ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" This difference in ellipse shape was noted in Schombert (2007), but these difference ellipses are not enough explain the large surface brightness differences found in the galaxy sample (numerical experiments with ellipses in 2MASS data displays only a 1 to difference in intensities)."," This difference in ellipse shape was noted in Schombert (2007), but these difference ellipses are not enough explain the large surface brightness differences found in the galaxy sample (numerical experiments with ellipses in 2MASS data displays only a 1 to difference in intensities)."3" There are a few extreme cases (e.g. LSB galaxy, NGC 3109), but in general ellipticals have fairly constant eccentricities."," There are a few extreme cases (e.g. LSB galaxy, NGC 3109), but in general ellipticals have fairly constant eccentricities."4" However, there are large differences in the quoted intensity values per radius between the 2MASS project and our study."," However, there are large differences in the quoted intensity values per radius between the 2MASS project and our study."5" These differences range from small to up to60%,, greatest at the lowest intensity values."," These differences range from small to up to, greatest at the lowest intensity values."6"where e4, and es, are the two parameters used to define the ellipticity. as explained below.","where $a_{1\epsilon}$ and $a_{2\epsilon}$ are the two parameters used to define the ellipticity, as explained below."7" From the elliptical lens potential οι(6)=zr,). we can caleulatete the elliptical deflection angle (see § 3.2): Notice (hat (he expressions above hold foranv definition of ay, anc es."," From the elliptical lens potential $\varphi_\epsilon(x)\equiv\varphi(x_\epsilon)$, we can calculatete the elliptical deflection angle (see $\S$ 3.2): Notice that the expressions above hold forany definition of $a_{1\epsilon}$ and $a_{2\epsilon}$."8 Here. we follow Golse&Ixneib(2002) who. in order to be able to analvtically derive (he convergence ancl shear. chose the following elliptical parameters: which for small values of ellipticity€ results in (he same ellipticity along the ry as the standard elliptical model of wilh e—1—b/a. where e and b ave (he semianajor ancl semi-minor axis of the projected elliptic potential. respectively.," Here, we follow \citet{GolKne02} who, in order to be able to analytically derive the convergence and shear, chose the following elliptical parameters: which for small values of ellipticity$\epsilon$ results in the same ellipticity along the $x_1$ as the standard elliptical model of with $\epsilon=1-b/a$, where $a$ and $b$ are the semi-major and semi-minor axis of the projected elliptic potential, respectively."9 In the thin-lens approximation. we define 3 as the optical axis and (72.3)RE as the 3- Newtonian potential. with r=y?Hi+ 37.," In the thin-lens approximation, we define $\mathfrak{z}$ as the optical axis and $\Phi(R,\mathfrak{z})$ as the 3-dimensional Newtonian potential, with $r=\sqrt{R^2+\mathfrak{z}^2}$ ."10 The so-called reduced 2-dimensional potential which is defined in the dellector plane is given by (Schneider.Ehlers.&Falco1992) where c is thespeed of light. and @=(04.05) is (he angular position in the image plane.," The so-called reduced 2-dimensional potential which is defined in the deflector plane is given by \citep{SchEhlFal92} where $\mathfrak{c}$ is thespeed of light, and $\mathbf{\theta}=(\theta_1,\theta_2)$ is the angular position in the image plane."11" Dj. D.. and D,, are angular clistances of observer-observer-source. and deflector-source. respectively."," $D_{d}$ , $D_{s}$ , and $D_{ds}$ are angular distances of observer-deflector,observer-source, and deflector-source, respectively."12 The deflection angle o. convergence," The deflection angle $\mathbf{\alpha}$ , convergence"13energy distribution starting from the density. by caleulating what is the fraction of stellar mass at a given Ar from the centre.,"energy distribution starting from the density, by calculating what is the fraction of stellar mass at a given $\Delta r$ from the centre."14 Fig., Fig.15 | illustrates the geometry.," \ref{fig:scheme}16 illustrates the geometry."17 It can be easily shown that where ptr) is the spherically symmetric mass density of the star., It can be easily shown that where $\rho(r)$ is the spherically symmetric mass density of the star.18 The relation between the distribution of Ar and the distribution of energy Ε is simply given by: where AF is given by Eq. (3))., The relation between the distribution of $\Delta r$ and the distribution of energy $E$ is simply given by: where $\Delta E$ is given by Eq. \ref{eq:deltaE}) ).19 It is useful to introduce dimensionless quantities., It is useful to introduce dimensionless quantities.20" We then define €=-E/AE (where we have also included a minus sign because we are interested in material with negative specific energy) as our dimensionless energy. x=ΔΕΑ, as our radial coordinate within the star. x,=A,/R,c [as our dimensionless pericentre distance and ar=M/M, as our dimensionless mass."," We then define $\epsilon =21-E/\Delta E$ (where we have also included a minus sign because we are interested in material with negative specific energy) as our dimensionless energy, $x=\Delta r/R_{\star}$ as our radial coordinate within the star, $x_{\rm p}=R_{\rm p}/R_{\star}\gg 1$ as our dimensionless pericentre distance and $m=M/M_{\star}$ as our dimensionless mass."22" We also introduce a fiducial time unit 7;=SmR* and a dimensionlesstime τ=7/7y. as well as a fiducial IGM)density po7M,/R; and a dimensionless density P=/po."," We also introduce a fiducial time unit $T_0 = 2\pi(R_{\rm p}^3/GM_{\rm h})^{1/2}$ and a dimensionlesstime $\tau = T/T_0$, as well as a fiducial density $\rho_0=M_{\star}/R_{\star}^3$ and a dimensionless density $\hat{\rho}=\rho/\rho_0$."23" The outcome of the disruption event depends on the ""penetration factor 6=R,/N. that is the ratio of the pericenter distance to the tidal radius A,= ‘RL. where g=My/M, is the mass ratio between the black hole and the star."," The outcome of the disruption event depends on the 'penetration factor' $\beta=R_{\rm p}/R_{\rm24 t}$, that is the ratio of the pericenter distance to the tidal radius $R_{\rm t}=q^{1/3}R_{\star}$ , where $q=M_{\rm h}/M_{\star}$ is the mass ratio between the black hole and the star."25 In order to tidally disrupt the star we require BxV., In order to tidally disrupt the star we require $\beta\lesssim 1$.26" For example. for a mass ratio g=10°. we have B=| for Ry=LOOR,."," For example, for a mass ratio $q= 10^6$, we have $\beta=1$ for $R_{\rm p}=100 R_{\star}$."27" To give an idea of the numbers involved. we note that for Ry=1008;. My=LOS. M,=LM, and R,=Κ.Ο we have Tyx3.18107 yrs =0.11 days. while the unit for the accretion rate is M,/Py=3.1108M, /yr."," To give an idea of the numbers involved, we note that for $R_{\rm p}=100R_{\odot}$, $M_{\rm28 h}=10^6M_{\odot}$, $M_{\star}=1M_{\odot}$ and $R_{\star}=R_{\odot}$, we have $T_0 \approx 3.18~10^{-4}$ yrs $\approx 0.11$ days, while the unit for the accretion rate is $M_{\star}/T_0\approx 3.1~10^3M_{\odot}$ /yr."29 In these units. Eqs. (1). (24). (4) ," In these units, Eqs. \ref{eq:ET}) ), \ref{eq:MT}) ), \ref{eq:MR}) )"30and (59) become simply: The above simple set of equations therefore allows us to calculate the accretion rate onto the black hole as a function of the internal stellar structure., and \ref{eq:ME}) ) become simply: The above simple set of equations therefore allows us to calculate the accretion rate onto the black hole as a function of the internal stellar structure.31 In general. we expect the density to show a peak at small radii x and therefore a peak at small specitie energies €.," In general, we expect the density to show a peak at small radii $x$ and therefore a peak at small specific energies $\epsilon$."32 Since material at lower energies contributes to the accretion at later times. we can already predict what relative changes do we expect with respect to the standard ¢7? light curve.," Since material at lower energies contributes to the accretion at later times, we can already predict what relative changes do we expect with respect to the standard $t^{-5/3}$ light curve."33 In particular. we expect that if the star is more centrally condensed the flare should start with a relatively longer delay (less matter at large energies - small return time) and should have a shallower light curve (more matter at small energies - large return time).," In particular, we expect that if the star is more centrally condensed the flare should start with a relatively longer delay (less matter at large energies - small return time) and should have a shallower light curve (more matter at small energies - large return time)."34 However. unless the density is strongly diverging at small radii. we expect dir/dx=dmi/de to flatten at the lowest energies and therefore the light curve to approach a /7? profile at late times.," However, unless the density is strongly diverging at small radii, we expect $\de m/\de x= \de m/\de\epsilon$ to flatten at the lowest energies and therefore the light curve to approach a $t^{-5/3}$ profile at late times."35 As an example. we can use the above analytical formulae to calculate the specitic energy distribution and the accretion rate as a function of time predicted for some simple stellar models with known density profiles.," As an example, we can use the above analytical formulae to calculate the specific energy distribution and the accretion rate as a function of time predicted for some simple stellar models with known density profiles."36 We have thus considered simple polytropic spheres with ditferent indices y=5/3. I.4 and 4/3.," We have thus considered simple polytropic spheres with different indices $\gamma =375/3$, 1.4 and $4/3$."38 We have first solved numerically the Lane-Emden equation for the three cases and have then computed the various relevant quantities using Eq. (6))-€9)), We have first solved numerically the Lane-Emden equation for the three cases and have then computed the various relevant quantities using Eq. \ref{eq:dim1}) \ref{eq:dim4}) )39 above. assuming y=100.," above, assuming $x_{\rm p}=100$."40 The results are shown in Fig. 2.., The results are shown in Fig. \ref{fig:analytic}.41 The left panel shows the prediction for the energy distribution. where the solid line indicates the relatively non compact case y=S/3. the short-dashed line indicates y=1.4 and the dashed case shows the most compact case y= 4/3.," The left panel shows the prediction for the energy distribution, where the solid line indicates the relatively non compact case $\gamma=5/3$, the short-dashed line indicates $\gamma=1.4$ and the long-dashed case shows the most compact case $\gamma=4/3$ ."42 As can be seen. he energy distributions do extend up to &~|. but are not flat except at very low energies. the etfect becoming more pronounced or the more compact cases.," As can be seen, the energy distributions do extend up to $\epsilon \sim 1$, but are not flat except at very low energies, the effect becoming more pronounced for the more compact cases."43 The middle panel shows the predicted evolution of the mass accretion rate 7—dar/dr. for the three values of y with the same line styles as the left panel.," The middle panel shows the predicted evolution of the mass accretion rate $\dot{m}=\de m/\de \tau$, for the three values of $\gamma$ with the same line styles as the left panel."44 The red line shows or comparison a simple power law with index -5/3., The red line shows for comparison a simple power law with index -5/3.45 It can be seen hat indeed the light curves are slightly shallower that /°° and approach it only at late times., It can be seen that indeed the light curves are slightly shallower that $t^{-5/3}$ and approach it only at late times.46 This is even more evident in the right xnel. where we plot the power law index 7=dInzir/dIn for the hree cases.," This is even more evident in the right panel, where we plot the power law index $n=\de\ln\dot{m}/\de\ln\tau$ for the three cases."47 If we want to put some numbers on the estimates above. note that for our standard numerical values described above a time of | year corresponds to roughly 7.=3000.," If we want to put some numbers on the estimates above, note that for our standard numerical values described above a time of 1 year corresponds to roughly $\tau\approx 3000$."48 We then see that the yower law index after | year of the flare is η=—1.5 for y= 5/3. which is reasonably close to the expected -5/3.," We then see that the power law index after 1 year of the flare is $n\approx -1.5$ for $\gamma=5/3$ , which is reasonably close to the expected -5/3."49 However. such stellar model is probably unrealistic for a solar type star. whose structure is rather more similar toa y=4/3 polytrope. in which case. after | yearof the flare the power law index is still 7= —0.8.," However, such stellar model is probably unrealistic for a solar type star, whose structure is rather more similar toa $\gamma=4/3$ polytrope, in which case, after 1 year of the flare the power law index is still $n\approx -0.8$ ."50To evaluate. our. fragmentation criterion. we require the angular momentum of material within a collapsing turbulent core.,"To evaluate our fragmentation criterion, we require the angular momentum of material within a collapsing turbulent core."51 Although this is not included in the mocdels. we shall estimate angular momentum within hese models by ecneralizing a calculation by ALLOS (itself an analvtical version of the calculation. in the vein of 1987)).," Although this is not included in the models, we shall estimate angular momentum within these models by generalizing a calculation by ML05 (itself an analytical version of the calculation, in the vein of )."52 This calculation (presented in the. Appendix) notes that a core model specifies the turbulent velocity. dispersion a(r) as well as he density. profile p(r)., This calculation (presented in the Appendix) notes that a core model specifies the turbulent velocity dispersion $\sigma(r)$ as well as the density profile $\rho(r)$.53 For a special class of velocity fields one can compute the ensemble-averaged: specific: angular momentum and velocity dispersion., For a special class of velocity fields one can compute the ensemble-averaged specific angular momentum and velocity dispersion.54 The velocity field. must (e dsotropie: it must have a velocity dillerence. between any two points that scales as a(|ryτο)x[ryro regardless of the underlving density distribution: and its Cartesian components must be uncorrelated (oe. transport no average shear stress).," The velocity field must be isotropic; it must have a velocity difference between any two points that scales as $\sigma(|\mathbf r_1-\mathbf r_2|)\propto |\mathbf r_1-\mathbf55r_2|^\beta $ regardless of the underlying density distribution; and its Cartesian components must be uncorrelated (i.e., transport no average shear stress)."56 “Phe ensemble-averaged: specific angular momentum and. velocity dispersion. are calculated in equations (44))-(47))., The ensemble-averaged specific angular momentum and velocity dispersion are calculated in equations \ref{<j^2>}) \ref{<sigma^2>-angular}) ).57 We define theparameter 8; for a turbulent region of size £?: The rightmost expression involves root-mean-square ensemble averages over the turbulent velocity field. which are calculated in the Appendix.," We define the $\theta_j$ for a turbulent region of size $R$: The rightmost expression involves root-mean-square ensemble averages over the turbulent velocity field, which are calculated in the Appendix."58 Phe factor f; accounts for the cillerence between the ratio of rms averages and the ratio of amplitudes: since the amplitudes: are random variables. this includes both an overall offset. and a disperson.," The factor $f_j$ accounts for the difference between the ratio of rms averages and the ratio of amplitudes; since the amplitudes are random variables, this includes both an overall offset and a disperson."59" MEOS estimate logy,f;=0.088πο on the basis of a Gaussian model for the velocity Ποιά."," ML05 estimate $\log_{10} f_j =60-0.088^{+0.16}_{-0.49}$ on the basis of a Gaussian model for the velocity field."61 Our evaluation of the spin parameter is presented in the Appendix and summarized in figure 7 and table 7.., Our evaluation of the spin parameter is presented in the Appendix and summarized in figure \ref{jForCores} and table \ref{jOnRSigma}.62" Forà turbulence supported region with poxr"" one must have aryoxGALfrx7 ""oso dmdohf»14 (for 3/2)."," Fora turbulence supported region with $\rho\propto r^{-k_\rho}$ one must have $\sigma(r)^2 \propto G M(r)/r\propto r^{2-k_\rho}$, so $\beta=1-k_\rho/2\rightarrow 1/4$ (for $k_\rho\rightarrow 3/2$ )."63 In the core collapse model. each shell of matter accretes in sequence.," In the core collapse model, each shell of matter accretes in sequence."64 For each shell. the spin parameter is (see equation 49)).," For each shell, the spin parameter is (see equation \ref{powerlaw-thetaj-with-beta}) )."65 However. the last. shell to accrete naturally has the highest. angular momentum: as the disk. accumulates vector. angular um.26 may overestimate the disk. radius.," However, the last shell to accrete naturally has the highest angular momentum; as the disk accumulates vector angular \ref{thetajshell} may overestimate the disk radius."66 Moreover. although collapse is generally. super-Alfvénnic. magnetic braking may sap ) somewhat.," Moreover, although collapse is generally super-Alfvénnic, magnetic braking may sap $j$ somewhat."67 A rough lower bound on 8; is given by the specific angular momentum of the entire core. which corresponds to (also equation 49)).," A rough lower bound on $\theta_j$ is given by the specific angular momentum of the entire core, which corresponds to (also equation \ref{powerlaw-thetaj-with-beta}) )."68 Given upper and lower limits for 6;. we must decide which value to adopt.," Given upper and lower limits for $\theta_j$, we must decide which value to adopt."69 The remainder of this paper is intended to establish that fragmentation is inevitable in the outer reaches of massive-star disks. so we shall adopt the more conservative estimate (eq. 27)).," The remainder of this paper is intended to establish that fragmentation is inevitable in the outer reaches of massive-star disks, so we shall adopt the more conservative estimate (eq. \ref{thetajcore}) )."70 Please bear in mind that the upper bound to Ay is about four times larger., Please bear in mind that the upper bound to $R_d$ is about four times larger.71 The protostellar outflow will tend to remove low-j material (see also MLO05). but we expect this ellect to be rather minor and do not evaluate it.," The protostellar outflow will tend to remove $j$ material (see also ML05), but we expect this effect to be rather minor and do not evaluate it."72 For convenience we shall define a second: related quantity. οι by The factor o; defined here is related. to. the spin parameter 8; by ó;=Ra(I)8;CALGR)].," For convenience we shall define a second rotation-related quantity, $\phi_j$, by The factor $\phi_j$ defined here is related to the spin parameter $\theta_j$ by $\phi_j = R\sigma(R)^2\theta_j/[G M(R)]$."73" Lovdrostatic equilibrium. requires. Z20()?CAL(R)|=1/2th,Des]: therefore eiving ©;—0.067 in the fiducial case."," Hydrostatic equilibrium requires $ {R \sigma(R)^2 }/[{G M(R)}] = 1/[2(k_\rho-1)74\phi_B]$: therefore giving $\phi_j=0.067$ in the fiducial case."75 The disk acquires a final radius which is about L/40th of the core radius: in the fiducial. conservative case given by equation. (27)).," The disk acquires a final radius which is about 1/40th of the core radius: in the fiducial, conservative case given by equation \ref{thetajcore}) )."76 During acceretion. the disk radius remains proportional to the current racius of accretion:therefore al least on average.," During accretion, the disk radius remains proportional to the current radius of accretion;therefore at least on average."77 lt ds useful to know the column density scale in the infall for reference in the calculation of disk irraciation., It is useful to know the column density scale in the infall for reference in the calculation of disk irradiation.78" As discussed in MELOS. this is characterized by Nau(42,): the column outward from Z2; in à nonrotating infall of the same accretion rate."," As discussed in ML05, this is characterized by $\Sigma_{\rm sph}(R_d)$: the column outward from $R_d$ in a nonrotating infall of the same accretion rate."79 We find i... that the final infall column is comparable to the core column (see also AILO5).," We find i.e., that the final infall column is comparable to the core column (see also ML05)."80 Over the course of accretion. Finally. a note on the relation between a core’s density profile ancl its angular momentum scale.," Over the course of accretion, Finally, a note on the relation between a core's density profile and its angular momentum scale."81" Considering the range of values 1A,<2. the angular momentum of a turbulent sphere decreases sharply toward. zero as fk, approaches 2 and : approaches zero. as shown in figure 7."," Considering the range of values $1\leq82k_\rho\leq 2$, the angular momentum of a turbulent sphere decreases sharply toward zero as $k_\rho$ approaches 2 and $\beta$ approaches zero, as shown in figure \ref{jForCores}."83 Chis (rend is easily understood: when ;= 0. the velocity dillerencee between two points is independent of their separation and must therefore be contained in very scale motions as in an isothermal gas.," This trend is easily understood: when $\beta=0$ , the velocity difference between two points is independent of their separation and must therefore be contained in very small-scale motions as in an isothermal gas."84 Indeed. the threc-dimensional power spectrum scales as fo?7 and contains a divergent encrey at small scales as Pa3=Q0.," Indeed, the three-dimensional power spectrum scales as $k^{-3-2\beta}$ and contains a divergent energy at small scales as $\beta\rightarrow 0$."85 Angular momentunm is dominated bv the largest-scale motions that fit within the region of interest. ancl therefore. vanishes if turbulent energy. appears only at small scales.," Angular momentum is dominated by the largest-scale motions that fit within the region of interest, and therefore vanishes if turbulent energy appears only at small scales."86 However. a core whose hyelrostatic support is elfectively isothermal (3= 0) may still contain angular momentum duc to background turbulence if it is confined in a turbulent region with :> 0.," However, a core whose hydrostatic support is effectively isothermal $\beta=0$ ) may still contain angular momentum due to turbulence if it is confined in a turbulent region with $\beta>0$ ."87 This situation holds for thermally. supported: coreswithin turbulent molecular clouds. and. formed. the basis for the AMILO5 estimate of clisk radii in low-mass star formation.," This situation holds for thermally supported coreswithin turbulent molecular clouds, and formed the basis for the ML05 estimate of disk radii in low-mass star formation."88"a colour-magnitude diagram (CMD), the candidate companion star of ffalls near the zone of the main sequence stars with spectral type between B5 and B8-A09).","a colour-magnitude diagram (CMD), the candidate companion star of falls near the zone of the main sequence stars with spectral type between B5 and B8–A0."89". In this case of a BeXB system, the disc-like ring of matter surrounding the B star can modify its colour J—K by a largefactor (e.g.upto—0.5magin4U0115-63 ?).."," In this case of a BeXB system, the disc-like ring of matter surrounding the B star can modify its colour $J-K$ by a largefactor \citep[e.g. up to $-0.5$~mag in 4U~0115+63][]{Reigal07}."90 This is illustrated in Fig., This is illustrated in Fig.91" 9 by arrows of maximum length of 0.5 mag that strengthen the scenario of a B star located far away in the Galaxy, thus highly absorbed by the interstellar medium."," \ref{ima_cmd} by arrows of maximum length of 0.5 mag that strengthen the scenario of a B star located far away in the Galaxy, thus highly absorbed by the interstellar medium."92" In another case where the star would be located nearer to us (~1 kpc), thus with a lower extinction, the star would be a main sequence star of type KM."," In another case where the star would be located nearer to us $\sim 1$ kpc), thus with a lower extinction, the star would be a main sequence star of type KM."93" In that case, this star would probably not be the counterpart ofJ1749.1—2733,, because the large orbital period completely rules out the possibility of combining such KM star with this X-ray source."," In that case, this star would probably not be the counterpart of, because the large orbital period completely rules out the possibility of combining such KM star with this X-ray source."94 The possibility that the star is a red giant is also unlikely as it should combine a location far away in the Galaxy with low extinction., The possibility that the star is a red giant is also unlikely as it should combine a location far away in the Galaxy with low extinction.95" Spectroscopy of the candidate counterpart is needed to disentangle between the 2 possibilities, either a B star located far away in the Galaxy z8.5 kpc and strongly absorbed or a normal star located nearer to us."," Spectroscopy of the candidate counterpart is needed to disentangle between the 2 possibilities, either a B star located far away in the Galaxy $\gtrsim8.5$ kpc and strongly absorbed or a normal star located nearer to us."96" Still, because of the X-ray properties observed for aand the absence of any other candidate, the B star is favoured."," Still, because of the X-ray properties observed for and the absence of any other candidate, the B star is favoured."97" As the known BeXB have an earlier spectral type than B3 (?),, this would imply that the source is located at a very long distance of >8.5 kpc."," As the known BeXB have an earlier spectral type than B3 \citep{Negueruela98}, this would imply that the source is located at a very long distance of $>8.5$ kpc."98 Another argument in favour of the BeXB scenario is the reddening-free parameter ο=(J—H)—-1.70(H—Ks) (?).., Another argument in favour of the BeXB scenario is the reddening-free parameter $Q=(J-H)-1.70(H-K_{\mathrm{S}})$ \citep{Negueruelaal07a}.99" For candidate #55, Q~—0.9+0.1, thus suggesting a high IR excess."," For candidate 5, $Q\sim-0.9\pm0.1$, thus suggesting a high IR excess."100" Such excess is not expected in KM stars whose Q values lie between 0.4—0.5; however, a factor Q«0 is expected for Be stars."," Such excess is not expected in KM stars whose $Q$ values lie between 0.4–0.5; however, a factor $Q<0$ is expected for Be stars."101" Assuming a distance of 8.5 kpc, the 22-50 keV luminosity is 3x1026ergss! during the bright flare that occurred on MJD 52891 and 0.4—0.9x1026ergss! during the long outbursts, values typical of BeXB."," Assuming a distance of 8.5 kpc, the 22–50 keV luminosity is $3\times10^{36}\ \es$ during the bright flare that occurred on MJD 52891 and $0.4-0.9\times10^{36}\ \es$ during the long outbursts, values typical of BeXB."102" The 0.2-10 keV luminosity is 0.2x10°°ergss!, a factor 2-4 lower than inINTEGRAL."," The 0.2--10 keV luminosity is $0.2\times10^{36}\ \es$, a factor 2–4 lower than in."103". We point out that, in the case of a BeXB with typical outbursts of the order of ~1036ergss!, and if the system was located nearer to us (<8 kpc), wwould detect such a source with a 22-50 keV count rate >2s~!,, which is not the case."," We point out that, in the case of a BeXB with typical outbursts of the order of $\sim10^{36}\ \es$, and if the system was located nearer to us $\lesssim 8$ kpc), would detect such a source with a 22-50 keV count rate $\gtrsim 2$, which is not the case."104" In the case of a BeXB, sshows a high intrinsic absorption of Ny=20.1513x10?cm? that is quite uncommon in other BeXB."," In the case of a BeXB, shows a high intrinsic absorption of $\nh=20.1_{-1.3}^{+1.5}\times10^{22}\ \unit{cm}{-2}$ that is quite uncommon in other BeXB."105" Indeed, most of the BeXB have density columns closer to the galactic absorption with Ny~1-3xNg"" (seeFig.15of?).."," Indeed, most of the BeXB have density columns closer to the galactic absorption with $\nh\sim 1-3\times N_{\mathrm{H}} ^{\mathrm{Gal}}$ \citep[see Fig.~15 of][]{Bodagheeal07}. ."106 Only one BeXB exhibits such high absorption: 2S 1845-024., Only one BeXB exhibits such high absorption: 2S $-$ 024.107" The properties of this source are very similar to wwith Po»=242.18+0.01 d, outburst duration of ~13 d, Pspin=94.9 s (with episodes of spin-up and spin-down) and Ny=25€10x10?cm? (???,andreferencestherein).."," The properties of this source are very similar to with $P_{\mathrm{orb}}=242.18\pm0.01$ d, outburst duration of $\sim 13$ d, $P_{\mathrm{spin}}=94.9$ s (with episodes of spin-up and spin-down) and $\nh=25\pm10\times10^{22}\ \unit{cm}{-2}$ \citep[][and references therein]{Koyamaal90,Soffittaal98,Fingeral99}."108" They classified 2S 1845—024 as a BeXB (located at 10 kpc!) from its X-ray properties; however, no counterpart has been identified yet."," They classified 2S $-$ 024 as a BeXB (located at 10 ) from its X-ray properties; however, no counterpart has been identified yet."109" Thus, mmight be the first identified counterpart BeXB with high intrinsic absorption similar to the obscured SGXB revealed byINTEGRAL."," Thus, might be the first identified counterpart BeXB with high intrinsic absorption similar to the obscured SGXB revealed by."110".. Spectral properties of pulsars, either SGXB or BeXB, are very similar (seee.g.?).."," Spectral properties of pulsars, either SGXB or BeXB, are very similar \citep[see e.g.][]{Whiteal95}."111" As IBIS/ISGRI is not affected by absorption, aallowed a large population of obscured SGXB to be revealed with Ny values of =10?cm""."," As IBIS/ISGRI is not affected by absorption, allowed a large population of obscured SGXB to be revealed with $\nh$ values of $\gtrsim10^{23}\ \unit{cm}{-2}$."112" That such highly-absorbed BeXB have not been observed yet (?) is perhaps not so surprising since BeXB are mostly transient sources, and the sources must also be observed during the outbursts by another X-ray emission with high sensitivity at low energies (such as oor Chandra)) in order to constrain the absorption."," That such highly-absorbed BeXB have not been observed yet \citep{Bodagheeal07} is perhaps not so surprising since BeXB are mostly transient sources, and the sources must also be observed during the outbursts by another X-ray emission with high sensitivity at low energies (such as or ) in order to constrain the absorption."113 Such a population of obscured BeXB might still have to be revealed., Such a population of obscured BeXB might still have to be revealed.114" Indeed, the only BeXB among the ssources reported in Fig."," Indeed, the only BeXB among the sources reported in Fig."115 15 of ? is the 3rd highly-absorbed BeXB (after aand 2S 1845—024)., 15 of \citet{Bodagheeal07} is the 3rd highly-absorbed BeXB (after and 2S $-$ 024).116" All the X-ray properties observed in lead to classifing this object as an X-ray binary, most probably an HMXB with a Be companion star whose compact object is an NS."," All the X-ray properties observed in lead to classifing this object as an X-ray binary, most probably an HMXB with a Be companion star whose compact object is an NS."117 The only optical/NIR candidate counterpart located inside the best X-ray error circle is compatible with a B star located far inside the galaxy and suffering large extinction., The only optical/NIR candidate counterpart located inside the best X-ray error circle is compatible with a B star located far inside the galaxy and suffering large extinction.118" Besides, the lack of a supergiant companion and the duration/smoothnessof the outbursts rule out the classification of this source as an SEXT, as proposed in ? and ?.."," Besides, the lack of a supergiant companion and the duration/smoothnessof the outbursts rule out the classification of this source as an SFXT, as proposed in \citet{Zand05} and \citet{Sgueraal06}. ."119" Instead,"," Instead,"120observed scattering and (he observed emission properties of the dust in the coma.,observed scattering and the observed emission properties of the dust in the coma.121" Comet C/2007 N3 (Lulin) was observed on 2009 March 03 UT with the 2.3-2i Bok Telescope at Kil Peak National Observatory at heliocentric distance. rj,=1.45 AU and a eeocentrie distance. A=0.49 AU."," Comet C/2007 N3 (Lulin) was observed on 2009 March 03 UT with the 2.3-m Bok Telescope at Kitt Peak National Observatory at heliocentric distance, $r_{h} = 1.45$ AU and a geocentric distance, $\Delta=0.49$ AU."122 The comet was al a phase angle a=17.777., The comet was at a phase angle $\alpha=17.77^{\circ}$.123 The images were obtained with the 90prime Camera (Williamsοἱal.2004)... a prime focus imager built for the Bok Telescope.," The images were obtained with the 90prime Camera \citep{williams04}, a prime focus imager built for the Bok Telescope."124 At the time of observation. the 90prime camera. utilized a thinned back-iluminated CCD detector with 4064 x 4064 pixels with a pixel size of 15.0yam.," At the time of observation, the 90prime camera utilized a thinned back-illuminated CCD detector with 4064 $\times$ 4064 pixels with a pixel size of $15.0~\micron$."125" At prime focus the camera pixel scale is 0.45"" which vields a field of view of 30.5x30.5 square-arcnun.", At prime focus the camera pixel scale is $0.45^{\prime\prime}$ which yields a field of view of $\times$ 30.5 square-arcmin.126 The instrument was equipped wilh Cousins/Bessel svstem broadband V. aud 7 filters., The instrument was equipped with Cousins/Bessel system broadband $V$ and $I$ filters.127 Alulüiple exposures (3 images of 120 seconds in J band and 4 images in V. band: 1 ol 60 seconds and 3 of 120 seconds) were obtained of the nucleus and coma of the comet with the telescope tracking at the non-sidereal rate corresponding to the predicted motion of the comet provided by JPL in an airmass range of 1.08 to 1.11., Multiple exposures (3 images of 120 seconds in $I$ band and 4 images in $V$ band; 1 of 60 seconds and 3 of 120 seconds) were obtained of the nucleus and coma of the comet with the telescope tracking at the non-sidereal rate corresponding to the predicted motion of the comet provided by JPL in an airmass range of 1.08 to 1.11.128 All images were corrected [or overscan. bias and fLat-fielding with standard routines.," All images were corrected for overscan, bias and flat-fielding with standard routines."129 Due to the, Due to the130"young low-mass stars (such as the ongoing Spitzer/YSOVAR program, and future surveys, such as PAN-STARRS and LSST) will better constrain the expected variability of extincting disks around young brown dwarfs.priori,","young low-mass stars (such as the ongoing Spitzer/YSOVAR program, and future surveys, such as PAN-STARRS and LSST) will better constrain the expected variability of extincting disks around young brown dwarfs.,"131", it would be unlikely (and perhaps unfortunate) that 2MASS 1207 b, a system which is currently unique as the closest, youngest, extremely low-mass object, is inclined to our line of sight in a near edge-on configuration where it is “partially” extincted."," it would be unlikely (and perhaps unfortunate) that 2MASS 1207 b, a system which is currently unique as the closest, youngest, extremely low-mass object, is inclined to our line of sight in a near edge-on configuration where it is “partially"" extincted."132" In this section, we investigate the probability that a brown dwarf system is in a configuration such that its disk “partially” extincts the central source."," In this section, we investigate the probability that a brown dwarf system is in a configuration such that its disk “partially"" extincts the central source."133 We use our RADMC disk models for 2MASS 1207 b and calculate the extinction produced by the hypothetical disk when viewed at different inclinations varying from 0 to 90 degrees., We use our RADMC disk models for 2MASS 1207 b and calculate the extinction produced by the hypothetical disk when viewed at different inclinations varying from 0 to 90 degrees.134" In Figure [6] we show the H-band extinction predicted by the models as a function of disk inclination, for both flat and flared geometries."," In Figure \ref{extinction} we show the H-band extinction predicted by the models as a function of disk inclination, for both flat and flared geometries."135" We note that there are 3 distinct regions of each plot: an region, a region where the extinction rises sharply, and a region where the extinction levels off."," We note that there are 3 distinct regions of each plot: an region, a region where the extinction rises sharply, and a region where the extinction levels off."136" Physically, the partially extincted region begins when the outer edge of the disk moves into our line of sight towards the brown dwarf."," Physically, the partially extincted region begins when the outer edge of the disk moves into our line of sight towards the brown dwarf."137" As inclination continues to increase, the extinction towards the brown dwarf rises until the fully extincted region, where scattered light (which is assumed to be isotropic in RADMC) caps extinction even as opacity continues to rise."," As inclination continues to increase, the extinction towards the brown dwarf rises until the fully extincted region, where scattered light (which is assumed to be isotropic in RADMC) caps extinction even as opacity continues to rise."138" Based on this analysis, and assuming an isotropic distribution of disk inclinations, there is a probability that a brown dwarf with our flat disk model is unextincted (Ag —0-0.5 mags), a probability that it is partially extincted (Aq =0.5-6.0 mags), and a probability that it is fully extincted (Ay =6.0-7.1 mags)."," Based on this analysis, and assuming an isotropic distribution of disk inclinations, there is a probability that a brown dwarf with our flat disk model is unextincted $A_{H}=$ 0-0.5 mags), a probability that it is partially extincted $A_{H}=$ 0.5-6.0 mags), and a probability that it is fully extincted $A_{H}=$ 6.0-7.1 mags)."139" For the flared disk model, there is a probability that it is unextincted (Ay =0-0.5 mags), a probability that it is partially extincted (Ay —0.5-3 mags), and a probability that it is fully extincted (Aj —3-4 mags)."," For the flared disk model, there is a probability that it is unextincted $A_{H}=$ 0-0.5 mags), a probability that it is partially extincted $A_{H}=$ 0.5-3 mags), and a probability that it is fully extincted $A_{H}=$ 3-4 mags)."140" For brown dwarfs, the flat disk model is more accurate than the flared disk model (see Section B.1))."," For brown dwarfs, the flat disk model is more accurate than the flared disk model (see Section \ref{RADMC Disk Models}) )."141" Although the exact analysis depends strongly on disk flaring, the two cases presented here bracket the likely geometries."," Although the exact analysis depends strongly on disk flaring, the two cases presented here bracket the likely geometries."142" Assuming 2MASS 1207 b has a disk, but ignoring its under-luminosity as prior evidence for why it should have a near edge-on disk, the probability that 2MASS 1207 b's disk is in the inclination range that causes partial extinction is ~6.4%.."," Assuming 2MASS 1207 b has a disk, but ignoring its under-luminosity as prior evidence for why it should have a near edge-on disk, the probability that 2MASS 1207 b's disk is in the inclination range that causes partial extinction is $\sim$."143" This also neglects the fact that 2MASS 1207 A's disk is thought to be near edge-on, and disks in binaries tend to be"," This also neglects the fact that 2MASS 1207 A's disk is thought to be near edge-on, and disks in binaries tend to be"144In the interstellar medium (SM). dust grains are the most efficient absorber of stellar light.,"In the interstellar medium (ISM), dust grains are the most efficient absorber of stellar light."145 The spectral energy distributions and the radiative heating and cooling in galaxies are thus strongly regulated by the presence of dust (e.g.Yamasawaetal.20113., The spectral energy distributions and the radiative heating and cooling in galaxies are thus strongly regulated by the presence of dust \citep[e.g.][]{yamasawa11}.146. This means that the understanding of dust enrichment in galaxies is crucial in the studies of galaxy evolution., This means that the understanding of dust enrichment in galaxies is crucial in the studies of galaxy evolution.147 Dust enrichment in galaxies is governed by various processes depending on age. metallicity. citepdwek98..," Dust enrichment in galaxies is governed by various processes depending on age, metallicity, \\citep{dwek98}."148 In the earliest stage of galaxy evolution. dust is predominantly produced by supernovae (SNe) (e.g.Kozasaetal. 2009).. while at later epochs asymptotic giant branch (AGB) stars also contribute (Valianteetal.2009).," In the earliest stage of galaxy evolution, dust is predominantly produced by supernovae (SNe) \citep[e.g.][]{kozasa09}, while at later epochs asymptotic giant branch (AGB) stars also contribute \citep{valiante09}."149. The time-scale of dust destruction by SN shocks isafew.LO” yr2008). while that of dust supply from stellar sources is longer than | Gyr in the Milky Way (MeKee1989).," The time-scale of dust destruction by SN shocks is $\mbox{a few}\times 10^8$ yr, while that of dust supply from stellar sources is longer than 1 Gyr in the Milky Way \citep{mckee89}."150. Therefore. dust grains should grow in the ISM by the accretion of metals onto grains (Draine2009) to explain the existence of dust in the ISM.," Therefore, dust grains should grow in the ISM by the accretion of metals onto grains \citep{draine09}151 to explain the existence of dust in the ISM."152 The growth occurs most efficiently in molecular clouds. where the number density of hydrogen molecules is ~10 em? (Hirashita2000a).," The growth occurs most efficiently in molecular clouds, where the number density of hydrogen molecules is $\sim 10^3$ $^{-3}$ \citep{hirashita00}."153. This process is called ‘grain growth in clouds’ in this paper., This process is called `grain growth in clouds' in this paper.154 Observational pieces of evidence for the grain growth in clouds come from larger depletion of metal elements in cold elouds than in warm medium (SavageSembach 1996)., Observational pieces of evidence for the grain growth in clouds come from larger depletion of metal elements in cold clouds than in warm medium \citep{savage96}.155. A lot of chemical evolution models treat the evolution of dust content in galaxies., A lot of chemical evolution models treat the evolution of dust content in galaxies.156 These models usually include dust production by stars. grain growth in clouds. and dust destruction by SNe (e.g.Dwek1998:Inoue2003:Zhukovska.Gail.