ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 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."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.4 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.5 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."6 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.7 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).8 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.9 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."10 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."11 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.12 1997)., 1997).13 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."14 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."15 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)."16 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 1404.17 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. (181988).,1988).19 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."20 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).21" 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 $R_{\rm e}$ )."22 In, In23of Dlazars interpreted dn terms of cliscoutimuitics i a Povuting flux jet.,of Blazars interpreted in terms of discontinuities in a Poynting flux jet.24 We analyze ciffereut theoretical aud observational aspects connected wit1i such outbursts., We analyze different theoretical and observational aspects connected with such outbursts.25 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.26 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."27 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)."28 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)."29 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.30 1998)., 1998).31 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."32 1998: Lovelace et al., 1998; Lovelace et al.33 1987)., 1987).34 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).35 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."36 1997)., 1997).37 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 $B=(10^2-10^4)~{\rm G}$."38 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)."39 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)."40 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. (411987).,1987).42 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."43 1957)., 1987).44 The collimation is due to the toroidal component of maguetic field., The collimation is due to the toroidal component of magnetic field.45" 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 $E_r = - (v_j/c) B_0 [r_0/r_j(z)]$ 46or beating interactions between these.,or beating interactions between these.47" 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."48 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.49 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.50" 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."51" 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."52 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 $-$ 302.53 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.54" 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."55 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.56" '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."57 A more detailed discussion of this profile is given in Section 4., A more detailed discussion of this profile is given in Section 4.58" 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."59 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}.60 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.61 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.62 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.63 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.64 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.65 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.66" 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 $\sigma$."67" 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."68 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.69" 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."70 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.71 The subset of all those outbursts, The subset of all those outbursts72magnitude at random from the distributions shown in black in Figure A3.,magnitude at random from the distributions shown in black in Figure A3.73 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."74 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.75 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."76 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.77" 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 $\Delta_{o-i}(NUV-r)$ )."78 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}."79 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."80 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.81 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 $\sigma(NUV-r)<0.1$ )."82" 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)."83 The scatter in therecovered gradient is less than 0.2 mag., The scatter in therecovered gradient is less than 0.2 mag.84" When bs,«+ AS ", When $b_{50}<4$ \ref{fig:dnuvr_criteria} 85This 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.86 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.87" 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."88" 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."89 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 CZ07.90 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.91 6 (right panels)., \ref{fig:surfaceabundances1p25} (right panels).92" 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."93 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 3.1.2.94" 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}) )."95" 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."96" 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.97 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 $_{\rm t}$ ."98 Crude as it may, Crude as it may99characteristics 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 154.100 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.101 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."102 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."103 Such variations of plasma teniperature would be naturally explained by our model., Such variations of plasma temperature would be naturally explained by our model.104 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.105" 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."106" 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}) )"107 at 110 pe., at $140$ pc.108 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."109 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."110 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."111 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."112 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."113 Donitoetal.2010a.— for example of effects of variable jet flows)., \citealt{bom10} for example of effects of variable jet flows).114" 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.115 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.116 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."117 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.118 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 $\approx1''$."119" ""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."120 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."121 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.122 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."123" 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."124 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 $\beta = (p_{\rm sh}+\rho_{\rm125sh}u_{\rm sh}^2)/(B^2/8\pi) \approx 1$, where $B$ is the magnetic field strength, we derive $B\approx 5$ mG in the magnetic nozzle at the base of the jet."126 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}. ."127 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."128function of the “cloud” region.,"function of the “cloud"" region."129 The result is indicated by the solid line in the figure., The result is indicated by the solid line in the figure.130 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."131 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 $\sim0.1\,M_\odot$."132 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."133 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}."134 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."135 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."136 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.137 In addition (Bihainetal.2009) found a possible hint of a turnover al ~0.004. AZ.. also reminiscent of Figure &..," In addition \citep{bih09}138 found a possible hint of a turnover at $\sim0.004$ $M_\odot$, also reminiscent of Figure \ref{fig8}."139 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."140 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 $M_J$ ."141 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 mass142our 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."143 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.144 The pipeline corrected for auv simall residual shifts., The pipeline corrected for any small residual shifts.145 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.146 There were vpically 15 bright (16<£78 17) alignment stars yer duask used to alien asks., There were typically 4–5 bright $16<R<17$ ) alignment stars per mask used to align masks.147 They were put ino 1 square rather than 1”slits., They were put in $4\arcsec$ square rather than $1\arcsec$.148 The advantage of using alieumieut stars for flux calibration is that aliguiment stars and the targets were observed uuder exactly the sale conditions such as transparency and airmass., The advantage of using alignment stars for flux calibration is that alignment stars and the targets were observed under exactly the same conditions such as transparency and airmass.149" For cach imask. we first measured the spectral response frou, the spectra of standard star BD|28d1211. and extracted the spectra of the alignment stars."," For each mask, we first measured the spectral response from the spectra of standard star BD+28d4211, and extracted the spectra of the alignment stars."150 We then caleulatedthe couut-to-flux (eres bem7 +) ratios by scaling the spectra of the alizumoent stars to their broad-band photometry (7 or 2)., We then calculated the count-to-flux (erg $^{-1}$ $^{-2}$ $^{-1}$ ) ratios by scaling the spectra of the alignment stars to their broad-band photometry $i'$ or $z'$ ).151 The ratios amoug different alieunieut stars on a mask aeree within 0.1 mag., The ratios among different alignment stars on a mask agree within 0.1 mag.152 We also incorporated slit loss ( 0.21) iuto the couut-to-flux conversion ratios., We also incorporated slit loss $\sim0.24$ ) into the count-to-flux conversion ratios.153 The slit loss was estimated by ο a slit width of 17 and a stable Caussiau PSF of 1” (typical secine)., The slit loss was estimated by assuming a slit width of $1\arcsec$ and a stable Gaussian PSF of $1\arcsec$ (typical seeing).154 Finally the average of conversion ratios was applied to the spectra of other objects iu this mask., Finally the average of conversion ratios was applied to the spectra of other objects in this mask.155 Because the PSF is comparable to the slit width. the slit loss varies with varving secine. possible offsets between targets and slits. and even the sizes of targets.," Because the PSF is comparable to the slit width, the slit loss varies with varying seeing, possible offsets between targets and slits, and even the sizes of targets."156 We did not correct for these minor changes., We did not correct for these minor changes.157 Alone six ask nuages. one (the first one during which FCS failed) had more than twice lower slit throughput due to the £ülure of FCS or other unknown reasons.," Among six mask images, one (the first one during which FCS failed) had more than twice lower slit throughput due to the failure of FCS or other unknown reasons."158 We ideutified oue very bright LAE (out of 11 candidates} in this mask (No., We identified one very bright LAE (out of 14 candidates) in this mask (No.159 19 in Table 1 aud Figures l aud 2. see the following paragraphs). but we will not include this oue iu the analvsis of spatial density aud LE in the next section.," 19 in Table 1 and Figures 1 and 2, see the following paragraphs), but we will not include this one in the analysis of spatial density and LF in the next section."160 Iu the other five masks. we identified LS galaxies (out of 59 candidates) with prominent comission lines," In the other five masks, we identified 18 galaxies (out of 59 candidates) with prominent emission lines."161 Our 36 detection linit is about 0.7<10 ere bem2 at ~8500AL. ane is estimated as ollows.," Our $3\sigma$ detection limit is about $0.7 \times 10^{-17}$ erg $^{-1}$ $^{-2}$ at $\sim8500$, and is estimated as follows."162 The detection linüt depeuds on the shape of the lines. as narrower lines (for a eiven flux) are easier o ideutifv.," The detection limit depends on the shape of the lines, as narrower lines (for a given flux) are easier to identify."163 Iashikawactal.