ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 A otal of 13 overlapping fields in the two surveys are taken into account only once in the area curve calculation., A total of 13 overlapping fields in the two surveys are taken into account only once in the area curve calculation.3 The combined sample covers about =15ceg7 ancl comprises a otal of 46 unique entries.," The combined sample covers about $\approx 15 \, \rm deg^2$ and comprises a total of 46 unique entries."4 The logΝS is presented in Figure 3.., The $\log N - \log S$ is presented in Figure \ref{fig_lognlogs}.5 The differential “normal galaxy counts in the 2kkeV of the two combined surveys are fit hy a power law vielding a slope of 2.46-E0.13., The differential `normal' galaxy counts in the keV of the two combined surveys are fit by a power law yielding a slope of $-2.46\pm0.13$.6 This correspond to a slope of 1.4640.18 for the cumulative number counts. in agreementwith the results of Tajer et al. (," This correspond to a slope of $-1.46\pm0.13$ for the cumulative number counts, in agreementwith the results of Tajer et al. ("72005) at bright Utxes ane Llornschemeieret al. (,2005) at bright fluxes and Hornschemeier et al. (82003: 1.46.0%OS at the faint end. the latter sample based on the same selection criteria used here (log[xffone <2).,"2003; $-1.46^{+0.28}_{-0.30}$ ) at the faint end, the latter sample based on the same selection criteria used here $\log f_X /9f_{opt}<-2$ )."10 We further explore the statistical properties of the normal galaxy sample by deriving the X-ray luminosity. function (LE) using methods that are Lully described. by Ceorgantopoulos et al. (, We further explore the statistical properties of the normal galaxy sample by deriving the X-ray luminosity function (LF) using methods that are fully described by Georgantopoulos et al. (112005).,2005).12 We estimate both the binned X-rav LE using the technique of Page Carrera (2000) and the parametric Maximum. Likelihood fit. (Tammann. Sandage Yahil 1979) adopting a Schechter (1976) form for the luminosity function.," We estimate both the binned X-ray LF using the technique of Page Carrera (2000) and the parametric Maximum Likelihood fit (Tammann, Sandage Yahil 1979) adopting a Schechter (1976) form for the luminosity function."13 We first estimate the 0.5-2kkeV. LE. for the ΙΝΔΙΑ data alone., We first estimate the keV LF for the 1XMM data alone.14 Figure 4 plots our results in comparison with those from the combined. NIIS and. CDE data [rom Ceorgantopoulos et al. (, Figure \ref{fig_lf_comp} plots our results in comparison with those from the combined NHS and CDF data from Georgantopoulos et al. (152005) shifted to the kkeV. bane assuming bL-—Ls.,2005) shifted to the keV band assuming $\Gamma=1.8$.16 There is good agreement within the leo errors further suggesting that the area curve derived. in section 77. is adequate for statistical studies., There is good agreement within the $1\sigma$ errors further suggesting that the area curve derived in section \ref{sec_xray} is adequate for statistical studies.17 We note tha the two sources without spectroscopic redshift estimate are not used in this caleulation., We note that the two sources without spectroscopic redshift estimate are not used in this calculation.18 We improve the statistical reliability. of our LE estimates by combining our sample with both the NIIS and 23 2£0.2 galaxies selected in the kkeV. spectral band from the CDE-N and C€CDE-S. The CDE-N data are obtained from. Hornschemeier et al. (, We improve the statistical reliability of our LF estimates by combining our sample with both the NHS and 23 $z \la 0.2$ galaxies selected in the keV spectral band from the CDF-N and CDF-S. The CDF-N data are obtained from Hornschemeier et al. (192003) by selecting a total of 15 sources. with 0.5-2kkeV. band detection.,2003) by selecting a total of 15 sources with keV band detection.20 All of these systems have spectroscopic redshifts available., All of these systems have spectroscopic redshifts available.21 In the case of the CDE-S we select a total of S sources detected in the kkeV spectral band with logfy/fii<2 from the catalogue. presented. by. Rosati et. al. (, In the case of the CDF-S we select a total of 8 sources detected in the keV spectral band with $\log f_X /f_{opt}<-2$ from the catalogue presented by Rosati et al. (222001).,2001).23 Spectroscopic (total of 5) or. photometric (total of 3) redshifts are available from Szokoly et al. (, Spectroscopic (total of 5) or photometric (total of 3) redshifts are available from Szokoly et al. (242004) anc Zheng et al. (,2004) and Zheng et al. (252004) respectively.,2004) respectively.26 This combined sample is also split into absorption and emission line svstems to explore the LE for dillerent galaxy types., This combined sample is also split into absorption and emission line systems to explore the LF for different galaxy types.27" Our results are plotted in Figure 5 with the maximum likelihood best-fit parameters presented in Table 1.. where £L, is the break of Schechter function. à is the faint-end slope and ó, the normalisation."," Our results are plotted in Figure \ref{fig_lf_all} with the maximum likelihood best-fit parameters presented in Table \ref{tab_xlf}, where $L_\star$ is the break of Schechter function, $\alpha$ is the faint-end slope and $\phi_\star$ the normalisation."28" In the same table we give the X-ray emissivity (luminosity per. Alpe’) estimated by the relation j,=fP(L)LdL. where &(L) is the luminosity function."," In the same table we give the X-ray emissivity (luminosity per $\rm Mpc^3$ ) estimated by the relation $j_x=\int \Phi(L)~L~dL$ , where $\Phi(L)$ is the luminosity function."29" The le errors on L, and o are estimated [rom the regions around the best fit where the likelihood function changes by 94=0.5 (e.g. Press et al.", The $1\sigma$ errors on $L_\star$ and $\alpha$ are estimated from the regions around the best fit where the likelihood function changes by $\delta L=0.5$ (e.g. Press et al.30 1992)., 1992).31" Phe uncertainties in ó, and jy are approximated. by performing 200 bootstrap resamples of the data and. then estimating the Gsth percentiles around. the median.", The uncertainties in $\phi_\star$ and $j_X$ are approximated by performing 200 bootstrap resamples of the data and then estimating the 68th percentiles around the median.32 For a Gaussian clistribution these correspond to the 68 per cent confidence level., For a Gaussian distribution these correspond to the 68 per cent confidence level.33 ligure 5. also compares the X-ray. luminosity function of the combined IXMM|NIIS]CDE sample at. à mean redshift +=0.087 with the higher-z LE estimates of Norman et al. (, Figure \ref{fig_lf_all} also compares the X-ray luminosity function of the combined 1XMM+NHS+CDF sample at a mean redshift $z=0.087$ with the $z$ LF estimates of Norman et al. (342004).,2004).35 These. authors used Bayesian: statistical analysis to select normal galaxy candidates in the CDE-North and South and derived the first ever X-ray luminosity function for these systems in two redshift bins with mecdians >=0.26 and z=0.66 respectively., These authors used Bayesian statistical analysis to select normal galaxy candidates in the CDF-North and South and derived the first ever X-ray luminosity function for these systems in two redshift bins with medians $z=0.26$ and $z=0.66$ respectively.36 Their z<0.5 LE in Figure 5 is in fair agreement with ours at the faint end but civerges at brighter luminosities., Their $z<0.5$ LF in Figure \ref{fig_lf_all} is in fair agreement with ours at the faint end but diverges at brighter luminosities.37 This may suggest. (1) contamination of the Norman et al. (, This may suggest (i) contamination of the Norman et al. (382004) sample by ACNs at bright luminosities. (ii) bias in our sample against X-ray . ⊔∐↓⋅⋜⊢↓⊔⊔⊔⊔∪⊔⊳∖⊳∖∙∖⇁⊳∖↿∢⋅⊔↓⊳∖↿∖⋖⋅⊓↳≱⋡∠⇀∖∕∿↓∪⋖⋅↓⋅⋏↳≱≱∖⊐∣⋊⋅≼∙⋜⋯⋡∖⋖⋅∪⇂ pple1 ↿⇂↥∢⋅⇂∪⋏∙≟↿∖∡∕⊽⇀∖⇠∕⊽⊓↗∕∕⊐∖∕2 selection or (it) evolution of the normal ealaxy luminosity function.,"2004) sample by AGNs at bright luminosities, (ii) bias in our sample against X-ray ultra-luminous systems (e.g. $L_X \ga 10^{42} \rm \, erg \, s^{-1}$ ) because of the $\log (f_X /f_{opt})<-2$ selection or (iii) evolution of the normal galaxy luminosity function."39 In the latter case. the median redshift of the 2<0.5 subsample of Norman οἱ al," In the latter case, the median redshift of the $z<0.5$ subsample of Norman et al."40 .ds ρω=0.26 higher than our mean of 2=0.087., is $z_{median}=0.26$ higher than our mean of $z=0.087$.41 For luminosity evolution of the form (1|z) derived by Norman ct al. (, For luminosity evolution of the form $(1+z)^{2.7}$ derived by Norman et al. (422004). a source at 2=0.26 is expected to become about 1.5 times more luminous relative to z= 0.087.,"2004), a source at $z=0.26$ is expected to become about 1.5 times more luminous relative to $z=0.087$ ."43 Such a brightening can indeed. partially account for the observed dillerences.," Such a brightening can indeed, partially account for the observed differences."44 In ‘Table 1 wealso estimate a 0.5-2kkeV N-ray emissivity of (0.24.+0.02)10 and (0.22+0.03) for emission and absorption line svstenis respectively.," In Table \ref{tab_xlf} wealso estimate a keV X-ray emissivity of $(0.24\pm0.02)\times10^{38}$ and $(0.22\pm0.03) \times4510^{38} \rm \, erg \, s^{-1} \, Mpc^{-3}$ for emission and absorption line systems respectively."46 These values are lower than previous estimates., These values are lower than previous estimates.47 For example Ceoreakakis ο al. (, For example Georgakakis et al. (482003b) used: stacking,2003b) used stacking49of the plasma.,of the plasma.50" The backerouud metric is written by the Bover-Lindquist coordinates with e=G1I. where A—rt""n2inr|5a7. MNEP—067|a?>cos0» 0. aud a0 and e denote the mass aud angular moment per unit mass of the black hole. respectively."," The background metric is written by the Boyer-Lindquist coordinates with $c=G=1$, where $\Delta \equiv r^2 -2mr +a^2 $, $\Sigma \equiv r^2 +a^2\cos^2\theta$ , and $m$ and $a$ denote the mass and angular momentum per unit mass of the black hole, respectively."51 The dow with the above assuniptions streams along a magnetic feld line. which is expressed by a magnetic stream function W=W(;.0) with WV= constant: V is basically the toroidal commpoucut of the vector potential.," The flow with the above assumptions streams along a magnetic field line, which is expressed by a magnetic stream function $\Psi=\Psi(r,\theta)$ with $\Psi=$ constant; $\Psi$ is basically the toroidal component of the vector potential."52 Stationaritv. axisviunetry and ideal MITD couditiou require the existence of five constants of motion (e.g. Bekenstein Ότο 1978: Camenzind 1986a).," Stationarity, axisymmetry and ideal MHD condition require the existence of five constants of motion (e.g., Bekenstein Oron 1978; Camenzind 1986a)."53" These conserved quantities are the total enerev LY). the total augular moment L(0). the angular velocity of the field line ΟΡ} and the particle fiux through a flux tube yk). which are given by where B,,=(A/S)καFy, is the toroidal coupoucut of the maguctic field. D, is the poloidal coniponent of the maguetic field seeu bya lab-frame observer and py.5—n,"" Unos."," These conserved quantities are the total energy $E(\Psi)$, the total angular momentum $L(\Psi)$, the angular velocity of the field line $\Omega_F(\Psi)$ and the particle flux through a flux tube $\eta(\Psi)$, which are given by where $B_\phi \equiv (\Delta/\Sigma)\sin\theta\; F_{\theta r}$ is the toroidal component of the magnetic field, $B_p$ is the poloidal component of the magnetic field seen bya lab-frame observer and $\rho_w^2\equiv g_{t\phi}^2-g_{tt}g_{\phi\phi}$ ."54" The poloidal. compoucut «p of the velocity is defined by ue=ayei (Asap. 0). where we set a,>0 (u<0) for ingoine flows."," The poloidal component $u_p$ of the velocity is defined by $u_p^2\equiv -u_Au^A$ $A=r$, $\theta$ ), where we set $u_p>0$ $(u^r<0)$ for ingoing flows."55" For the polytropic equation of state with adiabatic iudex D. the relativistic specific euthalpy p is written as (see Caimenuzind 1987). where and iy, is the vest mass of the particle."," For the polytropic equation of state with adiabatic index $\Gamma$, the relativistic specific enthalpy $\mu$ is written as (see Camenzind 1987), where and $m_{\rm p}$ is the rest mass of the particle."56 The quautities labeled by “inj” are specified at a poiut injecting plasma as a plasina source., The quantities labeled by “inj” are specified at a point injecting plasma as a plasma source.57" The boundary coucitious should be given by a plasma source model (ο,ος, the accretion disk/corona model. pai-creationmodel. aud so on)."," The boundary conditions should be given by a plasma source model (e.g., the accretion disk/corona model, pair-creationmodel, and so on)."58 Thus. werequire the specification of the additional fifth coustaut of motion. 5: inm à cold Iit.we obtain Zi;>0 and jt>mp(— fie).," Thus, werequire the specification of the additional fifth constant of motion, $h_{\rm inj}$ ; in a cold limit,we obtain $h_{\rm inj}\to 0$ and $\mu\to m_{\rm p}\, (\equiv \mu_{\rm c})$ ."59degradation due to a generic log-normal error clistribution in the estimation of halo masses.),degradation due to a generic log-normal error distribution in the estimation of halo masses.)60 We use halo occupancy distribution mocdels to estimate the stochasticitv £ resulting from more traditional surveys which apply uniform weights to targeted galaxies., We use halo occupancy distribution models to estimate the stochasticity $E$ resulting from more traditional surveys which apply uniform weights to targeted galaxies.61 Phe mean I1IODs for Iuminositv-thresholded: samples and LRGs are remarkably useful. approximations to the optimal weight functions., The mean HODs for luminosity-thresholded samples and LRGs are remarkably useful approximations to the optimal weight functions.62 However. additional stochasticitv is introduced into the mass estimator by the random variations in halo occupancy about the mean.," However, additional stochasticity is introduced into the mass estimator by the random variations in halo occupancy about the mean."63 Hence [uminositv-selected: or LRG catalogs require z8. more redshifts to reach à given LE than a survey with perfect knowledge of halo masses for which the optimal weighting can be applied., Hence luminosity-selected or LRG catalogs require $\approx 3\times$ more redshifts to reach a given $E$ than a survey with perfect knowledge of halo masses for which the optimal weighting can be applied.64 In. contrast. LWODs for blue or emission-line galaxies do not resemble the optimal weights. and hence require =LOO. more redshift measurements than an optimally-weighted survey to obtain a given ££.," In contrast, HODs for blue or emission-line galaxies do not resemble the optimal weights, and hence require $\approx 100\times$ more redshift measurements than an optimally-weighted survey to obtain a given $E$."65 Rancom sub-sampling such galaxies to the same space density as LRGs vields ££ values that are 2. larger than those for LRGs., Random sub-sampling such galaxies to the same space density as LRGs yields $E$ values that are $2\times$ larger than those for LRGs.66 We also find that low-mass halos cannot reconstruct the shot noise contributed by the massive halos. setting an upper limit on the ficlelity of the mass reconstruction for surveys that fail to icentify the most massive clusters.," We also find that low-mass halos cannot reconstruct the shot noise contributed by the massive halos, setting an upper limit on the fidelity of the mass reconstruction for surveys that fail to identify the most massive clusters."67 Application of optimal halo weighting can be even more benelicial for studies of cross-correlation between eravitational potential (i.c. mass) and other cosmological signals. since these experiments gain rapidly as the stochasticity ££ drops below the Lo=0.5 needed to make voltunc-limited power-spectrum measurements. ?)..," Application of optimal halo weighting can be even more beneficial for studies of cross-correlation between gravitational potential (i.e. mass) and other cosmological signals, since these experiments gain rapidly as the stochasticity $E$ drops below the $E=0.5$ needed to make volume-limited power-spectrum measurements. \citet{Park10},"68 find. for example. that mass weighting halos can greatly accuracy in estimation of gravitational potential if the halo catalog extends down to zLOMΑΙ. or lower.," find, for example, that mass weighting halos can greatly accuracy in estimation of gravitational potential if the halo catalog extends down to $\approx10^{13}h^{-1}M_\odot$ or lower."69 Applving the optimal weight is obviously. ellicient. in reducing noise in the estimation of BAO from power spectra and in cross-correlation cosmological tests., Applying the optimal weight is obviously efficient in reducing noise in the estimation of BAO from power spectra and in cross-correlation cosmological tests.70 In future work we will extend this study to the use of redshift space distortions to measure the growth rate of structure (e.g.2)..., In future work we will extend this study to the use of redshift space distortions to measure the growth rate of structure \citep[e.g.][]{Okumura10}.71 We are also investigating the potential for galaxy marking and non-linear mass estimators to further improve the ability to trace large-scale structure with observational cata., We are also investigating the potential for galaxy marking and non-linear mass estimators to further improve the ability to trace large-scale structure with observational data.72 We thank Roman Seoccimarro for. providing the NYU simulations., We thank Roman Scoccimarro for providing the NYU simulations.73 This work is supported by DOL grant. FOO2-95ER40893. and grants. AST-0908027. and AS'T-)O0SN241 from the National Science. Foundation.," This work is supported by DOE grant DE-FG02-95ER40893, and grants AST-0908027 and AST-0908241 from the National Science Foundation."74 The Millennium. simulation used in this paper was carried. out as part of the programme of the Virgo Consortium on the tegalta supercomputer of the Computing Centre of the Alax-Planck-Society in Garching., The Millennium simulation used in this paper was carried out as part of the programme of the Virgo Consortium on the Regatta supercomputer of the Computing Centre of the Max-Planck-Society in Garching.75 We thanks John LHellv for wlping accessing the Millennium database., We thanks John Helly for helping accessing the Millennium database.76 YC thanks the rospitality of the Institute for Computational Cosmology in Durham University when this work was finishing., YC thanks the hospitality of the Institute for Computational Cosmology in Durham University when this work was finishing.77 Following ?.. we can calculate the Jeans mass where « is the tsothermal sound speed and p is the mass density.," Following , we can calculate the Jeans mass where $a$ is the isothermal sound speed and $\rho$ is the mass density."78 For -7x10? (see Sect. 3.1.3) , For $n = 7 \times 10^5$ (see Sect. \ref{g11:dentemp}) )79and T= 60 K. we obtain a Jeans mass of «1.8 M...," and $T =$ 60 K, we obtain a Jeans mass of $\sim$ 1.8 ."80" We find a gas mass (M,) to the Jeans mass (Mj) ratio larger than unity: other interferometric studies toward IRDCs report ΛΜ>| as well.", We find a gas mass $M_g$ ) to the Jeans mass $M_J$ ) ratio larger than unity; other interferometric studies toward IRDCs report $M_g/M_J > 1$ as well.81 From our interferometric observations at Imm. and taking a flux density equal to the 3c detection level. we derive a mass sensitivity limit of 0.4M.," From our interferometric observations at 1mm, and taking a flux density equal to the $\sigma$ detection level, we derive a mass sensitivity limit of 0.4."82.. Comparing this value with the Jeans mass. we note that our mass sensitivity limit is good enough to detect fragments of the order of the Jeans mass.," Comparing this value with the Jeans mass, we note that our mass sensitivity limit is good enough to detect fragments of the order of the Jeans mass."83" Figure + shows the integrated intensity map of the CH;OH 3,-I, quartet of lines middle).", Figure \ref{F3mm} shows the integrated intensity map of the $_{3}$ OH $2_{k} \rightarrow 1_{k}$ quartet of lines ).84" This emission presents three maxima: one of them is spatially coincident with the | and 3 mm continuum emission which peaks at (1755.00)). the other two are located at (13/11.00""7)) and (-9755.22722)."," This emission presents three maxima; one of them is spatially coincident with the 1 and 3 mm continuum emission which peaks at ), the other two are located at ) and $-$ 2)."85 We plot sample spectra at four different positions. including the three maxima and one position on the envelope (3777.- 33). inordertocomparelineprofiles. absolutelinestrengths. andtherelai δι—ΠΕ ," We plot sample spectra at four different positions, including the three maxima and one position on the envelope $-$ 3), in order to compare line profiles, absolute line strengths, and the relative strengths among lines."86transition that arises from a smaller region is also shown middle)., The high excitation $_3$ OH $2_{1} \rightarrow 1_{1}E$ transition that arises from a smaller region is also shown ).87" Line widths at and close to the three peak positions. are. jn average 5 with line profiles showing red- and/or blueshifted ""wings"". while in the outer parts of the envelope. e.g. at the (3/77.-7/33)323 position.2 ] ] ] thelinewidthisnarrower(~ ---. zseespectra analin Fig.; 4))."," Line widths at and close to the three peak positions are, in average $\sim$ 5 with line profiles showing red- and/or blueshifted “wings”, while in the outer parts of the envelope, e.g., at the $-$ 3) position, the line width is narrower $\sim$ 2; see spectra in Fig. \ref{F3mm}) )."88 In Fig., In Fig.89 5. we present the integratedintensity map of the strongest line CH3:OH 56— 46A., \ref{F1mm} we present the integratedintensity map of the strongest line $_{3}$ OH $_{0} \rightarrow$ $_{0}A$.90 The emission distribution ts as extendedas that of the | mm continuum and the CH;OH 2;— ΗΕ emissions., The emission distribution is as extendedas that of the 1 mm continuum and the $_3$ OH $_{1} \rightarrow$ $_{1}E$ emissions.91 We derived the rotational temperatures and methanol column, We derived the rotational temperatures and methanol column92km s! level.,km $^{-1}$ level.93 Some of these variations might be explained by an underestimate of our uncertainties., Some of these variations might be explained by an underestimate of our uncertainties.94 Alternatively these variations could be caused either by binaries or by instabilities/waves in the complex atmospheres of these super- and hypergiants., Alternatively these variations could be caused either by binaries or by instabilities/waves in the complex atmospheres of these super- and hypergiants.95 Using the five least variable yellow hypergiants and the LBV. we find a velocity dispersion for the massive stars in Westerlund | of σ=2.1722 km s! with a confidence limit of955t.. assuming no significant errors in measured radial velocity differences between the stars.," Using the five least variable yellow hypergiants and the LBV, we find a velocity dispersion for the massive stars in Westerlund I of $\sigma=2.1^{+3.4}_{-0.9}$ km $^{-1}$ with a confidence limit of, assuming no significant errors in measured radial velocity differences between the stars."96" In reality even these least variable stars show radial velocity variations between epochs of a few km s'. implying that the quoted velocity ""Sispersion is only an upper limit of the true velocity dispersion."," In reality even these least variable stars show radial velocity variations between epochs of a few km $^{-1}$, implying that the quoted velocity dispersion is only an upper limit of the true velocity dispersion."97" In Figure 5. the probability distribution of the velocity ""Sispersion from our measurements is compared to several estimates of the velocity dispersion which we expect in virial equilibrium.", In Figure \ref{fig:p_vdisp} the probability distribution of the velocity dispersion from our measurements is compared to several estimates of the velocity dispersion which we expect in virial equilibrium.98" These estimates have been calculated using ""Sifferent estimates of the total mass of Westerlund [. as well as different rough approximations of the effects of possible mass segregation and the effects of a velocity anisotropy. which is suggested by the observed spatial elongation of Westerlund I. For all of these cases the observations favor a subvirial cluster."," These estimates have been calculated using different estimates of the total mass of Westerlund I, as well as different rough approximations of the effects of possible mass segregation and the effects of a velocity anisotropy, which is suggested by the observed spatial elongation of Westerlund I. For all of these cases the observations favor a subvirial cluster."99 For the lower photometric mass estimate of ? the observations are consistent with the cluster in. virial equilibrium., For the lower photometric mass estimate of \citet{Gen11} the observations are consistent with the cluster in virial equilibrium.100 In all cases we exclude that Westerlund I is significantly supervirial. implying that the cluster is bound. has survived any recent gas expulsion.," In all cases we exclude that Westerlund I is significantly supervirial, implying that the cluster is bound, has survived any recent gas expulsion."101 Barring any violent interactions with other clusters or molecular clouds. Westerlund IL. which might be the most massive young cluster in our Galaxy. is expected to survive for billions of years.," Barring any violent interactions with other clusters or molecular clouds, Westerlund I, which might be the most massive young cluster in our Galaxy, is expected to survive for billions of years."102 The density distribution of both the massive and intermediate mass stars in Westerlund I has been shown to be elongated (??)