., In Sect. + 5. we present the resits of our, \ref{sec:5} we present the results of our +A GLF for the galaxies nominally associated with the absorbers can be constructed by calculating the absolute magnitude of each of the galaxies where an excess is observed. assuming they lie at the redshift of the absorber.,"A GLF for the galaxies nominally associated with the absorbers can be constructed by calculating the absolute magnitude of each of the galaxies where an excess is observed, assuming they lie at the redshift of the absorber." + After correcting for the effects of redshift evolution as described above. a 220.0 GLF is constructed which may be compared with the local GLF derived by Kochaneketal. (2001)..," After correcting for the effects of redshift evolution as described above, a $z$ =0.0 GLF is constructed which may be compared with the local GLF derived by \citet{2001ApJ...560..566K}." + There are two statistical corrections that must first be made before proceeding., There are two statistical corrections that must first be made before proceeding. + Firstly. although =the limiting absolute magnitude. corresponding to the A=20.0 apparent— magnitude— limit. does not vary enormously over the absorber redshift range. a number of the fainter galaxies detected in the lower redshift absorber fields could not have been detected at the redshifts of all the observed fields.," Firstly, although the limiting absolute magnitude, corresponding to the $K=20.0$ apparent magnitude limit, does not vary enormously over the absorber redshift range, a number of the fainter galaxies detected in the lower redshift absorber fields could not have been detected at the redshifts of all the observed fields." + Each galaxy is therefore weighted by the factor ANpossaης where Nopctect Is the number of absorber fields in which a galaxy of given absolute magnitude is detectable and Nei=30 is the total number of fields we," Each galaxy is therefore weighted by the factor $N_{\rm +Detect}/N_{\rm Field}$, where $N_{\rm Detect}$ is the number of absorber fields in which a galaxy of given absolute magnitude is detectable and $N_{\rm +Field}=30$ is the total number of fields we." + Secondly. from the field number density (Section ?2)) we expect 9.6 galaxies of the 30 galaxies detected within a 6700 radius of the background quasar not to be associated with the absorber. and we would like to account for these as best we can.," Secondly, from the field number density (Section \ref{sec:nummag}) ) we expect 9.6 galaxies of the 30 galaxies detected within a 0 radius of the background quasar not to be associated with the absorber, and we would like to account for these as best we can." + In what follows we designate Poin as the probability that the galaxy is associated with the absorber: the average value is =9.67/30= 0.32., In what follows we designate $P_{\rm Field}$ as the probability that the galaxy is associated with the absorber; the average value is $=9.6/30=0.32$ . + We can use our prior knowledge of the number- and number-magnitude counts of the field galaxies to predict for each of our galaxies a more accurate probability that it is an interloping field galaxy. and then weight the contribution of each galaxy to the GLF by individual 1.sia eiehtinefactors.," We can use our prior knowledge of the number-density and number-magnitude counts of the field galaxies to predict for each of our galaxies a more accurate probability that it is an interloping field galaxy, and then weight the contribution of each galaxy to the GLF by individual $1-P_{\rm Field}$ factors." + While we could combine the priors into a single w scheme. we chose to adopt algorithms based on each prior separately. to ensure that the GLF is not sensitive to the precise scheme for the assignment of the probabilities.," While we could combine the priors into a single weighting scheme, we chose to adopt algorithms based on each prior separately, to ensure that the GLF is not sensitive to the precise scheme for the assignment of the probabilities." + Combining the weighting schemes gave a consistent result., Combining the weighting schemes gave a consistent result. + The first weighting scheme accounts for the fact that the excess of galaxies around the target quasar is observed to be a function of distance from the quasar., The first weighting scheme accounts for the fact that the excess of galaxies around the target quasar is observed to be a function of distance from the quasar. + The individual 1ο. factors then take account of the increasing likelihood that a galaxy closer to the quasar is associated with an absorber than one further away., The individual $1-P_{\rm Field}$ factors then take account of the increasing likelihood that a galaxy closer to the quasar is associated with an absorber than one further away. +" Galaxies in each annulus (N920700—1700.1700— 2700.....8700- -6700) are assigned a value oft where pict, ithinand 05, are the predicted and observed number of galaxies w the annulus respectively.", Galaxies in each annulus $\Delta\theta$ 0- 0) are assigned a value of: where $n_{\rm Field}$ and $n_{Obs}$ are the predicted and observed number of galaxies within the annulus respectively. + The second scheme is based on our prior Knowledge of the apparent magnitude distribution of Av-band selected galaxies., The second scheme is based on our prior knowledge of the apparent magnitude distribution of $K$ -band selected galaxies. +" Adopting the form of the ἐν -band number counts from Cimattietal.(2002)... magnitude limits of A 215.0 and 20.0. and ordering the galaxies. 771.2.....30. by increasing magnitude. A. galaxies are assigned a value of: where ""yi is the predicted number of galaxies with A- apparent magnitudes between the limits for galaxy ¢ and the results are normalised such that «“ig=0.32."," Adopting the form of the $K$ -band number counts from \citet{2002A&A...392..395C}, magnitude limits of $K$ =15.0 and 20.0, and ordering the galaxies, $i$ =1,2,...,30, by increasing magnitude, $K$, galaxies are assigned a value of: where $n_{\rm Field, i}$ is the predicted number of galaxies with $K$ -band apparent magnitudes between the limits for galaxy $i$ and the results are normalised such that $=0.32$." + Figure Bashouwsthez OcumulativeC LEoblainedwilhoutapplginglheweighlingschemoes3.4The thecontinioushistogramusestheraenimbercounts: weighlinggalaaiesbuNpstatisticalmissingasa(NVgalaxiesviek|of results in the dotted histogram ie. a very small correction for the faintest objects., Figure \ref{fig:glf}$ $a$ shows the $z$ =0 cumulative GLF obtained without applying the weighting schemes: the continuous histogram uses the raw number counts; weighting galaxies by $N_{\rm Detect}/N_{\rm Field}$ results in the dotted histogram i.e. a very small correction for the faintest objects. + The overplotted lines indicate the cumulative GLF obtained by Kochaneketal.(2001). normalised appropriately for each histogram.," The overplotted lines indicate the cumulative GLF obtained by \citet{2001ApJ...560..566K}, normalised appropriately for each histogram." + Figure 3AbshowsthecumulativeC — Lboblainedaflterapplyinglhelwodi = — — — fferentweighli Ihecontinuoushistogramuscsweighlsaccording, Figure \ref{fig:glf}$ $b$ shows the cumulative GLF obtained after applying the two different weighting schemes: the continuous histogram uses weights according to spatial distribution and the dotted histogram according to apparent magnitude. +lospali, Clearly the shape of the GLF is independent of the weighting scheme adopted for the galaxies. +aldislri," Again, the predicted GLF is overplotted, normalised appropriately for each histogram." +bulion, The dashed line will be discussed in Section \ref{sec:ldcc}. +andther , The lack of any particularly large vertical displacements in any of the histograms shows that the form of the cumulative GLF is not dominated by a small number of galaxies with large weights. +"There is a clear excess in the number of galaxies brighter than Aly. reaching a factor +2 at My=23.5 and increasing to a factor of Bat AJ,=240"," There is a clear excess in the number of galaxies brighter than $M_K^*$, reaching a factor $\simeq2$ at $M_K=-23.5$ and increasing to a factor of $\simeq3$ at $M_K=-24.0$." + Given the signal-to-noise ratio of the target imaging was set in order to achieve detections of A'20 galaxies the quality of the images is not in general sufficient to provide much quantitative information on the morphologies of the galaxies., Given the signal-to-noise ratio of the target imaging was set in order to achieve detections of $K\simeq 20$ galaxies the quality of the images is not in general sufficient to provide much quantitative information on the morphologies of the galaxies. + Visual inspection ofFig., Visual inspection of Fig. + | and the SEXTRACTOR-ellipticities indicate the presence of a proportion of elongated images. suggesting that at least some of the galaxies possess luminous disk components.," 1 and the -ellipticities indicate the presence of a proportion of elongated images, suggesting that at least some of the galaxies possess luminous disk components." +" There are certainly examples of high surface brightness galaxies with substantial bulge components (e.g, SDSS J132323.78-002155.2. SDSS 1173559.954-573]05.9) and overall the /v-band images provide no strong evidence for a distribution of morphological properties that differ from those evident for the general population of ——A/ galaxies at 2~1 in imaging surveys."," There are certainly examples of high surface brightness galaxies with substantial bulge components (e.g. SDSS J132323.78-002155.2, SDSS J173559.95+573105.9) and overall the $K$ -band images provide no strong evidence for a distribution of morphological properties that differ from those evident for the general population of $\sim$$M^*$ galaxies at $z$$\sim$ 1 in imaging surveys." + A link between absorbers and interacting systems has been suggested (Bowen19910..., A link between absorbers and interacting systems has been suggested \citep{1991MNRAS.251..649B}. + Without redshifts to establish which of the galaxies among the seven absorbers with more than one galaxy within 6/00 are associated with the absorbers. it is difficult to perform a strong test for an excess of close pairs.," Without redshifts to establish which of the galaxies among the seven absorbers with more than one galaxy within 0 are associated with the absorbers, it is difficult to perform a strong test for an excess of close pairs." + The angular separations of the centers of the galaxies from ye absorbers are given in Col., The angular separations of the centers of the galaxies from the absorbers are given in Col. + 4 of Table 2.., 4 of Table \ref{tab:galcat}. + By assuming each galaxy is at the associated absorber redshift and converting ye angular separations into kpe. we can calculate the typical impact parameters.," By assuming each galaxy is at the associated absorber redshift and converting the angular separations into kpc, we can calculate the typical impact parameters." + Again. the galaxies are weighted using ye two different weighting schemes discussed above.," Again, the galaxies are weighted using the two different weighting schemes discussed above." + The median projected distance using separation- and magnitude-based weighting is kkpe and 2S5.3kkpe respectively. with ye value for the weighting based on separation smaller as expected.," The median projected distance using separation- and magnitude-based weighting is kpc and kpc respectively, with the value for the weighting based on separation smaller as expected." + However. the relatively small systematic difference gives confidence in the results and we adopt a value of 2442 kkpe for the median projected separation between the absorbers and the associated galaxies.," However, the relatively small systematic difference gives confidence in the results and we adopt a value of $\pm$ kpc for the median projected separation between the absorbers and the associated galaxies." + With chance projections constituting a third of the galaxy images within 600 of the absorbers extracting quantitative information concerning the relationship between galaxy luminosity. impact parameter —and absorber properties— is not really viable.," With chance projections constituting a third of the galaxy images within 0 of the absorbers extracting quantitative information concerning the relationship between galaxy luminosity, impact parameter and absorber properties is not really viable." + Inspection of the distribution of such parameters do not reveal any convincing trends but definitive conclusions must await the acquisition of redshifts for the galaxies., Inspection of the distribution of such parameters do not reveal any convincing trends but definitive conclusions must await the acquisition of redshifts for the galaxies. + The excess galaxies about the absorber quasars establishes an association between the absorbers and the observed galaxies but for approximately a third of the absorbers no associated galaxy is seen., The statistical excess of galaxies about the absorber quasars establishes an association between the absorbers and the observed galaxies but for approximately a third of the absorbers no associated galaxy is seen. + Potential explanations forthe nature of, Potential explanations forthe nature of +1n addition .G& Cen is the first elobular cluster for which the CASE project (Phompson et al.,"In addition, $\omega$ Cen is the first globular cluster for which the CASE project (Thompson et al." + 2001) determined. the istance., 2001) determined the distance. + The analysis of photometric ancl spectroscopic ata for an eclipsing binary OGLE «ας1 vicldecd an apparent distance modulus of (aAZ)=14.09+0.04 mag (Ixaluznv ο al., The analysis of photometric and spectroscopic data for an eclipsing binary OGLE GC17 yielded an apparent distance modulus of $(m-M)_V=14.09\pm0.04$ mag (Kaluzny et al. + 2002)., 2002). + Lt is the most precise ancl reliable istance determination for this cluster ancl will be used in our work for caculating the absolute magnitudes of SNPS belonging to w Con., It is the most precise and reliable distance determination for this cluster and will be used in our work for calculating the absolute magnitudes of SXPS belonging to $\omega$ Cen. + We will also use the mean color data erecdened witi the color excess £(D1)20.13 mag (Schlegel. Fink»iner Davis. 1998) to place individual objects in the 1-]t. ciagram.," We will also use the mean color data dereddened with the color excess $E(B-V)=0.13$ mag (Schlegel, Finkbeiner Davis, 1998) to place individual objects in the H-R diagram." + The full lis Of SAPS located in the field of w Centauri containing main periods. amplitudes. mean magnitudes and colors is provicl«d in Table 1.," The full list of SXPS located in the field of $\omega$ Centauri containing main periods, amplitudes, mean magnitudes and colors is provided in Table 1." + Fig., Fig. + 1 shows color-magnitude diagram arounm blue stragelers region of w Cen., 1 shows color-magnitude diagram around blue stragglers region of $\omega$ Cen. + Points and open circles derrole constant stars and SAPS. respectively.," Points and open circles denote constant stars and SXPS, respectively." + Not all stars in he SNPS region are variables., Not all stars in the SXPS region are variables. + Vhis is hardly surprising. as we have the same situation in the 9 Seuti domain.," This is hardly surprising, as we have the same situation in the $\delta$ Scuti domain." + Presumably these apparently. constant objects are very low amplituce pulsators., Presumably these apparently constant objects are very low amplitude pulsators. + Alany SX Phe stars exhibit multiple. periods. hence their analysis poses specific challenges., Many SX Phe stars exhibit multiple periods hence their analysis poses specific challenges. + Arguably the most advanced. project in terms of both extent of its photometry, Arguably the most advanced project in terms of both extent of its photometry +ccolumn density measured from the Lyman-o profile. (4) the DLA covering factor f. (5) the spin temperature 7;. or. for 21cm non-detections. the 30 lower limit to 7; (taking into account the DLA covering factor. when known). (6) the metallicity [Z/H (7) the dust depletion factor [Z/Fe]. (8) the transitions used |.for the [Z/H] and [Z/Fe] estimates. and (9) references for [Z/H] and [Zn/Fe] values.,"column density measured from the $\alpha$ profile, (4) the DLA covering factor $f$, (5) the spin temperature $\ts$, or, for 21cm non-detections, the $3\sigma$ lower limit to $\ts$ (taking into account the DLA covering factor, when known), (6) the metallicity [Z/H], (7) the dust depletion factor [Z/Fe], (8) the transitions used for the [Z/H] and [Z/Fe] estimates, and (9) references for [Z/H] and [Zn/Fe] values." + In all but two cases. Z—S.Zn. in order of preference.," In all but two cases, ${\rm Z} \equiv +{\rm Zn, S, Si}$, in order of preference." + The exceptions are the z—0.524 Si.DLAs towards 0235+164 and 08274243. where the metallicities are. respectively. from an X-ray spectrum (Junkkarinenetal.2004) and [Z/H]=|Fe/H]+0.4 [following Prochaskaetal. (2003a)]].," The exceptions are the $z \sim 0.524$ DLAs towards 0235+164 and 0827+243, where the metallicities are, respectively, from an X-ray spectrum \citep{junkkarinen04} and $=$ $+0.4$ [following \citet{prochaska03a}] ]." +" The sample contains I4 T, measurements and 12 lower limits. and 20 [Z/H] measurements. five upper limits. and one lower limit (towards 03114430: Ellisonetal. 2008))."," The sample contains 14 $\ts$ measurements and 12 lower limits, and 20 [Z/H] measurements, five upper limits, and one lower limit (towards 0311+430; \citealt{ellison08}) )." + Detailed references for the metallicities and spin temperatures are provided in Kanekar et al. prep.))., Detailed references for the metallicities and spin temperatures are provided in Kanekar et al. ). +" Note that the sample does not include four systems where the radio emission is clearly extended on scales >>I"". and the covering factor islikely to be low. f£<> 1''$, and the covering factor islikely to be low, $f << 1$; these are the 21cm absorbers at $z \sim 0.437$ towards 3C196 \citep{briggs01} and $z \sim 0.656$ towards 3C336 \citep{curran07a} (where the 21cm absorption arises towards extended lobes, with little radio flux density associated with the quasar core), and the 21cm non-detections at $z \sim 1.3911$ towards QSO 0957+561 and $z \sim 1.4205$ towards PKS 1354+258 \citep{kanekar03}." +". We have also excluded ""associated"" DLAs. lying within ~3000 oof the quasar. as conditions m these absorbers could be affected by their proximity to an active galactic nucleus."," We have also excluded “associated” DLAs, lying within $\sim 3000$ of the quasar, as conditions in these absorbers could be affected by their proximity to an active galactic nucleus." +" Preliminary. results of this study showing the correlation between 7, and [Z/H] were presented in KanekarChengalur (2005)..", Preliminary results of this study showing the anti-correlation between $\ts$ and [Z/H] were presented in \citet{kanekar05b}. + Curranetal.(2007b) later also found weak evidence for the anti-correlation. but did not have covering factor estimates for most high-z; DLAs. and hence could not rule out the effects of unknown covering factors.," \citet{curran07c} later also found weak evidence for the anti-correlation, but did not have covering factor estimates for most $z$ DLAs, and hence could not rule out the effects of unknown covering factors." + The results of the presentLetter are based on new 21em data on |] absorbers. and VLBI estimates of the DLA covering factor for most systems. and yield the first clear evidence for a relation between the metallicity and the ttemperature distribution m the absorbers.," The results of the present are based on new 21cm data on $11$ absorbers, and VLBI estimates of the DLA covering factor for most systems, and yield the first clear evidence for a relation between the metallicity and the temperature distribution in the absorbers." + Fig. I{[, Fig. \ref{fig:tszn}[ [ +A] shows 7; plotted versus [Z/H]| for the 26 DLAs of the full sample: it is apparent that low 7; values (<300 K) are obtained at high metallicities ([Z/H|2 —0.6). while high 7; values =700 K are found at low metallicities. [Z/H—1.,"A] shows $\ts$ plotted versus [Z/H] for the 26 DLAs of the full sample; it is apparent that low $\ts$ values $\lesssim 300$ K) are obtained at high metallicities $\gtrsim -0.6$ ), while high $\ts$ values $\gtrsim 700$ K are found at low metallicities, $\lesssim -1$." + We used the non-parametric generalized Kendall rank |correlation. statistic (Brownetal.1974:Isobe 1986).. as implemented in the package (the BHK statistic). to test for a correlation between 7; and |Z/H]. treating the latter as the independent variable.," We used the non-parametric generalized Kendall rank correlation statistic \citep{brown74,isobe86}, as implemented in the package (the BHK statistic), to test for a correlation between $\ts$ and [Z/H], treating the latter as the independent variable." + This allows limits in both variables to be treated consistently., This allows limits in both variables to be treated consistently. + Errors, Errors +Alter the four misfits the next two largest numerical anomalies are the dillerences between model and catalog distances relative to catalog uncertainties for M33 and 10:10.,After the four misfits the next two largest numerical anomalies are the differences between model and catalog distances relative to catalog uncertainties for M33 and IC10. + It is not unreasonable to expect that some distance measurements have errors well outside the catalog uncertainties. and (he low galactic latitude of ICLO may make this distance measurenient particularly problematic. though both Sanna et al (2008) and Wim et al. (," It is not unreasonable to expect that some distance measurements have errors well outside the catalog uncertainties, and the low galactic latitude of IC10 may make this distance measurement particularly problematic, though both Sanna et al (2008) and Kim et al. (" +2009) lind. distances to ICLO that are short of the model value in Table 1.,2009) find distances to IC10 that are short of the model value in Table 1. + The orbits of M33 and ICIO are strongly constrained) by measurements of their proper motions., The orbits of M33 and IC10 are strongly constrained by measurements of their proper motions. + These proper motions require corrections for the motions of the masers relative to the host galaxies., These proper motions require corrections for the motions of the masers relative to the host galaxies. + We can suggest no problem with this carefully done correction. but additional considerations of these valuable constraints on the orbits of M33 and ICLO and on the dvnamies of the Local Group certainly will be welcome.," We can suggest no problem with this carefully done correction, but additional considerations of these valuable constraints on the orbits of M33 and IC10 and on the dynamics of the Local Group certainly will be welcome." + Although the orbit of M33 fits demanding constraints from its redshift and proper motion as well as (he initial conditions. (he result is problematic.," Although the orbit of M33 fits demanding constraints from its redshift and proper motion as well as the initial conditions, the result is problematic." + The weight of the evidence informing the Local Universe Catalog is that M33 is more distant than. M31. but the model puts M33. closer.," The weight of the evidence informing the Local Universe Catalog is that M33 is more distant than M31, but the model puts M33 closer." + Also. the model has M33 approaching M31 for the first time since high redshift. while (he evidence is (hat these (wo galaxies passed close enough to have disturbed the disk of M183 ancl dian oul stellar and streams possibly connecting M33 {ο M31 (Rogstad et al.," Also, the model has M33 approaching M31 for the first time since high redshift, while the evidence is that these two galaxies passed close enough to have disturbed the disk of M33 and drawn out stellar and streams possibly connecting M33 to M31 (Rogstad et al." + 1976: MeConnachie et al., 1976; McConnachie et al. + 2009: Putman et al., 2009; Putman et al. + 2009: Richardson et al., 2009; Richardson et al. + 2011)., 2011). + To be considered is that some galaxies that are quite isolated [rom visible companions nevertheless have apparently disturbed. disks (Ixreckel et al., To be considered is that some galaxies that are quite isolated from visible companions nevertheless have apparently disturbed disks (Kreckel et al. + 2011). ancl that models for stellar halos can produce stellar streams (hat originated at high redshilt (Cooper et al.," 2011), and that models for stellar halos can produce stellar streams that originated at high redshift (Cooper et al." + 2010: Wane. Peebles. and Nusser 2011). when the galaxies were closer together.," 2010; Wang, Peebles, and Nusser 2011), when the galaxies were closer together." + Separating these phenomena [from (he possible effect of a more recent interaction of M31 and M33 is an interesting challenge for future work., Separating these phenomena from the possible effect of a more recent interaction of M31 and M33 is an interesting challenge for future work. + The model masses have problematic features. including the exceptionally large to-light ratio of NGC 135. and. since the model would have similar cireular. velocities in AIW and M3I. the dissimilar model masses.," The model masses have problematic features, including the exceptionally large mass-to-light ratio of NGC 185, and, since the model would have similar circular velocities in MW and M31, the dissimilar model masses." + Assessment of issues with masses must take account of three points., Assessment of issues with masses must take account of three points. + First. we have useful statistical measures of (he relation between total galaxy masses and the stellar masses and velocities. but the scatter in the relation lor individual galaxies is not al all well measured: it is to be explored by clvuamical analyses such as (his.," First, we have useful statistical measures of the relation between total galaxy masses and the stellar masses and velocities, but the scatter in the relation for individual galaxies is not at all well measured: it is to be explored by dynamical analyses such as this." + Second. our measure of the fit of the model to the constraints uses nominal values of (he galaxy masses (hat were thought to be particularly important for the dynamics.," Second, our measure of the fit of the model to the constraints uses nominal values of the galaxy masses that were thought to be particularly important for the dynamics." + The relaxation to a minimum of the V7 measure of fit can end up at a local mininiumn closer io the nominal mass than another local minimum al a more accurate mass., The relaxation to a minimum of the $\chi^2$ measure of fit can end up at a local minimum closer to the nominal mass than another local minimum at a more accurate mass. + The ellect is real even though the penalty of a mass adjustment is low., The effect is real even though the penalty of a mass adjustment is low. + An example is the small model mass of LGS 3. only of the stellar mass found by Hidalgo et al. (," An example is the small model mass of LGS 3, only of the stellar mass found by Hidalgo et al. (" +2011).,2011). + This may be a result of the nominal choice of a mass small enough not to matter., This may be a result of the nominal choice of a mass small enough not to matter. + Another example is the, Another example is the +Throughout our analvsis of these data. we adopt the “kinematic model for the moving lines. which assumes that (he changing Doppler shifts arise from the precession of the jet axis in 55433.," Throughout our analysis of these data, we adopt the “kinematic model” for the moving lines, which assumes that the changing Doppler shifts arise from the precession of the jet axis in SS433." + The simplest form of the kinematic mocdel takes into account five components: the jet velocity 9=©: the jet angle from the precessional axis 8. the inclination angle of the svstem with respect to the observers line of sight 7. the precession period P. and the epoch of zero precessional phase /j.," The simplest form of the kinematic model takes into account five components: the jet velocity $\beta = {v \over{c}}$; the jet angle from the precessional axis $\theta$, the inclination angle of the system with respect to the observer's line of sight $i$, the precession period $P$, and the epoch of zero precessional phase $t_0$." + The period and zero-phase epoch combine to give the precessional phase o=[odu+4., The period and zero-phase epoch combine to give the precessional phase $\phi = {{t - t_0} \over{P}}$. +" The resulting Doppler shifts obey the equation where 4=(1—32).!?,", The resulting Doppler shifts obey the equation where $\gamma = (1- \beta^2)^{-1/2}$. + 88433 exhibits “nodding” of the jets on a e6.5-dav period due to the 13-dax binary motion of 55433 (Cramptonetal.1980).. which are nol accounted for in this model.," SS433 exhibits “nodding” of the jets on a $\sim 6.5$ -day period \citep{Katz} due to the $\sim13$ -day binary motion of SS433 \citep{Crampton}, which are not accounted for in this model." + However. the effects of this nodding are essentially negligible lor long timescale studies of the jets such as ours.," However, the effects of this nodding are essentially negligible for long timescale studies of the jets such as ours." + We further mitigate the impact of nodding by applving a ταν boxcar smoothing filter to the individual Doppler shifts determined above., We further mitigate the impact of nodding by applying a 7-day boxcar smoothing filter to the individual Doppler shifts determined above. + We then used chi-squared minimization to find the best-lit parameters lor the kinematic model (Table 1)., We then used chi-squared minimization to find the best-fit parameters for the kinematic model (Table 1). + The resulting model fit is plotted. versus time along with the cata and residuals in Figures 2-3 lor τι and το., The resulting model fit is plotted versus time along with the data and residuals in Figures 2-3 for $z_1$ and $z_2$. + We plot the same moclel fit. data. and residuals versus precessional phase in Figure 4.," We plot the same model fit, data, and residuals versus precessional phase in Figure 4." + The resulting fit has a chi-squared residual per degree of freedom of 472=8.9. indicating (he presence of statistically significant residuals.," The resulting fit has a chi-squared residual per degree of freedom of $\chi^2_{\nu} = 8.9$, indicating the presence of statistically significant residuals." + ILowever. we can still use this fit to estimate uncertainties in the kinematic model parameters as follows.," However, we can still use this fit to estimate uncertainties in the kinematic model parameters as follows." + First. we scale all of the o. values by V8.9. so that the residuals have VIris=1.0. essentially by fiat.," First, we scale all of the $\sigma_z$ values by $\sqrt{8.9}$, so that the residuals have $\chi^2_{\nu-fix} = 1.0$, essentially by fiat." + We then take the uncertainties to be the range of a model parameter which introduces a total change οἱ ANS.=1.0.," We then take the uncertainties to be the range of a model parameter which introduces a total change of $\Delta +\chi^2_{fix} = 1.0$." + We also report these values in Table 1., We also report these values in Table 1. + This rescaling approach lor deriving ihe model parameter uncertainties is statistically valid im a strict sense only if the residuals are consistent. with Gaussian noise and are not correlated with anv model parameters in asvstamlic wav., This rescaling approach for deriving the model parameter uncertainties is statistically valid in a strict sense only if the residuals are consistent with Gaussian noise and are not correlated with any model parameters in a systamtic way. + If so. then the residuals would simply indicate that we have ignored one or more sources of noise in the svstem when estimating the uncertainties in the individual Doppler shifts.," If so, then the residuals would simply indicate that we have ignored one or more sources of noise in the system when estimating the uncertainties in the individual Doppler shifts." + As we show below. this is largely (rue. though we see some evidence of small (but statisticallv-significant) svstematic deviations from the kinematic model.," As we show below, this is largely true, though we see some evidence of small (but statistically-significant) systematic deviations from the kinematic model." + Thus. (he uncertainties in (he model parameters in Table 1 are likely to be good. but not perfect. statistical estimates.," Thus, the uncertainties in the model parameters in Table 1 are likely to be good, but not perfect, statistical estimates." + For the remainder of (he paper. we adopt the best-fit model parameters presented in Table 1.," For the remainder of the paper, we adopt the best-fit model parameters presented in Table 1." +motions are induced. via the cascade of the vorticity generated due to cosmological shocks during the formation of LSS. and the IGME is produced as a consequence of the amplification ol weak seed fields of any origin through the stretching of field lines by the flow motions.,"motions are induced via the cascade of the vorticity generated due to cosmological shocks during the formation of LSS, and the IGMF is produced as a consequence of the amplification of weak seed fields of any origin through the stretching of field lines by the flow motions." +" Then. it can be modeled that a fraction of the turbulent-flow energy. τν. is converted to ihe magnetic energy. oy. as where the conversion [actor. o. depends only on the eddy turnover number. ///q,."," Then, it can be modeled that a fraction of the turbulent-flow energy, $\varepsilon_{\rm turb}$, is converted to the magnetic energy, $\varepsilon_B$, as where the conversion factor, $\phi$, depends only on the eddy turnover number, $t/t_{\rm eddy}$." +" ]lere. the eddy: (turnover time is defined as (he reciprocal of the vorticity al driving scales. {ων=L/eveiving (=Vx ο),"," Here, the eddy turnover time is defined as the reciprocal of the vorticity at driving scales, $t_{\rm eddy} \equiv 1/\omega_{\rm driving}$ ${\vec \omega} \equiv {\vec \nabla}\times{\vec v}$ )." + The local vorticity and turbulent-flow energy density. were caleulated from the data of the structure formation simulations described above. and the age of the universe at the redshift z was used for /.," The local vorticity and turbulent-flow energy density were calculated from the data of the structure formation simulations described above, and the age of the universe at the redshift $z$ was used for $t$." + The functional form for the conversion factor was derived [rom a separate. incompressible. magnetohlivdrodvnamic (MIID) simulation of turbulence dvnamo (R03).," The functional form for the conversion factor was derived from a separate, incompressible, magnetohydrodynamic (MHD) simulation of turbulence dynamo (R08)." + Then. the magnetic energy density was calculated: according to Equation 1l.. and the strength of the IGAIF as B=Y&rey.," Then, the magnetic energy density was calculated according to Equation \ref{eq1}, and the strength of the IGMF as $B = \sqrt{8\pi\varepsilon_B}$." + The average strength οἱ the resulting model IGAIF for the WIIIM is (D).~10 nG or (pB)/(p)~0.1 iG αἱ 2=0., The average strength of the resulting model IGMF for the WHIM is $\langle B\rangle \sim 10$ nG or $\langle \rho B\rangle/\langle \rho\rangle \sim 0.1\ \mu$ G at $z=0$. + For the direction of the IGAMIF. we used (hat of the passive fields from structure formation simulations. in which weak seed fields were generated through the Biermann battery mechanism at cosmological shocks and evolved passively. ignoring the back-reaction. along with flow motions1993).," For the direction of the IGMF, we used that of the passive fields from structure formation simulations, in which weak seed fields were generated through the Biermann battery mechanism at cosmological shocks and evolved passively, ignoring the back-reaction, along with flow motions." +. The validity of our model IGME was discussed in details in ARLO., The validity of our model IGMF was discussed in details in AR10. + It was argued that our model IGME would produce reasonable results for the RAL through the cosmic web in the local universe., It was argued that our model IGMF would produce reasonable results for the RM through the cosmic web in the local universe. + The simulated passive fields reproduce the directions that show the expected correlation with those of vorticity., The simulated passive fields reproduce the directions that show the expected correlation with those of vorticity. + The RAI coherence length for the IGME in filaments is estimated to be a few to several x100 kpe at 2=0. which agrees with the estimation of 0109.," The RM coherence length for the IGMF in filaments is estimated to be a few to several $\times 100$ kpc at $z=0$, which agrees with the estimation of CR09." + It is a few times larger than the grid resolution of our simulations. 195fh! kpe.," It is a few times larger than the grid resolution of our simulations, $195\ h^{-1}$ kpc." + On the other hand. (he coherence length lor the IGME in clusters is expected to be a few x10 kpe (CRO9). which is smaller than the grid resolution.," On the other hand, the coherence length for the IGMF in clusters is expected to be a few $\times 10$ kpc (CR09), which is smaller than the grid resolution." + So the application of our moclel IGAIF to clusters would results in an erroneous estimation of RAL., So the application of our model IGMF to clusters would results in an erroneous estimation of RM. + However. here we study ihe RM through the cosmic web outside clusters. and so we will remove the contribution from clusters to RAI (see Section 2.8).," However, here we study the RM through the cosmic web outside clusters, and so we will remove the contribution from clusters to RM (see Section 2.8)." +" Our model predicts that the IGME for the WILAI was a bit stronger in (he past: for instance. (B)~30 nG for the gas with 10° IX «T 10"" IX at z=5 (see Figure 2 of ROX)."," Our model predicts that the IGMF for the WHIM was a bit stronger in the past; for instance, $\langle B\rangle \sim 30$ nG for the gas with $10^5$ K $< T <$ $10^7$ K at $z=5$ (see Figure 2 of R08)." + It is because the density of the WIIIM was higher in (he past. although the magnitudes of vorticity and the vortücal component of velocity. were smaller.," It is because the density of the WHIM was higher in the past, although the magnitudes of vorticity and the vortical component of velocity were smaller." + Our model also predicts stronger IGMF for the hot gas with T10* IX in the past., Our model also predicts stronger IGMF for the hot gas with $T > 10^7$ K in the past. + However. the IGMF averaged," However, the IGMF averaged" +"Within the standard cosmological model of structure formation. galaxy clusters trace regions where the hierarchical build. up of galaxies and their interaction with the inter-galactic medium (IGM) proceed at a somewhat faster rate compared to regions of the Universe with ""average densitv.","Within the standard cosmological model of structure formation, galaxy clusters trace regions where the hierarchical build up of galaxies and their interaction with the inter-galactic medium (IGM) proceed at a somewhat faster rate compared to regions of the Universe with `average' density." + Finding and observing high-redshift progenitors of galaxy clusters can provide invaluable information on the processes wvich led to their formation and evoution., Finding and observing high–redshift progenitors of galaxy clusters can provide invaluable information on the processes which led to their formation and evolution. + The most distant clusers to date have been identified out to zz;1.5 from deep X-ray and. infra-red Observations (e.g.90909).andreferencestl rein).," The most distant clusters to date have been identified out to $z\mincir 1.5$ from deep X–ray and infra-red observations \citep[e.g.][and references + therein]{2005ApJ...623L..85M,2008arXiv0804.4798E,2005ApJ...634L.129S}." + A yowerful technique. that extends hese studies to higher redshift. is to search for overdensities of emission line galaxies in the neighbourhood of luminous vigh-redshift radio galaxies (e.g.?)..," A powerful technique, that extends these studies to higher redshift, is to search for overdensities of emission line galaxies in the neighbourhood of luminous high-redshift radio galaxies \citep[e.g.][]{1998ApJ...504..139P}." + Although these regions are expected not to trace virialized clusters. hey likely identify he progenitors of oresent. day clusters. offering an unique opportunity to study he evolutionary processes which determine heir observational properties.," Although these regions are expected not to trace virialized clusters, they likely identify the progenitors of present day clusters, offering an unique opportunity to study the evolutionary processes which determine their observational properties." +" Recently. a number of observations of distant putative proto-clusters. like the one associated with the so-called “Spiderweb Galaxy"" at 52.16 (?.. MOG hereafter). uve demonstrated that these regions are characterised by intense dynamical and star formation activity (e.g. ?.. M06. 22.. and references therein)."," Recently, a number of observations of distant putative proto-clusters, like the one associated with the so–called “Spiderweb Galaxy” at $z=2.16$ \citealt{2006ApJ...650L..29M}, M06 hereafter), have demonstrated that these regions are characterised by intense dynamical and star formation activity (e.g. \citealt{2000A&A...361L..25P}, M06, \citealt{2007A&A...461..823V,2008ApJ...673..143O}, and references therein)." + On the theoretical side. modern cosmological hydrodynamical simulations are now reaching good enough resolution. and include detailed treatments of a number of astrophysical processes. to provide. an accurate descriptionum of. the assembly of: galaxy clusters.," On the theoretical side, modern cosmological hydrodynamical simulations are now reaching good enough resolution, and include detailed treatments of a number of astrophysical processes, to provide an accurate description of the assembly of galaxy clusters." + These simulations are now able to reproduce the basic properties observed for the bulk of the cluster galaxy population. at. low redshift. while generally predicting too massive and too blue BGCs. due to the absence on an efficient feedback mechanism that suppresses the star 'formation. activity L2.in these galaxies. at late times. (egT8.," These simulations are now able to reproduce the basic properties observed for the bulk of the cluster galaxy population at low redshift, while generally predicting too massive and too blue BGCs, due to the absence on an efficient feedback mechanism that suppresses the star formation activity in these galaxies at late times \citep[e.g.,][]{2006MNRAS.373..397S,2008MNRAS.tmp..793R}." + In this Letter we present results from high-resolution simulations of two proto—cluster regions at 2~ that we compare to observational results of the Spiderweb galaxy., In this Letter we present results from high–resolution simulations of two proto–cluster regions at $z\sim 2$ that we compare to observational results of the Spiderweb galaxy. + The aim of this analysis is to verify to what extent simulations of proto—cluster regions in a standard cosmological scenario resemble the observed properties of the Spiderweb complex., The aim of this analysis is to verify to what extent simulations of proto–cluster regions in a standard cosmological scenario resemble the observed properties of the Spiderweb complex. + Furthermore. we provide predictions for the properties of the proto intra-cluster medium (ICM). in view of future deep X-ray observations of high-redshift proto-cluster regions.," Furthermore, we provide predictions for the properties of the proto intra-cluster medium (ICM), in view of future deep X–ray observations of high–redshift proto-cluster regions." +Ty can lead to a higher energy conversion efficiency because of the effect on the resonance ellipses.,$T_{\rm w}$ can lead to a higher energy conversion efficiency because of the effect on the resonance ellipses. + The flux density drops slightly with increasing Ty as seen in panel (b) of Fig. 5.., The flux density drops slightly with increasing $T_{\rm w}$ as seen in panel (b) of Fig. \ref{fig_flux}. + Panel (e) in Fig., Panel (e) in Fig. + 5 shows the effect of the loss-cone angle on flux density., \ref{fig_flux} shows the effect of the loss-cone angle on flux density. + The rapid increase of flux density when the loss-coneangle (o) changes from 10° to 20° is the consequence of the significant increase in the size of the region of velocity space involved., The rapid increase of flux density when the loss-coneangle $\alpha_{\rm c}$ ) changes from $10^{\circ}$ to $20^{\circ}$ is the consequence of the significant increase in the size of the region of velocity space involved. + Quasi-linear diffusion influences a large number of particles and results in growth and amplification of some wave modes growing., Quasi-linear diffusion influences a large number of particles and results in growth and amplification of some wave modes growing. +" On the other hand, when a,>20°, the positive gradient in the perpendicular direction decreases so that the electromagnetic wave energy density can not be amplified effectively."," On the other hand, when $\alpha_{\rm c}>20^{\circ}$, the positive gradient in the perpendicular direction decreases so that the electromagnetic wave energy density can not be amplified effectively." +" The effect of pitch angle distribution slope is similar to that of the loss-cone angle, see panel (f) in Fig. 5.."," The effect of pitch angle distribution slope is similar to that of the loss-cone angle, see panel (f) in Fig. \ref{fig_flux}." +" In this section, we determine the possible range of the different parameters."," In this section, we determine the possible range of the different parameters." +" From Table 1,, there are at least 13 parameters that can influence the radio light curve of TVLM 513; we are able to reduce this number, however."," From Table \ref{tab_parameters}, there are at least 13 parameters that can influence the radio light curve of TVLM 513; we are able to reduce this number, however." +" Considering the contribution of the degenerate electron gas and the ionic Coulomb pressure, the radius is almost a constant around 0.1Ro, in the range of 0.08Ro to 0.11Re (?).."," Considering the contribution of the degenerate electron gas and the ionic Coulomb pressure, the radius is almost a constant around $R_{\rm \odot}$, in the range of $R_{\rm \odot}$ to $R_{\rm \odot}$ \citep{Chabrier00}." + The temperature of cold plasma is more difficult to determine., The temperature of cold plasma is more difficult to determine. +" In this work we assume it is around 106 K, similar to the typical temperature of the solar corona."," In this work we assume it is around $10^{6}$ K, similar to the typical temperature of the solar corona." +" On the other hand, if the coronal temperature waslower, this would favor wave propagation rather than damping."," On the other hand, if the coronal temperature waslower, this would favor wave propagation rather than damping." +" We set the initial wave energy Tw at a high level of 10/4 K. On the other hand, from Fig. 5,,"," We set the initial wave energy $T_{\rm w}$ at a high level of $10^{14}$ K. On the other hand, from Fig. \ref{fig_flux}," +" the flux density varies only slightly (a factor of 2) when Ty, changes from 10!° to 1015 K. We should however note that ? suggested that the ECM instability may be a viable source of quiescent unpolarized radio emission, indistinguishable in temporal and polarization characteristics from gyrosynchrotron radiation."," the flux density varies only slightly (a factor of 2) when $T_{\rm w}$ changes from $10^{10}$ to $10^{15}$ K. We should however note that \citet{Hallinan08} + suggested that the ECM instability may be a viable source of quiescent unpolarized radio emission, indistinguishable in temporal and polarization characteristics from gyrosynchrotron radiation." +" For convenience we adopt a plausible value of 0.1 for the ratio u of plasma frequency to gyrofrequency (/p/ fc), a value that permits unstable growth of the ECMI."," For convenience we adopt a plausible value of 0.1 for the ratio $u$ of plasma frequency to gyrofrequency $f_{\rm p} +/f_{\rm c}$ ), a value that permits unstable growth of the ECMI." +" If we focus on the observation frequency of 4.9 GHz, the magnetic field strength (B) has to be around 1750 G and the density of the cold background plasma is ~3x10? cm."," If we focus on the observation frequency of 4.9 GHz, the magnetic field strength $B$ ) has to be around 1750 G and the density of the cold background plasma is $\sim$ $\times10^{9}$ $^{-3}$." + Any change of u alone will not affect the maximum flux density for the fundamental X-mode and fundamental O-mode respectively., Any change of $u$ alone will not affect the maximum flux density for the fundamental $X$ -mode and fundamental $O$ -mode respectively. +" However, we stress that if we change the magnetic field strength (B), even keeping u at the same value, the maximum flux density will change because it depends on the cyclotron frequency."," However, we stress that if we change the magnetic field strength $B$ ), even keeping $u$ at the same value, the maximum flux density will change because it depends on the cyclotron frequency." + The size of the radio-emitting region A is associated with the time duration of the radio pulses., The size of the radio-emitting region $A$ is associated with the time duration of the radio pulses. +" Thus in the case of TVLM 513, we have A«(54.75At)' when the latitude of the active region is 30°."," Thus in the case of TVLM 513, we have $A\approx(54.75\Delta t)^{\gamma}$ when the latitude of the active region is $^{\circ}$." +" Changing the latitude to 70? gives Ax (21.62At)"".", Changing the latitude to $^{\circ}$ gives $A\approx(21.62\Delta t)^{\gamma}$ . + At is easily obtained from observations and is a more convenient parameter than A., $\Delta t$ is easily obtained from observations and is a more convenient parameter than $A$. + rue is a variable to describe the radius of a flux tube., $r_{\rm tube}$ is a variable to describe the radius of a flux tube. +" We expect there are distributions for plasma parameters (Th, ny) and loss-cone parameters (ας, N) in different flux tubes."," We expect there are distributions for plasma parameters $T_{\rm h}$ , $n_{\rm h}$ ) and loss-cone parameters $\alpha_{\rm c}$ , $N$ ) in different flux tubes." + The variation of different parameters can result in the oscillation of the observed flux density., The variation of different parameters can result in the oscillation of the observed flux density. + Smaller values for rupe leadto smoother simulated radio light curves (see Fig. 4))., Smaller values for $r_{\rm tube}$ leadto smoother simulated radio light curves (see Fig. \ref{fig_rtubev}) ). +Adams et al. (,Adams et al. ( +"2008) and Rein Papaloizou (2009), we assume that only the outermost planet experiences the torques arising from the disk.","2008) and Rein Papaloizou (2009), we assume that only the outermost planet experiences the torques arising from the disk." +" We also assume that the planets have near equal mass, in order to avoid the chaotic regime which comes into play for disparate masses (Papaloizou Szuszkiewicz 2005)."," We also assume that the planets have near equal mass, in order to avoid the chaotic regime which comes into play for disparate masses (Papaloizou Szuszkiewicz 2005)." +" In the limit of large damping rate for the resonance and neglecting effects from planet-planet interaction, the asymptotic value P of the probability for the resonance to be maintained is given by (Lecoanet et al."," In the limit of large damping rate for the resonance and neglecting effects from planet-planet interaction, the asymptotic value $P$ of the probability for the resonance to be maintained is given by (Lecoanet et al." + 2009): where Dg is the diffusion coefficient associated with the resonant angle diffusion and ty is the damping timescale for the resonance angle., 2009): where $D_\phi$ is the diffusion coefficient associated with the resonant angle diffusion and $\tau_d$ is the damping timescale for the resonance angle. +" This equation is valid at late times f>wo! where wo is the libration frequency of the resonant angles, as long as t>D; and D;>>Tq."," This equation is valid at late times $t\gg \omega_0^{-1}$ where $\omega_0$ is the libration frequency of the resonant angles, as long as $t \gg D_\phi^{-1}$ and $D_\phi^{-1}\gg \tau_d$." +" From the previous equation, we can estimate the maximum value of the diffusion coefficient for the sytem to remain bound in resonance with probability P=1."," From the previous equation, we can estimate the maximum value of the diffusion coefficient for the sytem to remain bound in resonance with probability $P=1$." + This reads: As shown in Adams et al. (, This reads: As shown in Adams et al. ( +"2008), Dg can be related to the diffusion coefficient Dj, associated with the diffusion of the outer planet’s angular momentum as: For moderate eccentricities, wo is given by: where e; is the eccentricity of the inner planet, qo=mo/M, and Ω; is the angular frequency of the innermost planet.","2008), $D_\phi$ can be related to the diffusion coefficient $D_{H,o}$ associated with the diffusion of the outer planet's angular momentum as: For moderate eccentricities, $\omega_0$ is given by: where $e_i$ is the eccentricity of the inner planet, $q_0=m_0/M_\star$ and $\Omega_i$ is the angular frequency of the innermost planet." +" In the previous equation, «=aj/do, (jo,ja) are integers which depend on the resonance being considered and fj(q@) results from the expansion of the disturbing function."," In the previous equation, $\alpha=a_i/a_o$, $(j_2,j_4)$ are integers which depend on the resonance being considered and $f_d(\alpha)$ results from the expansion of the disturbing function." +" In the case of the 3:2 resonance, we have j2=—2, j4=-1 and afy(a)~—1.54 (Murray Dermott 1999)."," In the case of the 3:2 resonance, we have $j_2=-2$ , $j_4=-1$ and $\alpha f_d(\alpha) \sim -1.54$ (Murray Dermott 1999)." +" In Eq. 7,,"," In Eq. \ref{eq:dphi}," +" Dy» can be expressed in terms of both the correlation timescale τε associated with the stochastic torques exerted on the outer planet and the standard deviation of the turbulent torque distribution c as: As discussed in Baruteau Lin (2010), σ, takes the following form when applied to the outermost planet: where gg=m,/M,, Σο is the value of the surface density at the position of the outer planet, Q, is the angular frequency of this planet and C is a constant."," $D_{H,o}$ can be expressed in terms of both the correlation timescale $\tau_c$ associated with the stochastic torques exerted on the outer planet and the standard deviation of the turbulent torque distribution $\sigma_{t}$ as: As discussed in Baruteau Lin (2010), $\sigma_t$ takes the following form when applied to the outermost planet: where $q_o=m_o/M_\star$, $\Sigma_o$ is the value of the surface density at the position of the outer planet, $\Omega_o$ is the angular frequency of this planet and $C$ is a constant." +" For a simulation using the same disk parameters as for model G1 and with y=6x10>, we find C~1.6x 107, which is close to the value found by Baruteau Lin (2010)."," For a simulation using the same disk parameters as for model G1 and with $\gamma=6\times 10^{-5}$, we find $C\sim 1.6\times 10^2$ , which is close to the value found by Baruteau Lin (2010)." +" Combining Eqs. 7,"," Combining Eqs. \ref{eq:dphi}," +",9 and 10 gives an expression for the diffusion coefficient associated with the diffusion of the resonant angle Do, in terms of the value for the turbulent forcing y."," \ref{eq:dj} and \ref{eq:sigmat} gives an expression for the diffusion coefficient associated with the diffusion of the resonant angle $D_\Phi$, in terms of the value for the turbulent forcing $\gamma$." +" This reads: with ga=nX,a2/M,.", This reads: with $q_d=\pi \Sigma_o a_o^2/M_\star$. +" Setting δω=ωρ/Ώο, we can rewrite the previous expression as: We notice that in the case where p=1, δω is comparable to the dimensionless width of the libration zone."," Setting $\delta \omega=\omega_0/ \Omega_o$, we can rewrite the previous expression as: We notice that in the case where $p=1$, $\delta \omega$ is comparable to the dimensionless width of the libration zone." +" Using the previous equation together with Eq. 6,,"," Using the previous equation together with Eq. \ref{eq:dphicrit}," +" we find that the critical value for the turbulent forcing above which the 3:2 resonance is disrupted is given by: In absence of turbulent forcing, we expect the amplitude of the resonant angles to scale as ΩςV2 (Peale1976)."," we find that the critical value for the turbulent forcing above which the 3:2 resonance is disrupted is given by: In absence of turbulent forcing, we expect the amplitude of the resonant angles to scale as $\Omega_o^{-1/2}$ (Peale1976)." +" According to Rein Papaloizou (2009), this implies thatthe damping timescale of the libration amplitude 7; is twice the migration"," According to Rein Papaloizou (2009), this implies thatthe damping timescale of the libration amplitude $\tau_d$ is twice the migration" + (c.g...Rocheetal.1991:2003:Snuthetal.20072)... (PAIIs.Leger&Puget1981:AlbunaudolaetTiclens2008).," \citep[e.g.,][]{roc91,lu03,smi07a}. \citep[PAHs,][]{leg84,all85,tie08}," +. (Ticlens2005). (e...Peetersetal.20014:Calzettial.2009).. (e...Povichetal.2007).. (ACN.Voit1992:1998).. (e.g.Scliweitzeretal.2006:Shial.2007.2009:Lutzct2008).," \citep{tie05} \citep[e.g.,][]{pee04,cal07,rie09}. \citep[e.g.,][]{pov07}. \citep[AGN,][]{voi92,gen98}. \citep[e.g.,][]{sch06, shi07, shi09, lut08}." +. Dulev&Williams(1981) (Allamandolaetal., \citet{dul81} \citep{all89}. +1989).. san sau pan out-of-plane bending modes., $\mu$ $\mu$ $\mu$ out-of-plane bending modes. +" While these features are cohmmonly attributed to PATIs. we use the simpler. more eeneral term ""aromatic to avoid making assuniptions about the detailed structure of the molecules."," While these features are commonly attributed to PAHs, we use the simpler, more general term “aromatic” to avoid making assumptions about the detailed structure of the molecules." + It is wortli noting. for example. that PAIT spectra from laboratory casurements and quantum chemical caleulatious are unable to amatch the range of astronomical spectra without artificial cuhauccments of the 6.2. 7.7. aud 8.6 quu feature strengths (e.g.Li&Draine2001).," It is worth noting, for example, that PAH spectra from laboratory measurements and quantum chemical calculations are unable to match the range of astronomical spectra without artificial enhancements of the 6.2, 7.7, and 8.6 $\mu$ m feature strengths \citep[e.g.,][]{li01}." +. Reeardless of this uncertaiutyv associated with uniquelv matching observed spectra with expectations for specific molectles. one can probe the properties of the aromatic carriers by measure the relative streneths of the cCluission features. which are expected to vary as a function of charge state (e.e..Bakesetal.2001).. molecular size (o...Draine&Li 2001).. aud molecular structure (ce...Vermeijetal.2002).," Regardless of this uncertainty associated with uniquely matching observed spectra with expectations for specific molecules, one can probe the properties of the aromatic carriers by measuring the relative strengths of the emission features, which are expected to vary as a function of charge state \citep[e.g.,][]{bak01}, molecular size \citep[e.g.,][]{dra01}, , and molecular structure \citep[e.g.,][]{ver02}." + Efforts to study varlatious dn aromatic feature streneths outside the Milky Way have focused. om star-forming ealaxies (o.g..Suuithetal.2007a:Gallianoct2008:Roschoomotal.2009:ODowdct 2009).. but the AGNs included in these studies have shown evidence for suppression of shorter wavelength features (c.e.. those at 6.2. 7.7. and &.6 yan) relative to those at longer wavelengths.," Efforts to study variations in aromatic feature strengths outside the Milky Way have focused on star-forming galaxies \citep[e.g.,][]{smi07a,gal08,ros09,odo09}, but the AGNs included in these studies have shown evidence for suppression of shorter wavelength features (e.g., those at 6.2, 7.7, and 8.6 $\mu$ m) relative to those at longer wavelengths." + For example. Simithctal.(2007a) studied a sanuple of 59 ealaxies from the Spitzer Tufrared Nearby Galaxy Survey (SINGS.EKenucuttetal.2003).. of which 12 have Sevfert nuclei aud 20 have low-ionization unclear emission-liue regious (LINERS). aud they fouud a tendency for the systems with reduced 6δ jan features to be associated with low-luuwinositv ACNs.," For example, \citet{smi07a} studied a sample of 59 galaxies from the Spitzer Infrared Nearby Galaxy Survey \citep[SINGS,][]{ken03}, of which 12 have Seyfert nuclei and 20 have low-ionization nuclear emission-line regions (LINERs), and they found a tendency for the systems with reduced 6–8 $\mu$ m features to be associated with low-luminosity AGNs." + Thev speculated on possible causes for this behiwvior. inchiding whether the ACN can modify the aromatic erain size distribution or serve as the excitation source for aromatic enissiou.," They speculated on possible causes for this behavior, including whether the AGN can modify the aromatic grain size distribution or serve as the excitation source for aromatic emission." + Similarly. ODowdetal.(2009) studied a sample of 92 sealaxies at 2~0.1fromtheSpitzer SDSS GALEN Spectroscopic Survey. iucludiug ασACN-dominated and20 composite svstems. and found that the AGNs exhibited lower 7.7/11.3 pan ratios.," Similarly, \citet{odo09} studied a sample of 92 galaxies at $z\sim0.1$fromtheSpitzer SDSS GALEX Spectroscopic Survey, including eightAGN-dominated and20 composite systems, and found that the AGNs exhibited lower 7.7/11.3 $\mu$ m ratios." + They interpreted this behavior asbeing consistent witl, They interpreted this behavior asbeing consistent with + They interpreted this behavior asbeing consistent witli, They interpreted this behavior asbeing consistent with +to be probed.,to be probed. + In future studies it would be of interest to determine Mn abundances in the most metal-rich w Cen population: for example. by analyzing Mn in the 2 most metal-rich red eiants studied to date (ROA 300. WFEI22068. and WFEI222679) by Pancino et al. (," In future studies it would be of interest to determine Mn abundances in the most metal-rich $\omega$ Cen population; for example, by analyzing Mn in the 3 most metal-rich red giants studied to date (ROA 300, WFI22068, and WFI222679) by Pancino et al. (" +2002).,2002). + The behavior of the manganese abundances in (hese more metal-rich stars will provide further insight into both the origins of Mn and the nature of star formation within w Cen during the final throes of its chemical evolution., The behavior of the manganese abundances in these more metal-rich stars will provide further insight into both the origins of Mn and the nature of star formation within $\omega$ Cen during the final throes of its chemical evolution. + MB thanks Dr. Frank Grupp for providing MAFAGS-OS model atmospheres for selected stars., MB thanks Dr. Frank Grupp for providing MAFAGS-OS model atmospheres for selected stars. + This research was supported in part bv the National Science Foundation (AST 06-46790 to KC and VVS)., This research was supported in part by the National Science Foundation (AST 06-46790 to KC and VVS). + DLL thanks the Robert A. Welch Foundation for support via grant. F-634., DLL thanks the Robert A. Welch Foundation for support via grant F-634. +Our understanding of hieh-redshif ealaxies Is erowiug at a vapid pace.,Our understanding of high-redshift galaxies is growing at a rapid pace. + By combining erotnd aud: space-based observations. all of the clectrouagnetic spectrum from the N-vavs to the radio ijs now bαπο used to select and study ealaxics iu fre early dadiverse.," By combining ground and space-based observations, all of the electromagnetic spectrum from the X-rays to the radio is now being used to select and study galaxies in the early universe." + Among the eveor-growiue number of μασ]τος]τε ealaxy popula10115. Lyman Break Calasxics {LBCs) pav dominant role. roni an astroplivsical aux from au oservatiowal point of view.," Among the ever-growing number of high-redshift galaxy populations, Lyman Break Galaxies (LBGs) play a dominant role, from an astrophysical and from an observational point of view." +" Receutlv. ? argued that bπο, star-forning eaaNICS ike LBCs may have jid the largest courilttion to the volommetric enerev outt of ealaxies at redshi daz2Ὁ, cluphasizing their muiporance for our τιderstanding of he cosunic star-formation history."," Recently, \citet{reddy07} argued that blue, star-forming galaxies like LBGs may have had the largest contribution to the bolometric energy output of galaxies at redshifts $\sim 2-3$, emphasizing their importance for our understanding of the cosmic star-formation history." + Observationallv. more han 1000 LBCs have s)ectroscopie recshifts at z—3 alone (e.g..?).. aud their eusenible properties. like their spatial clustering. huuinositv function. and average rest-rane UV spectral properies are kuown a unprecedented TCCISIOMN (eo.TTTT).," Observationally, more than 1000 LBGs have spectroscopic redshifts at $\sim 3$ alone \citep[e.g.,][]{steidel03}, and their ensemble properties, like their spatial clustering, luminosity function, and average rest-frame UV spectral properties are known at unprecedented precision \citep[e.g.,][]{adelberger05,shapley01,papovich01,shapley03}." + Very receutly.2 presented adaptive-optics assisted iuteeral-fiek spectroscopy. of the 2=3.3 ο DSF2237a-C2 using ¢JSIRIS ou the Ίνκας clescope.," Very recently,\citet{law07} presented adaptive-optics assisted integral-field spectroscopy of the $z= 3.3$ LBG DSF2237a-C2 using OSIRIS on the Keck telescope." + The picture that cimerges frou hese observations is ar from simple., The picture that emerges from these observations is far from simple. + ? point out that a resolutious of l kpe reached with adaptive optics. UV-selected: ze2.3 galaxies have irregular kinetics. which are likely rot dominated by large-scale eraviatioval motion. but ooerhaps are more relateL to mereie or eas-cooling.," \citet{law07} point out that at resolutions of $\sim 1$ kpc reached with adaptive optics, UV-selected $\sim 2-3$ galaxies have irregular kinematics, which are likely not dominated by large-scale gravitational motion, but perhaps are more related to merging or gas-cooling." + 7? however argue that at cast a subsample of blue. star-ornnes galaxies at somewhat lower redsufts. z~2. may show the sigus of large. s]itiallv-extenude«. rotating disks.," \citet{genzel06,nmfs06} however argue that at least a subsample of blue, star-forming galaxies at somewhat lower redshifts, $\sim 2$, may show the signs of large, spatially-extended, rotating disks." + Distiuguislhiug between tje wo scenarios is cüfficult. due o the low spatial resolution of the data reative to the size of the targets (seealso?)..," Distinguishing between the two scenarios is difficult, due to the low spatial resolution of the data relative to the size of the targets \citep[see +also][]{kronberger07}." +" Tere we present a sudv of one of the first z~3 LBCs described iu the literature. QU317-383. Ch, which was initially described by ?.."," Here we present a study of one of the first $\sim 3$ LBGs described in the literature, Q0347-383 C5, which was initially described by \citet{steidel96b}." + With R 223.52 mag. QU3I1T- ⋅≩≺∖⋅⊓⋅↱⊐∙∖∙⊲ ↕↴∖↴↖↖↽↕↑↕∐∐↑↕∐∖↑⋜↧∐∪↕⋟↑↕∐∖∿∐∣⋰∣⊲ ixiehtest LBCs.," With ${\cal R}=$ 23.82 mag, Q0347-383 C5 is within the tail of the $\sim 10$ brightest LBGs." +" WEPC2 imaging shows a relatively couples morphology. extending over 1""down to the faint surface briglituess detection limit of the image (150Xs through the P702W filter) aud a half light radius about a few teutis of an are second ?.."," WFPC2 imaging shows a relatively complex morphology, extending over $\sim 1$ down to the faint surface brightness detection limit of the image (18000s through the F702W filter) and a half light radius about a few tenths of an arc second \citet{pettini01}." + Exteuts tus larec are not rare along the bright LBC population and its halt-light radius is also ratlY typical (?).., Extents this large are not rare among the bright LBG population \citep{conselice03} and its half-light radius is also rather typical \citep{ferguson04}. +" stained lougshlit specLTOSCODV in the K-1xuxd for a sal saluple of z~3 LBCs. 1iclucdiug (03L7-383 C5. which was oue ou of two of their sources with spatially-exteuded speclan xd a velocity eracdicut of ~TO kms Lin the AA 959.5007 emission li1ο,"," \citet{pettini01} obtained longslit spectroscopy in the K-band for a small sample of $\sim 3$ LBGs, including Q0347-383 C5, which was one out of two of their sources with spatially-extended spectra and a velocity gradient of $\sim 70$ km $^{-1}$ in the $\lambda\lambda$ 4959,5007 emission line." + They placed a: hcluit on IL/ of PUP)<1.3«10τν cre E )τν, They placed a $\sigma$ limit on $\beta$ of $F(H\beta) < 1.7 \times 10^{-17}$ erg $^{-1}$ $^{-2}$. +" Usiug the nemiifrarecd sxctrograpli SINFONT ou he LA""LT. we obtained deep. spatially-resolved spectroscopy of —ie AX 959.5007. aud emission Bue."," Using the near-infrared spectrograph SINFONI on the VLT, we obtained deep, spatially-resolved spectroscopy of the $\lambda\lambda$ 4959,5007, and $\beta$ emission line." + This is οily +re second uuCl]isCC LBC with iutegral-Bield spectroscopy in the literaure with such observatious (?.discusshetheNeck.withalasereidestar.) Caven the τα] uuuTOS of LBCs with iutegral-Beld spectroscopy. aid the large observationa expense o stich observations. even the stidy of a singe object is aready a siguificaut sep forward.," This is only the second unlensed LBG with integral-field spectroscopy in the literature with such observations \citep[][discuss the z=3.2 LBG DSF2238a-C2, for which they obtained +rest-frame optical integral-field spectroscopy using OSIRIS on the Keck +with a laser guide star.]{law07} Given the small number of LBGs with integral-field spectroscopy, and the large observational expense of such observations, even the study of a single object is already a significant step forward." + Such obscYvationis overconue niaiv uncertainties relate to loneslt sλοςroscopy. ππο as 8it-losses. a allow us to trace the emission line uorphologv and kimeniaties across the two-dinieusiowl surface of the target.," Such observations overcome many uncertainties related to longslit spectroscopy, such as slit-losses, and allow us to trace the emission line morphology and kinematics across the two-dimensional surface of the target." + This makes them particularly suited to diseitanele the oteu complex chussion liue morphology of ligrredshitt galaxies., This makes them particularly suited to disentangle the often complex emission line morphology of high-redshift galaxies. + Throughout tie paper we adopt a flat Hy =70 kin + ? concordance cosiiooev with O4=U.7 and Qj;= 0.5., Throughout the paper we adopt a flat $_0 =$ 70 km $^{-1}$ $^{-3}$ concordance cosmology with $\Omega_{\Lambda} = 0.7$ and $\Omega_{M} = 0.3$ . + Tn this cosinoloev. Dy= 28 Cpe and Dy= 1.5 Cpe at z=3.23.," In this cosmology, $_L=$ 28 Gpc and $_A =$ 1.5 Gpc at z=3.23." + Tje size scale is 7.5 kpe +., The size scale is 7.5 kpc $^{-1}$. + The age of the universe at this redshift aud cosmological model is 1.9 Cor., The age of the universe at this redshift and cosmological model is 1.9 Gyr. + We obtained deep. sccine-limited IdK-baud spectroscopy of the z=3.2 LBC QU317-383. C5. using the," We obtained deep, seeing-limited K-band spectroscopy of the $=$ 3.2 LBG Q0347-383 C5, using the" +individually.,individually. + The results are then averaged together. similar to the method used for calculating ihe GCL from the individual CLs for a given object. as detailed in RO4b.," The results are then averaged together, similar to the method used for calculating the GCL from the individual CLs for a given object, as detailed in R04b." + The light curve morphology test is predicated on the theory that a variable quasar will tend to vary little on the Gime scale of an individual QUEST observing season (six (ο eieht weeks). but may vary significantly between observing seasons.," The light curve morphology test is predicated on the theory that a variable quasar will tend to vary little on the time scale of an individual QUEST observing season (six to eight weeks), but may vary significantly between observing seasons." + The opposite will tend to be true for periodie variable stars. which will tend to exhibit a higher level of variability during a single observing season. with the annual average magnitude remaining fairly constant [rom one vear to the next.," The opposite will tend to be true for shorter-term periodic variable stars, which will tend to exhibit a higher level of variability during a single observing season, with the annual average magnitude remaining fairly constant from one year to the next." + This is effectively a null detection test. similar to proper motion cuts to detect quasars.," This is effectively a null detection test, similar to proper motion cuts to detect quasars." + By rejecting variable objects which are detectably periodic. we still keep in consideration aperiodic variable objects. which will include those stellar variables which do not show periodic behavior. those whose periodicity was missed due to insufficient time sampling. ancl those which have periods longer than those sampled in the QVS.," By rejecting variable objects which are detectably periodic, we still keep in consideration aperiodic variable objects, which will include those stellar variables which do not show periodic behavior, those whose periodicity was missed due to insufficient time sampling, and those which have periods longer than those sampled in the QVS." + A light curve morphology. parameter. denoted by q;. is calculated.," A light curve morphology parameter, denoted by $q_i$ , is calculated." + q; is the ratio of two indices. both of which exploit the qualitative difference between periodic and aperioclic variables: a variance index. Vj. and a magnitude difference index. inj.," $q_i$ is the ratio of two indices, both of which exploit the qualitative difference between periodic and aperiodic variables: a variance index, $V_i$, and a magnitude difference index, $\Delta m_i$." + V; is the average ol the ratio of the global variance to the single observing season variance. weighted bv the percentage of total data points in a given observing season.," $V_i$ is the average of the ratio of the global variance to the single observing season variance, weighted by the percentage of total data points in a given observing season." + where .V; is the number of lisht curve points within a given observing season. σ is the standard deviation of the light curve points over the entire light curve σι is (lie standarcl deviation of light curve points within a given observing season. ancl (he index 7 runs over the three individual observing seasons.," where $N_i$ is the number of light curve points within a given observing season, $\sigma$ is the standard deviation of the light curve points over the entire light curve $\sigma_i$ is the standard deviation of light curve points within a given observing season, and the index $i$ runs over the three individual observing seasons." + Short-term periodic variables will see larger variations within an observing season. so σι and σ will be comparable. leading to smaller values lor V;.," Short-term periodic variables will see larger variations within an observing season, so $\sigma_i$ and $\sigma$ will be comparable, leading to smaller values for $V_i$." + Visual inspection of the representative light curves in relleex shows (hat an aperiodic light curve will tend to have a larger V; than a periodic variable., Visual inspection of the representative light curves in \\ref{lcex} shows that an aperiodic light curve will tend to have a larger $V_i$ than a periodic variable. + Am; compares the global standard deviation to the largest difference in mean magnitude between any (wo observing seasons., $\Delta m_i$ compares the global standard deviation to the largest difference in mean magnitude between any two observing seasons. +" where & is againthe global standard deviation and A«2,4, is the largest dillerence between single-observing-season average magnitudes.", where $\sigma$ is againthe global standard deviation and $\Delta\!<\!m\!>_{max}$ is the largest difference between single-observing-season average magnitudes. + Another visual inspection of, Another visual inspection of +"bearing turbulent eddy. τιοὐL/v i$ the characteristic convective time. and /n, is the radial size of the largest eddy at r with characteristic frequency of w or greater Ui,=Lmin(l.(2c; 27),","bearing turbulent eddy, $\tau_L \approx L/v$ is the characteristic convective time, and $h_\omega$ is the radial size of the largest eddy at $r$ with characteristic frequency of $\omega$ or greater $h_\omega = L \min\{1, (2\omega\tau_L)^{-3/2}\}$ )." + The gravity waves are evanescent in the convection zone. the region where they are excited.," The gravity waves are evanescent in the convection zone, the region where they are excited." +" Their wave-functions &, and & are thus proportional to ky!;exp(i[drk,)."," Their wave-functions $\xi_r$ and $\xi_h$ are thus proportional to $k_r^{-1/2} \, \exp \lp i\int \diff r \, k_r \rp$." + The above equation was derived under the assumption that the turbulence spectrum is Kolmogorov., The above equation was derived under the assumption that the turbulence spectrum is Kolmogorov. +" The momentum flux per unit frequency 7,"" is then The momentum spectra corresponding to the various stellar masses are shown in Fig.", The momentum flux per unit frequency ${{\cal F}_J}^R$ is then The momentum spectra corresponding to the various stellar masses are shown in Fig. +" 2 where £,=Anz,T is the momentum luminosity: note that some of the lower frequency waves have zero magnitude.", 2 where ${\cal L}_J=4\pi r_{\rm cz}^2 {\cal F}_J$ is the momentum luminosity; note that some of the lower frequency waves have zero magnitude. + This is due to the fact that the corresponding damping is too large to permit them to be waves., This is due to the fact that the corresponding damping is too large to permit them to be waves. + Spectrum characteristics evolve together with the structure of the convection zone which depends oi the stellar mass., Spectrum characteristics evolve together with the structure of the convection zone which depends on the stellar mass. + Low frequeney waves disappear when the stellar mass increases., Low frequency waves disappear when the stellar mass increases. + This is related to the fact that the surface convection zone then becomes thinner. leading to a larger thermal diffusivity just below it.," This is related to the fact that the surface convection zone then becomes thinner, leading to a larger thermal diffusivity just below it." + This in turn implies stronger damping (see Eq. 6) , This in turn implies stronger damping (see Eq. \ref{optdepth}) ) +and the disappearance of low frequency waves., and the disappearance of low frequency waves. + Furthermore. as stellar mass rises up to about 1.35M. (1.e.. Tay ~6400 K). so does the flux associated with a given frequency.," Furthermore, as stellar mass rises up to about $1.35~M_{\odot}$ (i.e., $T_{\rm eff} \sim $ 6400 K), so does the flux associated with a given frequency." + This 15 related to the rise of the luminosity with mass. and thus. of the energy in convective motions.," This is related to the rise of the luminosity with mass, and thus, of the energy in convective motions." + For even more massive stars. the flux associated with a given frequency remains about constant. but most low frequency waves are damped too rapidly to exist.," For even more massive stars, the flux associated with a given frequency remains about constant, but most low frequency waves are damped too rapidly to exist." + Let us recall that these results are obtained for stellar structures on the ZAMS. and that we have found no significant dependence of the wave spectrum with age on the main sequence: it can thus be considered as constant for the duration of the main sequence.," Let us recall that these results are obtained for stellar structures on the ZAMS, and that we have found no significant dependence of the wave spectrum with age on the main sequence; it can thus be considered as constant for the duration of the main sequence." + In this description. waves with frequencies up to NV. (the Brunt-Viáiisill frequency at the base of the convective envelope) can be excited.," In this description, waves with frequencies up to $N_c$ (the Brunt-Väiisällä frequency at the base of the convective envelope) can be excited." + However. the high-frequency waves will have little impact on momentum evolution: indeed. as frequencies increase. filtering by the shear layer (see 33) becomes less efficient and less differential.," However, the high-frequency waves will have little impact on momentum evolution; indeed, as frequencies increase, filtering by the shear layer (see 3) becomes less efficient and less differential." + Furthermore. damping is so small that it leads to only a small amount of momentum redistribution.," Furthermore, damping is so small that it leads to only a small amount of momentum redistribution." + Finally. as wave excitation diminishes with frequency. they carry much less momentum overall.," Finally, as wave excitation diminishes with frequency, they carry much less momentum overall." + These high-frequency waves will form standing waves. the g-modes of helio- and astero-seismology.," These high-frequency waves will form standing waves, the -modes of helio- and astero-seismology." + Greater uncertainties exist on wave generation via convective penetration., Greater uncertainties exist on wave generation via convective penetration. + The only theoretical estimates that exist have been made by Press (1981) and ia Lóppez Spruit (1991). and later used by Zahn et al. (," The only theoretical estimates that exist have been made by Press (1981) and a Lóppez Spruit (1991), and later used by Zahn et al. (" +1997).,1997). + It is the formulation we shall adopt here., It is the formulation we shall adopt here. + This deseription is based on the matching of wave pressure fluctuations with those of turbulent convection., This description is based on the matching of wave pressure fluctuations with those of turbulent convection. + Furthermore. it takes into account the combination of turbulent eddies of a given size to produce larger fluctuations.," Furthermore, it takes into account the combination of turbulent eddies of a given size to produce larger fluctuations." + The range of horizontal scales available is thus 0 iC 6 7 EN where ( is the spherical harmonic number associated with the largest convective scale and ως 1s the corresponding convective frequency., The range of horizontal scales available is thus 0 < < _u _u = _c where $\ell_c$ is the spherical harmonic number associated with the largest convective scale and $\omega_c$ is the corresponding convective frequency. + Turbulence is assumed to follow a Kolmogorov spectrum. all frequencies with w7c. thus being available.," Turbulence is assumed to follow a Kolmogorov spectrum, all frequencies with $\omega \ge \omega _c$ thus being available." + The associated energy flux 7; is and the corresponding angular momentum flux is still given by Eq. (2).," The associated energy flux ${{\cal F}_E}^P$ is ^P, = 1- ^2 and the corresponding angular momentum flux is still given by Eq. \ref{mom_flux}) )." + Let us stress that the fluxes caleulated here are somewhat uncertain. especially in the second case.," Let us stress that the fluxes calculated here are somewhat uncertain, especially in the second case." + Indeed. it is well known that the “structure” of convection. which contains e.g. plumes that travel down across the whole convection zone. 1s not well reproduced by the mixing length model even though the convective velocities are more or less correct (e.g. Hurlburt etal.," Indeed, it is well known that the “structure” of convection, which contains e.g. plumes that travel down across the whole convection zone, is not well reproduced by the mixing length model even though the convective velocities are more or less correct (e.g. Hurlburt etal." + 1986)., 1986). + However. their differential properties should have," However, their differential properties should have" +Shown in Figure 13 is the image correlation [uncetion for the source galaxies. where the galaxies have again been broadly distributed in redshilt space and a flat A-dominated universe has been adopted.,"Shown in Figure 13 is the image correlation function for the source galaxies, where the galaxies have again been broadly distributed in redshift space and a flat $\Lambda$ -dominated universe has been adopted." + Solid squares show the results for the full. multiple-deflection calculations ancl open circles show the results for the single-deflection calculations in which the sources have been lensed by only the closest lenses.," Solid squares show the results for the full, multiple-deflection calculations and open circles show the results for the single-deflection calculations in which the sources have been lensed by only the closest lenses." + From Figure 13. then. it is clear that for angular separations 6Z5 aresec. the single-delleetion calculations vield essentially no contribution of galaxv-galaxy lensing to the cosmic shear.," From Figure 13, then, it is clear that for angular separations $\theta \gtrsim 5$ arcsec, the single-deflection calculations yield essentially no contribution of galaxy-galaxy lensing to the cosmic shear." + That is. if multiple deflections were nol important in galaxv-galaxy lensing. one would expect that on scales greater (han 5 arcsec. galaxies alone would not contribute to cosmic shear.," That is, if multiple deflections were not important in galaxy-galaxy lensing, one would expect that on scales greater than 5 arcsec, galaxies alone would not contribute to cosmic shear." + Ilence. cosmic shear on scales ereater (han 5 arcsec would be expected to be largely independent of the gravitational potentials of the halos of field galaxies.," Hence, cosmic shear on scales greater than 5 arcsec would be expected to be largely independent of the gravitational potentials of the halos of field galaxies." + Llowever. the full. multiple-deflection calculations in Figure 13 show that galaxv-galaxy lensing can. indeed. induce substantial correlations in the source images on scales greater than 5 arcsec.," However, the full, multiple-deflection calculations in Figure 13 show that galaxy-galaxy lensing can, indeed, induce substantial correlations in the source images on scales greater than 5 arcsec." +" Furthermore. the degree of lensing-induced image alignment is stronglv. affected by (he characteristic parameters (hat are adopted [for the halos of £5, lenses."," Furthermore, the degree of lensing-induced image alignment is strongly affected by the characteristic parameters that are adopted for the halos of $L_B^\ast$ lenses." + In addition to (he image correlation function. the top hat shear variance is common measure of cosmic shear.," In addition to the image correlation function, the top hat shear variance is common measure of cosmic shear." +" Here /7, is the power spectrum of the projected mass densitv of the universe. J; is a Bessel function of the first kind. and 8 is the radius of the circular aperture over which the mean is computed."," Here $P_\kappa$ is the power spectrum of the projected mass density of the universe, $J_1$ is a Bessel function of the first kind, and $\theta$ is the radius of the circular aperture over which the mean is computed." + In an observational data set. the function is computed as for all galaxies within a circular aperture of radius 9 on the sky.," In an observational data set, the function is computed as for all galaxies within a circular aperture of radius $\theta$ on the sky." + Solid squares in Figure 14 show the shear top hat. variance due to galaxv-galaxy. lensing alone. obtained [rom full. multiple-dellection ealeula(ions.," Solid squares in Figure 14 show the shear top hat variance due to galaxy-galaxy lensing alone, obtained from full, multiple-deflection calculations." + Again. sources have been broadly distributed in redshift and a flat A-dominated. universe is adopted.," Again, sources have been broadly distributed in redshift and a flat $\Lambda$ -dominated universe is adopted." +" Also shown for comparison (crosses connected by dotted line) are the measured values of (52) obtained by Fu et ((2008) for galaxies in the CFIIT Legacy Survey with a median redshift z,,=0.83.", Also shown for comparison (crosses connected by dotted line) are the measured values of $\left < \gamma^2 \right>$ obtained by Fu et (2008) for galaxies in the CFHT Legacy Survey with a median redshift $z_m = 0.83$. + Although this is somewhat lower than the meclian redshift of the source galaxies in (he Monte Carlo simulations. it is sullicientlv similar (hat it is reasonable to compare the observational and (theoretical results directlv.," Although this is somewhat lower than the median redshift of the source galaxies in the Monte Carlo simulations, it is sufficiently similar that it is reasonable to compare the observational and theoretical results directly." +" From Figure 14. the small-scale contribution of galaxy-galaxy lensing to (57) depends quite strongly on the parameters adopted for the halos of L5, galaxies. and scales roughly"," From Figure 14, the small-scale contribution of galaxy-galaxy lensing to $\left< \gamma^2 \right>$ depends quite strongly on the parameters adopted for the halos of $L_B^\ast$ galaxies, and scales roughly" +oworder moments through incomplete cancellation (Feldman&Watkins1994.1998)... an effect which up to now has not been quantified.,"low–order moments through incomplete cancellation \citep{fw94,fw98}, an effect which up to now has not been quantified." + Another drawback of this approach is that il utilizes only a fraction of the available information., Another drawback of this approach is that it utilizes only a fraction of the available information. + An alternative method is to. perform a likelihood analvsis using all of the velocity information (Jaffe&Ixaiser1995)., An alternative method is to perform a likelihood analysis using all of the velocity information \citep{jk95}. +.. An obvious danger here is that retaining smallscale. ionlinear contributions to the velocities can lead to unpredictable biases which can skew the results (Croft&Efstathiou1994).," An obvious danger here is that retaining small–scale, nonlinear contributions to the velocities can lead to unpredictable biases which can skew the results \citep{C&E}." +. This method also has the disadvantage of becoming unwieldy for surveys larger (han about a thousand objects., This method also has the disadvantage of becoming unwieldy for surveys larger than about a thousand objects. + While advances in computing will nuake this less of a problem in the future. clearly a less timeintensive method is desirable.," While advances in computing will make this less of a problem in the future, clearly a less time–intensive method is desirable." + In this paper we describe a new method lor the analysis of peculiar velocities which is designed to separate large ancl small scale velocity information in an optimal wav., In this paper we describe a new method for the analysis of peculiar velocities which is designed to separate large and small scale velocity information in an optimal way. + The nethod utilizes KarhunenLoevve methods of data compression to construct aset of moments out of the velocities which are minimally sensitive to small scale power: (hese moments can then be used in a likelihood analvsis., The method utilizes Karhunen–Loèvve methods of data compression to construct a set of moments out of the velocities which are minimally sensitive to small scale power; these moments can then be used in a likelihood analysis. + Overall sensitivity of the set of moments to small scales is quantified. and can be controlled through the imunber of moments retained in the analvsis.," Overall sensitivity of the set of moments to small scales is quantified, and can be controlled through the number of moments retained in the analysis." + since the number of moments kept is (wpically much smaller than the number of velocities in the survey. this method has the added advantage of being much more efficient than a full analvsis of thedata.," Since the number of moments kept is typically much smaller than the number of velocities in the survey, this method has the added advantage of being much more efficient than a full analysis of thedata." + KarhunenLoévve methods (lxennev&Keeping1954:KendallStuart1969). have recently become popular in cosmology.," Karhunen–Loèvve methods \citep{KK,KS} have recently become popular in cosmology." + A general diseussion of their use in the analvsis of large data sets was done by Tegmark.Tavl, A general discussion of their use in the analysis of large data sets was done by \citet{TTH}. +or&Ileavens(1997).. In addition. Loeévve methods have been applied to the Las Campanas Bedshift Survey. &Landy 2000).. to velocity field survevs (Πο[πια& 2001).. aud to the decorrelation of the power spectrum (IluniltonTeemark 2000).," In addition, Karhunen--Lo\`evve methods have been applied to the Las Campanas Redshift Survey \citep{matsubara00}, to velocity field surveys \citep{hz00,silberman01}, and to the decorrelation of the power spectrum \citep{H00,HT00}." +. Although we use the same general method. our take on the formalism is «quite different.," Although we use the same general method, our take on the formalism is quite different." + Taking advantage of the compression techniques aud (the Fisher information matrix (Fisher1935).. we filler out smallscale. nonlinear velocity modes and retain only information regarding the largescale modes.," Taking advantage of the compression techniques and the Fisher information matrix \citep{fisher}, we filter out small–scale, nonlinear velocity modes and retain only information regarding the large–scale modes." + This paper is organized as follows., This paper is organized as follows. + In Sec., In Sec. + 2. we review likelihood methods lov the analvsis of peculiar velocities., \ref{sec-like} we review likelihood methods for the analysis of peculiar velocities. + In Sec., In Sec. + 3. we discuss methods of data compression., \ref{sec-compress} we discuss methods of data compression. + In Sec. 4..," In Sec. \ref{sec-select}," + we describe criteria for the selection of a set of optimal moments., we describe criteria for the selection of a set of optimal moments. + In Sec., In Sec. + 5. we describe the power spectrum model that will be used for our analysis. and in Sec.," \ref{sec-pow} we describe the power spectrum model that will be used for our analysis, and in Sec." + G we discuss the application of our method to peculiar velocity data., \ref{sec-anal} we discuss the application of our method to peculiar velocity data. + In Sec., In Sec. + 7 we show results [rom performing our analvsis on sinnlated catalogs that illustrate the effects of small.scale. nonlinear power and the effectiveness of our method of analvsis in removing these effects.," \ref{results} we show results from performing our analysis on simulated catalogs that illustrate the effects of small–scale, nonlinear power and the effectiveness of our method of analysis in removing these effects." + Finally. in Sec.," Finally, in Sec." + 3 we sumniarize and discuss our results., \ref{sec-conc} we summarize and discuss our results. + several studies have used likelihood methods for the analysis of peculiar velocity data (see. e.g.. Ixaiser (1958))).," Several studies have used likelihood methods for the analysis of peculiar velocity data (see, e.g., \citet{Kaiser88}) )." + Here we review the most straightforward analvsis of this type: one that works directly. with the observed lineofsight peculiar velocities., Here we review the most straightforward analysis of this type; one that works directly with the observed line–of–sight peculiar velocities. +" Suppose that we are eiven a set of N objects wilh positions r; ancl lineofsieht peculiar velocities οἱ, ", Suppose that we are given a set of $N$ objects with positions ${\bf r}_{i}$ and line–of–sight peculiar velocities $v_i$ . +We assume that the observed. velocity v; is of the form, We assume that the observed velocity $v_{i}$ is of the form +11996).,1996). + The profiles of DDO 43 resemble (hose of a few SedSim galaxies with exponential profiles shown by Elmegreen ((1996)., The profiles of DDO 43 resemble those of a few Scd–Sm galaxies with exponential profiles shown by Elmegreen (1996). + We present UDV surface photometry in Figure 4.., We present UBV surface photometry in Figure \ref{fig:ubv}. + To measure (the surface photometry we used ellipses with a position angle of6.5°.. a ratio of minor to major axis ratio θα ol 0.70. and a semi-major axis step size of 11.," To measure the surface photometry we used ellipses with a position angle of, a ratio of minor to major axis ratio $b/a$ of 0.70, and a semi-major axis step size of ." +"3"". The b/a. position angle. and center were determined [rom an outer isophote on a 2x block-averaged version of the V-band image."," The $b/a$, position angle, and center were determined from an outer isophote on a $2\times2$ block-averaged version of the V-band image." +" The surface photometry aud colors have been corrected [or reddening using a total E(B-V),=E(B-V);+0.05. where the foreground reddening E(D— V); is 0.055 (Burstein lleiles 1934) and we add 0.05 [or nominal internal reddening."," The surface photometry and colors have been corrected for reddening using a total $-$ $_t$ $-$ $_f$$+$ 0.05, where the foreground reddening $-$ $_f$ is 0.055 (Burstein Heiles 1984) and we add 0.05 for nominal internal reddening." + We use the reddening law of Cardelli. Clavton. Mathis (1989) and A/E(D—V)23.1.," We use the reddening law of Cardelli, Clayton, Mathis (1989) and $_V$ $-$ $=$ 3.1." + Thus. Ay: is 0.33 and E(U-—D) is 0.0.," Thus, $_V$ is 0.33 and $-$ B) is 0.07." + From the reddening-corrected D-band surface photometry αι we measure Ro; to be3177.. which is 990 pe at the galaxy.," From the reddening-corrected B-band surface photometry $\mu_{B_0}$ we measure $_{25}$ to be, which is 990 pc at the galaxy." + Our radius is smaller than that given by RC3., Our radius is smaller than that given by RC3. + The llolmberg radius. Ry. originally defined to a photographic surface brightness. is measured al an equivalent D-band surface brightness jj;=26.7—0.14908V).," The Holmberg radius, $_H$, originally defined to a photographic surface brightness, is measured at an equivalent B-band surface brightness $\mu_B = 26.7 - +0.149(B-V)$." +" For a (B-V),y of 0.32. the Holmberg radius is determined at a 4765, of 26.65 magnitudes of one 7."," For a $-$ $_0$ of 0.32, the Holmberg radius is determined at a $\mu_{B_0}$ of 26.65 magnitudes of one $^{-2}$." +" We find an Ry of 53""7.. which is 1.4 kpe at the galaxy."," We find an $_H$ of , which is 1.4 kpc at the galaxy." + Integrated properties of DDO 43 are listed in Table 2.., Integrated properties of DDO 43 are listed in Table \ref{tab:int}. + We fit an exponential disk to νο. and the fit is shown in Figure 4..," We fit an exponential disk to $\mu_{V_0}$, and the fit is shown in Figure \ref{fig:ubv}. ." + DDO 43 is fit well with an exponential disk profile having a central surface brightness ji of 22.440.2 magnitudes of one 7 and a disk scale length. Ry of 430450 pe., DDO 43 is fit well with an exponential disk profile having a central surface brightness $\mu_0$ of $\pm$ 0.2 magnitudes of one $^{-2}$ and a disk scale length $_D$ of $\pm$ 50 pc. + Both these values are normal lor Im ealaxies (IIunter Elinegreen 2004. de Jong 1996).," Both these values are normal for Im galaxies (Hunter Elmegreen 2004, de Jong 1996)." + DDO 43's integrated colors are tvpical of Im galaxies (see Figure 2 of IIunter. 1997)., DDO 43's integrated colors are typical of Im galaxies (see Figure 2 of Hunter 1997). + Integrated values are given in Table 2.. and annular colors are shownin Figure 4..," Integrated values are given in Table \ref{tab:int}, and annular colors are shownin Figure \ref{fig:ubv}." + As in most irregulars. the colors are. within the uncertainties. constant with radius.," As in most irregulars, the colors are, within the uncertainties, constant with radius." + Dwo-dimensional color ratio images furthersubstantiate that (here is nolarge-scale pattern to the colors., Two-dimensional color ratio images furthersubstantiate that there is nolarge-scale pattern to the colors. +"""anthropic principle” on (he grounds that it is “nol a scientific theory” in Chat it ""does not make testable predictions”.",“anthropic principle” on the grounds that it is “not a scientific theory” in that it “does not make testable predictions”. + Such arguments reflect a deep mistuclerstanding of the nature of scientific inquiry., Such arguments reflect a deep misunderstanding of the nature of scientific inquiry. + Of course. the anthropic principle is not a scientific theory. and obviously in itself makes no testable predictions.," Of course, the anthropic principle is not a scientific theory and obviously in itself makes no testable predictions." + Rather it is a framework for theoretical speculation., Rather it is a framework for theoretical speculation. + Any profoundly new theory will be preceded by theoretical speculation. or even groping. helore it can be properly formulated.," Any profoundly new theory will be preceded by theoretical speculation, or even groping, before it can be properly formulated." + Such fall formulations may require additional universes and αἱ (he same time make predictions about our universe., Such full formulations may require additional universes and at the same time make predictions about our universe. +" If there are one or (wo such predictions that are verified. ancl these are minimally entangled with the hypothesis of other universes. one might maintain the hope that a new theory will emerge that predicts the same things about our universe but avoids the ""embarrassment of other universes."," If there are one or two such predictions that are verified, and these are minimally entangled with the hypothesis of other universes, one might maintain the hope that a new theory will emerge that predicts the same things about our universe but avoids the “embarrassment” of other universes." + But if these correct predictions multiply. and if they become deeply entanelecl wilh the existence other universes. then (he other universes will come to be accepted. in the same wav that we currently accept (he “reality” of the magnetic vector potential. despite the [act Chat il was originally introduced as a mathematical convenience.," But if these correct predictions multiply, and if they become deeply entangled with the existence other universes, then the other universes will come to be accepted, in the same way that we currently accept the “reality” of the magnetic vector potential, despite the fact that it was originally introduced as a mathematical convenience." + Of course. it is also possible (hat nothing will come of the anthropic-principle speculation. in which case it would join the ranks of the vast majority of such speculations in the waste bin of theoretical physics.," Of course, it is also possible that nothing will come of the anthropic-principle speculation, in which case it would join the ranks of the vast majority of such speculations in the waste bin of theoretical physics." + In this context. it is useful to catalog physical constants that would be (post-Iacto) explained bv the anthropic principle. assunmüng (hat many universes wilh verv different physical constants do exist.," In this context, it is useful to catalog physical constants that would be (post-facto) explained by the anthropic principle, assuming that many universes with very different physical constants do exist." + In 1967. the great Soviet. physicist Andrei Sakharov identified three conditions for barvogenesis.," In 1967, the great Soviet physicist Andrei Sakharov identified three conditions for baryogenesis." + In the early universe. (here were exactly equal numbers of barvons and and these both approximately equaled the number of photons.," In the early universe, there were exactly equal numbers of baryons and anti-baryons, and these both approximately equaled the number of photons." + Today. (he number ol photons is roughly unchanged. but essentially all of the anti-barvons have annihilated with barvons.," Today, the number of photons is roughly unchanged, but essentially all of the anti-baryons have annihilated with baryons." + From (he presently observed baryon/photon ratio. we therefore learn that somehow during those early times. about one in a billion anti-barvons was converted into a barvon.," From the presently observed baryon/photon ratio, we therefore learn that somehow during those early times, about one in a billion anti-baryons was converted into a baryon." + Sakharovs (1967) three necessary conditions were 1) barvon-number violating process. 2) violation of charge-paritv (CP) svimnietry. 3) out-ol-equilibrium thermodynamics.," Sakharov's (1967) three necessary conditions were 1) baryon-number violating process, 2) violation of charge-parity (CP) symmetry, 3) out-of-equilibrium thermodynamics." + The first condition is obvious., The first condition is obvious. + The third is also obvious. since in thermodynamic equilibrium detailed balance ensures (hat every. barvon-violating process will be countered by barvon violation going in the other direction.," The third is also obvious, since in thermodynamic equilibrium detailed balance ensures that every baryon-violating process will be countered by baryon violation going in the other direction." + The second is less obvious., The second is less obvious. + Under the CP svinmetry. a given particle's anti-particle will behave exactly as the particle does. provided we consider anti-particles of the opposite parity.," Under the CP symmetry, a given particle's anti-particle will behave exactly as the particle does, provided we consider anti-particles of the opposite parity." + In quantum mechanics. CPT svinmetry is essentially a mathematical identity.," In quantum mechanics, CPT symmetry is essentially a mathematical identity." + That is. the above svnunetry must hold if in addition. the," That is, the above symmetry must hold if, in addition, the" +We acknowledge useful discussions with Manuel Merchánn ancl Michael Balogh.,We acknowledge useful discussions with Manuel Merchánn and Michael Balogh. + We thanks the anonymous lieferec for a detail revision that helped. to improve this paper., We thanks the anonymous Referee for a detail revision that helped to improve this paper. + This work was partially supported by the Consejo Nacional ce Investigaciones Cientifficas vy Péecnicas. Agencia de. Promociónn de Ciencia vy ‘Pecnologfaa. Funcdacionn Antorchas and Secretariaa de Ciencia v. Γόσσμίσα cde [a Universidad: Nacional de Corrcdoha.," This work was partially supported by the Consejo Nacional de Investigaciones ficas y Téccnicas, Agencia de Promociónn de Ciencia y a, Fundaciónn Antorchas and a de Ciencia y Téccnica de la Universidad Nacional de Córrdoba." +by one or more small impacts and spread across a fraction of the asteroid surface as lallback debris.,by one or more small impacts and spread across a fraction of the asteroid surface as fallback debris. + While we possess no proof that (his is the origin of the near infrared spectral features on either Themis or Cvbele. the inevitabilitv of impact and the simplicity of the impact excavation model provide ample motivation lor an expanded search [or ice-like absorptions in. and outgassing from. the asteroids.," While we possess no proof that this is the origin of the near infrared spectral features on either Themis or Cybele, the inevitability of impact and the simplicity of the impact excavation model provide ample motivation for an expanded search for ice-like absorptions in, and outgassing from, the asteroids." +"shows the correlation between the gamma-ray luminosity and the encounter rate, and the correlation coefficient is 0.71.","shows the correlation between the gamma-ray luminosity and the encounter rate, and the correlation coefficient is 0.71." +" Figure 7b and Figure 7c show the correlations between L, and the combined factor, i.e. [ewpn, where wy; are optical and IR photon energy density respectively."," Figure 7b and Figure 7c show the correlations between $L_{\gamma}$ and the combined factor, i.e. $\Gamma_{c}w_{ph}$ , where $w_{ph}$ are optical and IR photon energy density respectively." +" The correlation coefficients for Figure 7b and Figure 7c are 0.79 and 0.82 respectively, which show stronger correlations when the soft photon energy density is included."," The correlation coefficients for Figure 7b and Figure 7c are 0.79 and 0.82 respectively, which show stronger correlations when the soft photon energy density is included." + These results support that the inverse Compton scattering mechanism is at least one of the major gamma-ray emission process in globular clusters., These results support that the inverse Compton scattering mechanism is at least one of the major gamma-ray emission process in globular clusters. +" KSC is supported by a GRF grant of Hong Kong Government under HKU700908P, DOC and VAD are partly supported by the RFBR grant 08-02-00170-a, the NSC-RFBR Joint Research Project RP09N04 and 09-02-92000-HHC-a and by the grant of a President of the Russian Federation ""Scientific School of Academician V.L.Ginzburg"", and AKHK is supported partly by the National Science Council of the Republic of China (Taiwan) through grant NSC96-2112-M007-037-MY3."," KSC is supported by a GRF grant of Hong Kong Government under HKU700908P, DOC and VAD are partly supported by the RFBR grant 08-02-00170-a, the NSC-RFBR Joint Research Project RP09N04 and 09-02-92000-HHC-a and by the grant of a President of the Russian Federation ""Scientific School of Academician V.L.Ginzburg"", and AKHK is supported partly by the National Science Council of the Republic of China (Taiwan) through grant NSC96-2112-M007-037-MY3." +The two groups of QSOs in our sample are well suited to search for large under-dense regions in the IGM.,The two groups of QSOs in our sample are well suited to search for large under-dense regions in the IGM. + Previous attempts to detect under-dense regions in the fforest have searched for regions without absorption lines along a singlesight., Previous attempts to detect under-dense regions in the forest have searched for regions without absorption lines along a single. +. They looked for portions of spectra where the observed number of absorption lines was significantly smaller then the expected number from synthetic spectra (Carswell&Rees1987;CrottsOs-al. 2001).," They looked for portions of spectra where the observed number of absorption lines was significantly smaller then the expected number from synthetic spectra \citep{carswell87,crotts87,ostriker88,cristiani95,kim01}." + A strong improvement of the statistical significance of each detection can be provided by the simultaneous presence of an under-dense region along several closesight., A strong improvement of the statistical significance of each detection can be provided by the simultaneous presence of an under-dense region along several close. +. This would allow the detection of smaller under-dense regions maintaining a high confidence level., This would allow the detection of smaller under-dense regions maintaining a high confidence level. +" As done in the previous section, we focused our attention on searching for common under-dense regions among the oof the Triplet and among all the possible groups of pprovided by the Sextet."," As done in the previous section, we focused our attention on searching for common under-dense regions among the of the Triplet and among all the possible groups of provided by the Sextet." +" Following Rollindeetal.(2003),, we can define an under-dense region along single aas a portion of the spectruma between A; and Ae, where the normalized flux f is higher than the specific threshold (f—oy), where is the average flux in the fforest and oy is fthe value of the flux uncertainty."," Following \citet{rollinde03}, we can define an under-dense region along a single as a portion of the spectrum between $\lambda_{i}$ and $\lambda_{e}$ , where the normalized flux ${\it f}$ is higher than the specific threshold $(\bar{f} - \sigma_f)$, where $\bar{f}$ is the average flux in the forest and $\sigma_f$ is the value of the flux uncertainty." + Note also that at z~2 regions above the mean density correspond on average to regions below the mean flux level of high resolution spectra (Vieletal.2008)., Note also that at $z\sim 2$ regions above the mean density correspond on average to regions below the mean flux level of high resolution spectra \citep{viel2008}. +". Since the SNR of the spectra analyzed by Rollindeetal.(2003) is much larger than that of our spectra (15—70 vs. 4—15 respectively), this simple procedure for the detection of under-dense regions cannot be adopted in the present case."," Since the SNR of the spectra analyzed by \citet{rollinde03} is much larger than that of our spectra $15-70$ vs. $4-15$ respectively), this simple procedure for the detection of under-dense regions cannot be adopted in the present case." +" Indeed, the fluctuations due to the flux noise cause the splitting of single large under-dense regions into several smaller regions, preventing their detection."," Indeed, the fluctuations due to the flux noise cause the splitting of single large under-dense regions into several smaller regions, preventing their detection." +" In order to reveal the presence of under-dense regions in our spectra, we have developed the following method."," In order to reveal the presence of under-dense regions in our spectra, we have developed the following method." +" The spectra are smoothed with a median filter characterized by a very short kernel length, only three pixels."," The spectra are smoothed with a median filter characterized by a very short kernel length, only three pixels." +" After the smoothing, common under-dense regions are looked for with the method described above (always adopting the same average flux and flux uncertainty)."," After the smoothing, common under-dense regions are looked for with the method described above (always adopting the same average flux and flux uncertainty)." +" Then, the spectra are smoothed again and again searched for common voids."," Then, the spectra are smoothed again and again searched for common voids." + This process is iterated several times., This process is iterated several times. + T'he results are shown in Fig., The results are shown in Fig. + 12 where we have reported the size of the bigger common under-dense region found in the Triplet and in the $3-S5-86 group of Sextet QSOs as a function of the number of times the spectra have been smoothed., \ref{fig:smooth} where we have reported the size of the bigger common under-dense region found in the Triplet and in the S3-S5-S6 group of Sextet QSOs as a function of the number of times the spectra have been smoothed. + We report only the result concerning the S3-S5-S6 group because it is the only one in which a significant under-dense region has been detected., We report only the result concerning the S3-S5-S6 group because it is the only one in which a significant under-dense region has been detected. +" We can see how, after an initial linear growth of the size of the common under-dense region, a step behaviour occurs in both the series of data."," We can see how, after an initial linear growth of the size of the common under-dense region, a step behaviour occurs in both the series of data." +" Steps occur whenever two separate under-dense regions are merged together, that is when the absorption line (both real or spurious) lying between them is smoothed out by the n-th action of the median filter."," Steps occur whenever two separate under-dense regions are merged together, that is when the absorption line (both real or spurious) lying between them is smoothed out by the n-th action of the median filter." +" We can notice also how, after ~10 smoothings, the size of the under-dense regions in both the Triplet and the S3-S5-96 group reaches an ""asymptotic"" value."," We can notice also how, after $\sim 10$ smoothings, the size of the under-dense regions in both the Triplet and the S3-S5-S6 group reaches an ”asymptotic” value." + Each asymptotic rate corresponds to the size of a common under-dense region enclosed between two strong lines (not necessarily belonging to the same spectrum) requiring a large number of smoothings to be cancelled., Each asymptotic rate corresponds to the size of a common under-dense region enclosed between two strong lines (not necessarily belonging to the same spectrum) requiring a large number of smoothings to be cancelled. +" A series of simulations has been carried out in order to evaluate the minimum value of the column density N(HijoftheLyman—a llines surviving after 6 and 8 smoothing processes in the Triplet and the $3-S5-S6 group, respectively."," A series of simulations has been carried out in order to evaluate the minimum value of the column density $N($ $)$ of the lines surviving after 6 and 8 smoothing processes in the Triplet and the S3-S5-S6 group, respectively." +" First, a mock spectrum has been created placing several lines characterized by an increasing log N(H1), from12tol5bystepsof0.05, andcentralwavelengthsseparatedby10"," First, a mock spectrum has been created placing several lines characterized by an increasing $\log N($ $)$, from 12 to 15 by steps of 0.05, and central wavelengths separated by 10." + ," Line profiles have been modeled with a Gaussian, since we were interested only in the centre of the lines and not in reproducing correctly their wings." +2001);; the dependence of the simulation results from this parameter is negligible., The Doppler parameter$b$ was set to a value of 20 \citep{kim01}; the dependence of the simulation results from this parameter is negligible. +adapted to estimate error bars.,adapted to estimate error bars. + We perform 1000 \Toute-Carlo draws and do a wavelet analysis on each of the 100 draws., We perform 1000 Monte-Carlo draws and do a wavelet analysis on each of the 1000 draws. + We choose as limits to the error bars the ) and. 90 percentiles of the distributions thus obtaiuect., We choose as limits to the error bars the 10 and 90 percentiles of the distributions thus obtained. + These are shown on the top panel of Fie. 12.., These are shown on the top panel of Fig. \ref{fadda}. + The dip jerefore appears to boe statistically tomsignificant., The dip therefore appears to be statistically significant. + However. Us. bootstrap techuique. gives. too large a weight. to the observed realization: m particular. if à gap is preseut im 10 data. uo draw will be able to fill it.," However, this bootstrap technique gives too large a weight to the observed realization; in particular, if a gap is present in the data, no draw will be able to fill it." + We have therefore applied a second method., We have therefore applied a second method. + As a first step. we have wavelet reconstructed the luminosity πιοοι. climinating the three smallest scales.," As a first step, we have wavelet reconstructed the luminosity function eliminating the three smallest scales." + The distribution obtaimed im this way does uot show auv dip., The distribution obtained in this way does not show any dip. + We have then performed 1000 Monte-Carlo draws ollowius this profile. and again have done a wavelet analysis on cach of these draws.," We have then performed 1000 Monte-Carlo draws following this profile, and again have done a wavelet analysis on each of these draws." + The result of this method isshown in Fig., The result of this method isshown in Fig. + 12. (bottom uel), \ref{fadda} (bottom panel). + The dip clearly appears outside the error bar region. muplviug that the probability to obtain such a eature from such a parent sample(devoid of dips} is sunaller than 0.001: even the luminosity function drawn at a larger scale (dashed line in Fig. 12))," The dip clearly appears outside the error bar region, implying that the probability to obtain such a feature from such a parent sample (devoid of dips) is smaller than 0.001; even the luminosity function drawn at a larger scale (dashed line in Fig. \ref{fadda}) )" + shows a shallower mt still significant dip., shows a shallower but still significant dip. + A comparable dip: was found: in: the Iuniuosity: fiction: of: several clusters., A comparable dip was found in the luminosity function of several clusters. +" We- give: in: Table: E2. the positionskl of] the. for. Ro» baud. absolute magnitudes recalculateddashed when. . for a. IIubble coustaut of 501 kimi s Alpej, Error. Dhuumositv∙∙⋅ functious:. drawn in; the D baud have heen shifted to the R baud assumiug R=1.7 for all clusters except Virgo. a typical value for cllipticals. taken as the dominaut. cluster population."," We give in Table \ref{dip} the positions of the dips for R band absolute magnitudes recalculated when necessary for a Hubble constant of 50 km $^{-1}$ $^{-1}$; luminosity functions drawn in the B band have been shifted to the R band assuming $-$ R=1.7 for all clusters except Virgo, a typical value for ellipticals, taken as the dominant cluster population." +. For TVireo. where spirals- are dominant.H we took B. R=.»lL.," For Virgo, where spirals are dominant, we took $-$ R=1.4." + No- -. K-corvectionor Galactic. absorption correction were inchided. suce this is ouky a rough comparison.," No K-correction or Galactic absorption correction were included, since this is only a rough comparison." + It is ⋅⋅interesting⋅ to note that the dips⋅ in⋅ the lmninosity⋅ functions are found at comparable absolute maguitudes in all these clusters within a rauge of only one magnitudo., It is interesting to note that the dips in the luminosity functions are found at comparable absolute magnitudes in all these clusters within a range of only one magnitude. + The only cluster that we found iu the literature having a dip at a significantly. different absolute magnitude is ABCC 196., The only cluster that we found in the literature having a dip at a significantly different absolute magnitude is ABCG 496. + As inentioned above. the dip position derived from he redshift catalogue differs from that derived from the CCD imaging catalogue in ABCC 85.," As mentioned above, the dip position derived from the redshift catalogue differs from that derived from the CCD imaging catalogue in ABCG 85." + This apparent discrepancy is nmiost likely accounted for bv the fact hat the latter corresponds to a auch smaller ceutral region. and suggests that cuviromucutal effects modify the unumositv function iu this cluster (see below).," This apparent discrepancy is most likely accounted for by the fact that the latter corresponds to a much smaller central region, and suggests that environmental effects modify the luminosity function in this cluster (see below)." + These dips do not all secu to have the same width: he dip found in the luminosity function of Shapley 8 is notably broader. while shallower dips (or at least Hattenines) are found in the luminosity functions of Vireo and ABCC 963.," These dips do not all seem to have the same width: the dip found in the luminosity function of Shapley 8 is notably broader, while shallower dips (or at least flattenings) are found in the luminosity functions of Virgo and ABCG 963." + Towever the aethods used dy hese various authors are quite different from ors: σττν haveNET redone(H theB analysisη.lu describedvec]B by- Bivianoix. CtB al.+ (, However the methods used by these various authors are quite different from ours; we have redone the analysis described by Biviano et al. ( +"1995)TOXOF, in1 theH Coma'. cluster.ov usingjd theH wavelet-avpoele Pecoustruction technique: the corresponding luninosity function is displaved in Fig.",1995) in the Coma cluster using the wavelet reconstruction technique; the corresponding luminosity function is displayed in Fig. + 9 aud the dip has a shape wotably;- broader⋅⊀∖⋅ than; that; of: ABCG301 85., \ref{fdlz} and the dip has a shape notably broader than that of ABCG 85. +NR The above facts suggest that the bright galaxy distributions i these clusters have roughly comparable properties. but also that they differ from a cluster to @hother. and even from one region to another in a. given cluster.," The above facts suggest that the bright galaxy distributions in these clusters have roughly comparable properties, but also that they differ from a cluster to another, and even from one region to another in a given cluster." + This is also the case for the relative abundances of galaxy types. which depend on the local density aud/or 04 the global properties of cach cluster.," This is also the case for the relative abundances of galaxy types, which depend on the local density and/or on the global properties of each cluster." + Iu fact. a simple model based on the shapes of the Inuinosity fuuctiouns of the various galaxy types aud on their relative proportious (c.g. Bolin Schiuidt 1995. Jevjen Tanuuann 1997. aud references therein) cau roughlv account for the dip in the Iuninositv function.," In fact, a simple model based on the shapes of the luminosity functions of the various galaxy types and on their relative proportions (e.g. Böhhm Schmidt 1995, Jerjen Tammann 1997, and references therein) can roughly account for the dip in the luminosity function." + By using ouly three kinds of Iuuinosity fictions. aud adjusting the relative proportions of these three types of galaxies. it is easy to recover a Dunünositv function with a similar shape to that observed.," By using only three kinds of luminosity functions, and adjusting the relative proportions of these three types of galaxies, it is easy to recover a luminosity function with a similar shape to that observed." + As an example. such a tov-luminosity function is given in ολ in this case. we have used:," As an example, such a toy-luminosity function is given in \ref{toy2}; ; in this case, we have used:" +"with respect to the average powerlaw for sampling frequencies f<0.005—0.01 days"".",with respect to the average powerlaw for sampling frequencies $f\lesssim0.005-0.01$ $^{-1}$. + In combination with the information from the flux distributions (Sect., In combination with the information from the flux distributions (Sect. + 5.1: Fig. 2.. 3))," 5.1; Fig. \ref{fig_fluxdist1}, \ref{fig_fluxdist2}) )" +" this strongly suggests that ""quiescent high-frequency and “flaring” low-frequency emission have to be treated as separate source states.", this strongly suggests that “quiescent” high-frequency and “flaring” low-frequency emission have to be treated as separate source states. + This conclusion deviates from the more simple picture drawn by other studies (e.g.. Hufnagel Bregman 1992:: Uttley et al. 2002))," This conclusion deviates from the more simple picture drawn by other studies (e.g., Hufnagel Bregman \cite{hufnagel1992}; Uttley et al. \cite{uttley2002}) )" + that treat AGN time series and power spectra as uniform red-noise distributions., that treat AGN time series and power spectra as uniform red-noise distributions. + However. a physical dichotomy of quiescent vs. flaring source states has been suggested for the near-infrared emission observed from the Galactic nuclear black hole. Sagittarius A* (e.g. Gillessen et al. 2006::," However, a physical dichotomy of quiescent vs. flaring source states has been suggested for the near-infrared emission observed from the Galactic nuclear black hole, Sagittarius A* (e.g. Gillessen et al. \cite{gillessen2006};" + Trippe et al. 2007::, Trippe et al. \cite{trippe2007}; + Dodds-Eden et al. 201 11).," Dodds-Eden et al. \cite{doddseden2011}) )," + and has been hotly debated since then (compare. e.g.. Meyer et al.," and has been hotly debated since then (compare, e.g., Meyer et al." + 2007. vs. Meyer et al. 2008)., \cite{meyer2007} vs. Meyer et al. \cite{meyer2008}) ). + We also note that a segregation of distinct source states is well-known for the case of Galactic microquasars., We also note that a segregation of distinct source states is well-known for the case of Galactic microquasars. +" These sources mirror many properties of AGN (taking into account scaling with the black hole mass) and their emission shows distinct states that are ususally classified as ""hard"" and ""soft"" according to their X-ray spectral properties (e.g.. Tananbaum et al. 1972::"," These sources mirror many properties of AGN (taking into account scaling with the black hole mass) and their emission shows distinct states that are ususally classified as “hard” and “soft” according to their X-ray spectral properties (e.g., Tananbaum et al. \cite{tananbaum1972};" + Mirabel Rodriguez 1998.1900:: Takeuchi Mineshige 1998)).," Mirabel Rodriguez \cite{mirabel1998,mirabel1999}; Takeuchi Mineshige \cite{takeuchi1998}) )." + A possible explanation for this transition (Klein-Wolt et al. 2002)), A possible explanation for this transition (Klein-Wolt et al. \cite{kleinwolt2002}) ) + is the difference between the ejection of fairly localized knots from the black hole vicinity (leading to X-ray and radio flares) and the ejection of quasi-contiuous. extended jets that are initially optically thick (leading. to “plateaus” in the X-ray and radio lighteurves).," is the difference between the ejection of fairly localized knots from the black hole vicinity (leading to X-ray and radio flares) and the ejection of quasi-continuous, extended jets that are initially optically thick (leading to “plateaus” in the X-ray and radio lightcurves)." + For nicro-quasars. these events happen on timescales from minutes (minimum time between the ejection of knots) to tens of days (maximum length of “plateau” phases observed): for AGN. corresponding phenomena would have to occur on timescales of years — thus deviating strongly from a simple linear black-hole mass scaling relation — in order to be consistent with our observations.," For micro-quasars, these events happen on timescales from minutes (minimum time between the ejection of knots) to tens of days (maximum length of “plateau” phases observed); for AGN, corresponding phenomena would have to occur on timescales of years – thus deviating strongly from a simple linear black-hole mass scaling relation – in order to be consistent with our observations." +" Notably. the ""flare"" and “high-frequency” regimes of the power spectra are consistent with having the same powerlaw index though on different (by factors 22-3 in spectral power) energy levels."," Notably, the “flare” and “high-frequency” regimes of the power spectra are consistent with having the same powerlaw index though on different (by factors $\approx$ 2–3 in spectral power) energy levels." + This indicates that both emission regimes. although they appear to be physically disconnected. are caused by intrinsically stochastic processes with similar correlation properties.," This indicates that both emission regimes, although they appear to be physically disconnected, are caused by intrinsically stochastic processes with similar correlation properties." + Remarkably. the three sources in question — 3C 111. 3C 273. and 3C 454.3 -- are also those for which we find the (temporarily) fattest spectral indices. indicating optically thick emission.," Remarkably, the three sources in question – 3C 111, 3C 273, and 3C 454.3 – are also those for which we find the (temporarily) flattest spectral indices, indicating optically thick emission." + We tested the presence or absence of time lags between the |.3- and 3-mm fluxes by means of a correlation analysis (cf., We tested the presence or absence of time lags between the 1.3-mm and 3-mm fluxes by means of a correlation analysis (cf. + Eq. 8))., Eq. \ref{eq_dcf}) ). +" We can exclude the presence of significant — referring here to a 3c confidence level — offsets in time for four of our targets. namely 09234392, 3C ΤΙ. 3C 273. and 3C 345 (see Fig. 8))."," We can exclude the presence of significant – referring here to a $3\sigma$ confidence level – offsets in time for four of our targets, namely 0923+392, 3C 111, 3C 273, and 3C 345 (see Fig. \ref{fig_timelag}) )." + This statement holds within accuracies (referring to the ranges of timelags consistent with a zero offset within the 3c confidence band) of few tens of days., This statement holds within accuracies (referring to the ranges of timelags consistent with a zero offset within the $3\sigma$ confidence band) of few tens of days. + Our results are consistent with those obtained by the time delay analyses of Tornikoski et al. (1994)), Our results are consistent with those obtained by the time delay analyses of Tornikoski et al. \cite{tornikoski1994}) ) + and Hovatta et al. (2008)), and Hovatta et al. \cite{hovatta2008}) ) + in the em- range., in the cm-radio range. + Hovatta et al. (2008)), Hovatta et al. \cite{hovatta2008}) ) +" conclude that those limits on time delays. both in the em- and mm-regimes. can be understood in the frame of the semi-empiric “generalized shock model"" by Valtaoja et al. (1992))."," conclude that those limits on time delays, both in the cm- and mm-regimes, can be understood in the frame of the semi-empiric “generalized shock model” by Valtaoja et al. \cite{valtaoja1992}) )." + For the remaining two sources. 