(2011) generated two composite comission lines for their z~5.7 aud 6.5 LAEs aud found hat the two lines were very similar., \citet{kas11} generated two composite emission lines for their $z\sim5.7$ and 6.5 LAEs and found that the two lines were very similar.164 We create a eenission model image with the shape of the composite 2~6.5 LAE profile., We create a emission model image with the shape of the composite $z\sim6.5$ LAE profile.165 We then scale this model image aud mit a muuber of them outo the spectral images., We then scale this model image and put a number of them onto the spectral images.166 The fiux indt is determined by detecting these simulated eenission from the spectral inages., The flux limit is determined by detecting these simulated emission from the spectral images.167 Briefly we ford one ealaxv out of LL candidates in the mask with verv low hroughput aud found 18 galaxies out of 59 candidates in he other five masks., Briefly we found one galaxy out of 14 candidates in the mask with very low throughput and found 18 galaxies out of 59 candidates in the other five masks.168 The remaining candidates do not show anv continu chussion nor line eniüssion. so we were not able to ideutifv them.," The remaining candidates do not show any continuum emission nor line emission, so we were not able to identify them."169 Figure 1 shows the thumbnail images of these galaxies in two broad bands // and z iud oue uarrow baud NB921., Figure 1 shows the thumbnail images of these galaxies in two broad bands $i'$ and $z'$ and one narrow band NB921.170 They were barely detected in the απ images aud totally invisible iu the BWR bands., They were barely detected in the $i'$ -band images and totally invisible in the $BVR$ bands.171 Most of them were also barely detected in the NB921 baud., Most of them were also barely detected in the NB921 band.172 Figure 2 shows the DETAIOS spectra and the redshifts of the 19 ealaxies., Figure 2 shows the DEIMOS spectra and the redshifts of the 19 galaxies.173 The spectra have been flux calibrated and are placed on an absolute flux scale using aliguinent stars., The spectra have been flux calibrated and are placed on an absolute flux scale using alignment stars.174 We can clearly see asviunetrv in the emission lines of relatively xieht galaxies., We can clearly see asymmetry in the emission lines of relatively bright galaxies.175 This is the indicator of the ccluission line at high redshift due to strong neutral interealactic medium (ICM) absorption bluewaird of the iuc., This is the indicator of the emission line at high redshift due to strong neutral intergalactic medium (IGM) absorption blueward of the line.176 The nou-detection iu deep BVRR nuages uplies hat they are not likely low-redshift contaminants., The non-detection in deep $BVR$ images implies that they are not likely low-redshift contaminants.177 Iu addition. the large wavelength coverage rules out the osspbilitv that the detected lines are one of theΤΠ...A5OQ7.. or lines.," In addition, the large wavelength coverage rules out the possibility that the detected lines are one of the, or lines."178Oi} The high resolution of the spectra also cusures that hey are not ddoublets., The high resolution of the spectra also ensures that they are not doublets.179 Ii a few cases in Figure 2 there are some residual sky lines recsviud of that appear like emission lines., In a few cases in Figure 2 there are some residual sky lines redward of that appear like emission lines.180 They are not the AGN cature À1210. because at 2~6 the comission line is ~170 ανν.," They are not the AGN feature $\lambda$ 1240, because at $z\sim6$ the emission line is $\sim170$ away."181 Table 1 lists the galaxy coordinates. redshifts. aud z baud magnitudes. as well as other properties that will be described below.," Table 1 lists the galaxy coordinates, redshifts, and $z'$ -band magnitudes, as well as other properties that will be described below."182 This galaxy sample spaus a redshift range 6xz6.1 and a inaguitude range of 25.1x 27., This galaxy sample spans a redshift range $6 \le z \le 6.4$ and a magnitude range of $25.1 \le z' \le 27$ .183 Redshift for cach galaxy is measured from the lliue center using a Caussian profile to fit the top ~50% of the line from the peak (the rest-frame line center is assumed to be 1216 Aj)., Redshift for each galaxy is measured from the line center using a Gaussian profile to fit the top $\sim50$ of the line from the peak (the rest-frame line center is assumed to be 1216 ).184 Note that the no., Note that the no.185 19 ealaxy in our lst is no., 13 galaxy in our list is no.186 2 in the photometric sample of Shiniasakuetal.(2005)., 2 in the photometric sample of \citet{shi05}.187. We measure observed line fixes by integrating the sspectra over rest-frame 1215.2 (=12160.8) to 1217.2 (—1216|1.2)À., We measure observed line fluxes by integrating the spectra over rest-frame 1215.2 (=1216–0.8) to 1217.2 (=1216+1.2).188. We do not correct for ICAL absorption dueward of the lune., We do not correct for IGM absorption blueward of the line.189 Table 1 shows the flux neasurenmienuts and the Iuminosities derived from the observed fluxes., Table 1 shows the flux measurements and the luminosities derived from the observed fluxes.190 Most. of he galaxies iu our suuple have the fluxes in a range of (0.7~2.1).10.I erg t caconrparable to the ‘fluxes in the SDF «—6.5 LAE sample al. 2006).," Most of the galaxies in our sample have the fluxes in a range of $(0.7\sim2.4) \times 10^{-17}$ erg $^{-1}$ $^{-2}$,comparable to the fluxes in the SDF $z\sim6.5$ LAE sample \citep{kas06}."191. The strongest ecuuission liue (5.8«10.I eres | 2) in our sample is as bright as the strongest LAEs from laree LAE surveys of Ouchietal.(2009).. Παetal. (2010).. and Kashikawaetal.(201 1).. indicating that it represcuts the bright eud of LAEs at 2>6.," 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 $z>6$."192 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}. .193 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.194 We estimate the rest-frame equivalent widths (ENs) using the observed, We estimate the rest-frame equivalent widths (EWs) using the observed195Mathysetal.(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.196 550 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}.197lsseda(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.198bypomcoholdanovdibissS€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.199 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.200 (OU 47 magnetic Ap/Bp stars with resolved Zeeman splitting., \citet{Mathys04} noted only 47 magnetic Ap/Bp stars with resolved Zeeman splitting.201 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.202 This comes from our survey of, This comes from our survey of203The orbit ellipGicily also influences (he similarity between the (wo cluster tails.,The orbit ellipticity also influences the similarity between the two cluster tails.204 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."205 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."206 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."207 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."208 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)."209 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."210 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."211 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."212 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."213 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 $0.4r_b$ ."214 The density profiles are very similar to (hat, The density profiles are very similar to that215 , 216In 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.)"217 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."218 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."219 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.220 1., 1.221 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.222 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.223 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}) )."224 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.225 The result of the test is displaved in Fig., The result of the test is displayed in Fig.226 2. which shows a surprisingly Gght correlation. as predicted by Eq.(1).," 2, which shows a surprisingly tight correlation, as predicted by Eq.(1)."227 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."228 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.229 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."230 The small standard deviation obtained in Fig., The small standard deviation obtained in Fig.231 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.232 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."233 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."234 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."235 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}) )."236 We also note that the strictly dillerential character, We also note that the strictly differential character2370.5<AsyoyX1.6 and Ayx0.15 which reduces the i. range away from »=1.0.,$0.5\le A_{2000} \le1.6$ and $A_K\le0.15$ which reduces the $A_v$ range away from $n=1.0$.238 In general. we mareinalize over attenuation. Lie. we chose the best fit parameters within the definedJ ranges that minimizefof: qD when fittingJH the SEII+ and IME.," In general, we marginalize over attenuation, i.e., we chose the best fit parameters within the defined ranges that minimize $\chi^2$ when fitting the SFH and IMF."239 Iu this section. we sununarize the important parameters and ranecs considered in our analysis aud show the effect of varving some of the parameters.," In this section, we summarize the important parameters and ranges considered in our analysis and show the effect of varying some of the parameters."240 Figure 5 shows the effects of varving one parameter on the syuthetic spectra (normalized at the ναι}. with respect to a model of (D.να.i5) = (1.3. 2.5.0. 0.018. 0.35. 1.0).," Figure \ref{fig:example-variations} shows the effects of varying one parameter on the synthetic spectra (normalized at the band) with respect to a model of $(\Gamma,\beta,\alpha,\bar{Z},A_v,n)$ = (1.3, 2.5, 0, 0.018, 0.35, 1.0)."241 Over our chosen Z.parameter ranges. varving the IME slope P. has the largest effect on the UV- colors. with 3 having the second largest effect.," Over our chosen parameter ranges, varying the IMF slope $\Gamma$ has the largest effect on the $-$ colors, with $\beta$ having the second largest effect."242 The ietallicitv has the largest effect on the -ccolors., The metallicity has the largest effect on the $-$colors.243 First. we fit to the UV-to-optical huninositv deusitv measurements of Sullivanetal.(2000):Dlautonct(2003b) with different near-IR measurements. considered separately: (a) using the Coleetal.(2001). A-band result (compilation designated iy Y: (b) using the Wnaue(2003) result (compilation SBIT). aud: (ο) using the Colectal. J bandresalt(compilationSBC 7) aud not including the :-band measurement which is included iu the first two compilations.," First, we fit to the UV-to-optical luminosity density measurements of \cite{sullivan00,blanton03} with different near-IR measurements, considered separately: (a) using the \cite{cole01} $K$ -band result (compilation designated $_K$ ); (b) using the \cite{huang03} result (compilation SBH), and; (c) using the \citeauthor{cole01} $J$ -band result (compilation $_J$ ) and not including the $z$ -band measurement which is included in the first two compilations."244 Examples of fitted spectra are shown in Figure 6.., Examples of fitted spectra are shown in Figure \ref{fig:example-fits}.245 This shows that the uear-IR luuinosity density measurements can be fitted. primarily by varving metallicity. while the UWV-to-optical spectrum reais approximately the same.," This shows that the near-IR luminosity density measurements can be fitted, primarily by varying metallicity, while the UV-to-optical spectrum remains approximately the same."246" Within the range of metallicity considered here Zsuu)) the best ft is obtained to the SBC, data."," Within the range of metallicity considered here ), the best fit is obtained to the $_K$ data."247 Tere. all the measurements are within about lo of the svuthetic magnitudes.," Here, all the measurements are within about $1\sigma$ of the synthetic magnitudes."248 The new results of Blautonctal. and this analysis resolves the major discrepancy noted by Wright(2001) between the optical aud ucar-IR huuinositv densities., The new results of \cite{blanton03} and this analysis resolves the major discrepancy noted by \cite{Wright01} between the optical and near-IR luminosity densities.249 However. there is a siguificaut discrepancy between the Tawaii and the 2\TASS K-baud huninosity densities aud a discrepancy between the J-baud result and the z-banud/ A-baud results.," However, there is a significant discrepancy between the Hawaii and the 2MASS $K$ -band luminosity densities and a discrepancy between the $J$ -band result and the $z$ $K$ -band results."250 Neither of the iuftrared surveys is ideal for comparison with the SDSS survey results., Neither of the infrared surveys is ideal for comparison with the SDSS survey results.251 The 2\EASS survey is too shallow Guedian 2~0.05 at the Πιτ of the extended source catalog) for direct comparison with the :=0.1 analysis and the Tawail survey soes deeper but las a sienificantly simialler area sqdeg))., The 2MASS survey is too shallow (median $z\sim0.05$ at the limit of the extended source catalog) for direct comparison with the $z=0.1$ analysis and the Hawaii survey goes deeper but has a significantly smaller area ).252" Note that the Sullivanctal. ivesult only uses about 200 ealaxies but it is consistent with the ""0 band result.", Note that the \citeauthor{sullivan00} result only uses about 200 galaxies but it is consistent with the $^{0.1}u$ band result.253 Improved surveys are needed to resolve the near-IR bhunuinuositv deusitv discrepancies and to reduce the uucertaiuties i UV. buninositv deusities., Improved surveys are needed to resolve the near-IR luminosity density discrepancies and to reduce the uncertainties in UV luminosity densities.254 We first look at constraints on the metallicity and IMF for a eiven cosmic ΕΗ (uareinalizine over dust attenuation)., We first look at constraints on the metallicity and IMF for a given cosmic SFH (marginalizing over dust attenuation).255" We compute u ando deteriuine the confidence levels of A4? = (1.0. 2.3. 6.2. 11.8) corresponding to (68.3%)) L-paramecter aud(68.3%..99.73%)) 2-pusuneter confidence Πές,"," We compute $\chi^2$ and determine the confidence levels of $\Delta\chi^2$ = (1.0, 2.3, 6.2, 11.8) corresponding to ) 1-parameter and,) 2-parameter confidence limits."256 The resulting contours are shown in Figure 7 for a cosmic SEIT with 9=2.5 anda=0 (Hoge2002:Steideletal.1999).," The resulting contours are shown in Figure \ref{fig:Z-imf+0} for a cosmic SFH with $\beta=2.5$ and $\alpha=0$ \citep{Hogg02,steidel99}."257". As expected. the best fit metallicity is dependent ou the near-IR data: the SDC, data has a best fit metallicity aroundZsxuu: SDII data. >2Zsxun.. 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, $<1$ ."258". 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}.259. 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.260 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}."261 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."262 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}. .263 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}. .264 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"265~s107 would produce similar effects.,"$\Omega_{dust}^{igm} \sim 3266\times 10^{-5}$ would produce similar effects."267 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.268" 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 $N \simeq269n\pi R^2D$ , where $D\approx 2400h_{65}^{-1}\,$ Mpc is the distance to $z=0.5$ in an $\Omega=0.2$ universe."270 Now consider galaxies with sΓΗ.DApe? (Lin et al.," Now consider galaxies with $n = 0.008h_{65}^3(1+z)^3\,{\rm271 Mpc^{-3}}$ (Lin et al."272 1996)., 1996).273 For N12zl this uuplies R>πι.ταν?ο” ," For $N^{1/2} \ga 1$ this implies $R274\ga 70h_{65}^{-1}[(1+z)/1.5]^{-3/2}\,{\rm kpc}$."275Escape 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."276 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.277" 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 $\Delta \sim2780.2/\sqrt{300} = 0.01$."279 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.280 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 $\delta281\sim 100$ is characteristic of the bulk of the metal-rich gas."282" 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.283 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.284 Ti Ro<TO kpc. most extinction takes place in a σα. nnnuber of clumps. in particular in the halo of the supernova host galaxy.," If $R \la 70$ kpc, most extinction takes place in a small number of clumps, in particular in the halo of the supernova host galaxy."285 For dust of deusitv Ὁως=vos107 unifornlv distributed in radius R=©«100kpc halos of galaxies with ο=Οδ.