..," The density distribution of both the massive and intermediate mass stars in Westerlund I has been shown to be elongated \citep{Neg10,Gen11}."103 Here we will calculate the effect of this elongation on the dynamical mass calculation of Westerlund IL. using an ellipsoidal densityprofile.," Here we will calculate the effect of this elongation on the dynamical mass calculation of Westerlund I, using an ellipsoidal densityprofile."104 Such a profile is suggested by ?.. who fitted a density profile to their stellar density distribution of Westerlund I. where the lines of constant densities lie along ellipses instead of circles.," Such a profile is suggested by \citet{Gen11}, who fitted a density profile to their stellar density distribution of Westerlund I, where the lines of constant densities lie along ellipses instead of circles."105 To limit the number of free parameters as well as greatly simplify the equations. we will assume that one of the axis of the ellipsoid lies along the line of sight.," To limit the number of free parameters as well as greatly simplify the equations, we will assume that one of the axis of the ellipsoid lies along the line of sight."106 The other two axes are then the axes found by ? in the plane of the sky., The other two axes are then the axes found by \citet{Gen11} in the plane of the sky.107 We define the length of the semi-major axis found by ? as αι. the length of the semi-minor axis as a2 and than have αν as the length along the line of sight. which ts a unconstrained by observations.," We define the length of the semi-major axis found by \citet{Gen11} as $a_1$ , the length of the semi-minor axis as $a_2$ and than have $a_3$ as the length along the line of sight, which is a unconstrained by observations."108 For an ellipsoidal cluster in. virial) equilibrium. the elongation implies a velocity anisotropy. which is given by the tensor form of the virial theorem where 2KjjMayr Is the tensor form of the kinetic energy along the axis / and W;; is the potential energy tensor.," For an ellipsoidal cluster in virial equilibrium the elongation implies a velocity anisotropy, which is given by the tensor form of the virial theorem where $2 K_{jj}=M_{\rm dyn} \sigma_j^2$ is the tensor form of the kinetic energy along the axis $j$ and $W_{jj}$ is the potential energy tensor."109 For an ellipsoidal system this potential can be split up in a product of two factors (seeeq2.144in2): (1) which only depends on the axial ratios of the cluster: and (11) which is independent of the cluster's ellipticity or along which axis the potential energy tensor is calculated and only depends on the density dropoff along a single axis. which we take to be the observed semi-major axis.," For an ellipsoidal system this potential can be split up in a product of two factors \citep[see eq 2.144 in][]{Bin08}: (i) which only depends on the axial ratios of the cluster; and (ii) which is independent of the cluster's ellipticity or along which axis the potential energy tensor is calculated and only depends on the density dropoff along a single axis, which we take to be the observed semi-major axis."110 In functional form this corresponds to with where the A; are a complex function of the axial ratios given by Table 2.1 in ?.., In functional form this corresponds to with where the $A_j$ are a complex function of the axial ratios given by Table 2.1 in \citet{Bin08}.111 Note that the equations in this table assume «|>doa3. Which will make it necessary to rearrange the indices. if the axis along the line of sight is not the smallest.," Note that the equations in this table assume $a_1>a_2>a_3$, which will make it necessary to rearrange the indices, if the axis along the line of sight is not the smallest."112Because g does not depend on the ag» and a3 we can calculate this term for the sphericalcase. where we set a> and «3 to aj. For a spherical cluster we have A;= 2/3. so fitia3.αν)=1 and W;;=+W. (e.g.?) (2). ? 2..,"Because $g$ does not depend on the $a_2$ and $a_3$ we can calculate this term for the sphericalcase, where we set $a_2$ and $a_3$ to $a_1$ For a spherical cluster we have $A_j=2/3$ , so $f_{j}(a_1,a_2,a_3)=1$ and $W_{jj}=\frac{1}{3}W$ \citep[e.g.][]{Por10} \citep{Por10} \citet{Bra08} \citet{Gen11},"113density of ~2 g cm-?.,"density of $\sim1142$ g $^{-3}$."115" The largest KBOs have bulk densities of about 2 g cm-?, which is similar to the density predicted from cosmochemical estimates of the rock to ice ratio in the outer solar system (??).."," The largest KBOs have bulk densities of about 2 g $^{-3}$, which is similar to the density predicted from cosmochemical estimates of the rock to ice ratio in the outer solar system \citep{McKinnon1997,McKinnon2008}."116" Although the internal structures of large KBOs are unknown (?),, strong water features on the surfaces of the largest bodies suggest that they have differentiated (?).."," Although the internal structures of large KBOs are unknown \citep{Leinhardt2008}, strong water features on the surfaces of the largest bodies suggest that they have differentiated \citep{McKinnon2008}."117" Hence, in this work, we consider collisions between differentiated bodies only in the high resolution simulations."," Hence, in this work, we consider collisions between differentiated bodies only in the high resolution simulations."118" The material in the rocky cores were modeled using a tabulated version of the molecular ANEOS equation of state for SiOz (?),, and the ice mantles were modeled with the tabular 5-Phase equation of state for H3O (?).."," The material in the rocky cores were modeled using a tabulated version of the molecular ANEOS equation of state for $_{2}$ \citep{Melosh2007}, and the ice mantles were modeled with the tabular 5-Phase equation of state for $_{2}$ O \citep{Senft2008}."119" The internal temperature profile is dependent on the ice to rock ratio and the viscosity of ice; models indicate that temperatures for a Charon size body are generally low (e.g.,<300Kafter4Ga?).."," The internal temperature profile is dependent on the ice to rock ratio and the viscosity of ice; models indicate that temperatures for a Charon size body are generally low \citep[e.g., $<300$~K after1204~Ga][]{McKinnon2008}."121" As a result, a constant initial temperature of 150 K was chosen."," As a result, a constant initial temperature of 150 K was chosen."122 The bodies were initialized with hydrostatic pressure profiles., The bodies were initialized with hydrostatic pressure profiles.123 They were then allowed to settle in isolation for many dynamical times at which point all particles have negligible velocities s!) at the specified temperature., They were then allowed to settle in isolation for many dynamical times at which point all particles have negligible velocities (cms $^{-1}$ ) at the specified temperature.124" The number of (cmsparticles ranged from ~1.2x10? to ~4x10° (~ 24-36 particles per target a sufficient resolution to resolve shock heating and radius)the formation of family members, and the results were checked for sensitivity to resolution."," The number of particles ranged from $\sim 1.2 \times 10^{5}$ to $\sim 4125\times 10^{5}$ $\sim$ 24-36 particles per target radius) a sufficient resolution to resolve shock heating and the formation of family members, and the results were checked for sensitivity to resolution."126" As in all previous studies of giant impacts, the materials are hydrodynamic discussion in §3.3))."," As in all previous studies of giant impacts, the materials are hydrodynamic (see discussion in \ref{sec:cth}) )."127" The GADGET (seesimulations were run as long as was practically feasible, normally about 60 simulation hours."," The GADGET simulations were run as long as was practically feasible, normally about 60 simulation hours."128" At this time, the collision and mass loss process was complete; however, more time was needed to determine the long-term orbital stability of material bound to the largest object."," At this time, the collision and mass loss process was complete; however, more time was needed to determine the long-term orbital stability of material bound to the largest object."129 The N-body code was used to integrate the orbiting fragments for thousands of spin periods of the largest remnant., The N-body code was used to integrate the orbiting fragments for thousands of spin periods of the largest remnant.130 The GADGET output was translated and handed off topkdgrav., The GADGET output was translated and handed off to.131". In previous work on asteroid family formation, pairs of particles were merged into a single particle after each particle-particle collision to reduce computation time (resulting in artificial perfectly spherical collision remnants)."," In previous work on asteroid family formation, pairs of particles were merged into a single particle after each particle-particle collision to reduce computation time (resulting in artificial perfectly spherical collision remnants)."132" In this work, because of the significant elongation in the largest remnant, the shape and rotation rate needed to be preserved for the orbital evolution calculation, and particle merging could not be used."," In this work, because of the significant elongation in the largest remnant, the shape and rotation rate needed to be preserved for the orbital evolution calculation, and particle merging could not be used."133" Hence, the calculation utilized inelastic collisions (§2.2)) to pkdgravpreserve the shape and gravitational potential of the largest remnant."," Hence, the calculation utilized inelastic collisions \ref{sec:lowres}) ) to preserve the shape and gravitational potential of the largest remnant."134" However, the number of particles in the largest remnant in the GADGET simulation 10° particles) is too large to integrate in (~because of the computational expense of calculating the collisions within the largest remnant."," However, the number of particles in the largest remnant in the GADGET simulation $\sim 10^5$ particles) is too large to integrate in because of the computational expense of calculating the collisions within the largest remnant."135" Therefore, the largest remnant was de-resolved to contain ~105 particles by placing a grid over the body and placing all particles within a grid cell into a single particle."," Therefore, the largest remnant was de-resolved to contain $\sim 10^3$ particles by placing a grid over the body and placing all particles within a grid cell into a single particle."136" Each merged particle had a mass equal to the combined mass, a position equal to the center of mass position, and velocity vector equal to the center of mass velocity."," Each merged particle had a mass equal to the combined mass, a position equal to the center of mass position, and velocity vector equal to the center of mass velocity."137 The spin and shape of the largest remnant was preserved., The spin and shape of the largest remnant was preserved.138 The mass of the largest remnant using inelastic collisions was compared with a perfect merging collision outcome to test the stability of the handoff., The mass of the largest remnant using inelastic collisions was compared with a perfect merging collision outcome to test the stability of the handoff.139 The mass of the largest remnant was very similar in both cases., The mass of the largest remnant was very similar in both cases.140 The shape and ice-to-rock ratio of individual smaller remnants (the satellites and family members) were not resolved in the SPH simulation., The shape and ice-to-rock ratio of individual smaller remnants (the satellites and family members) were not resolved in the SPH simulation.141" Hence, the self-gravitating remnants outside of the largest remnant were merged into single particles."," Hence, the self-gravitating remnants outside of the largest remnant were merged into single particles."142" In this mannner, the de-resolved calculation allowed the stability simulation topkdgrav run for thousands of orbits in a reasonable amount of time."," In this mannner, the de-resolved calculation allowed the stability simulation to run for thousands of orbits in a reasonable amount of time."143 The impact conditions and outcomes of the resolution numerical simulations of possible Haumea-forming impact events are summarized in Table 1.., The impact conditions and outcomes of the low-resolution numerical simulations of possible Haumea-forming impact events are summarized in Table \ref{tab:pkd}.144" The last column of the table, collision type, describes the general class of the collision."," The last column of the table, collision type, describes the general class of the collision."145" We found three different collision outcomes in our restricted parameter space (see $4 for further discussion): 1)merge — the projectile and target merge after initial impact with little or no mass loss; 2) — the projectile initially hits the target with a large impact parameter and then separates, the projectile is decelerated, but remains relatively intact, and subsequently recollides at a much slower velocity resulting in a merger and a fast-spinning body; 3) — the projectile and target hit but do not lose enough energy to remain bound to each other."," We found three different collision outcomes in our restricted parameter space (see \ref{sec:disc} for further discussion): 1) – the projectile and target merge after initial impact with little or no mass loss; 2) – the projectile initially hits the target with a large impact parameter and then separates, the projectile is decelerated, but remains relatively intact, and subsequently recollides at a much slower velocity resulting in a merger and a fast-spinning body; 3) – the projectile and target hit but do not lose enough energy to remain bound to each other."146 The impact parameters that produced elongated bodies with a total mass and spin period similar to Haumea tend to be of the graze and merge category., The impact parameters that produced elongated bodies with a total mass and spin period similar to Haumea tend to be of the graze and merge category.147" Thus, collisions that form a Haumea-like body are found in a distinctly different parameter space than catastrophic disruption events."," Thus, collisions that form a Haumea-like body are found in a distinctly different parameter space than catastrophic disruption events."148 High-resolution hybrid simulations of the most successful collision scenarios for forming a Haumea-like planet were conducted to investigate the properties of the satellites and family members (Table 2))., High-resolution hybrid simulations of the most successful collision scenarios for forming a Haumea-like planet were conducted to investigate the properties of the satellites and family members (Table \ref{tab:sims}) ).149 A time series from an example collision simulation (sim., A time series from an example collision simulation (sim.150" 4) is presented in Fig. 2,"," 4) is presented in Fig. \ref{fig:tile},"151 which displays the materials in cross-section looking down on the collision plane., which displays the materials in cross-section looking down on the collision plane.152" The last frame, which has been rotated by ninety degrees to show the collision outcome edge-on, shows the surfaces of the largest remnant and the debris field."," The last frame, which has been rotated by ninety degrees to show the collision outcome edge-on, shows the surfaces of the largest remnant and the debris field."153" During the collision, the rocky cores of the progenitor bodies merge, and the resulting primary body spins so quickly that it sheds icy mantle material from the ends in many small clumps."," During the collision, the rocky cores of the progenitor bodies merge, and the resulting primary body spins so quickly that it sheds icy mantle material from the ends in many small clumps."154 Some of this material is gravitationally bound and some escapes from the primary., Some of this material is gravitationally bound and some escapes from the primary.155" In this scenario, the satellites and family members do not originate from the initial contact; instead, they are spun off after the subsequent merger."," In this scenario, the satellites and family members do not originate from the initial contact; instead, they are spun off after the subsequent merger."156" As a result, the V of the family members are small; in other words, the ejection velocities of the fragments are not much greater than the escape velocity of the merged primary."," As a result, the $_\infty$ of the family members are small; in other words, the ejection velocities of the fragments are not much greater than the escape velocity of the merged primary."157 The analytic and numerical results show that the optimum parameter space to form a Haumea-like planet is in an encounter slightly more energetic than merging between comparably sized bodies., The analytic and numerical results show that the optimum parameter space to form a Haumea-like planet is in an encounter slightly more energetic than merging between comparably sized bodies.158" Some of the merging cases that are close to the transition to graze and merge also produce an elongated, fast-spinning largest"," Some of the merging cases that are close to the transition to graze and merge also produce an elongated, fast-spinning largest"159however. be as a lower limit.,"however, be regarded as a lower limit."160 Therefore the number density of AGNs in the local regardeduniverse is considered to be larger than previously thought., Therefore the number density of AGNs in the local universe is considered to be larger than previously thought.161 3., 3.162 N-rav. properties of low luminosity AGNs and black hole mass 3.] X-ray spectra We summarize of LLAGNs using galaxies from which X-ray emission is dominatedX-ray by propertiesAGNs., X-ray properties of low luminosity AGNs and black hole mass 3.1 X-ray spectra We summarize X-ray properties of LLAGNs using galaxies from which X-ray emission is dominated by AGNs.163 X-ray images of these galaxies are consistent with point like in the hard. X-ray band and ratios are also similar to luminous , X-ray images of these galaxies are consistent with point like in the hard X-ray band and ratios are also similar to luminous Seyferts.164We use data of (1) NGC 315. 1097. 3031. 3079. 3147. 3998. 4203. 4450. Sevferts.4579. 4594. 4639. 4736. 5033. IC 1459 and (2)NGC€ 1052. 2273. 2639. 4258. 4941.," We use data of (1) NGC 315, 1097, 3031, 3079, 3147, 3998, 4203, 4450, 4579, 4594, 4639, 4736, 5033, IC 1459 and (2)NGC 1052, 2273, 2639, 4258, 4941."165 The absorption column densities [or galaxies in the eroup (1) and group (2) are Ny<107 and Ng10757. respectively.," The absorption column densities for galaxies in the group (1) and group (2) are $<10^{23}$ and $>10^{23}$, respectively."166 We classify these subclasses as “Pvpe 1 and 2 LLAGNs. respectively.," We classify these subclasses as Type 1 and Type 2 LLAGNs, respectively."167 TypeThe luminosity of indices for Pype 1 AXGNSs is shown in Fig 3., The luminosity dependence of photon indices for Type 1 AGNs is shown in Fig 3.168 The data for dependenceluminous photonSevlert | are taken from Nandra et al. , The data for luminous Seyfert 1 galaxies are taken from Nandra et al. (169,1997b).170Phe of ealaxiescolumn clensitics is also shown in 3. (1, The histogram of absorption column densities is also shown in Fig 3.171997b).These histogramindicate that absorption of Type 1 LLAGNs have Figquite similar figuresphoton indices to N-rayluminous spectraACGNs., These figures indicate that X-ray spectra of Type 1 LLAGNs have quite similar photon indices to luminous AGNs.172 The indices of 2 LLAGNSs also show no luminosity dependence. photonalthough errors for Typeindices are large for both Luminous and low luminosity Type 2 AGNs.," The photon indices of Type 2 LLAGNs also show no luminosity dependence, although errors for indices are large for both luminous and low luminosity Type 2 AGNs."173 The absorption column densities range from 107 to 1073 and there exists LLAGNSs both with absorption and small as in galaxies., The absorption column densities range from $10^{20}$ to $10^{24}$ and there exists LLAGNs both with heavy absorption and small absorption as in Seyfert galaxies.174 Note that the heavypresent sample is not absorptionand that the Sevfertdistribution of absorption column densities does not completerellect the optical depths and geometry of the obscuring matter around, Note that the present sample is not complete and that the distribution of absorption column densities does not reflect the optical depths and geometry of the obscuring matter around LLAGNs.175Thus X-ray LLACGNSs.continuum of LLAGNs are similar to luminous AGNs., Thus X-ray continuum shape of LLAGNs are quite similar to luminous AGNs.176 On the other hand. iron shapeIx emission line propertiesquite ancl variability in 1 LLAGNs are cdillerent from luminous AGNs.," On the other hand, iron K emission line properties and variability in Type 1 LLAGNs are different from luminous AGNs."177 No iron Ix. emissionType is detected from our Tvpe 1 LLAGN sample except for significantNGC, No significant iron K emission is detected from our Type 1 LLAGN sample except for NGC1781400IX and 12001 [or mixing coellicients of A..=10? and A..