3C 454.3 (after 2005.2; cf.," For the remaining two sources, 3C 454.3 (after 2005.2; cf." + Fig. 9)), Fig. \ref{fig_dcf3C454.3}) ) + and 3C 84. we do find indication that the. 1.3-mm emission preceeds the 3-mm emission by =55 days (3C 454.3) and =300 days (3C 84).," and 3C 84, we do find indication that the 1.3-mm emission preceeds the 3-mm emission by $\approx55$ days (3C 454.3) and $\approx300$ days (3C 84)." + We note that the result for 3C 454.3 is consistent with the results by Tornikoski et al. (1994)), We note that the result for 3C 454.3 is consistent with the results by Tornikoski et al. \cite{tornikoski1994}) ) + and Hovatta et al. (2008)), and Hovatta et al. \cite{hovatta2008}) ) + who do not find a time delay in their radio lightcurves: the data of Hovatta et al. (2008)), who do not find a time delay in their radio lightcurves; the data of Hovatta et al. \cite{hovatta2008}) ) +" end in 2005.3. just at the beginning of the ""flare phase"" of 3C 454.3."," end in 2005.3, just at the beginning of the “flare phase” of 3C 454.3." + For 3C 454.3. we suspect variations of the optical depth with frequency as the principal cause for the time delay.," For 3C 454.3, we suspect variations of the optical depth with frequency as the principal cause for the time delay." + Adiabatically expanding plasmas become optically thin. at higher energies first. introducing a systematic time delay between two lighteurves obtained at two frequencies with the high-frequency emission leading.," Adiabatically expanding plasmas become optically thin at higher energies first, introducing a systematic time delay between two lightcurves obtained at two frequencies with the high-frequency emission leading." + Details depend on various parameters. notably the electron energy distribution. the optical depth at a reference frequency. the magnetic field strength. the electron density. and the emission region size (van der Laan 1966)).," Details depend on various parameters, notably the electron energy distribution, the optical depth at a reference frequency, the magnetic field strength, the electron density, and the emission region size (van der Laan \cite{vanderlaan1966}) )." + This mechanism has been incorporated into the shock-in-jet model by Marscher Gear (1985)); proper quantitative treatment takes into account the combination of Compton. synehrotron. and adiabatic cooling (e.g.. Fromm et al. 2011..," This mechanism has been incorporated into the shock-in-jet model by Marscher Gear \cite{marscher1985}) ); proper quantitative treatment takes into account the combination of Compton, synchrotron, and adiabatic cooling (e.g., Fromm et al. \cite{fromm2011}," + and references therein)., and references therein). + Our interpretation is supported by the fact that the spectral index shows fast variability from inverted to almost optically thin spectral indices in. 2005-2007 and remains in the optically thick regime after2007°., Our interpretation is supported by the fact that the spectral index shows fast variability from inverted to almost optically thin spectral indices in 2005–2007 and remains in the optically thick regime after. +. This is in agreement with the results by Jorstad et al. (2010)), This is in agreement with the results by Jorstad et al. \cite{jorstad2010}) ) + who find time delays up to «215 days between 37 GHz and 230 GHz lightcurves. with the 230 GHz emission leading.," who find time delays up to $\approx$ 215 days between 37 GHz and 230 GHz lightcurves, with the 230 GHz emission leading." + For 3C 84. the answer is less clear.," For 3C 84, the answer is less clear." + High-resolution radio-interferometric observations let Asada et al. (20060) , High-resolution radio-interferometric observations let Asada et al. \cite{asada2006}) ) +conclude that the lightcurve. as observed until 2001. is in agreement with adiabatic cooling of an expanding radio lobe.," conclude that the lightcurve, as observed until 2001, is in agreement with adiabatic cooling of an expanding radio lobe." + The rise of the emission around 2005 nicely agrees with observations of the ejection of a new radio jet component in 2005 (agal et al. 2010))., The rise of the emission around 2005 nicely agrees with observations of the ejection of a new radio jet component in 2005 (Nagai et al. \cite{nagai2010}) ). + Those observations are à priori in agreement with optical depth variations in the context of the shock-in-jet model., Those observations are a priori in agreement with optical depth variations in the context of the shock-in-jet model. + However. we note the unusually large time delay of +300 days — assuming the result of the DCF analysis ts correct.," However, we note the unusually large time delay of $\approx$ 300 days – assuming the result of the DCF analysis is correct." + Such a large delay suggests additional travel time effects given by the geometry of the emission region., Such a large delay suggests additional travel time effects given by the geometry of the emission region. + If the emission is composed of various components emitted from spatially separate zones. according time lags may occur.," If the emission is composed of various components emitted from spatially separate zones, according time lags may occur." + Given the observed time offsets of 300 days. this would suggest a spatial extension of the emission region of the order of one light-year.," Given the observed time offsets of $\approx$ 300 days, this would suggest a spatial extension of the emission region of the order of one light-year." +experiment when e.g. the capabilities of breaking moce parameter degeeneracies come into focus.,experiment when e.g. the capabilities of breaking model parameter degeneracies come into focus. + By then the survey parameters and the analysis strategies should. not change radically anvmore. but only in relatively small steps au only a few parameters at a time.," By then the survey parameters and the analysis strategies should not change radically anymore, but only in relatively small steps and only a few parameters at a time." + Lo that holds true. the general form of the posterior is only moderately. mocifiec under these changes. so that one can continue to use the optimal Box-C'ox parameters determined from the initial ful likelihood analysis.," If that holds true, the general form of the posterior is only moderately modified under these changes, so that one can continue to use the optimal Box-Cox parameters determined from the initial full likelihood analysis." + The Box-Cox-Fisher analvsis is repeated: for. severa survey configurations that each ciller in one or two parameters from the fiducial survey by about 10/4.," The Box-Cox-Fisher analysis is repeated for several survey configurations that each differ in one or two parameters from the fiducial survey by about $10\,\%$." + These changes are accounted for in the Fisher matrix. but we retain the values of the Box-Cox. parameters. determined. for the fiducial survey.," These changes are accounted for in the Fisher matrix, but we retain the values of the Box-Cox parameters determined for the fiducial survey." + AX full likelihood. analvsis is computed: as well for every. configuration. but solely for the purpose of assessing the accuracy of the forecast.," A full likelihood analysis is computed as well for every configuration, but solely for the purpose of assessing the accuracy of the forecast." +" We mocdifv the fiducial cosmology by lowering £34, by lot."," We modify the fiducial cosmology by lowering $\Omega_{\rm m}$ by $10\,\%$." + AX slightly. deeper survey is analysed. increasing Syed to l. which also increases the number density of galaxies and. consequently reduces the noise contribution.," A slightly deeper survey is analysed, increasing $z_{\rm med}$ to 1, which also increases the number density of galaxies and consequently reduces the noise contribution." + Applying the scaling found by(2007). the deeper survey has n4=3754aremin27.," Applying the scaling found by, the deeper survey has $\bar{n}_{\rm g}=37.4\,{\rm arcmin}^{-2}$." + Moreover we consider the case of discarding the highest angular frequency bins in the analysis. reducing fas to STOO.," Moreover we consider the case of discarding the highest angular frequency bins in the analysis, reducing $\ell_{\rm max}$ to 8700." + Finally. we increase the survey size by LO%.," Finally, we increase the survey size by $10\,\%$." + Analogously to the foregoing section. we employ. the Ixullback-Leibler divergence to compare the Box-Cox-Fisher result with the posterior from the full likelihood analysis.," Analogously to the foregoing section, we employ the Kullback-Leibler divergence to compare the Box-Cox-Fisher result with the posterior from the full likelihood analysis." +" As is evident from Table2. Dy, for the marginal distributions and the posterior in the Oy,ax plane remains constant to good approximation in all cases."," As is evident from Table, $D_{\rm KL}$ for the marginal distributions and the posterior in the $\Omega_{\rm m}-\sigma_8$ plane remains constant to good approximation in all cases." + One of the most. likely modifications in. mock. weak lensing analyses is a change in the statistic usec as the observable., One of the most likely modifications in mock weak lensing analyses is a change in the statistic used as the observable. + We switch to the frequently crploved correlation function € which is related. to the power spectrum. via where Jy is the Bessel function of the first. kind. of order 0., We switch to the frequently employed correlation function $\xi_+$ which is related to the power spectrum via where $J_0$ is the Bessel function of the first kind of order 0. + The covariance of the correlation Function can directlv be determined [rom equation (18). as detailed in(2008).," The covariance of the correlation function can directly be determined from equation ), as detailed in." + We intend to roughly use the same angular scales as in the power spectrum analysis and thus consider the range larcmin«065deg. divided into 50 logarithmically spaced bins.," We intend to roughly use the same angular scales as in the power spectrum analysis and thus consider the range $1\,{\rm arcmin}<\theta<5\,{\rm deg}$, divided into 50 logarithmically spaced bins." + Note that this range of angular scales does not ensure a similar information content because the angular separation bins are strongly. correlated., Note that this range of angular scales does not ensure a similar information content because the angular separation bins are strongly correlated. + Aloreover we now use Population Monte-Carlo sampling with to create a random sample of size LO” from the full posterior in order to determine optimal Box-Cox parameters. via equation (6)., Moreover we now use Population Monte-Carlo sampling with to create a random sample of size $10^5$ from the full posterior in order to determine optimal Box-Cox parameters via equation ). + The results are. presented. in. Fig.4. finding again excellent agreement between Dox-Cox-Fisher results and full posterior.," The results are presented in $\,$, finding again excellent agreement between Box-Cox-Fisher results and full posterior." + H£ the optimal Box-C'ox parameters that were obtained for the power spectrum analysis in Section are used instead. one arrives at constraints of similar quality.," If the optimal Box-Cox parameters that were obtained for the power spectrum analysis in Section are used instead, one arrives at constraints of similar quality." + Pherefore the Box-Cox-Fisher formalism should also be robust with respect to a change in the weak lensing statistic emploved in the Fisher matrix., Therefore the Box-Cox-Fisher formalism should also be robust with respect to a change in the weak lensing statistic employed in the Fisher matrix. + As a final test for the practical applicability of the novel forecasting method. we have to verily that it is accurate for à higher-cimoensional posterior.," As a final test for the practical applicability of the novel forecasting method, we have to verify that it is accurate for a higher-dimensional posterior." +" Hence we drop the assumption of a spatially Dat. Universe and vary the density. parameter of dark energy. Q3. as well as ης in addition to £3, and ax."," Hence we drop the assumption of a spatially flat Universe and vary the density parameter of dark energy, $\Omega_\Lambda$, as well as $n_{\rm s}$ in addition to $\Omega_{\rm m}$ and $\sigma_8$." + We perform the analysis as in the foregoing case. using again CosmoPMC to create about LO? random samples of 1¢ four-dimensional posterior to determine in total 8 Box-ο.'ox parameters.," We perform the analysis as in the foregoing case, using again CosmoPMC to create about $10^6$ random samples of the four-dimensional posterior to determine in total 8 Box-Cox parameters." + The confidence contours of the marginalised) posterior istributions for all possible pairs of cosmological parameters are shown in 5.," The confidence contours of the marginalised posterior distributions for all possible pairs of cosmological parameters are shown in $\,$." + The DBox-Cox-Fisher formalism. vields contours that are able to adopt arbitrary gaiipes anc represent the four-dimensional posterior veuratelv. including the non-linear degeneracies in the r3aax and OXna planes.," The Box-Cox-Fisher formalism yields contours that are able to adopt arbitrary shapes and represent the four-dimensional posterior accurately, including the non-linear degeneracies in the $\Omega_{\rm m}-\sigma_8$ and $\Omega_\Lambda-n_{\rm s}$ planes." + The only significant iscrepancies between the Fisher-basecl contours and. the confidence levels. derived. from. the Monte-Carlo: sample appears in regions where the posterior declines. slowly. e.g. for large Ow or small ox.," The only significant discrepancies between the Fisher-based contours and the confidence levels derived from the Monte-Carlo sample appears in regions where the posterior declines slowly, e.g. for large $\Omega_{\rm m}$ or small $\sigma_8$." + The fraved contour lines indicate that these regions are still sparsely sampled by CosmoPMC., The frayed contour lines indicate that these regions are still sparsely sampled by CosmoPMC. + “Phis could. imply that the Monte-Carlo sample is not suited to allow for a determination of optimal Box-Cox parameters which lead. to an accurate posterior shape in these regions., This could imply that the Monte-Carlo sample is not suited to allow for a determination of optimal Box-Cox parameters which lead to an accurate posterior shape in these regions. + Alternatively. the Box-Cox-Fisher formalism might well be robust enough to produce a precise representation of the posterior also where it is shallow. so," Alternatively, the Box-Cox-Fisher formalism might well be robust enough to produce a precise representation of the posterior also where it is shallow, so" +"young, relatively loose GC, that is in an environment significantly different from a typically dense GC.","young, relatively loose GC, that is in an environment significantly different from a typically dense GC." +" We anticipate here that our analysis reveals that BSS in Arp 2 do share the same distribution of RGB and horizontal branch (HB) stars, and are more concentrated than main sequence (MS) This paper is organized as follows."," We anticipate here that our analysis reveals that BSS in Arp 2 do share the same distribution of RGB and horizontal branch (HB) stars, and are more concentrated than main sequence (MS) This paper is organized as follows." + In Sect., In Sect. +" 2 we illustrate how we collected and analyzed our data, while in Sect."," 2 we illustrate how we collected and analyzed our data, while in Sect." + 3 we present star counts in Arp 2 to measure its size., 3 we present star counts in Arp 2 to measure its size. + The CMD of Arp 2 is presented and discussed in Sect., The CMD of Arp 2 is presented and discussed in Sect. +" 4, whereas the definition of BSS, and their statistics is discussed in Sect."," 4, whereas the definition of BSS, and their statistics is discussed in Sect." +" 6, which, also, comments on and summarizes our findings."," 6, which, also, comments on and summarizes our findings." +" CCD BVI images were acquired with the EFOSC2 camera mounted on the Nasmyth focus of the ESO NTT telescope on the night of August 8, 2008."," CCD BVI images were acquired with the EFOSC2 camera mounted on the Nasmyth focus of the ESO NTT telescope on the night of August 8, 2008." +" The CCD is a 1030x 1038 array with a scale of 0.24 arcsec, allowing to cover 4.1x4.1 arcmin on the sky."," The CCD is a $\times$ 1038 array with a scale of 0.24 arcsec, allowing to cover $\times$ 4.1 arcmin on the sky." + This allows us to cover a field centered on Arp 2 slightly larger than the previous observations by Buonanno et al. (, This allows us to cover a field centered on Arp 2 slightly larger than the previous observations by Buonanno et al. ( +1994).,1994). +" We used multiple exposures of 30 and 1200 secs for the B filter, and 30 and 900 both for V and I filters."," We used multiple exposures of 30 and 1200 secs for the B filter, and 30 and 900 both for V and I filters." +" As an illustration, an I filter, 900 sec, raw image is shown in Fig."," As an illustration, an I filter, 900 sec, raw image is shown in Fig." + 1., 1. +" The night was photometric, and we calibrated our photometry against the Landolt (1992) standard field Mark A and PG 2213, observed several times during the night."," The night was photometric, and we calibrated our photometry against the Landolt (1992) standard field Mark A and PG 2213, observed several times during the night." + Arp 2 was observed during an observational run focused ona different science when the principal target was not visible., Arp 2 was observed during an observational run focused on a different science when the principal target was not visible. + Data have been reduced in the standard way., Data have been reduced in the standard way. +" Image preparation (trimming, bias and flatfield) was done using the IRAF package, while photometry was extracted by using DAOPHOT and ALLSTAR (Stetson 1987)."," Image preparation (trimming, bias and flatfield) was done using the IRAF package, while photometry was extracted by using DAOPHOT and ALLSTAR (Stetson 1987)." +" We obtained a final catalog with 4580 entries having 2000.0 Equatorial coordinates, and B, V and I magnitudes together with associated uncertainties."," We obtained a final catalog with 4580 entries having 2000.0 Equatorial coordinates, and B, V and I magnitudes together with associated uncertainties." + These latter have been calculated following the prescriptions described in Patat Carraro (2001)., These latter have been calculated following the prescriptions described in Patat Carraro (2001). +" Our optical catalogue was cross-correlated with 2MASS, which resulted in a final catalog including BV and JHks magnitudes."," Our optical catalogue was cross-correlated with 2MASS, which resulted in a final catalog including $BVI$ and $JHK_{s}$ magnitudes." +" As a by product, pixel (detector) coordinates were converted to RA and DEC for J2000.0 equinox, thus providing 2MASS-based Finally, completeness corrections were determined by running artificial star experiments on the data."," As a by product, pixel (detector) coordinates were converted to RA and DEC for J2000.0 equinox, thus providing 2MASS-based Finally, completeness corrections were determined by running artificial star experiments on the data." +" The data-set was divided in two regions, inner (inside 1 arcmin) and outer (beyond 1 arcmin), and completeness was computed for these two different regions, which, due to the nature of the object, are expected to be differently affected by star crowding (Carraro et al."," The data-set was divided in two regions, inner (inside 1 arcmin) and outer (beyond 1 arcmin), and completeness was computed for these two different regions, which, due to the nature of the object, are expected to be differently affected by star crowding (Carraro et al." + 2007)., 2007). +" Basically, we created several artificial images by adding artificial stars to the original frames."," Basically, we created several artificial images by adding artificial stars to the original frames." +" These stars were added at random positions, and had the same color and luminosity distribution of the true sample."," These stars were added at random positions, and had the same color and luminosity distribution of the true sample." +" To avoid generating overcrowding, in each experiment we added up to of the original number of stars."," To avoid generating overcrowding, in each experiment we added up to of the original number of stars." +" Depending on the frame (short or deep exposures), between 1000-5000 stars were added."," Depending on the frame (short or deep exposures), between 1000-5000 stars were added." +" In this way we have estimated that the completeness level of our photometry in the outer region is down to V = 23.00, and better than down to V = 23.50."," In this way we have estimated that the completeness level of our photometry in the outer region is down to $V$ = 23.00, and better than down to $V$ = 23.50." +" As for the inner region, we found that the completeness is down to V = 22.40, and better than down to V = 22.80."," As for the inner region, we found that the completeness is down to $V$ = 22.40, and better than down to $V$ = 22.80." + We used our photometry to study the cluster stars radial distribution., We used our photometry to study the cluster stars radial distribution. +" Accordingto Harris (1996), Arp 2 has a concentration c=0.90, an half-mass radius = 1.91 arcmin, and a core and tidal radius of 1.59 and 12.65 arcmin, respectively."," Accordingto Harris (1996), Arp 2 has a concentration $c$ =0.90, an half-mass radius = 1.91 arcmin, and a core and tidal radius of 1.59 and 12.65 arcmin, respectively." + Therefore we expect our photometry to cover just the inner part of the cluster., Therefore we expect our photometry to cover just the inner part of the cluster. + The radial density profile we constructed is shown in Fig., The radial density profile we constructed is shown in Fig. + 2., 2. + It has been derived following the method described in Seleznev (1994)., It has been derived following the method described in Seleznev (1994). +" This method employs numerical differentiation of the best mean-square polynomial fit for N(r), the number of stars in circles of radius r in the plane of the sky."," This method employs numerical differentiation of the best mean-square polynomial fit for N(r), the number of stars in circles of radius r in the plane of the sky." +" The center of the cluster was taken at the detector coordinates (512,512) which corresponds to a=1928"" 44°, ὃ=—30?21'14"" (J2000.0)."," The center of the cluster was taken at the detector coordinates (512,512) which corresponds to $\alpha=19^h~28^m~44^s$ , $\delta=-30^{o}21^{\prime}~14^{\prime\prime}$ (J2000.0)." + Vertical bars, Vertical bars +to be real),to be real.) + Experiments with adopting different IAVS dark currents aud with methods for dealing with detector memory effects made little difference to the spectra., Experiments with adopting different LWS dark currents and with methods for dealing with detector memory effects made little difference to the spectra. + The clino-pyroxene optical coustauts of Roike ot al. (1993)), The clino-pyroxene optical constants of Koike et al. \cite{koike}) ) + show a broad feature around 60 gan (sce also Cohen ct al. 1999)).," show a broad feature around 60 $\mu$ m (see also Cohen et al. \cite{cohen}) )," + but this peaks at longer wavelengths than the crystalline water ice band. aud so is not a likely carrier for the CRE 2199 aud WX Psc features.," but this peaks at longer wavelengths than the crystalline water ice band, and so is not a likely carrier for the CRL 2199 and WX Psc features." + Similarly. the 62-441 features in OIII27.8. OII26.5 and GL 5379 do uot need an additional loue-waveleneth couniponueut. so the Ixoike pyroxcue is uot necessary to fit these spectra.," Similarly, the $\mu$ m features in OH127.8, OH26.5 and GL 5379 do not need an additional long-wavelength component, so the Koike pyroxene is not necessary to fit these spectra." + The Jagecr et al. (1998)), The Jägger et al. \cite{jaeger}) ) + laboratory data do not reproduce the broad 6O-yan band seen in the I&oike data. so the feature may uot be real.," laboratory data do not reproduce the broad $\mu$ m band seen in the Koike data, so the feature may not be real." + Iu general. we find that the observed features iu Fie.," In general, we find that the observed features in Fig." + 5 are narrower than our fits. sugecsting that we have overestimated the coutiuuua level in this wavelcueth," \ref{icefig} + are narrower than our fits, suggesting that we have overestimated the continuum level in this wavelength" +such cillerential expansion losses would depress the diffuse radio conünuum flux density in (he west. as observed.,"Such differential expansion losses would depress the diffuse radio continuum flux density in the west, as observed." + Free-lree absorption. svichrotron aging and expansion losses will all manifest themselves in the spectral behavior of the radio emission from (he two nuclei.," Free-free absorption, synchrotron aging and expansion losses will all manifest themselves in the spectral behavior of the radio emission from the two nuclei." + Detailed high-sensitivity spectral mapping αἱ 0.1 aresecond resolution will be needed to further constrain these phenomena in the Arp 220 nuclei., Detailed high-sensitivity spectral mapping at 0.1 arcsecond resolution will be needed to further constrain these phenomena in the Arp 220 nuclei. + This may soon be possible with the expanded bandwidths and sensitivitv of the e-MERLLIN instrument., This may soon be possible with the expanded bandwidths and sensitivity of the e-MERLIN instrument. + On a cautionary note. Iree-Iree absorption will preferentially depress the fIux densities of the RSN in the western nucleus.," On a cautionary note, free-free absorption will preferentially depress the flux densities of the RSN in the western nucleus." + Η these reduced flux densities fall below our detection Limit for some new sources up lo a vear old. the inferred supernova rate in the western nucleus vill be depressed relative to that in the east.," If these reduced flux densities fall below our detection limit for some new sources up to a year old, the inferred supernova rate in the western nucleus will be depressed relative to that in the east." + The only wax to discover if our census of new supernovae is complete. and therefore if our inferred supernova rate estimates are unbiased between the (wo nuclei. is to see if increased imaging sensitivitv. vields increased rates of appearance of new sources.," The only way to discover if our census of new supernovae is complete, and therefore if our inferred supernova rate estimates are unbiased between the two nuclei, is to see if increased imaging sensitivity yields increased rates of appearance of new sources." + This will be feasible in coming vears as bandwidths for VLBI systems continue {ο improve., This will be feasible in coming years as bandwidths for VLBI systems continue to improve. + To summarize our conclusions [rom this section. our images of RSNe trace an energetic starburst in progress in both Arp 220 nuclei.," To summarize our conclusions from this section, our images of RSNe trace an energetic starburst in progress in both Arp 220 nuclei." + Regarding the Iuminositv ratio between the nuclei. comparison of our data wilh mid-IR. imaging data leads to a consistent picture of a 3:1 ratio of westfeast luminosities.," Regarding the luminosity ratio between the nuclei, comparison of our data with mid-IR imaging data leads to a consistent picture of a 3:1 ratio of west/east luminosities." + A starburst origin for the bulk of the Arp 220 bolometric luminosity is supported by this comparison., A starburst origin for the bulk of the Arp 220 bolometric luminosity is supported by this comparison. + The failure of the diffuse radio continuum enussion to exhibit a similar 3:1 ratio can be understood in terms of dillerential [ree-Iree absorption. and more speculatively. in terms of differential svuchrotvon plasma expansion losses.," The failure of the diffuse radio continuum emission to exhibit a similar 3:1 ratio can be understood in terms of differential free-free absorption, and more speculatively, in terms of differential synchrotron plasma expansion losses." + The starburst galaxy AIS? lies al a distance of only 3.2 Alpe. and as such is amenable to detailed study at much lower Iuminositv levels.," The starburst galaxy M82 lies at a distance of only 3.2 Mpc, and as such is amenable to detailed study at much lower luminosity levels." + It is the only other galaxy in which large nunmbers of compact sources have been detected., It is the only other galaxy in which large numbers of compact sources have been detected. + Despite the obvious difference in the scale of the phenomenon. (here are striking similarities. ancl we deem a comparison of the two galaxies to. be useful.," Despite the obvious difference in the scale of the phenomenon, there are striking similarities, and we deem a comparison of the two galaxies to be useful." + The [ar infrared. luminosity of ΜΙΣΟ is 2.8xΟΦΗ. (Telesco 1983). which is roughly 50 times lower than that of Arp 220.," The far infrared luminosity of M82 is $\times +10^{10}L_{\odot}$ (Telesco 1988), which is roughly 50 times lower than that of Arp 220." + The star formation rate is therefore expected to be lower bv a comparable factor. and with a consequently lower supernova rate. one expects (o see a population of supernova remnants (hat is much older and fainter (han that in Arp 220.," The star formation rate is therefore expected to be lower by a comparable factor, and with a consequently lower supernova rate, one expects to see a population of supernova remnants that is much older and fainter than that in Arp 220." + Qualitatively. this is exactly what is found.," Qualitatively, this is exactly what is found." +At the outset we need to determine in which theoretical regime of maser polarization propagation our observational data reside.,At the outset we need to determine in which theoretical regime of maser polarization propagation our observational data reside. + Specifically. (here are several kev parameters (hat determine (his theoretical interpretive framework.," Specifically, there are several key parameters that determine this theoretical interpretive framework." + These include the relative magnitude of the stimulated emission rate. A. the eumulative collisional and radiative decay. rate. D. and the Zeeman rate. gQ (Goldreich.Ixeelev.&Kwan1973:Watson2002).," These include the relative magnitude of the stimulated emission rate, $R$, the cumulative collisional and radiative decay rate, $\Gamma$, and the Zeeman rate, $g\Omega$ \citep{goldreich73,watson02}." +. To estimate 2. we adopt equation 1 of Plambeck.Wright.&Rao(2003). to derive the stimulated emission rate of the v—1.J=10 SiO transition as: where Z5; is (he maser brightness temperature and dQ is the estimated maser beaming angle.," To estimate $R$, we adopt equation 1 of \citet{plambeck03} to derive the stimulated emission rate of the $v=1,\ J=1-0$ SiO transition as: where $T_B$ is the maser brightness temperature and $d\Omega$ is the estimated maser beaming angle." + The relative magnitude of 2 and D defines the degree of maser saturation. with saturation increasing lor increasing n," The relative magnitude of $R$ and $\Gamma$ defines the degree of maser saturation, with saturation increasing for increasing $\frac{R}{\Gamma}$." + The vibrational radiative transitions e—(e1) for low-J rotation levels have radiative decay rates D~5e | (Iwan 1992)..," The vibrational radiative transitions $v \to (v-1)$ for low-J rotation levels have radiative decay rates $\Gamma \sim 5 v$ $^{-1}$ \citep{kwan74,elitzur92}. ." + These radiative decay rates dominate over SiO-II5 or S1O-II collisional de-excitation., These radiative decay rates dominate over $_2$ or SiO-H collisional de-excitation. +" From the collisional rate equations in Elitzur(1980)... we calculate POi. and q(0)=1 lor 0 5. and Stokes Q changes sign.- the observed EVPAT on the plane of the skv switches [rom parallel to the projected magnetic field (0<0,.) to perpendicular to the projected magnetic field (0>05) (Goldreich.Elitzur 1992)."," At a break angle, $\theta_F +\approx 55^\circ$, defined as the point where $\sin^2\theta_F=\frac{2}{3}$ , and Stokes $Q$ changes sign, the observed EVPA on the plane of the sky switches from parallel to the projected magnetic field $\theta < \theta_F)$ to perpendicular to the projected magnetic field $\theta > \theta_F)$ \citep{goldreich73,elitzur92}." +. We note that this changeof EVPA over 90° has been detected observationally by Vlemmings&Diamond(2006) [or a water maser component in the source ΑΛΦΑ. The degree of saturation n required to achieve the the limiting magnitude of fractional linear polarization differs however betweenthe (svo theoretical models ofmaser polarization propagation (Nedoluha&Watson1990:Elitzur 1996)...," We note that this changeof EVPA over $^\circ$ has been detected observationally by \citet{vlemmings06a} + for a water maser component in the source W43A. The degree of saturation $\frac{R}{\Gamma}$ required to achieve the the limiting magnitude of fractional linear polarization differs however betweenthe two theoretical models ofmaser polarization propagation \citep{nedoluha90,elitzur96}. ." + A saturation of nizz30 is required, A saturation of $\frac{R}{\Gamma} \approx 30$ is required +absorptions and fringes (in thinned CCDs) were removed by using templates constructed from spectra of bright carly tvpe stars (6. Carinac. ¢ Ophiuci or & Puppis) observed immecdiatelyv after or before η Car.,"absorptions and fringes (in thinned CCDs) were removed by using templates constructed from spectra of bright early type stars $\theta$ Carinae, $\zeta$ Ophiuci or $\zeta$ Puppis) observed immediately after or before $\eta$ Car." + For the 2003 event. we also used spectra taken with the spectrographs REOSC (It = 25 km 1j and EDASIM (R — T km +) attached to the 2.15-m CASLEO telescope (Argentina). and spectra taken at CTIO with the 4.0-m Echelle Spetrograph (15 — 8 km s land at Magellan with MIIXIS Spectrograph (R= 12 kms Ly.," For the 2003 event, we also used spectra taken with the spectrographs REOSC (R = 25 km $^{-1}$ ) and EBASIM (R = 7 km $^{-1}$ ) attached to the 2.15-m CASLEO telescope (Argentina), and spectra taken at CTIO with the 4.0-m Echelle Spetrograph (R = 8 km $^{-1}$ ) and at Magellan with MIKE Spectrograph (R = 12 km $^{-1}$ )." + For the 1997/8 event. we used spectra collected at La Silla/EO with CAL-CES (R= I2 km +).," For the 1997/8 event, we used spectra collected at La Silla/ESO with CAT-CES (R = 12 km $^{-1}$ )." + For the 1992 event. we also used spectra collected with the ΕΙΛΙΕΤΗΟΡ spectrograph attached to the 50-em telescope (ESO/Chile) with a fiber diameter ~5 aresec and spectral resolution — 12 km |.," For the 1992 event, we also used spectra collected with the FLASH/HEROS spectrograph attached to the 50-cm telescope (ESO/Chile) with a fiber diameter $\sim5$ arcsec and spectral resolution R = 12 km $^{-1}$." + On several occasions we used FEROS spectrographRo attached to 1 1.52-m telescope at La Silla to cover the entire optical =vindow' at resolution' l5 — 12. kms 1., On several occasions we used FEROS spectrograph attached to the 1.52-m telescope at La Silla to cover the entire optical window at resolution R = 12 km $^{-1}$. + 3clore measuring the spectral features. we degraded the Esvectra to a dispersion of 0.39. pixel+.," Before measuring the spectral features, we degraded the spectra to a dispersion of 0.39 $^{-1}$." + ‘Vhis step was =[udot really necessary but it helped facilitate the adoption of 10 same limits between the narrow and broad components. nd positioning of the stellar continuum. when measuring 10 spectra.," This step was not really necessary but it helped facilitate the adoption of the same limits between the narrow and broad components, and positioning of the stellar continuum, when measuring the spectra." + Since we adopted the observations collected a LNA Observatory as a reference. we added data from other sources only in the case where they merged smoothly to the ine intensity curve.," Since we adopted the observations collected at LNA Observatory as a reference, we added data from other sources only in the case where they merged smoothly to the line intensity curve." + This criterion was fulfilled by almos | ground-based observations. confirming our expectation hat slit widths in the range lL3 arcsec width woulc give the same results independent of the position angle ~AL) of the slit.," This criterion was fulfilled by almost all ground-based observations, confirming our expectation that slit widths in the range $1-3$ arcsec width would give the same results independent of the position angle (P.A.) of the slit." + This happens because the main emitting region is smaller than 1 aresee and has a huge contras o the surrounding Homunculus nebula and. also because 1ο seeing [whm is Larger than 1 arcsec. smearing ou Ίο emitting region.," This happens because the main emitting region is smaller than $1$ arcsec and has a huge contrast to the surrounding Homunculus nebula and also because the seeing fwhm is larger than $1$ arcsec, smearing out the emitting region." + In a forthcoming paper (on the long erm behavior of the spectral lines) we will present the complete list of observations from the entire campaign anc a table with individual measurements., In a forthcoming paper (on the long term behavior of the spectral lines) we will present the complete list of observations from the entire campaign and a table with individual measurements. + Fig., Fig. + laa displays spectra representative of the high ancl low excitation states. showing the disappearance of the high excitation lines ane enhancement of P Cyeni absorption profiles during the minimum.," \ref{highlow}a a displays spectra representative of the high and low excitation states, showing the disappearance of the high excitation lines and enhancement of P Cygni absorption profiles during the minimum." + Fie., Fig. + Ibb shows spectra in the blue for the high excitation state of 1995 and for the low excitation state of 1997 and 1970 (see also Daminelietal.(1998). for the Lull spectral range 3850.11000. A)., \ref{highlow}b b shows spectra in the blue for the high excitation state of 1995 and for the low excitation state of 1997 and 1970 (see also \citet{b29} for the full spectral range 3850–11000 ). + Spectra from the Space Telescope Imaging Spectrometer (STIS) on the. ave available for the 2003.49. and. 1997.95. events. though or consisteney we do not include them here since the slit width is much narrower than used in the erouncl-owed: observations. seumpling only a part of the inner circumstellar nebulosity.," Spectra from the Space Telescope Imaging Spectrometer (STIS) on the are available for the 2003.49 and 1997.95 events, though for consistency we do not include them here since the slit width is much narrower than used in the ground-based observations, sampling only a part of the inner circumstellar nebulosity." + Phese data are of course important or disentangling stellar from circumstellar variations. and ave been more Lully described in Nielsenetal.(2007a).. delsenetal. (2007b).. Gulletal. (2006).. ancl Davidsonal. (2005).," These data are of course important for disentangling stellar from circumstellar variations, and have been more fully described in \citet{nielsenetal07}, \citet{krister07}, \citet{gull06}, and \citet{kd05}." +. Since the wind of the primary star is resolved by he STIS slit and the slit’s position angle varied in cilferent visits. care must be taken when comparing line profiles rom cillerent epochs.," Since the wind of the primary star is resolved by the STIS slit and the slit's position angle varied in different visits, care must be taken when comparing line profiles from different epochs." + This applies to the lower excitation ransitions. formed far from the central source(s) that mav o subject to spatial asvmametries.," This applies to the lower excitation transitions, formed far from the central source(s) that may be subject to spatial asymmetries." + All the data processing ancl measurements were done in the standard. way using LRA packages., All the data processing and measurements were done in the standard way using IRAF packages. + Narrow lines were modeled by Gaussian fitting ancl deblenced from the broad. components., Narrow lines were modeled by Gaussian fitting and deblended from the broad components. + Since they are seated on top of broad line. profiles. which are themselves variable. we referred their equivalent widths (EW) to the local stellar continuum. in order that these measurements correspond to line flux normalized to the local stellar continuum. instead of classical equivalent width.," Since they are seated on top of broad line profiles, which are themselves variable, we referred their equivalent widths (EW) to the local stellar continuum, in order that these measurements correspond to line flux normalized to the local stellar continuum, instead of classical equivalent width." + As in the case of EW. this. kind. of measurement is translated into line Dux when multiplied by the stellar continuum flux.," As in the case of EW, this kind of measurement is translated into line flux when multiplied by the stellar continuum flux." + Because of this. we use the simple designation of equivalent width in place of normalized line Ες.," Because of this, we use the simple designation of equivalent width in place of normalized line flux." + Broad line emission. profiles were separated. from the narrow components. when they existed. and their equivalent widths and baricenters (for radial velocities) were measured by direct integration along the line profile.," Broad line emission profiles were separated from the narrow components, when they existed, and their equivalent widths and baricenters (for radial velocities) were measured by direct integration along the line profile." + Raclial velocities are in the heliocentric reference svsten., Radial velocities are in the heliocentric reference system. + Lt is dillicult to attribute errors to single measurements. as the main source is systematic. not statistical.," It is difficult to attribute errors to single measurements, as the main source is systematic, not statistical." + Phe spectra were well exposed. in order that. photon noise is very. low. except in the violet. region.," The spectra were well exposed, in order that photon noise is very low, except in the violet region." + The major source of error is linked to the stellar continuum. because of line blendings and changes in relative intensity of linc/continuum. as the," The major source of error is linked to the stellar continuum, because of line blendings and changes in relative intensity of line/continuum, as the" +listed in Table 2..,listed in Table \ref{tab:colors}. + They are compared with previous large-scale cirrus Byoo/Byeo color measurements (2) and CIB colors from the ?) empirical model of galaxy evolution., They are compared with previous large-scale cirrus $B_{100}/B_{160}$ color measurements \citep{1996AA...312..256B} and CIB colors from the \citet{2003MNRAS.338..555L} empirical model of galaxy evolution. + On seales «95 aremin. our results are consistent with the CIB prediction of ?)..," On scales $<$ 95 arcmin, our results are consistent with the CIB prediction of \citet{2003MNRAS.338..555L}." + However. there is a discrepancy on scales > 95 aremin between our results and those of ?).. which we attribute to real changes in cirrus properties from one field to another.," However, there is a discrepancy on scales $>$ 95 arcmin between our results and those of \citet{1996AA...312..256B}, which we attribute to real changes in cirrus properties from one field to another." + ?) found that Byoo/δι=0.25£0.01 across the whole Taurus complex. whereas locally. they found that the same ratio varies from 0.27 to 0.5.," \citet{2009ApJ...701.1450F} found that $B_{100}/B_{160}=0.25\pm0.01$ across the whole Taurus complex, whereas locally, they found that the same ratio varies from 0.27 to 0.5." + 2?) computed colors in several small regions of the sky surrounding nearby galaxies (70.1 deg). and they also found varying colors from one field to another: from Byoo/Boo = 0.36 to Byoo/ Bygo=0.60.," \citet{2009ApJ...695..469B} computed colors in several small regions of the sky surrounding nearby galaxies $\sim$ 0.1 deg), and they also found varying colors from one field to another: from $B_{100}/B_{160}$ = 0.36 to $B_{100}/B_{160}$ =0.60." + In both cases. they explained these differences by a variation of the interstellar radiation. field and/or the abundance of very small and big grains.," In both cases, they explained these differences by a variation of the interstellar radiation field and/or the abundance of very small and big grains." + To compare the cirrus power spectrum obtained using IRIS data at 100 pm with our 160 pm power spectrum. we rescale the 100 gam power spectrum by BVOdesTOI?228des|o0.cirris and then by (Byoo/Byoo)= (1/0.35)-. the large-scale color that corresponds to the cirrus color in our field.," To compare the cirrus power spectrum obtained using IRIS data at 100 $\mu$ m with our 160 $\mu$ m power spectrum, we rescale the 100 $\mu$ m power spectrum by $B_{100, cirrus}^{10 deg^2}/B_{100, cirrus}^{225 deg^2}$ and then by $(B_{160}/B_{100})^2 = (1/0.35)^2$ , the large-scale color that corresponds to the cirrus color in our field." + We show this comparison in Fig., We show this comparison in Fig. +" 12. and observe that they are in good agreement for k «0.02 aremin| (i.e. in the “cirrus regime"")."," \ref{fig:pk_mips_iris_sc} and observe that they are in good agreement for $k<$ 0.02 $^{-1}$ (i.e. in the ""cirrus regime"")." + Unfortunately. the statistics of the large scales at 160 jim are quite poor and do not allow us to quantify the quality of the argument.," Unfortunately, the statistics of the large scales at 160 $\mu$ m are quite poor and do not allow us to quantify the quality of the argument." + The dust that is heated by the interstellar radiation field and emits in the IR is mixed with neutral hydrogen., The dust that is heated by the interstellar radiation field and emits in the IR is mixed with neutral hydrogen. + Thus. the IR emission of the cirrus is strongly correlated with the 21 em line.," Thus, the IR emission of the cirrus is strongly correlated with the 21 cm line." + ?) showed that this correlation is tight at high Galactic latitudes at 60 and 100 ym. This correlation has often been used to study dust properties. for instance by ?)» who derived the dust spectrum associated with In this section. we use GBT data at 21 em to derive the FIR emission of the cirrus. which is then removed from our data at 100 jim and 160 jm in Sect. ??..," \citet{1988ApJ...330..964B} showed that this correlation is tight at high Galactic latitudes at 60 and 100 $\mu$ m. This correlation has often been used to study dust properties, for instance by \citet{1996AA...312..256B} who derived the dust spectrum associated with In this section, we use GBT data at 21 cm to derive the FIR emission of the cirrus, which is then removed from our data at 100 $\mu$ m and 160 $\mu$ m in Sect. \ref{par:removal}." + In the ELAIS NI field. there are three distinguishable velocity components : the local component. an intermediate velocity cloud (IVC). and a high velocity cloud (HVC).," In the ELAIS N1 field, there are three distinguishable velocity components : the local component, an intermediate velocity cloud (IVC), and a high velocity cloud (HVC)." + We first compute their integrated emission by adding all velocity channels with -14 km/s . begins to be seen in directions where Njjj>2x10 em and T,>12K (e.g.. 2). ?).. 2). it is unlikely that there are significant amounts of H» in our field."," The brightness temperature ofthe line is always $\leq 8.9$ K. Since molecular hydrogen, $H_2$ , begins to be seen in directions where $N_{HI} > 2 \times 10^{20}$ $^{-2}$ and $T_b > 12$ K (e.g., \citet{2006ApJ...636..891G}, \citet{2002A&A...389..393L}, \cite{2005AJ....129.1968L}) ), it is unlikely that there are significant amounts of $H_2$ in our field." +" Therefore. we can apply the decomposition following 2j where /, is the infrared map. Ni(X.v) is the column density of the i-the component. a is the emissivity of component ; at wavelength οἱ. and ον.y) ts à residual term (offset + CIB)."," Therefore, we can apply the decomposition following \cite{2005ApJ...631L..57M} + where $I_{\lambda}$ is the infrared map, $N_{HI}^i(x,y)$ is the column density of the $i$ -the component, $\alpha_\lambda^i$ is the emissivity of component $i$ at wavelength $\lambda$, and $C_{\lambda}(x,y)$ is a residual term (offset + CIB)." +" The correlation coefficients αι are estimated using a y minimization"".", The correlation coefficients $\alpha_\lambda^i$ are estimated using a $\chi^2$ . +" The error bars given by the [DL function are valid only if the noise of the 7; maps is Gaussian and if the noise affecting Ny, is negligible.", The error bars given by the IDL function are valid only if the noise of the $I_{\lambda}$ maps is Gaussian and if the noise affecting $_{HI}$ is negligible. + This may not be the case as the maps contain the IRIS or MIPS instrumental noise and CIB anisotropies., This may not be the case as the maps contain the IRIS or MIPS instrumental noise and CIB anisotropies. + ?) carried out Monte Carlo simulations to estimate the errors in αι for IRIS 100 and 60 um and determined the coefficients by which they multiplied the error bars found assuming a Gaussian noise., \citet{2011A&A...536A..24P} carried out Monte Carlo simulations to estimate the errors in $\alpha_\lambda^i$ for IRIS 100 and 60 $\mu$ m and determined the coefficients by which they multiplied the error bars found assuming a Gaussian noise. + We multiply our errors by these coefficients at 60 and 100 jim. For MIPS at 160 um.we take the mean of the 100 and 350 jm coefficients determined by ?).. as thesecoefficients vary only slightly with wavelength.," We multiply our errors by these coefficients at 60 and 100 $\mu$ m. For MIPS at 160 $\mu$ m,we take the mean of the 100 and 350 $\mu$ m coefficients determined by \citet{2011A&A...536A..24P}, , as thesecoefficients vary only slightly with wavelength." + They are on theorder of The emissivities αἱ are computedat 60. 100. and 160 um in the ELAIS NI/MIPS field (1.9. ELAIS NI field restricted to," They are on theorder of The emissivities $\alpha^i_{\lambda}$ are computedat 60, 100, and 160 $\mu$ m in the ELAIS N1/MIPS field (i.e. ELAIS N1 field restricted to" +in saturating the CCD which then requires de-focusing the telescope to distribute the image of the star over more pixels.,in saturating the CCD which then requires de-focusing the telescope to distribute the image of the star over more pixels. +" De-focusing has certain advantages, such as reducing the impact of pixel-to-pixel and intra-pixel sensitivity variations, but it also significantly increases the sky and CCD readout noise (Southworthetal.2009)."," De-focusing has certain advantages, such as reducing the impact of pixel-to-pixel and intra-pixel sensitivity variations, but it also significantly increases the sky and CCD readout noise \citep{southworth2009}." +". In addition, de-focusing is not routinely possible on some telescopes (e.g the VLT) aand it can not be done with crowded fields."," In addition, de-focusing is not routinely possible on some telescopes (e.g the VLT) and it can not be done with crowded fields." +" More importantly for fast photometry, time averaging can also only be used in circumstances where the intrinsic variability of the target has a much longer time scale than the scintillation."," More importantly for fast photometry, time averaging can also only be used in circumstances where the intrinsic variability of the target has a much longer time scale than the scintillation." +" As scintillation is caused by the spatial intensity fluctuations crossing the pupil boundary, the time scale is determined by the wind speed of the turbulent layer."," As scintillation is caused by the spatial intensity fluctuations crossing the pupil boundary, the time scale is determined by the wind speed of the turbulent layer." +" Dravinsetal.(1997a,b,1998) studied the temporal autocorrelation of the scintillation pattern at astronomical sites and found that the power is mainly located between 10 and 100 Hz but actually spans many orders of magnitude."," \citet{Dravins1997,Dravins1997b,Dravins1998} studied the temporal autocorrelation of the scintillation pattern at astronomical sites and found that the power is mainly located between 10 and 100 Hz but actually spans many orders of magnitude." + Differential photometric measurements can be made by normalising with a nearby comparison star (e.g. Henry 2000)., Differential photometric measurements can be made by normalising with a nearby comparison star (e.g. \citeauthor{Henry2000} 2000). + This is not to reduce the scintillation but to correct for transparency variations in the atmosphere., This is not to reduce the scintillation but to correct for transparency variations in the atmosphere. +" However, this actually makes the scintillation noise worse as it is inherently caused by high altitude layers and therefore will have a very small angle of coherence iin the optical (typically ~ 1"")."," However, this actually makes the scintillation noise worse as it is inherently caused by high altitude layers and therefore will have a very small angle of coherence in the optical (typically $\sim1^{\prime\prime}$ )." +" Here we propose a technique, called *conjugate-plane photometry"" to reduce scintillation noise by increasing the aangle of coherence up to ~0.5°, allowing the intensity variations of the target star to be corrected by a comparison star."," Here we propose a technique, called “conjugate-plane photometry” to reduce scintillation noise by increasing the angle of coherence up to $\sim0.5^{\circ}$, allowing the intensity variations of the target star to be corrected by a comparison star." + Our technique offers a relatively simple way of routinely obtaining space-quality photometry from the ground for a fraction of the price and with much larger telescope apertures., Our technique offers a relatively simple way of routinely obtaining space-quality photometry from the ground for a fraction of the price and with much larger telescope apertures. + In section 2 we describe the scintillation reduction method., In section 2 we describe the scintillation reduction method. + Section 3 shows the results of simulations of our correction technique., Section 3 shows the results of simulations of our correction technique. +" The expected performance of the system for a theoretical extrasolar planet transit, and simulation results using a real atmospheric profile are shown in section 4."," The expected performance of the system for a theoretical extrasolar planet transit, and simulation results using a real atmospheric profile are shown in section 4." + Finally in section 5 we discuss the design of a prototype which will be tested at the NOT on La Palma in September 2010., Finally in section 5 we discuss the design of a prototype which will be tested at the NOT on La Palma in September 2010. + High altitude turbulence in the atmosphere distorts the plane wavefronts of light from a star which is effectively at infinity., High altitude turbulence in the atmosphere distorts the plane wavefronts of light from a star which is effectively at infinity. + As the wavefronts propagate these phase aberrations evolve into intensity variations which we view with the naked eye as twinkling., As the wavefronts propagate these phase aberrations evolve into intensity variations which we view with the naked eye as twinkling. +" Wavefronts incident on a telescope pupil have both phase variations, caused by the integrated effect of light passing though the whole vertical depth of the atmosphere, and intensity variations, caused predominantly by the light diffracting through high altitude turbulence and interfering at the ground."," Wavefronts incident on a telescope pupil have both phase variations, caused by the integrated effect of light passing though the whole vertical depth of the atmosphere, and intensity variations, caused predominantly by the light diffracting through high altitude turbulence and interfering at the ground." +" Phase variations are normally considered more significant as they dramatically affect the spatial resolution of images, and this has led to the development of adaptive optics."," Phase variations are normally considered more significant as they dramatically affect the spatial resolution of images, and this has led to the development of adaptive optics." + The intensity variations across the pupil are effectively averaged together when the light is focused and therefore have less effect., The intensity variations across the pupil are effectively averaged together when the light is focused and therefore have less effect. + A larger aperture implies more spatial averaging (which is why stars twinkle less when observed through a telescope than with the naked eye)., A larger aperture implies more spatial averaging (which is why stars twinkle less when observed through a telescope than with the naked eye). +" However, these small intensity fluctuations do become significant when one is concerned with high precision photometry."," However, these small intensity fluctuations do become significant when one is concerned with high precision photometry." + Consider now the effect of these intensity variations in more detail., Consider now the effect of these intensity variations in more detail. +" If we ignore diffraction, then a flat wavefront which is the same size as the telescope pupil at a given high altitude, in the absence of atmospheric turbulence, will propagate in a direction normal to the wavefront and will be collected by the telescope pupil (see figure 1))."," If we ignore diffraction, then a flat wavefront which is the same size as the telescope pupil at a given high altitude, in the absence of atmospheric turbulence, will propagate in a direction normal to the wavefront and will be collected by the telescope pupil (see figure \ref{fig:scintillation1}) )." + Now consider the effect of atmospheric distortion., Now consider the effect of atmospheric distortion. + Phase aberrations cause diffraction in different directions and hence produce scintillation., Phase aberrations cause diffraction in different directions and hence produce scintillation. + Effectively light from one part of the original wavefront is redirected to other parts of the pupil., Effectively light from one part of the original wavefront is redirected to other parts of the pupil. +" This in itself is not a significant problem for photometry, as the integrated intensity across the pupil is the same."," This in itself is not a significant problem for photometry, as the integrated intensity across the pupil is the same." +" The problem occurs either when rays from the wavefront at high altitude propagate away from the telescope pupil, and are lost, or conversely when high altitude areas away from the telescope pupil area propagate into the telescope pupil at the ground."," The problem occurs either when rays from the wavefront at high altitude propagate away from the telescope pupil, and are lost, or conversely when high altitude areas away from the telescope pupil area propagate into the telescope pupil at the ground." +" These effects lead to a decrease and increase in intensity, respectively, and at any one instant both of these effects will be occurring (see figure 1))."," These effects lead to a decrease and increase in intensity, respectively, and at any one instant both of these effects will be occurring (see figure \ref{fig:scintillation1}) )." + The turbulence is blown across the field of view of the telescope producing an overall change in intensity as a function of time., The turbulence is blown across the field of view of the telescope producing an overall change in intensity as a function of time. +" As a thought experiment, to show the basic concept behind our proposal, if we could place an aperture which is smaller than the telescope pupil in the sky at the altitude of high turbulence then this change in intensity could be dramatically reduced."," As a thought experiment, to show the basic concept behind our proposal, if we could place an aperture which is smaller than the telescope pupil in the sky at the altitude of high turbulence then this change in intensity could be dramatically reduced." +" In this case, the rays that would have"," In this case, the rays that would have" +will provide an extra pressure support to the ICM.,will provide an extra pressure support to the ICM. + While rising buovantly towards the cluster outskirts ancl heating the surrounding eas. this clramatically reduces the amount of gas that can be accreted by the central DII.," While rising buoyantly towards the cluster outskirts and heating the surrounding gas, this dramatically reduces the amount of gas that can be accreted by the central BH." + Successively. C]t pressure will ect clissipated and. gas will start to cool again leacing to higher BILAR. values. until another bubble is triggered. and the evcle is repeated.," Successively, CR pressure will get dissipated and gas will start to cool again leading to higher BHAR values, until another bubble is triggered, and the cycle is repeated." + Note that at late times due to this behaviour of bubbles there is some residual star formation activity and the DII growth is not as elliciently terminated as it is the case for thermal bubbles., Note that at late times due to this behaviour of CR bubbles there is some residual star formation activity and the BH growth is not as efficiently terminated as it is the case for thermal bubbles. + The bottom panels of Figure 2. show how the profiles of gas density. temperature and entropy are alfected hy CR bubbles.," The bottom panels of Figure \ref{iso_profiles} show how the profiles of gas density, temperature and entropy are affected by CR bubbles." + Phe racial temperature profile is always decreasing towards the central regions in the runs with CR. bubbles. reflecting the fact that a significant fraction of non-thermal pressure builds up there.," The radial temperature profile is always decreasing towards the central regions in the runs with CR bubbles, reflecting the fact that a significant fraction of non-thermal pressure builds up there." + However. the gas density can either be increased or reduced relative to the thermal case. depending on whether £g is higher than {πι at a given instant.," However, the gas density can either be increased or reduced relative to the thermal case, depending on whether $P_{\rm CR}$ is higher than $P_{\rm +th}$ at a given instant." + Finally. the gas entropy is also somewhat reduced in the innermost regions. mainly being driven by the variations in temperature.," Finally, the gas entropy is also somewhat reduced in the innermost regions, mainly being driven by the variations in temperature." +" Overall. the simulation with a Latter Ch spectrum shows a more significant imprint of Cllts on the ICM. as expected due to the more pronounced. high-energy teil of the CR. momentum distribution. so that a significant level of Pop, can be maintained for a longer time interval."," Overall, the simulation with a flatter CR spectrum shows a more significant imprint of CRs on the ICM, as expected due to the more pronounced high-energy tail of the CR momentum distribution, so that a significant level of $P_{\rm CR}$ can be maintained for a longer time interval." + There are two primary dissipation processes for the CR particle population., There are two primary dissipation processes for the CR particle population. + One is given by individual electron scatterings in the Coulomb fields. of CIS. particles and by small momentum transfers. through exeitations of plasma oscillations. which is especially cllicicnt in the low momenttun tail of the Cl population (7)..," One is given by individual electron scatterings in the Coulomb fields of CR particles and by small momentum transfers through excitations of plasma oscillations, which is especially efficient in the low momentum tail of the CR population \citep{Gould1972}." +. The other important CR energv loss process is clue το inelastic collisions of Clts on nucleons. where hadronic interactions srocluce pions that are. then ultimately dissipated: into radiation as well as thermal heat (e.g.?)..," The other important CR energy loss process is due to inelastic collisions of CRs on nucleons, where hadronic interactions produce pions that are then ultimately dissipated into radiation as well as thermal heat \citep[e.g.][]{Ensslin2007}." + Xdditionallv. he process of MIID wave-mecliated cosmic-ray heating (?) could be relevant for the C1. particle population within the xibbles (seee.g.2).. that we do not consider in this work.," Additionally, the process of MHD wave-mediated cosmic-ray heating \citep{Loewenstein1991} could be relevant for the CR particle population within the bubbles \citep[see e.g.][]{Guo2007}, that we do not consider in this work." + In order to gauge the relative importance of these loss oocesses we have performed two additional test runs where, In order to gauge the relative importance of these loss processes we have performed two additional test runs where +For each reduced and registered image of an ADI sequence. a reference PSF has to be built from (he images of the same sequence.,"For each reduced and registered image of an ADI sequence, a reference PSF has to be built from the images of the same sequence." + The wav that Chis reference PSF is built is of eveal importance since il directly. affects the noise attenuation performance., The way that this reference PSF is built is of great importance since it directly affects the noise attenuation performance. + We have used (wo methods to construct the reference PSF., We have used two methods to construct the reference PSF. + The first method is simply to take the median of all the images of the sequence., The first method is simply to take the median of all the images of the sequence. + II enough field rotation has occurred during the sequence so (hat an eventual point source has moved by at least (wice its full width at half maximum (EWILIM). then (his point source will be largely rejected by the median which will leave only the average PSF.," If enough field rotation has occurred during the sequence so that an eventual point source has moved by at least twice its full width at half maximum (FWHM), then this point source will be largely rejected by the median which will leave only the average PSF." +" The minimum racial separation al which this occurs is noted A2,;,.", The minimum radial separation at which this occurs is noted $R_{\rm{min}}$. + Since the median is taken over a large number of images. the pixel-to-pixel noise (i.e. PSF. flat Ποια. dark and sky. Poisson noises and detector readout noise) of the relerence image is much less than that of anv individual image.," Since the median is taken over a large number of images, the pixel-to-pixel noise (i.e. PSF, flat field, dark and sky Poisson noises and detector readout noise) of the reference image is much less than that of any individual image." + Thus this first method minimizes the noise in regions where the residuals are limited bv pixel-to-pixel noise., Thus this first method minimizes the noise in regions where the residuals are limited by pixel-to-pixel noise. + However. since a sequence (vpically lasts more than an hour. the relerence PSF only has modest quasi-static speckle correlation with the individual images of (he sequence.," However, since a sequence typically lasts more than an hour, the reference PSF only has modest quasi-static speckle correlation with the individual images of the sequence." + The second method is to take the median of only a lew images as close in (ime as possible but for which the displacement due to field rotation between the images is. al a eiven separation. at least 1.5 PSF FWIIM.," The second method is to take the median of only a few images as close in time as possible but for which the displacement due to field rotation between the images is, at a given separation, at least 1.5 PSF FWHM." + This displacement. ensures (hat the flux inside the PSF core of an eventual point source is not significantly reduced by (he subtraction., This displacement ensures that the flux inside the PSF core of an eventual point source is not significantly reduced by the subtraction. +" The lime 7,44, required for such field rotation is Function of the separation angle [rom the target. the target azimuth A and zenith distance z and (he telescope latitude ©."," The time $\tau_{\rm{min}}$ required for such field rotation is function of the separation angle from the target, the target azimuth $A$ and zenith distance $z$ and the telescope latitude $\phi$." + The rotation rate i (degree/minute) of the FOV is obtained [rom the time derivative of the parallactic angle and is given (McLean1997). by Figure 1 is provided as a reference to determine the time interval for observations from the summit of the Mauna hea., The rotation rate $\psi$ (degree/minute) of the FOV is obtained from the time derivative of the parallactic angle and is given \citep{mclean1997} by Figure 1 is provided as a reference to determine the time interval for observations from the summit of the Mauna Kea. + This second technique provides better quasi-static speckle noise allenuation since (he relerence PSF is built using images acquired al short time intervals., This second technique provides better quasi-static speckle noise attenuation since the reference PSF is built using images acquired at short time intervals. + llowever. the pixel-to-pixel noise of the reference image max not be negligible compared to that of an individual image.," However, the pixel-to-pixel noise of the reference image may not be negligible compared to that of an individual image." + The first method is optimized [or regions where (he residuals are limited bv noise while (he second is optimized lor regions where the residuals are still limited by speckle noise., The first method is optimized for regions where the residuals are limited by pixel-to-pixel noise while the second is optimized for regions where the residuals are still limited by speckle noise. + The combination of both techniques into a single reduction algorithin will be, The combination of both techniques into a single reduction algorithm will be +of the one-species method in comparison with the “individual-species method as explained below.,of the one-species method in comparison with the `individual-species method' as explained below. +" The ""individual-species"" method adopts the grain size distribution of individual species and the evolution of grain size distribution is separately calculated for individual species (note that the grain size distribution summed over all the species other than carbonaceous grains is adopted for ‘silicate’ in the one-species method).", The `individual-species' method adopts the grain size distribution of individual species and the evolution of grain size distribution is separately calculated for individual species (note that the grain size distribution summed over all the species other than carbonaceous grains is adopted for `silicate' in the one-species method). + In calculating the evolution of grain size distribution of a certain species. the total mass density of the species relative to the gas density is assumed to be the total dust-to-gas ratio (but the grain size distribution after shattering is normalized again to recover the correct mass ratio of each species).," In calculating the evolution of grain size distribution of a certain species, the total mass density of the species relative to the gas density is assumed to be the total dust-to-gas ratio (but the grain size distribution after shattering is normalized again to recover the correct mass ratio of each species)." + This treatment maximizes the production of small grains for non-Si species. which have smaller sizes than Si. but minimizes the production of small Si grains.," This treatment maximizes the production of small grains for non-Si species, which have smaller sizes than Si, but minimizes the production of small Si grains." + Thus. this method is suitable to examine the maximum possible contribution from non-Si small grains to the UV extinction curve.," Thus, this method is suitable to examine the maximum possible contribution from non-Si small grains to the UV extinction curve." +" In author.reftigisize; ndividual.. (ie πα-|em speciesandindividual— ccomparcethegqrainsizedislribulionspredic[gspecicsmethodsforny =0.1 and 1 ""at S Myr."," In \\ref{fig:size_individual}, we compare the grain size distributions predicted by the one-species and individual-species methods for $\nH =0.1$ and 1 $^{-3}$ at 5 Myr." + For ng.=10 7. the difference between the two methods is negligible because non-Si grains contribute little to the total grain abundance.," For $\nH =10$ $^{-3}$, the difference between the two methods is negligible because non-Si grains contribute little to the total grain abundance." + From the figure. we observe that the difference is relatively large in the case of my=0.1em 7.," From the figure, we observe that the difference is relatively large in the case of $\nH =0.1$ $^{-3}$ ." + This is because the fraction of non-Si grains is larger for my=O.l 5? than for lem . In UHsha, This is because the fraction of non-Si grains is larger for $\nH =0.1$ $^{-3}$ than for $\nH =1$ $^{-3}$. +tteredreffigext;ndieidual. . weshowtbeertinclioncurvescaleutatedbyl helagongeteqdas," In \\ref{fig:ext_individual}, we show the extinction curves calculated by the two methods." +The extinction Seescurves πα...are shown inFig.ipereresefB2. We observe Ala speciesmethodlendlobesteeperihanthoscoftheone specicsmethod, We observe that the extinction curves of the individual-species method tend to be steeper thanthose of the one-species method. + Ascanbesceninthe figure. lhesteeperslopecomesf roni negligiblyuottimismallat À niRAMIStum Sigrainsindicatedbyothers!," As can be seen in the figure, the steeper slope comes from the contribution from the non-Si grains indicated by `others'." +" Lntheindividual speciesmelhod. thesizedistribulionofeachnon Sispecies. whichhasalarger fractionofsmeallgrainsthanthatof Si, This iscalculate dscparately. solhal the ""(esEAEgional smalinon Sigrainsiscnhanced"," In the individual-species method, the size distribution of each non-Si species, which has a larger fraction of small grains than that of Si, is calculated separately, so that the production of small non-Si grains is enhanced." +" M enolethatlhe rcal'grainsizedistribulionuw thorpaper, αυhas Doi.béen typesetIRSA so", We note that the `real' grain size distribution would lie between the results of the two methods. +"fthetren SEN HENAXRfile ΜΠΛΕprepared Αςby ""pprorimealclreei speciesmelhod)isiusti fied forng Lem4", This means the approximate treatment adopted in the text one-species method) is justified for $\nH\ga 1$ $^{-3}$. + For ng=OL . because the contribution from non-Si species is significant. the error of the one-species method is at most ~10 at Ac0.2qum. and ~40¢ at A~0.1pum.," For $\nH\la 0.1$ $^{-3}$, because the contribution from non-Si species is significant, the error of the one-species method is at most $\sim 10$ at $\lambda\sim 0.2~\micron$, and $\sim 40$ at $\lambda\sim 0.1~\micron$." + In order to overcome this uncertainty. we should develop a different scheme that could treat the collisions between multiple species (in our case. 9 species). which the current scheme cannot treat in a reasonable computational time.," In order to overcome this uncertainty, we should develop a different scheme that could treat the collisions between multiple species (in our case, 9 species), which the current scheme cannot treat in a reasonable computational time." + The size distribution of shattered fragmentsis assumed to be a power law with an exponent of à(., The size distribution of shattered fragmentsis assumed to be a power law with an exponent of $-\alpha_\mathrm{f}$. + As we discuss in the text. the steepening of extinction curve becomes prominent if the power-law exponent (p) of the grain size distribution around @~0.03pum is steeper than ~3 (Section 4.13).," As we discuss in the text, the steepening of extinction curve becomes prominent if the power-law exponent $p$ ) of the grain size distribution around $a\sim 0.03~\micron$ is steeper than $\sim 3$ (Section \ref{subsec:steep}) )." + Jonesetal.(1996) have shown that the size distribution after shattering is not sensitive to aj., \citet{jones96} have shown that the size distribution after shattering is not sensitive to $\alpha_\mathrm{f}$. +" They also argue that o, slightly larger than3 is robust against the change of the cratering flow parameters in shattering (a;=3.3is adoptedin the text).", They also argue that $\alpha_\mathrm{f}$ slightly larger than 3 is robust against the change of the cratering flow parameters in shattering $\alpha_\mathrm{f}=3.3$is adopted in the text). + Nevertheless it would be interesting to examine if p>3 is realized even if we assume ay« 3., Nevertheless it would be interesting to examine if $p>3$ is realized even if we assume $\alpha_\mathrm{f}<3$ . +" Here we examine the smallest exponent adopted in Joneset (1996). à,=2.5 as an extreme case."," Here we examine the smallest exponent adopted in \citet{jones96}, , $\alpha_\mathrm{f}=2.5$ as an extreme case." + The ambient hydrogen number density is fixed to ng=Lem7. Jonesetal.(1996)..," The ambient hydrogen number density is fixed to $\nH =1~\mathrm{cm}^{-3}$ \\ref{fig:size_alpha}, \citet{jones96}. \\ref{fig:ext_alpha}." +were chosen due to considerations of computational cost and are not intended to be representative of the relative fraction of bodies in the planetesimal disk in any way.,were chosen due to considerations of computational cost and are not intended to be representative of the relative fraction of bodies in the planetesimal disk in any way. + The initial conditions were drawn from the eight multi-resonant states that were identified by Batygin&Brown as being compatible with an instability formation (2010)model., The initial conditions were drawn from the eight multi-resonant states that were identified by \citet{2010ApJ...716.1323B} as being compatible with an instability formation model. +" The planetesimals were initialized on near-coplanar, near-circular orbits (e~sini 1078)."," The planetesimals were initialized on near-coplanar, near-circular orbits $e \sim \sin i \sim 10^{-3}$ )." +" The self-gravity of the planetesimal swarm was neglected to reduce computational cost of the experiments, as 30 permutations of each initial condition were integrated."," The self-gravity of the planetesimal swarm was neglected to reduce computational cost of the experiments, as 30 permutations of each initial condition were integrated." +" Batygin&Brown(2010) used the presence of scattering events between an ice giant and gas giant, followed by a transient phase of high eccentricity,a as a proxy for whether successful formation of the classical Kuiper belt can occur."," \citet{2010ApJ...716.1323B} used the presence of scattering events between an ice giant and a gas giant, followed by a transient phase of high eccentricity, as a proxy for whether successful formation of the classical Kuiper belt can occur." + Further constraints on the initial conditions can be placed by considering the reproduction of the outer solar systems’ secular eigenmodes., Further constraints on the initial conditions can be placed by considering the reproduction of the outer solar systems' secular eigenmodes. + Particular difficulty has been found in ensuring that the amplitude of Jupiters gs mode is larger than that of the gg mode (Morbidellietal.2009).., Particular difficulty has been found in ensuring that the amplitude of Jupiters $g_5$ mode is larger than that of the $g_6$ mode \citep{2009A&A...507.1041M}. +" Having completed all of the integrations, we checkedthe relative amplitudes of the gs and the gg modes in all solutions."," Having completed all of the integrations, we checkedthe relative amplitudes of the $g_5$ and the $g_6$ modes in all solutions." +" Surprisingly, we found that despite a transient period of instability and gas giant/ice giant scattering, the (3:2 3:2 and the (5:3 4:3 4:3) initial conditions did not reproduce the secular architecture of the planets, in neither this set nor in the set of integrations of Batygin&Brown(2010).."," Surprisingly, we found that despite a transient period of instability and gas giant/ice giant scattering, the (3:2 3:2 and the (5:3 4:3 4:3) initial conditions did not reproduce the secular architecture of the planets, in neither this set nor in the set of integrations of \citet{2010ApJ...716.1323B}." +" If Jupiter and Saturn were indeed initially locked in the 3:2 MMR, as hydrodynamic simulations suggest (Massetson2008),, only the (3:2 3:2 5:4) and (3:2 4:3 4:3) initial conditions are left as a viable options for the starting state of the solar system."," If Jupiter and Saturn were indeed initially locked in the 3:2 MMR, as hydrodynamic simulations suggest \citep{2001MNRAS.320L..55M, 2007Icar..191..158M, 2008A&A...482..333P}, only the (3:2 3:2 5:4) and (3:2 4:3 4:3) initial conditions are left as a viable options for the starting state of the solar system." +" As already discussed in section 2, interactions between the cold outer disk and the outer-most ice-giant are largely independent of the starting condition, since scattering in a successful simulation always sets the planets onto orbits that are close to that of the current solar system, but with moderate eccentricities."," As already discussed in section $2$, interactions between the cold outer disk and the outer-most ice-giant are largely independent of the starting condition, since scattering in a successful simulation always sets the planets onto orbits that are close to that of the current solar system, but with moderate eccentricities." +" Consequently, we did not restrict our analysis to any particular initial condition."," Consequently, we did not restrict our analysis to any particular initial condition." +" Out of our set of 180 integrations, in 8 cases, primordially cold objects were able to retain unexcited orbits in addition to the gas-giant eigenmodes being reproduced correctly."," Out of our set of $180$ integrations, in $8$ cases, primordially cold objects were able to retain unexcited orbits in addition to the gas-giant eigenmodes being reproduced correctly." +" Here, we focus on two representative integrations: one starting from the (2:1 4:3 4:3) initial condition (Figure 5) and another starting from the (5:3 4:3 3:2) initial condition 6)."," Here, we focus on two representative integrations: one starting from the (2:1 4:3 4:3) initial condition (Figure 5) and another starting from the (5:3 4:3 3:2) initial condition (Figure 6)." +" In both cases, the cold classical population is (Figureproduced, but the wedge is only formed in the simulation that starts from the (2:1 4:3 4:3) initial condition (although it is somewhat smaller than its observed counterpart)."," In both cases, the cold classical population is produced, but the wedge is only formed in the simulation that starts from the (2:1 4:3 4:3) initial condition (although it is somewhat smaller than its observed counterpart)." +" Note, that the formation of the wedge has little to do with the initial condition - rather, its production is a random process."," Note, that the formation of the wedge has little to do with the initial condition - rather, its production is a random process." +" Similarly, the exact degree of excitation of the cold population’s inclinations is sensitively dependent on the details of Neptune’s evolution, which is chaotic."," Similarly, the exact degree of excitation of the cold population's inclinations is sensitively dependent on the details of Neptune's evolution, which is chaotic." +" Thus, the fact that the wedge is reproduced in one simulation and the degree of excitation of the inclinations is reproduced in another are unrelated results."," Thus, the fact that the wedge is reproduced in one simulation and the degree of excitation of the inclinations is reproduced in another are unrelated results." + A vast majority (> 90%) of the objects in the cold classical region (ie. a2 42AU) are retained in our simulations on stable orbits., A vast majority $>90\%$ ) of the objects in the cold classical region (i.e. $a \gtrsim 42$ AU) are retained in our simulations on stable orbits. +" On the contrary, only about a few thousandth of the particles in the inner disk are emplaced onto stable orbits in the Kuiper belt region."," On the contrary, only about a few thousandth of the particles in the inner disk are emplaced onto stable orbits in the Kuiper belt region." +" This implies that in order to self-consistently study the formation of the Kuiper belt, N>>3000 is needed."," This implies that in order to self-consistently study the formation of the Kuiper belt, $N \gg 3000$ is needed." +" Unfortunately, the required resolution is not computationally feasible."," Unfortunately, the required resolution is not computationally feasible." +" However, the problem can still be addressed by the use of “tracer” simulations, an approach already utilized in the context of Kuiper belt formation by Levisonetal. (2008).."," However, the problem can still be addressed by the use of “tracer"" simulations, an approach already utilized in the context of Kuiper belt formation by \cite{2008Icar..196..258L}. ." + In a tracer simulation the planets and planetesimals are not self-consistently evolved in time., In a tracer simulation the planets and planetesimals are not self-consistently evolved in time. +" Rather, the"," Rather, the" +parallax and for AAJ) as a funetion of B—V and 98(U—Εως using only Hyades dwarfs aud field halo dwarls.,parallax and for $\Delta M_V$ as a function of $B-V$ and $\delta(U-B)_{0.6}$ using only Hyades dwarfs and field halo dwarfs. + The uniform patteru amoung the various relatious is that the slope. AAA/A[Fe/H]. varies with both 8—V and [Fe/H].," The uniform pattern among the various relations is that the slope, $\Delta M_V/\Delta$ [Fe/H], varies with both $B-V$ and [Fe/H]." + Using the final differential calibration applied at 8—V = Q.70 between [Fe/H] = +0.39 and —0.50. the average AA)/A[Fe/H] = 0.63. smaller than the value fouud by Percivaletal.(2003).," Using the final differential calibration applied at $B-V$ = 0.70 between [Fe/H] = +0.39 and $-0.50$, the average $\Delta M_V/\Delta$ [Fe/H] = 0.63, smaller than the value found by \citet{pe03}." +. The result is even more extreme if the change is translated toa B—V ratio because the average tail sequence slope defined by the main sequence data of ]xaratas&Schuster(2006).. weighted toward the bluer end of the main sequence. is 5.5. leading toM(B—V)/A[Fe/ H]-0.115.," The result is even more extreme if the change is translated to a $B-V$ ratio because the average main sequence slope defined by the main sequence data of \citet{ka06}, weighted toward the bluer end of the main sequence, is 5.5, leading to$\Delta(B-V)/\Delta$ $ = 0.115$." + Independent of the sensitivity of A4- with [Fe/H] at a given B—V. does the absolute scale of the parallax sample generate plausible distauce moduli for well-studied clusters?," Independent of the sensitivity of $M_V$ with [Fe/H] at a given $B-V$, does the absolute scale of the parallax sample generate plausible distance moduli for well-studied clusters?" + The obvious initia test case is tlie Hyacles., The obvious initial test case is the Hyades. + Because of the respectable nuuber of stars witli a metallicity approximating that of the Hyades. we cau follow an approach similar to that for the solar metallicity sample ii the previous section.," Because of the respectable number of stars with a metallicity approximating that of the Hyades, we can follow an approach similar to that for the solar metallicity sample in the previous section." + All stars with [Fe/H] within x0.05 dex of the Hyades metallicity have beet identified. adjusted in AA to the metallicity of the Hyades and theu compared to the Hyades inai sequence relation.," All stars with [Fe/H] within $\pm$ 0.05 dex of the Hyades metallicity have been identified, adjusted in $M_V$ to the metallicity of the Hyades and then compared to the Hyades main sequence relation." + What is the Hyades metallicity?, What is the Hyades metallicity? + We have identifiel Hyades stars within our catalog thirougl a comparison with two sources of Hyades inembers., We have identified Hyades stars within our catalog through a comparison with two sources of Hyades members. + From 15 Hyades stars that overlap with the spectroscopic catalog of Taylor(2005).. [Fe/H] = 0.129 + 0.029 on our system.," From 18 Hyades stars that overlap with the spectroscopic catalog of \citet{tay05}, [Fe/H] = 0.129 $\pm$ 0.029 on our system." + The average offset oL —0.031 dex is essentially identical to the predicted. value of —0.032 dex. from the relation [or the entire catalog as derived in Sec., The average offset of $-0.031$ dex is essentially identical to the predicted value of $-0.032$ dex from the relation for the entire catalog as derived in Sec. + 2., 2. + From 10 stars that overlap with the catalog utilized by Piusonneaultetal...(200D).. [Fe/H] = 0.137 x 0.010.," From 10 stars that overlap with the catalog utilized by \citet{pi04}, [Fe/H] = 0.137 $\pm$ 0.040." + We will adopt [Fe/H] = 2-0.13 for the Hyades as celined by our spectroscopic scale., We will adopt [Fe/H] = +0.13 for the Hyades as defined by our spectroscopic scale. + For the Hyacdes main sequence we have adopted the meau relation derived by 1).. equivalent to a parallax-deliued true modulus of Gr—M) = 3.33. with two moclilicatious.," For the Hyades main sequence we have adopted the mean relation derived by \citet{pi04}, equivalent to a parallax-defined true modulus of $(m-M)_0$ = 3.33, with two modifications." + As detailed in Sec., As detailed in Sec. + 2. the Pinsonneaultetal.(2001) photometric scale exhibits small offsets relative to the convertedTycho-2 BV. system that delines our sample.," 2, the \citet{pi04} photometric scale exhibits small offsets relative to the converted $BV$ system that defines our sample." + We have adjusted the Hyades nean relation to our scale by acting 0.009 mae in 8—V. aud decreasing V by 0.020 mag., We have adjusted the \citet{pi04} Hyades mean relation to our scale by adding 0.009 mag in $B-V$ and decreasing $V$ by 0.020 mag. + This is equivalent to shiftiug the original relation in My: at a eiven color by —0.06 nag., This is equivalent to shifting the original relation in $M_V$ at a given color by $-0.06$ mag. + Fig., Fig. + 6 shows a plot of the residuals. in the seuse CALgyades—Advaita). as a Dunctiou of B—V for parallax stars with [Fe/H] between +0.08 and +O0.18. adjusted in AA: to [Fe/H] = 20.13 using / NAANFe/H]2 1.01.," 6 shows a plot of the residuals, in the sense $(M_{VHyades} - M_{VField})$, as a function of $B-V$ for parallax stars with [Fe/H] between +0.08 and +0.18, adjusted in $M_V$ to [Fe/H] = +0.13 using $\Delta M_V/\Delta$ $ = 1.04$ ." + A color-depeudent asymmetry among the residuals is obvious., A color-dependent asymmetry among the residuals is obvious. + On the uegative side of the distribution. there is an extremely sharp edge to the residuals wear —0.15 mae," On the negative side of the distribution, there is an extremely sharp edge to the residuals near $-0.15$ mag" +The time variation in the fiue structure constant has been studied: several times since first beiug proposed bv ?..,The time variation in the fine structure constant has been studied several times since first being proposed by \citet{gamow67}. + Observational upper bounds on its time variation as well as several theoretical frameworks that consider a as a dynamical field. have been published (au exhaustive list can be found in (27) and references there in).," Observational upper bounds on its time variation as well as several theoretical frameworks that consider $\alpha$ as a dynamical field have been published (an exhaustive list can be found in \citep{landau02:tesis,uzan03} and references there in)." + Although still dispted. the claim that à was sinaller in the past is an exciting perspective. (?2)..," Although still disputed, the claim that $\alpha$ was smaller in the past is an exciting perspective, \citep{MurphyWebbFlambaum2003}." + Declistelns theorv (7). which is based ou a ΠΤΙΟΙ of niuinial liypothesis of highly accepted plysical principles. is m a sense represcutative of may low cucrey theories iuspired by eraud uuification schemes.," Beckenstein's theory \citep{Beckens82}, which is based on a number of minimal hypothesis of highly accepted physical principles, is in a sense representative of many low energy theories inspired by grand unification schemes." + Tn this work. we derive equations that govern the energy exchauge between matter. the scalar field. aud the electromagnetic field.," In this work, we derive equations that govern the energy exchange between matter, the scalar field, and the electromagnetic field." + Although we do not analyze the precise mechanism of clerev release. we assunie hat the work done bv the scalar field is racdiated away in an efficient wav. as for the rotochenmical heating of neutron stars due to the spin down of the star (?7)..," Although we do not analyze the precise mechanism of energy release, we assume that the work done by the scalar field is radiated away in an efficient way, as for the rotochemical heating of neutron stars due to the spin down of the star \citep{Reisenegger1995,FernandezReisenegger2005}." + Iu section 2.. we briciy review Deckeusteius heory. as well as the cosimological time evolutiou of 4 hat it oediets.," In section \ref{sec:alfadot}, we briefly review Beckenstein's theory, as well as the cosmological time evolution of $\alpha$ that it predicts." + Iu section 3.. we derive a generalized version of the Povutiug theorem for the clectromaguetic feld. aud from the conservation of the total enerevanonmioeutuni ensor we fud how the energv flow of matter is modified x the scalar field.," In section \ref{sec:Edot}, we derive a generalized version of the Poynting theorem for the electromagnetic field, and from the conservation of the total energy-momentum tensor we find how the energy flow of matter is modified by the scalar field." + In section LL. we discuss the magnetic enerev of matter using a simple nuclear model.," In section \ref{sec:Eem-Mat}, we discuss the magnetic energy of matter using a simple nuclear model." +" Iu section D, we study the thermal historv of the Earth iu the oxeseuce of Dekeusteiu's scalar field."," In section \ref{sec:CoolEarth}, we study the thermal history of the Earth in the presence of Bekenstein's scalar field." + We also describe iu section 6 the results we obtained for the outer planets., We also describe in section \ref{sec:outerplanets} the results we obtained for the outer planets. + Finally in section 7 we sunmnuiuize our conclusions., Finally in section \ref{sec:conclusions} we summarize our conclusions. + We briefly review Bekeusteius forimalisni and its mediction for the cosmological time variation of a., We briefly review Bekenstein's formalism and its prediction for the cosmological time variation of $\alpha$. + Although we consider galactic as well as terrestrial phenomena. we can nevertheless couficlently assume that hey track the cosimological[m] evolution of a. (?)..," Although we consider galactic as well as terrestrial phenomena, we can nevertheless confidently assume that they track the cosmological evolution of $\alpha$, \citep{ShawBarrow2006}." + ? proposes to modify Maxwell's theory by introducing afield e that dynamically describes the variation of a., \citet{Beckens82} proposes to modify Maxwell's theory by introducing a field $\epsilon$ that dynamically describes the variation of $\alpha$. + The oundational hypothesis are the following(??):: Sting theories aud the like iu which there are other fundamental leneth scales. force us to set aside condition T.," The foundational hypothesis are the following\citep{Beckens82,landau02:tesis}: String theories and the like in which there are other fundamental length scales, force us to set aside condition \ref{item:Planck}. ." + These hypothesis uniquely lead to the action where, These hypothesis uniquely lead to the action where +Lon while showed that a classical bulge is not necessary [or a SMDILIL to exist.,"$L,n$ while showed that a classical bulge is not necessary for a SMBH to exist." + Pseudobulges are central components of late tvpe galaxies with disk features and it is believed that they follow a separate formation path to the classical bulges with which they can coexist., Pseudobulges are central components of late type galaxies with disk features and it is believed that they follow a separate formation path to the classical bulges with which they can coexist. + For a review of the properties of pseudobulges see?., For a review of the properties of pseudobulges see. +". The first estimation of the Ad, £ relation in the near- was established by using three band images from the Two Micron All Sky Survey DoFfor a sample of Lao37 earlv- and late- type galaxies.", The first estimation of the $M_{\rm bh}$ $L$ relation in the near-IR was established by using three band images from the Two Micron All Sky Survey for a sample of 37 early- and late- type galaxies. + The intrinsic scatter of their correlation ranges from ~O.5clex to ~0.3dex depending on the subsample selection., The intrinsic scatter of their correlation ranges from $\sim$ 0.5dex to $\sim$ 0.3dex depending on the subsample selection. + refined the Adin £ relation bv using updated. Adiga measurements ancl modifving the photometry of the data set ancl finding an intrinsic scatter of —0.30dex., refined the $M_{\rm bh}$ $L$ relation by using updated $M_{\rm bh}$ measurements and modifying the photometry of the data set and finding an intrinsic scatter of $\sim$ 0.30dex. +" More recently anc in addition to the Αι L relation found a relation between the galaxy light. concentration nm (Sérrsic index) and Ada, with a comparable intrinsic scatter of 0.31dex.", More recently and in addition to the $M_{\rm bh}$ $L$ relation found a relation between the galaxy light concentration $n$ (Sérrsic index) and $M_{\rm bh}$ with a comparable intrinsic scatter of 0.31dex. +" In the review by the Ay on relation was shown to be as accurate on predicting Afi as the Adj, @ relations.", In the review by the $M_{\rm bh}$ $n$ relation was shown to be as accurate on predicting $M_{\rm bh}$ as the $M_{\rm bh}$ $\sigma$ relations. +" and applied both the AAW n and Ady, £ relations respectively to derive the nearby SMDIL mass. functions for the Alillennium Galaxy Catalogue (22)) and. derived individual SAIBLL mass measurements for a sample of 1743 ealaxies.", and applied both the $M_{\rm bh}$ $n$ and $M_{\rm bh}$ $L$ relations respectively to derive the nearby SMBH mass functions for the Millennium Galaxy Catalogue ) and derived individual SMBH mass measurements for a sample of 1743 galaxies. + While the mass functions agreed well within the cited. errors. the comparison of the derived. SALBLE masses on a galaxy by galaxv basis showed ᾱ- low consistency between the two predictors.," While the mass functions agreed well within the cited errors, the comparison of the derived SMBH masses on a galaxy by galaxy basis showed a low consistency between the two predictors." + Γον explained that the lack of correlation is in part due to the scatter introduced. by combining elliptical and disk galaxies. the uncertainty of separating the bulge component from the disk component. and due to the intrinsic scatter of the Ai L.η correlations at optical wavelengths.," They explained that the lack of correlation is in part due to the scatter introduced by combining elliptical and disk galaxies, the uncertainty of separating the bulge component from the disk component, and due to the intrinsic scatter of the $M_{\rm bh}$ $L,n$ correlations at optical wavelengths." + In this paper we aim to reconstruct the Ay L.n relations in the neal by using high. resolution UIXIICE Infrared. Deep Sky Survey. (UIKIDSS.. ?2)). images which extend significant deeper (— 2nmag/aresec?) than the previous studies based. on 2ALASS.," In this paper we aim to reconstruct the $M_{\rm bh}$ $L,n$ relations in the near-IR by using high resolution UKIRT Infrared Deep Sky Survey (UKIDSS, ) images which extend significant deeper $\sim2$ $^2$ ) than the previous studies based on 2MASS." + We specifically. choose near-LR photometry because galaxy profiles. should be less perturbed by voung star populations ancl by dust attenuation relative to optical passhancs (?))., We specifically choose near-IR photometry because galaxy profiles should be less perturbed by young star populations and by dust attenuation relative to optical passbands ). + Thereby vielding a lower intrinsic scatter and enabling more accurate SALDIL mass function determinations from the application of these relations to large surveys (c.g. GAALA see ?))., Thereby yielding a lower intrinsic scatter and enabling more accurate SMBH mass function determinations from the application of these relations to large surveys (e.g. GAMA see ). + Section 2. describes the cata selection ancl the data reduction., Section \ref{sec:2} describes the data selection and the data reduction. + —Section 3. describes the methodology. [or measuring radial surface-brightness profiles for our 29 galaxies using (?)) ancl presents information from the literature for our sample., Section \ref{sec:3} describes the methodology for measuring radial surface-brightness profiles for our 29 galaxies using ) and presents information from the literature for our sample. + In Section 4. we explore the Ala L.n correlations and compare with previous studies.," In Section \ref{sec:4} we explore the $M_{\rm bh}$ $L,n$ correlations and compare with previous studies." + Finally. Section 5 summarises our conclusions and suggests possible direction for further studs.," Finally, Section \ref{sec:5} summarises our conclusions and suggests possible direction for further study." + We extract calibrated Ix-band images from. UIXIDSS for 29 ealaxies for which SAIBLI masses have been measured., We extract calibrated K-band images from UKIDSS for 29 galaxies for which SMBH masses have been measured. + These galaxies are a subsample of the host. galaxy population. where the mass of the SMDII has been measured. using a direct. method.," These galaxies are a subsample of the host galaxy population, where the mass of the SMBH has been measured using a direct method." + The full sample consists of 86 galaxies with SMLDIIS ancl 9 galaxies with intermediate massive black holes (LMDBID. as presented by GOLO and references therein.," The full sample consists of 86 galaxies with SMBHs and 9 galaxies with intermediate massive black holes (IMBH), as presented by GO10 and references therein." + The wide-Lield. images were obtained using the Wide Field Lnfrared Camera (NECΑΛ) (2)) on the 3.8-2m United Ixingdom Infra-red Telescope CUINIICE) as part of the Large Area Survey UINIDSS-LAS (?7))., The wide-field images were obtained using the Wide Field Infrared Camera (WFCAM) ) on the 3.8-m United Kingdom Infra-red Telescope (UKIRT) as part of the Large Area Survey UKIDSS-LAS ). + The pixel size of cach detector is 0.4 arcsec with a gain of 4.50. ADU and a read noise of 25 ADU., The pixel size of each detector is $~$ arcsec with a gain of 4.5 $^{-}$ /ADU and a read noise of 25 ADU. + The properties of our galaxy sample are listed in ‘Table 1.., The properties of our galaxy sample are listed in Table \ref{table:first}. + We include galaxies with SMDLILI masses measured with stellar kinematics. gas kinematics. water masers. stellar proper. motion ancl reverberation mapping (see ‘Table 6)).," We include galaxies with SMBH masses measured with stellar kinematics, gas kinematics, water masers, stellar proper motion and reverberation mapping (see Table \ref{table:masses}) )." + The masses for NGCO2778. Ναςτὸ. NGCAS64. C4697 anc NGCSS45 have been modified. from their initial published. values due to an update of their distances (see COLO).," The masses for NGC2778, NGC4473, NGC4564, NGC4697 and NGC5845 have been modified from their initial published values due to an update of their distances (see GO10)." + Our sample includes 15 elliptical galaxies and 14 disk galaxies (see Table 1)., Our sample includes 15 elliptical galaxies and 14 disk galaxies (see Table 1). + We also include for reference. only the Milkv Wavy xwameters derived. from other studies., We also include for reference only the Milky Way parameters derived from other studies. + In. particular. the SMIDLIL mass is (4.32:0.3)10M... for à distance of 0.0083Mpc (?)). the bulge luminosity is (4.041.22107L... at 2.2//m (2)) and the Séresie index 025U.22 (27))," In particular, the SMBH mass is $(4.3 \pm 0.3)10^{6} \rm M_{\odot}$ for a distance of 0.0083Mpc ), the bulge luminosity is $(4.0 \pm 1.2)10^{8} \rm L_{\odot}$ at $\mu$ m ) and the Sérrsic index $^{+0.26 }_{- 0.22 }$ )." +a ‘The accuracy to which we can determine the sky background dictates the depth to which we can profile cach galaxy., The accuracy to which we can determine the sky background dictates the depth to which we can profile each galaxy. + We measure the sky backerounc by manually placing 40 - 50 xxes (I0 x. 10 pixels) at locations around each galaxy. using he task imexamine., We measure the sky background by manually placing 40 - 50 boxes (10 x 10 pixels) at locations around each galaxy using the task imexamine. + Phe sky. value we then adopt is he mean of the median values from cach box (see Figure for details)., The sky value we then adopt is the mean of the median values from each box (see Figure \ref{fig:sky} for details). + Phe boxes are selected to lic away from stars. he faint halo of the galaxy. neighbouring galaxies that may exist and to be uniformly. distributed around each image.," The boxes are selected to lie away from stars, the faint halo of the galaxy, neighbouring galaxies that may exist and to be uniformly distributed around each image." +" Some images (Νοτν, NOGOC3245.. NGC4258. αςΟΡ} have ai noticeable background. gradient."," Some images (NGC2778, NGC3245, NGC4258, NGC7052) have a noticeable background gradient." + We correct the gradient with the use of a (?)) Cully resolved: background map., We correct the gradient with the use of a ) fully resolved background map. + To ensure that the subtraction, To ensure that the subtraction +were measured αἱ a dillerent limiüng surface brightness. a correction of +0.178 in log was applied to the Broeils and Rhee data.,"were measured at a different limiting surface brightness, a correction of +0.178 in log r was applied to the Broeils and Rhee data." + This was determined by jointly correlating the radii and the masses ancl finding the minimum dispersion., This was determined by jointly correlating the radii and the masses and finding the minimum dispersion. + This correction is well within the uncertainties quoted by Begum et al., This correction is well within the uncertainties quoted by Begum et al. + in their discussion of this problem., in their discussion of this problem. + Fig., Fig. +" 2 shows the resulting relation between 2 log rj, ande Ay.", 2 shows the resulting relation between 2 log $_{HI}$ and log $_{HI}$. + The solid line has a slope of 1 while a least squares fit for Chis slope gives 0.994+0.012 for all 137 galaxies., The solid line has a slope of 1 while a least squares fit for this slope gives $~\pm~0.012$ for all 137 galaxies. + The logaritlimic intercept (log M-2log r) is 0.846zE0.132., The logarithmic intercept (log M-2log r) is $~\pm~0.132$. + Hence: in agreement with DBegum et al., Hence in agreement with Begum et al. + (he HI surface density appears to be remarkably constant over nearly 5 orders of magnitude in mass., the HI surface density appears to be remarkably constant over nearly 5 orders of magnitude in mass. +" Note (hat this face-on surface density is not to be confused with X, above where il represents the column density.", Note that this face-on surface density is not to be confused with $\Sigma_{o}$ above where it represents the column density. + Equation (6) above implies (hat if A is a constant then a relation between 2 log V and log r should determine its value., Equation (6) above implies that if $\lambda$ is a constant then a relation between 2 log V and log r should determine its value. + Fig.3 shows such a plot., Fig.3 shows such a plot. + Possibly a more familiar wav (o look at this relation is (o eliminate r by using the relationship established in Fie.2., Possibly a more familiar way to look at this relation is to eliminate r by using the relationship established in Fig.2. +" Since rxMU? equation (6) implies MoxWi, ie. an HI Tullv-Fisher relation is predicted.", Since $\propto M^{1/2}$ equation (6) implies $\propto V_{rot}^{4}$ i.e. an HI Tully-Fisher relation is predicted. + This is shown in Fie.4., This is shown in Fig.4. + The solid line in both Figs 3 4 has a slope of 1., The solid line in both Figs 3 4 has a slope of 1. + Least squares fit to the data with ρω>41.7kms|! (ie. above the dashed lines) give +0.078 in Fig.3 and 4089 1n Fig.," Least squares fit to the data with $_{rot} > 41.7~km~s^{-1}$ (i.e. above the dashed lines) give $~\pm~0.078$ in Fig.3 and $~\pm~ +0.089$ in Fig." +" ,", 4. + Both regressions included: 109 galaxies., Both regressions included 109 galaxies. +" The logarithmic intercepts are (log 1-2 log V,,,)— +0.250 and (log M-4 log +0.515.", The logarithmic intercepts are (log r-2 log $_{rot}$ )= $~\pm~0.250$ and (log M-4 log $~\pm~0.515$. +" Solving for A from each one obtains A=61.3.435.307)pe and A=61.4.+363(T/p)pe respectively,"," Solving for $\lambda$ from each one obtains $\lambda=61.3~\pm~35.3(T_{4}/\mu)~pc$ and $\lambda=61.4 +~\pm~36.3(T_{4}/\mu)~pc$ respectively." + Although the uncertainties are large (he numerical difference is small given the light correlation seen in Fig., Although the uncertainties are large the numerical difference is small given the tight correlation seen in Fig. + 2., 2. + Given this value of A the time scale arguments above are justified., Given this value of $\lambda$ the time scale arguments above are justified. + It should be noted however that the condition for Iragmentation will be violated Lor values of Z/Z. not much below 0.01., It should be noted however that the condition for fragmentation will be violated for values of $_{\odot}$ not much below 0.01. + This provides a natural explanation for (he observed abundance threshold of (his order below which elobular clusters are not observed a point also made by Gann (1930)., This provides a natural explanation for the observed abundance threshold of this order below which globular clusters are not observed a point also made by Gunn (1980). + Returning to equation (9) the Jean's mass becomes Mj—3.742.1xΟΤΙ)M.," Returning to equation (9) the Jean's mass becomes $_{J}=3.7~\pm~2.1\times10^ +{6}(T_{4}/\mu)^{2}~M_{\odot}$ ." + Allowing for a gas to star formation elliciency of no0.07 results in a predicted elobulur cluster mass upper limit of Alege2.641.5OurM.," Allowing for a gas to star formation efficiency of $\eta\sim0.07$ results in a predicted globular cluster mass upper limit of $_{GC}\sim2.6~\pm~1.5\times10^ +{5}(T_{4}/\mu)^{2}~M_{\odot}$." + Degimn et al. (, Begum et al. ( +2008a) have also noted that the dwarl irregular galaxies with the lowest rotational velocities (i.e. those below the dashed line in Figs 3 4) lie below the extrapolatedecl baryonic Tully-Fisher relation.,2008a) have also noted that the dwarf irregular galaxies with the lowest rotational velocities (i.e. those below the dashed line in Figs 3 4) lie below the extrapolated baryonic Tully-Fisher relation. + If all of the galaxies are rotationally supported. then Where a is the ratio of the total mass enclosed within rj; to the gas mass.," If all of the galaxies are rotationally supported, then $_{rot}^{2}=\alpha GM_{HI}/r_{HI}$ where $\alpha$ is the ratio of the total mass enclosed within $_{HI}$ to the gas mass." + Given the relatively tight relation in Fig.2 (he increased scatter in Figs 3 4 can be understood as due to variations in this ratio., Given the relatively tight relation in Fig.2 the increased scatter in Figs 3 4 can be understood as due to variations in this ratio. + In order to account for the data below the dashed lines. either the gas is not fully rotationallv supported or there is a svstematic shift in the value of a towards a lower value inspite of the Geht correlation between(he HI radius ancl mass," In order to account for the data below the dashed lines, either the gas is not fully rotationally supported or there is a systematic shift in the value of $\alpha$ towards a lower value inspite of the tight correlation betweenthe HI radius and mass" +NGC 5055: see Fig.,NGC 5055; see Fig. + 1)., 1). + For this purpose. we have selected the Astro-Physics Starfire (APS) 1G0EDESG. a short focal length (£/7). 16 em-aperture relractor that provides a FOV of ~ 73.7 x 110.6 aremin (see Table 1).," For this purpose, we have selected the Astro-Physics Starfire (APS) 160EDF6, a short focal length (f/7), 16 cm-aperture refractor that provides a FOV of $\sim$ 73.7 $\times$ 110.6 arcmin (see Table 1)." + Each telescope is equipped with a commercially available CCD camera., Each telescope is equipped with a commercially available CCD camera. + The primary survey camera of (he Black Dird Observatory (BBO) is the SBIG STL-11000. which uses a Kodak IXAI-11000M imaging sensor.," The primary survey camera of the Black Bird Observatory (BBO) is the SBIG STL-11000, which uses a Kodak KAI-11000M imaging sensor." + This sensor consists of a 4008 x 2672 pixel array with 9 x 9 micron pixels., This sensor consists of a 4008 $\times$ 2672 pixel array with 9 $\times$ 9 micron pixels. + Some of the other facilities use a 16-megapixel camera manufactured bv Apogee Instruments. of Roseville (California).," Some of the other facilities use a 16-megapixel camera manufactured by Apogee Instruments, of Roseville (California)." + The Rancho del Sol (RdS) observatory uses (he Alta-LAFO9000 imaging sensor with 3056 x 3056 pixels with 12 x 12 micron., The Rancho del Sol (RdS) observatory uses the Alta-KAFO9000 imaging sensor with 3056 $\times$ 3056 pixels with 12 $\times$ 12 micron. + The Moorook (Mrlx) observatory uses a similar CCD camera. the Apogee Alla-LAF16803 with 4096 x 4096 pixels and a smaller pixel size (9 x 9 micron).," The Moorook (MrK) observatory uses a similar CCD camera, the Apogee Alta-KAF16803 with 4096 $\times$ 4096 pixels and a smaller pixel size (9 $\times$ 9 micron)." + The tidal stream detection strategv ancl the procedures used for data acquisition aud reduction of the data are the same as those described in our previous papers from this project (Martinez-Deleado οἱ al., The tidal stream detection strategy and the procedures used for data acquisition and reduction of the data are the same as those described in our previous papers from this project (Martinez-Delgado et al. + 2008: 2009)., 2008; 2009). + In summary. (his strategy strives lor multiple deep exposures of each target using a wide bandpass. high throughput. clear optical filter wilh a near-IR cut-off. also known as aL. The typical cumulative exposure limes are in (he ranee of 6 to 11 hours.," In summary, this strategy strives for multiple deep exposures of each target using a wide bandpass, high throughput, clear optical filter with a near-IR cut-off, also known as a. The typical cumulative exposure times are in the range of 6 to 11 hours." + Data reduction followed stanclard techniques described in (he afore-mentioned papers., Data reduction followed standard techniques described in the afore-mentioned papers. + The list of targets. together with the telescopes and total exposure time used in each case are given in Table 2.," The list of targets, together with the telescopes and total exposure time used in each case are given in Table 2." + Photometric calibration of the luminance filler CL) images is not currently available., Photometric calibration of the luminance filter $L$ ) images is not currently available. +" 50. lo assess (heir depth: and (vpical quality in terms of backeround and [LIat-fielding. we relied on images of six of our galaxies Ναςος, NGCI1084. NGC3521. NGCU2106. NGCH651 and NGC5866 obtained by the Sloan Digital Sky Survey ( SDSS. York et al."," So, to assess their depth and typical quality in terms of background and flat-fielding, we relied on images of six of our galaxies — NGC1055, NGC1084, NGC3521, NGC4216, NGC4651 and NGC5866 — obtained by the Sloan Digital Sky Survey ( SDSS, York et al." + 2000: Data Release 7. Abazajian οἱ al.," 2000; Data Release 7, Abazajian et al." + 2009)., 2009). +regular gaps. due to the Earth occultation of the satellite. we binned the data in orbit-lone bins (~5400 s) to obtain an evenly sampled. light curve. containing 551 points.,"regular gaps, due to the Earth occultation of the satellite, we binned the data in orbit-long bins $\sim 5400$ s) to obtain an evenly sampled light curve, containing 551 points." + To check the stability of the detector through this month-long observation. we compared the ratios between the light curves from cdilferent detectors.," To check the stability of the detector through this month-long observation, we compared the ratios between the light curves from different detectors." + While SIS0. GIS2 and GISS showed consistent. light. curves. we observed. discrepancies between these and SISI in all energy bands.," While SIS0, GIS2 and GIS3 showed consistent light curves, we observed discrepancies between these and SIS1 in all energy bands." + The ratio between the SISI light curve and the light curves from all other detectors shows a lincarly decreasing trend. of amplitude ~10/4 as measured from the start to the end of the observation.," The ratio between the SIS1 light curve and the light curves from all other detectors shows a linearly decreasing trend, of amplitude $\sim10$ as measured from the start to the end of the observation." + We therefore combined only SISO. CIS2 and GISS data. in each energy band. to produce the final light curves.," We therefore combined only SIS0, GIS2 and GIS3 data, in each energy band, to produce the final light curves." + ‘Phe combined. binned anc background-subtracted keV light curve is shown in Fig. 2..," The combined, binned and background-subtracted $0.7--10$ keV light curve is shown in Fig. \ref{asca_lc}." + Phe average count rates for the soft. medium and hard light curves are 2 0.82 and 0.24 counts/s respectively and the average exposure fraction is23X.," The average count rates for the soft, medium and hard light curves are 2.7, 0.82 and 0.24 counts/s respectively and the average exposure fraction is." +. The PSD and other variability. properties of this data set have been studied by c.g. Papadakis(2002):Eclelsonetal.," The PSD and other variability properties of this data set have been studied by e.g. \citet{Papadakis_ark,Edelson}." + (2002).. Fluxes in dillerent encrey bands may vary in a similar wav and can do it simultaneously. or with a delay.," Fluxes in different energy bands may vary in a similar way and can do it simultaneously, or with a delay." + Time lags and coherence between two simultaneous ime series ο).(0. can be estimated. using the cross spectrum C'(f)=ο. where S(f) and. Hf) are he Fourier transforms of the respective light curves.," Time lags and coherence between two simultaneous time series $s(t),h(t)$ can be estimated using the cross spectrum $C(f)= +S^*(f)H(f)$, where $S(f)$ and $H(f)$ are the Fourier transforms of the respective light curves." + The coherence 572 forB discretely. sampled time. series. is. caleulated as follows: where Reeη) and LImet(f;j) ave the real and imaginary parts of the cross spectrum C'(f) ancl angle brackets represent averaging over independent. measurements. either at consecutive frequencies in a frequency bin or equal [requencies from different light curve segments.," The coherence $\gamma ^2$ for discretely sampled time series is calculated as follows: where ${\rm Re}_C (f_{i})$ and ${\rm Im}_C (f_{i})$ are the real and imaginary parts of the cross spectrum $C(f)$ and angle brackets represent averaging over independent measurements, either at consecutive frequencies in a frequency bin or equal frequencies from different light curve segments." + The argument of the cross spectrum defines the phase lags: o(f;)=avg€(Cf. and from here the time lags. τί]. are calculated as: The cross spectrum produces estimates of the coherence ancl time lags as a function of Fourier frequency. or equivalently. of time-scale.," The argument of the cross spectrum defines the phase lags: $\phi( f_{i})=\arg{\langle C(f_{i})\rangle}$, and from here the time lags, $\tau(f_i)$, are calculated as: The cross spectrum produces estimates of the coherence and time lags as a function of Fourier frequency, or equivalently, of time-scale." + Vaughan&Nowak(1997) and Nowaketal.(1999) discuss the interpretation of these measurcments in detail— and provide error estimates for data with observational noise., \citet{Vaughan_coh} and \citet{Nowak_lags} discuss the interpretation of these measurements in detail and provide error estimates for data with observational noise. + We used the methods described therein to estimate the error bars on the time lags., We used the methods described therein to estimate the error bars on the time lags. + We used data to compute lags and coherence in the 10°107 Lz frequeney range and data for the 107107 Lz frequeney range.," We used data to compute lags and coherence in the $10^{-6} +-10^{-4}$ Hz frequency range and data for the $10^{-4} -10^{-2}$ Hz frequency range." + Asa first step we used the 07.2.0 keV and 2.010.0 keV bbancs to obtain the highest possible signal-to-noise in the light. curves., As a first step we used the $0.7-2.0$ keV and $2.0-10.0$ keV bands to obtain the highest possible signal-to-noise in the light curves. + As the lags and coherence are often. we used light. curves with the same as the bbands (see Section 2.1).," As the lags and coherence are often energy-dependent, we used light curves with the same as the bands (see Section 2.1)." +A new opportunity to study stellar processes near massive black holes (MBHs) arises with the anticipated detection of gravitational waves (GWs) by the Laser Interferometer Space Antenna (LISA).,A new opportunity to study stellar processes near massive black holes (MBHs) arises with the anticipated detection of gravitational waves (GWs) by the Laser Interferometer Space Antenna (LISA). + LISA will be a space-based detector in orbit around the Sun. consisting of three satellites five million kilometres apart.," LISA will be a space-based detector in orbit around the Sun, consisting of three satellites five million kilometres apart." + It will be sensitive to GWs in a frequency range 10ΤΗ;10? Hz., It will be sensitive to GWs in a frequency range $10^{-4}\Hz\lesssim f\lesssim 10^{-2}$ Hz. + An important source of GWs for LISA is the inspiral of compact objects onto MBHs in galactic nuclei (e.g. Hils&Bender 1995:: Sigurdsson&Rees 1997: Ivanov. 2002:: Freitag 2003: Hopman&Alexander 2005.. 20062... 2006b:: Amaro-Seoaneetal. 2007:: see Hopman 2006 for a review).," An important source of GWs for LISA is the inspiral of compact objects onto MBHs in galactic nuclei (e.g. \citeauthor{Hil95} \citeyear{Hil95}; ; \citeauthor{Sig97} \citeyear{Sig97}; ; \citeauthor{Iva02} \citeyear{Iva02}; \citeauthor{Fre03} + \citeyear{Fre03}; \citeauthor{Hop05} \citeyear{Hop05}, \citeyear{Hop06}, \citeyear{Hop06b}; \citeauthor{Ama07} + \citeyear{Ama07}; see \citeauthor{Hop06c} + \citeyear{Hop06c} for a review)." +" These are sources on highly eccentric orbits with periapses slightly larger than the Schwarzschild radius rg=2GM,c of the MBH. where M, is the mass of the MBH."," These are sources on highly eccentric orbits with periapses slightly larger than the Schwarzschild radius $r_{S}=2GM_{\bullet}/c^2$ of the MBH, where $M_{\bullet}$ is the mass of the MBH." + The star dissipates energy due to GW emission. and as a result spirals in.," The star dissipates energy due to GW emission, and as a result spirals in." + Such extreme mass ratio inspirals CEMRIs) can be observed by LISA to cosmological distances if the orbital period of the star is shorter than PX107 sec (Finn&Thorne 2000: Barack&Cutler 2004: Gairetal. 2004: Glampedakis 2005)).," Such extreme mass ratio inspirals (EMRIs) can be observed by LISA to cosmological distances if the orbital period of the star is shorter than $P\lesssim 10^4$ sec \citeauthor{Fin00} + \citeyear{Fin00}; \citeauthor{Bar04b} \citeyear{Bar04b}; \citeauthor{Gai04} \citeyear{Gai04}; \citeauthor{Gla05} + \citeyear{Gla05}) )." + LISA will detect hundreds to thousands of such captures over its projected 3-5 yr mission life time 2004:Gair 20050.," LISA will detect hundreds to thousands of such captures over its projected 3-5 yr mission life time \citep{Gai04, + Gai08}." + For most of the inspiral the emitted GW's are not observable by LISA., For most of the inspiral the emitted GWs are not observable by LISA. + These GW give rise to a source of confusion noise. possibly obscuring other types of GW sources.," These GWs give rise to a source of confusion noise, possibly obscuring other types of GW sources." + The shape and overall magnitude of this EMRI background has been studied by Barack&Cutler (2004).., The shape and overall magnitude of this EMRI background has been studied by \citet{Bar04b}. . + They do not study the dynamical requirements of inspiral. but scale their result with possible EMRI rates of Freitag(2001. 2003).," They do not study the dynamical requirements of inspiral, but scale their result with possible EMRI rates of \citet{Fre01, Fre03}." +. Therefore noise of stars that do not eventually spiral in is not included., Therefore noise of stars that do not eventually spiral in is not included. + Rubboetal.(2006). show that stars on long periods of a few years and nearly radial orbits that carry them near the Schwarzschild radius of the MBH. emit bursts of GWS that for the Galactic centre will give a signal to noise ratio larger than 5.," \citet{Rub06} show that stars on long periods of a few years and nearly radial orbits that carry them near the Schwarzschild radius of the MBH, emit bursts of GWs that for the Galactic centre will give a signal to noise ratio larger than 5." + Taking into account processes determining the inner radius of the density profile as well as mass segregation effects. Hopmanetal.(2007) find that stellar mass black holes (BHs) have a burst rate of order Lye|. while the rate is ZO. yr! for main sequence stars (MSs) and white dwarfs (WDs).," Taking into account processes determining the inner radius of the density profile as well as mass segregation effects, \citet{Hop07} find that stellar mass black holes (BHs) have a burst rate of order $1$ $^{-1}$, while the rate is $\lesssim 0.1$ $^{-1}$ for main sequence stars (MSs) and white dwarfs (WDs)." + Individual bursts from. star-MBH fly-bys may be detected from our own Galactic centre. but it is unlikely they will be observed from other galactic nuclei.," Individual bursts from star-MBH fly-bys may be detected from our own Galactic centre, but it is unlikely they will be observed from other galactic nuclei." + However. the accumulation of all bursts of all galaxies in the universe gives rise to an eXtreme mass ratio burst background (EMBB).," However, the accumulation of all bursts of all galaxies in the universe gives rise to an extreme mass ratio burst background (EMBB)." + Since the energy emitted per event is much higher for inspirals compared to fly-bys. but the event rate is much lower (Alexander&Hopman 2003). it is nota priori clear whichof these dominates the confuse background.," Since the energy emitted per event is much higher for inspirals compared to fly-bys, but the event rate is much lower \citep{Ale03b}, , it is nota priori clear whichof these dominates the confuse background." + In this paper we studythe contribution of these fly-bys to the GW background., In this paper we studythe contribution of these fly-bys to the GW background. + In, In +Filled diamonds indicate radial profile measurements.,Filled diamonds indicate radial profile measurements. +" Data for 7 nearby spirals from Wong&Blitz(2002) are shown in red, those for M51 from Schuster in green and those for 66946 from Crosthwaite&Turner(2007) in purple."," Data for 7 nearby spirals from \citet{WONG02} are shown in red, those for M51 from \citet{SCHUSTER07} in green and those for 6946 from \citet{CROSTHWAITE07} in purple." +" Wong&Blitz(2002) derive ffrom eemission, Schusteretal.(2007) from RC emission, and Crosthwaite&Turner from FIR emission."," \citet{WONG02} derive from emission, \citet{SCHUSTER07} from RC emission, and \citet{CROSTHWAITE07} from FIR emission." + Small points represent (2007)aperture data., Small points represent aperture data. + Blue points show ppc-sized aperture measurements from Kennicutt(2007) of star forming regions in the spiral arms of 55194 (M51)., Blue points show pc-sized aperture measurements from \citet{KENNICUTT07} of star forming regions in the spiral arms of 5194 (M51). + They infer Xsrn from a combination of aand eemission., They infer $\Sigma_{\rm SFR}$ from a combination of and emission. +" Green points show 500ppc apertures from Rahmanetal.(2010), who sample mainly the spiral arms of 44254."," Green points show pc apertures from \citet{RAHMAN10}, who sample mainly the spiral arms of 4254." + The points shown here reflect aas derived from FUV and eemission., The points shown here reflect as derived from FUV and emission. + Red points indicate ppc apertures covering the central 4.1x kkpc? of 55194 (M51) from Blancetal., Red points indicate pc apertures covering the central $4.1\times4.1$ $^{2}$ of 5194 (M51) from \citet{BLANC09}. + They infer ffrom extinction (2009)..corrected eemission using integral field unit observations., They infer from extinction corrected emission using integral field unit observations. + The left panel of Figure 3 labels these various studies and overplots our data., The left panel of Figure \ref{fig:lit} labels these various studies and overplots our data. + Figure 3 shows that these measurements sweep out a distinct part of Xsgg-Xgo space., Figure \ref{fig:lit} shows that these measurements sweep out a distinct part of $\Sigma_{\rm SFR}$ $\Sigma_{\rm H2}$ space. +" Most data scatter between THz,=10? and 10? yr and our measurements lie near the center of the distribution.", Most data scatter between $\tau_{\rm Dep}^{\rm H2} = 10^9$ and $10^{10}$ yr and our measurements lie near the center of the distribution. + The right panel in Figure 3 shows this most clearly: we take the simplistic approach of treating all of the literature data equally (shown as gray points) and construct the same running median that we use on our own data., The right panel in Figure \ref{fig:lit} shows this most clearly: we take the simplistic approach of treating all of the literature data equally (shown as gray points) and construct the same running median that we use on our own data. + The literature average (red points) agrees strikingly well with our measurements (black points)., The literature average (red points) agrees strikingly well with our measurements (black points). + This implies that our results are robust with respect to the choice of tracers or experimental setup., This implies that our results are robust with respect to the choice of tracers or experimental setup. +" The literature sample as a whole also suggests that Toe,©2.3 Gyr in nearby disks and that Top is a fairly weak function of ΣΗ2.", The literature sample as a whole also suggests that $\tau_{\rm Dep}^{\rm H2} \approx 2.3$ Gyr in nearby disks and that $\tau_{\rm Dep}^{\rm H2}$ is a fairly weak function of $\Sigma_{\rm H2}$. +" Using new IRAM 30m CO J=2>1 maps from the HERACLES survey, we determine the relation between ssurface density,€go,, and SFR surface density,Xsrn,, in 30 nearby disk galaxies."," Using new IRAM 30m CO $J=2\rightarrow1$ maps from the HERACLES survey, we determine the relation between surface density, and SFR surface density, in 30 nearby disk galaxies." + T'his significantly extends the number of galaxies (by more than a factor of four) and the range of galaxy properties probed compared to Bigieletal. , This significantly extends the number of galaxies (by more than a factor of four) and the range of galaxy properties probed compared to \citet{BIGIEL08}. . +We present our main results for a common physical (2008)..resolution of kkpc., We present our main results for a common physical resolution of kpc. +" We find a remarkably constant molecular gas consumption time TDop©2.35 Gyr (including helium) with a 1σ scatter of ddex (e 75%) and little dependence of 754,on Xo over the range Xg» 5-100 Mo pc7?.", We find a remarkably constant molecular gas consumption time $\tau_{\rm Dep}^{\rm H2} \approx 2.35$ Gyr (including helium) with a $\sigma$ scatter of dex $\approx 75\%$ ) and little dependence of $\tau_{\rm Dep}^{\rm H2}$ on $\Sigma_{\rm H2}$ over the range $\Sigma_{\rm H2} \sim 5$ $100$ $_\odot$ $^{-2}$. +" 'This extends and reinforces the conclusions of Bigielal.(2008) and Leroyetal.(2008) that the star formation rate per unit H2 in the disks of massive star-forming galaxies is, to first order, constant."," This extends and reinforces the conclusions of \citet{BIGIEL08} and \citet{LEROY08} + that the star formation rate per unit $_2$ in the disks of massive star-forming galaxies is, to first order, constant." +" We interpret this as strong, yet indirect, evidence that the disks of nearby spiral galaxies are populated by GMCs forming stars in a relatively uniform manner."," We interpret this as strong, yet indirect, evidence that the disks of nearby spiral galaxies are populated by GMCs forming stars in a relatively uniform manner." + We caution that theseresults are specific to disk galaxies and scales on which we average over many GMCs — they may be expected to break down at very high surface densities and, We caution that theseresults are specific to disk galaxies and scales on which we average over many GMCs — they may be expected to break down at very high surface densities and +"We have discovered a new bright transient N-rav. source in M31 at R.A.=00:43:09.940 40.65"". Dec.—41:23:32.49 £0.66"".","We have discovered a new bright transient X-ray source in M31 at R.A.=00:43:09.940 $\pm 0.65''$, Dec.