|2)?Alpe7. the extinction to the galaxy center is which gives the required extinction for $£=1 and XVmL As long as ©m0 there will uot be large dispersion due to different galactic radii in the supernovac. but inhomogencitics in the dust distribution in the halo could be iÀuportaut.," For dust of density $\Omega_{dust} = \chi\times 10^{-5}$ uniformly distributed in radius $R=\xi \times 100\,{\rm kpc}$ halos of galaxies with $n = 0.008h_{65}^3(1+z)^3\,{\rm Mpc^{-3}}$, the extinction to the galaxy center is which gives the required extinction for $\xi \approx 1$ and $\chi286\approx 4.$ As long as $\xi \ga 0.1$ there will not be large dispersion due to different galactic radii in the supernovae, but inhomogeneities in the dust distribution in the halo could be important."287" The supernova results could could be explained by such halos with a smaller O,5,4. but this would require that the halos are somewhat larger at low :. aud that all halos at 2~0.5 have similar colin cleusity through them."," The supernova results could could be explained by such halos with a smaller $\Omega_{dust}$, but this would require that the halos are somewhat larger at low $z$, and that all halos at $z\sim2880.5$ have similar column density through them."289 This scenario does uot ποσα to be as natural an explanation as a niore unifori dust distribution. but i relays a possibility.," This scenario does not seem to be as natural an explanation as a more uniform dust distribution, but it remains a possibility."290" Leaving aside these uncertainties. the essential result of my calculation is that a truucated-MBN clistribution of Draine Lee dust with «,,;,20.1. uniforiilv distributed and with —(45)~Ls10? can account for the supernovaQu dinuuine i an O=0.2 universe withou excessive reddenimg."," Leaving aside these uncertainties, the essential result of my calculation is that a truncated-MRN distribution of Draine Lee dust with $a_{min} \ga 0.1$, uniformly distributed and with $\Omega_{dust}^{igm}(z=0.5) \simeq 4\times 10^{-5}$ can account for the supernova dimming in an $\Omega=0.2$ universe without excessive reddening."291 Whether the induced dispersion in extinction is too large depeuds crucially on the (uncertain) distance to which ejected dust can escape from the galaxies in which it formis. aud on the chuupiness of the resulting distribution.," Whether the induced dispersion in extinction is too large depends crucially on the (uncertain) distance to which ejected dust can escape from the galaxies in which it forms, and on the clumpiness of the resulting distribution."292" Au intergalactic dust distribution of the magnitude requirec to explain fje supernova resuls would have other cosimoloeical inplicatious,", An intergalactic dust distribution of the magnitude required to explain the supernova results would have other cosmological implications.293 For iustauccanv intergalactic dust couponeut wil absorb energv fiui the optical/UV nckgrouid aud reewit the enerev in f1ο FIR/inicrowave.," For instance, any intergalactic dust component will absorb energy from the optical/UV background and re-emit the energy in the FIR/microwave."294 Calculation of the evolution of the cosmic mean density field shows (Aguirre Taian. in preparation) that the dust considered in this paper will not lead to measurable CMB spectral but stead adds (significantly) o the CIB.," Calculation of the evolution of the cosmic mean density field shows (Aguirre Haiman, in preparation) that the dust considered in this paper will not lead to measurable CMB spectral but instead adds (significantly) to the CIB."295 The FIRAS distortion limits can. however. iuit dust types with high FIR cuissivity. since these lave ower equilibrium temperatures.," The FIRAS distortion limits can, however, limit dust types with high FIR emissivity, since these have lower equilibrium temperatures."296 Note also that while the SER estimates correct for dust extinction (0.8. Madau. Pozetti Dickiusou 1998: Pettini 1999 and references therein). these correctious would not account for intergalactie dust.," Note also that while the SFR estimates correct for dust extinction (e.g. Madau, Pozetti Dickinson 1998; Pettini 1999 and references therein), these corrections would not account for intergalactic dust."297 Iuterealactic absorption of ο. lauagatcic]0.5 Ὁ (see fig. 5)), Intergalactic absorption of $\sim 0.1 - 1$ mag at $z \sim 0.5-5$ (see fig. \ref{fig-depth}) )298 would imply an SER aud hence metal density a factor of ~2 higher than that eiven iu rofsec-nietals.., would imply an SFR – and hence metal density – a factor of $\sim 2$ higher than that given in \\ref{sec-metals}.299 Future observations of supernovae can investigate the iuportaunce of intergalactic dust im two wavs., Future observations of supernovae can investigate the importance of intergalactic dust in two ways.300" First. accurate ligh-: observatious iu rest-frame R-baud or longer waveleugths should reveal the dust with propertics of the model developed here,"," First, accurate $z$ observations in rest-frame $R$ -band or longer wavelengths should reveal the dust with properties of the model developed here."301 As shown in fie. L.," As shown in fig. \ref{fig-reds},"302" the E(I yeddeuiug to.=0.5 is z0.25 for both pure eraphite dust (with d,,;,=0.06 pau) or for silicate|graphite (with με=OL gan)."," the $E(B-R)/B$ reddening to $z=0.5$ is $\approx3030.25$ for both pure graphite dust (with $a_{min} = 0.06\mic$ ) or for silicate+graphite (with $a_{min}=0.1\mic$ )."304 Therefore high-: supernova should have E(DR) values 0.05 mae higher than the low-: sample., Therefore $z$ supernova should have $E(B-R)$ values 0.05 mag higher than the $z$ sample.305 The effect iu B.I would be even strouger., The effect in $B-I$ would be even stronger.306 Nou-sphlierical eraius (of which the needles of Αθ are an example) could provide erev opacity into R-baud ancl bevoud. but are constrained limits ou f£u-iufrared/1iicrowave emission (Aeuirre Taian. in preparation).," Non-spherical grains (of which the needles of A99 are an example) could provide grey opacity into $R$ -band and beyond, but are constrained limits on far-infrared/microwave emission (Aguirre Haiman, in preparation)."307 Figure 5 includes the deviation of the it of R99 from the O=0.2 model (dashed line)., Figure \ref{fig-depth} includes the deviation of the fit of R99 from the $\Omega=0.2$ model (dashed line).308 The differeuce between this hue audthe dust optical depththen iudicates the deviation at high : of the dust model frou the cosmological coustaut (Q4= 0.72) model at +=1.5 the difference is ~0.2.0.3 mae.," The difference between this line andthe dust optical depththen indicates the deviation at high $z$ of the dust model from the cosmological constant $\Omega_\Lambda = 0.72$ ) model; at $z=1.5$ the difference is $\simeq3090.2-0.3$ mag."310 This possible difference should be testable ouce a significant ummber of +1 supernovae are measured., This possible difference should be testable once a significant number of $z > 1$ supernovae are measured.311 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"312correctly 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.313 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."314 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."315 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 $2\times31610^5$ yr, followed by a phase of conservative evolution) gives results consistent with several features of SNR1006."317 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.318 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."319 CD is verv indebted for α CIRIT grant., CB is very indebted for a CIRIT grant.320"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}.321 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 $r \sim 1.2$."322" 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."323" 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}) )."324 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)."325 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."326" 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."327 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."328 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."329" 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 $e_i/e_o \sim 0.6$."330 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.331 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.332 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."333 The bottom right panel of Fig., The bottom right panel of Fig.334 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.335 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."336 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."337 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 $q \ge 1$.338 Fig., Fig.339" 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 $m_o=5$ $\mearth$.340 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."341 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 $t\sim 5\times 10^4$."342" 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 $t \sim 3\times343 10^4$ which coincide with the planets being temporary captured in the 2:1 and 3:2 resonances."344" 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."345 Nonetheless. comparing Figs.," Nonetheless, comparing Figs."346 | 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 $m_o$."347 Fig., Fig.348 3 and Fig., \ref{run3} and Fig.349" 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.350" 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 $a_o\sim 1.6$."351" 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 $t\sim 1.4 \times 10^4$ ."352" 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."353 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}) )"354 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.355 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."356 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.357 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."358 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 Run4.359 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)."360 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)."361 Fig., Fig.362" 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 $m_o=10\;\mearth$.363 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 $t \sim 2\times36410^4$."365 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 $e_i$.366 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."367 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.368 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 $q\ge3691$ ."370 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"371The 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)."372 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."373 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."374 At (160 jim). some objects are not detected.," At (160 $\mu$ m), some objects are not detected."375 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."376 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}."377 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).378 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."379 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}."380 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}) ).381 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 ).382" 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, $(140/100)_\mathrm{cl}$."383 We can also take two colours for our BCD sample., We can also take two colours for our BCD sample.384 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."385 Thus. we apply the following corrections.," Thus, we apply the following corrections."386 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 $T_\mathrm{d}$."387 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 $T_\mathrm{d}((65/90)_\mathrm{cl},\,\beta )$ ."388 We adopt .?l and 2., We adopt $\beta =1$ and 2.389" 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."390 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.391" 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."392 In reffig:elrdat.. we show the colourcolour relation for the sample.," In \\ref{fig:clrdat}, we show the colour–colour relation for the sample."393 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}394 for the Milky Way (the Galactic plane with Galactic latitudes of $|b|<5^\circ$ ) and the Magellanic Clouds in \\ref{fig:clrdat}."395 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)."396 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)."397 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."398 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}) ).399 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."400 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}) )."401 We present the dependence of FIR colours on ISRF., We present the dependence of FIR colours on ISRF.402 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.403 In, In404so 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."405 po depends ou / through αμ., $\rho_o$ depends on $\hbar$ through $a_o$.406 This is the mass of the cold planet of Παππα radius., This is the mass of the cold planet of maximum radius.407 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."408 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.409 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.410 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.411" 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 $M_p=6.24 \times41210^{30}gm$."413 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.,"414 1995)., 1995).415 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 $gm\416cm^{-3}$."417" 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.418 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 $8\rho_o$.419" 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 $\hbar$.420 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.421 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).422 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 $7.0423\times 10^9$ for the radius of a body of mass $M_J=1.899 \times42410^{30} {\rm gm}$ 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."425"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. (4262003) and Calvet et al. (,2003) and Calvet et al. (4272004) in nearby star forming regions.,2004) in nearby star forming regions.428 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 $\dot429M_{\rm acc}$ 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.,"430 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.,"431 in preparation)., in preparation).432 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."433" 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.434" 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 $\dot m_{\rm}=\dot M_{\rm435acc}/m$, as a function of time for the PMS objects in 346 (circles) and for Galactic stars in Taurus (crosses; from Calvet et al."436 2000) and Trumpler 37 (squares: from Sicilia-Aguilar et al., 2000) and Trumpler 37 (squares; from Sicilia-Aguilar et al.437 2006)., 2006).438 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."439 in preparation)., in preparation).440 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 $\pm 1 \,441\sigma$ 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."442 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."443 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 $-7.7 \pm4440.6$ respectively for 346, the Dor region and the Galaxy."445 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."446 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."447 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.448 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 $\dot M_{\rm acc}$.449 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.,"450 in preparation)., in preparation).451 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."452 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.453 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."454 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}455 we can estimate the total mass accreted by a star over the time span from birth to the ZAMS."456 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.457 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."458 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."459 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."460 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."461 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.462 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."463 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.464 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 <o><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 $<\phi> \simeq 0.28$."465 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).466 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."467 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.468 In the range 0.4 , In the range $0.4$ 469"lie al V4,,,2227. 