&Trieloff2008:Calura.Pipino.&Matteucci2008:Asanoetal.201 1..," These models usually include dust production by stars, grain growth in clouds, and dust destruction by SNe \citep*[e.g.][]{dwek98,inoue03,zhukovska08,calura08,157asano11}."158 Most of the models which consider the grain growth in clouds indicate that this process dominates the dust budget at sub-solar or solar metallicities., Most of the models which consider the grain growth in clouds indicate that this process dominates the dust budget at sub-solar or solar metallicities.159 The grain growth occurs through the accretion of metals. so that the increasing rate of grain mass by the accretion of metals is proportional not only to the metallicity but also to the grain surface-to-volume ratio. which is very sensitive to the grain size distribution.," The grain growth occurs through the accretion of metals, so that the increasing rate of grain mass by the accretion of metals is proportional not only to the metallicity but also to the grain surface-to-volume ratio, which is very sensitive to the grain size distribution."160 Most models so far assume a certain grain size distribution or a typical grain size to estimate the surface-to-volume ratio., Most models so far assume a certain grain size distribution or a typical grain size to estimate the surface-to-volume ratio.161 However. since the dominant processes governing the grain size distribution should vary with age and metallicity (ODonnell&Mathis1997:Hirashitaetal.2010:Yamasawa 2011). it is expected that a variety of grain size distributions emerge in a complex way depending on age and metallicity.," However, since the dominant processes governing the grain size distribution should vary with age and metallicity \citep{odonnell97,hirashita10,yamasawa11}, it is expected that a variety of grain size distributions emerge in a complex way depending on age and metallicity."162 The first source of dust in the history of galaxy evolution is SNe. and the dust grains produced by," The first source of dust in the history of galaxy evolution is SNe, and the dust grains produced by"163emission indicating that there may be infall of matter back onto the star (see?)..,emission indicating that there may be infall of matter back onto the star \citep[see][]{Lobel2001}.164 The rotation rate of Betelgeuse has also been reported in the literature (e.g.2)..," The rotation rate of Betelgeuse has also been reported in the literature \citep[e.g.][]165{Uitenbroek1998}."166 More recently. Zeeman observations also reveal unambiguously. that there exists a magnetic field on the surface of Betclecuse (see??)..," More recently, Zeeman observations also reveal unambiguously, that there exists a magnetic field on the surface of Betelgeuse \citep[see][]{Auriere2010, 167Petit2011}."168 These observations naturally raise several questions regarding the role that magneto-rotational effects might play in the stars wind., These observations naturally raise several questions regarding the role that magneto-rotational effects might play in the star's wind.169 Thus overall. we see that there are several unanswered. questions regarding the nature of the outfLow from Detelgeuse.," Thus overall, we see that there are several unanswered questions regarding the nature of the outflow from Betelgeuse."170 Here. we present the very. first. mocel integrating ΑΗ) and rotational ellects with a dust-driven wind scenario for Betelgeuse.," Here, we present the very first model integrating MHD and rotational effects with a dust-driven wind scenario for Betelgeuse."171 The aim of the current study is to shed a new light on these issues and attempt to answer. at least some of these concerns.," The aim of the current study is to shed a new light on these issues and attempt to answer, at least some of these concerns."172 In this study. we find that the presence of a small magnetic field. on the order of what was recently discovered: of about LG (see2). is sullicient to drive material from close to the stellar surface up and out of its gravity well. by means of à magneto-rotational wind.," In this study, we find that the presence of a small magnetic field, on the order of what was recently discovered; of about $1$ G \citep[see][]{Auriere2010}, is sufficient to drive material from close to the stellar surface up and out of its gravity well, by means of a magneto-rotational wind."173" Dust condensation later occurs at large distances from the star (~ 3072,) which finally results in a hivbrid-MIID-cust-driven outflow.", Dust condensation later occurs at large distances from the star $\sim 30R_0$ ) which finally results in a hybrid-MHD-dust-driven outflow.174 This model provides a possible alternative resolution of this issue (sce??7)..," This model provides a possible alternative resolution of this issue \citep[see][]175{Harper2009,Guandalini2006,Jura1984}."176 Ht is to be mentioned at the very outset. that this model is merely suggested as an mechanism that can play a role in transport of stellar material and is not intended to supplant the altogether feasible models involving MIID or acoustic waves as likely candidates.," It is to be mentioned at the very outset, that this model is merely suggested as an mechanism that can play a role in transport of stellar material and is not intended to supplant the altogether feasible models involving MHD or acoustic waves as likely candidates."177 The theoretical model that we developed for intermediate mass asvniptlotic-giant-branch (ACB) stars (see7) has been extended to tackle the case of a supergiant like Betelecuse.," The theoretical model that we developed for intermediate mass asymptotic-giant-branch (AGB) stars \citep178[see][]{Thirumalai2010} has been extended to tackle the case of a supergiant like Betelgeuse."179 The reader is referred to our earlier work (see7) for details of the model., The reader is referred to our earlier work \citep[see][]{Thirumalai2010} for details of the model.180 Llere we shall present only the salient features of the theory., Here we shall present only the salient features of the theory.181 We also fine that. the wind velocities that are obtained from the model are in σου agreement with current estimates (c.g.777)," We also find that the wind velocities that are obtained from the model are in good agreement with current estimates \citep[e.g.][]{Harper2009,Falceta2002,Plez2002}."182 For the purposes of modelling. there are some marked dilferences that Detelgeuse exhibits from. a run-of-the-mill AGB star.," For the purposes of modelling, there are some marked differences that Betelgeuse exhibits from a run-of-the-mill AGB star."183 For example. Betelgeuse is much. more massive (15M.. 7)) than an intermediate mass AGB star.," For example, Betelgeuse is much more massive $\sim 15 \mathrm{M}_{\odot}$, \citealt{Smith2009}) ) than an intermediate mass AGB star."184 lt also has a far more extended ancl cooler atmosphere., It also has a far more extended and cooler atmosphere.185 More importantly. the cust condensation radius is much arther out. in terms of stellar radii. from the photosphere in comparison to a canonical AGB star.," More importantly, the dust condensation radius is much farther out, in terms of stellar radii, from the photosphere in comparison to a canonical AGB star."186 In. the former. he primary process governing mass-loss is the raciation oressure on dust erains that form at close distances from the hotosphere. tvpically no greater than 10725. coupled with strong stellar. pulsation.," In the former, the primary process governing mass-loss is the radiation pressure on dust grains that form at close distances from the photosphere, typically no greater than $10 R_0$, coupled with strong stellar pulsation."187 The presence of à magnetic field hen has the effect. of plaving a secondary role governing he gas cynamics., The presence of a magnetic field then has the effect of playing a secondary role governing the gas dynamics.188 In an AGB star. the hybrid-MILD-dust-driven mechanism is such. that without the onset of dust formation. it is not. possible to achieve an outflow and thereafter. the predominant energy. exchange in the wind is between the magneto-rotational and gravitational components (seeFig.5of?)..," In an AGB star, the hybrid-MHD-dust-driven mechanism is such, that without the onset of dust formation, it is not possible to achieve an outflow and thereafter, the predominant energy exchange in the wind is between the magneto-rotational and gravitational components \cite[see Fig.~5 of][]{Thirumalai2010}."189 In such a scenario. it was seen quite crucially. that dust forniation must occur prior to the hybrid. models sonic point ancl concomitantly. it was seen hat the dust. parameter. Py was required. to be less than unity for achieving a hybricl wind.," In such a scenario, it was seen quite crucially, that dust formation must occur prior to the hybrid model's sonic point and concomitantly, it was seen that the dust parameter, $\Gamma_d$ was required to be less than unity for achieving a hybrid wind."190 Such is not the case for Detelgeuse where observations find only a small amount of dust inside ro2530Ry., Such is not the case for Betelgeuse where observations find only a small amount of dust inside $ r \stackrel{_<}{_\sim} 25-30~R_0 $.191 In our earlier study. we had. additionally. investigate he possibility of locating the dust condensation radius outside the fast Alfvénn point.," In our earlier study, we had additionally investigated the possibility of locating the dust condensation radius outside the fast Alfvénn point."192 LO was shown that such a ivbrid wind is entirely theoretically possible. given typica xwameters of an AGB star (seeFig.9of7).," It was shown that such a hybrid wind is entirely theoretically possible, given typical parameters of an AGB star \cite[see Fig.~9 of][]{Thirumalai2010}."193 It was concluded therein that while such a scenario is unlikely for a vpical AGB star it may well apply to an altogether cdilleren vpe of stellar wind., It was concluded therein that while such a scenario is unlikely for a typical AGB star it may well apply to an altogether different type of stellar wind.194 Ht is this second type of hvbrid-MILD-dust-driven. model that is adapted: herein to formulate a stellar elllux scenario for Detelgeuse. with dust. formation occurring at a large distance 30Ay. from the star.," It is this second type of hybrid-MHD-dust-driven model that is adapted herein to formulate a stellar efflux scenario for Betelgeuse, with dust formation occurring at a large distance $\sim 30~R_0$, from the star."195 Our theoretical model can be summed up as follows (the interested reader is referred to 2. [or the steps involve in the derivation)., Our theoretical model can be summed up as follows (the interested reader is referred to \citet{Thirumalai2010} for the steps involved in the derivation).196 We imagine that we are looking down upon the two-dimensional equatorial plane of Deteleeuse., We imagine that we are looking down upon the two-dimensional equatorial plane of Betelgeuse.197 Therein. we assume that the magnetic field and the gas (aux dust) velocity. are. functions of purely the radial. distance from the centre of the star.," Therein, we assume that the magnetic field and the gas (and dust) velocity are functions of purely the radial distance from the centre of the star."198 Phe poloidal (co-Iatitudinal) components of these vectors vanish: this is the fundamenta assumption behind the canonical Weber-Davis (see?.here-afterWD) model for our sun.," The poloidal (co-latitudinal) components of these vectors vanish; this is the fundamental assumption behind the canonical Weber-Davis \citep199[see][hereafter WD]{WD67} model for our sun."200 The gas forms the [irs Hui and carries the magnetic field., The gas forms the first fluid and carries the magnetic field.201 However. unlike the sun. in the atmosphere of. Detelgeuse. embedded: within the gas is à second fluid: the dust.," However, unlike the sun, in the atmosphere of Betelgeuse, embedded within the gas is a second fluid; the dust."202 The two Εμάς co-exis ancl are coupled to each other through drag., The two fluids co-exist and are coupled to each other through drag.203 In an evolvec supergiant like Betclecuse. the circumstellar atmosphere is cool enough (2 100019} that dust @rains can condense ou of the surrounding eas (e.g.2222?)..," In an evolved supergiant like Betelgeuse, the circumstellar atmosphere is cool enough $\stackrel{_<}{_\sim}1000$ K) that dust grains can condense out of the surrounding gas \citep[e.g.][]{Bester1991,Bester1996,Danchi1994,Harper2009,Skinner1997}."204 In fact. direct imagine has enabled. estimates for the inner cust shell temperature to be ~700 Ix at around ~3042 (e.g.2)..," In fact, direct imaging has enabled estimates for the inner dust shell temperature to be $\sim 700~$ K at around $\sim 30R_0$ \citep[e.g.][]{Bloemhof1984}."205 Stellar radiation [rom the interior impinging upon the dust grains. can impar enough momentum to power these exiguous solar sails ancl propel them outward through the surrounding gaseous matter.," Stellar radiation from the interior impinging upon the dust grains, can impart enough momentum to power these exiguous solar sails and propel them outward through the surrounding gaseous matter."206 However. whilst moving through the gas. the dus the gas along with it. resulting in a prodigious an combined mass elllux of both dust. anc gas. [rom the star: the so-called dust-driven wind.," However, whilst moving through the gas, the dust the gas along with it, resulting in a prodigious and combined mass efflux of both dust and gas, from the star; the so-called dust-driven wind."207 Ht is to be kept in. mind. that the clust-to-gas mass-ratio is small: for Betelecuse. i is expected. to be on the order of zzο1015.10?5 or so (see2)..," It is to be kept in mind, that the dust-to-gas mass-ratio is small; for Betelgeuse, it is expected to be on the order of $\approx 6\times 20810^{-4} - 5 \times 10^{-3}$ or so \citep[see][]{Harper2001}."209 Additionally. the dust. &rains in our mocle are assumed to be spherical in shape. thus presenting a circular cross-section for radiation pressure to act upon.," Additionally, the dust grains in our model are assumed to be spherical in shape, thus presenting a circular cross-section for radiation pressure to act upon."210 The surface temperature of DBetelgeuse (Z5) plavs a key role in determining the hybrid wind. parameters. such as the bulk eas velocity at the base of the wind and the location ofthe critical points (see below).," The surface temperature of Betelgeuse $T_0$ ) plays a key role in determining the hybrid wind parameters, such as the bulk gas velocity at the base of the wind and the location of the critical points (see below)."211 We also assume that the gas has the thermocdsnamic equation of state of a polvtrope. with a polvtropic index 5c1. where a value of unity represents the isothermal limit.," We also assume that the gas has the thermodynamic equation of state of a polytrope, with a polytropic index $\gamma > 1$, where a value of unity represents the isothermal limit."212 We model the IHuid [low as an inviscid one and the eleetrodynamic properties of the [uid are taken to obey ideal MEID. Le. there is no Lorentz force acting on the Duid and the electric and magnetic forces balance cach other completely.," We model the fluid flow as an inviscid one and the electrodynamic properties of the fluid are taken to obey ideal MHD, i.e., there is no Lorentz force acting on the fluid and the electric and magnetic forces balance each other completely."213 Additionally. the mocel requires as input. a number of observed quantities. such as the mass of the star. --s rotation rate. the surface magnetic field strength and the miass-loss rate.," Additionally, the model requires as input, a number of observed quantities, such as the mass of the star, its rotation rate, the surface magnetic field strength and the mass-loss rate."214 These and other parameters for Betolgcuse are listed in Table 1., These and other parameters for Betelgeuse are listed in Table 1.215 With these ingredients. upon examining 1e Euler equations for [uid Pow for both the dust ancl the," With these ingredients, upon examining the Euler equations for fluid flow for both the dust and the"216Recent microlensing results from the NLACTIO collaboration suggest that in the context of a spherical isothermal model for the Galactic halo. some significant fraction of the halo is composed of objects with masses of about QAAL. (Alcocketal.1996)..,"Recent microlensing results from the MACHO collaboration suggest that in the context of a spherical isothermal model for the Galactic halo, some significant fraction of the halo is composed of objects with masses of about $0.4 M_{\odot}$ \cite{MACHOmass}."217 Such masses are consistent with several astrophysical candidates for. ΔΙΑΟν low mass main sequence stars. white carts. and black holes.," Such masses are consistent with several astrophysical candidates for MACHOs – low mass main sequence stars, white dwarfs, and black holes."218 Each of these candidates. however. is subject to a variety of constraints that present serious challenges for succesful models in which they form a significant fraction of the halo.," Each of these candidates, however, is subject to a variety of constraints that present serious challenges for succesful models in which they form a significant fraction of the halo."219 Low mass main sequence stars. should. be easily visible. and recent direct searches for these stars limit. their contribution to the halo to be less than 3% (Flynnetal.1996:να&Freese 1996).," Low mass main sequence stars should be easily visible, and recent direct searches for these stars limit their contribution to the halo to be less than $3\%$ \cite{halostars,reddwarfs}."220. The limits on halo white dwarl stars are much looser., The limits on halo white dwarf stars are much looser.221 Very old white chwarls would be cool and faint enough to have evaced direct. detection. thus far and. vet still be present in the halo in significant numbers (Gralletal.1997:Adams&Laughlin1906:Chabricret 1996)..," Very old white dwarfs would be cool and faint enough to have evaded direct detection thus far and yet still be present in the halo in significant numbers \cite{whitedwarfs,IMFproblem2,whitedwarfs2}."222 The progenitors of these white dwarfs presumably formed as a very carly generation of stars., The progenitors of these white dwarfs presumably formed as a very early generation of stars.223 This scenario has its own problems. however.," This scenario has its own problems, however."224 The progenitor stars would. have produced: copious amounts of metal enriched gas. which is not seen in the Galactic abuncanees (lHlegyiet.al.1986:Cibson&," The progenitor stars would have produced copious amounts of metal enriched gas, which is not seen in the Galactic abundances \cite{metals,metals2}."225Aloulel 1997)... ας the Galaxy. of this metal enriched. eas would require a strong Calactic wind at the appropriate time (Fieldsetal.1996)., Ridding the Galaxy of this metal enriched gas would require a strong Galactic wind at the appropriate time \cite{brianmodel}.226. In. addition. this scenario requires a stellar mass function for the halo stars that is peaked at à much higher mass than is observed. in the disk today.," In addition, this scenario requires a stellar mass function for the halo stars that is peaked at a much higher mass than is observed in the disk today."227 Unless the initial mass function is stronely suppressed. for low masses we should still sce the low mass main sequence stars that would have been produced. along with the higher mass white cwarf progenitor stars (vuet.al.1990:Adams&Laughlin 1996).," Unless the initial mass function is strongly suppressed for low masses we should still see the low mass main sequence stars that would have been produced along with the higher mass white dwarf progenitor stars \cite{IMFproblem,IMFproblem2}."228. Primordial black hole candidates require a fine tuning of the initial distribution of density perturbations. although there has been some recent work on black holes formec at the QCD phase transition (Joclanizik1997)..," Primordial black hole candidates require a fine tuning of the initial distribution of density perturbations, although there has been some recent work on black holes formed at the QCD phase transition \cite{Jedamzik}."229 In this paper we explore an alternative explanation or the relatively long term event. durations seen by the MACHO group., In this paper we explore an alternative explanation for the relatively long term event durations seen by the MACHO group.230 NLACTIO mass estimates are derived from he observed event duration. withthe of assumptiona model or the MLACTIO distribution and velocity structure.," MACHO mass estimates are derived from the observed event duration, with the assumption of a model for the MACHO distribution and velocity structure."231 The event duration is a function not only of the mass of the ens. but also of the distance to the lens and its tranverse (with respect to the line of sight) velocity.," The event duration is a function not only of the mass of the lens, but also of the distance to the lens and its tranverse (with respect to the line of sight) velocity."232 Without the aciditional information obtained. for example. by a parallax or binary lens event. in which case the velocity of the lensing object can sometimes be extracted ancl an. independent estimate of the distance to the lens. the mass of an individual event cannot be determined directlv.," Without the additional information obtained, for example, by a parallax or binary lens event, in which case the velocity of the lensing object can sometimes be extracted and an independent estimate of the distance to the lens, the mass of an individual event cannot be determined directly."233 The distance along the lensing tube and tranverse velocity are known only in a statistical sense (for a given model). and therefore only," The distance along the lensing tube and tranverse velocity are known only in a statistical sense (for a given model), and therefore only"234Since early studies of X-ray sources in the Milkv Way it has been known that GC's are a rich source of LAINBs (e.g.Clark 1975).,Since early studies of X-ray sources in the Milky Way it has been known that GCs are a rich source of LMXBs \citep[e.g.][]{Clark}.235.. To explain the populations observed. in the Milky. Way (Liuetal.2001.andreferenceswithin).. its GC's need to be two orders magnitude more ellicient at. forming LAINBs than other Galactic regions.," To explain the populations observed in the Milky Way \citep[][and references within]{Liu}, its GCs need to be two orders magnitude more efficient at forming LMXBs than other Galactic regions."236 Theorists have long argued that the likely reason for this is that GC LAINBs are formed mainly through dvnamical interactions instead of the evolution of primordial binaries (c.g.Clark1975:Fabian.bunt&Hut 1987)..," Theorists have long argued that the likely reason for this is that GC LMXBs are formed mainly through dynamical interactions instead of the evolution of primordial binaries \citep[e.g.][]{Clark,Fabian,Sutantyo,Hills,Verbunt}."237 The dynamical processes which can form LMXBD systems include the neutron star capturing a donor star through tidal capture: exchange interactions: and direct collisions., The dynamical processes which can form LMXB systems include the neutron star capturing a donor star through tidal capture; exchange interactions; and direct collisions.238 These interactions are likely to be very common in the cores of GC's where the stellar densities are relatively high., These interactions are likely to be very common in the cores of GCs where the stellar densities are relatively high.239 Studies of the 13 bright LAIN in the Milkv Way CC's are consistent with cvnamical formationBs scenarios., Studies of the 13 bright LMXBs in the Milky Way GCs are consistent with dynamical formation scenarios.240 In the era it has been possible to study much ereater numbers of LAINBs by looking at extra-galactic X-rav sources., In the era it has been possible to study much greater numbers of LMXBs by looking at extra-galactic X-ray sources.241 Observations of nearby. galaxies generally show large numbers of LANDs associated with their GC's (e.g.thereviewofFabbiano 2006).., Observations of nearby galaxies generally show large numbers of LMXBs associated with their GCs \citep[e.g. the review of][]{Fabbiano}.242 From these studies it has been possible to identify relationships between the properties of a cluster and the probability that it will contain a LAINB., From these studies it has been possible to identify relationships between the properties of a cluster and the probability that it will contain a LMXB.243 In both the Milkv Way anc nearby galaxies it has been found that LAINBs favour brighter (anc hence more massive) GC's (ος.Sarazinetal.2003:Ixim2006:Smitsetal.2006:Ixundu.Maccarone.&Zepl 2007).," In both the Milky Way and nearby galaxies it has been found that LMXBs favour brighter (and hence more massive) GCs \citep[e.g.][]{Sarazin,Kim06,Smits,Kundu07}."244. The likely reason for this is that higher mass clusters will generally have more stellar interactions and therefore form more LMXNDs through dynamical interactions., The likely reason for this is that higher mass clusters will generally have more stellar interactions and therefore form more LMXBs through dynamical interactions.245 It has also been suggested that higher mass clusters will retain more of the neutron stars they produce., It has also been suggested that higher mass clusters will retain more of the neutron stars they produce.246 “Phis is because more massive clusters will generally have higher escape velocities and neutron stars may be formed with Large kick velocities., This is because more massive clusters will generally have higher escape velocities and neutron stars may be formed with large kick velocities.247 However it is possible for neutron stars to form with lower velocities via electron-capture supernovae (c.g.Pfahl.Rappaport.&Pocl-slaclowski2002:Ivanovactal.," However it is possible for neutron stars to form with lower velocities via electron-capture supernovae \citep[e.g.][]{Pfahl,Ivanova}."248 2008).. If cvnamical formation is the primary method of formine LAINBs in GC's. we expect there to be a strong correlation between the stellar collision rate of a cluster and the presence of a LAINB.," If dynamical formation is the primary method of forming LMXBs in GCs, we expect there to be a strong correlation between the stellar collision rate of a cluster and the presence of a LMXB."249 ‘Vhe stellar collision rates in GCs will be dominated. by collisions in their cores (where the stellar. densities are highest)., The stellar collision rates in GCs will be dominated by collisions in their cores (where the stellar densities are highest).250 Unfortunately. clue to their small sizes and large distances [rom us. resolving the cores of extra-galactie GC's requires very good spatial resolution.," Unfortunately, due to their small sizes and large distances from us, resolving the cores of extra-galactic GCs requires very good spatial resolution."251 Some previous work has tried to infer collision rates without resolving the cluster cores, Some previous work has tried to infer collision rates without resolving the cluster cores252other one has positive helicity.,other one has positive helicity.253 Thus. irrespective of the details of the physical processes during leptogenesis. produced number η. of neutrinos with positive helicity έν)=+1 vs. produced number Η.. of neutrinos with negative helicity 2(vay)2—1 is roughly 2/n-=OCIO). (," Thus, irrespective of the details of the physical processes during leptogenesis, produced number $n_{+}$ of neutrinos with positive helicity $\lambda (\nu_{M})=+1$ vs. produced number $n_{-}$ of neutrinos with negative helicity $\lambda (\nu_{M})=-1$ is roughly $n_{+}/n_{-} = {\cal O}(10)$. ("2544) It is easy to estimate number of neutrinos and other particles at the epoch of neutrino decoupling (22):: We conclude that the spin density of the matter is dominated by the spin of the light neutrinos with an excess of the positive helicity states.,"4) It is easy to estimate number of neutrinos and other particles at the epoch of neutrino decoupling \citep{Kolb,Palle1}: We conclude that the spin density of the matter is dominated by the spin of the light neutrinos with an excess of the positive helicity states."255" In addition. the sum of the orbital angular momenta of particles vanishes because of the isotropy of the Universe at that moment of the evolution,"," In addition, the sum of the orbital angular momenta of particles vanishes because of the isotropy of the Universe at that moment of the evolution."256 The averaging procedure for spin of cosmic fluids (2).. lepton and CP violations. together with the positive helicity abundance. guarantee the nonvanishing spin. as well as nonvanishing torsion because of their algebraic relations within Einstein-Cartan equations.," The averaging procedure for spin of cosmic fluids \citep{Kerlick}, lepton and CP violations, together with the positive helicity abundance, guarantee the nonvanishing spin, as well as nonvanishing torsion because of their algebraic relations within Einstein-Cartan equations."257 This asymmetry is a seed for the small vorticity with the well defined chirality that we define later., This asymmetry is a seed for the small vorticity with the well defined chirality that we define later.258" It is clear that any cosmic observer measures different axis of vorticity. but a chirality of the vorticity 1s well defined invariant quantity for any observer, ("," It is clear that any cosmic observer measures different axis of vorticity, but a chirality of the vorticity is well defined invariant quantity for any observer. ("2595) The particles that can compete with neutrinos in abundances are the background photons.,5) The particles that can compete with neutrinos in abundances are the background photons.260 However. photons. as a massless gauge boson particles. do not generate the torsion in à gauge invariant way (?).. (," However, photons, as a massless gauge boson particles, do not generate the torsion in a gauge invariant way \citep{Hayashi}. ("2616) Electromagnetic and strong forces. as well as the Riemann curvature of spacetime induced by the metric alone. are chirally-symmetric interactions and cannot alter the chirality of vorticity in later stages of evolution after neutrino decoupling.,"6) Electromagnetic and strong forces, as well as the Riemann curvature of spacetime induced by the metric alone, are chirally-symmetric interactions and cannot alter the chirality of vorticity in later stages of evolution after neutrino decoupling."262 Vorticity induced by spin density within EC cosmology (see equations below) acts as a seed for vortical motions of cosmic particles and as a seed for the angular momenta of galaxies. clusters..... Universe (???)..," Vorticity induced by spin density within EC cosmology (see equations below) acts as a seed for vortical motions of cosmic particles and as a seed for the angular momenta of galaxies, clusters,..., Universe \citep{Peebles,Binney,Kolb}."263 Torsion grows together with a grow of large scale structures at late stages of the structure formation because the torsion is then dominated by the orbital angular momenta of large scale structures. (, Torsion grows together with a grow of large scale structures at late stages of the structure formation because the torsion is then dominated by the orbital angular momenta of large scale structures. (2647) A term of EC equations linear in torsion (spin) allows us to uniquely determine chirality of the vorticity.,7) A term of EC equations linear in torsion (spin) allows us to uniquely determine chirality of the vorticity.265 Namely. this is possible to achieve because of the relation derived at spacelike infinity and its vicinity (?2)..," Namely, this is possible to achieve because of the relation derived at spacelike infinity and its vicinity \citep{Palle4,Penrose}."266 The present Universe is in the matter dominated epoch with O(1071). while the spacelike infinity is at ΤΑ2e)=0K.," The present Universe is in the matter dominated epoch with $T_{\gamma, 0}=2.73\ K,\ \frac{\rho_{\gamma, 0}}{\rho_{m, 0}}=267{\cal O}(10^{-4})$ , while the spacelike infinity is at $T_{\gamma}(R=\infty)=0\ K$."268 Evidently. the present state of the Universe is in the vicinity of the spacelike infinity.," Evidently, the present state of the Universe is in the vicinity of the spacelike infinity."269implications of this line for the accretion flow geometry in this source. and explore connections to the recent observation of the Seyfert-I AGN MCG-6-30-15 (Wilms et al.,"implications of this line for the accretion flow geometry in this source, and explore connections to the recent observation of the Seyfert-I AGN MCG–6-30-15 (Wilms et al."270 2001)., 2001).271 We observed XTE J1650—500 with on 13 September. 2001. from 15:45:25-21:4 (UT) for à total exposure of 21.4 ks.," We observed XTE $-$ 500 with on 13 September, 2001, from 15:45:25–21:41:04 (UT) for a total exposure of 21.4 ks."272 We did not operate1:04. the EPIC-MOS2 camera or the Optical Monitor to preserve telemetry., We did not operate the EPIC-MOS2 camera or the Optical Monitor to preserve telemetry.273The EPIC-MOS] camera was operated in timing mode but suffered a full scientific buffer nearly continuously due to the high flux.,The EPIC-MOS1 camera was operated in timing mode but suffered a full scientific buffer nearly continuously due to the high flux.274 Full spectral results from the Reflection Grating Spectrometer (RGS. 0.33-2.5 keV) will be reported in a separate paper.," Full spectral results from the Reflection Grating Spectrometer (RGS, 0.33–2.5 keV) will be reported in a separate paper."275" To prevent photon pile-up. the EPIC-pn camera was operated in ""burst mode with the ""thin"" optical filter in place (for more information on the pn camera. see Stüdder et al."," To prevent photon pile-up, the EPIC-pn camera was operated in “burst” mode with the “thin” optical filter in place (for more information on the pn camera, see Stüdder et al."276 2001)., 2001).277 Only one CCD of the pn camera ts active in burst mode. and spatial information is only recorded in one dimension.," Only one CCD of the pn camera is active in burst mode, and spatial information is only recorded in one dimension."278 Burst mode has a time resolution of 7 srs. but a duty cycle of approximately3%.," Burst mode has a time resolution of 7 $\mu$ s, but a duty cycle of approximately."279 We extracted source counts using a box region centered on the source position (with X an Y half-widths of 1694 and 28. respectively. in DET units).," We extracted source counts using a box region centered on the source position (with X an Y half-widths of 1694 and 28, respectively, in DET units)."280 Two background regions adjacent to the source position were selected., Two background regions adjacent to the source position were selected.281 Single and double events were included for analysis., Single and double events were included for analysis.282 Standard pn filtering was accomplished with the procedure assuming a source position of 16750'01.0.—4957?45* (Castro-TiradoEEP. et al.," Standard pn filtering was accomplished with the procedure EP, assuming a source position of $16^{\circ} 50' 01.0'', -49^{h} 57^{m}28345^{s}$ (Castro-Tirado et al."284 2001: Groot et al., 2001; Groot et al.285 2001)., 2001).286 We measured a source count rate of 2557.0+1.9 counts s!. and a background count rate of 151.5£0.5 counts s.," We measured a source count rate of $2557.0\pm 1.9$ counts $^{-1}$ , and a background count rate of $151.5\pm 0.5$ counts $^{-1}$."287 Calibrated event lists were custom-made at MPE using SAS-5.3a., Calibrated event lists were custom-made at MPE using $\alpha$.288 The source and background spectra were created with SAS-5.2.0., The source and background spectra were created with SAS–5.2.0.289 Spectra were grouped based both on a requirement for counts per channel (20) and on the maximum number of spectral channels sampling the pn energy resolution (3)., Spectra were grouped based both on a requirement for counts per channel (20) and on the maximum number of spectral channels sampling the pn energy resolution (3).290 This is the first spectral analysis to. be reported from an observation which employed burst mode., This is the first spectral analysis to be reported from an observation which employed burst mode.291 Despite the peculiarities of this mode. the instrumental effective area and the energy response. and charge transfer inefficiency (CTD correction do not differ from more standard modes (Kirsch et al.," Despite the peculiarities of this mode, the instrumental effective area and the energy response, and charge transfer inefficiency (CTI) correction do not differ from more standard modes (Kirsch et al."292 2002)., 2002).293" Therefore. ""full frame"" mode response matrices were created to model the instrument response using SAS-5.2.0."," Therefore, “full frame” mode response matrices were created to model the instrument response using SAS–5.2.0."294 The spectral fits reported herein were made using XSPEC version. 11.1.0 (Arnaud 1996)., The spectral fits reported herein were made using XSPEC version 11.1.0 (Arnaud 1996).295 Quoted errors correspond. to A\*21.0., Quoted errors correspond to $\Delta~\chi^{2}=1.0$.296 Below 0.5 keV and above 10.0 keV. deviations were seen in the residuals regardless of the spectral model used.," Below 0.5 keV and above 10.0 keV, deviations were seen in the residuals regardless of the spectral model used."297 We therefore restricted our analysis to the 0.5—10.0 keV band., We therefore restricted our analysis to the 0.5–10.0 keV band.298 We note a feature at 2.34 keV which appears as an emission line., We note a feature at 2.34 keV which appears as an emission line.299 The detector effective area changes sharply at this energy and the line is well-fit by a zero-width Gaussian. suggesting that the feature is instrumental.," The detector effective area changes sharply at this energy and the line is well-fit by a zero-width Gaussian, suggesting that the feature is instrumental."300 In examining the EPIC-pn and RGS data of XTE J1650—500. we find oxygen to be 13*1 under-abundant. neon to be 1626€ over-abundant. and iron to be 45+5% under-abundant relative to solar values along this line of sight (assuming abundances as measured by Anders Grevesse 1989).," In examining the EPIC-pn and RGS data of XTE $-$ 500, we find oxygen to be $13^{+1}_{-5}$ under-abundant, neon to be $16_{-6}^{+8}$ over-abundant, and iron to be $45\pm 5$ under-abundant relative to solar values along this line of sight (assuming abundances as measured by Anders Grevesse 1989)."301 The RGS spectrum reveals that the oxygen edge location is more consistent with 0.536 keV than the expected 0.532 keV: this has also been noted in fits to Chandra data of Cygnus X-1 (Schulz et al., The RGS spectrum reveals that the oxygen edge location is more consistent with 0.536 keV than the expected 0.532 keV; this has also been noted in fits to Chandra data of Cygnus X-1 (Schulz et al.302 2001. Miller et al.," 2001, Miller et al."303 2002)., 2002).304 We therefore fixed the oxygen edge to be at 0.536 keV in all fits., We therefore fixed the oxygen edge to be at 0.536 keV in all fits.305 All other elements are found to have abundances consistent with solar values., All other elements are found to have abundances consistent with solar values.306" Absorption in the ISM was modeled using the ""vphabs model in XSPEC (with the abundance of oxygen set to zero. and an additional edge to model the oxygen absorption at 0.536 keV)."," Absorption in the ISM was modeled using the “vphabs” model in XSPEC (with the abundance of oxygen set to zero, and an additional edge to model the oxygen absorption at 0.536 keV)."307 We measure an effective neutral hydrogen column density of Ny27.80.2«107! atoms em., We measure an effective neutral hydrogen column density of $N_{H}=7.8\pm 0.2\times 10^{21}$ atoms $^{-2}$.308 Fits with the standard multicolor accretion disk black body (hereafter. MCD: Mitusda et al.," Fits with the standard multicolor accretion disk black body (hereafter, MCD; Mitusda et al."309 1984) plus power-law model to the 0.5-10.0 keV spectrum were statistically unacceptable (\7=513.4 for 233 d.of.)., 1984) plus power-law model to the 0.5–10.0 keV spectrum were statistically unacceptable $\chi^{2}=513.4$ for 233 d.o.f.).310 The data/model ratio for this model is shown in Figure 1., The data/model ratio for this model is shown in Figure 1.311 The emission line profile in this data/model ratio is similar to that observed in Cygnus X-1 with the High Energy Transmission Grating Spectrometer (Miller et al., The emission line profile in this data/model ratio is similar to that observed in Cygnus X-1 with the High Energy Transmission Grating Spectrometer (Miller et al.312 2002). and similar to line profiles seen in some AGNs with (see. e. g.. Iwasawa et al.," 2002), and similar to line profiles seen in some AGNs with (see, e. g., Iwasawa et al."313 1996: Weaver. Gelbord. Yagoob 2001).," 1996; Weaver, Gelbord, Yaqoob 2001)."314 Gaussian emission line and smeared edge (see Ebisawa et al., Gaussian emission line and smeared edge (see Ebisawa et al.315 1994) components were added to the model., 1994) components were added to the model.316 The addition of these components improved the fit significantly (4=314.8 for 225 d.o.f.)., The addition of these components improved the fit significantly $\chi^{2}=314.8$ for 225 d.o.f.).317" Using this model. we measure an inner disk color temperature of KT=0.322+0.004. keV. and an MCD normalization of 3.9""?i«107."," Using this model, we measure an inner disk color temperature of $kT=0.322\pm 0.004$ keV, and an MCD normalization of $3.9^{+0.3}_{-1.3}\times 10^{4}$."318 The measured power-law index is T=2.097045: the normalization of this component is measured to be 3.10.2 ph ems keV! at | keV. The 0.5-10.0 keV flux of the MCD component is 0.36255.107 ere en? sl. and that for the power-law component is," The measured power-law index is $\Gamma=2.09^{+0.03}_{-0.09}$; the normalization of this component is measured to be $3.1\pm 0.2$ ph $^{-2}$$^{-1}$ $^{-1}$ at 1 keV. The 0.5–10.0 keV flux of the MCD component is $0.36^{+0.03}_{-0.12}\times 10^{-8}$ erg $^{-2}$ $^{-1}$ , and that for the power-law component is"319indicator of whether there are any companions or not.,indicator of whether there are any companions or not.320" Our simulations show that 67 per cent of svstems with IN,70.75 have at least one spectroscopically confirmed. companion. while 76. per cent. of the systems. with Ny.