=41:23:32.49 $\pm 0.66''$." + We have named the source CNOMSI JO04309.9+412332)0 and given it the shorter name of 13-127., We have named the source CXOM31 J004309.9+412332 and given it the shorter name of r3-127. + This source was active for at least 5 months during 2004. but it has not been seen before or since. even in survevs with limiting fluxes nearly a factor of 100 fainter than our brightest detection of r3-12T.," This source was active for at least 5 months during 2004, but it has not been seen before or since, even in surveys with limiting fluxes nearly a factor of 100 fainter than our brightest detection of r3-127." + The observed X-ray lighteurve was double-peaked. hinting (hat (his source may be of a similar nature to some Galactic NRNe with complex lighteurves like NTE J1550-564 or GRO J1655-40 2004).," The observed X-ray lightcurve was double-peaked, hinting that this source may be of a similar nature to some Galactic XRNe with complex lightcurves like XTE J1550-564 or GRO J1655-40 \citep{mcclintock2004}." +. The X-ray spectrum of the source was soft. as is tvpical for LMXDs.," The X-ray spectrum of the source was soft, as is typical for LMXBs." + It was well-fitted bv both absorbed power-law ancl absorbed disk blackbodsy models. although the absorbed disk blackbocly fits were somewhat better.," It was well-fitted by both absorbed power-law and absorbed disk blackbody models, although the absorbed disk blackbody fits were somewhat better." + The spectrum appeared mareinally softer curing the second half of the 5-month outburst., The spectrum appeared marginally softer during the second half of the 5-month outburst. + The best fit model had an inner disk temperature of 0.8 keV and an absorption-corrected 0.37 keV peak Iuminositv of 1.1x10* erg ! on 04-Oct-2004., The best fit model had an inner disk temperature of 0.8 keV and an absorption-corrected 0.3–7 keV peak luminosity of $\times$ $^{37}$ erg $^{-1}$ on 04-Oct-2004. + CoordinatedLST ACS observations of the position of r3-127 revealed no stars brighter that MgcO.1. confirming 138-127 is not an HMXND.," Coordinated ACS observations of the position of r3-127 revealed no stars brighter that $_B\sim0.1$, confirming r3-127 is not an HMXB." + The observations also detected. one variable star al high confidence within the error ellipse of (he N-vav outburst., The observations also detected one variable star at high confidence within the error ellipse of the X-ray outburst. + This star is (he strongest candidate counterpart of (he X-ray transient source., This star is the strongest candidate counterpart of the X-ray transient source. + The counterpart candidate brightened when our data suggest the N-rav. source was faint. but the complexitv. of the lighteurve suggests such optical variations are reasonable.," The counterpart candidate brightened when our data suggest the X-ray source was faint, but the complexity of the lightcurve suggests such optical variations are reasonable." + The highest optical ancl X-ray luminosity measurements vield a prediction for the orbital period of 13-127 of 5 days., The highest optical and X-ray luminosity measurements yield a prediction for the orbital period of r3-127 of $^{+3.7}_{-1.2}$ days. + This predicted. period range is large. and it includes the periods of many Galactic LAINB (ransient svstenis.," This predicted period range is large, and it includes the periods of many Galactic LMXB transient systems." + The location and outburst date of r3-127. along with those of the other transient sources followed with 4STin 2004 (s1-36. r2-70. and 12-71: Williamsetal.2005a.b.c.. respectively). are consistent with the spatial distribution aud rate of transients measured in (2004)..," The location and outburst date of r3-127, along with those of the other transient sources followed with in 2004 (s1-86, r2-70, and r2-71; \citealp{williams2005bh1,williams2005bh2,williams2005bh4}, respectively), are consistent with the spatial distribution and rate of transients measured in \citet{williams2004hrc}." + We continue to find... 1 new transient source each month. ancl about half of them are in the bulge (within ~7 “of the nucleus).," We continue to find $\lap$ 1 new transient source each month, and about half of them are in the bulge (within $\sim$ $'$ of the nucleus)." + None of these recent events has appeared in a cluster or shown a high-mass secondary. suggesting that the outbursts are not associated with star formation.," None of these recent events has appeared in a cluster or shown a high-mass secondary, suggesting that the outbursts are not associated with star formation." + Support for this work was provided by NASA through erant number GO-9087 from the Space Telescope Science Institute and through erant number GO-3103X [rom the X-Ray Center., Support for this work was provided by NASA through grant number GO-9087 from the Space Telescope Science Institute and through grant number GO-3103X from the X-Ray Center. + MIRG acknowledges support from NASA LTSÀ grant. NAG5-10839., MRG acknowledges support from NASA LTSA grant NAG5-10889. + JEM acknowledges support from NASA ADP erant NNG-O5GB31C., JEM acknowledges support from NASA ADP grant NNG-05GB31G. +emission (see below). aud show the resultant images in Figure 1..,"emission (see below), and show the resultant images in Figure \ref{im}." + Although taken with the same instrument. the data sets span a range of exposure times aud oll-anis distances.," Although taken with the same instrument, the data sets span a range of exposure times and off-axis distances." + Iu the case of the data. we mace use of ouly the EPIC-PN data. from the standard. pipeline in the XMM-SÁS calibration package.," In the case of the data, we made use of only the EPIC-PN data, from the standard pipeline in the XMM-SAS calibration package." + These data were liltered in the energy range kkeV. aud the resultant unages are also shown iu Figure 1...," These data were filtered in the energy range keV, and the resultant images are also shown in Figure \ref{im}." + We performed no further processing ou auy of these archival data. aud use them only [or comparisou purposes while looking lor transient sources (8??)).," We performed no further processing on any of these archival data, and use them only for comparison purposes while looking for transient sources \ref{bob}) )." + Iu addition to the six observations discussed iu this paper. there were two observations by aud two byXMAI-Newton.," In addition to the six observations discussed in this paper, there were two observations by and two by." + The data were taken in continuous-clocking iode. aud so are not useful for analysis either of exteuced emission or faint. [ield sources because of the much higher background.," The data were taken in continuous-clocking mode, and so are not useful for analysis either of extended emission or faint field sources because of the much higher background." + For theXA observations. tlie spacecraft orientation was such that the locations of faint field sources shown in Fieuree 1 were not iimaged.e aud againe the PSF is too broad aud the background too Ligh to see extended. emission.," For the observations, the spacecraft orientation was such that the locations of faint field sources shown in Figure \ref{im} were not imaged, and again the PSF is too broad and the background too high to see extended emission." + We cousider neither observation furtlier. except to note the poiut source [lux measured byChandra. below.," We consider neither observation further, except to note the point source flux measured by, below." + From the tages in Figure 1.. it appears that iis a bright unresolved point source with extended emission around it: the extended emission is seen most clearly in the latest observation (bottom right pauel).," From the images in Figure \ref{im}, it appears that is a bright unresolved point source with extended emission around it; the extended emission is seen most clearly in the latest observation (bottom right panel)." + We split our results into three sectious: the spectrum of the bright point source. which is essentially unaffected by [aint exteuclec enission. the properties of the extended emission. which includes some contribution by the bright sources PSF. aud a description ofthe trausieut sources iu the field.," We split our results into three sections: the spectrum of the bright point source, which is essentially unaffected by faint extended emission, the properties of the extended emission, which includes some contribution by the bright source's PSF, and a description of the transient sources in the field." + From the ACIS data of 2009 October 30. we extracted the spectrum of the poiut-like source correspondiug to5039.. centered at R.A.=276256278. decl.=—1E8ISTI (12000). using the CLAO taskpsextract.," From the ACIS data of 2009 October 30, we extracted the spectrum of the point-like source corresponding to, centered at ${\rm R.A.}=276\fdg56278$, ${\rm decl.}=-14\fdg84871$ (J2000), using the CIAO task." + We picked background regions far from the source. aud as [ree of point sources as possible. vet large enough (total area 51.100 aresec?) that the background spectrum be well-determined.," We picked background regions far from the source, and as free of point sources as possible, yet large enough (total area 51,100 $^2$ ) that the background spectrum be well-determined." + The extraction regions are shown on Figure 1.., The extraction regions are shown on Figure \ref{im}. + We fitted an absorbed. power-law (PL) model to the spectrum. extracted from the r=5” aperture. using the package.," We fitted an absorbed power-law (PL) model to the spectrum, extracted from the $r=5\arcsec$ aperture, using the package." + We grouped the counts iu 25-count bius aud [fitted in the, We grouped the counts in 25-count bins and fitted in the +law (tBeuermaunetal.1999).. IHere. is the flux at ay aud ἂν are respectively the pre-breakFy aud post-breakty. light curve slopes aud i is a numerical factor controlling the sharpucss of the break.,"law \citep{Beuermann1999}, Here, $F_j$ is the flux at $t_j$, $-\alpha_1$ and $-\alpha_2$ are respectively the pre-break and post-break light curve slopes and $n$ is a numerical factor controlling the sharpness of the break." + The light curve break occurs when the jet euters the sidewavys expaudiug regime (calledexponentialregineiuRhoads1999) aud the observer receives light from the entire jet surface., The light curve break occurs when the jet enters the sideways expanding regime \citep[called exponential regime in][]{Rhoads1999} and the observer receives light from the entire jet surface. + The break time can be approximated as that point in time when 0=1/T. where 0 is the opening anele of the jet aud D is the Loreutz factor of the relativistically moving shock frout.," The break time can be approximated as that point in time when $\theta\approx 1/\Gamma$, where $\theta$ is the opening angle of the jet and $\Gamma$ is the Lorentz factor of the relativistically moving shock front." + Using analytical approximations frou Johannessonctal.(2005) we find that where £y is the total enerev injected iuto the jet. ay is the constant interstellar πούπι particle density. Jy is the initial opening angle of the jet in radians aud+ is the redshift of the burst.," Using analytical approximations from \citet{Johannesson2006} we find that where $E_0$ is the total energy injected into the jet, $n_0$ is the constant interstellar medium particle density, $\theta_0$ is the initial opening angle of the jet in radians and$z$ is the redshift of the burst." + This formulation differs slightly from the oue eiven in Rhoads(1999).. because we choose to use the energv injected iuto the jet rather than the isotropic equivalentοποίον iu order to better isolate Jy in the equation.," This formulation differs slightly from the one given in \citet{Rhoads1999}, because we choose to use the energy injected into the jet rather than the isotropic equivalentenergy in order to better isolate $\theta_0$ in the equation." +" As is often done when fitting CRB afterelows (οιο,Wi-jersetal.1997:Beuecrimaun1999:Zeh 2005).. we fitted the svuthetic B-baud light curves with both a sharply broken power law as in equation (1)) aud a sxinoothlv joined broken power law as m equation (2))."," As is often done when fitting GRB afterglows \citep[e.g.][]{Wijers1997,Beuermann1999,Zeh2005}, we fitted the synthetic R-band light curves with both a sharply broken power law as in equation \ref{eq:brapp}) ) and a smoothly joined broken power law as in equation \ref{eq:Beuermann}) )." +" These will hereafter be referred to as sharp fits and snooth fits. respectively,"," These will hereafter be referred to as sharp fits and smooth fits, respectively." + The Levenhbere-\larquardt uethod of Pressetal.(1996) was used to nüuinmuize 1ο A7 value of the fit in both cases., The Levenberg-Marquardt method of \citet{nr} was used to minimize the $\chi^2$ value of the fit in both cases. + Althoush the y.arting point of the fitting procedure was chosen as 10 theoretically correct values of tj. 64. a2 and Fy. it lid not result in an acceptable fit iu every case.," Although the starting point of the fitting procedure was chosen as the theoretically correct values of $t_j$, $\alpha_1$, $\alpha_2$ and $F_j$, it did not result in an acceptable fit in every case." + Ouly rose events where the 4? per deerce of freedom is less ian d for the smooth fits aud 2 for the sharp fits were selected for further study., Only those events where the $\chi^2$ per degree of freedom is less than 1 for the smooth fits and 2 for the sharp fits were selected for further study. + A higher threshold was used or the sharp fits since the numerically. eeuerated lelt curves are very sinooth aud uot well represented by a sharply broken power law (see fimeuro 1))., A higher threshold was used for the sharp fits since the numerically generated light curves are very smooth and not well represented by a sharply broken power law (see figure \ref{fig:exlc}) ). + About half of the fits fulfilled those requirements in both cases., About half of the fits fulfilled those requirements in both cases. + Since GRB afterglow measurements normally extend from a few hours after the burst to about a mouth. we limited our data aud f; to this time range in the fitting procedure.," Since GRB afterglow measurements normally extend from a few hours after the burst to about a month, we limited our data and $t_j$ to this time range in the fitting procedure." + Using equation (3)). it can be shown that this range also limits the range of derivable opening angles to about 1.57-157.. depending on other burst parameters.," Using equation \ref{eq:t_jet}) ), it can be shown that this range also limits the range of derivable opening angles to about -, depending on other burst parameters." + With real data. this range of opening angles can be further reduced if there is a bright underline host or a supernova component making the afterglow light difficult to observe.," With real data, this range of opening angles can be further reduced if there is a bright underlying host or a supernova component making the afterglow light difficult to observe." +" The results for from the fitting procedure cau be used to find an estimatef; of the opening augle of the jet by inverting equation (3)). IHere. the opening angle is denoted by 0; to distinguish it from the known initial opening angle of the burst. Oy. frou, our munerical model calculation. although theoretically they should be equal."," The results for $t_j$ from the fitting procedure can be used to find an estimate of the opening angle of the jet by inverting equation \ref{eq:t_jet}) ), Here, the opening angle is denoted by $\theta_j$ to distinguish it from the known initial opening angle of the burst, $\theta_0$ , from our numerical model calculation, although theoretically they should be equal." +" The results for the derived. slopes. a, and 6». cau be used to find the value of p and equation (1)) gives two different. values. pp=(L3)|dl and po=ay."," The results for the derived slopes, $\alpha_1$ and $\alpha_2$, can be used to find the value of $p$ and equation \ref{eq:brapp}) ) gives two different values, $p_1 = (4/3)\alpha_1+1$ and $p_2 = \alpha_2$." + Comparison of the values obtained this way frou the fitting procedure to the paraueters known from the nunuerical model is shown in figure 2. as the distribution ofrelative differences between the derived parameters and the kuown model parauneters App. Apo/p aud Αθ. where," Comparison of the values obtained this way from the fitting procedure to the parameters known from the numerical model is shown in figure \ref{fig:differences} as the distribution ofrelative differences between the derived parameters and the known model parameters: $\Delta +p_1/p$ , $\Delta p_2/p$ and $\Delta \theta_j/\theta_0$ , where" +through coagulation in a high-density cuviromment (Abüolmo ot al.,through coagulation in a high-density environment (Maiolino et al. + 200110). and/or siugle-photou destruction of siall eraius in the strong high-euergv radiation feld (Laor Draine 1993).," 2001b), and/or single-photon destruction of small grains in the strong high-energy radiation field (Laor Draine 1993)." + Iu the exteuded scatteriug region seen ii our Wages. the latter would be conceivable. though the former πο! uot be the case.," In the extended scattering region seen in our images, the latter would be conceivable, though the former might not be the case." + It is possible that ταν chargnmg ac rcating of dust erains by the AGN continu is able to sclectively destroy parts of the dust population (Ixrolik Rhoads 2001)., It is possible that X-ray charging and heating of dust grains by the AGN continuum is able to selectively destroy parts of the dust population (Krolik Rhoads 2001). + We have presented UST iniagiug polarimetry data of the Sevtert 2 ealaxy Mxk 3., We have presented HST imaging polarimetry data of the Seyfert 2 galaxy Mrk 3. + The UV and near-UV radiation is highly polarized. aud he polarization position angle distribution is controsvinnetric. consistent with scattering of radiation frou a compact source.," The UV and near-UV radiation is highly polarized, and the polarization position angle distribution is centrosymmetric, consistent with scattering of radiation from a compact source." + We have determined he location of the hidden uneleus as the center of lis centrosvunuetiic pattern., We have determined the location of the hidden nucleus as the center of this centrosymmetric pattern. +" The polarized fiux is extended out to over 37 (—1 kpc) from the imcleus. but most of it is from the region within ~1"" (—300 pe) from the nucleus."," The polarized flux is extended out to over $3''$ $\sim 1$ kpc) from the nucleus, but most of it is from the region within $\sim 1''$ $\sim 300$ pc) from the nucleus." + The polarized fux distributions in the two road baud filters are foun to be different. aud roni these two images we have obtained the color map of the polarized fiux.," The polarized flux distributions in the two broad band filters are found to be different, and from these two images we have obtained the color map of the polarized flux." + In the southern edee region. the color is significantly redder han a Sevfert 1l color. indicating reddening.," In the southern edge region, the color is significantly redder than a Seyfert 1 color, indicating reddening." + Iu contrast. the color seems to be bluened i some regions. sugecsting optically-thin dust scatteriug.," In contrast, the color seems to be bluened in some regions, suggesting optically-thin dust scattering." + ILowever. some bright kuots have a color similar to that of a Sevfert 1 uncleus. which woul inply erav scattering.," However, some bright knots have a color similar to that of a Seyfert 1 nucleus, which would imply gray scattering." + The receu Chandra observation sugeests rather large amount of extended X-rav scattered continmuuu., The recent Chandra observation suggests rather large amount of extended X-ray scattered continuum. + The ratio of the UV. scatterer flux to this XN-rav scattered. flux is simular to tha of Sevtert 1s., The ratio of the UV scattered flux to this X-ray scattered flux is similar to that of Seyfert 1s. + This indicates rather low scaeringo efücieucy iu the UV. much lower than the optically-thin scatteriug by Calactic dust.," This indicates rather low scattering efficiency in the UV, much lower than the optically-thin scattering by Galactic dust." + These two properties. naunelv the erav scattering aud low UV scatteriug efficiency. might be explained bv chuupy opaque dust scatteriug. or alternatively these could be intrinsic to nuclear dust grains which nüsht have a size distribution donuünated by large eram.," These two properties, namely the gray scattering and low UV scattering efficiency, might be explained by clumpy opaque dust scattering, or alternatively these could be intrinsic to nuclear dust grains which might have a size distribution dominated by large grains." +" Ποπονο, a simple explanation bv electron scattering is also viable."," However, a simple explanation by electron scattering is also viable." + Support for this work was provided bx NASA through erant GO-6702 to L. Nav from the Space Telescope Scicuce Institute. which is operated by AURA. Inc.. under NASA contract. NAS5-26555.," Support for this work was provided by NASA through grant GO-6702 to L. Kay from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555." + This work is based on observations with the NASA/ESA ITubble Space Telescope. obtained at the Space Telescope Science Tustitute.," This work is based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute." + The authors appreciate Masao Sako who kindly looked at the Chandra data upon our request., The authors appreciate Masao Sako who kindly looked at the Chandra data upon our request. + The authors also thank the referee for carefully reading the manuscript aud providing helpful commucuts., The authors also thank the referee for carefully reading the manuscript and providing helpful comments. + This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated bv the Jet Propulsion Laboratory. California Tustitute of Technology. under coutract with the National Acronautics and Space Aciiuistration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." + ALIS. was a Guest User. Canadian Astronomy Data Centre. which is operated by the Terzhbere Iustitute of Astroplivsics. National Research Council of Canada.," M.K. was a Guest User, Canadian Astronomy Data Centre, which is operated by the Herzberg Institute of Astrophysics, National Research Council of Canada." +series c(/) is an IMFE (IIuangetal.L998).,series $x(t)$ is an IMF \citep{Huang1998}. +. An IME satisfies the following (wo conditions: (1) the number of extrema and the number of zero crossings must be identical or differ bv one: and (2) at any of the points in the series. (he mean value of the upper envelope (defined by the local maxima) and the lower envelope (defined bv the local minima) is zero (IIuangetal.1993).," An IMF satisfies the following two conditions: (1) the number of extrema and the number of zero crossings must be identical or differ by one; and (2) at any of the points in the series, the mean value of the upper envelope (defined by the local maxima) and the lower envelope (defined by the local minima) is zero \citep{Huang1998}." +. Because the real data are usually not IME. it is diffieult to directly apply the Hilbert transform on primary data in most cases.," Because the real data are usually not IMF, it is difficult to directly apply the Hilbert transform on primary data in most cases." + To address this issue. proposed the EXD method to decompose a time series into several IMESs such that the Hilbert Transform is applicable.," To address this issue, \citet{Huang1998} proposed the EMD method to decompose a time series into several IMFs such that the Hilbert Transform is applicable." + The EMD method. assumes that any time series consists of some oscillatory components., The EMD method assumes that any time series consists of some oscillatory components. + The decomposition scheme utilizes the actual (nme series lor (he construction ol the decomposition base rather than decomposing it into a prescribed set of base hunctions., The decomposition scheme utilizes the actual time series for the construction of the decomposition base rather than decomposing it into a prescribed set of base functions. +" The decomposition is achieved by iterative ""sifüng processes for extracting modes by identification of local extrema and subtraction of local means (παςetal.1993).", The decomposition is achieved by iterative “sifting” processes for extracting modes by identification of local extrema and subtraction of local means \citep{Huang1998}. +. The iterations are terminated by a criterion of convergence., The iterations are terminated by a criterion of convergence. + For details of the sifting. relerence is here made to IInangetal.(1998).," For details of the sifting, reference is here made to \citet{Huang1998}." +". Under the procedures of EMD. (he original time series wl) is decomposed according to where ¢;s are IMIFs ancl 7, is a residue."," Under the procedures of EMD, the original time series $x(t)$ is decomposed according to where $c_i$ 's are IMFs and $r_n$ is a residue." + For a time series with infinite length. the decomposition satisfies the properties that the decomposed components are orthogonal to each other and form a complete set.," For a time series with infinite length, the decomposition satisfies the properties that the decomposed components are orthogonal to each other and form a complete set." + For a (ime series with finite length: however. the orthogonality of the decomposition max not strictly hold.," For a time series with finite length; however, the orthogonality of the decomposition may not strictly hold." + In this case. we mininüze the orthogonality index (OI) defined by to make (he decomposition “unique.," In this case, we minimize the orthogonality index (OI) defined by to make the decomposition “unique”." + Furthermore. if the original data is noisy or contains high-Irequency intermittent signals. (he decomposition may suffer the mode mixing," Furthermore, if the original data is noisy or contains high-frequency intermittent signals, the decomposition may suffer the mode mixing" +where Apis the dillerence in velocity between the top and bottom of the accretion evlinder and rà=CAL(T2|0: is the accretion radius.,where $\Delta \rho$ is the difference in velocity between the top and bottom of the accretion cylinder and $r_A=GM/(v^2+c_s^2)$ is the accretion radius. + Numerical simulations confirm that this formula is correct to order of magnitude (Πο 1999)., Numerical simulations confirm that this formula is correct to order of magnitude (Ruffert 1999). + Phe observed density luetuations in our galaxy scale as op/p(L107em)? (Armstrong. Rickett. Spangler 1995). extending down to a scale of ~107 em.," The observed density fluctuations in our galaxy scale as $\delta \rho /\rho \sim (L/10^{18} {\rm cm})^{1/3}$ (Armstrong, Rickett, Spangler 1995), extending down to a scale of $\sim 10^{8}$ cm." + The exponent of this scaling is nearly consistent with a Ixolmogorov spectrum of density (Dubinski et al., The exponent of this scaling is nearly consistent with a Kolmogorov spectrum of density (Dubinski et al. + 1995)., 1995). +" Evaluating this at £=2ry. we can then find the radius of the resulting accretion disce. raise. by equating the angular momentum oft the gas"" withEM the Keplerian-de angular""END momentum due to the black""au hole. lige,—=vCfMra.B """," Evaluating this at $L=2 r_A$, we can then find the radius of the resulting accretion disc, $r_{\rm disc}$, by equating the angular momentum of the gas with the Keplerian angular momentum due to the black hole, $l_{\rm Kep} = +\sqrt{GMr_{\rm disc}}$." +"pThis1 gives""e So. we see that a disce will almost always form in interstcllar accretion."," This gives So, we see that a disc will almost always form in interstellar accretion." + A similar argument is given in Fujita et al. (, A similar argument is given in Fujita et al. ( +1998) for the case of molecular clouds. for which the slope of velocity Huctuations is similar to that expected by a Ixolmogorov spectrum (Larson 1981).,"1998) for the case of molecular clouds, for which the slope of velocity fluctuations is similar to that expected by a Kolmogorov spectrum (Larson 1981)." + Ehe neutral interstellar medium seems to follow a power-law with a similar slope (Lazarian Pogosvan 2000). which will also lead to non-zero accreted angular momentum: however. the length scales probed in molecular anc atomic gas are much larger than the scale of the accretion radius.," The neutral interstellar medium seems to follow a power-law with a similar slope (Lazarian Pogosyan 2000), which will also lead to non-zero accreted angular momentum; however, the length scales probed in molecular and atomic gas are much larger than the scale of the accretion radius." + The aceretion time scale for the clisk scales as fy=Och(GALMice)E)1/2(raiseAh)? where f is the height. of the disc ancl ass is the ratio of the viscous stress to the pressure in the disk.," The accretion time scale for the disk scales as $t_{d} = +\alpha_{SS}^{-1}(GM/r_{\rm disc}^3)^{-1/2} +(r_{\rm disc}/h)^2 $ where $h$ is the height of the disc and $\alpha_{SS}$ is the ratio of the viscous stress to the pressure in the disk." + H£ the velocity and censity fields of the ISAT are incoherent on the scale of these Ductuations. then the angular momentum can change on a time scale of {ων=rie as gas will be accereted with the angular momentum vector pointing in a dillerent direction after this time scale.," If the velocity and density fields of the ISM are incoherent on the scale of these fluctuations, then the angular momentum can change on a time scale of $t_a=r_A/v$ as gas will be accreted with the angular momentum vector pointing in a different direction after this time scale." +" Thus. the angular momentum of the disc can be reduced due to a random walk of the accreted angular momentum vector i£ £,«fy."," Thus, the angular momentum of the disc can be reduced due to a random walk of the accreted angular momentum vector if $t_a \ll t_d$." + We estimate which indicates that there may only be a slight reduction in the angular momentum since these time scales are comparable., We estimate which indicates that there may only be a slight reduction in the angular momentum since these time scales are comparable. + The residual angulare momentum means that we use spherical-accretion formulae for the luminosity. but we must estimate the ellicieney. of the accretion disc that forms.," The residual angular momentum means that we use spherical-accretion formulae for the luminosity, but we must estimate the efficiency of the accretion disc that forms." +" We assume that the black holes radiate a spectrum with spectral index a=1. where £5x£9"". consistent with the typical spectrum. of black-hole X-ray binaries. so that equal energy. is emitted per unit. decade of energy."," We assume that the black holes radiate a spectrum with spectral index $\alpha=1$, where $F_\nu \propto \nu^{-\alpha}$, consistent with the typical spectrum of black-hole X-ray binaries, so that equal energy is emitted per unit decade of energy." +" We cleline Li, as the luminosity from 1 to 1000 Rad (13.6 eV). so the ellicienev is Goa=LionGuo)."," We define $L_{\rm ion}$ as the luminosity from 1 to 1000 Ryd (13.6 eV), so the efficiency is $\epsilon_{\rm ion}= L_{\rm ion}/(\dot M c^2)$." + Estimates of the accretion rate in Cvgnus X-1 indicate that it is accreting with an X-ray ellicienev of cia~LO+ (Shapiro “Veukolsky 1983)., Estimates of the accretion rate in Cygnus X-1 indicate that it is accreting with an X-ray efficiency of $\epsilon_{\rm ion}\sim 10^{-1}$ (Shapiro Teukolsky 1983). + However. at low accretion rates the density of the gas decreases. so it may not be able to cool. reducing the radiative clliciency.," However, at low accretion rates the density of the gas decreases, so it may not be able to cool, reducing the radiative efficiency." + By estimating the mass aeeretion rates in black-hole X-ray binaries and. X-ray. Iuminosities in the quiescent state. Lasota (2000) concludes that the 2]O keV elliciency is about 2.10° assumine that this luminosity is solely due to accretion. implying ei;10.7.," By estimating the mass accretion rates in black-hole X-ray binaries and X-ray luminosities in the quiescent state, Lasota (2000) concludes that the 2–10 keV efficiency is about $2\times 10^{-6}$ assuming that this luminosity is solely due to accretion, implying $\epsilon_{\rm ion} \sim 10^{-5}$." + Low upper limits on the X-ray Bondi-acceretion elliciencics are inferred for some supermassive black holes in elliptical galaxies (Loewenstein et al., Low upper limits on the X-ray Bondi-accretion efficiencies are inferred for some supermassive black holes in elliptical galaxies (Loewenstein et al. + 2001)., 2001). +" The Galactic-centre black hole has an N-rav ellicieney of ~4.102."" in the 210 keV band for a Bondi-Llovle accretion rate of LOM. * (Baganoll et al."," The Galactic-centre black hole has an X-ray efficiency of $\sim 4\times +10^{-8} - 2\times10^{-6}$ in the 2–10 keV band for a Bondi-Hoyle accretion rate of $10^{-6} {\rm M}_\odot$ $^{-1}$ (Baganoff et al." + 2001)., 2001). + Thus. we parameterize our results in ternis of an unknown X-ray elliciency.," Thus, we parameterize our results in terms of an unknown X-ray efficiency." + For certain ranges of parameters. the disc may be unstable to the hydrogen-ionisation disc instability (Lasota 2001). creating intermittent outbursts of higher Iuminosity between long periods of quiescence. with changes in luminosity of 10”.," For certain ranges of parameters, the disc may be unstable to the hydrogen-ionisation disc instability (Lasota 2001), creating intermittent outbursts of higher luminosity between long periods of quiescence, with changes in luminosity of $10^{5}$." + We will discuss the possible effect this may have on the number of detectable sources in section 6.2., We will discuss the possible effect this may have on the number of detectable sources in section 6.2. + The gas in the vicinity of the black hole will be heated by the ionising radiation field produced by accretion., The gas in the vicinity of the black hole will be heated by the ionising radiation field produced by accretion. + Lf the temperature rises enough. then the accretion radius. and thus the acerction rate. will decrease (Shvartsman 1971. Ostriker et al.," If the temperature rises enough, then the accretion radius, and thus the accretion rate, will decrease (Shvartsman 1971, Ostriker et al." + 1976)., 1976). + For an a=lL spectrum. the mean opacity from 1-1000 νά of neutral eas with cosmic abundance is tou=3.87101 cm?2 per hydrogen atom.," For an $\alpha=1$ spectrum, the mean opacity from 1-1000 Ryd of neutral gas with cosmic abundance is $\sigma_{\rm cold}=3.87\times 10^{-18}$ $^{2}$ per hydrogen atom." + The heating rate is then given bv Lf=Longesaa/(AxAU). where 2 is the distance [rom the black hole.," The heating rate is then given by $H=L_xn_H\sigma_{\rm cold} +/(4\pi R^2)$, where $R$ is the distance from the black hole." + Por teniperatures smaller than ~105 Ix and for a small ratio of radiation energy. density to gas energy. density. the heating rate ereatly. exceeds the cooling rate.," For temperatures smaller than $\sim 10^4$ K and for a small ratio of radiation energy density to gas energy density, the heating rate greatly exceeds the cooling rate." + Consider a [uid element. directly in front of the path of a moving black hole., Consider a fluid element directly in front of the path of a moving black hole. + As the black hole approaches with velocity ος the ratio of the total heating rate to the initial energy. density. eo of the gas is where ei4 is the total energy density absorbed by a [uid element (neglecting cooling). e= ικα Land Y=7410 Ix. Thus. even for small elliciencies the gas is strongly heated outside the accretion radius.," As the black hole approaches with velocity $v$ , the ratio of the total heating rate to the initial energy density, $e_0$ of the gas is where $e_{\rm tot}$ is the total energy density absorbed by a fluid element (neglecting cooling), $v=v_{40} 40$ km $^{-1}$ and $T=T_4 10^4$ K. Thus, even for small efficiencies the gas is strongly heated outside the accretion radius." + Once HE and He areionized. the," Once H and He areionized, the" +lligh-energv. gamma ravs traveling cosmological distances can interact with the diffuse UV. optical. ancl LR radiation fields in) clectron-positron pair production interactions. leading to an ellective optical depth for VILE sources (Nikishoy1962:Gould&Sehireder1967).,"High-energy gamma rays traveling cosmological distances can interact with the diffuse UV, optical, and IR radiation fields in electron-positron pair production interactions, leading to an effective optical depth for VHE sources \citep{nikishov62,gould&schreder67}." +. A recent technique in gamma-ray astronomy has been to use observations of relatively nearby. blazars observed by. Imaging Atmospheric Cherenkov Telescopes (LACIES) to constrain the EBL (e.g. Aharonianetal.2006:Mazin&Raue2007:Albertct 2008a)).," A recent technique in gamma-ray astronomy has been to use observations of relatively nearby blazars observed by Imaging Atmospheric Cherenkov Telescopes (IACTs) to constrain the EBL (e.g. \citealp{aharonian06,mazin&raue07,albert08}) )." + While blazars have been the primary target of efforts to detect. the cllects of EBL attenuation in high-cnerey spectra. another exciting possibility is to see these same elfects in observations of GRBs.," While blazars have been the primary target of efforts to detect the effects of EBL attenuation in high-energy spectra, another exciting possibility is to see these same effects in observations of GRBs." + Until recently. limitations on the cllective areas and energy ranges of high-energv experiments. and their ability to respond sulliciently quickly to transient. events have hindered observations at GeV energies that might reveal evidence of this phenomenon.," Until recently, limitations on the effective areas and energy ranges of high-energy experiments, and their ability to respond sufficiently quickly to transient events have hindered observations at GeV energies that might reveal evidence of this phenomenon." + The EGRET experiment on theObservatory (CORO) operated with energy range 20 MeV GeV and elleetive area ~LOO0 eng., The EGRET experiment on the ) operated with energy range 20 MeV--30 GeV and effective area $\sim$ 1000 $^2$. + This experiment detected. a total of 5 bursts above 30 MeV. in 4+ vears of operation. including 4 individual photons above 1: GeV (Dingus1995).," This experiment detected a total of 5 bursts above 30 MeV in 4 years of operation, including 4 individual photons above 1 GeV \citep{dingus95}." +. While these EGRET detections do suggest the presence. of a verv-high energy. component in the spectrum of some CGltDs. it is dillicult to craw more conclusions due to the small number of hish-energv. gamma ," While these EGRET detections do suggest the presence of a very-high energy component in the spectrum of some GRBs, it is difficult to draw more conclusions due to the small number of high-energy gamma rays detected." +CORO detected thousands of GBs at energies between 20 keV and 2 MeV. (Paciesasetal.1999).," At the same time, the BATSE instrument on CGRO detected thousands of GRBs at energies between 20 keV and 2 MeV \citep{paciesas99}." +.. Phe mission jas been finding bursts at arate of about S per month since its launch in December 2004 at energies between 15 and 150 keV. (Sakamotoetal.2008)., The mission has been finding bursts at a rate of about 8 per month since its launch in December 2004 at energies between 15 and 150 keV \citep{sakamoto08}. +. Until. the launch of the in. 2008. the only other possibility. to view ügh-energv emüssion from GitBs was with grouncd-based," Until the launch of the in 2008, the only other possibility to view high-energy emission from GRBs was with ground-based" +images. the data were divided into annular rings one pixel wide.,"images, the data were divided into annular rings one pixel wide." + Within each annulus. we can calculate the mean. meclian or mode of the histogram.," Within each annulus, we can calculate the mean, median or mode of the histogram." + Cosmic rav events appear as outliers and. are therefore easily removed., Cosmic ray events appear as outliers and are therefore easily removed. + We achieved better results when removing the high density of stars across the field due to the low galactic latitude., We achieved better results when removing the high density of stars across the field due to the low galactic latitude. + For all fields. we obtained a short exposure image through the blocking filter without the etalon.," For all fields, we obtained a short exposure image through the blocking filter without the etalon." + This enabled. us to identify compact sources and to mask out these pixels., This enabled us to identify compact sources and to mask out these pixels. + Typically of the pixels were removed in this way., Typically of the pixels were removed in this way. + In order to) demonstrate. that the Uatliclding was adequate. we divided. cach summed. image into loft. and right. halves and then. cillerenced them (see Fig.," In order to demonstrate that the flatfielding was adequate, we divided each summed image into left and right halves and then differenced them (see Fig." + 2a)., \ref{left_right}$ $a$ ). + 1 heresidual forthebiiqhtesttineislessthanl'ofpeakintensil, The residual for the brightest line is less than of peak intensity. + Her ΠΠ ΤΙ sdas aml 0.061s," Across the full bandpass, the residual has a dispersion of 0.9 cts." + Lhe posit appears to be real (see below)., The positive residual feature at $\lambda$ 6564.12 appears to be real (see below). + In Fig., In Fig. + 2b. weshowourbestmodetfillothella line from the D lamp.," \ref{left_right}$ $b$, we show our best model fit to the line from the D lamp." + Once again. the residual is better than of peak intensity.," Once again, the residual is better than of peak intensity." + While our spectral bandpass is only40A... it. comprises tvpically 3 4 OLL lines. a &eocoronal line. Revnolds laver emission at both aand Nu|AG548.. and 2 continuum features from scattered. solar ancl lunar light.," While our spectral bandpass is only, it comprises typically $-$ 4 OH lines, a geocoronal line, Reynolds layer emission at both and, and $-$ 2 continuum features from scattered solar and lunar light." + Phese features. provide fundamental calibrations of serendipitous detections within the band., These features provide fundamental calibrations of serendipitous detections within the band. + f ΠΟΙΟ hrs rotationally excited. OLL molecules in the mesosphere and, The OH emission arises from vibrationally and rotationally excited OH molecules in the mesosphere and +Narrow-line Sevlert 1 galaxies (NLSIs) belong to a ubiquitous class of N-rav. luminous AGNs whose extreme spectral ancl variability properties have been the subject of intensive,Narrow-line Seyfert 1 galaxies (NLS1s) belong to a ubiquitous class of X-ray luminous AGNs whose extreme spectral and variability properties have been the subject of intensive +In Vig.,In Fig. + we compare the square of the sound speed.ος. of dillerent. solar models evolving within the presence of a halo of WIAIPS and the solar standard model. (Brun. ‘Turek-Chiezze Morel 1998).," 1, we compare the square of the sound speed,$c_s^2$, of different solar models evolving within the presence of a halo of WIMPs and the solar standard model (Brun, Turck-Chièzze Morel 1998)." + The changes induced by the presence of WIALPs are concentrated in the inner core within of the solar radius. typically seen in the profiles of the temperature. density and molecular weight.," The changes induced by the presence of WIMPs are concentrated in the inner core within of the solar radius, typically seen in the profiles of the temperature, density and molecular weight." + Indeed. the NIMPS are thermalized within the solar core and. are on Weplerian orbits around. the solar. center. interacting through clastic scattering with the solar nuclei. such as helium. anc thereby. providing an alternative mechanism of energy. transport other than radiation.," Indeed, the WIMPs are thermalized within the solar core and are on Keplerian orbits around the solar center, interacting through elastic scattering with the solar nuclei, such as helium, and thereby providing an alternative mechanism of energy transport other than radiation." + The result is a nearly Hat. temperature cistribution. leading to an isothermal core.," The result is a nearly flat temperature distribution, leading to an isothermal core." + Consequently. the central temperature is reduced.," Consequently, the central temperature is reduced." + “This reduction. of temperature has two main consequences: since central pressure support must be maintained. due to the hydrostatie equilibrium. the central density is increased in the solar models with WIAIPs. and since less hydrogen is burnt at the centre of the Sun. the central helium abundance ancl the central molecular weight are smaller than in standard solar models.," This reduction of temperature has two main consequences: since central pressure support must be maintained, due to the hydrostatic equilibrium, the central density is increased in the solar models with WIMPs, and since less hydrogen is burnt at the centre of the Sun, the central helium abundance and the central molecular weight are smaller than in standard solar models." + The increase of the central density and hydrogen partially olfset the ellect of lowering the central temperature in the central. production of energy., The increase of the central density and hydrogen partially offset the effect of lowering the central temperature in the central production of energy. + In fact. this is the reason why minor changes are required. to the initial helium abundance and. the mixing-length. parameter in order to produce a solar model of the Sun with the observed. luminosity anc solar radius.," In fact, this is the reason why minor changes are required to the initial helium abundance and the mixing-length parameter in order to produce a solar model of the Sun with the observed luminosity and solar radius." + This reaclily leads to a balance between the temperature. and the molecular weight in the core. leading to the peculiar profile of the square of the sound. speed. ezExαμ.," This readily leads to a balance between the temperature, and the molecular weight in the core, leading to the peculiar profile of the square of the sound speed, $c_s^2\propto T/\mu$." + This seers to be the case for most of the solar models within WIMP halos., This seems to be the case for most of the solar models within WIMP halos. + The balance between the temperature. and molecular weight is critical for the profile in the center of the star. leading to some of the profiles presented in lig.," The balance between the temperature and molecular weight is critical for the profile in the center of the star, leading to some of the profiles presented in Fig." + 1., 1. + In the same figure. we display the inversion of the sound. speed: obtained. from the data of the three seismic experiments on board the SOLIO satellite.," In the same figure, we display the inversion of the sound speed obtained from the data of the three seismic experiments on board the SOHO satellite." + Ht. follows from our analvsis that the presence of WIMPs in the solar core »oduces Changes in the solar sound speed of the same order | magnitude as the dilference between the sound. speed. of he standard solar model and the inverted sound speed., It follows from our analysis that the presence of WIMPs in the solar core produces changes in the solar sound speed of the same order of magnitude as the difference between the sound speed of the standard solar model and the inverted sound speed. + I is important to remark that the inversion of the sound speed still presents some uncertainty in the central region due to 10 lack of seismic data. mainly due to the small number of coustic modes that reach the nuclear region.," It is important to remark that the inversion of the sound speed still presents some uncertainty in the central region due to the lack of seismic data, mainly due to the small number of acoustic modes that reach the nuclear region." + Furthermore. 10 inversions are not very reliable at the surface. above ON'A of the solar radius. due to a poor description of the interaction of acoustic waves with the radiation field and the urbulent convection. namely. in the superadiabatie region (Lopes Gough 2001).," Furthermore, the inversions are not very reliable at the surface, above $98 \%$ of the solar radius, due to a poor description of the interaction of acoustic waves with the radiation field and the turbulent convection, namely, in the superadiabatic region (Lopes Gough 2001)." + Llowever. we can establish. with certainty that the difference between the inverted: souric specd and the theoretical sound speed is known with a xecision of 0.34 in the solar interior. within 95% of the solar radius.," However, we can establish with certainty that the difference between the inverted sound speed and the theoretical sound speed is known with a precision of $0.3\%$ in the solar interior, within $95\% $ of the solar radius." + Phe evolution of the Sun in a halo of WIAIPs wil increase the evacuation of energy. [rom the solar core., The evolution of the Sun in a halo of WIMPs will increase the evacuation of energy from the solar core. + The ΑΗΟν will work as a cold bridge! between the core and the more external lavers of the Sun., The WIMPs will work as a 'cold bridge' between the core and the more external layers of the Sun. + The magnitude of the effec is proportional to the total number of WIALPs concentratec in the solar core., The magnitude of the effect is proportional to the total number of WIMPs concentrated in the solar core. + Nevertheless. even if some systematic clleet is present in the inversion of the sound. speed. the presence of WIMPSs in the solar core leads to a quite differen nucleosvnthesis history from the solar standard model case. and from that to a peculiar radial profile of the sound speed.," Nevertheless, even if some systematic effect is present in the inversion of the sound speed, the presence of WIMPs in the solar core leads to a quite different nucleosynthesis history from the solar standard model case, and from that to a peculiar radial profile of the sound speed." + In this wav. the ellect of NIMPSs in the solar core can be inferred on the basis of seismic diagnostics. such as the inversion of the square of the sound. speed. among other possible techniques.," In this way, the effect of WIMPs in the solar core can be inferred on the basis of seismic diagnostics, such as the inversion of the square of the sound speed, among other possible techniques." + The proposed method constitutes a new way to cliscntanele the contribution of dillerent non-barvonic particles to the dark matter., The proposed method constitutes a new way to disentangle the contribution of different non-baryonic particles to the dark matter. + The luminosity in the core of the Sun is presently known with a precision of one part in 10.7., The luminosity in the core of the Sun is presently known with a precision of one part in $10^{-3}$. + In the coming vears. it is very likely that the new seismic data available from the SOLO experiments. will allow us to obtain a seismic model of the Sun with an accuracy of 10.7.," In the coming years, it is very likely that the new seismic data available from the SOHO experiments, will allow us to obtain a seismic model of the Sun with an accuracy of $10^{-5}$." + In such conditions. the Sun can and should be used as an excellent probe [or dark matter in our own galaxy.," In such conditions, the Sun can and should be used as an excellent probe for dark matter in our own galaxy." + In Figs., In Figs. + 2 and 3. we compute the ratio of the NEMI luminosity against the Suns luminosity produced in the inner core of 54 of the solar racius.," 2 and 3, we compute the ratio of the WIMP luminosity against the Sun's luminosity produced in the inner core of $5\%$ of the solar radius." + A significative region of the σα!ae) plot shows changes in the solar luminosity of the order of 10. 7., A significative region of the $\sigma_{scat}-\langle\sigma_{a}v\rangle$ plot shows changes in the solar luminosity of the order of $10^{-3}$ . + This order of magnitude on the Luminosity produced in the solar, This order of magnitude on the luminosity produced in the solar +field variables.,field variables. + That is. we evolve be12jh [or J=l....ny aud &—Loebut i=Lien+1.," That is, we evolve $b^x_{i-1/2,j,k}$ for $j=1,...,n_y$ and $k=1,...,n_z$ $i=1,...,n_x+1$." + This is useful for three reasons., This is useful for three reasons. + First. this allows V+b to be computed over all cells.," First, this allows $\grad \cdot \bvec$ to be computed over all cells." +" Secoud. to update 57i12A the fluxes 05, are needed at in the boundary cells (see fig.1)) with 7—n,01/2."," Second, to update $b^y_{n_x,j+1/2,k}$ the fluxes $v_y b_x$ are needed at in the boundary cells (see \ref{fig:grid}) ) with $i=n_x+1/2$." + Third. 6 can be interpolated to cell centers without the need to specify olf erid values.," Third, $\bvec$ can be interpolated to cell centers without the need to specify off grid values." +" ""nee the TVD limiters are noulinear. sinusoidal waveforms cau teud to become “clipped”. or )oxy-loosine."," Since the TVD limiters are nonlinear, sinusoidal waveforms can tend to become “clipped"", or boxy-looking." + We find that these uoulinear distortious cau be minimized by using constant flux reezit& speed. set to be the maxitmut1 along that acvection line.," We find that these nonlinear distortions can be minimized by using constant flux freezing speed, set to be the maximum along that advection line." + Additional stability can |ye ealned N multilying the flux freezing speed by a coistant multiplicative factor. although: this llCreases he num1yer of time steps needed ai lakes he code uore diffusive.," Additional stability can be gained by multiplying the flux freezing speed by a constant multiplicative factor, although this increases the number of time steps needed and makes the code more diffusive." + Empirically we find that SInoot1i& the velocity field which acvecs the uaeietic ield cau lead to less clamping of the slow noce., Empirically we find that smoothing the velocity field which advects the magnetic field can lead to less damping of the slow mode. + h ‘oduction rums. we have fotud ai OCCas]onal failure of the code when the Courant ¢'oncditiou is pusle too close to the limit.," In production runs, we have found an occasional failure of the code when the Courant condition is pushed too close to the limit." + In the operator sxit approach. the time step is lixed at the beginning of a double tiue step. and determined f‘om te Courant coudition at the beginning.," In the operator split approach, the time step is fixed at the beginning of a double time step, and determined from the Courant condition at the beginning." + Diuing the lesep. this condition may chauge. leadiug ο an instability if it exceeds the initial coustraint.," During the time step, this condition may change, leading to an instability if it exceeds the initial constraint." + Qur solution las been to be sulliciently «‘onservative using a choice of ος0.7., Our solution has been to be sufficiently conservative using a choice of $\lesssim 0.7$. + A more efficient JTOCedure woud be to measure the change in the Courant couditiou during the sweeps. aid use his as an iudicator in subsequent ime steps.," A more efficient procedure would be to measure the change in the Courant condition during the sweeps, and use this as an indicator in subsequent time steps." + And should a given sweep step be instable. ole Call always break it into twosubsteps.," And should a given sweep step be instable, one can always break it into two substeps." + We have implementec a Cully distribited version in MPI., We have implemented a fully distributed version in MPI. + After a full set of operato ‘sib one dimeusiou. we update the buller zoles.," After a full set of operators in one dimension, we update the buffer zones." + Εςx hydrodynamies. ouly 3 bulfler cells are requi‘ect.," For hydrodynamics, only 3 buffer cells are required." + The magnetic fiek requires inerpolation.L. aL we use 16 buíler cels for magnetized) simulatious.," The magnetic field requires interpolation, and we use 16 buffer cells for magnetized simulations." + A full three dimeusioual «O1dain cdecomposition is implemented. where we update the bulles in the appropriate clirectiou aler each dimensioiil operator.," A full three dimensional domain decomposition is implemented, where we update the buffers in the appropriate direction after each dimensional operator." + Since only large [aces are comuninicatect. latency of σοιinunuication is negligible. bi signficant bandwidth is required to move tle buffer zones.," Since only large faces are communicated, latency of communication is negligible, but signficant bandwidth is required to move the buffer zones." + The comununicatio1 is perlo1ned asvuchronously. aud computatlous proceed during the comununicatlo1 stage.," The communication is performed asynchronously, and computations proceed during the communication stage." + Witlin each ode. OyenMP is used to utilize multiple processors in a node without the ox'erhead ο bLer cells ancl οςLULLCatlous.," Within each node, OpenMP is used to utilize multiple processors in a node without the overhead of buffer cells and communications." + We tested the paralleliuplementatiou onthe CITA Melxeuzie beowull cluster., We tested the parallel implementation on the CITA McKenzie beowulf cluster. + The maiiu cluster has 256 nodes of dual Lute Pentitiu-1 Neo1 processors running at 2.1 Ghz. 1 GB of RAM. dual eigabit ethernet. and 80 GB of disk.," The main cluster has 256 nodes of dual Intel Pentium-4 Xeon processors running at 2.4 Ghz, 1 GB of RAM, dual gigabit ethernet, and 80 GB of disk." + The networkiug consists of bristles of 16 machines with oue eigabit port counected to a switch., The networking consists of bristles of 16 machines with one gigabit port connected to a switch. + The second gigabit port is used to intercounect the bristles in a, The second gigabit port is used to interconnect the bristles in a +tail to the thermal Maxwelian electron enerey clistriution.,tail to the thermal Maxwellian electron energy distribution. + Many of these hybrid models (e.g...Bechareketal.1990:Cridere1997:GierlinskiPoutanenPoutaneu&Coopi1998:Coppi1999) teud to je rather ad hoc. in that they assume some acceeraed (or non-Aaxwejan) particle populaion and then pre)ceed to explore the subsequent consequences.," Many of these hybrid thermal/non-thermal models \citep[e.g.,][]{bednarek90,crider97,gierlinski97,poutanen98a,poutanen98b,coppi99} tend to be rather ad hoc, in that they assume some accelerated (or non-Maxwellian) particle population and then proceed to explore the subsequent consequences." + Typicalvy. altough not always. the ixithermal poptlation takes the form of a iu tie. electron energy istribution.," Typically, although not always, the nonthermal population takes the form of a power-law in the electron energy distribution." + Suc1 a clistribtion is similar to that seen. for example. iu solar Mares (e.s..Copοἱ1999).," Such a distribution is similar to that seen, for example, in solar flares \citep[e.g.,][]{coppi99}." +. Both Crideretal.(1997) and Poutanen&Coppi(1098) have shown that a Maxwellian plus power-law [ο‘in fo“| he electron euergy distribution can be adapted o lit a composite COIPTEL-OSSE spectrunn ome ‘venus X-1., Both \citet{crider97} and \citet{poutanen98b} have shown that a Maxwellian plus power-law form for the electron energy distribution can be adapted to fit a composite COMPTEL-OSSE spectrum of Cygnus X-1. + Oilers have considered dhivsical mecharIslas N which uou-thermal electron cistributious might ye deveoped., Others have considered physical mechanisms by which non-thermal electron distributions might be developed. + For example. bohe stochastic particle acceleraion (Dermer.Miller.&Li1996:Li.Ixusuose&Liane1996) axl MHD twbulence (Li&liler1997) have been proposed as nechanisims for directly acceleratine te electrons.," For example, both stochastic particle acceleration \citep{dermer96,li96} and MHD turbulence \citep{li97} have been proposed as mechanisms for directly accelerating the electrons." + The iou »oulatioi might also couribute to he non-thermal electon distributiou 1 tlie case where a two-teniperature plasma deveops (e.g..197I:Shapiro.LielitinauandEardley1976:Csrabarti&Titarchuk 1995).," The ion popoulation might also contribute to the non-thermal electron distribution in the case where a two-temperature plasma develops \citep[e.g.,][]{dahlbacka74,shapiro76,chakrabarti95}." +. In this situation. the ion poptlation ay reacl a temperature of AT;~10P Is. 'esultiug in z production rom protou-proton iiteractions (e.g..Eilik19850:&IvaalosL983).," In this situation, the ion population may reach a temperature of $kT_i \sim 10^{12}$ K, resulting in $\pi^o$ production from proton-proton interactions \citep[e.g.,][]{eilik80,eilik83}." +. The « component then eads. via ploou-photon interactions jetweeu the z-«lecay. photous axb the X-ray. photous. to »oduction of energetic (noithermal) € pairs.," The $\pi^o$ component then leads, via photon-photon interactions between the $\pi^o$ -decay photons and the X-ray photons, to production of energetic (nonthermal) $e^{+}-e^{-}$ pairs." + Jordain&Roques(1991) used this concept o fit te hard. X-ray tails «X not only Cygnus X-1. bu uso GRO JO1[224-32 aud GX 339-1. as neastted by both SIGMA aid OSSE.," \citet{jourdain94} used this concept to fit the hard X-ray tails of not only Cygnus X-1, but also GRO J0422+32 and GX 339-4, as measured by both SIGMA and OSSE." + While retaining tle standard STSO spectrum to explain the emissiMl a ergles below 200 keV. they used z procuction to generate the uouthermal pairs ieeced to je spectruin at eiergies above ~200 keV. Tje histo'N of Cyenus N-1 is also riddled with uucoi1ued reports of very inteuse. very broad Ine eilission in the regionu arouxl 1 MeV. [ar exceediug hat which would be expected [rom a simple extrapolatiou «X the low energv continuum specir1 (e.g..Lingetal.1987:MeConnell [902).," While retaining the standard ST80 spectrum to explain the emission at energies below 200 keV, they used $\pi^o$ production to generate the nonthermal pairs needed to fit the spectrum at energies above $\sim 200$ keV. The history of Cygnus X-1 is also riddled with unconfirmed reports of very intense, very broad line emission in the region around 1 MeV, far exceeding that which would be expected from a simple extrapolation of the low energy continuum spectrum \citep[e.g.,][]{ling87,mcconnell89,owens92}." +. The broad MeV ure observed by HEAO-3 1987) occured uuder alb unitisul source condition when both the hard aud soft. X-ray fluxes wee ow., The broad MeV feature observed by HEAO-3 \citep{ling87} occured under an unusual source condition when both the hard and soft X-ray fluxes were low. + Liang&Dermer(LOSS) iierpreted the feature as evideuce for the presence of a very lert (GET.~LOO keV) palr«lominatec cloud in the inner region o ‘the accretion cisk., \citet{liang88} interpreted the feature as evidence for the presence of a very hot $kT_e \sim 400$ keV) pair-dominated cloud in the inner region of the accretion disk. + Lua this moclel. pai uay escape the system ail produce a weak narrow. aunililation feature in the cold surrouucli ueciun (Dermer&Liaug1989).," In this model, pairs may escape the system and produce a weak narrow annihilation feature in the cold surrounding medium \citep{dermer89}." +. Such a feature was also σιeoested in the HEAO-3 spectrum (Li .., Such a feature was also suggested in the HEAO-3 spectrum \citep{ling89}. + Melia&Misra(1993) extened this model by cousklering a more realistic hermally stratiied cloud., \citet{melia93} extended this model by considering a more realistic thermally stratified cloud. +" These ""MeV bumps."" h:we uot been seen by auy of the experiments c=[un he Compton Catinna-Ray Observatory (CORO) (l1cConnelletal.19914:Phlips1996:etal. 1997)."," These “MeV bumps,” have not been seen by any of the experiments on the Compton Gamma-Ray Observatory (CGRO) \citep{mcconnell94,phlips96,ling97}." +. Any such emission must therefore be ]Dnie-vaable (c.L.Harrisetal.1993).," Any such emission must therefore be time-variable \citep[c.f.,][]{harris93}." +". Although the‘e have been uo recent observatiols of au ""MeV bump"" iu tle spectrum of Cygnus X-1l. the contiuuiur flux levels that are now generally ο5erved around 1 MeV. still indicate a substantial barcleune of the hieh energy. spectrin1"," Although there have been no recent observations of an “MeV bump” in the spectrum of Cygnus X-1, the continuum flux levels that are now generally observed around 1 MeV still indicate a substantial hardening of the high energy spectrum." + The extent to which the spectrum barcenus, The extent to which the spectrum hardens +adio sources are born. grow and sleep.,"Radio sources are born, grow and sleep." + This evolutionary process can be interred frou the diversity of known radio sources: compact svnunuetrie objects are likely to be voung radio sources (Readlead et al. 1996):, This evolutionary process can be inferred from the diversity of known radio sources: compact symmetric objects are likely to be young radio sources (Readhead et al. \cite{readhead}) ); +" Fanaroft-Rilev radio galaxies of type I and II (Fanaroff Riley 1971)) may be cousidered ""adult sources: finally. relic sources are probably associated with galaxies which have ceased their uuclear activity (I&onissiuov Cubauov 1991: Iburis et al. 1993))."," Fanaroff-Riley radio galaxies of type I and II (Fanaroff Riley \cite{fanaroff}) ) may be considered “adult” sources; finally, relic sources are probably associated with galaxies which have ceased their nuclear activity (Komissarov Gubanov \cite{komissarov}; Harris et al. \cite{harris}) )." + If we believe that the activity iu radio-loud active galactic nuclei is the result of accretion outo a compact massive object. likely a black hole. he life of a radio source would be subordinated to he accretion vate.," If we believe that the activity in radio-loud active galactic nuclei is the result of accretion onto a compact massive object, likely a black hole, the life of a radio source would be subordinated to the accretion rate." + The vanishing of accretion would lead a former radio source to a “dormant” or hibernation phase., The vanishing of accretion would lead a former radio source to a “dormant” or hibernation phase. + Such a picture is supported by the increasing uunuboer of massive dark objects detected in inactive galaxies (see Ikoinenudy Richstone 1995))., Such a picture is supported by the increasing number of massive dark objects detected in inactive galaxies (see Kormendy Richstone \cite{kormendy}) ). + However. interaction aud mereie with neighboring galaxies cau trieeer the activity. aud eventually produce a transition frou a dormant to an active phase (Stockton Alackeuty 1983:: Dalicall ct al.," However, interaction and merging with neighboring galaxies can trigger the activity, and eventually produce a transition from a dormant to an active phase (Stockton Mackenty \cite{stockton}; Bahcall et al." + L997 and references therein)., \cite{bahcall} and references therein). + Under such a scenario. it should be expected that a iunber of radio sources with clear evidences of having owed through different phases curing their lifetime are found.," Under such a scenario, it should be expected that a number of radio sources with clear evidences of having passed through different phases during their lifetime are found." + A promising candidate is the radio source 3C338. with a large-scale structure. apparently unrelated o the present nuclear activity (Cüovauniui et al. 1998)].," A promising candidate is the radio source 3C338, with a large-scale structure apparently unrelated to the present nuclear activity (Giovannini et al. \cite{giovannini}) )." + Other sources. like 3€219 (Clarke et al. 19923) ," Other sources, like 3C219 (Clarke et al. \cite{clarke2}) )" +or 3€32.1 (Buduick 1985]. show indication of episodic events oossjblv resulting from an alteruatiou of hieh aud low activity phases.," or 3C33.1 (Rudnick \cite{rudnick2}) ), show indication of episodic events possibly resulting from an alternation of high and low activity phases." + Iu this paper. we present VLA observations of the radio source «1520620. made within the frame of the study of a new sample of large aneular size radio galaxies (Lara et al.," In this paper, we present VLA observations of the radio source J1835+620, made within the frame of the study of a new sample of large angular size radio galaxies (Lara et al.," + in preparation) selected from the NRAO VLA Sky Survey (NVSS: Condon et al. 1998))., in preparation) selected from the NRAO VLA Sky Survey (NVSS; Condon et al. \cite{nvss}) ). + Optical maging aud spectroscopy of the host ealaxy made at the Caliy Alto Observatory are also preseuted., Optical imaging and spectroscopy of the host galaxy made at the Calar Alto Observatory are also presented. + No previous studies ofthis radio source have been found in the literature., No previous studies of this radio source have been found in the literature. + J1835|620 presents. as its iain peculiarity. clear sigus of two distinct phases of unclear activity.," J1835+620 presents, as its main peculiarity, clear signs of two distinct phases of nuclear activity." + We made coutimmiun observations of J1835|620 with the VLA iu its D- and C-coufiguratious at 1.1. 1.9 and 8.5 CGIIz (see Table 1. for details).," We made continuum observations of J1835+620 with the VLA in its B- and C-configurations at 1.4, 4.9 and 8.5 GHz (see Table \ref{obs} for details)." + Tho radio sources ὃς250 and/or 3€18 served as primary flux density calibrators., The radio sources 3C286 and/or 3C48 served as primary flux density calibrators. + The interferometric phases of J18235|620 were calibrated using the nearby radio sources JL927|612 (at l.l and, The interferometric phases of J1835+620 were calibrated using the nearby radio sources J1927+612 (at 1.4 and +The [Nel] 12.8jn emission line has been suggested as a potential new probe of the planet formation region of circumstellar disks.,The [NeII] $12.8\micron$ emission line has been suggested as a potential new probe of the planet formation region of circumstellar disks. + It is a potentially powerful diagnostic because (he neon in disks is expected to be filly in the gas phase and in atomic form., It is a potentially powerful diagnostic because the neon in disks is expected to be fully in the gas phase and in atomic form. + In addition. the [Νο 12.8jan line probes warm. ionized gas. conditions which are believed to characterize the upper atmosphere of the inner disks surrounding classical T Tauri stars (Glassgold. Najila. Igea 2007: Meijerink. Glassgold. Najita 2008) and disk photoevaporative flows (Alexander 2008).," In addition, the [NeII] $12.8\micron$ line probes warm, ionized gas, conditions which are believed to characterize the upper atmosphere of the inner disks surrounding classical T Tauri stars (Glassgold, Najita, Igea 2007; Meijerink, Glassgold, Najita 2008) and disk photoevaporative flows (Alexander 2008)." + Because it is sensitive to low column densities of gas. [Nell] may also be a usefu probe of residual gas surrounding weak-line T Tauri stars or gas in the optically thin regions ol transitional disks.," Because it is sensitive to low column densities of gas, [NeII] may also be a useful probe of residual gas surrounding weak-line T Tauri stars or gas in the optically thin regions of transitional disks." + Glassgold et ((2007) predicted that the inner regions (<20 AAU? of classical T Tauri disks (hat are irraciated by stellar N-ravs would produce strong [Nell enussion that could be detected with theTelescope., Glassgold et (2007) predicted that the inner regions $< 20$ AU) of classical T Tauri disks that are irradiated by stellar X-rays would produce strong [NeII] emission that could be detected with the. + Comparably strong [Nell, Comparably strong [NeII] +"I3""a Laurikainen E.. Salo Le. Buta R.. Ixnapen J. HH. 2011. MNIUAS. 418. 1452 I3IA Martinez-Valpuesta L. Ixnapen JL. Buta R. 2007. AJ. 134. 1863 IS Alartig AL. Bournaucl FE. 2010. ApJ. 714. 275 IS? Moore B.. Ixatz N.. Lake G.. Dressler A.. Oemler A. 1996. Nat.","[54] Laurikainen E., Salo H., Buta R., Knapen J. H. 2011, MNRAS, 418, 1452 [55] Martinez-Valpuesta I., Knapen J.H., Buta R. 2007, AJ, 134, 1863 [56] Martig M., Bournaud F. 2010, ApJ, 714, 275 [57] Moore B., Katz N., Lake G., Dressler A., Oemler A. 1996, Nat." +" 379. 613 I3 Naab T.. Trujillo IL. 2006. NINILAS. 369. 625 ῥὲ Naab T.. Ikhochfar οι, Burkert A. 2006. ApJ. 636. SI ο"" Nair P.D.. van den Berg S.. Abraham It. 2010. ApJ. 715. 606 Guo Q.. White S.. Bovlan-Ixolehin AL. De Lucia €i. Ixaulfmann G.. Lemson C.. Li €.. Springcl V.. Weinmann $8. NIULAS. 413. 101 Salo LL. Rautiainen P.. Buta It. Purcell G.D.. Cobb"," 379, 613 [58] Naab T., Trujillo I. 2006, MNRAS, 369, 625 [59] Naab T., Khochfar S., Burkert A. 2006, ApJ, 636, 81 [60] Nair P.B., van den Berg S., Abraham R.G. 2010, ApJ, 715, 606 [61] Guo Q., White S., Boylan-Kolchin M., De Lucia G., Kauffmann G., Lemson G., Li C., Springel V., Weinmann S. 2011, MNRAS, 413, 101 [62] Salo H., Rautiainen P., Buta R., Purcell G.B., Cobb" +he »profile becomes a uull profile for both axial aud oroidal fields.,the profile becomes a null profile for both axial and toroidal fields. + Oue should bear im mind that the polarized efficiencies. are upper Buits to the polarizatious tat would. actually be measured. see the efficiencies are with reference to the scattered light ouly aud do not take account of the direct starlight . ↥⋅∪⋯↕∐∖↴∖↴⋅↖↽↴," One should bear in mind that the polarized efficiencies are upper limits to the polarizations that would actually be measured, since the efficiencies are with reference to the scattered light only and do not take account of the direct starlight from the system." +∖↴↑↸∖⋯∙∺∐⋯∖↑∐↕↴∖↴↴∖↴↑⋜∐⋅∐∶↴∙∐↑↕↴∖↴↸∖⊼↻↸∖↸⊳↸∖≼↧ . ⋅ ⋅⋝⋅ ο be largely unpolarized. its contribution acts to “dilute” the polarization substantially below the cficicucy levels reported here.," Since this starlight is expected to be largely unpolarized, its contribution acts to “dilute” the polarization substantially below the efficiency levels reported here." + For example. if the ine is relatively weak at of. the coutim£.uu evel. then the expected measured polarizatious⋅⋅ would have fractional values at about 1/5 of the cficicucy values. resulting in line polarizations of −≱∣⋰∣↕∪↥↙∣↗∕ar rivedfor aad or less fora.," For example, if the line is relatively weak at of the continuum level, then the expected measured polarizations would have fractional values at about 1/5 of the efficiency values, resulting in line polarizations of around for and or less for." +".. As percent polarizations. such values would appear to be easily iieasurable, but i practice vere are several challenges."," As percent polarizations, such values would appear to be easily measurable, but in practice there are several challenges." + First. a spectral resolution vieldiug several points acrossthe polarized xofile is needed.," First, a spectral resolution yielding several points across the polarized profile is needed." + οσατοαν disks have rotation specds of order 500 km +., Circumstellar disks have rotation speeds of order 500 km $^{-1}$. + A requisite velocity resolution of perhaps 50 lau s! would then be iceded. implying a resolving power of A/AAzx G000.," A requisite velocity resolution of perhaps 50 km $^{-1}$ would then be needed, implying a resolving power of $\lambda/\Delta \lambda \approx 6000$ ." + Tarringtou Ixuhln (20092) have demoustrated jit such resolving powers can be achieved in spectropolarimetry: however. the next requirement is that of Ποιο suitable scattering lines.," Harrington Kuhn (2009a) have demonstrated that such resolving powers can be achieved in spectropolarimetry; however, the next requirement is that of finding suitable scattering lines." +" The very oeinteresting effects secu in the sample of IEuxiug""EU ÍIuhu (20094)x exploits a relatively uew effect . ⋅⋅ ⋅ ∪↕↸∖∐∐⋜⋯↸⊳↸∖≼⋯↕⋜∐⋅↕∑⋜↧⊓∪∐↑∐⋜↧↑↕↴∖↴↸⊳∪⋃↸⊳↕≼∐∖∐↑↖∏↑∐⋅⋅ ⋅ ↥⋅↸∖∶↴∙⊾↕∪∐↴∖↴∪↕⋟∐∶↴∙⊾∐∖↥⋅∐↕∐∖⋜∏⋝↴∖↴∪↥⋅↻↑↕∪∐∙⋜↧↸⊳∪∐↴∖↴↸∖≺∣⋯∖∐↸⊳↸∖∪↕⋡ optical pumping effects."," The very interesting effects seen in the sample of Harrington Kuhn (2009a) exploits a relatively new effect of enhanced polarization that is coincident with regions of higher line absorption, a consequence of optical pumping effects." + For the Maule effect. or even for non-niaegnetie resonance scattering. lines that are predominantly scattering are needed.," For the Hanle effect, or even for non-magnetic resonance scattering, lines that are predominantly scattering are needed." + For hot star disks. such as the disks of Be stars. resonance scattering Ies are generally to be found at UV. waveleugths.," For hot star disks, such as the disks of Be stars, resonance scattering lines are generally to be found at UV wavelengths." + This requires space-bornue spectropoludneters., This requires space-borne spectropolarimeters. + Although the Wiscousin Ultraviolet Photo-Polarimeter Experiuenut AVUPPE) obtained exciting new results frou UV polarinctry. its resolving power was ouly about 200 (Nordsieck 11991).," Although the Wisconsin Ultraviolet Photo-Polarimeter Experiment (WUPPE) obtained exciting new results from UV polarimetry, its resolving power was only about 200 (Nordsieck 1994)." + A new UV spectropolarimeter called the Far-Ultvaviolet SpectroPolarimecr (FUSP) is a sounding rocket payload that wil have a resolving power of about 1800 (Nordsicc 1998)., A new UV spectropolarimeter called the Far-Ultraviolet SpectroPolarimeter (FUSP) is a sounding rocket payload that will have a resolving power of about 1800 (Nordsieck 1998). + Although possibly two low for circumstcllar disks. it will be suitable for stuclving scattering ine polarizations from high velocity stellar wiud sources.," Although possibly two low for circumstellar disks, it will be suitable for studying scattering line polarizations from high velocity stellar wind sources." + As noanatter of practical analysis. low should spectropolarimetric data best be managed to measure a Tanle effect?," As a matter of practical analysis, how should spectropolarimetric data best be managed to measure a Hanle effect?" + Plotting the velocity shifted polarizations in the sspace appears to be most promising., Plotting the velocity shifted polarizations in the space appears to be most promising. + The sequencing of the analysis for scattering Tues from disk sources might proceed as follows:, The sequencing of the analysis for scattering lines from disk sources might proceed as follows: +"classification of cach clusters iufall patteru: ""clean or clusters with few backeround aud foreground ealaxies. ""juteriediate for clusters with apparent iufall patterus mt significant contanuuation from either related larec-scale structure or foreground and backerouncl objects. and “none” for clusters with nuo appareut iufall pattern.","classification of each cluster's infall pattern: “clean” for clusters with few background and foreground galaxies, “intermediate” for clusters with apparent infall patterns but significant contamination from either related large-scale structure or foreground and background objects, and “none” for clusters with no apparent infall pattern." +" Below. we demonstrate that the caustic techuique can ο applied. successfully το clusters classified here as ""óuteriediate or ""none: our classification scheme is thus arly conservative."," Below, we demonstrate that the caustic technique can be applied successfully to clusters classified here as “intermediate” or “none”; our classification scheme is thus fairly conservative." + We use this classification scheme.only o show the dependence of the iufall pattern appearauce on cluster nass and the sampling depth., We use this classification scheme to show the dependence of the infall pattern appearance on cluster mass and the sampling depth. + Figue ?7 shows the dependence of this subjective Classification ou N-ray luminosity aud redshift., Figure \ref{cirslxz} shows the dependence of this subjective classification on X-ray luminosity and redshift. +" As expected from the depth of SDSS (52.1). there are few ""clean infall patterus where SDSS samples shallower thi A.|1."," As expected from the depth of SDSS $\S \ref{sdssdesc}$ ), there are few “clean” infall patterns where SDSS samples shallower than $M_*+1$." + We therefore define a “courplete” sample selected by Nevay flux fy73410 Mere temο (0.1-2.1 keV) and redshift (2 <0.10).," We therefore define a “complete” sample selected by X-ray flux $f_X\geq 3\times +10^{-12}$ erg $^{-1}$ $^{-2}$ (0.1-2.4 keV) and redshift $z\leq$ 0.10)." + The CIRS sample contains clusters: the vast majority of this sample or )) contain “clea” infall patterus aud oulv three }) show no obvious infall pattern., The CIRS sample contains clusters; the vast majority of this sample or ) contain “clean” infall patterns and only three ) show no obvious infall pattern. + Of the three clusters in the latter category. two are enibedded i larger structures (NGC1636 in the outskirts of the Virgo cluster and À2067 in the outskirts of A2061. part of the CorBor supercluster) and one (AL291) is a possible mereing cluster with two newly concentric coniponents separated by ~2000 kms1 (sce 51 for details).," Of the three clusters in the latter category, two are embedded in larger structures (NGC4636 in the outskirts of the Virgo cluster and A2067 in the outskirts of A2061, part of the CorBor supercluster) and one (A1291) is a possible merging cluster with two nearly concentric components separated by $\sim$ 2000 $\kms$ (see $\S$ \ref{individual} for details)." + Iu $2.2 we are able to identify caustics in of the CIRS clusters., In $\S$ 3.2 we are able to identify caustics in of the CIRS clusters. + Figure ?? also shows the CAIRNS X-rav huudnositv and redshift liuits., Figure \ref{cirslxz} also shows the CAIRNS X-ray luminosity and redshift limits. + The three CIRS clusters imeetiug this criteria were studied by CAIRNS (A119. Al6s. aud A2199).," The three CIRS clusters meeting this criteria were studied by CAIRNS (A119, A168, and A2199)." + Figure ?? demonstrates the expanded parameter space covered bythe CIRS sample., Figure \ref{cirslxz} demonstrates the expanded parameter space covered by the CIRS sample. +" Table 7 lists the clusters in the CIRS sample. their A-rayv positions. huninosities. and temperatures (when available). their central redshifts aud velocity dispersions (see below). aud the projected radius Within which the SDSS DRI spectroscopic survey Ron,provides complete spatial coverage."," Table \ref{sample} lists the clusters in the CIRS sample, their X-ray positions, luminosities, and temperatures (when available), their central redshifts and velocity dispersions (see below), and the projected radius $R_{comp}$ within which the SDSS DR4 spectroscopic survey provides complete spatial coverage." + For several clusters. the caustic pattern disappears bevoud because of this edge effect.," For several clusters, the caustic pattern disappears beyond $R_{comp}$ because of this edge effect." + Figures ??--?? «how the Roomyracdius-redshift diagraims for the CIRS sample., Figures \ref{allcirs1}- \ref{allcirs6} show the radius-redshift diagrams for the CIRS sample. + Vertical lines in some panels indicate the radius within which the DRL spectroscopic footprint provides complete coverage of the iufall region: the absence of a caustic pattern iu sole clusters bevoud this lait is due to iconiplete spatial coverage., Vertical lines in some panels indicate the radius within which the DR4 spectroscopic footprint provides complete coverage of the infall region; the absence of a caustic pattern in some clusters beyond this limit is due to incomplete spatial coverage. + Another factor which determines the presence or absence of a “clean” iufall pattern is the surrounding laree-scale structure., Another factor which determines the presence or absence of a “clean” infall pattern is the surrounding large-scale structure. + For example. the redshift-racdins diagrams of evoups within the infall reeious of more massive clusters reflect the kinematics of the clusters iufall region (ec...A2199.see 7).," For example, the redshift-radius diagrams of groups within the infall regions of more massive clusters reflect the kinematics of the cluster's infall region \citep[e.g., A2199, see][]{rines02}." + The CIRS sample contains several of these systems: NCGCGIOT and À2197 in the iufall reeion of A2199. NCC1636 in the infall region of Virgo. NGC5813 iu the infall region of NCC5816. aud. A2067 in the infall region of À2061.," The CIRS sample contains several of these systems: NGC6107 and A2197 in the infall region of A2199, NGC4636 in the infall region of Virgo, NGC5813 in the infall region of NGC5846, and A2067 in the infall region of A2061." + ALL7T3 aud ALL90 are close aud likely bound., A1173 and A1190 are close and likely bound. + Two clusters. ÀAI035 and À1291. show evidence of two iufall patterus in the projected racdius-redshift diagrais.," Two clusters, A1035 and A1291, show evidence of two infall patterns in the projected radius-redshift diagrams." + We label the two compoucuts A aud D with A indicating the lower redshift component., We label the two components A and B with A indicating the lower redshift component. + The caustic algorithm finds ALO35B and ÀÁI291À to be the larger conrponents: we use these components when compiling results for the CIRS sample., The caustic algorithm finds A1035B and A1291A to be the larger components; we use these components when compiling results for the CIRS sample. + We discuss these systenis iu more detail in 9l., We discuss these systems in more detail in $\S \ref{individual}$. +] Similar to CAIRNS. the CIRS clusters show iufall patterns ΙΟ. amore well defined than those of the simulations of D99.," Similar to CAIRNS, the CIRS clusters show infall patterns much more well defined than those of the simulations of D99." + Because infall patterus are better defined in a low-density universe (D99). a possible explanation for this discrepancy is that the real universe has a smaller matter deusity than the simulations.," Because infall patterns are better defined in a low-density universe (D99), a possible explanation for this discrepancy is that the real universe has a smaller matter density than the simulations." + Another possibility is that the seuiu-aualytic ealaxy formation recipes used in D99 are inaccurate around massive clusters., Another possibility is that the semi-analytic galaxy formation recipes used in D99 are inaccurate around massive clusters. + We briefly review the method DC and D99 developed to estimate the mass profile of a galaxw cluster bv identifving caustics in redshift space., We briefly review the method DG and D99 developed to estimate the mass profile of a galaxy cluster by identifying caustics in redshift space. + The method assumes that clusters form: in a hierarchical process., The method assumes that clusters form in a hierarchical process. + Application of the method requires only ealaxy redshifts and sky coordinates., Application of the method requires only galaxy redshifts and sky coordinates. + Tov models of simple spherical iufall onto clusters produce sharp chhaucements in the phase space density around the system., Toy models of simple spherical infall onto clusters produce sharp enhancements in the phase space density around the system. + These euliucements. kuowiui as caustics. appear as a trumpct shape iu scatter plots of redshift versus projected clustercentiic radius (?77)..," These enhancements, known as caustics, appear as a trumpet shape in scatter plots of redshift versus projected clustercentric radius \citep{kais87,rg89}." + DG aud D99 show that raucdou motions smooth out the sharp pattern expected from simple spherical iufall iuto a deuse envelope in the redshift-radius diagram (seealso 7)..," DG and D99 show that random motions smooth out the sharp pattern expected from simple spherical infall into a dense envelope in the redshift-radius diagram \citep[see +also][]{vh98}." + The edges of this cuvelope cau be interpreted as the escape velocity as a function of radius., The edges of this envelope can be interpreted as the escape velocity as a function of radius. + Galaxies outside the caustics are also outside the turnaround radius., Galaxies outside the caustics are also outside the turnaround radius. + The caustic techuique provides a well-defined bouudiry between the infall region and interlopers: oue may think of the technique as a imethod for defining membership that eives the cluster mass profile as a byproduct., The caustic technique provides a well-defined boundary between the infall region and interlopers; one may think of the technique as a method for defining membership that gives the cluster mass profile as a byproduct. + The amplitude Ati) of the caustics is half of the distance between the upper aud lower caustics in redshift space., The amplitude $\mathcal{A} \mathnormal{(r)}$ of the caustics is half of the distance between the upper and lower caustics in redshift space. +" Assuming splicrical symuuetry. Ate) is related to the cluster gravitational potential o(r) by where (0)=1lo;r)oi) is the velocity anisotropy paralcter aud og and σι, are the tangential and radial velocity dispersions respectively."," Assuming spherical symmetry, $\mathcal{A} \mathnormal(r)$ is related to the cluster gravitational potential $\phi (r)$ by where $\beta (r) = 1- [\sigma_\theta^2(r)/\sigma_r^2(r)]$ is the velocity anisotropy parameter and $\sigma_\theta$ and $\sigma_r$ are the tangential and radial velocity dispersions respectively." + DG. show that the mass of a spherical shell of radii fry. 7| within the iufall region is the integral of the square of the amplitude Ar) ΠΟΠΠ) = where £42:0.5 is a filling factor with a umuerical value estimated from simulations.," DG show that the mass of a spherical shell of radii $r_0,r$ ] within the infall region is the integral of the square of the amplitude $\mathcal{A} +\mathnormal{(r)}$ GM(40.3 need their Houdashelt values increased. on mean. by +305+69 K (s.d.).," If the stars are split into the two groups based on the Houdashelt results discussed in Section 6.3, the 12 stars with Houdashelt-scale values of $> +0.3$ need their Houdashelt values increased, on mean, by $+305 \pm 69$ K (s.d.)," + while the remaining 43 stars require a mean change of 212+113 K (s.d.)., while the remaining 43 stars require a mean change of $-12 \pm 113$ K (s.d.). + The resulting |O/Fe] vs. [Fe/H] plot is shown in Figure 13., The resulting [O/Fe] vs. [Fe/H] plot is shown in Figure 13. + The calculation of the random errors given in Tables 11 and 12 and shown in Figure 12 and 13 required changes to the method used in Section 6.2., The calculation of the random errors given in Tables 11 and 12 and shown in Figure 12 and 13 required changes to the method used in Section 6.2. + We determined the random error in by considering the uncertainties in the oxygen equivalent widths and inΜν., We determined the random error in by considering the uncertainties in the oxygen equivalent widths and in. +". However. when calculating the errors for the O, and O, abundances. we needed to add three terms to Equation 4 that took into account the correlation between the error in the oxygen equivalent widths on one hand. andTyyy.. and [n/H] on the other."," However, when calculating the errors for the $_p$ and $_f$ abundances, we needed to add three terms to Equation 4 that took into account the correlation between the error in the oxygen equivalent widths on one hand, and, and [m/H] on the other." + Α comparison between our oxygen abundances for all three temperature scales and those of several earlier works is given in Figure 14., A comparison between our oxygen abundances for all three temperature scales and those of several earlier works is given in Figure 14. + With a few exceptions. the points lie on parallel tracks to the 45-degree line.," With a few exceptions, the points lie on parallel tracks to the 45-degree line." + The effect of changes in the temperature. for example. can be seen by comparing the top. middle. and lower panels.," The effect of changes in the temperature, for example, can be seen by comparing the top, middle, and lower panels." + As the temperature increases. the forbidden line oxygen abundances shift to higher abundances. while the permitted line abundances shift to lower abundances.," As the temperature increases, the forbidden line oxygen abundances shift to higher abundances, while the permitted line abundances shift to lower abundances." + King(1993). proposed a temperature scalethat would resolve the discrepancy between the forbidden and permitted lines., \citet{k93} proposed a temperature scalethat would resolve the discrepancy between the forbidden and permitted lines. +" His calibration of Tyay-colorrelationshipsisvalid forstarswithT.-,>5470 K. so thereare only 5stars within our sample that can be compared to the King(1993) scale."," His calibration of $-$ color relationships is valid for stars with $\mteff > 5470$ K, so thereare only 5stars within our sample that can be compared to the \citet{k93} scale." + The differences. TauHoe Ting. are +352 K. +260 K. +180 K. +165 K. and —140 K for a mean difference of 163+185 K. King provides specific values for three more stars in common with this sample.," The differences, $_{\rm Ad Hoc} -$ $_{\rm King}$, are $+352$ K, $+260$ K, $+180$ K, $+165$ K, and $-140$ K for a mean difference of $163 \pm 185$ K. King provides specific values for three more stars in common with this sample." + If all eight stars are considered. the Ad Hoe scale is +147+142 K warmer. and there is only a weak significance to the correlation between the two scales.," If all eight stars are considered, the Ad Hoc scale is $+147 \pm 142$ K warmer, and there is only a weak significance to the correlation between the two scales." + While the overlap in samples is small. the evidence suggests that the King and Ad Hoe temperature scales are not in general agreement. even though both scales agree that increased values can resolve the oxygen problem.," While the overlap in samples is small, the evidence suggests that the King and Ad Hoc temperature scales are not in general agreement, even though both scales agree that increased values can resolve the oxygen problem." + The ad hoc temperature scale was picked to solve the oxygen problem. but we must examine whether the scale reasonable when compared to other observations or the predictions of stellar evolution.," The ad hoc temperature scale was picked to solve the oxygen problem, but we must examine whether the scale reasonable when compared to other observations or the predictions of stellar evolution." + In Figure 15. we plot the vs. plane for all three parameter scales.," In Figure 15, we plot the vs. plane for all three parameter scales." + Also plotted are 10 and 12 Gyr o-enhanced isochrones from VandenBerg(2000) for [Fe/H] 2 -0.84. —1.54. and —2.31.," Also plotted are 10 and 12 Gyr $\alpha$ -enhanced isochrones from \citet{v00} for [Fe/H] $= -0.84$ , $-1.54$ , and $-2.31$ ." + This range spans the observed [Fe/H] range for most of the target, This range spans the observed [Fe/H] range for most of the target +Lx bin (even for very coarse bins). and. in. part. because we compute e over a large range in logL a typical mock sample leads to many empty bins.,"$L_X$ bin (even for very coarse bins), and in part because we compute $\Phi$ over a large range in $\mathrm{log}L_X$, a typical mock sample leads to many empty bins." + This implies.x. in a given bin. many points (corresponding to many mock samples) at ᾧ—0.," This implies, in a given bin, many points (corresponding to many mock samples) at $\Phi=0$." + The distribution of the non-zero values is determined by the correlation. with perhaps a factor of 2 or so spread (l or 2 svstems in that bin) and with some additional scatter [rom the distribution of the weights.," The distribution of the non-zero values is determined by the correlation, with perhaps a factor of 2 or so spread (1 or 2 systems in that bin) and with some additional scatter from the distribution of the weights." + Therefore. the clistribution of values in a given bin cannot tell us the error on ® in that bin. and more work is needed (see Section 5.2)).," Therefore, the distribution of values in a given bin cannot tell us the error on $\Phi$ in that bin, and more work is needed (see Section \ref{sec:simphi}) )." + Llere we present the results of the calculations described in section 3. above., Here we present the results of the calculations described in Section \ref{sec:rho} above. + We will elaborate on the interpretation and limitations of these results in Section 5.., We will elaborate on the interpretation and limitations of these results in Section \ref{sec:fluxl}. + The probability distribution function of po resultingfrom 1ο caleulation described. above is shown in Fig. 2.., The probability distribution function of $\rho_0$ resultingfrom the calculation described above is shown in Fig. \ref{fig:rhopdf}. + As already noted. we find that the distances errors dominate the total uncertainty in po. although the small sample size also contributessignificantly.," As already noted, we find that the distances errors dominate the total uncertainty in $\rho_0$, although the small sample size also contributessignificantly." +" Phe mode. median. and mean of the istribution are 2.310"". ΕΕ10 and 7.4 .and are marked by solid lines."," The mode, median, and mean of the distribution are $2.3 \times 10^{-6}$, $4.4 \times 10^{-6}$ and $7.4 \times 10^{-6}\,\mathrm{pc^{-3}}$ , and are marked by solid lines." +" The dashed lines at 22.]0 ""and LO.10.pe show a I-0 confidence interval (the 16th and S4th percentile points of the distribution)"," The dashed lines at $2.2 \times 10^{-6}$ and $1.0 \times 10^{-5}\,\mathrm{pc^{-3}}$ show a $\sigma$ confidence interval (the 16th and 84th percentile points of the distribution)." +" Considering the large errors. our p estimate of ΕΕονn0""pc3"" resultingB from. the combined+ RBS1 and NEPwae survey is in reasonable agreement with the value found. by Schwopeetal.(2002) when omitting the two systems for which they estimated very small distances."," Considering the large errors, our $\rho$ estimate of $4.4^{+5.9}_{-2.0} \times 10^{-6}\,\mathrm{pc^{-3}}$ resulting from the combined RBS and NEP survey is in reasonable agreement with the value found by \cite{SchwopeBrunnerBuckley02} when omitting the two systems for which they estimated very small distances." + We will compare the new estimate with the higher value we found from the NEP survey alone in some detail in Section 5.3.., We will compare the new estimate with the higher value we found from the NEP survey alone in some detail in Section \ref{sec:consistent}. + Considering short- and long-period CVs separately (even assuming that TW Pie. RDBS490. RDS1411. and 4€) Iii are all short-period. systems). we find that the space density. estimate is dominated by long-period systems: po of long-period CVs is roughly 1.2 times that of short-period svstems (this is cliscussecl further in Section 6)).," Considering short- and long-period CVs separately (even assuming that TW Pic, RBS490, RBS1411, and IQ Eri are all short-period systems), we find that the space density estimate is dominated by long-period systems; $\rho_0$ of long-period CVs is roughly 1.2 times that of short-period systems (this is discussed further in Section \ref{sec:disc}) )." +" If we use a single Galactic scale-height of 260 pe for all systems. we find po=3.81510""pe this is not significantly cilferent from the result when using cilferent scale heights for long- and. short-periocd CVs."," If we use a single Galactic scale-height of 260 pc for all systems, we find $\rho_0 = 3.8^{+5.3}_{-1.9} \times 10^{-6}\,\mathrm{pc^{-3}}$; this is not significantly different from the result when using different scale heights for long- and short-period CVs." +" Similarly. if we correct for the possible distance biases listed in Table 2.. the resulting po is insignificantly dilferent. namely 10""pe ."," Similarly, if we correct for the possible distance biases listed in Table \ref{tab:bias}, the resulting $\rho_0$ is insignificantly different, namely $4.0^{+5.3}_{-2.0} \times 10^{-6}\,\mathrm{pc^{-3}}$ ." + The same calculation that gives po also vields 9e. as explained in Section. 3.2.1..," The same calculation that gives $\rho_0$ also yields $\Phi$, as explained in Section \ref{sec:1overvmax}." + Phe X-ray luminosity function. obtained from this calculation (assuming f=260pc for all CVs) is shown in Fig. 3..," The X-ray luminosity function obtained from this calculation (assuming $h=260\,\mathrm{pc}$ for all CVs) is shown in Fig. \ref{fig:obsphi}." + We also plot there the log(Lxferes1j estimates of the 20 detected CVs. in order to show the size of the errors in these values.," We also plot there the $\mathrm{log}(L_X/\mathrm{erg\,s^{-1}})$ estimates of the 20 detected CVs, in order to show the size of the errors in these values." + The uncertainty in Ly has the ellect of smoothing features in the luminosity function., The uncertainty in $L_X$ has the effect of smoothing features in the luminosity function. + This explains. for example. why the inferred Luminosity function its à gradual turn-over at the faint Ly end. rather than a sharp cut-olf at. the faintest observed Ly value.," This explains, for example, why the inferred luminosity function has a gradual turn-over at the faint $L_X$ end, rather than a sharp cut-off at the faintest observed $L_X$ value." + Lh we integrate this histogram. we find 6.1.19pe. a number xtween the median and mean of the py distribution.," If we integrate this histogram, we find $6.1 \times 10^{-6}\,\mathrm{pc^{-3}}$, a number between the median and mean of the $\rho_0$ distribution." + As explained in Section 3.2.3.. this calculation does not wovicle the uncertainty on 9. hence we do not show error xus on the histogram in Fig. y ," As explained in Section \ref{sec:test}, this calculation does not provide the uncertainty on $\Phi$, hence we do not show error bars on the histogram in Fig. \ref{fig:obsphi}. ." +Furthermore.although he result does not change significantly if we correct lor he possible distance biases discussed in Section 2.1.1.. the uminosity. function. probably still sullers from Malmeaquist- biases. ancl while the turnover at the faint end might," Furthermore,although the result does not change significantly if we correct for the possible distance biases discussed in Section \ref{sec:dbias}, , the luminosity function probably still suffers from Malmquist-type biases, and while the turnover at the faint end might" +The stellar mass and age are estimated as follows: for each stellar evolutionary model we compute the functional where the subseripts obs and mod refer to the observed values and theoretical (model) values respectively (e.g.?)..,The stellar mass and age are estimated as follows: for each stellar evolutionary model we compute the functional where the subscripts $obs$ and $mod$ refer to the observed values and theoretical (model) values respectively \citep[e.g.][]{Lastennet-2002}. + The o values are taken from ?.., The $\sigma$ values are taken from \citet[][]{Sousa-2008}. + The solution is obtained by minimizing the above function., The solution is obtained by minimizing the above function. + For each star the final mass anc age is obtained when the prediction of the theoretical stellar model is inside the observational error bar. i.e.. y(M.r)«2.," For each star the final mass and age is obtained when the prediction of the theoretical stellar model is inside the observational error bar, i.e., $\chi^2 (M,t) < 2$." + In Table | we present the derived values for mass and age in our sample., In Table \ref{tab1} we present the derived values for mass and age in our sample. + The typical (relative) errors bars of our estimations are Mc; in mass and 0.5 Gyr and 1.0 Gyr. respectively. for ages lower and higher than 5 Gyr.," The typical (relative) errors bars of our estimations are $M_{\sun}$ in mass and 0.5 Gyr and 1.0 Gyr, respectively, for ages lower and higher than 5 Gyr." + This level of precision is possible because of the very small (relative) errors in the stellar parameters derived for the solar analogues in 2.., This level of precision is possible because of the very small (relative) errors in the stellar parameters derived for the solar analogues in \citet[][]{Sousa-2008}. + We note however that we are not taking into account variations in parameters like the mixing length and helium abundance., We note however that we are not taking into account variations in parameters like the mixing length and helium abundance. + Changes in these parameters could lead to errors in the stellar masses and ages (e.g.?).., Changes in these parameters could lead to errors in the stellar masses and ages \citep[e.g.][]{Fernandes-2004}. + In order to check our methodology. we applied the stellar evolutionary models from the Padova group. computed with the web interface dealing with stellar isochrones and their derivatives (http://stev.oapd.tnaf.1t/egi-bin/emd) to the stars of our sample.," In order to check our methodology, we applied the stellar evolutionary models from the Padova group, computed with the web interface dealing with stellar isochrones and their derivatives (http://stev.oapd.inaf.it/cgi-bin/cmd) to the stars of our sample." + Taking into account that the Padova models are constrained to metal abundance lower than Z « 0.03. we have arbitrarily chosen a subsample of 27 stars to cover the range of mass and age of the stars in the paper.," Taking into account that the Padova models are constrained to metal abundance lower than Z $<$ 0.03, we have arbitrarily chosen a subsample of 27 stars to cover the range of mass and age of the stars in the paper." + In Figs., In Figs. + | and 2 we show the comparison between masses and ages respectively. using the CESAM and Padova models.," \ref{masses} and \ref{ages} we show the comparison between masses and ages respectively, using the CESAM and Padova models." + In addition we also include a comparison to the values published in ? and ? (with this latter we have 41 stars in common)., In addition we also include a comparison to the values published in \citet[][]{Sousa-2008} and \citet[][]{Valenti-2005} (with this latter we have 41 stars in common). + A very good agreement exists between all sets of values. except for the ages of ? which seem to be constrained to values closer to the Sun age.," A very good agreement exists between all sets of values, except for the ages of \citet[][]{Valenti-2005} which seem to be constrained to values closer to the Sun age." + The reason for this is not clear: this discussion is out of the scope of the present paper., The reason for this is not clear; this discussion is out of the scope of the present paper. + However. if the age span of the stars in our sample were smaller (taking the values from Valenti Fischer). it would strengthen the results discussed below.," However, if the age span of the stars in our sample were smaller (taking the values from Valenti Fischer), it would strengthen the results discussed below." + reftabl shows the values of mass and age derived for the stars in. this. work and their lithium. abundances (?).., \\ref{tab1} shows the values of mass and age derived for the stars in this work and their lithium abundances \citep[][]{Israelian-2009}. + The sample studied here corresponds to the majority of solar analogues studied in ?.., The sample studied here corresponds to the majority of solar analogues studied in \citet[][]{Israelian-2009}. + However. here we only considered those belonging to the HARPS sample (60).," However, here we only considered those belonging to the HARPS sample $\sim$ 60)." + For these stars we have the best uniform stellar parameters (?).. assuring the total consistency of our results.," For these stars we have the best uniform stellar parameters \citep[][]{Sousa-2008}, assuring the total consistency of our results." + Four stars in the sample were also exeluded since no reliable masses and ages could be derived 228701. 778558. 996423. 1143114).," Four stars in the sample were also excluded since no reliable masses and ages could be derived 28701, 78558, 96423, 143114)." + The top panel in Fig., The top panel in Fig. + 3. shows the lithium abundance plotted against the effective temperature for the stars presented in Table 1.., \ref{fig_calibration_proc} shows the lithium abundance plotted against the effective temperature for the stars presented in Table \ref{tab1}. + This result is almost indistinguishable from 11 in 2.., This result is almost indistinguishable from 1 in \citet[][]{Israelian-2009}. + There 1s a general tendency for lower temperature stars to present on average lower lithium abundances. an expected result (seee.g.22)..," There is a general tendency for lower temperature stars to present on average lower lithium abundances, an expected result \citep[see e.g.][]{Pinsonneault-1990, Sestito-2005}." + It is also evident that the stars that host planets are distributed in the lower region of the plot. while the stars with no evidence for planetary companions are spreac over the entire diagram.," It is also evident that the stars that host planets are distributed in the lower region of the plot, while the stars with no evidence for planetary companions are spread over the entire diagram." + In the middle plot of Fig., In the middle plot of Fig. + 3. we present the lithium abundance as a function of the derived stellar age., \ref{fig_calibration_proc} we present the lithium abundance as a function of the derived stellar age. + As expected. the bulk of the stars are old.," As expected, the bulk of the stars are old." + The HARPS sample was chosen to avoic active (younger) stars due to the higher difficulty in searching for planets i these objects (e.g.?).., The HARPS sample was chosen to avoid active (younger) stars due to the higher difficulty in searching for planets in these objects \citep[e.g.][]{Santos-2000a}. + Interestingly à few younger objects are seen in the left part of this panel («2 GGyr). a region where no lithium-depleted star is seen.," Interestingly a few younger objects are seen in the left part of this panel $<$ Gyr), a region where no lithium-depleted star is seen." + This suggests a lithium. abundance dependence with age., This suggests a lithium abundance dependence with age. + Above an age of -2GGyr. however. we observe a wider dispersion in lithium for all stars in the plot. and no correlation Is seen.," Above an age of $\sim$ Gyr, however, we observe a wider dispersion in lithium for all stars in the plot, and no correlation is seen." +For these five galaxies. we see no obvious correlation between the amount of substructure and cluster-ceutric distance. as shown iu Figure 6.. AIST.,"For these five galaxies, we see no obvious correlation between the amount of substructure and cluster-centric distance, as shown in Figure \ref{environ}." + ALLO. aud M89 have significantly more substructure lhuuinositv than the others. although iu the case of AIST aud ALLY. the substructures contribute mach less to the total huninosity of the salaxies.," M87, M49, and M89 have significantly more substructure luminosity than the others, although in the case of M87 and M49, the substructures contribute much less to the total luminosity of the galaxies." + Neither M81 nor. M86 appear to have appreciable substructure. either im total or fractional huuinositv.," Neither M84 nor M86 appear to have appreciable substructure, either in total or fractional luminosity." + A model where substructure survival depends simply ou clusterceutric distance is clearly too simplistic to explain the features seen in these Vireo ellipticals., A model where substructure survival depends simply on cluster-centric distance is clearly too simplistic to explain the features seen in these Virgo ellipticals. +" However, AIST is not simply in the cluster potential. it livescenter of the cluster."," However, M87 is not simply in the cluster potential, it lives of the cluster." + In this privileged. position. it experiences a constant rain of sanaller satellite ealaxies fallne in at high velocities. which will be tidally stripped aud leave behiud long streamers such as those seen extending to the NW of AINT.," In this privileged position, it experiences a constant rain of smaller satellite galaxies falling in at high velocities, which will be tidally stripped and leave behind long streamers such as those seen extending to the NW of M87." + Unlike the long-lived structures around isolated ealaxies. streamers duside an active cluster euvirouimeut are dispersed rapidly via interactions with other cluster members. typically within a few crossing times (Ruddick. 2009).," Unlike the long-lived structures around isolated galaxies, streamers inside an active cluster environment are dispersed rapidly via interactions with other cluster members, typically within a few crossing times (Rudick 2009)." + Iu this position. MS? has both high creation rates aud high destruction rates for its diffuse substructure. so that the window of opportunity for observing cold streams around ALS? will be short.," In this position, M87 has both high creation rates and high destruction rates for its diffuse substructure, so that the window of opportunity for observing cold streams around M87 will be short." + While the amount of substructure does not seen to correlate with cluster-ceutric radius. there are interesting xtterus iu the morphological properties of the diffuse ight iu these ellipticals.," While the amount of substructure does not seem to correlate with cluster-centric radius, there are interesting patterns in the morphological properties of the diffuse light in these ellipticals." + NM9 aud M89 both have complex shell structures out to large radius. where the material would be loosely bound to the host galaxy.," M49 and M89 both have complex shell structures out to large radius, where the material would be loosely bound to the host galaxy." + Any strong idal forces that would occur duriug a galaxys passage iouegh the cluster would likely be sufficient to strip or at least significantly perturb the shells (see. Milios 2001).," Any strong tidal forces that would occur during a galaxy's passage through the cluster would likely be sufficient to strip or at least significantly perturb the shells (see, Mihos 2004)." + The sharpness of the shells aud the long dynamical nuescales in the outskirts of these ealaxies (~ 0.5 Gar) argue that these galaxies have not passed through ιο dense Virgo Core in the recent past., The sharpness of the shells and the long dynamical timescales in the outskirts of these galaxies $\sim$ 0.5 Gyr) argue that these galaxies have not passed through the dense Virgo Core in the recent past. + Iu contrast. we see little evidence for sharp shelblike structures im AINT. MS6. or ADSL.," In contrast, we see little evidence for sharp shell-like structures in M87, M86, or M84." + Living at the ceuter of Virgo. AIST experiences repeated chcounters with cluster galaxies. and any dynamically delicate feature will quickly be cdestroved.," Living at the center of Virgo, M87 experiences repeated encounters with cluster galaxies, and any dynamically delicate feature will quickly be destroyed." + In the radial streams visible to the wortlavest of AST. we are likely secing very recent stripping of ealaxies falling in on racial orbits.," In the radial streams visible to the northwest of M87, we are likely seeing very recent stripping of galaxies falling in on radial orbits." + The nature of the streams observed in M87 aud. M86 is qualitatively different as well., The nature of the streams observed in M87 and M86 is qualitatively different as well. + M8S7'8 NW aud WNW streams can be traced out to ~ 1 degree (275 kpe) from the center of M87. while M8G6's streams are nach simaller.," M87's NW and WNW streams can be traced out to $\sim$ 1 degree (275 kpc) from the center of M87, while M86's streams are much smaller." + The longest. the N Stream. extends ffrom M86. while the others are much smaller in leneth (only a few arcninutes in size) aud closer to M86.," The longest, the N Stream, extends from M86, while the others are much smaller in length (only a few arcminutes in size) and closer to M86." + \loving at such a high velocity near or through the cluster core. AISG simply may not be able to hang ou to exteuded debris.," Moving at such a high velocity near or through the cluster core, M86 simply may not be able to hang on to extended debris." +" The chister tidal feld may casily strip these streams, or they may lack coherency simply because of the motion of M86."," The cluster tidal field may easily strip these streams, or they may lack coherency simply because of the motion of M86." + A coherent stream at 300 kpe would have an orbital period of a few Gyr. a timescale over which M86 would have moved a few AIpe through the cluster.," A coherent stream at 300 kpc would have an orbital period of a few Gyr, a timescale over which M86 would have moved a few Mpc through the cluster." + The combination of tidal effects aud. MS6's high speed motion through the cluster would iuake it difficult for M86 to retain lighly extended streamers., The combination of tidal effects and M86's high speed motion through the cluster would make it difficult for M86 to retain highly extended streamers. + Substructure is not the full story of the diffuse light πι Vireo cllipticals. of course.," Substructure is not the full story of the diffuse light in Virgo ellipticals, of course." + Because these features are likely to be short-lived iu a dynamically complex euvironnieut like a galaxy cluster. they will nix iuto a nore diffuse. extended euvelope.," Because these features are likely to be short-lived in a dynamically complex environment like a galaxy cluster, they will mix into a more diffuse, extended envelope." + Whether or not this euvelope is a dviiauicallv or structurally distinct eutitv roni the galaxy itself is a subject of considerable debate., Whether or not this envelope is a dynamically or structurally distinct entity from the galaxy itself is a subject of considerable debate. + Conzalez (2005) argue that in clusters with clear BCGs. the intracluster light settles iuto a structurally distinct compoucut from the ealaxian light of the BCC. and inodel the two compoucuts using distinet +t!! xofiles.," Gonzalez (2005) argue that in clusters with clear BCGs, the intracluster light settles into a structurally distinct component from the galaxian light of the BCG, and model the two components using distinct $r^{1/4}$ profiles." + They fud that. im their sample of BCCs. the outer profile typically contains of the total uninositv. and has au effective radius 10.LO times larecr hau the immer component.," They find that, in their sample of BCGs, the outer profile typically contains $\sim$ of the total luminosity, and has an effective radius 10–40 times larger than the inner component." + If we consider MBT in this way. we fiud a smaller fraction of light iu the extended envelope (50%)) than typical in the Conzalez siuuple.," If we consider M87 in this way, we find a smaller fraction of light in the extended envelope ) than typical in the Gonzalez sample." + However. Virgo is somewhat different from those BCC clusters. iu that it has a number of comparably bright ealaxies (M8T at the center: M86 projected aawav: and MI9 tto the south).," However, Virgo is somewhat different from those BCG clusters, in that it has a number of comparably bright galaxies (M87 at the center; M86 projected away; and M49 to the south)." + With multiple bright galaxies aud. both spatial aud kinematic substructure. Virgo may represeut a dynamically less-evolved progenitor to the Conzalez clusters. in which case the lower fraction of light in the envelope may be a signature of au still-developiug ICL Rudick 2006).," With multiple bright galaxies and both spatial and kinematic substructure, Virgo may represent a dynamically less-evolved progenitor to the Gonzalez clusters, in which case the lower fraction of light in the envelope may be a signature of an still-developing ICL Rudick 2006)." + This iufereuce echoes that of IK09. who arene based on the systematics of MB? Sérrsic fit that the ealaxy is at best only aweek cD ealaxy.," This inference echoes that of K09, who argue based on the systematics of M87's Sérrsic fit that the galaxy is at best only a cD galaxy." + Iu this context. it is also interesting to look at ALL9.," In this context, it is also interesting to look at M49." + AII9 is the dominant galaxy in the Vireo Southern Extension (VSE). and somewhat more luninous than AIST.," M49 is the dominant galaxy in the Virgo Southern Extension (VSE), and somewhat more luminous than M87." + Tf clusters build through the hierarchical accretion of sub-chuups. the sub-chuups themselves may have their own diffuse lieht component. as suggested in the simulations by Rucick (2006).," If clusters build through the hierarchical accretion of sub-clumps, the sub-clumps themselves may have their own diffuse light component, as suggested in the simulations by Rudick (2006)." + Tf the VSE is an evolved group now being accreted into the Virgo cluster. it may have a structure similar to (albeit smaller tha) that of the BCC clusters of Gouzalez (2005).," If the VSE is an evolved group now being accreted into the Virgo cluster, it may have a structure similar to (albeit smaller than) that of the BCG clusters of Gonzalez (2005)." +" Aud iudeed. the 2dV ft for ALL9 shows a higher fraction of light )) iu the outer component than docs M87. but with a auch smaller characteristic scale (r0,,;0(M 49) = ro ualMST))."," And indeed, the 2dV fit for M49 shows a higher fraction of light ) in the outer component than does M87, but with a much smaller characteristic scale $r_{e,out}$ (M49) = $r_{e,out}$ (M87))." + While these results are cousisteut with a scenario of a gradual. on-going buiktup of ICL in Virgo. there are several important caveats.," While these results are consistent with a scenario of a gradual, on-going buildup of ICL in Virgo, there are several important caveats." + First. the 2dV profiles are not clearly superior to regular Sérrsic fits. aud the justification for dividing hunünositv iuto an imucr and outer component based ou these fits is not strong.," First, the 2dV profiles are not clearly superior to regular Sérrsic fits, and the justification for dividing luminosity into an inner and outer component based on these fits is not strong." + Even he choice of functional form for the division is the source of some debate Seigar (2007) areue that an inner Sérrsic | outer exponential ft is a better description of he lisht profile for cD ealaxies., Even the choice of functional form for the division is the source of some debate – Seigar (2007) argue that an inner Sérrsic + outer exponential fit is a better description of the light profile for cD galaxies. +" However. given the fact hat the additional free parameter of the 20V fit over the Sérrsic fit did not result in significautly better profile fits or our galaxies. we do not pursue these higher order fits rere,"," However, given the fact that the additional free parameter of the 2dV fit over the Sérrsic fit did not result in significantly better profile fits for our galaxies, we do not pursue these higher order fits here." + Given our results. we paint a plausible picture of the dynamics of the galaxies within the Virgo Cluster.," Given our results, we paint a plausible picture of the dynamics of the galaxies within the Virgo Cluster." + Sitting at the ceuter of the cluster. ALS7 experiences a rain of sanaller galaxies which are being tidally stripped by the cluster potential. leading to the long ciffuse streams secu to the NW of ALS7.," Sitting at the center of the cluster, M87 experiences a rain of smaller galaxies which are being tidally stripped by the cluster potential, leading to the long diffuse streams seen to the NW of M87." + Due to encounters with other galaxies, Due to encounters with other galaxies +"of existence L,,5,€L«ον.","of existence $ L_{min} < { L } +< L_{max} $." + In this distribution the mode is at μμ., In this distribution the mode is at $L_{min}$ . + section 2.2 first introduces the 2D Voronoi diagrams and then describes the mathematical details (hat allow us to deduce (wo new physical functions lor luminosity of galaxies and section 3. reports a first test based on the SDSS photometric catalog.," Section \ref{luminosity_my} + first introduces the 2D Voronoi diagrams and then describes the mathematical details that allow us to deduce two new physical functions for luminosity of galaxies and Section \ref{test} reports a first test based on the SDSS photometric catalog." + In Section 4 the red-shift dependence of (he Schechter ΠΟΙΟ aud the first new function are explored in detail., In Section \ref{secz} the red-shift dependence of the Schechter function and the first new function are explored in detail. + Section 5 reports the mass evaluation for galaxies based on the first luminosity finetion as well as a new formula for the limiting mass., Section \ref{secmass} reports the mass evaluation for galaxies based on the first luminosity function as well as a new formula for the limiting mass. + Section 6. summnmarises ihe results., Section \ref{conclusions} summarises the results. + The first paragraph briefly introduces the 2D Voronoi diagrams as produced by two tvpes of seeds., The first paragraph briefly introduces the 2D Voronoi diagrams as produced by two types of seeds. +" These two statistical distributions adopted to fit the area of the irregular Voronoi polveons can be taken as a starting point to construct (wo luminosity functions Lor galaxies,", These two statistical distributions adopted to fit the area of the irregular Voronoi polygons can be taken as a starting point to construct two luminosity functions for galaxies. + When the seeds are randomly and uncorrelated distributed. are called Poisson Voronoi diagrams.," When the seeds are randomly and uncorrelated distributed, are called Poisson Voronoi diagrams." + A great number of natural phenomena are described by Poisson Voronoi diagrams. we cite some of them: lattices in quantum fiekl theory. see Drouffe&Itzvkson(1984) conductivity and percolation in granular composites. see Jerauldetal.(1984a) ancl Jeraukletal. (1984b):: modelling growth of metal clusters on amorphous substrates. see Dicenzo&Wertheim(1989):the statistical mechanics of simple glass forming svstems in 2D. see Henischeletal.(2007): modelling of material interface evolution in grain growth of polvervstalline materials. see Lee&Chen(2006).," A great number of natural phenomena are described by Poisson Voronoi diagrams, we cite some of them: lattices in quantum field theory, see \cite{Drouffe1984} ; conductivity and percolation in granular composites, see \cite{Jerauld1984_a} and \cite{Jerauld1984_b}; ; modelling growth of metal clusters on amorphous substrates, see \cite{Dicenzo1989};the statistical mechanics of simple glass forming systems in 2D, see \cite{Hentschel2007}; modelling of material interface evolution in grain growth of polycrystalline materials, see \cite{Lee2006}." +. When the seeds are randomly and uncorrelated distributed. are called Poisson Voronoi diagrams.," When the seeds are randomly and uncorrelated distributed, are called Poisson Voronoi diagrams." + A great number of natural phenomena are described by Poisson Voronoi diagrams . we cite some of them: lattices in quantum field theory. see Droulle&Itzvkson(1984): conductivity and percolation in eranular composites. see Jerauldetal.(1984a). ancl Jerauldοἱal.(1984b):: modelling erowth of metal clusters on amorphous substrates. see Dicenzo&Wertheim(1989): the statistical mechanics of simple elass forming svstems in 2D. see IHentscheletal.(2001): modelling of malerial interlace evolution in grain growth of polverystalline materials. see (2006).," A great number of natural phenomena are described by Poisson Voronoi diagrams , we cite some of them: lattices in quantum field theory, see \cite{Drouffe1984} ; conductivity and percolation in granular composites, see \cite{Jerauld1984_a} and \cite{Jerauld1984_b}; modelling growth of metal clusters on amorphous substrates, see \cite{Dicenzo1989}; the statistical mechanics of simple glass forming systems in 2D, see \cite{Hentschel2007}; modelling of material interface evolution in grain growth of polycrystalline materials, see \cite{Lee2006}." +. À review of the Voronoi diagrams applied to the spatial distribution ofthe galaxies can be foundin Zaninetti(2006).. IIere weare interested in (he fragmentation of a 2D laver, A review of the Voronoi diagrams applied to the spatial distribution ofthe galaxies can be foundin \cite{Zaninetti2006}.. Here weare interested in the fragmentation of a 2D layer +variations in ayand 75.,variations in $m_1$and $m_2$. +" We found that decreasing T by 100 K causes the masses to grow by 7—10%.. while an increase in My, by -0.1 mag makes them larger by 10—[5%."," We found that decreasing $T$ by 100 K causes the masses to grow by $7-10$, while an increase in $M^o_{bol}$ by $-0.1$ mag makes them larger by $10-15$." +. At à first glance. focusing on semi-detached systems seems too restrictive.," At a first glance, focusing on semi-detached systems seems too restrictive." + To see it clearly. suppose that the visible component is entirely contained within its Roche lobe.," To see it clearly, suppose that the visible component is entirely contained within its Roche lobe." +" Then in order to recover M5, we would have to increase the orbital separatiol a.", Then in order to recover $M^o_{bol}$ we would have to increase the orbital separation $a$. + Since the period P is fixed. the masses would have to increase. too.," Since the period $P$ is fixed, the masses would have to increase, too." + To keep the observed velocity amplitude constant. the inclination / would have to decrease.," To keep the observed velocity amplitude constant, the inclination $i$ would have to decrease." +" For that reason. and also because the visible component would now be less deformed. AV, would also decrease."," For that reason, and also because the visible component would now be less deformed, $\Delta V_c$ would also decrease." + This way the range of q for which the ratio ΑΙΑΗ=1 could be extended onto fits which for semi-detached systems yield Α.Α>1., This way the range of $q$ for which the ratio $\Delta V_c/\Delta V_{obs}\approx1$ could be extended onto fits which for semi-detached systems yield $\Delta V_c/\Delta V_{obs}>1$. + 1 principle. it is even possible that //; and #2 derived for some mass ratio g#qp from detached fits could be smaller tha m(9) and m3Gp).," In principle, it is even possible that $m_1$ and $m_2$ derived for some mass ratio $q\ne q_b$ from detached fits could be smaller than $m_1^{sd}(q_b)$ and $m_2^{sd}(q_b)$." + However. upon verifying this possibility we found that in most cases the detached fit results in either too low an amplitude for the light-curve or masses larger tha those obtained for gp. so that the extension of the g-range I:non marginal (1f any).," However, upon verifying this possibility we found that in most cases the detached fit results in either too low an amplitude for the light-curve or masses larger than those obtained for $q_b$, so that the extension of the $q$ -range is marginal (if any)." + We conclude that the errors in the mass limit caused by neglecting detached configurations are smaller tha those related to bolometric corrections or the color-temperature scale., We conclude that the errors in the mass limits caused by neglecting detached configurations are smaller than those related to bolometric corrections or the color-temperature scale. + Another possible source of errors is the assumption that the whole light output of the system originates in the component responsible for the observed spectrum., Another possible source of errors is the assumption that the whole light output of the system originates in the component responsible for the observed spectrum. + The components of the only system in our sample in which two sets of velocities could be measured differ in brightness by AM=| mag.," The components of the only system in our sample in which two sets of velocities could be measured differ in brightness by $\Delta +M\approx 1$ mag." + Assuming that in the remaining systems AM.=2 mag causes their brighter components to be dimmer by 0.16 mag.," Assuming that in the remaining systems $\Delta M = +2$ mag causes their brighter components to be dimmer by 0.16 mag." +" The corresponding decrease in masses. estimated from the general relation between mass and M7, mentioned earlier. amounts to 15-20."," The corresponding decrease in masses, estimated from the general relation between mass and $M^o_{bol}$ mentioned earlier, amounts to $15-20$." + Quantitative results of the analysis are shown in Tables 3-13. and discussed in Sect. 3.3..," Quantitative results of the analysis are shown in Tables 3-13, and discussed in Sect. \ref{sect: Results}." + The bestfits are indicated with an asterisk in the last column of each table. and the corresponding computed light and velocity curves are displayed in Figs. 3.. 4.. 