28.",lie at $_{nuc}$$\simeq$ 27–28.470 None were identified as variable abovethe 30 threshold in our survey., None were identified as variable abovethe $\sigma$ threshold in our survey.471 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.472 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."473 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."474 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."475 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).476 The measured variability signilicance of 633.1218 0.350., The measured variability significance of is $\sigma$.477 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.478 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.479" 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.480 Of the 16 variables. optical spectra exist lor 13.," Of the 16 variables, optical spectra exist for 13."481 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."482 Almost all of the remaining 12 show emission lines in their spectra., Almost all of the remaining 12 show emission lines in their spectra.483 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)."484 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."485 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)."486 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."487 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)."488 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."489 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)."490 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."491"The expressions for D, up to n=6 are given below.",The expressions for $D_n$ up to $n=6$ are given below.492" 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)."493" 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."494" 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$ ."495 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).496" 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$ )."497" 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."498"(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."499" 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."500 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.501" 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.502 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.503" 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."504" 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."505 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.506" 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."507 This is equivalent to having aninfinite number terms in the Edgeworth expansion., This is equivalent to having aninfinite number terms in the Edgeworth expansion.508" In numerical implementations, however,"," In numerical implementations, however,"509the 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}$."510 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.511 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.512 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."513" 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."514 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."515 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.516 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.517" 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."518 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}."519. 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.520 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."521 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."522 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."523 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."524 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}. ."525Spectral οσο effects are ignored here.,Spectral edge effects are ignored here.526 Eq., Eq.527 BLO agai refers to the pure power-law spectra case., \ref{eq:alphanu2} again refers to the pure power-law spectra case.528 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$."529" 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."530" 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 $r<R$ ) is given by an integration over the spherical emission volume $V$: where ${\rm Ei}(x)$ denotes the exponential integral."531 The total uuuber of svuchrotron photons within the source is then eiven by External photon fields do not penetrate the source completely for frequencies idu the svuchrotron sclabsorption frequency regine., The total number of synchrotron photons within the source is then given by External photon fields do not penetrate the source completely for frequencies in the synchrotron self-absorption frequency regime.532" A homogeneous COSLLUC background brightuess Seyi) produces a photon. field witlin the source according to where d(r.)) is the distance of a point at radius + from the source surface at radius A in the direction ο,"," A homogeneous cosmic background brightness $S_{\rm CB}(\nu)$ produces a photon field within the source according to where $d(r,\Omega)$ is the distance of a point at radius $r$ from the source surface at radius $R$ in the direction $\Omega$."533" The volume aud ceutral line-ofsight integrated number deusities can be approximated by These approximations have au accuracy of 1054 and they are asvinptotically correct for 7=τν]>0 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 $\tau534\rightarrow \infty$."535 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$.536 This relation is assumed to hold exactly in the monochromatic approximation., This relation is assumed to hold exactly in the monochromatic approximation.537 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."538 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$."539 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."540 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."541 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."542 The up-scattered CMD photons are nüssing at CXMB frequencies., The up-scattered CMB photons are missing at CMB frequencies.543 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.544 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)$ ."545where 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."546 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$."547 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$."548 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."549 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}.550" 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."551 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$."552 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."553" 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.554 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}."555" 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)$."556 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.557 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."558 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."559 Fig. 2).," Fig. \ref{fig_qval}) ),"560 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."561 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$ ."562 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"563without irraclialon effects included.,without irradiation effects included.564 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."565 2001)., 2004).566 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).567" 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."568 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.569 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$ ).570 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}) )."571 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."572 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$ )."573 Radius determinations of lot-Neptunes could. thus distinguish between different ormation scenarios., Radius determinations of hot-Neptunes could thus distinguish between different formation scenarios.574 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."575" 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$ ).576 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.577 The internal couposition also strongv affects the evolution of the planet., The internal composition also strongly affects the evolution of the planet.578 The sequence witi initial niass, The sequence with initial mass579" 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."580 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)."581 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."582 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."583 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.584 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)."585 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).586 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.587 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.588" 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)."589 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)."590 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.591 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."592 The sourceof theBHmass or velocity dispersion of the, The sourceof theBHmass or velocity dispersion of the593"110"" to 110” where it intersects the CND at the same velocity.",$''$ to $''$ where it intersects the CND at the same velocity.594 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)."595 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.596 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."597 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}.598. 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.599 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."600 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.601" 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$."602 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.603 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."604 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."605 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}) ).606 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.607 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."608 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.609 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."610 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.611" 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}$."612 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}613 in (1,1) and (2,2)."614 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."615 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}$."616 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."617 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.618" 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''$."619 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."620" Eiission from the CND is is seen from SO"" to 180"".", Emission from the CND is is seen from $''$ to $''$.621 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."622 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. (623T.1) aud (2.2) slow the same kinematics.,"1,1) and (2,2) show the same kinematics."624 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}$ ."625"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."626 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.627 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)."628" 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''$."629" 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 $''$.630 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.631 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.632 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.633" Overall. we detect three plivsical connections to the ΝΕΟ,"," Overall, we detect three physical connections to the CND."634 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.635" 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).636 SELextends northwiuds aud kinematically connects to the eastern lobe of the CND., SE1extends northwards and kinematically connects to the eastern lobe of the CND.637" 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."638" 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 $''$."639" 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 $''$ ."640 This feature is within 2 pe in projected distance frou Ser A*., This feature is within 2 pc in projected distance from Sgr A*.641" 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.642 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 $''$ ).643 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."644" 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 $''$ .645" At 125"". there is cunission from 50 aus το | 40s +."," At $''$ , there is emission from –50 km $^{-1}$ to +40 km $^{-1}$ ."646 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"647 their inflated radii., their inflated radii.648 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."649 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."650 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.651 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).652 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."653 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."654 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.655 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."656 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."657 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."658 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."659 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 =660({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_{\rm661eq}$ ."6623elore 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."663. 