«0.75. do not have any companions."," Our simulations show that 67 per cent of systems with $N_w > 0.75$ have at least one spectroscopically confirmed companion, while 76 per cent of the systems with $N_w < 0.75$ do not have any companions."321 We suspect that many of the incorrect associations are due to late-tvpe galaxies that are not identified well bv our colour clistributions., We suspect that many of the incorrect associations are due to late-type galaxies that are not identified well by our colour distributions.322" N,, for each lens svstem is recorded in Table 1..", $N_w$ for each lens system is recorded in Table \ref{table_lens_properties}.323" Phere is a noticeable trend for lenses with steeper density. profiles to have higher values of IN, (Figure. 2)).", There is a noticeable trend for lenses with steeper density profiles to have higher values of $N_w$ (Figure \ref{figure_lens_neighbors}) ).324 Furthermore. none of the shallower than isothermal lenses are found to be associated with a companion galaxy.," Furthermore, none of the shallower than isothermal lenses are found to be associated with a companion galaxy."325 A simple linear regression of the data (after setting NY.=1 for the svstenis with Nc 1) finds that the trend is real with 98.3 per cent confidence., A simple linear regression of the data (after setting $N_w = 1$ for the systems with $N_w > 1$ ) finds that the trend is real with 98.3 per cent confidence.326 A comparison saniple of non-Lens fields was mace for each lens system to provide an external. comparison., A comparison sample of non-lens fields was made for each lens system to provide an external comparison.327 For cach lens. the same analysis as described above was performed on 200 SDSS galaxies at the same redshift as the SLACS lens and with a measured stellar velocity dispersion within 20 of the lens velocity dispersion.," For each lens, the same analysis as described above was performed on 200 SDSS galaxies at the same redshift as the SLACS lens and with a measured stellar velocity dispersion within 20 of the lens velocity dispersion."328 In. some cases the number of comparison fields meeting these criteria is less than 200. in which case we used all fields that do meet the criteria.," In some cases the number of comparison fields meeting these criteria is less than 200, in which case we used all fields that do meet the criteria."329" The composite distribution of IN, for all of the comparison samples is shown in Figure 3: a Ixolmogorov-Smirnov (Ix-8) test was unable to distinguish between the distributions.", The composite distribution of $N_w$ for all of the comparison samples is shown in Figure \ref{figure_comp_neighbors}; a Kolmogorov-Smirnov (K-S) test was unable to distinguish between the distributions.330 A proper characterization of the global environment of a lens system would determine the velocity dispersion for the group that the lens resides in as well as the distance of the lens from the centre of the group., A proper characterization of the global environment of a lens system would determine the velocity dispersion for the group that the lens resides in as well as the distance of the lens from the centre of the group.331 Neither of these can be quantified without spectroscopically defining the group membership: we are only able to perform this analvsis for the lowest redshift’ lenses. (Section. 2.2.3))., Neither of these can be quantified without spectroscopically defining the group membership; we are only able to perform this analysis for the lowest redshift lenses (Section \ref{section_spectroscopy}) ).332" Nevertheless. we attempt to characterize the ""richness! of the global environment by emploving a weighting scheme similar to the one used for the local environment."," Nevertheless, we attempt to characterize the `richness' of the global environment by employing a weighting scheme similar to the one used for the local environment."333 The same colour distributions are used and the analysis only dillers by the weight termi used to penalize the racial olfset from the lens: the distance weighting for the global environment is with dy set to 350 tkpe. approximately the virial radius for moderate redshift) groups (c.g.Auger 2007a).," The same colour distributions are used and the analysis only differs by the weight term used to penalize the radial offset from the lens; the distance weighting for the global environment is with $d_0$ set to 350 kpc, approximately the virial radius for moderate redshift groups \citep[e.g.,][]{augera}."334. The group richness. 2. is the sum of all of the incliviclual weights and is recorded in Table 1..," The group richness, $R$ , is the sum of all of the individual weights and is recorded in Table \ref{table_lens_properties}."335" While IN, can be interpreted approximately as the number of neighbouring galaxies for each lens. /! should not be interpreted as the number of galaxies in the group. though it is a proxyfor the density of early-type galaxies at a particular redshift."," While $N_w$ can be interpreted approximately as the number of neighbouring galaxies for each lens, $R$ should not be interpreted as the number of galaxies in the group, though it is a proxyfor the density of early-type galaxies at a particular redshift."336uncertainties (compareRahmanetal. or a correct treatment of the uncertainties associated 2010)with physical parameter estimation.,"uncertainties \citep[compare][]{RAHMAN10}337 or a correct treatment of the uncertainties associated with physical parameter estimation."338" Bearing these caveats in mind, a rough parameterization may still be useful to the reader."," Bearing these caveats in mind, a rough parameterization may still be useful to the reader."339" If we apply a simple linear regression in log space and the function μη=Ax(Eua/10Mgpc72)"" to the binned kpc data (red points in the lower right panel of Figure 1)), we find Az4.4x107? Mo yr! kpc? and Nx1.0."," If we apply a simple linear regression in log space and the function $\Sigma_{\rm SFR} = A \times \left( \Sigma_{\rm H2} / {\rm340 10 M}_\odot~{\rm pc}^{-2}\right)^N$ to the binned kpc data (red points in the lower right panel of Figure \ref{fig:combined}) ), we find $A\approx4.4 \times341 10^{-3}$ $_\odot$ $^{-1}$ $^{-2}$ and $N\approx1.0$."342 This is not rigorous: we have treated the observable “yo as an independent variable and we discarded information in the process of binning., This is not rigorous: we have treated the observable $\Sigma_{\rm H2}$ as an independent variable and we discarded information in the process of binning.343 However the fit does reasonably bisect the data., However the fit does reasonably bisect the data.344" We find similar results fitting the individual measurements where we are complete with N varying by +0.2 and A varying by ~30%, depending mainly on how the fit is constructed."," We find similar results fitting the individual measurements where we are complete with $N$ varying by $\pm 0.2$ and $A$ varying by $\sim 30\%$, depending mainly on how the fit is constructed."345" The results of this fitting can be distilled to what is immediately apparent from the plot: a characteristic Top~2.3 Gyr and a power law index close to unity, so that the data extend parallel to the dashed lines of fixed in Figure 1.."," The results of this fitting can be distilled to what is immediately apparent from the plot: a characteristic $\tau_{\rm Dep}^{\rm H2} \sim3462.3$ Gyr and a power law index close to unity, so that the data extend parallel to the dashed lines of fixed $\tau_{\rm Dep}^{\rm H2}$ in Figure \ref{fig:combined}."347" The global index close to unity implies 75>,that the ratio of Xj to Ugrr does not change much as a function of ye across our data.", The global index close to unity implies that the ratio of $\Sigma_{\rm H2}$ to $\Sigma_{\rm SFR}$ does not change much as a function of $\Sigma_{\rm H2}$ across our data.348 We quantify this by comparing Top to “ye where we are complete >5 Mo ," We quantify this by comparing $\tau_{\rm Dep}^{\rm H2}$ to $\Sigma_{\rm349 H2}$ where we are complete $\Sigma_{\rm H2} >3505$ $_\odot$ $^{-2}$ )."351Figure 2 plots the individual measurements(Sy2 along pc?)with a running median and scatter; both show little or no systematic variation of as a function of “ye across the range studied., Figure \ref{fig:tau} plots the individual measurements along with a running median and scatter; both show little or no systematic variation of $\tau_{\rm Dep}^{\rm H2}$ as a function of $\Sigma_{\rm H2}$ across the range studied.352" The Τβο,rank correlation coefficient relating Tob=Xg»/Xarn to Xgo is r=0.09+0.01 in our kpc data, i.e., the two quantities are only very weakly correlated."," The rank correlation coefficient relating $\tau_{\rm Dep}^{\rm H2} = \Sigma_{\rm H2} /353\Sigma_{\rm SFR}$ to $\Sigma_{\rm H2}$ is $r = 0.09 \pm 0.01$ in our kpc data, i.e., the two quantities are only very weakly correlated."354" 'These results extend those found by B08 and Leroyal. (2008),, who also found a roughly constant ratio for a smaller, less diverse sample."," These results extend those found by B08 and \citet{LEROY08}, who also found a roughly constant ratio $\Sigma_{\rm H2} /355\Sigma_{\rm SFR}$ for a smaller, less diverse sample."356" Based on Xu2/Xsrndetailed studies of Local Group galaxies2010), they speculated that the approximately linear rrelation arises because star formation in disk galaxies takes place in a relatively uniform population of GMCs."," Based on detailed studies of Local Group galaxies, they speculated that the approximately linear relation arises because star formation in disk galaxies takes place in a relatively uniform population of GMCs."357" Given typical GMC masses of ~10°-10® Mo and sizes of ~50 pc, each of our resolution elements likely averages over at least a few — and often many — GMCs."," Given typical GMC masses of $\sim 10^5$ $10^6$ $_\odot$ and sizes of $\sim 50$ pc, each of our resolution elements likely averages over at least a few — and often many — GMCs."358" Thus, in this scenario the relationship between Xg» and Xsrn reduces to a counting exercise: Xgs corresponds to a different number of GMCs inside different resolution elements, rather than to changing physical conditions in the molecular gas."," Thus, in this scenario the relationship between $\Sigma_{\rm H2}$ and $\Sigma_{\rm SFR}$ reduces to a counting exercise: $\Sigma_{\rm H2}$ corresponds to a different number of GMCs inside different resolution elements, rather than to changing physical conditions in the molecular gas."359" This also naturally explains the weak dependence of our results on spatial scale, whichmerely determines the number of GMCs per resolution element but leaves the average fixed constant TBep intact (compare B08 for a detailed discussion)."," This also naturally explains the weak dependence of our results on spatial scale, whichmerely determines the number of GMCs per resolution element but leaves the average fixed constant $\tau_{\rm Dep}^{\rm H2}$ intact (compare B08 for a detailed discussion)."360" This scenario does not contradict earlier results finding that Top depends on Sy2 or Mmgo: the strongest measurements of variable TBep come from LIRGs and ULIRGs (e.g.,Kennicutt1998;Gao&Solomon2004),, systems with ssurface densities significantly exceeding those studied here and where the assumption of a uniform GMC population likely breaks down."," This scenario does not contradict earlier results finding that $\tau_{\rm Dep}^{\rm H2}$ depends on $\Sigma_{\rm H2}$ or $M_{\rm361 H2}$: the strongest measurements of variable $\tau_{\rm362 Dep}^{\rm H2}$ come from LIRGs and ULIRGs \citep[e.g.,][]{KENNICUTT98A,gao04}, systems with surface densities significantly exceeding those studied here and where the assumption of a uniform GMC population likely breaks down."363" Departures are also expected on scales of individual molecular clouds, where only a small fraction of the molecular gas actively forms stars (e.g.,Heidermanetal.2010)."," Departures are also expected on scales of individual molecular clouds, where only a small fraction of the molecular gas actively forms stars \citep[e.g.,][]{Heiderman10}."364". We will show in the next section, however, that for normal disk galaxies and on scales greater than a few 100ppc our results agree remarkably well with previous measurements of Top "," We will show in the next section, however, that for normal disk galaxies and on scales greater than a few pc our results agree remarkably well with previous measurements of $\tau_{\rm Dep}^{\rm H2}$."365"As described in Section 1, many studies have examined the relationship between molecular gas and star formation in nearby disk galaxies over the last decade."," As described in Section \ref{sec:intro}, many studies have examined the relationship between molecular gas and star formation in nearby disk galaxies over the last decade."366 The emphasis on power law fits has somewhat obscured the basic question of whether these data fundamentally agree or disagree regarding which part of “Myo—Ugrr space is occupied by local disk galaxies.," The emphasis on power law fits has somewhat obscured the basic question of whether these data fundamentally agree or disagree regarding which part of $\Sigma_{\rm367 H2}-\Sigma_{\rm SFR}$ space is occupied by local disk galaxies."368" To address this point, Figure 3 shows our binned data (big points with error bars) along with a wide compilation of recent measurements."," To address this point, Figure \ref{fig:lit} shows our binned data (big points with error bars) along with a wide compilation of recent measurements."369 We adjust all literature measurements to share our adopted aand stellar IMF but otherwise leave the data unchanged.," We adjust all literature measurements to share our adopted and stellar IMF (Kroupa), but otherwise leave the data unchanged."370" These points (Kroupa),therefore reflect a wide range of star formation tracers, sampling schemes and physical scales."," These points therefore reflect a wide range of star formation tracers, sampling schemes and physical scales."371 We plot averages over whole galaxies as triangles., We plot averages over whole galaxies as triangles.372 These include 57 normal spiral galaxies (green) and 15 starburst galaxies (blue) from Kennicutt(1998).., These include 57 normal spiral galaxies (green) and 15 starburst galaxies (blue) from \citet{KENNICUTT98A}.373 Kennicutt estimates Xspg from Ha for normal spirals and IR (1998)emission for starbursts.," \citet{KENNICUTT98A} estimates $\Sigma_{\rm374 SFR}$ from $\alpha$ for normal spirals and IR emission for starbursts."375" We also show 236 pointings towards spirals from Murgiaetal.(2002,pur- and towards 80 small nearby spirals and dwarfs from Leroyetal.(2005,red) (2003)..", We also show 236 pointings towards spirals from \citet[][purple]{MURGIA02} and towards 80 small nearby spirals and dwarfs from \citet[][red]{LEROY05} .376". Both data sets have ~(1996),50” resolution, corresponding to ~ 1-4 kpc, and use 1.4 GHz radio continuum (RC) emission to estimate USFR-"," Both data sets have $\sim 50\arcsec$ resolution, corresponding to $\sim1$ $4$ kpc, and use 1.4 GHz radio continuum (RC) emission to estimate $\Sigma_{\rm SFR}$ ."377While the ML Eddineton bias estimate for individual sources is straight forward. we conceutrate on the application of the source flux redistribution matrix.,"While the ML Eddington bias estimate for individual sources is straight forward, we concentrate on the application of the source flux redistribution matrix."378 This procedure follows the staudard data calibration. exposure map coustruction. source detection. aud backgrouud image generation (e.g... Wang et al.," This procedure follows the standard data calibration, exposure map construction, source detection, and background image generation (e.g., Wang et al."379 2003. 2001: see also Figs.," 2003, 2004; see also Figs."380 1-3)., 1-3).381" We adopt 2,=10°.", We adopt $P_{th} = 10^{-6}$.382" From the ACIS-I observation — Abell 2125. we detect SL. LS. aud 93 sources in the 0.52, 2-5. and 0.5-8 keV baucls. respectively."," From the ACIS-I observation of Abell 2125, we detect 81, 48, and 93 sources in the 0.5-2, 2-8, and 0.5-8 keV bands, respectively."383 From the ACIS-S observation of NGC (σοι. 80. 65. and. 112 sources are detected in the 0.3-1.5. 1.5-T. aud 0.3-7 keV bands. respectively.," From the ACIS-S observation of NGC 4594, 80, 65, and 112 sources are detected in the 0.3-1.5, 1.5-7, and 0.3-7 keV bands, respectively."384 After removing duplicates (spatial coincicleuces) iu the detections. we lind a total of 99 aud 115 unique sources in the Abell 2125 and NGC 1591 liekds (Figs.," After removing duplicates (spatial coincidences) in the detections, we find a total of 99 and 115 unique sources in the Abell 2125 and NGC 4594 fields (Figs."385 ] aud 2b)., 1 and 2b).386 We then apply the procedure described in 81 to generate the required fIux redistribution matrix LOS1) for each source detection baud (e.g.. Fig.," We then apply the procedure described in 4 to generate the required flux redistribution matrix $R(J,I)$ for each source detection band (e.g., Fig."387 6). which can then be used to study the nuimber-flux relatious in the fields.," 6), which can then be used to study the number-flux relations in the fields."388the travel time between adjacent pinning sites. which are the atomic nuclei in (he solid crust ol a neutron star) is much shorter than the associated relaxation time.,"the travel time between adjacent pinning sites, which are the atomic nuclei in the solid crust of a neutron star) is much shorter than the associated relaxation time."389 Thus the vortices. under (he assumed pinning conditions. (ake part in the relaxation processwhole. even though each undergoes an intermittent evele of movements and halts.," Thus the vortices, under the assumed pinning conditions, take part in the relaxation process, even though each undergoes an intermittent cycle of movements and halts."390 The relaxation (me. in (he absence of any. pinning. is deduced from a solution of the vortex equation of motion (Eq.," The relaxation time, in the absence of any pinning, is deduced from a solution of the vortex equation of motion (Eq."391" 3) for the radial r;(/) and azimuthal 6,(/) components of the vortex position in polar coordinates. as a [function of time / Alpar Souls. 1935: JJahan-Miri 1993): where O-subseripts indicate initial values at /=0 corresponding to an assumed departure from an earlier state of co-rotation of the supertluid (vortices) and the crust. and τει "," 3) for the radial $r_{\rm v}(t)$ and azimuthal $\phi_{\rm v}(t)$ components of the vortex position in polar coordinates, as a function of time $t$ \markcite{as88} Alpar Sauls 1988; \markcite{mj98}J Jahan-Miri 1998): where 0-subscripts indicate initial values at $t=0$ corresponding to an assumed departure from an earlier state of co-rotation of the superfluid (vortices) and the crust, and $K = { \rho_{\rm s}392\kappa n_{\rm v} \over \ \rho_{\rm c}} \ {\tau_v}$ ."393The relaxation time το needed [or the simultaneous re-adiustment of the vortices in both radial and azimuthal directions in response to the exiting torque on the superthaid. ie.," The relaxation time $\tau_{\rm D}$ needed for the simultaneous re-adjustment of the vortices in both radial and azimuthal directions in response to the exiting torque on the superfluid, ie."394" (he dvnamieal coupling time scale. is given as where =L. and any=20,22 have been used. omitüng the zero subscripts."," the dynamical coupling time scale, is given as where ${ \rho_{\rm s} \over \ \rho_{\rm c}} ={I_{\rm s} \over \395I_{\rm c}}$, and $\kappa n_{\rm v} = 2 \Omega_{\rm s} \approx 2396\Omega_{\rm c}$ have been used, omitting the zero subscripts."397 In the case of pining. the racial position of each vortex changes according to the same equation l4. between ils successive pinned states. followed by a halt in idis motion until unpinning again.," In the case of pining, the radial position of each vortex changes according to the same equation 14, between its successive pinned states, followed by a halt in its motion until unpinning again."398" For definiteness. we assume the twpical time period /, that any given vortex undergoes a pinning/unpinnineg cvcle is much shorter than the sought relaxation (ime scale of (he svstem."," For definiteness, we assume the typical time period $t_{\rm c}$ that any given vortex undergoes a pinning/unpinning cycle is much shorter than the sought relaxation time scale of the system."399 This should be the relevant limit lor (he case considered. eiven the microscopic distances between pinning centers which set (he the order οἱ magnitude of the tvpical distance that is travelled by an unpinned vortex before re-pinning.," This should be the relevant limit for the case considered, given the microscopic distances between pinning centers which set the the order of magnitude of the typical distance that is travelled by an unpinned vortex before re-pinning."400 This length scale together with the (tvpical relative (radial as well as azimuthal) velocities of (hie vortices will respect (o the crust will set the period /.. for a given unpinning probability £.," This length scale together with the typical relative (radial as well as azimuthal) velocities of the vortices with respect to the crust will set the period $t_{\rm401c}$, for a given unpinning probability $\xi$."402 Thus. one needs to do some averaging over successive movements and stationary states of each vortex in order io infer an exponential-like Gane behavior for its radial displacement. hence deducing a dvnamical relaxation ime. comparable (ο (he case of no pining.," Thus, one needs to do some averaging over successive movements and stationary states of each vortex in order to infer an exponential-like time behavior for its radial displacement, hence deducing a dynamical relaxation time, comparable to the case of no pining."403" We trv three different averaging methods. which nevertheless give consistent results at least for the relevant limiting CASES,"," We try three different averaging methods, which nevertheless give consistent results at least for the relevant limiting cases."404"from the asvamptotie solutions of Eqs 10 11 indicate a relative rotation difference AQ,, such that where _ is the steady-state spin-down rate of either component.",from the asymptotic solutions of Eqs 10 11 indicate a relative rotation difference $\Delta \Omega_{\rm ss}$ such that where = - is the steady-state spin-down rate of either component.405 The latter relation (Eq., The latter relation (Eq.406 13) is however expressing a general dynamical relation. applicable also to the case of a superfIuid component. with (hie reservation that the relative rotation of (he vortices (not the superfIuid) and the crust would be (he relevant quantity.," 13) is however expressing a general dynamical relation, applicable also to the case of a superfluid component, with the reservation that the relative rotation of the vortices (not the superfluid) and the crust would be the relevant quantity."407 In contrast to the above formulation of a (two-component svstem. the dynamical coupling lime scale of a superíIuid is associated. with (he relaxation of ils vortices (o their new positions. in response to (he existing torque on the superfluid.," In contrast to the above formulation of a two-component system, the dynamical coupling time scale of a superfluid is associated with the relaxation of its vortices to their new positions, in response to the existing torque on the superfluid."408 The added: complexity is due to the fact that. unlike (he particles of a normal component. (he relaxation of vortices involves both their azimuthal as well radial displacements.," The added complexity is due to the fact that, unlike the particles of a normal component, the relaxation of vortices involves both their azimuthal as well radial displacements."409 Moreover. in (he case of random unpinning a further complication is that only. a fraction of the total vortices are effectively moving. at any given (ime.," Moreover, in the case of random unpinning a further complication is that only a fraction of the total vortices are effectively moving, at any given time."410" For a pinned superfIuid with a total number density of the vortices ny. per unit area. random unpinning events al a rate £ may result in a statistical population ol [ree potentially movable vortices. with a munber density y=£n, (Ex."," For a pinned superfluid with a total number density of the vortices $n_{\rm v}$, per unit area, random unpinning events at a rate $\xi$ may result in a statistical population of free potentially movable vortices, with a number density $n_{\rm m} = \xi n_{\rm411v}$ (Eq."412 5). al any given time while ||<cg.," 5), at any given time while $|\omega| < \omega_{\rm413crit}$."414 Likewise. looking at any given vortex over a large enough time period (larger than the associated pinning/unpinning intervals). it would move ancl take part in the relaxation process for onlv a fraction £ of the (me. and spends the rest of it. (1—£) fraction. as stationary pinned aud decoupled.," Likewise, looking at any given vortex over a large enough time period (larger than the associated pinning/unpinning intervals), it would move and take part in the relaxation process for only a fraction $\xi$ of the time, and spends the rest of it, $(1-\xi)$ fraction, as stationary pinned and decoupled."415" The drag force on any uinpinned moving vortex is nevertheless (he same as in the normal case when all of the vortices are [free and mobile. under (he same assumed conditions for (he scattering processes and relative velocities (sane T, odd Myo)."," The drag force on any unpinned moving vortex is nevertheless the same as in the normal case when all of the vortices are free and mobile, under the same assumed conditions for the scattering processes and relative velocities (same $\tau_v$ and $v_{\rm rel}$ )."416 Also. the instantaneous kinematic contribution of the vortices in the superíIuid spin frequency is the same irrespective of their pinning/unpinning states.," Also, the instantaneous kinematic contribution of the vortices in the superfluid spin frequency is the same irrespective of their pinning/unpinning states."417 Therefore. the equation of motion of each vortex. governing the time behavior of ils racial displacement between successive pinning events. would be exactly (he same as in (he absence of any pinning (Eq.," Therefore, the equation of motion of each vortex, governing the time behavior of its radial displacement between successive pinning events, would be exactly the same as in the absence of any pinning (Eq."418 14. below).," 14, below)."419 A superfIuid rotational relaxation would nevertheless be achieved via rearrangement of the (radial) positions ofalf vortices., A superfluid rotational relaxation would nevertheless be achieved via rearrangement of the (radial) positions of vortices.420 The distinction between a pinned subgroup and another unpinned is meaningful only for (he instantaneous considerations. aud not for a long term relaxation process.," The distinction between a pinned subgroup and another unpinned is meaningful only for the instantaneous considerations, and not for a long term relaxation process."421 This would be further justified if the vortices (being indistinguishable (hid entities) are required to maintain a locally uniform density ancl more so if the time between successive pinning/unpinnings for each vortex (being of the order of, This would be further justified if the vortices (being indistinguishable fluid entities) are required to maintain a locally uniform density and more so if the time between successive pinning/unpinnings for each vortex (being of the order of422where [/] is the number density (molecules *) of each species 7.,where $[i]$ is the number density (molecules $^{-3}$ ) of each species $i$ .423" The rates (7) of the forward reaction ancl reverse reaction are given by where , and , ave the kinetic rate coellicients Lor the forward and reverse reactions. respectively."," The rates $\nu$ ) of the forward reaction and reverse reaction are given by where $k_{f}$ and $k_{r}$ are the kinetic rate coefficients for the forward and reverse reactions, respectively."424 When the system is operating at equilibrium. the forward reaction rate is equal to the reverse reaction rate: which is an expression of the principle of microscopic reversibility.," When the system is operating at equilibrium, the forward reaction rate is equal to the reverse reaction rate: which is an expression of the principle of microscopic reversibility."425 Substitution into the equilibrium constant expression (2)) gives an equation often found in textbooks. (hat can be used to determine reverse reaction rate coefficients.," Substitution into the equilibrium constant expression \ref{eq:eqcon}) ) gives an equation often found in textbooks, that can be used to determine reverse reaction rate coefficients."426 However. it is important to note that thermodynamic tabulations containing equilibrium constants (A) ave generally calculated. assuming units of pressure (e.g..l-barconstant-pressurereference 1993).. whereas reaction rate coellicients (/) are generally reported in units of number density.," However, it is important to note that thermodynamic tabulations containing equilibrium constants $K$ ) are generally calculated assuming units of pressure \citep[e.g., 1-bar constant-pressure reference state,][]{chase1998}, whereas reaction rate coefficients $k$ ) are generally reported in units of number density."427 For reactions containing dillerent iunbers of reactants and products. omission of the appropriate pressure-correc(ion terms in equation (6)) will result in incorrect rate coefficients for the reverse reaction.," For reactions containing different numbers of reactants and products, omission of the appropriate pressure-correction terms in equation \ref{eq:reversibility}) ) will result in incorrect rate coefficients for the reverse reaction."428 For example.several authors consider [1+ICO4-M—CIHI4O4 as the rate-limiting step for CO—CIL; conversion in substellar atmospheres (Yungetal.1983:Griffith&Yelle1999:Dézardetal.2002:Cooper&Showman2006:Line 2010).. where M represents anv third body.," For example,several authors consider $\textrm{H}+\textrm{H}_{2}\textrm{CO}+\textrm{M}\rightarrow 429\textrm{CH}_{3}\textrm{O} + \textrm{M}$ as the rate-limiting step for $\textrm{CO}\rightarrow 430\textrm{CH}_{4}$ conversion in substellar atmospheres \citep{yung1988,griffith1999,bezard2002,cooper2006,line2010}, where M represents any third body."431 The rate coefficient lor this termolecular reaction has not been measured experimentally. but it can be calculated from the rate coefficient. of the reverse reaction CIHI4O04M — I+ οςο + M investigated by Pageetal.(1989).," The rate coefficient for this termolecular reaction has not been measured experimentally, but it can be calculated from the rate coefficient of the reverse reaction $\textrm{CH}_{3}\textrm{O} + 432\textrm{M}$ $\rightarrow$ H + $_2$ CO + M investigated by \citet{page1989}."433.. As pointed out by Bézarel (2002).. the pressure-correction term was omitted bv Griffith&Yelle(1999) in their reversal. ancl therefore Griffith&Yelle(1999) have adopted an incorrect rate coefficient in (heir treatment of CO quench kinetics on Gliese 229D. Lineetal.(2010) make a similar error in their (treatment of quench kinetics on ILD 189733b and derive a two-body rate coefficient (whichwassubsequentlyadoptedbyMacdhusudhan&Seager2011.forGJ436b) for the three-body reaction I4Ε.Ο+M.," As pointed out by \citet{bezard2002}, the pressure-correction term was omitted by \citet{griffith1999} in their reversal, and therefore \citet{griffith1999} have adopted an incorrect rate coefficient in their treatment of CO quench kinetics on Gliese 229B. \cite{line2010} make a similar error in their treatment of quench kinetics on HD 189733b and derive a two-body rate coefficient \citep[which was subsequently adopted by][for GJ 436b]{madhusudhan2011} for the three-body reaction $\textrm{H}+\textrm{H}_{2}\textrm{CO}+\textrm{M}$."434 However. because Lineetal.(2010) consider a quench level (hat is near 1 bar. theiromission of (he pressure-correction terni is mostly offset by (heir omission of the [M] term when calculating the rate of H--H3CO--M.," However, because \citet{line2010} consider a quench level that is near 1 bar, theiromission of the pressure-correction term is mostly offset by their omission of the [M] term when calculating the rate of $\textrm{H}+\textrm{H}_{2}\textrm{CO}+\textrm{M}$ ."435 Nevertheless. such errors," Nevertheless, such errors"436seems that BLR cloud densities and sizes in different AGN must span at least a three order-of-magnitude range.,seems that BLR cloud densities and sizes in different AGN must span at least a three order-of-magnitude range.437 We would like to thank Hagai Netzer and Brad Peterson for helpful discussions., We would like to thank Hagai Netzer and Brad Peterson for helpful discussions.438cosluic strings. cosmic necklaces. aud superheavy long-lived relic particles.,"cosmic strings, cosmic necklaces, and superheavy long-lived relic particles."439 The idea belind these models is that relies of the very carly universe. topological deects (TDs) or superlieavy relic (SUR) particles. produced after or at the eud of inflation. can decay today. auc generate UITECTis.," The idea behind these models is that relics of the very early universe, topological defects (TDs) or superheavy relic (SHR) particles, produced after or at the end of inflation, can decay today and generate UHECRs."440 Defects. such as cosmic strings. domain walls. aud maguctic monopoles. can be generated hrough the Wiiile mechanisni as syiunietries are broken with the expansion aud cooling of the universe.," Defects, such as cosmic strings, domain walls, and magnetic monopoles, can be generated through the Kibble mechanism as symmetries are broken with the expansion and cooling of the universe."441 Topologically stable defects can survive to the present and decompose iito their constituent fields as they collapse. anuihilate. or reach critical current im the case of superconducting cosmic strings.," Topologically stable defects can survive to the present and decompose into their constituent fields as they collapse, annihilate, or reach critical current in the case of superconducting cosmic strings."442 The decay products. superheavy gauge aud higesao bosons. decay iuto jets of hadrous. mostlv pious.," The decay products, superheavy gauge and higgs bosons, decay into jets of hadrons, mostly pions."443 Pious in the ]ets subsequently decay into >-ravs. clectrous. aud ucutrinos.," Pions in the jets subsequently decay into $\gamma$ -rays, electrons, and neutrinos."444 Only a few perceu of the hadrois are expected. o be nucleous., Only a few percent of the hadrons are expected to be nucleons.445 Typical features of hese scenarios ave a predominant release o rays aud uottrinos aud a QCD yagiuentation spectrum which is considerably harder than t1e case of Zevatron shock acceleration., Typical features of these scenarios are a predominant release of $\gamma$ -rays and neutrinos and a QCD fragmentation spectrum which is considerably harder than the case of Zevatron shock acceleration.446 ZeV euergies are not a challenge for top-down nodels since svauinetryv wreaking scaes at the cud of inflation typically are >>107! oV (typical X- masses vary between ~E107720δη7 eV)., ZeV energies are not a challenge for top-down models since symmetry breaking scales at the end of inflation typically are $\gg 10^{21}$ eV (typical X-particle masses vary between $\sim 10^{22-25}$ eV).447"T Fitting.+ fie observed flux of CHECRs is the real challenge since the vpieal distauc‘es between TDs is he Ilorizon scale. 1, e.. about several Cx."," Fitting the observed flux of UHECRs is the real challenge since the typical distances between TDs is the Horizon scale, i. e., about several Gpc."448 The low flux hurts proposals owed ou ordinary aud superconducting cosnüc strings which are distributed hroughout spaceTD in Table 2)., The low flux hurts proposals based on ordinary and superconducting cosmic strings which are distributed throughout space in Table 2).449 Mouo)oles usiallv suffer the opposite problem. they would in general be too uuuerous.," Monopoles usually suffer the opposite problem, they would in general be too numerous."450 Inflation succeeds iu dilutiug the number density of monopoles aud makes them too rare for UITEC'R xodnuctioi., Inflation succeeds in diluting the number density of monopoles and makes them too rare for UHECR production.451 To reach the observed UIIECR. flux. mouopole nodels usually involve some degree of fine tuning.," To reach the observed UHECR flux, monopole models usually involve some degree of fine tuning."452 If euoieh monopoles and autinmonopoles survive from the early inverse. thev may form a bound state. naued 1onopoloniuu. hat can cecav generating UMECRs.," If enough monopoles and antimonopoles survive from the early universe, they may form a bound state, named monopolonium, that can decay generating UHECRs."453 The liοια of nionopoloja Ίαν be too short for this scenario to succeed iuless they are connected by strings! Once two sviunietry breaking scales are invoked. a combination of horizou scales gives του to reasonable ummber deusities.," The lifetime of monopolonia may be too short for this scenario to succeed unless they are connected by \cite{PO99}454 Once two symmetry breaking scales are invoked, a combination of horizon scales gives room to reasonable number densities."455 This can be arranged for cosluic strings that end iu monopoles making a monopole string network or even more clearly for cosmic uccklaces?? Cosmic necklaces are hivbrid defects where cach monopole is conneced to two strings τοππιο beads on a cosmic string necklace.," This can be arranged for cosmic strings that end in monopoles making a monopole string network or even more clearly for cosmic \cite{BV97}456 Cosmic necklaces are hybrid defects where each monopole is connected to two strings resembling beads on a cosmic string necklace."457 Necklace uetworks may evolve to configurations that can fi the UIIECR flux wueich is ulnuatelv eenerated bv the annililation of monopoles with autinonopoles trapped iu- the yoyAG Iu these |OSCOLAIdOS. DIOtous doiiuunate the fh xiuthelowerejerev side of the GZIX cutoff while photous cud to dominate at ieior energies de»udiue ou the radio bacseround (see Figure 9 aud in Table 2).," Necklace networks may evolve to configurations that can fit the UHECR flux which is ultimately generated by the annihilation of monopoles with antimonopoles trapped in the \cite{BV97,BBV98} In these scenarios, protons dominate the flux in the lower energy side of the GZK cutoff while photons tend to dominate at higher energies depending on the radio background (see Figure 9 and in Table 2)."458 Tf future data cau settle the composition of, If future data can settle the composition of459mostly due to bremsstrahlung.,mostly due to bremsstrahlung.460To separate the WILIINM. Grom these (wo phases we need {ο identify (he emission lines. ancl (his sets the requirement on (he energy. resolution of any instrument designed (o study the WIIIM.,"To separate the WHIM from these two phases we need to identify the emission lines, and this sets the requirement on the energy resolution of any instrument designed to study the WHIM."461 An energv resolution of a few eVs is necessary to resolve single lines. in particular if we want to identify the triplet al ο570 eV. the main tracer of the WILIM.," An energy resolution of a few eVs is necessary to resolve single lines, in particular if we want to identify the triplet at $\sim 570$ eV, the main tracer of the WHIM."462 We generated [four sets of identical simulations. with the metallicity as the only parameter that was changed. using the models described in section 3..," We generated four sets of identical simulations, with the metallicity as the only parameter that was changed, using the models described in section \ref{metal-models}."463" For simplicity. we refer to those models as ""DBorgani. ""Croft. “Scatter”. and ""Cen""."," For simplicity we refer to those models as “Borgani”, “Croft”, “Scatter”, and “Cen”."464 To evaluate the contribution of the WIIIM to the total diffuse. N-rav. emission we compared our simulations will results from (he X-ray Quantum Calorimeter (XQC) souncine rocket program (AleCammon et al., To evaluate the contribution of the WHIM to the total diffuse X-ray emission we compared our simulations with results from the X-ray Quantum Calorimeter (XQC) sounding rocket program (McCammon et al.465 2002) and the ROSAT All Sky Survey (ASS - Snowdnen et al., 2002) and the $ROSAT$ All Sky Survey (RASS - Snowdnen et al.466 1994)., 1994).467 NOC is the only current mission using high resolution microcalorimeters for the study. of the DXD in the οποιον range 50-2000 eV. while RASS is the most accurate. survey below 1 keV and are considered the benchmarks for any soft DXD studies.," XQC is the only current mission using high resolution microcalorimeters for the study of the DXB in the energy range 50-2000 eV, while RASS is the most accurate X-ray survey below 1 keV and are considered the benchmarks for any soft DXB studies."468 The most recent. NQC published results (MeConmmon et al., The most recent XQC published results (McCammon et al.469 2002) predict a surface brightness of in the 0.880-0.950 keV οποιον band., 2002) predict a surface brightness of in the 0.380-0.950 keV energy band.470 In table 1. we report the surface brightness predicted bv the four simulations in the same enerev band and the predicted Πας in the RASS R4 and #5 bands (Snowcnen et al., In table \ref{surf-bright} we report the surface brightness predicted by the four simulations in the same energy band and the predicted flux in the RASS $R4$ and $R5$ bands (Snowdnen et al.471" 1994) in units of "" photons ! 7 (the default RASS units).", 1994) in units of $^{-6}$ photons $^{-1}$ $^{-2}$ (the default RASS units).472" The average RASS flux in the R44-R5 bands is ~ 139 "" photons | >7.", The average RASS flux in the R4+R5 bands is $\sim$ 139 $^{-6}$ photons $^{-1}$ $^{-2}$.473 The Dorgani model has the lowest brightness. 