5 ," The bestfits are indicated with an asterisk in the last column of each table, and the corresponding computed light and velocity curves are displayed in Figs. \ref{fig: bs1}, \ref{fig: bs2}," +and 6.. along with the observational data.," \ref{fig: sd} and \ref{fig: +tms}, along with the observational data." +V214.. Assuming that the visible component is the secondary results in computed light-curve amplitudes consistently much too low., Assuming that the visible component is the secondary results in computed light-curve amplitudes consistently much too low. +" Assuming that it is the primary makes the difference between AV,,, and AV, smaller. but still unacceptable."," Assuming that it is the primary makes the difference between $\Delta V_{obs}$ and $\Delta +V_c$ smaller, but still unacceptable." +" In order to make AV, larger. we are forced to look for solutions in which both components contribute to the observed ellipticity effect."," In order to make $\Delta V_c$ larger, we are forced to look for solutions in which both components contribute to the observed ellipticity effect." +" Based on the simplest possible assumption that the system is in contact. we apply the following procedure: i) set qz 1) adjust a so that the combined M, of the system is 2.44 mag: in) adjust / so that the computed velocity curve agrees with the observed one: 1v) check if the computed light curve agrees with the observed one."," Based on the simplest possible assumption that the system is in contact, we apply the following procedure: i) set $q$; ii) adjust $a$ so that the combined $M_{bol}$ of the system is 2.44 mag; iii) adjust $i$ so that the computed velocity curve agrees with the observed one; iv) check if the computed light curve agrees with the observed one." + The fits are shown in Table 3.. and we conclude that the available data favor a system with a rather large mass ratio. which must have undergone significant mass transfer (and may still be transferring mass at a low rate).," The fits are shown in Table \ref{tab: V214c}, and we conclude that the available data favor a system with a rather large mass ratio, which must have undergone significant mass transfer (and may still be transferring mass at a low rate)." + Obviously. the sum a=omy+mo should not exceed two turnoff masses of the youngest population of w Cen. re. 1.84. M4. (Norris2004).," Obviously, the sum $m=m_1+m_2$ should not exceed two turnoff masses of the youngest population of $\omega$ Cen, i.e. 1.84 $M_\odot$ \citep{nor04}." +". Given the rather large errors in the mass estimates due to uncertainties in T and M7,. one may accept that this requirement is fulfilled by at least the first two fits in Table 3..V251.."," Given the rather large errors in the mass estimates due to uncertainties in $T$ and $M^o_{bol}$, one may accept that this requirement is fulfilled by at least the first two fits in Table \ref{tab: V214c}." +" Like in the previous cases. assuming that the spectrum originates in the secondary we find that for all g values AV, is much smaller than AY,,,."," Like in the previous cases, assuming that the spectrum originates in the secondary we find that for all $q$ values $\Delta V_c$ is much smaller than $\Delta V_{obs}$." + Assigning the spectrum to the primary leads to the results displayed in Table 4.., Assigning the spectrum to the primary leads to the results displayed in Table \ref{tab: V251p}. + As the total mass is markedly smaller than 1.84. M... we seem to have a system which not only underwent mass transfer. but also lost a significant amount of V254.," As the total mass is markedly smaller than 1.84 $M_\odot$, we seem to have a system which not only underwent mass transfer, but also lost a significant amount of ." +. Assuming that the spectrum originates from. the secondary leads once more to amplitude ratios AV./AVa. which for all mass ratios are much smaller than unity., Assuming that the spectrum originates from the secondary leads once more to amplitude ratios $\Delta V_c/\Delta V_{obs}$ which for all mass ratios are much smaller than unity. + Upon adopting that the source of the spectrum is the primary we get the results displayed in Table 5.. which suggests that V254 is similar to," Upon adopting that the source of the spectrum is the primary we get the results displayed in Table \ref{tab: V254p}, , which suggests that V254 is similar to" +(0.7imag from the stellar locus). which relax the signal to noise requirements cousiderably.,"$\sim 0.7~\mag$ from the stellar locus), which relax the signal to noise requirements considerably." + Tf gamma ray bursts are highly collimated. we expect to observe many more atterglows than GRBs (Rhoads 1997).," If gamma ray bursts are highly collimated, we expect to observe many more afterglows than GRBs (Rhoads 1997)." + The search for such “orphan afterelows is an muportaut aud lareely modelindependent1Weὰ way-xX of “toasttestingeo GRBCORB collimation., The search for such “orphan afterglows” is an important and largely model-independent way of testing GRB collimation. +«Mnatfi Color-based techniques will be a valuable addition to orphan afterglow searches., Color-based techniques will be a valuable addition to orphan afterglow searches. +" Aftcrglows remain rare phenomena even iu extreme collimation scenarios, and in order to find one it will be lecessary to survey a large area of sky that will contain many quasars."," Afterglows remain rare phenomena even in extreme collimation scenarios, and in order to find one it will be necessary to survey a large area of sky that will contain many quasars." +" Thus. orphan afterglow searches must combine variability with color tests o be reliable,"," Thus, orphan afterglow searches must combine variability with color tests to be reliable." +" When enough filters are observed simultaneously in a field where au archival first epoch is available. it will be possible to identify rew sources. test their colors for cousistenev witli a power law spectruii and start intensive followup of any viable afferelow candidates,"," When enough filters are observed simultaneously in a field where an archival first epoch is available, it will be possible to identify new sources, test their colors for consistency with a power law spectrum, and start intensive followup of any viable afterglow candidates." + This will allow uuch greater confidence in the ideutification of orphan afterglows than is presently possible. since good spectra and Light curves can then be used ο distinguish real afterglows from variable stars. ugh redshift supernovae. active galactic uncle. wicrolensing events. and other optically variable SOULCOS.," This will allow much greater confidence in the identification of orphan afterglows than is presently possible, since good spectra and light curves can then be used to distinguish real afterglows from variable stars, high redshift supernovae, active galactic nuclei, microlensing events, and other optically variable sources." + As au illustrative example. cousider Sloan Digital Sky Survey (SDSS: see Iuapp et al 1999).," As an illustrative example, consider Sloan Digital Sky Survey (SDSS; see Knapp et al 1999)." + The SDSS southern strip will cover an area ~200 degree? to about 22ud magnitude iu 5 broadband filters many ( 15) times., The SDSS southern strip will cover an area $\sim 200$ $^2$ to about 22nd magnitude in 5 broadband filters many $\sim 45$ ) times. + The known CRB rate is ~3 per sky per αν. and bright afterelows remain above 22nd magnitude for a period ~| davs.," The known GRB rate is $\sim 3$ per sky per day, and bright afterglows remain above 22nd magnitude for a period $\sim 4$ days." + Thus the southern strip has an effective ⋝⊐⊽p ∙∙↴↔ . ↪≧↸∖↥⋅∐⋜∏⋝↸∖↕∙≋∙∙↕≧⋜∐⋅↑∪↕∐∐∙≼⊲," Thus the southern strip has an effective coverage of $4 \times 10^4 \hbox{degree}^2 +\day$." +"∙∙↕≻↕⊑∏⋝↥⋅↕∑↕∪∙∫⇀⋈ survey will. cover --10 degree? ...m a single ↴⋅⋝⋅niaegius""n epoch.", The northern SDSS survey will cover $10^4$ $^2$ in a single imaging epoch. +" Fortunately, GRB afterglows would likely be targeted for spectra based on their quasar-like colors. vielding a second epoch."," Fortunately, GRB afterglows would likely be targeted for spectra based on their quasar-like colors, yielding a second epoch." + The northern survey thus provides another ~|<10!deeree?day.," The northern survey thus provides another $\sim 4 +\times 10^4 \hbox{degree}^2 \day$." + Both parts together would be expected to detect ~6 CRB afterelows., Both parts together would be expected to detect $\sim 6$ GRB afterglows. + If GRBs are tightly collimated (opening angles = 107). the expected number of orphan afterglows rises to Z25.," If GRBs are tightly collimated (opening angles $\la 10^\circ$ ), the expected number of orphan afterglows rises to $\ga 25$." + By using the color space properties to ideutifv these afterglows. such a survey can place strong Ημες on the collimation anele aud hence euergev requireciieuts of eiiuua pav bursts.," By using the color space properties to identify these afterglows, such a survey can place strong limits on the collimation angle and hence energy requirements of gamma ray bursts." + Color-based searches will allow faster ideutification of many emiunia ray burst afterelows., Color-based searches will allow faster identification of many gamma ray burst afterglows. + Liteusive followup of these afterglows can then beein earlier and at brighter fax levels. viclding a larger sample ofbursts for which spectroscopic redshifts aud well measured spectral energy. distributious: (iuchiding: roughly svuoptic data at X-rav. optical. uea-infrared. subiuillieter. aud radio waveleneths) can be obtained.," Intensive followup of these afterglows can then begin earlier and at brighter flux levels, yielding a larger sample of bursts for which spectroscopic redshifts and well measured spectral energy distributions (including roughly synoptic data at X-ray, optical, near-infrared, submillimeter, and radio wavelengths) can be obtained." + Such data sets are crucial to detailed studies of afterglow plivsics., Such data sets are crucial to detailed studies of afterglow physics. + Additionally. sinele-epoch color-based searches may vield a more easily characterized statistical suuple of afterglow detections and nondetectious than is currently available.," Additionally, single-epoch color-based searches may yield a more easily characterized statistical sample of afterglow detections and nondetections than is currently available." + Such samples will allow reliable studies of the population properties of eamuna rav burst afterelows. and therebv open the wav for new insights into the uature of euuna rav bursts.," Such samples will allow reliable studies of the population properties of gamma ray burst afterglows, and thereby open the way for new insights into the nature of gamma ray bursts." + Tthauk Sangecta Malbotra for extensive discussions and comments on an carly draft of this paper: Audy Fruchter for suggesting a harder look at IR excess methods: aud Mauro Ciavalisco. Arjun Dey. Norm Crogiu. aud Richard Cree for additional discussious.," I thank Sangeeta Malhotra for extensive discussions and comments on an early draft of this paper; Andy Fruchter for suggesting a harder look at IR excess methods; and Mauro Giavalisco, Arjun Dey, Norm Grogin, and Richard Green for additional discussions." + Finally. I thank Arne Hendon aud the USNOtm GRD team for providiusc» freely the photometric calibration data for CRB fields that allowed the first cuypirical test of this iethod.," Finally, I thank Arne Henden and the USNO GRB team for providing freely the photometric calibration data for GRB fields that allowed the first empirical test of this method." +" This work was supported by au Institute Fellowship at The Space Telescope Science. Institute (STScI). which is operated by AURA under NASA coutract NAS 5-26555,"," This work was supported by an Institute Fellowship at The Space Telescope Science Institute (STScI), which is operated by AURA under NASA contract NAS 5-26555." +total and spectral solar irradiance.,total and spectral solar irradiance. + The groups needed for capturing the salient features of the solar spectral variability are: the quiet sun. sunspots (umbra and penumbra). and bright magnetic structures (faculae and the network).," The groups needed for capturing the salient features of the solar spectral variability are: the quiet sun, sunspots (umbra and penumbra), and bright magnetic structures (faculae and the network)." + Models such as the SATIRE (Spectral And Total Irradiance Reconstruction) models are also based on the same assumption and have been successfully employed to compute the evolution of the solar irradiance from days to millennia ?.., Models such as the SATIRE (Spectral And Total Irradiance Reconstruction) models are also based on the same assumption and have been successfully employed to compute the evolution of the solar irradiance from days to millennia \cite{krivova2003}. + However. while SATIRE models employ the intensities of each atmospheric component to compute the emission at a given wavelength. we use a more empirical and data-driven approach based on an artificial neural network (ANN).," However, while SATIRE models employ the intensities of each atmospheric component to compute the emission at a given wavelength, we use a more empirical and data-driven approach based on an artificial neural network (ANN)." + The main advantage of using an ANN instead of the intensities of each atmospheric component is the flexibility to recognize and predict temporal patterns from near-real time solar disk magnetograms and intensity images., The main advantage of using an ANN instead of the intensities of each atmospheric component is the flexibility to recognize and predict temporal patterns from near-real time solar disk magnetograms and intensity images. + The model. however. needs to be trained with real data so our assumption here ts that the spectra from SORCE are indeed the true representation of the SSL.," The model, however, needs to be trained with real data so our assumption here is that the spectra from SORCE are indeed the true representation of the SSI." + We employ a Layer-Recurrent Network (LRN) to model the complex relationships between the evolution of the bipolar magnetic structures (input) and the solar irradiance (output)., We employ a Layer-Recurrent Network (LRN) to model the complex relationships between the evolution of the bipolar magnetic structures (input) and the solar irradiance (output). + We follow the original structure proposed by ?.., We follow the original structure proposed by \cite{elman90}. . + Figure | presents a schematic representation of the LRN architecture., Figure \ref{Fig_ann} presents a schematic representation of the LRN architecture. + The network has two layers with one neuron in each layer., The network has two layers with one neuron in each layer. + While the network uses a nonlinear transfer function (hyperbolic tangent - ton) for the first laver. a linear transfer function is employed for the output layer.," While the network uses a nonlinear transfer function (hyperbolic tangent - $tanh$ ) for the first layer, a linear transfer function is employed for the output layer." + Additionally. there is a feedback loop. with a single delay. around the first layer.," Additionally, there is a feedback loop, with a single delay, around the first layer." + This feedback introduces memory in the system and helps the stabilizing the spectra when the inputs suffer from outliers., This feedback introduces memory in the system and helps the stabilizing the spectra when the inputs suffer from outliers. + The output of the first layer («aj;) at the discrete time instant f; is computed taking into account weighted input (Wp). the bias (54) and the weighted feedback (αι).," The output of the first layer $a_{1,i}$ ) at the discrete time instant $t_i$ is computed taking into account weighted input ${\boldsymbol W} {\boldsymbol p}$ ), the bias $b_1$ ) and the weighted feedback $L a_{1,i-1}$ )." + The input of the network is the n-element vector p., The input of the network is the n-element vector $p$. + The elements of the input vector p; are multiplied by weights w;., The elements of the input vector $p_j$ are multiplied by weights $w_j$. + The weighted values are then summed., The weighted values are then summed. + In this way. we can express mathematically the output of the first layer às The output of the second layer (o). which is the irradiance at a given wavelength and at a given discrete time ({1. 57). is represented by a linear combination In principle. solar disk magnetograms and intensity images can be employed directly as the input of the network.," In this way, we can express mathematically the output of the first layer as The output of the second layer $a_{1,i}$ ), which is the irradiance at a given wavelength and at a given discrete time $I(\lambda,t_i)$ ), is represented by a linear combination In principle, solar disk magnetograms and intensity images can be employed directly as the input of the network." + However. this would imply in a very large number of coefhicients to be determined. which is not computationally efficient.," However, this would imply in a very large number of coefficients to be determined, which is not computationally efficient." + One alternative is the transformation of the input images into a set of features., One alternative is the transformation of the input images into a set of features. + This process. which is known as feature extraction. isa form," This process, which is known as feature extraction, isa form" +The huuinositv fictions aud hnunuiuositv densities of the local universe are available at both wavelengths (0.2 and jan).,The luminosity functions and luminosity densities of the local universe are available at both wavelengths (0.2 and 60 $\mu$ m). + Therefore we can conipare sonie of their properties to the characteristics of individual sealaxies., Therefore we can compare some of their properties to the characteristics of individual galaxies. + The 60 gan local luminosity function aud density at z=0 have heen caleulated by Saunders ct al. (1990))., The 60 $\mu$ m local luminosity function and density at z=0 have been calculated by Saunders et al. \cite{saunders}) ). + The 0.2 iaa luminosity function aud density have been derived by Trever et al. (1998)), The 0.2 $\mu$ m luminosity function and density have been derived by Treyer et al. \cite{treyer}) ) + at à πασά z20.15., at a mean z=0.15. + From hese studies we can calculate the ratio of the local luminosity densities P0Po.ο at zt.," From these studies we can calculate the ratio of the local luminosity densities $\rm \rho_{60} +/\rho_{0.2}$ at z=0." + To this aim we correct the UV density for the redshift evolution., To this aim we correct the UV density for the redshift evolution. + From Madau et al. (1998)), From Madau et al. \cite{madau}) ) + we estimate that the Iuuinosity deusity increases by a factor L540.2 from z=0 to z=0.15 which is consistent with the estimates of Lilly et al. (1996)), we estimate that the luminosity density increases by a factor $\sim 1.5\pm 0.2$ from z=0 to z=0.15 which is consistent with the estimates of Lilly et al. \cite{lilly}) ) + aud. Cowie et al. (1999))., and Cowie et al. \cite{cowie}) ). + Applving this factor to the estimate of Trever et al., Applying this factor to the estimate of Treyer et al. + we obtain py»=ο10*hL.: /Mpe?., we obtain $\rm \rho_{0.2}=4.6\pm 2.0 ~10^7~h~L\odot/Mpc^3$ . + With poy=L2+ we find poofpoy2=0.9+0. bat z=0.," With $\rm \rho_{60}= +4.2\pm 0.4~10^7~h~L\odot/Mpc^3$ we find $\rm \rho_{60}/\rho_{0.2} = 0.9 \pm +0.4$ at z=0." + Iu the same way. frou pry=5.6+0.6107hiLAIpe? (Saunders et al. 19903).," In the same way, from $\rm \rho_{FIR}=5.6\pm 0.6~10^7~h~L\odot/Mpc^3$ (Saunders et al. \cite{saunders}) )," + wecalculate ppppo:=1.24.5.," we calculate $\rm \rho_{FIR}/\rho_{0.2} = +1.2\pm 0.5$." + Povpuo is reported in figures 2 aud:, $\rm \rho_{60}/\rho_{0.2}$ is reported in figures 2 and 3. + The ratio appears lower than almost all the ratios found for individual galaxies and is svstematically lower than all the median values calculated for increasing 60. pau huuinosity (figure 3V., The ratio appears lower than almost all the ratios found for individual galaxies and is systematically lower than all the median values calculated for increasing 60 $\mu$ m luminosity (figure 3). +"Universe, Our sample is FIR selected since we have searched for FIR galaxies detected in UV. therefore a bias toward Ίος FIR to UV flux ratio is expected and this bias Increases as we solec brighter ealaxies (figure 2)."," Our sample is FIR selected since we have searched for FIR galaxies detected in UV, therefore a bias toward large FIR to UV flux ratio is expected and this bias increases as we select brighter galaxies (figure 2)." + For conrparison. we can also re-consider the sample used by Duat Xu (1996)): he galaxies were primarily selected to have a UV ineasureiment and then searched in the IRAS database.," For comparison, we can also re-consider the sample used by Buat Xu \cite{buxu}) ): the galaxies were primarily selected to have a UV measurement and then searched in the IRAS database." + Ouly galaxies detected both in UV and FIR are considered., Only galaxies detected both in UV and FIR are considered. + Whereas the selection biases of this sample are very complicated since the primary selection is on the UV he bias toward the FIR is certainly less strong than for he IRAS/FOCA sample., Whereas the selection biases of this sample are very complicated since the primary selection is on the UV the bias toward the FIR is certainly less strong than for the IRAS/FOCA sample. +" Tn figure | the histograms of FryΕν ratio are reported for three sauples: the IRAS/FOCA sample (solid Πιο), the IVE/TRAS templates of Meurer et al. (1999)) ("," In figure 4 the histograms of $\rm F_{FIR}/F_{UV}$ ratio are reported for three samples: the IRAS/FOCA sample (solid line), the IUE/IRAS templates of Meurer et al. \cite{meurheck}) ) (" +dotted Ime) aud the sample of Buat Xu (dashed line).,dotted line) and the sample of Buat Xu (dashed line). + We can see that almost all the IRAS/FOCAÀ ealaxies aud he local IUE/IRAS templates exhibit a arecr ratio than he ratio of the ocal luminosity densities pri/ po». , We can see that almost all the IRAS/FOCA galaxies and the local IUE/IRAS templates exhibit a larger ratio than the ratio of the local luminosity densities $\rm \rho_{FIR}/\rho_{0.2}$ . +The situation is less extreme for the Buat Xu sample for which the median of the Frin/Fuy fux ratio is 1.66. vauslating to aye Οmag (0.91 mae with the 'Onuula of Meurer et al).," The situation is less extreme for the Buat Xu sample for which the median of the $\rm F_{FIR}/F_{UV}$ flux ratio is 1.66, translating to $\rm +a_{0.2}=0.71 ~mag$ (0.94 mag with the formula of Meurer et al.)." + This difference in the FIR aud UV properties of the samples explains the rather ow extinction found by Buat Na for this sauple as conrpared with those obained by Meurer et al., This difference in the FIR and UV properties of the samples explains the rather low extinction found by Buat Xu for this sample as compared with those obtained by Meurer et al. + The mean property of the local Universe im terms FIR to UV huninosity deusity ratio is not well represeuted by the saunples of galaxies considered here., The mean property of the local Universe in terms FIR to UV luminosity density ratio is not well represented by the samples of galaxies considered here. + Therefore much caution must be taken to estimate elobal correction for extinction to be applied to the Iuminositv function., Therefore much caution must be taken to estimate global correction for extinction to be applied to the luminosity function. + An explanation for the discrepaucy. between the Fey/Fy.2 ratio of individual galaxies aud the ratio of the local uunmnositv densities is that it is not the same galaxies which form the bulk of the UV. enudsson on one had and the FIR cunission ou the other haud., An explanation for the discrepancy between the $\rm F_{60}/F_{0.2}$ ratio of individual galaxies and the ratio of the local luminosity densities is that it is not the same galaxies which form the bulk of the UV emission on one hand and the FIR emission on the other hand. +" Indeed. the aree difference found in the shape of the two Iunuinositv ""ucetious is consistent with this explanation as already discussed iu Buat Burearella (19983)."," Indeed, the large difference found in the shape of the two luminosity functions is consistent with this explanation as already discussed in Buat Burgarella \cite{bubu}) )." + The adopted value of PoofPoe depeuds on the reliability of the 1unuinositv functions and is subject to some uncertainties.," The adopted value of $\rm +\rho_{60}/\rho_{0.2}$ depends on the reliability of the luminosity functions and is subject to some uncertainties." + Nevertheless very large modifications must be invoked to nake cousistent fιο Foo/Eo» ratios in our IRAS/FOCA sample aud the mean value of the local universe., Nevertheless very large modifications must be invoked to make consistent the $\rm F_{60}/F_{0.2}$ ratios in our IRAS/FOCA sample and the mean value of the local universe. + Moreover it would not explain the trend found of an increase of the Fou/Fuy.2 ratio with the FIR luninositv of the ealaxics., Moreover it would not explain the trend found of an increase of the $\rm F_{60}/F_{0.2}$ ratio with the FIR luminosity of the galaxies. + We have evaluated the contributionto the Iuuinositv function and the huuinosivdensity at 0.2 san (resp., We have evaluated the contributionto the luminosity function and the luminositydensity at 0.2 $\mu$ m (resp. + μα) of the galaxies as a function of their intrinsic, $\mu$ m) of the galaxies as a function of their intrinsic +This paper provides a pedagogical introduction to barvon acoustic oscillations (DAO). accessible to readers not necessarily familiar with details of large seale structure in the universe.,"This paper provides a pedagogical introduction to baryon acoustic oscillations (BAO), accessible to readers not necessarily familiar with details of large scale structure in the universe." + In addition. it summarizes some of the current issues plus and minus — with the use of BAO as a cosmological probe of the nature of dark energy.," In addition, it summarizes some of the current issues – plus and minus – with the use of BAO as a cosmological probe of the nature of dark energy." + For more quantitative. technical discussions of these issues. seeWhite(2005)..," For more quantitative, technical discussions of these issues, see\citet{mwhite05}." +bbetween visual miniunni and maxi.,between visual minimum and maximum. + This was already suggested. by. Lamers (1997). albeit a coustaut value of jj was auticipated.," This was already suggested by Lamers (1997), albeit a constant value of $\eta$ was anticipated." + Oi present calculations cannot be used to model the observed LBV variations. because we have assuned solar netallicities. whereas the LBVs are known to have an chhanced Πο aud N abundance (e.g.o Suuth et al.," Our present calculations cannot be used to model the observed LBV variations, because we have assumed solar metallicities, whereas the LBVs are known to have an enhanced He and N abundance (e.g. Smith et al." + 1991)., 1994). + Aloreover. «nce nost LBVs have already. suffered. severe uass loss in the past. their L./M. ratio will be higher iui for normal OB supereiauts.," Moreover, since most LBVs have already suffered severe mass loss in the past, their $L_*/M_*$ ratio will be higher than for normal OB supergiants." + Thisis incaus that LBVs are closer to their Eddiugton Lut. which oue may expect o have an effect on aalso.," This means that LBVs are closer to their Eddington limit, which one may expect to have an effect on also." + These combined effects explain the lack of a consistent behaviour of for LBV variations so far., These combined effects explain the lack of a consistent behaviour of for LBV variations so far. + Especially since it is not sure hat L. really remains coustant during the variations (see Lamers 19905)., Especially since it is not sure that $L_*$ really remains constant during the variations (see Lamers 1995). + We have investigated the nature of the observed. jump iu je ratio v4γιος Of the winds of xupergiauts near spectral ype Bl., We have investigated the nature of the observed jump in the ratio $\ratio$ of the winds of supergiants near spectral type B1. + Calculations for wind models of OB superegiauts show vat around Dig=25000Ts the mass-loss rate ipuups due to au iucrease in the Ime acceleration of Fe yclow the sonic poiut., Calculations for wind models of OB supergiants show that around $\teff = 25~000~\rm K$ the mass-loss rate jumps due to an increase in the line acceleration of Fe below the sonic point. + This jump iu is found in three different series of imuodoels., This jump in is found in three different series of models. +" Du allcases. je wind efficiency number gj=Alen(L.fe) mereases significantly, by about a actor of 2 to 3. if ddecreases froun about 27 500 I to about 22 500. Ik. Observations show that the ratio v4τις drops bv a factor of two around spectral type Bl."," In allcases, the wind efficiency number $\eta= \Mdot \vinf /(L_*/c)$ increases significantly, by about a factor of 2 to 3, if decreases from about 27 500 K to about 22 500 K. Observations show that the ratio $\ratio$ drops by a factor of two around spectral type B1." + Applving these values for v4/v. We predict a bi-stabilitv Jump iu oof about a factor of five.," Applying these values for $\ratio$, we predict a bi-stability jump in of about a factor of five." + So lis expected to increase by about this factor between 27 500 aud 22 500 Ix. We have argued that the mass loss is determined by the radiative acceleration in the subsonic part of the wind. ic. below rx1.038...," So is expected to increase by about this factor between 27 500 and 22 500 K. We have argued that the mass loss is determined by the radiative acceleration in the subsonic part of the wind, i.e. below $r \simeq 1.03 R_*$." + We found that this radiative acceleration ix dominated by the contribution of the Fe lines., We found that this radiative acceleration is dominated by the contribution of the Fe lines. + Therefore lis very sensitive to both the metal abundance aud to the ionization equilibrium of Fe., Therefore is very sensitive to both the metal abundance and to the ionization equilibrium of Fe. + Our models show that the ionization fraction of Fe and the subsonic radiative acceleration mereases steeply between ως 27 500 aud 25 000 Ik. This explains the calculated increase in lin this narrow tfeniperature range., Our models show that the ionization fraction of Fe and the subsonic radiative acceleration increases steeply between = 27 500 and 25 000 K. This explains the calculated increase in in this narrow temperature range. + The exact temperature of the bi-stability jump is somewhat ambiguous., The exact temperature of the bi-stability jump is somewhat ambiguous. + Observations indicate that the juu occurs around spectral type Bl. corresponding to Tig c 21 000 I& (Lamers et al.," Observations indicate that the jump occurs around spectral type B1, corresponding to $\teff$ $\simeq$ 21 000 K (Lamers et al." + 1995)., 1995). + If one would not completely trust the value of v4/vi« for the star IID 109867 (number 91 in Lamers et al. (, If one would not completely trust the value of $\ratio$ for the star HD 109867 (number 91 in Lamers et al. ( +1995)). because of its relatively large error bar. then Tig of the observed jump can casily occur at a few KI hieher.,"1995)), because of its relatively large error bar, then $\teff$ of the observed jump can easily occur at a few kK higher." + In fact we caunot expect the bi-stability jump to occur at one aud the same temperature for all limunosity classes; because the jump is sensitive to the lonization balance (uainly of Fe 111) iu the subsonic region ofthe wind aud hence to the eravity of the star.," In fact we cannot expect the bi-stability jump to occur at one and the same temperature for all luminosity classes, because the jump is sensitive to the ionization balance (mainly of Fe ) in the subsonic region of the wind and hence to the gravity of the star." + Our models predict that the jump will occur near Tig ~ 25 000 Ix. ITowever. this is sensitive to the assuniptions of the models: the adopted masses aud Imunuinosities aud to the assumption of the modified nebular approximation for the calculation of the ionization equilibrium of irou (sec Sect. 1D).," Our models predict that the jump will occur near $\Teff$ $\simeq$ 25 000 K. However, this is sensitive to the assumptions of the models: the adopted masses and luminosities and to the assumption of the modified nebular approximation for the calculation of the ionization equilibrium of iron (see Sect. \ref{sec:isa}) )." + A muore consistent treatment of the ionization and excitation equilibrium of the Fe-group elemoeuts may have two effects: ppredicted οι AL may alter. aud Tig at which the ionization ratio of e.c. Fe flips. may shift.," A more consistent treatment of the ionization and excitation equilibrium of the Fe-group elements may have two effects: predicted from $\Delta L$ may alter, and $\teff$ at which the ionization ratio of e.g. Fe flips, may shift." + Nevertheless. iu view of the very encouraging results using the modified nebular approximation iu the modeling of UV inctal-line forests (de I&oter et al.," Nevertheless, in view of the very encouraging results using the modified nebular approximation in the modeling of UV metal-line forests (de Koter et al." + 1998). we expect the error in at which the dominant ionization of Fe switches from to to be at mos a few ΚΙ. Furthermore. if a more consistent treatment would vield a change in this would most likely produce a systematic shift.," 1998), we expect the error in at which the dominant ionization of Fe switches from to to be at most a few kK. Furthermore, if a more consistent treatment would yield a change in this would most likely produce a systematic shift." + Since we are esseutiallv iuterested in relative shifts in M. we do uot expect that our conclusions reearcding the nature of the bi-stability jump would be affected.," Since we are essentially interested in relative shifts in $\mdot$, we do not expect that our conclusions regarding the nature of the bi-stability jump would be affected." + It is relevant to mention that Leitherer et al. (, It is relevant to mention that Leitherer et al. ( +1950) calculated atiuosphierie models for LBVs and. suggested that he recombination of von C»eroup elements fom doubly to sinely ionized stages. which according to them. occurs around 10 000 Tx. can explain Hucreases when LBVs approach thei maxima states.,"1989) calculated atmospheric models for LBVs and suggested that the recombination of iron group elements from doubly to singly ionized stages, which according to them, occurs around = 10 000 K, can explain increases when LBVs approach their maximum states." + We have found a Fe ionization/reconibiuation effect around == 25 000 Is for normal supereiauts., We have found a Fe ionization/recombination effect around = 25 000 K for normal supergiants. + We also anticipate that somewhere. at a lower value of a sIndlar jonization/recombination effect will occur for FeΠΠ. causing asecond bistabilitv jump.," We also anticipate that somewhere, at a lower value of a similar ionization/recombination effect will occur for Fe, causing a bi-stability jump." + Lamers et al. (, Lamers et al. ( +1995) already. mentioned the possible existeuce of a second bi-stability jump ivound == 10 000 I& from their determinations ofνους. but the observational evidence for this second jump was meaere.,"1995) already mentioned the possible existence of a second bi-stability jump around = 10 000 K from their determinations of, but the observational evidence for this second jump was meagre." + Possibly. this second jump real aud we anticipate that this second jump could very well originate ποια a Fe ionizationrecombination effect.," Possibly, this second jump real and we anticipate that this second jump could very well originate from a Fe ionization/recombination effect." + Furthermore. we have shown that the clements C.N and O are important line drivers in the part of the wind. whereas the part of the wind is donunated by the Ine acceleration due o Fe.," Furthermore, we have shown that the elements C, N and O are important line drivers in the part of the wind, whereas the part of the wind is dominated by the line acceleration due to Fe." + relliojensshowsanoverlayoftheobserver'sskyontheorbilalplaned =π/3 anda photon trajectory (null geodesic) that connects the source ancl the observer.,\\ref{fig_lens} shows an overlay of the observer's sky on the orbital plane $\theta = \pi/2$ and a photon trajectory (null geodesic) that connects the source and the observer. + The position angles of the lens. source star. and image are depicted as 5. 2. and a. and they are related (o ry and 94; by the followings.," The position angles of the lens, source star, and image are depicted as $\gamma$, $\beta$, and $\alpha$ , and they are related to $r_0$ and $\delta\varphi$ by the followings." +" where D, and D, ave the (radial) distances to the lens mass A/ and the source star [rom the observer.", where $D_\ell$ and $D_s$ are the (radial) distances to the lens mass $M$ and the source star from the observer. +" In the linear order small angle approximation. (he equations (22)) and (23)) become b= -4)):: D(a -- Dy = varphi(D, — D)("," In the linear order small angle approximation, the equations \ref{eqLensOne}) ) and \ref{eqLensTwo}) ) become b = ); D_s - ) = (D_s - )." +94) Using the Einstein deflection angle dy=46M/ry and ry=b—GAL&b. the familiar single lens equation is obtained. α," Using the Einstein deflection angle $\delta\varphi = 4GM/r_0$ and $r_0 = b - GM \approx b$, the familiar single lens equation is obtained. -" +ντι i) L\\)-—c— Given the angular positions of a source (2) anda lens (5). (here are usually (wo solutions for a: the source. lens. and (wo images are collinear in (he skv.," = - ) Given the angular positions of a source $\beta$ ) and a lens $\gamma$ ), there are usually two solutions for $\alpha$; the source, lens, and two images are collinear in the sky." + If the periastron distance ry—ReΊλια. however. the lens and source are aligned along the line of sight (9= 5). and the image forms on a ring due to the svimmetry around the axis connecting the observer and the mass M.," If the periastron distance $r_0 = R_E=D_1 \alpha_E$, however, the lens and source are aligned along the line of sight $\beta = \gamma$ ), and the image forms on a ring due to the symmetry around the axis connecting the observer and the mass $M$." + The angular radius of the ring image is given bv ap. (, The angular radius of the ring image is given by $\alpha_E$. ( +"There are two solutions a=tay, lor 0—7/2. and the axial svammnetry allows (wo solutions lor each value of @=[0.7] resulting in solutions of two half circles of the same radius ap.","There are two solutions $\alpha = \pm \alpha_E$ for $\theta = \pi/2$, and the axial symmetry allows two solutions for each value of $\theta = [0, \pi]$ resulting in solutions of two half circles of the same radius $\alpha_E$." + See for à wav to understand the transition [rom two images to two hall-circle images.), See \\ref{secBreak} for a way to understand the transition from two images to two half-circle images.) + The circular image is known as Einstein ring. hence the subscript E in ap.," The circular image is known as Einstein ring, hence the subscript $E$ in $\alpha_E$." + The oOeravily of the mass Mmakes the egeometry of the space around itspherical and focuses photons from the source to the observer: The source and observer are the two focal, The gravity of the mass $M$makes the geometry of the space around itspherical and focuses photons from the source to the observer; The source and observer are the two focal +(Weibetal2007:VauderWerf2010).,"\citep{Weiss.etal2007,VanDerWerf.etal2010}." +. Since hieh TLO abundauces can be generated in both. PDRs and NDRs (Aleijerink&Spaans2005j.. our data do not distinguish directly between these models.," Since high $\HtO$ abundances can be generated in both PDRs and XDRs \citep{Meijerink.Spaans2005}, our data do not distinguish directly between these models." + However. while N-vavs casily traverse and heat large σοι densities of gas. they are iueffiient at heating the dust. and dust temperatures higher than ~50I& are hard to achieve over extended regious (Yan1997:Meijeriuk&Spaans 2005)..," However, while X-rays easily traverse and heat large column densities of gas, they are inefficient at heating the dust, and dust temperatures higher than $\sim50\K$ are hard to achieve over extended regions \citep{Yan1997,Meijerink.Spaans2005}. ." + The hieh dust temperature of ~220Ix over a ~550pe radius region is more casily achieved in PDRs. generated by widespread star formation iu chuups of dense eas throughout the ciremuuitclear gas disk.," The high dust temperature of $\sim220\K$ over a $\sim550\pc$ radius region is more easily achieved in PDRs, generated by widespread star formation in clumps of dense gas throughout the circumnuclear gas disk." + Regions of several 100pe radius. with high 100sau optical depths. are locally found only iu the central reeious of ULIRGs (Solomonetal.1997).," Regions of several $100\pc$ radius, with high $100\mum$ optical depths, are locally found only in the central regions of ULIRGs \citep{Solomon.etal1997}." + The fact that in this study we find such a region in a QSO. provides support for the scenario where ULIRCs form the birtliplaces of OSOs (Saucersetal.1988).," The fact that in this study we find such a region in a QSO, provides support for the scenario where ULIRGs form the birthplaces of QSOs \citep{Sanders.etal1988}." +. If our sugeestion that the extended warm dust contimmi is eenerated by ΕΠ star formation πι APALO8279|5255 is correct. this star formation is takine place in the presence of the strong and pore N-ray radiation field generatedby the ACN (Callagheretal.shown2002:TlasinecrChartas 2002).," If our suggestion that the extended warm dust continuum is generated by circumnuclear star formation in $\APM{08279{+}5255}$ is correct, this star formation is taking place in the presence of the strong and penetrative X-ray radiation field generated by the AGN \citep{Gallagher.etal2002,Hasinger.etal2002,Chartas.etal2002}." +. As |x Tocuk&Spaaus(2010).. iu this situation yagiuentation is iulibited aud a top-heavy stellar Initial Mass Function is expected to result.," As shown by \citet{Hocuk.Spaans2010}, in this situation fragmentation is inhibited and a top-heavy stellar Initial Mass Function is expected to result." + It 3s possible hat this effect accounts for the extraordinary far-IR huninosity Epp=5«1057L. (corrected for eravitational amplification) of APALO8279|5255., It is possible that this effect accounts for the extraordinary far-IR luminosity $\LFIR=5\times10^{13}\Lsun$ (corrected for gravitational amplification) of $\APM{08279{+}5255}$. +" We rote also that iu the chumps iu our model. both turbulent Xessure Pan9DoH Gvhere p ds. the mass density+ of. he gas clump aud σι pon/23its turbulent velocity dispersion) and radiation pressure σωμα~Tolc (where σ is he Stefau-Boltzimanu constant and e the speed of light) exceed the thermal pressure Pay,~myky bv a larec factor."," We note also that in the clumps in our model, both turbulent pressure $\qu{P}{turb}\sim \rho\sigma_v^2/3$ (where $\rho$ is the mass density of the gas clump and $\sigma_v$ its turbulent velocity dispersion) and radiation pressure $\qu{P}{rad}\sim \tau_{100}\sigma\Td^4/c$ (where $\sigma$ is the Stefan-Boltzmann constant and $c$ the speed of light) exceed the thermal pressure $\qu{P}{th}\sim \nHt k\Tg$ by a large factor." + Inserting uunibers from) our best-fit model we fud that Pu3«10Scregein.7 while Pra~Paaκ107ergei7.," Inserting numbers from our best-fit model, we find that $\qu{P}{th}\sim 3\times 10^{-8}\un{erg}\pcmcub$, while $\qu{P}{turb}\sim\qu{P}{rad}\sim3\times +10^{-7}\un{erg}\pcmcub$ ." + Radiation pressure therefore plays an important role iu the clwnamics of the circumauuclear eas cloud., Radiation pressure therefore plays an important role in the dynamics of the circumnuclear gas cloud. + If the clumps are indeccl forming stars. as we are sugeesting.the star formation process is then close to Eddington-limited. in agreement with the model developed by Thompsonctal.(2005) for starburst reelons surrounding a supermassive black hole.," If the clumps are indeed forming stars, as we are suggesting,the star formation process is then close to Eddington-limited, in agreement with the model developed by \citet{Thompson.etal2005} for starburst regions surrounding a supermassive black hole." + Qur study demonstrates low raciiatively exited IT2O lines can be used to reveal the presence of extended infrared-opaque regions in galactic nuclei (even without spatially resolving these regions)., Our study demonstrates how radiatively exited $\HtO$ lines can be used to reveal the presence of extended infrared-opaque regions in galactic nuclei (even without spatially resolving these regions). + Furthermore. we can derive local couditious in the infrarec-opaque nuclear eas disk. which in the present case indicates close to Eddineton-lanited star formation.," Furthermore, we can derive local conditions in the infrared-opaque nuclear gas disk, which in the present case indicates close to Eddington-limited star formation." + While for local ealaxies observations frou space will remain necessary to observe the Πο lines. the Atacama Large Millimeter Array will make this diagnostic readily available iu ealaxies with sufficient redshift. without the aid of eravitational lensiug.," While for local galaxies observations from space will remain necessary to observe the $\HtO$ lines, the Atacama Large Millimeter Array will make this diagnostic readily available in galaxies with sufficient redshift, without the aid of gravitational lensing." + DR acknowledges support frou NASA through a Spitzer erant., DR acknowledges support from NASA through a Spitzer grant. + We thank Melanie Waips for expert assistance withthe IRAM data reduction. aud Rodrigo Ibata for providing the NICMOS image used in ," We thank Melanie Krips for expert assistance withthe IRAM data reduction, and Rodrigo Ibata for providing the NICMOS image used in ." +We also thank Nauder Ticlens for commenting on au earlier version of this paper., We also thank Xander Tielens for commenting on an earlier version of this paper. +Using Eq.,Using Eq. + 11. we can write or where Therefore. the derivative in the first term in Eq.," \ref{eq:perturb_m} we can write or where Therefore, the derivative in the first term in Eq." + 10 becomes In the second term in Eq., \ref{eq:sph_rad_tran_m} becomes In the second term in Eq. + 10. there is 7!=(ro+ory!., \ref{eq:sph_rad_tran_m} there is $r^{-1} = (r_0 + \delta r)^{-1}$. + Because we assume that 0r«ry. we can perform a binomial expansion of r. keeping only the first two terms. to get by using Eq. 2..," Because we assume that $\delta r \ll r_0$, we can perform a binomial expansion of $r^{-1}$, keeping only the first two terms, to get by using Eq. \ref{eq:dm}." + Using these. the spherical radiative. transfer. equation. including perturbations. becomes Clearing the I[/(1+6mm’) term and expanding Eq. 22..," Using these, the spherical radiative transfer equation, including perturbations, becomes Clearing the $1/(1 + \delta m^{\prime})$ term and expanding Eq. \ref{eq:sph_rad_tran_pert}," + ignoring terms with second-order perturbations. gives Note that the left hand side of Eq.," ignoring terms with second-order perturbations, gives Note that the left hand side of Eq." + 23. contains and the right hand side has and these equal each other because they are just the two sides of Eq., \ref{eq:sph_rad_tran_pert_expand} contains and the right hand side has and these equal each other because they are just the two sides of Eq. + 10. for the current structure., \ref{eq:sph_rad_tran_m} for the current structure. + Canceling these out of Eq., Canceling these out of Eq. + 23 leaves the first-order perturbation of the spherical equation of radiative transfer The first angular moment of the first-order perturbation equation is obtained by multiplying Eq., \ref{eq:sph_rad_tran_pert_expand} leaves the first-order perturbation of the spherical equation of radiative transfer The first angular moment of the first-order perturbation equation is obtained by multiplying Eq. + 26 by jc and integrating over all µ. to get Dividing Eq.," \ref{eq:sph_rad_tran_1} by $\mu$ and integrating over all $\mu$, to get Dividing Eq." + 27— by Καν). and integrating over all frequencies. we obtain We now assume that the correct choice of 072 will make the left hand side of Eq.," \ref{eq:sph_pert_moment_1} by $k_0(\nu)$ and integrating over all frequencies, we obtain We now assume that the correct choice of $\delta m$ will make the left hand side of Eq." + 28 go to zero., \ref{eq:sph_moment_1_int} go to zero. + That is. we assume that the perturbations of the radiation field. 6K and 0J. vanish when the correct atmospheric structure is obtained.," That is, we assume that the perturbations of the radiation field, $\delta K$ and $\delta J$, vanish when the correct atmospheric structure is obtained." + These assumptions are equivalent to the assumptions used in ?.. equation 25. and in ?.. equation 7.5.," These assumptions are equivalent to the assumptions used in \citet{1964SAOSR.167...83A}, equation 25, and in \citet{1970SAOSR.309.....K}, equation 7.5." + This leaves the right hand side of Eq., This leaves the right hand side of Eq. +" 28 as a differential equation for ov. where and with, being the radially dependent Eddington flux that we need to achieve."," \ref{eq:sph_moment_1_int} as a differential equation for $\delta m$, where and with being the radially dependent Eddington flux that we need to achieve." + The general solution to Eq., The general solution to Eq. + 29 is where rii is an integration variable., \ref{eq:delta_r_deq} is where $\tilde{m}$ is an integration variable. + The correction for the mass column density found above has assumed that all the energy is carried by radiation., The correction for the mass column density found above has assumed that all the energy is carried by radiation. + If the atmospheric. temperature is cool enough. significant amounts of energy can also be carried by convection in the deeper. less transparent levels of the atmosphere.," If the atmospheric temperature is cool enough, significant amounts of energy can also be carried by convection in the deeper, less transparent levels of the atmosphere." + calculates the convective energy transport by the mixing length approximation., calculates the convective energy transport by the mixing length approximation. + The equations in ?. do not contain the radial variable explicitly. but they do contain the surface gravity. g. which now varies with r.," The equations in \citet{1970SAOSR.309.....K} do not contain the radial variable explicitly, but they do contain the surface gravity, $g$, which now varies with $r$." + However. the implementation of those equations replaces e in terms of the total pressure. which now includes the geometry.," However, the implementation of those equations replaces $g$ in terms of the total pressure, which now includes the geometry." + Therefore. there is no need to modify the original code to include convection in the spherical temperature correction. and Eq.," Therefore, there is no need to modify the original code to include convection in the spherical temperature correction, and Eq." + 29 remains the same. with the addition of convective terms in the coefficients do.bo and co as follows:," \ref{eq:delta_r_deq} remains the same, with the addition of convective terms in the coefficients $a_0, \ b_0$ and $c_0$ as follows:" +To constrain the underlviung stellar population. we consider a suite of svnthetic stellar population models generated using the Druzual&Charlot(2003) spectral library.,"To constrain the underlying stellar population, we consider a suite of synthetic stellar population models generated using the \citet{bc03} + spectral library." + We adopt a Salpeter initial mass function wilh a range of metallicity from 1/5 solar to solar and a range of star formation history [vom a single burst to an exponentially declining star formation rate of e-Iolding tme 300 Myr., We adopt a Salpeter initial mass function with a range of metallicity from 1/5 solar to solar and a range of star formation history from a single burst to an exponentially declining star formation rate of e-folding time 300 Myr. + We include no dust in our svntlietic spectra., We include no dust in our synthetic spectra. + Comparing the observed narrow-band features ancl broad-band photometry with model predictions allows us lo constrain the stellar age in galaxy C., Comparing the observed narrow-band features and broad-band photometry with model predictions allows us to constrain the stellar age in galaxy $G^*$. + The results are presented in Figure 3.. where the observed spectral energy distribution of the galaxy is shown in the top panel together with the best-fit model.," The results are presented in Figure \ref{fig:model}, where the observed spectral energy distribution of the galaxy is shown in the top panel together with the best-fit model." + The bottom panel of Figure 3. shows the likelihood distribution function versus stellar age. indicating that the last major episode of star formation occurred at 2 1.3 Gyr ago.," The bottom panel of Figure \ref{fig:model} shows the likelihood distribution function versus stellar age, indicating that the last major episode of star formation occurred at $\approx$ 1.3 Gyr ago." + The velocity dispersion along the slit angle was 460 km !. suggesting that G is a massive galaxv.," The velocity dispersion along the slit angle was 460 km $^{-1}$, suggesting that $G^*$ is a massive galaxy." + The absolute A-band magnitude is Mjzz—23.3 mag. imiplving il is 1.6 { lor early-twpe galaxies (Ixochanekοἱal.2001).," The absolute $K$ -band magnitude is $M_K \approx -23.3$ mag, implying it is 1.6 $L_*$ for early-type galaxies \citep{kpf+01}." +". The best-fit stellar population and age sugeest ML,=2.2. leading to a total stellar mass of 7x10!5-2?M. ."," The best-fit stellar population and age suggest $M/L_K = 2.2$, leading to a total stellar mass of $7 +\times 10^{11} h^{-2}_{71} M_{\sun}$ ." + With a rest[rame equivalent width of IIó Wi=2.9450.5 aand [OL] Wea=3.220.5A.. the classification of G* is closest to K. though could be consistent with γα (formerly part of the Α΄ class) (following Fig.," With a restframe equivalent width of $\delta$ $W_{\rm rest}= 2.9 \pm 0.5$ and [OII] $W_{\rm +rest}= 3.2\pm 0.5$, the classification of $G^*$ is closest to `k', though could be consistent with `k+a' (formerly part of the `E+A' class) (following Fig." + 4 of 1999))., 4 of \citealt{dsp+99}) ). + We aclvance (he hypothesis that G* hosted the birth of the progenitor of 060502D. which travelled an appreciable distance from its birthsite belore producing the GRD event.," We advance the hypothesis that $G^*$ hosted the birth of the progenitor of 060502B, which travelled an appreciable distance from its birthsite before producing the GRB event." +" Al a redshift of 2=0.237. the offset of the ART position from the center of the galaxy (17.05""+ 4.36"")) corresponds to r=73B419 he! kpe in projection."," At a redshift of $z=0.287$, the offset of the XRT position from the center of the galaxy $17.05\arcsec \pm 4.36$ ) corresponds to $r = 73 \pm 19$ $h_{71}^{-1}$ kpc in projection." +" With a fence of (4.02:0.5)xLO Sere 7. the total energy release in 5-ravs assuming a unity A-correction is Big,=(79410)x107 erg."," With a fluence of $(4.0 \pm 0.5) +\times 10^{-8}$ erg $^{-2}$, the total energy release in $\gamma$ -rays assuming a unity $k$ -correction is $E_{\rm iso, \gamma} += (79 \pm 10) \times 10^{47}$ erg." + Our proposed association is based on both probabilistic and associative erounds., Our proposed association is based on both probabilistic and associative grounds. + This is supported by a dvnamical calculation in 84.., This is supported by a dynamical calculation in \ref{sec:conc}. + Even with the relatively large offset observed between 060502D and C. the rarity ol bright galaxies on the sky suggests an association.," Even with the relatively large offset observed between 060502B and $G^*$, the rarity of bright galaxies on the sky suggests an association." + Based onour PAIRITEL photometry. the putative host G has an apparent magnitude of A = 15.23.," Based onour PAIRITEL photometry, the putative host $G^*$ has an apparent magnitude of $K$ = 15.23." + The sky density of galaxies, The sky density of galaxies +United States Naval Observatory. and the University of Washington.,"United States Naval Observatory, and the University of Washington." +The absorption scenario is however far from being confirmed: the fact that absorption is more often seeu in radio loud objects ie. those which more likely lost a relativistic jet. raises the question of why these jets are not able to remove the eas in their vicinity.,"The absorption scenario is however far from being confirmed: the fact that absorption is more often seen in radio loud objects, i.e. those which more likely host a relativistic jet, raises the question of why these jets are not able to remove the gas in their vicinity." +" Another problem is the apparent absence of extinction at lower euergies (that is. UV and optical). if absorption is indeed. prescut in these objects. and ""e""]in particular iu Swift 3302: indeed. the shape of s optical spectrum. once corrected for the Galactic extinction. sugecsts a local column deusity which is much lower than that inferred from the Xrav data analysis (this value would inuply a V -baud rest-frame extinction “ly~ LO Lag. assulung he Galactic extinction law)."," Another problem is the apparent absence of extinction at lower energies (that is, UV and optical), if absorption is indeed present in these objects, and in particular in Swift $-$ 3302: indeed, the shape of its optical spectrum, once corrected for the Galactic extinction, suggests a local column density which is much lower than that inferred from the X–ray data analysis (this value would imply a $V$ -band rest-frame extinction $A_V \sim$ 40 mag, assuming the Galactic extinction law)." + This effec nav however be partly alleviated by the fact that. at high redshift. the chemical composition of the cust is substantially cüfferent from hat of the Milkv. Wav. thus producing an optical-UV extinction law radically at variance with that of our Galaxy (6.8. Calzetti ct al.," This effect may however be partly alleviated by the fact that, at high redshift, the chemical composition of the dust is substantially different from that of the Milky Way, thus producing an optical-UV extinction law radically at variance with that of our Galaxy (e.g., Calzetti et al." + 1998: Alaioliuo et al., 1998; Maiolino et al. + 2001)., 2001). + Au alternative interpretation or the deficit of soft photous has been put forward for blazars. do. that the observed shape is due to intrinsic curvature of the iuverse Compton chussion (Fabian et al.," An alternative interpretation for the deficit of soft photons has been put forward for blazars, i.e. that the observed shape is due to intrinsic curvature of the inverse Compton emission (Fabian et al." + 2001: see also Tavecchio et al., 2001; see also Tavecchio et al. + 2007 for a recent investigation made using this model}., 2007 for a recent investigation made using this model). +" Iudeed. a low οποιον cutoff in the relativistic particle distribution at req, would produce a flattening im the scattered προςπα below voi. o spudPE1)l where Py ds the Lorentz factor. m4 the frequency of the seed photous aud : the redshift of the source."," Indeed, a low energy cutoff in the relativistic particle distribution at $\gamma_{\rm cut}$ would produce a flattening in the scattered spectrum below $\nu_{\rm obs}$ $\sim$ $\nu_{\rm ex} \cdot \Gamma_{\rm +L}^2 \cdot \gamma_{\rm cut}^2 \cdot (z + 1)^{-1}$, where $\Gamma_{\rm L} $ is the Lorentz factor, $\nu_{\rm ex}$ the frequency of the seed photons and $z$ the redshift of the source." + If mx. is 1027 IIz. the break observed in Swift 3302 iuplies. for Loreutz factors in the range LO50. that 560442 a few.," If $\nu_{\rm ex}$ is $\approx$ $^{15}$ Hz, the break observed in Swift $-$ 3302 implies, for Lorentz factors in the range 10–50, that $\gamma_{\rm cut} \approx$ a few." + A different description of the source SED. again iu je asstuuption of the intrinsic curvature hivpothesis. cau vo mnade assundug a log-parabolie distribution for the cluitting clectrous. iu the form F(E) 2 KEαἱLogE) (Massaro ct al.," A different description of the source SED, again in the assumption of the intrinsic curvature hypothesis, can be made assuming a log-parabolic distribution for the emitting electrons, in the form $F$ $E$ ) = $K \cdot E^{-(a+b \cdot Log\,E)}$ (Massaro et al." + 2006: Tramacere et al., 2006; Tramacere et al. + 2007). where eds je power law slope at | keV and bids the curvature below dis enierev.," 2007), where $a$ is the power law slope at 1 keV and $b$ is the curvature below this energy." + As an example. in Fie.," As an example, in Fig." + 5 we overplotted on the SED a log-parabolic distribution with & = 0.55 aud 5 = 1.6., 5 we overplotted on the SED a log-parabolic distribution with $a$ = 0.55 and $b$ = 0.6. + We however defer the detailed analysis of the itrinsic curvature of the Xrav spectrum of Swift 3302 ο a Subsequent paper., We however defer the detailed analysis of the intrinsic curvature of the X–ray spectrum of Swift $-$ 3302 to a subsequent paper. + We conclude this Section by briefly commenting ou iespectral evolution seen when comparing the IBIS and the BAT spectra: apparently. the source Xray spectrin steepeus when it gets fainter.," We conclude this Section by briefly commenting on thespectral evolution seen when comparing the IBIS and the BAT spectra: apparently, the source X–ray spectrum steepens when it gets fainter." + The observed Xray variability iu both flix aud spectrum reported here for Swift J1656.3-3302 is unusual. though not unprecedented in FSRO.," The observed X--ray variability in both flux and spectrum reported here for Swift J1656.3-3302 is unusual, though not unprecedented in FSRQs." + Indeed. a iuuber of other high-: blazars show the same behavior. such as RN Osll (2 = L2: Yuan et al.," Indeed, a number of other $z$ blazars show the same behavior, such as RX $-$ 0844 $z$ = 4.2; Yuan et al." + 2005) and GB DII2S|1217 (2 = L7: Worsley et al., 2005) and GB B1428+4217 $z$ = 4.7; Worsley et al. + 2006) aud. in more recent studies. RBS 315 (: = 2.7: Tavecchio et al.," 2006) and, in more recent studies, RBS 315 $z$ = 2.7; Tavecchio et al." + 2007) aud QSO 0836|710 ες = 2.2: Sambruna et al., 2007) and QSO 0836+710 $z$ = 2.2; Sambruna et al. + 2007)., 2007). + This variability could be due to langes iu the clectron distribution at low energies. or iiv be a hint of the presence of an extra compoucut. which becomes stronger or weaker as the source brightuess changes.," This variability could be due to changes in the electron distribution at low energies, or may be a hint of the presence of an extra component, which becomes stronger or weaker as the source brightness changes." + Through optical follow-up observations we lave been able to identify the newly discovered hard Xταν source Swift 3302 with a blazar at : = 2.1., Through optical follow-up observations we have been able to identify the newly discovered hard X–ray source Swift $-$ 3302 with a blazar at $z$ = 2.4. + Spectral evolution is observed when comparing the Swift/DAT and ZNTECRAL/IDIS data. with the Xrav spectrum nudergoine softeniug whenthe enission becomes faiuter.," Spectral evolution is observed when comparing the Swift/BAT and /IBIS data, with the X–ray spectrum undergoing softening whenthe emission becomes fainter." + The source xoadbanud X'eznuniarav spectrüuni is well described by a power law of index DP— 1.6., The source broadband X–/gamma–ray spectrum is well described by a power law of index $\Gamma \sim$ 1.6. +" The source is extremely brigh with a 20LOO keV observers frame luminosity of ~ 104% ereOo 1|, asstmingc» isotropic enissiou."," The source is extremely bright with a 20–100 keV observer's frame luminosity of $\sim$ $^{48}$ erg $^{-1}$, assuming isotropic emission." + The source SED is typical of high buuinosity blazars. as it has two peaks: the lower (svuchrotrou) oue likely located at infrared frequencies. aud the hieher (inverse Compton) one positioned above a few lunered keV. The spectral curvature detected in the Nrav spectrum of the object can either be intrinsic aud due to the distribution of the enüttiug electrous. or associated with the presence of absorption local to the source aud produced by a colin deusity of à —T «107 7. higher than that typically observed iu hieh-: blazars.," The source SED is typical of high luminosity blazars, as it has two peaks: the lower (synchrotron) one likely located at infrared frequencies, and the higher (inverse Compton) one positioned above a few hundred keV. The spectral curvature detected in the X–ray spectrum of the object can either be intrinsic and due to the distribution of the emitting electrons, or associated with the presence of absorption local to the source and produced by a column density of a $\sim$ $\times$ $^{22}$ $^{-2}$, higher than that typically observed in $z$ blazars." + A] of he observational evidence gathered so far therefore points to Swift 3302 being another case of a distant luminous blazar selected. at οαλ energies., All of the observational evidence gathered so far therefore points to Swift $-$ 3302 being another case of a distant luminous blazar selected at gamma--ray energies. + It ds also the farthest object. among the previously unidentified sources. whose nature has con. determined through optical spectroscopy.," It is also the farthest object, among the previously unidentified sources, whose nature has been determined through optical spectroscopy." +of the Lyman break imiposed onu tlie 52ος‘tra of high redshilt gal:indies by the [GM makes the exact shape of the ⋯∐⇂≺↵∏⊽∖⇁∎ug galaxy spectrun almost irreley.aut.,of the Lyman break imposed on the spectra of high redshift galaxies by the IGM makes the exact shape of the underlying galaxy spectrum almost irrelevant. + To account for the elfects of the IGM. we use the prescription of Madau(1995)..," To account for the effects of the IGM, we use the prescription of \citet{madau}." + Having onyo a small number of templates can cause aliasing in photometjc redshifis., Having only a small number of templates can cause aliasing in photometric redshifts. + The‘efore. 10 new teuplates have been created in between each pair of the six origiuil templates.," Therefore, 10 new templates have been created in between each pair of the six original templates." + There are a total of 51 templates., There are a total of 51 templates. + The spectral eierey distributioi derived from tje. observed maguituces of each object is compared to each template spectrum iu turi., The spectral energy distribution derived from the observed magnitudes of each object is compared to each template spectrum in turn. +" The best matching spectrum. aud heuce the redshift. "" . .⋅⋅ ↥⊳∖≼⇂≺↵↕↩↓⋅∐∐∐↩≺⇂∣≻⊽∖⇁∐∐∐∐⋯∠⋯∑≟∖−⋜↕⊳∖≺⇂≺↵ ined by the following equation: ∖∖↽∐≺↵↕⋅≺↵∣↥⊳∖↕∐≺↵⊳∖↥↽≻≺↵∢∙⋃⋅⋜↕↥↕⊽∖⊽↥↽≻≺↵⋅∶↕⊳∖↕∐≺↵↓⋅≺↵≺⇂⊳∖∐∐∎↕⋅⋀∖⊽∙∕⋅↥⊳∖↕∐≺↵⋯∐∐∣⋈↵↓⋅∩↥∎↓∐↕≺↵↕⋅⊳∖⋅∌↴∣⋅⋜↕∐≺⇂∪↙⋰↙ are respectively the flux and the uncertainty in the flux in each baudpass of the observed galaxy. Tj is the flux in each bandpass of the template beiug considered. aud a is a uormalizatiou [actor given by: Figure 1. shows a comparison of the photometric redshifts with the 39 publislied spectroscopi redshifts."," The best matching spectrum, and hence the redshift, is determined by minimizing $\chi^2$ as defined by the following equation: where $t$ is the spectral type, $z$ is the redshift, $N_f$ is the number of filters, $F_i$ and $\sigma_{F_i}$ are respectively the flux and the uncertainty in the flux in each bandpass of the observed galaxy, $T_i$ is the flux in each bandpass of the template being considered, and $\alpha$ is a normalization factor given by: Figure \ref{fig:f1} shows a comparison of the photometric redshifts with the 39 published spectroscopic redshifts." +" These were tasei [rom the worxof Vauzellaetal.(2005).. LeFevreetal.(200 1).. SzokoN . Croometal. (2001).. Stauw""ayelal.(200 L).. and Stolgeretal.(2001) as compiled bN Rettura(2001).."," These were taken from the workof \citet{vanzcdfs}, \citet{olfcdfs}, \citet{szocdfs}, \citet{croomcdfs}, \citet{stancdfs}, and \citet{strolger} as compiled by \citet{cdfszlist}." + The filed points show ojects with sect'e redshfts., The filled points show objects with secure redshifts. + The open points show objects where the spectroscopic redshift ideutific:lon is less secur'e for one of a uuuber of reasous., The open points show objects where the spectroscopic redshift identification is less secure for one of a number of reasons. +" The most COMMON Leasou is that he “redshift quaity flag"" given|1 tlie reevalll pziper was low (lor exampT quality—1 or 2 in LeFevreetal.(2001 ).", The most common reason is that the “redshift quality flag” givenin the relevant paper was low (for example quality=1 or 2 in \citet{olfcdfs}) ). + Furher. both objecs from he Szokolyetal.(2001 paper are identified as €llasad sor ΑΝ.," Further, both objects from the \citet{szocdfs} + paper are identified as quasars or AGN." + Since we do not include such templates in our photometri redshift met1ος. it woud be slightly surorisiug if we could measre accurate photometric redslifW. for these ojjects.," Since we do not include such templates in our photometric redshift method, it would be slightly surprising if we could measure accurate photometric redshifts for these objects." + Iu Lac both objects slow good agreement. bt are indicated with open poiuW. anyway.," In fact both objects show good agreement, but are indicated with open points anyway." + Finedly. the position of one of tle spectroscopic redshif objects lies directly between two objects whic1 are resolved in the HST images.," Finally, the position of one of the spectroscopic redshift objects lies directly between two objects which are resolved in the HST images." + These objects are jergec in lower resolution images., These objects are merged in lower resolution images. + Taking into account ouly the objecs withsecure recdshilts. the photometric redshift error is X12) with no catastrophic [αἱlures.," Taking into account only the objects withsecure redshifts, the photometric redshift error is $\sigma_z = 0.06 (1+z)$ with no catastrophic failures." + Takiug into accotit all the objects increases this to (12). with 2 catastrophic [αἱures for 39 objects.," Taking into account all the objects increases this to $\sigma_z = 0.12 (1+z)$, with 2 catastrophic failures for 39 objects." + The resauiplecd images. aud the catalog with photometry ancl yhotometric redshifts are available on the web a> inl.," The resampled images, and the catalog with photometry and photometric redshifts are available on the web at: ." + Also available at this site are the SWarp αἱ4 configuration files., Also available at this site are the and configuration files. + toa Lagrangian fluid element is which in this case reduces to The correspoudiug Lagrangian form of the contiuuity equation is Combining equatious (5)) aud (7)). we obtain the sealing relation For isotropic expansion (2= 1). Bx07%.,"to a Lagrangian fluid element is which in this case reduces to The corresponding Lagrangian form of the continuity equation is Combining equations \ref{eq:induction_special}) ) and \ref{eq:continuity_special}) ), we obtain the scaling relation For isotropic expansion $\varepsilon = 1$ ), $B\propto +\varrho^{2/3}$." + In the case where the horizontal expansion rate is much larger than that of the vertical expansion rate we have ><1l. so that B.xνο.," In the case where the horizontal expansion rate is much larger than that of the vertical expansion rate we have $\varepsilon \ll 1$, so that $B\propto +\sqrt{\varrho}$ ." +" For a field strength of LO kG at o=1x10. το 7 (density at >=—7.5 Min). the linear scaling relation gives. for op,~LxI0. 'g . a photospheric fiekl streneth of 10 C. This is evidently too weak compared to what is found iu the simulation aud to what is observed. both of which give emergiug horizontal field streneths ou the order of a few hundred € 2003).."," For a field strength of $10$ kG at $\varrho=4\times 10^{-4}$ g $^{-3}$ (density at $z=-7.5$ Mm), the linear scaling relation gives, for $\varrho_{\rm ph}\sim 4\times 10^{-7}$ g $^{-3}$, a photospheric field strength of $\sim 10$ G. This is evidently too weak compared to what is found in the simulation and to what is observed, both of which give emerging horizontal field strengths on the order of a few hundred G \citep{Lites:EmergingFieldsVector,Kubo:EmergingFluxRegion}. ." + The second scaling relation Bx02* vields more consistent. values for emeregiug horizontal field streugths., The second scaling relation $B\propto \varrho^{\frac{1+\varepsilon}{2+\varepsilon}}$ yields more consistent values for emerging horizontal field strengths. + For 2=0 (zero expansion in the vertical direction) aud ¢=1 (isotropic expansion). a density drop of 10° vields horizontal photospheric field strengths of B=100 G and B=300 Ci. respectively.," For $\varepsilon = 0$ (zero expansion in the vertical direction) and $\varepsilon=1$ (isotropic expansion), a density drop of $10^3$ yields horizontal photospheric field strengths of $B=100$ G and $B=300$ G, respectively." + Figure 6. shows a joint probability deusity fuuctiou (JPDF) ofthe horizontal field strength versus mass censity saipled at the mid-plaue 1=0 between /=1 and /28 hours., Figure \ref{fig:rhoB_scaling} shows a joint probability density function (JPDF) of the horizontal field strength versus mass density sampled at the mid-plane $x=0$ between $t=1$ and $t=8$ hours. + Poiuts with low values of specific entropy. (s<9.75x 105) have been excluded since they correspond to plasma that has undergoue radiative cooling at the surface., Points with low values of specific entropy $s < 9.75\times10^8$ ) have been excluded since they correspond to plasma that has undergone radiative cooling at the surface. + The iaximuu imaguetic field strengtli oL 21 kG corresponds to the field strength at the axis of the torus that is introduced through the bottom boundary., The maximum magnetic field strength of $21$ kG corresponds to the field strength at the axis of the torus that is introduced through the bottom boundary. +" The solid aud dashed lines correspoud to the scaling relations Box\/o aud Bxo7""> respectively.", The solid and dashed lines correspond to the scaling relations $B\propto \sqrt{\varrho}$ and $B\propto \varrho^{2/3}$ respectively. +". The latter scaling. relation. is. clearly too steep aud uuderestimates. the field. strengllis at photospheric deusities (ap,zLx10* [n]g om"").", The latter scaling relation is clearly too steep and underestimates the field strengths at photospheric densities $\varrho_{\rm ph}\approx 4\times 10^{-7}$ g $^{-3}$ ). + The square-root scaling relation provides a much better match to the JPDF., The square-root scaling relation provides a much better match to the JPDF. + This result is consistent with the fact that the plasina experiences predominantly horizontal expausion (2 close to zero) cduriug its rise to the surface (see Fig. 5) , This result is consistent with the fact that the plasma experiences predominantly horizontal expansion $\varepsilon $ close to zero) during its rise to the surface (see Fig. \ref{fig5}) ). +Figure7 shows bow the arrival of buoyant. magneticplasma at tle photospliere leads to a trausieut pressure excess which drives divergiug horizontal flows about the flux emergence site.," Figure\ref{fig:outflows} shows how the arrival of buoyant, magneticplasma at the photosphere leads to a transient pressure excess which drives diverging horizontal flows about the flux emergence site." + The, The +disk 15 formed out of the parent envelope. part of the infalling material aceretes close enough to the star that it is heated to more than 800 or 1200 K and can be erystallised.,"disk is formed out of the parent envelope, part of the infalling material accretes close enough to the star that it is heated to more than 800 or 1200 K and can be crystallised." + However. the observations show significant fractions of crystalline dust at least out to radit corresponding to a temperature of 100K.," However, the observations show significant fractions of crystalline dust at least out to radii corresponding to a temperature of 100." +. Crystalline dust is also found in comets. which are formed in regions much colder than 800 K (??)..," Crystalline dust is also found in comets, which are formed in regions much colder than 800 K \citep{wooden99a,keller06a}." + This suggests an efficient radial mixing mechanism to transport erystalline material from the hot inner disk to the colder outer parts (222)..," This suggests an efficient radial mixing mechanism to transport crystalline material from the hot inner disk to the colder outer parts \citep{nuth99a,bockelee02a,keller04a}." + An argument against large-scale radial mixing was recently provided by spatially resolved observations with the Spitzer Space Telescope., An argument against large-scale radial mixing was recently provided by spatially resolved observations with the Spitzer Space Telescope. + ? found a clear radial dependence in the relative abundances of forsterite and enstatite. two common specific forms of crystalline silicate.," \citet{bouwman08a} found a clear radial dependence in the relative abundances of forsterite and enstatite, two common specific forms of crystalline silicate." + If both are formed in the hot inner disk and then transported outwards. one would expect the same relative abundances throughout the entire disk.," If both are formed in the hot inner disk and then transported outwards, one would expect the same relative abundances throughout the entire disk." + Hence. the observed radial dependence argues in favour of a localised crystallisation mechanism such as heating by shock waves triggered by gravitational instabilities (??)..," Hence, the observed radial dependence argues in favour of a localised crystallisation mechanism such as heating by shock waves triggered by gravitational instabilities \citep{harker02a,desch05a}." + However. the observations do not completely rule out the possibility of crystallisation in the hot inner disk followed by radial mixing: at best. they provide an upper limit to how much crystalline dust can be formed that way.," However, the observations do not completely rule out the possibility of crystallisation in the hot inner disk followed by radial mixing; at best, they provide an upper limit to how much crystalline dust can be formed that way." + In. another set of Spitzer observations. crystalline spectroscopic features in the 20-30 region were detected three times more frequently than the crystalline feature at 11.3 (2)...," In another set of Spitzer observations, crystalline spectroscopic features in the 20–30 region were detected three times more frequently than the crystalline feature at 11.3 \citep{olofsson09a}." + This is unexpected. because shorter wavelengths trace warmer material at shorter distances from the protostar. where all models predict the crystalline fractions to be larger.," This is unexpected, because shorter wavelengths trace warmer material at shorter distances from the protostar, where all models predict the crystalline fractions to be larger." + The crystalline. 11.3 feature may be partially shielded by the amorphous 10 feature. but Olofsson et sshowed that this alone cannot explain the observations.," The crystalline 11.3 feature may be partially shielded by the amorphous 10 feature, but Olofsson et showed that this alone cannot explain the observations." + A full compositional analysis (Olofsson et ssubm.), A full compositional analysis (Olofsson et subm.) +" is required to shed more light on this ""erystallinity paradox"".", is required to shed more light on this “crystallinity paradox”. + In the model of?.. erystallisation occurs right from the time when the disk is first formed.," In the model of, crystallisation occurs right from the time when the disk is first formed." + Indeed. because the disk is very small at that time. its dust is hot and nearly fully erystalline.," Indeed, because the disk is very small at that time, its dust is hot and nearly fully crystalline." + As the collapse proceeds and the disk's outer radius grows. an ever larger fraction of the infalling material does not come close enough to the star anymore to be heated above 800K.," As the collapse proceeds and the disk's outer radius grows, an ever larger fraction of the infalling material does not come close enough to the star anymore to be heated above 800." +. In the absence of strong shocks. this results in amorphous dust being mixed in with the erystalline material.," In the absence of strong shocks, this results in amorphous dust being mixed in with the crystalline material." + Hence. the crystalline fraction averaged over the entire disk is expected to decrease with time.," Hence, the crystalline fraction averaged over the entire disk is expected to decrease with time." + There is tentative observational support for an age-crystallinity anticorrelation (??).. but this ἐς far from conclusive (??)..," There is tentative observational support for an age-crystallinity anticorrelation \citep{vanboekel05a,apai05a}, but this is far from conclusive \citep{bouwman08a,watson09a}." + One should of course consider the fact that observations do not probe the entire disk., One should of course consider the fact that observations do not probe the entire disk. + If the model results from are interpreted over a limited part of the disk. such as the 10-20 AU region. they show only a small difference in the crystalline fractions at | and 3 Myr.," If the model results from are interpreted over a limited part of the disk, such as the 10–20 AU region, they show only a small difference in the crystalline fractions at 1 and 3 Myr." + Add to that the uncertainties in the ages for individual objects. and it is clear that the model results cannot be said to conflict the observational data.," Add to that the uncertainties in the ages for individual objects, and it is clear that the model results cannot be said to conflict the observational data." + The crystalline fractions obtained by were all on the high end of the observed range of1-30... unless unreasonably high initial rotation rates were adopted for the envelope or the disk temperature was lowered artificially.," The crystalline fractions obtained by were all on the high end of the observed range of, unless unreasonably high initial rotation rates were adopted for the envelope or the disk temperature was lowered artificially." + If we accept that only part of the silicates in the outer disk originate in the hot inner region — so the other part. formed in situ. can account for the observed radial abundance variations — the discrepancy between the model and the observations becomes even larger.," If we accept that only part of the silicates in the outer disk originate in the hot inner region – so the other part, formed in situ, can account for the observed radial abundance variations – the discrepancy between the model and the observations becomes even larger." + In. the following. we show that we obtain more realistic crystalline fractions with our new method.," In the following, we show that we obtain more realistic crystalline fractions with our new method." + The two main differences between the old method of and our new method are (1) the treatment of the disk as a multidimensional object instead ofjust a flat accretion surface and (2) the improved solution to the problem of sub-Keplerian accretion refsec:eqs))., The two main differences between the old method of and our new method are (1) the treatment of the disk as a multidimensional object instead of just a flat accretion surface and (2) the improved solution to the problem of sub-Keplerian accretion \\ref{sec:eqs}) ). + The former has the largest impact on the crystallisation., The former has the largest impact on the crystallisation. + In case of a fully flat disk. material falls in along ballistic trajectories until it hits the midplane at or inside the centrifugal radius.," In case of a fully flat disk, material falls in along ballistic trajectories until it hits the midplane at or inside the centrifugal radius." + If the vertical extent of the disk is taken into account. the infalling material hits the disk before it can flow all the way to the midplane.," If the vertical extent of the disk is taken into account, the infalling material hits the disk before it can flow all the way to the midplane." + Because part of the disk often spreads beyond the centrifugal radius. especially at early times 1)). accretion now occurs at much larger radit.," Because part of the disk often spreads beyond the centrifugal radius, especially at early times ), accretion now occurs at much larger radii." + This ts visualised in3.. which shows the mass loading onto the disk at Fig. yr (0.23 £4) after the onset of collapse.," This is visualised in, which shows the mass loading onto the disk at } yr (0.23 $\tacc$ ) after the onset of collapse." +" The model parameters are those of the default model of?:: an initial cloud core mass My of 2.5 Ms. a rotation rate Qo of {κ107"" sl. and a sound speed c, of 0.23 kms!."," The model parameters are those of the default model of: an initial cloud core mass $M_0$ of 2.5 $M_\odot$, a rotation rate $\Omega_0$ of } , and a sound speed $\cs$ of 0.23 km." +. The centrifugal radius at yr is 2.2 AU. but the disk has already spreac to 32AU.," The centrifugal radius at } yr is 2.2 AU, but the disk has already spread to 32." +. Accretion occurs across the entire disk. although most mass falls in at small radii.," Accretion occurs across the entire disk, although most mass falls in at small radii." + If the vertical structure of the disk is ignored whet calculating the source function. as happened in the old methoc of?.. the infall trajectories continue along the dotted lines.," If the vertical structure of the disk is ignored when calculating the source function, as happened in the old method of, the infall trajectories continue along the dotted lines." + They all intersect the midplane inside of Αι., They all intersect the midplane inside of $R_\el{c}$. + In this case. that means all accretion takes place inside the “annealing radius” (Ras. the radius corresponding to 800 K) and all dust ts turned into crystalline form.," In this case, that means all accretion takes place inside the “annealing radius” $R_\el{ann}$, the radius corresponding to 800 K) and all dust is turned into crystalline form." + In the new method. only of the accreting material comes inside of Rj44. so the disk gains a much smaller amount of crystalline dust.," In the new method, only of the accreting material comes inside of $R_\el{ann}$, so the disk gains a much smaller amount of crystalline dust." + The crystalline fractions obtained with the new method are compared to the results from in4., The crystalline fractions obtained with the new method are compared to the results from in. +. In both cases. the inner part of the disk. out to à few AU. ts fully crystalline.," In both cases, the inner part of the disk, out to a few AU, is fully crystalline." + This is followed by a near-powerlaw decrease as crystalline material is mixed to larger radit., This is followed by a near-powerlaw decrease as crystalline material is mixed to larger radii. + At a few tens of AU. the crystallinity levels off to a base value that remains roughly constant to the outer edge of the disk. where the curves are terminated.," At a few tens of AU, the crystallinity levels off to a base value that remains roughly constant to the outer edge of the disk, where the curves are terminated." +" The increase in crystallinity towards large radit in the original curves is an artifact from the pre-infall low-density seed ""6isk (used for reasons of numerical stability) and occurs only in those regions where the surface density is anyway nearly zero.", The increase in crystallinity towards large radii in the original curves is an artifact from the pre-infall low-density seed disk (used for reasons of numerical stability) and occurs only in those regions where the surface density is anyway nearly zero. + This increase ts therefore irrelevant., This increase is therefore irrelevant. + Due to the use of an improved numerical integration scheme. it is no longer present in the new curves.," Due to the use of an improved numerical integration scheme, it is no longer present in the new curves." + At each of the three time steps plotted in4.. the new crystallinity outside of a few AU is lower than the old one.," At each of the three time steps plotted in, the new crystallinity outside of a few AU is lower than the old one." + For example. at 1O AU and 3.1 Myr. the fraction is," For example, at 10 AU and 3.1 Myr, the fraction is" +ealaxics:— nuclei galaxies: struct The collisional coustruction of. galaxies from. the merger of thonght to 2 conimion occurrence lessorin the palaisUniverse.,galaxies: nuclei — galaxies: structure} The collisional construction of galaxies from the merger of lesser galaxies is thought to be a common occurrence in the Universe. +Is Coupled bewith ↑∐∖↻↥⋅↸∖↴∖↴↸∖↕∐⊳↸∖∪↕⋟⋜↧↴∖↴↿∏⋉∖↥⋅↕⊔⋜↧↴∖∷∖↴↕↖⇁↸∖∐⋯⊳↨↘↽∐∪↕↸∖⋖≋⋀∖∐≧∐⋝ ⋜↧↑���∐↸∖∐↸∖⋜∐⋅↑∪↕⋟⊔∪↴∖↴↑∶↴∙⊾⋜↧↕⋜⋯↕↸∖↴∖↴≺↕↘⊽∪↥⋅⋯↸∖∐↧⋅↖↽∙∖↽ ↕⊰↕↸⊳∐∖↴↑∪∐↸∖↕∩∩⋅↱≻∶⋀∖↕⋜↧∶↴∙⊾∪↥⋅↥⋅↕⋜∐⊔∖↑⋜↧↕∙∐∩∩≺∖∖⋅↕⊰↕↸⊳∐∖↴↑∪↕∐∖ ↸∖⋜↧↕∙↕⊽≝↭≺∖∖⋝∙≺∐↴∖↴↴∖↴∏≻⋜↧↑↕∪↕∐↸∖↴∖∷∖↴∐∐∖↥⋅∶↴∙⊾↸∖↥⋅↴∖↴∐⋜↧↖↽↸∖↴⋝↸∖↸∖∐ prope pu tote ⋯∪∪↴∖↴↸∖≼↧↑∪↸∖⊼≻↕⋪↧↕↕↑∐↸∖≼⇂⋪∐⊔⋪↧∩⊾↸∖≺↧∐⋯⊳↕↸∖↕↕↕∩⊾↕⋪⋯↑ M elliptical galaxies (e.g... Lauer et Aaenr11995. Faber al. Rest ansot al. ellipt," Coupled with the presence of a supermassive black hole (SMBH) at the heart of most galaxies (Kormendy Richstone 1995; Magorrian et 1998, Richstone et 1998), dissipationless mergers have been proposed to explain the damaged nuclei in giant elliptical galaxies (e.g., Lauer et 1995, Faber et 1997, Rest et 2001)." +"icalAlthough some ealaxv ""core-depletion is due to the SMDII(s) dining on stars that venture to close (e.g. Magorrian & 1999: Zhao. IHachnelt. & 2002: Yu 2003). it is primarily from the eravitational slingshot effect that the coalescing SAIBIIs from the preanerged ealaxics have on stars while they themselves sink to the bottom of the potential well of the newly wed galaxy (Begeliuan. Dlaudford. Rees 1980: Ebisuzaki. Alalsino. Okuunua 1901: Makino Ebisuzaki 1996: Quinlan 1996: Quinlan Heruquist 1997)."," Although some galaxy “core-depletion” is due to the SMBH(s) dining on stars that venture to close (e.g., Magorrian Tremaine 1999; Zhao, Haehnelt, Rees, 2002; Yu 2003), it is primarily from the gravitational slingshot effect that the coalescing SMBHs --- from the pre-merged galaxies — have on stars while they themselves sink to the bottom of the potential well of the newly wed galaxy (Begelman, Blandford, Rees 1980; Ebisuzaki, Makino, Okumura 1991; Makino Ebisuzaki 1996; Quinlan 1996; Quinlan Hernquist 1997)." + Theory predicts that the orbital decay of two ↴∖↴⋯⊳∐≋⋀∖∐≧∐↴∖↴↴∖↴∐∪∏↕≼↧↸∖⋅↿≱↸∖↸⊳⋜↧⋯↥⋅↸∖⋯⋜↧↴∖↴↴∖↴↥⋅⋯∶↴⋁↕∐⋅↖↽ ↸∖≺∣∏⋜↧↕↑∪↑∐↸∖↸⊳∪∐∐⋝↕⋯∖≺↴⋝↕⋜↧↸⊳↘↽∐∪↕↸∖⊔⋜↧↴∖↴↴∖↴↸∖↴∖↴⋖⊡⋝↕↴∖↴∏∑⋜∐↘↽↕∙ ⋀∖↕⋜∐↘↽↕∐∪∙∙∖↽≼≓∐↘↽∏∐∐∐⋅⋜↧↕∩," Theory predicts that the orbital decay of two such SMBHs should eject a core mass roughly equal to the combined black hole masses (Ebisuzaki, Makino, Okumura 1991; Milosavljević Merritt 2001)." +"≝∐∶⋀∖↕∐∪↴∖↴⋜↧↖↽↕⋅↾↸∖↖↽↕↸↗⊳∙∖↽⋀∖↕↸∖∐⋅↕⇈ ⊇∩∩⊔∙≼⊲↿∐⋅↥⋅↸∖∐↑⋯↸∖⋜↧↴∖↴↿↥⋅↸∖∐∐∖∐↑↴∖↴∪↕≯∐↸∖∩∖∐↥⋅⋜↧↕↴∖↴↑↸∖∐⋜∐⋅ ≼↧↸∖∱∎⊔⊳↕↑⋜∐⋅↸∖⋜⋯∪↥⋅≼∐∖↥⋅∪↕≯⊔⋜↧∶↴∙⊾∐↕↑∏∩∖↕⋜∐⋅∶↴∙⊾↸∖↥⋅↑∐⋜⋯ the central SAIBIT↴ mass. suggesting⋅ that iuost galaxies⋅⋅ have⋅‘ undergone multiple. (z8-. etdigest10) majoraucrgers (Milosavljevió Moeriitt 2001: Alilosavljevió et 22002: Ravindranath. Πο, Filippeuko 2002)."," Current measurements of the central stellar deficit are an order of magnitude larger than the central SMBH mass, suggesting that most elliptical galaxies have undergone multiple $\approx$ 8-10) major-mergers (Milosavljević Merritt 2001; Milosavljević et 2002; Ravindranath, Ho, Filippenko 2002)." + This result. however. is at odds with popular models of hierarchial structure formation. which predict an average of oulv 1 (dissipationless) major-merecr event for huuinous," This result, however, is at odds with popular models of hierarchial structure formation, which predict an average of only 1 (dissipationless) major-merger event for luminous" +HES91).,. +. Except for some galaxies in Virgo. all the galaxies in the HES97 sample are located in low densitv environments (either loose groups or isolated).," Except for some galaxies in Virgo, all the galaxies in the HFS97 sample are located in low density environments (either loose groups or isolated)." + In Table 2. we compare their results (395 galaxies. excluding the galaxies in Virgo) with ours.," In Table \ref{tbl2} we compare their results (395 galaxies, excluding the galaxies in Virgo) with ours." +" In the HHES97 sample. the BLAGNs were classified as such by Iloetal.(1997b).. based on the detection of a broad LL, component."," In the HFS97 sample, the BLAGNs were classified as such by \citet{ho97b}, based on the detection of a broad $_{\alpha}$ component." + To be consistent with our definition. all (hese galaxies were classified as Svl.," To be consistent with our definition, all these galaxies were classified as Sy1." + Also for comparison sake. (he narrow emission lines galaxies in the IIFS97 sample were reclassified using the criteria described in sect. 2..," Also for comparison sake, the narrow emission lines galaxies in the HFS97 sample were reclassified using the criteria described in sect. \ref{sec2}." + The fraction BLAGN/NLAGN in the IIFS97 sample is and the ratio Svl/Sv2 isGLY., The fraction BLAGN/NLAGN in the HFS97 sample is and the ratio Sy1/Sy2 is. +.. There is consequently a clear deficiency of BLAGNs in CGs., There is consequently a clear deficiency of BLAGNs in CGs. + This also appears as an extremely large dillerence in the number of ον]. as compared to Sv2 galaxies., This also appears as an extremely large difference in the number of Sy1 as compared to Sy2 galaxies. + This phenomenon is quite intriguing considering that there is no deficit of AGNs as a whole in COs: AGNs in the ICG. in the UZC-CG compared to in the IIFS9O7 sample.," This phenomenon is quite intriguing considering that there is no deficit of AGNs as a whole in CGs: AGNs in the HCG, in the UZC-CG compared to in the HFS97 sample." + Comparable ratios (Sv1/8y2 νο )) were obtained bv Sorrentinoetal.(2006.SRROG) in the field. with a slight increase in “loose groups” (Svl/Sv2 )).," Comparable ratios (Sy1/Sy2 $\backsim$ ) were obtained by \citet[SRR06]{sor06} in the field, with a slight increase in “loose groups” (Sy1/Sy2 $\backsim$ )." + In the nearby (20.33) sample of SDSS AGN galaxies covering four orders of Iuminositv and similar environments as SRROG. H105 determined a ratio BLAGN/NLAGN of and a ratio Svl/Sv2 of54%.," In the nearby $<$ 0.33) sample of SDSS AGN galaxies covering four orders of luminosity and similar environments as SRR06, H05 determined a ratio BLAGN/NLAGN of and a ratio Sy1/Sy2 of." +.. Assuming BLAGNs are slightly favored at higher Iuminosity these hieh ratios are comparable to those found by HESOT., Assuming BLAGNs are slightly favored at higher luminosity these high ratios are comparable to those found by HFS97. + Our results suggest there is an important deficit of BLAGNs in our two CG samples as compared to similar survevs in (he field., Our results suggest there is an important deficit of BLAGNs in our two CG samples as compared to similar surveys in the field. + This result confirm the tendency first encountered bv Cozioletal.(1998.2000).," This result confirm the tendency first encountered by \citet{coz98,coz00}." +. To verily that the lack of BLAGNs in CGs can not be induced by differences in observation. reduction or analvsis methods we have investigated thoroughly these possibilities.," To verify that the lack of BLAGNs in CGs can not be induced by differences in observation, reduction or analysis methods we have investigated thoroughly these possibilities." + Comparison of the UZC-CG sample with the survev made by HO05 is sale. because our SDSS data derive from the same telescope. reduction and analysis methods (including template subtraction) as theirs.," Comparison of the UZC-CG sample with the survey made by H05 is safe, because our SDSS data derive from the same telescope, reduction and analysis methods (including template subtraction) as theirs." + The ratio BLAGN/NLAGN is in our sample compared to for the sample of H05. which is already a huge difference.," The ratio BLAGN/NLAGN is in our sample compared to for the sample of H05, which is already a huge difference." + A possible effect due to difference in spectral resolution can also be excluded., A possible effect due to difference in spectral resolution can also be excluded. + have used high resolution (2.5 À)) spectra. but made tests with two others low resolution set-ups," \citet{ho97b} have used high resolution (2.5 ) spectra, but made tests with two others low resolution set-ups" +"refsec-obs}). gives P=3.641. (statistical error L.l%)) aud Opa=2437° (statistical error 11) at F275WN. P—5.1ELX (statistical error )) aud (py=62x25"" (stiistical error 67) at E312W. Therefore. the polarization detection is mareinal. but the blob couk be oluized with the 1.54 level. since our error estimation would be couscrvative. as discussed iu Iisiinoto (1999).","), gives $P = 3.6 \pm 4.4$ (statistical error ) and $\theta_{\rm PA} = 2 \pm 37\degr$ (statistical error $11\degr$ ) at F275W, $P = 5.1 \pm 4.3$ (statistical error ) and $\theta_{\rm +PA} = 6 \pm 25\degr$ (statistical error $6\degr$ ) at F342W. Therefore, the polarization detection is marginal, but the blob could be polarized with the $4-5$ level, since our error estimation would be conservative, as discussed in Kishimoto (1999)." + Figues 5. and 6 show the polarized fiux distribution through the F275W and F312W filter. respectively.," Figures \ref{fig_mrk3_f275_pf} and \ref{fig_mrk3_f342_pf} show the polarized flux distribution through the F275W and F342W filter, respectively." + The three polarizer images for each filter were smoothed by a Caussian with a FWIIA of 10 pixels (~ 0.711). and polarized fux was calculated with a 5 pixel bin.," The three polarizer images for each filter were smoothed by a Gaussian with a FWHM of 10 pixels $\sim 0.''14$ ), and polarized flux was calculated with a 5 pixel bin." + The polarized flux has been debiased following Simuno1s Stewart (1985): namely corrected by a factor| of (1(opf/Da))? (opis astaistical error. obs is an observed polarization).," The polarized flux has been debiased following Simmons Stewart (1985); namely corrected by a factor of $(1 - (\sigma_P/P_{\rm obs})^2)^{1/2}$ $\sigma_P$ is a statistical error, $P_{\rm obs}$ is an observed polarization)." + The regions with Pousfop<1 are masked out., The regions with $P_{\rm obs}/\sigma_P < 1$ are masked out. + The contours of the I image with the ΕΟΝ filter are drawn iuboth of the feures. to make the comparison of the Wo xolarized flux distribution easier.," The contours of the $I$ image with the F342W filter are drawn in both of the figures, to make the comparison of the two polarized flux distribution easier." +" The gravscal CIs incar in both nuages. with a )ea at the sane και [~(0.76, 0.71)]."," The grayscale is linear in both images, with a peak at the same pixel $\sim (0.''6, -0.''1)$ ]." + The peak polarized. flux in the F312W filter is lower by a factor of {75 han that in the F275W filter (after the Calactic reddening correction with Γρy= 0.188).," The peak polarized flux in the F342W filter is lower by a factor of 0.75 than that in the F275W filter (after the Galactic reddening correction with $E_{B-V} = +0.188$ )." +" Nost of the polarize flux (roughlv ~ 7054)) is coming roin the region within ~1"" (~ 300 pc) from the cleus. aid the polarized fux is greater on the west side than he east side."," Most of the polarized flux (roughly $\sim 70$ ) is coming from the region within $\sim 1''$ $\sim$ 300 pc) from the nucleus, and the polarized flux is greater on the west side than the east side." + The polarized flax distribution is different iu hese two filters., The polarized flux distribution is different in these two filters. + From. tje nuages with these two filters. we ca ¢erive the color distributions o the ooludzed flux. which is shown in Figure 7..," From the images with these two filters, we can derive the color distributions of the polarized flux, which is shown in Figure \ref{fig_mrk3_pfcolor}." +" The ratio of the polarized flux in the F275W fi]ter o that in the E312W filter has Όσοι couverteL to he spectral iudex à (E,x »"").", The ratio of the polarized flux in the F275W filter to that in the F342W filter has been converted to the spectral index $\alpha$ $F_{\nu} \propto \nu^{\alpha}$ ). + The spectraliudex ras been corrected for tfje Galactic reddening of Γρy=0.188 (NED: Schlegel ct al., The spectral index has been corrected for the Galactic reddening of $E_{B-V} = 0.188$ (NED; Schlegel et al. + 1995)., 1998). +" The resulting iudex rauge shown in the figure 1s fr""Oli 3.1 to |1.2.", The resulting index range shown in the figure is from $-3.1$ to $+1.2$. + This color map is a composite| of three differeut bius with three different sootinus., This color map is a composite of three different bins with three different smoothing. + We have convolved three polarizer images for each filter with a Gaussian of PFWIIM. 10. 20. 10 pixe and generated the color map with 20. 10. 5 pInc bius. respectively. and stacked them iuto one plot.," We have convolved three polarizer images for each filter with a Gaussian of FWHM 40, 20, 10 pixel and generated the color map with 20, 10, 5 pixel bins, respectively, and stacked them into one plot." + For cach bin case. the regions with the forma l-c uncertiintv (caIculatec using the smoothed image counts) in the specral index simaller than 2 are shown. but the actual nucertaity for the regions show1 is estinted to © less than —1 by biuniug the inuages with the smoothing FWIIM size.," For each bin case, the regions with the formal $\sigma$ uncertainty (calculated using the smoothed image counts) in the spectral index smaller than 2 are shown, but the actual uncertainty for the regions shown is estimated to be less than $\sim 1$ by binning the images with the smoothing FWHM size." + For the error caleulatioj we have ucelected the error source () described im retsec-obs.. because of he rather heavy siioothiug.," For the error calculation, we have neglected the error source (4) described in \\ref{sec-obs}, because of the rather heavy smoothing." + The caveat is that t1ο color at the regions with largeoO iuteusitv eracienut should he taken with caution. since it would have itheuce roni the spatial blurriue of the bright recion.," The caveat is that the color at the regions with large intensity gradient should be taken with caution, since it would have influence from the spatial blurring of the bright region." +" We also mace the color“lap without ans sooting and obtaiue a consisteut nap. thremel he features are much clearer in the nap froini slneotlec Huaces,"," We also made the color map without any smoothing and obtained a consistent map, though the features are much clearer in the map from smoothed images." + Therefore we oilv show he latter., Therefore we only show the latter. + We also eerrerated the total Πας color imap. which is shown in Figure 8..," We also generated the total flux color map, which is shown in Figure \ref{fig_mrk3_tfcolor}." + The color las been corrected for f1ο Cadacic reddening., The color has been corrected for the Galactic reddening. + The same procedure as or the polarized flux color map was taken. except he threshold for the formal 1-0 uncertainutv int he iudex which was set to 1.," The same procedure as for the polarized flux color map was taken, except the threshold for the formal $\sigma$ uncertainty in the index which was set to 1." +" In the ceutral 1"" radis reeion. the actual uucertaimty is estimated to )o less than 0.3."," In the central $1''$ radius region, the actual uncertainty is estimated to be less than 0.3." + The spectral iudex range 1s found to be 5.0~2.2. seulficautly redder than tlie polarized fhx.," The spectral index range is found to be $-5.0 \sim -2.2$, significantly redder than the polarized flux." + The color Is τον red at aroun the location o: the hidden nucleus (~5.0: see the previous subsection). aud lis red color is extended to the souh.," The color is very red at around the location of the hidden nucleus $\sim -5.0$; see the previous subsection), and this red color is extended to the south." + This is probably due to an euhauced extinelon., This is probably due to an enhanced extinction. + The red color seclus to be also exte1eed aloue the nortr-:outh direction., The red color seems to be also extended along the north-south direction. + On the other liuc. the color tends to e bluer at tho regions adjacent to some bright clouds. ou the opposite sicle of the direction o the nucleus especially the eas sicle of the southeastern lol aud tljo west sido «oft the western xieht blob.," On the other hand, the color tends to be bluer at the regions adjacent to some bright clouds, on the opposite side of the direction to the nucleus: especially the east side of the southeastern blob and the west side of the western bright blob." + However. he interpreation of the otal flux color iu general is uncertain while he overall ved color could be partly duc ο the contribution from old stellar population in the jost ealaxy. tjo slnall-spatialscale color variation could be caused by the narrow-line contamination in our two filteys (μου refsec-obs)).," However, the interpretation of the total flux color in general is uncertain: while the overall red color could be partly due to the contribution from old stellar population in the host galaxy, the small-spatial-scale color variation could be caused by the narrow-line contamination in our two filters (see \\ref{sec-obs}) )." + Therefore we will not attempt to interpret the total flux color map in this uper., Therefore we will not attempt to interpret the total flux color map in this paper. + We will discuss the polarized flux color map in rofsec-disc.., We will discuss the polarized flux color map in \\ref{sec-disc}. . +"Discovered ou 1906 February 21. main-belt asteroid (596) Scheila has a diameter of d=113.30 kan (Tedescoetαἱ. 2001)... an orbital period of Poy,=5.0L vears. a seninajor axis of «=2.927 AU. an eccentricity of c—0.165. an inclination of /=11.66 ‘and a Tisseraud piraueter (with respect to Jupiter) of T;=3.209.","Discovered on 1906 February 21, main-belt asteroid (596) Scheila has a diameter of $d=113.34$ km \citep{ted04}, an orbital period of $P_{\rm orb}=5.01$ years, a semimajor axis of $a=2.927$ AU, an eccentricity of $e=0.165$, an inclination of $i=14.66^{\circ}$, and a Tisserand parameter (with respect to Jupiter) of $T_J=3.209$." + On 2010 December 10.1. observations bv LLarsou using the 0.68 11 Catalina Scliunidt telescope showed that Scheila was exhibiting comet-like activity.," On 2010 December 10.4, observations by Larson using the 0.68 m Catalina Schmidt telescope showed that Scheila was exhibiting comet-like activity." + Examination of archived Catalina data indicated that the oject also appeared diffuse on December 3. but was polit-source-ike on October l5. November 2. and November 11 (Larson2010).," Examination of archived Catalina data indicated that the object also appeared diffuse on December 3, but was point-source-like on October 18, November 2, and November 11 \citep{lar10}." +. If its activi vds truly cometary. Scheila wotId be the rewest member of the small class of objects known as Inalu-bel comets CMDBCs). whiclji are objects that exhibit comeary activity(6.9.. dust cinissio1) due to he μιblination of volatile ices. but occupy stable orbits eutirelv confined to the main asteroid bolt (Fie. 5)).," If its activity is truly cometary, Scheila would be the newest member of the small class of objects known as main-belt comets (MBCs), which are objects that exhibit cometary activity, dust emission) due to the sublimation of volatile ices, but occupy stable orbits entirely confined to the main asteroid belt (Fig. \ref{mbcs_aei}) )." +" AIDC's are unikelv to originate in the outer soar svsteni ike oher comets. aud are probably native to the main olt. (Fornancezefal,2002:Taghighipour2009)."," MBCs are unlikely to originate in the outer solar system like other comets, and are probably native to the main belt \citep{jfer02,hag09}." +. Their activity ds )elieved. to be trigecrec bv nupacts that excavate subsurface volaile material (probablywaterice:Prialuik&Roseuore2009:Schorelocer 2008).. exposing it to direct solar heatine. driving sublimation aud comet-like dust emission {sich&Jewitt2006).," Their activity is believed to be triggered by impacts that excavate subsurface volatile material \citep[probably water ice;][]{pri09,sch08}, exposing it to direct solar heating, driving sublimation and comet-like dust emission \citep{hsi06}." +. Noting the strong correlation )tween activity and proximity to peribelion for all currently known AIBCs. however. Ichctal.(20011b) proosed. the alternate )ossibilitv that activity is iu fact ]xni depeudeut on helioceutric distance. and onlv peaks during the post-perihelio- portion of cach MBC's orbit due to he finite time required for solar tieriual waves to proweate through insulaine surface material before reach the subsurface reservoirs of volatie Inateria below.," Noting the strong correlation between activity and proximity to perihelion for all currently known MBCs, however, \citet{hsi11b} proposed the alternate possibility that activity is in fact primarily dependent on heliocentric distance, and only peaks during the post-perihelion portion of each MBC's orbit due to the finite time required for solar thermal waves to propagate through insulating surface material before reach the subsurface reservoirs of volatile material below." + Currently. both livpotjoses are consistent witi the available evidence. though we note the first hivpohesis could be ruled out (at least as a universally applicable explaration for MDC activiv imnodulation) bv the deterwination of a pole orienation for an MBC that is inconsistent with seasonal nocation of activity(i.e.. where peak activity does not occur near a solstice position. as required by the seasonal nocation hvpothnesis. but near an equinox position).," Currently, both hypotheses are consistent with the available evidence, though we note the first hypothesis could be ruled out (at least as a universally applicable explanation for MBC activity modulation) by the determination of a pole orientation for an MBC that is inconsistent with seasonal modulation of activity, where peak activity does not occur near a solstice position, as required by the seasonal modulation hypothesis, but near an equinox position)." + Likewise. the seconL hypothesis could be ruled out as a universal explanaticπι for MBC activity modulation bv he discovery of an MBC which exhibits peak activity xior to reaching pevilelion.," Likewise, the second hypothesis could be ruled out as a universal explanation for MBC activity modulation by the discovery of an MBC which exhibits peak activity prior to reaching perihelion." + To date. gas enission has never cen directly detected or an MBC (60.4...2011).," To date, gas emission has never been directly detected for an MBC \citep[{\it e.g.},." + This present lack of spectroscopic confirmation of outeassing is largely due to the faintuess of MDC activity. requiring extremely sensitive observations.," This present lack of spectroscopic confirmation of outgassing is largely due to the faintness of MBC activity, requiring extremely sensitive observations." + Cas detection effort» are further colplicated by the transience of MBC activity. requiring that spectroscopic observations beo secured soon after new MDCsS are discovered. something that has only been achieved for the more recent discoveries.," Gas detection efforts are further complicated by the transience of MBC activity, requiring that spectroscopic observations be secured soon after new MBCs are discovered, something that has only been achieved for the more recent discoveries." + Since rapid gas dissipation timescales mean that dust cussion may coutinuce lone after active sublimation has actually ceased. even those observations," Since rapid gas dissipation timescales mean that dust emission may continue long after active sublimation has actually ceased, even those observations" +There ave four independent parameters {ο be varied in our dimensionless cartesian svstem.,There are four independent parameters to be varied in our dimensionless cartesian system. +" These include ¢,. which measures the relative influence of Coriolis and viscous forces; H. which measures (he aspect ratio of the channel and therefore the colatitude of the equatorial boundary of the polar cap: C,(R). the linear rotational. velocity imposed at (his boundary: and WV,(A). representing the meridional flow imposed (there."," These include $\epsilon_n$, which measures the relative influence of Coriolis and viscous forces; $R$, which measures the aspect ratio of the channel and therefore the colatitude of the equatorial boundary of the polar cap; $U_n(R)$, the linear rotational velocity imposed at this boundary; and $\Psi_n(R)$, representing the meridional flow imposed there." +" To estimate the range ol e,, of interest. we use for O the core rotation rate of the Sun. 2.6xLOὃν+ and for 4H the depth of the convection zone. 2xI0!em.10 "," To estimate the range of $\epsilon_n$ of interest, we use for $\Omega$ the core rotation rate of the Sun, $2.6\times 10^{-6} {\rm s}^{-1}$ and for $H$ the depth of the convection zone, $2 \times 10^{10} {\rm cm}$." +"Then the range of ej, is given by 6.53xLOMa/v.", Then the range of $\epsilon_n$ is given by $6.53 \times 10^{15}n/\nu$. +" :Therefore. for. the range LO!<,»10Memzs>! for. η=1. the lowest verticalκ mode. we get 6.53x10!>e10.653."," Therefore for the range $10^{11}<\nu<10^{16} {\rm cm}^2\,{\rm s}^{-1}$ for $n=1$ the lowest vertical mode, we get $6.53 \times 10^4>\epsilon_1> 0.653$." + The most plausible values for v in the convection zone of the Sun are inB the range 107>—10!emn?s.," The most plausible values for $\nu$ in the convection zone of the Sun are in the range $10^{12}-10^{14} {\rm cm}^2\,{\rm s}^{-1}$." +! A typical dimensional meridional flow speed observed in midlatitudes near the boundary of our polar cap falls in the range -5 to -20 ms+ (the negative sign is for [low toward the left hand edge of the channel. corresponding to poleward flow in the polar cap).," A typical dimensional meridional flow speed observed in midlatitudes near the boundary of our polar cap falls in the range -5 to -20 ${\rm m}\,{\rm s}^{-1}$ (the negative sign is for flow toward the left hand edge of the channel, corresponding to poleward flow in the polar cap)." + Relative to (he core rotation rate. a surface linear rotational flow speed at similar latitudes would be in the range -20 to -90 ms |. What dimensionless values these correspond to vary according to what value of ν we assume.," Relative to the core rotation rate, a surface linear rotational flow speed at similar latitudes would be in the range -20 to -90 ${\rm m}\,{\rm s}^{-1}$ What dimensionless values these correspond to vary according to what value of $\nu$ we assume." + For Sms|H and ν of 10!em?s.H! we get a dimensionless velocity of one unit and a streamfinction of 1/z units.," For $5\,{\rm m}\,{\rm s}^{-1}$ and $\nu$ of $10^{11}\, {\rm cm}^2\,{\rm s} +^{-1}$ we get a dimensionless velocity of one unit and a streamfunction of $1/\pi$ units." + For a dimensional speed of 90ms+ and v ο s.1. the dimensionless velocity is 1.8x10 ‘units.," For a dimensional speed of $90\, {\rm m}\,{\rm s}^{-1}$ and $\nu$ of $10^{15} {\rm cm}^2\,{\rm s}^{-1}$, the dimensionless velocity is $1.8 \times 10^{-4}$ units." + The streamfunction associated with. a peak meridional∙∙ [low of ⊳∙20ms! and vy=105em?9s tis: +x10.!/z.," The streamfunction associated with a peak meridional flow of $20\,{\rm m}{\rm s}^{-1}$ and $\nu=10^{15}\, {\rm cm}^2\, +{\rm s}^{-1}$ is $4 \times 10^{-4}/\pi$." + :The results that Follow will be for parameter values within these ranges and for even higher viscosity. in order to show the full range of behavior of the solution with respect to node number and location.," The results that follow will be for parameter values within these ranges and for even higher viscosity, in order to show the full range of behavior of the solution with respect to node number and location." +" In the case of the differential rotation linear velocity imposed at the side boundary. we must decide the relative amplitudes of the z independent part Cj and the z-dependent part U,."," In the case of the differential rotation linear velocity imposed at the side boundary, we must decide the relative amplitudes of the $z$ independent part $U_0$ and the $z$ -dependent part $U_n$." + This choice will be guided by observations., This choice will be guided by observations. + Whatever the choice. only the z dependent part of C has dynamical consequences for the meridional [low ancl the position of its nodes.," Whatever the choice, only the $z$ dependent part of $U$ has dynamical consequences for the meridional flow and the position of its nodes." + Our results are of (wo types: displays of the latitude positions of all the nodes in the streaanfunction as functions of the parameters of the problem. and contour plots of that streaanfunction.," Our results are of two types: displays of the latitude positions of all the nodes in the streamfunction as functions of the parameters of the problem, and contour plots of that streamfunction." + We discuss node position first., We discuss node position first. + We focus on solutions lor which the boundary forcing is chosen wilh »=1. corresponding to a primary meridional circulation cell that has poleward flow in the upper half of the polar cap.and equatorward flow in the lower half.," We focus on solutions for which the boundary forcing is chosen with $n=1$, corresponding to a primary meridional circulation cell that has poleward flow in the upper half of the polar cap,and equatorward flow in the lower half." +To produce a meridional flow in the polar cap that contains »21 requires forcing al the,To produce a meridional flow in the polar cap that contains $n>1$ requires forcing at the +bbZ.. and ,", and =." +mee 22., See 2. + The nonvanishing elements of9o;; may now be calculated., The nonvanishing elements of$\delta\sigma_{ij}$ may now be calculated. + The diagonal elements are -— = (v−uet) REPRE)ὸ = IBNjo and the off-diagonal elements are (, The diagonal elements are = = - ) = ) and the off-diagonal elements are . + The diagonal elements are -— = (v−uet) REPRE)ὸ = IBNjo and the off-diagonal elements are (2, The diagonal elements are = = - ) = ) and the off-diagonal elements are . + The diagonal elements are -— = (v−uet) REPRE)ὸ = IBNjo and the off-diagonal elements are (22, The diagonal elements are = = - ) = ) and the off-diagonal elements are . + The diagonal elements are -— = (v−uet) REPRE)ὸ = IBNjo and the off-diagonal elements are (22), The diagonal elements are = = - ) = ) and the off-diagonal elements are . +detected in the 0.5-2 keV αμ aid are thus 1ot iucluded iu the nuuber-fHux relation extrapolated from the same band.,detected in the 0.5-2 keV band and are thus not included in the number-flux relation extrapolated from the same band. +" Unforuately, he poor uumber statistics of such sources detected iu the field prevents us [rom placing :1 tight coustraint ou their population."," Unfortunately, the poor number statistics of such sources detected in the field prevents us from placing a tight constraint on their population." + lu addition. one also expects all intrinsic cosmic variance 1 the source number clensity from one field to anXher. typically =6 depeudiug ou the ΕΟΝ. eiergy baud. alic SOULCe detection limit of observaious (see Yaug et al.," In addition, one also expects an intrinsic cosmic variance in the source number density from one field to another, typically $\gtrsim 6\%$, depending on the FoV, energy band, and source detection limit of observations (see Yang et al." + 2003) ancl references therei., 2003 and references therein). +" Thereft)'6e. even in are atively deep exposure sich as the Abell 2125 observation. the nuuber of interlope ""Caluot be p'ecieted ac‘curately."," Therefore, even in a relatively deep exposure such as the Abell 2125 observation, the number of interlopers cannot be predicted accurately." + The relative uncertaity in the uum»er of iuterlopers |)eCOlnes evel &‘eater for an ACIS-S observation. because of bot 1its small FoV (at leasl or the BI CCD #77 chip alone) aud its different euergv response [rot rihe FICCDs of tve ACIS-L. Tlere ]s1 ot yet a nuimber-flux relation constructed or ACIS-S detecte interlcpers.," The relative uncertainty in the number of interlopers becomes even greater for an ACIS-S observation, because of both its small FoV (at least for the BI CCD 7 chip alone) and its different energy response from the FI CCDs of the ACIS-I. There is not yet a number-flux relation constructed for ACIS-S detected interlopers." + Neve‘theless. an a»proxitiate estimate is ofteu required.," Nevertheless, an approximate estimate is often required." + Oue may Se an approach sitvilar to the one described above for the ACIS-I 0.5-8 keV baud., One may use an approach similar to the one described above for the ACIS-I 0.5-8 keV band. + By adopting a atio of the ACIS-S Q.3-Y keV to ACIS-I 0.5-2 keV count ‘ates as 2.2 (Fig., By adopting a ratio of the ACIS-S 0.3-7 keV to ACIS-I 0.5-2 keV count rates as $\sim 2.2$ (Fig. +" 9b). [or example. we iud that the expececd uunber of interlopers is Ve,~16 in the NGC 1591 observation. compared with 112 sources detected in the 0.3-7 keV band."," 9b), for example, we find that the expected number of interlopers is $N_{s,b} \sim 16$ in the NGC 4594 observation, compared with 112 sources detected in the 0.3-7 keV band." + Althouel the relative uncertainty in the expected uunber of interlopers is statistically large. the bulk of the detected sources are clearly associated with the galaxy.," Although the relative uncertainty in the expected number of interlopers is statistically large, the bulk of the detected sources are clearly associated with the galaxy." + To facilitate a comparison with the analysis by Di Stefano et al. (, To facilitate a comparison with the analysis by Di Stefano et al. ( +2003). we also exclude sources that have beet identified as foregroud sars as well as the nucleus aud globular clisters of NGC 0801.,"2003), we also exclude sources that have been identified as foreground stars as well as the nucleus and globular clusters of NGC 4594." + Fig., Fig. + 10 presents the nunber-[fltx relation for the remainine νι=90 soure etected in the 0.3-7 keV. banc., 10 presents the number-flux relation for the remaining $N_s = 90$ sources detected in the 0.3-7 keV band. + We calculate the re-distibution matdx. by using Eq.," We calculate the re-distribution matrix, by using Eq." + 19 witl ANS4—16 as estimated above aud the 2M1ASS. Is-ba16| iuwage (Fig.," 19 with $N_{s,b} = 16$ as estimated above and the 2MASS K-band image (Fig." + 2a) as tlὁ galactic source proability listribution., 2a) as the galactic source probability distribution. + Foregrouid stars in the image are 'emoved appὈδίμιαely with a 9x9 pixel inecdian ter (pixel size — 5»)., Foreground stars in the image are removed approximately with a $\times$ 9 pixel median filter (pixel size = 5). + The predicted iuerloper coutribution ls small ancl is thus ]xec in the subsequent ΕΣ analysis., The predicted interloper contribution is small and is thus fixed in the subsequent number-flux analysis. + First. we mocle the galactic COMPO.ient. Using a single power law xl get the best [it as fall error bars are at the lo coulfideuce level): the C-statistic value 17.0 for 9 degrees of (reedom cau ouly be rejected statistically at a coulideuce ~92©.," First, we model the galactic component, using a single power law and get the best fit as (all error bars are at the $1\sigma$ confidence level); the C-statistic value 17.0 for 9 degrees of freedom can only be rejected statistically at a confidence $\sim 92\%$." + Consideriug al the additional uncertainties that are not included in the analysis (e.tGee) iuterloper subtraction errors). we consider the siugle power law fit is still reasonably acceptable.," Considering all the additional uncertainties that are not included in the analysis (e.g., interloper subtraction errors), we consider the single power law fit is still reasonably acceptable." + Next. we fit the observed. uumber-Iux relation with a brokeu power law (see also Di Stefano et al.," Next, we fit the observed number-flux relation with a broken power law (see also Di Stefano et al." + 2003J.," 2003)," +There have been countless papers in recent vears discussing he matter distribution in galaxies and. in particular. the contributions of both the stellar disc and the dark matter ido.,"There have been countless papers in recent years discussing the matter distribution in galaxies and, in particular, the contributions of both the stellar disc and the dark matter halo." + Any attempt to model the structure of a galaxy with multiple components is limited by the information provided w the light we receive., Any attempt to model the structure of a galaxy with multiple components is limited by the information provided by the light we receive. + This introduces degeneracies in the mass distribution when we compare the Lew constrained xwameters with the large number of unknowns., This introduces degeneracies in the mass distribution when we compare the few constrained parameters with the large number of unknowns. + One technique that has been used to. side-step. this oblem is to assume a maximal disc (quantified in Sackett 1997). whereby the disc contributes the majority of the rotation (75-95%)) at the radius of its maximum circular speed.," One technique that has been used to side-step this problem is to assume a maximal disc (quantified in Sackett 1997), whereby the disc contributes the majority of the rotation ) at the radius of its maximum circular speed." + This definition takes into account the contribution to the inner rotation curve of a bulge component., This definition takes into account the contribution to the inner rotation curve of a bulge component. + Various studies have challenged: and supported this view and they will be discussed in Section ??.., Various studies have challenged and supported this view and they will be discussed in Section \ref{max}. + Observations of rotation curves of galaxies gave the irst hints of the existence of dark matter., Observations of rotation curves of galaxies gave the first hints of the existence of dark matter. + In the 1960s ane TOs. extensive studies of the circular rotation of spiral ealaxies suggested the need for dark matter to account [or he missing cdvnamical mass (e.g. see Rubin et al.," In the 1960s and 70s, extensive studies of the circular rotation of spiral galaxies suggested the need for dark matter to account for the missing dynamical mass (e.g. see Rubin et al." + 1962: Lubin. Ford Thonnard. 1978: Faber Gallagher. 