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."664 “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."665 Note that. the actors were not included in Figs., Note that the factors were not included in Figs.666 2. and 3 above. (, \ref{relstar_matches1} and \ref{relstar_matches2} above. (667Phe LAWS calibration is in disagreement with the one,The LW3 calibration is in disagreement with the one668 (c.c.T) (e.g...7?7?j..," \citep[e.g.,][]{Mateo98} \citep[e.g.,][]{Mateo98,Lokas09,Walker_etal09}."669 (e.g...7) (e.e..2). ο7)..," \citep[e.g.,][]{Grcevich_Putman09} \citep[e.g.,][]{Mateo98} \citep[e.g.,][]{Grebel00}."670 (e.g.?77?77?777) (?).. inodel(?) Tn," \citep[e.g.,][]{Einasto_etal74,Faber_Lin83,Mayer_etal01,Kravtsov_etal04,671 Mayer_etal06,Mayer_etal07,Klimentowski_etal09,Kazantzidis_etal11}672 \citep{D'Onghia_etal09}."673 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."674 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."675 Iuteractions aud mergers between galaxies ma constitute such a mechianisui., Interactions and mergers between galaxies may constitute such a mechanism.676 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}."677. 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}."678 ?. 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.679 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 M31.680 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."681 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."682 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.683line 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.684 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.685 [6] and [7/))., \ref{fig:evo} and \ref{fig:Si_evo}) ).686 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$.687" 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."688 By just comparing the two leftmost panels in Fig., By just comparing the two leftmost panels in Fig.689" 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."690 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.691" 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."692 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 0.11.693 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 from694iuner-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.695 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.696" 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."697 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."698 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."699 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}) ),"700 aud 142 miu for NTE 0929-311 (Calloway et al. 2002))., and 42 min for XTE J0929-314 (Galloway et al. \cite{galetal}) ).701 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."702" 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."703 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?5<Xx:1011»οσα.," Narayan Heyl \cite{nh02}) ) compute instability of accretion onto a hypothetical $10M_\odot$ star with a surface of radius between $(9/8)R_S$ and $3R_S$, and report that for a range of accretion rates compatible with observations of X-ray novae, the star is expected to give rise to an X-ray burst if the accreted column density is $10^9\,{\rm g/cm^2}\le\Sigma\le 10^{11}\,{\rm704g/cm^2}$."705 Frou this.. he authors conclude that black hole eaucdidates cannot have a surface. as they do not exhibit N-rav bursts.," From this, the authors conclude that black hole candidates cannot have a surface, as they do not exhibit X-ray bursts."706" Que COUCCELL 19 that the authors do not present the results separately for the lowest colt density considered. 10?οσα”, aud the higher values 1019οαμ” and +10H&/eau?2 forJ a 10A. star with. a 3s. radius.. the nass transferred iu the transient outburst ~6«107!Pefe?D correspouds o 6⋅«E10'oPe/cm?. so the N-raw mast expected at one of he higher colin deusities may. in fact. not occur during a SNT outburst."," One concern is that the authors do not present the results separately for the lowest column density considered, $10^9\,{\rm g/cm^2}$, and the higher values $10^{10}\,{\rm g/cm^2}$ and $10^{11}\,{\rm g/cm^2}$ —for a $10M_\odot$ star with a $3R_S$ radius, the mass transferred in the transient outburst $\sim 6\times10^{24}\,{\rm g/cm^2}$ corresponds to $6\times10^9\,{\rm g/cm^2}$, so the X-ray burst expected at one of the higher column densities may, in fact, not occur during a SXT outburst."707 However. there is a nore fundamental doubt as to the relevance of the result.," However, there is a more fundamental doubt as to the relevance of the result."708 Since the minima radius of Q-star is Lb Ry (Miller et al. 1998)).," Since the minimum radius of Q-star is 1.4 $R_S$ (Miller et al. \cite{msn98}) ),"709 Naravan Πο] (2002)) consider not ouly objects composed of matter whose properties have been described by Bahcall ct al. (1990)), Narayan Heyl \cite{nh02}) ) consider not only objects composed of matter whose properties have been described by Bahcall et al. \cite{bls90}) )710 Dut also more colupact configurations whose microscopic propertics are uot known at all., but also more compact configurations whose microscopic properties are not known at all.711 Therefore there is no reason to asstuuce that the surface of such objects is composed. of ordinary matter aud is in the temperature ranee required for X-ray bursts to occur., Therefore there is no reason to assume that the surface of such objects is composed of ordinary matter and is in the temperature range required for X-ray bursts to occur.712 The stellar surface could be too co to support a thermonuclear runaway., The stellar surface could be too cold to support a thermonuclear runaway.713 As a matter of fact. the accreted matter could be couverted right away to a nore exotic form. as it would be on contact with quark matter in the color-locked phase (Alford. Rajagopal Wilezck. 1995.. Rapp ct al.," As a matter of fact, the accreted matter could be converted right away to a more exotic form, as it would be on contact with quark matter in the color-locked phase (Alford, Rajagopal Wilczek \cite{arw}, Rapp et al."714 1998). or with the skin of a gravastar (Mazur Mottola 2001.. see below).," 1998), or with the skin of a gravastar (Mazur Mottola \cite{MM01}, , see below)."715 This could happen even at zero density. contrary to the lwpothesis advanced by Naravan IIevl (2002)).," This could happen even at zero density, contrary to the hypothesis advanced by Narayan Heyl \cite{nh02}) )."716 No nuclei: uo bursts.," No nuclei, no bursts."717" Mazur aud Mottola (2001)) have receutly found a new static. spherically οποίαο, solution of Eiusteimis Ποια equations."," Mazur and Mottola \cite{MM01}) ) have recently found a new static, spherically symmetric, solution of Einstein's field equations."718 A eravastar. as it is called. has the standard vacuum Scliawarzschild exterior. aud an interior filled with matter that has the equation of state p=p.," A gravastar, as it is called, has the standard vacuum Schwarzschild exterior, and an interior filled with matter that has the equation of state $\rho = -p$."719" The interior is described by the de Sitter solution. and is matched to the exterior vacunni solution iu a very thin shell of thickness ou the order of the Planck eugth. Ap=LGSLO σσ,"," The interior is described by the de Sitter solution, and is matched to the exterior vacuum solution in a very thin shell of thickness on the order of the Planck length, $\lambda_P = 1.6 \times72010^{-33}$ cm."721 The eravastar has uo horizon or sineularity., The gravastar has no horizon or singularity.722 Its vieid surface is located at a radius just slightly ercater than the eravitational radius. R=Rs|frp. f~2.," Its rigid surface is located at a radius just slightly greater than the gravitational radius, $R_* = R_S + f\lambda_P$, $f \sim 2$."723 There are several purely theoretical objections that one could raise against eravastars. none of them conclusive.," There are several purely theoretical objections that one could raise against gravastars, none of them conclusive."724 For example. stcllaranass eravastars have cutropy smaller than ordinary stars with the same masses aud this would require extremely efficieut cooling before eravastars could form during stellar collapse.," For example, stellar-mass gravastars have entropy smaller than ordinary stars with the same masses and this would require extremely efficient cooling before gravastars could form during stellar collapse."725 There is no observational way to distiuguish what wav seen to be a Sclawarzschild black-hole from a exavastar., There is no way to distinguish what may seem to be a Schwarzschild black-hole from a gravastar.726 To see lis. let us denote the surface redshift by For astroplivsically interesting eravastars. with lass greater than M. bie. Rg>34105 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."727" 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."728 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."729 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.730 , 731"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) \equiv732k_z(0)/k_x$, $\varepsilon \equiv (k_z z_0)^{-1}$, $\sigma^2 \equiv733(C_s/C_A)^2$ , $N^2 \equiv (N_{BV}/C_Ak_x)^2$."734" 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$, $d735\equiv i{\hat \varrho}/\rho_0$, ${\cal P} \equiv i{\hat736p}/\rho_0C_s^2$, $e \equiv -k_x {\hat s}/(\partial_zs_0)$, $\tau737\equiv k_xC_At$, ${\cal K}_y(\tau) \equiv {\cal K}_y(0) - {\cal738R}\tau$ , ${\cal K}_z(\tau) \equiv {\cal K}_z(0) - R\tau$."739 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},740d, e, \cal P$ )."741 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. (74214) [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) $\alpha743\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."744 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.745 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."746 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.747 ARIILT5S8« ~ , $\sim$ 748This 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."749" 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$ ."750 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)."751 This mav imply that the errors were overestimated by Alcocketal.(2001)., This may imply that the errors were overestimated by \citet{alcock01}.752. 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."753 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."754. 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."755 Onlv alter these tests are successfully concluded do we combine the data., Only after these tests are successfully concluded do we combine the data.756 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."757 These data have already been analvzed by and Gould(2004)., These data have already been analyzed by \citet{alcock01} and \citet{gould04}.758. 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$ ).759 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.760 We repeat (his procedure until all 3.50 outliers are removed.," We repeat this procedure until all $3.5\,\sigma$ outliers are removed."761 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$."762 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."763 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$.764 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"765and 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."766 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."767 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$."768 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."769 The fractal nature of the accreting matter acts against multitransonicity., The fractal nature of the accreting matter acts against multitransonicity.770 Nevertheless. this does not preclude transonicity itself.," Nevertheless, this does not preclude transonicity itself."771 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."772 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."773 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."774 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."775 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}."776. 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}.777. 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."778 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."779 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."780 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}."781 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.782 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."783 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).784 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.785 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."786 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.787" 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}788 for spherically symmetric flows, and applied successfully later to thin disc flows \citep{ray03,crd06,rbcqg}."789. 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."790 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$ ."791 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$.792 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}."793.. 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.794 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."795 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."796 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"797steepening 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}.798 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}."799. 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.800 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.801 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."802 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}) )."803 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}) )."804 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}.805. 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.806 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."807 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.808 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.809 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?810 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."811" 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."812 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.813" 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."814 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."815 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."816 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 establish817preseut.,present.818 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."819" 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."820 As s1OWll in Figs., As shown in Figs.821" | 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}$ )."822Dowever. 