0.77£0.04 tin the 0.380-0.950 keV energy range. and can be used to put a lower limit to the WIIIM emission.," The Borgani model has the lowest brightness, $0.77\pm0.04$ in the 0.380-0.950 keV energy range, and can be used to put a lower limit to the WHIM emission."474 We remind that even if (his model has a hieh average metallicity at low densities (as shown in Fig., We remind that even if this model has a high average metallicity at low densities (as shown in Fig.475 6 and table 1)). most of the particles actually have no metals due to the poor diffusion of metals to low density regions in the hvdrodynamie code.," \ref{metallicity-vs-density} and table \ref{surf-bright}) ), most of the particles actually have no metals due to the poor diffusion of metals to low density regions in the hydrodynamic code."476 Moreover. the few particles with metals have low densitv and. since enission goes as clensily squared. (hev give litle contribution as well.," Moreover, the few particles with metals have low density and, since emission goes as density squared, they give little contribution as well."477 The Croft model predicts a relatively low emission as well. 1.84+0.08," The Croft model predicts a relatively low emission as well, $1.84\pm0.08$."478 This model was designed to work at high redshift (2~ 3). where (he gas is still rather poor in metals.," This model was designed to work at high redshift $z\sim3$ ), where the gas is still rather poor in metals."479 Although being somewhat unrealistic. (his model is a test of intermediate metallicitv.," Although being somewhat unrealistic, this model is a test of intermediate metallicity."480 The Seatter model. on the other hand. was created [or gas al 2=0. and slightly overestimates (he observed metalliites at 0<z«0.5 (Z~0.3Z. lor groups and clusters and Z~O.1Z. for diffuse gas. as seen in 1)). but it gives much higher metallicities (possib=<," The Scatter model, on the other hand, was created for gas at $z=0$, and slightly overestimates the observed metallicites at $0<z<0.5$ $\textrm{Z}\sim 0.3 \textrm{Z}_\odot$ for groups and clusters and $\textrm{Z}\sim0.1\textrm{Z}_\odot$ for diffuse gas, as seen in \ref{introduction}) ), but it gives much higher metallicities (possibly"481e»20—100 kpe.,$\sim 20 - 100$ kpc.482 If dense cold gas is injected into the ICM. e.g. by ram pressure stripping from galaxies (e.g.. Soker 11991) or cooling on the ~LOO kpe scale. it can sink to (he center of the cluster on a time scale no shorter than ~100 kpc/ 1000 kins ~108 vr.," If dense cold gas is injected into the ICM, e.g., by ram pressure stripping from galaxies (e.g., Soker 1991) or cooling on the $\sim 100$ kpc scale, it can sink to the center of the cluster on a time scale no shorter than $\sim 100$ kpc/ 1000 km $\sim 10^8$ yr."483 This limits the rate at which cold eas can accumulate in the ICM. on the 100 kpe scales., This limits the rate at which cold gas can accumulate in the ICM on the 100 kpc scales.484" The accumulation rate (i.e.. the difference between the sources and sinks of cold gas) is constrained (o be no more than about 4x10+ M,L|."," The accumulation rate (i.e., the difference between the sources and sinks of cold gas) is constrained to be no more than about $4 \times 10^{-4}$ $_\odot$."485" This suggests (1) if cold. elouds are not efficiently. destroved. injection of cold gas into the hot ICM (by any mechanism. including cooling) on the LOO kpe scales is verv low ~10.4? M, Ίντι or (2) any cold clouds on the 100 kpe scales are efficiently re-heated or destroved (e.g.. Loewenstein Fabian 1990): and (3) the dense nebulae in the cluster center are produced by gas which is deposited or which coolssitu."," This suggests (1) if cold clouds are not efficiently destroyed, injection of cold gas into the hot ICM (by any mechanism, including cooling) on the 100 kpc scales is very low $\sim 10^{-4}$ $_\odot$ /yr; or (2) any cold clouds on the 100 kpc scales are efficiently re-heated or destroyed (e.g., Loewenstein Fabian 1990); and (3) the dense nebulae in the cluster center are produced by gas which is deposited or which cools."486 We present LIST STIS long-slit spectroscopy of the line in A426. AL795 ancl A2597.," We present HST STIS long-slit spectroscopy of the line in A426, A1795 and A2597."487 We detect ten aabsorplion svstenis towards (he nucleus of NGC1215 with estimated column densities in the range NUL)~107 to Lot!7..., We detect ten absorption systems towards the nucleus of NGC1275 with estimated column densities in the range $N(HI) \sim 10^{12}$ to $10^{14}$.488 These svstems could not have been detected in the 2] em line. but are easily detected in aabsorption.," These systems could not have been detected in the 21 cm line, but are easily detected in absorption."489 Most of the detected features are located in the broad wines of (he emission line and are bevond the velocity range of the emission line filaanents., Most of the detected features are located in the broad wings of the emission line and are beyond the velocity range of the emission line filaments.490 The detected absorption svslelus are most consistent wilh associated nuclear absorption svstems., The detected absorption systems are most consistent with associated nuclear absorption systems.491 Further observations of variability and. /or the metal lines are necessary (o confirm this hypothesis., Further observations of variability and /or the metal lines are necessary to confirm this hypothesis.492 We do not detect the feature al rreported by Johnstone Fabian (1995) aud interpreted as being due to Fermi-acceleratedLya., We do not detect the feature at reported by Johnstone Fabian (1995) and interpreted as being due to Fermi-accelerated.493. If real. this feature is variable and would be consistent with an intrinsic absorbing svslenm.," If real, this feature is variable and would be consistent with an intrinsic absorbing system."494 There is very little absorption at the svstemic velocity of NGCI275 (Ieature 8 contains NIIT)o3x101 7))., There is very little absorption at the systemic velocity of NGC1275 (feature 8 contains $N(HI) \sim 3\times 10^{12}$ ).495 This implies that the very large column densities detected in the 2] em line avoid the line of sight to the nuclear eenitiing region and are likely detected against (he parsec scale radio jet., This implies that the very large column densities detected in the 21 cm line avoid the line of sight to the nuclear emitting region and are likely detected against the parsec scale radio jet.496 This atomic gas may be located in a cireiumnuclear disk or torus., This atomic gas may be located in a circumnuclear disk or torus.497Forty vears after its discovery. the 2175 interstellar absorption baud still Inspires new efforts in search of a model carrvicr which could satisty all the (s01ietiiies apparently contradictory) observational constraints.,"Forty years after its discovery, the 2175 interstellar absorption band still inspires new efforts in search of a model carrier which could satisfy all the (sometimes apparently contradictory) observational constraints."498" Among the latest eudeavours. we note several papers on fullerenes/buckvonious models ο, Wada and Tokunaga (2006). Chhowalla et al. (2003).."," Among the latest endeavours, we note several papers on fullerenes/buckyonions models (e.g. Wada and Tokunaga \cite{wad} , Chhowalla et al. \cite{chh},"499 Ruiz et al. (2005)..X ," Ruiz et al. \cite{rui}, ,"500Li et al.(2008)))., Li et \cite{li}) ).501 On the other hand. an improved approach of the polvervstalline eraphite (PC) model was described by Papoular aud Papoular (20081.," On the other hand, an improved approach of the polycrystalline graphite (PG) model was described by Papoular and Papoular \cite{pp}."502 However. to this da. only a few authors have proposed a solution to the most difficult puzzle iu this domain. viz.," However, to this day, only a few authors have proposed a solution to the most difficult puzzle in this domain, viz."503 the relative narrowness of most IS (interstellar) features aud the observed variations of their width from 0.7 to 13 yan + together with the constancy of the coutral wavelength at L6 jun. | (or 5.7 eV) to better than 2 , the relative narrowness of most IS (interstellar) features and the observed variations of their width from 0.7 to 1.3 $\mu$ $^{-1}$ together with the constancy of the central wavelength at 4.6 $\mu$ $^{-1}$ (or 5.7 eV) to better than 2 $\%$ .504To our knowledge. the latest amoung them are Sorrell (1990). aud Moeunella et al. ((1998))).," To our knowledge, the latest among them are Sorrell \cite{sor} and Mennella et al. \cite{men}) )."505 Sorrell proposed monosized carbon eraius eraplhütized by UV starlight., Sorrell proposed monosized carbon grains graphitized by UV starlight.506 Meunella et al., Mennella et al.507 reasoned that au ordered material like eraplite is too hard to conceive in space aud prefer UV-processed )carbon grains (BCC: bip carrier carbons)., reasoned that an ordered material like graphite is too hard to conceive in space and prefer UV-processed carbon grains (BCC: bump carrier carbons).508 Based on anu original approach to their previous spectral reflectance measurements of various samples (Menunella et al. (1996))).," Based on an original approach to their previous spectral reflectance measurements of various samples (Mennella et al. \cite{men96}) ),"509 they cane up with a series of dielectric fictions from which they derived plasiuon resonance profiles that fit observations remarkably well., they came up with a series of dielectric functions from which they derived plasmon resonance profiles that fit observations remarkably well.510 At about the same time. Duley and Sealira (1998). studied a large nuuber of different theoretical carbon structures similar to those of PAID molecules but with various degrees of hydrogenation. ionization and defects. of which they computed the diclectric fictions (using the discrete dipole approximation) and deduced the corresponding bump spectral profiles.," At about the same time, Duley and Seahra \cite{dul} studied a large number of different theoretical carbon structures similar to those of PAH molecules but with various degrees of hydrogenation, ionization and defects, of which they computed the dielectric functions (using the discrete dipole approximation) and deduced the corresponding bump spectral profiles."511 While some of these exhibit the bump at the right waveleneth. none fulfill the feature width constraints.," While some of these exhibit the bump at the right wavelength, none fulfill the feature width constraints."512 Again. noue exhibit feature widths uarrower than 1 µια | (their Fig.," Again, none exhibit feature widths narrower than 1 $\mu$ $^{-1}$ (their Fig."513 16)., 16).514 These authors note that hydrogenation and defects increase the feature width and decrease its intensity. which concurs with previous measurements by Blanco et al.," These authors note that hydrogenation and defects increase the feature width and decrease its intensity, which concurs with previous measurements by Blanco et al."515 (1996) and Schuaiter et al. (1996)., \cite{bla} and Schnaiter et al. \cite{sch96}.516.. As this whole picture seenis o be at odds with Meunella et al, As this whole picture seems to be at odds with Mennella et al.517s favourable conclusion regarding the same ype of materials. the issue will be taken up iu the Discussion below.,"'s favourable conclusion regarding the same type of materials, the issue will be taken up in the Discussion below."518 The PG model of Papoular and Papoular (2009). is neither based ou the xerfectly ordered terrestrial eraphite nor on amorphous livdrogenated carbon., The PG model of Papoular and Papoular \cite{pp} is neither based on the perfectly ordered terrestrial graphite nor on amorphous hydrogenated carbon.519 Tt is. inade of. pure. mainly. sp9 carbon in. a disordered. structure.," It is made of pure, mainly $^{2}$ carbon in a disordered structure."520 Hore. based on classical results of solid stateplivsies. aswell as on new experiueutal findings," Here, based on classical results of solid statephysics, aswell as on new experimental findings"521spectrum (Percivaletal. 2009:; Reidetal.2009).,spectrum \cite{Percival2009}; ; \cite{Reid2009}) ).522 It. 15 therefore legitimate to wonder whether our conclusions can be appreciably modified with this new information., It is therefore legitimate to wonder whether our conclusions can be appreciably modified with this new information.523 However. there are some reasons that this is not anticipated.," However, there are some reasons that this is not anticipated."524 A comparison of the columns in Tables 2..3 and 4 reveals that our results are not sensitive to different data combinations: using the three data sets (CMB. P(A). SN Ia) or using only two (either CMB and P(k) or CMB and SN Ia) leads to nearly identical constraints. differences in preferred parameters being at most 1.5 «c. less than the worse systematic difference discussed below.," A comparison of the columns in Tables \ref {Table_wi02wf1}, \ref{Table_wi01wf1} and \ref{Table_wi0wf1} reveals that our results are not sensitive to different data combinations: using the three data sets (CMB, $P(k)$, SN Ia) or using only two (either CMB and $P(k)$ or CMB and SN Ia) leads to nearly identical constraints, differences in preferred parameters being at most 1.5 $\sigma$, less than the worse systematic difference discussed below."525 Since preferred cosmological parameters from most recent analysis are entirely consistent with our previous analysis (Ferramachoetal. 2009)). it is reasonable to assume that using the new data would make virtually no difference.," Since preferred cosmological parameters from most recent analysis are entirely consistent with our previous analysis \cite{FBZ}) ), it is reasonable to assume that using the new data would make virtually no difference."526 Our general conclusion is. maybe not surprisingly. that the concordance model ts doing well and that possible variation in dark energy is unlikely.," Our general conclusion is, maybe not surprisingly, that the concordance model is doing well and that possible variation in dark energy is unlikely."527 A final word of caution though: In the present analysis we used the constraint from the power spectrum of LRG (Tegmarketal. 2006))., A final word of caution though: In the present analysis we used the constraint from the power spectrum of LRG \cite{T06}) ).528 However. Ferramacho et al. (," However, Ferramacho et al. ("5292009) noticed that the use of the correlation function could lead to preferred values which differ up to 2c from the ones obtained with the power spectrum.,2009) noticed that the use of the correlation function could lead to preferred values which differ up to $2\sigma$ from the ones obtained with the power spectrum.530 Therefore. our 2c ranges can be regarded as indicative of possible systematic effects.," Therefore, our $2\sigma$ ranges can be regarded as indicative of possible systematic effects."531 We have no certainty however that this systematic difference could not be larger for varying dark energy models., We have no certainty however that this systematic difference could not be larger for varying dark energy models.532 The difference i the clustering properties between red and blue galaxies is also a subject that calls for caution in the detailed interpretatio of data (Sánchez&Cole2008:: Percivaletal. 2007)). eve if recent analysis tends to weaken earlier discrepancies (Percivaletal. 2009)).," The difference in the clustering properties between red and blue galaxies is also a subject that calls for caution in the detailed interpretation of data \cite{SanchezCole}; \cite{PercivalDR5}) ), even if recent analysis tends to weaken earlier discrepancies \cite{Percival2009}) )."533 Improvements of constraints on dark energy from future experiments would have to control 1 an extremely accurate way their systematics to infer robust constraints onthe variation of dark energy., Improvements of constraints on dark energy from future experiments would have to control in an extremely accurate way their systematics to infer robust constraints onthe variation of dark energy.534appropriately by the number density of galaxies within that bin.,appropriately by the number density of galaxies within that bin.535" As noted in 2, the 3D weak lensing problem can be reduced to a one-dimensional problem, by taking as our data vector the (noisy) lensing convergence along each line of sight, which is related to the density contrast through Equation(9)."," As noted in \ref{sec:theory}, the 3D weak lensing problem can be reduced to a one-dimensional problem, by taking as our data vector the (noisy) lensing convergence along each line of sight, which is related to the density contrast through Equation."536". Therefore, we take d=&;;(z) and R=Q, and consider each line of sight in our images independently."," Therefore, we take $\boldsymbol{d} = \boldsymbol{\kappa}_{ij}(z)$ and $\mathbf{R} = \mathbf{Q}$, and consider each line of sight in our images independently."537" Further, as discussed previously, we take ® to be a ó-function dictionary."," Further, as discussed previously, we take $\boldsymbol{\Phi}$ to be a $\delta$ -function dictionary."538" In our simulations, clusters are placed into a region where the mean density in the absence of the cluster is equal to the mean density of the Universe at that redshift."," In our simulations, clusters are placed into a region where the mean density in the absence of the cluster is equal to the mean density of the Universe at that redshift."539" In other words, ó is constrained to be greater than zero in all our simulations."," In other words, $\delta$ is constrained to be greater than zero in all our simulations."540" Therefore, the projection onto the convex set C in algorithm applies a positivity constraint at each iteration."," Therefore, the projection onto the convex set $\mathcal{C}$ in algorithm \ref{alg:inversion} applies a positivity constraint at each iteration."541" Clearly, a one-dimensional implementation throws away information, as we do not account at all for the correlation between neighbouring lines of sight that will arise in the presence of a large structure in the image; however, reducing the problem to a single dimension is fast and easy to implement, and allows us to test the efficacy of the algorithm using a particularly simple basis function through which we impose sparsity."," Clearly, a one-dimensional implementation throws away information, as we do not account at all for the correlation between neighbouring lines of sight that will arise in the presence of a large structure in the image; however, reducing the problem to a single dimension is fast and easy to implement, and allows us to test the efficacy of the algorithm using a particularly simple basis function through which we impose sparsity."542" A fully three-dimensional treatment of the problem, with more accurate noise modelling (see below) will be the subject of a future work."," A fully three-dimensional treatment of the problem, with more accurate noise modelling (see below) will be the subject of a future work."543" However, the algorithm used is entirely general; therefore, with appropriate choice of a three-dimensional basis set and taking d=γ(θ,2) and R=Pa-Q, one can implement this algorithm as a fully three-dimensional treatment of the data with no modification to the algorithm itself."," However, the algorithm used is entirely general; therefore, with appropriate choice of a three-dimensional basis set and taking $\boldsymbol{d} = \boldsymbol{\gamma}(\bt,z)$ and $\mathbf{R} = \mathbf{P_{\gamma\kappa}Q}$, one can implement this algorithm as a fully three-dimensional treatment of the data with no modification to the algorithm itself."544" We assume that the redshifts of the sources are known exactly, so there is no correlation between the noise in each source bin."," We assume that the redshifts of the sources are known exactly, so there is no correlation between the noise in each source bin."545" Therefore, the covariance matrix of the noise along the line of sight is diagonal, with where Apia is the pixel area, ng(z;) is the number density of sources in the bin at redshift σι, and c. is the intrinsic dispersion in galaxy ellipticity, taken throughout to be 0.2."," Therefore, the covariance matrix of the noise along the line of sight is diagonal, with where $A_{pix}$ is the pixel area, $n_g(z_i)$ is the number density of sources in the bin at redshift $z_i$, and $\sigma_\gamma$ is the intrinsic dispersion in galaxy ellipticity, taken throughout to be $0.2$."546 This covariance matrix is used in the evaluation of the data fidelity constraint in our algorithm above., This covariance matrix is used in the evaluation of the data fidelity constraint in our algorithm above.547 Note that the covariance matrix is only diagonal if the galaxy redshifts are known exactly., Note that the covariance matrix is only diagonal if the galaxy redshifts are known exactly.548" In practice, photometric redshift errors mean that each redshift slice in the data is likely to be contaminated with a few galaxies whose redshift error bars overlap with neighbouring redshift bins."," In practice, photometric redshift errors mean that each redshift slice in the data is likely to be contaminated with a few galaxies whose redshift error bars overlap with neighbouring redshift bins."549" In this case, the covariance matrix will have additional, non-diagonal elements that are non-zero."," In this case, the covariance matrix will have additional, non-diagonal elements that are non-zero."550" This is straightforward to model, however, for the chosen method of photometric redshift estimations, and our algorithm is entirely general regarding the form of the covariance matrix."," This is straightforward to model, however, for the chosen method of photometric redshift estimations, and our algorithm is entirely general regarding the form of the covariance matrix."551" Therefore, the problem of photometric redshift errors is readily tractable in our method, and will be presented in a future work."," Therefore, the problem of photometric redshift errors is readily tractable in our method, and will be presented in a future work."552 The noise in the reconstruction is controlled and suppressed by two parameters in the algorithm described in Figure 2 and Appendix AppendixB:., The noise in the reconstruction is controlled and suppressed by two parameters in the algorithm described in Figure \ref{fg:alg_schem} and Appendix \ref{sec:implementation}.553". The first, and most important of these parameters is the data fidelity control parameter, c."," The first, and most important of these parameters is the data fidelity control parameter, $\epsilon$."554" 'This parameter controls how well the data are fit by the reconstruction, with e—0 implying a perfect fit to the data, which is not possible in the presence of noise."," This parameter controls how well the data are fit by the reconstruction, with $\epsilon = 0$ implying a perfect fit to the data, which is not possible in the presence of noise."555 Figure 4 demonstrates the effect of varying ε in the reconstruction of two lines of sight from our simulations., Figure \ref{fg:epsilon} demonstrates the effect of varying $\epsilon$ in the reconstruction of two lines of sight from our simulations.556" Clearly, when is small, the algorithm attempts to fit each data point more eclosely which, in the presence of noise, can result in overfitting of the data (as seen in line of sight 1) and hence false detections along the line of sight."," Clearly, when $\epsilon$ is small, the algorithm attempts to fit each data point more closely which, in the presence of noise, can result in overfitting of the data (as seen in line of sight 1) and hence false detections along the line of sight."557" On the other hand, a large e may result in a solution that is not a good fit to the data (as seen in line of sight 2)."," On the other hand, a large $\epsilon$ may result in a solution that is not a good fit to the data (as seen in line of sight 2)."558" The second parameter used to control the noise is the soft threshold parameter A, which is used in the algorithm to impose the sparsity prior."," The second parameter used to control the noise is the soft threshold parameter $\lambda$, which is used in the algorithm to impose the sparsity prior."559" A threshold set excessively high will result in a null solution, whilst a threshold set fairly low will allow for more false detections of noise peaks along a given line of sight."," A threshold set excessively high will result in a null solution, whilst a threshold set fairly low will allow for more false detections of noise peaks along a given line of sight."560" The appropriate value for this threshold should be related to the expected fluctuations in the density contrast resulting from noise variations, and should scale with the signal to noise in the image."," The appropriate value for this threshold should be related to the expected fluctuations in the density contrast resulting from noise variations, and should scale with the signal to noise in the image."561" Note that while ε strongly affects the accuracy of the estimation in reproducing the underlying density contrast, A simply affects the sparsity of the solution."," Note that while $\epsilon$ strongly affects the accuracy of the estimation in reproducing the underlying density contrast, $\lambda$ simply affects the sparsity of the solution."562" In other words, changing A will not greatly affect the reconstructions of true density peaks, but may affect the number of false detections and noise peaks seen."," In other words, changing $\lambda$ will not greatly affect the reconstructions of true density peaks, but may affect the number of false detections and noise peaks seen."563" Also note that a thresholding A does not imply that density peaks with 6«A will not be detected, as soft thresholding is only applied to one part of the estimate of the solution."," Also note that a thresholding $\lambda$ does not imply that density peaks with $\delta < \lambda$ will not be detected, as soft thresholding is only applied to one part of the estimate of the solution."564The dependence of the star formation rate on eas density on large scales is a subject. of intense observational and theoretical investigation. as it is both an important input for models of galaxy formation and evolution and chemical evolution calculations. as well as a critical test for theories of interstellar medium evolution and star formation.,"The dependence of the star formation rate on gas density on large scales is a subject of intense observational and theoretical investigation, as it is both an important input for models of galaxy formation and evolution and chemical evolution calculations, as well as a critical test for theories of interstellar medium evolution and star formation."565" Let us define the surface density of the star formation rate. Msp. as the mass of eas being converted into stars per unit time per unit surface area. and Ma, as the total gas mass per unit surface area."," Let us define the surface density of the star formation rate, $\dot{\Sigma}_{\rm SF}$, as the mass of gas being converted into stars per unit time per unit surface area, and $\Sigma_{\rm gas}$ as the total gas mass per unit surface area."566 The two quantities have been found to obey a non-linear. power-law relation: where mau81.5 for a large range of surface densities and system morphologies.," The two quantities have been found to obey a non-linear, power-law relation: where $n_{\rm gas} \approx 1.5$ for a large range of surface densities and system morphologies."567 This correlation is known as the WKennicutt-Schmidt law of star. formation. (Schmidt 1959. Ixennicutt. 1989).," This correlation is known as the Kennicutt-Schmidt law of star formation (Schmidt 1959, Kennicutt 1989)."568 The star formation law has been established through observations of the global star formation and gas density in dillerent. galaxies (e.g. Wennicutt 1998. Misiriotis et 22004. Ixomugi et 22005): of local gas ancl star formation densities in dillerent galaxies (e.g. Wong and Blitz 2002. Doissier et 22003): and. of local σας and. star formation densities within a single galaxy (e.g. Misiriotis et 22006 in the case ofthe Milky. Way. Schuster et 22007 in the case of. M51).," The star formation law has been established through observations of the global star formation and gas density in different galaxies (e.g. Kennicutt 1998, Misiriotis et 2004, Komugi et 2005); of local gas and star formation densities in different galaxies (e.g. Wong and Blitz 2002, Boissier et 2003); and of local gas and star formation densities within a single galaxy (e.g. Misiriotis et 2006 in the case of the Milky Way, Schuster et 2007 in the case of M51)."569" ""Traditionally. this correlation has been interpreted. in the literature as à result of the density dependence of the star-[ormation timescale."," Traditionally, this correlation has been interpreted in the literature as a result of the density dependence of the star-formation timescale."570 The star formation rate density can be expressed as a ratio of the density of the gas available [or star formation over a timescale relevant to the conversion of the available gas to stars., The star formation rate density can be expressed as a ratio of the density of the gas available for star formation over a timescale relevant to the conversion of the available gas to stars.571 Examples of such timescales that have been suggested in this framework are the free-fall timescale. the turbulence crossing time over the scale height of the galaxy. the collapse timescale of large expanding shells with low Mach. number (see c.g. Elmeerecn 2002b and references therein). the orbital timescale of the galactic disk (Silk 1997). and the timescale for gas accumulation along magnetic Lux tubes parallel to spiral arms. into the vallevs created. by the magnetic. Iavleigh-Tavlor. (Parker) instability (see e.g. Shu ct al.," Examples of such timescales that have been suggested in this framework are the free-fall timescale, the turbulence crossing time over the scale height of the galaxy, the collapse timescale of large expanding shells with low Mach number (see e.g. Elmegreen 2002b and references therein), the orbital timescale of the galactic disk (Silk 1997), and the timescale for gas accumulation along magnetic flux tubes parallel to spiral arms, into the valleys created by the magnetic Rayleigh-Taylor (Parker) instability (see e.g. Shu et al."572 2007)., 2007).573 These timescalesaff scale as the inverse square root of density. resulting in an overall scaling. of the star formation density as σας density to the 1.5.," These timescales scale as the inverse square root of density, resulting in an overall scaling of the star formation density as gas density to the $1.5$."574 A more elaborate treatment based. on the same principle was presented by Ixrumholz anc Melxee (2005)., A more elaborate treatment based on the same principle was presented by Krumholz and McKee (2005).575" ""This interpretation of the star formation law is very tempting because it is conceptually simple. and elegant. and because it gives the same result. for. several cülferent"," This interpretation of the star formation law is very tempting because it is conceptually simple and elegant, and because it gives the same result for several different"576We eximine elobal incompressible axisvnuuelric perturbations of a differentially rotating MIID plasma with radial density gradients.,We examine global incompressible axisymmetric perturbations of a differentially rotating MHD plasma with radial density gradients.577 His shown that the standard magnetorotational instability. (MBRI) criterion drawn [rom the local dispersion relation is often misleacdine.," It is shown that the standard magnetorotational instability, (MRI) criterion drawn from the local dispersion relation is often misleading."578 If (he equilibria magnetic field is either purelv axial or purely toroidal. the problem reduces to finding the elobal radial eigenvalues of an elfective potential.," If the equilibrium magnetic field is either purely axial or purely toroidal, the problem reduces to finding the global radial eigenvalues of an effective potential."579 The standard Ixeplerian profile including the origin is mathematically ill-posed. and (hus anv solution will depend strongly on (he inner boundary.," The standard Keplerian profile including the origin is mathematically ill-posed, and thus any solution will depend strongly on the inner boundary."580 We find a class of unstable modes localized by the form of the rotation and density. profiles. with reduced dependence on boundary conditions. Subjectheadings:MILD.," We find a class of unstable modes localized by the form of the rotation and density profiles, with reduced dependence on boundary conditions. \end{abstract}\tikzmark{mainBodyEnd107}581\tikzmark{mainBodyStart108}\keywords{MHD,"582 instabilities. accretion disks lt is often stated that the Magnetorotational Instability (AIRD) (Chandrasekhar1961:Balbus&Hawley1991.hereafterDII91) in accretion disks is a local iistability. ie. normal modes are driven unstable by the local value of the rotational flow syear.," instabilities, accretion disks}\tikzmark{mainBodyEnd111}583 584\tikzmark{mainBodyStart112}\begin{document} It is often stated that the Magnetorotational Instability (MRI) \citep[][hereafter BH91]{Chandrasekhar:1961,Balbus:1991}585 in accretion disks is a `local' instability, i.e. normal modes are driven unstable by the local value of the rotational flow shear."586 huplicit in this analvsis is (he assumption that equilibrium rotation ancl density vary over a much larger spatial scale than the mode wavelength., Implicit in this analysis is the assumption that equilibrium rotation and density vary over a much larger spatial scale than the mode wavelength.587 Although it has been shown 1iab short-wavelength linear local MAI modes can drive global turbulence in (he nonlinear regime (BalbusHawlev 2001).. it is worthwhile to study. linear instabilities wil1 large raclial extent," Although it has been shown that short-wavelength linear local MRI modes can drive global turbulence in the nonlinear regime \citep{BH98,2001ApJ...554..534H}, it is worthwhile to study linear instabilities with large radial extent"588almost completely locked up in CO).,almost completely locked up in CO).589 In environments denser than TMC-1. gas-phase species freeze out more rapidly onto dust due to mereased collision rates. and this can become an important driver of large-molecule chemistry: Assuming equal sticking probabilities for all species involved in gas-grain collisions. lighter species (including atomic oxygen) travel at higher velocities and therefore freeze out more quickly than the heavier. slower-moving carbon. chains.," In environments denser than TMC-1, gas-phase species freeze out more rapidly onto dust due to increased collision rates, and this can become an important driver of large-molecule chemistry: Assuming equal sticking probabilities for all species involved in gas-grain collisions, lighter species (including atomic oxygen) travel at higher velocities and therefore freeze out more quickly than the heavier, slower-moving carbon chains."590 Because O is à primary destructive reactant for carbon-chain-bearing species. their abundances rise as oxygen freezes out.," Because O is a primary destructive reactant for carbon-chain-bearing species, their abundances rise as oxygen freezes out."591" This is known as the ""freeze-out peak"" (e.g.?).. and may be a plausible explanation for the large carbon chain abundances observed in Cha-MMS| and other dense cores."," This is known as the `freeze-out peak' \citep[\eg][]{bro90}, and may be a plausible explanation for the large carbon chain abundances observed in Cha-MMS1 and other dense cores."592 Evidence in favour of a freeze-out-peak chemistry in Cha-MMS1 is given by the CO depletion and large NH: abundance (?).., Evidence in favour of a freeze-out-peak chemistry in Cha-MMS1 is given by the CO depletion and large $_3$ abundance \citep{ten06}.593 Alternatively. ?? hypothesised that elevated carbon chain abundances in L1527 arise as a result of heating by the newly- protostar IRAS 04368-2557.," Alternatively, \citet{sak08,sak09} hypothesised that elevated carbon chain abundances in L1527 arise as a result of heating by the newly-formed protostar IRAS 04368+2557."594 Once the outer envelope reaches a temperature >30 K. it is theorised that. grain-surface methane begins to sublimate. which then reacts with gas-phase C to form hydrocarbon ions.," Once the outer envelope reaches a temperature $\gtrsim30$ K, it is theorised that grain-surface methane begins to sublimate, which then reacts with gas-phase $^+$ to form hydrocarbon ions."595" These subsequently engage in ion-molecule reactions and give rise to a so-called ""warm carbon-chain chemistry’ (WCCC).", These subsequently engage in ion-molecule reactions and give rise to a so-called `warm carbon-chain chemistry' (WCCC).596 Chemical models show that this mechanism is capable of producing elevated abundances of unsaturated hydrocarbons including polyynes and cyanopolyynes in the warm regionssurrounding low-mass protostars (?).., Chemical models show that this mechanism is capable of producing elevated abundances of unsaturated hydrocarbons including polyynes and cyanopolyynes in the warm regionssurrounding low-mass protostars \citep{has08}.597 The detection of high-excitation-energy carbon chain emission lines in L1527 by ?— is consistent with this theory., The detection of high-excitation-energy carbon chain emission lines in L1527 by \citet{sak08} is consistent with this theory.598 High-excitation lines. have not yet been detected in Cha-MMS1. but we are presently undertaking new observations to search for them.," High-excitation lines have not yet been detected in Cha-MMS1, but we are presently undertaking new observations to search for them."599 The HCiN /=10-9 map of Cha-MMS1I published by ? shows a north-south elongation in the peak emission contour./— which covers both the location of the protostar and the more southerly peak in our observed HC3N /=4-3 map.," The $_3$ N $J=10-9$ map of Cha-MMS1 published by \citet{kon00} shows a north-south elongation in the peak emission contour, which covers both the location of the protostar and the more southerly peak in our observed $_3$ N $J=4-3$ map."600" The /=4-3 emission originates from a rotational energy level (E,) only 4.3 K above the ground state. whereas the J=10-9 emission originates from Εμ=24 K and therefore provides evidence for a significant contribution to the HC3N emission from warmer. more excited gas heated by the protostar."," The $J=4-3$ emission originates from a rotational energy level $E_u$ ) only 4.3 K above the ground state, whereas the $J=10-9$ emission originates from $E_u=24$ K and therefore provides evidence for a significant contribution to the $_3$ N emission from warmer, more excited gas heated by the protostar."601 It is possible that carbon chain abundances may be enhanced as a result of WCCC in this region., It is possible that carbon chain abundances may be enhanced as a result of WCCC in this region.602" However. ? did not detect any emission from the high-excitation (E,=52 K) J=15-14 line of HC3N. which indicates that any warm and dense region must be small compared with the 37” SEST beam."," However, \citet{kon00} did not detect any emission from the high-excitation $E_u=52$ K) $J=15-14$ line of $_3$ N, which indicates that any warm and dense region must be small compared with the $37''$ SEST beam."603 According to the physical model of protostar evolution by ?. during the FHSC stage soon before the protostar begins fusion. the temperature reaches above 30 K at radial distances from the core Ray<20 AU.," According to the physical model of protostar evolution by \citet{mas00}, during the FHSC stage soon before the protostar begins fusion, the temperature reaches above 30 K at radial distances from the core $R_{30}\lesssim20$ AU."604 The protostar subsequently ignites and warms the surrounding envelope over time., The protostar subsequently ignites and warms the surrounding envelope over time.605 After 2x107 yr. Raw is predicted to increase to ~1000 AU. and increases further during the late stages of the Class 0 phase. but by a relatively smaller amount.," After $2\times10^4$ yr, $R_{30}$ is predicted to increase to $\sim1000$ AU, and increases further during the mid-to-late stages of the Class 0 phase, but by a relatively smaller amount."606 The Mopra beam HWHM of =40” corresponds to 6000 AU at the distance of Cha-MMSI. so emission from the cool. extended outer envelope of the (collapsing) protostar dominates the observed spectra. and any emission from the compact methane-sublimation region (inside R35) would be severely diluted regardless of the evolutionary state of the protostar. making the WCCC signature difficult to detect.," The Mopra beam HWHM of $\approx40''$ corresponds to 6000 AU at the distance of Cha-MMS1, so emission from the cool, extended outer envelope of the (collapsing) protostar dominates the observed spectra, and any emission from the compact methane-sublimation region (inside $R_{30}$ ) would be severely diluted regardless of the evolutionary state of the protostar, making the WCCC signature difficult to detect."607 In the case of Cha-MMS] (with its very low luminosity). the warm region close to the protostar is probably too small to make a significant contribution to our observed emission.," In the case of Cha-MMS1 (with its very low luminosity), the warm region close to the protostar is probably too small to make a significant contribution to our observed emission."608 Our non-detection of the more highly-excited emission lines of CoH (with Εξ31 K) is not surprising given the expected beam dilution., Our non-detection of the more highly-excited emission lines of $_6$ H (with $E_u=31$ K) is not surprising given the expected beam dilution.609 On the other hand. if Cha-MMSI contains a VeLLO undergoing episodie aceretion. the size of the warm (methane-sublimation) region is predicted to vary in accordance with the accretion rate (seeforexample.?)