1979).," 1962; Rubin, Ford Thonnard 1978; Faber Gallagher 1979)." + The fatness of rotation curves beyond the optical edge of hese spirals contracicted the expected Ixeplerian Fall-olf., The flatness of rotation curves beyond the optical edge of these spirals contradicted the expected Keplerian fall-off. + In he 1980s and 90s. many groups used large scale structure to deduce the expected properties of dark matter particles and applied these to N-body simulations (Peebles 1984: Navarro. Frenk White 1996).," In the 1980s and 90s, many groups used large scale structure to deduce the expected properties of dark matter particles and applied these to N-body simulations (Peebles 1984; Navarro, Frenk White 1996)." + Phe subsequent caleulated profiles can be compared with the results of observations for consistency., The subsequent calculated profiles can be compared with the results of observations for consistency. + The firm determination. of a general trend in the eatures of rotation curves. as distinct from a few abnormal systems. requires the accumulation of cata from many galaxies with varving morphological tvpes.," The firm determination of a general trend in the features of rotation curves, as distinct from a few abnormal systems, requires the accumulation of data from many galaxies with varying morphological types." + Salucci Burkert (2000) constructed ‘universal rotation curves’ (URCs) with luminosity as the only free parameter. [rom observations of ~ 1100 rotation curves.," Salucci Burkert (2000) constructed `universal rotation curves' (URCs) with luminosity as the only free parameter, from observations of $\sim$ 1100 rotation curves." + From these URCs. hey were able to subtract constant mass-to-light ratio disces from the surface brightness distributions of observed galaxies. and derive the expected. contribution from dark matter.," From these URCs, they were able to subtract constant mass-to-light ratio discs from the surface brightness distributions of observed galaxies, and derive the expected contribution from dark matter." + Salucci (2001) found the dark matter haloes were required to have large core regions in order to [fit the universal curves., Salucci (2001) found the dark matter haloes were required to have large core regions in order to fit the universal curves. + Core radii of 3-4 disc scale lengths were ound to be consistent with observations for large spiral ealaxies., Core radii of 3-4 disc scale lengths were found to be consistent with observations for large spiral galaxies. + The use of gravitational lensing to disassemble a galaxy iw been used recently by Alaller et al. (, The use of gravitational lensing to disassemble a galaxy has been used recently by Maller et al. ( +2000).,2000). + Their analysis of the cloubly imaged system D1600|484 cic not ve a unique solution due to the necessity. of invoking he Tullv. Fisher relation for rotational information. the arge errors on the position angle of the major components and the perturbing elfect of a nearby galaxy.," Their analysis of the doubly imaged system B1600+434 did not have a unique solution due to the necessity of invoking the Tully Fisher relation for rotational information, the large errors on the position angle of the major components and the perturbing effect of a nearby galaxy." + In. addition. he constraint of only two images limits the number of known parameters.," In addition, the constraint of only two images limits the number of known parameters." + Their work. however. illustrated the utilisation. of lensing to break the disc/halo. degeneracy.," Their work, however, illustrated the utilisation of lensing to break the disc/halo degeneracy." + They found a high. probability for à sub-maximal disc. ancl he need for some degree of a constant density core in he centre of the dark matter halo.," They found a high probability for a sub-maximal disc, and the need for some degree of a constant density core in the centre of the dark matter halo." + These results pave the wav lor our work and demonstrate the ability to solve for he mass distribution given à reasonable number of known )aranmeters., These results pave the way for our work and demonstrate the ability to solve for the mass distribution given a reasonable number of known parameters. +Although the observer's spiral will be shifted by an angle o either counter (leading ficldlines) or with (trailing Leldlines) the direction of rotation. it is clear [rom equation (26) that in either case only for ϐGe= can there be two physical roots to equation (25).,"Although the observer's spiral will be shifted by an angle $\Phi$ either counter (leading fieldlines) or with (trailing fieldlines) the direction of rotation, it is clear from equation (26) that in either case only for $\theta<\theta_{max}=\frac{r_{*}}{r_{lc}}$ can there be two physical roots to equation (25)." + As 6 peduces. the double roots will begin with those at rj=re| κor.) aad ro—0 and end with in the limit «V.," As $\theta$ reduces, the double roots will begin with those at $r_{1}=r_{*}+\Phi{r_{lc}}$ $0. this corresponds to 365)«0. and we can close the contour in the lower half-plane.," For $\xi>0$, this corresponds to $\Im(s) < 0$, and we can close the contour in the lower half-plane." + If instead €«0. the requirement is S65)>0. and we can close the contour in the upper half-plane.," If instead $\xi<0$, the requirement is $\Im(s) > 0$, and we can close the contour in the upper half-plane." + So for a given &. only the poles lying in the corresponding half-plane contribute to the sum of residues.," So for a given $\xi$, only the poles lying in the corresponding half-plane contribute to the sum of residues." +" We encode this behaviour in the factor where for the Heaviside step function. we use the convention If all poles s, are simple. we can calculate the residues by the winding numbers w, =1for the upper and Wy =-for the lower contour. the full integral is then This result holds for most relevant combinations of input power spectra and lag parameters."," We encode this behaviour in the factor where for the Heaviside step function we use the convention If all poles $s_n$ are simple, we can calculate the residues by Inserting the winding numbers $w_n=1$ for the upper and $w_n=-1$ for the lower contour, the full integral is then This result holds for most relevant combinations of input power spectra and lag parameters." + For other cases. we derive a generalised result of a very similar functional form. that also holds for multiple poles. in appendix AppendixA:..," For other cases, we derive a generalised result of a very similar functional form, that also holds for multiple poles, in appendix \ref{sec:multipoles}." + We were unable to further simplify the limit of the infinite sum in the probability distribution function (22))., We were unable to further simplify the limit of the infinite sum in the probability distribution function \ref{eq:univar_derivation_pxifinal}) ). + However. as long as the power spectrum decreases at least like £7? for large &. our numerical implementation of the sum formulae. as described in Sect. 4..," However, as long as the power spectrum decreases at least like $k^{-2}$ for large $k$, our numerical implementation of the sum formulae, as described in Sect. \ref{sec:numerical}," + showed that the probability distribution function converges as well., showed that the probability distribution function converges as well. + In practice. it is therefore possible to truncate the series at some maximum mode number NV without losing much precision.," In practice, it is therefore possible to truncate the series at some maximum mode number $N$ without losing much precision." + Also. it is obvious from Eq. (22))," Also, it is obvious from Eq. \ref{eq:univar_derivation_pxifinal}) )" + that for large & a single mode will always dominate the sum. sothat asymptotically. the distribution is not Gaussian. p(é)οeT. but instead exponential. p(£)e:eee!," that for large $\xi$, a single mode will always dominate the sum, sothat asymptotically, the distribution is not Gaussian, $p(\xi) \propto \eto{-\xi^2}$, but instead exponential, $p(\xi) \propto \eto{-\xi / \left(2C_{\mathrm{max}}\right)}$." + We also note at this point that Eq. (22)), We also note at this point that Eq. \ref{eq:univar_derivation_pxifinal}) ) +" depends on the field size L. separation x and power spectrum P(|k,|) only through the ratios x/£ and P(Kk,D/L. as can be seen from the definition of C, in Eq. (16))."," depends on the field size $L$, separation $x$ and power spectrum $P(|k_n|)$ only through the ratios $x/L$ and $P(|k_n|)/L$ , as can be seen from the definition of $C_n$ in Eq. \ref{eq:derivation_cnfactors}) )." + When we present numerical results in the further course of this article. we therefore give these quantities only.," When we present numerical results in the further course of this article, we therefore give these quantities only." + Furthermore. in the case of a Gaussian power spectrum. wecan directly state Lcrp asthe relevant quantity.," Furthermore, in the case of a Gaussian power spectrum, wecan directly state $L \, \sigma_P$ asthe relevant quantity." + For such a power spectrum with Lop=150 and a separation v= 0. Fig.," For such a power spectrum with $L \, \sigma_P=150$ and a separation $x=0$ , Fig." + | demonstratesthe convergence behaviour of the distribution function., \ref{fig:univar_derivation_pxi_x0_g075} demonstratesthe convergence behaviour of the distribution function. + In. this. case. the," In this case, the" +The pulsars galactic planar aud polar velocity components relative (o its standard οἱ res( ave 247 km/s almost directly away trom the galactic center and 51 km/s toward the ealactic North Pole. respectively. (,"The pulsar's galactic planar and polar velocity components relative to its standard of rest are 247 km/s almost directly away from the galactic center and 51 km/s toward the galactic North Pole, respectively. (" +This is signilicantlv larger than the measured velocity in (he solar svstem barycenter frame because (he pulsars standard of rest velocity fortuitously cancels much of the pulsars peculiar velocity with respect to il.),This is significantly larger than the measured velocity in the solar system barycenter frame because the pulsar's standard of rest velocity fortuitously cancels much of the pulsar's peculiar velocity with respect to it.) + The svstemic velocity ol 1012160 is significantly larger than other well-measurecl double neutron star binary svslem velocities. including the JOT37-3037 (transverse velocity 10 kim/s: Stairs οἱ al.," The systemic velocity of B1913+16 is significantly larger than other well-measured double neutron star binary system velocities, including the J0737-3037 (transverse velocity 10 km/s; Stairs et al." + 2006). J1518+4905 (Uransverse velocity 25 km/s: Janssen et al.," 2006), J1518+4905 (transverse velocity 25 km/s; Janssen et al." + 2008). and. B1534+12 (transverse velocily 122 km/s: Thorsett et al.," 2008), and B1534+12 (transverse velocity 122 km/s; Thorsett et al." + )2005) svstems., 2005) systems. + We have analyzed the full set of Arecibo timing data on pulsar D19134-16 to derive the best values of all measurable quantities., We have analyzed the full set of Arecibo timing data on pulsar B1913+16 to derive the best values of all measurable quantities. + A significant proper motion has finally been determined., A significant proper motion has finally been determined. + A small eliteh was observed in the pulsar's timing behavior. the second known elitch in the population of recycled. pulsars.," A small glitch was observed in the pulsar's timing behavior, the second known glitch in the population of recycled pulsars." + The measured rate of orbital period decay continues to be almost precisely the value predicted by general relativity. providing conclusive evidence for the existence of gravitational radiation.," The measured rate of orbital period decay continues to be almost precisely the value predicted by general relativity, providing conclusive evidence for the existence of gravitational radiation." +" Uncertainties in galactic accelerations now dominate the error budget in D. and are likely to do so until the pulsar distance can be measured more accurately,"," Uncertainties in galactic accelerations now dominate the error budget in $\dot P_b$, and are likely to do so until the pulsar distance can be measured more accurately." + We expect that the Shapiro gravitational propagation delay will vield additional tests of relativistic gravity within a few more vears., We expect that the Shapiro gravitational propagation delay will yield additional tests of relativistic gravity within a few more years. +also matched with the values obtained frou the elobal III profiles.,also matched with the values obtained from the global HI profiles. + Keeping the center aud systemic velocity fixed. we fitted for the inclination aud position angle (PA) in cach vine.," Keeping the center and systemic velocity fixed, we fitted for the inclination and position angle (PA) in each ring." +" For IKK98 250. seeping inclination as a free parameter in the tilted rine ft gave unphysical results. hence. the kinematical iuclinatiou of the galaxy was fixed to the value estimated from the ITI morphology. viz NU""."," For KK98 250, keeping inclination as a free parameter in the tilted ring fit gave unphysical results, hence, the kinematical inclination of the galaxy was fixed to the value estimated from the HI morphology, viz $80^\circ$." + Note that at such lieh inclination aneles. the uucertaintv im iuclination iis only a small effect on the derived rotation curve (Beeeman 1989).," Note that at such high inclination angles, the uncertainty in inclination has only a small effect on the derived rotation curve (Begeman 1989)." + For example. if we fix the inclination to 7V. the derived rotation curve is the sane. within the error bars.," For example, if we fix the inclination to $70^\circ$, the derived rotation curve is the same, within the error bars." + Fits for the position anele eave a value of ~2617 Gn good agreement with tha derived from the optical nage). with no svstematic variation across the galaxy.," Fits for the position angle gave a value of $\sim 267^\circ$ (in good agreement with that derived from the optical image), with no systematic variation across the galaxy." +" The rotation curves (derived with the PA and inclination fixed to the values of 267° alc so"") are shown in Fig. 5||", The rotation curves (derived with the PA and inclination fixed to the values of $267^\circ$ and $80^\circ$ ) are shown in Fig. \ref{fig:vrot1}[ [ +À].,A]. + Note that the rotation curves derived from the differeut resolution velocity fields match within the errorbars. sugeestiug hat. iu spite of beige hiehlv inclined. the effects of eam smeariug are not significant.," Note that the rotation curves derived from the different resolution velocity fields match within the errorbars, suggesting that, in spite of being highly inclined, the effects of beam smearing are not significant." + The final adopted rotation curve is shown in Fig. 5|[, The final adopted rotation curve is shown in Fig. \ref{fig:vrot1}[ [ +A] as a solid line.,A] as a solid line. +" For IWIS98 251. the inclination was ound to be 65"" Qvlich agrees with that derived from cllipse fitting to the HII morphology. see Sect. 3.1))."," For KK98 251, the inclination was found to be $65^{\circ}$ (which agrees with that derived from ellipse fitting to the HI morphology, see Sect. \ref{ssec:HI_dis}) )," + with no systematic variation with the radius., with no systematic variation with the radius. + The vost fit position angle was 2307 at all radii. except in the outermost regious of the ealaxy where it changes to ~215°.," The best fit position angle was $\sim 230^\circ$ at all radii, except in the outermost regions of the galaxy where it changes to $\sim 215^\circ$." +" Iguoriug this relatively simall change. (which in any case has uceligible effect on the derived. velocities). the rotation curve was derived by keeping the inclination aud PA fixed at 657 iid 2307 respectively,"," Ignoring this relatively small change, (which in any case has negligible effect on the derived velocities), the rotation curve was derived by keeping the inclination and PA fixed at $65^{\circ}$ and $230^{\circ}$ respectively." + Fig. 6[[, Fig. \ref{fig:vrot2}[ [ +À] shows the rotation curves for KIx98 251. derived from the various resolution velocity fields.,"A] shows the rotation curves for KK98 251, derived from the various resolution velocity fields." + Note that all the rotation curves match within the errorbars., Note that all the rotation curves match within the errorbars. + Recall that IKI&98 251 shows slisht kincimatical lopsidedness., Recall that KK98 251 shows slight kinematical lopsidedness. + Consistent with this. the rotation curve derivec incdependcutly for the approaching aud receding sides are sheltly different. althoueh the iffercnce is evervwhere less thau 3.5|.," Consistent with this, the rotation curve derived independently for the approaching and receding sides are slightly different, although the difference is everywhere less than 3.5." + For the purpose of mass modchnue. we have used a inea of the rotation curves for the two sides.," For the purpose of mass modeling, we have used a mean of the rotation curves for the two sides." + The errorbars on he mean rotation curve were obtained by adding quadratically the uncertaintv reported by the Ποπιο ft as well as he difference iu rotation velocities between the approaching aud receding side., The errorbars on the mean rotation curve were obtained by adding quadratically the uncertainty reported by the tilted-ring fit as well as the difference in rotation velocities between the approaching and receding side. + For highly inclined galaxies. rotation velocities derived frou the titles rue fits to the velocity field) could underestimate the true rotation velocities. hence iu such cases the rotation curve is often estimated by fittiug to the hieh velocity οσο of the enmüssiou (e.g. Saucid Allen 1979).," For highly inclined galaxies, rotation velocities derived from the titled ring fits to the velocity field could underestimate the true rotation velocities, hence in such cases the rotation curve is often estimated by fitting to the high velocity edge of the emission (e.g. Sancisi Allen 1979)." + While this method is well suited to large ealaxies with fla rotation curves. it i not appropriate for ealaxies with solid body rotation.," While this method is well suited to large galaxies with flat rotation curves, it is not appropriate for galaxies with solid body rotation." + Both the velocity field of IKIK98 250 as well as the rotation curve derived frou the tilted ring fit iudicate solid body rotation. hence. stead of using the οσο fitting technique. the rotation curve or WIN98 250 was derived. by. interactively fitting to the PV diagram. using the task INSPECTOR in GIPSY (see Fig ΠΙΑ.," Both the velocity field of KK98 250 as well as the rotation curve derived from the tilted ring fit indicate solid body rotation, hence, instead of using the `edge fitting' technique, the rotation curve for KK98 250 was derived by interactively fitting to the PV diagram, using the task INSPECTOR in GIPSY (see Fig \ref{fig:PV}[ [A])." + The PA aud the iuclination in the interactive fittine were fixed to the values used in the tilted mime fit., The PA and the inclination in the interactive fitting were fixed to the values used in the tilted ring fit. + The derived rotation curve matches. within the errorbars. o that derived from the tilted rime ft.," The derived rotation curve matches, within the errorbars, to that derived from the tilted ring fit." + As a further check of the robustuess of the derived rotation curve. a node data cube for ΤΙΣ 250 was coustructed using he adopted rotation curve and the observed HI column density profile. with the task GCALAIOD in GIPSY.," As a further check of the robustness of the derived rotation curve, a model data cube for KK98 250 was constructed using the adopted rotation curve and the observed HI column density profile, with the task GALMOD in GIPSY." + The HOCLE data cube was smoothed to a beam of 26%421” resolution and the moment maps were derived in the same uauner as for the real data., The model data cube was smoothed to a beam of $''\times21''$ resolution and the moment maps were derived in the same manner as for the real data. + Fig. 8||, Fig. \ref{fig:model1}[ [ +D] shows the derived LLOCLC velocity field for IKIX98 250.,B] shows the derived model velocity field for KK98 250. + A residual (data-model) velocity field is shown in Fig. S[|, A residual (data-model) velocity field is shown in Fig. \ref{fig:model1}[ [ +C|: as can be seen. the uodel velocity field provides a good match to the observed Ποια.,"C]; as can be seen, the model velocity field provides a good match to the observed field." +of the line center.,of the line center. + These red photons cau still have a probability of expericucing resonant scatterings in the intall region around the halo aud being shifted to the blue side., These red photons can still have a probability of experiencing resonant scatterings in the infall region around the halo and being shifted to the blue side. + The surface brightucss profile on scales <1htMIpe is expected to be contributed by these photous., The surface brightness profile on scales $\lesssim 1\hMpc$ is expected to be contributed by these photons. + The probability of such scatterings depends ou the 1iaguitude of the shitt aud the iufall velocity around the halo., The probability of such scatterings depends on the magnitude of the shift and the infall velocity around the halo. + For sources in LottTAL. halos. even with a |Go initial line shift (thin dashed curves in Figure 9)). the flattening part in the surface brightucss profile cau still be clearly seen (left panel). although the majority of the observed photons are from the ceutral region (right panel).," For sources in $10^{11}\hMsun$ halos, even with a $+6\sigma$ initial line shift (thin dashed curves in Figure \ref{fig:initfreq}) ), the flattening part in the surface brightness profile can still be clearly seen (left panel), although the majority of the observed photons are from the central region (right panel)." + We verity that for a [3.50 initial Bine shift (not shown iu the plot) the contribution from the central region to the total Iuniinosity is =1056.. less thau that from the extended. cunission.," We verify that for a $+3.5\sigma$ initial line shift (not shown in the plot) the contribution from the central region to the total luminosity is $\lesssim$, less than that from the extended emission." + If we take this as a threshold for the profile to change frou point-like to extended. it would correspond to ~250kus|.," If we take this as a threshold for the profile to change from point-like to extended, it would correspond to $\sim 250\kms$." + If the wavelength shift of the initial photos is ni the range of £30. the resultant surface briehtuess istribution is not scusitive to the initial wavelength. as shown by the solid curves in Figure 9..," If the wavelength shift of the initial photons is in the range of $\pm 3\sigma$, the resultant surface brightness distribution is not sensitive to the initial wavelength, as shown by the solid curves in Figure \ref{fig:initfreq}." + This is easy to understand: photons starting at a wavelength shift #30 uudergo many scatterines in the core. leading to a istributiou that loses memory of the original wavelcueth and to a nearly constant surface brightuess profile.," This is easy to understand: photons starting at a wavelength shift $\pm 3\sigma$ undergo many scatterings in the core, leading to a distribution that loses memory of the original wavelength and to a nearly constant surface brightness profile." + But photons with a larger initial wavelength deviation are not scattered cuough times to be redistributed in this wav before they escape., But photons with a larger initial wavelength deviation are not scattered enough times to be redistributed in this way before they escape. + Therefore. tlhe predicted profile should be reliable except when many photous are cluitted from the central galaxy with a wavelength shift of several times the velocity dispersion.," Therefore, the predicted profile should be reliable except when many photons are emitted from the central galaxy with a wavelength shift of several times the velocity dispersion." + To climinate most of the extended emission around the galaxies. the initial line shifts (after/ plotous escape the ISM) need to be larger than 250kus| for halos of LOMA TALL.," To eliminate most of the extended emission around the galaxies, the initial line shifts (after photons escape the ISM) need to be larger than $250\kms$ for halos of $10^{11}\hMsun$ ." + Galactic winds can have the effect of shifting emission toward red (c.g...Ver-hamuneetal.2006:Dijkstra&νο 2010).," Galactic winds can have the effect of shifting emission toward red \citep[e.g.,][]{Verhamme06,Dijkstra10}." +".. From observations of i:~3 galaxies. Steideletal.(2010) fud that the interstellar absorption line shifts with respect to the Ta-defined ealaxy systemic redshift bv 165211008+ GQnean + standard deviation) for ealaxies of barvon inass (stars plus cold sas) ranging frou ~«1019AZ, to~3«10H:AZ,"," From observations of $z\sim 3$ galaxies, \citet{Steidel10} find that the interstellar absorption line shifts with respect to the $\alpha$ -defined galaxy systemic redshift by $165 \pm 140 \kms$ (mean $\pm$ standard deviation) for galaxies of baryon mass (stars plus cold gas) ranging from $\sim 1\times 10^{10}\Msun$ to $\sim 3\times 10^{11}\Msun$." + The uncertainty of velocity ucasured for individual galaxies is estimated to be 130kms 1., The uncertainty of velocity measured for individual galaxies is estimated to be $\sim 130\kms$ . + Tf the wind is confined in a region uot far yon the ISAL the above observational results indicate hat the imitial shift in ciission could be above ~300kus1.," If the wind is confined in a region not far from the ISM, the above observational results indicate that the initial shift in emission could be above $\sim 300\kms$." + Dowever. even in such a case. the shift may rot be sufficieut for pliotous to completely decouple roni the circunegalactic aud intergalactic cuviromments. depending on the spatial distribution of the wind.," However, even in such a case, the shift may not be sufficient for photons to completely decouple from the circumgalactic and intergalactic environments, depending on the spatial distribution of the wind." + Observationally. the outflowing neutral gas of the wind is rot isotropic. usually collimated ina bipolar fashion (6.9..Veilleux&Rupke 2002).," Observationally, the outflowing neutral gas of the wind is not isotropic, usually collimated in a bipolar fashion \citep[e.g.,][]{Bland88,Shopbell98,Veilleux02}." +. It is likely that cussion escaping in directions other than the wind would gain onlv a simaller recsviurd shift. aud the source would still vccolmme extended in the end.," It is likely that emission escaping in directions other than the wind would gain only a smaller redward shift, and the source would still become extended in the end." + The wind effect ou the spatial distribution of emission is also expected to be ess slenificaut for sources before reionization than those after reionization. since the higher neutral density boosts he scattering optical depth.," The wind effect on the spatial distribution of emission is also expected to be less significant for sources before reionization than those after reionization, since the higher neutral density boosts the scattering optical depth." + It is also possible that the wiud could reach scales uuch larger than the ISM. (e.g...Steideletal.2010).," It is also possible that the wind could reach scales much larger than the ISM \citep[e.g.,][]{Steidel10}." +. Tn such a case. the initial hine shüfts (after photous CRape the ISM) is not much affected bv the wind. mt the wind alters the distribution aud dynamics of jeutral eas in the circumealactic region aud therefore the details iu the radiative transfer process.," In such a case, the initial line shifts (after photons escape the ISM) is not much affected by the wind, but the wind alters the distribution and dynamics of neutral gas in the circumgalactic region and therefore the details in the radiative transfer process." + While the surface briehtuess profile of emission may chauge accordingly. the extended enüssou should remain as a generic feature.," While the surface brightness profile of emission may change accordingly, the extended emission should remain as a generic feature." + Such a possibility deserves further investigations using high resolution galaxy formation simulations with a wind prescription., Such a possibility deserves further investigations using high resolution galaxy formation simulations with a wind prescription. + A change in the initial line profile can lead to a change in the observed Iuuinosity aud therefore the observed luninosity function., A change in the initial line profile can lead to a change in the observed luminosity and therefore the observed luminosity function. + However. as discussed in Paper L α combination of changes in the star formation prescription used. the stellar EME adopted. and the dust extinction is able to keep the predicted luminosity function to match the observed one.," However, as discussed in Paper I, a combination of changes in the star formation prescription used, the stellar IMF adopted, and the dust extinction is able to keep the predicted luminosity function to match the observed one." + On the other haud. the chauge in the iuitid Lue profile can alter the streneth of the coupling between the observed chussion and the circumealactic aud iterealactic environments.," On the other hand, the change in the initial line profile can alter the strength of the coupling between the observed emission and the circumgalactic and intergalactic environments." + This would show up in the clustering of LAEs (Paper ID. which provides an interesting wav to constrain the initial line profile aud the effect of ealactic wincl.," This would show up in the clustering of LAEs (Paper II), which provides an interesting way to constrain the initial line profile and the effect of galactic wind." + For the iain results in this paper. our radiative trauster caleulation is performed im a 10075PAIpe” simulation box. where eas propertics (density. temperature.aud peculiar velocity) are sampled," For the main results in this paper, our radiative transfer calculation is performed in a $100^3 \VhMpc$ simulation box, where gas properties (density, temperature,and peculiar velocity) are sampled" +either mixed hydrogen/helium or pure helium ignitions.,either mixed hydrogen/helium or pure helium ignitions. + The presence of a substantial amount of hydrogen leads to a factor of two greater expansion because of the lower mean molecular weight (jj24/3 for pure He: µz0.6 for solar composition)., The presence of a substantial amount of hydrogen leads to a factor of two greater expansion because of the lower mean molecular weight $\mu=4/3$ for pure He; $\mu\approx 0.6$ for solar composition). + CB noted that the largest frequency shifts observed (fractional frequency shifts Αννz 0.896)) were difficult to achieve with pure He ignitions. requiring temperatures at the base of the burning shell extremely close to the limiting value from radiation pressure at the start of the burst.," CB noted that the largest frequency shifts observed (fractional frequency shifts $\Delta\nu/\nu\approx 0.8$ ) were difficult to achieve with pure He ignitions, requiring temperatures at the base of the burning shell extremely close to the limiting value from radiation pressure at the start of the burst." + However. they also noted that no burst oscillations have been seen during Type I X-ray bursts with long (>20 s) cooling tails. characteristic of hydrogen burning (which is limited by beta decays during the rp process: Bildsten 1998). perhaps indicating a preponderance of He bursts amongst those which show oscillations.," However, they also noted that no burst oscillations have been seen during Type I X-ray bursts with long $\gtrsim 20\ {\rm s}$ ) cooling tails, characteristic of hydrogen burning (which is limited by beta decays during the rp process; Bildsten 1998), perhaps indicating a preponderance of He bursts amongst those which show oscillations." + Thus they suggested that understanding the largest frequency shifts observed as being due to hydrostatic expansion together with rigid rotation might prove problematic., Thus they suggested that understanding the largest frequency shifts observed as being due to hydrostatic expansion together with rigid rotation might prove problematic. + Recently. two sources have shown extremely large frequency shifts.," Recently, two sources have shown extremely large frequency shifts." + Wijnands. Strohmayer. Franco. (2001) found an increase of ~5Hz in the 567 Hz burst oscillation from MXB 1658-298.," Wijnands, Strohmayer, Franco (2001) found an increase of $\approx 5\ {\rm Hz}$ in the 567 Hz burst oscillation from MXB 1658-298." + In addition to being a large frequency shift (Av/vzz 0.9%)). the spin evolution in this burst was unusual. with a rapid frequency increase occuring several seconds into the burst tail.," In addition to being a large frequency shift $\Delta\nu/\nu\approx 0.9$ ), the spin evolution in this burst was unusual, with a rapid frequency increase occuring several seconds into the burst tail." + This frequeney shift is a little larger than the rigidly-rotating mixed H/He models of CB., This frequency shift is a little larger than the rigidly-rotating mixed H/He models of CB. + Galloway et al. (, Galloway et al. ( +2001) discovered a 270 Hz burst oscillation from the dipping source 4U 1916-053.,2001) discovered a 270 Hz burst oscillation from the dipping source 4U 1916-053. + During 4 seconds in the burst decay. the frequency increased by 3.6 Hz. à fractional shift of1.3%.. by far the largest fractional frequency shift observed so far.," During 4 seconds in the burst decay, the frequency increased by 3.6 Hz, a fractional shift of, by far the largest fractional frequency shift observed so far." + Comparing with the results of CB. Galloway et al. (," Comparing with the results of CB, Galloway et al. (" +2001) pointed out that the expansion implied by this frequency shift is larger than expected if the atmosphere rotates rigidly. especially given that the measured peak flux of the X-ray burst is sub-Eddington (z0.5 Fray). and that the orbital period of this source (z:50mins: Walter et al.,"2001) pointed out that the expansion implied by this frequency shift is larger than expected if the atmosphere rotates rigidly, especially given that the measured peak flux of the X-ray burst is sub-Eddington $\approx 0.5\ {\rm F_{\rm Edd}}$ ), and that the orbital period of this source $\approx 50\ {\rm mins}$; Walter et al." + 1982; White Swank 1982; Grindlay et al., 1982; White Swank 1982; Grindlay et al. + 1988) implies a hydrogen-poor companion (Nelson. Rappaport. Joss 1986) and therefore a small fraction of hydrogen present at ignition.," 1988) implies a hydrogen-poor companion (Nelson, Rappaport, Joss 1986) and therefore a small fraction of hydrogen present at ignition." + —1 this paper. we present new calculations of the hydrostatic expansion and resulting spin-down of the neutron star atmosphere.," In this paper, we present new calculations of the hydrostatic expansion and resulting spin-down of the neutron star atmosphere." + In $2. we describe an error in CB’s calculation of the change in the moment of inertia of the burning shell. and show that the values of spin-down calculated by CB are a factor of two too large.," In 2, we describe an error in CB's calculation of the change in the moment of inertia of the burning shell, and show that the values of spin-down calculated by CB are a factor of two too large." + Comparing the new results with observations. we show that. even when hydrogen is present at ignition.shifts.," Comparing the new results with observations, we show that, even when hydrogen is present at ignition,." + We then go on to consider different neutron star masses and equations of state., We then go on to consider different neutron star masses and equations of state. + In $3. we derive the angular momentum conservation law 1n general relativity. presenting analytic results for slow rotation. and numerical calculations of rapidly-rotating stars.," In 3, we derive the angular momentum conservation law in general relativity, presenting analytic results for slow rotation, and numerical calculations of rapidly-rotating stars." + We compare our results with recent work by Heyl (2000) and Abramowiez. Kluzniak. Lasota (2001).," We compare our results with recent work by Heyl (2000) and Abramowicz, Kluzniak, Lasota (2001)." + In $4. we show how to include general relativity and rapid rotation 1n the equations describing the structure of the atmosphere.," In 4, we show how to include general relativity and rapid rotation in the equations describing the structure of the atmosphere." + We then rescale our fiducial results of 32 to different neutron star masses and equations of state. before presenting some detailed models and rotational profiles.," We then rescale our fiducial results of 2 to different neutron star masses and equations of state, before presenting some detailed models and rotational profiles." + We again show that the expected spin-down due to angular momentum conservation is smaller than the observed frequency drifts if the atmosphere rotates rigidly., We again show that the expected spin-down due to angular momentum conservation is smaller than the observed frequency drifts if the atmosphere rotates rigidly. + We discuss the implications of our results in $5., We discuss the implications of our results in 5. + In this section. we first show that CB made an error of a factor of two in their calculation of the change in the moment of inertia during a Type I X-ray burst. and then compare the new spin down calculations with observations.," In this section, we first show that CB made an error of a factor of two in their calculation of the change in the moment of inertia during a Type I X-ray burst, and then compare the new spin down calculations with observations." + Consider a spherical shell at the surface of the star. (, Consider a spherical shell at the surface of the star. ( +The arguments of this section are unaffected by including the centrifugal distortion of the isobaric surfaces.),The arguments of this section are unaffected by including the centrifugal distortion of the isobaric surfaces.) + The mass of the shell is and its moment of Inertia 1s where the factor of 2/3 comes from integrating over angles., The mass of the shell is and its moment of inertia is where the factor of $2/3$ comes from integrating over angles. + Following CB. we adopt a plane-parallel approximation for the thin atmosphere. and write Á=R+<. keeping only first order terms in z/R.," Following CB, we adopt a plane-parallel approximation for the thin atmosphere, and write $r=R+z$ , keeping only first order terms in $z/R$." + Changing integration variables from radius r to column depth v. where dv2—-pdr. equation (2)) reduces to CB's equation (19) for the moment of inertia.," Changing integration variables from radius $r$ to column depth $y$, where $dy=-\rho\,dr$ , equation \ref{eq:I}) ) reduces to CB's equation (19) for the moment of inertia." + If the angular momentum of the atmosphere. /O. is conserved. the spin-down is given by comparing its moment of inertia before the burst with that during the burst. AQ/O2—AZ/T.," If the angular momentum of the atmosphere, $I\Omega$, is conserved, the spin-down is given by comparing its moment of inertia before the burst with that during the burst, $\Delta\Omega/\Omega=-\Delta I/I$." + The error in CB's ealeulation of the change in moment of inertia arises because they assume that the total column depth of the atmosphere is constant during the burst., The error in CB's calculation of the change in moment of inertia arises because they assume that the total column depth of the atmosphere is constant during the burst. + We now show that this is not the case when the mass of the layer is conserved., We now show that this is not the case when the mass of the layer is conserved. + We write the mass of the shell as where Ay is the total column depth. and we define a mass- thickness (2j=[ονΑν.," We write the mass of the shell as where $\Delta y$ is the total column depth, and we define a mass-weighted thickness $\avz=\int z(y) dy/\Delta y$." + If the vertical extent of the layer (x) changes. so must its total column depth Av if the total mass M ts conserved.," If the vertical extent of the layer $\avz$ changes, so must its total column depth $\Delta y$ if the total mass $M$ is conserved." + Physically. a thin spherical shell has a greater surface area If 1t moves radially outwards. and so must have a lower column depth in order to conserve its total mass.," Physically, a thin spherical shell has a greater surface area if it moves radially outwards, and so must have a lower column depth in order to conserve its total mass." + By taking the column depth at the base during the burst to be the same as that before the burst. CB unwittingly increased the mass of the layer during the burst. and so overestimated the change in its moment of inertia.," By taking the column depth at the base during the burst to be the same as that before the burst, CB unwittingly increased the mass of the layer during the burst, and so overestimated the change in its moment of inertia." + Rather than including the change in the column depth of the layer explicitly. we write the mass element in equation (2)) as dit2ARR.dy. so that there isa unique correspondence between mass and column depth.," Rather than including the change in the column depth of the layer explicitly, we write the mass element in equation \ref{eq:I}) ) as $dm=4\pi R^2\ dy$, so that there is a unique correspondence between mass and column depth." +" The moment of inertia is then where the integration limits are now held fixed during the burst. thereby keeping the mass of the layer constant. M=ERAAy =47R-(1,—¥,)."," The moment of inertia is then where the integration limits are now held fixed during the burst, thereby keeping the mass of the layer constant, $M=4\pi R^2\Delta +y=4\pi R^2(y_b-y_t)$ ." + We have checked the validity of this expression by integrating the full spherical equations for this problem., We have checked the validity of this expression by integrating the full spherical equations for this problem. + In this paper. we adopt a plane-parallel approximation because it allows us to straightforwardly incorporate the general relativistic angular momentum conservation law.," In this paper, we adopt a plane-parallel approximation because it allows us to straightforwardly incorporate the general relativistic angular momentum conservation law." + The spin changes during the burst result from changes in the verticalextent ofthe atmosphere. which are described by the second term of equation (4)).," The spin changes during the burst result from changes in the verticalextent ofthe atmosphere, which are described by the second term of equation \ref{eq:right}) )." + Equation (19) of CB has a factor, Equation (19) of CB has a factor +5truciu BStrueiu Cnr Cnr Cnr Cnr σα1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures ,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt} + " +excess of light of about 6.3 per cent in V. and 4.4 per cent in D.,excess of light of about 6.3 per cent in $V$ and 4.4 per cent in $B$. + Vhese figures are actually very close to the values derived from the light curve analysis. and the colour behaviour is also reproduced. thus giving additional physical meaning to the best-fitting parameters obtained.," These figures are actually very close to the values derived from the light curve analysis, and the colour behaviour is also reproduced, thus giving additional physical meaning to the best-fitting parameters obtained." + The uncertainties in the parameters presented in Table 2 were carefully. evaluated by means of two. cülferent approaches., The uncertainties in the parameters presented in Table \ref{tab:CDTau} were carefully evaluated by means of two different approaches. + On the one hand. the WD program viclds the standard: error associated to each adjusted: parameter.," On the one hand, the WD program yields the standard error associated to each adjusted parameter." + On the other hand. the error can also be estimated: as the r.nis.," On the other hand, the error can also be estimated as the r.m.s." + scatter ofal£ the parameter sets corresponding to the iterations between the first solution and the Last. iteration (about 100)., scatter of the parameter sets corresponding to the iterations between the first solution and the last iteration (about 100). + We shall mention that this is. in general. larger than the res.," We shall mention that this is, in general, larger than the r.m.s." + scatter of the solutions alone. i.e. those that fulfill the criterion previously. described.," scatter of the solutions alone, i.e. those that fulfill the criterion previously described." + We conservatively adopted the uncertainty as twice whichever of the two error estimates was the largest., We conservatively adopted the uncertainty as twice whichever of the two error estimates was the largest. + Phe ranis., The r.m.s. + scatters of the residuals in the light curve fit are 0.011 mag (7= 292) for both D anc V., scatters of the residuals in the light curve fit are 0.011 mag $n=292$ ) for both $B$ and $V$. + Fig., Fig. + 2 shows the light curve fit to the observed. D. anc V dillerential photometry and the corresponding residuals. where no systematic trends are observed.," \ref{fig:lcCD} shows the light curve fit to the observed $B$ and $V$ differential photometry and the corresponding residuals, where no systematic trends are observed." + We shall compare our analysis with that. of. Woo (1976). Güllmen et al. (," We shall compare our analysis with that of Wood (1976), Güllmen et al. (" +1980) and. Russo et al. (,1980) and Russo et al. ( +1981).,1981). + Regarding the first two works. significant. dillerences exis in the inclination and in the fractional radii.," Regarding the first two works, significant differences exist in the inclination and in the fractional radii." + The inclination is 1° larger in our solution. rx is also 0.010 larger in our case. but ry is about 0.005 smaller. the latter implying a large change in the ratio of radii.," The inclination is $^{\circ}$ larger in our solution, $r_{\rm A}$ is also 0.010 larger in our case, but $r_{\rm B}$ is about 0.005 smaller, the latter implying a large change in the ratio of radii." + However. our computed elements are in very good agreement with those of Russo οἱ al. (," However, our computed elements are in very good agreement with those of Russo et al. (" +1981).,1981). + They. also emploved the WD program (although an earlier version) to analyse the light. curves. while the other authors used. Woods model.," They also employed the WD program (although an earlier version) to analyse the light curves, while the other authors used Wood's model." + Thus. the reason for the discrepancy in the solutions is probably related to intrinsic cüllerences of the models.," Thus, the reason for the discrepancy in the solutions is probably related to intrinsic differences of the models." + The radii of Wood. (1976). and Güllmen et al. (, The radii of Wood (1976) and Güllmen et al. ( +1980) leac to a physically unlikely situation [or a detached system. with a secondary component. too evolved when compared to the primary (loggyzlog gy).,"1980) lead to a physically unlikely situation for a detached system, with a secondary component too evolved when compared to the primary $\g_{\rm A} \ga \g_{\rm B}$ )." +Witt&Gordon(1996) found that it is necessary to model interstellar dust as a multi-phase medium.,\citet{Witt1996} found that it is necessary to model interstellar dust as a multi-phase medium. +" To achieve this, a small fraction (15 total filling factor) of clumps of high density dust is randomly placed into a field of low density dust with 100 times lower density in the global dust geometries mentioned previously."," To achieve this, a small fraction (15 total filling factor) of clumps of high density dust is randomly placed into a field of low density dust with 100 times lower density in the global dust geometries mentioned previously." +" Without the clumpiness, the effectiveness of dust absorption would be overestimated."," Without the clumpiness, the effectiveness of dust absorption would be overestimated." +" In this study, we exclusively use clumpy dust distributions."," In this study, we exclusively use clumpy dust distributions." + The optical depth averaged over all sightlines (from infinity to the center of the geometry) is normalized to the desired value ofTy., The optical depth averaged over all sightlines (from infinity to the center of the geometry) is normalized to the desired value of. +. We use the spectral evolutionary synthesis (SES) model PEGASE 2 (Fioc&Rocca-Volmerange1997) as the stellar input to our model.," We use the spectral evolutionary synthesis (SES) model PEGASE 2 \citep{PEGASE} + as the stellar input to our model." + We model starbursts of various ages with solar and 1/5 solar metallicity and the Padova evolutionary tracks., We model starbursts of various ages with solar and 1/5 solar metallicity and the Padova evolutionary tracks. +" An old galaxy may contain both old stellar populations and young stellar populations, although the latter is expected to be much less abundant considering that the typical timescale for gas depletion is about 3 Gyr (Pflamm-Altenburg&K"," An old galaxy may contain both old stellar populations and young stellar populations, although the latter is expected to be much less abundant considering that the typical timescale for gas depletion is about 3 Gyr \citep{Pflamm2009}." +roupa The time-dependent profile of star formation could be 2009)..modeled as an exponentially decaying burst (Searleetal.1973;Conti2003).," The time-dependent profile of star formation could be modeled as an exponentially decaying burst \citep{exp_time1973,exp_time2003}." +". However, since we want to model the characteristics (the luminosity of stellar populations at a certain age, we use instantaneousratios) starbursts."," However, since we want to model the characteristics (the luminosity ratios) of stellar populations at a certain age, we use instantaneous starbursts." +" To bracket the possible real world scenarios, we model the extreme cases of very young (1 Myr) and very old (13 Gyr) starburst populations."," To bracket the possible real world scenarios, we model the extreme cases of very young (1 Myr) and very old (13 Gyr) starburst populations." +" Gas continuum and emission of recombination lines, as calculated by PEGASE, are included."," Gas continuum and emission of recombination lines, as calculated by PEGASE, are included." + See Gordonetal.(1999) for a detailed discussion on how we use spectral evolutionary synthesis models with our dusty radiative transfer model., See \citet{Gordon1999} for a detailed discussion on how we use spectral evolutionary synthesis models with our dusty radiative transfer model. +" The dust extinction curve for stars in the Milky Way (MW), Small and Large Magellanic Clouds (SMC and LMC) are found to have overall similar shapes with significant variation in the UV etal.2003)."," The dust extinction curve for stars in the Milky Way (MW), Small and Large Magellanic Clouds (SMC and LMC) are found to have overall similar shapes with significant variation in the UV \citep{Gordon2003}." +. There are two distinct features (Gordonthat differentiate the different types of dust., There are two distinct features that differentiate the different types of dust. +" The first one is the 2175 bbump, which is found to vary in strength on average between the MW diffuse ISM/LMC general (strong bump), LMC2 (near 30 Dor)/SMC Wing (weak bump), and SMC Bar (no bump)."," The first one is the 2175 bump, which is found to vary in strength on average between the MW diffuse ISM/LMC general (strong bump), LMC2 (near 30 Dor)/SMC Wing (weak bump), and SMC Bar (no bump)." +" The second is the far UV rise, which generally varies in strength inversely with the 2175 bbump."," The second is the far UV rise, which generally varies in strength inversely with the 2175 bump." + Dust properties can be influenced by star forming activity and metallicity., Dust properties can be influenced by star forming activity and metallicity. +" In particular, Gordonetal.(1997) found that the SMC Bar type dust (lacking a 2175 describes the starburst galaxies better than either bbump)the LMC or MW type dust."," In particular, \citet{Gordon1997} found that the SMC Bar type dust (lacking a 2175 bump) describes the starburst galaxies better than either the LMC or MW type dust." +" From the GMASS survey, Nolletal.(2009) found that there is a wide range of UV dust properties, including those that are intermediate between SMC Bar and LMC2 type dusts."," From the GMASS survey, \citet{Noll2009} found that there is a wide range of UV dust properties, including those that are intermediate between SMC Bar and LMC2 type dusts." +" Modeling results show that the type of dust can affect the strength of PAH features (Draineetal.2007),, which in turn affects the IR observations."," Modeling results show that the type of dust can affect the strength of PAH features \citep{Draine2007}, which in turn affects the IR observations." +" As a result, it is important to choose an appropriate dust type for our study, and to explore the sensitivity of our results to the dust type."," As a result, it is important to choose an appropriate dust type for our study, and to explore the sensitivity of our results to the dust type." +" To span the whole range of known dust properties, we use SMC Bar type dust and Milky Way"," To span the whole range of known dust properties, we use SMC Bar type dust and Milky Way" +2.3 pointings were performed. cach month with a typical duration of ~35 ks per observation. and a separation of 12 weeks.,"$2-3$ pointings were performed each month with a typical duration of $\sim3-5$ ks per observation, and a separation of $\sim1-2$ weeks." + From 2009 November onwards. the cadence was lowered to one observation per month with a longer exposure time when possible (see Table 12).," From 2009 November onwards, the cadence was lowered to one observation per month with a longer exposure time when possible (see Table \ref{tab:obs}) )." + iis detected. in the NRL observations at. count rates. of ~(15).10?countss, is detected in the XRT observations at count rates of $\sim(1-5)\times10^{-2}~\cnts$. + All Suwifr//NIWE observations were obtained in. the photon-counting (pc) mode ancl were processed. using the with standard quality cuts (event grade 0.12)., All /XRT observations were obtained in the photon-counting (pc) mode and were processed using the with standard quality cuts (event grade 0–12). + Using (v. 2.4). we extracted source spectra from a circular region with a racius of 35 aresec (15 pixels). which optimises the signal to noise ratio at the observed count rates2007).," Using (v. 2.4), we extracted source spectra from a circular region with a radius of 35 arcsec $\sim15$ pixels), which optimises the signal to noise ratio at the observed count rates." +. Corresponding background events were averaged over three source-free regions of similar shape and size., Corresponding background events were averaged over three source-free regions of similar shape and size. + Emploving the toolXRTENPOMAL.. we ereated exposure maps to account for the elfective area of the CDD. while arfs generated with account for vignetting and point-spread-function corrections.," Employing the tool, we created exposure maps to account for the effective area of the CDD, while arfs generated with account for vignetting and point-spread-function corrections." + The latest rmf (v. 11) was obtained from the database., The latest rmf (v. 11) was obtained from the database. + Due to low statistics. it is not possible το identify eclipses in the llightcurves.," Due to low statistics, it is not possible to identify eclipses in the lightcurves." + Therefore. we used the ephemeris of to determine during. which observations eclipses were occurring (see Table 1)).," Therefore, we used the ephemeris of to determine during which observations eclipses were occurring (see Table \ref{tab:obs}) )." + To caleulate the correct non-eclipse time-averaged. [uxes. the exposure times of these observations were reduced with the duration of the eclipses contained in the data (500 s ifa full eclipse was present. but less if only. part of an eclipse was expected).," To calculate the correct non-eclipse time-averaged fluxes, the exposure times of these observations were reduced with the duration of the eclipses contained in the data (500 s if a full eclipse was present, but less if only part of an eclipse was expected)." + Furthermore. oobservations obtained within a 2-day time span were sunumed to improve the data Phis scons justified. since the celata do not reveal any spectral changes on such time scales (see Section ??))," Furthermore, observations obtained within a 2-day time span were summed to improve the data This seems justified, since the data do not reveal any spectral changes on such time scales (see Section \ref{subsec:spectraldata}) )." + We fitted the spectral data in the 0.510 keV. energy range using1996)., We fitted the spectral data in the 0.5–10 keV energy range using. +.. Phis software package facilitates fitting a spectral model simultaneously to multiple data files. which cach have their own response anc background. files.," This software package facilitates fitting a spectral model simultaneously to multiple data files, which each have their own response and background files." + As is common practise. we fit the delata with all spectral parameters tied between the differen detectors (νο. the mocdel parameters are not allowed to vary independently between the PN ancl two MOS. detectors).," As is common practise, we fit the data with all spectral parameters tied between the different detectors (i.e., the model parameters are not allowed to vary independently between the PN and two MOS detectors)." + For all fits throughout this paper. we included the cllec of neutral hydrogen absorption. Ny. along the line of sigh using the model with the default abundances ancl cross-sections1992).," For all fits throughout this paper, we included the effect of neutral hydrogen absorption, $N_{\mathrm{H}}$, along the line of sight using the model with the default abundances and cross-sections." +. We first investigate the shape of the quiescent spectrum of bby considering the oobservation. which provides the highest statistics.," We first investigate the shape of the quiescent spectrum of by considering the observation, which provides the highest statistics." + A single absorbed. powerlaw in NSPEC)) provides an acceptable fit to the data (AL=1.3 for 466 d.o.£)., A single absorbed powerlaw in ) provides an acceptable fit to the data $\chi^2_{\nu}=1.3$ for 466 d.o.f.). + However. he spectral index is unusually large for an N-rav. binary (Po—4.7 X0.1) and suggests that the spectrum has a hermal shape.," However, the spectral index is unusually large for an X-ray binary $\Gamma=4.7\pm0.1$ ) and suggests that the spectrum has a thermal shape." + Using a simple absorbed. blackhock niocel.BBODYRAD.. results in an adequate [it (42.—L2 for 466 cho).," Using a simple absorbed blackbody model, results in an adequate fit $\chi^2_{\nu}=1.2$ for 466 d.o.f.)," + although the inferred. emitting region has a much smaller racius than expected ora neutron star (2.4 km or distances of 510 kpe)., although the inferred emitting region has a much smaller radius than expected for a neutron star $\sim2-4$ km for distances of $5-10$ kpc). + Nevertheless. it is thought that radiative transfer effects. in he neutron star atmosphere cause the emergent spectrum to deviate from a blackbocdy1999).," Nevertheless, it is thought that radiative transfer effects in the neutron star atmosphere cause the emergent spectrum to deviate from a blackbody." +. There are several neutron star atmosphere models available withinNSPEC.. which vield equivalent results2007).," There are several neutron star atmosphere models available within, which yield equivalent results." +. In the remainder of this work. we concentrate on fitting the data with a neutron star atmosphere model 2006).," In the remainder of this work, we concentrate on fitting the data with a neutron star atmosphere model ." +. The model consists of five parameters. which are the neutron star mass and radius (Mys and yz). the elfective temperature in the neutron star [rame 1οι. non-redshifted: AYig). the source distance (2) and a normalisation factor. which parametrizes the fraction. of the surface that is radiating.," The model consists of five parameters, which are the neutron star mass and radius $M_{\mathrm{NS}}$ and $R_{\mathrm{NS}}$ ), the effective temperature in the neutron star frame (i.e., non-redshifted; $kT_{\mathrm{eff}}$ ), the source distance $D$ ) and a normalisation factor, which parametrizes the fraction of the surface that is radiating." + We keep the latter fixed. at 1 throughout this work. which corresponds to the entire neutron star surface emitting.," We keep the latter fixed at 1 throughout this work, which corresponds to the entire neutron star surface emitting." + The cllective temperature as seen bv an observer at infinity is given by Kip=Kal| os). where 1|2=(dRoRxs)7 is the eravitational redshift factor. with Ro=26Mgys/c being the Schwarzschilel radius. € the gravitational constant ancl c the speed. of light.," The effective temperature as seen by an observer at infinity is given by $kT^{\infty}_{\mathrm{eff}}= kT_{\mathrm{eff}}/(1+z)$ , where $1+z = (1-R_{\mathrm{s}}/R_{\mathrm{NS}})^{-1/2}$ is the gravitational redshift factor, with $R_{\mathrm{s}}=2GM_{\mathrm{NS}}/c^2$ being the Schwarzschild radius, $G$ the gravitational constant and $c$ the speed of light." + The delata is well-fittecd by an absorbed model (A5=Ll for 466 d.o.[).," The data is well-fitted by an absorbed model $\chi^2_{\nu}=1.1$ for 466 d.o.f.)," + although significant resicluals above the model fit are present for energies <23 keV. We model this non-thermal emission by adding a powerlaw component. which significantly improves the fit (x5=1.0 for 464 clo:," although significant residuals above the model fit are present for energies $\gtrsim2-3$ keV. We model this non-thermal emission by adding a powerlaw component, which significantly improves the fit $\chi^2_{\nu}=1.0$ for 464 d.o.f.;" + an F-test suggests a c110.1! probability of achieving this level of improvement by chance)., an F-test suggests a $\sim1\times10^{-14}$ probability of achieving this level of improvement by chance). + oobservations carriedout in 2008 mid-October. three weeks prior to this oobservation. also indicated the presence of a non-thermal," observations carriedout in 2008 mid-October, three weeks prior to this observation, also indicated the presence of a non-thermal" +switch on the high voltage. select telemetry rate and perform calibrations.,"switch on the high voltage, select telemetry rate and perform calibrations." + These cobunand sequences are generated by a liehly automated observation scheduling system which optimizes source selection. manages solid state recorder space. aud builds the command uploads.," These command sequences are generated by a highly automated observation scheduling system which optimizes source selection, manages solid state recorder space, and builds the command uploads." + The USA data processing system is also highly automated., The USA data processing system is also highly automated. + As data appear at TIirtlaud. files are automatically retreived via FTP aud the first several processing steps are performed.," As data appear at Kirtland, files are automatically retreived via FTP and the first several processing steps are performed." + Quicklook data are checked for anomalous conditions aud the USA team is alerted by e-mail if problems occur., Quicklook data are checked for anomalous conditions and the USA team is alerted by e-mail if problems occur. + Subsequently. observations are extracted from the Level 0 archive. couverted to FITS. aud distributed to the scientific analysis ceuters. includiug NRL aud SLAC.," Subsequently, observations are extracted from the Level 0 archive, converted to FITS, and distributed to the scientific analysis centers, including NRL and SLAC." + A Science Working Group (SWC) las been established to help optimize the scientific potential of USA., A Science Working Group (SWG) has been established to help optimize the scientific potential of USA. + The SWCG determines scientific priorities for observing targets. subject to certain constraints.," The SWG determines scientific priorities for observing targets, subject to certain constraints." + Scheduling of tarects during the USA mission will he consistent with experiment science objectives. priorities. aud mission operations capabilities.," Scheduling of targets during the USA mission will be consistent with experiment science objectives, priorities, and mission operations capabilities." + Telemetry formats will be selected to support overall «yjectives., Telemetry formats will be selected to support overall objectives. + USA has the flexibility to respond quickly to some targets of opportunity with approximately al23 day turnaround after the decision to revise the observing plan., USA has the flexibility to respond quickly to some targets of opportunity with approximately a 1–3 day turnaround after the decision to revise the observing plan. + The SWC decides whether to respond to potential targets of opportunity aud also identities instances when coordinated observations with eround-hased observers. CGRO. RATE. or other ARGOS instruments are scientifically advantageous.," The SWG decides whether to respond to potential targets of opportunity and also identifies instances when coordinated observations with ground-based observers, CGRO, RXTE, or other ARGOS instruments are scientifically advantageous." + The USA team is receptive to collaborations to make better use of the data. but the small size of the eroup does not allow us to operate a conventional euest observer facility.," The USA team is receptive to collaborations to make better use of the data, but the small size of the group does not allow us to operate a conventional guest observer facility." + The ARGOS launch aud deplovinent went flawlessly. but since then several problems have surfaced with various subsystems.," The ARGOS launch and deployment went flawlessly, but since then several problems have surfaced with various subsystems." +" Conerally, the spacecraft has been very robust aud has autonomously sated itself when preseuted with dramatic disturbances. such as a battery exploding on the electric propulsion experiment aud diving the USA Detector 2 gas leak."," Generally, the spacecraft has been very robust and has autonomously safed itself when presented with dramatic disturbances, such as a battery exploding on the electric propulsion experiment and during the USA Detector 2 gas leak." + Tere we will just sunuuarize the issues aud describe Low hey affect the operation of USA., Here we will just summarize the issues and describe how they affect the operation of USA. + Shortly after humnch. it was discovered that the GPS receiver is unable to stay ocked on to the GPS solution aud provide good navigation information.," Shortly after launch, it was discovered that the GPS receiver is unable to stay locked on to the GPS solution and provide good navigation information." + This xoblem was traced to an unexpectedly large input level to the receiver which causes cross correlation errors Which disrupt the solution., This problem was traced to an unexpectedly large input level to the receiver which causes cross correlation errors which disrupt the solution. + Generally the receiver will lock ou. then oscillate between uavigation and acquisition mode for a period of a few uinutes to a few hours before losing the solution completely.," Generally the receiver will lock on, then oscillate between navigation and acquisition mode for a period of a few minutes to a few hours before losing the solution completely." + To recover the time resolution required for many of the USA objectives. new software was uploaded o the satellite to make it safer to initialize the receiver repeatedly.," To recover the time resolution required for many of the USA objectives, new software was uploaded to the satellite to make it safer to initialize the receiver repeatedly." + Currently the receiver is initialized | times per dax., Currently the receiver is initialized 4 times per day. + Software is being developed to be able to interpolate times using the onboard clock to recover precise absolute times between xeriods when the receiver is locked ou to a &ood solution., Software is being developed to be able to interpolate times using the onboard clock to recover precise absolute times between periods when the receiver is locked on to a good solution. + A problem was discovered with the Scanning Torizou Sensors which ave used o coutrol the pitch and roll of the satellite., A problem was discovered with the Scanning Horizon Sensors which are used to control the pitch and roll of the satellite. + They are more radiation seusitive han expected and expericuce data dropouts or return incorrect data caving most massages through the South Atlantic Anomaly (SAA)., They are more radiation sensitive than expected and experience data dropouts or return incorrect data during most passages through the South Atlantic Anomaly (SAA). + This causes the spacecraft to, This causes the spacecraft to +we first assemble the imeredicuts needed to model the stochastic CAV backeround from MBO binaries. aud in rofsecistraiuspec we prescut the results of our calculations.,"we first assemble the ingredients needed to model the stochastic GW background from MBH binaries, and in \\ref{sec:strainspec} we present the results of our calculations." + In roefseciPT we discuss the detection of gravitational radiation with a Pulsar Timine Array and the status of current experiments., In \\ref{sec:PT} we discuss the detection of gravitational radiation with a Pulsar Timing Array and the status of current experiments. + In the concluding section we discuss the theoretical and observational prospects for a better understanding of the various ingredients to our calculations and micasurements., In the concluding section we discuss the theoretical and observational prospects for a better understanding of the various ingredients to our calculations and measurements. + First. we need to define the teriuinologv for a stochastic eravitational wave background spectrum that has been preseuted in the literature in a variety of wavs(c.g... ???7)).," First, we need to define the terminology for a stochastic gravitational wave background spectrum that has been presented in the literature in a variety of ways, \citet{Burke75,AllenRomano99,Maggiore00}) )." +" A single CW is denoted by the trausverse-traceless part of the uctric perturbation. ως.τὸ=fy(f)mI|fi.(te,(x). where plus sigus aud crosses refer to the two polarization degrees of freedom of a gravitational wave. aud the 67; are basis tensors for the polarizations which are ΠιοΊος of the direction of propagation of the exavitational wave. k."," A single GW is denoted by the transverse-traceless part of the metric perturbation, $h_{ab}({\bf x},t)=h_{+}(t)e^+_{ab}({\bf k}) + +h_{\times}(t)e^\times_{ab}({\bf k})$, where plus signs and crosses refer to the two polarization degrees of freedom of a gravitational wave, and the $e^i_{ab}$ are basis tensors for the polarizations which are functions of the direction of propagation of the gravitational wave, ${\bf k}$." + The two amplitudes combine with the two coordinate directions aud the polarization position angle to vield five independent parameters of the sineleavave metric perturbation., The two amplitudes combine with the two coordinate directions and the polarization position angle to yield five independent parameters of the single-wave metric perturbation. + The stochastic background will excite. both wave couponents equally aud vaudomly Qf)j|7)2=Ch.[75 aud Geyjho)=0. aud all directious. and position augles will be equally likels-," The stochastic background will excite both wave components equally and randomly $\langle |h_+|^2 \rangle = \langle +|h_\times|^2 \rangle$ and $\langle h^*_+ h_\times\rangle=0$, and all directions and position angles will be equally likely." + The total power spectral density of gravitational waves. ορ (7). is defined by where bptf) is the Fourier transform of the P=|.« polarization component of the metric straiu tensor at frequency f. aud à is the Dirac delta function Gwhich comes from our Fourier conventions aud tle definition of S)(f} as a spectral deusitv with uuits of inverse frequency).," The total power spectral density of gravitational waves, $S_h(f)$ , is defined by where ${\tilde h}_P(f)$ is the Fourier transform of the $P=+,\times$ polarization component of the metric strain tensor at frequency $f$, and $\delta$ is the Dirac delta function (which comes from our Fourier conventions and the definition of $S_h(f)$ as a spectral density with units of inverse frequency)." + There are two spectra couventious in the literature: “two-sided” (defined for |f| 100 AU) planetesimal belts responsible for the bulk of the mid-IR and emission respectively (???).. However, therefar-"," Current analysis of the debris system suggests inner (R $<$ 20 AU) and outer (R $>$ 100 AU) planetesimal belts responsible for the bulk of the mid-IR and far-IR/sub-mm emission respectively \citep{Greaves98, Stapelfeldt04, Kalas05}." +IR/sub-mm is plenty of room for additional gas/ice giant planets in the system.," However, there is plenty of room for additional gas/ice giant planets in the system." + Our upper limits rule out masses greater than 2 between ~13-40 AU., Our upper limits rule out masses greater than 2 between $\sim$ 13-40 AU. + ? suggest ju;that gas giants could end up at large separations due to planet-planet scattering., \citet{Chatterjee08} suggest that gas giants could end up at large separations due to planet-planet scattering. +" In this scenario, the largest planets in the system tend to stay put and smaller planets end up in large, eccentric orbits."," In this scenario, the largest planets in the system tend to stay put and smaller planets end up in large, eccentric orbits." + Our results suggest this may not be an explanation for the location of Fomalhaut b. ? have explored the hypothesis that most planetary systems are “packed” in the sense that any orbit dynamically stable on timescales of order the age of the system or longer are inhabited., Our results suggest this may not be an explanation for the location of Fomalhaut b. \citet{BarnesGreenberg07} have explored the hypothesis that most planetary systems are “packed” in the sense that any orbit dynamically stable on timescales of order the age of the system or longer are inhabited. + This implies that the planet formation process is very efficient indeed and is consistent with numerical integration of the orbits in our own solar system , This implies that the planet formation process is very efficient indeed and is consistent with numerical integration of the orbits in our own solar system \citep{Laskar96}. +This hypothesis found recent confirmation in the discovery(?).. of HD 74156 d (?) of the mass and orbit predicted., This hypothesis found recent confirmation in the discovery of HD 74156 d \citep{Bean08} of the mass and orbit predicted. +" If Fomalhaut has a multiplanet system spaced like the Solar system and HR 8799 systems (giant planets spaced logarithmically, spaced by ~0.25+00.05 dex in a), one would naively predict interior planets at radii 65, ~35, 20 AU.Spitzer"," If Fomalhaut has a multiplanet system spaced like the Solar system and HR 8799 systems (giant planets spaced logarithmically, spaced by $\sim$ $\pm$ 0.05 dex in $a$ ), one would naively predict interior planets at radii $\sim$ 65, $\sim$ 35, $\sim$ 20 AU." + detected evidence of a warm inner disk at «20 AU (?).., detected evidence of a warm inner disk at $<$ 20 AU \citep{Stapelfeldt04}. + It is tempting to speculate that Fomalhaut's inner disk is likewise being perturbed by another planet., It is tempting to speculate that Fomalhaut's inner disk is likewise being perturbed by another planet. +" If Fomalhaut indeed has a packed system of planets between its inner AU) and outer AU) debris belts, our M-band («20results suggest that (7133planets in the 713-40 AU range are less than «2"," If Fomalhaut indeed has a packed system of planets between its inner $<$ 20 AU) and outer $>$ 133 AU) debris belts, our M-band results suggest that planets in the $\sim$ 13-40 AU range are less than $<$ 2" +eenmission line iu a large sample of local disk aud irregular ealaxies. aud to compare it with the distribution of older stars.,"emission line in a large sample of local disk and irregular galaxies, and to compare it with the distribution of older stars." + pprovides esscutially a snapshot view of SF activity. since it is powered by massive stars with nain SOCUICTICC lifetimes of —105 vears.," provides essentially a snapshot view of SF activity, since it is powered by massive stars with main sequence lifetimes of $\sim$ $^7$ years." + This can cause problems with the interpretation of the pproperties of iudividual galaxies. since the enisxion is driven by a small unuiber of regions with short lifetimes. and so the stochastic uncertainties are substantial.," This can cause problems with the interpretation of the properties of individual galaxies, since the emission is driven by a small number of regions with short lifetimes, and so the stochastic uncertainties are substantial." + Thus the approach adopted here is to look at the mean properties of at least several ealaxies of the same type. giving a statistical basis for studies of the distribution of SF. the erowth of disks. aud the effects of bars on the SF process.," Thus the approach adopted here is to look at the mean properties of at least several galaxies of the same type, giving a statistical basis for studies of the distribution of SF, the growth of disks, and the effects of bars on the SF process." + The ealaxies used are a field sample. and hence the effects of environmoeut should be zinall. though some of the galaxies do have fairly close companions.," The galaxies used are a field sample, and hence the effects of environment should be small, though some of the galaxies do have fairly close companions." +" These will be studied iu a subsequeut paper (CF. IT. Knapen P. A. James ApJ παέτος, Paper VII)."," These will be studied in a subsequent paper (J. H. Knapen P. A. James ApJ submitted, Paper VIII)." + All data are taken from the CGCalaxy Survey (Tacs). a survey of 327 nearby galaxies (plus a further 7 sereudipitouslv observed objects) which rave been imiaged in both the liue aud the R-band continu.," All data are taken from the Galaxy Survey GS), a survey of 327 nearby galaxies (plus a further 7 serendipitously observed objects) which have been imaged in both the line and the $R$ -band continuum." + The narrow-band filters used cucompassed the aand neighbouring lues. which should be borne in mind when iuterpretiug he narrow-band fiux distriibutious in the present paper.," The narrow-band filters used encompassed the and neighbouring lines, which should be borne in mind when interpreting the narrow-band flux distributions in the present paper." + For convenicnce. this combined emission is referred to as throughout.," For convenience, this combined emission is referred to as throughout." + The GS sample coutaims all Hubble types Toni Sü/a o hu aud galaxies are sclected to have icliocentrie recession velocities less thau 3000 kin 1, The GS sample contains all Hubble types from S0/a to Im and galaxies are selected to have heliocentric recession velocities less than 3000 km $^{-1}$. + All ealaxies were observed with the 1.0 metre Jacobus ΊναXevu Teescope (JIT). part of the Isaac Newton Croup of Telescopes (ING) situaed on La Paha i the Cauv Islands.," All galaxies were observed with the 1.0 metre Jacobus Kapteyn Telescope (JKT), part of the Isaac Newton Group of Telescopes (ING) situated on La Palma in the Canary Islands." + The selectiou aud the observation of he souple are discussed in Paper L The overall aim of the survev ds to quantifv as lly as possible the star formation properties in field galaxies at the current epoch., The selection and the observation of the sample are discussed in Paper I. The overall aim of the survey is to quantify as fully as possible the star formation properties in field galaxies at the current epoch. + Elie Παζ papers have looked at total SF rates and Πα equivalent widths 1i galaxies (Paper I). aud the contributions of galaxies of differeut types to the integrated SF rate (SER) per unit volume of the local Universe (Paper IV).," Earlier GS papers have looked at total SF rates and $\alpha$ equivalent widths in galaxies (Paper I), and the contributions of galaxies of different types to the integrated SF rate (SFR) per unit volume of the local Universe (Paper IV)." + Whereas previous papers derived from the HaS have mainly focussed on inteerated SE properties or each of the galaxies studied. fjo present paper will focus ou the spatial resolution of SF provided by the iuaeiug technique.," Whereas previous papers derived from the GS have mainly focussed on integrated SF properties for each of the galaxies studied, the present paper will focus on the spatial resolution of SF provided by the imaging technique." + This will be done first fwough au analysis of three concentration indices applied to both the Fi-baud and ]lieht distinitions. and then through more detailed study of mean normalised radial light distributions for galaxies of cach morphological type. aud for barred aud wnbarred ealaxies.," This will be done first through an analysis of three concentration indices applied to both the $R$ -band and light distributions, and then through more detailed study of mean normalised radial light distributions for galaxies of each morphological type, and for barred and unbarred galaxies." + Some results frou the earlier paovers that are relevant for the preseut study will first be sununarised., Some results from the earlier papers that are relevant for the present study will first be summarised. + Paper I contained a brief analysis of the effect of bars ou total SERs of galaxies. aud ou the equivaeut width of eenission.," Paper I contained a brief analysis of the effect of bars on total SFRs of galaxies, and on the equivalent width of emission." + Bars eive modest. barely siguificant increases i both quantities overall: however. barred galaxies of types Sab Se inclusive were found to have larger SFRs by factors 1.52.0 compared with uubarred galaxies of the same types.," Bars give modest, barely significant increases in both quantities overall; however, barred galaxies of types Sab – Sc inclusive were found to have larger SFRs by factors 1.5–2.0 compared with unbarred galaxies of the same types." + The SER per galaxy is highest in intermediate disk types with classifications of She aud Sc., The SFR per galaxy is highest in intermediate disk types with classifications of Sbc and Sc. + In Paper IV it was found that these same types also dominate the SER density. ie... SFR per unit volume of the local Universe. sunned over all Hubble types.," In Paper IV it was found that these same types also dominate the SFR density, i.e., SFR per unit volume of the local Universe, summed over all Hubble types." + Disk regions. defined as those ling more than 1 kpe from the centres of galaxies. were found to contribute more than of the total SE currently occurring in the local Universe.," Disk regions, defined as those lying more than 1 kpc from the centres of galaxies, were found to contribute more than of the total SF currently occurring in the local Universe." + Sample aand A-baud images of several galaxies from the WaGs database are presented in Paper LE. aud a large umber of images of those galaxies that have hosted superuovae are preseuted in the online version of another paper in this SOTIOS (?.PaperIID..," Sample and $R$ -band images of several galaxies from the GS database are presented in Paper I, and a large number of images of those galaxies that have hosted supernovae are presented in the online version of another paper in this series \citep[][Paper III]{paper3}." + These provide a good indication of the overall quality of the data used iu the sresent analysis. and in the interests of brevity no images are shown in the present paper.," These provide a good indication of the overall quality of the data used in the present analysis, and in the interests of brevity no images are shown in the present paper." + The structure of this paper is as follows., The structure of this paper is as follows. + Section 2 contaius an investigation of three concentration iudices. which are appied to both aud HR-Wux light distributions.," Section 2 contains an investigation of three concentration indices, which are applied to both and $R$ -band light distributions." + The strength of correlation beween indices aud EIubble type is studied. leacineC» to. preliminary conclusions on the relative distributions of vouns aud old stellar οριαος as a function of eaaxy type.," The strength of correlation between indices and Hubble type is studied, leading to preliminary conclusions on the relative distributions of young and old stellar populations as a function of galaxy type." + The effect of stroug bars on the racial distribuion of SF as traced by these iudices is also aualvsec., The effect of strong bars on the radial distribution of SF as traced by these indices is also analysed. + Section 3 looks at 11621 radial xofiles as a more detailed tracer of stellar distributions., Section 3 looks at mean radial profiles as a more detailed tracer of stellar distributions. + aud -baud mean profiles. biuned by type. are preseuted for the full sequence of spiral types. and compared for barred aud uubarred types. leadiug to the identification of an effect on profiles for bars iu SBb types that is particularly marsed in xofiles but al«| clear in the R-biuc heht distributions.," and $R$ -band mean profiles, binned by type, are presented for the full sequence of spiral types, and compared for barred and unbarred types, leading to the identification of an effect on profiles for bars in SBb types that is particularly marked in profiles but also clear in the $R$ -band light distributions." + The effect. of coΠΕ errors on profiles is iso studied m tjs section., The effect of continuum-subtraction errors on profiles is also studied in this section. + Section | contains a detailed investigation of he central aud bar-eid CC4ulssiou in SBI| galaxies., Section 4 contains a detailed investigation of the central and bar-end emission in SBb galaxies. + Section 5 «'ontadus a discussion of sole of the lnain results. aud he conclusions are presented im Sec.," Section 5 contains a discussion of some of the main results, and the conclusions are presented in Sect." + 6., 6. +can show that (see Appendix) where 5 is the number density of sightlines and the v; involve the power spectrum and its integral in a Kk shell. k—AK/2«|k|k+Ak/2.,"can show that (see Appendix) where $\bar{n}$ is the number density of sightlines and the $v_j$ involve the power spectrum and its integral in a $\mathbf{k}$ shell, $k-\Delta k/2<|\mathbf{k}|>0. (4)) the ordinary wave propagates rectilinearly as well."," As was already mentioned, for large enough angles $\theta \gg \theta_{*}$ \ref{thetaQ}) ) the ordinary wave propagates rectilinearly as well." +" From this condition and the solution of the equation above one can find Here ωρο is the plasma frequency near the star surface, and index ’em’ corresponds to the quantities on the generation level."," From this condition and the solution of the equation above one can find Here $\omega_{{\rm p}0}$ is the plasma frequency near the star surface, and index 'em' corresponds to the quantities on the generation level." +" Besides, the dimensionless factor where the angle 0m is measured from the magnetic axis, determines the position of the radiation point within the polar cap."," Besides, the dimensionless factor where the angle $\theta_{m}$ is measured from the magnetic axis, determines the position of the radiation point within the polar cap." +" The angle 20,(co) the angular width of thebeam.", The angle $2 \theta_{\perp}(\infty)$ the angular width of the. +" Finally, the ""tearing off” level l, defined by the condition 0=0, is equals to It gives Thus, this level locates much than the level of the formation of the outgoing polarization res.~1000R (7)."," Finally, the ""tearing off"" level $l_{\rm t}$ defined by the condition $\theta = \theta_{*}$ is equals to It gives Thus, this level locates much than the level of the formation of the outgoing polarization $r_{\rm esc} \sim 1000 \, R$ \ref{resc}) )." +" In more detail the procedure we have used is describedjet in Appendix A. For reasonable parameters of the plasma filling the pulsar magnetosphere one can neglect the effect of curvature of magnetic field while considering the propagation of radio waves (see, e.g., Beskin 1999)."," In more detail the procedure we have used is described in Appendix A. For reasonable parameters of the plasma filling the pulsar magnetosphere one can neglect the effect of curvature of magnetic field while considering the propagation of radio waves (see, e.g., Beskin 1999)." +" On the other hand, as the level of the formation of the outgoing polarization resc (7)) locates in the vicinity of the light cylinder (Cheng Ruderman 1979; Barnard 1986), it is necessary to include into consideration the nonzero external electric field (Petrova Lyubarskii 2000)."," On the other hand, as the level of the formation of the outgoing polarization $r_{\rm esc}$ \ref{resc}) ) locates in the vicinity of the light cylinder (Cheng Ruderman 1979; Barnard 1986), it is necessary to include into consideration the nonzero external electric field (Petrova Lyubarskii 2000)." + In this paragraph z-axis is selected along the direction of magnetic field and the wave vector lies in zz-plane., In this paragraph $z$ -axis is selected along the direction of magnetic field and the wave vector lies in $xz$ -plane. + Our goal is to find the permittivity tensor of relativistic plasma in perpendicular uniform magnetic and electrical fields., Our goal is to find the permittivity tensor of relativistic plasma in perpendicular uniform magnetic and electrical fields. + In the derivation we take into account the fact that in the strong enough magnetic field the unpertubated motion, In the derivation we take into account the fact that in the strong enough magnetic field the unpertubated motion +Solar prominences and filaments are large-scale magnetic structures of the solar corona.,Solar prominences and filaments are large-scale magnetic structures of the solar corona. +" The main issues regarding the physics. dynamics, and modeling of these coronal inhabitants have been recently reviewed by Labrosseetal.(2010) and Mackayetal.(2010)."," The main issues regarding the physics, dynamics, and modeling of these coronal inhabitants have been recently reviewed by \citet{labrossereview} and \citet{mackay}." +". High-resolution observations reveal that prominences and filaments are formed by long (5""—20"") and thin 0.6) fine structures, usually called threads."," High-resolution observations reveal that prominences and filaments are formed by long $5'' - 20''$ ) and thin $0''.2 - 0''.6$ ) fine structures, usually called threads." +" Although the existence of the fine structure of prominences was discovered long time ago (e.g..Menzel&Wolbach1960;Enevold1976),, its properties and dynamics could only be studied in more detail with recent high-resolution observations."," Although the existence of the fine structure of prominences was discovered long time ago \citep[e.g.,][]{menzel60,engvold76}, its properties and dynamics could only be studied in more detail with recent high-resolution observations." +" The fine structures show up as dark ribbons in H« images of filaments on the solar disk from the Swedish Solar Telescope (e.g..Lin2004:etal.2007,2008.2009)..and as bright features in observations of prominences in the solar limb from the Solar Optical Telescope aboard the Hinode satellite ίο.ο..Okamotoetal.2007;Berger2008:ChaeNing 2010).."," The fine structures show up as dark ribbons in $\alpha$ images of filaments on the solar disk from the Swedish Solar Telescope \citep[e.g.,][]{lin04,lin07,lin08,lin09}, and as bright features in observations of prominences in the solar limb from the Solar Optical Telescope aboard the Hinode satellite \citep[e.g.,][]{okamoto,berger,chae,ning,brigi}." +" Statistical studies Show that the orientation of threads with respect to the filament long axis can significantly vary within the same filament (Lin2004),, with 20 degrees a mean value typically reported."," Statistical studies show that the orientation of threads with respect to the filament long axis can significantly vary within the same filament \citep{lin04}, with 20 degrees a mean value typically reported." +" Vertical threads are more commonly seen in quiescent prominences (¢c.g.,2008:Chaeetal.2008) whereas horizontal threads are usually observed in active region prominences (e.g..Okamotoetal."," Vertical threads are more commonly seen in quiescent prominences \citep[e.g.,][]{berger,chae} whereas horizontal threads are usually observed in active region prominences \citep[e.g.,][]{okamoto}." +2007).. Schmiederetal.(2010). recently pointed out that vertical threads might actually be a pile up of horizontal threads which seem to be vertical structures when projected on the plane of the sky., \citet{brigi} recently pointed out that vertical threads might actually be a pile up of horizontal threads which seem to be vertical structures when projected on the plane of the sky. +" However, this is still a matter of controversy."," However, this is still a matter of controversy." +" Since threads are observed in both spines and barbs, it is believed that they are the basic building blocks of prominences and filaments (Engvold2004)."," Since threads are observed in both spines and barbs, it is believed that they are the basic building blocks of prominences and filaments \citep{engvold2004}." +". Theoretically, the fine structures have been modeled as magnetic flux tubes anchored in the solar photosphere (e.g..Ballester&Priest1989:Rempeletal.1999),, which are only partially filled with the cool (~10° K) filament material, while the rest of the tube is occupied by hot coronal plasma."," Theoretically, the fine structures have been modeled as magnetic flux tubes anchored in the solar photosphere \citep[e.g.,][]{ballesterpriest,rempel}, which are only partially filled with the cool $\sim 10^4$ K) filament material, while the rest of the tube is occupied by hot coronal plasma." + Therefore. the magnetic field 1s oriented along the axis of the fine structure.," Therefore, the magnetic field is oriented along the axis of the fine structure." + This modelis conceptuallyin agreement with the idea that the dense prominence material is trapped in dips near the apex of a magnetic arcade connecting two photospheric regions of opposite magnetic polarity., This model is conceptually in agreement with the idea that the dense prominence material is trapped in dips near the apex of a magnetic arcade connecting two photospheric regions of opposite magnetic polarity. +" The dips are supposed to correspond to the observed threads, which are piled up to form the prominence body."," The dips are supposed to correspond to the observed threads, which are piled up to form the prominence body." + It has also been suggested trom differential emission measure studies that each thread might be surrounded by its own prominence-corona transition region (PCTR) where the plasma physical properties would abruptly vary from prominence to coronal conditions (Cirigliano 2004)., It has also been suggested from differential emission measure studies that each thread might be surrounded by its own prominence-corona transition region (PCTR) where the plasma physical properties would abruptly vary from prominence to coronal conditions \citep{cirigliano}. +. Prominence threads are highly dynamic (see.e.g..Heinzel2007:Engvold2008).," Prominence threads are highly dynamic \citep[see, e.g.,][]{heinzel,engvold}." +". For example. transverse thread oscillations and propagating waves along the threads seem to be ubiquitous in prominences, which have been interpreted in terms of magnetohydrodynamic (MHD) waves (see 2010).."," For example, transverse thread oscillations and propagating waves along the threads seem to be ubiquitous in prominences, which have been interpreted in terms of magnetohydrodynamic (MHD) waves \citep[see the reviews by][]{ballester, oliver, arreguiballester}. ." +" Mass flows along threads,"," Mass flows along threads," +Based ou the above three tests. we conclude that our method recovers accurate estimates of the population velocity-cispersion (distribution parameters.,"Based on the above three tests, we conclude that our method recovers accurate estimates of the population velocity-dispersion distribution parameters." + Our method of determining pid;logy)0) incorporates an explicit marginalizatiou over redshiff error. aud propagates all observational unecrtainty iu the velocity dispersion of a given galaxy.," Our method of determining $p(\vec{d}_i | \log_{10} \sigma)$ incorporates an explicit marginalization over redshift error, and propagates all observational uncertainty in the velocity dispersion of a given galaxy." + Our biuning iu redshift and absolute iaguitude introduces additional error possibilities that we must account for., Our binning in redshift and absolute magnitude introduces additional error possibilities that we must account for. + In the case of redshift. the errors are negligible relative to the biu width of A:=0.01. and are unlikely to contribute any artificial broadeniug to our determination of the redshift depeudence of à ands.," In the case of redshift, the errors are negligible relative to the bin width of $\Delta z = 0.04$, and are unlikely to contribute any artificial broadening to our determination of the redshift dependence of $m$ and $s$." + The absolute maeitucde errors are. however. non-neslieible iu comparison to the magnitude bin width of AMI=OL. and thus we use the following technique to estimate and colmpcusate for the broadening effect of the observational scattering of galaxies between absolutce-anagnitude bius (sce Figure 1)).," The absolute magnitude errors are, however, non-negligible in comparison to the magnitude bin width of $\Delta \rm M_V = 0.1$, and thus we use the following technique to estimate and compensate for the broadening effect of the observational scattering of galaxies between absolute-magnitude bins (see Figure \ref{fig:gal_dist}) )." + Suppose Gres} are the true values within a biu. aud Gna.sq) are the values that we determine in the presence of absolute-nagnitude errors.," Suppose $(m, s)$ are the true values within a bin, and $(m_1, s_1)$ are the values that we determine in the presence of absolute-magnitude errors." + We assiunue that where di aud ds are the biases introduced by magnitude errors., We assume that where ${\delta}m$ and ${\delta}s$ are the biases introduced by magnitude errors. + To estimate and remove these biases. we add additional raudom errors to all our galaxy absolute magnitudes AA to eive where e i8 a normally distributed random ΠΕ with mean O0 aud standard deviation 1. aud ολ are the ealaxy-by-ealaxy absolute-niaguitude errors estinated by (propagated from SDSS apparent maguitude errors).," To estimate and remove these biases, we add additional random errors to all our galaxy absolute magnitudes $M_V$ to give where ${\epsilon}$ is a normally distributed random number with mean 0 and standard deviation 1, and ${\delta}M_V$ are the galaxy-by-galaxy absolute-magnitude errors estimated by (propagated from SDSS apparent magnitude errors)." + We repeat our analysis. binning instead ino aud denoting the new distribution parameter resultsMp. by i0» and s».," We repeat our analysis, binning instead in $M_V^\prime$, and denoting the new distribution parameter results by $m_2$ and $s_2$ ." +" We assume these new determinations are related to my, ancl sy in the salue Way as iy and sy are related to e and s. which tuples that Thus the biases due to absolute magnitude errors ài and és can be removed to vield Iu practice. we find tvpical values for di of 0.01. and for ds of 0.0L."," We assume these new determinations are related to $m_1$ and $s_1$ in the same way as $m_1$ and $s_1$ are related to $m$ and $s$, which implies that Thus the biases due to absolute magnitude errors ${\delta}m$ and ${\delta}s$ can be removed to yield In practice, we find typical values for ${\delta}m$ of 0.01, and for ${\delta}s$ of 0.04." + Iun this section we present the results of the application of our lierarchical Bayesian velocitv-dispersion distribution measurementtechnique to the approximately 103.000 ealaxies in our LOZ sample aud 330.000 ealaxies in our CALASS sample.," In this section we present the results of the application of our hierarchical Bayesian velocity-dispersion distribution measurementtechnique to the approximately 103,000 galaxies in our LOZ sample and 330,000 galaxies in our CMASS sample." + The LOZ sample extends to 20.5., The LOZ sample extends to $z \approx 0.5$. + The 2D coutour ots of a and s (Figure 7)) and scatter plots in different redshift bius (Figure 8)) show that the mean m ds strouglv. correlated with absolute iiagnuitude. while he iutriusic scatter 5 shows uo siguificaut variation.," The 2D contour plots of $m$ and $s$ (Figure \ref{fig:loz}) ) and scatter plots in different redshift bins (Figure \ref{fig:scatter-loz}) ) show that the mean $m$ is strongly correlated with absolute magnitude, while the intrinsic scatter $s$ shows no significant variation." + Tracks of constaut stellar mass assuming the LRG stellar population model of Marastonetal.(2009) rave also been over-plotted in Figure 7.. aud used to convert from an absoluteauagnitude to a stellar-uass vascline in Figure &..," Tracks of constant stellar mass assuming the LRG stellar population model of \citet{Maraston09} + have also been over-plotted in Figure \ref{fig:loz}, and used to convert from an absolute-magnitude to a stellar-mass baseline in Figure \ref{fig:scatter-loz}." +" Galaxies in the LOZ sample have estimated stellar masses between approximately 10137, and 1012JJ...", Galaxies in the LOZ sample have estimated stellar masses between approximately $10^{11} M_\sun$ and $10^{12} M_\sun$. +" To quantity the variation of the a aud 5 parameters with redshift and absolute maeuitude. we consider a simple model specified by: with the ""0 superscriptdenoting the LOZ sample specifically."," To quantify the variation of the $m$ and $s$ parameters with redshift and absolute magnitude, we consider a simple model specified by: with the “0” superscriptdenoting the LOZ sample specifically." +" Performine alinear least squares fit to the individual biu data points. we obtain We can translate the resulting scaling iuto the standard form for the PIR. with huninosity Lx0"" by recognizing that.= "," Performing alinear least squares fit to the individual bin data points, we obtain We can translate the resulting scaling into the standard form for the FJR, with luminosity $L \propto \sigma^x$ by recognizing that $x = -0.4 / A_m^0$." +The resulting value of —1.552:0.06 is in reasonable 0.1/49..agreement with the canonical local-universe value ofc=£L., The resulting value of $x = 4.55 \pm 0.06$ is in reasonable agreement with the canonical local-universe value of $x = 4$. + Thus. BOSS low-z LRGs define an FJR whose slope and scatter has little dependence ou redshift and huuinositv: there is correspondingly little evidence for dynamicalevolution iu this sample since roughly z— 0.5.," Thus, BOSS low-z LRGs define an FJR whose slope and scatter has little dependence on redshift and luminosity; there is correspondingly little evidence for dynamicalevolution in this sample since roughly $\rm z=0.5$ ." + The CMASS ealaxy sample extends frou τ50.3 to zz (ks. , The CMASS galaxy sample extends from $z \approx 0.3$ to $z \approx 0.8$ . +The results of our σ distribution parameter nieasurenaents are shown in Fieures 9 aud 10.. once," The results of our $\sigma$ distribution parameter measurements are shown in Figures \ref{fig:CMASS} and \ref{fig:scatter-CMASS}, , once" +"We first estimated the (Sain). which is the fraction of binary svslelus wilh a mass ralio (,;, luge enough to make them clearly distinguishable from (he sinele-star ADS.","We first estimated the $\xi_{min}$ ), which is the fraction of binary systems with a mass ratio $q_{min}$ large enough to make them clearly distinguishable from the single-star MS." +" It is clear that the value of q,;, depends directly on the photometric errors and £,,;5, represents onlv a sub-samiple of (he whole population of binaries. but it has the advantage of being a purely observational quantity."," It is clear that the value of $q_{min}$ depends directly on the photometric errors and $\xi_{min}$ represents only a sub-sample of the whole population of binaries, but it has the advantage of being a purely observational quantity." + In (his case we deline (he as the set of stus located in the CMD between the following boundaries (see erav region in Fig. 3)):, In this case we define the as the set of stars located in the CMD between the following boundaries (see gray region in Fig. \ref{regions}) ): + the left-hand boundary is (he line corresponding to a color difference from the MISRL equal to three times the photometric error αἱ any magnitude level (right dashed line): the risht-hand boundary is the line at a color difference from the eequal-mass binary sequence equal to three times (he photometric error: Che upper and lower boundaries are sel by the lareest ancl (he smallest primary mass (corresponding to the quoted bright and faint euis of the various magnitude ranges along the MSRL). combined with all the possible mass ratios.," the left-hand boundary is the line corresponding to a color difference from the MSRL equal to three times the photometric error at any magnitude level (right dashed line); the right-hand boundary is the line at a color difference from the equal-mass binary sequence equal to three times the photometric error; the upper and lower boundaries are set by the largest and the smallest primary mass (corresponding to the quoted bright and faint cuts of the various magnitude ranges along the MSRL), combined with all the possible mass ratios." +" la other words. (he “binary population” includes all binary svstenis with primary mass set by the considered magnitude ranges and wilh qj,;,Xq1. also Lalàng into account the effect of photometric errors."," In other words, the “binary population” includes all binary systems with primary mass set by the considered magnitude ranges and with $q_{min}\le q\le 1$, also taking into account the effect of photometric errors." + For each of the considered radial bins and magnitude ranges we estimated the minimum binary fraction by performing all the steps described in Sect., For each of the considered radial bins and magnitude ranges we estimated the minimum binary fraction by performing all the steps described in Sect. + ?? ancl. in much more detail. in S07.," \ref{analysis} and, in much more detail, in S07." + The resul(s are presented in Table L.., The results are presented in Table \ref{tab:fmin}. +" As is apparent. £,,;, monotonically decreases from the center to the outskirts. in agreement with previous findings aud with theoretical predictions (see Sect. ??))."," As is apparent, $\xi_{min}$ monotonically decreases from the center to the outskirts, in agreement with previous findings and with theoretical predictions (see Sect. \ref{discuss}) )." + Inthe magnitude range. such a radial variation ranges from ~QU. al rry.," Inthe magnitude range, such a radial variation ranges from $\sim 6\%$ at $rr_h$." +" There also seems (o be a trend with magnitude. especially in the central bin. where £,,;, varies [rom ~8% in the range. to ~5 in (he one."," There also seems to be a trend with magnitude, especially in the central bin, where $\xi_{min}$ varies from $\sim 8\%$ in the range, to $\sim 5\%$ in the one." +" llowever. since the photometric error depends on magnitude. the value of q,,;, changes in (he considered luminosity ranges: for decreasing luminosity. q,,5; varies from 0.5 to 0.6 in both the ACS and the WFPC2 samples."," However, since the photometric error depends on magnitude, the value of $q_{min}$ changes in the considered luminosity ranges: for decreasing luminosity, $q_{min}$ varies from 0.5 to 0.6 in both the ACS and the WFPC2 samples." + Hence. the derived. values of μμ are neither strictly comparable to one other. nor to the estimates presented in different works.," Hence, the derived values of $\xi_{min}$ are neither strictly comparable to one other, nor to the estimates presented in different works." + We have therefore computed the faction of binaries with mass ratios larger (han a fixed value q=0.6 (£205)., We have therefore computed the fraction of binaries with mass ratios larger than a fixed value $q=0.6$ $\xi_{\geq0.6}$ ). + This value has been chosen as a compromise between having enough statistics and avoiding contamination [rom single stars (indeed. the line corresponding to g=0.6 in the CAD always runs to the right-hand sile of the MS population boundary).," This value has been chosen as a compromise between having enough statistics and avoiding contamination from single stars (indeed, the line corresponding to $q=0.6$ in the CMD always runs to the right-hand side of the MS population boundary)." +" In this case the “binary population"" is made up of stars that. in the CMD. are located between the line of constant q=0.6 (left boundary: see dotted lines in Fig. 2))"," In this case the “binary population” is made up of stars that, in the CMD, are located between the line of constant $q=0.6$ (left boundary; see dotted lines in Fig. \ref{regions}) )" + and the right-hand boundary defined above., and the right-hand boundary defined above. + Its ratio with respect to the total number of stars gives (he lraction of binaries wilh q>0.6. which is presented in Table 2..," Its ratio with respect to the total number of stars gives the fraction of binaries with $q\ge0.6$, which is presented in Table \ref{tab:fq06}." +" Obviously. the obtained values are smaller (han (he corresponding minimum lIractions £,,5, in Table 1.."," Obviously, the obtained values are smaller than the corresponding minimum fractions $\xi_{min}$ in Table \ref{tab:fmin}. ." + We also note that the same behaviors discussed above are still present. (hus again suggesting that the trend with magnitude could," We also note that the same behaviors discussed above are still present, thus again suggesting that the trend with magnitude could" +presented in Figures 5 and 6..,presented in Figures \ref{figure5} and \ref{figure6}. + The good «quality. seeing of the complementary V-band Wide Field image allowed us to detect aud study the galaxy population in the field of NGC 4576 down to faint levels., The good quality seeing of the complementary V-band Wide Field image allowed us to detect and study the galaxy population in the field of NGC 4576 down to faint levels. + Source extraction was performed using the software (Bertin&Arnouts1996).. which uses a routine based on neural network generated weights for star-galaxy separation.," Source extraction was performed using the software \citep{Bertin96}, which uses a routine based on neural network generated weights for star-galaxy separation." + Detections were checked visually and objects with the parameter greater than 0.5 were deemed to be definitely stellar and therefore discarded., Detections were checked visually and objects with the parameter greater than 0.5 were deemed to be definitely stellar and therefore discarded. + All objects with a major axis <2” and with a magnitude outside the range 17xnn22 (corresponding to —]1.8) were not processed further since they are most likely background objects.," All objects with a major axis $\leq$ and with a magnitude outside the range $17 \leq m_V +\leq 22$ (corresponding to $-16.8 \geq M_V \geq -11.8$ ) were not processed further since they are most likely background objects." + Furtheron. all known galaxy members of the Abell 1631 cluster were removed from the list.," Furtheron, all known galaxy members of the Abell 1631 cluster were removed from the list." + Applving these selection criteria we idenlily 115 galaxies as group member candidates in addition to the objects studied wilh the 3.6m. For candidate objects where neither redshift information is available nor an unambiguous association to the NGC 4756 group is possible. we provide their identification and (he measure of their accurate astrometric position useful for redshift followup.," Applying these selection criteria we identify 115 galaxies as group member candidates in addition to the objects studied with the 3.6m. For candidate objects where neither redshift information is available nor an unambiguous association to the NGC 4756 group is possible, we provide their identification and the measure of their accurate astrometric position useful for redshift followup." + The WINGS project is indeed performing a spectroscopic study of a set of nearby clusters up to their outskirts. including the Abell 1631 field. and will determine therefore the group menbership.," The WINGS project is indeed performing a spectroscopic study of a set of nearby clusters up to their outskirts, including the Abell 1631 field, and will determine therefore the group membership." + Notice (hat Zabludoff&Mulchaey.(1998). studied the galaxy. population in a small nunber of groups.," Notice that \citet{zab98} + studied the galaxy population in a small number of groups." +" They. found a significantly higher number of faint galaxies (20-50 members down to magnitudes as faint as Mj2 -14 +5loey, μη) in X-ray detected eroups. most of which are earlv-tvpes. than in groups without hot IGM."," They found a significantly higher number of faint galaxies (20-50 members down to magnitudes as faint as $_B \approx$ -14 $_{10}$ $_{100}$ ) in X-ray detected groups, most of which are early-types, than in groups without hot IGM." + We consequently expect to [ind a significant population of dwarl galaxies also in the NGC 4756 group (see X-ray properües in 4.3)., We consequently expect to find a significant population of dwarf galaxies also in the NGC 4756 group (see X-ray properties in 4.3). + We further determine (he accurate photometric properties οἱ the candidate galaxies., We further determine the accurate photometric properties of the candidate galaxies. + Several studies in the literature start toanalvze the photometric, Several studies in the literature start toanalyze the photometric +with a metalpoor =—0.7) and old (7>6 Gyr) star population. (Vazdekisefal.(1996).Vazdekiset (1997))).,"with a metalpoor $\,\,\approx -0.7$ ) and old $T>6$ Gyr) star population. \cite{va,va03}) )." + Clearly. imaging at much higher spatial resolution. e.g. with HST. is required to obtain more reliable colors close to the center and to corroborate the presence of a disky subcomponent.," Clearly, imaging at much higher spatial resolution, e.g. with HST, is required to obtain more reliable colors close to the center and to corroborate the presence of a disky subcomponent." + Also. spectroscopy in a wavelength region better suited for constraining the mean age and metallicity of the stellar population is prerequisite to fully understand the origin of these KDCs.," Also, spectroscopy in a wavelength region better suited for constraining the mean age and metallicity of the stellar population is prerequisite to fully understand the origin of these KDCs." + Finally. it should be noted that neither galaxy shows any dust features.," Finally, it should be noted that neither galaxy shows any dust features." + The internal dynamics of a steady-state axisymmetric stellar system are described by a gravitational potential (c.z). that determines the stellar orbits. and the distribution. function (DF) Ftr.v)drdv. which gives the number density of stars in phase space ((@.=) are cylindrical coordinates).," The internal dynamics of a steady-state axisymmetric stellar system are described by a gravitational potential $\psi(\varpi,z)$, that determines the stellar orbits, and the distribution function (DF) $F(\vec{r},\vec{v})\,d\vec{r}\,d\vec{v}$, which gives the number density of stars in phase space $(\varpi,z)$ are cylindrical coordinates)." + Roughly speaking. the DF distributes the stars over all possible orbits.," Roughly speaking, the DF distributes the stars over all possible orbits." + According to the Jeans theorem. the DF can be written as a function of the isolating integrals of motion.," According to the Jeans theorem, the DF can be written as a function of the isolating integrals of motion." + An axisymmetric potential generally allows only two such integrals; the binding energy E and the z-component of the angular momentum L-., An axisymmetric potential generally allows only two such integrals; the binding energy $E$ and the $z$ -component of the angular momentum $L_z$. + More freedom to distribute stars over phase space can be gained if a third integral of motion exists., More freedom to distribute stars over phase space can be gained if a third integral of motion exists. + Therefore. we work in spheroidal coordinates and approximate the gravitational potential by a Sticekel potential which allows the existence of a third integral. denoted by /:;.," Therefore, we work in spheroidal coordinates and approximate the gravitational potential by a Stäcckel potential which allows the existence of a third integral, denoted by $I_3$." + Round galaxies are modeled more efficiently in a spherical geometry. in which case the DF is conveniently taken to be a function of E. L.. and L. the total angular momentum.," Round galaxies are modeled more efficiently in a spherical geometry, in which case the DF is conveniently taken to be a function of $E$, $L_z$, and $L$, the total angular momentum." + The L--dependence of the DF allows the construction of rotating and slightly flattened stellar systems., The $L_z$ -dependence of the DF allows the construction of rotating and slightly flattened stellar systems. + FS373. which has a significantly flattened appearance on the sky. is modeled using an axisymmetrie Sticckel potential while FS76 is treated as a system with a spherical gravitational potential.," FS373, which has a significantly flattened appearance on the sky, is modeled using an axisymmetric Stäcckel potential while FS76 is treated as a system with a spherical gravitational potential." + Of course. a galaxy with a KDC need not be axisymmetric but in the context of equilibrium models such an assumption is inevitable: also. the isophotes do not indicate that these galaxies are significantly non-axisymmetric.," Of course, a galaxy with a KDC need not be axisymmetric but in the context of equilibrium models such an assumption is inevitable; also, the isophotes do not indicate that these galaxies are significantly non-axisymmetric." + A detailed account of the method we employed to construct the spheroidal coordinate system and Sticckel potential that give the best fit to a given axisymmetric potential can be found in Dejonghe&deZeeuw(1988).etal.(1996).. and DeBruyneefaf.(2001).," A detailed account of the method we employed to construct the spheroidal coordinate system and Stäcckel potential that give the best fit to a given axisymmetric potential can be found in \cite{dz88,de96}, and \cite{deb01}." +. In brief. we deproject the observed surface brightness distribution. derived from an I-band image. assuming the galaxy to be axisymmetric and viewed edge-on.," In brief, we deproject the observed surface brightness distribution, derived from an I-band image, assuming the galaxy to be axisymmetric and viewed edge-on." + The total mass density. including dark matter. is parameterized as the spatial lumimosity density multiplied by a spatially varying mass-to-light ratio with the parameters A and B to be estimated from the data and g the axis ratio of the luminosity density distribution.," The total mass density, including dark matter, is parameterized as the spatial luminosity density multiplied by a spatially varying mass-to-light ratio with the parameters $A$ and $B$ to be estimated from the data and $q$ the axis ratio of the luminosity density distribution." + The gravitational potential is obtained by decomposing the total mass density in spherical harmonies., The gravitational potential is obtained by decomposing the total mass density in spherical harmonics. + Finally. we fit a Stücckel potential to this gravitational potential.," Finally, we fit a Stäcckel potential to this gravitational potential." + For a spherical galaxy (qd=1). the deprojection of the surface brightness profile reduces to solving an Abel’s integral equation (Binney&Tremaine(1987).. eq. (," For a spherical galaxy $q=1$ ), the deprojection of the surface brightness profile reduces to solving an Abel's integral equation \cite{bt}, eq. (" +1B-57b)).,1B-57b)). + The gravitational potential follows from Binney&Tremaine(1987).. eq. (," The gravitational potential follows from \cite{bt}, eq. (" +2-22).,2-22). + For a given potential. we wish to find the DF that best reproduces the kinematical information.," For a given potential, we wish to find the DF that best reproduces the kinematical information." +" The DF is written as a weighted sum of basis functions F=Y;c;F; and the coefficients c; are determined by minimizing the quantity with obs; an observed data point. c, the 1-c errorbar on that data point. and obs;; the corresponding value calculated from the # basis function. subject to the constraint that the DF be positive everywhere 1n phase space."," The DF is written as a weighted sum of basis functions $F = \sum_i c_i \, F_i$ and the coefficients $c_i$ are determined by minimizing the quantity with ${\rm obs}_l$ an observed data point, $\sigma_l$ the $\sigma$ errorbar on that data point, and ${\rm obs}_{l,i}$ the corresponding value calculated from the $i^{\rm th}$ basis function, subject to the constraint that the DF be positive everywhere in phase space." + For a spherical potential. we used the basis functions ΕΕ.L)=ΕπΙΙ and F&«E.L.)=EID. with integer powers. to construct the DF (DeBruyneetal. (2004))).," For a spherical potential, we used the basis functions $F_i(E,L) = +E^{\alpha_i} L^{\beta_i}$ and $F_j(E,L_z) = E^{\alpha_j} +L_z^{\beta_j}$, with integer powers, to construct the DF \cite{deb04}) )." + The three-integral DF in a Stücckel potential on the other hand was built with basis functions of the form ΕΚΕ.Lis)=EVLEP. with integer powers (Dejongheetaf. (1996))).," The three-integral DF in a Stäcckel potential on the other hand was built with basis functions of the form $F_i(E,L_z,I_3) += E^{\alpha_i} L_z^{\beta_i} I_3^{\gamma_i}$, with integer powers \cite{de96}) )." + In the case of FS76. the models are fitted directly to the observed major and minor axis spectra (DeRijcke&Dejonghe (1998))). making the best possible use of all the kinematical information contained in the spectra.," In the case of FS76, the models are fitted directly to the observed major and minor axis spectra \cite{dr0}) ), making the best possible use of all the kinematical information contained in the spectra." + The axisymmetric models for FS373 are much more complex and computationally time-consuming and we opted to use the observed surface brightness distribution and the velocity dispersion and mean velocity profiles along both major and minor axis (Le. the central second and first order moments of the LOSVDs.nor the Gaussian parameters) as kinematical input for the modeling code.," The axisymmetric models for FS373 are much more complex and computationally time-consuming and we opted to use the observed surface brightness distribution and the velocity dispersion and mean velocity profiles along both major and minor axis (i.e. the central second and first order moments of the LOSVDs, the Gaussian parameters) as kinematical input for the modeling code." + As a further constraint. we used the central fourth order moment of the LOSVDs. calculated from the kinematic parameters up to η.," As a further constraint, we used the central fourth order moment of the LOSVDs, calculated from the kinematic parameters up to $h_4$ ." + We use a Quadratic Programming technique to find the optimal values for the c; using a library of hundreds of linearly independent basis functions. making this method essentially non-parametric.," We use a Quadratic Programming technique to find the optimal values for the $c_i$ using a library of hundreds of linearly independent basis functions, making this method essentially non-parametric." + This is repeated for about 100 different (A. B)-pairs. covering the relevant part of parameter space.," This is repeated for about 100 different $A,B$ )-pairs, covering the relevant part of parameter space." + This allows us to define the range of models (and hence mass distributions) that are consistent with the data and to determine which model gives the best fit to the data., This allows us to define the range of models (and hence mass distributions) that are consistent with the data and to determine which model gives the best fit to the data. + The major-axis velocity dispersion and mean velocity profiles of the best models for FS373 and FS76 are compared with the observed kinematics in Fig. 11.., The major-axis velocity dispersion and mean velocity profiles of the best models for FS373 and FS76 are compared with the observed kinematics in Fig. \ref{modelps}. +" From these best models. we estimate the mass within a 1.5 KR, sphere of FS76 at 2.975x10 (at the confidence level) and that of FS373 at 6.2704M..x10""M..."," From these best models, we estimate the mass within a 1.5 $R_{\rm e}$ sphere of FS76 at $2.9^{{+0.5}}_{{-1.7}} \times 10^9 M_\odot$ (at the confidence level) and that of FS373 at $6.2^{{+2.3}}_{{-1.3}} \times 10^9 M_\odot$." + Both galaxies require the presence of à dark matter halo. albeit not à very massive one. in order to reproduce the observed outwardly rising velocity dispersion profiles.," Both galaxies require the presence of a dark matter halo, albeit not a very massive one, in order to reproduce the observed outwardly rising velocity dispersion profiles." + For FS76 we find a B-band mass-to-light ratio M/Lp=7.812M./Lp; while for FS373 we find Μην=74ΤΗ. /Lg;;.," For FS76 we find a B-band mass-to-light ratio $M/L_B = +7.8^{{+1.3}}_{{-4.6}} M_\odot/L_{B,\odot}$ while for FS373 we find $M/L_B = 7.4^{{+2.8}}_{{-1.5}} M_\odot/L_{B,\odot}$ ." + These models agree very well with the data and reproduce the central dip in the velocity dispersion. the bump in the velocity profile. and. in the case of FS373. the inward rise of the ellipticityprofile.," These models agree very well with the data and reproduce the central dip in the velocity dispersion, the bump in the velocity profile, and, in the case of FS373, the inward rise of the ellipticityprofile." + In. both galaxies. this requires the presence of a fast rotating cold subcomponent in," In both galaxies, this requires the presence of a fast rotating cold subcomponent in" +Optical survevs such as the Sloan Digital Skv Survey (SDSS: York et al.,Optical surveys such as the Sloan Digital Sky Survey (SDSS; York et al. + 2000) and je. Digitized Palomar Sky Survey (Djorgovskietal.1999) have revealed large samples οἱ quasi-stellar objects out to z6., 2000) and the Digitized Palomar Sky Survey \citep{DJO99} have revealed large samples of quasi-stellar objects out to $z \sim 6$. +" Studies by Fanetal.(2002) and Fanetal.(2006). have V.i0wn that al such a hieh redshift we are approaching the epoch of reionization. the edge of je. ""dark ages”. when the first stars and massive black holes were formed."," Studies by \citet{FAN02} and \citet{FCK06} have shown that at such a high redshift we are approaching the epoch of reionization, the edge of the “dark ages”, when the first stars and massive black holes were formed." + Observations of hieh redshift QSOs at mun and sub-mim wavelengths have shown (hat a V.ignificant [raction (~ 305) of the sources are strong emitters of Fur-infrared (PIR) radiation. which is thermal emission [rom warm dust.," Observations of high redshift QSOs at mm and sub-mm wavelengths have shown that a significant fraction $\sim 30\%$ ) of the sources are strong emitters of far-infrared (FIR) radiation, which is thermal emission from warm dust." +" These sources have luminosities Lyy,>107RiechersL, and molecular gas masses greater than LOMAL. (Solomon&Vandenetal. 2006)."," These sources have luminosities $L_{\rm FIR} > 10^{12}~L_{\odot}$, and molecular gas masses greater than $10^{10}~M_{\odot}$ \citep{SV05,RD06}." +. Moreover. the large reservoirs of warm gas ancl dust in (hese objects have led to the hypothesis that these are starburst galaxies wilh massive star formation rates on the order of 1000 AL.vr.+ (Bertoldietal.2003:Beelenοἱ2006:Carillial. 2003).," Moreover, the large reservoirs of warm gas and dust in these objects have led to the hypothesis that these are starburst galaxies with massive star formation rates on the order of 1000 $M_{\odot}~{\rm yr}^{-1}$ \citep{BER03,BEE06,CAR04,WAL03}." +. Animportant question regarding these high-z QSOs is whether the dust heating mechanism is dominated by a central AGN. or starburst activity in the QSO host galaxies.," An important question regarding these $z$ QSOs is whether the dust heating mechanism is dominated by a central AGN, or starburst activity in the QSO host galaxies." + The high resolution of Very Long Baseline Interlerometryv (VLBI) observations permits a detailed look at the physical structures in the most distant cosmic sources., The high resolution of Very Long Baseline Interferometry (VLBI) observations permits a detailed look at the physical structures in the most distant cosmic sources. + Also. sensitive VLBI continuum observations can be used to determine the nature of the energy source(s) in these galaxies al radio frequencies.," Also, sensitive VLBI continuum observations can be used to determine the nature of the energy source(s) in these galaxies at radio frequencies." + To date. several high redshift QSOs have been imaged at milliarcsecond resolution (Frey2003:Momjianetal.2004:Beelen 2005).," To date, several high redshift QSOs have been imaged at milliarcsecond resolution \citep{FRE97,FRE03,MOM04,BEE04,MOM05}." +. These are (he highest resolution studies of such distant QSOs by Far., These are the highest resolution studies of such distant QSOs by far. + In this paper. we present sensitive," In this paper, we present sensitive" +Tt then follows that if the PAIL size distribution is similar across our sample. that the grain size distribution must be fairly long-lived ancl stable.,"It then follows that if the PAH size distribution is similar across our sample, that the grain size distribution must be fairly long-lived and stable." + We compare the global PAIL racliance ratios in our sample galaxies with a collection of similar measurements that probe a wide variety of sources From Suaithetal.(2007).. Galliano (2008).. Gordonetal.(2008).. and Intetal.(2010).," We compare the global PAH radiance ratios in our sample galaxies with a collection of similar measurements that probe a wide variety of sources from \citet{Smith07a}, , \citet{Galliano08}, , \citet{Gordon08}, and \citet{Hunt10}." +. From (hiis comparison. we see evidence for a similar PAIL size distribution across the range of objects explored. which includes spirals. AGN. cdiwarls. and II IL regions.," From this comparison, we see evidence for a similar PAH size distribution across the range of objects explored, which includes spirals, AGN, dwarfs, and H II regions." + The ionization indices vary signilicantlv within (hese different sources., The ionization indices vary significantly within these different sources. + Taken together. these properties suggest that the local environment has a greater impact on the intensity of PATI emission than does the metallicity or the history ol PAIL formation/destruetion in a given galaxy or region.," Taken together, these properties suggest that the local environment has a greater impact on the intensity of PAH emission than does the metallicity or the history of PAH formation/destruction in a given galaxy or region." + We also examine PAIL emission on a spatially resolved. basis by extracting maps of PAII features and emission lines in our sample galaxies., We also examine PAH emission on a spatially resolved basis by extracting maps of PAH features and emission lines in our sample galaxies. + Examining both individual pixels (in regions of hieh S/N) and apertures of physical radius 52.5 pe. we find that the (7.7 jm)/(11.3 jm) ratio (a probe of ionization index or radiation field strength) varies by a factor of ~5 across our sample.," Examining both individual pixels (in regions of high S/N) and apertures of physical radius 52.5 pc, we find that the (7.7 $\mu$ m)/(11.3 $\mu$ m) ratio (a probe of ionization index or radiation field strength) varies by a factor of $\sim$ 5 across our sample." + The grain size distribution (using the (8.6 jmi)/(6.2. jm) ratio as a diagnostic) shows only very minor variations over this range., The grain size distribution (using the (8.6 $\mu$ m)/(6.2 $\mu$ m) ratio as a diagnostic) shows only very minor variations over this range. + This agrees with the interpretations lound for other galaxies and suggests that there is very little change in the PAIL carrier size distribution as a function of radiation field strength., This agrees with the interpretations found for other galaxies and suggests that there is very little change in the PAH carrier size distribution as a function of radiation field strength. + Previous works have suggested that the relative intensities of the main PALIT features are essentially constant within a given galaxy (see references in 3 and 4 above)., Previous works have suggested that the relative intensities of the main PAH features are essentially constant within a given galaxy (see references in \ref{S3} and \ref{S4} above). + Our examination of the ISM in the three clwarl galaxies of (his sample supports (his interpretation., Our examination of the ISM in the three dwarf galaxies of this sample supports this interpretation. + In comparing the PDAIL/PAIT ratios at a spatial resolution of 52.5 pe. we find very few regions that display. statistically significant deviations from (he mean within a given svstem (no variations exceed (he 3.50 level. and most are at the 2a level or lower).," In comparing the PAH/PAH ratios at a spatial resolution of 52.5 pc, we find very few regions that display statistically significant deviations from the mean within a given system (no variations exceed the $\sigma$ level, and most are at the $\sigma$ level or lower)." + In contrast to the diverse environmental variations seen between regions in our sample. ihe PAIL band ratios are constant. within each galaxy.," In contrast to the diverse environmental variations seen between regions in our sample, the PAH band ratios are constant within each galaxy." +" The apparently simple conclusions of this work mask a great deal of complexity in the canonically ""simple"" 19M of dwarl galaxies.", The apparently simple conclusions of this work mask a great deal of complexity in the canonically “simple” ISM of dwarf galaxies. + The uniformity of metal abundance in these svslenms is well-docunented but has not vel been explained., The uniformity of metal abundance in these systems is well-documented but has not yet been explained. + The present work suggests that this uniformity also extends to the properties of the carriers of the PAII bands., The present work suggests that this uniformity also extends to the properties of the carriers of the PAH bands. +" When examining each of these svstemis. we find a remarkably wide variety of physical conditions: some star Formation regions are UV-bright while others are deeply embedded: some regions have widespread ionizing photons while others are apparently quiescent, some regions are dominated by the red stellar continuum. while others have SEDs that rise steeply towaud the far-IR."," When examining each of these systems, we find a remarkably wide variety of physical conditions: some star formation regions are UV-bright while others are deeply embedded; some regions have widespread ionizing photons while others are apparently quiescent; some regions are dominated by the red stellar continuum while others have SEDs that rise steeply toward the far-IR." + In response to these diverse local conditions. the intensity of the PAIL emission features do in [act change markedly. in line wilh expectations based on the strengthofthe," In response to these diverse local conditions, the intensity of the PAH emission features do in fact change markedly, in line with expectations based on the strengthofthe" +individual spectra were co-aclded and eviddecl onto a uniform 15 grid.,individual spectra were co-added and gridded onto a uniform 15” grid. + Linear baselines were removed [rom line-[ree channels., Linear baselines were removed from line-free channels. + All spectra are presented on the antenna temperature (77| scale., All spectra are presented on the antenna temperature $T_A^*$ ) scale. + To convert to main-beam brightness temperatures. one should divide the antenna temperatures by the main-beam elliciency of 0.49 (Laddetal.2005).," To convert to main-beam brightness temperatures, one should divide the antenna temperatures by the main-beam efficiency of 0.49 \citep{Ladd2005}." +. System temperatures for the observations were ~180—300 Ix. which vielded a (vpical rms noise of Z4—0.14 Ix in each spectral channel.," System temperatures for the observations were $\sim 180 - 300$ K, which yielded a typical rms noise of $T_A^* = 0.14$ K in each spectral channel." + The Mopra integrated intensity. maps closely correspond to the regions of mid-IK. extinction (Figure 1))., The Mopra integrated intensity maps closely correspond to the regions of mid-IR extinction (Figure \ref{figure1}) ). + The map consists of fainter. uniform emission associated with (he filament. upon which compact. brighter regions we call “cores” are superposed.," The map consists of fainter, uniform emission associated with the filament, upon which compact, brighter regions we call “cores” are superposed." + Gaussian lits to the lines demonstrate that every position witliin Nessie las essentially the same radial velocity. —38 43.4 ((Fieure 1)).," Gaussian fits to the lines demonstrate that every position within Nessie has essentially the same radial velocity, $-38$ $\pm 3.4$ (Figure \ref{figure1}) )." + I the Clemens rotation curve is used. (his velocity corresponds to a kinematic distance of 3.1 kpc (Clemens1985).," If the Clemens rotation curve is used, this velocity corresponds to a kinematic distance of 3.1 kpc \citep{Clemens1985}." +. The molecular cores in Nessie are often associated stau-Iormation activity., The molecular cores in Nessie are often associated star-formation activity. + Specifically. many cores show the presence of excess 4.5 jan emission called. “green fuzzies.” which indicates shocked eas (e.g.. Noriega-Crespoοἱal.2004;Marstonet 2004)). and. bright 24 yon point sources. which indicate an embedded protostar (e.g.. Chambersetal. 2009)).," Specifically, many cores show the presence of excess 4.5 $\mu$ m emission called “green fuzzies,” which indicates shocked gas (e.g., \citealt{Noriega-Crespo2004,Marston2004}) ), and bright 24 $\mu$ m point sources, which indicate an embedded protostar (e.g., \citealt{Chambers2009}) )." + The cores do not appear to be randomly spaced. within the filament. but instead have a characteristic spacing.," The cores do not appear to be randomly spaced within the filament, but instead have a characteristic spacing." + The filament is (hus reminiscent of a string with beads Chat are spaced sparsely but. approximately uniformly along ils length., The filament is thus reminiscent of a string with beads that are spaced sparsely but approximately uniformly along its length. + We used (he clumplind2d algorithm with a threshold of seven times the rms noise and 2.50 increments (Williams on the integrated intensity map to identify 12 molecular cores (see Figure 1)), We used the clumpfind2d algorithm with a threshold of seven times the rms noise and $\sigma$ increments \citep{Williams1994} on the integrated intensity map to identify 12 molecular cores (see Figure \ref{figure1}) ). + The exact choice of clumplfind. parameters will result in the identification of slightly more or fewer cores. but (he resulting core spacing is quite insensitive to reasonable input parameters.," The exact choice of clumpfind parameters will result in the identification of slightly more or fewer cores, but the resulting core spacing is quite insensitive to reasonable input parameters." + Since (he cores are relatively isolated and well separated. cblumplind works well and identifies the cores (hat one would tend to select by eve.," Since the cores are relatively isolated and well separated, clumpfind works well and identifies the cores that one would tend to select by eye." + The positions and selected properties of the cores are listed in Table 1.., The positions and selected properties of the cores are listed in Table \ref{coretable}. + Columns | and 2 give the Galactic coordinates of the position of peak integrated LINC intensity in each core. Column 3 the peak HNC integrated intensity. Columns 4 and 5 (he angular size and physical extent. Column 6 the LTE mass (see Section 4)). and Column 7 whether or not the core contains a 24 jmi point source.," Columns 1 and 2 give the Galactic coordinates of the position of peak integrated HNC intensity in each core, Column 3 the peak HNC integrated intensity, Columns 4 and 5 the angular size and physical extent, Column 6 the LTE mass (see Section \ref{Discussion}) ), and Column 7 whether or not the core contains a 24 $\mu$ m point source." + The mean projected spacing between cores is roughly 4.5 pe., The mean projected spacing between cores is roughly 4.5 pc. + Although we prefer to use the molecular gas clamps as our indicator of core spacing. since," Although we prefer to use the molecular gas clumps as our indicator of core spacing, since" +Conservation of angular momentum gives nM)=rp (rp)o,Conservation of angular momentum gives )=r_f ). +w Combining these two results we find In the fluid limit. we assume the dark matter is in hydrostatic equilibrium in the initial and final states.," Combining these two results we find In the fluid limit, we assume the dark matter is in hydrostatic equilibrium in the initial and final states." + We neglect heat transfer. so that the entropy of the dark matter at fixed mass shell is invariant [or a monatomic ideal gas. and r; and ry are related by mass conservation (eqn. (D)).," We neglect heat transfer, so that the entropy of the dark matter at fixed mass shell is invariant ), where $S$ is given by for a monatomic ideal gas, and $r_i$ and $r_f$ are related by mass conservation (eqn. \ref{masscon}) )." + These assumptions are valid provided the condensation of baryons takes place on a timescale slow relative (o the dvnamical time. but. fast. compared to the heat conduction. timescale (equ. (3))).," These assumptions are valid provided the condensation of baryons takes place on a timescale slow relative to the dynamical time, but fast compared to the heat conduction timescale (eqn. \ref{ttherm}) ))." + IE /p is thecondensation time. these approximations hold where Qr). Uvedr," If $t_{B}$ is thecondensation time, these approximations hold where $t_{dyn}\left(r\right)\lesssim t_{B}\lesssim \tau\left(r\right) t_{dyn}\left(r\right)$ ." +ostatic equilibrium of the dark matter component implies, Hydrostatic equilibrium of the dark matter component implies P M ; or +A very useful space throughout our analysis will be the truncated anisotropic (parabolic) space Dο that we celine here.,"A very useful space throughout our analysis will be the truncated anisotropic (parabolic) Lizorkin-Triebel space $\widetilde{F}^{s}_{p,q}$ that we define here." +" The basic dillerence between £5, and £5, is that in n we ont the term op*« and ouly take in consideration the terms 6;xu. jz1."," The basic difference between $F^{s}_{p,q}$ and $\widetilde{F}^{s}_{p,q}$ is that in $\widetilde{F}^{s}_{p,q}$ we omit the term $\phi_{0}*u$ and only take in consideration the terms $\phi_{j}*u$, $j\geq 1$." + Sobolev embecdcings of parabolic Lizorkin-Triebel and Besov spaces are shown by the next two lemimnas., Sobolev embeddings of parabolic Lizorkin-Triebel and Besov spaces are shown by the next two lemmas. +vvalues are matched as best as possible.,values are matched as best as possible. + For models 1300 (Figs 2aa-b) and n1000 (Figs 2ec-£) . the PPDEs have steep increases. resulting in peaks that do not correspond to the peaks in the PPDEs.," For models n300 (Figs \ref{pdfpans}a a-b) and n1000 (Figs \ref{pdfpans}e e-f), the PDFs have steep increases, resulting in peaks that do not correspond to the peaks in the PDFs." + The PDEs ofthe other simulations. n300-Z03. 