=I0! em? /s. respectively. compared to 1000 Ix in the case of equilibrium chemistry.,"K and $\,$ K for mixing coefficients of $K_{zz}=10^2$ and $K_{zz}=10^4\,$ $^2$ /s, respectively, compared to $\,$ K in the case of equilibrium chemistry."179 The jm band of NIL; appears ab Tayο 1000IN [or A.Z107 /s. instead of IK. Because of the the relatively [Lat equilibrium abundance profile of NII;. (his result is nearly independent of A...," The $\,\mu$ m band of $_3$ appears at $\Teff \wig< 1000\,$ K for $K_{zz}\wig> 10^2\,$ $^2$ /s, instead of $\,$ K. Because of the the relatively flat equilibrium abundance profile of $_3$, this result is nearly independent of $K_{zz}$ ."180" While NIL, can be depleted by more than one order of magnitude (for τω=5001). the pam fealtves remain strong (Fig."," While $_3$ can be depleted by more than one order of magnitude (for $\Teff=800\,$ K), the $\,\mu$ m features remain strong (Fig."181 3)., 3).182 Spectroscopy with the URS instrument on SIRTF between 5 and jm will complete the sampling of the spectral enerev distribution of brown dwarls.," Spectroscopy with the IRS instrument on SIRTF between 5 and $\,\mu$ m will complete the sampling of the spectral energy distribution of brown dwarfs."183" From our analysis of our nucLIR. svuthetic spectra. we find that the new data will: 1) clearly reveal the presence of Nll; in T dwarls. despite the strong depletion due to vertical transport in the atmosphere. 2) likely detect the silicate cloud ~10 pam im micd-L cwarls and put strong constraints on (he vertical structure of the cloud. 3) lead to a much more complete picture of non-equilibrium chemistry among CO. CIL. sO. Ne and NIL. 4) show COs in low-gravityv. high metallicity (argels near the L/T (ransiGion. 5) reveal interesting species such as I5. CII4D. and ihe I, CIA opacity. and 6) possibly discover brown clwarl stratospheres through emission from trace species such as COs. LCN, HCO. Colla. Coll; Cols and CIHISO. Furthermore. we predict that: 7) a strong band of PIL, at yan falls in the IRAC band 2. 8) IRAC photometry will be most useful for objects below 1. and 9) photospheric spectra of brown chwarls are of very little interest bevond jam. The mid-IR. spectral window is rich in diagnostics of brown dwarl atmospheres."," From our analysis of our mid-IR synthetic spectra, we find that the new data will: 1) clearly reveal the presence of $_3$ in T dwarfs, despite the strong depletion due to vertical transport in the atmosphere, 2) likely detect the silicate cloud $\sim 10\,\mu$ m in mid-L dwarfs and put strong constraints on the vertical structure of the cloud, 3) lead to a much more complete picture of non-equilibrium chemistry among CO, $_4$, $_2$ O, $_2$ and $_3$ , 4) show $_2$ in low-gravity, high metallicity targets near the L/T transition, 5) reveal interesting species such as $_2$ S, $_3$ D, and the $_2$ CIA opacity, and 6) possibly discover brown dwarf stratospheres through emission from trace species such as $_2$, HCN, HCO, $_2$ $_2$, $_2$ $_4$, $_2$ $_6$ and $_2$ O. Furthermore, we predict that: 7) a strong band of $_3$ at $\,\mu$ m falls in the IRAC band 2, 8) IRAC photometry will be most useful for objects below $\,$ K, and 9) photospheric spectra of brown dwarfs are of very little interest beyond $\,\mu$ m. The mid-IR spectral window is rich in diagnostics of brown dwarf atmospheres."184 Our understanding of these cool neighbors will grow dramatically with our first mid-IB. observations with SIRTF., Our understanding of these cool neighbors will grow dramatically with our first mid-IR observations with SIRTF.185 We thank Richard Freedman for providing the molecular opacities used in this caleulation and the SIRTFE/IBRS instrument team for informative discussions., We thank Richard Freedman for providing the molecular opacities used in this calculation and the SIRTF/IRS instrument team for informative discussions.186 This work was supported in part ον NASA grants NAG2-6007 and NAG5-8919 and NSF grant. AST 00-36288(MSM) and by NSF grant AST 00-86437 UxL)., This work was supported in part by NASA grants NAG2-6007 and NAG5-8919 and NSF grant AST 00-86288(MSM) and by NSF grant AST 00-86487 (KL).187 Part of this workwas supported by the United States Department of Energy. uider contract W-7405-ENG-36, Part of this workwas supported by the United States Department of Energy under contract W-7405-ENG-36188and constrain the origin of those lines. and test X-ray reverberation mapping in a large sample of ACGNs.,"and constrain the origin of those lines, and test X-ray reverberation mapping in a large sample of AGNs."189 We are very grateful to an anonymous. referee for helpful comments to improve the manuscript substantially., We are very grateful to an anonymous referee for helpful comments to improve the manuscript substantially.190 We hank the discussion. ancl suggestion from. Prof J. AL. Wane.," We thank the discussion and suggestion from Prof. J. M., Wang."191" This work is supported by the Natural Science. Foundation of China under grant m""MEIN11003022. deseeand he Guoshoujing Telescope.", This work is supported by the National Natural Science Foundation of China under grant 11003022 and the Guoshoujing Telescope.192 The (formerly named the Large Sky Area Multi-Objeet. Fiber Speetroscopic Telescope: LAMOST) is. funded. by the tional Development and Reform Commission. operated and managed by the hey Laboratory of Optical Astronomy. «λος CAS.," The Guoshoujing Telescope (formerly named the Large Sky Area Multi-Object Fiber Spectroscopic Telescope; LAMOST) is funded by the National Development and Reform Commission, operated and managed by the Key Laboratory of Optical Astronomy, NAOC, CAS."193 This research. has mace use of. results obtained withChandra. and.Suzaku. which are collaborative missions contributed by the USA (NASA). he ESA member states and the space agencies of Japan (JANA).," This research has made use of results obtained with, and, which are collaborative missions contributed by the USA (NASA), the ESA member states and the space agencies of Japan (JAXA)."1942005).. as in BOLO (see 6 of that paper for further. details).,", as in BO10 (see 6 of that paper for further details)."195" However. we modify the forcing and damping to take into account the z-direction. and instead of forcing an m=2 wave in the equatorial plane. we now have in Cartesian coordinates (with i7art|g 27). which is applied in the region Οδ,xrxO.rsu."," However, we modify the forcing and damping to take into account the $z$ -direction, and instead of forcing an $m=2$ wave in the equatorial plane, we now have in Cartesian coordinates (with $r^{2} = x^{2}+y^{2}+z^{2}$ ), which is applied in the region $0.85r_{box} \leq r \leq 0.9r_{box}$."196 We study a region rg.z:Phar.Moor]. where ro.=1.5. in arbitrary units (not the same as 3)).," We study a region $x,y,z \in197[-r_{box},r_{box}]$, where $r_{box}=1.5$, in arbitrary units (not the same as \ref{lineartheory3D}) )."198 For rz0Οων the solution is damped to zero bv using a parabolic smoothing function. as in BOLO.," For $r > 0.9r_{box}$ the solution is damped to zero by using a parabolic smoothing function, as in BO10."199 We primarily use a resolution of 256° or which the simulations were possible to run on a single Intel Core i7 machine. utilising all 8 cores. with a tvpical run time of several weeks to resolve a hundred: wave crossing times.," We primarily use a resolution of $256^{3}$, for which the simulations were possible to run on a single Intel Core i7 machine, utilising all 8 cores, with a typical run time of several weeks to resolve a hundred wave crossing times."200" We set uw=1 and choose a typical LOW wavelength of A,= 0.15. giving approximately S wavelengths within the box."," We set $\omega = 1$ and choose a typical IGW wavelength of $\lambda_{r} = 0.15$ , giving approximately 8 wavelengths within the box."201" The value of A, is chosen to be slightly larger than that used in most of the 2D caleulations.", The value of $\lambda_{r}$ is chosen to be slightly larger than that used in most of the 2D calculations.202 This increases the number of grid points within a wavelenth of the primary wave. partially ollsetting the reduction in resolution that results [rom using a smaller. number of grid. points per dimension than in 2D. Choosing larger wavelengths than this is found to result in unwanted elfects from the proximity of the forcing region. which modifies the linear solution.," This increases the number of grid points within a wavelenth of the primary wave, partially offsetting the reduction in resolution that results from using a smaller number of grid points per dimension than in 2D. Choosing larger wavelengths than this is found to result in unwanted effects from the proximity of the forcing region, which modifies the linear solution."203" The viscosity. ancl radiative diffusion coellicients. at. least one of which must be implemented in the code for numerical stability. ave chosen to be vy=4.10"" and &=0."," The viscosity and radiative diffusion coefficients, at least one of which must be implemented in the code for numerical stability, are chosen to be $ \nu = 4 \times20410^{-6}$ and $\kappa = 0$."205 An otherwise identical setup is used as in BOLO. except using Esoherical geometry instead of evlindrical geometry.," An otherwise identical setup is used as in BO10, except using spherical geometry instead of cylindrical geometry."206 We have confirmed that the linear solution is well reproduced: with us numerical setup., We have confirmed that the linear solution is well reproduced with this numerical setup.207 In this section we ceseribe the results of the numerica simulations., In this section we describe the results of the numerical simulations.208We analyse the results of the simulations using the INC/ON decomposition ceseribecl in. Xppencdix A. and reconstruct the solutions from. the compute IWOW amplitudes to compare with the simulation data. as described therein.,"We analyse the results of the simulations using the IW/OW decomposition described in Appendix \ref{refcoeff}, and reconstruct the solutions from the computed IW/OW amplitudes to compare with the simulation data, as described therein."209" From: preliminary investigation. we finc that n=23x(57À,.)&0.2 ts required. for breaking. so a variety of simulations are. performed. with forcing amplitudes either side of this value."," From preliminary investigation, we find that $\tilde{f}_{r}210\equiv f_{r} 2\pi/(\omega^{2}\lambda_{r}) \gtrsim 0.2$ is required for breaking, so a variety of simulations are performed with forcing amplitudes either side of this value."211 The basic results of these simulations are that the wave rellects approximately perfectly from the centre of the star if the amplitude of the wave is smaller than a certain critical value. which is fou to correspond with that required for isentropic overturning.," The basic results of these simulations are that the wave reflects approximately perfectly from the centre of the star if the amplitude of the wave is smaller than a certain critical value, which is found to correspond with that required for isentropic overturning."212 Above this value. wave breaking and critical laver formation occur.," Above this value, wave breaking and critical layer formation occur."213" This picture is identical to that in 2D. For a low-amplitude simulation. with max(7,) below the critical value for isentropic overturning (using — 0.1). we plot the variation in amplitudes of the IWs anc OWs. and also the reconstructed solutions in Fig 1.."," This picture is identical to that in 2D. For a low-amplitude simulation, with $\tilde{u}_{r}$ ) below the critical value for isentropic overturning (using $\tilde{f}_{r} =2140.1$ ), we plot the variation in amplitudes of the IWs and OWs, and also the reconstructed solutions in Fig \ref{256lam15fr01t49AinAout}."215 We analyse the results using the method described in Appencix A.. choosing a time once transients have been sulliciently. damped. and standing waves have formed.," We analyse the results using the method described in Appendix \ref{refcoeff}, choosing a time once transients have been sufficiently damped and standing waves have formed."216" The decay in radius is roughly. (though slightly smaller than) that which would be expected [rom viscous damping. by the fractional amount where e,=CArz/(zx7) is the (constant asymptotic) radial group velocity. for a wave of the given wavelength."," The decay in radius is roughly (though slightly smaller than) that which would be expected from viscous damping, by the fractional amount where $c_{g,r} = C\lambda_{r}^{2}/(2\pi^{2})$ is the (constant asymptotic) radial group velocity, for a wave of the given wavelength."217 As in 2D. we have confirmed. this explanation by running simulations without viscosity. which are found to not exhibit this decay (though these simulations eventually become numerically unstable ify =5s0).," As in 2D, we have confirmed this explanation by running simulations without viscosity, which are found to not exhibit this decay (though these simulations eventually become numerically unstable if $\nu=\kappa=0$ )."218 Using a smaller viscosity is also found. to reduce the wavelength-scale oscillations around the mean slope., Using a smaller viscosity is also found to reduce the wavelength-scale oscillations around the mean slope.219 These result. from the fact that the lincar solution to the forced wave problem is no longer exact in the presence of viscosity., These result from the fact that the linear solution to the forced wave problem is no longer exact in the presence of viscosity.220 We find that increasing the number of erid points within each shell (hy reducing the values Of ο and Fuss) slightly reduces the vertical extent of these oscillations. because this averages out the errors that result. from the assumption that the inviscid linear solution is exact.," We find that increasing the number of grid points within each shell (by reducing the values of $i_{step},j_{step}$ and $k_{step}$ ) slightly reduces the vertical extent of these oscillations, because this averages out the errors that result from the assumption that the inviscid linear solution is exact."221 However. increasing the number of erid points within each shell has negligible effect on the mean slope.," However, increasing the number of grid points within each shell has negligible effect on the mean slope."222 The spatial structure of the solutions. in. three dimensions in the wry-plane is very similar to that in two dimensions. as can be seen in Fig.," The spatial structure of the solutions in three dimensions in the $xy$ -plane is very similar to that in two dimensions, as can be seen in Fig."223 2 (which can be compared with Fig., \ref{256lam15fr01t35xy} (which can be compared with Fig.224 3 in BOLO)., 3 in BO10).225 In Fig. 3..," In Fig. \ref{256lam15fr01t35xz},"226" we plot m, on the .ez-plane.", we plot $\tilde{u}_{\phi}$ on the $xz$ -plane.227 This shows that the magnitude of the azimuthal velocity peaks at @=7/2. due to the latitudinal form of YF.," This shows that the magnitude of the azimuthal velocity peaks at $\theta = \pi/2$, due to the latitudinal form of $Y_{2}^{2}$."228 From the calculation in 3.2.. we expect the cllects of nonlinearity to be much weaker than the elects of viscosity for small-amplitude waves which do not cause convective overturning.," From the calculation in \ref{weaklynonlinear}, we expect the effects of nonlinearity to be much weaker than the effects of viscosity for small-amplitude waves which do not cause convective overturning."229 Since the cllects of weak nonlinearity are very small. it is cillicult to quantitatively confirm the results in 3 using. for example. an extension of the method deseribed in Appendix A for multiple / and m. values.," Since the effects of weak nonlinearity are very small, it is difficult to quantitatively confirm the results in \ref{weaklynonlinear}, , using, for example, an extension of the method described in Appendix \ref{refcoeff} for multiple $l$ and $m$ values."230 Nevertheless. we have qualitatively confirmed the result that the rellection is coherent ancl nearly. perfect. (in that ὃντε 1) for amplitudes below that required. for overturning the stratification.," Nevertheless, we have qualitatively confirmed the result that the reflection is coherent and nearly perfect (in that $\mathcal{R} \approx 1$ ) for amplitudes below that required for overturning the stratification."231 As in 2D we do not observe any instabilities that act on the waves when they have insullicient amplitude to overturn the stratification., As in 2D we do not observe any instabilities that act on the waves when they have insufficient amplitude to overturn the stratification.232 In this case. the waves can form global modes in the RZ.," In this case, the waves can form global modes in the RZ."233 In high-amplitucle simulations. in which the wave amplitude exceeds the overturning criterion. the wave overturns the stratification during part of its evele and a rapid instability acts on the wave. which leads to wave breaking within 13 wave periods.," In high-amplitude simulations, in which the wave amplitude exceeds the overturning criterion, the wave overturns the stratification during part of its cycle and a rapid instability acts on the wave, which leads to wave breaking within $1-3$ wave periods."234" “Vhis causes the rapid (within several wave »eriods) deposition of primary wave angular momentum. which spins up the mean How to Q,, Ovhich corresponds with he orbital angular frequency of the planet) ancl produces a critical laver."," This causes the rapid (within several wave periods) deposition of primary wave angular momentum, which spins up the mean flow to $\Omega_{p}$ (which corresponds with the orbital angular frequency of the planet) and produces a critical layer."235 This critical laver acts as an absorbing barrier or IN as is shown from Vig. 4..," This critical layer acts as an absorbing barrier for IWs, as is shown from Fig. \ref{256lam15fr1t45AinAout},"236 which plots the variation in amplitudes. of the IW and OW. and also thereconstructed wave solutions (which can be contrasted with Fig. 1)).," which plots the variation in amplitude of the IW and OW, and also thereconstructed wave solutions (which can be contrasted with Fig. \ref{256lam15fr01t49AinAout}) )."237 Once he critical laver has formed. we find Ass]& Lbs]. The central regions are not well described by the linearmocel.," Once the critical layer has formed, we find $|A_{out}| \ll |A_{in}|$ The central regions are not well described by the linearmodel,"238Blue compact dwarf galaxies (BCDs) generally host compact and ongoing star formation activities in metal-poor and gas- environments (Sargent&Searle1970:vanZee.Skillman.&Salzer 1998).,"Blue compact dwarf galaxies (BCDs) generally host compact and ongoing star formation activities in metal-poor and gas-rich environments \citep*{sargent70,vanzee98}."239 Because both low metallicity and rich gas content indicate an early evolutionary stage. BCDs can be used as nearby laboratories of primeval galaxies which should exist at high redshift.," Because both low metallicity and rich gas content indicate an early evolutionary stage, BCDs can be used as nearby laboratories of primeval galaxies which should exist at high redshift."240 In some BCDs. the most active class of star formation is taking place in super star clusters (SSCs)galaxies.," In some BCDs, the most active class of star formation is taking place in super star clusters (SSCs)."241 IL Zw 40 is a well studied BCD with a low oxygen abundance. 12|log(O/I1Il)=8.13 (Thuan&Izotov2005).," II Zw 40 is a well studied BCD with a low oxygen abundance, $12+\log (\mathrm{O/H})=8.13$ \citep{thuan05}."242.. This galaxy hosts a high star formation activity associated with the SSCs in the centre., This galaxy hosts a high star formation activity associated with the SSCs in the centre.243" At centimetre wavelengths. the central star-forming region in IT Zw 40 is compact and optically thick for free-free absorption. and is categorized as a ""supernebula! or ""ultradense rregion (Turner.Ho.&Beck1998:KobulnickyJohnson1999)."," At centimetre wavelengths, the central star-forming region in II Zw 40 is compact and optically thick for free–free absorption, and is categorized as a `supernebula' or `ultradense region' \citep{turner98,kobulnicky99}."244. Such a dense and compact star formation activity is called “active” mode in Huntetal.(2003) and Hirashita&Hunt(2004)., Such a dense and compact star formation activity is called `active' mode in \citet{hunt03} and \citet{hirashita04}.245. IT Zw 40 is also classified as a Wolf-Rayet galaxy: the Wolf-Rayet feature indicates that the typical age of the current starburst is a few Myr (Vacca&Conti1992)., II Zw 40 is also classified as a Wolf-Rayet galaxy: the Wolf-Rayet feature indicates that the typical age of the current starburst is a few Myr \citep{vacca92}.246 Buckalew.Kobulnickv.&Dufour(2005) derived an age of 2.6 Myr from the Ha and H.? equivalent widths., \citet{buckalew05} derived an age of 2.6 Myr from the $\alpha$ and $\beta$ equivalent widths.247 The Br equivalent width also shows age 3 Myr (Vanzietal. 2008).., The $\gamma$ equivalent width also shows age $\la 3$ Myr \citep{vanzi08}. .248 Stellar spectral synthetic models support young ages ~2 Myr. although there is an underlying old stellar population (Westeraetal. 2004).," Stellar spectral synthetic models support young ages $\sim 2$ Myr, although there is an underlying old stellar population \citep{westera04}."249 In order to trace dense “embedded” star-formation activities. optically thin star formation indicators are useful. such as far-infrared (FIR) dust luminosity (e.g.Kennicutt1998:Inoue.Hi-rashita.&Kamaya2000) and radio (thermal plus non-thermal) luminosity (Condon1992).," In order to trace dense `embedded' star-formation activities, optically thin star formation indicators are useful, such as far-infrared (FIR) dust luminosity \citep[e.g.][]{kennicutt98,inoue00} and radio (thermal plus non-thermal) luminosity \citep{condon92}."250. Indeed. there is a correlation between FIR and radio luminosities in nearby star-forming galaxies (e.g..deJongetal.1985:Helou.Soifer.&Rowan-Robinson 1985). which is naturally explained if both luminosities are strongly connected with star formation activities (ΝΙΚ1989).," Indeed, there is a correlation between FIR and radio luminosities in nearby star-forming galaxies \citep[e.g.,][]{dejong85,helou85}, which is naturally explained if both luminosities are strongly connected with star formation activities \citep{volk89}."251". However. the studies of radio—FIR relation are biased to objects with FIR detection (e.g.Condon 1992), which means that a significant dust enrichment has already occurred."," However, the studies of radio–FIR relation are biased to objects with FIR detection \citep[e.g.][]{condon92}, which means that a significant dust enrichment has already occurred."252" Therefore. the evolution of radio—FIR relation in young primeval galaxies is not yet clear,"," Therefore, the evolution of radio–FIR relation in young primeval galaxies is not yet clear."253 The gas density. the magnetic field strength. and the energy density of cosmic ray electrons affect the evolution of radio emission on various time-scales 2010). while the dust enrichment plays a role to increase the FIR luminosity (Hirashita&Hunt2008).," The gas density, the magnetic field strength, and the energy density of cosmic ray electrons affect the evolution of radio emission on various time-scales , while the dust enrichment plays a role to increase the FIR luminosity \citep{hirashita_hunt08}."254. There have been some observational studies on the evolution of radio—FIR relation along the cosmic age., There have been some observational studies on the evolution of radio–FIR relation along the cosmic age.255 The radio—FIR relation at moderate and high redshifts ἐς +) is broadly similar to that at thehe localloca! UniversUniverse Cg.GarrettJarrettnn2002:GrunpionimTupprontwa|DM2003:Ibarometal.2008:Murphy2009:Michalowski.Watson.&Hjorth 2010).. although there is also a slight indication of evolution (Vlahakis. 