..," On the other hand, if Cha-MMS1 contains a VeLLO undergoing episodic accretion, the size of the warm (methane-sublimation) region is predicted to vary in accordance with the accretion rate \citep[see for example,][]{lee07}."610 Therefore. if MMS| is presently at or near to à minimum in the accretion rate cycle. there may still be abundant carbon chains around the protostar. left over from a previous epoch of WCCC that occurred when the aceretion rate and protostar luminosity were greater. and the size of Rao correspondingly larger.," Therefore, if Cha-MMS1 is presently at or near to a minimum in the accretion rate cycle, there may still be abundant carbon chains around the protostar, left over from a previous epoch of WCCC that occurred when the accretion rate and protostar luminosity were greater, and the size of $R_{30}$ correspondingly larger."611 It must be emphasised. however. that the ‘cold’ carbon chain emission peaks (see Figures 2. to 4)) are offset from the protostar centre. so WCCC is an unlikely explanation for the majority of the carbon-chain-rich material surrounding Cha-MMS1].," It must be emphasised, however, that the `cold' carbon chain emission peaks (see Figures \ref{fig:hc3n_map} to \ref{fig:c3s_map}) ) are offset from the protostar centre, so WCCC is an unlikely explanation for the majority of the carbon-chain-rich material surrounding Cha-MMS1."612 Smaller telescope beam sizes combined with the observation of high excitation-energy lines to probe warmer gases will be required for further analysis of the carbon chemistry mside the putative methane sublimation zone and warm inner envelope of Cha-MMSI., Smaller telescope beam sizes combined with the observation of high excitation-energy lines to probe warmer gases will be required for further analysis of the carbon chemistry inside the putative methane sublimation zone and warm inner envelope of Cha-MMS1.613 The polyyne anions C;H and ΟΠΗ were not detected., The polyyne anions $_4$ $^-$ and $_6$ $^-$ were not detected.614 Three-sigma upper limits on their respective anton-to-neutral ratios are [C)H- /[/C4H] < and [CoH |/[CoH] «106c.. which include the errors in the observed abundances of the neutral species.," Three-sigma upper limits on their respective anion-to-neutral ratios are $_4$ $^-$ $_4$ H] $<$ and $_6$ $^-$ $_6$ H] $<$, which include the errors in the observed abundances of the neutral species."615 The largest anion-to-neutral ratios observed in any astronomical source so far (for both species) have been in L1527 where [CH ]/|C4H] = (2) and [CoH |/[CoH] = (2x. which are consistent with our results.," The largest anion-to-neutral ratios observed in any astronomical source so far (for both species) have been in L1527 where $_4$ $^-$ $_4$ H] = \citep{agu08} and $_6$ $^-$ $_6$ H] = \citep{sak08c}, which are consistent with our results."616 In chemical models for dense clouds (e.g.??). the observed CgH™ anion-to-neutral ratios (on the order of a few percent) are reproduced with good accuracy.," In chemical models for dense clouds \citep[\eg][]{mil07,har08}, the observed $_6$ $^-$ anion-to-neutral ratios (on the order of a few percent) are reproduced with good accuracy."617" However. our non-detection of C,H™ provides a new example of the observed C,H anion-to-neutral ratio being substantially less than predicted by theory (see?).."," However, our non-detection of $_4$ $^-$ provides a new example of the observed $_4$ H anion-to-neutral ratio being substantially less than predicted by theory \citep[see][]{her08}."618 Methanol is found in the gas phase in dense molecular clouds. prestellar cores and in the vicinity of protostars. with column densities ~10?— em (e.g.2??)..," Methanol is found in the gas phase in dense molecular clouds, prestellar cores and in the vicinity of protostars, with column densities $\sim10^{13}-10^{15}$ $^{-2}$ \citep[\eg][]{fri88,mar05,buc06}."619 However. most of the methanol in cold. dense protostellar envelopes is found in the form of ice (?)..," However, most of the methanol in cold, dense protostellar envelopes is found in the form of ice \citep{boo08}."620 Its formation gas-phase chemistry is inefficient (2).. and methanol is widely believed to be formed by successive hydrogenation of CO on cold dust grain surfaces.," Its formation gas-phase chemistry is inefficient \citep{gep06}, and methanol is widely believed to be formed by successive hydrogenation of CO on cold dust grain surfaces."621 Its appearance in the gas phase in cold regions has been hypothesised to be due to cosmic-ray-induced desorption. reactive desorption. or heating in grain-grain collisions. whereas inside protostellar envelopes. heating of the material to temperatures >100 K results in complete evaporation of the ices (e.g.?)..," Its appearance in the gas phase in cold regions has been hypothesised to be due to cosmic-ray-induced desorption, reactive desorption, or heating in grain-grain collisions, whereas inside protostellar envelopes, heating of the material to temperatures $\gtrsim100$ K results in complete evaporation of the ices \citep[\eg][]{rod03}."622 The CH;OH map in Figure 3. does not rule out the existence of methanol in warm gas in the vicinity of the protostar. but similar to the carbon-chain-bearing species. the fact that the emission peak is offset by ~10 AU shows that protostellar heating probably does not explain the majority of the observed methanol.," The $_3$ OH map in Figure \ref{fig:ch3oh_map} does not rule out the existence of methanol in warm gas in the vicinity of the protostar, but similar to the carbon-chain-bearing species, the fact that the emission peak is offset by $\sim10^4$ AU shows that protostellar heating probably does not explain the majority of the observed methanol."623 The lack of spatial correlation between the CH;OH and carbon chain distributions matches the observations made by ?.. who used chemical models to infer the physical and chemical histories of HC3N-rich. and CH;OH-rich gas clumps.," The lack of spatial correlation between the $_3$ OH and carbon chain distributions matches the observations made by \citet{buc06}, , who used chemical models to infer the physical and chemical histories of $_3$ N-rich and $_3$ OH-rich gas clumps."624 The observed methanol peak offset in Cha-MMS|] is consistent with the theory presented by, The observed methanol peak offset in Cha-MMS1 is consistent with the theory presented by625the X-ray corona of AB Dor based on the potential field extrapolation. combined with different N-rav inodoels for coronal loops.,"the X-ray corona of AB Dor based on the potential field extrapolation, combined with different X-ray models for coronal loops."626 The poteutial field extrapolation is a useful tool to obtain a first order approximation of the larec-scale structure of a stellar corona based ou its surface maeuetic nap., The potential field extrapolation is a useful tool to obtain a first order approximation of the large-scale structure of a stellar corona based on its surface magnetic map.627 The approach taken by [ussainetal.(2007) is justified due to the fact that the major part of the coronal X-rav cluission is expected to originate from he simaller closed loops near the surface. which are usually in a uear-potenutial state (in the static case where ootpoiut motions aud other short-term motions are not aken into account).," The approach taken by \cite{Hussain07} is justified due to the fact that the major part of the coronal X-ray emission is expected to originate from the smaller closed loops near the surface, which are usually in a near-potential state (in the static case where footpoint motions and other short-term motions are not taken into account)."628 There are. however. good reasons o attempt a more plvsical approach for describing stellar coronac.," There are, however, good reasons to attempt a more physical approach for describing stellar coronae."629 First. the potential field approximation (by itself) provides information only about the magnetic field of the system. and does not address energy dissipation through driving a wind.," First, the potential field approximation (by itself) provides information only about the magnetic field of the system, and does not address energy dissipation through driving a wind."630 Second. the location of the source surface is uot well defined. aud third. when considering a complete description of the physics involved. including conservatiou of mass. mnionenutun. and energy. one needs to take iuto account the effects of coronal heating and stellar wind acceleration. the stretching of the feld lines bv the liehly couductive coronal plasiia to a non-poteutial state. as well as the effects of rapid rotation in stars like AB Dor.," Second, the location of the source surface is not well defined, and third, when considering a complete description of the physics involved, including conservation of mass, momentum, and energy, one needs to take into account the effects of coronal heating and stellar wind acceleration, the stretching of the field lines by the highly conductive coronal plasma to a non-potential state, as well as the effects of rapid rotation in stars like AB Dor."631 Tere we extend the work of IIussnotal.(2007) and present a complete three-dinenusioual MaenetolydroDvuamic (ATID) siuulation of the corona of AD Dor based ou its observed surface magnetic field distribution., Here we extend the work of \cite{Hussain07} and present a complete three-dimensional MagnetoHydroDynamic (MHD) simulation of the corona of AB Dor based on its observed surface magnetic field distribution.632 For our simulation. we use a elobal MIID model developed for the solar corona. which provides a sel&cousistent stellar wind solution driven by surface magnetic field maps.," For our simulation, we use a global MHD model developed for the solar corona, which provides a self-consistent stellar wind solution driven by surface magnetic field maps."633 The cud result is a steady state. AIIID. nou-poteutial solution of the corona aud wind of AD Dor. which includes the distribution of the complete set of physical parameters in the siuulation domain.," The end result is a steady state, MHD, non-potential solution of the corona and wind of AB Dor, which includes the distribution of the complete set of physical parameters in the simulation domain."634 This more conplete solution provides a better understanding of the large-scale. coronal structure., This more complete solution provides a better understanding of the large-scale coronal structure.635 We highlelt the differences between the coronae of voune stars like AB Dor aud the solar corona due to rapid rotation of the former., We highlight the differences between the coronae of young stars like AB Dor and the solar corona due to rapid rotation of the former.636 We also provide realistic caleulatious of the possible mass loss rates for AB Dor. parameterized ly the coronal base density.," We also provide realistic calculations of the possible mass loss rates for AB Dor, parameterized by the coronal base density."637 We present the numerical model and the observational constraints used in the simulation in Section 2.., We present the numerical model and the observational constraints used in the simulation in Section \ref{sec:Simulation}.638" The results are presented in Section 3.. aud the main fiudiues are discussed in Section ἐν,"," The results are presented in Section \ref{sec:Results}, and the main findings are discussed in Section \ref{sec:Discussion}."639 We couclude this work iu Section 5.., We conclude this work in Section \ref{sec:Conclusions}.640 The simulation of AB Dor is done using the solar corona model by Cohenetal.(2007.20051. which is part of the Space Weather \odcling Framework (SWAIF) (Tothetal.2005). and is based on the generic MIID model by (Powelletal.1999).," The simulation of AB Dor is done using the solar corona model by \citet{cohen07, cohen08b}, which is part of the Space Weather Modeling Framework (SWMF) \citep{toth05} and is based on the generic MHD model by \citep{powell99}."641. The model is driven bv surface magnetic field maps. aud the initial condition for the maenetic field. as well as the volumetric energv input for the stellar wind acceleration. is based ou the distribution of the poteutial field.," The model is driven by surface magnetic field maps, and the initial condition for the magnetic field, as well as the volumetric energy input for the stellar wind acceleration, is based on the distribution of the potential field."642 Iu addition. the boundary condition for the surface plasima density. po. is scaled with the maguetic field so that the plasima at closed field regions is more deuse than iu open field regions. as observed for the solar case1995).," In addition, the boundary condition for the surface plasma density, $\rho_0$, is scaled with the magnetic field so that the plasma at closed field regions is more dense than in open field regions, as observed for the solar case."643. Tn the solar case. the source surface is usually set to be at r=2.5R..," In the solar case, the source surface is usually set to be at $r=2.5R_\odot$."644 Iu the case of AB Dor however. the surface distribution of the maeuetic field contains larec regions with strong field.," In the case of AB Dor however, the surface distribution of the magnetic field contains large regions with strong field."645" Therefore. we expect loops on AB Dor to be much larger than solar loops so we choose to set the source surface at r=1048,."," Therefore, we expect loops on AB Dor to be much larger than solar loops so we choose to set the source surface at $r=10R_\star$."646 This should not have any effect on the nou-poteutial. MIID solution since the poteutial field only serves at the initial condition.," This should not have any effect on the non-potential, MHD solution since the potential field only serves at the initial condition."647 The MIID solution is mostly affected by the distribution of euergev deposited iuto the stellar wind. and this cnereization is not sensitive to the location of the source surface as long as it is set above the the height of the largest closed loops.," The MHD solution is mostly affected by the distribution of energy deposited into the stellar wind, and this energization is not sensitive to the location of the source surface as long as it is set above the the height of the largest closed loops."648" However. setting the source surface below the actual size of the loops (at r=2.5/8, for example). forces more field lines to be open and as a result. cach plasiua cell iu the stellar wind is over-enereized. resulting iu solutions with uurealistically fast stellar winds."," However, setting the source surface below the actual size of the loops (at $r=2.5R_\star$ for example), forces more field lines to be open and as a result, each plasma cell in the stellar wind is over-energized, resulting in solutions with unrealistically fast stellar winds."649 A selfeousisteut wind acceleration in the code is obtained by assuming an enipirical relation between the magnetic flux tube expansion and the terminal stellar wind originating from that flux tube., A self-consistent wind acceleration in the code is obtained by assuming an empirical relation between the magnetic flux tube expansion and the terminal stellar wind originating from that flux tube.650 Wang&Shec-lev(1990) and Aree&Pizzo(2000) have derived an clupirical formula that relates the final solar wiud distribution. «4. to the flux tubeexpansion factor. fi.," \cite{wangy90} and \cite{argepizzo00} have derived an empirical formula that relates the final solar wind distribution, $u_{sw}$, to the flux tubeexpansion factor, $f_s$."651" The factor f, is the ratio of the inaguetie flux of a particular flux tube at r=Ry. aud at r=R,. where Ry. is the height of the source surface."," The factor $f_s$ is the ratio of the magnetic flux of a particular flux tube at $r=R_{ss}$ and at $r=R_\star$ , where $R_{ss}$ is the height of the source surface."652 The empirical mecthoc described above predicts the spherical distribution of the solar wind speed at ¢»x., The empirical method described above predicts the spherical distribution of the solar wind speed at $r\rightarrow \infty$.653 Tt is reasonable to assume that far from the Sun (or star). the total euergyv. equals to the bulk kinetic energy of the plasiua. while on the solar surface. t he total energy. equals to the cuthalpy of the fluid. miuus the eravitational potential euergv (the kinetic energy is zero).," It is reasonable to assumed that far from the Sun (or star), the total energy equals to the bulk kinetic energy of the plasma, while on the solar surface, t he total energy equals to the enthalpy of the fluid, minus the gravitational potential energy (the kinetic energy is zero)."654" By adopting the couservatiou of total energv along a streamline (Bernoulli Iutegral). we can relate the final solar wind speed. we, aud the surface value of polvtropic index. 59. assunüuse the boundary conditions for the surface tenmiperature. Zu. are known: Or with IHere hy being the Doltzuiumn coustaut. 50, the proton mass. and G the eravitational constant."," By adopting the conservation of total energy along a streamline (Bernoulli Integral), we can relate the final solar wind speed, $u_{sw}$ and the surface value of polytropic index, $\gamma_0$, assuming the boundary conditions for the surface temperature, $T_0$, are known: or with Here $k_b$ being the Boltzmann constant, $m_p$ the proton mass, and $G$ the gravitational constant."655 Closeto the Sun. the value of 5 is observed to be about unity. (the plasima is hiehlv turbulent). while at 1] AU 5 has a value closer to 1.5 (Tottenotal.1995. 1996).," Closeto the Sun, the value of $\gamma$ is observed to be about unity, (the plasma is highly turbulent), while at 1 AU $\gamma$ has a value closer to 1.5 \citep{totten95,totten96}."656. This observed modulation in > can be related to the powering of the solar wind. in the manner that the larger the eracdicut iu 5 along a flux tube. the faster the wind flows aloug that tube.," This observed modulation in $\gamma$ can be related to the powering of the solar wind, in the manner that the larger the gradient in $\gamma$ along a flux tube, the faster the wind flows along that tube."657 Based on this assiuption. and on the relation preseuted in Eq. 1.. ," Based on this assumption, and on the relation presented in Eq. \ref{BI}, ,"658it ispossible to construct a volumetric heating function. £-(ry.1). iu a wavy that the observed volumetric acceleration of the solar wind can be recovered.," it ispossible to construct a volumetric heating function, $E_\gamma(\gamma_0,\mathbf{r})$ , in a way that the observed volumetric acceleration of the solar wind can be recovered."659 The additional term E.>(0 a8 63/2, The additional term $E_\gamma \rightarrow 0$ as $\gamma \rightarrow 3/2$ .660at4050A.,at.661. Since the resolution of the spectral models we chose is (μου 3. 2)). we binned cach composite into bbins. and then removed. bins which included: the bright emission lines. principally aandΟΠΗ.," Since the resolution of the spectral models we chose is (see \ref{sec:modelling}) ), we binned each composite into bins, and then removed bins which included the bright emission lines, principally and."662 We estimated the errors on the {lux in each wavelength. bin by measuring the IMS of the 14 original pixels which were included in cach bin., We estimated the errors on the flux in each wavelength bin by measuring the RMS of the 14 original pixels which were included in each bin.663 We chose to perform the fits to the models over the wavelength rangeA... based on our desire to fit he same wavelength region in all spectra: a total of 33 independent data points in cach spectrum were used in the EN," We chose to perform the fits to the models over the wavelength range, based on our desire to fit the same wavelength region in all spectra; a total of 33 independent data points in each spectrum were used in the fits."664 Composites for. the matched: sample of. racio-quiet sources 2.2)) were created in exactly the same manner: his data set serves as à control sample to see how the stellar »opulation varies in the absence of a powerful radio source., Composites for the matched sample of radio-quiet sources \ref{sec:matched}) ) were created in exactly the same manner; this data set serves as a control sample to see how the stellar population varies in the absence of a powerful radio source.665 To determine if the presence of an active nucleus alfects the galaxy. we compared the composites formed from the radio-oud sample and the matched radio-quiet sources 2.2)).," To determine if the presence of an active nucleus affects the galaxy, we compared the composites formed from the radio-loud sample and the matched radio-quiet sources \ref{sec:matched}) )."666 The most basic test is to use à simple «72 test. το [ind he probability that a pair of composites come from the same underlying distribution., The most basic test is to use a simple $\chi^2$ test to find the probability that a pair of composites come from the same underlying distribution.667 Each of the eighteen. raclio-oucl composite spectra (Table 1)) was compared with the corresponding raclio-quiet counterpart., Each of the eighteen radio-loud composite spectra (Table \ref{tab:composites}) ) was compared with the corresponding radio-quiet counterpart.668 All composites were consistent with being from the same distribution. except the D4 composite formed from the highest-power radio sources. where the x52=.3.5.," All composites were consistent with being from the same distribution, except the D4 composite formed from the highest-power radio sources, where the $\chi_\nu^2=3.5$."669 This Mooinitial evidence. suggests that. with. the exception of the very highest-power radio sources. there is no evidence of dillerence between galaxies containing an active AGN and those that do not.," This initial evidence suggests that, with the exception of the very highest-power radio sources, there is no evidence of difference between galaxies containing an active AGN and those that do not."670 We modelled the observed continuum as an old. population plus a blue component due to a second population of stars of a younger age. using models from the library (DBruzualX.&Charlot1993).," We modelled the observed continuum as an old population plus a blue component due to a second population of stars of a younger age, using models from the library \citep{bc93}."671. Of the moclels in their library. we used the ones with a Salpeter initial mass function with mass limits of 0.1 and aand solar metallicity. using the Gunn&Stevker(1983) stellar spectral atlas.," Of the models in their library, we used the ones with a Salpeter initial mass function with mass limits of 0.1 and and solar metallicity, using the \citet{gs83} stellar spectral atlas."672 We used (wo single-age stellar populations. representing instantaneous bursts of star formation.," We used two single-age stellar populations, representing instantaneous bursts of star formation."673 The old population was represented by a single-age population of age 7100 Myr. the vounger stars by a population with a range of ages (10. 20. 50. 70. 100. 200. 500. του. 1000. 2000 or 5000 Avr).," The old population was represented by a single-age population of age 7000 Myr, the younger stars by a population with a range of ages (10, 20, 50, 70, 100, 200, 500, 700, 1000, 2000 or 5000 Myr)."674" The exact age of the ""old"" population is not critical. since the spectrum changes little at these ages: we chose 7 Gyr since at the highest redshift in our sample (2= 0.76) the age of he universe was 7 Cyr."," The exact age of the “old” population is not critical, since the spectrum changes little at these ages; we chose 7 Gyr since at the highest redshift in our sample $z=0.76$ ) the age of the universe was 7 Gyr."675 We assembled the model spectra rom the library. ancl binned them to the sane resolution as the observed spectra.," We assembled the model spectra from the library, and binned them to the same resolution as the observed spectra."676 Since the observed continuum is modelled as the sum of wo populations. we assumed cach composite is represented as à 7000 Myr population plus some fraction f of à vounger population with age τι our task is to determine f and T for cach composite.," Since the observed continuum is modelled as the sum of two populations, we assumed each composite is represented as a 7000 Myr population plus some fraction $f$ of a younger population with age $\tau$; our task is to determine $f$ and $\tau$ for each composite."677 This parametrisation is unlikely. to »* à realistic representation of the stellar. populations of hese galaxies., This parametrisation is unlikely to be a realistic representation of the stellar populations of these galaxies.678 However. the exact form. of the models is not important. because our study is a test.," However, the exact form of the models is not important, because our study is a test,"679This work was supported by NASA eraut NACG5-7150.,This work was supported by NASA grant NAG5-7150.680 A. S. wishes to recognize support from the Natural Sciences aud Engiueeriug Research Council of Canada., A. S. wishes to recognize support from the Natural Sciences and Engineering Research Council of Canada.681and for states up to the 155; configuration for He-like ions.,and for states up to the 1s5g configuration for He-like ions.682 Ni and are included only for the ealeulation of the ionization balance: currently no bound-bound transitions for these ions are treated., Ni and are included only for the calculation of the ionization balance; currently no bound-bound transitions for these ions are treated.683 For Fe. utomie data were taken from which provides atomic dati from the project for ions of astrophysical interest.," For Fe, atomic data were taken from which provides atomic data from the project for ions of astrophysical interest."684 These data also contain levels for n.<5 of Fe but include more highly excited contigurations of Fe than CHIANTI tup to the Is10h configuration., These data also contain levels for $n \leq 5$ of Fe but include more highly excited configurations of Fe than CHIANTI (up to the 1s10h configuration).685 Atomic data for Fe and were also taken from TIPBASE: however. no states involving excitation of electrons from the Is shell are included for either of these ions.," Atomic data for Fe and were also taken from TIPBASE; however, no states involving excitation of electrons from the 1s shell are included for either of these ions."686 Ground configuration. photoionization cross-sections were described by the fits from ?.. except for Ni for which fits from ? were adopted.," Ground configuration photoionization cross-sections were described by the fits from \citet{verner96}, except for Ni for which fits from \citet{verner95} were adopted."687 For excited states. photoionization cross-sections were computed using a hydrogenic approximation for all ions.," For excited states, photoionization cross-sections were computed using a hydrogenic approximation for all ions."688 Since bound-free absorption from excited states was not included in the MC simulations. these excited state cross-sections are only needed for the computation of macro atom transition probabilities (see Section 3.3.4).," Since bound-free absorption from excited states was not included in the MC simulations, these excited state cross-sections are only needed for the computation of macro atom transition probabilities (see Section \ref{sect_reemiss}) )."689 The fraction of recombinations which go directly to the ground state. C. wasobtained from the hydrogenic calculations of ?..," The fraction of recombinations which go directly to the ground state, $\zeta$, wasobtained from the hydrogenic calculations of \citet{martin88}."690 In this section we present detailed results pertaining to one particular instance of our model., In this section we present detailed results pertaining to one particular instance of our model.691 The complete set of adopted input parameters for our example model is give in Table 2.., The complete set of adopted input parameters for our example model is give in Table \ref{tab_param}.692 The black-hole mass. source X-ray luminosity and primary power-law index are all chosen to be reasonable for Mrk 766. the object for which we make a detailed comparison in Section 8 CM~4.37109 M. ΗΕ~107 ergs 1 TIED~2:38 [21h ," The black-hole mass, source X-ray luminosity and primary power-law index are all chosen to be reasonable for Mrk 766, the object for which we make a detailed comparison in Section \ref{sect_mrk766} $M_{\mbox{\scriptsize bh}} \sim 4.3 \times 10^6$ $_{\odot}$ \citealt{wang01}] ]; $L_{X} \sim 10^{43}$ ergs $^{-1}$ \citealt{pounds03b}] ]; $\Gamma \sim 2.38$ \citealt{miller07}] ])."693We assume that f.—1. which is characteristic of radiatively driven flows.," We assume that $f_{v} = 1$, which is characteristic of radiatively driven flows."694" Furthermore. since we wish to consider outflow features with shifts corresponding to ος<O.le. we require flow launching radii 2;2007, — hence we adopt rain=LOOr, and Unas,=150r."," Furthermore, since we wish to consider outflow features with shifts corresponding to $v_{\infty} \simgt 0.1 c$, we require flow launching radii $\simlt 200 r_g$ – hence we adopt $r_{\mbox{\scriptsize min}} = 100 r_g$ and $r_{\mbox{\scriptsize max}}695= 150 r_g$."696" Physically, 77. and ;7 should depend on the acceleration mechanism and location — however. since such properties are unknown. we adopt /7,=rin and 5=1. as appropriate for the simple case of an acceleration which occurs on the scale of the system."," Physically, $R_{v}$ and $\beta$ should depend on the acceleration mechanism and location – however, since such properties are unknown, we adopt $R_{v} = r_{\mbox{\scriptsize min}}$ and $\beta = 1$, as appropriate for the simple case of an acceleration which occurs on the scale of the system."697 It is assumed that ro[ons such that eg=0 can be adopted in the numerical simulations., It is assumed that $v_{0} \ll v_{\infty}$ such that $v_{0} = 0$ can be adopted in the numerical simulations.698" For the example model. we adopt a polar opening angle of 45 deg (i.e. d— rind. a moderate mass-loss rate QU=01M. ) and electron temperature 7=3-10"" K. The effects of varying these parameters will be discussed in Section 5.."," For the example model, we adopt a polar opening angle of 45 deg (i.e. $d = r_{\mbox{\scriptsize min}}$ ), a moderate mass-loss rate $\dot{M} = 0.1$ $_{\odot}$ $^{-1}$ ) and electron temperature $T_e = 3 \times 10^6$ K. The effects of varying these parameters will be discussed in Section \ref{sect_grid}."699 The ionization state is very important since it determines the distribution of line opacity within the outflow., The ionization state is very important since it determines the distribution of line opacity within the outflow.700 Fig., Fig.701 2. shows the computed ionization fraction of Fe K-shell ions (i.e. Fe + XXVD in the example model., \ref{fig_ion} shows the computed ionization fraction of Fe K-shell ions (i.e. Fe + ) in the example model.702 There is significant variation in the ionization state in the wind., There is significant variation in the ionization state in the wind.703 The edge of outflow closest to the rotation (2-) axis is most highly ionized since it sees unattenuated X-ray radiation rom the continuum source., The edge of outflow closest to the rotation $z$ -) axis is most highly ionized since it sees unattenuated X-ray radiation from the continuum source.704 In the outermost parts of the wind the ionization state is high and relatively uniform: although far from he X-ray source. these regions have low density which disfavours recombination.," In the outermost parts of the wind the ionization state is high and relatively uniform: although far from the X-ray source, these regions have low density which disfavours recombination."705 Across the wind. there is a significant ionization gradient since each layer progressively shields those below it from he X-ray source.," Across the wind, there is a significant ionization gradient since each layer progressively shields those below it from the X-ray source."706 The very lowest ionization material occurs near he .g-plane on the outer edge of the wind — this region has both he highest densities and the most effective shielding from the ray source., The very lowest ionization material occurs near the $xy$ -plane on the outer edge of the wind – this region has both the highest densities and the most effective shielding from the X-ray source.707 Fig., Fig.708 3 shows spectra computed for the example model., \ref{fig_spec} shows spectra computed for the example model.709 These were obtained by binning the emergent MC quanta by angle relative to the polar axis (61., These were obtained by binning the emergent MC quanta by angle relative to the polar axis $\theta$ ).710 The first eight angular bins shown each cover equal solid angle. specifically they encompass Acos@=0.1 while the ninth covers the equatorial range O«cose0.3.," The first eight angular bins shown each cover equal solid angle, specifically they encompass $\Delta \cos711\theta = 0.1$ while the ninth covers the equatorial range $0 < \cos712\theta < 0.2$."713 During the MC simulations. the number of interactions was recorded for eachquantum.," During the MC simulations, the number of interactions was recorded for eachquantum."714 This information has been used to divide the spectra into “direct” (meaning quanta which underwent no interactions) and “scattered” components (note that this includes packets that underwent number of type of physical event, This information has been used to divide the spectra into “direct” (meaning quanta which underwent no interactions) and “scattered” components (note that this includes packets that underwent number of type of physical event715Lithium abundances iu stellar atimnosplieres are key observables iu astroplivsics. eiving crucial information onu stellar evolution and mixing. stellar and Big Bane micleosvuthesis. cosnüc ray spallation. and perhaps even planet formation (e.g.222).,"Lithium abundances in stellar atmospheres are key observables in astrophysics, giving crucial information on stellar evolution and mixing, stellar and Big Bang nucleosynthesis, cosmic ray spallation, and perhaps even planet formation \citep[e.g.][]{1993PhST...47..186L, 1994A&A...288..860C, 2010Ap&SS.328..193M}."716 Such abundauces are interpreted from observations of the few Li I ines found iu stellar spectra. and to obtain accurate results. if is iuportant to account for departures from οσα] thermodynamic equilibiun (LTE) (???).. ," Such abundances are interpreted from observations of the few Li I lines found in stellar spectra, and to obtain accurate results, it is important to account for departures from local thermodynamic equilibrium (LTE) \citep{1984A&A...130..319S,1994A&A...288..860C, Lind2009}."717Reliable uodelliug of line formation iu non-LTE requires detailed snowledee of all important radiative and collisional o»ocesses on the atom of interest. Li.," Reliable modelling of line formation in non-LTE requires detailed knowledge of all important radiative and collisional processes on the atom of interest, Li."718 The collisional processes are particularly challeugiug., The collisional processes are particularly challenging.719 For mauyv wears following the pionecring study of ?.. the muportauce of inelastic hydrogen collisions was a major uncertaintw.," For many years following the pioneering study of \citet{1984A&A...130..319S}, the importance of inelastic hydrogen collisions was a major uncertainty."720 Detailed quantum scattering caleulatious of Li!UW collisions (7). ancl application to 10n-LTE modelling (?1) have allowed this question to be answered. aud it was found that direct excitations bv hydrogen collisious essentially have no influcuce.," Detailed quantum scattering calculations of Li+H collisions \citep{H+Li} and application to non-LTE modelling \citep{2003A&A...409L...1B,Lind2009} have allowed this question to be answered, and it was found that direct excitations by hydrogen collisions essentially have no influence."721 However. a related charec-exchange process Li(35)|I=Li!IL was shown to be nuportant. resulting iu differences in derived abunudanuces of about 0.05 dex im solar-metallicity stars and 0.1 dex in iuctal-poor stars.," However, a related charge-exchange process $\mathrm{Li(3s)} + \mathrm{H} \rightleftharpoons \mathrm{Li}^+ + \mathrm{H}^-$ was shown to be important, resulting in differences in derived abundances of about 0.05 dex in solar-metallicity stars and 0.1 dex in metal-poor stars."722 Moreover. it was found that the results were not scusitive to uncertainties in the data for this process.," Moreover, it was found that the results were not sensitive to uncertainties in the data for this process."723 When the rate coeffideut was altered bv factors in keeping with the expected uncertainty in the theoretical calculation. the effects ou the line formation were practically ueelieible (<0.01 dex du derived abundances).," When the rate coefficient was altered by factors in keeping with the expected uncertainty in the theoretical calculation, the effects on the line formation were practically negligible $< 0.01$ dex in derived abundances)."724 Thus. barring there being additional iportaut collisional processes on Li we are unaware of. the uncertainties regarding collisional data lic. perhaps. with the clectrou collisions.," Thus, barring there being additional important collisional processes on Li we are unaware of, the uncertainties regarding collisional data lie, perhaps, with the electron collisions."725 The question of quautifving these has only been touched wpou briefly in the past., The question of quantifying these has only been touched upon briefly in the past.726 ? made calculations exploring the sensitivity of their results fo various input parameters. mceludiug collision cross sections.," \citet{1994A&A...288..860C} made calculations exploring the sensitivity of their results to various input parameters, including collision cross sections."727 They identified the oscillator strengths of the lines of interest (6708 and GLOL AJ) and the photoionization cross sections frou 25 aud 2p as the most iuportaut atomic data in determine the uncertainties of their calculations., They identified the oscillator strengths of the lines of interest (6708 and 6104 ) and the photoionization cross sections from $2s$ and $2p$ as the most important atomic data in determining the uncertainties of their calculations.728 They estimate an οπου iu the abundance corrections of less han 0.01 dex arising frou these sources., They estimate an error in the abundance corrections of less than 0.01 dex arising from these sources.729 That the sensitivity to collisional cross sections was explored. though no discussed: explicitly iuplies even smaller uncertainties due to collisiou cross sections. mt details have not CCL oiblished.," That the sensitivity to collisional cross sections was explored, though not discussed explicitly implies even smaller uncertainties due to collision cross sections, but details have not been published."730 This study and others (e.g.77) lnake use of emupiricallv. corrected calculations bv ? aud ? for excitation iud ?/ or similar for iouization.," This study and others \citep[e.g.][]{1984A&A...130..319S, Lind2009} make use of empirically corrected calculations by \citet{1962ApJ...136..906V} and \citet{Park1971} for excitation and \citet{1976asqu.book.....A} or similar for ionization."731 (ναι the ereat astroplivsica oeuportance of Li abundances aud the considerable advauces in calculation methods for electrou scattering in the mterveniug period. in particular advanced close-coupling methods that are able to account for effects of coupling to the target contimun. we considere it worthwhile aud mucdent to accurately quantity the macertaintics associated with the electron collision data.," Given the great astrophysical importance of Li abundances and the considerable advances in calculation methods for electron scattering in the intervening period, in particular advanced close-coupling methods that are able to account for effects of coupling to the target continuum, we considered it worthwhile and prudent to accurately quantify the uncertainties associated with the electron collision data."732 Iu this paper we examine the electron collision data in the literature. aud perform a new Ranatrix calculation. ia order to accurately estimate the uncertaimties in such calculations.," In this paper we examine the electron collision data in the literature, and perform a new $R$ -matrix calculation, in order to accurately estimate the uncertainties in such calculations."733 The data are then used in non-LTE Li I line formation uodelling to assess the resulting uncertainties in stellar Li abundances., The data are then used in non-LTE Li I line formation modelling to assess the resulting uncertainties in stellar Li abundances.734 Iu this section we examine the existing data for excitation and ionization bv electron nupact used iu non-LTEÉ calculations., In this section we examine the existing data for excitation and ionization by electron impact used in non-LTE calculations.735 We compare with advanced close-coupling calculations including our owl. calculations for the excitation processes and prescut the details., We compare with advanced close-coupling calculations including our own calculations for the excitation processes and present the details.736 There are a umber of existing calculations for clectron-iupact excitation Lifal)|«>Lic)6c. though ouly relatively receutlv have there been anv large-scale calculations inchiding a sienificant αν of excited states.," There are a number of existing calculations for electron-impact excitation $\mathrm{Li}(nl) + e \rightarrow \mathrm{Li}(n^\prime l^\prime) + e$, though only relatively recently have there been any large-scale calculations including a significant number of excited states."737 Two advanced close-coupling methods have been used. namely convergent close-coupling (CCC. 73) aud Π- ," Two advanced close-coupling methods have been used, namely convergent close-coupling (CCC, \citealt{PhysRevA.46.6995}) ) and $R$ "738Other asviumetries. especially departures from a dominant axis of svmuuetry could be intrinsic to the explosion process.,"Other asymmetries, especially departures from a dominant axis of symmetry could be intrinsic to the explosion process."739 The departures from the dominant axis could come from hunps of Ni that produce irregularities in the excitation., The departures from the dominant axis could come from lumps of $^{56}$ Ni that produce irregularities in the excitation.740 These. in turn. would be clues to the nature of the thermonuclear burning (hat drives the explosion.," These, in turn, would be clues to the nature of the thermonuclear burning that drives the explosion."741 Within the class οἱ Mey models. it is believed that the explosion is triggered by compressional heating near the WD center. and that the burning front starts as a subsonic cleflagration.," Within the class of $M_{Ch}$ models, it is believed that the explosion is triggered by compressional heating near the WD center, and that the burning front starts as a subsonic deflagration."742 The time evolution of the burning front is still an open question., The time evolution of the burning front is still an open question.743 The issue is whether the deflagration lront burns through the entire WD (Nomoto.Thielemann.