201. ancl nlOO. show comparable gradients at low aandNoo. but at high values the PPDESs drop more rapidly thanNoo.," The PDFs of the other simulations, n300-Z03, n300-Z01, and n100, show comparable gradients at low and, but at high values the PDFs drop more rapidly than." +. In those PDEs showing a steep decline inW.. at high CO column densities there is little or no corresponding CO emission. even though there is good correspondence at. lower values (due in part to the choice of the aand aaxis ranges).," In those PDFs showing a steep decline in, at high CO column densities there is little or no corresponding CO emission, even though there is good correspondence at lower values (due in part to the choice of the and axis ranges)." + PDEs showing a much steeper eracicnt bevond the ppeak compared to the ppeak can be attributed to saturation of the CO line: as a result of saturation. regions with very high mmav have similar intensities to regions with lower (but still high)Ico. producing a PDF which appears to have a 7piled-up profile at some highWe.," PDFs showing a much steeper gradient beyond the peak compared to the peak can be attributed to saturation of the CO line: as a result of saturation, regions with very high may have similar intensities to regions with lower (but still high), producing a PDF which appears to have a “piled-up” profile at some high." + Such PDE shapes are clearly evident in the mocderatelv low metallicity (n300-ZÜ3) and very [ow density (100) cloud simulations., Such PDF shapes are clearly evident in the moderately low metallicity (n300-Z03) and very low density (n100) cloud simulations. + For the simulation with very low metallicity. (n300-Z01) for which the aand PPDESs appear to be correlated. there is no evidence of a saturation feature.," For the simulation with very low metallicity (n300-Z01) for which the and PDFs appear to be correlated, there is no evidence of a saturation feature." + We have shown that there is no simple correlation between aandNeo. focusing on models with dillerent. metallicities and densities.," We have shown that there is no simple correlation between and, focusing on models with different metallicities and densities." + Of course. the background radiation field also allects the formation of CO. due to UV. photodissociation (?.PaperLD)..," Of course, the background radiation field also affects the formation of CO, due to UV photodissociation \citep[][Paper + II]{vanDishoeck&Black88}." + Figure 3. shows theNyy. Noo. and hhistograms from models n300. n300-UV ancl n300-UVMIOO (see Table 1)).," Figure \ref{highUV} shows the, and histograms from models n300, n300-UV10, and n300-UV100 (see Table \ref{exptab}) )." + These models only 10.differ in their background. UV. radiation field strengths. with values of Go = 1. 10. and 100 times the Galactic estimate 10.5 erg 7s +).," These models only differ in their background UV radiation field strengths, with values of $_0$ = 1, 10, and 100 times the Galactic estimate $\times 10^{-3}$ erg $^{-2}$ $^{-1}$ )." + All simulations have similar log-normal cdeistributions., All simulations have similar log-normal distributions. + Simulations with higher UV fields have more extended PPDEFs. and thereby lowered maxima in the pprobabilities.," Simulations with higher UV fields have more extended PDFs, and thereby lowered maxima in the probabilities." + This occurs because stronger UV radiation is able to penetrate further into the cloud to dissociate CO. resulting in more regions with low CO densities.," This occurs because stronger UV radiation is able to penetrate further into the cloud to dissociate CO, resulting in more regions with low CO densities." + Similarly. the cdeistributions are more extended. for models with brighter UV backgrounds. with fewer regions with high vvalues.," Similarly, the distributions are more extended for models with brighter UV backgrounds, with fewer regions with high values." + These results simply follow the trend. previously discussed: models. with a wice range in CO abundances demonstrate a lack of correlation between aand PPDEs., These results simply follow the trend previously discussed: models with a wide range in CO abundances demonstrate a lack of correlation between and PDFs. + The lack of correlation in the PDEs primarily occur at the highest densities and intensities (with the exception of n300-ZO1. but see last paragraph of this subsection). though at lower densities gas is optically thin resulting in a correlation between aandNeo.," The lack of correlation in the PDFs primarily occur at the highest densities and intensities (with the exception of n300-Z01, but see last paragraph of this subsection), though at lower densities gas is optically thin resulting in a correlation between and." + Clouds. with lower metallicity. lower overall densitv.. higher UV. background. or a combination of these factors have much more distributed CO abundances. resulting in greater discrepancies between the aand PPDEs.," Clouds with lower metallicity, lower overall density, higher UV background, or a combination of these factors have much more distributed CO abundances, resulting in greater discrepancies between the and PDFs." + Keeping this general trend in mind. in our subsequent analysis we will focus on the models with Co =l1.," Keeping this general trend in mind, in our subsequent analysis we will focus on the models with $_0$ = 1." + We now turn our attention to the aand pproperties of simulation. n300-Z03 (Figs., We now turn our attention to the and properties of simulation n300-Z03 (Figs. + 2cc-d)., \ref{pdfpans}c c-d). + There is a relatively large spread inNoo. whieh also has a clear double peak. at ουNoo)s 14.5 and 16.5 (with similar probabilities).," There is a relatively large spread in, which also has a clear double peak, at $\log(N_{\rm CO}) \approx$ 14.5 and 16.5 (with similar probabilities)." + Further. though the PPDE appears to correlate well with the PPDE at low CO density (or low intensity) values. the peak in σος not correlate well with the peak inNoo.," Further, though the PDF appears to correlate well with the PDF at low CO density (or low intensity) values, the peak in does not correlate well with the peak in." + A closer inspection of the aancl images for Model n300-Z03. shown in Figure daa-b. further reveals the correlation at. low densities. and lack of correlation- at high densities.," A closer inspection of the and images for Model n300-Z03, shown in Figure \ref{compfigs}a a-b, further reveals the correlation at low densities, and lack of correlation at high densities." + In the low intensity range 3< log(W) 1. marked by solid lines in Figure 2dd. an increase in ecorresponds to a similar increase in iin the 12 x logCNco)) x 14 range.," In the low intensity range $-3 \leq$ log(W) $\leq \, -$ 1, marked by solid lines in Figure \ref{pdfpans}d d, an increase in corresponds to a similar increase in in the 12 $\leq$ ) $\leq$ 14 range." + These aand vvalues are indicated by solid contours in Figure 4.. showing excellent correspondence.," These and values are indicated by solid contours in Figure \ref{compfigs}, showing excellent correspondence." + However. at higher intensities. ddoes not faithfully trace the high rregions.," However, at higher intensities, does not faithfully trace the high regions." + Phe PDE of intensities at log(VV)) zc 1.5. marked by a dashed line in Figure 2dd. decreases sharply. whereas log(Neoo)) continues to increase.," The PDF of intensities at ) $\geq$ 1.5, marked by a dashed line in Figure \ref{pdfpans}d d, decreases sharply, whereas ) continues to increase." + The clashed contours in Figure 4 mark the corresponding regions in the aancl mniaps.," The dashed contours in Figure \ref{compfigs} + mark the corresponding regions in the and maps." + In some of the filaments (e.g. near the bottom). the contours mark similar regions.," In some of the filaments (e.g. near the bottom), the contours mark similar regions." + However. in the most dense regions (c.g. the laree over-dense region in the top right). the area within the ccontour is noticeably smaller than that encompassed in the nunap.," However, in the most dense regions (e.g. the large over-dense region in the top right), the area within the contour is noticeably smaller than that encompassed in the map." + The detailed morphology in the region enconmpassed by the dashed contour also shows stark cillerences between the observed. CO. intensities. and intrinsic CO column densities., The detailed morphology in the region encompassed by the dashed contour also shows stark differences between the observed CO intensities and intrinsic CO column densities. + These dilferences at high densities are a direct consequence of the optically thick nature of the Ilinc., These differences at high densities are a direct consequence of the optically thick nature of the line. + Similar discrepancies are present in a —-MW ccomparison of all the models., Similar discrepancies are present in a - comparison of all the models. + In some cases. such as model cloud. with very low metallicity. n300-Z01 shown in Figure jj. the apparent. correlation in PDEs at low densities does not translate into a correlation in the 2D maps.," In some cases, such as model cloud with very low metallicity, n300-Z01 shown in Figure \ref{pdfpans}j j, the apparent correlation in PDFs at low densities does not translate into a correlation in the 2D maps." + As stated. the aancd PPDESs were plotted with abscissas chosen to best match the PDEs at low densities and intensities. and so any apparent correlation may only be coincidental.," As stated, the and PDFs were plotted with abscissas chosen to best match the PDFs at low densities and intensities, and so any apparent correlation may only be coincidental." + ln summary. we have shown that at low censities. CO emission traces the distribution of CO molecules well. since the CO line is optically thin.," In summary, we have shown that at low densities, CO emission traces the distribution of CO molecules well, since the CO line is optically thin." + However. at high densities. the line becomes optically thick. resulting in an intensity threshold.," However, at high densities, the line becomes optically thick, resulting in an intensity threshold." +" ""hus. CO intensity does not neatly trace the highest density. gas."," Thus, CO intensity does not neatly trace the highest density gas." + Further. there is generally no simple correlation in the distribution of CO and mumolecules.since," Further, there is generally no simple correlation in the distribution of CO and molecules,since" +PPETER Goanmia-ray bursts (GRBs) are potential sources of ultra-high-energy cosmic rays (UILECTis.Waxman1995;Χο.1995:Milerom&Usov 1996).,"Peter Gamma-ray bursts (GRBs) are potential sources of ultra-high-energy cosmic rays \citep[UHECRs,][]{wax95,vie95,mil96}." +". While the required local UIIECT enissivilv Is ο”~0.8x10!ereMpeντ tat proton energy ope10! eV &Dahcall1998:Dermer 2007).. the local GRB rate may be in the range of 0.05—1Gpe""vr! (Daigneetal.2006:Le&Dermer2007:GuettaPiran2007)."," While the required local UHECR emissivity is $\varepsilon_{\rm p}^2 d\dot{N}_{\rm p}/d\varepsilon_{\rm p} \simeq 0.8 \times 10^{44}\ {\rm erg\ Mpc^{-3} yr^{-1}}$ at proton energy $\varepsilon_{\rm p} \sim 10^{19}$ eV \citep{wax98,der07}, the local GRB rate may be in the range of $0.05-1\ {\rm Gpc^{-3} yr^{-1}}$ \citep{dai06,le07,gue07}." +".. Assuming py=2 lor the power-law index of accelerated protons. the necessary. total isolropic-equivalent energy in protons would be £j,~2x10?!—310? erg when integrated over 2j~10?—10?"" eV. Compared to the isotropic-equivalent οποίον released as gamma-rays. typically E.~1003 ere. (his indicates that the accelerated protons must dominate the energy budget of GRBs in order for them to be viable sources of VITECRs."," Assuming $p_{\rm p}=2$ for the power-law index of accelerated protons, the necessary total isotropic-equivalent energy in protons would be $E_{\rm p} \sim 2 \times 10^{54} - 3 \times 10^{55}$ erg when integrated over $\varepsilon_{\rm p} \sim 10^9 - 10^{20}$ eV. Compared to the isotropic-equivalent energy released as gamma-rays, typically $E_\gamma \sim 10^{53}$ erg, this indicates that the accelerated protons must dominate the energy budget of GRBs in order for them to be viable sources of UHECRs." + Although E2;/E.=10—100 in GRBs may appear physically demanding. a number ol considerations provide some justification (Totani1905:Asanoetal.2009).," Although $E_{\rm p}/E_\gamma \ga 10 - 100$ in GRBs may appear physically demanding, a number of considerations provide some justification \citep{tot98,asa09}." +. First. in the popular internal shock model where the prompt MeV. eamma-ravs are attributed to svachrotron radiation from electrons accelerated in shocks within the GRB outflow Mészáros 2006).. the efficieney. with which the electrons are energized may be limited in comparison with the total available energy. which is the cdissipated fraction of the bulk kinetic energv conveved. predominantly by protons.," First, in the popular internal shock model where the prompt MeV gamma-rays are attributed to synchrotron radiation from electrons accelerated in shocks within the GRB outflow \citep{pir05,mes06}, the efficiency with which the electrons are energized may be limited in comparison with the total available energy, which is the dissipated fraction of the bulk kinetic energy conveyed predominantly by protons." + Since simple Coulomb collisions are inelleclive in (rausferrine the enerev of (he protons to the electrons within a dynamical timescale. it has been generally assumed that (his can occur through some plasma instabilities with efficiencies e;~ 0.1-0.5.," Since simple Coulomb collisions are ineffective in transferring the energy of the protons to the electrons within a dynamical timescale, it has been generally assumed that this can occur through some plasma instabilities with efficiencies $\epsilon_{\rm e} \sim 0.1$ $0.5$." + However. this is bv no means physically. guaranteed. so we are motivated to consider the possibility of proton-donminated GRBs with e.<0.1 and explore ils consequences.," However, this is by no means physically guaranteed, so we are motivated to consider the possibility of proton-dominated GRBs with $\epsilon_{\rm e} \ll 0.1$ and explore its consequences." + Note (hat a high proton-to-electron ratio is not only observed in Galactic cosmic rays and inferred in supernova remnants (Aharonianetal...2006).. but also theoretically expected. at least for nonrelativistic shocks (Blandford1994:Levinson1996).," Note that a high proton-to-electron ratio is not only observed in Galactic cosmic rays and inferred in supernova remnants \citep{aha06}, but also theoretically expected, at least for nonrelativistic shocks \citep{bla94,lev96}." + The prompt emission spectra of GRBs are known to be generally well described by the so-called Band model. consisting of a hard. low-energy. power-law part. a softer. high-energy," The prompt emission spectra of GRBs are known to be generally well described by the so-called Band model, consisting of a hard, low-energy power-law part, a softer, high-energy" +We have provided a physical reconstruction of the large-scale solar magnetic field and the open heliospheric flux since 1700 with a surface flux transport model with sources based on sunspot number data and on the statistical. properties. of the sunspot groups in the RGO photoheliographic results.,We have provided a physical reconstruction of the large-scale solar magnetic field and the open heliospheric flux since 1700 with a surface flux transport model with sources based on sunspot number data and on the statistical properties of the sunspot groups in the RGO photoheliographic results. + The model has been validated through comparison. with reconstructions based on the actual sunspot group record and with directly measured or observationally inferred quantities., The model has been validated through comparison with reconstructions based on the actual sunspot group record and with directly measured or observationally inferred quantities. + Our source term. S. is based on the semi-synthetic sunspot group record of Paper I. It in turn is based upon correlations between the cycle amplitudes ard eycle phase. and sunspot group areas. emergence latitudes and tilt angles.," Our source term, $S$, is based on the semi-synthetic sunspot group record of Paper I. It in turn is based upon correlations between the cycle amplitudes and cycle phase, and sunspot group areas, emergence latitudes and tilt angles." + Hence while the surface evolution described by the SFTM model ts linear. our model of the source term 1troduces nonlinearities into the reconstruction.," Hence while the surface evolution described by the SFTM model is linear, our model of the source term introduces nonlinearities into the reconstruction." + These nonlinearities partly explain why the reconstruction for the period from 1874 to 1976 has polar field reversals each cycle without the heed to invoke variations im the meridional flow (2). or extra terms which cause the field to decay (?).., These nonlinearities partly explain why the reconstruction for the period from 1874 to 1976 has polar field reversals each cycle without the need to invoke variations in the meridional flow \citep{Wang02} or extra terms which cause the field to decay \citep{Schrijver02}. + This was also found in CJSSIQ., This was also found in CJSS10. + The sunspot numbers are less reliable prior to 1874. anc we needed to," The sunspot numbers are less reliable prior to 1874, and we needed to" +ssec.,sec. +" The data obtained by the two EPIC MOS cameras suffered from very severe pile up, but the operation of the pn camera was switched to timing mode and yielded a measured average, background corrected EPIC-pn count rate of 1348.0+0.3 cts sec! (?),, with variations by (?).."," The data obtained by the two EPIC MOS cameras suffered from very severe pile up, but the operation of the pn camera was switched to timing mode and yielded a measured average, background corrected EPIC-pn count rate of $1\,348.0 \pm 0.3$ cts $^{-1}$ \citep{OEA03}, with variations by \citep{LEA06}." +" The RGS count rates were about 57 cts sec, and the unabsorbed flux was 1.5x107? erg cm2 -l, consistent with the flux measured 16 days earlier with "," The RGS count rates were about 57 cts $^{-1}$, and the unabsorbed flux was $1.5 \times 10^{-9}$ erg $^{-2}$ $^{-1}$, consistent with the flux measured 16 days earlier with \citep{LEA06}." +Most of the variability is well represented as a combination(?).. of oscillations at a set of discrete frequencies lower than 1.7mmHz (?)., Most of the variability is well represented as a combination of oscillations at a set of discrete frequencies lower than mHz \citep{LEA06}. + At least five frequencies preserve their coherence over the 16 days time interval between the two observations., At least five frequencies preserve their coherence over the 16 days time interval between the two observations. +" The 13324ssec period detected with could be split into two periods, of 13310.1ssec and 13371.6ssec, both of which are consistent in the data but it may not have been resolved "," The sec period detected with could be split into two periods, of sec and sec, both of which are consistent in the data but it may not have been resolved \citep{LEA06}." +"In that article we suggested that a period in the power (?)..spectrum of both light curves at the frequency of 20.75 mmHz (corresponding to 13371.6ssec) is the spin period of the white dwarf in the system, and that other observed frequencies are signatures of non-radial white dwarf pulsations."," In that article we suggested that a period in the power spectrum of both light curves at the frequency of $\simeq$ mHz (corresponding to sec) is the spin period of the white dwarf in the system, and that other observed frequencies are signatures of non-radial white dwarf pulsations." +" The X-ray evolution was followed with ssec long exposures with the LETG in July and September 2003 and in February 2004, and with a 300000ssec observation with in September 2004."," The X-ray evolution was followed with sec long exposures with the LETG in July and September 2003 and in February 2004, and with a sec observation with in September 2004." +" By this time, the nova X-ray luminosity had decayed by 5 orders of magnitude, but the period of e1370 ssec was still detectable."," By this time, the nova X-ray luminosity had decayed by 5 orders of magnitude, but the period of $\approx 1\,370$ sec was still detectable." +" However, the S/N of the RGS spectra at this epoch was very poor."," However, the S/N of the RGS spectra at this epoch was very poor." +" We have performed a NLTE spectral analysis of the grating spectra obtained between 2003 March and 2004 February, with NLTE model-atmosphere techniques."," We have performed a NLTE spectral analysis of the grating spectra obtained between 2003 March and 2004 February, with NLTE model-atmosphere techniques." + The model-atmosphere code and the construction of the model atoms that are used are described in2., The model-atmosphere code and the construction of the model atoms that are used are described in. +1.. An attempt to determine photospheric parameters with a fit procedure is presented in3., An attempt to determine photospheric parameters with a fit procedure is presented in. +"1.. This is followed by a detailed investigation of the observed, flux-calibrated spectrum ofsKsect:fine."," This is followed by a detailed investigation of the observed, flux-calibrated spectrum of." +. In we describe how our models fit the and observations to interpret the post-nova evolution in the 18 months after the outburst ofSgr., In we describe how our models fit the and observations to interpret the post-nova evolution in the 18 months after the outburst of. +". A previous analysis of LETG-S observations of citepPEA05,, done with the NLTE models with solar abundances, reached=580kK.."," A previous analysis of LETG-S observations of \\citep{PEA05}, done with the NLTE models with solar abundances, reached." +" The fit of the model to the data was still poor, and this is not surprising because in the phase directly after the outburst,i."," The fit of the model to the data was still poor, and this is not surprising because in the phase directly after the outburst,." +"e.. when the H burning is still on-going (for years), the surface composition of the WD is poorly known, but it is very unlikely to be solar."," when the H burning is still on-going (for years), the surface composition of the WD is poorly known, but it is very unlikely to be solar." +" With the code, the nova atmosphere is approximated as an expanding, but stationary in time structure."," With the code, the nova atmosphere is approximated as an expanding, but stationary in time structure." +" Recently, ? presented a new version of that considers mass-loss as well as velocity fields."," Recently, \citet{VRN10} presented a new version of that considers mass-loss as well as velocity fields." +" In the future, such codes will become a powerful tool for the analysis and understanding of novae and other supersoft sources."," In the future, such codes will become a powerful tool for the analysis and understanding of novae and other supersoft sources." +" However, in order to make progress, we decided to neglect the velocity field, and to use our static NLTE models to investigate basic parameters like and surface composition."," However, in order to make progress, we decided to neglect the velocity field, and to use our static NLTE models to investigate basic parameters like and surface composition." +" This is not fully justified because especially in the first spectra the lines were significantly blue-shifted, but our aim is at least a qualitative modeling of the and observations done between 2003 March and 2004 February."," This is not fully justified because especially in the first spectra the lines were significantly blue-shifted, but our aim is at least a qualitative modeling of the and observations done between 2003 March and 2004 February." +" We started with the highest S/N spectrum, the one obtained with the RGS gratings on April 4 2003, that we used as a template to adjust the abundances."," We started with the highest S/N spectrum, the one obtained with the RGS gratings on April 4 2003, that we used as a template to adjust the abundances." +" We then proceeded to fit also the spectra with the same model, checking whether the abundances we obtained were suitable, and adjusting ffor each epoch."," We then proceeded to fit also the spectra with the same model, checking whether the abundances we obtained were suitable, and adjusting for each epoch." +" In this way, we obtained the evolution ofT.g,, and the duration of the constant bolometric luminosity phase."," In this way, we obtained the evolution of, and the duration of the constant bolometric luminosity phase." +" For a reliable analysis of X-ray observations of the hottest white dwarfs, detailed NLTE model-atmospheres that consider opacities of all elements from hydrogen up to the iron-group elements (cf.?) are required."," For a reliable analysis of X-ray observations of the hottest white dwarfs, detailed NLTE model-atmospheres that consider opacities of all elements from hydrogen up to the iron-group elements \citep[cf\.][]{R03} + are required." +" Thus, for our analysis, we employed the plane-parallel, static models calculated with the Tübbingen NLTE Model-Atmosphere Package (?)."," Thus, for our analysis, we employed the plane-parallel, static models calculated with the Tübbingen NLTE Model-Atmosphere Package \citep[\tmap\footnote{http://astro.uni-tuebingen.de/$^\sim$rauch/TMAP/TMAP.html},." +" The construction of model atoms which are used TMAP!,,within ffollows ?..", The construction of model atoms which are used within follows \citet{RD03}. + Some details for these extremely hot model atmospheres in the rrange are summarized briefly in the following., Some details for these extremely hot model atmospheres in the range are summarized briefly in the following. +" Since the surface composition is unknown, we started with the calculation of exploratory H+He+C+N+0O models and later included Ne, Mg, Si, S, as well as the iron-group elements."," Since the surface composition is unknown, we started with the calculation of exploratory H+He+C+N+O models and later included Ne, Mg, Si, S, as well as the iron-group elements." + The iron-group elements (Sc — Ni) and Ca are treated with a statistical method (7) and are represented by one generic model atom., The iron-group elements (Sc – Ni) and Ca are treated with a statistical method \citep{RD03} and are represented by one generic model atom. +" Beside an element selection, also the construction of the model atoms has to be performed with care."," Beside an element selection, also the construction of the model atoms has to be performed with care." + An, An +| for dillerent. values of the inclination angle.,\ref{light_curve_gamma_h} for different values of the inclination angle. + For low inclination angles (tel mass). VHE plotous euiitted from apastron go through less circumstellar hydrogen than those emitted [rom periastrou.," For low inclination angles (high mass), VHE photons emitted from apastron go through less circumstellar hydrogen than those emitted from periastron." + 'Ehis results in minimum attenuation uear apastron. as can be seen iu figure L.," This results in minimum attenuation near apastron, as can be seen in figure \ref{light_curve_gamma_h}." + From this figure it is clear that the emiissiol peak corresponding to a cauonical L.OAL. neutron star is ouly imarginally supported by observatio15., From this figure it is clear that the emission peak corresponding to a canonical $1.5M_{\odot}$ neutron star is only marginally supported by observations. + We take the inclination angle. characteristic density. and normalization [actor as [ree parameters.," We take the inclination angle, characteristic density, and normalization factor as free parameters." + We find the iuclination :uigle to be 7<28° (Ms> BAL.) at the S056 €oufidence level (CL) iu the context of this model. aid ic3E (Alo 2.5M..) at the 99% CL.," We find the inclination angle to be $i< 28^\circ$ $M_2>3M_\odot$ ) at the $89\%$ confidence level (CL) in the context of this model, and $i<34^{\circ}$ $M_2>2.5M_{\odot}$ ) at the $99\%$ CL." + Tese liinits are no iu good agreement with the ueuron star scenario generally [avored [or the b'oad-baikd. spectii mitplies!., These limits are not in good agreement with the neutron star scenario generally favored for the broad-band spectrum it. +. However. our restIts are still consistent with other observational coustraiuts (107<7« 607) (Casares.elal.2005). olXained. [rom optical spectroscopy.," However, our results are still consistent with other observational constraints $10^{\circ}7 erg L 2 in. reasonable agreement with. ju independent estimate.," This value is within one standard deviation of the mean flux of the R08 emitters, $3.7\times10^{-18}$ erg $^{-1}$ $^{-2}$ , in reasonable agreement with that independent estimate." + Phe average luminosity of Lye Επτους causing DLAS in the line-ol-sieht to background WOs is similar or perhaps even somewhat larger than 1ο average Luminosity of [aint Lye emitters in the ROS sample., The average luminosity of $\alpha$ emitters causing DLAS in the line-of-sight to background QSOs is similar or perhaps even somewhat larger than the average luminosity of faint $\alpha$ emitters in the R08 sample. + Thus. contrary to the claim by Rahmani ct al. our present analysis lends additional support to the conclusions w Rauch et al 2008 that their Lya emitters largely overlap with the host.galaxies of DLAS.," Thus, contrary to the claim by Rahmani et al, our present analysis lends additional support to the conclusions by Rauch et al 2008 that their $\alpha$ emitters largely overlap with the hostgalaxies of DLAS." +position is only 11 aresec.,position is only 11 arcsec. + Object. 1 is only LO aresee from. the X-ray. position (see the finder chart in Figure 1(f))., Object 1 is only 10 arcsec from the X-ray position (see the finder chart in Figure 1(f)). + On 1998 February 3 we obtained a lla spectrum. of Object 1., On 1998 February 3 we obtained a $\alpha$ spectrum of Object 1. + “Phe spectrum. shown in Figure 3(0). has a strong llo emission line. with (Llaj=-60AX.," The spectrum, shown in Figure 3(e), has a strong $\alpha$ emission line, with $\alpha$ )=-60." +. The peak of the llo line is at a wavelength of 6566.0£0.5A.. corresponding to a velocity of 148223 km +.," The peak of the $\alpha$ line is at a wavelength of $\pm$ 0.5, corresponding to a velocity of $\pm$ 23 km $^{-1}$." + These data confirm that Object Lis a Be star in the SAIC., These data confirm that Object 1 is a Be star in the SMC. + As this is the only such object within several arcmiinutes of the X-ray position. we ientify object Las the optical counterpart. and confirm a Je/N-rav binary nature for this X-ray source.," As this is the only such object within several arcminutes of the X-ray position, we identify object 1 as the optical counterpart, and confirm a Be/X-ray binary nature for this X-ray source." + This source was discovered. by ENOSAT during. deep observations of the LAIC N-4 region in 1983. (Pakull οἱ al., This source was discovered by EXOSAT during deep observations of the LMC X-4 region in 1983 (Pakull et al. + 1985)., 1985). + It was detected. again in 1985 by the SL2 NLP experiment., It was detected again in 1985 by the SL2 XRT experiment. + The lack of detection in ENOSAT observations mace between these dates demonstrates the transient nature of the source., The lack of detection in EXOSAT observations made between these dates demonstrates the transient nature of the source. + The object was identified with a Be star hy Pakull (private communication)., The object was identified with a Be star by Pakull (private communication). + The counterpart. proposed by Pakull is the northern component of a close double., The counterpart proposed by Pakull is the northern component of a close double. + The components of this double are marked. 1 and 2 in Figures 1(g)., The components of this double are marked 1 and 2 in Figures 1(g). + The positions of the two objects in the diagram show that both are early type stars., The positions of the two objects in the diagram show that both are early type stars. + With our chosen criterion of a Be star having R-lla=0.2 then Object 1 is the onlyBe star within the N-ray. error circle. with R-lla = 0.21. Object 2 has R-Lla = 0.15: within the uncertainties however. our data do not favour one object over another as emission line objects.," With our chosen criterion of a Be star having $\alpha \ge 0.2$ then Object 1 is the onlyBe star within the X-ray error circle, with $\alpha$ = 0.21, Object 2 has $\alpha$ = 0.15; within the uncertainties however, our data do not favour one object over another as emission line objects." + On 1998 February 3 we obtained. a spectrum of the Northern component of the double., On 1998 February 3 we obtained a spectrum of the Northern component of the double. + The resulting spectrum shown in Figure ο) confirms the presence of Ho. emission. with (lla) = -10.0X1.0A.," The resulting spectrum shown in Figure 3(f) confirms the presence of $\alpha$ emission, with $\alpha$ ) = $\pm$ 1.0." +. The line is centered on a wavelength of 7250.5A. corresponding to à velocity of 23. km l.," The line is centered on a wavelength of $\pm$ 0.5, corresponding to a velocity of $\pm$ 23 km $^{-1}$." + On 1998 FebruaryH 5 we obtained. a low resoluion. Hux calibrated spectrum. of this object. (shown in Figure 5)). showing Lh? also in emission. with IENV(.7) = -0.54+0.2 A..," On 1998 February 5 we obtained a low resoluion, flux calibrated spectrum of this object (shown in Figure \ref{0531_low}) ), showing $\beta$ also in emission with $\beta$ ) = $\pm$ 0.2." + No spectrum has vet been obtained. of the Southern component of the double., No spectrum has yet been obtained of the Southern component of the double. + In order to determine which object is the counterpart to the N-rav. source. it will be necessary to obtain an X-ray position to sub-aresecond accuracy. possible with the forthcoming“LYALL mission. or to find optical/infrared variations in one of the objects which correlate with N-rav behaviour.," In order to determine which object is the counterpart to the X-ray source, it will be necessary to obtain an X-ray position to sub-arcsecond accuracy, possible with the forthcoming mission, or to find optical/infrared variations in one of the objects which correlate with X-ray behaviour." + This source was discovered. with the scanning moculation collimator by Johnston. Bradt Doxsey (1979).," This source was discovered with the scanning modulation collimator by Johnston, Bradt Doxsey (1979)." + The brightest object within the X-ray error circle (star 1 in Figure 1.. and in Figure 6 of Johnston. Braclt Doxscv 1979) was found to be a variable BO-L star (van der Wis et al.," The brightest object within the X-ray error circle (star 1 in Figure \ref{finders}, and in Figure 6 of Johnston, Bradt Doxsey 1979) was found to be a variable B0-1 star (van der Klis et al." + 1983 and references therein) but. no emission. lines have been observed. in its spectrum to identity it as a Be star., 1983 and references therein) but no emission lines have been observed in its spectrum to identify it as a Be star. + van cler Whis et al. (, van der Klis et al. ( +1983) published photometry which showed a negative correlation between optical magnitudes ancl colour indices. twpical of Be stars whose variability is due to variations in the circumstellar disc.,"1983) published photometry which showed a negative correlation between optical magnitudes and colour indices, typical of Be stars whose variability is due to variations in the circumstellar disc." + Phe authors expressed concern at the lack of other obvious Be star spectral characteristics. but suggested that the object may be a Be star in a low state of activity.," The authors expressed concern at the lack of other obvious Be star spectral characteristics, but suggested that the object may be a Be star in a low state of activity." + Anemission-colouwr diagram for objects in the field was created as previously. described., An diagram for objects in the field was created as previously described. + In the 4 arcminute radius area searched. only one object displavs the colours indicative ofa Be star.," In the 4 arcminute radius area searched, only one object displays the colours indicative of a Be star." + This object is identified as Object Lin Figure L.. and corresponds to the Object 1 o£ Johnson. Bradt Doxey (1979).," This object is identified as Object 1 in Figure \ref{finders}, and corresponds to the Object 1 of Johnson, Bradt Doxey (1979)." + We obtained optical spectra of this object in. 1998 February. these are shown in Figures 3(g) and 6..," We obtained optical spectra of this object in 1998 February, these are shown in Figures 3(g) and \ref{h0544_low}." + The lla line is clearlv. in emission. with an equivalent width measurecl from. the medium. resolution spectrum. (Figure 3(9)) of EW(Lla) = -S.7+1.0A.," The $\alpha$ line is clearly in emission, with an equivalent width measured from the medium resolution spectrum (Figure 3(g)) of $\alpha$ ) = $\pm$ 1.0." + The profile is double peaked with a peak separation of 1812-30 km 1. the mean velocity of these peaks is 282020 kms 1. consistent with the LAIC velocity of 275 km eiven by Westerlund (1997). but lower than the 360042 km s measured for. Balmer," The profile is double peaked with a peak separation of $\pm$ 30 km $^{-1}$, the mean velocity of these peaks is $\pm$ 20 km $^{-1}$ , consistent with the LMC velocity of 275 km $^{-1}$ given by Westerlund (1997), but lower than the $\pm$ 42 km $^{-1}$ measured for Balmer" +Extragalactic Database (NED).,Extragalactic Database (NED). + We were also able to use an uuipublisbed image obtained with the WIYN for NGC 3215. and the minor-axis ucar-intrared surtace-brightuess profile of the Milkv. Way published by veut. Dame. Fazio (1991). makine a total of 23 galaxies with uscable data.," We were also able to use an unpublished image obtained with the WIYN for NGC 3245, and the minor-axis near-infrared surface-brightness profile of the Milky Way published by Kent, Dame, Fazio (1991), making a total of 23 galaxies with useable data." + A full discussion of the images for individual galaxies. along with reduction procedures aud the extracted light xofiles. analysis aud model fitting for cach galaxy. will be resented in Erwin et ((2001).," A full discussion of the images for individual galaxies, along with reduction procedures and the extracted light profiles, analysis and model fitting for each galaxy will be presented in Erwin et (2001)." + Bricfiv. we fitted ellipses o the isophotes. allowing the position angle aud ellipticitv o vary with radius.," Briefly, we fitted ellipses to the isophotes, allowing the position angle and ellipticity to vary with radius." + The resulting light profiles were heu fitted with a Sérrsic (1968) pli uodel., The resulting light profiles were then fitted with a Sérrsic (1968) $r^{1/n}$ model. +" We modeled disk galaxy profiles with a combined (seeing-couvolved) cxpoucutial disk aud ri"" bulge.", We modeled disk galaxy profiles with a combined (seeing-convolved) exponential disk and $r^{1/n}$ bulge. + For wo galaxies with strong bars. we used the lieht profile derived from cuts along an axis perpendicular to the bar: his produced much. better fits and avoided most of the xw contribution.," For two galaxies with strong bars, we used the light profile derived from cuts along an axis perpendicular to the bar; this produced much better fits and avoided most of the bar contribution." + The iuuer arc secoud of the profiles was eencrallv excluded from the fit. since these regious are often dominated by relatively flat cores. bright nuclear disks. or nuclear poiut-sources (c.g.. Rest et 22001. and referenecs therein) none of which can be modeled with Sevrsic profiles.," The inner arc second of the profiles was generally excluded from the fit, since these regions are often dominated by relatively flat cores, bright nuclear disks, or nuclear point-sources (e.g., Rest et 2001, and references therein), none of which can be modeled with Sérrsic profiles." + We are thus measuring the overall concentration of the bulec. independent of auv separate central stellar components like nuclear disks.," We are thus measuring the overall concentration of the bulge, independent of any separate central stellar components like nuclear disks." + Only two ealaxies could not be successfully inodeled., Only two galaxies could not be successfully modeled. + The final set of 21 galaxies with well-fitted profiles is eiveu in Table 2.., The final set of 21 galaxies with well-fitted profiles is given in Table \ref{table1}. + We then computed the concentration of the best-fittiug rl qnodels using the ceutral concentration index first preseuted in Trujillo. Graham Caon (2001) aud further developed in Graham et ((20013.," We then computed the concentration of the best-fitting $r^{1/n}$ models using the central concentration index first presented in Trujillo, Graham Caon (2001b) and further developed in Graham et (2001)." + This iudex measures the light concentration within a bulee's halflieht radius (τα is the ratio of flux inside some fraction à of the halt radius to the total flux inside the haltlieht radius., This index measures the light concentration within a bulge's half-light radius $r_e$ ): it is the ratio of flux inside some fraction $\alpha$ of the half-light radius to the total flux inside the half-light radius. +" For an rl!"" qnodel. this iudex can be analytically defined as where vis the shape parameter of the £L"" model and b, is derived nunericalle from the expression I(20)223(2n0.5,) where Poa) aud 5(o..0) are respectively the eaa function aud the incomplete eauuna function (Abramowitz Steenun L961). ("," For an $r^{1/n}$ model, this index can be analytically defined as where $n$ is the shape parameter of the $r^{1/n}$ model and $b_n$ is derived numerically from the expression $\Gamma (2n)$$=$$2\gamma +(2n,b_n)$ where $\Gamma(a)$ and $\gamma(a,x)$ are respectively the gamma function and the incomplete gamma function (Abramowitz Stegun 1964). (" +This index. Ihe measured enipiricallv. without the use of Sérvrsic models. but for bulges in disk galaxies this would first require successful two-dimensional modeling aud subtraction of disks. bars. etc.),"This index be measured empirically, without the use of Sérrsic models, but for bulges in disk galaxies this would first require successful two-dimensional modeling and subtraction of disks, bars, etc.)" + The parameter a can be auy value between 0 aud 1. aud defines what level of conceutration is being measured.," The parameter $\alpha$ can be any value between 0 and 1, and defines what level of concentration is being measured." + Following Graham et ((2001). we used a value of a= 1/3.," Following Graham et (2001), we used a value of $\alpha = 1/3$ ." +" We did however explore a range of values. finding that a=1/3 roughly produced the minima vertical scatter in the logAi,C,(a) correlation."," We did however explore a range of values, finding that $\alpha = 1/3$ roughly produced the minimum vertical scatter in the $\log M_{\rm bh}-C_{r_e}(\alpha)$ correlation." + €.(1/3) is then simply the ratio of flux inside one-third of the halflight radius to the dux inside the eutire halfleht radius. G, $C_{r_e}(1/3)$ is then simply the ratio of flux inside one-third of the half-light radius to the flux inside the entire half-light radius. ( +vhich is of course half the total bulge luminosity).,which is of course half the total bulge luminosity). +" The €,(1/3) values are listed iu the final coluunu of Table 2..", The $C_{r_e}(1/3)$ values are listed in the final column of Table \ref{table1}. +" Because these values are analytically derived from the best-fittine Sérrsic iudex a. the uncertainty in C,(1/3) depends directly ou the unecrtainty in aud is derived by standard propagation of errors."," Because these values are analytically derived from the best-fitting Sérrsic index $n$, the uncertainty in $C_{r_e}(1/3)$ depends directly on the uncertainty in $n$ and is derived by standard propagation of errors." + Exror estimates for are based ou the results of Caon. Capaccioli. D'Onofrio (1993). who found a typical uncertaintv of ~25% wheu fitting with Sérrsc profiles.," Error estimates for $n$ are based on the results of Caon, Capaccioli, D'Onofrio (1993), who found a typical uncertainty of $\sim25\%$ when fitting with Sérrsic profiles." + For Séórrsje values of 9 between 2 aud 11. this corresponds to a uncertainty in the bulee conceutration.," For Sérrsic values of $n$ between 2 and 11, this corresponds to a uncertainty in the bulge concentration." +" For comparison with the known SMDII massvelocity ispersion relation. we also list the velocity dispersious σ, and corresponding errors for cach galaxy: these are taken from Alerritt Ferrarese (2001b) and thus incorporate the equivaleut-aperture correction described in Ferrarese Merritt (2000)."," For comparison with the known SMBH mass–velocity dispersion relation, we also list the velocity dispersions $\sigma_{c}$ and corresponding errors for each galaxy; these are taken from Merritt Ferrarese (2001b) and thus incorporate the equivalent-aperture correction described in Ferrarese Merritt (2000)." + As Merritt Ferrarese (2001a) showed. these values differ. on average. by only ~ from the σι values used by Cebhardt et ((2000).," As Merritt Ferrarese (2001a) showed, these values differ, on average, by only $\sim1$ from the $\sigma_{e}$ values used by Gebhardt et (2000)." + Correlations between SAMBIT iass and bulec concentration are presented in Figure 3: for comparison. we also show the correlations between SAIBIT mass and velocity dispersion for the same galaxies.," Correlations between SMBH mass and bulge concentration are presented in Figure \ref{fig1}; for comparison, we also show the correlations between SMBH mass and velocity dispersion for the same galaxies." + We used the bisector lincarreeression routine from Akritas Borshady (1996) to fit a line to these correlations., We used the bisector linear-regression routine from Akritas Bershady (1996) to fit a line to these correlations. + This regression routine treats both variables equally. aud allows for iutrinsic scatter as well as measurement errors iu the data: as Merritt Forrarese (2001a) poimt out. it is eenerally the best method to use when there are errors in both variables.," This regression routine treats both variables equally, and allows for intrinsic scatter as well as measurement errors in the data; as Merritt Ferrarese (2001a) point out, it is generally the best method to use when there are errors in both variables." + Using theorfhogonal regrosson analvsis of Akrtas Dershady (1996) and the orthogonal distance reeression routine FITENY of Press et (1950) alternate iethods for data sets with errors in both variables eave consistent results., Using the regression analysis of Akritas Bershady (1996) and the orthogonal distance regression routine FITEXY of Press et (1989) --- alternate methods for data sets with errors in both variables — gave consistent results. + We computed the Pearson correlation cocfiicicut r and Spearman rauk-order correlation cocfiicicut κ. both of which are given in Figure 3..," We computed the Pearson correlation coefficient $r$ and Spearman rank-order correlation coefficient $r_s$, both of which are given in Figure \ref{fig1}." + The Spearman cocfiicicut is preferred as it is more robust to outliers anc does not presuppose a huear relation., The Spearman coefficient is preferred as it is more robust to outliers and does not presuppose a linear relation. + The best linear fit to the whole sample is logΕπ..., The best linear fit to the whole sample is $\log M_{\rm bh} = 6.81(\pm0.95)C_{r_e}(1/3) + 5.03\pm0.41$. + Figure 3 shows that the correlation between black hole mass and bulee concentration is extremely good as good as or better than that between black hole mass aud velocity dispersion., Figure \ref{fig1} shows that the correlation between black hole mass and bulge concentration is extremely good — as good as or better than that between black hole mass and velocity dispersion. + In addition. the low 47 value of 0.82 suggests a scatter consistent with the measurement errors alone. inplviue negligible intrinsic scatter (as Ferrarese Merritt 2000 claimed for the SAIBIT velocity dispersion relation).," In addition, the low $\chi^{2}$ value of 0.82 suggests a scatter consistent with the measurement errors alone, implying negligible intrinsic scatter (as Ferrarese Merritt 2000 claimed for the SMBH – velocity dispersion relation)." + This couclusiou does. however. depeud ou how well determined the errors are: see Erwin et 22001.," This conclusion does, however, depend on how well determined the errors are; see Erwin et 2001." + Data points at the extreme euds of a correlation can be verv useful for determining the true slope. due to the weieltthey leud. but by the same token they cau heavily bias the data to produce a iuisleacding slope if they thoiiselves have not been well determined’..," Data points at the extreme ends of a correlation can be very useful for determining the true slope, due to the weightthey lend, but by the same token they can heavily bias the data to produce a misleading slope if they themselves have not been well ." + We have, We have +eergs!) with hightemperatures (T.=2—7x10° K).,erg$^{-1}$ ) with hightemperatures $T=2-7 \times 10^{5}$ K). +models. in which the effect of the magnetic field enters only in an indirect way. through an assumed suppression of envelope convection.,"models, in which the effect of the magnetic field enters only in an indirect way, through an assumed suppression of envelope convection." + The stability against high radial order pulsations of a number of main-sequence models of different masses was considered., The stability against high radial order pulsations of a number of main-sequence models of different masses was considered. + For each model with unstable high radial order modes. the frequency of the mode with largest growth rate was taken as a reference for the typical frequencies that may be expected to be observed in that region of the HR diagram.," For each model with unstable high radial order modes, the frequency of the mode with largest growth rate was taken as a reference for the typical frequencies that may be expected to be observed in that region of the HR diagram." + The reference frequencies are shown in Fig., The reference frequencies are shown in Fig. + 16 where we overplotted the three models discussed in the previous sections., \ref{fig:HRDiagram} where we overplotted the three models discussed in the previous sections. + It is clear that the reference frequencies decrease as the star evolves. a phenomenon that is in great part (but not totally) explained by the increase in stellar radius tailed discussion). ," It is clear that the reference frequencies decrease as the star evolves, a phenomenon that is in great part (but not totally) explained by the increase in stellar radius \cite[see][for a detailed discussion]{cunha02}. ." +From Fig., From Fig. + 16 it can be seen that the star is near the terminal age main sequence. as expected from its low effective temperature and surface gravity.," \ref{fig:HRDiagram} it can be seen that the star is near the terminal age main sequence, as expected from its low effective temperature and surface gravity." + That provides a natural explanation for the low frequency of the modes observed in 110195926. when compared to those seen in the majority of roAp stars.," That provides a natural explanation for the low frequency of the modes observed in 10195926, when compared to those seen in the majority of roAp stars." + 110195926 shows the power of the precision of theKepler johetometrie data., 10195926 shows the power of the precision of the photometric data. +" While its principal pulsation at 7, could have been discovered in ground-based observations. only the πας oecision of the data has allowed us to see examine the rotational multiplet of οι. with all the mode geometry information that contains."," While its principal pulsation at $\nu_1$ could have been discovered in ground-based observations, only the $\mu$ mag precision of the data has allowed us to see examine the rotational multiplet of $\nu_1$, with all the mode geometry information that contains." + And v could not be detected from ground-based shotometry., And $\nu_2$ could not be detected from ground-based photometry. +" It is the separation between. and comparison of. 7, and vo that lead to the remarkable suggestion that the pulsation axes of hese two modes do not coincide."," It is the separation between, and comparison of, $\nu_1$ and $\nu_2$ that lead to the remarkable suggestion that the pulsation axes of these two modes do not coincide." + This is a viable hypothesis for his star supported by the improved oblique pulsator model (2)., This is a viable hypothesis for this star supported by the improved oblique pulsator model \citep{bigot02}. +. No other pulsating star has ever been noted to have different pulsation axes for different modes., No other pulsating star has ever been noted to have different pulsation axes for different modes. + In the simple oblique pulsator model (2) the pulsation axis of the star coincides with its magnetic axis., In the simple oblique pulsator model \citep{kurtz82} the pulsation axis of the star coincides with its magnetic axis. + The simple case for the rotational light variations of a7 CCVn stars is also for spots that are concentric about the magnetic and pulsation poles., The simple case for the rotational light variations of $\alpha^2$ CVn stars is also for spots that are concentric about the magnetic and pulsation poles. + It has been clear for decades that magnetic Ap stars often have global fields that are more complex than dipoles. and that the spot structure is more detailed than two spots at the poles.," It has been clear for decades that magnetic Ap stars often have global fields that are more complex than dipoles, and that the spot structure is more detailed than two spots at the poles." + Recently. ? Palshowed that the spots of the roAp star a CCir do not coincide with its pulsation axis.," Recently, \citet{brunttetal09} showed that the spots of the roAp star $\alpha$ Cir do not coincide with its pulsation axis." +" We now see for 110195926 that 7, rotational light minimum in brightness coincides with maximum pulsation amplitude. whereas for vo maximum pulsation amplitude coincides with one of the rotational maxima in brightness."," We now see for 10195926 that $\nu_1$ rotational light minimum in brightness coincides with maximum pulsation amplitude, whereas for $\nu_2$ maximum pulsation amplitude coincides with one of the rotational maxima in brightness." + These indicate that the modes are in alignment with spots. but not with the same ones. and there is no simple symmetry to the spot structure.," These indicate that the modes are in alignment with spots, but not with the same ones, and there is no simple symmetry to the spot structure." + No other roAp star so obviously shows these effects., No other roAp star so obviously shows these effects. + The number of stars with rotational multiplets is small., The number of stars with rotational multiplets is small. + 66532. 33831 and 11217 are the best cases.," 6532, 3831 and 1217 are the best cases." + For the first two there is only one pulsation mode. while the latter shows at least 6 modes that have been modelled with distorted modes of different spherical degree. but with no thought to use differing pulsation axes (2)..," For the first two there is only one pulsation mode, while the latter shows at least 6 modes that have been modelled with distorted modes of different spherical degree, but with no thought to use differing pulsation axes \citep{saioetal10}." + In light of the result here for 110195926. it will be worth revisiting the interpretation of the frequency multiplets for 11217.," In light of the result here for 10195926, it will be worth revisiting the interpretation of the frequency multiplets for 1217." + The theory of the interaction of rotation. pulsation and magnetic fields is complex.," The theory of the interaction of rotation, pulsation and magnetic fields is complex." +" ? presented the improved oblique pulsator model incorporating both rotation and magnetic field in the relatively weak field case where 5,LkKG. They showed that the pulsation axis is not necessarily the magnetic axis of the star.", \cite{bigot02} presented the improved oblique pulsator model incorporating both rotation and magnetic field in the relatively weak field case where $B_p \sim 1$ kG. They showed that the pulsation axis is not necessarily the magnetic axis of the star. + In their formalism. the inclination of the dipole mode depends on how the centrifugal frequency shift compares to the difference between magnetic eigenmode frequencies of consecutive azimuthal orders m. Le. NPΠΕ”.," In their formalism, the inclination of the dipole mode depends on how the centrifugal frequency shift compares to the difference between magnetic eigenmode frequencies of consecutive azimuthal orders $m$, i.e. $\Delta^{\rm mag}_{n,l}=\omega^{\rm mag}_{n,l,m}-\omega^{\rm mag}_{n,l,m+1}$." +" At a given rotation rate. the difference between magnetic and centrifugal shifts is a function of the magnetic strength J, and of the frequency."," At a given rotation rate, the difference between magnetic and centrifugal shifts is a function of the magnetic strength $B_p$ and of the frequency." + Therefore. strictly speaking two consecutive magnetic overtones of the same degree / must have different inclinations with respect to the magnetic field axis.," Therefore, strictly speaking two consecutive magnetic overtones of the same degree $l$ must have different inclinations with respect to the magnetic field axis." + However. as shown in ?.. the difference 777 is very small in most cases. Which indicates that consecutive ARNmodes have roughly the same inclination.," However, as shown in \citet{bigotetal00}, the difference $\Delta^{\rm mag}_{n,l} - \Delta^{\rm +mag}_{n\pm 1,l}$ is very small in most cases, which indicates that consecutive modes have roughly the same inclination." +" Since v, and v2 have different amplitude ratios we conclude that the two modes have different axes.", Since $\nu_1$ and $\nu_2$ have different amplitude ratios we conclude that the two modes have different axes. + One possibility to explain this is to consider that the two modes are perpendicular., One possibility to explain this is to consider that the two modes are perpendicular. +" Since we found that the 7, mode is a dipole almost linearly polarized close to the magnetic axis. a simple interpretation for having a mode at ο with a different pulsation axis would have been an orthogonal dipole mode."," Since we found that the $\nu_1$ mode is a dipole almost linearly polarized close to the magnetic axis, a simple interpretation for having a mode at $\nu_2$ with a different pulsation axis would have been an orthogonal dipole mode." + However. we could not find satisfactory agreement in fitting both amplitude ratios simultaneously for οι and ο. which shows that this hypothesis has to be discarded.," However, we could not find satisfactory agreement in fitting both amplitude ratios simultaneously for $\nu_1$ and $\nu_2$, which shows that this hypothesis has to be discarded." + A mode of degree /=3 is also a possibility. but the phase reversal of v occurring between times of pulsation amplitude maxima. as seen in reffig:phamp2.. and as deduced from the amplitudes of the / requency triplet given in reftab:nu2fit.. suggests the simple geometry of a dipole.," A mode of degree $l=3$ is also a possibility, but the phase reversal of $\nu_2$ occurring between times of pulsation amplitude maxima, as seen in \\ref{fig:phamp2}, and as deduced from the amplitudes of the $\nu_2$ frequency triplet given in \\ref{tab:nu2fit}, suggests the simple geometry of a dipole." + Another possible explanation. for the «difference in the oulsation axes of the two modes observed could come from an effect found by ?. and ?.., Another possible explanation for the difference in the pulsation axes of the two modes observed could come from an effect found by \citet{cunha00} and \citet{saiogautschy04}. + They clearly showed that at specific Tequencies. which depend on the magnetic field strength. two modes of consecutive radial order are very differently affected by he magnetic field.," They clearly showed that at specific frequencies, which depend on the magnetic field strength, two modes of consecutive radial order are very differently affected by the magnetic field." + In those cases. the relative size of magnetic and centrifugal shifts is likely to be strongly moditiedfrom one overtone to the next. and the pulsation axes of the two consecutive," In those cases, the relative size of magnetic and centrifugal shifts is likely to be strongly modifiedfrom one overtone to the next, and the pulsation axes of the two consecutive" +"In real observations. the derived value of AZ, will differ rom the true one due to several ellects.","In real observations, the derived value of $M_{\rm ap}$ will differ from the true one due to several effects." +" First. the intrinsic ellipticity distribution of the source galaxies causes noise in he measurement of AZ, which is given by (28))."," First, the intrinsic ellipticity distribution of the source galaxies causes noise in the measurement of $M_{\rm ap}$ which is given by \ref{sigma}) )." + Second. he number of source galaxies in the [filter will have at cast Possonian noise.," Second, the number of source galaxies in the filter will have at least Possonian noise." + And third. halos are not isolated. but here will be perturbing mass inhomogencitics along the inec-of-sight to the halo.," And third, halos are not isolated, but there will be perturbing mass inhomogeneities along the line-of-sight to the halo." + Comparing the first. two sources of errors. the first dominates (see Schneider ct al. (," Comparing the first two sources of errors, the first dominates (see Schneider et al. (" +1998)). and so we consider a as the uncertainty with which we can measure JM.,"1998)), and so we consider $\sigma_{\rm c}$ as the uncertainty with which we can measure $M_{\rm ap}$." + The third. source of error cannot be modelled analytically. but must. be estimated. through ray-tracing simulations such as those carried out by Jain. Seljak White (1998).," The third source of error cannot be modelled analytically, but must be estimated through ray-tracing simulations such as those carried out by Jain, Seljak White (1998)." +" Then. by taking into account only the noise coming from the intrinsic cllipticity distribution of the source galaxies. we assume that the deviation AM, between the true value of AM, and the measured one Aq is Gaussian. In Figure 6 we have plotted the convolution NC⇁May.8) of AN(AL.@) with the distribution (40)) for the filter scale 9. In comparison with the non-convolved. function. (see Figure 5)) the values of (41)) are only slightly enhanced for the values of AZ; we areinterested in. (e.g... Ma,0.04.0.08)."," Then, by taking into account only the noise coming from the intrinsic ellipticity distribution of the source galaxies, we assume that the deviation $\Delta M_{\rm ap}$ between the true value of $M_{\rm ap}$ and the measured one $\hat M_{\rm ap}$ is Gaussian, In Figure \ref{numbermapcon} we have plotted the convolution $\hat N(> \hat M_{\rm ap}, \theta)$ of $N(>M_{\rm ap}, \theta)$ with the distribution \ref{prob}) ) for the filter scale $\theta=2'$, In comparison with the non-convolved function (see Figure \ref{numbermap}) ) the values of \ref{numberhat}) ) are only slightly enhanced for the values of $M_{\rm ap}$ we areinterested in (e.g., $M_{\rm ap}=0.04,0.08$ )." +" Therefore. in the following discussion. we shall neglect the difference between the distributions of Mj, and Alay."," Therefore, in the following discussion we shall neglect the difference between the distributions of $M_{\rm ap}$ and $\hat M_{\rm ap}$." + We shall now discuss whether [rom measuring the number density of haloes above a given threshold. AL... one can distinguish between the various cosmological models mentioned at the beginning of this section.," We shall now discuss whether from measuring the number density of haloes above a given threshold $M_{\rm ap}$, one can distinguish between the various cosmological models mentioned at the beginning of this section." +" From 55 and 6. we see that the EdS models with o;=0.6 and P=0.25 hereafter EdS(0.6.0.25). and with ox=1 and b=0.25 hereafter EdS(1.0.25)]. have à considerably lower and higher. respectively. number density of haloes for given Ala, than the three other models."," From 5 and 6, we see that the EdS models with $\sigma_8=0.6$ and $\Gamma=0.25$ [hereafter EdS(0.6,0.25)], and with $\sigma_8=1$ and $\Gamma=0.25$ [hereafter EdS(1,0.25)], have a considerably lower and higher, respectively, number density of haloes for given $M_{\rm ap}$ than the three other models." +" From the numbers in Table 1. considering a value of AZ,=0.04 or signal-o-noise of 5. it is clear that these two cosmologics can x distinguished. significantly (by which we mean that the Poisson error bars do not overlap) from the other three already with 1 deg? of a deep imaging survey."," From the numbers in Table 1, considering a value of $M_{\rm ap}=0.04$ or signal-to-noise of 5, it is clear that these two cosmologies can be distinguished significantly (by which we mean that the Poisson error bars do not overlap) from the other three already with 1 ${\rm deg}^2$ of a deep imaging survey." + To distinguish tween the other three cosmologies LEds(0.6.0.5). OCDAM. ACDAI]. a larger-area survey is needed.," To distinguish between the other three cosmologies [EdS(0.6,0.5), OCDM, $\Lambda$ CDM], a larger-area survey is needed." +" Taking the projected MBEGACAAL survey with its expected 25 deg? as an example (Moellier et 11998). one sees from the numbers in Table lthat at AZ,=0.08 (signal-to-noise of 10). this survey is more than sullicient to allow a clear distinction of these hree cosmologies."," Taking the projected MEGACAM survey with its expected 25 ${\rm deg}^2$ as an example (Mellier et 1998), one sees from the numbers in Table 1 that at $M_{\rm ap}=0.08$ (signal-to-noise of 10), this survey is more than sufficient to allow a clear distinction of these three cosmologies." + We therefore conclude that the currently xanned. wide-field. imaging surveys will allow to separate tween the most popular currently discussed. cosmological models., We therefore conclude that the currently planned wide-field imaging surveys will allow to separate between the most popular currently discussed cosmological models. + In order to get a more precise handle on the values of the cosmological parameters and/or the shape of the initial power spectrum. more detailed information may be used.," In order to get a more precise handle on the values of the cosmological parameters and/or the shape of the initial power spectrum, more detailed information may be used." +" Assuming that the haloes giving rise to moeasurenients of Maj, are not completely. dark. but. cluster-like (though possibly with a broad. range of mass-to-light. ratios). one might be able to identify a measured halo with a galaxy overdensity on the sky and/or in redshift. and thus determine the redshift of the corresponding halo. using either. photometric redshift techniques or spectroscopy."," Assuming that the haloes giving rise to measurements of $M_{\rm ap}$ are not completely dark, but cluster-like (though possibly with a broad range of mass-to-light ratios), one might be able to identify a measured halo with a galaxy overdensity on the sky and/or in redshift, and thus determine the redshift of the corresponding halo, using either photometric redshift techniques or spectroscopy." + In this case. the redshift dependence of the halo distribution can be measured.," In this case, the redshift dependence of the halo distribution can be measured." +" As shown in and 3.. the redshift evolution of the halo density as probed bv AZ, is quite different in. the cosmologies considered. here."," As shown in \\ref{ndachx} and \ref{ndach1}, , the redshift evolution of the halo density as probed by $M_{\rm ap}$ is quite different in the cosmologies considered here." + 1n Table 1 we have also cisplaved the number of, In Table \ref{table} we have also displayed the number of +"It is worth to emphasize that if accretion streams are not uniform in density, the chromospheric absorption triggers a selection effect, absorbing preferentially the X-ray emission from high density plasma components.","It is worth to emphasize that if accretion streams are not uniform in density, the chromospheric absorption triggers a selection effect, absorbing preferentially the X-ray emission from high density plasma components." +" In addition, since the chromospheric absorption does not equally affect the different density tracers (e.g. and He-like triplets; see right panels in Fig. 6)),"," In addition, since the chromospheric absorption does not equally affect the different density tracers (e.g. and He-like triplets; see right panels in Fig. \ref{fig:lum_massrate}) )," +" we expect that, in general, the results of the use of these tracers may differ significantly (see also discussion at the end of Sect. 4))."," we expect that, in general, the results of the use of these tracers may differ significantly (see also discussion at the end of Sect. \ref{sec4}) )." +U band. because showed that. at shorter wavelengths. it is impossible to fit the HB of with one single population of fixed helium content.,"$U$ band, because showed that, at shorter wavelengths, it is impossible to fit the HB of with one single population of fixed helium content." + Therefore. the fit was performed in the V versus (hereafter vs.) (B— V) plane. where the closest match was found by assuming that (m-M)y=15.7 and E(B— V)z0.15. in good agreement with?.," Therefore, the fit was performed in the $V$ versus (hereafter vs.) $B-V$ ) plane, where the closest match was found by assuming that $_\mathrm{V}$ =15.7 and $B-V$ )=0.15, in good agreement with." +. The fit is shown in the lower panel of Figure 1.., The fit is shown in the lower panel of Figure \ref{f_cmd}. + The temperature of each target was then estimated from the point of the model ZAHB closest to the observed position., The temperature of each target was then estimated from the point of the model ZAHB closest to the observed position. + Varying M)y and E(B— V) between values that still gave a reasonably good fit. we estimated that the uncertainty in the temperature should be on the order of10%.," Varying $_\mathrm{V}$ and $B-V$ ) between values that still gave a reasonably good fit, we estimated that the uncertainty in the temperature should be on the order of." +. The temperature derived for each star is given in Table 4.., The temperature derived for each star is given in Table \ref{t_datatarg}. + In the selected sample. there are eight stars hotter than 200000 K and. following the canonical definition. they. can be considered EHB stars.," In the selected sample, there are eight stars hotter than 000 K and, following the canonical definition, they can be considered EHB stars." + However. in the CMD of there is no underpopulated region in correspondence to this temperature as in. for example. andM80.. where the EHB is separated from cooler HB stars.," However, in the CMD of there is no underpopulated region in correspondence to this temperature as in, for example, and, where the EHB is separated from cooler HB stars." + In contrast. identified two clear gaps in at about V218.4 (~ 165500 K) and Vz20 («250000 K). called GI and G2 respectively. by ?.," In contrast, identified two clear gaps in at about $V$ =18.4 $\sim$ 500 K) and $V$ =20 $\sim$ 000 K), called G1 and G2 respectively, by ." +. The cluster blue HB is thus divided into three sections. called EBTI (Tay <165500 K). EBT2 (160000 and nya, are constant in the logarithms of the Coulomb andbremsstrahlung losses are (see. e.g.. Brunettietal. (2001))): where"," For time-independent acceleration, the analytic solution of equation \ref{Eloss}) ) with the condition that $\gamma$ and $n_{gas}$ are constant in the logarithms of the Coulomb andbremsstrahlung losses are (see, e.g., \citet{bru01}) ): where" +where nj;=|n. neutrons may be transformed into protons and via clectroweak processes.,"where $n_{\rm b}^\mu = n_n^\mu+n_p^\mu$, neutrons may be transformed into protons and via electroweak processes." + The fastest process is the direct. Urea process where (is electron or muon., The fastest process is the direct Urca process where $\ell$ is electron or muon. + When the beta equilibrium is reached. the two reactions occur at the same rate.," When the beta equilibrium is reached, the two reactions occur at the same rate." + In degenerate dense matter. this process is allowed for sullicienthy large proton fractions owing to the requirement that both momentum and energy has to be conserved (2)..," In degenerate dense matter, this process is allowed for sufficiently large proton fractions owing to the requirement that both momentum and energy has to be conserved \citep{lattimer-91}." + When these reactions are forbidden. the slower moclifiec Crea process prevails involving an additional spectator nucleon IN. (neutron or proton).," When these reactions are forbidden, the slower modified Urca process prevails involving an additional spectator nucleon $N$ (neutron or proton)." +" Phe relaxation time of these beta processes for npe matter. neglecting. nucleon supertluicity.eq. is. approximately. given. by 77D~oe207,ob* s and 77V!ta&ops7, months for⋅ the direct. and modified Urea processes respectively. where Zo is the temperature in units of 107 Ex (2).."," The relaxation time of these beta processes for $npe$ matter, neglecting nucleon superfluidity, is approximately given by $\tau^{(D)} \sim 20 T_9^{-4}$ s and $\tau^{(M)} \sim T_9^{-6}$ months for the direct and modified Urca processes respectively, where $T_9$ is the temperature in units of $10^9$ K \citep{yakovlev-01}." + Electrons and muons are transformed into each other via the lepton mocdified Urea processes where .X. is either a nucleon or a lepton (the direct. process is kinematically forbidden)., Electrons and muons are transformed into each other via the lepton modified Urca processes where $X$ is either a nucleon or a lepton (the direct process is kinematically forbidden). + The relaxation time associated with electromagnetic processes. of the order of LO77 5 (2).. is much smaller than the characteristic time-scales of the neutron star phenomena considered here. so that the matter can be treated as electrically neutral.," The relaxation time associated with electromagnetic processes, of the order of $10^{-22}$ s \citep{easson-79b}, is much smaller than the characteristic time-scales of the neutron star phenomena considered here, so that the matter can be treated as electrically neutral." + Εις condition reads In the newlv-born proto-neutron stars. the temperatures are of the order of ~104 I& or higher so that the equilibrium is reached in à few microseconds for the mocdified Urea process or ten times less for the direct Urea.," This condition reads In the newly-born proto-neutron stars, the temperatures are of the order of $\sim 10^{11}$ K or higher so that the equilibrium is reached in a few microseconds for the modified Urca process or ten times less for the direct Urca." + As the star cools down to temperatures ~10? Ix after 107—107 vears. the relaxation times rise dramatically to about 20 seconds for the direct Urea ancl several months for the modified. Urea.," As the star cools down to temperatures $\sim 10^{9}$ K after $10^3-10^4$ years, the relaxation times rise dramatically to about 20 seconds for the direct Urca and several months for the modified Urca." + Besides when the temperature falls below the critical threshold. for the onset of superlluiditv. the relaxation times increase exponentially (2)...," Besides when the temperature falls below the critical threshold for the onset of superfluidity, the relaxation times increase exponentially \citep{villain-05}." + As à consequence. for the short time-scales ~1...100 milliseconds relevant for oscillations of mature neutron stars (like the recently observed QPOs in SCR). the composition of the star remains essentially frozen and the constituents can therefore be assumed to be separately conserved which entails by Eqs. (76))," As a consequence, for the short time-scales $\sim 1-100$ milliseconds relevant for oscillations of mature neutron stars (like the recently observed QPOs in SGR), the composition of the star remains essentially frozen and the constituents can therefore be assumed to be separately conserved which entails by Eqs. \ref{eq.baryon.cons}) )" + and (80)). that the other currents are also conserved μην=0 and με=0 (remembering that the leptons are co-moving with the protons).," and \ref{eq.neutrality}) ), that the other currents are also conserved $\nabla_\mu n_n^\mu = 0$ and $\nabla_\mu n_\mu^\mu = 0$ (remembering that the leptons are co-moving with the protons)." + Let us remark that the lepton number is not conserved unlike the barvon number. because the neutron star matter is transparent to neutrinos (except for the first few seconds after its birth into a hot proto-neutron star).," Let us remark that the lepton number is not conserved unlike the baryon number, because the neutron star matter is transparent to neutrinos (except for the first few seconds after its birth into a hot proto-neutron star)." + The initial equilibrium composition of the neutron star core is obtained from the condition of electro neutrality (80)) and the conditions that the chemical allinities corresponding to the above processes should vanish (?).., The initial equilibrium composition of the neutron star core is obtained from the condition of electro neutrality \ref{eq.neutrality}) ) and the conditions that the chemical affinities corresponding to the above processes should vanish \citep{CCIII-05}. + Phe chemical allinity = ofa given reaction S is defined by (7) where N= and £* are the relevant particle creation numbers and the energies per particle. respectively.," The chemical affinity ${\cal A}^{_\Xi}$ of a given reaction $\Xi$ is defined by \citep{CCIII-05} where $N^{_\Xi}_{_{\rm X}}$ and ${\cal E}^{_{\rm X}}$ are the relevant particle creation numbers and the energies per particle, respectively." + As pointed out by 7.. the problem arises of determining the reference frame with respect to which the energies £* have to be measured. when some of the constituents (here neutrons and charged particles) are moving with dillerent velocities.," As pointed out by \citet{CCIII-05}, the problem arises of determining the reference frame with respect to which the energies ${\cal E}^{_{\rm X}}$ have to be measured when some of the constituents (here neutrons and charged particles) are moving with different velocities." + Since the relative velocity between the two Iuids is expected to be small compared to the ΕΙ velocities. we assume for simplicity in this section that the particles are all co-moving with 4-velocity a!)," Since the relative velocity between the two fluids is expected to be small compared to the fluid velocities, we assume for simplicity in this section that the particles are all co-moving with 4-velocity $u^\mu$." + I is then natural to define the energy per particle as £*=4 x3.," It is then natural to define the energy per particle as ${\cal E}^{_{\rm X}}=-u^\mu \pi^{_{\rm X}}_{\, \mu}$ ." + In the Newtonian case. using Eq. (25))," In the Newtonian case, using Eq. \ref{eq.piq.comoving}) )" + we thus have where the chemical potential of a particle species x is defined by Eq. (23))., we thus have where the chemical potential of a particle species $_{\rm X}$ is defined by Eq. \ref{eq.muX}) ). + Since the mass is conserved in any chemical reaction = involving particles. the corresponding chemical allinity (82)) reduces to In therelativistic case. the energy. per particle obtained from Iq. (48))," Since the mass is conserved in any chemical reaction $\Xi$ involving particles, the corresponding chemical affinity \ref{eq.def.Axi}) ) reduces to In therelativistic case, the energy per particle obtained from Eq. \ref{eq.pi.rel.comoving}) )" + is given by, is given by +We first solve the problem (1)) just as described by CKE. and ect the quarter-period shown iu Fig.2.,"We first solve the problem \ref{pme}) ) just as described by CKF, and get the quarter-period shown in Fig.2." + Next we note that for our periodic pulsar the uet poloidal current is always zero bv sviuiuetry. aud sve are actually free to Choose αν value for the SL poloidal current.," Next we note that for our periodic pulsar the net poloidal current is always zero by symmetry, and we are actually free to choose any value for the SL poloidal current." + For example. Fig.2 shows the FFE inaenetosphere with zero poloidal current iu theSL?.," For example, Fig.3 shows the FFE magnetosphere with zero poloidal current in the." +. The ambiguityOo of the FFE maguctosphereOo is worrisome., The ambiguity of the FFE magnetosphere is worrisome. + Much worse is that all FFE maenetospheres are actually unphysical. because no matter how big the postulated SL poloidal curent. the electromagnetic field inevitably becomes at laree enough distances from the lielit cevliuder.," Much worse is that all FFE magnetospheres are actually unphysical, because no matter how big the postulated SL poloidal current, the electromagnetic field inevitably becomes at large enough distances from the light cylinder." + ludeed. since the EFE inagnuetie surfaces are also the equipoteutials. the electric field at large distances from the liebt exliuder depends only on 2. while both poloidal and toroidal components of he maeuctic field decrease as rt at laree r.," Indeed, since the FFE magnetic surfaces are also the equipotentials, the electric field at large distances from the light cylinder depends only on $z$, while both poloidal and toroidal components of the magnetic field decrease as $r^{-1}$ at large $r$." + For normal pulsars. isolated aud spherical. as calculated by FFE or the ligh-couductivity SEE. he open magnetic surfaces diverge from cach other at large r. allowing the electric feld to decrease in such a way that the clectromaguetic field apparently remains everywhere maguetic-ike. except in the equator outside the lieht cvlinder.," For normal pulsars, isolated and spherical, as calculated by FFE or the high-conductivity SFE, the open magnetic surfaces diverge from each other at large $r$, allowing the electric field to decrease in such a way that the electromagnetic field apparently remains everywhere magnetic-like, except in the equator outside the light cylinder." + But for our periodic pulsar. the neighboring uaguetie surfaces cannot diverge to more than a ialf-period.," But for our periodic pulsar, the neighboring magnetic surfaces cannot diverge to more than a half-period." + The SFE magnetosphere8 is calculated as described w Cuauzinov (2011a). only now we use periodic vertical boundary couditions. change the shape of he star. aud choose the external toroidal current Howiue within the star iu such a wav as to roughly reproduce the characteristic width of the sigu-definite regions of c on the stellar surface.," The SFE magnetosphere is calculated as described by Gruzinov (2011a), only now we use periodic vertical boundary conditions, change the shape of the star, and choose the external toroidal current flowing within the star in such a way as to roughly reproduce the characteristic width of the sign-definite regions of $\psi$ on the stellar surface." + The xuwanmeters of the ποσα) simulation (in ternis of the augular velocity of the star Ο with «=1 and with ο=1 in Fig.1) are Fig.l shows that now. in the SFE maenetosphere. the electromaguetic field becomes clectric-like oulv iu the SLs (planes :=2h outside the helt cxlinder).," The parameters of the numerical simulation (in terms of the angular velocity of the star $\Omega$, with $c=1$ and with $\Omega =1$ in Fig.1) are Fig.1 shows that now, in the SFE magnetosphere, the electromagnetic field becomes electric-like only in the SLs (planes $z=2k$ outside the light cylinder)." + The cutire Povuting flux is nowdauped!.. thus allowing the magnetic surfaces (equipoteutials) to close. and the electric field. to decrease.," The entire Poynting flux is now, thus allowing the magnetic surfaces (equipotentials) to close, and the electric field to decrease." +" Just like for isolated pulsars. the solution is eiveu by ""EFE with correct boundary coucditious at SL” (Cauzinoy 201110)."," Just like for isolated pulsars, the solution is given by “FFE with correct boundary conditions at SL” (Gruzinov 2011b)." + Large Povutiug flux damping is inevitable for cvliudical musars., Large Poynting flux damping is inevitable for cylindrical pulsars. +" It seems uulikelv that the very existence of the local SL damping cau be decided bv the elobal geometry,", It seems unlikely that the very existence of the local SL damping can be decided by the global geometry. + Therefore. SEE rather than pure FFE iust be in the right for real pulsars.," Therefore, SFE rather than pure FFE must be in the right for real pulsars." + The final word. obviously. belongs to microphysics. which is anyway needed to calculate the pulsar cluission.," The final word, obviously, belongs to microphysics, which is anyway needed to calculate the pulsar emission." + If SEE is right. the microplivsics handles an order-unuitv fraction of energw. at least right bevoud the light cvlincer.," If SFE is right, the microphysics handles an order-unity fraction of energy, at least right beyond the light cylinder." + I thank Anatoly Spitkovsky for a valuable bit of information., I thank Anatoly Spitkovsky for a valuable bit of information. +The NEW profile has a 3-D density defined by where and e is the concentration parameter. defined as ους.,"The NFW profile has a 3-D density defined by where and $c$ is the concentration parameter, defined as $c=R_{200}/r_s$ ." + For a ogiven choice of virial mass. the virial radius ouo is computed from the definition in Equationi 17..," For a given choice of virial mass, the virial radius $R_{200}$ is computed from the definition in Equation \ref{eq:mvir}." + JXe[ore defining the convergence. it ds. useful to introduce some shorthand notation.," Before defining the convergence, it is useful to introduce some shorthand notation." + First. we define w«= |£|/r.=|0]/0.. where |0|= [£|/Da.," First, we define $x\equiv |\mbox{\boldmath{$ $}}|/r_s=|\bt|/\theta_s$, where $|\bt|=|\mbox{\boldmath{$ $}}|/D_{\rm d}$." +" Second. we define a normadisationzLagtert ΩΙ hliczeonvergence is give We now consider the expected behaviour of the PA, signal for a given mass mocel. aperture size and filter shape."," Second, we define a normalisation factor: In this notation, the convergence is given by where and the first flexion is given by We now consider the expected behaviour of the $\fmap$ signal for a given mass model, aperture size and filter shape." + For convenience. we shall consider only apertures that lie along the r-axis. ie. the position vector from the centre of the lens to the centre of the aperture is given by Χους.," For convenience, we shall consider only apertures that lie along the $x$ -axis, i.e. the position vector from the centre of the lens to the centre of the aperture is given by ${\bf x_0}=x_0 \ihat$." +" This is a valid simplification because the lenses under consideration all have circular symmetry. hence the racial profile of the LAL, signal along any given axis will provide a complete ceseription of the expected signal."," This is a valid simplification because the lenses under consideration all have circular symmetry, hence the radial profile of the $\fmap$ signal along any given axis will provide a complete description of the expected signal." + The clisplacement vector ofa point within the aperture with respect to the centre of the aperture is denoted by y=yeosoe|gsinój3., The displacement vector of a point within the aperture with respect to the centre of the aperture is denoted by ${\bf y}=y\cos\phi\ihat+y\sin\phi\jhat$. + Thus. the separation between the centre of the lens and a given point within the aperture may be expressed as @=xo|yGro|gcosó) ysino7.," Thus, the separation between the centre of the lens and a given point within the aperture may be expressed as $\bt={\bf x_0}+{\bf y}=(x_0+y\cos\phi)\ihat+y\sin\phi\jhat$ ." + The Ucxion vector always points along the cirection of 0. Lo: and. by definition. ]t is important to note that [7] will. itself. generally be dependent on μοι jg. and ©. as it is a function of 6.," The flexion vector always points along the direction of $\bt$ , i.e.: and, by definition, It is important to note that $|{\cal F}|$ will, itself, generally be dependent on $x_0$, $y$, and $\phi$, as it is a function of $\bt$." +" Thus. rewriting Equation 10.. FAM, is given by As can be seen above. in general the [exion aperture mass is rather dillicult to evaluate analytically. even for the simple case of a singular isothermal lens (unless the aperture is centred. on the lens: this special case is discussed below)."," Thus, rewriting Equation \ref{eq:mflex}, $\fmap$ is given by As can be seen above, in general the flexion aperture mass is rather difficult to evaluate analytically, even for the simple case of a singular isothermal lens (unless the aperture is centred on the lens; this special case is discussed below)." + Therefore. in order to characterise its behaviour under different mass models. aperture scales and filter shapes. it is necessary to evaluate the signal numerically.," Therefore, in order to characterise its behaviour under different mass models, aperture scales and filter shapes, it is necessary to evaluate the signal numerically." + To do this. for each. combination of virial mass. mass model. aperture size and. filter. shape. we consider. 200 apertures evenly spaced in the range ry=07.2007].," To do this, for each combination of virial mass, mass model, aperture size and filter shape, we consider 200 apertures evenly spaced in the range $x_0=[0'',200'']$." + At each aperture location. we use a uniform ranclon number eenerator to generate 1000 y positions with 2xgy;ft. and select those that lie within the aperture (ic. those with H). so that the signal is evaluated on a uniform distribution of points within the aperture.," At each aperture location, we use a uniform random number generator to generate 1000 $\by$ positions with $-R\le y_i\le R$, and select those that lie within the aperture (i.e. those with $|\by|\le R$ ), so that the signal is evaluated on a uniform distribution of points within the aperture." +" At each point. the E-mocle Iexion with respect to the centre of the aperture is computed. and the PAZ, signal at org evaluated according lo where ois the number density of points within the aperture."," At each point, the E-mode flexion with respect to the centre of the aperture is computed, and the $\fmap$ signal at $x_0$ evaluated according to where $n$ is the number density of points within the aperture." + As only a finite number of points are being evaluated. this measure can be rather noisy.," As only a finite number of points are being evaluated, this measure can be rather noisy." + To reduce the noise. for each value of wg. the signal is estimated for 200cülferent sets of randomlv-sampled data points. and the median value taken as an estimate of the signal.," To reduce the noise, for each value of $x_0$, the signal is estimated for 200different sets of randomly-sampled data points, and the median value taken as an estimate of the signal." +" Phe resulting FA, signal is plotted in Figure 1. for a sample of cluster mass Lenses with Aloo=1075ΤΑ. f=3 and R=1207."," The resulting $\fmap$ signal is plotted in Figure \ref{fg:apmass_ex} for a sample of cluster mass lenses with $M_{200}=10^{15}h^{-1}M_\odot$, $l=3$ and $R=120''$." + Lt is immediately apparent that the Ες differ greatly both in amplitude and in effective width., It is immediately apparent that the $\fmap$ profiles differ greatly both in amplitude and in effective width. + Therefore. comparison of these two features should provide information about the underlying lens mass and density profile.," Therefore, comparison of these two features should provide information about the underlying lens mass and density profile." +" We take the radius at which the signal gocs to zero as à proxy [or the elfective width of the £M, profile in cach case.", We take the radius at which the signal goes to zero as a proxy for the effective width of the $\fmap$ profile in each case. + Other contours. such as the width at half the maximum signal or the radius of the minimum signal. could be used: however. we selected the zero-signal contour as both easily identifiable and. convenient to fit.," Other contours, such as the width at half the maximum signal or the radius of the minimum signal, could be used; however, we selected the zero-signal contour as both easily identifiable and convenient to fit." + The profiles shown in the figure are not well-fit by a single analytic function., The profiles shown in the figure are not well-fit by a single analytic function. + It is possible to fit these curves with a Chebyshey series of high order (720: T. Neuven. comm.)).," It is possible to fit these curves with a Chebyshev series of high order $\sim 20$; T. Nguyen, )." + However. the signal is equally well-fit (and. in some cases. better fit) bv à piecewise continuouspolynomial function. with a different: polynomial behaviour seen for duooasis ABC αυ Whore roojy ds the value ΟΕ ο at which the minimum signal is seen.," However, the signal is equally well-fit (and, in some cases, better fit) by a piecewise continuouspolynomial function, with a different polynomial behaviour seen for $x_0x_{0,min}$ , where $x_{0,min}$ is the value of $x_0$ at which the minimum signal is seen." + We find that, We find that +rotary vacuum feedthrough (Ferrolluidies FES1-122190A) by a feedback controlled Ixollmorgen U9MA Servo Disc DC motor with high-altitude brushes mounted outside the receiver.,rotary vacuum feedthrough (Ferrofluidics FE51-122190A) by a feedback controlled Kollmorgen U9M4 Servo Disc DC motor with high-altitude brushes mounted outside the receiver. +" The orientation of the motor shaft. and therefore the ΕΛΛΤΟ, was measurecl with a I6-bit Gurley A258 optical encoder."," The orientation of the motor shaft, and therefore the HWP, was measured with a 16-bit Gurley A25S optical encoder." + The LP was held in place near the Lyot stop with a Itulon-J sleeve bearing embedded in a 0.4 inch thick clisk of Zote foam., The HWP was held in place near the Lyot stop with a Rulon-J sleeve bearing embedded in a 0.4 inch thick disk of Zote foam. + A sapphire bearing was used in NLVNIPOL-0 but was later found to exhibit less favorable vibrational properties., A sapphire bearing was used in MAXIPOL-0 but was later found to exhibit less favorable vibrational properties. + This foam clisk was mounted in the optical path perpendicular to the chief rav., This foam disk was mounted in the optical path perpendicular to the chief ray. + A polished. hardened-stecl sewing needle was passed through a center drilled hole in the LWP: the assembly resembled a toy top.," A polished, hardened-steel sewing needle was passed through a center drilled hole in the HWP; the assembly resembled a toy top." + One end of the needle was slipped into the Itulon-J sleeve and the other end was rigidly coupled to the driveshaft with 907 epoxy., One end of the needle was slipped into the Rulon-J sleeve and the other end was rigidly coupled to the driveshaft with 907 epoxy. + Phe driveshaft had. three main parts., The driveshaft had three main parts. + Between the ΗΝ and the tertiary mirror. the driveshaft was made of thin wall CLO tubing (wall thickness ~ 0.005 in).," Between the HWP and the tertiary mirror, the driveshaft was made of thin wall G10 tubing (wall thickness $\simeq$ 0.005 in)." + The thin fiberglass G10 material minimized both the thermal load on the LAV? and the optical cross-section of the exposed. driveshaft. while retaining the desired torsional clriveshalt stillness.," The thin fiberglass G10 material minimized both the thermal load on the HWP and the optical cross-section of the exposed driveshaft, while retaining the desired torsional driveshaft stiffness." + A bearing assembly was mounted at the back of the tertiary mirror to act as a thermal intercept and to provided necessary mechanical stability for the driveshaft., A bearing assembly was mounted at the back of the tertiary mirror to act as a thermal intercept and to provided necessary mechanical stability for the driveshaft. + Phe bearing was mace of Rulon-J (Vespel SP3) lor NLANIPOL-1 (NLAXIPOL-0)., The bearing was made of Rulon-J (Vespel SP3) for MAXIPOL-1 (MAXIPOL-0). + Insicle this bearing. the driveshaft was macde of polished steel. sputter coated with MoS»: the shaft material was cromoly steel (titanium. nitride coated. tungsten. carbide) for ALANIPOL-1 (ALANIPOL-0).," Inside this bearing, the driveshaft was made of polished steel, sputter coated with $_{2}$; the shaft material was cromoly steel (titanium nitride coated tungsten carbide) for MAXIPOL-1 (MAXIPOL-0)." + Between the tertiary mirror ancl the rotary vacuum feedthrough at the cryostat shell the driveshalt was again made of GLO tubing to minimize the thermal load on the LWP and the liquid helium bath., Between the tertiary mirror and the rotary vacuum feedthrough at the cryostat shell the driveshaft was again made of G10 tubing to minimize the thermal load on the HWP and the liquid helium bath. + Laboratory testing was carried out to test the vibrational properties of the clrivetrain assembly. at liquid. helium temperatures., Laboratory testing was carried out to test the vibrational properties of the drivetrain assembly at liquid helium temperatures. + A mock-up of the drivetrain was constructed and installed in a liquid helium ervostat., A mock-up of the drivetrain was constructed and installed in a liquid helium cryostat. + With this setup. two bearing materials. Rulon-J and Vespel SP3. were studied with microphones mounted near the bearings inside the crvostat.," With this setup, two bearing materials, Rulon-J and Vespel SP3, were studied with microphones mounted near the bearings inside the cryostat." + Rulon-J was chosen as the tight drivetrain bearing material because of the low noise performance it exhibited over several consecutive davs of testing., Rulon-J was chosen as the flight drivetrain bearing material because of the low noise performance it exhibited over several consecutive days of testing. + During the ~22 hour. ALANIPOL-O flight the NASA cata transmitter failed. sporadically because of a broken solder connection., During the $\sim$ 22 hour MAXIPOL-0 flight the NASA data transmitter failed sporadically because of a broken solder connection. + As a result. only a few 10 minute sections of bolometer data were successfully recorded: we did not realize enough integration time for CAIB measurements.," As a result, only a few $\sim$ 10 minute sections of bolometer data were successfully recorded; we did not realize enough integration time for CMB measurements." + The flight did provide us with the opportunity to check the in-Hight polarimeter performance and to test the new davtime pointing camera. the sun shielding strategy and the LAW) driveshaft motor and encoder.," The flight did provide us with the opportunity to check the in-flight polarimeter performance and to test the new daytime pointing camera, the sun shielding strategy and the HWP driveshaft motor and encoder." + During the ALANIPOL-1 Hight. we executed four dillerent. tvpes of telescope scans: a planet scan. a dipole scan. a CALB scan and a foreground dust scan.," During the MAXIPOL-1 flight, we executed four different types of telescope scans: a planet scan, a dipole scan, a CMB scan and a foreground dust scan." + During the planet scan. the gondola vawed sinusoidally 2.57 peak-to-peak in azimuth at a slowly-rising elevation for 1 hour.," During the planet scan, the gondola yawed sinusoidally $^{\circ}$ peak-to-peak in azimuth at a slowly-rising elevation for $\sim$ 1 hour." + The scan period was 18 seconds., The scan period was 18 seconds. + During this time. Jupiter passed through the field-of-view of the instrument and was detected by the bolometers.," During this time, Jupiter passed through the field-of-view of the instrument and was detected by the bolometers." + This data set will be used to map the beam shape of cach photometer ancl calibrate the bolometer time streams given the known millimeter-wave intensity of Jupiter., This data set will be used to map the beam shape of each photometer and calibrate the bolometer time streams given the known millimeter-wave intensity of Jupiter. + We performed both daytime ancl nighttime observations of Jupiter., We performed both daytime and nighttime observations of Jupiter. + The CAIB dipole was scanned by rotating the gondola 360° in azimuth while holding the telescope at a constant elevation of 36° for 22 minutes., The CMB dipole was scanned by rotating the gondola $^{\circ}$ in azimuth while holding the telescope at a constant elevation of $^{\circ}$ for 22 minutes. + A second 10 minute scan was performed at an clevation of 50°., A second $\sim$ 10 minute scan was performed at an elevation of $^{\circ}$. + “Phe period of a single rotation was LS seconds., The period of a single rotation was 18 seconds. + With this data set we will calibrate the bolometer time streams given the large. known CAIB dipole signal.," With this data set we will calibrate the bolometer time streams given the large, known CMB dipole signal." + For the €MD and dust scans. the telescope tracked a guide star as it swept across the sky.," For the CMB and dust scans, the telescope tracked a guide star as it swept across the sky." + Simultaneouslv. the gonclola vawed 2 peak-to-peak in azimuth with a pertocl of LO seconds.," Simultaneously, the gondola yawed $^{\circ}$ peak-to-peak in azimuth with a period of 10 seconds." + This telescope motion combined with the inherent sky rotation produced bow tie shaped maps., This telescope motion combined with the inherent sky rotation produced bow tie shaped maps. + To improve cross-linking. the telescope elevation dithered periodically about the elevation of the guide star by + 0.27 with an elevation change ocurring every LO minutes.," To improve cross-linking, the telescope elevation dithered periodically about the elevation of the guide star by $\pm$ $^{\circ}$ with an elevation change ocurring every 10 minutes." + Table 1. summarizes the scan length and the expected dust. contribution for the five regions observed during NLAXIPOL-1., Table \ref{table:scans} summarizes the scan length and the expected dust contribution for the five regions observed during MAXIPOL-1. + Regions with strong cust contamination will be used to characterize this foreground signal., Regions with strong dust contamination will be used to characterize this foreground signal. + ‘Lo monitor the bolometer temperature dependence of the calibration. a fixed intensity millimeter-wave Lamp mounted near the focal plane was switched on for LO seconds every 22 minutes.," To monitor the bolometer temperature dependence of the calibration, a fixed intensity millimeter-wave lamp mounted near the focal plane was switched on for 10 seconds every 22 minutes." + The relationship between the magnitude of the subsequent bolometer response and the known bolometer temperature. will be ascertained. during data analysis., The relationship between the magnitude of the subsequent bolometer response and the known bolometer temperature will be ascertained during data analysis. + The responsivity of cach bolometer sample will be interpolated given this relative calibration and the absolute Jupiter and CAB dipole calibrations., The responsivity of each bolometer sample will be interpolated given this relative calibration and the absolute Jupiter and CMB dipole calibrations. + The purpose of this section is to demonstrate the viability of the instrument., The purpose of this section is to demonstrate the viability of the instrument. + Five minutes of NLANXIPOL-0 time stream data from one 140 Cllz photometer are plotted in the upper left panel of Figure 6.., Five minutes of MAXIPOL-0 time stream data from one 140 GHz photometer are plotted in the upper left panel of Figure \ref{fig:data}. + When this data is replottecl versus LAP angle. the systematic olfsets become apparent (upper right panel).," When this data is replotted versus HWP angle, the systematic offsets become apparent (upper right panel)." +If the radiating particles are heavy nuclei. then the efficiency of inverse bremsstralline would be increased ly the factor Z? but the arect material lvdrogen would have an abundance j=l. so that for a given flux. of inverse bremsstrahhme energetic protous would xoduce roughly au order of magnitude less fux iu lines thaw do cnerectic Carbon or Oxveeu nuclei.,"If the radiating particles are heavy nuclei, then the efficiency of inverse bremsstrahlung would be increased by the factor $Z^2$ but the target material hydrogen would have an abundance $\eta=1$, so that for a given flux of inverse bremsstrahlung energetic protons would produce roughly an order of magnitude less flux in lines than do energetic Carbon or Oxygen nuclei." +" If only energetic carbon nuclei were responsible for the eutire observed soft contiuuuu then the nuplied flux of line Cluission from the inner radian of the Galactic plane would he Likewise we obtain for energetic oxygen uuclei Due to the sinaller excitation cross sections the implied line fluxes for other heavy nuclei would be lower. so that depending ou the abundances of heavy nuclei iu low-enerev cosnüc ravs in the inner Calaxy an actual ""average"" line flux would be Z10.οplieui/sec."," If only energetic carbon nuclei were responsible for the entire observed soft continuum then the implied flux of line emission from the inner radian of the Galactic plane would be Likewise we obtain for energetic oxygen nuclei Due to the smaller excitation cross sections the implied line fluxes for other heavy nuclei would be lower, so that depending on the abundances of heavy nuclei in low-energy cosmic rays in the inner Galaxy an actual ""average"" line flux would be $\ga 10^{-3}\ {\rm ph./cm^2/sec}$." + If ou the other haud a large population of low-energy protons is responsible for the soft omission. then the nuplied dux of line emission from the mner radian of the Galactic plane would be assuming a solar abundance of Carbou (ge:=3.6: 1) and Oxveen (jo=8.510. 1) (Crevesse Anders 1989).," If on the other hand a large population of low-energy protons is responsible for the soft emission, then the implied flux of line emission from the inner radian of the Galactic plane would be assuming a solar abundance of Carbon $\eta_C =3.6\cdot 10^{-4}$ ) and Oxygen $\eta_O =8.5\cdot 10^{-4}$ ) (Grevesse Anders 1989)." + Note trat these estimates for the line flux have been caIculated uxiug the limits of the particle spectrin as in Eq.l. ie. assundue that no energetic particles exis with energies below £4=0.03. aud therefore they should be taken as lower Inaits.," Note that these estimates for the line flux have been calculated using the limits of the particle spectrum as in Eq.4, i.e. assuming that no energetic particles exist with energies below $E_1=0.03$, and therefore they should be taken as lower limits." + Tt the low-energy protons are enriched by heavier uuclei with a differential intensity ratio correspouding to solar abundances. the estimate im Eq.10 would be doubled aud one would observe broad aud narrow lines at simular flux levels.," If the low-energy protons are enriched by heavier nuclei with a differential intensity ratio corresponding to solar abundances, the estimate in Eq.10 would be doubled and one would observe broad and narrow lines at similar flux levels." + The results of the OSSE aud COMPTEL experiments ou line eiuission folowing the de-excitation of carbou and oxveen nuclei are still preliminary., The results of the OSSE and COMPTEL experiments on line emission following the de-excitation of carbon and oxygen nuclei are still preliminary. + The OSSE team has reported a 3a upoer limit for narrow lines from the iuner radiau of the Calactic plane (Harris et al., The OSSE team has reported a $\sigma$ upper limit for narrow lines from the inner radian of the Galactic plane (Harris et al. + 1996) For broad lines. i.e. cherectic Carbon aud Oxvecu uuclei. the wpper Πιτ is aout bisher.," 1996) For broad lines, i.e. energetic Carbon and Oxygen nuclei, the upper limit is about higher." + COMPTEL data have revealed some ikication for an excess 3-7 MeV flux from the Calactic ridge at a level of (Blocmen Bykov 1997. Blocien et al.," COMPTEL data have revealed some indication for an excess 3-7 MeV flux from the Galactic ridge at a level of (Bloemen Bykov 1997, Bloemen et al." + 1997) These lanits strouglv exclude a large population of low-cnerev heavy nuclei causing the observed soft continu., 1997) These limits strongly exclude a large population of low-energy heavy nuclei causing the observed soft continuum. + Inverse broiisstralilung of protons seeciis to be weakly excluded as the implied liue fiux is a factor of 2 hieher than he 30 OSSE limit., Inverse bremsstrahlung of protons seems to be weakly excluded as the implied line flux is a factor of 2 higher than the $\sigma$ OSSE limit. + The main sources of uncertaintv im the implied line flux are: a) the abundance of Carbon aud. Oxvecn in the iuner Cilaxy. b) he fracjon of the soft οσοπα which is truly cüffuse cussion. aud ο) the true low-energv nuit of the power-law spectrum in Eq.1.," The main sources of uncertainty in the implied line flux are: a) the abundance of Carbon and Oxygen in the inner Galaxy, b) the fraction of the soft continuum which is truly diffuse emission, and c) the true low-energy limit of the power-law spectrum in Eq.1." + The imetallicitv in the iuuer Calaxy is higher than in solar vicinity (Shaver et al., The metallicity in the inner Galaxy is higher than in solar vicinity (Shaver et al. + 1983). so that we can expect Carbon aud Oxveen abundances to be higher than solar.," 1983), so that we can expect Carbon and Oxygen abundances to be higher than solar." + This would lead to a higher line fiux and thereby increase the discrepancy between implied flux and the observational limits., This would lead to a higher line flux and thereby increase the discrepancy between implied flux and the observational limits. + The broad longitude cüstriliion of the soft continu indicates that it isi clutter roughlv lomoecucously throughou the Calactic disk., The broad longitude distribution of the soft continuum indicates that it is emitted roughly homogeneously throughout the Galactic disk. + Iu he remaining discussion we may therefore assunue a nietaicity like that near the molecular ring at about lkpe galactocentric radius. which is roughly a factor 2 ueher than solar (Shaver ot al.," In the remaining discussion we may therefore assume a metallicity like that near the molecular ring at about 4 kpc galactocentric radius, which is roughly a factor 2 higher than solar (Shaver et al." + 1983)., 1983). + The main contribution to the implied line fiux in Lq.10 comes from excitations of ambient Oxvecu wiclei., The main contribution to the implied line flux in Eq.10 comes from excitations of ambient Oxygen nuclei. + Due to the weak cucrev dependence of the Oxvecu excitation cross section the line flax depends on the ower luit of the proton spectrmu roughly as X£jvs , Due to the weak energy dependence of the Oxygen excitation cross section the line flux depends on the lower limit of the proton spectrum roughly as $\propto E_1^{-0.8}$. +Therefore. the predicted line flux would haxinonize with the observational Iuuits oulv if £y were 70.1. which ueans that the continWun cussion below 50 keV could iot be eutirely caused w inverse brenisstraliluug.," Therefore, the predicted line flux would harmonize with the observational limits only if $E_1$ were $\ge 0.1$, which means that the continuum emission below 50 keV could not be entirely caused by inverse bremsstrahlung." + For cCucrgics above E=0.3 hne contimuni chussion following pioi production aud decay provides another coustraint on the uuuber of energetic protons iu the Calaxy., For energies above E=0.3 the continuum emission following pion production and decay provides another constraint on the number of energetic protons in the Galaxy. + The combined data o| ECRET. OSSE. aud COAPTEL show that he luminosity of the Galaxy at a few hundred MeV. is about twice as much as that at 30 keV (Purcell ct al.," The combined data of EGRET, OSSE, and COMPTEL show that the luminosity of the Galaxy at a few hundred MeV is about twice as much as that at 30 keV (Purcell et al." + 1996)., 1996). + For protous with less han 100 MeV energv we can assume the Galaxy to act as a thick target (Pohl 1993). thusthe particle spectra. is ouly determined by the euergv losses.," For protons with less than 100 MeV energy we can assume the Galaxy to act as a thick target (Pohl 1993), thusthe particle spectrum is only determined by the energy losses." + Frou the welshown enerev dependeuce of Ionization and Coulon osses (IIecitley 1951: Butler Birmingham 1962) we ca- infer that an QXEο) injection spectrum ds required o iualutain an NVXE£L5 equilibrimm spectrum., From the well-known energy dependence of Ionization and Coulomb losses (Heitler 1954; Butler Birmingham 1962) we can infer that an $Q\propto E^{-3.3}$ injection spectrum is required to maintain an $N\propto E^{-1.8}$ equilibrium spectrum. + The uuirosity at a few hundred MeV ploonu energv thel shoud scale to that at 30 keV like the ratico of the radiatiol efficiency. times injected energv in the appropriate energv uds., The luminosity at a few hundred MeV photon energy then should scale to that at 30 keV like the ratio of the radiation efficiency times injected energy in the appropriate energy bands. + Cuven the results for the mean deusity aud escape Ποιος of cosmic ravs (Webber et al., Given the results for the mean density and escape lifetime of cosmic rays (Webber et al. +" 1992) we cau estimate that for z""-productiou 4~0.02.", 1992) we can estimate that for $\pi^0$ -production $\eta \simeq 0.02$. + For inverse xenmisstrahluug at 30 keV the radiation efficiency cau be calculated to be yx1:10 ., For inverse bremsstrahlung at 30 keV the radiation efficiency can be calculated to be $\eta \simeq 4\cdot 10^{-5}$ . + Therefore we obtiiu, Therefore we obtain +Fig.,Fig. + 7 in Cordes&Lazio(2003)., 7 in \citet{cl03}. +. We found that the limiting value of DM is about 150 pc cm? and we present our reasoning below., We found that the limiting value of $DM$ is about 150 pc $^{-3}$ and we present our reasoning below. +" The typical duty cycle of normal pulsars is 596, which for our shortest period (20 ms) gives a pulse window of about 1 ms."," The typical duty cycle of normal pulsars is $\sim5\%$, which for our shortest period (20 ms) gives a pulse window of about 1 ms." + We assumed arbitrarily the value of 10 per cent (0.1 ms) of this value as the maximum possible broadening due to high DM., We assumed arbitrarily the value of 10 per cent (0.1 ms) of this value as the maximum possible broadening due to high $DM$. + According to Fig., According to Fig. + 7 in Cordes&Lazio(2003) this corresponds to dispersion measure value DM~150 pc cm?., 7 in \citet{cl03} this corresponds to dispersion measure value $DM\sim150$ pc $^{-3}$. +" Of course, the number of pulsars with period close to 20 ms in thewhole sample is comparatively small, so probably the DM limit can be slightly higher."," Of course, the number of pulsars with period close to 20 ms in thewhole sample is comparatively small, so probably the $DM$ limit can be slightly higher." +" Increasing the maximum DM value to 170 pc cm? would extend the number of pulse-widths by less than 10 per cent, which seems to be irrelevant in our statistical analysis."," Increasing the maximum $DM$ value to 170 pc $^{-3}$ would extend the number of pulse–widths by less than 10 per cent, which seems to be irrelevant in our statistical analysis." +" However, for DM~200 pc cm? the pulse broadening would be about 1 ms, which is evidently too much."," However, for $DM\sim200$ pc $^{-3}$ the pulse broadening would be about 1 ms, which is evidently too much." +" Thus, we construct our new pulse-width database using the value of 150 pc cm? as the limit for DM in our sample."," Thus, we construct our new pulse–width database using the value of 150 pc $^{-3}$ as the limit for $DM$ in our sample." +" The new database contains pulse-widths used by GH96 and KGM04, extended by pulse-widths from SwinburneIntermediate — Latitude Pulsar Survey (Edwards 2001),, Parkes Southern Pulsar Survey I — III (Manchester (1996),, Lyneetal. (1988),, D'Amicoetal. (1998))),"," The new database contains pulse–widths used by GH96 and KGM04, extended by pulse–widths from SwinburneIntermediate – Latitude Pulsar Survey \citep{swinburne}, , Parkes Southern Pulsar Survey I – III \citet{southern1}, , \citet{southern2}, , \citet{southern3}) )," +lig.,Fig. +" 3 shows the entropy landscape for QQ. Vul. constructed assuming an inclination of 72. from which we derive optimum masses of AJ, = 0.66 M. and A» = 0.42 M.."," \ref{fig:landscapes} shows the entropy landscape for QQ Vul, constructed assuming an inclination of $^{\circ}$, from which we derive optimum masses of $M_1$ = 0.66 $_{\odot}$ and $M_2$ = 0.42 $_{\odot}$." + We adopt these masses and inclination. for the reconstruction in Section 5.2.., We adopt these masses and inclination for the reconstruction in Section \ref{qqvulmap}. +" The derived masses. however. decrease smoothly as the inclination is increased to 907 and cover the range AM, = 0.580.66 M... Ado = 0.340.44 M. al à constant ο = 0.63."," The derived masses, however, decrease smoothly as the inclination is increased to $^{\circ}$ and cover the range $M_1$ = 0.58–0.66 $_{\odot}$, $M_2$ = 0.34–0.44 $_{\odot}$ at a constant $q$ = 0.63." + This agrees well with. and is better constrained than. the masses of A4; = 356 M. andAle = 0.3040.10 AL. estimated by ?..," This agrees well with, and is better constrained than, the masses of $M_1$ = $^{+0.21}_{-0.16}$ $_{\odot}$ and$M_2$ = $\pm$ 0.10 $_{\odot}$ estimated by \citet{catalan99}." +" The white-chvarl mass we derive agrees with the values of Al, = Oda M. (7). and Aly = 0.59 M. (?).. but is almost half that of ? and ? who obtained M, = 1.22 Al. and AZ, = 1.1L3 M.. respectively."," The white-dwarf mass we derive agrees with the values of $M_1$ = $^{+0.44}_{-0.09}$ $_{\odot}$ \citep{mukai87} and $M_1$ = 0.59 $_{\odot}$ \citep{mouchet93}, but is almost half that of \citet{cropper98} and \citet{wu95} who obtained $M_1$ = 1.22 $_{\odot}$ and $M_1$ = 1.1–1.3 $_{\odot}$, respectively." + The two latter mass determinations make use of the N-ravs emitted from the accreting white dwarf and involve fitting model spectra to the observed X-ray spectra. and are therefore subject to uncerlsing assumptions in the moclel.," The two latter mass determinations make use of the X-rays emitted from the accreting white dwarf and involve fitting model spectra to the observed X-ray spectra, and are therefore subject to underlying assumptions in the model." + The mass ratio of ¢ = 0.63 obtained in this work is in excellent agreement with previous determinations. including q = O0.5440.14 (7) and q — 0.450.67 determined by ?. from Doppler tomography ancl polarimetry.," The mass ratio of $q$ = 0.63 obtained in this work is in excellent agreement with previous determinations, including $q$ = $\pm$ 0.14 \citep{catalan99} and $q$ = 0.45–0.67 determined by \citet{schwope00} from Doppler tomography and polarimetry." + The Roche tomogram of QQ Vul is presented in Fig., The Roche tomogram of QQ Vul is presented in Fig. +" 6 and shows a distinct. reduction in the Na I absorption around he L, point which can be explained by irraciation from he white dwarl and accretion regions ionising the Na Lon he inner lace of the secondary. as in ANI Ler."," \ref{fig:qqvulrdisp} + and shows a distinct reduction in the Na I absorption around the $L_1$ point which can be explained by irradiation from the white dwarf and accretion regions ionising the Na I on the inner face of the secondary, as in AM Her." + The etllects of irradiation also appear to be slightly stronger on the trailing iemisphere. suggesting that the leading hemisphere may be yartially shielded bv the accretion stream or curtain.," The effects of irradiation also appear to be slightly stronger on the trailing hemisphere, suggesting that the leading hemisphere may be partially shielded by the accretion stream or curtain." + Another notable feature is a bright patch on the leading iemisphere. corresponding to an increased. Na L fux deficit around phase 0.75.," Another notable feature is a bright patch on the leading hemisphere, corresponding to an increased Na I flux deficit around phase 0.75." + A similar feature can also be seen in the omogram of IP Peg (Eis. 8)), A similar feature can also be seen in the tomogram of IP Peg (Fig. \ref{fig:ippegrdisp}) ) + and larger lux deficits at ὦ Ξ 0.75 than at oO = 0.25 have also been reported for the Na 1. doublet in IE Cas (2). and in the TiO lisht curves of Z Cha (?).., and larger flux deficits at $\phi$ = 0.75 than at $\phi$ = 0.25 have also been reported for the Na I doublet in HT Cas \citep*{catalan99b} and in the TiO light curves of Z Cha \citep{wade88}. + In their study of QQ Vul using the same data used in his work. ? found that their surface maps derived. [rom racial-velocitv curve fitting did not give satisfactory [its o the velocities and. line fluxes between orbital phases © = (k6 and ὁ = 0.5.," In their study of QQ Vul using the same data used in this work, \citet{catalan99} found that their surface maps derived from radial-velocity curve fitting did not give satisfactory fits to the velocities and line fluxes between orbital phases $\phi$ = 0.6 and $\phi$ = 0.8." + The bright patch seen. around. phase 1.75 in Fig., The bright patch seen around phase 0.75 in Fig. + Gis almost. certainly the cause of their unsatisfactory fits., \ref{fig:qqvulrdisp} is almost certainly the cause of their unsatisfactory fits. + ? attributed. this discrepancy to the »esence of starspots., \citet{catalan99} attributed this discrepancy to the presence of starspots. + Εις interpretation is almost certainly wrong. however. as an increase in the Na LE flux deficit is inconsistent with a star-pot. as the Na LE flux deficit. is known to decrease with later spectral type (2). ancl star-spots are generally cooler than the surrounding photosphere.," This interpretation is almost certainly wrong, however, as an increase in the Na I flux deficit is inconsistent with a star-spot, as the Na I flux deficit is known to decrease with later spectral type \citep{brett93} and star-spots are generally cooler than the surrounding photosphere." + Therefore. à starspot should appear as a dark feature in the omograms. (," Therefore, a starspot should appear as a dark feature in the tomograms. (" +Although spots hotter than the photosphere mave also been imaged. e.g. 2)).,"Although spots hotter than the photosphere have also been imaged, e.g. \citealt{donati92}) )." + The reality of the spot. feature can be assessed. in Fie. 7.," The reality of the spot feature can be assessed in Fig. \ref{fig:qqvulerr1}," + which shows the significance map when we take he comparison level as the average intensity on the outer remisphere. avoiding both the region that appears to be irracliatec and the bright patch.," which shows the significance map when we take the comparison level as the average intensity on the outer hemisphere, avoiding both the region that appears to be irradiated and the bright patch." + This shows that the bright xuch is not significant., This shows that the bright patch is not significant. + Phe significance map does. however. show that the irradiated inner hemisphere is real and there is evidence for stronger irradiation of the trailing hemisphere.," The significance map does, however, show that the irradiated inner hemisphere is real and there is evidence for stronger irradiation of the trailing hemisphere." +" As with AM Ler. the reduction in absorption around the £L, point can be explained. by irradiation from. the white dwarf and accreting regions ionising the Na Lon the inner lace of the secondary. with possible shielding bv the accretion stream/curtain reducing the ellect on the leading hemisphere."," As with AM Her, the reduction in absorption around the $L_1$ point can be explained by irradiation from the white dwarf and accreting regions ionising the Na I on the inner face of the secondary, with possible shielding by the accretion stream/curtain reducing the effect on the leading hemisphere." + The optimum. svstemice velocity. as shown in Fig. l..," The optimum systemic velocity, as shown in Fig. \ref{fig:incl}," + is km s+., is --9 km $^{-1}$. + This is significanth: different from the values of 56 -E d kms+ obtained by ? and 31 τ km s.+ obtained bv ?. , This is significantly different from the values of 56 $\pm$ 4 km $^{-1}$ obtained by \citet*{martin87} and 31 $\pm$ 7 km $^{-1}$ obtained by \citet{martin89}. . +Fie., Fig. + d. also shows that we have been unable to determine the inclination of LP Peg., \ref{fig:incl} also shows that we have been unable to determine the inclination of IP Peg. + This is due to the small variations in the line strength over the orbital evele. which provides our only constraint on the inclination before taking into consideration the eclipse width.," This is due to the small variations in the line strength over the orbital cycle, which provides our only constraint on the inclination before taking into consideration the eclipse width." + The reconstructions clo.," The reconstructions do," +the flux density of GB 1428|422 at 15 11: on about 50 occasions between 1998 April and December (unfortunately much later than the LURE pointing).,the flux density of GB 1428+422 at 15 GHz on about 50 occasions between 1998 April and December (unfortunately much later than the HRI pointing). + These observations. usually of short duration (tvpically « Lh). were mace during gaps in the regular schedule of the telescope.," These observations, usually of short duration (typically $<$ 1 h), were made during gaps in the regular schedule of the telescope." + A more detailed description of the observing technique is given in Pooley Fender (L997)., A more detailed description of the observing technique is given in Pooley Fender (1997). + The flux.density scale of the observations was established by a nearby observation of either 3€ 48 or 3€ 286., The flux–density scale of the observations was established by a nearby observation of either 3C 48 or 3C 286. + Similar datasets have shown that the overall calibration in such cases has an remes., Similar datasets have shown that the overall calibration in such cases has an r.m.s. + scatter of less than 3 per cent., scatter of less than 3 per cent. + In Fig., In Fig. + 2 the Hux density of GB 142s|422 is plotted: significant variability can be detected with an amplitude of 40 per cent over about three months. and 15 per cent on timescale of ten davs.," 2 the flux density of GB 1428+422 is plotted: significant variability can be detected with an amplitude of $\sim$ 40 per cent over about three months, and $\sim$ 15 per cent on timescale of ten days." + We therefore conclude that the significant. variability on short timescales detected both in the X.rav and radio bands stronely confirms the identification of GB 1428|4217 witha blazar., We therefore conclude that the significant variability on short timescales detected both in the X–ray and radio bands strongly confirms the identification of GB 1428+4217 with a blazar. + In the following we will then consider the variability and spectral. properties of this source. and compare them with those of nearby blazars. with the aim to gain insight both on the physics and evolutionary behavior of this class of AG," In the following we will then consider the variability and spectral properties of this source, and compare them with those of nearby blazars, with the aim to gain insight both on the physics and evolutionary behavior of this class of AGN." + 1n addition to the broad. band D ancl Ro magnitudes (and monochromatic continuum flux at a rest frame wavelength of 1500) reported by Hook AleMahon (1998). we present here J. ff and £A observations.," In addition to the broad band B and R magnitudes (and monochromatic continuum flux at a rest frame wavelength of ) reported by Hook McMahon (1998), we present here $J$, $H$ and $K$ observations." + They were carried out on LOOT March 26 with the United WKinecdom Infra-IHed. Telescope (VINER) using the 2567 Lash array based camera IRCAAS in the O.28aresee/pixel mode. with exposure limes per waveband of 900 s. The data underwent. dark subtraction. [lat-ieklüing. anc mosaicing of the cdithered images using the Starlink LACXMDI software.," They were carried out on 1997 March 26 with the United Kingdom Infra-Red Telescope (UKIRT) using the $256^{2}$ InSb array based camera IRCAM3 in the 0.28arcsec/pixel mode with exposure times per waveband of 900 s. The data underwent dark subtraction, flat-fielding, and mosaicing of the dithered images using the Starlink IRCAMDR software." + Photometry was carried out using apertures of diameter 5 arcsec calibrated. against similarly analyzecl standard stars. fron Casali llawarden (1992)., Photometry was carried out using apertures of diameter 5 arcsec calibrated against similarly analyzed standard stars from Casali Hawarden (1992). + In Table. 1. we list. the observed magnitudes and derived uxes.," In Table 1, we list the observed magnitudes and derived fluxes." +" The spectral index over the range covered by the optical and LR data is ~0.0 GP,oxν73.", The spectral index over the range covered by the optical and IR data is $\sim$ 0.0 $F_{\nu} \propto \nu^{-\alpha}$ ). + This is bluer than the canonical ayy of 0.7 (eg., This is bluer than the canonical $\alpha_{\rm uv}$ of 0.7 (eg. + Fall. Pei MeMahbon 1989) which means that there is no evidence for reddening over the rest [rame spectral rangeA...," Fall, Pei McMahon 1989) which means that there is no evidence for reddening over the rest frame spectral range." + The spectral energy distribution. (SED) of this source already pointed: towards its identification. with a blazar (Fabian et al., The spectral energy distribution (SED) of this source already pointed towards its identification with a blazar (Fabian et al. + 1997. 1998).," 1997, 1998)." + In particular. Fabian et al. (," In particular, Fabian et al. (" +1998) showed that the (poorly. sampled. anc not. simultaneous) SED of GB 1425]4217 can be accounted for as nonthermal svnehrotron and. inverseCompton emission from a relativistically moving source. forming two broad. peaks in μήν). as characteristic of blazars.,"1998) showed that the (poorly sampled and not simultaneous) SED of GB 1428+4217 can be accounted for as non--thermal synchrotron and inverseCompton emission from a relativistically moving source, forming two broad peaks in $\nu +F(\nu)$, as characteristic of blazars." + However. no constraints on its size were available at the time.," However, no constraints on its size were available at the time." + The X.ray variability imescale inferred. from our ROSAT observations sets instead a significant upper limit on the dimension., The X–ray variability timescale inferred from our ROSAT observations sets instead a significant upper limit on the dimension. + We herefore re-consider the modeling of the SED and find that a broad. band energy. distribution and at Xray spectrum consistent with the data can still be found adopting a simple 10mogeneous mocel., We therefore re-consider the modeling of the SED and find that a broad band energy distribution and flat X–ray spectrum consistent with the data can still be found adopting a simple homogeneous model. + As an example of the results obtained. in Fig.," As an example of the results obtained, in Fig." + 3 we show the SED from one of the specific models (see caption) proposed by Fabian ct al. (, 3 we show the SED from one of the specific models (see caption) proposed by Fabian et al. ( +1998). where the intrinsic dimensions ancl Doppler factor are of order. f?