2010).," The radio–FIR relation at moderate and high redshifts $z\la 4$ ) is broadly similar to that at the local Universe \citep*[e.g.][]{garrett02,gruppioni03,ibar08,256murphy09,michalowski10}, although there is also a slight indication of evolution \citep{vlahakis07,seymour09,michalowski10}."257.The disadvantage of high-z observations is the difficulty in deriving quantities related to galaxy evolution (tage. metallicity. ete.)," The disadvantage of $z$ observations is the difficulty in deriving quantities related to galaxy evolution (age, metallicity, etc.)"258 with high accuracy., with high accuracy.259 On the other hand.studies of nearby metal-poor dwarf galaxies as ‘laboratories’ of primeval galaxies," On the other hand,studies of nearby metal-poor dwarf galaxies as `laboratories' of primeval galaxies"260 for svstematies is always open ended. and in these we Checking one new check we have recently performed.,"Checking for systematics is always open ended, and in these Proceedings we merely present one new check we have recently performed."261 ProceedingsIt concerns he merelyso-called present templates., It concerns the so-called systematic templates.262 The procedure Leading from the time series to a CMD svstematic as well as the map. an estimate of the systematic ellects mappossibly produces. the final product.," The procedure leading from the time series to a CMB map produces, as well as the map, an estimate of the systematic effects possibly plaguing the final product."263 These “systematic for DALR are well plaguingdocumented 0D. and display strongly Gaussian cmplates”structures. tracing the DAR patterns.," These “systematic templates” for DMR are well documented ), and display strongly non-Gaussian structures, tracing the DMR scanning patterns."264 The svstematic templates have negligible scanningpower., The systematic templates have negligible power.265 The worst effect. in he worst channel has a rms of about 6 pH at the 95% confidence level., The worst effect in the worst channel has a rms of about 6 $\mu K$ at the $95\%$ confidence level.266 Lt is unlikely that these effects could corrupt spectrums estimates., It is unlikely that these effects could corrupt power spectrum estimates.267 «onetheless it is well known that a non-Gaussian powerpattern with negligible power πια out over a Gaussian map with much larger »ower., Nonetheless it is well known that a non-Gaussian pattern with negligible power may visually stand out over a Gaussian map with much larger power.268 mawSimilarly it visuallycould. that these svstematies. while irrelevant or the of power happenspectrum estimation. could be responsible for he observed purposenonCGaussian bispectra. derived from ΟΛΗ maps.," Similarly it could happen that these systematics, while irrelevant for the purpose of power spectrum estimation, could be responsible for the observed nonGaussian bispectra, derived from DMR maps."269 In order to address this problem. we subjected the systematic templates o two tests.," In order to address this problem, we subjected the systematic templates to two tests."270 Firstly we computed the £7 spectra for the templates., Firstly we computed the $I^3_\ell$ spectra for the templates.271 The resulting. { are well outside the Gaussian. prediction. but. they do not correlate with the DMB observed. £7.," The resulting $I^3_\ell$ are well outside the Gaussian prediction, but they do not correlate with the DMR observed $I^3_\ell$."272 Secondly. we added or subtracted hese templates enhanced by a factor of up to 4 to DMI maps.," Secondly, we added or subtracted these templates enhanced by a factor of up to 4 to DMR maps."273 The effect on the £7 was always found to be , The effect on the $I^3_\ell$ spectrum was always found to be negligible.274This shows that the systematic elfeets spectrumdocumented in. have not only negligible.negligible but also elect on the 0]order statistics which we have power.studied.," This shows that the systematic effects documented in have not only negligible power, but also negligible effect on the higher order statistics which we have studied."275" To be negligiblemore we have higherapplied the above tests to [or svsteniaties in 53,1. specific53D. 9024. ancl 90."," To be more specific we have applied the above tests to templates for systematics in $53A$, $53B$, $90A$, and $90B$, separately."276 This is the templatessensible thing to do. given that the templates are separately.correlated. from. to ," This is the sensible thing to do, given that the templates are highly correlated from pixel to )."277We have considered the ellect of instrumenthighly to pixelthe pixel(Earth 0]). field: any unknown elfects at the spacecraft susceptibilityperiod: errors in the magneticcalibration associated with long-term drifts. and spincalibration errors at the orbit and errors due to incorrect removal of the COBE and. spinEarth. frequency: errors in for emissions from the DopplerEarth. and Dopplercllects: signals:artifacts due to correctinguncertainty in the correction for the correlation eclipsecreated by the low-pass filter on the," We have considered the effect of instrument susceptibility to the Earth magnetic field; any unknown effects at the spacecraft spin period; errors in the calibration associated with long-term drifts, and calibration errors at the orbit and spin frequency; errors due to incorrect removal of the COBE Doppler and Earth Doppler signals; errors in correcting for emissions from the Earth, and eclipse effects; artifacts due to uncertainty in the correction for the correlation created by the low-pass filter on the"278formulated the shock-acceleration for the arbitrary shock speeds without the cilfusion approximation.,formulated the shock-acceleration for the arbitrary shock speeds without the diffusion approximation.279 Their theories include the non-clillusive effect. which is important for relativistic shocks anc reproduce the same result. in the non-relativistic limit., Their theories include the non-diffusive effect which is important for relativistic shocks and reproduce the same result in the non-relativistic limit.280 Both of them are constructed in two parts., Both of them are constructed in two parts.281 First. they calculated {μονp). Gugto.p) ) which denotes the conditional. probability. that a particle entering into the upstreani (downstream) along a direction fto Will leave toward the downstream (upstream) along a direction yr.," First, they calculated $ P_u(\mu_0,\mu)$ $ P_d(\mu_0,\mu)$ ) which denotes the conditional probability that a particle entering into the upstream (downstream) along a direction $\mu_0$ will leave toward the downstream (upstream) along a direction $\mu$."282" They used. some phenominological scattering models to calculate. 2, and. £2).", They used some phenominological scattering models to calculate $P_u$ and $P_d$.283 Second. they calculated a power-law index using cdillerent wavs.," Second, they calculated a power-law index using different ways."284 Peacock(1981) calculated a power-law index assuming that particles cross a shock front many times and an energv-gain of cach step is fully uncorrelated (Peacock’s approximation)., \citet{b17} calculated a power-law index assuming that particles cross a shock front many times and an energy-gain of each step is fully uncorrelated (Peacock's approximation).285 Ixato&Taka-hara(2001). used. Peacock's approximation., \citet{b9} used Peacock's approximation.286 On the other hand. Vietri(2003). solved the transport equation exactly and caleulated: a power-law index (Vietri's. formulation).," On the other hand, \citet{b20} solved the transport equation exactly and calculated a power-law index (Vietri's formulation)."287 Le considered correlation among energv-gains of a particle., He considered correlation among energy-gains of a particle.288 Le used his original formulation to calculate a power-law index., He used his original formulation to calculate a power-law index.289 Vietri's formulation gives the dillerent. result. [rom Peacock's approximation in general but. both approaches eive the same result in the Newtonian limit (see also Blasi (2005)))., Vietri's formulation gives the different result from Peacock's approximation in general but both approaches give the same result in the Newtonian limit (see also \citet{b6}) ).290" To calculate a power-law index. we have to calculate D. and D, using5 some scattering5 models."," To calculate a power-law index, we have to calculate $P_u$ and $P_d$ using some scattering models."291" Kato&""Taka-hara(2001) considered the large-angle5 scattering5 in. both the upstream and the downstream to calculate >, and D, (Model A).", \citet{b9} considered the large-angle scattering in both the upstream and the downstream to calculate $P_u$ and $P_d$ (Model A).292 Ehe. large-angle scattering. model mimics the scattering in strongly. turbulent fields., The large-angle scattering model mimics the scattering in strongly turbulent fields.293 Lt is often supposed that the turbulence can be strong in astrophysical shock environments (see Ellisonet.al.(1990)... ancl references therein).," It is often supposed that the turbulence can be strong in astrophysical shock environments (see \citet{b7}, and references therein)."294 In this model. the initial information of the distribution function is lost when particles are scattered.," In this model, the initial information of the distribution function is lost when particles are scattered."295 S0 an enerev-gain factor of each step is uncorrelated., So an energy-gain factor of each step is uncorrelated.296 Moreover. Gallant&Achterbere(1999) pointed. oul necessity to consider the regular dellection as lar as relativistic shocks are concerned (Model D).," Moreover, \citet{b8} pointed out necessity to consider the regular deflection as far as relativistic shocks are concerned (Model B)."297 It was understood that return of the particles to a shock surface from the upstream region can be warranted even in the absence of scattering. provided background. magnetic fields are at an angle with the shock normal.," It was understood that return of the particles to a shock surface from the upstream region can be warranted even in the absence of scattering, provided background magnetic fields are at an angle with the shock normal."298 This is due to the fact particles return to the shock surface from the upstream by the regular cdellection before scattering occurs., This is due to the fact particles return to the shock surface from the upstream by the regular deflection before scattering occurs.299 In this paper. we examine how the variance of the energv-gain [actor inlluences the dillerence between Vietri's formulation and. Peacock’s approximation.," In this paper, we examine how the variance of the energy-gain factor influences the difference between Vietri's formulation and Peacock's approximation."300 Ht is useful to know when we can use Peacock's approximation because Peacock's approximation is simple to cderive a power-law index., It is useful to know when we can use Peacock's approximation because Peacock's approximation is simple to derive a power-law index.301 It is also important to understand Vietri's formulation and. Peacock’s approximation in detail because we can examine validity of the works in which Peacock’s approximation is used., It is also important to understand Vietri's formulation and Peacock's approximation in detail because we can examine validity of the works in which Peacock's approximation is used.302" First. we calculate. 77, ancl £2, in model A (where the Llarge-angle scattering occurs at both sides of a shock) which is suitable lor examining the cllect of the variance of the energv-gain [actor because there is no ellect of the correlation in this model."," First, we calculate $P_u$ and $P_d$ in model A (where the large-angle scattering occurs at both sides of a shock) which is suitable for examining the effect of the variance of the energy-gain factor because there is no effect of the correlation in this model."303 Phen we calculate a power-law index using both Peacock’s approximation and Vietri's. formulation., Then we calculate a power-law index using both Peacock's approximation and Vietri's formulation.304 Next. we consider model 3. where the large-angle scattering occurs in the downstream. and a particle is deflected by. large-scale. magnetic fields. in the upstream.," Next, we consider model B where the large-angle scattering occurs in the downstream and a particle is deflected by large-scale magnetic fields in the upstream."305 We calculate probability. functions and a power-law index using Peacock’s approximation anc Vietri's formulation in the same wav as the case of mocdel AX. Finally. we examine how the power-law index derived from Peacock’s approximation dilfers from the one derived from Vietri's formulation to examine the cllect of the variance.," We calculate probability functions and a power-law index using Peacock's approximation and Vietri's formulation in the same way as the case of model A. Finally, we examine how the power-law index derived from Peacock's approximation differs from the one derived from Vietri's formulation to examine the effect of the variance."306 In moclel X. we see that the variance allects the dillerence between Peacock's approximation and Vietri's formulation. and explain what the effect of the variance means physically.," In model A, we see that the variance affects the difference between Peacock's approximation and Vietri's formulation, and explain what the effect of the variance means physically."307 ‘To examine the above fact. we show the power-law index changing the shock velocity from a non-relativistic one to a hiehly-relativistic one.," To examine the above fact, we show the power-law index changing the shock velocity from a non-relativistic one to a highly-relativistic one."308" Morlino..Blasi&Vietri(2007) calculated: a power-law index with 0.04Pos.x19 considering the regular dellection. where 3, is the shock velocity and E; is the Lorentz factor of the shock velocity."," \citet{b16} calculated a power-law index with $0.04\leq\Gamma_s\beta_s\leq10$ considering the regular deflection, where $\beta_s$ is the shock velocity and $\Gamma_s$ is the Lorentz factor of the shock velocity."309 We extend this calculation to the highhy-relativistic range., We extend this calculation to the highly-relativistic range.310 The plan of this paper is as follows., The plan of this paper is as follows.311 In section 2 we briclly summarize the theoretical framework introduced in Wato&Vakahara(2001)., In section 2 we briefly summarize the theoretical framework introduced in \citet{b9}.312. We also review Peacock’s approximation ancl Vietri's formulation., We also review Peacock's approximation and Vietri's formulation.313 Ln section 38. first. we consider the large angle scattering in both the upstream and the downstream.," In section 3, first, we consider the large angle scattering in both the upstream and the downstream."314 Next. we consider the regular dellection in the upstream and the large angle scattering in the downstream.," Next, we consider the regular deflection in the upstream and the large angle scattering in the downstream."315 We also discuss what makes Peacock’s approximation inadequate., We also discuss what makes Peacock's approximation inadequate.316 Discussion and conclusion are presented in section 4., Discussion and conclusion are presented in section 4.317 In this paper we use the shock-acceleration formulation which is applicable to any value of the shock speed. in the static situation and caleulate a power-law index. using Peacockapproximation and Vietri's formulation., In this paper we use the shock-acceleration formulation which is applicable to any value of the shock speed in the static situation and calculate a power-law index using Peacock'approximation and Vietri's formulation.318 We assume the test. particle approximation ancl adopt the large-angle scattering., We assume the test particle approximation and adopt the large-angle scattering.319 We also consider the regular deflection hy scale magnetic fields. (, We also consider the regular deflection by large-scale magnetic fields. (320we take the unit e= 1) First. we have to determine a shock structure by solving jump conditions and an equation of state. (,"we take the unit $c=1$ ) First, we have to determine a shock structure by solving jump conditions and an equation of state. ("321c.g.irk& (1999))) Relativistic jump conditions are written as Number densities (n). pressure (p) and energy. densities (c) are all measured in the comoving frame of the plasma we refer to. while the Lorentz factor (E) is measured in the shock frame.,"e.g.,\citet{b11}) ) Relativistic jump conditions are written as Number densities (n), pressure (p) and energy densities $\epsilon$ ) are all measured in the comoving frame of the plasma we refer to, while the Lorentz factor $\Gamma$ ) is measured in the shock frame."322 Ehe indices uw and d refer to the upstream and downstream plasmas respectively., The indices 'u' and 'd' refer to the upstream and downstream plasmas respectively.323" For simplicity. we consider the case of a strong shock (Le. upstream plasma is cold). so that p,—0 and e~ nim."," For simplicity, we consider the case of a strong shock (i.e., upstream plasma is cold), so that $p_u=0$ and $\epsilon\sim n_um$ ."324 We use an equation of state which was introduced by νήσο (1951).., We use an equation of state which was introduced by \citet{b18}. .325 The basic assumption is that the plasma consists of a, The basic assumption is that the plasma consists of a326In this section we study the likelihood of association between UIIECIRs and the 453 AGNs identified in the IFGL. i.e. the sources in the [LAC catalog within the PAO Ποιά of view.,"In this section we study the likelihood of association between UHECRs and the 453 AGNs identified in the 1FGL, i.e. the sources in the 1LAC catalog within the PAO field of view."327 Figure 6 shows the skv map in Galactic coordinates of the PAO events and the LILAC sources., Figure \ref{fig:1lacmap} shows the sky map in Galactic coordinates of the PAO events and the 1LAC sources.328 These AGNs are located αἱ distances ranging from z20.001 (the nearest LLAC AGN is NGC 253) up to z&3.2. which corresponds to the FSRQ blazar PIxXS. 0336-017 (Abdoetal.20L0b).," These AGNs are located at distances ranging from $z \approx 0.001$ (the nearest 1LAC AGN is NGC 253) up to $z \approx 3.2$, which corresponds to the FSRQ blazar PKS 0336-017 \citep{1lac}."329. The left panel of Figure 8 shows the correlation signal of the PAO events with all {LAC AGNs., The left panel of Figure \ref{fig:agn} shows the correlation signal of the PAO events with all 1LAC AGNs.330" There is a maximal association between the (wo data sets at the angular scale ic2.4? (Le. P reaches a minimal value P480.01. corresponding to 54,4;=2.69)."," There is a maximal association between the two data sets at the angular scale $\psi \approx 2.4^\circ$ (i.e. $P$ reaches a minimal value $P_{\rm min} \approx 0.01$, corresponding to $S_{\rm max}=2.6\sigma$ )."331 Within 2.4. 1? events correlate with all the AGNs without distinction of distance or AGN class. whereas 6.5 correlations are expected by chance.," Within $2.4^\circ$, 12 events correlate with all the AGNs without distinction of distance or AGN class, whereas 6.5 correlations are expected by chance."332 The middle panel of Figure 8. shows the correlation signal with the 367 LLAC blazars., The middle panel of Figure \ref{fig:agn} shows the correlation signal with the 367 1LAC blazars.333 There is no significant correlation (i.e. ο< lo) between blazars and VITECRs that cannot be explained bv an isotropic flux of cosmic ravs., There is no significant correlation (i.e. $S<1\sigma$ ) between blazars and UHECRs that cannot be explained by an isotropic flux of cosmic rays.334 We also study (he amount of correlation obtained when cross-correlating separately the two classes of blazars. BL Lacertae and FSRQ. with the PAO UILECHIs.," We also study the amount of correlation obtained when cross-correlating separately the two classes of blazars, BL Lacertae and FSRQ, with the PAO UHECRs."335 We obtained for the 169 BL Lacertae LILAC sources a quite similar correlation signal to that of all blazars (1.6. consistent with chance correlations)., We obtained for the 169 BL Lacertae 1LAC sources a quite similar correlation signal to that of all blazars (i.e. consistent with chance correlations).336 If we select onlv FSRQ sources. we have a sample of 198 FSRQ objects. which increases (he sienilicance ol the correlation up to 2.30 at i26.57.," If we select only FSRQ sources, we have a sample of 198 FSRQ objects, which increases the significance of the correlation up to $2.3\sigma$ at $\psi \approx 6.5^\circ$."337 It is interesting to note that LLAC FSRQ blazars are located al 2>0.15. well outside the GZlIx horizon.," It is interesting to note that 1LAC FSRQ blazars are located at $z>0.15$, well outside the GZK horizon."338 Therefore. we should not expect an association of these objects with the arrival directions of UIIECHTUs.," Therefore, we should not expect an association of these objects with the arrival directions of UHECRs."339 The right5 panel of Figure5 3. displavs the amount of cross-correlation between the subset of 86 AGNs consisting of non blazars (i.e. 17 misaligned jet sources such as the radio galaxies Centaurus-entaurus A and M87)AIST) together with the (heAGNsAGNs that(hat |have not been beeniclentiliedidentified vet (69 sources)., The right panel of Figure \ref{fig:agn} displays the amount of cross-correlation between the subset of 86 AGNs consisting of non blazars (i.e. 17 misaligned jet sources such as the radio galaxies Centaurus A and M87) together with the AGNs that have not been identified yet (69 sources).340sources) The lower panel shows that the correlation significance raises above 1o in the range eX. , The lower panel shows that the correlation significance raises above $1\sigma$ in the range $2^\circ \lesssim \psi \lesssim 7.5^\circ$ .341"In particular. the probability signal reaches the mininnun value P4,25x10.! (Suas= 3.50) al c223.27. with 8 observed PAO event correlations. whereas only 2.9 chance correlations are expected."," In particular, the probability signal reaches the minimum value $P_{\rm min} \approx 5 \times 10^{-4}$ $S_{\rm max}=3.5\sigma$ ) at $\psi \approx 3.2^\circ$, with 8 observed PAO event correlations, whereas only 2.9 chance correlations are expected."342 These PAO events are correlated with 7 AGNs. of which Cen A. 4C--04.77 and NGC 4945 are the only sources whose AGN types are known.," These PAO events are correlated with 7 AGNs, of which Cen A, 4C+04.77 and NGC 4945 are the only sources whose AGN types are known."343 Protons or nuclei with energies above 60 EeV interact with the cosmic microwave background and suffer the GZlIx effect: a strong attenuation of their [αν for distant sources, Protons or nuclei with energies above 60 EeV interact with the cosmic microwave background and suffer the GZK effect: a strong attenuation of their flux for distant sources344Uncertainties in Tedecony and the total H-band magnitude are estimated from the range in values obtained from the fixed-n residual-corrected profiles.,"Uncertainties in $r_{e, deconv}$ and the total $H$ -band magnitude are estimated from the range in values obtained from the $n$ residual-corrected profiles."345" The errorsgiven in Table 1 are the rms errors of the best-fit parameters from all of the fits, and give an indication of the systematic errors due to differences between the observed surface brightness profile and the Sérrsic models used in the fitting procedure."," The errorsgiven in Table \ref{tab:prop}346 are the rms errors of the best-fit parameters from all of the fits, and give an indication of the systematic errors due to differences between the observed surface brightness profile and the Sérrsic models used in the fitting procedure."347 The uncertainty in n is estimated using simulations: we add random sky noise to the observed galaxy image., The uncertainty in $n$ is estimated using simulations: we add random sky noise to the observed galaxy image.348" This is repeated several times, resulting in a number of images, on each of which we perform the fitting procedure described above."," This is repeated several times, resulting in a number of images, on each of which we perform the fitting procedure described above."349 The uncertainty given in Table 1 is two times the rms error of the best-fit parameter from all of the fits., The uncertainty