&Yokoi1984) or makes a transition into a supersonic detonation mode. as suggested in the celaved detonation (DD) model (IXhokhlov1991:Yamaokaetal.1992).," The issue is whether the deflagration front burns through the entire WD \citep{NTY:1984} or makes a transition into a supersonic detonation mode, as suggested in the delayed detonation (DD) model \citep{Khokhlov:1991,Yamaoka:1992}."744". DD models have been found to reproduce the optical and infrared light curves and spectra of ""typical? SNe la reasonably well (Hótlich.|1995b:IxXhokhlov1996:Nugentetal.1997:Wheeler1993:Lentz 2001)."," DD models have been found to reproduce the optical and infrared light curves and spectra of “typical"" SNe Ia reasonably well \citep{Hoeflich:94D, HofKho:1996, Nugent:1997, Wheeler:IR,Lentz:2001}."745. The propagation of a detonation front is well understood (Gamezo.Wheeler.Khokhlov.1999:Sharpe 2001).. but the description of the deflaeration front aud the deflagration to detonation transition (DDT) pose problems.," The propagation of a detonation front is well understood \citep{Gamezo:1999,Sharpe:2001}, but the description of the deflagration front and the deflagration to detonation transition (DDT) pose problems."746 Significant progress has been made toward a better understanding of the plvsics of thermonuclear flames., Significant progress has been made toward a better understanding of the physics of thermonuclear flames.747 The front has been found to be Ravleigh-Tavlor (RT) unstable. increasing the effective speed of the burning front. (Nomoto et al.," The front has been found to be Rayleigh-Taylor (RT) unstable, increasing the effective speed of the burning front (Nomoto et al."748 1976) ancl also. perhaps. imposing density imregularities (plumes) on the structure that could be reflected in the polarimetry.," 1976) and also, perhaps, imposing density irregularities (plumes) on the structure that could be reflected in the polarimetry."749 Starting from static WDs. hydrodynamic ealeulations of the deflagration[routs have been performed in 2-D (Reinecke.Hillebraudt.&Niemever1999) and 3-D (Livne1995. 2002).," Starting from static WDs, hydrodynamic calculations of the deflagrationfronts have been performed in 2-D \citep{Reinecke:1999} and 3-D \citep{Livne:1993, Khokhlov:1995, Khokhlov:2002}."750. RT instabiliies govern the morphology of the burning front and the effective burning speed is verv sensitive to the energy release by (he [uel. aud therefore to the local C/O ratio (IXhokhlov.2002).," RT instabilities govern the morphology of the burning front and the effective burning speed is very sensitive to the energy release by the fuel, and therefore to the local C/O ratio \citep{Khokhlov:2002}."751. Therefore. the actual flame propagation will depend on the detailed chemical structure of the progenitor.," Therefore, the actual flame propagation will depend on the detailed chemical structure of the progenitor."752 Three-dimensional models (IxXhokhlov2002) sugeest (hat plumes of burned matter are [frozen out in the expansion., Three-dimensional models \citep{Khokhlov:2002} suggest that plumes of burned matter are frozen out in the expansion.753 These plumes. rich in Ni. could be the source of dispersion around any dominant polarization axis.," These plumes, rich in $^{56}$ Ni, could be the source of dispersion around any dominant polarization axis."754 On the other hand. optical and IB. data on the sub-Iuminous. but significantly polarized SN 1900ν (Ilowelletal.2001).. seem to be at odds with these models of the deflagration phase that predict signilicant mixing of the inner lavers of the WD prior to detonation.," On the other hand, optical and IR data on the sub-luminous, but significantly polarized SN 1999by \citep{Howell:99by}, seem to be at odds with these models of the deflagration phase that predict significant mixing of the inner layers of the WD prior to detonation."755 Whether this confliet exists for normally bright SN Ia remains to be seen., Whether this conflict exists for normally bright SN Ia remains to be seen.756 The transition to detonation is thought to occur earlier in normallv-bright events. giving less time for the RT structure to develop.," The transition to detonation is thought to occur earlier in normally-bright events, giving less time for the RT structure to develop."757 This might allow clumps of °°Ni to develop that could. drive the dispersion in polarization vectors without causing intolerably large distortions of the fIux spectrum., This might allow clumps of $^{56}$ Ni to develop that could drive the dispersion in polarization vectors without causing intolerably large distortions of the flux spectrum.758 Pre-conditioning of the WD may alfect the nature of both normal ancl subluminous 5Ne Ia. Such pre-conditioning may involve (he main sequence mass and metallicitv of the progenitor WD (Dominguezetal.2001:Llóflich.19983:Iwamoto 1999).. the," Pre-conditioning of the WD may affect the nature of both normal and subluminous SNe Ia. Such pre-conditioning may involve the main sequence mass and metallicity of the progenitor WD \citep{Dominguez:2001,Hoeflich:1998, Iwamoto:1999}, , the"759From this comparison we can salely conclude. that hree (out of four) of the sub-populations along the LB of GC 2808 can be identified as the progeny ofthree distinct stellar populations with different initial helium abundances in the range Y—0.24 0.40.,From this comparison we can safely conclude that three (out of four) of the sub-populations along the HB of NGC 2808 can be identified as the progeny of three distinct stellar populations with different initial helium abundances in the range $Y=0.24$ –0.40.760 The specific values used (Y 248. 0.30. O40) were set bv the model data base. and we have not attempted to determine. values of Y which rest fit the data.," The specific values used $Y=0.248$ , 0.30, 0.40) were set by the model data base, and we have not attempted to determine values of $Y$ which best fit the data."761 The adopted: values are consistent. with what found from the photometry of the ALS (Picotto ct al., The adopted values are consistent with what found from the photometry of the MS (Piotto et al.762 2007)., 2007).763 This conclusion is independent of any assumption about the mass-LIoss cllicieney of their RGB progenitors., This conclusion is independent of any assumption about the mass-loss efficiency of their RGB progenitors.764 Our findings are also in agreement with He abundances reported on the basis of different indicators along the ID (like cilference in colour or Z;45) by DBragaglia et al. (, Our findings are also in agreement with He abundances reported on the basis of different indicators along the RGB (like difference in colour or $T_{\rm eff}$ ) by Bragaglia et al. (7652010).,2010).766 The consistency with these results also justifies our choice. (in principle arbitrary) to fix the distance (and extinction) bv matching the 3=0.248 LB population to the RILB., The consistency with these results also justifies our choice (in principle arbitrary) to fix the distance (and extinction) by matching the $Y=0.248$ HB population to the RHB.767" Had we tried to match these ""normal-He models to. e.g. the BUB population. it would have been impossible then to match the RUB stars with models with any reasonable value of Y."," Had we tried to match these “normal-He” models to, e.g. the BHB population, it would have been impossible then to match the RHB stars with models with any reasonable value of $Y$."768 As a second step of our analysis. we determined. the mean mass of the BIID and ELD sub-populations. bw producing svnthetic LBs in the same way as described before. and matching the mode of both the Ευ and the (mirlsu mansus) distributions.," As a second step of our analysis, we determined the mean mass of the BHB and EHB sub-populations, by producing synthetic HBs in the same way as described before, and matching the mode of both the $m_{F336W}$ and the $m_{F160BW}-m_{F555W}$ ) distributions."769 The svnthetic sample compared to the 11112 component has been calculated: using the 3—0.30 LED tracks. while for the ELLB we emploved the )=0.0 tracks. including the cllect of levitation in both cases.," The synthetic sample compared to the BHB component has been calculated using the $Y=0.30$ HB tracks, while for the EHB we employed the $Y=0.40$ tracks, including the effect of levitation in both cases."770 Figure 9 compares the observed. (shaded. histogram) and theoretical (solid histogram) star counts as a function oÉ massa and the (nein mess) for the BIB and he bluce ENB component.," Figure \ref{teo6}771 compares the observed (shaded histogram) and theoretical (solid histogram) star counts as a function of $m_{F336W}$ and the $m_{F160BW}-m_{F555W}$ ) for the BHB and the bluer EHB component."772 An indirect estimate of mass-loss experienced by each sub-population can then be obtained by comparing the mean mass on the LLB and the mass at the TO (lor an age of GGwvr)., An indirect estimate of mass-loss experienced by each sub-population can then be obtained by comparing the mean mass on the HB and the mass at the TO (for an age of Gyr).773 A summary of the values obtained or RUB. BUB and. EMLB sub-populations is reported. in ‘Table 1.," A summary of the values obtained for RHB, BHB and EHB sub-populations is reported in Table 1."774 Under these assumptions we found a mean amount of ROB mass-loss ranging from (AAI)=0.15 for both the UID and ΤΗ stars. to £NÀZ?=0.20 for the ELLB stars.," Under these assumptions we found a mean amount of RGB mass-loss ranging from $\langle \Delta M \rangle=0.15$ for both the RHB and EHB stars, to $\langle \Delta M \rangle=0.20$ for the EHB stars."775" Finally. in order to verify whether the RIED. BIHID and EMB populations are the progeny of the red. mean and que. MS. respectively, we have compared the star counts iong the LIB. with those reported. by Piotto ct al. ("," Finally, in order to verify whether the RHB, BHB and EHB populations are the progeny of the red, mean and blue MS, respectively, we have compared the star counts along the HB, with those reported by Piotto et al. ("7762007) iong the MS.,2007) along the MS.777 In our sample we found: (NeaΑΗων= 1.10.1. and (NeuesNene).=3-940.7.," In our sample we found: $(N_{\rm778RHB}/N_{\rm BHB})_{\rm obs}=1.1 \pm 0.1$ , and $(N_{\rm RHB}/N_{\rm779EHB})_{\rm obs}=3.9 \pm 0.7$."780 Starting [rom the (served ALS number counts. and after applying corrections accounting for the cdillerent evolutionary Lifetimes along he ROB and among the WB populations (i.e. how the ifetime varies as a function of Y and mass) the expected number of stars along the LIB would be: (ΑπΑΗων=3.7QT£04 and GNnun/NEenun)oso=3.3EEdE0.5.," Starting from the observed MS number counts, and after applying corrections accounting for the different evolutionary lifetimes along the RGB and among the HB populations (i.e., how the lifetime varies as a function of $Y$ and mass) the expected number of stars along the HB would be: $(N_{\rm RHB}/N_{\rm BHB})_{\rm exp}= 3.7781\pm 0.4$ and $(N_{\rm RHB}/N_{\rm EHB})_{\rm exp}=3.3 \pm 0.5$."782 Clearly. while he two values of (Δημου/Nene) are compatible. it is not possible to reconcile the observed and the expected values of (ΑμήνΑρης).," Clearly, while the two values of $(N_{\rm RHB}/N_{\rm EHB})$ are compatible, it is not possible to reconcile the observed and the expected values of $(N_{\rm RHB}/N_{\rm BHB})$."783 Phe ACS cata usec by Piotto et al. (, The ACS data used by Piotto et al. (7842007) are stronely oll-centred. (re~ 200%) with respect ο Cow.,2007) are strongly off-centred $r \sim 200\arcsec$ ) with respect to $C_{\rm grav}$.785 As shown by 109. the ratio Nnan/Npap roughly doubles for r>907.," As shown by I09, the ratio $N_{\rm786RHB}/N_{\rm BHB}$ roughly doubles for $r>90\arcsec$."787" ""Phis may be a possible explanation Lor he observed. discrepancy.", This may be a possible explanation for the observed discrepancy.788 However the progenitor masscs or RIB ancl BUB are respectively 0.847. and 0.76AL. (sce Table 1).," However the progenitor masses for RHB and BHB are respectively $0.84\,M_\odot$ and $0.76\,M_\odot$ (see Table 1)."789 Dynamical evolution of the cluster. should cause the μηνNea to decrease as rr increases. just the opposite of what was found by 109.," Dynamical evolution of the cluster should cause the $N_{\rm RHB}/N_{\rm BHB}$ to decrease as $r$ increases, just the opposite of what was found by I09."790 A more detailed: stuck: of racial variations in LB sub-populations extending over the full cluster could. be illuminating., A more detailed study of radial variations in HB sub-populations extending over the full cluster could be illuminating.791 I0 would also be quite interesting to check whether the triple MS varies with position in the cluster., It would also be quite interesting to check whether the triple MS varies with position in the cluster.792 The CMDs in Figs., The CMDs in Figs.793 7 and S show verv clearly that DIIK stars are not reproduced. by any of the theoretical models. this sub-population is systematically hotter than he hottest. point along the ΛΙΝ.," \ref{teo4} and \ref{teo5} show very clearly that BHk stars are not reproduced by any of the theoretical models, this sub-population is systematically hotter than the hottest point along the ZAHBs."794 To shed more light on he nature of these stars. in Fig.," To shed more light on the nature of these stars, in Fig."795 LO we compare the observed number count distributions for the BILk sub-population in he FIGOBIW. P336W and £555M magnitudes. with a svnthetie sample with Yo—0.40. a mean mass CMgp?=461M. (ie. the minimum possible mass of LLB objects or our models at this metallicity) and zero dispersion.," \ref{teo7} we compare the observed number count distributions for the BHk sub-population in the $F160BW$, $F336W$ and $F555W$ magnitudes, with a synthetic sample with $Y=0.40$, a mean mass $\langle M_{\rm HB} \rangle=0.461 M_{\odot}$ (i.e. the minimum possible mass of HB objects for our models at this metallicity) and zero dispersion."796 Lt is impossible to match the observed. distributions in all three ilters., It is impossible to match the observed distributions in all three filters.797 This inability of LB models. to. reproduce the BILk »opulation suggests that these are not genuine LED stars. and it leads us to identify these objects as hot-IEashers (1)Cruz et al.," This inability of HB models to reproduce the BHk population suggests that these are not genuine HB stars, and it leads us to identify these objects as hot-flashers (D'Cruz et al."798 1996: Brown ct al., 1996; Brown et al.799 2001. 2010: Cassisi ct al.," 2001, 2010; Cassisi et al."800 2003: Moehler οἱ al., 2003; Moehler et al.801 2004)., 2004).802 Llot-flashers are stars that. experience strong mass-loss during the RGB phase. leave the branch. before the occurrence of the Le-lash. and move quickly to the Lle-core white chart cooling curve. where they experience a He-IDash under conditions of strong electron degeneracy in their core.," Hot-flashers are stars that experience strong mass-loss during the RGB phase, leave the branch before the occurrence of the He-flash, and move quickly to the He-core white dwarf cooling curve, where they experience a He-flash under conditions of strong electron degeneracy in their core."803 ‘This scenario was envisaged earlier by Castellani, This scenario was envisaged earlier by Castellani804that the Scalo IMP is not suitable for these galaxies (6.8. Afatteucci Cübson. 1995).,"that the Scalo IMF is not suitable for these galaxies (e.g. Matteucci Gibson, 1995)."805 Table 6 shows the results of the model I (Salpeter IME). whereas Table 7 shows the results of the mocel II (x20.95 IME).," Table 6 shows the results of the model I (Salpeter IMF), whereas Table 7 shows the results of the model II (x=0.95 IMF)."806 These models have been computed by assuming the same à and the same wv as for the Milk Wavy., These models have been computed by assuming the same $\alpha$ and the same $n$ as for the Milky Way.807 Iu particular. iu the first column we report the initial ealactic huninous mass. in the second column the nova rate dn units of vr lin CoL," In particular, in the first column we report the initial galactic luminous mass, in the second column the nova rate in units of $\rm yr^{-1}$, in Col."808 3 the bhuninositv specific nova rate. in Col.," 3 the luminosity specific nova rate, in Col."809 { the SN Ia rate in units of (1007).! id iu Col., 4 the SN Ia rate in units of $\rm (100yr)^{-1}$ and in Col.810" 5 and 6 the SN Ia rate in units of οΑρ and οαν. respectively,"," 5 and 6 the SN Ia rate in units of $SNu_B$ and $SNu_K$, respectively."811 The predicted lova rates are quite large for massive ellipticals rangingo between 300 and 1000 nova vr which is about a factor 3-10 larger than it is derived from observations., The predicted nova rates are quite large for massive ellipticals ranging between 300 and 1000 nova $\rm yr^{-1}$ which is about a factor 3-10 larger than it is derived from observations.812 If these values were realistic. the discrepancy could be partially due to ui observational bias affecting the ground based nova survevs due to poor spatial resolution aud bright limutine magnitude.," If these values were realistic, the discrepancy could be partially due to an observational bias affecting the ground based nova surveys due to poor spatial resolution and bright limiting magnitude."813 An indication in this direction comes from the nova rate of ALS? recently provided by Shara Zurck (2002) ou the basis of IST archive images. which is a factor 23 larger than previous ground-based estimates (sco Table 1).," An indication in this direction comes from the nova rate of M87 recently provided by Shara Zurek (2002) on the basis of HST archive images, which is a factor 2–3 larger than previous ground-based estimates (see Table 1)."814 Another οκτν is that in carly type ealaxies the recurrence time between two cousecutive nova explosions is considerably longer than in late spirals as a consequence of the different stellar population frou which novae originate., Another possibility is that in early type galaxies the recurrence time between two consecutive nova explosions is considerably longer than in late spirals as a consequence of the different stellar population from which novae originate.815 This sugecstionOO is supported both w observational aud theoretical erounds., This suggestion is supported both by observational and theoretical grounds.816 Frou oue side Ducrbeck (1990) and Della Valle et al. (, From one side Duerbeck (1990) and Della Valle et al. (817"1992. 1991) have denionstrated. on the basis of galactic and extragalactic ji0vaà observations. the existeuce of two populations of rovac: fast and bright novae belonging to ""disk stellar sopulation aud slow aud faint novae which originate roni a ""bulge stellar population.","1992, 1994) have demonstrated, on the basis of galactic and extragalactic nova observations, the existence of two populations of novae: fast and bright novae belonging to `disk' stellar population and slow and faint novae which originate from a `bulge' stellar population."818 In particular. the latter authors (see also Della Valle Livio 1998) sugeestecOO that nlee novae could originate from relatively light WDs. ikelv in the range of masses of pp)x09M.. while rovace iu the disk axise frou massive WDs (fib;— 1.4...," In particular, the latter authors (see also Della Valle Livio 1998) suggested that bulge novae could originate from relatively light WDs, likely in the range of masses of $\langle M_{WD}819\rangle \leq 0.9M_\odot$ while novae in the disk arise from massive WDs $\langle M_{WD}820\rangle \geq 1 M_\odot$ )."821 From the other side. Truran (1990. sce also Bitter et al.," From the other side, Truran (1990, see also Ritter et al."822 1991) has found that the mass of the WD and he recurrence tiue between the outbursts are inversely xoportioual., 1991) has found that the mass of the WD and the recurrence time between the outbursts are inversely proportional.823" Ta order to match the ‘theoretical’ with ""ορσα. rates, one needs to lower either a or n or th."," In order to match the `theoretical' with `empirical' rates, one needs to lower either $\alpha$ or $n$ or both."824" For example for M87 the match between predicted and observed rates can be achieved by increasing the recurrence time between two consecutive outhursts. to T,~3l5105 va."," For example for M87 the match between predicted and observed rates can be achieved by increasing the recurrence time between two consecutive outbursts, to $T_r\sim 3-1\cdot 10^5$ yr."825" This is about 103 times larger than assunued for novae m the ""disk of the Galaxy.", This is about 10–3 times larger than assumed for novae in the `disk' of the Galaxy.826 Iu this wax. both the predictions of models I aud IL for a luminous mass in the range 1-6 101537. axe in very eood agreement with the preliminary new estimate fron Shara Zurek (2002) of the nova rate for M8ST.," In this way, both the predictions of models I and II, for a luminous mass in the range 4-6 $\cdot 10^{11}M_{\odot}$ are in very good agreement with the preliminary new estimate from Shara Zurek (2002) of the nova rate for M87."827" In fact. AINT cau be modeled both as an elliptical galaxy with huninous mass ~[5108AL. and Rej;—6 kpe or with huninous mass ~6-101.AZ, and 44~ 7 kpe (Colin Ryzhov 1997)."," In fact, M87 can be modeled both as an elliptical galaxy with luminous mass $\sim 4\cdot 10^{11}~M_{\odot}$ and $R_{eff}\sim 6$ kpc or with luminous mass $\sim 6\cdot 10^{11}~M_{\odot}$ and $828R_{eff}\sim$ 7 kpc (Cohen Ryzhov 1997)."829 The predictions of these two models do, The predictions of these two models do830"1990111: where Al is the minimum halo mass of the LBCGs under consideration. &—LAS|aR WV,=WALA). and V(Αη) is the 4/7same asj in equation 3...",": where $M$ is the minimum halo mass of the LBGs under consideration, $k=\sqrt{k_x^2+k_y^2+k_w^2}$, $W_{xy}=W(k_x)\,W(k_y)$, and $W(k_i)$ is the same as in equation \ref{eq:window}."831 The power measured in the simulation. however. includes an additional. scale-independent component from Poisson noise.," The power measured in the simulation, however, includes an additional, scale-independent component from Poisson noise."832" This. too. can be caleulated analytically as and subtracted olf. ο is the ST halo mass function of LAL hosts with mass greater than Al and llere. e. can be any length scale and. represents the depth of the skewer for which στ=§N(»Al))n>AL)ase,nus is the Poisson variance in the number of LAEs."," This, too, can be calculated analytically as and subtracted off, where $\bar{n}(>M)$ is the ST halo mass function of LAE hosts with mass greater than $M$ and Here, $a_z$ can be any length scale and represents the depth of the skewer for which $\sigma^2_P=\left<N\left(>M\right)\right>=\bar{n}\left(>M\right)\,a_x\,a_y\,a_w$ is the Poisson variance in the number of LAEs."833 Since. Ota)xLfaw. and so PippoissonfAl) is approximately independent of αμ. as expected.," Since, $Q(a_w)\propto1/a_w$, and so $P_{\rm 1D,Poisson}(M)$ is approximately independent of $a_w$, as expected."834 From equation 5.. we can see that the LD power spectrum at a given scale is a complicated convolution of shorter wavelength modes with the window function.," From equation \ref{eq:power1D}, we can see that the 1D power spectrum at a given scale is a complicated convolution of shorter wavelength modes with the window function."835 This integration washes out anv features. that may have existed at. small scales., This integration washes out any features that may have existed at small scales.836 Thus. we expect the 1D spectrum to be relatively featureless and smooth.," Thus, we expect the 1D spectrum to be relatively featureless and smooth."837 We analyze the power spectrum for as many skewers through our simulation box that can be packed. into the 143Mpc size. 177 and 15? for >=6 and 2=10. respectively. before rotating the box to anew orientation and collecting additional sets of skewers.," We analyze the power spectrum for as many skewers through our simulation box that can be packed into the $143\,\mpc$ size, $17^2$ and $15^2$ for $z=6$ and $z=10$, respectively, before rotating the box to a new orientation and collecting additional sets of skewers."838 As in 8€?77.. this scheme is cquivalent to choosing an infinite number of skewers cach placed: randomly on the face of the simulation box.," As in \ref{sec:pdist}, this scheme is equivalent to choosing an infinite number of skewers each placed randomly on the face of the simulation box."839 The argument also applies to additional skewers gained through rotation of the simulation volume., The argument also applies to additional skewers gained through rotation of the simulation volume.840 Figures 5. and 6 compare analytic ancl simulation calculations of the 1D power spectrum and bias after cosmic reionization is assumed to be completed ἐς= 6) and in its carly stages at 2=10. respectively.," Figures \ref{fig:bias1D_z6} and \ref{fig:bias1D_z10} compare analytic and simulation calculations of the 1D power spectrum and bias after cosmic reionization is assumed to be completed $z=6$ ) and in its early stages at $z=10$, respectively."841" In. both figures. the black (blue) lines represent values for à minimum o luminosity of Lp,aas=101(10)erg8 corresponding to Mya,=16Q'(G4«107)AJ. at c=6 and Maasm82504107/022107) at z=10."," In both figures, the black (blue) lines represent values for a minimum $\alpha$ luminosity of $L_{\rm L\!\alpha,min}=10^{40}\,(10^{41})\,\rm{ergs/s}$ corresponding to $M_{\rm halo}=1.6\times10^9\,(6.4\times10^9)\,\msun$ at $z=6$ and $M_{\rm halo}=8.2\times10^8\,(3.2\times10^9)\,\msun$ at $z=10$."842 While LAEs are currently. detected to approximatelyA. this luminosity at >=6. future surveys should be able to probe down to the same luminosity at 2=10.," While LAEs are currently detected to approximately this luminosity at $z=6$, future surveys should be able to probe down to the same luminosity at $z=10$."843 Solid lines show the average log of the Poisson subtracted power spectrum (represented. as Nip(h)—k Pupils) measured from 35177 and 31572 skewers for z=6 and z=LO. respectively.," Solid lines show the average log of the Poisson subtracted power spectrum (represented as $\Delta^2_{\rm 1D}(k)=k\,P_{\rm 1D}(k)/\pi$ ) measured from $3\times17^2$ and $3\times15^2$ skewers for $z=6$ and $z=10$, respectively."844 The factor of 53 comes from additional independent. skewers we obtained from rotating the simulation box., The factor of $3$ comes from additional independent skewers we obtained from rotating the simulation box.845 Lone-dashed lines indicate the estimated 1.0 variation in the log of the amplitude of the power spectrum from skewer-to-skewer., Long-dashed lines indicate the estimated $1-\sigma$ variation in the log of the amplitude of the power spectrum from skewer-to-skewer.846 For clarity. these lines are only shown for αμα10!ores/s. but they are about the same size for {ΠινLoaouin=1l . ⋅ ⋅ ↓∪⋖⋅↓⋅⋏∙≟⊳∖⊳∖⊳⇀∖⊔⋖⊾⊳∖↿↓," For clarity, these lines are only shown for $L_{\rm L\,\alpha,min}=10^{40}\,\rm{ergs/s}$, but they are about the same size for $L_{\rm L\,\alpha,min}=10^{41}\,\rm{ergs/s}$."847⊔↓⋜⋯⋅∪⇂⇂↓↥⋖⊾↓≻∪∖∖⋎⋖⋅↓⋅⇂↓⋅∪⊔↓⋜↧ single skewer will fall within the 10 bounds 68 percent of the time., An estimate of the power from a single skewer will fall within the $1-\sigma$ bounds $68$ percent of the time.848 The standard deviation of the log of the power is approximately the same for all redshift ancl luminosity threshold. combinations we considered. with σ=0.4: it is also approximately independent. of scale., The standard deviation of the log of the power is approximately the same for all redshift and luminosity threshold combinations we considered with $\sigma\approx0.4$; it is also approximately independent of scale.849" Phe precision to which one is able to recover the true mean power spectrum is given by the standard error: σι,=σενNSuuuou.", The precision to which one is able to recover the true mean power spectrum is given by the standard error: $\sigma_e=\sigma/\sqrt{N_{skewers}}$.850 assuming that our estimate of the standard. deviation is close to the true value and given our number of independent skewers. we were able to estimate the mean of the log of the power to within a.zz0.02.," Assuming that our estimate of the standard deviation is close to the true value and given our number of independent skewers, we were able to estimate the mean of the log of the power to within $\sigma_e\approx0.02$ ."851 The level of error in measuring the power informs whether the 1D power contains suflicient information to distinguish between galaxies οἱ dillerent— masses ancl luminosities., The level of error in measuring the power informs whether the 1D power contains sufficient information to distinguish between galaxies of different masses and luminosities.852" This cdilferentiability dis. important in constraining the mass-Iuminosity. relationship anc happens when the standard: errors for cach power spectrum. using Nokewers independent. fields-of-view (in this case all having climensions.: of⋅⋅∕⋅∕ 3.43.49 are small enough that rev don't overlap:rlam: Ίμῃprao|—=(Grai|a0)/ENGYates. Where. yr andκ a, are the mean— and standard. deviations of the log of he power for the luminosity thresholds corresponding to Lpsauin=dO""ergs/s."," This differentiability is important in constraining the mass-luminosity relationship and happens when the standard errors for each power spectrum using $N_{\rm skewers}$ independent fields-of-view (in this case all having dimensions of $3.4'\times3.4'$ ) are small enough that they don't overlap: $\left|\mu_{41}-\mu_{40}\right|=(\sigma_{41}+\sigma_{40})/\sqrt{N_{\rm skewers}}$, where $\mu_x$ and $\sigma_x$ are the mean and standard deviations of the log of the power for the luminosity thresholds corresponding to $L_{\rm L\,\alpha,min}=10^x \rm{ergs/s}$."853 On the largest scales probed. the mean of the log of the power differs by =0.23 for both redshifts (with a weak scale dependence) and (648ayy0.," On the largest scales probed, the mean of the log of the power differs by $\approx0.23$ for both redshifts (with a weak scale dependence) and $\sigma_{41}\approx\sigma_{40}\approx0.4$."854 ‘Thus. approximately 12 independent skewers are needed to distinguish between the two luminosity thresholds based on heir LD power spectrum.," Thus, approximately 12 independent skewers are needed to distinguish between the two luminosity thresholds based on their 1D power spectrum."855 The short-dashed green. (red) line shows the analytic power-spectrum according το linear perturbation theory. with the same luminosity threshold as the black (blue) line.," The short-dashed green (red) line shows the analytic power-spectrum according to linear perturbation theory, with the same luminosity threshold as the black (blue) line."856 With no fit other than the calculations described above. the analytic predictions match the data from the simulations quite well on the largest scales.," With no fit other than the calculations described above, the analytic predictions match the data from the simulations quite well on the largest scales."857 As soon as nonlincaritics dominate on small scales. the simulation results and. the analviie caleulations diverge in their predictions.," As soon as nonlinearities dominate on small scales, the simulation results and the analytic calculations diverge in their predictions."858 However. it is important to note that the nonlinearities at work are on even smaller scales than the deviation scale due to aliasing.," However, it is important to note that the nonlinearities at work are on even smaller scales than the deviation scale due to aliasing."859 In the bottom panels of Figures 5. and 6.. we show the halo bias. measured from the simulation (solid lines) and compare the results to the analytic ST. caleulation (short-dashed lines).," In the bottom panels of Figures \ref{fig:bias1D_z6} and \ref{fig:bias1D_z10}, we show the halo bias, measured from the simulation (solid lines) and compare the results to the analytic ST calculation (short-dashed lines)."860" Here, PEARY is Che linear analytic ealeulation of the 1D dark matter power from equation (5)) with bap(Al)=1."," Here, $P^{\rm analytic}_{\rm 1D,dm}$ is the linear, analytic calculation of the 1D dark matter power from equation \ref{eq:power1D}) ) with $b_{\rm eff}(M)=1$."861 These plots show the same trend. as in the upper panels with increasing civergence between simulation ancl analytic calculations on small scales., These plots show the same trend as in the upper panels with increasing divergence between simulation and analytic calculations on small scales.862" ""This is precisely the result obtained from the full three-cimensional power by Trac&Con (2007).", This is precisely the result obtained from the full three-dimensional power by \citet{TC07}.863. However. note that the linear and. nonlinear values do not match up exactly for Luauiaottcres/s al 2=6.," However, note that the linear and nonlinear values do not match up exactly for $L_{\rm L\,\alpha,min}=10^{41}\,\rm{ergs/s}$ at $z=6$."864 The ST mass function is not a perfect fit over al masses and so it results in a slight deviation in the derivec bias., The ST mass function is not a perfect fit over all masses and so it results in a slight deviation in the derived bias.865 This elfect also manifests itself in the upper panel as à small deviation on large scales between the simulation anc analytic power for the same luminosity and recishift., This effect also manifests itself in the upper panel as a small deviation on large scales between the simulation and analytic power for the same luminosity and redshift.866 A striking aspect of the LD power spectrum illustrate in the top panels is that. for the 3.40.3.4. field-ol-view. it remainsrelatively [lat and. featureless over a range of A-valucs spanning an orcer-ol-magnitude or more.," A striking aspect of the 1D power spectrum illustrated in the top panels is that, for the $3.4'\times3.4'$ field-of-view, it remainsrelatively flat and featureless over a range of $k$ -values spanning an order-of-magnitude or more."867 This smoothness is expected since both the aliasing of small-scale, This smoothness is expected since both the aliasing of small-scale868The gravitational potential of a planet can be expanded in a Fourier series in azinmthal angle € and time /.,The gravitational potential of a planet can be expanded in a Fourier series in azimuthal angle $\theta$ and time $t$.869" Each term of this series is proportional to cospin(—O;,,1)] and has a radius dependent amplitude 6;,,(r)."," Each term of this series is proportional to $\cos[m(\theta-\Omega_{l,m}t)]$ and has a radius dependent amplitude $\phi_{l,m}(r)$ ."870" The mean motion Q,A is (he unique pattern speed for a planet with a circular orbit.", The mean motion $\Omega_p$ is the unique pattern speed for a planet with a circular orbit.871" From here on. subscripts p and d will denote planet ancl disk. respectively,"," From here on, subscripts $p$ and $d$ will denote planet and disk, respectively."872" Pattern. speeds for a planet which moves on an eccentric orbit may contain harmonics of the epicvclie frequency 5, and are denoted by 0,,,=Q,+0—mjr,,/im."," Pattern speeds for a planet which moves on an eccentric orbit may contain harmonics of the epicyclic frequency $\kappa_p$ and are denoted by $\Omega_{l,m}=\Omega_p + (l-m)\kappa_p/m$."873" To first order in eccentricity ορ. each value of mcontributes three components. a principal one with pattern speed Oy,=Qp whose amplitude 0, is independent of ej. and two first order components wilh pattern Er,/im whose amplitudes 6,,24,, ave proportional to e."" Two kinds of resonance are associated with each potential component."," To first order in eccentricity $e_p$, each value of $m$contributes three components, a principal one with pattern speed $\Omega_{m,m}=\Omega_p$ whose amplitude $\phi_{m,m}$ is independent of $e_p$, and two first order components with pattern $\Omega_{m\pm 1,m}=\Omega_p \pm \kappa_p/m$ whose amplitudes $\phi_{m\pm 1,m}$ are proportional to $e_p$ Two kinds of resonance are associated with each potential component."874" Corotation resonances occur where the pattern speed matches the angular velocitw of the disk material. Op,=Ou."," Corotation resonances occur where the pattern speed matches the angular velocity of the disk material, $\Omega_{l,m}=\Omega_d$."875 A disk particle located at a corotation resonance experiences a constant torcque which causes the radius of its orbit to change but does not excite its epievclie motion., A disk particle located at a corotation resonance experiences a constant torque which causes the radius of its orbit to change but does not excite its epicyclic motion.876" Lindblad resonances occur where the disks angular velocity differs from the pattern speed such that (0,—QO7,,)=ery."," Lindblad resonances occur where the disk's angular velocity differs from the pattern speed such that $m(\Omega_d-\Omega_{l,m})=\pm\kappa_d$."877 The two Lindblad resonances associated wilh each potential component are distinguished by the adjectives inner and outer and are often denoted as {1 and OLR., The two Lindblad resonances associated with each potential component are distinguished by the adjectives inner and outer and are often denoted as $ILR$ and $OLR$.878 A disk particle located at a Lindblad resonance is subject to radial and azimuthal perturbation forces which vary at its epicvelic Ireeuency., A disk particle located at a Lindblad resonance is subject to radial and azimuthal perturbation forces which vary at its epicyclic frequency.879 These excite its epicvelic motion and also change its semimajor axis., These excite its epicyclic motion and also change its semimajor axis.880" Each m has nine resonances associated with it: three potential components ó,,,, and Oy24,5 0M {του resonances for each potential component."," Each $m$ has nine resonances associated with it: three potential components $\phi_{m,m}$ and $\phi_{m\pm 1,m}$, and three resonances for each potential component."881 Table 3. describes some properties of these resonances., Table \ref{t:afterglow} describes some properties of these resonances.882" Each potential component is constant in aflame rotating with its pattern speed ης. so ils perturbations of the disk's angular momentum Z/,; and energy. Ly must preserve the"," Each potential component is constant in aframe rotating with its pattern speed $\Omega_{l,m}$ , so its perturbations of the disk's angular momentum $H_d$ and energy $E_d$ must preserve the"883the cdeusity distribution SF2 (see Sec.,the density distribution SF2 (see Sec.884 3)) αμα the assumption of staucdard caudles used [for the illustration in Figure 1.. one would estimate a maximum redshift of ~1.1 lor the softest bursts aud 3.1 for the hardest. bursts.," 3) and the assumption of standard candles used for the illustration in Figure \ref{fig1}, one would estimate a maximum redshift of $\sim 1.4$ for the softest bursts and $\sim 3.4$ for the hardest bursts."885 Wit1 ie given [lux limit of the BD2 sample. the soft. bursts are therefore of lower luminosity aud tie hard bursts of higher luminosity.," With the given flux limit of the BD2 sample, the soft bursts are therefore of lower luminosity and the hard bursts of higher luminosity."886 We conclude tliat the spectral tudes is a luminosity iudicator aud that there exists a luminosity-harduess correlation., We conclude that the spectral index is a luminosity indicator and that there exists a luminosity-hardness correlation.887 At this stage we cannot show the luulnosity-harduess correlation explicitly due to the dearth of observed redshifts., At this stage we cannot show the luminosity-hardness correlation explicitly due to the dearth of observed redshifts.888 Ouce we have derived the GRB luminosity Bunction. we will produce au explicit luminosity-harcuess correlation tlirougl Simulation. see Sec.," Once we have derived the GRB luminosity function, we will produce an explicit luminosity-hardness correlation through simulation, see Sec."889 5., 5.890 Could the correlation of 1 be a cousequence of the shape of the spectrum of GRBs?, Could the correlation of on be a consequence of the shape of the spectrum of GRBs?891" The typical GRB photon spect""un is often characterized as the Baud spectrum 1993).. with low energyslope —1. higl ellergy sope —2 and break energy near 150 keV. At low redshift. this spectrum will have au observed between —1 aud —2. while at higli redshift it will be —2."," The typical GRB photon spectrum is often characterized as the Band spectrum \citep{ban93}, with low energyslope $\sim-1$, high energy slope $\sim-2$ and break energy near 150 keV. At low redshift, this spectrum will have an observed between $-1$ and $-2$, while at high redshift it will be $-2$."892 Thus more clistaut bursts will |ave softer spectra. which is the opposite of our findiug above.," Thus more distant bursts will have softer spectra, which is the opposite of our finding above."893 Previous suclies of the correlation beween ha‘cluess aud global GRB properties Lave beeu based ou the relation or on-- 0[teu involving duration-harduess classes (Belli1996:Ixouveliotou.etal.1993.Pencdletoret1998:Tavani 1998).," Previous studies of the correlation between hardness and global GRB properties have been based on the relation or on, often involving duration-hardness classes \citep{bel92,bel96,kou93,kou96,pen98,tav98}."894. Amone the three Classes considered by Tavaui(1993).. classes B and C contained GRBs with Του>2.5 s similar to the BD2 GRBs detected at a time scale of 1021 ms.," Among the three classes considered by \citet{tav98}, classes B and C contained GRBs with $T_{90} > 2.5$ s similar to the BD2 GRBs detected at a time scale of 1024 ms."895 The |ard bursts iu class B had =0.39 while the κο bursts in class C had =6).12. showing the same trend as seen iu Figure 2..," The hard bursts in class B had $= 0.29$ while the soft bursts in class C had $= 0.42$, showing the same trend as seen in Figure \ref{fig2}."896 Also ofinterest is the study by Pencletonοἱal.