—5.101 em and 8—20. respectively.,"1998), where the intrinsic dimensions and Doppler factor are of order $R\sim 5\times 10^{16}$ cm and $\delta \sim 20$, respectively." + As already pointed out w Fabian et al., As already pointed out by Fabian et al. + the parameters inferred from the moceling are globally consistent with those deduced for larger samples οἱ blazars at lower redshifts (Chisellini et αἱ., the parameters inferred from the modeling are globally consistent with those deduced for larger samples of blazars at lower redshifts (Ghisellini et al. + 1998)., 1998). + A further hint that beaming is involved is given by the rate of change of luminosity. AL/A/25.101 erg s7.The simple ellicieney limit (Fabian 1979: Brandt et al.," A further hint that beaming is involved is given by the rate of change of luminosity, $\Delta L/\Delta t \approxgt 5\times 10^{41}$ erg $^{-2}$.The simple efficiency limit (Fabian 1979; Brandt et al." + 1999) then vields a radiative cllicieney for the source z 20 per cent if only the luminosity in the ROSAT band. is considered. and about ten times higher if one consider the total XNrav luminosity.," 1999) then yields a radiative efficiency for the source $\approxgt$ 20 per cent if only the luminosity in the ROSAT band is considered, and about ten times higher if one consider the total X–ray luminosity." + A closer comparison can now be made between the spectral properties of GB 1428|H217 and those of nearby. blazars., A closer comparison can now be made between the spectral properties of GB 1428+4217 and those of nearby blazars. + Dillerences can give important hints on the evolution in the intrinsic or environmental properties of radioloud AGN., Differences can give important hints on the evolution in the intrinsic or environmental properties of radio–loud AGN. +" Llere we consider as quantitative SED indicators the broad. banc spectral inclices’.. 0,5. Ao. and a..."," Here we consider as quantitative SED indicators the broad band spectral , $\alpha_{\it ro}$ , $\alpha_{\it ox}$ and $\alpha_{\it rx}$." +" Because of the uncertainties due to the Εικ variability we estimate the range spanned by 6,5. av. and a... by considering the extremesof theobserved radio anc X.ray"," Because of the uncertainties due to the flux variability we estimate the range spanned by $\alpha_{\it ro}$ , $\alpha_{\it ox}$ and $\alpha_{\it rx}$ , by considering the extremesof theobserved radio and X–ray" +was determined as in (2010).. using a Monte Carlo approach.,"was determined as in , using a Monte Carlo approach." + Each pixel in (he error vector produced by the SDSS spectroscopic reduction pipeline was multiplied by a lactor between 0 and 1. drawn from a normalized distribution.," Each pixel in the error vector produced by the SDSS spectroscopic reduction pipeline was multiplied by a factor between 0 and 1, drawn from a normalized distribution." + This new vector was then added to the data vector ancl the indices were remeasured., This new vector was then added to the data vector and the indices were remeasured. + This process was repeated. 100 times and the standarc deviation was taken to be the uneertainty., This process was repeated 100 times and the standard deviation was taken to be the uncertainty. + Naturally. Che resultant uncertainties are related to (he S/N of the spectra: uncertainties for the high-5/N spectra were much lower than the tvpical uncertainties found in the literature.," Naturally, the resultant uncertainties are related to the S/N of the spectra; uncertainties for the high-S/N spectra were much lower than the typical uncertainties found in the literature." + For (his reason. recent studies have sometimes smoothed their histograms to make them more directly comparable to past studies.," For this reason, recent studies have sometimes smoothed their histograms to make them more directly comparable to past studies." + S1ioothing the histogram also helps eliminate anv artificial substructure in the distribution created bv small number statistics. while additionally accounting for unidentified sources of uncertainty.," Smoothing the histogram also helps eliminate any artificial substructure in the distribution created by small number statistics, while additionally accounting for unidentified sources of uncertainty." + In Figure 4. the clusters are arranged in order of increasing metallicity. from left to right. top to bottom. and represent the 08(3839)N distribution on the RGB [ον each cluster.," In Figure \ref{figdcngenhist}, the clusters are arranged in order of increasing metallicity, from left to right, top to bottom, and represent the $\delta$ $_{\rm N}$ distribution on the RGB for each cluster." + Many of these clusters have been studied previously. so comparisons can be made with our present observations.," Many of these clusters have been studied previously, so comparisons can be made with our present observations." + reported a bimodal distribution in CN indices in M3 and M13 on the upper RGB (stars more Iuminous (han the IB)., reported a bimodal distribution in CN indices in M3 and M13 on the upper RGB (stars more luminous than the HB). + This observation lor M3 was confined on the upper RGB by ancl(1999)... and on the lower RGB of M3 by(1984).," This observation for M3 was confirmed on the upper RGB by and, and on the lower RGB of M3 by." +. also report. CN. bimodality among M13 RGB stars. and the proportions of CN-strong stars we observe in these (wo clusters agree well with those reported by(1981).," also report CN bimodality among M13 RGB stars, and the proportions of CN-strong stars we observe in these two clusters agree well with those reported by." +. M2 was studied by and shown to have a bimodal CN distribution. also matching in proportion io that seen in our data.," M2 was studied by and shown to have a bimodal CN distribution, also matching in proportion to that seen in our data." + Studies of MT1 bv (1982)..(2005).. and all report. CN. bimodality on the RGB.," Studies of M71 by , and all report CN bimodality on the RGB." + Evidence for bimodality is found in our data as well. at the same level as observed for 47 Tuc1979).. which is of," Evidence for bimodality is found in our data as well, at the same level as observed for 47 Tuc, which is of" +out that the true plateau from the continuum radiation is best observed in the y--band filter.,out that the true plateau from the continuum radiation is best observed in the -band filter. +" Since we are using the and I--filter, it is possible that the plateau phase does not exist in the R and J-bands due to the influence of the emission lines during the course of decline."," Since we are using the and -filter, it is possible that the plateau phase does not exist in the $R$ and $I$ -bands due to the influence of the emission lines during the course of decline." +" To summarize, we have classified 42 nova candidates and find to be S-class, to be C-class, to be O-class and to be J-class, while ? find to be S-class, to be C-class, to be O-class and to be J-class in their sample."," To summarize, we have classified 42 nova candidates and find to be S-class, to be C-class, to be O-class and to be J-class, while \cite{2010AJ....140...34S} find to be S-class, to be C-class, to be O-class and to be J-class in their sample." + Recurrent novae are potential supernovae progenitors (?).., Recurrent novae are potential supernovae progenitors \citep{2010ApJS..187..275S}. + We compare the position of our nova candidates with the catalog by ??.. ," We compare the position of our nova candidates with the catalog by \cite{2007A+A...465..375P, 2010AN....331..187P}." +We have found 4 recurrent novae candidates by selecting novae in the literature which are located within 1 arcsec to our nova candidates (see Table 8 and Fig. 11))., We have found 4 recurrent novae candidates by selecting novae in the literature which are located within 1 arcsec to our nova candidates (see Table \ref{tab.recurrent-nova} and Fig. \ref{fig.RNe}) ). +" Among the potential recurrent nova candidates N29 has 3 outbursts in 12 years, which would be an unprecedented short period."," Among the potential recurrent nova candidates N29 has 3 outbursts in 12 years, which would be an unprecedented short period." +" As pointed out by ?,, the outburst appears earlier in UV and Ha than in the R- which does not fit very well to the nova scheme."," As pointed out by \cite{2009ATel.2286....1H}, the outburst appears earlier in UV and $\alpha$ than in the $R$ -band which does not fit very well to the nova scheme." +" They thus suggest an alternative scheme, that this event could be a dwarf nova in the Milky Way."," They thus suggest an alternative scheme, that this event could be a dwarf nova in the Milky Way." + N19 has 4 outbursts detected so far., N19 has 4 outbursts detected so far. +" Because the short time separation between the first two outbursts, ? have doubted its nova nature and suggested it to be a U Gem type foreground Galactic dwarf nova."," Because the short time separation between the first two outbursts, \cite{1989SvAL...15..382S} have doubted its nova nature and suggested it to be a U Gem type foreground Galactic dwarf nova." +" However, the spectroscopic observations of the 4th outburst in 2010 (?) have confirmed it as a He/N spectroscopic class nova located in M31."," However, the spectroscopic observations of the 4th outburst in 2010 \citep{2010ATel.3006....1S} have confirmed it as a He/N spectroscopic class nova located in M31." +" In addition, ? have also reported the SSS turn-on ~ 15 days after the first optical detection in 2010."," In addition, \cite{2010ATel.3038....1P} + have also reported the SSS turn-on $\sim$ 15 days after the first optical detection in 2010." +" To test how likely an uncorrelated nova is falling into the 1 arcsec area, we perform a test by using the upper-right quarter of our pointing F1, which has the highest M31 light contribution from the bulge and contains 42 novae."," To test how likely an uncorrelated nova is falling into the 1 arcsec area, we perform a test by using the upper-right quarter of our pointing F1, which has the highest M31 light contribution from the bulge and contains 42 novae." +" The ratio of the area occupied by the 10 circle of these 42 novae to the total area of this quarter (300x300 arcsec”), implies the chance of an uncorrelated nova to coincide with an existing nova is low (1.5: 1000)."," The ratio of the area occupied by the $\farcs$ 0 circle of these 42 novae to the total area of this quarter $\times$ 300 $^2$ ), implies the chance of an uncorrelated nova to coincide with an existing nova is low (1.5: 1000)." + As most of the recurrent novae are not found in this quadrant (see Fig., As most of the recurrent novae are not found in this quadrant (see Fig. +" 4 and Table 8)), the chance of coincidence is even smaller for the majority of the recurrent nova candidates."," \ref{fig.all} and Table \ref{tab.recurrent-nova}) ), the chance of coincidence is even smaller for the majority of the recurrent nova candidates." +" Note that we use stricter selection criteria to search for recurrent novae, thus we have less candidates than presented by ??.. ?"," Note that we use stricter selection criteria to search for recurrent novae, thus we have less candidates than presented by \cite{2007A+A...465..375P, 2010AN....331..187P}." + suggested that recurrent novae all bear the plateau light curve., \cite{2006ApJS..167...59H} suggested that recurrent novae all bear the plateau light curve. +" However, in our light curve we did not detect evident plateaus."," However, in our light curve we did not detect evident plateaus." + The main reason is we do not have comprehensive coverage of the light curves., The main reason is we do not have comprehensive coverage of the light curves. +" Despite of the lack of highly sampled observation, it would be hard to find such plateaus because the light curves in or are contaminated bythe bright emission lines."," Despite of the lack of highly sampled observation, it would be hard to find such plateaus because the light curves in or are contaminated bythe bright emission lines." + ? thus advocate observations in Strómmgren y-band (centered at 547 nm) since it is designed to cut the strong emission lines in the wide V bandpass filter and can follow the continuum flux more accurately., \cite{2008ASPC..401..206H} thus advocate observations in Strömmgren $y$ -band (centered at 547 nm) since it is designed to cut the strong emission lines in the wide $V$ bandpass filter and can follow the continuum flux more accurately. +" However, the Strómmgren y-filter is narrow and requires longer exposure time, so we use the J-filter instead of the Strómmgren y-filter for the confirmation of microlensing event from achromaticity when the WeCAPP was initiated."," However, the Strömmgren $y$ -filter is narrow and requires longer exposure time, so we use the $I$ -filter instead of the Strömmgren $y$ -filter for the confirmation of microlensing event from achromaticity when the WeCAPP was initiated." + In this section we present the rate of decline for our nova sample., In this section we present the rate of decline for our nova sample. +" Due to the observing gaps before some of the apparent maxima, it is hard to recover the true maximum fluxes during the nova eruption."," Due to the observing gaps before some of the apparent maxima, it is hard to recover the true maximum fluxes during the nova eruption." +" Nevertheless, the apparent maxima can serve as a lower limit of the true maxima."," Nevertheless, the apparent maxima can serve as a lower limit of the true maxima." + One can derive upper limits for the {2 values (the time required for the nova to faint by two magnitudes) if the apparent maxima are taken as the true maxima., One can derive upper limits for the $t_2$ values (the time required for the nova to faint by two magnitudes) if the apparent maxima are taken as the true maxima. +" We have retrieved the t2 values for our sample as follows: we perform a linear fitting on the decline part of each light curve and determine the rate of decline, dm/dt (in units of magnitude/day)."," We have retrieved the $t_2$ values for our sample as follows: we perform a linear fitting on the decline part of each light curve and determine the rate of decline, dm/dt (in units of magnitude/day)." + We then use dm/dt to derive the t9 value relative to the observed maximum magnitude for all the novae., We then use dm/dt to derive the $t_2$ value relative to the observed maximum magnitude for all the novae. + The result is shown in Fig. 13.., The result is shown in Fig. \ref{fig.mmrd_all}. +" Besides the linear fitting, we also applied the universal decline law proposed by ? to retrieve the {ο value from the observed magnitude at the apparent maximum."," Besides the linear fitting, we also applied the universal decline law proposed by \cite{2006ApJS..167...59H} to retrieve the $t_2$ value from the observed magnitude at the apparent maximum." +" This procedure can only be done for 30 S-class novae, because the fitting routine fails to find a solution for other classes."," This procedure can only be done for 30 S-class novae, because the fitting routine fails to find a solution for other classes." + The result is shown in Fig. 14.. , The result is shown in Fig. \ref{fig.mmrd_s-class}. . +"The reader should keep in mind, that Fig."," The reader should keep in mind, that Fig." +" 13 or 14 does not give the exact MMRD relation, but serves as an upper limit in the {ο and lower limit in the magnitude."," \ref{fig.mmrd_all} or \ref{fig.mmrd_s-class} does not give the exact MMRD relation, but serves as an upper limit in the $t_2$ and lower limit in the magnitude." +Very-high-energy (££.z100 GeV) cosmic-ray | lose their energy rapidly via inverse Compton scattering and synchrotron radiation resulting in short cooling time and hence range.,Very-high-energy $E\gtrsim100$ GeV) cosmic-ray $^{1}$ lose their energy rapidly via inverse Compton scattering and synchrotron radiation resulting in short cooling time and hence range. + Therefore. they must come from a few nearby sources (Shen1970.Aharonianetal.1995.Kobayashi 2004)).," Therefore, they must come from a few nearby sources \cite{shen, AAV, Kobayashi}) )." + Recently. the ATIC collaboration reported the measurement of an excess in the electron spectrum (Changetal. 2008)).," Recently, the ATIC collaboration reported the measurement of an excess in the electron spectrum \cite{atic2}) )." + The excess appears as a peak in E P(E) where Φ is the differential electron flux: it can be approximated às a component with a power law index around 2 and a sharp cutoff around 620 GeV. Combined with the excess in the positron fraction neasured by PAMELA (Adrianietal. 2009)). the peak feature of the ATIC measurement has been interpreted in terms of a dark matter signal or a contribution of a nearby pulsar (e.g. Aalyshevetal.2009 and references given there).," The excess appears as a peak in $^3$ $\Phi$ (E) where $\Phi$ is the differential electron flux; it can be approximated as a component with a power law index around 2 and a sharp cutoff around 620 GeV. Combined with the excess in the positron fraction measured by PAMELA \cite{pamela}) ), the peak feature of the ATIC measurement has been interpreted in terms of a dark matter signal or a contribution of a nearby pulsar (e.g. \cite{Interpretation} and references given there)." + In the case of dark matter. the structure in the electron spectrum can be explained as caused by dark matter annihilation into low nultiplicity final states. while i the case of a pulsar scenario the structure arises from a competition between energy loss processes of pulsar electrons (which impose an energy cutoff depending on pulsar age) and energy-dependent diffusion (which favors high-energy particles in case of more distant The possibility to distinguish between a nearby electron source and a dark matter explanation with imaging atmospheric Cherenkov telescopes has been discussed by Hall&Hooper2008..," In the case of dark matter, the structure in the electron spectrum can be explained as caused by dark matter annihilation into low multiplicity final states, while in the case of a pulsar scenario the structure arises from a competition between energy loss processes of pulsar electrons (which impose an energy cutoff depending on pulsar age) and energy-dependent diffusion (which favors high-energy particles in case of more distant The possibility to distinguish between a nearby electron source and a dark matter explanation with imaging atmospheric Cherenkov telescopes has been discussed by \cite{hall}." + Imaging atmospheric Cherenkov telescopes have five orders of magnitude larger collectior areas than balloon and satellite experiments and can therefore measure TeV electrons with excellent statistics., Imaging atmospheric Cherenkov telescopes have five orders of magnitude larger collection areas than balloon and satellite experiments and can therefore measure TeV electrons with excellent statistics. + Hall anc Hooper assume that a structure in the electron spectrum should be visible even in the presence of a strong backgrounc of misidentified nucleonic cosmic rays., Hall and Hooper assume that a structure in the electron spectrum should be visible even in the presence of a strong background of misidentified nucleonic cosmic rays. + However. the assumption of a smooth background is oversimplified: 1 typical analyses the background rejection varies strongly with energy and without reliable control or better subtraction of the background. decisive results are difficult to achieve.," However, the assumption of a smooth background is oversimplified; in typical analyses the background rejection varies strongly with energy and without reliable control or better subtraction of the background, decisive results are difficult to achieve." + In a recent publication. the High Energy Stereoscopic System (H.E.S.S.) collaboration has shown that such a subtraction is indeed possible. reporting a measurement of the electron spectrum 1αυ] the range of 700 GeV to 5 TeV (Aharonianetal. 2008)).," In a recent publication, the High Energy Stereoscopic System (H.E.S.S.) collaboration has shown that such a subtraction is indeed possible, reporting a measurement of the electron spectrum in the range of 700 GeV to 5 TeV \cite{paper1}) )." + Here an eXtension of the H.E.S.S. measurement towards lower energies is presented. partially covering the range of the reported ATIC excess.," Here an extension of the H.E.S.S. measurement towards lower energies is presented, partially covering the range of the reported ATIC excess." + H.E.S.S. (Hinton2004)) is a system of four imaging atmospheric Cherenkov telescopes in Namibia., H.E.S.S. \cite{HESS}) ) is a system of four imaging atmospheric Cherenkov telescopes in Namibia. + While designed for the measurement of y-ray initiated air-showers. 1t can be used to neasure cosmic-ray electrons as well.," While designed for the measurement of $\gamma$ -ray initiated air-showers, it can be used to measure cosmic-ray electrons as well." + The basic properties of the analysis of cosmic-ray electrons with H.E.S.S. have been presented in. Aharonianetal., The basic properties of the analysis of cosmic-ray electrons with H.E.S.S. have been presented in \cite{paper1}. +2008... For the analysis. data from extragalactic fields (with a minimum of 7° above or below the Galactic plane) are used excluding any know! or potential y- ray source in order to avoid an almost indistinguishable y-ray contribution to the electron signal.," For the analysis, data from extragalactic fields (with a minimum of $^\circ$ above or below the Galactic plane) are used excluding any known or potential $\gamma$ -ray source in order to avoid an almost indistinguishable $\gamma$ -ray contribution to the electron signal." + As the diffuse extragalactic y-ray background ts strongly suppressed by pair creatior on cosmic radiation fields (Coppi&Aharonian1997)). its contribution to the measured flux can be estimatec following Coppi&Aharonian1997. to be less than 6%. assuming a blazar spectrum of an unbroken powerlaw up to 3 TeV with a Gausian spectral index distributior centered at F=—2.] with σι=0.35.," As the diffuse extragalactic $\gamma$ -ray background is strongly suppressed by pair creation on cosmic radiation fields \cite{BLLacs}) ), its contribution to the measured flux can be estimated following \cite{BLLacs} to be less than $6\%$, assuming a blazar spectrum of an unbroken powerlaw up to 3 TeV with a Gausian spectral index distribution centered at $\Gamma = -2.1$ with $\sigma_{\Gamma} = 0.35$." + For an improvec rejection of the hadronic background a Random Forest algorithm (Breiman&Cutler 2004)) 1s used., For an improved rejection of the hadronic background a Random Forest algorithm \cite{Forest}) ) is used. + The algorithm uses Image information to estimate the & of each event., The algorithm uses image information to estimate the $\zeta$ of each event. + Since some of the image parameters used to derive the € parameter are energy dependent. also ¢ depends on energy.," Since some of the image parameters used to derive the $\zeta$ parameter are energy dependent, also $\zeta$ depends on energy." + To derive an electron spectrum. a cut on Z of &£>0.6 is applied and the number of electrons is determined in independent energy bands by a fit of the distribution in Z with contributions of simulated electrons and protons.," To derive an electron spectrum, a cut on $\zeta$ of $\zeta > 0.6$ is applied and the number of electrons is determined in independent energy bands by a fit of the distribution in $\zeta$ with contributions of simulated electrons and protons." + The contribution of heavier nuclei is sufficiently suppressed for €>0.6 as not to play a role., The contribution of heavier nuclei is sufficiently suppressed for $\zeta>0.6$ as not to play a role. + The result does not depend on the particular choice of Zi., The result does not depend on the particular choice of $\zeta_\mathrm{min}$. + For an extension of the spectrum towards lower energies. the analysis has been modified to improve the sensitivity at low energies.," For an extension of the spectrum towards lower energies, the analysis has been modified to improve the sensitivity at low energies." + In the event selection cuts. the minimum image amplitude has been reduced from 200 to 80 photo electrons to allow for lower energy events.," In the event selection cuts, the minimum image amplitude has been reduced from 200 to 80 photo electrons to allow for lower energy events." + In order to guarantee good shower reconstruction. only events with a reconstructed distance from the projected core position on the ground to the array center of less than 100 m are included.," In order to guarantee good shower reconstruction, only events with a reconstructed distance from the projected core position on the ground to the array center of less than 100 m are included." + Additionally. only data taken between 2004 and 2005 are used.," Additionally, only data taken between 2004 and 2005 are used." + The reason is that the H.E.S.S. mirror reflectivity degrades over time and a reduced light yield corresponds to an increased energy threshold., The reason is that the H.E.S.S. mirror reflectivity degrades over time and a reduced light yield corresponds to an increased energy threshold. + The new data and event selection reduces the event statistics but enables to lower the analysis threshold to 340 GeV. The effective collection area at 340 GeV is z4x107 nj., The new data and event selection reduces the event statistics but enables to lower the analysis threshold to 340 GeV. The effective collection area at 340 GeV is $\approx 4 \times 10^{4}$ $^2$. + With a live-time of 77 hours of good quality data. a total effective exposure of =2.2x10’ méssrss is achieved at 340 GeV. Owing to the steepness of the electron spectrum. the measurement at lower energies is facilitated by the comparatively higher fluxes.," With a live-time of 77 hours of good quality data, a total effective exposure of $\approx 2.2\,\times\, 10^7$ $^{2}$ s is achieved at 340 GeV. Owing to the steepness of the electron spectrum, the measurement at lower energies is facilitated by the comparatively higher fluxes." + The Z distribution in the energy range of 340 to 700 GeV is shown in Fig. 1.., The $\zeta$ distribution in the energy range of 340 to 700 GeV is shown in Fig. \ref{fig1}. +deviation.,deviation. +" The amplitude of velocity perturbations is fixed by a constant injection rate of kinetic energy as in the prescription of Mac Low (1999), with the difference that we use a distinct random seed at each driving time."," The amplitude of velocity perturbations is fixed by a constant injection rate of kinetic energy as in the prescription of Mac Low (1999), with the difference that we use a distinct random seed at each driving time." +" The kinetic energy input rate is chosen as to approximately maintain a desired rms sonic Mach number M, which is expressed with respect to the sound speed at 104 K, c,=9.1 km s-!."," The kinetic energy input rate is chosen as to approximately maintain a desired rms sonic Mach number $M$, which is expressed with respect to the sound speed at $10^4$ K, $c_s=9.1$ km $^{-1}$." +" Note that dividing the box size by c,, we find a time unit of to=10.8 Myr."," Note that dividing the box size by $c_s$, we find a time unit of $t_0 = 10.8$ Myr." +" In all the simulations presented in §??,, the fluid is initially at the rest, the density and the temperature are uniform and have thermally unstable values (ng=1 επιὉ, Το=2399 K)."," In all the simulations presented in \ref{sec:results}, the fluid is initially at the rest, the density and the temperature are uniform and have thermally unstable values $n_0=1$ $^{-3}$, $T_0=2399$ K)." +" In this section we present results from one set of five simulations with 512? grid points and five different values of M namely 0.2, 0.6, 1.3, 4.0, and 4.5 (i.e from 0.41, 1.22, 2.65, 8.16, and 9.2 when computed with respect to the sound speed at the initial temperature)."," In this section we present results from one set of five simulations with $512^3$ grid points and five different values of $M$ namely 0.2, 0.6, 1.3, 4.0, and 4.5 (i.e from 0.41, 1.22, 2.65, 8.16, and 9.2 when computed with respect to the sound speed at the initial temperature)." + In Figure 1 column) we show two dimensional cuts of the density field for each simulation., In Figure \ref{fig:imagenes5} ) we show two dimensional cuts of the density field for each simulation. + Allthe images have been done with the same color scale., Allthe images have been done with the same color scale. +" As expected, lower M simulations show a smaller density contrast and sharper boundaries between dense regions and its surroundings, due to the relatively undisturbed development of TI."," As expected, lower $M$ simulations show a smaller density contrast and sharper boundaries between dense regions and its surroundings, due to the relatively undisturbed development of TI." +" The later behavior is better appreciated in Figure 2,, where different color scales have been used and where contours at temperatures delimiting the thermally unstable regime have been placed."," The later behavior is better appreciated in Figure \ref{fig:imagenes2}, where different color scales have been used and where contours at temperatures delimiting the thermally unstable regime have been placed." +" In this figure it also can be seen that for low M simulations, thermally unstable gas does just exist at the boundaries between gas at the two thermally stable regimes."," In this figure it also can be seen that for low $M$ simulations, thermally unstable gas does just exist at the boundaries between gas at the two thermally stable regimes." +" We denote by P,(k) the integrated power spectrum, i.e., the integral over spherical shells with radius &=|k| of the squared Fourier transform of the physical quantity a and for simplicity, we refer to P,(k) as the “Power Spectrum""."," We denote by $P_{a}(k)$ the integrated power spectrum, i.e., the integral over spherical shells with radius $k=|{\bf k}|$ of the squared Fourier transform of the physical quantity $a$ and for simplicity, we refer to $P_{a}(k)$ as the “Power Spectrum”." +" As usual, k=(kz,ky,kz) is the wave-vector."," As usual, ${\bf k}=(k_x,k_y,k_z)$ is the wave-vector." +" This convention is frequently used (e.g. Kim Ryu 2005, Kitsionas et al."," This convention is frequently used (e.g. Kim Ryu 2005, Kitsionas et al." +" 2009) but is not universal, sometimes (e.g. Hennebelle Audit 2007) the power spectrum is defined by the quantity pa(k)«k!~?P,(k), where D is the dimension of the distribution, which is the non integrated power spectrum."," 2009) but is not universal, sometimes (e.g. Hennebelle Audit 2007) the power spectrum is defined by the quantity $p_{a}(k)\propto k^{1-D}P_{a}(k)$, where $D$ is the dimension of the distribution, which is the non integrated power spectrum." +" For reference, for Kolmogorov turbulence py(k)οςk-H/? whereas Py(18)ος5/3,"," For reference, for Kolmogorov turbulence $p_{\bf v}(k)\propto k^{-11/3}$ whereas $P_{\bf v}(k)\propto k^{-5/3}$." + All the power spectra presented bellow are temporally averaged results., All the power spectra presented bellow are temporally averaged results. + The time intervals used for each simulation are listed in Table 3 in units of the corresponding turbulent crossing time tub., The time intervals used for each simulation are listed in Table \ref{tab:tiempos} in units of the corresponding turbulent crossing time $t_{\rm turb}$. +" We define tup=ltor/(Mcs) with lg,=ὄθρο being the characteristic scale of the turbulent forcing.", We define $t_{\rm turb}=l_{\rm for}/(M c_s)$ with $l_{\rm for}= 50$ pc being the characteristic scale of the turbulent forcing. + In this table we also present the final time reached by each simulation and the number of snapshots we use to compute the average., In this table we also present the final time reached by each simulation and the number of snapshots we use to compute the average. + In Figure 3 we present the Mach number as a function of time for the five simulations presented in next two sections., In Figure \ref{fig:machrms} we present the Mach number as a function of time for the five simulations presented in next two sections. +" The x-axis has to units in order to emphasize that, in these units, much longer integration times have been used for lower values of M."," The x-axis has $t_0$ units in order to emphasize that, in these units, much longer integration times have been used for lower values of $M$." +" In to units, the lower limit of the time interval used for averaging power spectra (i.e. the lower limit in the third column of Table 3)) corresponds to 10.0, 5.0, 2.3, 1.0, and 1.0 for M equal to 0.2, 0.6, 1.3, 4.0, and 4.5, respectively."," In $t_0$ units, the lower limit of the time interval used for averaging power spectra (i.e. the lower limit in the third column of Table \ref{tab:tiempos}) ) corresponds to 10.0, 5.0, 2.3, 1.0, and 1.0 for $M$ equal to 0.2, 0.6, 1.3, 4.0, and 4.5, respectively." + It can thus be seen from the figure that the power spectra have been averaged in a stationary regime., It can thus be seen from the figure that the power spectra have been averaged in a stationary regime. +" Time averaged density power spectra P,, are shown in Figure 4 along with power law least-squares fits computed for 41 and a probabilityof detecting a planet requires ο>2.2.," Assuming 24 two-dimensional observations equally spaced over the mission and an orbital period shorter than the mission duration, they found that a probability of detecting a planet requires $S \ge 1$ and a probabilityof detecting a planet requires $S \ge 2.2$." + The Sozzetti (2002) simulatious detect a planet when the best fit model with no planets can be rejected by a 47 test with confidence., The Sozzetti (2002) simulations detect a planet when the best fit model with no planets can be rejected by a $\chi^2$ test with confidence. + Since the target lists that we consider iuclude 120 to 1111 stars. a False alarm rate is unacceptably high.," Since the target lists that we consider include 120 to 1144 stars, a false alarm rate is unacceptably high." + We prefer to raise he detectionthreshold of Sozzetti (2002) by a factor 1.5. toS>3.3. which gives a negligible false alarm rate (770.15€ ). according ο Our Owl simulations.," We prefer to raise the detectionthreshold of Sozzetti (2002) by a factor $1.5$, to$S \ge 3.3$, which gives a negligible false alarm rate $\simeq0.1\%$ ), according to our own simulations." + According to the simulations of Sozzetti (2002). estimating tle mass and orbital parameters o within of the actual parameters for of the planets requires S>5.," According to the simulations of Sozzetti (2002), estimating the mass and orbital parameters to within of the actual parameters for of the planets requires $S \ge 5$." + To measure the mass of a planet accurate to within with probability requires Stox> , To measure the mass of a planet accurate to within with probability requires $S \ge 22$. +To measure the mass and orbital parameters to within 105€ with 95% probability requires $>33., To measure the mass and orbital parameters to within $10\%$ with $95\%$ probability requires $S \ge 33$. + We have couducted our own simulations. which verify the main fincines of Sozzetti (2002).," We have conducted our own simulations, which verify the main findings of Sozzetti (2002)." + We agree that ο>33 is required to measure the mass aud orbit: parameters to within LOY with ϱ probability., We agree that $S \ge 33$ is required to measure the mass and orbital parameters to within $10\%$ with $95\%$ probability. + We also find that the mass ancl orbital parameters Can be measured to within LO% with 50% probability when S26., We also find that the mass and orbital parameters can be measured to within $10\%$ with $50\%$ probability when $S \simeq 6$. + Thus. for many planets there is a significant chance that their orbits will be measured. even lor 59 significantly smaller than the thresholds given by Sozzetti (2002).," Thus, for many planets there is a significant chance that their orbits will be measured, even for $S$ significantly smaller than the thresholds given by Sozzetti (2002)." + We use our own simulations to estimate the probability of detecting or measuring the mass and/or orbital parameters for a given signal S (Ford 2003)., We use our own simulations to estimate the probability of detecting or measuring the mass and/or orbital parameters for a given signal $S$ (Ford 2003). + We approximate the probability ol detecting a planet or measuring its mass or orbital parameters based ou a fit with the fuuetional form p- where b. c. 2. and > are parameters obtained [roin fitting to the results of our own simulations aud are listed in table 1.," We approximate the probability of detecting a planet or measuring its mass or orbital parameters based on a fit with the functional form P = ], where $b$, $c$, $\beta$, and $\gamma$ are parameters obtained from fitting to the results of our own simulations and are listed in table 1." + Different values of these fit parameters are used depending on whether the probability is for detecting a planet. measuriug its mass aud orbital parameters with <30% accuracy. measuring its mass with <1066 accuracy. or measuring its mass and orbital parameters with <10% accuracy.," Different values of these fit parameters are used depending on whether the probability is for detecting a planet, measuring its mass and orbital parameters with $\le 30\%$ accuracy, measuring its mass with $\le 10\%$ accuracy, or measuring its mass and orbital parameters with $\le 10\%$ accuracy." + For orbital periods comparable to or longer than the mission lifetime (ήδη). the astrometri signature required for a detection or measurement iucreases.," For orbital periods comparable to or longer than the mission lifetime $P_{\mathrm{ML}}$ ), the astrometric signature required for a detection or measurement increases." +" To account for this effect we have divided our simulations according to the ratio of the planet's orbital period. £. to P, (see Table 1)."," To account for this effect we have divided our simulations according to the ratio of the planet's orbital period, $P_p$, to $P_{\mathrm{ML}}$ (see Table 1)." + We use different. values of 6. c. 2. aud 5 for each category.," We use different values of $b$ , $c$ , $\beta$ , and $\gamma$ for each category." + While it is clearly possible to detect the astrometric wobble iuduced by a planet with au orbital period much louger than the, While it is clearly possible to detect the astrometric wobble induced by a planet with an orbital period much longer than the +The behaviour of individual fast charged particles in magnetic turbulence is relevant (o a number of problems in plasma astrophvsies. from the solar wind (e.g.Bruno&Carbone2005) to interstellar medium (e.g.Elmegreen&Scalo2004). and cosmic ravs at highest energv (e.g.Fraschetti2008).,"The behaviour of individual fast charged particles in magnetic turbulence is relevant to a number of problems in plasma astrophysics, from the solar wind \citep[e.g.][]{bc05} to interstellar medium \citep[e.g.][]{es04} and cosmic rays at highest energy \citep[e.g.][]{f08}." +. Llowever. in contrast to cosmic ravs with energies bevond the GeV scale. a (thorough understanding of the particle transport properties can be attained only in interplanetary space. where measurements of both magnetic turbulence," However, in contrast to cosmic rays with energies beyond the GeV scale, a thorough understanding of the particle transport properties can be attained only in interplanetary space, where measurements of both magnetic turbulence" +unresolved LMXBs.,unresolved LMXBs. + If the ratio of LMXB X-ray emission to that of the gas is the same as that at kpe distances from the nucleus. based on Section 3.2 we would expect S+3% of the luminosity at keV (discounting that in PLI) to be from LMXBs. and our model fitting would be folding this into PL2.," If the ratio of LMXB X-ray emission to that of the gas is the same as that at kpc distances from the nucleus, based on Section \ref{sec:gasspectra} we would expect $8\pm 3$ of the luminosity at 0.3-2 keV (discounting that in PL1) to be from LMXBs, and our model fitting would be folding this into PL2." + However. since we measure PL2 to contribute 39+4% of the 0.3-2 keV luminosity (again discounting PLI). we consider it unlikely that LMXBs dominate the soft non-gaseous emission.," However, since we measure PL2 to contribute $39\pm 4$ of the 0.3–2 keV luminosity (again discounting PL1), we consider it unlikely that LMXBs dominate the soft non-gaseous emission." + This conclusion is also consistent with the luminosity function of ss LMXBs presented by Giordanoetal.(2003).., This conclusion is also consistent with the luminosity function of s LMXBs presented by \citet{giordano}. + Instead we focus on the evidence that PL? is jet related., Instead we focus on the evidence that PL2 is jet related. + We note that PL2 is detected in the ddata but is not separated from thermal emission in the larger PSF ofXMM-Newton., We note that PL2 is detected in the data but is not separated from thermal emission in the larger PSF of. +. A nominal extraction circle for point sources in iis 30 aresec in radius. and we can see the issue with reference to the spectral components in Fig.," A nominal extraction circle for point sources in is $30$ arcsec in radius, and we can see the issue with reference to the spectral components in Fig." + 7. by recognizing that an eextraetion would be like scaling the dotted line of the thermal emission up by a factor of ~600 relative to the dot-dashed line of PL2., \ref{fig:corespec} by recognizing that an extraction would be like scaling the dotted line of the thermal emission up by a factor of $\sim 600$ relative to the dot-dashed line of PL2. + This is a common difficulty for detecting relatively weak soft AGN components withXMAM-Newton., This is a common difficulty for detecting relatively weak soft AGN components with. +. For a similar reason. the early observations with the still larger PSFs of the PPSPC and ddid not find that the power-law emission (needed in addition to thermal gas) contains a component that is heavily absorbed.," For a similar reason, the early observations with the still larger PSFs of the PSPC and did not find that the power-law emission (needed in addition to thermal gas) contains a component that is heavily absorbed." + VLBI mapping of hhas found a parsec-scale radio jet and counterjet that are well aligned with their kpe-seale counterparts and. straddle an unresolved core (Jones&Wehrle1997)., VLBI mapping of has found a parsec-scale radio jet and counterjet that are well aligned with their kpc-scale counterparts and straddle an unresolved core \citep{jwehrle}. + The core has an inverted spectrum and varies in intensity by or more. whereas the scale jet emission is optically thin (Jonesetal.2001: 20013.," The core has an inverted spectrum and varies in intensity by or more, whereas the pc-scale jet emission is optically thin \citep{jones, piner}." + In observations at 5 GHz taken in 1999 the core had a flux density of ~50 mJy while the pe-sealejet and counterjet emission totalled ~300 mJy (Jonesetal.2001).," In observations at 5 GHz taken in 1999 the core had a 5-GHz flux density of $\sim +80$ mJy while the pc-scale jet and counterjet emission totalled $\sim +300$ mJy \citep{jones}." +. In the X-ray. PLI is ten times more luminous than PL2 but more highly absorbed.," In the X-ray, PL1 is ten times more luminous than PL2 but more highly absorbed." + It is logical to assume that it arises from a region no larger than the unresolved radio core measured with VLBI., It is logical to assume that it arises from a region no larger than the unresolved radio core measured with VLBI. + If we then take PL2 as primarily arising from the parsec-scale jet and counterjet. the ratio of radio to X-ray flux density is (3.5oe)107. in agreement with the value of ~LS.107 for the kpe-scale structures (Section 3.39).," If we then take PL2 as primarily arising from the parsec-scale jet and counterjet, the ratio of radio to X-ray flux density is $(3.5 +^{+0.6}_{-2.5}) \times 10^4$, in agreement with the value of $\sim 1.8 \times +10^4$ for the kpc-scale structures (Section \ref{sec:xjet}) )." + The validity of such a comparison rests on neither radio nor X-ray fluxes having varied by a large factor between measurements taken some years apart., The validity of such a comparison rests on neither radio nor X-ray fluxes having varied by a large factor between measurements taken some years apart. + While we cannot be sure of this. particularly since the separation between observations is comparable with the dynamical timescale of the component. we note that no X-ray variability is measured in PL? over 8 years.," While we cannot be sure of this, particularly since the separation between observations is comparable with the dynamical timescale of the component, we note that no X-ray variability is measured in PL2 over 8 years." + In Figure 8 we show the data for the jet and counterjet of Figure 5 in the form of a ratio of X-ray to radio emission. and have added a data-point at the core which uses X-ray counts from PL? and radio emission from the jet and counterjet.," In Figure \ref{fig:xrratio} we show the data for the jet and counterjet of Figure \ref{fig:xrprofile} in the form of a ratio of X-ray to radio emission, and have added a data-point at the core which uses X-ray counts from PL2 and radio emission from the pc-scale jet and counterjet." + Given that PL? is roughly 40 times brighter than an average jet and counterjet data point. it is remarkable that its ratio of X-ray to radio emission agrees as well as it does with the ratio for the extended emission.," Given that PL2 is roughly 40 times brighter than an average jet and counterjet data point, it is remarkable that its ratio of X-ray to radio emission agrees as well as it does with the ratio for the extended emission." + This supports the idea that ΡΙ arises from the pe-scale jet and counterjet through a mechanism similar to that operating on kpe scales., This supports the idea that PL2 arises from the pc-scale jet and counterjet through a mechanism similar to that operating on kpc scales. + We have estimated the counts and hardness ratio over 0.3 — 5 keV for component PL2., We have estimated the counts and hardness ratio over 0.3 – 5 keV for component PL2. + To do this we adopted the best-fitting model parameter values and used theFAKEIT task in with appropriate response files and exposures to simulate the counts in the bands 0.3-1 keV and 1—5 keV for the 2008 and 2000 observations. which we then combined.," To do this we adopted the best-fitting model parameter values and used the task in with appropriate response files and exposures to simulate the counts in the bands 0.3–1 keV and 1–5 keV for the 2008 and 2000 observations, which we then combined." + Uncertainties were estimated through further simulations that took into account the uncertainties in the model parameters in the spectral fit., Uncertainties were estimated through further simulations that took into account the uncertainties in the model parameters in the spectral fit. + As compared with the jet and counterjet. where bins of width 4.7 aresec and length 3 arcsec contain less than 100 counts (Fig. 59) ," As compared with the jet and counterjet, where bins of width 4.7 arcsec and length 3 arcsec contain less than 100 counts (Fig. \ref{fig:xrprofile}) )," +PL2 contains 1450 counts.," PL2 contains $\sim +1450$ counts." + The hardness ratio |0.31) is shown as the filled cirele with its error bar in Figure 6.., The hardness ratio $+0.31$ ) is shown as the filled circle with its error bar in Figure \ref{fig:hardness}. + It is noteworthy that the X-ray hardness is comparable to that of the inner parts of the resolved jet and counterjet. lending additional weight to the idea that PL2 represents the bright extension of the jets into the unresolved core.," It is noteworthy that the X-ray hardness is comparable to that of the inner parts of the resolved jet and counterjet, lending additional weight to the idea that PL2 represents the bright extension of the jets into the unresolved core." + In comparison the thermal emission is much softer: the hardness ratio in the thermal component in the core (using the same method as for PL2» is. 0.010.003. and the galaxy gus in the region defined in Section 3.2. has a hardness ratio of 0.51troi Cle errors).," In comparison the thermal emission is much softer: the hardness ratio in the thermal component in the core (using the same method as for PL2) is $-0.61\pm0.03$, and the galaxy gas in the region defined in Section \ref{sec:gasspectra} has a hardness ratio of $-0.51^{+0.03}_{-0.05}$ $1\sigma$ errors)." + Component PLI is much harder than PL2 due to high absorption. with few counts between 0.3 and | KeV. and so has a hardness ratio of |1.0.," Component PL1 is much harder than PL2 due to high absorption, with few counts between 0.3 and 1 keV, and so has a hardness ratio of $+1.0$." + We emphasize that PL? has an X-ray hardness ratio that follows the trend seen in the resolved jet., We emphasize that PL2 has an X-ray hardness ratio that follows the trend seen in the resolved jet. + Here we consider the radio and X-ray emission from the jet and counterjet. as extracted from the regions defined in Section 3.3..," Here we consider the radio and X-ray emission from the jet and counterjet, as extracted from the regions defined in Section \ref{sec:xjet}." +" A power-law extrapolation to higher frequencies of the radio emission. with a spectral index of a3€Pt,=0.56 (Wall&Pea-cock 1985)1.. falls above the X-ray emission. but consistency with the X-ray ean be found by applying a spectral break. o. of similar size in the jet and counterjet."," A power-law extrapolation to higher frequencies of the radio emission, with a spectral index of $\alpha^{5~\rm GHz}_{2.7~\rm GHz} = 0.56$ \citep{wall}, falls above the X-ray emission, but consistency with the X-ray can be found by applying a spectral break, $\Delta\alpha$, of similar size in the jet and counterjet." + Figure 9 shows the result of applying Aa=0.5. as expected for the simplest case of continuous injection where the electrons are losing energy by synchrotron radiation and inverse Compton scattering.," Figure \ref{fig:sed} shows the result of applying $\Delta\alpha=0.5$, as expected for the simplest case of continuous injection where the electrons are losing energy by synchrotron radiation and inverse Compton scattering." + The predictions for inverse-Compton X-ray emission are insensitive to the form of the electron spectrum at high energies. and we have estimated the minimum-energy magnetic field and the inverse Compton yield," The predictions for inverse-Compton X-ray emission are insensitive to the form of the electron spectrum at high energies, and we have estimated the minimum-energy magnetic field and the inverse Compton yield" +after the transition c,In the real Universe the local temperature of the radiation fluid fluctuates. +ompleted. is T doni —2M : This nucleatiou distance ," We decompose the local temperature $T(t,{\bf x})$ into the mean temperature $\bar{T}(t)$ and the perturbation $\delta T(t,{\bf x})$." +the spatialscale forbar," The temperature contrast is denoted by $\Delta +\equiv \delta T/ \bar{T}$ ." +von nunboer iuhomiogeucities. simulations setsthat real-world QCDthe density iust," On subhorizon scales in the radiation dominated epoch, each Fourier coefficient $\Delta(t,k)$ oscillates with constant amplitude, which we denote by $\Delta_T(k)$." + change Lattice rapidlyiu imply temperaturein interval. ασ n qu—5€ul. . (5)2 tu where tyτα = GM Sas)!2with thecucrey density phase.," Inflation predicts a Gaussian distribution, We find \cite{norm} for the COBE normalized \cite{Bennett} rms temperature fluctuation of the radiation fluid (not of cold dark matter) $\Delta_T^{\rm rms} = 1.0 \times 10^{-4}$ for a primordial Harrison-Zel'dovich spectrum." + This behaviorof thesound syspeedbeiug increases the nucleation distance becauseof the proportion," The change of the equation of state prior to the QCD transition modifies the temperature-energy density relation, $\Delta = c_s^2 \delta\varepsilon /(\varepsilon + p)$ ." +"ality Διx 1 [302 (T;)]τν, Iuthe thiucwall approximat", We may neglect the pressure $p$ near the critical temperature since $p \ll \varepsilon_{\rm q}$ at $T_{\rm c}$. +ionthe uncleation action has the following explicit expression: much , On the other hand the drop of the sound speed enhances the amplitude of the density fluctuations proportional to $c_s^{-1/2}$ \cite{SSW2}. +during supercoolne. thefollowing relationholdsfor the supercooliug and uucleatiouscales: AfiAtA.," Putting all those effects together and allowing for a tilt in the power spectrum, the COBE normalized rms temperature fluctuation reads where $k_0 = (aH)_0$." + gl23 Anni Tere we denoteby," For a Harrison-Zel'dovich spectrum $n=1$ ) and $3 c_s^2 = 0.1$ , we find $\Delta_T^{\rm rms} \approx 2 \times 10^{-5}$." + Aa relative (dimensionless) temperature intervalaud byAf a dimeusionful time," A small scale cut-off in the spectrum of primordial temperature fluctuations comes from collisional damping by neutrinos \cite{Weinberg,SSW2}." +" interval. S$= 5(€T,)", The interaction rate of neutrinos is $\sim G_{\rm F}^2 T^5$. + isthe critical nucleation action., This has to be compared with the angular frequency $c_s k_{\rm ph}$ of the acoustic oscillations. + 5 = O(100). Surface tension sipereooling isAy.= 2.3 «10 +.From Eq., At the QCD transition neutrinos travel freely on scales $l_{\nu} \approx 4 \times 10^{-6} d_{\rm H}$ . +(5))it followsthat Aq 1.5410.9. Substituting3c?= 0.1itoEq. (3)).," Fluctuations below the diffusion scale of neutrinos are washed out, In Ref." + we fiudAfime = 1.5 «10.Offor the durationofthe nucleation period. Thenucleation distance dependsouthe tuknown velocityejasdaEq. (2))., \cite{SSW2} the damping scale from collisional damping by neutrinos has been calculated to be $k^{\rm ph}_{\nu} = 10^4 H$ at $T=150$ MeV. The estimate \ref{diff}) ) is consistent with this damping scale. + Withthe value 0.1foreyoar., We assume $l_{\rm smooth} = 10^{-4} d_{\rm H}$. +thenucleation distancedanehom wouldhavethe value2.9& 10. 97g., The compression timescale for a homogeneous volume $\sim l_{\rm smooth}^3$ is $\delta t = \pi l_{\rm smooth}/c_s \sim 10^{-3} t_{\rm H}$. + One shouldtake these values with caution.due to large uncertaintiesin{ audo., Since $\delta t \gg \Delta t_{\rm nuc}$ the temperature fluctuations are frozen with respectto the time scale of nucleations. + Asour referenceset 6 |paranuetersswe take: Ay.1005 Anne 1059., As longas $l_{\rm smooth}$ exceeds the Fermi scale homogeneous bubble nucleation applies withinthese small homogeneous volumes. +Af 10fg, This is a +Af 10fg., This is a +not all lares studied by Aarnio require star-disk interaction. the longest flares in the COUP high-contrast flare saniple could be stablized by a circumstellar disk in (he scenario presented in 855.1.,"not all flares studied by Aarnio require star-disk interaction, the longest flares in the COUP high-contrast flare sample could be stablized by a circumstellar disk in the scenario presented in 5.1." +" We have already discussed (he bias in this sample towards high Iuminosity flares: these intense [lares on YSOs max be analogs to so-called ""superflares"" seen on magnelically active main sequence stars.", We have already discussed the bias in this sample towards high luminosity flares; these intense flares on YSOs may be analogs to so-called “superflares” seen on magnetically active main sequence stars. +" Schaefer (2000) apply the term 7superflare"" to flares will energies ranging from 10** to 10 eres on main sequence stars of spectral class F8 to Q8 with no close binary companion and no evidence [ον rapid rotation.", Schaefer (2000) apply the term “superflare” to flares with energies ranging from $10^{33}$ to $10^{38}$ ergs on main sequence stars of spectral class F8 to G8 with no close binary companion and no evidence for rapid rotation. + Osten (2007) reported the detection of an X-ray. superflare on the active binary system II Pegasi., Osten (2007) reported the detection of an X-ray superflare on the active binary system II Pegasi. + The II Peg superflare radiated 6x10° eres. the vast majoritv of which was radiated at energies less than 10 keV (see figure 4 of Osten 200T).," The II Peg superflare radiated $6 \times 10^{36}$ ergs, the vast majority of which was radiated at energies less than 10 keV (see figure 4 of Osten 2007)." + This value is comparable to the average energy radiated by flares in our sample. 1.66x10' eres.," This value is comparable to the average energy radiated by flares in our sample, $1.66 \times 10^{36}$ ergs." + It is thus tempting to draw an analogy between the YSO [Lares in our sample and supertlares like those reported on II Peg. aud so we can compare superllare characteristics (o our flare sample.," It is thus tempting to draw an analogy between the YSO flares in our sample and superflares like those reported on II Peg, and so we can compare superflare characteristics to our flare sample." + The reported II Peg superflare temperature is somewhat higher (han observed (not peak) temperatures in our sample: various model fits to II Peg vield flare temperatures between 118 and 152 MIN. consistent with the highest observed temperature in our sample of 126 + 30 MI.," The reported II Peg superflare temperature is somewhat higher than observed (not peak) temperatures in our sample: various model fits to II Peg yield flare temperatures between 118 and 152 MK, consistent with the highest observed temperature in our sample of 126 $\pm$ 30 MK." + The entire II Peg superflare only lasted for 11 ks. which is closer to (he average e-fold decay time of [Iare events in our sample. not their entire duration.," The entire II Peg superflare only lasted for 11 ks, which is closer to the average e-fold decay time of flare events in our sample, not their entire duration." +" Based on 6.4 keV emission. Osten report a loop length range of 0.5 — 1.3 2, for the superflare. which falls within the ranee of loop lengths observed in our sample. 0.2 — 3 R,."," Based on 6.4 keV emission, Osten report a loop length range of 0.5 $-$ 1.3 $R_{\star}$ for the superflare, which falls within the range of loop lengths observed in our sample, 0.2 $-$ 3 $R_{\star}$." +" Osten use n, of about 10"" 7. consistent with our sample's median plasma density of 1.2xLO! 7."," Osten use $n_e$ of about $10^{11}$ $^{-3}$, consistent with our sample's median plasma density of $1.2 \times 10^{11}$ $^{-3}$." + Using the values for plasma density. ancl observed. temperature reported by Osten et al..," Using the values for plasma density and observed temperature reported by Osten et al.," + equation 14 can be used (o estimate that the II Pee superflare is confined by a magnetic field of about 50 G. which is also consistent with the magnetic field strengths observed in our sample.," equation 14 can be used to estimate that the II Peg superflare is confined by a magnetic field of about 50 G, which is also consistent with the magnetic field strengths observed in our sample." + Finally. Osten estimate that superflares like the one on II Pegasi occur once every 5.4 montis. considerably more frequent than the value of one flare every three vears calculated in 844 [or our sample.," Finally, Osten estimate that superflares like the one on II Pegasi occur once every 5.4 months, considerably more frequent than the value of one flare every three years calculated in 4 for our sample." + Although similar flare characteristics do not guarantee identical Hare production mechanisms. if Il Peg max. be considered representative of superflares on other active MS stars. such superflares seem analogous to the flares in our sample.," Although similar flare characteristics do not guarantee identical flare production mechanisms, if II Peg may be considered representative of superflares on other active MS stars, such superflares seem analogous to the flares in our sample." +and 90 GIIz upgraded.OVRO observations. respectively.,"and 90 GHz upgraded observations, respectively." + Lastly. the contour labeled “SZA|OVRO is the result of simultaneously fitting all four uperaded OVRO aud SZA mock observations.," Lastly, the contour labeled “SZA+OVRO” is the result of simultaneously fitting all four upgraded OVRO and SZA mock observations." +" First. it ids obvious that the ""current mock observational data do not tightly— constrain and @. aud. furthermore. these parameters are stronely correlated. as found when modeling genuineBIMA/OVRO data (sec. c.g. Fig."," First, it is obvious that the “current” mock observational data do not tightly constrain $\beta$ and $\theta_c$ and, furthermore, these parameters are strongly correlated, as found when modeling genuine data (see, e.g., Fig." + Ὁ of Crego et al., 3 of Grego et al. +" 2000: Fie,", 2000; Fig. + 2 of Caceo ct al, 2 of Grego et al. + 2001)., 2001). + This 0.1iu eives us confidence that we have produced realistic mock. observations., This 0.1in gives us confidence that we have produced realistic mock observations. +" The huge degeneracy in the ;/0, plane is why a nuniber authors elect to use N-rav coustraiuts ou these parameters mstead or. iu the case of Reese et al. ("," The large degeneracy in the $\beta-\theta_c$ plane is why a number authors elect to use X-ray constraints on these parameters instead or, in the case of Reese et al. (" +2000: 2002). use a sinuultaueous fit to both N-rav and SZ effect data.,"2000; 2002), use a simultaneous fit to both X-ray and SZ effect data." +" However. data from the upcoming aud the uperadedOVRO array will be able to place muuch tighter coustraimts on these parameters (compare the ""OVRO aud ""SZÁ"" coutours with the ""current? contour)."," However, data from the upcoming and the upgraded array will be able to place much tighter constraints on these parameters (compare the “OVRO” and “SZA” contours with the “current” contour)." +" Note that the correlation between 2 aud 0, remains for the audOVRO ""data. but its size las been dramatically reduced."," Note that the correlation between $\beta$ and $\theta_c$ remains for the and “data”, but its size has been dramatically reduced." + A sinultaucous fit to both the aud uperadedOVRO data vields even better constraints on these parameters (shaded region)., A simultaneous fit to both the and upgraded data yields even better constraints on these parameters (shaded region). +" To get au idea of how well the future SZ effect data can constrain ivy. the cutropy floor level. we use the coufidence voluue (3. 0.. yy) for the “SZA|OVRO™ contour to ""measure yy and 5,444."," To get an idea of how well the future SZ effect data can constrain $K_0$, the entropy floor level, we use the confidence volume $\beta$, $\theta_c$ , $y_0$ ) for the “SZA+OVRO” contour to “measure” $y_0$ and $S_{\nu,arc}/f_{\nu}$." + The inferred statistical uncertaüntv associated with the central Compton parameter and integrated SZ effect fiux deusity within the central 1/ for this cluster is only about and155€. respectively.," The inferred statistical uncertainty associated with the central Compton parameter and integrated SZ effect flux density within the central $1\arcmin$ for this cluster is only about and, respectively." +" Comparing this to the predicted 5,/f,Yo relations (Figure 2 of MDIIDO3). it should. therefore. be possible to constrain the entropy floor level of this cluster to within 50-75 keV cii? or so."," Comparing this to the predicted $S_{\nu,arc}/f_{\nu}-y_0$ relations (Figure 2 of MBHB03), it should, therefore, be possible to constrain the entropy floor level of this cluster to within 50-75 keV $^2$ or so." + This is comparable with statistical uncertainties associated with N-ray mnieasurements of nearby clusters;, This is comparable with statistical uncertainties associated with X-ray measurements of nearby clusters. + This is remarkable considering that no N-rav “data” was used in the analysis aud the cluster Hes at ;=1., This is remarkable considering that no X-ray “data” was used in the analysis and the cluster lies at $z = 1$. + We also fud that reasonably accurate measurements of Ay are possible for clusters all he wav out to 2~2., We also find that reasonably accurate measurements of $K_0$ are possible for clusters all the way out to $z \sim 2$. + The aud upgradedOVRO array will be excellen ools for probing the non-gravitational cutropy of distau clusters., The and upgraded array will be excellent tools for probing the non-gravitational entropy of distant clusters. +" Because X-ray data will not be requires o coustrain the shapes of the SZ effect surface xiehtuess profiles of clusters observed with these Xauned interferometers. comparisons of data to predictec scalines (suchas S,,4:-/fp,—go) will provideindependent constraints on the properties of the iutracluster eas."," Because X-ray data will not be required to constrain the shapes of the SZ effect surface brightness profiles of clusters observed with these planned interferometers, comparisons of data to predicted scalings (such as $S_{\nu,arc}/f_{\nu}-y_0$ ) will provide constraints on the properties of the intracluster gas." + It wil hen also be possible to take advantage of the redslüft-independence of the SZ effect aud monitor the evolution of nou-gravitational processes in clusters right back to the epoch of cluster formation itself., It will then also be possible to take advantage of the redshift-independence of the SZ effect and monitor the evolution of non-gravitational processes in clusters right back to the epoch of cluster formation itself. + Up until now. measurements (both direct and imdirect) of the eutropv floors of massive galaxy clusters have been iuited to X-ray observations.," Up until now, measurements (both direct and indirect) of the entropy floors of massive galaxy clusters have been limited to X-ray observations." + Furthermore. these past X-rav studies have ecuecrally focused on nearby (2~0) clusters aud. as such. little is known about the evolution of he eutropy foor (aud the non-eravitational processes that xoduce it) with cosmuüc time.," Furthermore, these past X-ray studies have generally focused on nearby $z \sim 0$ ) clusters and, as such, little is known about the evolution of the entropy floor (and the non-gravitational processes that produce it) with cosmic time." + In the companion paper. we explored the extent to which the thermal Sunvaev-Zeldovich effect is modified by the presence of al eutropy Hoor.," In the companion paper, we explored the extent to which the thermal Sunyaev-Zeldovich effect is modified by the presence of an entropy floor." + Because it depends differently ou the temperature uid deusitv of ICAL and. also. because it ds redshitt-oeidependeut. the SZ effect could potentially be a very overful. iudependent test of the eutropy floors of even je most distant galaxy clusters.," Because it depends differently on the temperature and density of ICM and, also, because it is redshift-independent, the SZ effect could potentially be a very powerful, independent test of the entropy floors of even the most distant galaxy clusters." + The ceutral focus of the prescut paper was to compare our theoretical relations from MDIIDOS (iuncludiug one ji can potentially be measured through SZ effect observations ouly) to available high redshift SZ effect data your the literature to cetermune if the SZ effect data support the presence of au cutropy floor and. if so. how does the inferred level of that floor compare with that required to match local X-ray treuds.," The central focus of the present paper was to compare our theoretical relations from MBHB03 (including one that can potentially be measured through SZ effect observations only) to available high redshift SZ effect data from the literature to determine if the SZ effect data support the presence of an entropy floor and, if so, how does the inferred level of that floor compare with that required to match local X-ray trends." + This is the first time such a comparison has been done and we have made use of the largest compilation of high « SZ effect. clusters to date., This is the first time such a comparison has been done and we have made use of the largest compilation of high $z$ SZ effect clusters to date. + A detailed analvsis of seven differcut SZ effect scaling relations indicates that the cutropy floor in clusters with OIE2S078 is between 300 keV cum? 0$ )." +m, Let us consider the matching conditions for the perturbations at the front. +mi mms (mg. (πα.," The perturbation in the position of the front can be expressed as $\delta x_{f}\propto e^{i\,(k_{y}\,y-\omega\,t)}$, and thus the velocity perturbations normal and tangential to the front are given by The matching conditions of the front are perturbed version of mass and momentum flux conservation laws: We modify the equation \ref{PRH1}) ) for the following physical reasons." + m (—. um., The discontinuous-front approximation can be justified when we consider a perturbation whose wavelength is longer than the thickness of the front; the structure of the front is hardly deformed under such a perturbation. + πα (NEN μπα EENE EE | (7 ," Thus, the mass flux passing through the front will not changed, because it is determined by the structure of the front (eq. \ref{Q}) ))" +SSS NM α παπα παπα ὃοπα μα μα πα πα μπα 5 πα 5l M Ej," Substituting equations \ref{PL1}) \ref{PVT}) ) into equations \ref{PRH2}) \ref{PRH1b}) ), we obtain the characteristic equation where" +mean RLQRQQ black-hole mass difference in narrow luminosity bins (0.3 dex width) it was confirmed that the black-hole mass difference is consistent with a constant 0.16 dex off-set over the full luminosity range.,mean $-$ RQQ black-hole mass difference in narrow luminosity bins (0.3 dex width) it was confirmed that the black-hole mass difference is consistent with a constant 0.16 dex off-set over the full luminosity range. + The measured difference in mean black-hole mass between the RLQ and RQQ samples is predominantly due to fact that the FWHM of the low-ionization H.? and MgII emission lines of the RLQs are 20% larger than in the RQQs of the same optical luminosity., The measured difference in mean black-hole mass between the RLQ and RQQ samples is predominantly due to fact that the FWHM of the low-ionization $\beta$ and MgII emission lines of the RLQs are $\simeq 20\%$ larger than in the RQQs of the same optical luminosity. + The conclusion that ΕΙΩς exhibit broader low-ionization emission lines than RQQs is in good agreement with many previous studies (teg., The conclusion that RLQs exhibit broader low-ionization emission lines than RQQs is in good agreement with many previous studies (eg. + Boroson Green 1992: Corbin 1997: MeLure Dunlop 2002: Sulentic et al., Boroson Green 1992; Corbin 1997; McLure Dunlop 2002; Sulentic et al. + 2003)., 2003). + However. although the velocity-width difference between RLQs and RQOs has been noted previously. because of potential selection effects. attributing this directly to a difference in black-hole mass has been problematic.," However, although the velocity-width difference between RLQs and RQQs has been noted previously, because of potential selection effects, attributing this directly to a difference in black-hole mass has been problematic." + For example. given that the FWHM of low-ionization emission lines in RLQs are known to be influenced by viewing angle (Wills Browne 1986: Brotherton et al.," For example, given that the FWHM of low-ionization emission lines in RLQs are known to be influenced by viewing angle (Wills Browne 1986; Brotherton et al." + 1996). the velocity-width difference between RLQs and RQOSs could potentially be an orientation effect produced by comparing radio and optically selected samples.," 1996), the velocity-width difference between RLQs and RQQs could potentially be an orientation effect produced by comparing radio and optically selected samples." +" However. as discussed in Section 2. here both samples have been selected consistently by the SDSS ""gri colour algorithm. with targeted FIRST sources deliberately excluded."," However, as discussed in Section 2, here both samples have been selected consistently by the SDSS $ugri$ colour algorithm, with targeted FIRST sources deliberately excluded." + Combined with the excellent sample matching in terms of optical luminosity and redshift. the influence of potential orientation effects should therefore be minimized.," Combined with the excellent sample matching in terms of optical luminosity and redshift, the influence of potential orientation effects should therefore be minimized." + Consequently. the simplest interpretation of these new results is that at a fixed optical luminosity RLQs do. on average. harbour more massive black-holes than RQQs. accreting at a commensurately lower fraction of their Eddington limit.," Consequently, the simplest interpretation of these new results is that at a fixed optical luminosity RLQs do, on average, harbour more massive black-holes than RQQs, accreting at a commensurately lower fraction of their Eddington limit." +" Irrespective of the virial black-hole mass estimates presented here. it could reasonably be argued that the correlation between bulge and black-hole mass CM, Mig) and the well known A> relation for powerful radio galaxies (Lilly Longair 1984) immediately imply that RLQs should harbour black holes with masses 210""M..."," Irrespective of the virial black-hole mass estimates presented here, it could reasonably be argued that the correlation between bulge and black-hole mass $M_{bh}-M_{bulge}$ ) and the well known $K-z$ relation for powerful radio galaxies (Lilly Longair 1984) immediately imply that RLQs should harbour black holes with masses $\gtsim 10^{8}\Msun$." + The recent Willott et al. (, The recent Willott et al. ( +2003) study showed that the radio-galaxy fyz relation is consistent with the passive evolution of a 3£' elliptical formed at high redshift ἐς2 5).,2003) study showed that the radio-galaxy $K-z$ relation is consistent with the passive evolution of a $\simeq 3L^{\star}$ elliptical formed at high redshift $z\geq5$ ). + Therefore. if the predictions of orientation-based unification are correct. the host-galaxies of RLQs of comparable radio luminosity should have similar ἐν band luminosities.," Therefore, if the predictions of orientation-based unification are correct, the host-galaxies of RLQs of comparable radio luminosity should have similar $K-$ band luminosities." +" Notably. using the MeLure Dunlop (2002) fit to the AlinMig, relation. the mean black-hole mass of the RLQ sample corresponds to a A. band bulge luminosity of 3.8d:0.5"" (assuming a z=0 colour of ffA.=2.7: Bruzual Charlot 2003). in good agreement with the Willott et al."," Notably, using the McLure Dunlop (2002) fit to the $M_{bh}-M_{bulge}$ relation, the mean black-hole mass of the RLQ sample corresponds to a $K-$ band bulge luminosity of $3.8\pm0.5 L^{\star}$ (assuming a $z=0$ colour of $R-K=2.7$; Bruzual Charlot 2003), in good agreement with the Willott et al." + A—2 relation., $K-z$ relation. + Moreover. it is also interesting to compare the RLQ black-hole mass estimates derived here with those derived via host-galaxy luminosities for a complete sample of 41 20.5 radio galaxies by MeLure et al. ," Moreover, it is also interesting to compare the RLQ black-hole mass estimates derived here with those derived via host-galaxy luminosities for a complete sample of 41 $z\simeq 0.5$ radio galaxies by McLure et al. (" +2004).,2004). + Based on HST imaging of radio galaxies spanning the same range of radio luminosities as the current RLQ sample. the mean black-hole mass was determined to be =SSY+0.04. in excellent agreement with the mean black-hole mass of the RLQ sample derived here.," Based on HST imaging of radio galaxies spanning the same range of radio luminosities as the current RLQ sample, the mean black-hole mass was determined to be $<\log (M_{bh}/\Msun)>=8.87\pm0.04$, in excellent agreement with the mean black-hole mass of the RLQ sample derived here." + In addition to comparisons with radio galaxy studies. it is also possible to compare the black-hole mass difference between the RLQ and RQQ samples determined here with imaging studies of quasar host-galaxies.," In addition to comparisons with radio galaxy studies, it is also possible to compare the black-hole mass difference between the RLQ and RQQ samples determined here with imaging studies of quasar host-galaxies." + The most accurate quasar host-galaxy studies are those based on high-resolution HST imaging data (eg., The most accurate quasar host-galaxy studies are those based on high-resolution HST imaging data (eg. + Dunlop et al., Dunlop et al. + 2003: Schade et al., 2003; Schade et al. + 2000: Disney et al., 2000; Disney et al. + 1995)., 1995). + Among the various HST-based host galaxy studies. the Dunlop et al. (," Among the various HST-based host galaxy studies, the Dunlop et al. (" +2003) study has the advantage of featuring RLQ and RQQ samples which have well matched redshift - optical luminosity distributions.,2003) study has the advantage of featuring RLQ and RQQ samples which have well matched redshift - optical luminosity distributions. + Based on the results of this /?. band imaging study. the hosts of RLQs are typically 2O.4 mags brighter than their ΕΟΟ counterparts.," Based on the results of this $R-$ band imaging study, the hosts of RLQs are typically $\simeq 0.4$ mags brighter than their RQQ counterparts." +" Combining this with the MeLure Dunlop (2002) fit to the Mu,Mig, relation implies that RLQ and RQQ black-hole masses should differ by =0.2 dex. in good agreement with the virial-based results derived here."," Combining this with the McLure Dunlop (2002) fit to the $M_{bh}-M_{bulge}$ relation implies that RLQ and RQQ black-hole masses should differ by $\simeq 0.2$ dex, in good agreement with the virial-based results derived here." + In Fig 2. we plot both the radio-loudness 7 parameter and absolute radio luminosity versus black-hole mass for the RLQ and RQQ samples., In Fig \ref{fig2} we plot both the radio-loudness $\mathcal{R}$ parameter and absolute radio luminosity versus black-hole mass for the RLQ and RQQ samples. + In order to assess the significance of the apparent correlations in the presence of upper limits we have applied the generalized. Kendall's 7 test in the ASURV package (Isobe. Feigelson Nelson 1986).," In order to assess the significance of the apparent correlations in the presence of upper limits we have applied the generalized Kendall's $\tau$ test in the ASURV package (Isobe, Feigelson Nelson 1986)." +" The Kendall's 7 test detects a highly significant correlation in both cases. returning values of τς0.0497(7.60) andr =0.0697(11.40) forthe Δι and Lu;My, correlations respectively."," The Kendall's $\tau$ test detects a highly significant correlation in both cases, returning values of $\tau=0.0497\,\,(7.6\sigma)$ and $\tau=0.0697\,\, (11.4\sigma)$ for the $\mathcal{R}-M_{bh}$ and $L_{5GHz}-M_{bh}$ correlations respectively." + The detection of a signiticant correlation between black-hole mass and radio-loudness is in good agreement with the Lacy et al. (, The detection of a significant correlation between black-hole mass and radio-loudness is in good agreement with the Lacy et al. ( +2001) study of the combined FBQS+PG sample.,2001) study of the combined FBQS+PG sample. +" Furthermore. it can be seen from Fig 2aa that the RLQs are virtually exclusively confined to Mi,=10M... as previously found by Laor (2000). Lacy et al. ("," Furthermore, it can be seen from Fig \ref{fig2}a a that the RLQs are virtually exclusively confined to $M_{bh}\geq 10^{8}\Msun$, as previously found by Laor (2000), Lacy et al. (" +2001). Boroson (2002) and McLure Dunlop (2002).,"2001), Boroson (2002) and McLure Dunlop (2002)." +" Qualitatively. the fraction of RQOs with A7,10M. is 4c0.4. whereas the equivalent fraction of RLQs is only +1.0."," Qualitatively, the fraction of RQQs with $M_{bh}\leq 10^{8}\Msun$ is $9.2\% \pm 0.4$, whereas the equivalent fraction of RLQs is only $3.7\% \pm 1.0$." +" In fact. if the definition of radio-loud is restrictec to only those quasars with Lscra.>>107 !sr + only two objects have Ai,<107M. € 1%)."," In fact, if the definition of radio-loud is restricted to only those quasars with $L_{5GHz}>10^{24}$ $^{-1}$ $^{-1}$ only two objects have $M_{bh}\leq 10^{8}\Msun$ $<1\%$ )." + This result. combined with the radio galaxy fyz relation (e.g. Jarvis et al.," This result, combined with the radio galaxy $K-z$ relation (e.g. Jarvis et al." + 2001: Willot et al., 2001; Willott et al. + 2003). strengthens the claim that regardless of the exac nature of the black-hole mass - radio luminosity relationship in luminous quasars. sample selection based on high radio luminosity is effective in isolating the largest black holes. and presumably hos galaxies. at all epochs (eg.," 2003), strengthens the claim that regardless of the exact nature of the black-hole mass - radio luminosity relationship in luminous quasars, sample selection based on high radio luminosity is effective in isolating the largest black holes, and presumably host galaxies, at all epochs (eg." + MeLure 2003)., McLure 2003). +" In contrast to the results found here. we note that Woo Urry (2002) found no indication ofa RAZ), correlation in their study of a heterogeneous sample of 747 quasars in the redshift interval )€z«2.5."," In contrast to the results found here, we note that Woo Urry (2002) found no indication of a $\mathcal{R}-M_{bh}$ correlation in their study of a heterogeneous sample of 747 quasars in the redshift interval $0l)pz. where P pressure. p — deusitv. © specific internal cherey. + adiabatic iudex.," The flow of matter in this system can be described by Euler equations with equation of state for ideal gas $P=(\gamma-1)\rho\varepsilon$, where $P$ -- pressure, $\rho$ – density, $\varepsilon$ – specific internal energy, $\gamma$ – adiabatic index." + To mimic the radiative loss of enerev we adopt the value of + close to 1: 5=1.01. which corresponds to the near-isothermuc case (Sawada. Matsuda DHachisu+ sppd10986P3: Mpolteni.B rBelvedere Lauzafune 19910: Bisikalo et al.," To mimic the radiative loss of energy we adopt the value of $\gamma$ close to 1: $\gamma=1.01$, which corresponds to the near-isothermic case (Sawada, Matsuda Hachisu $^{\cite{spiral1}}$; Molteni, Belvedere Lanzafame $^{\cite{diego91}}$ ; Bisikalo et al." + 199704 )., $^{\cite{dima97}}$ ). +" To obtaiu the nunerical solution of the system of equations We use the RoeOsher TVD scheme of a high approximation order (Roe ""HP1986P3: Chakravarthy Osher- 1985[H1) with Eiufeldt modification (Eiufeld? 19511),", To obtain the numerical solution of the system of equations we used the Roe--Osher TVD scheme of a high approximation order (Roe $^{\cite{roe86}}$; Chakravarthy Osher $^{\cite{osher85}}$ ) with Einfeldt modification (Einfeldt $^{\cite{einfeldt88}}$ ). + The original svsteii of equations were writtenin a dimensionless form., The original system of equations were writtenin a dimensionless form. +" To do this. the spatial variables were normalized to the distance between the components ο, the time variables were normalized to the reciprocal angular velocity of the system ο,+, aud the deusifv was normalized to its value in the inner Lagrangian point L4."," To do this, the spatial variables were normalized to the distance between the components $A$, the time variables were normalized to the reciprocal angular velocity of the system ${\Omega}^{-1}$, and the density was normalized to its value in the inner Lagrangian point $L_1$." + The gas flow was simulated| over a parallelepipedon [odeAPSVode.ARALS[sssTL] (calculations were conducted only in the top halfspace).," The gas flow was simulated over a parallelepipedon $[\slantfrac{1}{2}A\ldots +\slantfrac{3}{2}A]\times[-\slantfrac{1}{2}A\ldots +\slantfrac{1}{2}A]\times[0\ldots \slantfrac{1}{4}A]$ (calculations were conducted only in the top half-space)." + The sphere with a radius of represeutius the accretor was cut out of the calculation domain., The sphere with a radius of $\slantfrac{1}{100}A$ representing the accretor was cut out of the calculation domain. +" The boundary aud the initial couditious were determined as follows: (1) we adopted free-outflow coucditious at the accretor and at the outer boundary of the caleulatiou conia: (1) on the first stage in eridpoiut corresponding to £4 we injected the matter with parameters p=ptL4). V,—c(L4). Vy=T= 0. whereο) is a gas speed of souud in Li poit: (i) for this stage we used rarefied ckeround eas with the following parameters po=102p(La). Py=10!ptEie?(hy)fs. Vy=0 as the initial couditious: (iv) on he secondstage when steady-state regime is reached at the moment of tino f=ty we decreased the deusity of the injected matter ο the value p—py."," The boundary and the initial conditions were determined as follows: (i) we adopted free-outflow conditions at the accretor and at the outer boundary of the calculation domain; (ii) on the first stage in gridpoint corresponding to $L_1$ we injected the matter with parameters $\rho=\rho(L_1)$, $V_x=c(L_1)$, $V_y=V_z=0$ , where$c(L_1)$ is a gas speed of sound in $L_1$ point; (iii) for this stage we used rarefied background gas with the following parameters $\rho_0=10^{-5}\cdot\rho(L_1)$, $P_0=10^{-4}\rho(L_1)c^2(L_1)/\gamma$, ${\bmath V}_0=0$ as the initial conditions; (iv) on the secondstage when steady-state regime is reached at the moment of time $t=t_0$ we decreased the density of the injected matter to the value $\rho=\rho_0$." +" The analysis of considered problemi shows hat the eas dyvnanidcal solutiou for the senüdetached dinary is defined bv. three dimensionless parameters (Bisikalo ct al. 1998503, 19990):"," The analysis of considered problem shows that the gas dynamical solution for the semidetached binary is defined by three dimensionless parameters (Bisikalo et al. $^{\cite{dima98b}}$, $^{\cite{dima99}}$;" +" Lubow Shu 197511 y he mass ratio gq=Mo/Mi. the Lubow-Shu paraleter €=(Ly)AO (Lubow Shu 19758 H5, and the adiabatic index. +."," Lubow Shu $^{\cite{lubowshu75}}$ ): the mass ratio $q=M_2/M_1$, the Lubow-Shu parameter $\epsilon=c(L_1)/A\Omega$ (Lubow Shu $^{\cite{lubowshu75}}$ ), and the adiabatic index $\gamma$." + The vahe of the adiabatie iudex was discussed. above and we used the value 5= 1.01., The value of the adiabatic index was discussed above and we used the value $\gamma=1.01$ . + Analysis of our previous results (Bisikalo et al., Analysis of our previous results (Bisikalo et al. + 190511. 19990shows that the madi characteristic features of 32D eas dynamical flow structure are qualitatively the same in wide range of parametersq aud e.," $^{\cite{dima98b}}$ ,$^{\cite{dima99}}$ )shows that the main characteristic features of 3D gas dynamical flow structure are qualitatively the same in wide range of parameters$q$ and $\epsilon$ ." + Therefore for the model simulation we chose them as follows: qEE —l.6€-—-_1 yy.," Therefore for the model simulation we chose them as follows: $q=1$ , $\epsilon=\slantfrac{1}{10}$ ." + To evaluae the influence of the viscosity ou the solution. several runs with cdiffereut spatial resolution were conducted.," To evaluate the influence of the viscosity on the solution, several runs with different spatial resolution were conducted." + The Euler, The Euler +ihe mass distribution in a galaxy ancl hence its dark matter content (e.g.. Degeman 1987. kent 1936. 1987. Geehan et al.,"the mass distribution in a galaxy and hence its dark matter content (e.g., Begeman 1987, Kent 1986, 1987, Geehan et al." + 2006)., 2006). + The thickness of the gas laver. on the other hand. depends on the vertical gravitational force and (races the potential perpendicular to the mid-plane (e.g.. Naravan Jog 2002 a).," The thickness of the gas layer, on the other hand, depends on the vertical gravitational force and traces the potential perpendicular to the mid-plane (e.g., Narayan Jog 2002 a)." + In this work. we use the rotation curves as well as (he radial distribution of the thickness of the III gas laver in the outer galaxy (o study the shape and density profile of the dark matter halo in M31.," In this work, we use the rotation curves as well as the radial distribution of the thickness of the HI gas layer in the outer galaxy to study the shape and density profile of the dark matter halo in M31." + In a disk plus bulge plus halo model of an external galaxy. the disk and the bulge can be mostly studied observationally.," In a disk plus bulge plus halo model of an external galaxy, the disk and the bulge can be mostly studied observationally." + Therefore. (he rotation curve and the verücal III scale height. data effectively complement each other to determine (he dark matter halo distribution of a galaxy uniquely.," Therefore, the rotation curve and the vertical HI scale height data effectively complement each other to determine the dark matter halo distribution of a galaxy uniquely." + In the past. the idea of studying the dark matter halo properties by using the outer ealactic ILE flaring data has been used to explore tha halos of NGC 4244 (Olling 1996). NGC 891 (Decquaert Combes 1997). and the Galaxy (Olline Merrifield 2000. 2001).," In the past, the idea of studying the dark matter halo properties by using the outer galactic HI flaring data has been used to explore tha halos of NGC 4244 (Olling 1996), NGC 891 (Becquaert Combes 1997), and the Galaxy (Olling Merrifield 2000, 2001)." + Llowever. the III seale height. distribution was mainlv used to constrain the oblateness of the halo. and not its other parameters such as the power-law index.," However, the HI scale height distribution was mainly used to constrain the oblateness of the halo, and not its other parameters such as the power-law index." + In some cases. the gas gravity and even the stellar eravily was ignored (Becquaert Combes 1997) in determining (he net ealactic potential. and hence (he gas scale height. distribution.," In some cases, the gas gravity and even the stellar gravity was ignored (Becquaert Combes 1997) in determining the net galactic potential, and hence the gas scale height distribution." + These issues were taken care of in determining (he Galactic halo parameters bv Naravan et al (2005)., These issues were taken care of in determining the Galactic halo parameters by Narayan et al (2005). + Using the gravitationallv-coupled. 3-component Galactic disk model (Naravan Jog 2002 b). various density profiles of the halo were investigated. and an attempt was made to obtain the halo parameters. which provided the best fit (in the least square sense) {ο the observed 111 scale height distribution.," Using the gravitationally-coupled, 3-component Galactic disk model (Narayan Jog 2002 b), various density profiles of the halo were investigated, and an attempt was made to obtain the halo parameters, which provided the best fit (in the least square sense) to the observed HI scale height distribution." + Finally. conformity with the shape of the observed rotation curves was used to remove the degeneracies in the best-fit values obtained bv the first constraint.," Finally, conformity with the shape of the observed rotation curves was used to remove the degeneracies in the best-fit values obtained by the first constraint." + Also. unlike some of the previous models. the sell-gravitv of the eas was included in (he analvsis.," Also, unlike some of the previous models, the self-gravity of the gas was included in the analysis." + From (heir study Naravan el al. (, From their study Narayan et al. ( +"2005) concluded (hat a spherical halo. with a densitw falling, off more rapidly than an isothermal halo. provides (he best fit to the available data.","2005) concluded that a spherical halo, with a density falling off more rapidly than an isothermal halo, provides the best fit to the available data." + This study was based on the HI scale heieht data (hen available upto 24 kpe from Wouterloot οἱ al. (, This study was based on the HI scale height data then available upto 24 kpc from Wouterloot et al. ( +1990).,1990). + Nalberla et al. (, Kalberla et al. ( +2007) have confirmed this by. using (heir recent extended II scale height data upto 40 kpc. and have also included a dark matter rine which (hev claim is needed (o explain the observed HI scale height distribution in the Galaxy.,"2007) have confirmed this by using their recent extended HI scale height data upto 40 kpc, and have also included a dark matter ring which they claim is needed to explain the observed HI scale height distribution in the Galaxy." + In (his paper. we apply the above approach to investigate the dark matter halo properties of the Andromeda galaxy (M31 or NGC 224).," In this paper, we apply the above approach to investigate the dark matter halo properties of the Andromeda galaxy (M31 or NGC 224)." + Here we use both the rotation curve and the LI scale height data as rigorous constraints simultaneously aud scan the entire parameter space svstematically so as to obtain the best-fit halo parameters., Here we use both the rotation curve and the HI scale height data as rigorous constraints simultaneously and scan the entire parameter space systematically so as to obtain the best-fit halo parameters. + In addition to (he various density profiles. we also (rv to fit. various shapes of the halo which was not done by Naravan et al. (," In addition to the various density profiles, we also try to fit various shapes of the halo which was not done by Narayan et al. (" +2005).,2005). + Earlier studies on M31 (Widrow et al., Earlier studies on M31 (Widrow et al. + 2003. Widrow Dubinski 2005. Geehan et al.," 2003, Widrow Dubinski 2005, Geehan et al." +the most important constrains on the stellar dynamo.,the most important constrains on the stellar dynamo. + Our results show the possibility of using helioseisnuc observations of the meridional circulation for the diagnostic purpose of the solar dynamo. because the dynamo properties significantly depends on the depth of the flow stagnation point.," Our results show the possibility of using helioseismic observations of the meridional circulation for the diagnostic purpose of the solar dynamo, because the dynamo properties significantly depends on the depth of the flow stagnation point." + This work was supported by NASA LWS NNN09AJ85G erant and partially by RFBR grant. 10-02-00148-a., This work was supported by NASA LWS NNX09AJ85G grant and partially by RFBR grant 10-02-00148-a. +svstem.,system. +" We define dimensionless variables via so that the svstem of equations (34)) becomes The boundary conditions at y=0 are r=re,q=f=O0.", We define dimensionless variables via so that the system of equations \ref{eq:RBODE}) ) becomes The boundary conditions at $\eta = 0$ are $r=r_{zz}=f=q=\theta = 0$ . + Solutions very close to the wall (9gx1) satisly: These simple relationships provide an ideal wav of calibrating each of the three constants C5. ος and ἐν individually (see Section. 3.4)). by analysing the power-law behaviour of the near-wall profiles of experimental or numerical data.," Solutions very close to the wall $(\eta \ll 1)$ satisfy: These simple relationships provide an ideal way of calibrating each of the three constants $C_\nu$, $C_{\nu\kappa}$ and $C_\kappa$ individually (see Section \ref{s:calibration}) ), by analysing the power-law behaviour of the near-wall profiles of experimental or numerical data." + Solutions far away from the boundary. laver. can be expanded as where l]lowever. unlike ry. f; and qo the constant £5 cannot be determined. without a numerical calculation. of the bouncary-laver solution for ηΞO(1).," Solutions far away from the boundary layer can be expanded as where However, unlike $r_0$, $f_1$ and $q_0$ the constant $\theta_0$ cannot be determined without a numerical calculation of the boundary-layer solution for $\eta = O(1)$." + The sealing laws obtained for rf. € and q far from the wall are expected on dimensional grounds. and recover the well-known solution of Priestlev (1954).," The scaling laws obtained for $r$, $f$, $\theta$ and $q$ far from the wall are expected on dimensional grounds, and recover the well-known solution of Priestley (1954)." + They are analogous to the universal “loe-law” solutions for turbulent shear Llows past a wall (e.g. Schlichting. 1979).," They are analogous to the universal “log-law” solutions for turbulent shear flows past a wall (e.g. Schlichting, 1979)." + ὃν comparing profiles of r. f and q with laboratory or numerical experiments. one can constrain some of the unknown coellicients. [C54 (see Section 3.4)).," By comparing profiles of $r$, $f$ and $q$ with laboratory or numerical experiments, one can constrain some of the unknown coefficients $\{C_i\}$ (see Section \ref{s:calibration}) )." + The heat [lux through the svstem in Bavleigh.Dénnard convection is commonly measured by the. cümensionless Nusselt’ number which compares the total heat Dux with the conductive, The heat flux through the system in Rayleigh–Bénnard convection is commonly measured by the dimensionless Nusselt number which compares the total heat flux with the conductive +ClussilO eniss10 enis curs enissbxl i102 Studies of optical emission lines in quasars have revealed strong correlations between emission line properties. that are possibly related to the central accreting black hole svstem.,"cmssi10 cmss10 cmr8 cmr8 cmssbx10 2 \def\ref{\par\noindent\hangindent 15pt} + = 12pt Studies of optical emission lines in quasars have revealed strong correlations between emission line properties, that are possibly related to the central accreting black hole system." + Boroson Cireen (1992) used the Bright Quasar Sample (BOS) and identified a set of optical emission line properties that vary together (optical Fell anc A5007 strengths. Lbs width and blue asymmetry). called the Boroson Creen cigenvector 1: (EVI).," Boroson Green (1992) used the Bright Quasar Sample (BQS) and identified a set of optical emission line properties that vary together (optical FeII and $\lambda 5007$ strengths, $\beta$ width and blue asymmetry), called the Boroson Green eigenvector 1 (EV1)." + Eigenvector 1l was found by Boller Drandt (1998) to correlate with properties (o. Loy).," Eigenvector 1 was found by Boller Brandt (1998) to correlate with X-ray properties $\alpha_x$, $_{2keV}$ )." + As the X-rays originate in the vicinity of the central black hole (at distances < 1001). hence eigenvector 1 is possibly linked to and. driven. by the central engine.," As the X-rays originate in the vicinity of the central black hole (at distances $< 100 R_{g}$ ), hence eigenvector 1 is possibly linked to and driven by the central engine." + To find the parameters of the central engine that drive cigenvector 1. we examined. first. objects with extreme EVI properties.," To find the parameters of the central engine that drive eigenvector 1, we examined first objects with extreme EV1 properties." + A class of Narrow-Line Sevíiert. 1 galaxies (NLSIs) is found to lie at the low IEV1 end of the Bright Quasar Sample studied by Boroson CGreen., A class of Narrow-Line Seyfert 1 galaxies (NLS1s) is found to lie at the low EV1 end of the Bright Quasar Sample studied by Boroson Green. + These objects exhibit. particularly narrow LL? line. of EWIIM E2000 Kms. strong Fell emission and /LL27 <3.," These objects exhibit particularly narrow $\beta$ line, of $ < $ 2000 km/s, strong II emission and $\beta$ $<$ 3." + Narrow Line Sevíiert. 1: galaxies. when compared. to typical AGN. show hotter and more pronounced. big blue bumps ancl steeper ray slopes.," Narrow Line Seyfert 1 galaxies, when compared to typical AGN, show hotter and more pronounced big blue bumps and steeper soft-X-ray slopes." + This can be explained due to higher ratios of their luminosity to the Eddington luminosity (ce. Pounds et al., This can be explained due to higher ratios of their luminosity to the Eddington luminosity (e.g. Pounds et al. + 1995). however there have also been attempts to explain the extreme properties and variability of the NLS1 class bv their high inclination angles to the line of sight (e.g. Brandt Gallagher. 2000).," 1995), however there have also been attempts to explain the extreme properties and variability of the NLS1 class by their high inclination angles to the line of sight (e.g. Brandt Gallagher, 2000)." + “Phis points towards either L/Lg or orientation as the primary driver of eigenvector 1., This points towards either $L/L_{Edd}$ or orientation as the primary driver of eigenvector 1. + For large accretion rates the matter of the accretion disk is more ionized. leading to an increase of the Ka line centroid energy above the neutral case value of 6.4 keV (sec Matt. Fabian Ross 1993. Zvveki," For large accretion rates the matter of the accretion disk is more ionized, leading to an increase of the $\alpha$ line centroid energy above the neutral case value of 6.4 keV (see Matt, Fabian Ross 1993, Żyycki" +(Qnean RAIS around 9%)). Q can be recovered with an accuracy better than (the accuracy on the RAIS is better than a lew %)).,"(mean RMS around ), Q can be recovered with an accuracy better than (the accuracy on the RMS is better than a few )." + llaving reconstructed the QPO Irequency evolution. one can compute the mean QPO parameters over (he observations. bv aligning all the 1G second PDS [or which a QPO frequency was estimated. directly. [rom a significant detection or by interpolation between (wo significant detections. separated by less (han 256 seconds. (see Figure 1)).," Having reconstructed the QPO frequency evolution, one can compute the mean QPO parameters over the observations, by aligning all the 16 second PDS for which a QPO frequency was estimated, directly from a significant detection or by interpolation between two significant detections, separated by less than 256 seconds, (see Figure \ref{fig1}) )." +" Increasing the latter value to καν, 512 seconds. does not lead to any changes in the fitted QPO parameters."," Increasing the latter value to say, 512 seconds, does not lead to any changes in the fitted QPO parameters." + The best fit results are listed in Table 1 and presented in Figure 2.., The best fit results are listed in Table \ref{tab1} and presented in Figure \ref{fig2}. + All the QPOs reported have a 422»5. and are therefore highlv significant.," All the QPOs reported have a $R>5$, and are therefore highly significant." + As can be seen from Figure 2.. despite some scatter. there is already evidence that above 800 IHIz the quality factor ancl (the RAIS amplitude of the QPO drops.," As can be seen from Figure \ref{fig2}, despite some scatter, there is already evidence that above 800 Hz the quality factor and the RMS amplitude of the QPO drops." + In addition to those hiehlv significant QPOs. we also note that there are hints for two additional single QPOs in the segments 93703-01-03-04 ancl 93703-01-05-06.," In addition to those highly significant QPOs, we also note that there are hints for two additional single QPOs in the segments 93703-01-03-04 and 93703-01-05-06." + No frequency drift corrections are possible for those two QPOs., No frequency drift corrections are possible for those two QPOs. + In (he first segment. v=905.0+4.4 114. Q=40.6419.3 lor an 2 ratio of2.9. whilein the second one v=548.8433.2. Q=2.741.6 for an £2 factor of --2.3.," In the first segment, $\nu=905.0\pm4.4$ Hz, $Q=40.6\pm19.3$ for an $R$ ratio of 2.9, while in the second one $\nu=548.3\pm33.2$, $Q=2.7\pm1.6$ for an $R$ factor of 2.3." + Being single and not very significant. it is difficult to draw any firm conclusions.," Being single and not very significant, it is difficult to draw any firm conclusions." + it cannot be excluded that thev are lower kllz QPOs. extending on both sides the frequency span of figure 2.. in which case one would expect them to have low Q [actors. as measured (with indeed the caveat that no drift correction could be applied. implving that the measured values are only lower limits on QQ).," However, it cannot be excluded that they are lower kHz QPOs, extending on both sides the frequency span of figure \ref{fig2}, in which case one would expect them to have low Q factors, as measured (with indeed the caveat that no drift correction could be applied, implying that the measured values are only lower limits on Q)." + The histogram of interpolated [requencies (measured over 16 seconds) is shown in Figure , The histogram of interpolated frequencies (measured over 16 seconds) is shown in Figure \ref{fig3}. +As can be seen. the frequency. span of the lower QPO. although comparable in breadth with other svstems. has not been sampled equally (there is a lack of observations around 50 111).," As can be seen, the frequency span of the lower QPO, although comparable in breadth with other systems, has not been sampled equally (there is a lack of observations around 750 Hz)." +" Grouping the data over constant frequency intervals is Cherefore not the optimum wav lo proceed,", Grouping the data over constant frequency intervals is therefore not the optimum way to proceed. + ae we have considered adjacent [requency intervals of varying widths. each including 200 QPO frequencies. allowing a better sampling of the peak of the equality factor versus frequency curve.," Instead we have considered adjacent frequency intervals of varying widths, each including 200 QPO frequencies, allowing a better sampling of the peak of the quality factor versus frequency curve." + The result is shown in Figure 4.., The result is shown in Figure \ref{fig4}. + As can be seen. the drops around 800 Lz of the QPO RAIS amplitude and quality factor are now much clearer ancl have significantly less scatter.," As can be seen, the drops around 800 Hz of the QPO RMS amplitude and quality factor are now much clearer and have significantly less scatter." + Thanks to our QPO tracking procedure. we can recover (he QPO Irequency on a (nmescale of 16 seconds. whereas Sannaetal.(2010) averaged as many 16 second PDS as required to enable a significant detection.," Thanks to our QPO tracking procedure, we can recover the QPO frequency on a timescale of 16 seconds, whereas \citet{sanna10mnras} averaged as many 16 second PDS as required to enable a significant detection." + This explains why on average we eel larger Q factors (han Sannaetal.(2010).. and hence a better description of its lrequency dependence.," This explains why on average we get larger Q factors than \citet{sanna10mnras}, and hence a better description of its frequency dependence." + Following Sannaetal.(2010).. we have shifted all (he 16 second PDS to search for the upper kllz QPO.," Following \citet{sanna10mnras}, we have shifted all the 16 second PDS to search for the upper kHz QPO." + Sannaetal.(2010) reported a 3.16. significance detection (single trial) with a frequency. separation of 25819 Iz.," \citet{sanna10mnras} + reported a $3.1\sigma$ significance detection (single trial) with a frequency separation of $258\pm 13$ Hz." + Using our procedure. (he significance of the," Using our procedure, the significance of the" +disentangle disk structure Irom opacity effects.,disentangle disk structure from opacity effects. + Both TW Iva aud ID 100546 will be prime protoplanetarv disk targets for the Atacama Large. Millimeter. Array. the next generation millimeter interferometer sited in northern Chile. whose construction has just started. and will continue for the next decade.," Both TW Hya and HD 100546 will be prime protoplanetary disk targets for the Atacama Large Millimeter Array, the next generation millimeter interferometer sited in northern Chile, whose construction has just started and will continue for the next decade." + We thank an anonvimous referee lor several suggestions that improved this paper., We thank an anonymous referee for several suggestions that improved this paper. + The Australia Telescope Compact Array. is part of the Australia Telescope. which is funded by ihe Commonwealth of Australia for operation as a national facility managed by CSIRO.," The Australia Telescope Compact Array is part of the Australia Telescope, which is funded by the Commonwealth of Australia for operation as a national facility managed by CSIRO." + Partial support for this work was provided by NASA Origins of Solar Svstems Program Grant NÀG5-L1777. bv the NRAO Foreign. Telescope Travel Fund. Program. by a NOVA ne(work 2 erant and a NWO-Spinoza grant.," Partial support for this work was provided by NASA Origins of Solar Systems Program Grant NAG5-11777, by the NRAO Foreign Telescope Travel Fund Program, by a NOVA network 2 grant and a NWO-Spinoza grant." + CMW acknowledges support of an Australian Research Council Fellowship., CMW acknowledges support of an Australian Research Council Fellowship. +eurow Line Sevfert 1 (NLSv1) are AGN with optical spectral properties similar to those of Sevfert 1. galaxies (Broad. Line Sevfert 1. BLSy1). except for having narrow Balmer lines ancl strong optical Fell lines (Osterbrock VETEgee 1985).,"Narrow Line Seyfert 1 (NLSy1) are AGN with optical spectral properties similar to those of Seyfert 1 galaxies (Broad Line Seyfert 1, BLSy1), except for having narrow Balmer lines and strong optical FeII lines (Osterbrock Pogge 1985)." + The classical definition of NLSv1 (Goodrich 1989) relies on three simple criteria: (1) the full width half maximum. (EWI) of the H1; line < 2000 km (ii) he OLLI] A5007/11; ratio <3: and (iii) unusually strong Fell., The classical definition of NLSy1 (Goodrich 1989) relies on three simple criteria: (i) the full width half maximum (FWHM) of the $_\beta$ line $<$ 2000 km $^{-1}$; (ii) the [OIII] $\lambda$ $_\beta$ ratio $<$ 3; and (iii) unusually strong FeII. + Phe NLSy1 and DLSy1 classes are not. conipletely distinct. for instance Vérron-C'etty Vérron (2006) notice a continuity between their optical spectral properties.," The NLSy1 and BLSy1 classes are not completely distinct, for instance Vérron-Cetty Vérron (2006) noticed a continuity between their optical spectral properties." + The most extreme characteristics of NLSy1I are seen in 10 X-ray domain (Gallo 2006)., The most extreme characteristics of NLSy1 are seen in the X-ray domain (Gallo 2006). + A strong and. variable sof excess enission below -—1 keV (George et al., A strong and variable soft excess emission below $\sim$ 1 keV (George et al. + 2000. Boller et al.," 2000, Boller et al." + 1996. Turner ct al.," 1996, Turner et al." + 1999) is more frequently. presen than in BLSvl (Leighly 1999)., 1999) is more frequently present than in BLSy1 (Leighly 1999). + Phe 2-10 keV spectral slope is usually stecper in NLSy1 with respect to BLSvl (Leighly 1999. Brandt et al.," The 2-10 keV spectral slope is usually steeper in NLSy1 with respect to BLSy1 (Leighly 1999, Brandt et al." + 1997) anda sharp spectral drop at abou 7 keV has been observed in some objects (Uttley et al., 1997) and a sharp spectral drop at about 7 keV has been observed in some objects (Uttley et al. + 2004. Longinotti et al.," 2004, Longinotti et al." + 2003. Boller et al.," 2003, Boller et al." + 2003. Boller et al.," 2003, Boller et al." + 2002)., 2002). + The complex NLSy1 A-ray spectrum has been explained in terms of relativistic blurred. disc rellection (c.g.. Fabian et al.," The complex NLSy1 X-ray spectrum has been explained in terms of relativistic blurred disc reflection (e.g., Fabian et al." + 2004) or ionized or neutral absorption either totally or partially covering the X-ray source (e.g. Gierlifsski Done 2004. “Tanaka ct al.," 2004) or ionized or neutral absorption either totally or partially covering the X-ray source (e.g., Gierlińsski Done 2004, Tanaka et al." + 2004)., 2004). +The reionisation of cosmic hyelrogen is commonly believed to have been due to UV photons produced by the first stars and quasars and was an important milestone in the history of the Universe (e.g...2)..,"The reionisation of cosmic hydrogen is commonly believed to have been due to UV photons produced by the first stars and quasars and was an important milestone in the history of the Universe \citep[e.g.,][]{bl2001}." + Relonisation starts with isolated regions of ionised hydrogen )) forming around. ealaxies and quasars. which later grow and merge. to. surround clusters of galaxies.," Reionisation starts with isolated regions of ionised hydrogen ) forming around galaxies and quasars, which later grow and merge to surround clusters of galaxies." + The reionisation process is complete when these regions overlap ancl fill the volume between galaxies., The reionisation process is complete when these regions overlap and fill the volume between galaxies. + Various experiments are currently underway to measure 21-cm emission from the pre-overlap intergalactic medium. (IGND. and. thus observe the evolution of the ionisation stucture directly., Various experiments are currently underway to measure 21-cm emission from the pre-overlap intergalactic medium (IGM) and thus observe the evolution of the ionisation stucture directly. + These experiments include the Low Frequency LOEAR]. the Murchison Widelicld (AIWA) and the Precision Array to Probe Epoch of (PAPER).," These experiments include the Low Frequency [LOFAR], the Murchison Widefield (MWA) and the Precision Array to Probe Epoch of (PAPER)." + Several probes of the reionisation epoch in redshifted 2i-em emission have been suggested. which include: observation of emission as a function of redshift averaged over a large area of skv: imaging of individual regions: observation of the power spectrum of. fluctuations.," Several probes of the reionisation epoch in redshifted 21-cm emission have been suggested, which include: observation of emission as a function of redshift averaged over a large area of sky; imaging of individual regions; observation of the power spectrum of fluctuations." + Observing emission as a function of redshift averaged. over a large area of sky provides a direct. probe of the evolution in the neutral fraction of the IGM. ancl is referred. to as he global step (???)..," Observing emission as a function of redshift averaged over a large area of sky provides a direct probe of the evolution in the neutral fraction of the IGM, and is referred to as the global step \citep{shaver1999,gnedin2004,furl2006a}." + Observation of individual regions in the image regime will probe quasar physics as well as the evolution of the neutral gas (???)..," Observation of individual regions in the image regime will probe quasar physics as well as the evolution of the neutral gas \citep{wl2004b,kohler2005,geil2008}." + Lhe most promising probe is the observation of the power spectrum of luctuations together with its evolution in redshift (sce.e.g. 7)..," The most promising probe is the observation of the power spectrum of fluctuations together with its evolution in redshift \citep[see, e.g.,][]{furl2006b}." + This observation would. trace the evolution of neutral eas with redshift as well as the topology of the reionisation »wocess via the spatial dependence of the statistics of recshifted: 21-cm. lluctuations (e.g..?2???7?)..," This observation would trace the evolution of neutral gas with redshift as well as the topology of the reionisation process via the spatial dependence of the statistics of redshifted 21-cm fluctuations \citep[e.g.,][]{tozzi2000,furl2004b,loeb2004,iliev2006,wm2007}." + In this paper we focus on the statistical signature of reionisation in 21-cm DOWEL spectra., In this paper we focus on the statistical signature of reionisation in 21-cm power spectra. + Due to theoretical uncertainties anc oa lack of observational evidence the exact role quasars play in the reionisation process is uncertain., Due to theoretical uncertainties and a lack of observational evidence the exact role quasars play in the reionisation process is uncertain. + Although relatively shor lived. (ἐν~LO?7 vvr) (see.eg.?.forareview). i is inferred. that. luminous quasars radiate close to. their Eddington limit (2). such that the ionising photon emission rate of Luminous quasars can be ~LO’ ss.1.," Although relatively short lived $t_{\rm q} \sim 10^{6-8}$ yr) \citep[see, e.g.,][for a review]{martini2004}, it is inferred that luminous quasars radiate close to their Eddington limit \citep[][]{kollmeier2006} such that the ionising photon emission rate of luminous quasars can be $\sim 10^{57}$ $^{-1}$." +" ""Phe observe quasar population cid not supply sullicent UV. photons to reionise the Universe at. z6 (e.g.777) even though quasars dominate the production. of ionising photons a 2<3."," The observed quasar population did not supply sufficent UV photons to reionise the Universe at $z > 6$ \citep[e.g.,][]{fan2001,dijkstra2004b,meiksin2005} even though quasars dominate the production of ionising photons at $z \lsim\,\,3$." + However. luminous quasars are known to exist at the edge of the reionisation epoch (?)..," However, luminous quasars are known to exist at the edge of the reionisation epoch \citep{fan2006}." + Moreover. these high-redshift quasars have a larec clustering bias (7).. implving that the ellect of their ionising contribution on the statistical signature of the epoch of reionisation may be significant," Moreover, these high-redshift quasars have a large clustering bias \citep{shen2007}, implying that the effect of their ionising contribution on the statistical signature of the epoch of reionisation may be significant" + (e.c.Richetal.2001). Brownctal.(2001a) Telescope GIST).," \citep[e.g.,][]{rich01} \citet{brown04a} )." + Iu general. ages of extragalactic star chusters are obtained by comparing integrated plotometry with models of simple stellar populations (SSPs).," In general, ages of extragalactic star clusters are obtained by comparing integrated photometry with models of simple stellar populations (SSPs)." + For exanrples. Maetal.(2001.2002a.b.c) and Jianectal.(2003). estimated ages for star clusters in ΑΠΟ aud ADU by comparing the SSP models of DC96 (Bruzual Charlot 1996. unpublished) with thei integrated photometric imeasurcments in the Beijine-Arizoua-Taiwan-Connecticut (BATC) photometric svstei deCaisetal.(2008a) determined ages and masses of star clusters iu the fossil starburst region D of M82 bv comparing thei observed cluster spectral energv distributions (SEDs) with the model predictions for au instantaneous burst of star formation (secalsodeCuijsetal. 200500)...," For examples, \citet{Ma01,Ma02a,Ma02b,Ma02c} and \citet{jiang03} estimated ages for star clusters in M33 and M31 by comparing the SSP models of BC96 (Bruzual Charlot 1996, unpublished) with their integrated photometric measurements in the Beijing-Arizona-Taiwan-Connecticut (BATC) photometric system; \citet{degrijs03a} determined ages and masses of star clusters in the fossil starburst region B of M82 by comparing their observed cluster spectral energy distributions (SEDs) with the model predictions for an instantaneous burst of star formation \citep[see also][]{degrijs03b,degrijs03c}." + Bisetal.(2003). and Bastianctal.(2005) derived ages. initial masses aud extinctions of AISI star cluster candidates by fitting SSP uodels (Leithereretal.1999). to their observed SEDs in six broad-baud aud two narrow-band filters from the Wide Field Planctary Camera-2 (WEPC2) onboard theHST.," \citet{bik03} and \citet{bastian05} + derived ages, initial masses and extinctions of M51 star cluster candidates by fitting SSP models \citep{Leitherer99} to their observed SEDs in six broad-band and two narrow-band filters from the Wide Field Planetary Camera-2 (WFPC2) onboard the." + Mactal.(20062). estinate ages aud inetallicities or 33 ΑΙΟΙ GCs by comparing between BCO3 models (Druzual&Charlot2003) and their BATC iulti-band photometric data., \citet{Ma06a} estimate ages and metallicities for 33 M31 GCs by comparing between BC03 models \citep{bru03} and their BATC multi-band photometric data. + Maetal.(2006b) derived the age and reddening value of the AIL GC 037-D327 based ou photometric aud BCO3 mceasureimoeuts in a large umber of broad- aud intermediate-band from the optical to the, \citet{Ma06b} derived the age and reddening value of the M31 GC 037-B327 based on photometric and BC03 measurements in a large number of broad- and intermediate-band from the optical to the +Kulkarni 1998).,Kulkarni 1998). + When the previously assumed constant component is removed. the overall light curve Is concave. in disagreement with a jet interpretation.," When the previously assumed constant component is removed, the overall light curve is concave, in disagreement with a jet interpretation." + If the last detection is interpreted as a different phenomenon (Kulkarni. 1999) then the remaining points show a rapid decline - 1n agreement with a jet.," If the last detection is interpreted as a different phenomenon (Kulkarni, 1999) then the remaining points show a rapid decline - in agreement with a jet." + In both GRB970228 and GRB970508 there was no observed break in the light curve as long as the afterglow could be observed., In both GRB970228 and GRB970508 there was no observed break in the light curve as long as the afterglow could be observed. + GRB970228 was observed byHST six months later. at which point it was still following a power-law decay as [17955 (Fruchter et al.," GRB970228 was observed by six months later, at which point it was still following a power-law decay as $t^{-1.14 \pm 0.05}$ (Fruchter et al." + 1998)., 1998). + GRB970508 was observed for 9 months to decline as ΓΙή (Zharikov et al..," GRB970508 was observed for 9 months to decline as $t^{-1.23 \pm 0.04}$ (Zharikov et al.," + 1998). at which point became as faint as its host galaxy.," 1998), at which point became as faint as its host galaxy." + This set a limit on the beaming in these events of (o71., This set a limit on the beaming in these events of $\theta _{0}\ge 1$. + The beaming factor is therefore less than an order of magnitude., The beaming factor is therefore less than an order of magnitude. + We have seen indication of a jet-like behavior in. three bursts., We have seen indication of a jet-like behavior in three bursts. + Two other bursts did not show any break in their optical light curves which have been observed for a long time., Two other bursts did not show any break in their optical light curves which have been observed for a long time. + In several other bursts the situation is inconclusive and their short afterglow is consistent with rather narrow jets., In several other bursts the situation is inconclusive and their short afterglow is consistent with rather narrow jets. + We suggest that jet-like behavior is the common one in GRBs., We suggest that jet-like behavior is the common one in GRBs. + Moreover. the range of possible beaming angles. from for GRB 980519. to 0~0.1 for GRB 990123 to 0>| for GRB 970228 and GRB 970508 is quite large.," Moreover, the range of possible beaming angles, from $\theta _{0}\le +0.1$ for GRB 980519, to $\theta \sim 0.1$ for GRB 990123 to $\theta \ge 1$ for GRB 970228 and GRB 970508 is quite large." +" These beaming angles are consistent with the limits set by searches for ""Orphan"" radio (Perna and Loeb. 1998) and X-ray (Grindlay 1999) afterglows."," These beaming angles are consistent with the limits set by searches for “Orphan” radio (Perna and Loeb, 1998) and X-ray (Grindlay 1999) afterglows." + The suggestion that GRBs are beamed has several implications., The suggestion that GRBs are beamed has several implications. +" First. this implies that the GRB ""inner engines? must include a collimation mechanism in addition. to. the required acceleration mechanism."," First, this implies that the GRB “inner engines” must include a collimation mechanism in addition to the required acceleration mechanism." + This makes the similarity between GRBs and some AGNs. more specifically Blazars. even greater.," This makes the similarity between GRBs and some AGNs, more specifically Blazars, even greater." + Second the beaming reduces the energy budget of this phenomenon., Second the beaming reduces the energy budget of this phenomenon. + Beaming of %~0.1 reduces the required energy by a factor of 400., Beaming of $\theta_0 \sim 0.1$ reduces the required energy by a factor of 400. + Interestingly. the evidence for jets arises most clearly in the two strongest bursts detected by BeppoSAX so far.," Interestingly, the evidence for jets arises most clearly in the two strongest bursts detected by BeppoSAX so far." + It may provide a hint on the energy budget and on the effect of beaming on the luminosity function., It may provide a hint on the energy budget and on the effect of beaming on the luminosity function. + GRB models based on “regular” compact objects become more appealing once more., GRB models based on “regular” compact objects become more appealing once more. + What would be the effects of beaming on the observed luminosity function. of GRBs and on possible. intrinsic correlations between different features of the source?, What would be the effects of beaming on the observed luminosity function of GRBs and on possible intrinsic correlations between different features of the source? + One might expect that different viewing angles might have a very strong effect on the observed luminosities and other characteristics of the GRBs., One might expect that different viewing angles might have a very strong effect on the observed luminosities and other characteristics of the GRBs. + However. as implied by the compactness problem typical initial Lorentz factors during the GRB. 506©100.," However, as implied by the compactness problem typical initial Lorentz factors during the GRB, $\gamma_0 \ge 100$." + An observer that is more than from58! away a GRB jet will practically miss the GRB., An observer that is more than }$ away from a GRB jet will practically miss the GRB. + Observers. within this range will see a weaker. softer and longer GRB.," Observers, within this range will see a weaker, softer and longer GRB." + However. Mao and Yi (1994) point out that if Jy>>s! then the fraction of bursts that are viewed “sideways” is rather small.," However, Mao and Yi (1994) point out that if $\theta_0 \gg \gamma_0^{-1}$ then the fraction of bursts that are viewed “sideways” is rather small." + It would be approximately 5!/0n. a few percent. if we use the value inferred for GRB 990123.," It would be approximately $\gamma_0^{-1} / \theta_0$, a few percent, if we use the value inferred for GRB 990123." + Thus this will introduce a small population of intrinsically weaker. softer and longer bursts.," Thus this will introduce a small population of intrinsically weaker, softer and longer bursts." + Since these bursts will be weaker. we expect that we would observe only a small fraction of them.," Since these bursts will be weaker, we expect that we would observe only a small fraction of them." +" This research was supported by the US-Israel BSF grant 95- by the Israeli Space Agency. by NASA grant NAGS-3516 and by the Sherman Fairchild Foundation,"," This research was supported by the US-Israel BSF grant 95-328, by the Israeli Space Agency, by NASA grant NAG5-3516 and by the Sherman Fairchild Foundation." +where Lig={μμlOLo ,where $L_{40} = L_{\rm sph}/10^{40}$ $^{-1}$. +"Figure 1 shows Af,/Lay and 6 as functions of m (using equations Ll and S)).", Figure 1 shows $M_1/L_{40}$ and $b$ as functions of $\dot m$ (using equations \ref{mass} and \ref{beam}) ). +" We see that οποίος ratios in the range 8.5«m20 imply stellar masses 1M.NN$m,$20 for the aceretors if the disc luminosity is. Z-107 "". and beaming ⋠⋅[actors in. the range |>b0.2."," We see that Eddington ratios in the range $8.5 < \dot m < 20$ imply stellar masses $1\msun \la m_1 \la +20$ for the accretors if the disc luminosity is $\la 10^{41}$ $^{-1}$, and beaming factors in the range $1 > b \ga 0.2$." + Llence stellarmass binaries with moderate Eddingtonx ratios and consequently modest beaming provide very good candidates for explaining ULXs., Hence stellar–mass binaries with moderate Eddington ratios and consequently modest beaming provide very good candidates for explaining ULXs. + We note from (10)) that the inferred luminosity Lon varies essentially only because of the sensitivity of the beaming factor b to m.," We note from \ref{lum}) ) that the inferred luminosity $L_{\rm + sph}$ varies essentially only because of the sensitivity of the beaming factor $b$ to $\dot m$." + Thus the bolometric luminosity varies only logarithmically above Le (assuming that the Eddington ratio always exceeds unity). but is spread over a smaller or ereater solid angle as m increases or decreases. the inferred luminosity.," Thus the bolometric luminosity varies only logarithmically above $L_E$ (assuming that the Eddington ratio always exceeds unity), but is spread over a smaller or greater solid angle as $\dot m$ increases or decreases, significantly altering the inferred luminosity." + Since significantlyAfaltering—mAlpx(ALfap. where η. the radiative ellicieney. is similar ( 0.1) for black holes and neutron stars. L note that that some ULXs could contain neutron stars. ancl could. even have lower absolute accretion rates for the same inferred luminosity.," Since $\dot M = \dot m\dot M_E \propto (M_1/\eta)\dot m$, where $\eta$, the radiative efficiency, is similar $\sim 0.1$ ) for black holes and neutron stars, I note that that some ULXs could contain neutron stars, and could even have lower absolute accretion rates for the same inferred luminosity." + From Fig., From Fig. + 1 we see that a LOAL. black hole with m—15 and a neutron star with mass Z2M. and m=30 produce similar inferred. laminosities. with the neutronstar svstem having an absolute accretion rate AL lower bv a [actor ~2.5 than the black hole.," 1 we see that a $10\msun$ black hole with $\dot m = 15$ and a neutron star with mass $\la +2\msun$ and $\dot m = 30$ produce similar inferred luminosities, with the neutron–star system having an absolute accretion rate $\dot M$ lower by a factor $\sim 2.5$ than the black hole." + The origin of this apparently. paradox. is that the latter system has a smaller beaming factor. (, The origin of this apparently paradox is that the latter system has a smaller beaming factor. ( +Put another wav. on Fie.,"Put another way, on Fig." + 1 the curves of constant AL are hyperbolac which cross the hyperbola describing 6.), 1 the curves of constant $\dot M$ are hyperbolae which cross the hyperbola describing $b$ .) + For ultrasoft ULXs with no detectable medium.energy Xray component. even white dwarf aceretors are possible. particularly since for them. 7 can be enhanced over the pure accretion vield. by nuclear burning of the accreting matter (c£ Fabbiane et al..," For ultrasoft ULXs with no detectable medium–energy X–ray component, even white dwarf accretors are possible, particularly since for them $\eta$ can be enhanced over the pure accretion yield by nuclear burning of the accreting matter (cf Fabbiano et al.," + 2003)., 2003). + Population studies of ULXs. have until now faced. the cilliculty that the beaming [actor 6 was not. determined. introducing a spurious degree of freedom.," Population studies of ULXs have until now faced the difficulty that the beaming factor $b$ was not determined, introducing a spurious degree of freedom." + Given. the connection (S)). we can now remove this.," Given the connection \ref{beam}) ), we can now remove this." +" We consider a population of ULXs with host ealaxy space density ny ""and assume that each host contains VW ULXs. with radiation beams oriented randomly."," We consider a population of ULXs with host galaxy space density $n_g$ $^{-3}$ and assume that each host contains $N$ ULXs, with radiation beams oriented randomly." + To be in the beam of one such object one has to search through ~L/Nb galaxies. i.e. a space volume ~l/nj4Nb.," To be in the beam of one such object one has to search through $\sim 1/Nb$ galaxies, i.e. a space volume $\sim 1 /n_g N b$." +" The nearest observed ULX is thus at a distance where mi,=m/10.", The nearest observed ULX is thus at a distance where $\dot m_1 = \dot m/10 $. +" Phe apparent Iuminositv of the ULX is where m,=AL/10M.. giving a maximum apparent bolometric ux These relations. together with the results of the previous Section. agree with the fact that ULXNs of apparent luminosity few. 107?107 are observed. in the Local Croup. and suggest that the tvpical intrinsic number N per host galaxy is at most a few."," The apparent luminosity of the ULX is where $m_* = M_1/10\msun$, giving a maximum apparent bolometric flux These relations, together with the results of the previous Section, agree with the fact that ULXs of apparent luminosity few $\times +10^{39} - 10^{41}$ $^{-1}$ are observed in the Local Group, and suggest that the typical intrinsic number $N$ per host galaxy is at most a few." + This is in line with estimates of the numbers of high.mass Xrav binaries in phases of rapid mass transfer on thermal or nuclear timescales (xing et al.," This is in line with estimates of the numbers of high–mass X–ray binaries in phases of rapid mass transfer on thermal or nuclear timescales (King et al.," + 2001: Rappaport et al..," 2001; Rappaport et al.," +. 2005). suggesting that these systems oller good. candidates: Lor explaining most if not all ULNs.," 2005), suggesting that these systems offer good candidates for explaining most if not all ULXs." + Ultimately one needs a population svnthesis calculation to verify that this picture produces the right numbers of svstems with the required moderate Eelelington ratios to produce the nearby ULXs., Ultimately one needs a population synthesis calculation to verify that this picture produces the right numbers of systems with the required moderate Eddington ratios to produce the nearby ULXs. + ]t is unclear to what value of ra one may safely extrapolate the boxi7 dependence inferred here., It is unclear to what value of $\dot m$ one may safely extrapolate the $b \propto \dot m^{-2}$ dependence inferred here. + This is an interesting question. as we know (cf Beeclman et al. 2006: Wing Aegelman. 