given in Table \ref{tab:prop} is two times the rms error of the best-fit parameter from all of the fits.350 Our results are the following: the galaxy is best fit by a Sérrsic profile with n=3.7., Our results are the following: the galaxy is best fit by a Sérrsic profile with $n=3.7$.351" Using the residual-corrected profile we find that the effective radius of the galaxy is Te,deconv=0.050 arcsec, which corresponds to Te0.42 kpc."," Using the residual-corrected profile we find that the effective radius of the galaxy is $r_{e, deconv} = 0.050$ arcsec, which corresponds to $r_{e, deconv} = 0.42$ kpc."352" If we fix the Sérrsic index to a constant deconvvalue, the inferred size does not vary substantially: redeconv varies from 0.31 kpc for n=9 to 0.51 kpc for n=1."," If we fix the Sérrsic index to a constant value, the inferred size does not vary substantially: $r_{e,deconv}$ varies from 0.31 kpc for $n=9$ to 0.51 kpc for $n=1$."353" Thus, the deviations from the best-fitting profile are <20%."," Thus, the deviations from the best-fitting profile are $< 20\%$."354 Our size estimate is therefore reasonably robust to deviations from the model profile., Our size estimate is therefore reasonably robust to deviations from the model profile.355 We have investigated the influence of PSF uncertainties; if we use PSFs extracted from other stars in the field we find variations in redeconv of «10%.," We have investigated the influence of PSF uncertainties; if we use PSFs extracted from other stars in the field we find variations in $r_{e, deconv}$ of $< 10\%$."356 We have used the Tiny Tim software to investigate the spatial dependence of the PSF independently., We have used the Tiny Tim software to investigate the spatial dependence of the PSF independently.357" We find that the derived effective radius changes very little with the position of the reference star used, with a maximum of in opposite corners of the field."," We find that the derived effective radius changes very little with the position of the reference star used, with a maximum of in opposite corners of the field."358 The difference in effective radius due to the distance between the reference star and the galaxy is less than1%., The difference in effective radius due to the distance between the reference star and the galaxy is less than.359. We therefore conclude that PSF errors do not present a significant problem in our analysis., We therefore conclude that PSF errors do not present a significant problem in our analysis.360 We now determine whether faint extended emission would be detected using our data., We now determine whether faint extended emission would be detected using our data.361" To this end we construct several simulated galaxy images which consist of two components; a compact component, described by an=4 Sérrsic profile with an effective radius roughly equal to the observed galaxy (see Table 1)), and an extended component, described by a Sérrsic profile with either n=4, Τε©3.5 kpc orn=1, τε&15 kpc."," To this end we construct several simulated galaxy images which consist of two components; a compact component, described by a $n=4$ Sérrsic profile with an effective radius roughly equal to the observed galaxy (see Table \ref{tab:prop}) ), and an extended component, described by a Sérrsic profile with either $n=4$, $r_e\approx 3.5$ kpc or $n=1$, $r_e\approx 15$ kpc."362 The extended component has a flux that is either or of the compact component’s flux., The extended component has a flux that is either or of the compact component's flux.363 The compact component’s flux is chosen such that the total flux of the two components is equal to the observed galaxy’s total flux., The compact component's flux is chosen such that the total flux of the two components is equal to the observed galaxy's total flux.364" The images are convolved with the PSF, and sky and readout noise are added."," The images are convolved with the PSF, and sky and readout noise are added."365" The images are then fit with a single Sérrsic profile using GALFIT, and a residual-corrected profile is constructed."," The images are then fit with a single Sérrsic profile using GALFIT, and a residual-corrected profile is constructed."366 By comparing the half-light radii obtained in this way to the intrinsic half-light radii we can quantify the sensitivity of our data to low surface brightness components., By comparing the half-light radii obtained in this way to the intrinsic half-light radii we can quantify the sensitivity of our data to low surface brightness components.367 The results of our simulated galaxy fits are shown in Figure 3.., The results of our simulated galaxy fits are shown in Figure \ref{fig:sim}. .368 The residual-corrected profiles closely follow, The residual-corrected profiles closely follow369" à. μ g,, Uzan2003)). (Savedoff", $\alpha$ $\mu$ $g_p$ \citealp{uzan03}) \citep{savedoff56}.370 α Kanekar(2008) Thompson1975:Wolfeetal.1976;Dzuba o: Murphyetal.(2004) [Aq/a|5.L+1.2)10.© (2)=1.75 Murphyetal.2003)). Srianandetal.2007:Molaro (Griest (Kanekaretal," $\alpha$ \citet{kanekar08b} \citealp{thompson75,wolfe76,dzuba99,darling03,chengalur03,kanekar04a,flambaum07b}) $\alpha$ \citet{murphy04} $\dal = (-5.4 \pm 1.2) 371\times 10^{-6}$ $\langle z \rangle = 1.75$ \citealp{murphy03}) \citealp{srianand07b,molaro08,murphy08b,kanekar10}) \citep{griest10}. \citep{kanekar04b,kanekar05alt},"372".2004: ~99.1% o. µ αν: Kanekar |AG/C)=(1.18d(0.16)«107 ~(0.217 Gμαην à. j; y,,. [Aqfal=(3.11.2)<10ο Murphyetal.(2004).. lower redshift."," $\sim 99.1$ $\alpha$ $\mu$ $g_p$ \citet{kanekar10b} $\left[\Delta G/G \right] = (-1.18 \pm 0.46) 373\times 10^{-5}$ $z \sim 0.247$ $G \equiv g_p [ \mu \alpha^2]^{1.85}$ $\alpha$ $\mu$ $g_p$ $\dal = (-3.1 \pm 1.2) \times 10^{-6}$ \citet{murphy04}, lower redshift."374 For three decades. ro-vibrational moleeular hydrogen (H») lines provided the sole method to directly probe changes in the proton-electron mass ratio (Thompson1975).," For three decades, ro-vibrational molecular hydrogen $_2$ ) lines provided the sole method to directly probe changes in the proton-electron mass ratio \citep{thompson75}."375. Unfortunately. few redshifted H» absorbers have been detected so far (e.g. Ledouxetal. 2003)). and. of these. only four have been found suitable to study changes in g (e.g. Ivanchiketal.2009:Malecetal.2010:Wendt&Molaro 2011).," Unfortunately, few redshifted $_2$ absorbers have been detected so far (e.g. \citealt{ledoux03}) ), and, of these, only four have been found suitable to study changes in $\mu$ (e.g. \citealt{ivanchik05,reinhold06,king08,thompson09,malec10,wendt11}) )."376 These results have also been controversial: Reinholdetal.(2006) obtained |Agr/pi]=(12.02:0.6)«100° from two absorbers at.2.63.0. Le. evidence for a larger value of µ at high redshift (see also Ivanchiketal. 2005)).," These results have also been controversial: \citet{reinhold06} obtained $\dmu = (+2.0 \pm 0.6) \times 10^{-5}$ from two absorbers at $z \sim 2.6 - 3.0$, i.e. evidence for a larger value of $\mu$ at high redshift (see also \citealt{ivanchik05}) )."377 However. independent re-analyses of these data by Kingetal.(2008) and Thompsonetal.(2009).. using improved wavelength calibration techniques. found no evidence for changes in ji.," However, independent re-analyses of these data by \citet{king08} and \citet{thompson09}, using improved wavelength calibration techniques, found no evidence for changes in $\mu$."378 Kingetal.(2008) obtain [Age/¢)=(12.643.0)«10.© from three absorbers at ;~2.63.0 (including the two systems of Reinholdetal. 2006)): note. however. that Wendtlaro(2011) argue that systematic errors have been in the latter analysis.," \citet{king08} obtain $\dmu = (+2.6 \pm 3.0) \times 10^{-6}$ from three absorbers at $z \sim 2.6 - 3.0$ (including the two systems of \citealt{reinhold06}) ); note, however, that \citet{wendt11} argue that systematic errors have been under-estimated in the latter analysis."379 A new laboratory technique to probe changes in gr was proposed by vanVeldhovenetal.(2004).. using inversior transitions of deuterated ammonia (ND).," A new laboratory technique to probe changes in $\mu$ was proposed by \citet{vanveldhoven04},, using inversion transitions of deuterated ammonia$_3$ )."380 Flambaum& adapted this technique to astrophysical circumstances. using ammonia (NH;) inversion lines anc rotational lines.," \citet{flambaum07b} adapted this technique to astrophysical circumstances, using ammonia $_3$ ) inversion lines and rotational lines."381 Rotational and inversion line frequencies have different dependences on µ. and a comparison betwee! the redshifts of NH; inversion lines and rotational (e.g. CO. HCO!. CS. etc) lines from asinglecosmologically-distantabsorbertsthussensitive tochangesin jj.," Rotational and inversion line frequencies have different dependences on $\mu$, and a comparison between the redshifts of $_3$ inversion lines and rotational (e.g. CO, $^+$, CS, etc) lines from asinglecosmologically-distantabsorberisthussensitive tochangesin $\mu$."382 OnlytworedshiftedNH;absorbers are currently known. at 2~0.685 towards BO218+357 (Henkeletal.2005) and :~(.586 towards BI830 210 (Henkeletal. 2008).," Onlytworedshifted$_3$absorbers are currently known, at $z \sim 0.685$ towards B0218+357 \citep{henkel05} and $z \sim 0.886$ towards $-$ 210 \citep{henkel08}."383.In both cases. the NH; detection spectra havebeenusedto obtain initialconstraints on changes in j/ (Murphyetal.2008a:Henkel 2009)..," .In both cases, the $_3$ detection spectra havebeenusedto obtain initialconstraints on changes in $\mu$ \citep{murphy08,henkel09}. ."384 Finally. the ammonia technique has also been used to search for spatial changes {πμ Levshakovetal.(2010) obtained the (conservative) constraint [Ayff]<3«10.7 from studies of multiple molecular clouds in the Galaxy.," Finally, the ammonia technique has also been used to search for spatial changes in $\mu$ : \citet{levshakov09} obtained the (conservative) constraint $\dmu < 3 \times 10^{-8}$ from studies of multiple molecular clouds in the Galaxy."385For that to occur. the trausfer of augular momentum from host star to exoplauet via tidal forces requires the rotation period of the star to be shorter than the orbital period of the planet.,"For that to occur, the transfer of angular momentum from host star to exoplanet via tidal forces requires the rotation period of the star to be shorter than the orbital period of the planet."386" Indeed. the median orbital period of the transiting plauets orbitiug the stars identified as anomalously slow projected rotators is Pcz3.2 days. while the median expected rotation period of their host stars is P.zm6.3 αν»,"," Indeed, the median orbital period of the transiting planets orbiting the stars identified as anomalously slow projected rotators is $P \approx 3.2$ days, while the median expected rotation period of their host stars is $P_{\ast}387\approx 6.3$ days."388 The presence of shghtly evolved stars among the host stars of transiting cxoplanets will also not produce false identifications as anomalously slow projected rotators., The presence of slightly evolved stars among the host stars of transiting exoplanets will also not produce false identifications as anomalously slow projected rotators.389 To see why. note that there are also slehth evolved stars in the control sample of SPOCS stars αμα recall that the threshold © required to ideutifv a star as an anomalously slow projected rotator was set by the aNd disagreement between model aud observation in the control sample.," To see why, note that there are also slightly evolved stars in the control sample of SPOCS stars and recall that the threshold $\Theta$ required to identify a star as an anomalously slow projected rotator was set by the maximum disagreement between model and observation in the control sample."390 Ii other words. the presence of slightly evolved stars has already: been accounted for iu setting the threshold.," In other words, the presence of slightly evolved stars has already been accounted for in setting the threshold."391 I plot in Figure 5. the distribution of the SPOCS suuple iu a theoretical IIR. diagram along with those transiting exoplauet hosts with trigonometric parallaxes., I plot in Figure \ref{fig05} the distribution of the SPOCS sample in a theoretical HR diagram along with those transiting exoplanet hosts with trigonometric parallaxes.392 I also iudicate the locations of those stellar hosts that I identified as anomalously slow projected rotators auc therefore potentially spin-orbit musalignecd systems., I also indicate the locations of those stellar hosts that I identified as anomalously slow projected rotators and therefore potentially spin-orbit misaligned systems.393 Figure 5 shows that many of the svstcms I identified as anomalously slow projected rotators appear to he evolving off of the zero-age main sequence (ZAMS).," Figure \ref{fig05}394 shows that many of the systems I identified as anomalously slow projected rotators appear to be evolving off of the zero-age main sequence (ZAMS)."395 Nevertheless. the fact that there are many stars in the control sample of SPOCS stars in similar evolutionary states sugeoests that the effects of stellar evolution on the rotation properties of evolved stars have already beeu accounted for ii iiv analysis.," Nevertheless, the fact that there are many stars in the control sample of SPOCS stars in similar evolutionary states suggests that the effects of stellar evolution on the rotation properties of evolved stars have already been accounted for in my analysis."396 Moreover. there are several hosts of trausitiug exoplanets that have evolved off of the ZAMS that I do not identify as anomalously slow projected rotators.," Moreover, there are several hosts of transiting exoplanets that have evolved off of the ZAMS that I do not identify as anomalously slow projected rotators."397 Collectively. these facts suggest that effects of stella: evolution cannot explain the rotation properties of the ten svstcis T identified as anomalously slow projected rotators.," Collectively, these facts suggest that effects of stellar evolution cannot explain the rotation properties of the ten systems I identified as anomalously slow projected rotators."398 Additional selection effects im either the SPOCS control sample or the transiting exoplauet sample are uulikely to affect this result., Additional selection effects in either the SPOCS control sample or the transiting exoplanet sample are unlikely to affect this result.399 Iudeed. the fact that SPOCS stars were preferentially selected to be those stars with sinall οποιο] esiné to euable high precision Doppler radial velocity measurements biases niv control sample o snaller esiu; at fixed stellar mass aud age.," Indeed, the fact that SPOCS stars were preferentially selected to be those stars with small enough $v\sin{i}$ to enable high precision Doppler radial velocity measurements biases my control sample to smaller $v\sin{i}$ at fixed stellar mass and age."400 However. since the candidate spin-orbit misaligned stars appear o have anomalously slow projected rotation. the bias acts against the false identification of a star as an anomalously slow projected rotator.," However, since the candidate spin-orbit misaligned stars appear to have anomalously slow projected rotation, the bias acts against the false identification of a star as an anomalously slow projected rotator."401 Though maenitude-inited transit survevs are biased toward stars slightly nore massive than the Sun. there are 276 stars in the control sample with AZ.=1.2M. to compare with.," Though magnitude-limited transit surveys are biased toward stars slightly more massive than the Sun, there are 276 stars in the control sample with $M_{\ast} \geq 1.2~M_{\odot}$ to compare with."402 Iu addition. though targeted transit surveys are biased oward less active stars. the control sample of SPOCS stars m similarly biased.," In addition, though targeted transit surveys are biased toward less active stars, the control sample of SPOCS stars in similarly biased."403 Trausit survevs should also not je biased toward evolved stars; as though both transit xobabilitv and transit duration increase linearly with rost stellar radius (favoring evolved svstenis). transit depth decreases quadratically with host stellar radius (favoring unevolved systems).," Transit surveys should also not be biased toward evolved stars, as though both transit probability and transit duration increase linearly with host stellar radius (favoring evolved systems), transit depth decreases quadratically with host stellar radius (favoring unevolved systems)."404 For that reason. the cliance of detecting a transiting planet is roughly iuscusitive to host stellar radius.," For that reason, the chance of detecting a transiting planet is roughly insensitive to host stellar radius."405 For the anomalously slow projected rotators identified in 822.5. I Bst in Table 2. the inchnation to the line 6| seht of the stellar rotation axis if the anomalous projected rotation is due fo spin-orbit uisalieumenut along the line of sight.," For the anomalously slow projected rotators identified in 2.3, I list in Table \ref{tbl-2} the inclination to the line of sight of the stellar rotation axis if the anomalous projected rotation is due to spin-orbit misalignment along the line of sight."406 I also note published RM lucasturements for four of the svsteius I identify as apparent slow projected rotators: ILAT-P-7. aud WASP-ll has been identified as a spin-orbit misaligned svsteni (Winnetal.2009b:Johnson2009)... while UD 17156 and TrES-I are consistent with spin-orbit alieuineut im the plane of the sky (Naritaetal.2009.2010).," I also note published RM measurements for four of the systems I identify as apparent slow projected rotators; HAT-P-7 and WASP-14 has been identified as a spin-orbit misaligned system \citep{win09b,joh09}, while HD 17156 and TrES-4 are consistent with spin-orbit alignment in the plane of the sky \citep{nar09,nar10}."407. Though IID 17156 is consistent with spin-orbit alieuuicut in the plane of the sky from RM mcasurcments. iuy technique measures iisalignment along the line of sight.," Though HD 17156 is consistent with spin-orbit alignment in the plane of the sky from RM measurements, my technique measures misalignment along the line of sight."408 There is other circmustautial evidence that WD 17156 is misaligned along the Lue of sieht., There is other circumstantial evidence that HD 17156 is misaligned along the line of sight.409 Fischeretal.(2007) iieasured a esiu/=2.6 kia Lon stellar radius R.=LATRS and used Ca IL Π and IN to infer a rotation period P..=12.8 davs.," \citet{fis07} measured a $v\sin{i}410= 2.6$ km $^{-1}$, a stellar radius $R_{\ast} = 1.47~R_{\odot}$ and used Ca II H and K to infer a rotation period $P_{\ast} = 12.8$ days."411 If the system has /=907. then a period P.=12.8 davs aud the inferred stellar radius HR.=1.17KR. nuaplies οsins=5.8 aus + (as compared to csin’=6.9 kins + expected sed on ivy simple model).," If the system has $i = 90^{\circ}$, then a period $P_{\ast} = 12.8$ days and the inferred stellar radius $R_{\ast} = 1.47~R_{\odot}$ implies $v\sin{i} = 5.8$ km $^{-1}$ (as compared to $v\sin{i} = 6.9$ km $^{-1}$ expected based on my simple model)."412 Clearly. it’s possible that iu lis case the activity indicator gives a spurious period estimate: still. if the ciscrepancy is due to uusalieuuen hen ἐκ=26° (as compared to ἐς=22° degrees from univ neasurenmoenut).," Clearly, it's possible that in this case the activity indicator gives a spurious period estimate; still, if the discrepancy is due to misalignment then $i_s = 26^{\circ}$ (as compared to $i_s = 22^{\circ}$ degrees from my measurement)."413 TrES-l is consistent with aliguiment iu the plane of he sky from measurements of the RAL effect., TrES-4 is consistent with alignment in the plane of the sky from measurements of the RM effect.414 However. hat is a different augle than that measured through iu analysis.," However, that is a different angle than that measured through my analysis."415" It could be that the ecometiy of the TrES- systei is apparently aligned in the plane of the sky bu uisalieued along the line of sight: alternatively, TYES- could simply be an anomalously slow rotator."," It could be that the geometry of the TrES-4 system is apparently aligned in the plane of the sky but misaligned along the line of sight; alternatively, TrES-4 could simply be an anomalously slow rotator."416 I find that teu of the 75 systems in Table 1 have anomalously slow projected rotation aud are likely spin-orbit misaligned aloug the line of sight., I find that ten of the 75 systems in Table \ref{tbl-1} have anomalously slow projected rotation and are likely spin-orbit misaligned along the line of sight.417 In contrast. the atest Rossiter-A\IcLanehlin measurements reported auc sunuuazrized in Traud et al. (," In contrast, the latest Rossiter-McLaughlin measurements reported and summarized in Triaud et al. ("4182010. submitted) sugecs iit cight of the 26 systems with RAL measurements lave significant spin-orbit müsalieuineut in the plaue of ie ska.,"2010, submitted) suggest that eight of the 26 systems with RM measurements have significant spin-orbit misalignment in the plane of the sky."419 The higher fraction of systems observed to be misaligned bv the RAL effect is expected. as the RA ffect can detect much smaller degrees of misaligniieu wan the coarser techuique described here.," The higher fraction of systems observed to be misaligned by the RM effect is expected, as the RM effect can detect much smaller degrees of misalignment than the coarser technique described here."420" Asstne for i6 ποιο! that the smallest degree of misaliguinen is technique cau identify is |/,,HaiCDOP (as sugeested by the minium difference from Table 2))."," Assume for the moment that the smallest degree of misalignment this technique can identify is $|i_p -421i_s|_{min} \approx 50^{\circ}$ (as suggested by the minimum difference from Table \ref{tbl-2}) )."422 Of ιο 26 systems with measureineuts of the RM effect. six wave |A|z50.," Of the 26 systems with measurements of the RM effect, six have $|\lambda| \gtrsim 50^{\circ}$."423 At the same time. the slightly higher incidence of mnüsalieued. svstenis iu the sample of RA ueasurenieuts iuieht be related to the fact that RA neasurements are resource intensive.," At the same time, the slightly higher incidence of misaligned systems in the sample of RM measurements might be related to the fact that RM measurements are resource intensive."424 That is. svstenuis hat ποσα to have a higher a priori probability of spiu-orbit musaliguiuent based on the current uuderstaudiug of spin-orbit misalignment (6.9. eccentric svstenis) are nore likely to be targeted for RM measurement.," That is, systems that seem to have a higher a priori probability of spin-orbit misalignment based on the current understanding of spin-orbit misalignment (e.g. eccentric systems) are more likely to be targeted for RM measurement."425 The fact hat this analvsis iucludes all known transiting exoplauct svstenus without the targeting biases inherent iu the current sample of RM measurements may even produce a less biased spin-orbit misaliguinent distribution., The fact that this analysis includes all known transiting exoplanet systems without the targeting biases inherent in the current sample of RM measurements may even produce a less biased spin-orbit misalignment distribution.426"c:2 MK for a solar twin with Lxz10?” erg s! to T= MK for a ZAMS star with Lx=(1—3)x10°° erg s! (Telleschietal,2005).",$\approx 2$ MK for a solar twin with $L_{\rm X} \approx 10^{27}$ erg $^{-1}$ to $T \approx 10$ MK for a ZAMS star with $L_{\rm X} = (1-3)\times 10^{30}$ erg $^{-1}$ \citep{telleschi05}.427". Consequently, S is expected to decrease toward higher activity levels (i.e., the line becomes progressively less important; Fig. 1))."," Consequently, $S$ is expected to decrease toward higher activity levels (i.e., the line becomes progressively less important; Fig. \ref{fig1}) )."428" This is indeed the case, the mostactive solar analog in the sample, 47 Cas B, showing S= 0.26, and the least active one, B Com, Sz1.21."," This is indeed the case, the mostactive solar analog in the sample, 47 Cas B, showing $S \approx 0.26$ , and the least active one, $\beta$ Com, $S\approx 1.21$."429" The values of S for WTTS and the two active, near-ZAMS stars 47 Cas B and EK Dra are similar, whereas for CTTS they are similar to inactive solar analogs with ages of z1 Gyr."," The values of $S$ for WTTS and the two active, near-ZAMS stars 47 Cas B and EK Dra are similar, whereas for CTTS they are similar to inactive solar analogs with ages of $\approx 1$ Gyr."430 Fig., Fig.431" 3aa shows the ratio between the intrinsic (unabsorbed) luminosities of the r and the Lya lines as a function of Lx, comparing with solar analogs from Telleschietal.