(1998) who defined NHE bursts as those hat have a marked lack of hish-energy [lux GE>300 keV). in contrast to HE bursts that lave a stroug high-energy flux.," Also of interest is the study by \citet{pen98} who defined NHE bursts as those that have a marked lack of high-energy flux $E > 300$ keV), in contrast to HE bursts that have a strong high-energy flux."897 Usiug the relations or both types they coucluded that HE usts are elel times more luminous than NHE bursts., Using the relations for both types they concluded that HE bursts are eight times more luminous than NHE bursts.898 TIis agrees qualitatively with our fiudiug hat hard bursts are more luminous than πο bursts., This agrees qualitatively with our finding that hard bursts are more luminous than soft bursts.899 We have not usec the durations or the duratiou-harduess classification of GRBs for the ollowiug reason., We have not used the durations or the duration-hardness classification of GRBs for the following reason.900 In the BD2 sample we define the duration of a GRB as the total time elapsed )etween the time of rigger aud the last time the burst flux exceeded the limitiug flux for triggeriug., In the BD2 sample we define the duration of a GRB as the total time elapsed between the time of trigger and the last time the burst flux exceeded the limiting flux for triggering.901 In our simulations iu which we move a burst out in distance to derive its.. we [ind that he duratiou decreases to arouud 1 or 2 secouds when last detected.," In our simulations in which we move a burst out in distance to derive its, we find that the duration decreases to around 1 or 2 seconds when last detected."902" Clearly. our definition of ""duration does not oroduce an absolute property of the burst."," Clearly, our definition of 'duration' does not produce an absolute property of the burst."903 Therefore. we have uot considered duration-harduess classes for the BD? GRBs.," Therefore, we have not considered duration-hardness classes for the BD2 GRBs."904" The BATSE Του aud Tey durations also suller from a ""[lueuce-duration"" bias according to Hakkilaetal.(2000).", The BATSE $T_{90}$ and $T_{50}$ durations also suffer from a “fluence-duration” bias according to \citet{hak00}.905. IL the derived duration of a given burst depeuds on its flux. then the values for bursts with a minimum observed duration have to be derived using two simultaneous limits (SclunidtLOGS)... ie. the flux limit aud the duration limit.," If the derived duration of a given burst depends on its flux, then the values for bursts with a minimum observed duration have to be derived using two simultaneous limits \citep{sch68},, i.e. the flux limit and the duration limit."906 Ienoring this requirement will eive rise to systematic errors in -, Ignoring this requirement will give rise to systematic errors in .907 Ienoring this requirement will eive rise to systematic errors in --, Ignoring this requirement will give rise to systematic errors in .908the negative value ofCu]leads to the positive polarization of X inpe collis,"To explain the $\Sigma^+$ polarization, we have to choose a small value of $C_{\{uu\}}^s$."909ions., We set the910"Thus, based on the current data it seems possible that the presence of OB stars is related to a low star to brown dwarf ratio, i.e. a higher abundancy of brown dwarfs.","Thus, based on the current data it seems possible that the presence of OB stars is related to a low star to brown dwarf ratio, i.e. a higher abundancy of brown dwarfs."911 This could be a sign that the radiation field of OB stars favours the formation of brown dwarfs., This could be a sign that the radiation field of OB stars favours the formation of brown dwarfs.912 It has been suggested that substellar and planetary-mass objects can be formed via photoerosion of cores by the ionizing radiation from an OB star (Whitworth&Zinnecker2004)., It has been suggested that substellar and planetary-mass objects can be formed via photoerosion of cores by the ionizing radiation from an OB star \citep{waz04}.913". At face value this would provide an additional formation channel for brown dwarfs in OB associations, lowering the star to brown dwarf ratio."," At face value this would provide an additional formation channel for brown dwarfs in OB associations, lowering the star to brown dwarf ratio."914" Given the substantial uncertainties in these ratios, this conclusion is certainly preliminary and needs to be substantiated by future surveys."," Given the substantial uncertainties in these ratios, this conclusion is certainly preliminary and needs to be substantiated by future surveys."915 We have carried out a survey for brown dwarfs in the MMyr old UpSco star forming region based on photometry and proper motions from a combination of the UKIDSS Galactic Cluster Survey and 2MASS., We have carried out a survey for brown dwarfs in the Myr old UpSco star forming region based on photometry and proper motions from a combination of the UKIDSS Galactic Cluster Survey and 2MASS.916 19 new substellar objects with estimated masses between 0.01 and 0.09M@ are identified., 19 new substellar objects with estimated masses between 0.01 and $M_{\sun}$ are identified.917 These objects are located in the southern part of the association which has not been covered by previous brown dwarf surveys., These objects are located in the southern part of the association which has not been covered by previous brown dwarf surveys.918 8 other objects with slightly higher proper motion have also been identified., 8 other objects with slightly higher proper motion have also been identified.919 These may be UpSco members with slightly higher dispersion velocity than the stellar members., These may be UpSco members with slightly higher dispersion velocity than the stellar members.920" Although spectroscopic confirmation has not been obtained yet, the level of contamination appears negligible."," Although spectroscopic confirmation has not been obtained yet, the level of contamination appears negligible."921" The ratio of stars to brown dwarfs in the South of UpSco was found to be 3.5779, in the same range as elsewhere in UpSco."," The ratio of stars to brown dwarfs in the South of UpSco was found to be $_{-1.3}^{+2.0}$, in the same range as elsewhere in UpSco."922" Comparing with literature findings, young clusters with OB associations tend to have lower ratios than clusters without OB stars, which might indicate that brown dwarf formation is a function of environment."," Comparing with literature findings, young clusters with OB associations tend to have lower ratios than clusters without OB stars, which might indicate that brown dwarf formation is a function of environment."923 The authors would like to thank Nicolas Lodieu of the Instituto de Astrofisica de Canarias and Isabelle Baraffe of the Centre de Recherche Astrophysique de Lyon for supplying model data., The authors would like to thank Nicolas Lodieu of the Instituto de Astrofisica de Canarias and Isabelle Baraffe of the Centre de Recherche Astrophysique de Lyon for supplying model data.924 This work was supported by the Science Foundation Ireland within the Research Frontiers Programme under grant no., This work was supported by the Science Foundation Ireland within the Research Frontiers Programme under grant no.925 10/RFP/AST2780., 10/RFP/AST2780.926" This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."927 We would also like to thank the UKIDSS Team for the excellent database they have made available to the community., We would also like to thank the UKIDSS Team for the excellent database they have made available to the community.928to a πα] underestimation of the nuuass of NGC 300 in Tully (1988) compared with more recent studies. Puche Carignan (1991) (the Tull (1988) value has been used in 55 for the sake of consistency with the other systems).,"to a small underestimation of the mass of NGC 300 in Tully (1988) compared with more recent studies, Puche Carignan (1991) (the Tully (1988) value has been used in 5 for the sake of consistency with the other systems)."929" It is certainly true hat the perhaps ‘relative steepness” of NGC 3008s source i1unuinositv distribution cau also be brought iuto line with he other svstems. if 2 or 3 of the questionable ""acc."," It is certainly true that the perhaps `relative steepness' of NGC 300's source luminosity distribution can also be brought into line with the other systems, if 2 or 3 of the questionable `acc.'"930 sources (see Table 5)) are removed., sources (see Table \ref{table_iden}) ) are removed.931" We have been here slightly conservative. in removing onlv sources we are απ sure do not belong to NGC 300 it nmuav well ος the case. and Fie.55 seems to bear this out. that a couple of the low luninosity sources may well not beloug o NGC 200,"," We have been here slightly conservative, in removing only sources we are fairly sure do not belong to NGC 300 $-$ it may well be the case, and 5 seems to bear this out, that a couple of the low luminosity sources may well not belong to NGC 300."932 Finally note that. although uo very bright sources are seen m NGC 300. none are also seen in the other normal. quiesceut galaxies M31 aud MJ.," Finally note that, although no very bright sources are seen in NGC 300, none are also seen in the other normal, quiescent galaxies M31 and M33."933 NGC 300 herefore. in terms of the Dunünositv distribution of its N-ray sources. appears nono way unusual.," NGC 300 therefore, in terms of the luminosity distribution of its X-ray sources, appears in no way unusual."934 The Sculptor group is probably the nearest small group of galaxies to our own Local Group. and the individual members have been studied in great detail.," The Sculptor group is probably the nearest small group of galaxies to our own Local Group, and the individual members have been studied in great detail."935 Nincimatical studies Puche Carignan 1988) have established the eroup to be made up of five major members (NGC 55. NGC 217. NGC 253. NGC 300 and NGC 7793).," Kinematical studies Puche Carignan 1988) have established the group to be made up of five major members (NGC 55, NGC 247, NGC 253, NGC 300 and NGC 7793)."936 Other «λαο galaxies. such as NGC 2 band NGC 15. were found to be more distant. and although dwarf galaxies do exist withiu Sculptor Lausten 11977). they contribute essentially. nothing to the eroup Cluission or dyvnanices.," Other smaller galaxies, such as NGC 24 and NGC 45, were found to be more distant, and although dwarf galaxies do exist within Sculptor Lausten 1977), they contribute essentially nothing to the group emission or dynamics."937 The Nav properties of the five members have been presented several times in the past Schlegel 11997: RPS97: Voeler Pietsch 1999: Pietsch 22000). and in discussing the PPSPC observations of NGC 7795 (Read Pietsch 1999. hereafter. RP99). a comparison of the Sculptor galaxies? ταν properties was presented. and it is well worth referring to RP99 here.," The X-ray properties of the five members have been presented several times in the past Schlegel 1997; RPS97; Vogler Pietsch 1999; Pietsch 2000), and in discussing the PSPC observations of NGC 7793 (Read Pietsch 1999, hereafter RP99), a comparison of the Sculptor galaxies' X-ray properties was presented, and it is well worth referring to RP99 here."938 A similar table to Table 5 of RP99 is eiven in Table 6.., A similar table to Table 5 of RP99 is given in Table \ref{table_scul}.939 Various physical. N-rav aud other uultiwavoeleusth properties for the five prominent Sculptor members are given.," Various physical, X-ray and other multi-wavelength properties for the five prominent Sculptor members are given."940 All N-raw information for NGC 300 is taken roni the preseut paper. while that for the remaining svstcms is taken οι RPSOT. apart from NGC 7793 (RP99).," All X-ray information for NGC 300 is taken from the present paper, while that for the remaining systems is taken from RPS97, apart from NGC 7793 (RP99)."941 Cüven in the last colui (12) is the logLxAy ratio. he neutral hydrogen mass values taken from Tully (1985).," Given in the last column (12) is the $\log{L_{X}/M_{\mbox{\small HI}} }$ ratio, the neutral hydrogen mass values taken from Tully (1988)."942 What is interesting as regards NGC 2300 i9 that now. the ealaxy appears more “normal than previously reported.," What is interesting as regards NGC 300 is that now, the galaxy appears more `normal' than previously reported."943 In RP99. the NCC 300 data reported. analysed in RPS97. assunucec a distance of MMypc (Tully 1988).," In RP99, the NGC 300 data reported, analysed in RPS97, assumed a distance of Mpc (Tully 1988)."944 Now we have assunued a distance. as described i the introduction. of MMppe. based on several authors more recent work.," Now we have assumed a distance, as described in the introduction, of Mpc, based on several authors' more recent work."945 Note that. correcting for the differeut assumed distances. the buuinositv for NGC 300 quoted here and that in the RPS97 survey. where ouly a part of the NGC 300 PSPC data was analysed (aud then only in a seni-autoniatie sense). agree rather well.," Note that, correcting for the different assumed distances, the luminosity for NGC 300 quoted here and that in the RPS97 survey, where only a part of the NGC 300 PSPC data was analysed (and then only in a semi-automatic sense), agree rather well."946 The most famous Sculptor amember is probably NGC 253. a lavee X-ray and far-infrared bright starburst ealaxy. while the remaining four svstenis are alb very sinu: plivsically simall. noxiual nou-starburst). late-type spirals (NGC 253 is also a late-tvpe spiral).," The most famous Sculptor member is probably NGC 253, a large X-ray and far-infrared bright starburst galaxy, while the remaining four systems are all very similar; physically small, normal non-starburst), late-type spirals (NGC 253 is also a late-type spiral)."947 The four normal Sculptor svstenis are also extremely simular in terms of their multivaveleusth properties., The four normal Sculptor systems are also extremely similar in terms of their multiwavelength properties.948 The narrow ranec in especially Lp. but also Ly. evident in Table 6 (excludiug NCC 253) is very striking (the larger range in Lere observed is partly due to properties of NGC 7795 - see RP99).," The narrow range in especially $L_{B}$ , but also $L_{X}$, evident in Table \ref{table_scul} (excluding NGC 253) is very striking (the larger range in $L_{FIR}$ observed is partly due to properties of NGC 7793 - see RP99)."949 Though this in itself is interesting. that the four jiormal Sculptor galaxies are extremely similar. and are herefore good examples of prototypical ποια. galaxies. what is xxhaps remarkable about NCC 300 is that it is he most “normal of the four.," Though this in itself is interesting, that the four normal Sculptor galaxies are extremely similar, and are therefore good examples of prototypical `normal' galaxies, what is perhaps remarkable about NGC 300 is that it is the most `normal' of the four."950 It is neither the brightest nor he dinunest galaxy in either the optical. the far-infrared or the N-rax baud.," It is neither the brightest nor the dimmest galaxy in either the optical, the far-infrared or the X-ray band."951 Similarly. it has neither the largest nor he smallest value of Lgig/Lp. Ly/Lp or Ly/Lg; flux ratio.," Similarly, it has neither the largest nor the smallest value of $L_{FIR}/L_{B}$, $L_{X}/L_{B}$ or $L_{X}/L_{FIR}$ flux ratio."952 Furthermore. studies aud mass modelling of the Sculptor group galaxies Puche Carignan 1991) have shown that NCC 300 lies nüdway in every parameter space. mnass-to-liehlt ratio ALLp. nunuass NNote also NCC 30078 midway logLy/Mjj ratio.," Furthermore, studies and mass modelling of the Sculptor group galaxies Puche Carignan 1991) have shown that NGC 300 lies midway in every parameter space, mass-to-light ratio $M/L_{B}$, mass Note also NGC 300's midway $\log{L_{X}/M_{\mbox{\small HI}} }$ ratio."953 As seen in Table 6.. the other three normal Sculptor ealaxies are muusnal in some wav: NGC 55 is X-ray bright. NCC 7793 is very &u-infrared bright aud NGC 217 is vorv far-infrared dim.," As seen in Table \ref{table_scul}, the other three normal Sculptor galaxies are unusual in some way; NGC 55 is X-ray bright, NGC 7793 is very far-infrared bright and NGC 247 is very far-infrared dim."954 NGC 300 however. is wholly remarkable. both in terms of how it compares with its Sculptor neighbours aud. as seeu in Sect. 1.2..," NGC 300 however, is wholly unremarkable, both in terms of how it compares with its Sculptor neighbours and, as seen in Sect. \ref{sec_disc2},"955 in how its N-ray source lminosity distribution compares with other nearby spiral galaxies., in how its X-ray source luminosity distribution compares with other nearby spiral galaxies.956 It is therefore perhaps one of the finest examples of a typical quiescent normal late-type spiral galaxy., It is therefore perhaps one of the finest examples of a typical quiescent normal late-type spiral galaxy.957 We have analysed all the PPSPC aud URI data from a field centred on the nearby face-on Sculptor galaxy NCC 300., We have analysed all the PSPC and HRI data from a field centred on the nearby face-on Sculptor galaxy NGC 300.958 29 PSPC aud IIRI sources are detected within the optical confines of the ealaxv., 29 PSPC and HRI sources are detected within the optical confines of the galaxy.959 Alauy of the sources appear to be variable and we attempt to classify aud identify the sources based ou their temporal and spectral properties and using other multi-waveleugth observations., Many of the sources appear to be variable and we attempt to classify and identify the sources based on their temporal and spectral properties and using other multi-wavelength observations.960 Iu addition to poiut source enissjon. some evidence for unresolved residual cussion is detected within NGC 300.," In addition to point source emission, some evidence for unresolved residual emission is detected within NGC 300."961 Our findines with reed to the observed poiut-source and unresolved emission cau be sumnananzed as follows: 1., Our findings with regard to the observed point-source and unresolved emission can be summarized as follows: 1.962 26 PSPC sources are detected within the D25 ellipse of NOC 300. as are LO IIRI sources(all but the very," 26 PSPC sources are detected within the D25 ellipse of NGC 300, as are 10 HRI sources(all but the very"963enough for our purposes.,enough for our purposes.964" Then at height : above the photosphere plz)=py,expCG.z/ Hui). where py, is the photospheric gas density.", Then at height $z$ above the photosphere $\rho(z)=\rho_{ph}\exp(-z/H_{ph})$ where $\rho_{ph}$ is the photospheric gas density.965 Using this result aud equation (30)) we find the photosphierie optical depth dz=-ΠΠ. from which it follows that," Using this result and equation \ref{eq:kappa}) ) we find the photospheric optical depth dz=, from which it follows that."966" As a byproduct of relation. (51)) one can rewrite equation (37)) as It then follows frou equations (17)) and (53)) that F;,,ELcT.", As a byproduct of relation \ref{eq:2_3}) ) one can rewrite equation \ref{eq:nabla_ph}) ) as It then follows from equations \ref{eq:nabla_cond}) ) and \ref{eq:nab_ph}) ) that $F_{in}\ll \sigma T_{ph}^4$.967" We are now iu position to evaluate £j, aud see how inadiation affects cooling of convective objects.", We are now in position to evaluate $F_{in}$ and see how irradiation affects cooling of convective objects.968 To do this we note that the inner boundary of the radiative zone is also the outer boundary of the convective iuterior., To do this we note that the inner boundary of the radiative zone is also the outer boundary of the convective interior.969 We asstuue that convective transport is so efficient that cutropy is throughout the iuner couvective zone. so that the EOS can be well represeuted by. P=Np? where A is the adiabatic constant.," We assume that convective transport is so efficient that entropy is throughout the inner convective zone, so that the EOS can be well represented by $P=K\rho^\gamma$ , where $K$ is the adiabatic constant."970" As a result. Pai and FZ), wast be related via (Τωνpy?=KP,1 hich. coupled with equations (37)). (12)). CI3)). and conclition (17)). vields the following expression for F;,,: Ίσα where Tutrinsic stella flux F5, exhibits an explicit latitudinal depeudeuce because it is a fuuctiou of 7,4,(0).As discussed. before; when 3<1 and Vy>θα transition to convection at some depth requires Vag."," As a result, $P_{ph}$ and $T_{ph}$ must be related via $(kT_{cb}/\mu)^\gamma=K P_{cb}^{\gamma-1}$ which, coupled with equations \ref{eq:nabla_ph}) ), \ref{eq:T_cb}) ), \ref{eq:P_cb}) ), and condition \ref{eq:nabla_cond}) ), yields the following expression for $F_{in}$ : , where Intrinsic stellar flux $F_{in}$ exhibits an explicit latitudinal dependence because it is a function of $T_{ph}(\theta)$.As discussed before, when $\beta<4$ and $\nabla_0>0$ a transition to convection at some depth requires $\nabla_0>\nabla_{ad}$ ."971 As a result.," As a result, )<0."972 On the other haud. when. >Lone also fuds Lo©<0 because Vy<0n this case.," On the other hand, when $\beta > 4$ one also finds $4-\xi<0$ because $\nabla_0<0$ in this case."973" Thus. in both situations £7, as Ty, increases."," Thus, in both situations $F_{in}$ as $T_{ph}$ increases."974 In other words. irrespective of the opacity behavior external radiation of the stellar surface stellar cooling. a result kuown frou the studies of radiated giant planets (Caullot 1996: Binrows 2000).," In other words, irrespective of the opacity behavior external irradiation of the stellar surface stellar cooling, a result known from the studies of irradiated giant planets (Guillot 1996; Burrows 2000)."975" Since external radiative zoue is rather thin compared to Rit umust contain negligible amount of mass compared with AZ,.", Since external radiative zone is rather thin compared to $R_\star$ it must contain negligible amount of mass compared with $M_\star$.976 Then the structure of fully couvective ΠΙΟ reeion of the star should be well described by the classical theory of polytropic spheres (Landau Lifshitz 198|: Ikippeuhahu 1991)., Then the structure of fully convective inner region of the star should be well described by the classical theory of polytropic spheres (Landau Lifshitz 1984; Kippenhahn 1994).977" In particular. adiabatic constant A C1 be related to the stellar massaud radius as K=c((s))GAL,: l. where Q(5)~ Lis à parameter set bv the equation of state of the eas."," In particular, adiabatic constant $K$ can be related to the stellar massand radius as ) G, where $\zeta(\gamma)\sim 1$ is a parameter set by the equation of state of the gas."978 Iu a particular case of convective vouug stars with fully ionized mterior characterized by 2=5/3 one has ¢(5/3)=0.1286 audRy., In a particular case of convective young stars with fully ionized interior characterized by $\gamma=5/3$ one has $\zeta(5/3)=0.1286$ and.979" Equatious (55)) aud (59)) unuanibiguouslv. deterinine cooling of the star as a function of stellar parameters RandAf,. temperature distributionat the photosphere T,(0). and opacity behavior iu the outer radiative zone."," Equations \ref{eq:F_in}) ) and \ref{eq:K}) ) unambiguously determine cooling of the star as a function of stellar parameters $R_\star$ and$M_\star$, temperature distributionat the photosphere $T_{ph}(\theta)$, and opacity behavior in the outer radiative zone."980 We now compare stellar cooling in the imacdiated case with that occuring in isolated stars.iu the abseuce of external illuuination.," We now compare stellar cooling in the irradiated case with that occurring in isolated stars,in the absence of external illumination."981" Iu the lattercaseTjj,= To. aud equation (53)) gives Vj=Vere(6| 1."," In the lattercase$T_{ph}=T_0$ , $F_{in}=F_0=\sigma T_0^4$ and equation \ref{eq:nab_ph}) ) gives $\nabla_{ph}=\nabla_{eff}=(\alpha+1)/8\sim 1$ ."982 Substituting this result iuto equations (12)). (13)). uxing adiabatic relation at the couvective-raciative boundary. and equation (52)) we fined," Substituting this result into equations \ref{eq:T_cb}) ), \ref{eq:P_cb}) ), using adiabatic relation at the convective-radiative boundary, and equation \ref{eq:P_ph}) ) we find . ."983None such errors have been reported in the literature. which is not a strong argument because ]lipparcos remains unparalleled at its level of global astrometric accuracy.,"None such errors have been reported in the literature, which is not a strong argument because Hipparcos remains unparalleled at its level of global astrometric accuracy."984 The major catalogs ol proper motions Tycho-2 (Urbanetal.2000) and UCAC (Zachariasetal.2004) are calibrated on Hipparcos stars: therefore. svstematic distortions of Hipparcos astrometry. if aly. are just copied over to these catalogs.," The major catalogs of proper motions Tycho-2 \citep{ur} and UCAC \citep{za} are calibrated on Hipparcos stars; therefore, systematic distortions of Hipparcos astrometry, if any, are just copied over to these catalogs."985 Raclio astrometric observations wilh VEDI have recently advanced (o a comparable level of accuracy. in positions and proper motions. aud being directly. tied to the ICRE. provide an independent test for the Lipparcos reference svstem (Bobolizetal.2006).," Radio astrometric observations with VLBI have recently advanced to a comparable level of accuracy in positions and proper motions, and being directly tied to the ICRF, provide an independent test for the Hipparcos reference system \citep{bo}."986. This important external check is unfortunately. limited by (he small number of optically bright radio stars. but the available accuracy of VLBI proper motions (approximately 1.7 !)) enables Boboltz et al.," This important external check is unfortunately limited by the small number of optically bright radio stars, but the available accuracy of VLBI proper motions (approximately $1.7$ ) enables Boboltz et al."987 to state that the relative spin of the Hipparcos proper motion svstem is much less (han 1. {about each axis., to state that the relative spin of the Hipparcos proper motion system is much less than 1 about each axis.988" This result confirms (hat the strong magnetic harmonic li,! representing a spin around the —Y direction. is not an artefact."," This result confirms that the strong magnetic harmonic $\vec{H}_1^{-1}$ representing a spin around the $-Y$ direction, is not an artefact."989 Another significant astrometrie development of late is the SPM3 catalog. which provides hieh «qualitv. absolute proper motions for a large sample of distant and faint stars. albeit in a small [Traction of the skv (Girardetal.2004).," Another significant astrometric development of late is the SPM3 catalog, which provides high quality absolute proper motions for a large sample of distant and faint stars, albeit in a small fraction of the sky \citep{spm}."990.. This catalog provides an independent view of the local stellar velocity field in the surveved area of the sky., This catalog provides an independent view of the local stellar velocity field in the surveyed area of the sky.991 As customary in studies of Galactic dynamics. we make use of the Galactic coordinate svslem (CX.1.Z) in which the NX axis is pointing Coward (he Galactic center. (he Y axis toward (he direcon of Galactic rotation. and (he Z axis toward the north pole.," As customary in studies of Galactic dynamics, we make use of the Galactic coordinate system $(X,Y,Z)$ in which the $X$ axis is pointing toward the Galactic center, the $Y$ axis toward the direction of Galactic rotation, and the $Z$ axis toward the north pole."992 For each star. a (rad of unit vectors (7.7.75)— is defined. with right righl))," For each star, a triad of unit vectors $(\vec{r},\vec{\tau_l},\vec{\tau_b})$ is defined, with ) )"993"calculations and three grid calculations are shown in Figures 6,, 7 and 8.","calculations and three grid calculations are shown in Figures \ref{fig:pdflin}, , \ref{fig:pdflog} and \ref{fig:pdftails}."994" The plots show the time average of individual PDFs computed at intervals of At=14/10, starting from 2t, when turbulence is reasonably well established (see Figures 1,, 3))."," The plots show the time average of individual PDFs computed at intervals of $\Delta t = t_{d}/10$, starting from $2 t_{d}$ when turbulence is reasonably well established (see Figures \ref{fig:vrms}, \ref{fig:coldens512}) )."995 This gives a total of 81 snapshots used in the averaging procedure., This gives a total of 81 snapshots used in the averaging procedure.996" For reference we compute the PDF for each code with a bin width of 0.1 in Inp, with the first bin starting at (Inp);,;;=—12."," For reference we compute the PDF for each code with a bin width of 0.1 in $\ln \rho$, with the first bin starting at $(\ln\rho)_{min} = -12$."997 For the grid results the volume weighted PDF is constructed simply by binning the grid cells according to the value of Inp., For the grid results the volume weighted PDF is constructed simply by binning the grid cells according to the value of $\ln \rho$.998" To obtain a volume weighted PDF in SPH it is necessary to weight the contribution of each particle by the volume element associated with that particle, m/p, which for equal mass particles is simply inversely proportional to the density."," To obtain a volume weighted PDF in SPH it is necessary to weight the contribution of each particle by the volume element associated with that particle, $m/\rho$, which for equal mass particles is simply inversely proportional to the density."999" To construct the PDF we therefore bin each particle according to the value of Inp and add a contribution of 1/p to the bin, normalising the resultant PDF such that the integral over all bins (i.e, the total probability) is unity."," To construct the PDF we therefore bin each particle according to the value of $\ln \rho$ and add a contribution of $1/\rho$ to the bin, normalising the resultant PDF such that the integral over all bins (i.e, the total probability) is unity."1000 This is different to the procedure used to construct density PDFs from SPH particles used both in the Potsdam comparison (?) (see however Fig., This is different to the procedure used to construct density PDFs from SPH particles used both in the Potsdam comparison \citep{kitsionasetal09} (see however Fig.1001" 11 in ?)) and by previous authors ?2?), whereby the SPH results were first interpolated to a grid and a PDF constructed as above for the grid-based results."," 11 in \citealt{kitsionasetal09}) ) and by previous authors \citep[e.g.][]{vsbpk03,klessen00,maclowetal98}, whereby the SPH results were first interpolated to a grid and a PDF constructed as above for the grid-based results."1002 The main disadvantage to interpolating to the grid is that the part of the high density tail of the SPH calculation that falls below the grid scale is removed., The main disadvantage to interpolating to the grid is that the part of the high density tail of the SPH calculation that falls below the grid scale is removed.1003" To retain this tail requires that PDFs be constructed from SPH particles by interpolating to a grid, though this is a perfectly valid procedure for computing volumetric quantities such as power spectra (see refsec:pspec))."," To retain this tail requires that PDFs be constructed from SPH particles by interpolating to a grid, though this is a perfectly valid procedure for computing volumetric quantities such as power spectra (see \\ref{sec:pspec}) )."1004 The PDFs thus constructed (Fig. 7)), The PDFs thus constructed (Fig. \ref{fig:pdflog}) )1005 show clearly a log-normal distribution in agreement with many previous calculations and with theoretical expectations (see above)., show clearly a log-normal distribution in agreement with many previous calculations and with theoretical expectations (see above).1006" Whilst the results are broadly similar for all calculations in the central regions around the mean density and in overall shape, clear differences may also be observed between codes and with resolution, particularly in the tails of the distribution (Fig. 8))."," Whilst the results are broadly similar for all calculations in the central regions around the mean density and in overall shape, clear differences may also be observed between codes and with resolution, particularly in the tails of the distribution (Fig. \ref{fig:pdftails}) )."1007 At the low density end (Fig. 8)), At the low density end (Fig. \ref{fig:pdftails}) )1008" the grid results tend to show a wide, low density tail, with probability densities with resolution."," the grid results tend to show a wide, low density tail, with probability densities with resolution."1009" By contrast, the SPH results show a narrower low density tail with probability densities that with resolution."," By contrast, the SPH results show a narrower low density tail with probability densities that with resolution."1010" Whilst both codes appear to be converging towards each other, it is clear that neither is well converged at the low density end (p/po< 0.01) at least for the resolutions used in this paper."," Whilst both codes appear to be converging towards each other, it is clear that neither is well converged at the low density end $\rho/\rho_{0} \lesssim 0.01$ ) at least for the resolutions used in this paper."1011 Thus the low density tail should not be used to fit the PDF width from either grid or SPH codes alone at these resolutions., Thus the low density tail should not be used to fit the PDF width from either grid or SPH codes alone at these resolutions.1012 Insteadwe measure the PDF width using the best fit around the mean, Insteadwe measure the PDF width using the best fit around the mean1013AI 31 and MW. GC's were measured on [Iux-calibrated spectra obtained. respectively. with the Blie Channel spectrograph. at MMT. and the Boller Chivens spectrograph on the Casseerain focus of the Bok telescope.,"M 31 and MW GCs were measured on flux-calibrated spectra obtained, respectively, with the Blue Channel spectrograph, at MMT, and the Boller Chivens spectrograph on the Cassegrain focus of the Bok telescope."1014 Iistrumental magnitudes were converted to the Lick svstem using observations of standard stars. in the usual way.," Instrumental magnitudes were converted to the Lick system using observations of standard stars, in the usual way."1015 We do not find any obvious wav in whieh the calibration of Ales measurements in Bursteinetal.(2004) data may be [aultv., We do not find any obvious way in which the calibration of $_2$ measurements in \cite{bu04} data may be faulty.1016 By the same token. the calibration of our own measurements for that index into the Lick svstem seems (o be «quite robust (upper panel of Figure 4)).," By the same token, the calibration of our own measurements for that index into the Lick system seems to be quite robust (upper panel of Figure \ref{zm31b}) )."1017 Llowever. an issue indeed seems to be present wilh the Bursteinetal.(2004) Mg» indices lor M 31 GCs.," However, an issue indeed seems to be present with the \cite{bu04} $_2$ indices for M 31 GCs."1018 This is further illustrated by Figure 13.. where Mg» measurements Irom different sources for M 31 and MW GCs are plotted against [Fe/H].," This is further illustrated by Figure \ref{mg2feh}, where $_2$ measurements from different sources for M 31 and MW GCs are plotted against [Fe/H]."1019 Iron abundances for the M 31 GCs were obtained by Caldwelletal.(2011) as described in Section 3.., Iron abundances for the M 31 GCs were obtained by \cite{ca10} as described in Section \ref{analysis}. .1020 For MW GCs. [Fe/II] comes from Carrettaetal.(2009).. whereas Mg» comes from different sources: MW. GCs from this work (grav error bars). AIW GCs from Duirsteinetal.(2004). (solid squares). M 31 GCs from Bursteinetal.(2004). (solid triangles). ancl M 31. GCs from Puziaοἱal.(2005) (open stars).," For MW GCs, [Fe/H] comes from \cite{ca09}, whereas $_2$ comes from different sources: MW GCs from this work (gray error bars), MW GCs from \cite{bu04} (solid squares), M 31 GCs from \cite{bu04} (solid triangles), and M 31 GCs from \cite{pu05}1021 (open stars)."1022 Clusters in M 31 and the MW are expected to occupy (he same locus in (his diagram. provided they have similar [Mg/Fe]. which is the case. as demonstrated by (2009).. Schiavonetal. (2011)... ancl Figure G..," Clusters in M 31 and the MW are expected to occupy the same locus in this diagram, provided they have similar [Mg/Fe], which is the case, as demonstrated by \cite{co09}, \cite{s11}, and Figure \ref{indb}."1023 As can be seen. the data by are in good agreement with our MW data. and so are the MW. data by (2004).," As can be seen, the data by \cite{pu05} are in good agreement with our MW data, and so are the MW data by \cite{bu04}."1024. However. the M 31 data by Bursteinetal.(2004). clearly depart from the overall trend. towards lower Mos. suggesting a zero point offset of about 0.05 mag in (hat index.," However, the M 31 data by \cite{bu04} clearly depart from the overall trend, towards lower $_2$, suggesting a zero point offset of about 0.05 mag in that index."1025 We conclude that the NII 3360 feature has similar strength in the spectra of M 31 and AMIW GCs of the same metallicitv., We conclude that the NH 3360 feature has similar strength in the spectra of M 31 and MW GCs of the same metallicity.1026 We suggest that the assertion that it may be stronger in the spectra of M 31 GCs derived from a zero point offset in Mes measurements in (2004)., We suggest that the assertion that it may be stronger in the spectra of M 31 GCs derived from a zero point offset in $_2$ measurements in \cite{bu04}.1027. M 31 and AIWGCs of different metallicities were compared in the NII vs Mes plane. which led to a perception that NII features seemed (arGlicially) stronger in," M 31 and MWGCs of different metallicities were compared in the NH vs $_2$ plane, which led to a perception that NH features seemed (artificially) stronger in"1028eas evolution with chemical reactions aud cooling is studied usine the model by Teemarketal. IIutclhiugsetal.(2002) anc Uirashita&Ferrara (2002).,"gas evolution with chemical reactions and cooling is studied using the model by \citet{Teg97}, , \citet{Hut02} and \citet{Hir02}."1029. We sunmniauize chemical reactions considered in this paper aud their rate cocficicuts (Rin=1... 11) iu Table 1..," We summarize chemical reactions considered in this paper and their rate coefficients $R_{n};n=1,\dots,11$ ) in Table \ref{tab:rea}."1030 The equations are based ou IHirashita&Ferrara(2002).. but we includethe effect of the dust size distribution on II» formation and the metal-line cooling process.," The equations are based on \citet{Hir02}, but we includethe effect of the dust size distribution on ${\rm H}_{2}$ formation and the metal-line cooling process."1031" The time evolution of the ionization degree is described as where fü=lefir, is the neutral fraction of lbydrogen.", The time evolution of the ionization degree is described as where $f_{0}=1-x-f_{{\rm H}_{2}}$ is the neutral fraction of hydrogen.1032 The terms ou the right-hand side are the rates of collisional ionization. recombination and photoionization.," The terms on the right-hand side are the rates of collisional ionization, recombination and photoionization."1033" Next. the time evolution of the molecular fraction is written as where the terms on the right-hand side are the IL, formation rate in gas phase. the IL. formation rate on dust eraius. the destruction rate in eas phase. aud the destruction rate by UV photons. aud the decreasing rate bv star formation.respectively."," Next, the time evolution of the molecular fraction is written as where the terms on the right-hand side are the ${\rm H}_{2}$ formation rate in gas phase, the ${\rm H}_{2}$ formation rate on dust grains, the destruction rate in gas phase, and the destruction rate by UV photons, and the decreasing rate by star formation,respectively."1034" These terms are giveu by aud The effective. formation rates of Is iucludiug the effect of destruction rate of IT aud IT] are aud respectively, and the destruction of IL]. due to II. collision is We will give the dust-to-gas mass ratio. D. aud the production rate of molecular hivdrogen via dust surface reaction. Rays. in Section 3.5 aud reaction rates of photo-process. D,(»=12.....15).iu Section 3.6.."," These terms are given by and The effective formation rates of ${\rm H}_{2}$ including the effect of destruction rate of ${\rm H}^{-}$ and ${\rm H}_{2}^{+}$ are and respectively, and the destruction of ${\rm H}_{2}^{+}$ due to ${\rm H}^{-}$ collision is We will give the dust-to-gas mass ratio, ${\cal D}$, and the production rate of molecular hydrogen via dust surface reaction, $R_{\rm dust}$, in Section \ref{subsec:formmol} and reaction rates of photo-process, $\Gamma_{n}(n=12,\dots,15)$,in Section \ref{subsec:rad}."1035 At temperature <104EK. the nain coolant is molecular hvdrogenu iu loxcAnctallicity eas.," At temperature $<10^{4}\ {\rm K}$ , the main coolant is molecular hydrogen in low-metallicity gas."1036" The cooling rate for molecular hydrogen. Ap. over the range LOK«T<I01K is given bv (Galli1995) where Tj,=log44(£7I). Glov"," The cooling rate for molecular hydrogen, $\Lambda_{{\rm H}_{2}}$, over the range $10{\rm K}\le T\le10^{4}{\rm K}$ is given by \citep{Gal98}1037 where $T_{\rm log}\equiv\log_{10}(T/{\rm K})$."1038er&Abel(2008) have receutlv eiven the IH» cooling rates which iuclude ITTs collision and UWUe collision odlsvavs. while the Calli&Palla(1998) rates iuclude only ITII» collisious.," \citet{Glo08} have recently given the ${\rm H}_{2}$ cooling rates which include ${\rm H}-{\rm H}_{2}$ collision and ${\rm H}_{2}-{\rm H}_{2}$ collision pathways, while the \citet{Gal98} rates include only ${\rm H}-{\rm H}_{2}$ collisions."1039 We απλο that he lower-linit of eas temperature is the CMD cluperature., We assume that the lower-limit of gas temperature is the CMB temperature.1040" At temperature T104 K. collisional excitation. Άγιος. and (less importantly) ionization of atomic ivdrogen. Ape: are muore dominant cooling oxocess than molecular hydrogen cooling aud are even by (Taianetal.1996) and respectively, where Ts is eas teniperaturein unitsof 10? Is."," At temperature $T\gtrsim10^{4}\ {\rm K}$ , collisional excitation, $\Lambda_{\rm H,ce}$ and (less importantly) ionization of atomic hydrogen, $\Lambda_{\rm H,ci}$ are more dominant cooling process than molecular hydrogen cooling and are given by \citep{Hai96} and respectively, where $T_{5}$ is gas temperaturein unitsof $10^{5}\ {\rm K}$ ."1041"A second reason for limiting the longitude is that the distance to the feature increases rapidly with distance from the anti-centre, making the sources fainter and appear closer to the plane so that there is less contrast with the other disc sources.","A second reason for limiting the longitude is that the distance to the feature increases rapidly with distance from the anti-centre, making the sources fainter and appear closer to the plane so that there is less contrast with the other disc sources."1042 The source densities in these regions will be very low requiring square degrees of sky to be covered to provide sufficient counts to give reasonable statistics., The source densities in these regions will be very low requiring square degrees of sky to be covered to provide sufficient counts to give reasonable statistics.1043" Therefore, the data has been taken from the SDSS release DR7 (Abazajian et al."," Therefore, the data has been taken from the SDSS release DR7 (Abazajian et al."1044 2009) with regions ~| square degree., 2009) with regions $\sim 1$ square degree.1045 As the regions are all well off the plane it has been assumed that the extinction is local and so all of the magnitudes have been corrected for extinction using the Galactic extinction model of Shlegel et al (1998)., As the regions are all well off the plane it has been assumed that the extinction is local and so all of the magnitudes have been corrected for extinction using the Galactic extinction model of Shlegel et al (1998).1046" Furthermore, the extinction is relatively small and a small residual error will not significantly affect the results, although it would make the sources appear at the wrong distance."," Furthermore, the extinction is relatively small and a small residual error will not significantly affect the results, although it would make the sources appear at the wrong distance."1047 Table 1 shows the position and assumed extinctions., Table 1 shows the position and assumed extinctions.1048" The positions/= 183°, b=21° and/=220° where used by Newberg et al. ("," The positions $l=183^\circ$ , $b=21^\circ $ and $l=220^\circ $ where used by Newberg et al. ("10492002); and the position at /=150° was used by Conn et al. (,2002); and the position at $l=150^\circ $ was used by Conn et al. (1050"2005), to support their “Monoceros stream”hypothesis.","2005), to support their “Monoceros stream”hypothesis."1051sull. the data is certainly very supportive of the view that lighting ordinances have been an elfective tool despite the population growth.,"Still, the data is certainly very supportive of the view that lighting ordinances have been an effective tool despite the population growth."1052 A comparison of our three datasets (1933. 