1999) that the wellstudied object 88433 has mnic3000107.," This is an interesting question, as we know (cf Begelman et al, 2006; King Begelman, 1999) that the well–studied object SS433 has $\dot m \sim +3000 - 10^4$." + Such values are tvpical for both thermaltimescale and nucleartimescale mass transfer from massive donor stars (Rappaport et al..," Such values are typical for both thermal--timescale and nuclear–timescale mass transfer from massive donor stars (Rappaport et al.," + 2005)., 2005). +" From the work of the previous Section. now scaling m as m=.LO""hy. the nearest such object. would be at a distance. where I have taken ny~0.02 Mipe as appropriate for L galaxies."," From the work of the previous Section, now scaling $\dot m$ as $\dot m += 10^4\dot m_4$, the nearest such object would be at a distance where I have taken $n_g \sim 0.02$ $^{-3}$ as appropriate for $L^*$ galaxies." + Vhe apparent isotropic luminosity of such an object. would be llence indistance and. apparent Luminosity the object would appear as an AGN., The apparent isotropic luminosity of such an object would be Hence indistance and apparent luminosity the object would appear as an AGN. + However. unlike a genuine AGN. there is no requirement that it should lie precisely in the nucleus of the host galaxy.," However, unlike a genuine AGN, there is no requirement that it should lie precisely in the nucleus of the host galaxy." + A possible candidate for such an object is the BL Lac system PINS 1413|135 (Perlman et al..," A possible candidate for such an object is the BL Lac system PKS 1413+135 (Perlman et al.," + 2002)., 2002). + With redshift >=0.24671 it has distance Dx=1000 3\Ipe ancl isotropic luminosity c1033eresto but lies at 13+4 mas from the centre of the host galaxy.," With redshift $z = 0.24671$ it has distance $D \simeq 1000$ Mpc and isotropic luminosity $\simeq +10^{44}~{\rm erg\, s}^{-1}$, but lies at $13 \pm 4$ mas from the centre of the host galaxy." + The work of this paper suggests that the beaming factor in superEelclington aceretion varies as bxrmi7., The work of this paper suggests that the beaming factor in super–Eddington accretion varies as $b \propto \dot m^{-2}$. + Phis seenis to be required by observations of the LowyYL correlation. and is reasonable on general &cometrical grounds.," This seems to be required by observations of the $L_{\rm soft} - T$ correlation, and is reasonable on general geometrical grounds." + The existence of this scaling means that observable. properties of ULXs depend essentially only on the Ededington ratio m., The existence of this scaling means that observable properties of ULXs depend essentially only on the Eddington ratio $\dot m$. + Lf this conclusion is valid. this removes the spurious degree of freeclom allowing one to choose 5 independently of 7 which has made svstematie parameter estimates dillieult in the past (e.g. Wing. 2008. where these two quantities are not connected).," If this conclusion is valid, this removes the spurious degree of freedom allowing one to choose $b$ independently of $\dot m$ which has made systematic parameter estimates difficult in the past (e.g. King, 2008, where these two quantities are not connected)." + Lt appears that most ULXs correspond to stellar mass systems accreting at Ecelineton ratios of order 10 —— 30. with corresponding beaming factors bz 0.1.," It appears that most ULXs correspond to stellar mass systems accreting at Eddington ratios of order 10 – 30, with corresponding beaming factors $b \ga 0.1$ ." + Lighmass X binaries containing black holes or neutron stars are excellent candidates. although population svnthesis studies," High–mass X--ray binaries containing black holes or neutron stars are excellent candidates, although population synthesis studies" +and have the potential for producing clusters.,and have the potential for producing clusters. +" In addition, the whole cloud of 9140 is also in gravitationally bound state."," In addition, the whole cloud of S140 is also in gravitationally bound state." +" By using the mean velocity width of 1.95 in FWHM all over the cloud and the projected extent of the cloud of 3.7 pc of the cloud, the virial mass of the cloud is estimated to be 1900Mo, which is by a factor of three smaller than the cloud mass of 6600Mo."," By using the mean velocity width of 1.95 in FWHM all over the cloud and the projected extent of the cloud of 3.7 pc of the cloud, the virial mass of the cloud is estimated to be 1900, which is by a factor of three smaller than the cloud mass of 6600." +" Following the CMF study in the OMC-1 region (Ikeda&Kitamura2009),, we applied the algorithm (Williamsetal.1994) to the three-dimensional (a-d-U_gsr) cube data."," Following the CMF study in the OMC-1 region \citep{ike09b}, we applied the algorithm \citep{wil94} + to the three-dimensional $\alpha$ $\delta$ $v_{\rm LSR}$ ) cube data." +" The algorithm can work well with reasonable parameters to identify cores or clumps, though several authors pointed out some shortcomings of theind."," The algorithm can work well with reasonable parameters to identify cores or clumps, though several authors pointed out some shortcomings of the." +" Pinedaetal.(2009) examined the behavior of the algorithm by changing the threshold level from 3 to 20 c, a wider range than Williamsetal.(1994) examined, and found that the power-law index of the mass function sensitively depends on the threshold for higher thresholds of > 5 σ."," \citet{pin09} examined the behavior of the algorithm by changing the threshold level from 3 to 20 $\sigma$, a wider range than \citet{wil94} examined, and found that the power-law index of the mass function sensitively depends on the threshold for higher thresholds of $>$ 5 $\sigma$." +" However, Ikeda&Kitamura(2009) demonstrated the weak dependence of core properties and CMF on the threshold in the reasonable range from 2 to 5 σ levels, which had been also shown in Pinedaetal.(2009)."," However, \citet{ike09b} demonstrated the weak dependence of core properties and CMF on the threshold in the reasonable range from 2 to 5 $\sigma$ levels, which had been also shown in \citet{pin09}." +". Therefore, we adopted the threshold level for the algorithm of 0.24 K, i.e., the 2 σ noise level of the cube data, which is recommended for identifying the core structure by Williamsetal.(1994) and falls in the robust and reasonable range derived by Ikeda&Kitamura(2009).."," Therefore, we adopted the threshold level for the algorithm of 0.24 K, i.e., the 2 $\sigma$ noise level of the cube data, which is recommended for identifying the core structure by \citet{wil94} + and falls in the robust and reasonable range derived by \citet{ike09b}." +" We adopted the grid spacing of the cube data of 22"".0, equal toA6,g,, i.e., full-beam sampling."," We adopted the grid spacing of the cube data of $''$ .0, equal to, i.e., full-beam sampling." + This is because Williamsetal.(1994) determined the optimal threshold of the 2 c level for the full-beam sampling case., This is because \citet{wil94} determined the optimal threshold of the 2 $\sigma$ level for the full-beam sampling case. + We also used the additional criteria introduced inIkedaetal.(2007) to reject ambiguous or fake core candidates whose size and velocity width are smaller than the," We also used the additional criteria introduced in\citet{ike07} + to reject ambiguous or fake core candidates whose size and velocity width are smaller than the" +Bavesian statistics encapsulate our understanding of the parameters in the model. prior to considering the data. indistribulions.,"Bayesian statistics encapsulate our understanding of the parameters in the model, prior to considering the data, in." + The is the product of the prior aud the likelihood. appropriately normalized.," The is the product of the prior and the likelihood, appropriately normalized." + The full posterior probability distribution in this problem requires solution to integrals in (he normalization that cannot be done analvlically., The full posterior probability distribution in this problem requires solution to integrals in the normalization that cannot be done analytically. + However. the uumormalized posterior probability distribution avoids these integrals and can be used to generale a Monte Carlo sample from the full posterior probability distribution.," However, the unnormalized posterior probability distribution avoids these integrals and can be used to generate a Monte Carlo sample from the full posterior probability distribution." + The techniques used to generate the sample are Markov. Chain techiiques., The techniques used to generate the sample are Markov Chain techniques. + The model for the infrared surface brightness calculation is developed by first substituting the infrared color index [or the visual color index in equation (6)) and then rearrange as follows where ο.D take the values given in equation (3)) and where we have replaced 1/r with π. the parallax in arcseconds.," The model for the infrared surface brightness calculation is developed by first substituting the infrared color index for the visual color index in equation \ref{eq:combined2}) ) and then rearrange as follows where $A,B$ take the values given in equation \ref{eq:ISB}) ) and where we have replaced $1/r$ with $\pi$, the parallax in arcseconds." + Within this model the likelihood. [unction is specified in a straightforward wav ancl is given in equation (12) of Barnes οἱ al., Within this model the likelihood function is specified in a straightforward way and is given in equation (12) of Barnes et al. +(2003).. We model the photometry and the racial velocity data as drawn [rom normal distributions with variances eiven by the observational uncertainties., We model the photometry and the radial velocity data as drawn from normal distributions with variances given by the observational uncertainties. + Because we do not (rust the quoted observational uncertainties. we introduce a hyper-parameter scale factor on each variance to model deviation in the scatter [rom that expected from the quoted uncertainties.," Because we do not trust the quoted observational uncertainties, we introduce a hyper-parameter scale factor on each variance to model deviation in the scatter from that expected from the quoted uncertainties." + The time variations of the photometry and radial velocities are modeled by Fourier series of unknown order on the pulsation phase., The time variations of the photometry and radial velocities are modeled by Fourier series of unknown order on the pulsation phase. + Barnes et al., Barnes et al. + discuss the priors adopted for each parameter of interest. but only one is relevant here.," discuss the priors adopted for each parameter of interest, but only one is relevant here." + It is well-known that Cepheids are distributed within the plane of the Galaxy wilh an exponential decrease in density. away [rom the plane., It is well-known that Cepheids are distributed within the plane of the Galaxy with an exponential decrease in density away from the plane. + We adopted a prior on distance that reflects the flattened density distribution with a scale height of τοzc10 pe., We adopted a prior on distance that reflects the flattened density distribution with a scale height of $70 \pm 10$ pc. + The results are insensitive (ο reasonable changes in the scale height., The results are insensitive to reasonable changes in the scale height. + The sampling strategy emploved in this work is Markov Chain Monte Carlo using the Aletropolis-Hastings anc Gibbs algorithms. as described in Barnes et al.," The sampling strategy employed in this work is Markov Chain Monte Carlo using the Metropolis-Hastings and Gibbs algorithms, as described in Barnes et al." +" The art in this approach is to find sampling methods that explore the posterior probability distributions fully ancl efficiently,", The art in this approach is to find sampling methods that explore the posterior probability distributions fully and efficiently. + Internal tests provide guidance on the completeness and efficiency of ihe sampling., Internal tests provide guidance on the completeness and efficiency of the sampling. + All the results presented here passed those tests., All the results presented here passed those tests. + In the customary manner. we chose a phase to improve the model selection efficiency.," In the customary manner, we chose a phase to improve the model selection efficiency." + To be consistent with the linear-bisector caleulation. we deleted [rom the Bavesian solution the photometry anclradial velocities in pulsation phase interval 0.8— 1.0.," To be consistent with the linear-bisector calculation, we deleted from the Bayesian solution the photometry andradial velocities in pulsation phase interval $0.8-1.0$ ." + In the, In the +supporting the fluorescent origin.,supporting the fluorescent origin. + Another fluorescent line is that of OTL at jan. which may be pumped by οἱ contimmun photons (7.andreferencestherein).," Another fluorescent line is that of I at $\,\mu$ m, which may be pumped by $\beta$ or continuum photons \citep[][and + references therein]{mcgregor1984}." +" Continuuin fluorescence predicts an ΟΠ 13164424 1.129,11 line ratio above unity."," Continuum fluorescence predicts an I $\,\mu$ m / $\,\mu$ m line ratio above unity." +" The 1.316,40 line is practically invisible in our SINFONT spectrum. which favors the Jj £uorescence."," The $\,\mu$ m line is practically invisible in our SINFONI spectrum, which favors the $\beta$ fluorescence." + If this is true. another OTI liue at should also be preseut.," If this is true, another I line at should also be present." + Iudeed. this liue is well visible in our FEROS spectra of LEup obtained between Apri aud June 2008 (?)..," Indeed, this line is well visible in our FEROS spectra of Lup obtained between April and June 2008 \citep{sicilia-aguilar2011}." +" Interestingly. both the and the pru Hines are visible even in quiescence, althoueh they are auch weaker than in outburst. inclicating that a sufficient amount of > radiation was present even im quiescence."," Interestingly, both the and the $\mu$ m lines are visible even in quiescence, although they are much weaker than in outburst, indicating that a sufficient amount of $\beta$ radiation was present even in quiescence." + The presence of .-pumpecd lines of neutral oxvgen indicates the presence of deuse warn regions enibedded in hot ionized plasma., The presence of $\beta$ -pumped lines of neutral oxygen indicates the presence of dense warm regions embedded in hot ionized plasma. + The MgII pau line may also be formed by UV. fluorescence.," The I $\,\mu$ m line may also be formed by UV fluorescence." + This requies that the Me pau transitions are also present.," This requires that the I $\,\mu$ m transitions are also present." + This is true for LLup., This is true for Lup. + However. collisional excitation may also play a role here. since the MeIT jan line is also visible.," However, collisional excitation may also play a role here, since the I $\,\mu$ m line is also visible." + We searched the spectzun of LEXLLup for shock-excited lines., We searched the spectrum of Lup for shock-excited lines. +" We found that the Il, line at 2.1218jan is not visible."," We found that the $_2$ line at $\,\mu$ m is not visible." + The line at 1.611072. may be present. but its wnambiguousΤΟΠ identification is difficult due to its closeness to the strong Drll2 line.," The [FeII] line at $\,\mu$ m may be present, but its unambiguous identification is difficult due to its closeness to the strong 12 line." + We checked the position-velocity diagram and the spectro-astrometric signal (see below) in order to ideutifv the location of the euissiou.," We checked the position-velocity diagram and the spectro-astrometric signal (see below) in order to identify the location of the $\,\mu$ m emission." + We found neither exteuded enüssioun nor gin.positional offset conrpared to the continui position., We found neither extended emission nor positional offset compared to the continuum position. + Thus. supposing that the line is deed preseut. at the time of our observations[Fell] the shock was still very close to the central source.," Thus, supposing that the [FeII] line is indeed present, at the time of our observations the shock was still very close to the central source." + This apparent lack of strong forbidden lines may be an indication that the cmission line region has a high density where forbidden lines are quenched (?7).., This apparent lack of strong forbidden lines may be an indication that the emission line region has a high density where forbidden lines are quenched \citep{nisini2005}. + Further mouitoriug of LLap may reveal shocks as they reach less deuse regions farther frou the central star. expanding iuto the medium around the disk.," Further monitoring of Lup may reveal shocks as they reach less dense regions farther from the central star, expanding into the medium around the disk." + The SINFONI data cubes can be used for spectro-astrometiy. ie. mieasurmng the position of the source as a function of wavelength.," The SINFONI data cubes can be used for spectro-astrometry, i.e. measuring the position of the source as a function of wavelength." + If ther Is extended emitting material moving at different velocities. the source position. measured at these velocities will deviate ον the position measured at coutimmin wavelengths.," If there is extended emitting material moving at different velocities, the source position measured at these velocities will deviate from the position measured at continuum wavelengths." + In case the cussion comes from a rotating disk. at certain wavelenetls. there will be a positive offset in the ceutroid. while at other waveleueths. there will be a negative offset.," In case the emission comes from a rotating disk, at certain wavelengths, there will be a positive offset in the centroid, while at other wavelengths, there will be a negative offset." + Thus. depeuding on whether we see the approaching or the receding part of the disk. the measured spectro-astronmietrie signal as a function of velocity will follow a typical sinusoidal pattern (seee.g.Fig.2in ?7).," Thus, depending on whether we see the approaching or the receding part of the disk, the measured spectro-astrometric signal as a function of velocity will follow a typical sinusoidal pattern \citep[see +e.g.~Fig.~2 in][]{pontoppidan2008}." + lIufall or outflow would. iu most cases. cause a positive oulv or negative ouly signal (seethemodeliugby ?)..," Infall or outflow would, in most cases, cause a positive only or negative only signal \citep[see the +modeling by][]{eisner2010}." + For certain ecometrics. a bipolar outflow could cause both positive aud negative offsets for different velocities. but the ceutroid displacement would be more linear (πουe.g.theexampleofW536Aq]in?)..," For certain geometries, a bipolar outflow could cause both positive and negative offsets for different velocities, but the centroid displacement would be more linear \citep[see e.g.~the example of V536\,Aql in][]{whelan2004}." + Binaries may also cause a non-zero spectro-astrometric sienal. but again. a positive ouly or uceative ouly signal (?7)..," Binaries may also cause a non-zero spectro-astrometric signal, but again, a positive only or negative only signal \citep{takami2003,brannigan2006}." + We analyzed several cussion lines iu the spectra of LLup with spectro-astrometric techuique., We analyzed several emission lines in the spectrum of Lup with spectro-astrometric technique. + Fig., Fig. + 5 shows some cxamples., \ref{fig:specast} shows some examples. + We found that ouly the lvdrogen lues indicate auv spectro-astrometric signal., We found that only the hydrogen lines indicate any spectro-astrometric signal. + ALetallic lues show a flat signal. which can be either due to gas close to the star. or slow-moving eas at larger distances.," Metallic lines show a flat signal, which can be either due to gas close to the star, or slow-moving gas at larger distances." + The fact that most of the metallic atoms are neutral supports the second possibility., The fact that most of the metallic atoms are neutral supports the second possibility. + The spectro-astrometric sienals plotted iu Fie., The spectro-astrometric signals plotted in Fig. + 8. for the Pao. Bre. aud 111 lines are all indicating rotating material.," \ref{fig:specast} for the $\,\beta$ , $\,\gamma$, and 11 lines are all indicating rotating material." + Since SINFONT contains no slit. our measurements do not suffer frou the artifacts usual for slit spectra. and the spectro-astrometric signal can be calculated for anv angle across the source.," Since SINFONI contains no slit, our measurements do not suffer from the artifacts usual for slit spectra, and the spectro-astrometric signal can be calculated for any angle across the source." + The results can be then used to calculate the position angle of the rotation axis. Le. the angle where the spectro-astrometric signal is constant 0.," The results can be then used to calculate the position angle of the rotation axis, i.e. the angle where the spectro-astrometric signal is constant 0." + Iu our case. this vields P.A. = 80+ 107. thus. the rotation axis is almost exactly east-west oriented.," In our case, this yields P.A. = $\,{\pm}\,$ $^{\circ}$, thus, the rotation axis is almost exactly east-west oriented." + Remarkably. the spectro-astrometric signals for the lvdrogen lies are all sviuuetric within the measurement uucertaimties. indicating that the brightuess and velocity distribution of lvdrogen gas around the ceutral star is azinuthallv synunetric.," Remarkably, the spectro-astrometric signals for the hydrogen lines are all symmetric within the measurement uncertainties, indicating that the brightness and velocity distribution of hydrogen gas around the central star is azimuthally symmetric." + Droad-baud poludmoetric images through the II filter were obtained for LLup using a shorter 9x) and a longer (253) exposure time., Broad-band polarimetric images through the H filter were obtained for Lup using a shorter s) and a longer s) exposure time. + The short exposure miages show that the distribution of the total intensity follows a Caussian profile., The short exposure images show that the distribution of the total intensity follows a Gaussian profile. + The profile of the long exposure images indicates that the inner region (within a radius of 3 pixels) of the source is saturated. but the rest of the profile is the same as for the short exposure nuages. sugeesting no extended cussion.," The profile of the long exposure images indicates that the inner region (within a radius of 3 pixels) of the source is saturated, but the rest of the profile is the same as for the short exposure images, suggesting no extended emission." + The Stokes Q and U images. as well as the polarized intensity nuages show no polarized dHieht whatsoever.," The Stokes Q and U images, as well as the polarized intensity images show no polarized light whatsoever." + This linits the II-baud degree of polarization for LLup below theinstrumental polarization (uot more than ))., This limits the H-band degree of polarization for Lup below theinstrumental polarization (not more than ). + This, This +packageSusDas.. provided by S'T5cl (the Space Telescope Science,"package, provided by STScI (the Space Telescope Science." +ute)?.. Figure 1. shows the Ciaussian smoothed and Iux-calibrated light curve from the far-UV. data., Figure \ref{fig:light} shows the Gaussian smoothed and flux-calibrated light curve from the far-UV data. + This light. curve was constructed by dividing the larger exposures into one-second bins. and by average the Huxes over the wavelength range. AA.," This light curve was constructed by dividing the larger exposures into one-second bins, and by average the fluxes over the wavelength range, –." + The light curve shows sharp. square-shaped eclipses. close to zero flux at mid-eclipse. and a very Hat. out-of-eclipse continuum. strongly suggesting that the UV. flux is dominated. by emission. from. (or very close to} the acereting WD.," The light curve shows sharp, square-shaped eclipses, close to zero flux at mid-eclipse, and a very flat out-of-eclipse continuum, strongly suggesting that the UV flux is dominated by emission from (or very close to) the accreting WD." + The folded light curve constructed from the combined data for all three HIST. orbits is. presented in the bottom panel., The folded light curve constructed from the combined data for all three HST orbits is presented in the bottom panel. + All further analysis was carried oul on the unsmoothed data. exeluding the eclipses.," All further analysis was carried out on the unsmoothed data, excluding the eclipses." + Crouncd-hasec optical observations were performed. at. the same time as the LIST observations. vielding a magnitude for 1507 of g=1s.444+0.02.," Ground-based optical observations were performed at the same time as the HST observations, yielding a magnitude for J1507 of $g = 18.44 \pm 0.02$." + This is consistent with SDSS. showing tha the system was in quiescence during the LIST observations.," This is consistent with SDSS, showing that the system was in quiescence during the HST observations." + The two top panels of Figure ὸ show the mean out-of eclipse spectrum (in black). for both the near- and far-UV.," The two top panels of Figure \ref{fig:spec} show the mean out-of eclipse spectrum (in black), for both the near- and far-UV." + The reduction was performed separately for the COS ane STIS data. and. the mean spectrum. for each. region were joined at. 1900 awwithout overlap for a total range of AA.," The reduction was performed separately for the COS and STIS data, and the mean spectrum for each region were joined at 1900 without overlap for a total range of –." + Phe COS data was rebinned slightly. to pix. to increase the οN ancl provide sullicient sampling of the Cl40L erating’s spectral resolution.," The COS data was rebinned slightly, to /pix, to increase the S/N and provide sufficient sampling of the G140L grating's spectral resolution." + Different clispersions were retained for the the far- and UV regions (0.2 pix ane 1.58 pix. respectively).," Different dispersions were retained for the the far- and near-UV regions (0.2 /pix and 1.58 /pix, respectively)." + The overall UV. speetrum for J1507 is relatively sparse in spectral lines;, The overall UV spectrum for J1507 is relatively sparse in spectral lines. + We identify CLL at 133! Sill at 1526.7 Hell at 1640.5. ATIEE at 1671 and Mel at 280tAA.," We identify CII at 1335, SiII at 1526.7 HeII at 1640.5, AlII at 1671 and MgII at 2800." +.. The strong emission feature near 1300 eds almost certainly due to geocoronal emission in the ο 1 1304 line that could. not. be cleanly removed. by the. pipeline background. subtraction., The strong emission feature near 1300 is almost certainly due to geocoronal emission in the O I 1304 line that could not be cleanly removed by the pipeline background subtraction. + Α model erick spanning the four Κον atmospheric parameters. effective. temperature (Zea). surface gravity (log g). metallicity (e/1]) and rotational velocity (¢ sins). was constructed. in order to. fit. the far- and. near-UV spectrum.," A model grid spanning the four key atmospheric parameters, effective temperature $T_{\text{eff}}$ ), surface gravity $\log g$ ), metallicity $[Fe/H]$ ) and rotational velocity $v \sin i$ ), was constructed in order to fit the far- and near-UV spectrum." + Atmospheric structures were calculated withTLUSsQY. with the spectral svnthesis being done with (7T: ?2)).," Atmospheric structures were calculated with, with the spectral synthesis being done with \citealp{1988CoPhC..52..103H}; \citealp{1995ApJ...439..875H}) )." + The grid consisted of: 12500 Ix. ssZ;4;£; 20000 Ix in steps of 500 Ix. 7.5 Ἐνlogg&9.5 in steps of 0.25. -2.0 SLe11] 0.0 in steps of 0.25. and 0 ο... 1000 Sin steps of 50 knissI.," The grid consisted of; 12500 K $\leappeq T_{\text{eff}} \leappeq$ 20000 K in steps of 500 K, 7.5 $\leappeq \log g \leappeq 9.5$ in steps of 0.25, -2.0 $\leappeq [Fe/H] \leappeq$ 0.0 in steps of 0.25, and 0 $^{-1} \leappeq v \sin i \leappeq$ 1000 $^{-1}$ in steps of 50 $^{-1}$." + Models at intermediate parameter values were constructed by linear interpolation on this grid., Models at intermediate parameter values were constructed by linear interpolation on this grid. + Pixels with non-zero data quality Hags set were excluded from our fits. as well as the regions around. the spectral lines. OL at. Clb at and the quasi-molecular LE feature at ~AA..," Pixels with non-zero data quality flags set were excluded from our fits, as well as the regions around the spectral lines, OI at CII at and the quasi-molecular H feature at $\sim$." + Before our models could be compared to the observed spectrum. they were convolved with a Gaussian filter to the spectral resolution appropriate to the COS (.— AA)) and STIS (.— AA)) data. and linearly interpolated onto the observational wavelength: scale.," Before our models could be compared to the observed spectrum, they were convolved with a Gaussian filter to the spectral resolution appropriate to the COS (< ) and STIS (> ) data, and linearly interpolated onto the observational wavelength scale." + In. general. our model fits did represent the main features of the data quite well. but the formal ovas somewhat high.," In general, our model fits did represent the main features of the data quite well, but the formal $\chi^{2}$ was somewhat high." + In order to obtain more realistic formal parameter errors. we ποΩς an intrinsic dispersion term to the Duxerrors in such a way that Xz 1.," In order to obtain more realistic formal parameter errors, we therefore added an intrinsic dispersion term to the fluxerrors in such a way that $\chi^{2}_{\nu}$ = 1." + This dispersion corresponds to about A fit to the far UV-region Nvields τω=14200£50 Ex. logg=S240.04.Fe/1H]124005 and esini=180+20 kmss|.," This dispersion corresponds to about A fit to the far UV-region – yields $T_{\text{eff}} = 14200 \pm 50$ K, $\log g = 8.2 \pm 0.04, [Fe/H] = -1.2 \pm 0.05 $ and $v \sin i = 180 \pm 20$ $^{-1}$." + These [it parameters provide a good approximation also for the spectrum out to where the spectrum may begin. to show dise. features., These fit parameters provide a good approximation also for the near-UV spectrum out to where the spectrum may begin to show disc features. + We adopt. these parameters as our. best-fit parameters., We adopt these parameters as our best-fit parameters. + The quoted errors. are formal errors. from the A7. fitting., The quoted errors are formal errors from the $\chi^{2}$ fitting. + Table 1 presents the best parameters along with their uncertainties., Table \ref{pars} presents the best parameters along with their uncertainties. + Phese uncertainties are larger than the formal errors. because. they include. our. best. estimates. of the systematic uncertainties associated. with different: choices of fitting windows.," These uncertainties are larger than the formal errors, because they include our best estimates of the systematic uncertainties associated with different choices of fitting windows." + However. there are several reasons for aclopting the parameters inferred from the fit to the COS far-UV data set as our best-bet estimates.," However, there are several reasons for adopting the parameters inferred from the fit to the COS far-UV data set as our best-bet estimates." + This region includes almost all line features. ancl is also most sensitive to changes in Zi and logg.," This region includes almost all line features, and is also most sensitive to changes in $T_{\text{eff}}$ and $\log g$." + Also. the far UV-region is more likely to represent. pure light from the WD. while towards. τω wavelengths. the spectrum could be affected by the dise am the bright spot.," Also, the far UV-region is more likely to represent pure light from the WD, while towards redder wavelengths, the spectrum could be affected by the disc and the bright spot." + Finally. fitting only the COS data removes any possibility that a mismatch in the αν calibration of COS and STIS could affect our results.," Finally, fitting only the COS data removes any possibility that a mis-match in the flux calibration of COS and STIS could affect our results." + The two top panels in Figure 2 show the best-fit moce in red. along with the mean out-of-eclipse spectrum. for J1507.," The two top panels in Figure \ref{fig:spec} show the best-fit model in red, along with the mean out-of-eclipse spectrum for J1507." + Ehe corresponding residuals between mocdel and data are plotted underneath. cach of the COS and STIS spectra regions. together with the I-7 error range marked in green.," The corresponding residuals between model and data are plotted underneath each of the COS and STIS spectral regions, together with the $\sigma$ error range marked in green." + The clips in the residuals at (1460. 1530. 1600 and. Care eaused by bad pixels in the data and these regions were excluded from our fits.," The dips in the residuals at (1460, 1530, 1600 and , are caused by bad pixels in the data and these regions were excluded from our fits." + As à comparison. a model showing," As a comparison, a model showing" +T=30.000 I aud μα=1O°L..,"$T = 30,000$ K and $L_{\rm bol} = 10^5 \lsun$." + Observations of the sstar cluster in the L’ band (7) showed that $2 has an excess of about 0.6 magnitudes (or 30 mJv for ος paralcters) m that band. compared with the “normal” colors of the «αποας stars.," Observations of the star cluster in the $L'$ band \citep{Genzel03} showed that S2 has an excess of about 0.6 magnitudes (or 30 mJy for S2's parameters) in that band, compared with the “normal” colors of the surrounding stars." + This excess could be due to contanunation of the star spectrum by the reprocessed cluission of the disk., This excess could be due to contamination of the star spectrum by the reprocessed emission of the disk. +" What we call below the ""observed spectral bunuimositv in 1 baud is then the blackbody cluission described aboveplus the excess neasured by ?..", What we call below the “observed spectral luminosity” in $L'$ band is then the blackbody emission described aboveplus the excess measured by \cite{Genzel03}. + The reprocessed disk eudssiou is a functiou of time., The reprocessed disk emission is a function of time. + The cooling time of the disk is much shorter than the stars orbital period (usually by orders of naenitude)., The cooling time of the disk is much shorter than the star's orbital period (usually by orders of magnitude). + The reprocessed emission can thou be calculated under the steady state asstuuption., The reprocessed emission can then be calculated under the steady state assumption. + The disk reprocessed spectruni is thus a fiction of ecoimoetry. ic. the distance between the star and the disk. 4.," The disk reprocessed spectrum is thus a function of geometry, i.e. the distance between the star and the disk, $d$." + For couvenience of this section. we introduce spherical coordinate svsteni iu which the disk plane coincides with the 0=7/2 plane. aud the star is at the 0= axis.," For convenience of this section, we introduce spherical coordinate system in which the disk plane coincides with the $\theta=\pi/2$ plane, and the star is at the $\theta=0$ axis." + The stars coordinates are thus (r. o. 0)=(4.0.0). (," The star's coordinates are thus $r$, $\phi$, $\theta) = (d,0,0)$. (" +Note that the black hole is offse from the center of these coordinates.),Note that the black hole is offset from the center of these coordinates.) + We asse local black body ciuuissivity for the disk., We assume local black body emissivity for the disk. + Iu this coordinate system the distance frou a point (ro.7/2) in the disk to the star is Yr?|d?.," In this coordinate system the distance from a point $(r,\phi,\pi/2)$ in the disk to the star is $\sqrt{r^2+d^2}$." + We thus treat the star as a point source aud the disk as an infinitely thin plane., We thus treat the star as a point source and the disk as an infinitely thin plane. + Clearly this approach is inaccurate for dZR.. but we neelect this due to very short duration of such a close approach.," Clearly this approach is inaccurate for $d\simlt R_*$, but we neglect this due to very short duration of such a close approach." +" The effective temperature of a ring with radius rin disk surface is where £, is the star luuinositv aud 6 is the Stefan-Boltzmann constant.", The effective temperature of a ring with radius $r$ in disk surface is where $L_\star$ is the star luminosity and $\sigma$ is the Stefan-Boltzmann constant. + Assmuine the black body eimissivity and inteerating over r. we arrive at the iutegrated multicolor black body disk spectimu.," Assuming the black body emissivity and integrating over $r$, we arrive at the integrated multicolor black body disk spectrum." + IH the disk is inclined at anele ἐν an additional factor of cos/ should be uxed.," If the disk is inclined at angle $i$, an additional factor of $\cos i$ should be used." + This simple approach (equation 1)) to calculating the disk spectrum is an approximation to the more realistic situation., This simple approach (equation \ref{Tdisk}) ) to calculating the disk spectrum is an approximation to the more realistic situation. +" At the temperatures given by equation L.. that are usual Tye,&10° K. the main agent respousible for the disk opacity and enuüssvitv is dust."," At the temperatures given by equation \ref{Tdisk}, that are usually $T_{disk}\simlt 10^3$ K, the main agent responsible for the disk opacity and emissivity is dust." + Iu reality the ionizing UV fux of the star will create a laver of conipletelvy ionized hivdrogen ou the top of the disk., In reality the ionizing UV flux of the star will create a layer of completely ionized hydrogen on the top of the disk. + The dominant role in this laver is plaved by the eas rather than the dust., The dominant role in this layer is played by the gas rather than the dust. + Within this thin laver. the recombination rate will balance the influx of ionizing photons from the star.," Within this thin layer, the recombination rate will balance the influx of ionizing photons from the star." + AsstunineC» temperature of order LO! IC for the layer. we ∐∐≼⊔∐⋜↕↑↕↑↴∖↴↸⊳∪↕∏⋯↕⊔∐∖↻↑⊔↴∖↴ where dys is distance between the star aud the disk iu units of 1027 cim. and yy is the lvdrogen unelei density in units of 101 3," Assuming temperature of order $10^4$ K for the layer, we find that its column depth is where $d_{15}$ is distance between the star and the disk in units of $10^{15}$ cm, and $n_{11}$ is the hydrogen nuclei density in units of $10^{11}$ $^{-3}$." + This coluun depth is orders of magnitude smaller hau that of the putative inactive disk. which was estimates by ? to be in the range Nyy~)Lo--OD4107'yd cii2 im order to produce huuinous. enough N-rav flares (depending on the distance from and talking model uucertaiunties iuto account).," This column depth is orders of magnitude smaller than that of the putative inactive disk, which was estimated by \cite{NCS03} to be in the range $N_H\sim 10^{22}-10^{25}$ $^{-2}$ in order to produce luminous enough X-ray flares (depending on the distance from and taking model uncertainties into account)." + The thin laver will re-enüt iu he optical aud the UV the incident stellar radiation., The thin layer will re-emit in the optical and the UV the incident stellar radiation. + Fraction of the UV. flux is emitted back out of the disk. and a fraction is enuütted towards the disk. penetrating deeper aud ionizing deeper lavers.," Fraction of the UV flux is emitted back out of the disk, and a fraction is emitted towards the disk, penetrating deeper and ionizing deeper layers." +" The flux re-elitted below the Lyman limit (aud below the correspouding thresholds for photo-ionizatiou of Ποια, Oxveen aud other abundant elements) can penetrate uuch deeper in the disk than the original ionizing stellar xàhotous."," The flux re-emitted below the Lyman limit (and below the corresponding thresholds for photo-ionization of Helium, Oxygen and other abundant elements) can penetrate much deeper in the disk than the original ionizing stellar photons." + This radiation will be absorbed chiefly bv the dust grains “deep” inside the disk aud then be emitted as he blackbody caleulated iu equation 1.., This radiation will be absorbed chiefly by the dust grains “deep” inside the disk and then be emitted as the blackbody calculated in equation \ref{Tdisk}. + Frou this discussion it is clear that in reality a fraction of the incident UV. radiation is reflected in the opticalUV baud., From this discussion it is clear that in reality a fraction of the incident UV radiation is reflected in the optical-UV band. + Correspondingly this fraction of the incideu radiation should not be counted iu equation 1..," Correspondingly, this fraction of the incident radiation should not be counted in equation \ref{Tdisk}." + However. or the stellar spectrum that we assume here. ic. the dackbody with T=30.000 EK. ouly about of he euergv ds ciitted at requeucies above the Lyman nuit. and therefore it seems that the shielding effec of the ionized laver should not be τον larec.," However, for the stellar spectrum that we assume here, i.e. the blackbody with $T=30,000$ K, only about of the energy is emitted at frequencies above the Lyman limit, and therefore it seems that the shielding effect of the ionized layer should not be very large." + Similarly. he dust scattering opacity could in certain wavelenetls exceed that for the dust absorption. aud then a siguificar yaction of the incident stellar radiation flux could be reflected back with uo change iu frequency.," Similarly, the dust scattering opacity could in certain wavelengths exceed that for the dust absorption, and then a significant fraction of the incident stellar radiation flux could be reflected back with no change in frequency." + However we calculated (using ? optical constants and a Mie code xovided by Ik. Dulleiioud) the dust opacity for several vpical erain sizes and found that this occurs in a rather warow range of conditions. aud hence we neglected. this effect.," However we calculated (using \citealp{Draine84} optical constants and a Mie code provided by K. Dullemond) the dust opacity for several typical grain sizes and found that this occurs in a rather narrow range of conditions, and hence we neglected this effect." + We also estimated the Brackett + (A= 2.1621) ine flux from this photo-ionized laver of eas., We also estimated the Brackett $\gamma$ $\lambda=2.16 \mu$ m) line flux from this photo-ionized layer of gas. + We used ie nuniber of ionizing photons appropriate for a BO star. a laver tenrperature of 10.000 I& aud the case D approxination (see?)..," We used the number of ionizing photons appropriate for a B0 star, a layer temperature of 10,000 K and the case B approximation \citep[see][]{Osterbrock89}." + The resulting equivaleut width of js is — GOA.. about twenty times larger Ενα the absorption in the DBr5 line from the star itself (secFig.1in ?)..," The resulting equivalent width of this is $\sim$ 60, about twenty times larger than the absorption in the $\gamma$ line from the star itself \citep[see +Fig. 1 in][]{Ghez03b}." +" In addition. we estimated the coutimuuna free-free eauission from the ploto-ionized laver to vield 2L,107? erg/sec at 2.2 gan. which is at the level of a few tenths of S2 spectral Iuniünositv (see Fig. 6))."," In addition, we estimated the continuum free-free emission from the photo-ionized layer to yield $\nu +L_\nu\sim 10^{35}$ erg/sec at 2.2 $\mu$ m, which is at the level of a few tenths of S2 spectral luminosity (see Fig. \ref{fig:nuLnuvsdist}) )," + above the current uncertainties in the flux of S2 (see ?).., above the current uncertainties in the flux of S2 \citep[see][]{Ott03}. . + Thus. if such a strong Brackett 5 and the free-free coutiuuunn enmission," Thus, if such a strong Brackett $\gamma$ and the free-free continuum emission" +almost. 3000 discovered) for which both parameters have been measured from microlensing data alone (Anetal.2003:IxXiibasοἱ2005).. and both of these were binary lenses.,"almost 3000 discovered) for which both parameters have been measured from microlensing data alone \citep{an02,kubas05}, and both of these were binary lenses." + The only known way toroutinely determine Oy: is by high-precision astrometric measurements of the microlensing event (logetal.1995:Mlivamoto&YoshiiWalkerPaczviski1998:Bodenetal. 1993).," The only known way to determine $\btheta_\e$ is by high-precision astrometric measurements of the microlensing event \citep{HNP95,MY95,Wa95,Pa98,BSV98}." +". The centroid of the microlensed images deviates [rom the source position by an amount and direction (hat vields both components of 0,..", The centroid of the microlensed images deviates from the source position by an amount and direction that yields both components of $\btheta_\e$. + The only known wav toroutinely determine zy is {ο make photometric measurements of the event [rom (wo locations separated by of order ὃς (Iefsdal1966:Gould1994).," The only known way to determine $\pi_\e$ is to make photometric measurements of the event from two locations separated by of order $\tilde r_\e$ \citep{Re66,gould94}." +. The difference in the event parameters then vields both the size of Pj ancl the direction of motion (he latter potentially confirming the direction extracted [rom 04)., The difference in the event parameters then yields both the size of $\tilde r_\e$ and the direction of motion (the latter potentially confirming the direction extracted from $\btheta_\e$ ). + Since Pj~O(AU). in practice this means placing a satellite in solar orbit.," Since $\tilde r_\e \sim O(\au)$, in practice this means placing a satellite in solar orbit." + Although there is a four-fold ambiguity in (he determination of me. this can be resolved by higher-order effects (Gould1995a).," Although there is a four-fold ambiguity in the determination of $\pi_\e$, this can be resolved by higher-order effects \citep{gould95a}." +". Moreover. measurement of (he direction of 0, also helps resolve this degeneracy."," Moreover, measurement of the direction of $\btheta_\e$ also helps resolve this degeneracy." + Gould&Salim(1999) showed that the combined with ground-based photometry. could determine both of these parameters with οσους ~3% precision with about 5 hours total obsrvation time lor bright (J~15) events having tvpical lens parameters.," \citet{gs99} showed that the combined with ground-based photometry, could determine both of these parameters with good $\sim 3\%$ precision with about 5 hours total obsrvation time for bright $(I\sim 15)$ events having typical lens parameters." + Moreover. thev showed that the same observations would also vield good measurements of πι and µ..," Moreover, they showed that the same observations would also yield good measurements of $\pi_s$ and $\bmu_s$." + Hence.SLA (combined with ground-based photometrv) could measure all (he required quantities for about 200 events with about 1000 hours of observing tine.," Hence, (combined with ground-based photometry) could measure all the required quantities for about 200 events with about 1000 hours of observing time." + Indeed. a5747 Wey Project has been awarded 1200 hours of observation (ime to carry out such observations.," Indeed, a Key Project has been awarded 1200 hours of observation time to carry out such observations." + The main objective of this project is to measure the bulge mass function but the same observations could cull out the handful of halo events that could be present in the same sample., The main objective of this project is to measure the bulge mass function but the same observations could cull out the handful of halo events that could be present in the same sample. +SIM has been descoped since Gould&Salim(1999) mace their analvsis., has been descoped since \citet{gs99} made their analysis. + The new performance is not precisely known but itis likely (hat the precision will degrade to something like ~5% for πι and ~LOW. for @ lor the canonical events considered by (1999)., The new performance is not precisely known but it is likely that the precision will degrade to something like $\sim 5\%$ for $\pi_\e$ and $\sim 10\%$ for $\theta_\e$ for the canonical events considered by \citet{gs99}. +. Moreover. it is unlikely that 200 /=15 events will be found cluring the 5-vear primarySZAL mission. and using Lnter sources (e.g.. £= 16.5) would futher degrade the precision by a factor 2.," Moreover, it is unlikely that 200 $I=15$ events will be found during the 5-year primary mission, and using fainter sources (e.g., $I=16.5$ ) would further degrade the precision by a factor 2." + Nevertheless. as E show below. this precision would be cuite adequate for distinguishing halo lenses.," Nevertheless, as I show below, this precision would be quite adequate for distinguishing halo lenses." + , +112. e.g. if the pulsed. radiation came from two antipoda poles on the NS.,"Hz, e.g. if the pulsed radiation came from two antipodal poles on the NS." + Although searches for à signal at half the burst oscillations frequency. the putative spin frequency of the neutron star (Miller1999).. in the power spectrum of the bursts in 4U 163653 vielded no positive result. (Strohmayer2001:Strohmaver&Markwardt 2002).. this option remainec viable.," Although searches for a signal at half the burst oscillations frequency, the putative spin frequency of the neutron star \citep{miller-sub}, in the power spectrum of the bursts in 4U 1636–53 yielded no positive result \citep{strohmayer-adspr, strohmayer-sub}, this option remained viable." +" When kllz QPOs and burst oscillations were discoverec in more sources. it became apparent that there was a systematic trend in how Av and 4, were related: For sources or which £j,2:400 Liz. Av2 6. whereas for sources for which wm<400 Lz. Av26/2."," When kHz QPOs and burst oscillations were discovered in more sources, it became apparent that there was a systematic trend in how $\Delta \nu$ and $\nu_b$ were related: For sources for which $\nu_b \simless 400$ Hz, $\Delta \nu \simeq \nu_b$ , whereas for sources for which $\nu_b \simmore +400$ Hz, $\Delta \nu \simeq \nu_b/2$." +" These two groups of sources were hen called “slow” and. ""fast rotators. respectively etal. 2001).."," These two groups of sources were then called “slow” and “fast” rotators, respectively \citep{muno}." + Related to this. it is interesting to note that when plotted against cach other. the frequencies of the kIIz QPOs in 19 cilferent sources all follow approximately the same relation (Belloni.Méndez.&Loman2005.2007:Zhangal. 2006).," Related to this, it is interesting to note that when plotted against each other, the frequencies of the kHz QPOs in 19 different sources all follow approximately the same relation \citep*{bmh05, bmh07, zhang06}." +". ""This is a priori unexpected if in cach source the requency of the upper and lower kllz QPOs were related o the spin frequency as v2νι|vs. given that 7, and η span more or less the same frequency range in all sources of «Iz QPOs. whereas the neutron stars in these systems have spins that span a large range of frequencies. 7.z200—620 11 (Chakrabartyetal. 2003).."," This is a priori unexpected if in each source the frequency of the upper and lower kHz QPOs were related to the spin frequency as $\nu_2 = \nu_1 ++ \nu_s$, given that $\nu_1$ and $\nu_2$ span more or less the same frequency range in all sources of kHz QPOs, whereas the neutron stars in these systems have spins that span a large range of frequencies, $\nu_s +\approx 200 - 620$ Hz \citep{chakrabarty-1808}. ." +" Alore kHz QPO data. and more precise QPO (requeney measurements. showed that at least in some sources Ay was not constant. but decreased. as the QPO frequencies increased (vanderWhisetal.1997:Méndez1999). and it was always significantly lower than either 1, (Méndez&vanderWlis1999). or ™,/2 (Móndez.vanderνα».&vanParaclijs 1998)."," More kHz QPO data, and more precise QPO frequency measurements, showed that at least in some sources $\Delta \nu$ was not constant, but decreased as the QPO frequencies increased \citep{vanderklis-scox-1, +mendez-1608}, and it was always significantly lower than either $\nu_b$ \citep{mendez-1728} or $\nu_b/2$ \citep*{mendez-1636}." +. Modifications of the sonic-point mocel (Lamb&Miller2001). could account. for this cüllerence. considering that the frequencies of the QPOs drift. slightly when the material that produces the QPOs crosses the sonic »ont. and falls onto the neutron star surface.," Modifications of the sonic-point model \citep{lamb} could account for this difference, considering that the frequencies of the QPOs drift slightly when the material that produces the QPOs crosses the sonic point and falls onto the neutron star surface." +" Three other results raised more serious issues against he sonic-point beat-frequeney model. and eventually rendered. it untenable: (1) Jonker.Méndez&vanderElis(2002) found that in 4U 163653. when the frequeney of the kHz QPOs decreases sulliciently. Av is significantly. higher han £,/2. which was difficult (if not impossible) to explain » the sonic-point model. even after the modifications introduced. by LambἂνMiller(2001): in the ΑΔΗ SAN JLSOS.43658. (i) Chakrabartyetal.(2003). found. that he frequeney of burst oscillations is equal to the NS spin requency (sceAlarkwarelt&Swank2003.forasimilarre- 338).. while (iii) Wijnancdsetal.(2003). detected: two simultaneous kIIz QPOs with a requency separation Av&p,ο."," Three other results raised more serious issues against the sonic-point beat-frequency model, and eventually rendered it untenable: (i) \cite*{jonker-1636} found that in 4U 1636–53, when the frequency of the kHz QPOs decreases sufficiently, $\Delta \nu$ is significantly higher than $\nu_b / 2$, which was difficult (if not impossible) to explain by the sonic-point model, even after the modifications introduced by \cite{lamb}; in the AMP SAX J1808.4–3658, (ii) \cite{chakrabarty-1808} + found that the frequency of burst oscillations is equal to the NS spin frequency \citep[see][for a similar result in another AMP, XTE +J1814--338]{markwardt-1814-iauc}, while (iii) \cite{wijnands-1808} + detected two simultaneous kHz QPOs with a frequency separation $\Delta +\nu \simeq \nu_s/2$." +" MO this is extended to other sources in which Av~™/2. it would also be true that [or hose £j,=7.. and hence Avzμ.ο."," If this is extended to other sources in which $\Delta \nu \simeq \nu_b/2$, it would also be true that for those $\nu_b += \nu_s$, and hence $\Delta \nu \simeq \nu_s/2$." + The sonic-point moclel could not explain this., The sonic-point model could not explain this. + But soon after the SAN JLSOS.43658. results were xiblished. a new model that reestablished a relation between he spin frequency of the NS and the κ ΟΡΟ. the sonic-»oint and spin-resonance model (Lamb&Miller 2003)... was ooposed (seealsoLeectal.2004)...," But soon after the SAX J1808.4–3658 results were published, a new model that reestablished a relation between the spin frequency of the NS and the kHz QPO, the sonic-point and spin-resonance model \citep{lamb-miller}, was proposed \citep[see also][]{lee}." + In this model. there is a resonance in the accretion disk at the radial distance at which the Ixeplerian orbital [requeney is equal to the neutron star spin frequency. minus the vertical epievelie frequency.," In this model, there is a resonance in the accretion disk at the radial distance at which the Keplerian orbital frequency is equal to the neutron star spin frequency minus the vertical epicyclic frequency." + This resonance could lead to either Av=vs. or Av=v2 depending on whether the disk How at the resonance radius is smooth or clumped., This resonance could lead to either $\Delta \nu = \nu_s$ or $\Delta \nu = \nu_s/2$ depending on whether the disk flow at the resonance radius is smooth or clumped. + In fact. the same source may in principle show both cases. but this has so far not. been observed.," In fact, the same source may in principle show both cases, but this has so far not been observed." + Almost in parallel with some of these explanations. and as a result of some of the dilliculties for. beat-frequencey models mentioned. above. a cdilferent class of models: was proposed. in which the frequencies of the kllz QPOs were associated to two of the three epievclic frequencies of general relativity. or a combination of those (e.g..Stella&Vietri1999)..," Almost in parallel with some of these explanations, and as a result of some of the difficulties for beat-frequency models mentioned above, a different class of models was proposed, in which the frequencies of the kHz QPOs were associated to two of the three epicyclic frequencies of general relativity, or a combination of those \citep[e.g.,][]{stella2}." +. In these models. the NS spin frequency plays no role in setting up the frequencies of the ΚΣ QPOs. except for the small corrections it. introduces to the epievelie frequencies.," In these models, the NS spin frequency plays no role in setting up the frequencies of the kHz QPOs, except for the small corrections it introduces to the epicyclic frequencies." + While these mocdels reproduce qualitatively the trends seen in the data. and. predicted other trends that were later on observed (Migliarietal.2003:Boutloukos2006).. they have problems to fit the data in detail.," While these models reproduce qualitatively the trends seen in the data, and predicted other trends that were later on observed \citep{migliari-1728, boutloukos-cirx1}, they have problems to fit the data in detail." + Phe main criticism to these mocdoels. however. has abwayvs been that. they do not explain the fact that in several sources Av&vs or Avc9ο (Lamb2003).," The main criticism to these models, however, has always been that they do not explain the fact that in several sources $\Delta \nu \simeq \nu_s$ or $\Delta \nu \simeq +\nu_s / 2$ \citep{lamb-jvp}." +. In other words. the criticism is that in these models the NS spin plavs no role in the mechanism that. produces the QPOs.," In other words, the criticism is that in these models the NS spin plays no role in the mechanism that produces the QPOs." + Recenth. Yinetal.(2007) compared the average frequeney separation. of the kllz QPOs. GN. with wv. in six systems in which these two quantities have been measured.," Recently, \cite{yin} compared the average frequency separation of the kHz QPOs, $\langle \Delta \nu \rangle$, with $\nu_s$ in six systems in which these two quantities have been measured." +" They suggest that. despite the low number of sources available for their analysis. (Ai) depends weakly on we. GN)00.206,|390 Lz."," They suggest that, despite the low number of sources available for their analysis, $\langle +\Delta\nu \rangle$ depends weakly on $\nu_s$, $\langle \Delta\nu \rangle +\simeq -0.20 \nu_s + 390$ Hz." + In summary. the history of models of the ΚΣ QPOs is a evele of attempts to explain the phenomenon in relation to the spin of the NS: each time that a new observation raised an issue against one such moclel. a mocliflication of that model. or a new model. was proposed that tried. to reestablish the role of the NS spin in the mechanism that produces the kIIz QPOs.," In summary, the history of models of the kHz QPOs is a cycle of attempts to explain the phenomenon in relation to the spin of the NS; each time that a new observation raised an issue against one such model, a modification of that model, or a new model, was proposed that tried to reestablish the role of the NS spin in the mechanism that produces the kHz QPOs." + After more than ten vears [rom the cliscovery of the kllz QPOs. a critical assessment of the current. paracignis is necessary.," After more than ten years from the discovery of the kHz QPOs, a critical assessment of the current paradigms is necessary." + Here we review all the values of Av and. f available in the literature in order to compare the slow/fast rotator paradigm with other possibilities., Here we review all the values of $\Delta\nu$ and $\nu_s$ available in the literature in order to compare the slow/fast rotator paradigm with other possibilities. + We suggest that the data may in fact show that there is no relation between NS spin and ΚΣ QPOs., We suggest that the data may in fact show that there is no relation between NS spin and kHz QPOs. + Actually. the cata appear to be consistent with a situation in which the average separation in [frequency of the kllz QPOs GN). is more or. less constant. independent of the spin of the neutron star in the system.," Actually, the data appear to be consistent with a situation in which the average separation in frequency of the kHz QPOs $\langle \Delta \nu \rangle$ is more or less constant, independent of the spin of the neutron star in the system." + The division between “slow ancl ιδ rotators may be an elfect of the low number of sources for which two simultaneous ΚΣ QPOs anc burst oscillations and/or pulsations in the persistent emission have been observed. and the fact that (Av) 1s independent of v..," The division between “slow” and “fast” rotators may be an effect of the low number of sources for which two simultaneous kHz QPOs and burst oscillations and/or pulsations in the persistent emission have been observed, and the fact that $\langle \Delta \nu \rangle$ is independent of $\nu_s$." + We use data from the literature., We use data from the literature. + For the rest of the paper we assume that the [requeneyο of burst oscillations isequal to the spin frequency of the neutron star.ος (see refintro)).," For the rest of the paper we assume that the frequency$\nu_b$ of burst oscillations isequal to the spin frequency of the neutron star,$\nu_s$ (see \\ref{intro}) )." + There are ten sources for which both Av ane vy have been measured., There are ten sources for which both $\Delta \nu$ and $\nu_s$ have been measured. + Pwo of these sources are the AALDPs SAN JISOS.43658 and NTE J1807294. six of them are the atoll sources 4U 160852. 4U 163653. 4U 170243. 4U 172834. WS 1731260. and 4U 191505," Two of these sources are the AMPs SAX J1808.4–3658 and XTE J1807–294, six of them are the atoll sources 4U 1608–52, 4U 1636–53, 4U 1702–43, 4U 1728–34, KS 1731–260, and 4U 1915–05" +We. note that in. the case where we do not restrict. the lag to lie within anv given range. the global significance is low.,"We note that in the case where we do not restrict the lag to lie within any given range, the global significance is low." + For example. it is not surprising that the S.4 Cllz versus X-ray CCE shows two peaks at greater than 95% loca confidence. since the corresponding elobal confidence at this evel is only 56%. so we expect a spurious peak in nearly half ofthe CCEs sampled from random light curves.," For example, it is not surprising that the 8.4 GHz versus X-ray CCF shows two peaks at greater than $\%$ local confidence, since the corresponding global confidence at this level is only $\%$, so we expect a spurious peak in nearly half of the CCFs sampled from random light curves." + Llowever the ocak corresponding to a negative lag of 140 days (ie. racio eading X-rav) cannot easily be explained with any physica model., However the peak corresponding to a negative lag of $\sim140$ days (i.e. radio leading X-ray) cannot easily be explained with any physical model. + When we presume that there must be a positive lag (radio lageing N-rav) - as we would indeed: predict. basec on our current understanding of the accretion disk/jet - his elobal significance level increases., When we presume that there must be a positive lag (radio lagging X-ray) - as we would indeed predict based on our current understanding of the accretion disk/jet - this global significance level increases. + Put another way. it is statistically unlikely that a spurious correlation shoutle appear in the range of lags which matches our physica expectations. as seems to be the case here.," Put another way, it is statistically unlikely that a spurious correlation should appear in the range of lags which matches our physical expectations, as seems to be the case here." + Therefore. we assume for the remainder of the paper that the correlation is real.," Therefore, we assume for the remainder of the paper that the correlation is real." +" Note that if the correlation is real. the lags can be well-determined: the significance o£ a lag and the significance of a correlation itself are unrelated. quantities. since a lag can be very well determined from just a single well-sampled ""event! (flare. or dip) in red noise data. if the data. are indeed: correlated."," Note that if the correlation is real, the lags can be well-determined: the significance of a lag and the significance of a correlation itself are unrelated quantities, since a lag can be very well determined from just a single well-sampled `event' (flare or dip) in red noise data, if the data are indeed correlated." + We will explore possible complexities in the disk/jet connection with respect to our calculated lags in section 5.1 To caleulate the cross-correlation between the two racio mands we used. the z-transformed discrete. correlation unction (ZDCE) of Alexander(1997).. see figure 3..," We will explore possible complexities in the disk/jet connection with respect to our calculated lags in section 5.1 To calculate the cross-correlation between the two radio bands we used the z-transformed discrete correlation function (ZDCF) of \cite{Alexander}, see figure \ref{CCF_radio}." + Note hat the two radio light curves are sampled at. the sanie ime: as noted. in Edelson&Wrolik(1988): to keep the normalisation correct for the DCE we need to omit the zero ag pairs as the errors between the two bands are correlated., Note that the two radio light curves are sampled at the same time: as noted in \cite{CCF_Paper}; to keep the normalisation correct for the DCF we need to omit the zero lag pairs as the errors between the two bands are correlated. + Therefore for convenience. (and. as the two methods. are comparable) we switch to the ZDCT which omits zero lagged ours., Therefore for convenience (and as the two methods are comparable) we switch to the ZDCF which omits zero lagged pairs. + We calculate the errors using the same method as described in section 4.1., We calculate the errors using the same method as described in section 4.1. + We thus find το=20.5+12.9 , We thus find $\tau_{cent}=20.5 \pm 12.9$ +The Virgo° Cluster is the second. brightest. extragalactic.? extended X-ray source in the 0.1.2.4 keV. ROSAT band. ancl the closest galaxy cluster (16.1 Alpe: Tonry 2001).,"The Virgo Cluster is the second brightest, extragalactic, extended X-ray source in the $0.1-2.4$ keV ROSAT band, and the closest galaxy cluster (16.1 Mpc; Tonry 2001)." + Ehe central galaxy of the Virgo Cluster. ALSST. hosts an active galactic nucleus (AGN) that exhibits compelling evidence for complex interactions with the surrounding cluster gas Bóhhringer 1995: Young 2002: Forman 2005. 2007).," The central galaxy of the Virgo Cluster, 87, hosts an active galactic nucleus (AGN) that exhibits compelling evidence for complex interactions with the surrounding cluster gas Böhhringer 1995; Young 2002; Forman 2005, 2007)." +" SST is. therefore. an object with which: to study AGN RENdriven processes AGN ""Dfeedback) that alfect the centers of galaxies anc galaxy. clusters."," 87 is, therefore, an object with which to study AGN driven processes AGN feedback) that affect the centers of galaxies and galaxy clusters." + The relatively cool. dense gas at the centers of many galaxy clusters emits copiously at. X-ray wavelengths.," The relatively cool, dense gas at the centers of many galaxy clusters emits copiously at X-ray wavelengths." + bo, In +The candidates’ final positions were determined with the ΗΑΕ taskzmeen£roid.,The candidates' final positions were determined with the IRAF task. + Positions of the objects were measured with data from the epoch in which the object. appeared brighter., Positions of the objects were measured with data from the epoch in which the object appeared brighter. + Two objects did not provide reliable centroids. suggesting that they were not strong detections and/or not point sources.," Two objects did not provide reliable centroids, suggesting that they were not strong detections and/or not point sources." + These candidates were removed. leaving a final list of 212 variable star candidates to be measured.," These candidates were removed, leaving a final list of 272 variable star candidates to be measured." + Aperture photometry was performed at theimcentroid position for each candidate using ihe IRAE taskphot., Aperture photometry was performed at the position for each candidate using the IRAF task. +" The aperture radius was 0.15"". and the annulus used to measure the skv brightness was from 0.30"" to 0.55""."," The aperture radius was $''$, and the annulus used to measure the sky brightness was from $''$ to $''$." + The photometry was performed identically for both epochs., The photometry was performed identically for both epochs. + These measurements vielded the ACS count rate for each candidate during each observation epoch., These measurements yielded the ACS count rate for each candidate during each observation epoch. + The count rates measured [rom the ACS images were converted to VEGA magnitudes using the calibration provided in the ACS. DataIHandbook., The count rates measured from the ACS images were converted to VEGA magnitudes using the calibration provided in the ACS Data. +. The VEGA magnitudes for ihe F435W filter is the ACS equivalent to the Johnson D magnitude., The VEGA magnitudes for the F435W filter is the ACS equivalent to the Johnson $B$ magnitude. + The final conversion formula was: where r is (he count rate measured byphof., The final conversion formula was: where $r$ is the count rate measured by. + Sources wilh D~27.8 were detected wilh 5o significance., Sources with $B\sim27.8$ were detected with $\sigma$ significance. + I took this to be the detection limit. only accepting detections brighter than this and assigning an upper-Himit D>27.8. to all non-detections.," I took this to be the detection limit, only accepting detections brighter than this and assigning an upper-limit $B>27.8$, to all non-detections." + The final 2 magnitudes [rom the second epoch were sublractecl from those of the first. ancl the photometric errors were added in quadrature.," The final $B$ magnitudes from the second epoch were subtracted from those of the first, and the photometric errors were added in quadrature." + No errors were assigned {ο non-detections., No errors were assigned to non-detections. + All of the candidates whose magnitudes changed by [four times (he root-stm-sequare ol their errors (or more) were included in the final catalog of variables given in Table 1.., All of the candidates whose magnitudes changed by four times the root-sum-square of their errors (or more) were included in the final catalog of variables given in Table \ref{cat}. + This requirement eliminated 3 candidates from the original list. reducing the catalog to 269 variable stars.," This requirement eliminated 3 candidates from the original list, reducing the catalog to 269 variable stars." + Finally. for all cases of stars detected in only one epoch. the four clithered ACS exposures of the detection epoch were inspected to ensure that these detections were nol cosmüc-ravs or artifacts from (he image processing.," Finally, for all cases of stars detected in only one epoch, the four dithered ACS exposures of the detection epoch were inspected to ensure that these detections were not cosmic-rays or artifacts from the image processing." + Real stars were seen in all of the individual raw exposures. while cosmic rays and artifacts were not.," Real stars were seen in all of the individual raw exposures, while cosmic rays and artifacts were not." + These inspections found, These inspections found +than a2 factor 1.5 is unphysical.,length variation larger than a factor 1.5 is unphysical. + We BoEF Elength determine limit for a pair of filters by plotting 3 t : ratio versus magnitude in one of the bands 1E 4 (see ," We determine the magnitude limit for a pair of filters by plotting the scale length ratio versus magnitude in one of the bands (see Fig. \ref{fig:magcut}) )," +and scan the values from the brighter to the Ε 3 fainter fixed bins of 0.2 magnitudes., and scan the values from the brighter to the fainter levels in fixed bins of 0.2 magnitudes. +" Once we reach C ————————— n a magnitude where less than of the scale length ratios is smaller than 0.67 or larger than 1.5 (i.e., above or below the horizontal dotted lines in Fig. 9)),"," Once we reach a magnitude where less than of the scale length ratios is smaller than 0.67 or larger than 1.5 (i.e., above or below the horizontal dotted lines in Fig. \ref{fig:magcut}) )," + we stop the scan and select this value for the faintest magnitude level in that band for which we trust the scale lengths., we stop the scan and select this value for the faintest magnitude level in that band for which we trust the scale lengths. +" As shown in Fig. 9,,"," As shown in Fig. \ref{fig:magcut}," +" this procedure very clearly demonstrates the noise in different bands, and how the values presented in table 3 have been established."," this procedure very clearly demonstrates the noise in different bands, and how the values presented in table \ref{tab:ugriz} have been established." +" In the given examples, the scale lengths in r- band when compared to i-band are complete to an r-band magnitude of 17.70 (indicated by the arrow), and the wu versus z-band is complete to an u-band magnitude of 16.29 (indicated by the arrow)."," In the given examples, the scale lengths in $r$ -band when compared to $i$ -band are complete to an $r$ -band magnitude of 17.70 (indicated by the arrow), and the $u$ versus $z$ -band is complete to an $u$ -band magnitude of 16.29 (indicated by the arrow)." +through to grever overall than any of the SAIC. LMC or AIW curves but with a strong feature (consistent with the low Z form presented by 7)) at high (2B 13. would. provide powerful constraints on mocels of star formation and chemical enrichment histories for. physical systems associated with metal absorbers over an extended range in column clensity.,"through to greyer overall than any of the SMC, LMC or MW curves but with a strong feature (consistent with the low $R_V$ form presented by \citet{1999PASP..111...63F}) ) at high $E(B-V)$ , would provide powerful constraints on models of star formation and chemical enrichment histories for physical systems associated with metal absorbers over an extended range in column density." + We would like to thank Bob. Carswell. Becky Canning. Dan Nestor. Max Pettini ancl Arthur. Wolfe for valuable cdisceussions.," We would like to thank Bob Carswell, Becky Canning, Dan Nestor, Max Pettini and Arthur Wolfe for valuable discussions." + JAIB acknowledges the award of a STEC rescarch studentship., JMB acknowledges the award of a STFC research studentship. + PCLE acknowledges support from the STEC-funded Galaxy Formation anc Evolution programme at the Institute of Astronomy., PCH acknowledges support from the STFC-funded Galaxy Formation and Evolution programme at the Institute of Astronomy. + This work has made extensive use of the Numerical Recipes €||. library and the Veusz scientific plotting package., This work has made extensive use of the Numerical Recipes C++ library and the Veusz scientific plotting package. + Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred. P. Sloan Foundation. the Participating Institutions. the National Acronautics and Space Administration. the National Science Foundation. the US Department of Energy. the Japanese Monbukagakusho. and the Alax Planck Society.," Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the US Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society." + The SDSS website is http:/www.scdss.org/. Phe SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions., The SDSS website is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. + The Participating Institutions are The University of Chicago. Fermilab. the Institute for Advanced Study. the Japan Participation Group. The Johns llopkins University. Los Alamos National Laboratory. the Max Planck Institute for Astronomy (MDPLX). the Max Planck Institute for. Astrophysics (MIA). New Mexico State University. the University of PBtsburgh.. Princeton University. the United States Naval Observatory. ancl the University of Washington.," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max Planck Institute for Astronomy (MPIA), the Max Planck Institute for Astrophysics (MPA), New Mexico State University, the University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington." +We sce that for a given offset. the cussion altitude is not uniquely determined. w Ay.,"We see that for a given offset, the emission altitude is not uniquely determined by $\Delta \varphi$." + Fora<60°. the same Ay is possible or two altitudes. while for a>607. a Whole interval of altitudes is possible.," For $\alpha \le 60^\circ$, the same $\Delta \varphi$ is possible for two altitudes, while for $\alpha \ge 60^\circ$, a whole interval of altitudes is possible." +" Thus the altitude is a multivalued ""unction of the offse Ay.", Thus the altitude is a multivalued function of the offset $\Delta \varphi$. +" It is wortlwhile to keep in niud that οιr plots when applied to a specific mulsar select a partic""lar rauge of the w-anxis.", It is worthwhile to keep in mind that our plots when applied to a specific pulsar select a particular range of the $x$ -axis. + This range is determined by both he period of the pusar ancl the assumed euiission altitude., This range is determined by both the period of the pulsar and the assumed emission altitude. + Clearly. for a given Cluission altitude. the co-rotation velocity wi] increase inversely with the pulsar )oriod.," Clearly, for a given emission altitude, the co-rotation velocity will increase inversely with the pulsar period." +" Now we turn to he comparison of A, xwith observations.", Now we turn to the comparison of $\Delta_{cc}$ with observations. + The core/coue phase offsets can coustrain only the difference between the two cnussion altitudes., The core/cone phase offsets can constrain only the difference between the two emission altitudes. + Therefore. it is not. possible to make a direct comparison of our results with observations so as to fit for individual pulsar parameters.," Therefore, it is not possible to make a direct comparison of our results with observations so as to fit for individual pulsar parameters." +side of a particular spiral arm.,side of a particular spiral arm. + This method has been used for NGCO6369. NGC6537. NGC6886 and NGC7027 (of the PNe which interest us).," This method has been used for NGC6369, NGC6537, NGC6886 and NGC7027 (of the PNe which interest us)." + This method 1s again limited to PNe near the galactic plane (see Gathier et al. (1986b)))., This method is again limited to PNe near the galactic plane (see Gathier et al. \cite{gath2}) ). + In addition use can be made of the average extinction (in magnitudes per kpe) in. various directions., In addition use can be made of the average extinction (in magnitudes per kpc) in various directions. + Such maps have been made by several authors but because a relatively limited number of stars are used. these maps are averages over relatively large areas and are more uncertain than when a small area is studied in depth.," Such maps have been made by several authors but because a relatively limited number of stars are used, these maps are averages over relatively large areas and are more uncertain than when a small area is studied in depth." + Results of this method are given for a large number of PNe by Pottasch (1984) and Sabbadin (1986).., Results of this method are given for a large number of PNe by Pottasch \cite{pott12} and Sabbadin \cite{sabbadin2}. + The results of these two authors generally agree when the same nebulae are compared., The results of these two authors generally agree when the same nebulae are compared. + We will use them when no other individual distance is available., We will use them when no other individual distance is available. + Another method of distance determination from the spectroscopic measurements of the central star., Another method of distance determination is from the spectroscopic measurements of the central star. + These measurements have already been discussed in section 3.1.5 for determining the central star temperatures for which. with the exception of NGC2392. reasonable agreement was obtained with the temperatures found from the nebular spectrum.," These measurements have already been discussed in section 3.1.5 for determining the central star temperatures for which, with the exception of NGC2392, reasonable agreement was obtained with the temperatures found from the nebular spectrum." + The same discussions (Pauldrach et al.(2004).. Kudritzki et al.(1997) and Mendez et al.(1988))) derive the distance and mass of various bright central stars.," The same discussions (Pauldrach et \cite{pauldrach}, Kudritzki et \cite{kudritzki} and Mendez et \cite{mendez}) ) derive the distance and mass of various bright central stars." + These distances are not included in the present discussion., These distances are not included in the present discussion. + The reason for this 1s the following., The reason for this is the following. + The large masses and distances found by Pauldrach et al., The large masses and distances found by Pauldrach et al. + are improbable., are improbable. + This has been convincingly demonstrated by citenapiwotzki.. who found that the kinematic properties of these nebulae are inconsistent with the masses and distances," This has been convincingly demonstrated by \\cite{napiwotzki}, who found that the kinematic properties of these nebulae are inconsistent with the masses and distances" +in the Cl 16014051 c]uste: field. as well as the entire photometric sample lor this cluster.,"in the Cl 1604+4321 cluster field, as well as the entire photometric sample for this cluster." + This time. however. we have usec the extrinsic error which is caleulated iudepende1ly for each galaxy.," This time, however, we have used the extrinsic error which is calculated independently for each galaxy." + By judiciously selecting the probability threshold. we cau maximize the cornjxleteuess (wuich is zz NNUC). while minimizing t1ο contanination (which is zz21%).," By judiciously selecting the probability threshold, we can maximize the completeness (which is $\approx 88\%$ ), while minimizing the contamination (which is $\approx 21\%$ )." + While we wotld clearly preer full completeness aud no coutamiration. this cluster demonstrates oue oft 1e strenigt150 “our {οςuleque. junely the ability to einpirially quantify both oir completeness anc contamitation.," While we would clearly prefer full completeness and no contamination, this cluster demonstrates one of the strengths of our technique, namely the ability to empirically quantify both our completeness and contamination." + In fact. our techuique predicts 37 cluster meinbers within the [ield of viev: of Oll COLibined image (see Figure 6)).," In fact, our technique predicts 37 cluster members within the field of view of our combined image (see Figure \ref{cl1604ef}) )." + If we ise the preclictious o‘deep number COULts (e.g.Driverefal.1995:Abalamefaf1996) to est]inate the coitamination due to foregrourd aud ockgrouud galaxies. νve esimate there should be 334ll cluster nembers iu tle image (note he large uncertainty 1 this statistical calculation). which is tje exact number that we find after correcting for contaiitallol and incompleteness 3Tx(1—2“ο... 90].," If we use the predictions of deep number counts \cite[\eg][]{driver95,smail95,abraham96} to estimate the contamination due to foreground and background galaxies, we estimate there should be $33\pm14$ cluster members in the image (note the large uncertainty in this statistical calculation), which is the exact number that we find after correcting for contamination and incompleteness $37 \times (1 - 21 \%) / 88 \% = 33$ ]." + \Ve have mace this comparison with the stalist]cal background correclon siuply i1 order to show that we are finding a reasonable uumber of cluster galaxies: however. uulike the backerouud correction tecluique. we have explicitly ideutilied the likely cluster members.," We have made this comparison with the statistical background correction simply in order to show that we are finding a reasonable number of cluster galaxies; however, unlike the background correction technique, we have explicitly identified the likely cluster members." + Ii this paper. we have presentec a uovel techuique lor the probabiistic determinatio 10Í cluster uembership base solely ou photometric redshift axl redshift error estimates.," In this paper, we have presented a novel technique for the probabilistic determination of cluster membership based solely on photometric redshift and redshift error estimates." + Our tecinique Cal ye tuned to either maximize the competeness of cluster member icentilicatio1 identify al actual cluster melibers). or. alternaively. to 1iuiize {1e contamination due o foree[n]LOULcL ale ockgrouud galaxies in the field.," Our technique can be tuned to either maximize the completeness of cluster member identification identify all actual cluster members), or, alternatively, to minimize the contamination due to foreground and background galaxies in the field." +" Futlermore. this tectuique provides a robist estimation [or tli the completeness and contaiiuaticyu [raclous of identified. cluser membe""s as a function of ikelihood."," Furthermore, this technique provides a robust estimation for both the completeness and contamination fractions of identified cluster members as a function of likelihood." + A comparison between our 1 huique witi tlie traditional techuique of staIstica oackerouud. correction shows remarkable :ereement. witl the caveat that our echuique actually kleutifies the galaxies vvhich are cluster nembes.," A comparison between our new technique with the traditional technique of statistical background correction shows remarkable agreement, with the caveat that our technique actually identifies the galaxies which are cluster members." + The results in thS paper are based on a1 emipirical prolometric redshilt estination. which we lavetsed because (a) we 1ave a reliable traiiug set [ron oIr extensive spectroscodic survey. and (b) hese photometric redshifts are less seusitiv to uncertaitties in spectra evolutio1 which can allect other redshift estiatici techniques.," The results in this paper are based on an empirical photometric redshift estimation, which we have used because (a) we have a reliable training set from our extensive spectroscopic survey, and (b) these photometric redshifts are less sensitive to uncertainties in spectral evolution which can affect other redshift estimation techniques." + Alternaive redshift estiniatlo techiniques. 1OWwever. Cau easily ye incorporated iuto he aleorithin. as all that is needed S a redshift esinate and a correspouding 'ecdshift error estimate," Alternative redshift estimation techniques, however, can easily be incorporated into the algorithm, as all that is needed is a redshift estimate and a corresponding redshift error estimate." +" .I1 the case of temslate photometric recslfts. the redslilt error could be determiued [rom either ile intrinsic clispersion iu the phoOluelric recashft relation1. au interpolation over the 4> [n]oOoocdnmess-ot-fi| parameter. or even more appropriately VOUwel a coubination"". of+ the 47> paralneter ald a Monte-Carlo bootstrap approach to mitlic pliotonetric uncertainty aucl template incompleteness."," In the case of template photometric redshifts, the redshift error could be determined from either the intrinsic dispersion in the photometric redshift relation, an interpolation over the $\chi^2$ goodness-of-fit parameter, or even more appropriately through a combination of the $\chi^2$ parameter and a Monte-Carlo bootstrap approach to mimic photometric uncertainty and template incompleteness." + Iu this case. however. caution must be isecL to màiuiulze auy possible systematic effects which might depeud ou various Puudamental assuuptious. such as the spectral type.," In this case, however, caution must be used to minimize any possible systematic effects which might depend on various fundamental assumptions, such as the spectral type." +we denoted uj(p) |and Gr. The existence of this limit will be confirmed upon obtaining the solution of eq.(24)) below.,Here we denoted ] and The existence of this limit will be confirmed upon obtaining the solution of \ref{dc:int2}) ) below. + First. we introduce the following notations can be rewritten as: uy x can be thus written as . Str. p) One sees (hat (he limit in eq.(25)) indeed exists and is equal to G=S/ic.. Furthermore. eq.(27)) describes à transition front on the particle distribution between its asviptotic value ο— Gal and g —0al£—x.," First, we introduce the following notations \ref{dc:int2}) ) then can be rewritten as: and its solution can be thus written as One sees that the limit in \ref{lim:g}) ) indeed exists and is equal to G=S/w. Furthermore, \ref{g:intern}) ) describes a transition front on the particle distribution between its asymptotic value g=G at and g=0 at." +. This front solution establishes as a result of particle losses caused by the lack of resonant waves towards the sub-shock as we argued discussing eqs.(19..20)).," This front solution establishes as a result of particle losses caused by the lack of resonant waves towards the sub-shock as we argued discussing \ref{dc3}, \ref{wke3}) )." + Note that according to the ordering in eq.(23)) we should set -rp(p) in Sr.p) when solving (26)) lor g(£) ancl we indeed must do it [or 1 as well as for all negative κQ.," Note that according to the ordering in \ref{order}) ) we should set (p) in S(x,p) when solving \ref{dc:int3}) ) for ) and we indeed must do it for 1 as well as for all negative <0." +. In the limitx... however. we may use the result (27)) for arbitrary (p) since it remains valid in this case. however. il merely states that in (his region the complete solution is represented by its “external” part GC.p) (eq.[25]).," In the limit, however, we may use the result \ref{g:intern}) ) for arbitrary (p) since it remains valid in this case, however, it merely states that in this region the complete solution is represented by its ” part G(x,p) \ref{lim:g}{ )." + This. in turn. is vet to be," This, in turn, is yet to be" +region located close to the compact object (IKhbaugulvan. Aharoniaun Bosch-Ramou 2008).,"region located close to the compact object (Khangulyan, Aharonian Bosch-Ramon 2008)." +" Iun this region. the naguctic feld (obtaired by equipartition) is extremoelv uel (of the order of 1""ay, "," In this region, the magnetic field (obtained by equipartition) is extremely high (of the order of $10^{7}$ G)." +This produces the imunediate cooling of primary electrons au significaut cooling of rotons., This produces the immediate cooling of primary electrons and significant cooling of protons. + [fi Fie., In Fig. + we show the cooling rates for both omnuary electrons arc protous iu he acceleration regio- as well the cooling aud decaving rate of secondary uiuons and pious.," \ref{fig:cool} we show the cooling rates for both primary electrons and protons in the acceleration region, as well as the cooling and decaying rate of secondary muons and pions." + The πλακα eucreies of the primary ouwticles are obtained equating the cooling rates to the acceleration rate. whic Las assuned to be produced by uildly relativistic shocss at the base of the jet through a first-order Feri meciuis.," The maximum energies of the primary particles are obtained equating the cooling rates to the acceleration rate, which is assumed to be produced by mildly relativistic shocks at the base of the jet through a first-order Fermi mechanism." + In this work we adopt au acceleration cficiency of the order of 10%.. which rougly corresponds to a shock velocity of 0.36 and a mean free pat1 snar to the Larnor radius.," In this work we adopt an acceleration efficiency of the order of 10, which rougly corresponds to a shock velocity of $0.3c$ and a mean free path similar to the Larmor radius." + We see that clectrous. even for sucha ligh acceleration efiicicicv. reach oulv Gey energies. whereas protons eau attain much higher energies. well into he PeV 1xuxdl.," We see that electrons, even for such a high acceleration efficiency, reach only GeV energies, whereas protons can attain much higher energies, well into the PeV band." + Qur model takes iuto account: 1) svuclirotron emission roni both types (electrons and protous) of primary outicles. as well as ciuission from secondary leptous (electrons. positrons. and nmous) aud hadrous (charged jois). 2) inverse Compton(IC) enussion frou all leptous in the strong total radiatiou fie di ithe cutting region. 3) yhoto-pair and phnotoaueson procuction by both protons and pious. 1) inelastic collisious between relativistic rotons m the jet and the cold material that forms most of he same outflow (see Bosch-Ramou. Romero Paredes 2006. for details of the plivsies of a cold matter domirated jet). 5) relativistic Dromsstralhluug from electrons and uuons. and 6) internal photon absorption iu the local radiation fields (calculated as in Aharonian. IKkbaugtIvan. Costamaute 2008). 7) re-Injecion of secondary pairs. which is negligible due to the low opacity of the proton-dominate jet (see Romero Vila 2008 for a discussion).," Our model takes into account: 1) synchrotron emission from both types (electrons and protons) of primary particles, as well as emission from secondary leptons (electrons, positrons, and muons) and hadrons (charged pions), 2) inverse Compton (IC) emission from all leptons in the strong total radiation field in the emitting region, 3) photo-pair and photo-meson production by both protons and pions, 4) inelastic collisions between relativistic protons in the jet and the cold material that forms most of the same outflow (see Bosch-Ramon, Romero Paredes 2006, for details of the physics of a cold matter dominated jet), 5) relativistic Bremsstrahlung from electrons and muons, and 6) internal photon absorption in the local radiation fields (calculated as in Aharonian, Khangulyan, Costamante 2008), 7) re-injection of secondary pairs, which is negligible due to the low opacity of the proton-dominated jet (see Romero Vila 2008 for a discussion)." + The effec of losses of nmnmons aud pious du a srone maguctic field ou the resulting eznuniae-ray aud secondary leptoi spectra has been receutlv ciscussed by Revuoso Romero (2008) and we adopt here their treatment., The effect of losses of muons and pions in a strong magnetic field on the resulting gamma-ray and secondary lepton spectra has been recently discussed by Reynoso Romero (2008) and we adopt here their treatment. + For the oher processes we follow the classical foriuulae (Bhuneuthal Could 1970). the ploto-meson production reatinent already used by Romero Vila (2008). aud he expressions eiveu bv IE&elucr. Aharonian. Bugavoy (2006) for pp iuteractious(this foriialisii is only valid for xoton chereies above 0.1 TeV: at lower energies we use he standard treatment).," For the other processes we follow the classical formulae (Blumenthal Gould 1970), the photo-meson production treatment already used by Romero Vila (2008), and the expressions given by Kelner, Aharonian, Bugayov (2006) for $pp$ interactions (this formalism is only valid for proton energies above 0.1 TeV; at lower energies we use the standard treatment)." + The ratio of relativistic protons to clectrous à in the jet is unknown and is used as the basic free parameter iu our model., The ratio of relativistic protons to electrons $a$ in the jet is unknown and is used as the basic free parameter in our model. +" We have calculated a umber of models for different acceleration efficiencies. aud a set of standard xuanmieters: black hole mass ~LO AL... accretion rate ~ ees! (1.6.. ~107 of the Eddington Iuuinosity). injection XE.17, viewing anele 307. jet bulk Loreutz actor DP1.5. aud location of the acceleration zone at upcmIU Cll (see Romero Vila 2008)."," We have calculated a number of models for different acceleration efficiencies, and a set of standard parameters: black hole mass $\sim 10$ $M_{\odot}$, accretion rate $\sim 10^{37}$ erg $^{-1}$ (i.e., $\sim 10^{-2}$ of the Eddington luminosity), injection $\propto E^{-1.5}$, viewing angle $30^\circ$, jet bulk Lorentz factor $\Gamma=1.5$, and location of the acceleration zone at $z_0\approx10^8$ cm (see Romero Vila 2008)." +" The transport equation is solved for all typesof particles,", The transport equation is solved for all typesof particles. + At steady state it roads: where foe Is the particle escape time frou the acceleration region (fc29Ate) ud Q is the injection fiction that can be normalized in accordance with the energv. budget of relativistic particles through: The minima kinetic energv is taken to be of the order of the rest 11ass enerev of the correspouding particle., At steady state it reads: where $t_{\rm{esc}}$ is the particle escape time from the acceleration region $t_{\rm{esc}}\approx \Delta z/v_{\rm{jet}}$ ) and $Q$ is the injection function that can be normalized in accordance with the energy budget of relativistic particles through: The minimum kinetic energy is taken to be of the order of the rest mass energy of the corresponding particle. + The equation for pions aud uous has an additional term. NCE.N(E.MffUta. that takes iuto accouit the| clecaydecay of the᾿ particles ou a timescale ta that depends ou the energy in the lab svsteun.," The equation for pions and muons has an additional term $N(E,z)/t_{\rm{dec}}$, that takes into account the decay of the particles on a timescale $t_{\rm{dec}}$ that depends on the energy in the lab system." + Iu general. variability cau be obtained introducing a variable injection QGE.f£).," In general, variability can be obtained introducing a variable injection $Q(E, t)$ ." + Ouce the uticle distributions are known. the radiative. output can be calculatedbon : mentioned. above.," Once the particle distributions are known, the radiative output can be calculated as mentioned above." + The internal attemation results photon annihilation: 5|Σε| , The internal attenuation results from photon annihilation: $\gamma + \gamma \rightarrow e^{-}+ e^{+}$. +"The opacity for a σα rav of enerev E. where p(e.2i) is the photon nuuber density at eneorev € and location z. 4=cos’. 0 is the angle between the momenta of the colliding photous. / is the y-ray photon pas and the cross section for the interaction is eiven by (οιο, Levinson 2006): ∐↸∖↥⋅↸∖∙↗∣↕↴∖↴↑∐↸∖↴∖↴↻↸∖↸∖≺↧∪↕⋡↑↕∐∖↸∖↕↸∖↸⊳⊓⋅∪∐∣↻∪↴∖↴↕⊓⋅∪∐↕∐↑↕∐∖ ↸⊳↸∖∐↑↸∖↥⋅∪↕⋟↕⊔∪∐∐∖∐⊓∐⊔↕≯↥⋅⋜⋯⊔∖∙↕∙↸∖∙∙ The threshold euergv εν is defined bv 3= i)—U."," The opacity for a gamma ray of energy $E_{\gamma}$ is: where $n(\epsilon, z)$ is the photon number density at energy $\epsilon$ and location $z$, $u=cos \vartheta$, $\vartheta$ is the angle between the momenta of the colliding photons, $l$ is the $\gamma$ -ray photon path, and the cross section for the interaction is given by (e.g. Levinson 2006): Here, $\beta$ is the speed of the electron/positron in the center of momentum frame, i.e., The threshold energy $\epsilon_{\rm th}$ is defined by $\beta=1$ with $\vartheta=0$." + Iu Fig., In Fig. + 2 we show the spectral cuerey distribution (SED) calculated for a proton dominated (α= 1000) jet. with a total power of 1075 ere 52 ," \ref{SED} we show the spectral energy distribution (SED) calculated for a proton dominated $a=1000$ ) jet, with a total power of $10^{37}$ erg $^{-1}$ ." +We show the different contributionsfrou all siguificaut cooling processes for all primary aud secondary particles. iu the case of two different acceleration efficicucics 9 (0.1 aud," We show the different contributionsfrom all significant cooling processes for all primary and secondary particles, in the case of two different acceleration efficiencies $\eta $ (0.1 and" +rels:obs)).,). + Given the limited span of these data. we are unable to clistinguish definitively among these models: (he exponentials appear superior. but (his is not statistically significant.," Given the limited span of these data, we are unable to distinguish definitively among these models; the exponentials appear superior, but this is not statistically significant." + For constant speed. as in 4433. models that predict intensity behavior with distance should be compared to data fit in age.," For constant speed, as in 433, models that predict intensity behavior with distance should be compared to data fit in age." + The model of a freely-expanding spherical cloud of magnetized relativistic plasma (vanderLaan1966).. which might be appropriate if the pieces of the jet behave as discrete non-interacting components. predicts that in the opticallv-thin regime the resulting svuchrotvon total intensity [alls off as r77. where p is the electron energy distribution exponent.," The model of a freely-expanding spherical cloud of magnetized relativistic plasma \citep{VanDerLaan}, which might be appropriate if the pieces of the jet behave as discrete non-interacting components, predicts that in the optically-thin regime the resulting synchrotron total intensity falls off as $r^{-2p}$ , where $p$ is the electron energy distribution exponent." + Since here p~2.4. this predicts a decay with a power law in component radius of index ~—4.8.," Since here $p \simeq 2.4$, this predicts a decay with a power law in component radius of index $\sim -4.8$." + Were the components freely expanding we would have rx7. which would then be ruled out by the data.," Were the components freely expanding we would have $r \propto \tau$, which would then be ruled out by the data." +" In the conical jet model ol IHjellming&Johnston(19883).. the intensity of the jet [alls off as dIox2""dz. where 2 is distance down (he jet. n=(rp—1)/(6+6d). and 6=0 and 0=1 correspond to freely-expancling and slowed expansion cases. respectively,"," In the conical jet model of \citet{HJ88}, the intensity of the jet falls off as $dI \propto z^{-m} \, dz$, where $z$ is distance down the jet, $m = (7p-1)/(6 + 6\delta) $, and $\delta = 0$ and $\delta = 1$ correspond to freely-expanding and slowed expansion cases, respectively." + For p=2.4. ὃ=0 corresponds lo m=2.6. and 6=1 to m=1.3.," For $p = 2.4$, $\delta = 0$ corresponds to $ m = 2.6$, and $\delta = 1$ to $m = 1.3$." +" Power fits to our data in this age range lie between the two cases,", Power fits to our data in this age range lie between the two cases. +" We also fit exponentials ancl power laws to the data for 250<7<800davs. ancl [lind for both jets Zi280days orà<4 where Bx7 "". mareinally incompatible with the freely expaucling sphere model."," We also fit exponentials and power laws to the data for $250 \leq \tau \leq 800\mbox{ days}$, and find for both jets $T_{1/2} \simeq 80\mbox{ days}$ or$a \leq 4$ where $B \propto \tau^{-a}$ , marginally incompatible with the freely expanding sphere model." + The principal results in (his paper are:, The principal results in this paper are: +"0.7 Alpe given in Georgie, et al. (",0.7 Mpc given in Georgiev et al. ( +1997).,1997). + Phe former is more likely to be a reliable distance estimate. as it was macde using the tip of the Recd-Ciant Branch instead of the brightest blue stars. so the high best-fit distance might. potentially constitute a problem for the standard MOND pir) (see‘Table 1)).," The former is more likely to be a reliable distance estimate, as it was made using the tip of the Red-Giant Branch instead of the brightest blue stars, so the high best-fit distance might potentially constitute a problem for the standard MOND $\mu(x)$ (seeTable \ref{tab-param}) )." +" ὃν allowing the distance to vary only within the 3.0 + 0.3 Alpe range we found that the standard fir) eives a relatively poor fit (yi,=141. which is however still much better than the constrained NEW fit). while the new μμ) gives a better fit (AZ,= 0.91): this fit can be further improved (xz,= 0.64) i£ aj is assunied to be 10 em 7 (see Faniaev et al."," By allowing the distance to vary only within the 3.0 $\pm$ 0.3 Mpc range we found that the standard $\mu(x)$ gives a relatively poor fit $\chi^2_{\rm red}=1.41$, which is however still much better than the constrained NFW fit), while the new $\mu(x)$ gives a better fit $\chi^2_{\rm red}=0.91$ ); this fit can be further improved $\chi^2_{\rm red}=0.64$ ) if $a_0$ is assumed to be $\times 10^{-8}$ cm $^{-2}$ (see Famaey et al." + 2006)., 2006). + Sealing up the contribution of the gaseous clisk gives a reasonably &ood fit. with a scaling factor for the gas surface density of ~13. in agreement with the results of Hoekstra et al. (," Scaling up the contribution of the gaseous disk gives a reasonably good fit, with a scaling factor for the gas surface density of $\sim 13$, in agreement with the results of Hoekstra et al. (" +2001).,2001). + A [it of the rotation curve was also made by assuming that the dark matter density can be described as a power-law (e.g. Simon et al., A fit of the rotation curve was also made by assuming that the dark matter density can be described as a power-law (e.g. Simon et al. + 2003). defined as pxor.," 2003), defined as $\rho \propto r^{\alpha}$." + This is not the case in most moclels of dark matter halos: a power-law fit will therefore provide a sort of average slope of the dark matter density profile over the range of radii probed by the rotation curve., This is not the case in most models of dark matter halos; a power-law fit will therefore provide a sort of average slope of the dark matter density profile over the range of radii probed by the rotation curve. + Note that the outcome of such a fit depends on the extension of the rotation curve: a more extended. rotation curve will have a steeper average slope., Note that the outcome of such a fit depends on the extension of the rotation curve: a more extended rotation curve will have a steeper average slope. + We fixed the stellar mass-to-light ratio at the average value between the two extremes found in 1e above fits: ML=0.9., We fixed the stellar mass-to-light ratio at the average value between the two extremes found in the above fits: $M/L=0.9$. + This quantity turns out not to have a great inlluence on o. since the disk dominates the kinematics only in the innermost few points.," This quantity turns out not to have a great influence on $\alpha$ , since the disk dominates the kinematics only in the innermost few points." + We linda=LIL+0-11 and yz.)=0.35. which however doesnol mean that NGC 3741 has a cuspy dark. matter halo.," We find $\alpha=-1.11\pm0.11$ and $\chi^2_{\rm red}=0.35$, which however does mean that NGC 3741 has a cuspy dark matter halo." + Indeed. at their respective core radius. a Burkert halo has a dlogp/dlogr=1.5. and a pseudo-isothermal halo has dlogpfdlogr=1.0.," Indeed, at their respective core radius, a Burkert halo has a $d{\rm log}\rho/d{\rm log}r=-1.5$, and a pseudo-isothermal halo has $d{\rm log}\rho/d{\rm log}r=-1.0$." + This shows that if the rotation curve extendsbeyond the core radius (such as in NGC 3741). the average slope. as measured by a power-law fit. will be much steeper than zero.," This shows that if the rotation curve extends the core radius (such as in NGC 3741), the average slope, as measured by a power-law fit, will be much steeper than zero." + On the other hand. for an NEW halo it is dillicult to reproduce an average slope close to -1. since its slope is already -2 at r=re (which is of the same order as the last measured radius of our NGC 3741 observations)," On the other hand, for an NFW halo it is difficult to reproduce an average slope close to -1, since its slope is already -2 at $r=r_s$ (which is of the same order as the last measured radius of our NGC 3741 observations)." + See eg. Fig., See e.g. Fig. + 3 of Navarro et al. (, 3 of Navarro et al. ( +2004) for the variation of the density slope with radius in ACDAL simulations of dwarf galaxies.,2004) for the variation of the density slope with radius in $\Lambda$ CDM simulations of dwarf galaxies. + The only wavs to reconcile an NEW profile with the observations are to have a very large r;. which means that either the virial mass has to be very high. or to decrease the concentration. which is at odds with the ACDAL predictions in the concordance cosmology.," The only ways to reconcile an NFW profile with the observations are to have a very large $r_s$, which means that either the virial mass has to be very high, or to decrease the concentration, which is at odds with the $\Lambda$ CDM predictions in the concordance cosmology." + NGC 3741 has therefore. evidence for a cored halo., NGC 3741 has therefore evidence for a cored halo. + This could be linked to the presence of a bar., This could be linked to the presence of a bar. + Indeed. barred galaxies seem to have somewhat shallower dark matter density. profiles (Swaters cet al.," Indeed, barred galaxies seem to have somewhat shallower dark matter density profiles (Swaters et al." + 2003). despite the uncertainties in the mass mocdels due to non-circular motions.," 2003), despite the uncertainties in the mass models due to non-circular motions." + However. there is no general agreement vet as to whether realistic bars can significantly Hatten the cusp (Weinberg Ixatz 2002. Sellwood 2006).," However, there is no general agreement yet as to whether realistic bars can significantly flatten the cusp (Weinberg Katz 2002, Sellwood 2006)." + We have presented. the analysis of HE observations of the nearby cwarl irregular galaxy 33741. performed at the WSR.," We have presented the analysis of HI observations of the nearby dwarf irregular galaxy 3741, performed at the WSRT." + Phe HE disk of this galaxy is very extended. the most extended ever observed in terms ofoptical scale length.," The HI disk of this galaxy is very extended, the most extended ever observed in terms of optical scale length." + The huge extension of the LL disk enables us to trace the rotation curve out to unprecedented. distances in terms of the size of the optical disk: the last radius at which we can trace the kinematics is 42 D-band exponential scale lengths. approximately 15 times Re.," The huge extension of the HI disk enables us to trace the rotation curve out to unprecedented distances in terms of the size of the optical disk: the last radius at which we can trace the kinematics is 42 B-band exponential scale lengths, approximately 15 times $_{25}$." + The HE disk displays a warp. which is very symmetric.," The HI disk displays a warp, which is very symmetric." + In order to derive the distribution and kinematics. we built model data cubes: with our choice of geometrical and kinematical parameters. the observed data cube is reproduced accurately.," In order to derive the distribution and kinematics, we built model data cubes; with our choice of geometrical and kinematical parameters, the observed data cube is reproduced accurately." + Some key features in the data cube are characteristic of non-circular motions. whose amplitude turns out to be of the order of 5...13¢.," Some key features in the data cube are characteristic of non-circular motions, whose amplitude turns out to be of the order of $\ldots$ 13." +. Their interpretation is non-trivial. but they are consistent with an inner bar and accreting outer material.," Their interpretation is non-trivial, but they are consistent with an inner bar and accreting outer material." + SubsequentIv. the standard rotation curve decomposition was performed.," Subsequently, the standard rotation curve decomposition was performed." + Phe (οσο) Surkert dark halo fits the data very well: the fit. performed. by taking the dark matter density distribution. predicted. by the ACDAL cosmological simulations [its badlv. unless the prediction of a correlation. between the concentration parameter and the virial mass is relaxed.," The (cored) Burkert dark halo fits the data very well; the fit performed by taking the dark matter density distribution predicted by the $\Lambda$ CDM cosmological simulations fits badly, unless the prediction of a correlation between the concentration parameter and the virial mass is relaxed." + Ln this case. however. the price to pay is a concentration parameter 2.5 0 below thepredicted e/—My relation and a high. virial mass (but poorly constrained) of 1075 AL. .," In this case, however, the price to pay is a concentration parameter 2.5 $\sigma$ below thepredicted $c-M_{\rm vir}$ relation and a high virial mass (but poorly constrained) of $^{11}$ $_{\odot}$ ." +Tsuji (2008)) for M7-8 giants.,Tsuji \cite{tsuji08}) ) for M7–8 giants. + We first attempted to explain the observed data with models with one additional CO layer but could not reproduce the spectrum and visibilities simultaneously., We first attempted to explain the observed data with models with one additional CO layer but could not reproduce the spectrum and visibilities simultaneously. +" Therefore, we attempted to explain the data with the models with two CO layers."," Therefore, we attempted to explain the data with the models with two CO layers." + Table 2 gives the range of the parameters searched in our modeling., Table \ref{table_param} gives the range of the parameters searched in our modeling. +" Note that the radius of the inner layer was set to be equal to or larger than 1.2 tto avoid an overlap with the MARCS photospheric model, which extends to 1.17 R,."," Note that the radius of the inner layer was set to be equal to or larger than 1.2 to avoid an overlap with the MARCS photospheric model, which extends to 1.17 ." +. Figure 7 shows a comparison between the observed data (data set #33) and the best-fit model., Figure \ref{marcs3000_wme_final} shows a comparison between the observed data (data set 3) and the best-fit model. +" The model intensity profiles and visibilities at three representative wavelengths (continuum, CO band head, and isolated CO line) are plotted in Fig. 8.."," The model intensity profiles and visibilities at three representative wavelengths (continuum, CO band head, and isolated CO line) are plotted in Fig. \ref{clvvisplot}." + This model is characterized by the inner CO layer at 1.2 wwith 2000 K and a CO column density of 2x107 aand the outer CO layer at 2.5 wwith 1900 K and a column density of 2x10?cm™?.., This model is characterized by the inner CO layer at 1.2 with 2000 K and a CO column density of $2\times10^{22}$ and the outer CO layer at 2.5 with 1900 K and a column density of $2\times10^{19}$. + The column densities of the inner and outer CO layer correspond to and of the CO column density in the MARCS photospheric model., The column densities of the inner and outer CO layer correspond to and of the CO column density in the MARCS photospheric model. +" We found the range of the radius, temperature and CO column density of the inner layer to be 1.2-1.25R,,, 1900-2100 K, and (1-2)x10?cm,, respectively."," We found the range of the radius, temperature and CO column density of the inner layer to be 1.2–1.25, 1900–2100 K, and $\times10^{22}$, respectively." +" The derived ranges for the radius, temperature, and CO column density of the outer layer are 2.5-3.0Κ.., 1500-2100 K, and 10?—10?9cm~?,, respectively."," The derived ranges for the radius, temperature, and CO column density of the outer layer are 2.5–3.0, 1500–2100 K, and $10^{19}$ $10^{20}$, respectively." +" As shown in Fig. 7,,"," As shown in Fig. \ref{marcs3000_wme_final}," + the observed visibilities and spectrum are well reproduced., the observed visibilities and spectrum are well reproduced. +" The model also predicts the CP to jump in the CO lines, in particular at the CO band head, as seen in the AMBER data."," The model also predicts the CP to jump in the CO lines, in particular at the CO band head, as seen in the AMBER data." + This can be explained as follows., This can be explained as follows. +" Figure 8bb shows that the inner CO layer, which is optically thick, makes the star appear larger in the CO band head than in the continuum by30%."," Figure \ref{clvvisplot}b b shows that the inner CO layer, which is optically thick, makes the star appear larger in the CO band head than in the continuum by." +". Then the longest baseline samples the second visibility lobe in the CO band head, as shown in Fig."," Then the longest baseline samples the second visibility lobe in the CO band head, as shown in Fig." + 8cc (red line and red triangle at a spatial frequency of ~100 arcsec!)., \ref{clvvisplot}c c (red line and red triangle at a spatial frequency of $\sim$ 100 $^{-1}$ ). + The phase in the second visibility lobe is π. while the phases on the shortest and middle baselines in the first visibility lobe are zero.," The phase in the second visibility lobe is $\pi$, while the phases on the shortest and middle baselines in the first visibility lobe are zero." + This results in a predicted CP of π for the CO band head and leads to the jumps in the CP as observed., This results in a predicted CP of $\pi$ for the CO band head and leads to the jumps in the CP as observed. +" Because the model is spherically symmetric, the observed π CPs and non-zero DPs are not."," Because the model is spherically symmetric, the observed $\pi$ CPs and non-zero DPs are not." +". However, the overall agreement in the spectrum, visibilities, and CP suggests that our model represents the approximate picture of the outer atmosphere of BK Vir."," However, the overall agreement in the spectrum, visibilities, and CP suggests that our model represents the approximate picture of the outer atmosphere of BK Vir." + It is impossible to uniquely constrain the detected inhomogeneous structure from our observations., It is impossible to uniquely constrain the detected inhomogeneous structure from our observations. +" However, we estimated the flux contribution of asymmetric features from the observed CPs as follows."," However, we estimated the flux contribution of asymmetric features from the observed CPs as follows." + We added a Gaussian-shaped spot to the best-fit model image in the CO lines and computed the visibility and CP at the observed baselines., We added a Gaussian-shaped spot to the best-fit model image in the CO lines and computed the visibility and CP at the observed baselines. + We changed the size and intensity of the Gaussian-shaped spot so that the observed non-zero/non-a CPs (40-100?)) can be reproduced without affecting the fit to the observed visibilities significantly., We changed the size and intensity of the Gaussian-shaped spot so that the observed $\pi$ CPs ) can be reproduced without affecting the fit to the observed visibilities significantly. + This experiment suggests that the flux contribution ofthe asymmetric feature is of the total, This experiment suggests that the flux contribution ofthe asymmetric feature is of the total +1993 and 2499 such objects within the «400 aresec? fields around 0322 and 4427 respectively.,1993 and 2499 such objects within the $\times$ 400 $^2$ fields around $-$ 0322 and $-$ 4427 respectively. +" We measured the flux of all objects in the isophotal aperture (for precise colour measurement) and in an ellipsoidal aperture with minor axis b5.0r,e and major axis «5.071. where is the first moment of the light distribution and e is the ellipticity (to get a measure of the total magnitudes)."," We measured the flux of all objects in the isophotal aperture (for precise colour measurement) and in an ellipsoidal aperture with minor axis $b=5.0 r_1 \epsilon$ and major axis $a=5.0 {r_1 \over \epsilon}$, where $r_1$ is the first moment of the light distribution and $\epsilon$ is the ellipticity (to get a measure of the total magnitudes)." +" As a minimum aperture radius. we used 1.5""."," As a minimum aperture radius, we used $1.5\arcsec$." + The fluxes measured in the large aperture are used to measure the total magnitudes of the objects., The fluxes measured in the large aperture are used to measure the total magnitudes of the objects. + We also derived error bars on colours as described in Fynbo et al. (, We also derived error bars on colours as described in Fynbo et al. ( +2002).,2002). +" For the final selection of LEGO candidates. we used the “narrow minus on-band broad"" versus ""narrow minus off-band broad"" colour/colour plot technique (Meller Warrer 1993: Fynbo et al."," For the final selection of LEGO candidates, we used the “narrow minus on-band broad” versus “narrow minus off-band broad” colour/colour plot technique ller Warren 1993; Fynbo et al." +" 1999, 2000. 2002 and Fig. 3))."," 1999, 2000, 2002 and Fig. \ref{colcol}) )." + In order to constrain where objects with no special spectral features in the narrow filter are in the diagram. we calculated colours basec on synthetic galaxy SEDs taken from the Bruzual Charlot (1995) models.," In order to constrain where objects with no special spectral features in the narrow filter are in the diagram, we calculated colours based on synthetic galaxy SEDs taken from the Bruzual Charlot (1995) models." + We have used models with ages ranging from a few Myr to 15 Gyr and with redshifts from 0 to 1.5 (oper squares in Fig. 4 3)), We have used models with ages ranging from a few Myr to 15 Gyr and with redshifts from 0 to 1.5 (open squares in Fig. \ref{colcol}) ) + and models with ages ranging from a few Mvr to 1 Gyr with redshifts from 1.5 to 3.0 (open triangles)., and models with ages ranging from a few Myr to 1 Gyr with redshifts from 1.5 to 3.0 (open triangles). + For the colours of high-redshift galaxies. we included the effect ο Ένα blanketing (Moller Jakobsen 1990: Madau 1995).," For the colours of high-redshift galaxies, we included the effect of $\alpha$ blanketing ller Jakobsen 1990; Madau 1995)." + Fig., Fig. + 3 shows the B(AB) versus R(AB) colour diagram for the simulated galaxy colours (left panels) and for the observed sources in the two target fields (middle and right panels)., \ref{colcol} shows the $-$ B(AB) versus $-$ R(AB) colour diagram for the simulated galaxy colours (left panels) and for the observed sources in the two target fields (middle and right panels). + The dashed line indicates where objects with a particular broad-band colour and either absorption (upper right) or emission (lower left) in the narrow filter will fall., The dashed line indicates where objects with a particular broad-band colour and either absorption (upper right) or emission (lower left) in the narrow filter will fall. + In the middle panel. we show the colour-colour diagram for all of the objects detected in the two fields.," In the middle panel, we show the colour-colour diagram for all of the objects detected in the two fields." + Due to the damped Lyo hine. 4427 has a large positive BCAB) colour and 1s hence seen in the upper right corner.," Due to the damped $\alpha$ line, $-$ 4427 has a large positive $-$ B(AB) colour and is hence seen in the upper right corner." + Due to Lyman-forest blanketing. the B-band flux of 0322 is suppressed hence decreasing its n(AB)-B(AB) colour.," Due to Lyman-forest blanketing, the B-band flux of $-$ 0322 is suppressed hence decreasing its n(AB)-B(AB) colour." + In the lower left part of the diagram. a large group of objects are found to lie significantly away from the locus of continuum objects.," In the lower left part of the diagram, a large group of objects are found to lie significantly away from the locus of continuum objects." + In the right panel. we show with the solid line the median B(AB) colour in the range 0$ 5 in the narrow-band image and whose $\sigma$ upper limit on $-$ B(AB) is below the line. + We detect 27 and 37 such objects in the 0322 and 4427 fields respectively which we consider as LEGO candidates in the following., We detect 27 and 37 such objects in the $-$ 0322 and $-$ 4427 fields respectively which we consider as LEGO candidates in the following. + The colours of the candidates are shown again in the two right panels., The colours of the candidates are shown again in the two right panels. + Follow-up Multi-Object Spectroscopy (MOS) of the previously described sample of LEGO candidates was carried out in visitor mode in July 10 — 13. 2002. with FORSI installed at the VLT telescope. unit Melipal.," Follow-up Multi-Object Spectroscopy (MOS) of the previously described sample of LEGO candidates was carried out in visitor mode in July 10 – 13, 2002, with FORS1 installed at the VLT telescope, unit Melipal." + The mask preparation was done using theSimulator., The mask preparation was done using the. + The field of 0322 was only visible at the beginning of the nights so we only had time for using three masks for the observations of this field., The field of $-$ 0322 was only visible at the beginning of the nights so we only had time for using three masks for the observations of this field. + Nevertheless. all but five candidates," Nevertheless, all but five candidates" +zero extinction for these ceutral stars.,zero extinction for these central stars. + Note that the mean extinction for the bright Magellanic Cloud PNe observed with theZ/ST is ο=0.19 (Shaw2006). so adopting a low extinction for this purpose is nof uureasonable., Note that the mean extinction for the bright Magellanic Cloud PNe observed with the is $c~=~$ 0.19 \citep{S:06} so adopting a low extinction for this purpose is not unreasonable. + Iu the waveleugth rauge under consideration. the LAIC and Calactic extinction Luvs are very simular (Ποπ1983).," In the wavelength range under consideration, the LMC and Galactic extinction laws are very similar \citep{How:83}." +. Thus. we used the interstellar extinction law of Savage&Mathis(1979). aud assumed that Ry= 3.1.," Thus, we used the interstellar extinction law of \cite{Sm:79} and assumed that $_{V}~=~3.1$ ." + The extinction in magnitudes CÀq-) is then Ay=2.26., The extinction in magnitudes $_{V}$ ) is then $_{V}~=~2.2 c$. + The transformation frou the instrmucutal STALIAC magnitude to the standard V-baud magnitude in the photometric Joliusou-Cousius UBVI system lias been derived using svuthetic photometry with IRAF/STSDAS SYNPIIOT by using a blackbody spectrum to represcut the Spectral Energy Distribution (SED) of the ceutral star., The transformation from the instrumental STMAG magnitude to the standard V-band magnitude in the photometric Johnson-Cousins UBVI system has been derived using synthetic photometry with IRAF/STSDAS SYNPHOT by using a blackbody spectrum to represent the Spectral Energy Distribution (SED) of the central star. + The procedure. which is described iu detail in Villaveretal.(2003).. basically cousists in obtaining a median of the V-50CCD colors for blackbodies between 300000 and 0000. Ids with the extinction values appropriate for cach source.," The procedure, which is described in detail in \cite{Vss:03}, basically consists in obtaining a median of the V-50CCD colors for blackbodies between 000 and 000 K with the extinction values appropriate for each source." + The uncertainty in the transformation has been added in quadrature to the error in the measured maguitude., The uncertainty in the transformation has been added in quadrature to the error in the measured magnitude. + When the central star is not detected (.0.. uo stellar PSF appears above the nebular level). we computed a lower limit to the ceutral star maeuitucde by measuring the fiw inside a stellar aperture at the geometric center of the uchula (i.c.. the most Likely position of the ceutral star).," When the central star is not detected (i.e., no stellar PSF appears above the nebular level), we computed a lower limit to the central star magnitude by measuring the flux inside a stellar aperture at the geometric center of the nebula (i.e., the most likely position of the central star)." + The lower lits to the magnitudes for those central stars that have uot been detected in our sample are presented in Table 2 where column (1) eives the object mame. colimus (2) aud (3) eive the lower limit magnitude of the ceutral star in the STALAG and Johuson-Cousins svsteiis respectively aud column (CL) eives the nebular extinction constant.," The lower limits to the magnitudes for those central stars that have not been detected in our sample are presented in Table 2 where column (1) gives the object name, columns (2) and (3) give the lower limit magnitude of the central star in the STMAG and Johnson-Cousins systems respectively and column (4) gives the nebular extinction constant." + Iu Table 3. we give the results of the photometry for the objects i which the central star has been etected.," In Table 3, we give the results of the photometry for the objects in which the central star has been detected." + Colima (1) gives the PN name. columnis (2) aud (3) eive the STAIAG and V magnitudes respectively as well as the associated errors.," Column (1) gives the PN name, columns (2) and (3) give the STMAG and $V$ magnitudes respectively as well as the associated errors." + The uncertainties includes the CCD noise (1.0. photon noise aud read noise). the systematic error (central star flux. Skv) aud the errors iu the calibration.," The uncertainties includes the CCD noise (i.e. photon noise and read noise), the systematic error (central star flux, sky) and the errors in the calibration." + The nebula extinction coustauts used to correct for the stellar extinction are listed in cohuun (1)., The nebular extinction constants used to correct for the stellar extinction are listed in column (4). + We have 6 objects (AIG 29. Mo 17. Sa 121. SMP 15. SMP 19. and SAIP 71) for which the ceutral star is detected. but at à mareinal level above the uchula (see footuote in Table 1).," We have 6 objects (MG 29, Mo 47, Sa 121, SMP 45, SMP 49, and SMP 74) for which the central star is detected, but at a marginal level above the nebula (see footnote in Table 1)." + The large errors obtained for these objects directly reflect the mucertainty oe ithe measurement of the stellar magnitude., The large errors obtained for these objects directly reflect the uncertainty in the measurement of the stellar magnitude. + As in previous papers we have estimated the temperature of the central star by using the method originally developed by Zaustra (ZaustraL931) which is extensively used in the literature G.c. Warman&1983:Staughellinietal. 2002b)).," As in previous papers we have estimated the temperature of the central star by using the method originally developed by Zanstra \citep{Zan:31} which is extensively used in the literature (i.e. \citealt{Hs:66,Kal:83,Svmg:02}) )." + The Zaustra temperature is an estimate of the ionizing flux from a star computed by comparing the fux of a nebular recombination line of hydrogen or helium to the stellar coutimmun flux in the V-baud assuniug a particular choice for the stellay spectral energy distribution. which iu our case is a blackbody.," The Zanstra temperature is an estimate of the ionizing flux from a star computed by comparing the flux of a nebular recombination line of hydrogen or helium to the stellar continuum flux in the $V$ -band assuming a particular choice for the stellar spectral energy distribution, which in our case is a blackbody." + The data needed for the temperature calculation have been taken from Shawetal.(2006) fluxes. nebular radii and extinction coustauts).," The data needed for the temperature calculation have been taken from \cite{Shaw:06} fluxes, nebular radii and extinction constants)." + The 1686 line fluxes were taken from Boroson.&Liebert (1989)... Meatheringham&Dopita (1991a).. Morgan&Parker (1998).. aud Leisy&Denueteld(2006).," The 4686 line fluxes were taken from \cite{BL}, \cite{MED}, \cite{Mp:98}, and \cite{Ld:06}." +. Iu order to assure the best results we have been very conscrvative with the uncertainties in the fluxes. quoted by the references;, In order to assure the best results we have been very conservative with the uncertainties in the fluxes quoted by the references. + We have supplemented the above with fuxes frou our unpublished. erouud-based. NTT spectra for SMP57.," We have supplemented the above with fluxes from our unpublished, ground-based NTT spectra for SMP57." + In Table 3. column (5) we list the £656 line intensity relative to = 100.," In Table 3, column (5) we list the 4686 line intensity relative to = 100," +(he parametric resonance occurring in the svstem.,the parametric resonance occurring in the system. + However. (he constancy of the QPOs frequency strouely supports the fact the thev are closely related to the black hole properties and independent of the Wow in the surrounding aceretion disk.," However, the constancy of the QPOs frequency strongly supports the fact the they are closely related to the black hole properties and independent of the flow in the surrounding accretion disk." + A hvdrodynamical general relativistic description is required to verily (his assessment and {ο check the behaviour of the accretion rate on the presence of certain QPOs., A hydrodynamical general relativistic description is required to verify this assessment and to check the behaviour of the accretion rate on the presence of certain QPOs. + This would be the continuation of the work begun by Maoetal...(2008)., This would be the continuation of the work begun by \citet{Mao2008}. +. Strictly speaking. at this stage. our model cannot estimate independently the angular momentum and (he mass of the black hole.," Strictly speaking, at this stage, our model cannot estimate independently the angular momentum and the mass of the black hole." + Nevertheless. applying it to some BIICs. we are able to give some constrain on their mass. assuming a non-rolating or a maximally rotating black hole.," Nevertheless, applying it to some BHCs, we are able to give some constrain on their mass, assuming a non-rotating or a maximally rotating black hole." + Following the work done by Maoetal.(2008)... we assume that the spiral density wave is launched close to the ISCO. at the location where the radial epievclic frequency is maximal. note (his radius Όμως.," Following the work done by \citet{Mao2008}, we assume that the spiral density wave is launched close to the ISCO, at the location where the radial epicyclic frequency is maximal, note this radius $r_{\rm max}$." + Che lrequency of the spiral density wave is equal to the local orbital frequency at ra. thus the speed of the density perturbation pattern is Ora (tpi).," The frequency of the spiral density wave is equal to the local orbital frequency at $r_{\rm max}$, thus the speed of the density perturbation pattern is $\Omega(r_{\rm max}, a_{\rm BH})$ ." +" Knowing the fundamental frequency O4, in the accretion disk lor a given black hole. the resonance condition Eq. (2))"," Knowing the fundamental frequency $\Omega_{\rm w}$ in the accretion disk for a given black hole, the resonance condition Eq. \ref{eq:ResPara}) )" + puts constrains on the relation between mass aud angular momentum by imposing QCyas.tpi)=Og.," puts constrains on the relation between mass and angular momentum by imposing $\Omega(r_{\rm max}, a_{\rm BH}) = \Omega_{\rm w}$." + This mass-angular momentum relation is shown in Fig., This mass-angular momentum relation is shown in Fig. + 1. for four DIICsS (GIAS19154-105. GRO J1655-40. NTE J1550-564. 111743-322) for which the fundamental frequency is known.," \ref{fig:MasseMomCin} for four BHCs (GRS1915+105, GRO J1655-40, XTE J1550-564, H1743-322) for which the fundamental frequency is known." + Lf we assume a black hole weakly or mildly rotating. Le. apy0.5 ΠΕ we find that for GRS 19154-105 its mass satisfies 13AL.