(2005) and the larger MS sample from Nessetal.(2004)."," \ref{fig3}a a shows the ratio between the intrinsic (unabsorbed) luminosities of the $r$ and the $\alpha$ lines as a function of $L_{\rm X}$, comparing with solar analogs from \citet{telleschi05} and the larger MS sample from \citet{ness04}."432". For the TTS of Telleschietal. (2007c),, a good approximation to compute L(O r) from L(O ντ) is L(O r) =0.55L(O vin)) (Porquetetal.,2001)."," For the TTS of \citet{telleschi07c}, a good approximation to compute $L$ $r$ ) from $L$ ) is $L$ $r$ ) $= 0.55L$ ) \citep{porquet01}."433".? The trend of a decreasing ratio with increasing Lx for MS stars is followed by the sample of WT'TS, while CTTS again show a significant excess."," The trend of a decreasing ratio with increasing $L_{\rm X}$ for MS stars is followed by the sample of WTTS, while CTTS again show a significant excess."434 This also holds if the the surface X-ray flux (Lx/[4m R2]) is used on the abscissa (not shown)., This also holds if the the surface X-ray flux $L_{\rm X}/[4\pi R_*^2]$ ) is used on the abscissa (not shown).435" In principle, a suppressed Lyo flux in CTTS would produce the same anomaly, but as we show in Fig."," In principle, a suppressed $\alpha$ flux in CTTS would produce the same anomaly, but as we show in Fig."436" 3bb, L(O vur)) of CTTS and WTTS both follow the same trend (rather than being suppressed for CTTS by a factor of 223-4), also indistinguishable from MS stars."," \ref{fig3}b b, $L$ ) of CTTS and WTTS both follow the same trend (rather than being suppressed for CTTS by a factor of $\approx$ 3–4), also indistinguishable from MS stars."437" Therefore, the CTTS is due to an excess in the flux."," Therefore, the CTTS is due to an excess in the flux."438" We also consider a sample of strongly accreting (TAX) sources that show an anomalous soft component additional to a much more strongly absorbed coronal component; the soft component contributes essentially all of the observed and Lyo flux; it has been interpreted as originating from the base of jets (Güdeletal,2007b)..", We also consider a sample of strongly accreting (TAX) sources that show an anomalous soft component additional to a much more strongly absorbed coronal component; the soft component contributes essentially all of the observed and $\alpha$ flux; it has been interpreted as originating from the base of jets \citep{guedel07b}.439" The low-resolution EPIC spectra are not useful to derive an S ratio, but the spectral fits are appropriate to estimate the luminosity in the dominant Lya line from the model."," The low-resolution EPIC spectra are not useful to derive an $S$ ratio, but the spectral fits are appropriate to estimate the luminosity in the dominant $\alpha$ line from the model."440 Overplotting L(O viit)) in Fig., Overplotting $L$ ) in Fig.441" 3bb shows a poor correlation, as should be expected because the coronal component shows a separate (harder) spectrum whose Lyo line is, however, entirely absorbed."," \ref{fig3}b b shows a poor correlation, as should be expected because the coronal component shows a separate (harder) spectrum whose $\alpha$ line is, however, entirely absorbed."442" All CTTS (except the two flaring ones) show an excess defined by an anomalously high ratio between the fluxes of the triplet and the Lya line, compared to WTTS and MS stars."," All CTTS (except the two flaring ones) show an defined by an anomalously high ratio between the fluxes of the triplet and the $\alpha$ line, compared to WTTS and MS stars."443" The anomaly refers to CTTS only, while WTTS show line ratios comparable with very active MS stars."," The anomaly refers to CTTS only, while WTTS show line ratios comparable with very active MS stars."444" In contrast, the correlation between L(O νι) and Lx is indistinguishable between CTTS, WTTS, and MS stars, suggesting that the CTTS soft excess is indeed due to an excess of cool material with TS2 MK rather than a relative suppression of the Lya line (e.g., due to resonance scattering)."," In contrast, the correlation between $L$ ) and $L_{\rm X}$ is indistinguishable between CTTS, WTTS, and MS stars, suggesting that the CTTS soft excess is indeed due to an excess of cool material with $T \la 2$ MK rather than a relative suppression of the $\alpha$ line (e.g., due to resonance scattering)."445 The strongly accreting TAX sources do not fit into this picture; strong absorption makes theircoronal and Lyo lines inaccessible., The strongly accreting TAX sources do not fit into this picture; strong absorption makes their and $\alpha$ lines inaccessible.446 Is the X-rayexcess described here the high-temperature equivalent of the UV/optical continuum and line excesses?, Is the X-ray described here the high-temperature equivalent of the UV/optical continuum and line excesses?447" We correlated L(O r), which is dominated by the excess emission, with UV Sirr,Silv,,Crv,, and A1958 continuum luminosities (all strongly dominated by excess emission) derived from fluxes presented by Valentietal.(2000),, applying the R=3.1 extinction law given by Cardellietal.(1989)."," We correlated $L$ $r$ ), which is dominated by the excess emission, with UV , and $\lambda$ 1958 continuum luminosities (all strongly dominated by excess emission) derived from fluxes presented by \citet{valenti00}, applying the $R=3.1$ extinction law given by \citet{cardelli89}."448. No correlation was found., No correlation was found.449" This is little surprising given that the UV excess luminosities amount to 10?—104 times the levels of *normal"" stars, with a large scatter over the entire range (Johns-Krulletal., 2000),, while the excessis comparatively small."," This is little surprising given that the UV excess luminosities amount to $10^2-10^4$ times the levels of “normal” stars, with a large scatter over the entire range \citep{johnskrull00}, , while the excessis comparatively small."450 Fig., Fig.451" 3 in fact suggests that for most CTTS reported here, the L(O r)/ L(O vu)) ratio is a factorof 23-4 that of equivalent MS stars, ie., L(Ovu r) scales with L(O vim)) as in MS stars, except that it is enhanced by a factor of z3- L("," \ref{fig3} in fact suggests that for most CTTS reported here, the $L$ $r$ $L$ ) ratio is a factorof $\approx$ 3–4 that of equivalent MS stars, i.e., $L$ $r$ ) scales with $L$ ) as in MS stars, except that it is enhanced by a factor of $\approx$3--4."452O vii)) in turn is “normal” and scales with Lx , $L$ ) in turn is “normal” and scales with $L_{\rm X}$ 453As primordial density fluctuations grow through eravitational Jeans instability within CDAI-like models. the web-like distribution of dark matter strongly inlluences the clustering of barvonic matter on large scales(Bietal.1992:Theunsetal.1998:Zhangct 1998)).,"As primordial density fluctuations grow through gravitational Jeans instability within CDM-like models, the web-like distribution of dark matter strongly influences the clustering of baryonic matter on large scales\citealt{Bi92,Cen92,Hernquist96,MiraldaEscude96,Theuns98,Zhang98}) )."454 After the epoch of hydrogen reionization. the hydrogen gas present in this barvonie component is highly ionized. leaving only a small fraction of the gas as neutral atoms in photoionization equilibrium within the intergalactic medium (LGAL).," After the epoch of hydrogen reionization, the hydrogen gas present in this baryonic component is highly ionized, leaving only a small fraction of the gas as neutral atoms in photoionization equilibrium within the intergalactic medium (IGM)."455 This clistribution of neutral hydrogen is observable as the forest of absorption lines in the spectra of high redshift QSOs (sce Rauch1998 or a review)., This distribution of neutral hydrogen is observable as the forest of absorption lines in the spectra of high redshift QSOs (see \citealt{Rauch98} for a review).456 Helium-4 is the second most abundant. nuclide in the Universe after. hydrogen. with a mass fraction of Y20.24 Walkeretal. 19913).," Helium-4 is the second most abundant nuclide in the Universe after hydrogen, with a mass fraction of $Y\simeq0.24$ \citealt{Walker91}) )."457 Following the onset of reionization. the structures responsible for the absorption seen in the forest should. also be observable as discrete absorption lines at the rest-frame wavelength of 304 Miralda-Aleiksin 1994)).," Following the onset of reionization, the structures responsible for the absorption seen in the forest should also be observable as discrete absorption lines at the rest-frame wavelength of $304$ \citealt{MiraldaEscudeOstriker90,MiraldaEscude93,MadauMeiksin94}) )."458 The development of space-based.—- UV-capable observatories in the 1990s led to the first. detection. of a possible Gunn-Peterson trough in. the. spectrum of Q0302003 bv Jakobsenetal.(1994) using the Faint Object Camera on. the(HST)., The development of space-based UV-capable observatories in the 1990s led to the first detection of a possible Gunn-Peterson trough in the spectrum of $\rm Q0302-003$ by \cite{Jakobsen94} using the Faint Object Camera on the.459 Uigher resolution studies of the same spectrum. using the CGoclarcd High. Resolution Spectrograph and the Space Telescope Imaging Spectrograph (STIS) on theHST. as well as spectral observations of HII 234794342 using the(FUSE). have all demonstrated. a strong correlation between resolved absorption features ane those seen in the forest. confirming theoretical predictions.," Higher resolution studies of the same spectrum using the Goddard High Resolution Spectrograph and the Space Telescope Imaging Spectrograph (STIS) on the, as well as spectral observations of $\rm HE$ $2347-4342$ using the, have all demonstrated a strong correlation between resolved absorption features and those seen in the forest, confirming theoretical predictions."460 Absorption from in the IGM hasso far been detected in six QSO spectra: PIS 19035. 692. (Tytleret.al.1995: L999)). IIS. 1700| 64. (Davidsenetal. 1996)) HIE 2347. 4342.," Absorption from in the IGM hasso far been detected in six QSO spectra; $\rm PKS$ $1935-692$ , \citealt{Tytler95,Jakobsen96,Anderson99}) ), $\rm HS$ $1700+64$ , \citealt{Davidsen96}) ) $\rm HE$ $2347-4342$ ,"461result. Applegate(1992) and Lanzaetal.(1998). developed a theory to explain the periodic pattern in O—C curves of these systems.,"result, \cite{app92} and \cite{lan98}462 developed a theory to explain the periodic pattern in $O-C$ curves of these systems."463 In thistheory.. a certain amount of angular momentum is periodically exchanged between the inner and the outer parts of the convection zone. and therefore the rotational oblateness of the star and hence the orbital period changes while the system's component goes through its activity cycles.," In this, a certain amount of angular momentum is periodically exchanged between the inner and the outer parts of the convection zone, and therefore the rotational oblateness of the star and hence the orbital period changes while the system's component goes through its activity cycles."464 However. the period changes of those Algols used by Hall(1989) were mainly derived from visual and photographie observations.," However, the period changes of those Algols used by \cite{hal89} were mainly derived from visual and photographic observations."4652000).. As new and more accurate observational material has accumulated since then. the present work. we will reproduce and improve the same diagram as Hall's (1989) of EA. EB and EW-type binaries based on the new collected data.," As new and more accurate observational material has accumulated since then, the present work, we will reproduce and improve the same diagram as Hall's (1989) of EA, EB and EW-type binaries based on the new collected data."466 We will check Hall's plot and discuss the cause of cyclical period changes., We will check Hall's plot and discuss the cause of cyclical period changes.467 Meanwhile. we will analyze the cyclical period change of the RS CVn-type binary WW Dra derived from the century-long historical record of the times of light minimum and discuss its plausible cause.," Meanwhile, we will analyze the cyclical period change of the RS CVn-type binary WW Dra derived from the century-long historical record of the times of light minimum and discuss its plausible cause."468 As discussed above. at present. the magnetic activity of one or both components (e.g.Applegate1992) or the light-travel time etfect(LTTE) via the presence of a third body are usually invoked to explain period changes of close binaries.," As discussed above, at present, the magnetic activity of one or both components \citep[e.g.,][]{app92} or the light-travel time effect(LTTE) via the presence of a third body are usually invoked to explain period changes of close binaries."469 Hall(1989) searched the orbital period changes of 101 Algol-type binaries in Giuricinetal...(1983)., \cite{hal89} searched the orbital period changes of 101 Algol-type binaries in \cite{giu83}.470. The samples of our study are made by he stars listed in Kreineretal.(2001).. the 101. Algol systems in Giuricinetal.(1983)... and the Algol-type binaries listed in Thanogluetal.(2006).," The samples of our study are made by the stars listed in \cite{kre01}, the 101 Algol systems in \cite{giu83}, and the Algol-type binaries listed in \cite{iba06}."471.. As selection criterion we considered stars that either show cyclical period changes or have secondary component of late spectral type., As selection criterion we considered stars that either show cyclical period changes or have secondary component of late spectral type.472 Finally. 182. EA-type (including he LOL Algol systems used by Hall (1989))). 43 EB-type. and 53 EW-type binaries were collected for this study.," Finally, 182 EA-type (including the 101 Algol systems used by \cite{hal89}) ), 43 EB-type, and 53 EW-type binaries were collected for this study."473 In this paper. the data of EA. EB. and EW-type binaries are oresented in Tables | - 3. respectively.," In this paper, the data of EA, EB, and EW-type binaries are presented in Tables 1 - 3, respectively."474 In Table 1. Column (1) and (7) give the systems we selected: (2) and (8) the secondary component's spectral type: (3) and (9) the mass ratio: (4) and (10) the form of the period change: (5) and CHE) the geometrical structure of the binary: semidetached binariestSD) or detached binariestD).. and (6) and (12) the reference for the ο—C information.," In Table 1, Column (1) and (7) give the systems we selected; (2) and (8) the secondary component's spectral type; (3) and (9) the mass ratio; (4) and (10) the form of the period change; (5) and (11) the geometrical structure of the binary: semidetached binaries(SD) or detached binaries(D), and (6) and (12) the reference for the $O-C$ information."475 In Table 2 and 3. Column (1) gives the systems we selected: (2) the secondary component's spectral type: (3) the mass ratio: (4) the form of the period change and (5) the reference for the O—C information.," In Table 2 and 3, Column (1) gives the systems we selected; (2) the secondary component's spectral type; (3) the mass ratio; (4) the form of the period change and (5) the reference for the $O-C$ information."476 The secondary component's spectral type (Sp.) anc the mass ratio (g)) are up to date values taken from one of these references: Kreineretal.(2001)... Giuricinetal. (1983). [banogluetal. (2006).. the reference given in corresponding table. and VizieR database!.," The secondary component's spectral type $\textrm{Sp}_{2}$ ) and the mass ratio ) are up to date values taken from one of these references: \cite{kre01}, \cite{giu83}, \cite{iba06}, the reference given in corresponding table, and VizieR database."477. Therefore. some of the secondary component's spectral types in Table | ditter from those in Giuricinetal.1953).," Therefore, some of the secondary component's spectral types in Table 1 differ from those in \cite{giu83}."478 Moreover. in the process of investigation. we reclassified severa systems as EB type or detached binaries with respect to Giuricineal.(1983). according to the mentioned more recent bibliography.," Moreover, in the process of investigation, we reclassified several systems as EB type or detached binaries with respect to \cite{giu83} according to the mentioned more recent bibliography."479 The plots of mass ratio(g}) vs. secondary component's spectra type (Sp.) for EA. EB. and EW-type binaries are displayed in Figs.," The plots of mass ) vs. secondary component's spectral type $\textrm{Sp}_{2}$ ) for EA, EB, and EW-type binaries are displayed in Figs."480 | - 3. respectively.," 1 - 3, respectively."481 The form of the period change follows the convention adopted by Hall(1989)., The form of the period change follows the convention adopted by \cite{hal89}.482.. A horizontal line € - ) indicates no period change. a forward slash € / } indicates a period increase only. a back slash € X ) indicates a period decrease only. a cross (X ) indicates both increase and decrease of the period. and a filled circle € e ) is used for systems for which we have inadequate data for judgement.," A horizontal line ( - ) indicates no period change, a forward slash ( / ) indicates a period increase only, a back slash ( $\setminus$ ) indicates a period decrease only, a cross ( $\times$ ) indicates both increase and decrease of the period, and a filled circle ( $\bullet$ ) is used for systems for which we have inadequate data for judgement."483 In Fig., In Fig.484 |. the magenta symbols are used for the semidetached Algol-type binaries and the black ones are for detached Algol-type binaries.," 1, the magenta symbols are used for the semidetached Algol-type binaries and the black ones are for detached Algol-type binaries."485 It is clear from Fig., It is clear from Fig.486 | that our plots do not support the conclusion derived by Hall(1989) that all cases of cyclical period changes are restricted to binaries with secondary component with spectral type later than F5., 1 that our plots do not support the conclusion derived by \cite{hal89} that all cases of cyclical period changes are restricted to binaries with secondary component with spectral type later than F5.487 There are cases among both semidetached and detached Algols in which the spectral type of the secondary component is earlier than F5. such as RW Cap Erdemetal.2007).. TX Her (Aketal.2004).. and it is expected that the number of these systems will grow rapidly as more new »servational data will be derived.," There are cases among both semidetached and detached Algols in which the spectral type of the secondary component is earlier than F5, such as RW Cap \cite[]{erd07}, TX Her \cite[]{ak04}, and it is expected that the number of these systems will grow rapidly as more new observational data will be derived."488 The presence of period changes also among systems with low-mass component of early-type stars for the period variation., The presence of period changes also among systems with low-mass component of early-type stars for the period variation.489 Among binaries with late-type component the orbital period variation can be due to either magnetic activity or LTTE., Among binaries with late-type component the orbital period variation can be due to either magnetic activity or LTTE.490 Whereas. among binaries with early-type components the LTTE is the more likely cause.," Whereas, among binaries with early-type components the LTTE is the more likely cause."491 Moreover. the validity of the Applegate mechanism has recently come into question (Lanza2005.2006).," Moreover, the validity of the Applegate mechanism has recently come into question \cite[]{lan05, lan06}."492. Lanza suggested that the Applegate mechanism should be rejected because if can not explain the orbital period modulations of classical RS CVn close binaries (Lanza005)., Lanza suggested that the Applegate mechanism should be rejected because it can not explain the orbital period modulations of classical RS CVn close binaries \cite[]{lan05}.493.. Afterwards he also found that the mechanism is inadequate to explain the cyclical yeriod changes of all close binaries with a late-type secondary (Lanza2006)., Afterwards he also found that the mechanism is inadequate to explain the cyclical period changes of all close binaries with a late-type secondary \cite[]{lan06}.494. Again. the Applegate mechanism predicted that here is a connection between the luminosity variation and the variation of period.," Again, the Applegate mechanism predicted that there is a connection between the luminosity variation and the variation of period."495 However. to date. no reliable connections were ‘ound in the literature.," However, to date, no reliable connections were found in the literature."496 Therefore. the most plausible explanation of the cyclical period changes is the LTTE via the presence of a hird body.," Therefore, the most plausible explanation of the cyclical period changes is the LTTE via the presence of a third body."497 We found that 48.9 of EA. 4.2 of EB and 64.2 of EW-type binaries have cyclical orbital period variation.," We found that 48.9 of EA, 44.2 of EB and 64.2 of EW-type binaries have cyclical orbital period variation."498 Tf we assume that such variations are related to the presence of a hird body through the LTTE. then we find that EW stars have the vighest probability to belong to multiple systems.," If we assume that such variations are related to the presence of a third body through the LTTE, then we find that EW stars have the highest probability to belong to multiple systems."499 These results are in agreement with the findings of Chambliss(1992b)., These results are in agreement with the findings of \cite{cha92b}.500. The detailed statistical numbers of cyclical period changes in close binary systems are displayed in Table 4., The detailed statistical numbers of cyclical period changes in close binary systems are displayed in Table 4.501 In the following sections.we present our investigation on the cyclical period change in the RS CVn-type binary WW Dra and discuss about its causes as the presence of a black hole companion.," In the following sections,we present our investigation on the cyclical period change in the RS CVn-type binary WW Dra and discuss about its causes as the presence of a black hole companion."502 WW Dra ( = HD 150708 = HIP 81519 = BD 460/1691. mag) was discovered to be an eclipsing binary by Harwooc (1916).," WW Dra ( = HD 150708 = HIP 81519 = BD $+ 60\,^{\circ} 1691$, $V_{max}=8.3\,mag$ ) was discovered to be an eclipsing binary by \cite{har16}."503 Studies based on photographie and photoelectric observations were carried out by Plaut(1940). Mezzettietal. (1979).. Mardirossianetal...(1980). and Tuncaetal. (19813.," Studies based on photographic and photoelectric observations were carried out by \cite{pla40}, \cite{mez79}, , \cite{mar80} and \cite{tun81}."504. Some of them also calculated the orbital anc physical elements of WW Dra. and the binary was confirmed to be a detached system composed of two sub-giant stars.," Some of them also calculated the orbital and physical elements of WW Dra, and the binary was confirmed to be a detached system composed of two sub-giant stars."505 The period variation of this binary was studied by Albayraketal.