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."823 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."824 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}.825 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."826 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$."827 As an exiunple. Fie.," As an example, Fig."828 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."829 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."830 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."831 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"832aabsorbers with redshifts 0.412.<20.84 by Nestoretal.(2006)..,absorbers with redshifts $0.42 < z < 0.84$ by \citet{2006astro.ph.10760N}.833" 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^*$ ."834" 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^*835\la L \la 2.0L^*$ ."836 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."837 The second result of the Nestor et al., The second result of the Nestor et al.838 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 \la83913L^*$."840 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.841 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."842 Thus. we find no evidence in our sample for any such excess.," Thus, we find no evidence in our sample for any such excess."843 Nestor et al., Nestor et al.844 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.845 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."846 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."847 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."848 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}."849 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).850" The absolute magniude corresponds to ~AL""0.5. or AZ (220)."," The absolute magnitude corresponds to $\simeq$$M^*-0.5$, or $M^*$ $z$ =0)."851 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."852 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$$M^*$ $z$ =0)+0.75."853 The KKde aperture corresponds closely to the spatial scale of our observed excess of galaxies and the average absolute magnitude of galaxies associated with al 30 absorbers is. 2M (220H40.2540.2., The kpc aperture corresponds closely to the spatial scale of our observed excess of galaxies and the average absolute magnitude of galaxies associated with all 30 absorbers is $\simeq$$M^*$ $z$ $\pm$ 0.2.854 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 (even855"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."856" 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)."857" 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."858" 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."859 This output is fed into the simulation at every iteration., This output is fed into the simulation at every iteration.860 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.861" 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."862" 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."863" 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}864 We create a spherical gas cloud with solar abundances at a distance of 10 parsec from a $^7 \rm M_{\odot}$ black hole."865 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.866" 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 $\rm P \propto \rho$."867 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.868" 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}."869" ? 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."870" 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."871" 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."872" 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."873" In this, heating is nearly immediate, since the timescale for heating is much shorter than the collapse time, thear<tg, and of the order of 107! years."," In this, heating is nearly immediate, since the timescale for heating is much shorter than the collapse time, $\rm t_{heat} \ll t_{ff}$, and of the order of $^{-1}$ years."874 All other conditions are the same for both simulations., All other conditions are the same for both simulations.875" The simulations are set up with an initial random, divergence-free turbulent velocity field and a characteristic FWHM of 5 km/s that agrees well with molecular clouds Observed in active regions (?).."," The simulations are set up with an initial random, divergence-free turbulent velocity field and a characteristic FWHM of 5 km/s that agrees well with molecular clouds observed in active regions \citep{2009A&A...503..459P}."876" These are supersonic flows with Mach numbers of up to 25, where the isothermal sound speed of the cloud is c,=0.19 km/s (for T=10K) and can go up to a maximum of 5 km/s when the cloud is heated by X-rays (T«10 K)."," These are supersonic flows with Mach numbers of up to 25, where the isothermal sound speed of the cloud is $\rm c_{s}=0.19$ km/s (for T=10K) and can go up to a maximum of 5 km/s when the cloud is heated by X-rays $\simeq$ $^{4}$ K)."877 We do not drive the turbulence but follow its decay., We do not drive the turbulence but follow its decay.878" The turbulence is applied over all scales with a power spectrum of P(k)ek, following the empirical laws for compressible fluids (???).. "," The turbulence is applied over all scales with a power spectrum of $\rm P(k) \propto k^{-4}$, following the empirical laws for compressible fluids \citep{1981MNRAS.194..809L, 1999ApJ...522L.141M, 2004ApJ...615L..45H}."879We start the simulations with a cloud that is in a stable Keplerian orbit around the black hole., We start the simulations with a cloud that is in a stable Keplerian orbit around the black hole.880 Shear that is introduced by the black hole is taken into account., Shear that is introduced by the black hole is taken into account.881" The maximum velocity difference imposed by the black hole, AVshear= 2.2 km/s across the cloud, is of the order of the applied initial turbulence."," The maximum velocity difference imposed by the black hole, $\triangle \rm v_{shear}=$ 2.2 km/s across the cloud, is of the order of the applied initial turbulence."882" This process keeps the turbulence strong to large dynamical times, ie., >1tg, 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."883" 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 $\sim$ $^{5} \rm ~cm^{-3}$."884 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.885" 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."886 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 $\rm cm^{-3}$.887" 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."888 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.889" 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."890 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.891" With the box size of 24 pc, the maximum spatial resolution becomes"," With the box size of 24 pc, the maximum spatial resolution becomes"892This section reviews the dynamical model and (he numerical action procedure.,This section reviews the dynamical model and the numerical action procedure.893 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.894 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.895 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.896 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."897 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 P09.898 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.899 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 $a_o=1$."900 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."901 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"902eficiency of the photoclectric heating.,efficiency of the photoelectric heating.903 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), $\chi \sim 1.6904\chi_0$ , where $\chi_0$ refers to the sum of the K cosmic background and the spectrum given by \citet{mezger82} and \citet{mathis83}."905. 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. (9062002). 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."907 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. ("9082002).,2002).909 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.910 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}."911 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.912 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.913 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."914 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.915 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."916 Other iuprovenients of our work. compared with Iugalls et al. (," Other improvements of our work, compared with Ingalls et al. ("9172002). are related to the euploved dust model.,"2002), are related to the employed dust model."918 We use the three component model of Li&Draine (2001).., We use the three component model of \citet{li01}. .919 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.920 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."921 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."922 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."923 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 d<Ax2) and uaintained with an external large scale random and solenoidal force. correlated at the largest scale urnover time.," Turbulence is set up as an initial large scale random and solenoidal velocity field (generated in Fourier space with power only in the range of wavenumbers $1\le K\le 2$ ) and maintained with an external large scale random and solenoidal force, correlated at the largest scale turn–over time."924 The initial deusitv aud maguetic field are uniform and the gas is assuined to be isothermal., The initial density and magnetic field are uniform and the gas is assumed to be isothermal.925 Details about the munerical method are given iu Padoan Nordluud (1999)., Details about the numerical method are given in Padoan Nordlund (1999).926 Experiuecuts are run for approximately 10 dynamical times m order to achieve a statistically relaxed state., Experiments are run for approximately 10 dynamical times in order to achieve a statistically relaxed state.927 The cloud models used in this work correspond to the final snapshot of cach siunlatiou., The cloud models used in this work correspond to the final snapshot of each simulation.928 The value of Ma is varied in ciffereut experiuüeuts bv varving the thermal energy., The value of $M_{\rm S}$ is varied in different experiments by varying the thermal energy.929 The initiali ris Alfvénnuic Mach nuniber τοας uchauged. A4=10.0. from run to run.," The initial rms Alfvénnic Mach number remains unchanged, $M_{\rm A}=10.0$, from run to run."930 The vohuueaveraged magnetic field streusth is constant in time because of the imposed fiux couservation., The volume–averaged magnetic field strength is constant in time because of the imposed flux conservation.931 The magnetic energv is dustead amplified., The magnetic energy is instead amplified.932" The initial value of the ratio of average magnetic and duae pressures is (PainGig,=0.005 for all runs. so all the runs are initially superAlfvéuuic."," The initial value of the ratio of average magnetic and dynamic pressures is $\langle P_{\rm m} \rangle _{\rm in} / \langle P_{\rm d} \rangle _{\rm933in}=0.005$ for all runs, so all the runs are initially super–Alfvénnic."934 The value of the same ratio at later times is larecr. due to the maguetic enerev amplification. but still significantly lower than wuitv (0.21. 0.1 and 0.12 for models A. B and C respectively).," The value of the same ratio at later times is larger, due to the magnetic energy amplification, but still significantly lower than unity (0.21, 0.14 and 0.12 for models $A$, $B$ and $C$ respectively)."935 The turbulence is therefore superAlfvénnic at al times., The turbulence is therefore super–Alfvénnic at all times.936 Supersonic and superAlfvénnic turbulence of an isothermal eas generates a highly inhomoecucous eas density distribution. with a deusitv contras of several orders of magnitude.," Supersonic and super–Alfvénnic turbulence of an isothermal gas generates a highly inhomogeneous gas density distribution, with a density contrast of several orders of magnitude."937 It has been shown to provide a eood description of the dynamics of molecular clouds aud of their highly fragimieutec nature (Padoanctal.1997a.b.1998.1999:Padoan&Nordlund 19995...," It has been shown to provide a good description of the dynamics of molecular clouds and of their highly fragmented nature \citep{pjn97, pnj97, padoan98, padoan99, Padoan+Nordlund99MHD}."938 Transhicent lieh latitude clouds (IILCS). such as the ones observed hy lugallsetal.(2002).. have been studied. thanks to their CO oenmission (Magnuaniοἳal.1996).," Translucent high latitude clouds (HLCs), such as the ones observed by \citet{ingalls02}, have been studied thanks to their CO emission \citep{magnani96}."939. Despite their lower gas density and oesunablv lavecr fraction ofgas in the atomic form.the clouds can still be approximately modeled with an isothermalequation of state.," Despite their lower gas density and presumably larger fraction ofgas in the atomic form,the clouds can still be approximately modeled with an isothermalequation of state."940 At densities above Lec5 the eas teniperature is expected, At densities above $^{-3}$ the gas temperature is expected941products produced at the TERAPIX data center located at the Institut d'Astrophysique de Paris.,products produced at the TERAPIX data center located at the Institut d'Astrophysique de Paris.942 The Isaac Newton Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofíssica de Canarias., The Isaac Newton Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofíssica de Canarias.943" This work 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."," This work 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."944 The Millennium Simulation databases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory., The Millennium Simulation databases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory.945companions.,companions.946 Alternatively. star formation may have been triMDecered by the radio lobe impacting tie interstellar uiecium. as suggestedMOD for Minkowski's object (ναι Breugel et al.," Alternatively, star formation may have been triggered by the radio lobe impacting the interstellar medium, as suggested for Minkowski's object (van Breugel et al."947 1985)., 1985).948 The fainter racio coutinuuin lobe of NGC 1110 extends to the northwest towards the ring (Smith 2000). howeven nal prese the resolution of the available radio continuum maps is not high enough to cdetermite its spati assoclal10i with the H II regions.," The fainter radio continuum lobe of NGC 4410 extends to the northwest towards the ring (Smith 2000), however, at present the resolution of the available radio continuum maps is not high enough to determine its spatial association with the H II regions."949 High resolution radio data would be useful to reveal tle allswer this questiou., High resolution radio data would be useful to reveal the answer to this question.950 The spectroscopic evidence for shocks or at least compressed gas iu the 1orthwester arc. however. supports this alternative hypothesis.," The spectroscopic evidence for shocks or at least compressed gas in the northwestern arc, however, supports this alternative hypothesis."951 Athid possibility is that the rine is the remnant o£ a third galaxy. which has bee1 torn apart by a collision., A third possibility is that the ring is the remnant of a third galaxy which has been torn apart by a collision.952 Iu this case. Ixuot #2 may be a third