1999 and 2009/10) highlights the robustness ol our current study.," A comparison of our three datasets (1988, 1999 and 2009/10) highlights the robustness of our current study."1053 In 1988. seven observations were made on a single night.," In 1988, seven observations were made on a single night."1054 In 1999. ien observations were made on three nearly consecutive nights.," In 1999, ten observations were made on three nearly consecutive nights."1055 In contrast. this study encompasses 30 observations on 6 nights and over a 15 month timespan.," In contrast, this study encompasses 30 observations on 6 nights and over a 15 month timespan."1056 Besides (hie increased baseline. our exposure times were longer by a factor of 23.," Besides the increased baseline, our exposure times were longer by a factor of $\sim$ 3."1057 Thus. after another decade passes. we hope to carry out a lest as rigorous as the one just completed.," Thus, after another decade passes, we hope to carry out a test as rigorous as the one just completed."1058 While the arid conditions of southern Arizona failed to stem the region's growth. our results show that (he skv brightness hasn't increased proportionally with the population.," While the arid conditions of southern Arizona failed to stem the region's growth, our results show that the sky brightness hasn't increased proportionally with the population."1059 Over the last (wo decades. both. Pima and. Maricopa Counties (which contain Tucson and Phoenix. respectively) have nearly doubled in size and Nogales ancl Santa Cruz County have experienced similar trends (U.S. Census Bureau: 1990. 2010).," Over the last two decades, both Pima and Maricopa Counties (which contain Tucson and Phoenix, respectively) have nearly doubled in size and Nogales and Santa Cruz County have experienced similar trends (U.S. Census Bureau: 1990, 2010)."1060" Llowever, Pima Countys 1974 Lighting ordinance. aud its successors in 1937. 2000 and 2005 along with similar regulations imposed bx the City of Tucson. have effectively stopped the impact of household. commercial and outdoor lights on the night sky."," However, Pima County's 1974 Lighting ordinance, and its successors in 1987, 2000 and 2005 along with similar regulations imposed by the City of Tucson, have effectively stopped the impact of household, commercial and outdoor lights on the night sky."1061 According to the Pima County Report (Davis et 22006). light pollution at Witt Peak has stabilized at 2005 levels and is expected to stay constant until at least 2030.," According to the Pima County Report (Davis et 2006), light pollution at Kitt Peak has stabilized at 2005 levels and is expected to stay constant until at least 2030."1062 Additionally. in 1974. Turnrose published absolute spectrometry of the Palomar night sky. al a time when Palomar was considered one of the premiere clark observing sites.," Additionally, in 1974, Turnrose published absolute spectrometry of the Palomar night sky, at a time when Palomar was considered one of the premiere dark observing sites."1063 Lis A4540 flix is equivalent to. 22.30 magnitudes 7 which is comparable to our A4550 magnitudes presented in Table 2.., His $\lambda$ 4540 flux is equivalent to 22.30 magnitudes $^{-2}$ which is comparable to our $\lambda$ 4550 magnitudes presented in Table \ref{tab:CompMags}.1064 Thus. Witt Peak is currently just as dark as Palomar was in the mid-70s.," Thus, Kitt Peak is currently just as dark as Palomar was in the mid-70s."1065 Astronomy has a major impact on Arizonas state economy = $2250 million in direct impact every vear as well as $11 billion in infrastructure (Eller College of Management. 2007).," Astronomy has a major impact on Arizona's state economy – 250 million in direct impact every year as well as 1 billion in infrastructure (Eller College of Management, 2007)."1066 Thus. the importance of keeping the skies dark extends far bevond the scope of Astronomy.," Thus, the importance of keeping the skies dark extends far beyond the scope of Astronomy."1067 Lighting ordinances have saved the Natt Peak night skv thus far. but as the populations of neiehboring towns increase and grow closer to (he mountain and as towns spring up around 1-10. it will become more and more difficult to maintain the current. light. pollution levels.," Lighting ordinances have saved the Kitt Peak night sky thus far, but as the populations of neighboring towns increase and grow closer to the mountain and as towns spring up around I-10, it will become more and more difficult to maintain the current light pollution levels."1068 Still. our results show that INitt Peak is essentially as dark now as it was in the late 19505 and if the lighting laws toughen as growth increases. there is no reason Witt Peak cant retain the pristine clark skies that Aden Meinel found so promising.," Still, our results show that Kitt Peak is essentially as dark now as it was in the late 1980s and if the lighting laws toughen as growth increases, there is no reason Kitt Peak can't retain the pristine dark skies that Aden Meinel found so promising."1069 The authors wish to thank the former Ixitt Peak Director. Buell Jannuzi. for encouraging ihem to obtain a new data set and lor being generous with the allocation of observing time (o make (his study possible.," The authors wish to thank the former Kitt Peak Director, Buell Jannuzi, for encouraging them to obtain a new data set and for being generous with the allocation of observing time to make this study possible."1070 Dr. Jannuzi has been a tireless proponent of keeping the skies over Witt Peak dark and working within (he community (o reduce light pollution through, Dr. Jannuzi has been a tireless proponent of keeping the skies over Kitt Peak dark and working within the community to reduce light pollution through1071shifted to an apparent magnitude scale using the mean of the e and r magnitudes of the comparison star.,shifted to an apparent magnitude scale using the mean of the $g$ and $r$ magnitudes of the comparison star.1072 We obtained 22 VLT spectra of JJ0039 on the night of 2007 August [5th and a further 7 spectra on the next night., We obtained 22 VLT spectra of J0039 on the night of 2007 August 15th and a further 7 spectra on the next night.1073 We have measured the profiles for radial velocity motion by cross-correlation against single and double Gaussian functions (Schneider&Young1980:Shafter1983).. as implemented inMOLLY.," We have measured the profiles for radial velocity motion by cross-correlation against single and double Gaussian functions \citep{SchneiderYoung80apj,Shafter83apj}, as implemented in."1074 The best results were obtained using a double Gaussian with widths aand separation €=2000kms!., The best results were obtained using a double Gaussian with widths and separation $\xi = 2000$.1075. We have fitted a spectroscopic orbit to the radial velocities using the code. which gives reliable error estimates for the optimised parameters (Southworthetal.2005).," We have fitted a spectroscopic orbit to the radial velocities using the code, which gives reliable error estimates for the optimised parameters \citep{Me+05mn}."1076 The radial velocities from the first night of VLT observations give an unambiguous period measurement of 90.69+0.67 mmin. and including the seven spectra from the second night gives a refined period of 91.39540.093 mmin.," The radial velocities from the first night of VLT observations give an unambiguous period measurement of $90.69 \pm 0.67$ min, and including the seven spectra from the second night gives a refined period of $91.395 \pm 0.093$ min."1077 The one-day alias solutions at 85.2 and 98.5 min can be ruled out. as they strongly disagree with the period from the data taken only on the first night and lead to radial velocity curves with a much increased scatter.," The one-day alias solutions at 85.2 and 98.5 min can be ruled out, as they strongly disagree with the period from the data taken only on the first night and lead to radial velocity curves with a much increased scatter."1078 The parameters of the best-fitting orbit are given in reftab:rvorbit.., The parameters of the best-fitting orbit are given in \\ref{tab:rvorbit}.1079 A. periodogram (Scargle1982) and phased radial velocity curve for the full dataset are shown in reffig:0039:rvplot.., A periodogram \citep{Scargle82apj} and phased radial velocity curve for the full dataset are shown in \\ref{fig:0039:rvplot}.1080" The velocity amplitude of this spectroscopic orbit. 39.244.2kms""! hhas been measured from the wings of the Ha emission line and is unlikely to accurately represent the motion of the WD: aceretion dise. asymmetries can induce spuriously large RV excursions even in the wings of emission lines."," The velocity amplitude of this spectroscopic orbit, $K_{\rm em} = 139.2 \pm 4.2$ has been measured from the wings of the $\alpha$ emission line and is unlikely to accurately represent the motion of the WD: accretion disc asymmetries can induce spuriously large RV excursions even in the wings of emission lines."1081 To investigate the reliability of the measurement we have constructed a diagnostic diagram (see Shafteretal.1986. and Thorstensen 2000)). where orbital solutions are plotted for a range of & ," To investigate the reliability of the measurement we have constructed a diagnostic diagram (see \citealt{Shafter++86apj} and \citealt{Thorstensen00pasp}) ), where orbital solutions are plotted for a range of $\xi$ "1082formation takes place at a higher redshift than in the HR runs. and then proceeds in a more efficient way.,"formation takes place at a higher redshift than in the HR runs, and then proceeds in a more efficient way."1083 Quite remarkably. the peak of star formation is even higher than for the highest resolution (VR) run.," Quite remarkably, the peak of star formation is even higher than for the highest resolution (VR) run."1084 Finally. results of the Lo8 run for the gas profiles are shown with the long-short-dashed curve in the bottom left panel of Fig. 6..," Finally, results of the 1o8 run for the gas profiles are shown with the long-short–dashed curve in the bottom left panel of Fig. \ref{fi:profs_res}."1085 Much like for the results on the cooled gas fraction. the resulting profiles are very similar to those of the MR and HR runs.," Much like for the results on the cooled gas fraction, the resulting profiles are very similar to those of the MR and HR runs."1086 Overall. the test on the degree of spurious gas heating from two-body relaxation confirms that à DM particle mass of at most ~10°1M. is sufficient to provide a reliable description of gas cooling within an already formed cluster of galaxies at low redshift.," Overall, the test on the degree of spurious gas heating from two–body relaxation confirms that a DM particle mass of at most $\simeq108710^9\msun$ is sufficient to provide a reliable description of gas cooling within an already formed cluster of galaxies at low redshift."1088 However. increasing the DM mass-resolution in order to reduce numerical heating of the gas from two-body encounters has a non—negligible effect on the number of resolved galaxies and on the star formation history. as a result of the better resolution of early structure formation.," However, increasing the DM mass–resolution in order to reduce numerical heating of the gas from two–body encounters has a non--negligible effect on the number of resolved galaxies and on the star formation history, as a result of the better resolution of early structure formation."1089 The comparatively low computational cost of the gravity part in a hydrodynamical simulation with radiative cooling. and the availability of large amounts of memory in modern supercomputers. may make it attractive to adopt a larger number of DM particles than gas particles in future simulation work.," The comparatively low computational cost of the gravity part in a hydrodynamical simulation with radiative cooling, and the availability of large amounts of memory in modern supercomputers, may make it attractive to adopt a larger number of DM particles than gas particles in future simulation work."1090 As we discussed in Section 2.. the initial Lagrangian particle distributions of the simulations of hhave been realized as a grid. while those of hhave been a glass.," As we discussed in Section \ref{sec:sims}, the initial Lagrangian particle distributions of the simulations of have been realized as a grid, while those of have been a glass."1091 The glass-based technique to generate initial conditions (ICs: 2)) aims at suppressing effects due to the regularity of the initial grid. which amplifies structure at the scale of the mean-interparticle separation.," The glass-based technique to generate initial conditions (ICs; ) aims at suppressing effects due to the regularity of the initial grid, which amplifies structure at the scale of the mean-interparticle separation."1092 In the glass scheme. particle positions are initially generated randomly in the simulation box. but are then evolved backwards in time until they reach an amorphous. minimum energy configuration where each particle experiences only vanishingly small forces.," In the glass scheme, particle positions are initially generated randomly in the simulation box, but are then evolved backwards in time until they reach an amorphous, minimum energy configuration where each particle experiences only vanishingly small forces."1093 The resulting irregular. particle distribution lacks prefered directions and should be less affected by the symmetries that occur in the grid method., The resulting irregular particle distribution lacks prefered directions and should be less affected by the symmetries that occur in the grid method.1094 In order to check the effect of using either one of the two techniques to generate ICs. we have rerun the CLS cluster with strong winds (SW). but this time starting from grid displacements.," In order to check the effect of using either one of the two techniques to generate ICs, we have rerun the CL5 cluster with strong winds (SW), but this time starting from grid displacements."1095 The results of this test are shown in Figure 10.. where we plot the corresponding star-formation histories (left panel) and the radial profiles of gas properties (right panels).," The results of this test are shown in Figure \ref{fi:grid_vs_glass}, where we plot the corresponding star–formation histories (left panel) and the radial profiles of gas properties (right panels)."1096 This comparison demonstrates that. at least at the resolution. relevant. for our simulations. the difference between using grid or glass ICs is very small.," This comparison demonstrates that, at least at the resolution relevant for our simulations, the difference between using grid or glass ICs is very small."1097 Looking at the details of the comparison. it turns out that tye grid-based run has a slightly higher star-formation at 2<6.," Looking at the details of the comparison, it turns out that the grid–based run has a slightly higher star–formation at $z\magcir10986$."1099 This may be due to a contribution of the small-scale fluctuation modes around the Nyquist frequency. which should collapse more efficiently in the grid case (and part of this may be artificial). favoring somewhat earlier cooling at high-z.," This may be due to a contribution of the small–scale fluctuation modes around the Nyquist frequency, which should collapse more efficiently in the grid case (and part of this may be artificial), favoring somewhat earlier cooling at $z$."1100 However. the star fractions within the cluster virial radius at >=0 are f;=0.17 for both runs.," However, the star fractions within the cluster virial radius at $z=0$ are $f_*=0.17$ for both runs."1101 The number of identified galaxies within the same region is 412 and 380 for the grid and glass runs. respectively.," The number of identified galaxies within the same region is 412 and 380 for the grid and glass runs, respectively."1102 This appears to confirm that grid-based ICs show slightly higher power on small scales. which. in turn. generates a slightly larger number of galaxies.," This appears to confirm that grid–based ICs show slightly higher power on small scales, which, in turn, generates a slightly larger number of galaxies."1103 As for the profiles of gas related quantities. we note that they also overlap quite closely.," As for the profiles of gas related quantities, we note that they also overlap quite closely."1104 The only noteworthy difference is that the positions of merging substructures vary., The only noteworthy difference is that the positions of merging substructures vary.1105 However. such differences in orbital timing are expected and common when different methods for the generation of ICs are used.," However, such differences in orbital timing are expected and common when different methods for the generation of ICs are used."1106 The general result of this comparison is that. at least at the resolution relevant for our cluster simulations. the effect of using either grid or glass ICs is very small. in any case negligible with respect to other numerical effects that we have explored in this paper.," The general result of this comparison is that, at least at the resolution relevant for our cluster simulations, the effect of using either grid or glass ICs is very small, in any case negligible with respect to other numerical effects that we have explored in this paper."1107 In this paper we have presented results from a large set of hydrodynamical simulations of galaxy clusters. carried out with the Tree+SPH codeGADGET-2.," In this paper we have presented results from a large set of hydrodynamical simulations of galaxy clusters, carried out with the Tree+SPH code."1108 Our simulations include radiative cooling. star formation and energy feedback by a phenomenological model for galactic winds.," Our simulations include radiative cooling, star formation and energy feedback by a phenomenological model for galactic winds."1109 The main target of our analysis has been the study of the stability of simulation results with respect to numerical parameters. such as mass resolution or gravitatiobal softening length.," The main target of our analysis has been the study of the stability of simulation results with respect to numerical parameters, such as mass resolution or gravitatiobal softening length."1110 We also considered different sources of numerical heating. and their interplay with the complex physical effects included.," We also considered different sources of numerical heating, and their interplay with the complex physical effects included."1111 As such. our analysis also represents a validation study of our previous results2).. which were based on a large cosmological box simulated a relatively low resolution.," As such, our analysis also represents a validation study of our previous results, which were based on a large cosmological box simulated a relatively low resolution."1112" Our simulated clusters span more than one order of magnitude in collapsed mass and several decades in mass resolution,", Our simulated clusters span more than one order of magnitude in collapsed mass and several decades in mass resolution.1113 A the highest resolution. the mass of the gas particles is mia.στ1.5«10h.! M... which allows us to resolve the virial region of a Virgo-like cluster with more than 2 million gas particles and at least as many dark-matter (DM) particles.," At the highest resolution, the mass of the gas particles is $m_{\rm gas}\simeq11141.5\times 10^7 h^{-1}{\rm M}_\odot$ , which allows us to resolve the virial region of a Virgo–like cluster with more than 2 million gas particles and at least as many dark–matter (DM) particles."1115 Our main results are concerned with the effects of resolution on the properties of the stellar populations and on the intra-cluster medium of the simulated galaxy clusters., Our main results are concerned with the effects of resolution on the properties of the stellar populations and on the intra–cluster medium of the simulated galaxy clusters.1116 They can be summarized as follows., They can be summarized as follows.1117 A further series of tests presented in this paper concerns the effect of numerical heating., A further series of tests presented in this paper concerns the effect of numerical heating.1118" The main results from these tests can be summarized as follows,", The main results from these tests can be summarized as follows.1119density wave theory.,density wave theory.1120" One of the few positive results is ?,, who find an age transition in M99."," One of the few positive results is \citet{Gonzalez1996}, who find an age transition in M99."1121" However ? analyse a sample of 13 spiral galaxies and find that in many galaxies, the colour gradients are opposite to the predictions of density wave theory (i.e. steeper on the leading side)."," However \citet{Mart2009} analyse a sample of 13 spiral galaxies and find that in many galaxies, the colour gradients are opposite to the predictions of density wave theory (i.e. steeper on the leading side)."1122" Furthermore, they often find that for a given galaxy, one spiral arm follows the predictions whilst the other does not (e.g. NGC 4254)."," Furthermore, they often find that for a given galaxy, one spiral arm follows the predictions whilst the other does not (e.g. NGC 4254)."1123" The results from our simulations show that in a tidally induced, or in a flocculent spiral, a clear transition in ages is not expected."," The results from our simulations show that in a tidally induced, or in a flocculent spiral, a clear transition in ages is not expected."1124" Thus the difficulty of finding a transition may simply reflect that those galaxies do not exhibit quasi-stationary density waves, but rather that their dynamics are more complex."," Thus the difficulty of finding a transition may simply reflect that those galaxies do not exhibit quasi-stationary density waves, but rather that their dynamics are more complex."1125" Alternatively the uncertainties may simply be too large to properly measure age differences, due to difficulties correcting for dust andHIL, and interarm star formation."," Alternatively the uncertainties may simply be too large to properly measure age differences, due to difficulties correcting for dust and, and interarm star formation."1126 The errors in their data are a sizable fraction of the gradients they show., The errors in their data are a sizable fraction of the gradients they show.1127" Thus age-dating techniques (e.g. ?7)) to directly measure the ages of stars may be a better, and more quantitative, way to differentiate between the theories of spiral arms."," Thus age-dating techniques (e.g. \citealt{Fall2009,Bastian2009}) ) to directly measure the ages of stars may be a better, and more quantitative, way to differentiate between the theories of spiral arms."1128" In fact, ? "," In fact, \citet{Kaleida2010} "1129with the V band measurements of the All Sky Automated Survey (ASAS;Pojmariski2002).,with the $V$ band measurements of the All Sky Automated Survey \citep[ASAS;][]{pojmanski02}.1130". For GK Per, we use the mean light curve of Campbell(1903) constructed from visual observations."," For GK Per, we use the mean light curve of \citet{campbell1903} constructed from visual observations."1131 We also include V373 Sct and its visual light curve published by Rosino(1978) and supplement it with AAVSO and AFOEV observations., We also include V373 Sct and its visual light curve published by \citet{rosino78} and supplement it with AAVSO and AFOEV observations.1132" To our knowledge, the above mentioned objects represent the best-observed novae exhibiting sufficient number of rebrightenings to study their timing evolution."," To our knowledge, the above mentioned objects represent the best-observed novae exhibiting sufficient number of rebrightenings to study their timing evolution."1133 Note that the error in a single visual estimate is usually assumed to be about 0.3 mag (Kissetal.1999) and we investigate events with amplitudes typically greater than 1 mag and defined by many observations of several observers., Note that the error in a single visual estimate is usually assumed to be about $0.3$ mag \citep{kissetal99} and we investigate events with amplitudes typically greater than $1$ mag and defined by many observations of several observers.1134 The rebrightenings we discuss here are robust., The rebrightenings we discuss here are robust.1135" In Figure 1,, we show the visual magnitudes of novae in our sample as a function of time."," In Figure \ref{fig:lc}, we show the visual magnitudes of novae in our sample as a function of time."1136" To illustrate a nova light curve with a smooth decline, we include a very fast nova, V1500 Cyg (Mattei 1993).."," To illustrate a nova light curve with a smooth decline, we include a very fast nova, V1500 Cyg \citep{mattei93}. ."1137" We plot moving-averaged data with bin size of 1 day, and we align the light curves so that the visual magnitude at the time of maximum tmax is 0 mag."," We plot moving-averaged data with bin size of $1$ day, and we align the light curves so that the visual magnitude at the time of maximum $\tmax$ is $0$ mag."1138" This procedure is potentially problematic in the case of V4745 Sgr and V2540 Oph, because the rebrightenings began shortly after discovery, unlike other novae."," This procedure is potentially problematic in the case of V4745 Sgr and V2540 Oph, because the rebrightenings began shortly after discovery, unlike other novae."1139" However, prediscovery ASAS observations of V4745 Sgr rule out the possibility that the true visual maximum was missed."," However, prediscovery ASAS observations of V4745 Sgr rule out the possibility that the true visual maximum was missed."1140" Given the overall similarity of light curves of both objects, wesuggest that the same is true for V2540 Oph and we set tmax for both objects to be approximately the time of discovery."," Given the overall similarity of light curves of both objects, wesuggest that the same is true for V2540 Oph and we set $\tmax$ for both objects to be approximately the time of discovery."1141" Importantly, an uncertainty of a couple of days in tmax does not affect any of our conclusions."," Importantly, an uncertainty of a couple of days in $\tmax$ does not affect any of our conclusions."1142" Shortly after maximum, the visual flux of novae decreases as a power-law function of time2005),, which can be observed as a linear decline in our Figure 1.."," Shortly after maximum, the visual flux of novae decreases as a power-law function of time, which can be observed as a linear decline in our Figure \ref{fig:lc}."1143" Several hundred days after tmax, the slope of the decline steepens, which is caused by a decrease in the wind mass-loss rate."," Several hundred days after $\tmax$, the slope of the decline steepens, which is caused by a decrease in the wind mass-loss rate."1144 The shell hydrogen burning stops shortly afterward (Hachisu&Kato2006)., The shell hydrogen burning stops shortly afterward \citep{hachisukato06}.1145. The rebrightenings start to occur approximately 20 days after the maximum., The rebrightenings start to occur approximately $20$ days after the maximum.1146" At this time, fast novae like GK Per or V1494 Aql have faded by about 4 visual magnitudes while the slow novae V2540 Oph and V4745 Sgr are still close to their maximal visual brightness."," At this time, fast novae like GK Per or V1494 Aql have faded by about 4 visual magnitudes while the slow novae V2540 Oph and V4745 Sgr are still close to their maximal visual brightness."1147" To investigate the nature of rebrightenings more closely, we plot in Figure 2 a blow-up of well-covered rebrightenings for V4745 Sgr, DK Lac ,and GK Per."," To investigate the nature of rebrightenings more closely, we plot in Figure \ref{fig:max} a blow-up of well-covered rebrightenings for V4745 Sgr, DK Lac ,and GK Per."1148 We see that the rise of brightness is much faster than the decline back to the base level., We see that the rise of brightness is much faster than the decline back to the base level.1149" Further, for all novae the amplitude of the rebrightenings ranges from 1.0 to 2.0 mag, without any obvious time dependence, although the duration of individual rebrightenings ranges from 2 days for GK Per to 10 days for V4745 Sgr."," Further, for all novae the amplitude of the rebrightenings ranges from $1.0$ to $2.0$ mag, without any obvious time dependence, although the duration of individual rebrightenings ranges from $2$ days for GK Per to $10$ days for V4745 Sgr."1150" We note that even for GK Per, where the time interval between the maxima is about 5 days, the individual rebrightenings are well separated by a period of essentially constant magnitude."," We note that even for GK Per, where the time interval between the maxima is about $5$ days, the individual rebrightenings are well separated by a period of essentially constant magnitude."1151" It should be noted, however, that the data for V603 Aql and V1494 Aql do not show the rebrightenings so clearly separated."," It should be noted, however, that the data for V603 Aql and V1494 Aql do not show the rebrightenings so clearly separated."1152 We attribute this to the lower quality of data available for these stars and to the averaging that smears out details in the light curves., We attribute this to the lower quality of data available for these stars and to the averaging that smears out details in the light curves.1153" Indeed, the phase of constant brightness stands out more clearly in unbinned data."," Indeed, the phase of constant brightness stands out more clearly in unbinned data."1154" Given this evidence, we consider the transition phase rebrightenings to be appropriatelydescribed as flares on top of a continuous underlying light curve."," Given this evidence, we consider the transition phase rebrightenings to be appropriatelydescribed as on top of a continuous underlying light curve."1155 Looking again at Figure 1 and particularly at the light, Looking again at Figure \ref{fig:lc} and particularly at the light1156The iudex of the velocitv-dispersiou-size relation is determined by. where 0 is the velocity-cdispersion of all particles having a relative distance r.,"The index of the velocity-dispersion-size relation is determined by, where $\sigma$ is the velocity-dispersion of all particles having a relative distance $r$."1157 Observations of the interstellar iiediuui suggest a constant index 6=dp on scales OO)=O(100) pe with 0.3τςὃνο0.5., Observations of the interstellar medium suggest a constant index $\delta=\delta_{\rm L}$ on scales ${\cal O}(0.1)-{\cal O}(100)$ pc with $0.3\la\delta_{\rm L} \la 0.5$.1158 This is expressed by Larsou's lw (c.g. Larsou 1981.. Scalo 19855.. Falgaroue Perault 1987.. Myers (οὐπα 1988)) Iu order ο preclude the effect of boundary conditions ou the scaling relations. upper aud lower cutoffs have to be taken iuto account.," This is expressed by Larson's law (e.g. Larson \cite{Larson81}, Scalo \cite{Scalo85}, Falgarone Perault \cite{Falgarone87}, Myers Goodman \cite{Myers88}) ) In order to preclude the effect of boundary conditions on the scaling relations, upper and lower cutoffs have to be taken into account."1159 The lower cutoff i given by the softening leugth., The lower cutoff is given by the softening length.1160 An upper cutoff arises from the final system size., An upper cutoff arises from the final system size.1161" Thus. the scope of application is for the velocity-dispersion-sizeaud the mass-size relation. e<<<2 Rog. aud €«ormRog/2. respectively, where Roy is the radius of the sphere centered at the origin which contaius 90% of the mass (see Παπνο Pfenniger 2001a))."," Thus, the scope of application is for the velocity-dispersion-sizeand the mass-size relation, $\epsilon<r<2R_{90}$ , and $\epsilon<r<R_{90}/2$, respectively, where $R_{90}$ is the radius of the sphere centered at the origin which contains $90\%$ of the mass (see Huber Pfenniger \cite{Huber01a}) )."1162 Tere. some N-body eravo-thermal experiments of svstenmis with weak dissipation. 1.6.. of svstenis in quasi-equilibrimui are preseuted.," Here, some $N$ -body gravo-thermal experiments of systems with weak dissipation, i.e., of systems in quasi-equilibrium are presented."1163 The results are compared with theoretical fiudiugs., The results are compared with theoretical findings.1164 Iu order to cover a range of energv with the same experiuent. a convenient wav is to introduce a weak global dissipation scheme allowing to describe a rauge of quasiequilibriun states.," In order to cover a range of energy with the same experiment, a convenient way is to introduce a weak global dissipation scheme allowing to describe a range of quasi-equilibrium states."1165 Were weal means that zi;2Tava. where ng is the dissipation time-scale.," Here weak means that $\tau_{\rm dis} \gg \tau_{\rm dyn}$, where $\tau_{\rm dis}$ is the dissipation time-scale."1166 Then. the results can be compared with theoretical equilibrium states.," Then, the results can be compared with theoretical equilibrium states."1167 Follana Laliena (2000)) examined theoretically the thermodvuaiics of sclberavitating svstemis with softened potcutials., Follana Laliena \cite{Follana00}) ) examined theoretically the thermodynamics of self-gravitating systems with softened potentials.1168 Thev soften the Newtonian potential bv keeping terms of au expansion in spherical Besscl functions (hereafter such a regularized potential is called a Follaua potential)., They soften the Newtonian potential by keeping $n$ terms of an expansion in spherical Bessel functions (hereafter such a regularized potential is called a Follana potential).1169 This reeularization allows the caleulation of the thermodvuamical quautities of a selt-eravitating svsteni., This regularization allows the calculation of the thermodynamical quantities of a self-gravitating system.1170 The form of their poteutial is similar to a Plunuuer potential with a corresponding softcuing leugth., The form of their potential is similar to a Plummer potential with a corresponding softening length.1171 Fie., Fig.1172 2 shows a softened Follana potential with v=10. and à Phuuimer poteutial with e=0.05.," \ref{folpot} shows a softened Follana potential with $n=10$, and a Plummer potential with $\epsilon = 0.05$."1173" Iu their theoretical work Follana Lalicua fouud for auld οποιο reguluization (κ 30) a phase transition below the critical cucrey 5,70.3235 in a region with uesative specific heat.", In their theoretical work Follana Laliena found for a mild enough regularization $n<30$ ) a phase transition below the critical energy $\varepsilon_c\approx -0.335$ in a region with negative specific heat.1174 The transition separates a high energv homogeneous phase from a low cnereyv collapsed phase with core-halo structure., The transition separates a high energy homogeneous phase from a low energy collapsed phase with core-halo structure.1175 We want to reproduce these fincines bv applying a Plunuuer potential (¢= 0)., We want to reproduce these findings by applying a Plummer potential $\xi=0$ ).1176 Furthermore. the effect of a smnall-scale repulsive force (62 1/3) is studied.," Furthermore, the effect of a small-scale repulsive force $\xi>1/3$ ) is studied."1177 For these purposes. simulations with a weak elobal dissipation streugth. a=0.025. are carried out.," For these purposes, simulations with a weak global dissipation strength, $\alpha=0.025$, are carried out."1178 The dissipation tine is then zi;=NOTdvn56.6TH. where the free fall time is. re=ris/ v2.," The dissipation time is then $\tau_{\rm dis} = 80\;\tau_{\rm dyn} = 56.6\;\tau_{\rm ff}$, where the free fall time is, $\tau_{\rm ff}=\tau_{\rm dyn}/\sqrt{2}$ ."1179 Before we discuss the results. let us bricthy present sole model properties.," Before we discuss the results, let us briefly present some model properties."1180 The initial state is a relaxed. unperturbed and confined N-body sphere with total ΙΟΥΝ ©= 1.," The initial state is a relaxed, unperturbed and confined $N$ -body sphere with total energy $\varepsilon=1$ ."1181In order to lollow the evolution of magnetic field topology. curing the reconnection we beein by showing in Figure 3. (he intersection of the fan surfaces with the z=0 plane.,In order to follow the evolution of magnetic field topology during the reconnection we begin by showing in Figure \ref{fig:fansz0} the intersection of the fan surfaces with the $z=0$ plane.1182 The strength of the flux ring increases linearly in time up to the final state which we have normalised as /=1., The strength of the flux ring increases linearly in time up to the final state which we have normalised as $t=1$.1183 We show the intersections bv. tracing field lines [rom each fan surface in (he close neighbourhood of the corresponding null which is possible since the disturbance is localised near the centre of the domain and so the eigenvalues associated with the nulls do not change in time., We show the intersections by tracing field lines from each fan surface in the close neighbourhood of the corresponding null which is possible since the disturbance is localised near the centre of the domain and so the eigenvalues associated with the nulls do not change in time.1184 In the images the [an surface of the lower null is coloured blue aud that of (he upper null in orange., In the images the fan surface of the lower null is coloured blue and that of the upper null in orange.1185 We first note (hat in the initial phase of the process the angle between (he fan surfaces decreases., We first note that in the initial phase of the process the angle between the fan surfaces decreases.1186 If the reconnection is weak (he process can stop in this phase without leading to anv change in the magnetic skeleton., If the reconnection is weak the process can stop in this phase without leading to any change in the magnetic skeleton.1187 However. a stronger reconnection event can lead to a further closing of the angle between the [an surfaces until thev intersect (at about /=0.44 in our model).," However, a stronger reconnection event can lead to a further closing of the angle between the fan surfaces until they intersect (at about $t=0.44$ in our model)."1188 Recall that erossings of the fan surfaces give the location of magnetic separators in (hat particular plane., Recall that crossings of the fan surfaces give the location of magnetic separators in that particular plane.1189 Hence the process creates (wo new separators and correspondingly (wo new magnetic flix domains., Hence the process creates two new separators and correspondingly two new magnetic flux domains.1190 In order to properly identilv the various fhix domains we label each of the distinct topological regions with the numbers I.VI. as shown in the lower-righthand image of Figure 3..," In order to properly identify the various flux domains we label each of the distinct topological regions with the numbers I–VI, as shown in the lower-right–hand image of Figure \ref{fig:fansz0}."1191 We shall examine the nature of these flux domains later in (his same section. but at this point it is already. possible to make some general statements about Chis tvpe of bifurcation.," We shall examine the nature of these flux domains later in this same section, but at this point it is already possible to make some general statements about this type of bifurcation."1192 Obviously the manner in which the fan planes can fold and intersect leads to the process always creating (or the reverse process annihilating) separators in pairs., Obviously the manner in which the fan planes can fold and intersect leads to the process always creating (or the reverse process annihilating) separators in pairs.1193 There is no way in which we can create a single new separator as long as the reconnection is localised. (, There is no way in which we can create a single new separator as long as the reconnection is localised. (1194This excludes that the whole domain under consideration is non-ideal aud (hat separators enter or leave the domain across the boundary).,This excludes that the whole domain under consideration is non-ideal and that separators enter or leave the domain across the boundary).1195relation.,relation.1196 Therefore. it is 1 principle possible to deduce the age of a star if its metallicity is known.," Therefore, it is in principle possible to deduce the age of a star if its metallicity is known."1197 This basic assumption of 1-zone chemical evolution models was dropped in our stochastic approach., This basic assumption of 1-zone chemical evolution models was dropped in our stochastic approach.1198 Therefore. 1t is not surprising that the well defined age-metallicity relation has to be replaced by a statistical relation.," Therefore, it is not surprising that the well defined age–metallicity relation has to be replaced by a statistical relation."1199 In Fig. 6..," In Fig. \ref{agemetal},"1200 the metallicity [Fe/H] of model stars is plotted against the time of their formation., the metallicity [Fe/H] of model stars is plotted against the time of their formation.

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