(1999) whoderived the parameters of the light time orbit., The period variation of this binary was studied by \cite{alb99} whoderived the parameters of the light time orbit.506 However. as," However, as"507carried by the charged particles in the plasma.,carried by the charged particles in the plasma.508 Before discussing screening. it is relevant (o explain how equation (23)) is satisfied in (he vacuunme-dipole and corotating-magnetosphere models.," Before discussing screening, it is relevant to explain how equation \ref{cf8}) ) is satisfied in the vacuum-dipole and corotating-magnetosphere models."509 For the inductive fields in vacuo. equation (23)) is satisfied with J=0.," For the inductive fields in vacuo, equation \ref{cf8}) ) is satisfied with ${\bi J}=0$."510 The inclusion of a magnetosphere can chanee all three terms in equation (23))., The inclusion of a magnetosphere can change all three terms in equation \ref{cf8}) ).511 We assume that the change to culB is less important than the changes (to the two terms on the right hand side., We assume that the change to $\curl{\bi B}$ is less important than the changes to the two terms on the right hand side.512 Ideal screening requires (hat the final term in equation (23)) be zero., Ideal screening requires that the final term in equation \ref{cf8}) ) be zero.513 This determines the screening current deusity as x)--- where Εμ.Xx) is the inductive electric field (hat would be present in the absence of screening.," This determines the screening current density as )= where ${\bi E}_{\rm ind}(t,{\bi x})$ is the inductive electric field that would be present in the absence of screening."514 In identilving the screening current by equation (24)). we effectively require that (he displacement. current in vacuo be replaced bv an identical J carried by: charges.," In identifying the screening current by equation \ref{scd1}) ), we effectively require that the displacement current in vacuo be replaced by an identical ${\bi J}$ carried by charges."515 If the plasma cannot supply (his current. then the displacement current is effectively unchanged from its value in vacuo. and Eg4(/.x) must have essentially the same value as in vacuo.," If the plasma cannot supply this current, then the displacement current is effectively unchanged from its value in vacuo, and ${\bi E}_{\rm ind} (t,{\bi x})$ must have essentially the same value as in vacuo."516 We argue below that in a pulsar magnetosphere. the parallel component of equation (24)) may be satislied. but the perpendicular component cannot be satisfied.," We argue below that in a pulsar magnetosphere, the parallel component of equation \ref{scd1}) ) may be satisfied, but the perpendicular component cannot be satisfied."517" For the corotation field. (he time-derivative of equation (12)) can be evaluated. using equation (13)). giving E,,(/.x)| (wlimesx)jdivE,κ]."," For the corotation field, the time-derivative of equation \ref{cf1}) ) can be evaluated using equation \ref{rf2}) ), giving )] )."518 One can rewrite equation (25)) in the form of equation (23)). and re-interpret it.," One can rewrite equation \ref{cf4}) ) in the form of equation \ref{cf8}) ), and re-interpret it."519 The interpretation is as a relation between the displacement current associated with E.x). the curl of the corotation-induced magnetic field. Bi.x)=(wxE00.κ). and the current density. pcexx. due to the corotating charge density.," The interpretation is as a relation between the displacement current associated with ${\bi E}_{\rm cor}(t,{\bi x})$, the curl of the corotation-induced magnetic field, ${\bi B}_{\rm cor}(t,{\bi x})=(\bomega\times{\bi x})\times{\bi E}_{\rm cor}(t,{\bi x})/c^2$, and the current density, $\rho_{\rm GJ}\bomega\times{\bi x}$, due to the corotating charge density."520 The corotationdnduced magnetic field is smaller than B(/.x) by a factor of order 72/r?. and can be neglected in ihe inner magnetosphere.," The corotation-induced magnetic field is smaller than ${\bi B}(t,{\bi x})$ by a factor of order $r^2/r_{\rm lc}^2$, and can be neglected in the inner magnetosphere."521 Thus equation (23)) is satisfied bv (he corotation fields alone., Thus equation \ref{cf8}) ) is satisfied by the corotation fields alone.522 This justifies the neglect of the corotation field in identifving the screening current given by equation (24))., This justifies the neglect of the corotation field in identifying the screening current given by equation \ref{scd1}) ).523The 6 Cep class member 1180642 has a visual magnitude of 8.3 and a dominant radial mode with V amplitude mmmag (Aerts 2000).,"The $\beta\,$ Cep class member 180642 has a visual magnitude of 8.3 and a dominant radial mode with $V$ amplitude mmag (Aerts 2000)."524 The additional observational characteristics of 1180642 we used as input for the seismic modelling were taken from Degroote et ((2009. ID andc Briquet et ((2009. ILD.," The additional observational characteristics of 180642 we used as input for the seismic modelling were taken from Degroote et (2009, I) and Briquet et (2009, II)."525 H was devoted to the analysise of the CoRoT light curve of the star., I was devoted to the analysis of the CoRoT light curve of the star.526 Three versions Cf a model deseription for the light curve were considered: one with classical prewhitening producing 127 significant frequencies. one with harmonics and combination frequencies of 11 independent frequencies. and one where time-dependent c£onplitudes and phases were allowed.," Three versions of a model description for the light curve were considered: one with classical prewhitening producing 127 significant frequencies, one with harmonics and combination frequencies of 11 independent frequencies, and one where time-dependent amplitudes and phases were allowed."527 After careful statistical evaluation taking into account penalties for the number of free parameters. the best fit to the CoRoT light curve was found to be the model based on 33 frequencies among which 11 were independent ones (which are repeated in reffreqs)). 3 were harmonics of the dominant frequency and 19 were combination frequencies (listed in 22 of PaperII and not repeated here).," After careful statistical evaluation taking into account penalties for the number of free parameters, the best fit to the CoRoT light curve was found to be the model based on 33 frequencies among which 11 were independent ones (which are repeated in \\ref{freqs}) ), 3 were harmonics of the dominant frequency and 19 were combination frequencies (listed in 2 of I and not repeated here)."528 The list of nine highest-amplitude independent stable frequencies contains the one of the dominant radial mode known prior to the CoRoT launch (Aerts 2000). eight frequencies in the range [6.1.8.5].. and two frequencies belowld'.. which could either be due to g modes or connected to the rotation of the star (or both) and agree to within a factor three.," The list of nine highest-amplitude independent stable frequencies contains the one of the dominant radial mode known prior to the CoRoT launch (Aerts 2000), eight frequencies in the range $[6.1,8.5]\,$, and two frequencies below, which could either be due to g modes or connected to the rotation of the star (or both) and agree to within a factor three."529 These ten frequencies have amplitudes roughly between 0.8 and mmmag ID. t.e.. far below the mmmag of the dominant mode.," These ten frequencies have amplitudes roughly between 0.8 and mmag I), i.e., far below the mmag of the dominant mode."530 The frequency spectrum was found to be atypical of a B Cep star. 1n the sense that ten sum and nine difference frequencies were also detected. in addition to three harmonies of the dominant frequency.," The frequency spectrum was found to be atypical of a $\beta\,$ Cep star, in the sense that ten sum and nine difference frequencies were also detected, in addition to three harmonics of the dominant frequency."531 Moreover. several of the combination frequencies were found to have locked phases. a characteristic expected for modes undergoing non-linear mode interaction with the large-amplitude dominant oscillation.," Moreover, several of the combination frequencies were found to have locked phases, a characteristic expected for modes undergoing non-linear mode interaction with the large-amplitude dominant oscillation."532 The 11 independent largest-amplitude frequencies found inthe space photometry are listed in reffreqs.. along with their mode identification obtained by Aerts (2000) and in IL and IL.," The 11 independent largest-amplitude frequencies found inthe space photometry are listed in \\ref{freqs}, along with their mode identification obtained by Aerts (2000) and in I and II."533 In this work. we consider the nine highest frequencies in that table for the modelling procedure. r.e.. the two frequencies below are not used.," In this work, we consider the nine highest frequencies in that table for the modelling procedure, i.e., the two frequencies below are not used."534 The total range of frequencies related to dominant independent modes and their combinations. covers [0.3.27.5]d..," The total range of frequencies related to dominant independent modes and their combinations covers $[0.3,27.5]\,$."535 In addition to these 33 frequencies. variations with time-dependent behaviour were found in the residual light curve. within the frequency range of the harmonies and the combination frequencies of the heat-driven modes (Belkacem et 22009: IL).," In addition to these 33 frequencies, variations with time-dependent behaviour were found in the residual light curve, within the frequency range of the harmonics and the combination frequencies of the heat-driven modes (Belkacem et 2009; I)."536 Belkacem et ((2009) determined a frequency spacing of for the range above dd™' and below and interpreted it in terms of solar-like oscillations caused by stochastic forcing due to convective motions in the outer stellar layers., Belkacem et (2009) determined a frequency spacing of for the range above $^{-1}$ and below and interpreted it in terms of solar-like oscillations caused by stochastic forcing due to convective motions in the outer stellar layers.537 In PaperΠΠ. a value for candidate frequency spacings was recomputed over the range [4.32.25.9] for the three types of prewhitening procedures and led to 1.05. 1.11. andcd.. with an uncertainty of -0.02 (the corresponding four spacing values are 13.5. 12.1. 12.9. and Hz).," In I, a value for candidate frequency spacings was recomputed over the range $[4.32,25.9]\,$ for the three types of prewhitening procedures and led to 1.05, 1.11, and, with an uncertainty of $\sim\,0.02\,$ (the corresponding four spacing values are 13.5, 12.1, 12.9, and $\mu$ Hz)."538 The physical interpretation of these spacings remains unclear. given that their value depends on the way the CoRoT light curve ts prewhitened.," The physical interpretation of these spacings remains unclear, given that their value depends on the way the CoRoT light curve is prewhitened."539 We return to this problem in refspacing.., We return to this problem in \\ref{spacing}.540 In Paperlll. we presented the results of an extensive ground-based multicolour photometric and. high-resolutior spectroscopic campaign that we have organised.," In II, we presented the results of an extensive ground-based multicolour photometric and high-resolution spectroscopic campaign that we have organised."541 This campaigt has led to the detection of three of the CoRoT frequencies 11 the photometry and nine in the spectroscopy. among then the fourth harmonie of the dominant frequency. which is not founc in the space photometry.," This campaign has led to the detection of three of the CoRoT frequencies in the photometry and nine in the spectroscopy, among then the fourth harmonic of the dominant frequency, which is not found in the space photometry."542 Empirical mode identifation. based o1 photometric amplitude ratios and on line-profile variability. lec to the results in reffreqs..," Empirical mode identifation, based on photometric amplitude ratios and on line-profile variability, led to the results in \\ref{freqs}."543 In particular. the frequency was identified with either an £=0 or €=3 mode from amplitude ratios. while the moment method was used to deduce information on the mode wavenumbers (6.1). the inclination angle. and the equatorial velocity for the frequencycd.," In particular, the frequency was identified with either an $\ell=0$ or $\ell=3$ mode from amplitude ratios, while the moment method was used to deduce information on the mode wavenumbers $(\ell,m)$, the inclination angle, and the equatorial velocity for the frequency."544. The seven possibilities listed in reffreqs occurred with à much higher probability than any of the other options for (£.11) and we allow any of those seven solutions in the modelling rather than taking only the best one.," The seven possibilities listed in \\ref{freqs} occurred with a much higher probability than any of the other options for $(\ell,m)$ and we allow any of those seven solutions in the modelling rather than taking only the best one."545 The average spectrum of 1180642 was also analysed in PaperllI to determine the fundamentalparameters of the star. as well as its current surface abundance pattern.," The average spectrum of 180642 was also analysed in II to determine the fundamentalparameters of the star, as well as its current surface abundance pattern."546 This resulted in Tuy=24500x 1000K. loge=3.45x 0.15. and Z€[0.0083. 0.0142]. where the interval for Z covers the," This resulted in $T_{\rm eff} = 24\,500 \pm 1\,000$ K, $\log\,g=3.45 \pm 0.15$ , and $Z\in547[0.0083,0.0142]$ , where the interval for $Z$ covers the"548Tere the subscript “O° corresponds to the initial moment (f= 0). subscript “1° to the moment of the beeinning of the evolution of maenetic field (f=ty2 0).,"Here the subscript ""0"" corresponds to the initial moment $t=0$ ), subscript ""1"" to the moment of the beginning of the evolution of magnetic field $t=t_1>0$ )."549 The assumptions about the sviuetry of the problem. are the same as in Section 2.., The assumptions about the symmetry of the problem are the same as in Section \ref{basiceq}.550 The process can be divided into the following three qualitatively different stages., The process can be divided into the following three qualitatively different stages.551 First is a pretty short wdrodvuamical collapse stage., First is a pretty short hydrodynamical collapse stage.552 At this stage the influence of the magnetic field on the process of the collapse of he cloud can be neglected. because the initial poloidal naguetic field is weak.," At this stage the influence of the magnetic field on the process of the collapse of the cloud can be neglected, because the initial poloidal magnetic field is weak."553 Iu the short time of collapse the oroidal component of the magnetic field. which appears o be due to the arising differeutial rotation is also weak at Us initial stage.," In the short time of collapse the toroidal component of the magnetic field, which appears to be due to the arising differential rotation is also weak at this initial stage."554" The second stage is the stage of a rather ""long twisting of magnetic feld due to the differeutial rotation of the cloud.", The second stage is the stage of a rather ”long” twisting of magnetic field due to the differential rotation of the cloud.555 The final third stage starts with je appearance of a conrpression Wave. moving from the oeΠΙΟ parts of the cloud to its periphery aloug a steeply ecreasing density backeround.," The final third stage starts with the appearance of a compression wave, moving from the inner parts of the cloud to its periphery along a steeply decreasing density background."556 Soon after its appearance. it transforms into the MIID shock wave. which cau push out a lieht euvelope of the protostar.," Soon after its appearance, it transforms into the MHD shock wave, which can push out a light envelope of the protostar."557 Simular cejection following formation of a rapidly rotating neutron star and a differentially rotating envelope. cau be interpreted as supernova explosion.," Similar ejection following formation of a rapidly rotating neutron star and a differentially rotating envelope, can be interpreted as supernova explosion."558 Simulations for different © consist of the calculation of oscillations of the cloud until formation of the differentially rotating equilibrium (without inagnetic feld) aud subsequent inclusion and twisting of the maenetic field.," Simulations for different $\xi$ consist of the calculation of oscillations of the cloud until formation of the differentially rotating equilibrium (without magnetic field), and subsequent inclusion and twisting of the magnetic field."559 The initial maeuetic field mist satisfy the condition of absence of magnetic charges divH=0., The initial magnetic field must satisfy the condition of absence of magnetic charges ${\rm div} {\bf H} = 0$.560 It also has to correspoud to the boundary conditious of the problem., It also has to correspond to the boundary conditions of the problem.561 The best choice would be dipole or quadrupole., The best choice would be dipole or quadrupole.562 While they satisfv initial and boundary conditions. they have snueuluities iu the origin of coordinates (+Ξ0.του.," While they satisfy initial and boundary conditions, they have singularities in the origin of coordinates $r=0,\> z=0$ )."563 Using such magnetic fields i umucrical simulations cau lead to loss of accuracy of calculations., Using such magnetic fields in numerical simulations can lead to loss of accuracy of calculations.564 To define the initial magnetic field we use the folowing iiethod., To define the initial magnetic field we use the following method.565 We defined toroidal curreut j- i the ceutral part of the core of the collapsed cloud by a formula: After ecttine the deffercutially rotating stationary solution for nommaeuetized cloud we use Bio-Savara aw CÀI)L(CA2)).0A5)). for calculation of the poloidal colmponents of the magnetic field Πω.Πιυ (Fie. 2)).," We defined toroidal current $j_\varphi$ in the central part of the core of the collapsed cloud by a formula: After getting the defferentially rotating stationary solution for nonmagnetized cloud we use Bio-Savara law \ref{biosavara}) \ref{biosavararas}) \ref{biosavr}) ) for calculation of the poloidal components of the magnetic field $H_{r0},\> H_{z0}$ (Fig. \ref{inimag}) )."566 This magnetic field is divereency free. but it is not force-ree and should be balanced at the initial moment.," This magnetic field is divergency free, but it is not force-free and should be balanced at the initial moment."567 Then we use the following method: we “turn on” the poloidal uaenetie feld Ly.Ley. but “switch off the equation or the evolution of the toroidal component 7L. iu (1)).," Then we use the following method: we ""turn on"" the poloidal magnetic field $H_{r0},\>H_{z0}$, but ""switch off"" the equation for the evolution of the toroidal component $H_\varphi$ in \ref{magmain}) )."568 Actually it. means that we define Z7.=0.Eul—(0.," Actually it means that we define $H_\varphi569\equiv 0,\> {{\rm d}H_\varphi \over {\rm d} t} \equiv 0$."570 From he physical poiut of view it 11eaus that we allow maguetic ποια lines to slip through the matter of the cloud iu the, From the physical point of view it means that we allow magnetic field lines to slip through the matter of the cloud in the571 ÀA 1 loss continues slowly after the common euvelope phase through magnetic braking aud gravitational radiation (Paczvüsshki 1967: Rappaport. Verbuut Joss 1983).," $\lambda\lambda$ \ref{tab1} loss continues slowly after the common envelope phase through magnetic braking and gravitational radiation (Paczyńsski 1967; Rappaport, Verbunt Joss 1983)."572 Through these augular momentum trausfer niecliinisaus. the companion stars Roche lobe descends upon and makes contact with the companion.," Through these angular momentum transfer mechanisms, the companion star's Roche lobe descends upon and makes contact with the companion."573 Contact initiates ballistic mass trausfer frou the companion star to the white dwarf through the immer Lagrangian point. at which time the object is classed a CV.," Contact initiates ballistic mass transfer from the companion star to the white dwarf through the inner Lagrangian point, at which time the object is classed a CV."574 Mass. transfer is stable and contiuues ecnerally util the companion becomes degenerate., Mass transfer is stable and continues generally until the companion becomes degenerate.575 Thus. CVs have broad importance for coustraining models of stellar evolution. binary evolution aud the chemical curichiment of the Galaxy.," Thus, CVs have broad importance for constraining models of stellar evolution, binary evolution and the chemical enrichment of the Galaxy."576 The CV plase has another important feature., The CV phase has another important feature.577 Ballistic material leaving the companion star cannot fall onto the white dwarf without losing aneular miomentmn., Ballistic material leaving the companion star cannot fall onto the white dwarf without losing angular momentum.578 Iu the absence of a powerful maeuctic field from the white dwarf. material does this through the shearing lavers of a ciretuustellar accretion disk (Shakura Suuvaev 1973).," In the absence of a powerful magnetic field from the white dwarf, material does this through the shearing layers of a circumstellar accretion disk (Shakura Sunyaev 1973)."579 Such disks occur in nature over a range of scales. from planet-buildiug disks around protostars to those that feed the distant quasars.," Such disks occur in nature over a range of scales, from planet-building disks around protostars to those that feed the distant quasars."580 However. CV disks are unique in that their optical light. dominates over both stellar companions. aud svstenis are typically nearby. withiu a kpe.," However, CV disks are unique in that their optical light dominates over both stellar companions, and systems are typically nearby, within a kpc."581 The mass trauster rate through the disk is often modulated by a viscously daiven lint evele (S1uak 1981). resulting in iuteuse. short-lived optical outbursts.," The mass transfer rate through the disk is often modulated by a viscously driven limit cycle (Smak 1984), resulting in intense, short-lived optical outbursts."582 Because of the observational detail available. CVs are primary tarects for monitor accretion disk behavior and testing accretion disk theory.," Because of the observational detail available, CVs are primary targets for monitoring accretion disk behavior and testing accretion disk theory."583 Using the unprecedented detail ofMepler quiescent-to-outburst light curves we cau test viscous accretion disk lait cvele models. quautify mass accretion rates. disk viscositv and trace the evolution of cooling and heating waves across the disk.," Using the unprecedented detail of quiescent-to-outburst light curves we can test viscous accretion disk limit cycle models, quantify mass accretion rates, disk viscosity and trace the evolution of cooling and heating waves across the disk."584Wepler will monitor the evolution of uperlmup periods throughout, will monitor the evolution of superhump periods throughout58522009).,2009).586 Indirect support for this prediction has come from the detection of the CF” molecular ion. by means of ground-based observations of its /=1-0. 