uucleus.," In this case, Knot $\#$ 2 may be a third nucleus."953 The relatively narrow optical line widths of liis source (Section 3.1). however. argues against this interpretation.," The relatively narrow optical line widths of this source (Section 3.4), however, argues against this interpretation."954 Iu the southeastern NCC £110 lobe. a prominent radio ‘hot spot” is found. coiucideut. with au jotical knot (Huimnel οἱ al.," In the southeastern NGC 4410 lobe, a prominent radio `hot spot' is found, coincident with an optical knot (Hummel et al."955 19856)., 1986).956 Huimnel et al. (, Hummel et al. (9571986) suggested that tliis odtical structure may je associated with the radio knot iu some manner.,1986) suggested that this optical structure may be associated with the radio knot in some manner.958 It is possible that tUs source is a “hot spot’ eultting optical svuchrotron emission. as is believed to be the case lor he odtical knots studied by keel Martini (1995). ODea et al. (," It is possible that this source is a `hot spot' emitting optical synchrotron emission, as is believed to be the case for the optical knots studied by Keel Martini (1995), O'Dea et al. ("9591999). and Lahhteemmakki Valtaoja (1999).,"1999), and Lähhteenmäkki Valtaoja (1999)."960" The 1.9 uil 1.5 GHz flux densities of t1ο NGC LILO knot a'e 2.5 mJy aud [41 u.Jv. respectively. with a spectral iudex à (E, x pj"") of 20.17."," The 4.9 and 1.5 GHz flux densities of the NGC 4410 knot are 2.5 mJy and 4.4 mJy, respectively, with a spectral index $\alpha$ $_{\nu}$ $\propto$ $\nu$$^{\alpha}$ ) of $-$ 0.47."961 The optical cotuterpart has an Rou lagude of 19 (333.2). iving an optical/1.0 GHz specral index of ~—0.31. similar to that inu he radio.," The optical counterpart has an R magnitude of $\sim$ 19 3.2), giving an optical/4.9 GHz spectral index of $\sim$$-$ 0.31, similar to that in the radio."962 The estimated iudex supports the idea that the optical emission is cle to syuchrotron eimission., The estimated index supports the idea that the optical emission is due to synchrotron emission.963" However. the NGC L110 knot is uuresolved iu our larrowbaud red imag[n]e (FWHM <0%99 ~ 100 pc). while the racio contiuuuu knot has a size of ~ 15"" (T kpc) (Humiuel et al."," However, the NGC 4410 knot is unresolved in our narrowband red image (FWHM $\le$ 9 $\sim$ 400 pc), while the radio continuum knot has a size of $\sim$ $''$ (7 kpc) (Hummel et al."964 LOSG). arguliD>oO agalust an association.," 1986), arguing against an association."965 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."966 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."967 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."968 1985: vat Bruegel Dey 1993: Ctaliam 1993)., 1985; van Bruegel Dey 1993; Graham 1998).969 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 $^{-1}$."970 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."971 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."972 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)."973 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"974 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"975 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"976the 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},"977 we get: where function G is defined as and, we get: where function $G$ is defined as and978suppressed 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.979 With these findiugs we calculate the cooling history of QNS and QS., With these findings we calculate the cooling history of QCNS and QS.980 The results are presented in Fie., The results are presented in Fig.981 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)."982 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.983 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.984 We have estimated the contributions of various quark processes to the enissivitv., We have estimated the contributions of various quark processes to the emissivity.985 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."986" 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 $Y_e <Y_{ec}$, the normal quark phase, and various color superconducting phases as the $uds$ -phase - small gaps” suggested by \citet{BL84}, , the CFL phase, and the 2SC phase, as suggested in recent works \citep{ARW98,RSSV98,S98,ARW99,RSSV99}."987. In all the cases we sce that Also the cooling curves for the case of small gaps. (A=O.1...1 MeV) disagree with the data., In all the cases we see that Also the cooling curves for the case of small gaps $\Delta = 0.1 \dots 1$ MeV) disagree with the data.988 Even if the CFL phase would be realised only in the deep interior region of a NS it would be problematic to satisty N-rav data., Even if the CFL phase would be realised only in the deep interior region of a NS it would be problematic to satisfy X-ray data.989 In this case the star would radiate mostly not from the surface but from the CFL region due to its extremely simall specific heat related to the Coldstone excitation., In this case the star would radiate mostly not from the surface but from the CFL region due to its extremely small specific heat related to the Goldstone excitation.990 Thus the cooling time would be determined by the heat trausport frou exterior regions to the center rather than by the cooling of the hadronic shell., Thus the cooling time would be determined by the heat transport from exterior regions to the center rather than by the cooling of the hadronic shell.991 Iun this respect the followiug remark ds in order., In this respect the following remark is in order.992 It is now believed that quark matter below LT.~50 MeV is in the color superconducting state characterized by a diquark condensate with laree euergv gaps (A~100 MeV) rather than ojus in the normal state or the superfiid state characterized by small gaps (As1 MeV)., It is now believed that quark matter below $T_c \sim 50$ MeV is in the color superconducting state characterized by a diquark condensate with large energy gaps $\Delta \sim 100$ MeV) rather than being in the normal state or the superfluid state characterized by small gaps $\Delta \lsim 1$ MeV).993 If so. one could thiuk that our above discussion of iorinal quark matter and of the case of a small eap has just pedagogic reasoning.," If so, one could think that our above discussion of normal quark matter and of the case of a small gap has just pedagogic reasoning."994 However. this is rot really so.," However, this is not really so."995 Indeed. besides the idea of abuormal y.ranec nuclei aud strange stars (Bociner1971:Witten1981:deRujulaandGlashow—1981) rere is the very similar idea of abnormal piou condensate nuclei aud stars with pion condeusate miclei. see (AGedal1971:Voskreseuskyv1977) aud je review (Migdaletal.1990).. chapters 15. 16.," Indeed, besides the idea of abnormal strange nuclei and strange stars \citep{B71,W84,RG84} there is the very similar idea of abnormal pion condensate nuclei and stars with pion condensate nuclei, see \citep{M71,VSC77} and the review \citep{MSTV90}, chapters 15, 16."996 The same relates to the kaon condensate objects., The same relates to the kaon condensate objects.997 Pion condensate systems cool down at about je same rate as eiven by QDU processes (for Yod0 7)., Pion condensate systems cool down at about the same rate as given by QDU processes (for $Y_e \sim 10^{-5}$ ).998 Besides. they cau be in the nonual state or iu the superfluid state characterized by very small eaps A=0.1 MeV. The cooling history of svstenis being in normal state is described by +ick solid curves on the lower panels of Figs.," Besides, they can be in the normal state or in the superfluid state characterized by very small gaps $\Delta \lsim 0.1$ MeV. The cooling history of systems being in normal state is described by thick solid curves on the lower panels of Figs."999 1 - 3., 1 - 3.1000 Thus we may also conclude that (bempe m normal A=0 stato with a crust) Stays with pion aud kaon condensate nuclei beime in the superfiuid state with eaps A=0.1 MeV are ruled out as objects being observed in N-ravs., Thus we may also conclude that (being in normal $\Delta =0$ state with a crust) Stars with pion and kaon condensate nuclei being in the superfluid state with gaps $\Delta \gsim 0.1$ MeV are ruled out as objects being observed in X-rays.1001 Three final remarks are iu order: Gi) It is conceivable that there are more colples collective effects which esseutially affect the specific heat and the huninositv., Three final remarks are in order: (i) It is conceivable that there are more complex collective effects which essentially affect the specific heat and the luminosity.1002 E.g. we calculated the mixed plotou-ghiou spectrum iu a siuplified model of two Abeclian gauge fields aud couchided that the mass of the excitation is laree. whereas oue cant exclude that iu the realistic nou-Abclian case there exists a photou-eluon excitation of a simall mass tha could leadto very officicn cooling via the mixed plioton-eluon decay process even by eq. (13)).," E.g., we calculated the mixed photon-gluon spectrum in a simplified model of two Abelian gauge fields and concluded that the mass of the excitation is large, whereas one can't exclude that in the realistic non-Abelian case there exists a photon-gluon excitation of a small mass that could leadto very efficient cooling via the mixed photon-gluon decay process given by eq. \ref{em-ph}) )."1003 The masses of hadronic quasi-Coldstone modesin CFL phase, The masses of hadronic quasi-Goldstone modesin CFL phase1004in the lowest redshift bin using isophotal fit PAs.,in the lowest redshift bin using isophotal fit PAs.1005 The results based on the random control sample in Figure 5 show that ó measured using all types of PAs are consistently zero across the redshift range., The results based on the random control sample in Figure \ref{fig:delta_z_random} show that $\delta$ measured using all types of PAs are consistently zero across the redshift range.1006" In Figure 6,, we plot the axis ratio of the satellite galaxies in different redshift bins."," In Figure \ref{fig:deltambz}, we plot the axis ratio of the satellite galaxies in different redshift bins."1007 The axis ratio determines how precisely the PAs are measured., The axis ratio determines how precisely the PAs are measured.1008" From Figure 6,, the axis ratio measured using the isophotal method does not vary much as redshift increases, indicating that the diminishing satellite alignment based on isophotal fit PAs is not due to the decreasing S/N at high redshift."," From Figure \ref{fig:deltambz}, the axis ratio measured using the isophotal method does not vary much as redshift increases, indicating that the diminishing satellite alignment based on isophotal fit PAs is not due to the decreasing S/N at high redshift."1009 'There are two possible explanations for the measured 6 in the low redshift bins., There are two possible explanations for the measured $\delta$ in the low redshift bins.1010 The first one is that the diffuse light from the BCGs affects the measurements of the PAs of the cluster satellite galaxies'., The first one is that the diffuse light from the BCGs affects the measurements of the PAs of the cluster satellite galaxies'.1011 This creates an artificial preference of major axes of the satellite galaxies., This creates an artificial preference of major axes of the satellite galaxies.1012" This contamination is most severe when the PAs are measured using isophotal fit, but less prominent when the PAs are measured using exponential fit and De Vaucouleurs fit."," This contamination is most severe when the PAs are measured using isophotal fit, but less prominent when the PAs are measured using exponential fit and De Vaucouleurs fit."1013 This is because the isophotal PAs are sensitive to the shape of the outer profile of galaxy while the model fit PAs are more determined by the inner profile of the galaxy., This is because the isophotal PAs are sensitive to the shape of the outer profile of galaxy while the model fit PAs are more determined by the inner profile of the galaxy.1014 'The second possible explanation to these results is the twisting of galaxy., The second possible explanation to these results is the twisting of galaxy.1015 This leads to different PAs when we use different methods., This leads to different PAs when we use different methods.1016 The outer rim of the galaxy is more susceptible to the tidal torque so that the alignment will show up when we use the isophotal fit PAs., The outer rim of the galaxy is more susceptible to the tidal torque so that the alignment will show up when we use the isophotal fit PAs.1017" One way to distinguish these two explanations is to look at the way ὃ depends on the absolute and apparent magnitudes of the BCG.To see this, we plot the measured ó for all the clusters with respect to apparent magnitudes and absolute magnitudes of the corresponding BCGs in the Figure 7 and Figure 8 respectively."," One way to distinguish these two explanations is to look at the way $\delta$ depends on the absolute and apparent magnitudes of the BCG.To see this, we plot the measured $\delta$ for all the clusters with respect to apparent magnitudes and absolute magnitudes of the corresponding BCGs in the Figure \ref{fig:deltarmaga} and Figure \ref{fig:deltarmagb} respectively."1018 One can see that ó shows a strong dependence on the apparent magnitude but not on the absolute magnitude., One can see that $\delta$ shows a strong dependence on the apparent magnitude but not on the absolute magnitude.1019" Therefore, we conclude that the 6 in the low redshift bins in Figure 4 is more likely resulted from the artifact of the PA measurement."," Therefore, we conclude that the $\delta$ in the low redshift bins in Figure \ref{fig:deltaz} is more likely resulted from the artifact of the PA measurement."1020" In Figure 9,, we show the absolute magnitude vs redsfhit for the BCGs."," In Figure \ref{fig:photozramag}, , we show the absolute magnitude vs redsfhit for the BCGs."1021anisotropic. indicating specifically a longitudinal (East-West) asviunetiv.,"anisotropic, indicating specifically a longitudinal (East-West) asymmetry."1022 If the radiation has a longitudinal asvuuuetry. if is reasonable to suspect that it may also have a latituclinal (North-South) asvuuuetry.," If the radiation has a longitudinal asymmetry, it is reasonable to suspect that it may also have a latitudinal (North-South) asymmetry."1023 The goal and scope of this article are limited to investigating the consequences of the following two lypotheses: Iu Section ??.. we analyze the properties of a model based on these two hypotheses.," The goal and scope of this article are limited to investigating the consequences of the following two hypotheses: In Section \ref{sec:Model}, we analyze the properties of a model based on these two hypotheses."1024 We find that. according this model. the muaxiumuu decay rate should occur in the ranee approximately September 6 to March δ.," We find that, according to this model, the maximum decay rate should occur in the range approximately September 6 to March 8."1025 Iu Section ??.. we compare this mocel with data from the BNL aud PTB experiments. and find that the phases of aN variability appear to be compatible with this model.," In Section \ref{sec:data}, we compare this model with data from the BNL and PTB experiments, and find that the phases of maximum variability appear to be compatible with this model."1026 We discuss these results iu Section [.., We discuss these results in Section \ref{sec:disc}.1027 It is couvenicnt to measure phase of the wear so as to run from 0 to 1., It is convenient to measure phase of the year so as to run from 0 to 1.1028" We denote bv o, the phase of the minium Sun-Earth distauce. aud by o4 a plase related to the solar axis of rotation."," We denote by $\phi_o$ the phase of the minimum Sun-Earth distance, and by $\phi_A$ a phase related to the solar axis of rotation."1029" Since the Suu-Earth distauce js a ln on January 3. 0,=0.008."," Since the Sun-Earth distance is a minimum on January 3, $\phi_o=0.008$."1030 The Earth has ιαππμ. exposure to the southern solar hemisphere ou March 6 and maximum exposure to he northern hemisphere on September 8. correspouding ο phases 0.178 and 0.687. respectively.," The Earth has maximum exposure to the southern solar hemisphere on March 6 and maximum exposure to the northern hemisphere on September 8, corresponding to phases 0.178 and 0.687, respectively."1031 The fact that he ciffereuce is not exactly 0.5 is due to the eccentricity of the Earth’s orbit., The fact that the difference is not exactly 0.5 is due to the eccentricity of the Earth's orbit.1032 Approximating the elliptical orbit wea circular orbit for the purpose of representing the North-South asvunuetiv. we adopt o4=0.183. which elves luaxinuun exposure to the southern hemisphere at phase 0.183. (March. 8) aud. maxima exposure to the rorthern hemisphere at phase 0.683 (September 6).," Approximating the elliptical orbit by a circular orbit for the purpose of representing the North-South asymmetry, we adopt $\phi_A=0.183$, which gives maximum exposure to the southern hemisphere at phase 0.183 (March 8) and maximum exposure to the northern hemisphere at phase 0.683 (September 6)."1033 We also point out that we are miplicitlv. invoking a hird hypothesis: The eccentricity of the Earth’s orbit leads to a variation in the dus of the hypothetical radiation iufiuenciug decay rates. normalized to mean value unity. given by wwhere €=(0.0331.," We also point out that we are implicitly invoking a third hypothesis: The eccentricity of the Earth's orbit leads to a variation in the flux of the hypothetical radiation influencing decay rates, normalized to mean value unity, given by where $C=0.0334$."1034" The variation of the flux due to a North-South asvuumetry is giveu by where the ""asviuuetry coefficient? ο ids chosen so that: Tt the average fiux is responsible for an increase in the decay rate by the simall “coupling cocficient™ TP. then he annual modulation of the decay rate P. normalized ο lnean value unity. is eiven by [We should note. however. that if is conceivable that the unknown radiation may act on some isotopes to reduce he decay rate."," The variation of the flux due to a North-South asymmetry is given by where the “asymmetry coefficient” $A$ is chosen so that: If the average flux is responsible for an increase in the decay rate by the small “coupling coefficient” $\Gamma$, then the annual modulation of the decay rate $R$, normalized to mean value unity, is given by [We should note, however, that it is conceivable that the unknown radiation may act on some isotopes to reduce the decay rate."1035 In this case the coupling cocticient E would be negative.|, In this case the coupling coefficient $\Gamma$ would be negative.]1036" We find from iuspection of this formula that. since oyo,f<0.5. the maxinin value of & is to be found oulv in the range o4,0.5""OX Or. equivalently. in the wo ranges Otooa aud o|0.5to1. 1,6. 0 £o 0.1825 aud ""dor83 to T."," We find from inspection of this formula that, since $|\phi_A-\phi_o|<0.5$, the maximum value of $R$ is to be found only in the range $\phi_A - 0.5 ~\rm{to}~\phi_A$ or, equivalently, in the two ranges $0 ~\rm{to}~\phi_A$ and $\phi_A + 0.5 ~\rm{to}~1$, i.e. 0 to 0.183 and 0.683 to 1."1037 The range oytoox|0.5.1.0. 0.1823 to 0.683.is Xddeu. [," The range $\phi_A ~\rm{to}~\phi_A + 0.5$, i.e. 0.183 to 0.683, is “forbidden.” ["1038For the case that the solar radiation acts to suppress the decay rate; these ranges would be |,"For the case that the solar radiation acts to suppress the decay rate, these ranges would be reversed.]"1039" Oue may uuderstand this result by noting that reversed.if we stu two sine waves. with pliases o4ando». the peak will be found in the range o4too» if Jo,οὐ)<0.5. and outside that range if Joy09]> 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 $|\phi_1-\phi_2|>0.5$ ."1040 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."1041 By comparing Eqs., By comparing Eqs.1042 | 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}."1043 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 1.1044" I£&=o,. the cocficicut Is zero. as we would expect."," If$\kappa=\phi_o$, the coefficient is zero, as we would expect."1045 Ife=oy. the coefficient is infinite. again as we would expect.," If $\kappa=\phi_A$, the coefficient is infinite, again as we would expect."1046 We also &ud from Eq., We also find from Eq.1047 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}. .1048"I£ &= o,. the factor is uuitv."," If $\kappa=\phi_o$ , the factor is unity."1049 Ife=oy or o4| 0.5. the factor is zero.," If $\kappa=\phi_A$ or $\phi_A+0.5$ , the factor is zero."1050parameters of the lower-frequency g-modes.,parameters of the lower-frequency $g$ -modes.1051 In total we detected 20 periodicities with 24., In total we detected 20 periodicities with $\geq$ 4.1052 All pre-whitened frequencies are listed in Table 3.., All pre-whitened frequencies are listed in Table \ref{freq_7668647}.1053 The bottom panel of Fig., The bottom panel of Fig.1054 6. still contains peaks with significant amplitude., \ref{ft_7668647} still contains peaks with significant amplitude.1055 However. all those peaks lie close to already—removed periodicities.," However, all those peaks lie close to already–removed periodicities."1056 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."1057 We did not attempt to pre-whiten those residual peaks., We did not attempt to pre-whiten those residual peaks.1058 The mean noise level in the tinal residual amplitude spectrum is mmma., The mean noise level in the final residual amplitude spectrum is mma.1059 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},"1060 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.1061 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.1062 Three remaining igh-frequency peaks lie slightly above the detection threshold., Three remaining high-frequency peaks lie slightly above the detection threshold.1063" 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."1064 The latter. if real. might be a signature of hybridity.," The latter, if real, might be a signature of hybridity."1065 In the low frequeney region we detected 24 peaks., In the low frequency region we detected 24 peaks.1066 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."1067 The list of detected peaks is given in Table 4.., The list of detected peaks is given in Table \ref{freq_10001893}.1068 The bottom panel of Fig., The bottom panel of Fig.1069 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.1070 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."1071 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."1072 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.1073 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.1074 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."1075 All peaks are listed inTable 5.., All peaks are listed inTable \ref{freq_8302197}. .1076 We can easily, We can easily1077al.,al.1078 1998)., 1998).1079 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."1080 2001)., 2001).1081 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.1082 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.1083 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."1084 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}) )1085 strongly suggests that they are directly related to cach other., strongly suggests that they are directly related to each other.1086 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)."1087 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."1088 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."1089 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.1090 Whatever rigecred this change. it only minorlv elected. the X-ray spectrum.," Whatever triggered this change, it only minorly effected the X-ray spectrum."1091 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."1092 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."1093 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.1094 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)."1095 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."1096 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."1097 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.1098 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."1099 2000: Remillard ct al., 2000; Remillard et al.1100 2001). GS. 1915|105 (1tcig et al.," 2001), GRS 1915+105 (Reig et al."1101 2000: Lin et al., 2000; Lin et al.1102 2000: Tomsick Ixaaret. 2001). NTE 11859|226 (Cui et al.," 2000; Tomsick Kaaret 2001), XTE J1859+226 (Cui et al."1103 2000). ancl GRS 1739278 (this study).," 2000), and GRS 1739–278 (this study)."1104 The phase lags show a large variety of behaviour., The phase lags show a large variety of behaviour.1105" 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)."1106 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)."1107 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."1108 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."1109 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.1110 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."1111 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."1112 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."1113 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."1114 19992.b: Cui ct al.," 1999a,b; Cui et al."1115 2000: LLoman et al., 2000; Homan et al.1116 2001: Strohmaver 2001)., 2001; Strohmayer 2001).1117 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."1118 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."1119 However. a search for such QPOs did not result in a," However, a search for such QPOs did not result in a"1120and 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}1121 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}."1122 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 $\Omega1123\equiv |\bOmega|$ is the angular frequency of rotation."1124" 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 $\hough(\mu;11250) \equiv \legen(\mu)$."1126 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."1127" 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."1128" 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."1129 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."1130 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."1131" 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 $\hough(\mu;\nu)$."1132 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)."1133 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}."1134 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."1135 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."1136 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."1137" 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."1138 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 $r$."1139 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.1140 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"1141with 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. (11421991) and Latter et al. (,1994) and Latter et al. (114301995).,1995).1144 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."1145" 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.1146 Iastuer et al. (, Kastner et al. (11471991) 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.1148 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 )."1149 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."1150" 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."1151 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.1152 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."1153 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."1154 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."1155 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."1156 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."1157 These observations are described in 82., These observations are described in 2.1158 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 4.1159 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.1160 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.1161 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}) )"1162 aud IIunt ct al. (1996))., and Hunt et al. \cite{Hea96}) ).1163 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."1164 199s).," \cite{VGCT97}1165 )."1166 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."1167 Data reduction was carried out usine the aud ARNICA (unt ct al., Data reduction was carried out using the and ARNICA (Hunt et al.1168 1991) software packages., 1994) software packages.1169 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}) ).1170 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 $\sim 15\%$."1171 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."1172 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.1173 1998)., 1998).1174 The accuracy ds I5.., The accuracy is $\sim$.1175 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.1176 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.1177 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}) ).1178" 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."1179 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 of1180(2010).,.1181. 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."1182 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.1183 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."1184 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."1185 In, In1186period to a negligible value.,period to a negligible value.1187 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."1188 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."1189 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."1190 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."1191 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."1192 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)."1193 This gave us a sample of 81 stars 1 (he mass ange., This gave us a sample of 81 stars in the mass range.1194. 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."1195 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."1196 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, $f(\tau_{disk})$."1197 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 $\tau_{disk}$."1198 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.1199 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."1200 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.

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