7=2-L and J=3-2 transitions towards the Orion bar (Neufeld et 22006) and of its /=1-0 transition towards several other UV-irradiated molecular clouds (Neufeld et 22010. in preparation).," Indirect support for this prediction has come from the detection of the $^+$ molecular ion, by means of ground-based observations of its $J=1-0$ , $J=2-1$ and $J=3-2$ transitions towards the Orion bar (Neufeld et 2006) and of its $J=1-0$ transition towards several other UV-irradiated molecular clouds (Neufeld et 2010, in preparation)."587 Because the presumptive production mechanism for CF ts the reaction these detections of CF” argue for a significant overlap of the regions where ΗΕ and C are both abundant. and thus for the presence of large HF abundances close to cloud surfaces where the C7/CO ratio is large.," Because the presumptive production mechanism for $^+$ is the reaction these detections of $^+$ argue for a significant overlap of the regions where HF and $^+$ are both abundant, and thus for the presence of large HF abundances close to cloud surfaces where the $^+$ /CO ratio is large."588 The detection of interstellar HF itself. however. is severely hampered by atmospheric absorption.," The detection of interstellar HF itself, however, is severely hampered by atmospheric absorption."589 Because HF has the smallest moment of inertia of any molecule containing a heavy element. its pure rotational transitions le at high frequencies inaccessible from ground-based observatories.," Because HF has the smallest moment of inertia of any molecule containing a heavy element, its pure rotational transitions lie at high frequencies inaccessible from ground-based observatories."590 To date. the only detection of interstellar HF has been obtained toward a single source by means of observations (Neufeld et 11997) performed with the(ISO).," To date, the only detection of interstellar HF has been obtained toward a single source by means of observations (Neufeld et 1997) performed with the."591 In that study. the /=2—| transition at 2.463 THz was detected in absorption toward the strong submillimeter continuum source Ser B2.," In that study, the $J=2-1$ transition at 2.463 THz was detected in absorption toward the strong submillimeter continuum source Sgr B2."592 Because the spectral coverage of did not extend to the 1.232 THz J=1—0 transition. the search for HF in absorption was impossible except in exceptional regions where the /=| state was significantly populated by radiative excitation.," Because the spectral coverage of did not extend to the 1.232 THz $J=1-0$ transition, the search for HF in absorption was impossible except in exceptional regions where the $J=1$ state was significantly populated by radiative excitation."593 The Heterodyne Instrument for the Far-Infrared(ΗΙΕΙΓ:: De Graauw et 22010). on board the (Pilbratt et 22010). provides access to the HF J=1—0 transition for the first time.," The Heterodyne Instrument for the Far-Infrared; De Graauw et 2010), on board the (Pilbratt et 2010), provides access to the HF $J=1-0$ transition for the first time."594 Thus. absorption line spectroscopy of bright submillimeter continuum sources. performed with HIFL can provide a sensitive probe of HF in its (J= 0).," Thus, absorption line spectroscopy of bright submillimeter continuum sources, performed with HIFI, can provide a sensitive probe of HF in its $J=0$ )."595" As part of the PRISMAS (""PRobing InterStellar Molecules with Absorption line Studies”) Key Program. we will exploit this new capability by performing HIFI observations of eight strong submillimeter continuum sources with sight-lines that are known to intercept foreground molecular material."," As part of the PRISMAS (”PRobing InterStellar Molecules with Absorption line Studies”) Key Program, we will exploit this new capability by performing HIFI observations of eight strong submillimeter continuum sources with sight-lines that are known to intercept foreground molecular material."596 In thisLetter. we present the first results of our search for hydrogen fluoride. obtained from observations of the sight-line to G10.6-0.4 (W31C).," In this, we present the first results of our search for hydrogen fluoride, obtained from observations of the sight-line to G10.6–0.4 (W31C)."597 G10.6-0.4 is a region of high-mass star-formation., G10.6–0.4 is a region of high-mass star-formation.598 It is one of three bright HII regions within the W31 complex. and an extremely luminous submillimeter and infrared continuum source: Wright. Fazio Low (1977) estimate its infrared luminosity as ~107L...," It is one of three bright HII regions within the W31 complex, and an extremely luminous submillimeter and infrared continuum source; Wright, Fazio Low (1977) estimate its infrared luminosity as $\sim 10^7 L_\odot$."599" Using observations of foreground HI 21 em absorption. Fish et ((2003) have obtained a kinematic distance estimate of 4.803 kpe for GIO.6-0.4. a value that places the source within the so-called 7-30 km s!"" spiral arm."," Using observations of foreground HI 21 cm absorption, Fish et (2003) have obtained a kinematic distance estimate of $4.8^{+0.4}_{-0.8}$ kpc for G10.6–0.4, a value that places the source within the so-called “–30 km $^{-1}$ ” spiral arm."600 The sight-line to G10.6-0.4 intersects several foreground molecular clouds. the arrangement of which has been elucidated by Corbel Eikenberry (2004: see their Figure 8).," The sight-line to G10.6–0.4 intersects several foreground molecular clouds, the arrangement of which has been elucidated by Corbel Eikenberry (2004; see their Figure 8)."601 Because G10.6-0.4 shows a large continuum flux at infrared and radio wavelengths. this sight-line has proven one of the most valuable in the Galaxy for the study of interstellar gas by absorption line spectroscopy.," Because G10.6–0.4 shows a large continuum flux at infrared and radio wavelengths, this sight-line has proven one of the most valuable in the Galaxy for the study of interstellar gas by absorption line spectroscopy."602" Indeed. line absorption by foreground gas has been detected over three and one-half decades in wavelength. from species as diverse às atomic oxygen (at 63 jm: Keene et 11999), CH- (J=1-Oat 36] um; Falgarone. Phillips Pearson 2005). HCO (/=1-0 at 3.36 mm: Keene et 11999; Godard et 22010). and atomic hydrogen (at 21 em: Fish et 22003)."," Indeed, line absorption by foreground gas has been detected over three and one-half decades in wavelength, from species as diverse as atomic oxygen (at 63 $\mu$ m; Keene et 1999), $^{13}$ $^+$ $J=1-0$ at 361 $\mu$ m; Falgarone, Phillips Pearson 2005), $^+$ $J=1-0$ at 3.36 mm; Keene et 1999; Godard et 2010), and atomic hydrogen (at 21 cm; Fish et 2003)."603 We observed the J=1—0 transition of HF. with rest frequency 1232.4763 GHz (Nolt et 11987). in the upper sideband of the Band 5a HIFI receiver.," We observed the $J=1-0$ transition of HF, with rest frequency 1232.4763 GHz (Nolt et 1987), in the upper sideband of the Band 5a HIFI receiver."604 To help determine whether any observed feature did indeed lie in the upper sideband. three observations were carried out with slightly different settings of the local oscillator (LO) frequency.," To help determine whether any observed feature did indeed lie in the upper sideband, three observations were carried out with slightly different settings of the local oscillator (LO) frequency."605 These observations. each with an on-source integration time of 75 s. were carried out on 2010 March 5. using the dual beam switch (DBS) mode and the Wide Band Spectrometer (WBS).," These observations, each with an on-source integration time of 75 s, were carried out on 2010 March 5, using the dual beam switch (DBS) mode and the Wide Band Spectrometer (WBS)."606 The WBS has a spectral resolution of 1.1 MHz. corresponding to à velocity resolution of 0.27kms! at the frequency of the HF J=1-0 transition.," The WBS has a spectral resolution of 1.1 MHz, corresponding to a velocity resolution of $0.27\, \rm km\,s^{-1}$ at the frequency of the HF $J=1-0$ transition."607" The telescope beam. of diameter ~18"" HPBW. was centered at a=18h10m28.75.0—-19""55’50.0""(J2000)."," The telescope beam, of diameter $\sim 18^{\prime\prime}$ HPBW, was centered at $\rm \alpha=18h\,10m\,28.7s, \delta = -19^0\, 55^\prime \,50.0^{\prime\prime} (J2000)$."608 The reference positions for these observations were located 3’ on either side of the source along an East-West axis: by taking the difference between the reference position spectra. we confirmed that the reference positions are devoid of measurable line or continuum emission at the frequencies of present interest.," The reference positions for these observations were located $^\prime$ on either side of the source along an East-West axis; by taking the difference between the reference position spectra, we confirmed that the reference positions are devoid of measurable line or continuum emission at the frequencies of present interest."609 The data were reduced using the standard Herschel pipeline to Level 2. providing fully calibrated spectra of the source.," The data were reduced using the standard Herschel pipeline to Level 2, providing fully calibrated spectra of the source."610 The Level 2 data were analysed further using the Herschel Interactive Processing Environment (HIPE). along with ancillary IDL routines that we have developed.," The Level 2 data were analysed further using the Herschel Interactive Processing Environment (HIPE), along with ancillary IDL routines that we have developed."611 The signals measured in the two orthogonal polarizations were in excellent agreement. as were spectra obtained at thethree LO settings when assigned to the upper sideband.," The signals measured in the two orthogonal polarizations were in excellent agreement, as were spectra obtained at thethree LO settings when assigned to the upper sideband."612 We combined the data from the three observations. and from both polarizations. to obtain an average spectrum.," We combined the data from the three observations, and from both polarizations, to obtain an average spectrum."613 We also note that for any experiment with finite beam size there will be a mixing of in the beam owing to the temperature fluctuations on the last scattering surface on scales smaller than the beam size. leading to inevitable v distortions ofmagnitude (2).," We also note that for any experiment with finite beam size there will be a mixing of in the beam owing to the temperature fluctuations on the last scattering surface on scales smaller than the beam size, leading to inevitable $y$ distortions ofmagnitude $\sim (\Delta614T/T)^2\sim 10^{-9}-10^{-10}$ ."615 In this paper we find new solutions for the Kompaneets equation describing the CMB spectral distortions arising from described above., In this paper we find new solutions for the Kompaneets equation describing the CMB spectral distortions arising from described above.616 A second mechanism results in a and heating of the electrons at low redshifts., A second mechanism results in a and heating of the electrons at low redshifts.617 At high redshifts Comptonization of CMB on the hotter electrons converts the distortion to a p-type distortion (2::2))., At high redshifts Comptonization of CMB on the hotter electrons converts the distortion to a $\mu$ -type distortion \citet{sz1970}; \citet{is1975}) ).618 We demonstrate below that two of distortions work against each in spectral distortions opposite signs but same spectral shape in any part of the CMB spectrum., We demonstrate below that two of distortions work against each in spectral distortions opposite signs but same spectral shape in any part of the CMB spectrum.619 The cooling of electrons and the corresponding spectral distortions are easy to calculate and only depend on the standard cosmological parameters. such as baryon to photon number density 15/ny and helium fraction. which decide the amount of energy losses by the CMB. the Hubble constant (Ho). and densities of constituents of the Universe. which in turn the expansion rate and thus the efficiency ofComptonization.," The cooling of electrons and the corresponding spectral distortions are easy to calculate and only depend on the standard cosmological parameters, such as baryon to photon number density $\nB/n_{\gamma}$ and helium fraction, which decide the amount of energy losses by the CMB, the Hubble constant $H_0$ ), and densities of constituents of the Universe, which in turn the expansion rate and thus the efficiency of."620" the energy released by dissipation of sound waves crucially depends on the power in small-scale fluctuations. and thus the spectral index (2,) in the standard cosmological model. in addition to the other parameters of the standard cosmological model. (2).."," the energy released by dissipation of sound waves crucially depends on the power in small-scale fluctuations, and thus the spectral index $\nS $ ) in the standard cosmological model, in addition to the other well-measured parameters of the standard cosmological model, \citep{wmap7}. ."621 It is interesting to note that for a spectrum with constant ης the energy release due to dissipation exceeds the energy losses to adiabatic cooling of baryons. and there is net heating of electrons.," It is interesting to note that for a spectrum with constant $\nS$ the energy release due to dissipation exceeds the energy losses to adiabatic cooling of baryons, and there is net heating of electrons."622 For a primordial spectrum with a running spectral index. the role of with colder electrons and Bose-Einstein condensation can become dominant. with the spectral distortions changing sign. and there can be net cooling of electrons and a corresponding decrease of CMB entropy per baryon (specific entropy).," For a primordial spectrum with a running spectral index, the role of with colder electrons and Bose-Einstein condensation can become dominant, with the spectral distortions changing sign, and there can be net cooling of electrons and a corresponding decrease of CMB entropy per baryon (specific entropy)."623 Additional increase in entropy during the recombination epoch due to superposition ofblackbodies. freestreaming as well as Silk damping and the second-order Doppler effect only produce y-type distortions and can be distinguished from the y distortions created m the earlier epoch.," Additional increase in entropy during the recombination epoch due to superposition of, freestreaming as well as Silk damping and the second-order Doppler effect only produce $y$ -type distortions and can be distinguished from the $\mu$ distortions created in the earlier epoch."624 We can obtain the energy losses due to adiabatic cooling of baryons under the assumption that Compton scattering. bremsstrahlung. and double Compton scattering can maintain full thermodynamic equilibrium between the electrons and photons.," We can obtain the energy losses due to adiabatic cooling of baryons under the assumption that Compton scattering, bremsstrahlung, and double Compton scattering can maintain full thermodynamic equilibrium between the electrons and photons."625 This is true to high accuracy atz>10° while at lower bremsstrahlung and double Compton scattering cannot Planck spectrum at all frequencies. Comptonization keeps electron," This is true to high accuracy at $z>10^6$ while at lower bremsstrahlung and double Compton scattering cannot Planck spectrum at all frequencies, Comptonization keeps electron"626If οταν bursts (CRBs) originate iu a deuse environment their Xrav afterelow spectra are modified. by absorption features and the imprinted edges cau be used to determine their redshifts.,If $\gamma$ -ray bursts (GRBs) originate in a dense environment their X–ray afterglow spectra are modified by absorption features and the imprinted edges can be used to determine their redshifts.627 Caven the time decay. law observed in the GRD Xray afterglows. the necessary S/N ratio to reveal an absorption feature can be achieved ouly if fιο XNray observation starts munediatelv after the burst itself. or if the collecting effective area of the detector is much lareer than 100 cu.," Given the time decay law observed in the GRB X–ray afterglows, the necessary S/N ratio to reveal an absorption feature can be achieved only if the X–ray observation starts immediately after the burst itself, or if the collecting effective area of the detector is much larger than 100 $^2$."628 We have simulated the observed spectiiuu by using the response niatriees of some future plauned missions. such as JET-N (A~200 cn? at 1.5 keV aud A~40 cur at S.l keV for the two telescopes: Citterio et al.," We have simulated the observed spectrum by using the response matrices of some future planned missions, such as JET-X $A\sim 200$ $^2$ at 1.5 keV and $A\sim62940$ $^2$ at 8.1 keV for the two telescopes; Citterio et al."630 1996). ANAF with Back Ihuninated (BI) CCDs CA~700 cui at 1.5 keV andl~10 cm? at 8.1 keV: Kelloge et al.," 1996), AXAF with Back Illuminated (BI) CCDs $A\sim 700$ $^2$ at 1.5 keV and $A\sim 40$ $^2$ at 8.1 keV; Kellogg et al."631 1997) aud NAIA with the EPIC detectors (A~3600 em? at 1.5 keV and 4~1500 cn? at 8.1 keV for three telescopes: Coudoin et al., 1997) and XMM with the EPIC detectors $A\sim 3600$ $^2$ at 1.5 keV and $A\sim 1500$ $^2$ at 8.1 keV for three telescopes; Gondoin et al.632 1996) aud assunuine: 7) F(100s)=105 ere 275 ! between 2 aud 10 keV at the beginning of the observation: //) a power law time decay of the flux x fol 77) au intrinsic (absorbed) power law spectrum of photon iudex P21 coustaut in time.," 1996) and assuming: $i)$ $F(100\,{\rm s})=10^{-8}$ erg $^{-2}$ $^{-1}$ between 2 and 10 keV at the beginning of the observation; $ii)$ a power law time decay of the flux $\propto t^{-1}$ ; $iii)$ an intrinsic (unabsorbed) power law spectrum of photon index $\Gamma=1$ constant in time."633 All the simulations reported here refer to observations of 10 ks., All the simulations reported here refer to observations of 10 ks.634" We siniulaB two differeut cases: a GRD afterglow a 2=0.25 and intrinsic Ny=3«1073 2 and 2= and Ng.=au1075 ,7. which. are relevant for. the oxvecu and iron οσο, respectively."," We simulated two different cases: a GRB afterglow at $z=0.25$ and intrinsic $N_{\rm H}=3\times 10^{21}$ $^{-2}$ and $z=4$ and $N_{\rm H}=10^{24}$ $^{-2}$, which are relevant for the oxygen and iron edge, respectively."635 A galactic coli1 density of 3.s4n1079 D2 has also been iucluded: (forJ an overview of he Ny values with BeppoSAN see Owens et al., A galactic column density of $3\times 10^{20}$ $^{-2}$ has also been included (for an overview of the $N_H$ values with BeppoSAX see Owens et al.636 1998)., 1998).637 Iu the case of the oxvecn edge (at 0.52 keV) he satellite energv band is extremely important iu order to recover he correct CRB vedshit., In the case of the oxygen edge (at 0.52 keV) the satellite energy band is extremely important in order to recover the correct GRB redshift.638 We keep fixed the ecee enorgles. even if in the case oτα warn absorber fit shoud be worse.," We keep fixed the edge energies, even if in the case of a warm absorber fit should be worse."639 Iu the case o: JET-X. the niMinti enerev of 0.3 keV nuits the maxiAui etectable reshift to ~0.7.," In the case of JET-X, the minimum energy of 0.3 keV limits the maximum detectable redshift to $\sim 0.7$."640 The influence of the eaOs:actic absorplon plavs also a crucial role. such that only fx low vales (<5s10389 3] we are able| fo diseutaugle the iitisic and the ealactic absorption.," The influence of the galactic absorption plays also a crucial role, such that only for low values $\lsim\, 5\times 10^{20}$ $^{-2}$ ) we are able to disentangle the intrinsic and the galactic absorption."641 Iu Fie., In Fig.642 | (lef side) we report tlre' contour plots in the Au> plane o the simulated λιωςels as observed with ciffereut X.rav satellites., 1 (left side) we report the contour plots in the $N_{\rm H}-z$ plane of the simulated models as observed with different X–ray satellites.643 The thiree contours refer to 1. 2 aud 3e coufidence levels.," The three contours refer to 1, 2 and $3\,\sigma$ confidence levels."644 In Fig., In Fig.645 lais shown the case ofthe JET-X telescope., 1a is shown the case of the JET-X telescope.646 It can be noted that the input redshift aud coluii density are not recovered satisfactoril., It can be noted that the input redshift and column density are not recovered satisfactorily.647 Iu particular. the presence of different absorption features (O. Ne. Mg. Si) results in the clongated coutour iu the BIL2 ypane.," In particular, the presence of different absorption features (O, Ne, Mg, Si) results in the elongated contour in the $N_{\rm H}-z$ plane."648 In the case of ANAF (Fig., In the case of AXAF (Fig.649 1b). the recovery of the CRB redshift is cased hy he higher throughput at low energies guaranteed by the BI CCDs.," 1b), the recovery of the GRB redshift is eased by the higher throughput at low energies guaranteed by the BI CCDs."650 The large effective area of NMM poses no probein for the ideutificatk ποτ1ο redshift (Fig., The large effective area of XMM poses no problem for the identification of the redshift (Fig.651 1c)., 1c).652 lu the czwe oft1e Fe edge there are less problems due to the fact tha bevoxd irou there are not promineat Is edges., In the case of the Fe edge there are less problems due to the fact that beyond iron there are not prominent K edges.653 This is testified by Fie., This is testified by Fig.654 1 Giehlt side). iu which for all the considered instrument the redshift aud the coluun density aro rocowvorCd wih a high degree of confidence.," 1 (right side), in which for all the considered instrument the redshift and the column density are recovered with a high degree of confidence."655 Note however that at fhese large redshift. the iron abundance iav be lower tha1 the solar value.," Note however that at these large redshift, the iron abundance may be lower than the solar value."656 Oxvecn and iron edges are the most prominent absorption features in the spectra ofNX.rav sources., Oxygen and iron edges are the most prominent absorption features in the spectra of X–ray sources.657 This iudividuates two almost distinct accessible part of the redshift)coluun density plane for CRB: one characterized by a moderate Ny~1022 1072 ? and 2~0.1 0.5 aud the other, This individuates two almost distinct accessible part of the redshift–column density plane for GRB: one characterized by a moderate $N_{\rm H}\sim 10^{21}$ $10^{22}$ $^{-2}$ and $z\sim 0.1$ $0.5$ and the other658calibration was based on measurements of the continuum emission of 448. assuming a flux density of JJy at GGHz (Ott et al.,"calibration was based on measurements of the continuum emission of 48, assuming a flux density of Jy at GHz (Ott et al."659 1994; see also 44.2)., 1994; see also 4.2).660 The absolute flux-density calibration is estimated to be accurate to within +15 from the spectra to remove residual baseline ripples., The absolute flux-density calibration is estimated to be accurate to within $\pm$ from the spectra to remove residual baseline ripples.661 Seven of the sources displayed in Table | did not reveal any spectral feature., Seven of the sources displayed in Table \ref{table1} did not reveal any spectral feature.662 In the case of absorption (see below). ec upper limits on the line-to-continuum flux density ratio range from ~0.01 for the sources with strongest continuum 44261. 11052. 11068) to almost unity for the source with the weakest continuum 55135).," In the case of absorption (see below), $\sigma$ upper limits on the line-to-continuum flux density ratio range from $\sim$ 0.01 for the sources with strongest continuum 4261, 1052, 1068) to almost unity for the source with the weakest continuum 5135)."663 We detected CH:OH absorption toward 33079., We detected $_3$ OH absorption toward 3079.664 The spectrum is shown in refspectrum.., The spectrum is shown in \\ref{spectrum}.665 Line parameters from Gaussian fits are presented in Table 2.., Line parameters from Gaussian fits are presented in Table \ref{table2}.666 The profile shows a relatively strong (~6 mmJy) narrow component near the systemic velocity at. Vsui (1127210) ss! (Irwin Seaquist 1991). and a weaker (~2mmJy) broader blue-shifted component displaced by ~100kkm ss~!.," The profile shows a relatively strong $\sim$ mJy) narrow component near the systemic velocity at $V_{\rm667systemic}$ = $\pm$ $^{-1}$ (Irwin Seaquist 1991), and a weaker $\sim$ mJy) broader blue-shifted component displaced by $\sim$ $^{-1}$."668 While the FWHP linewidths of the two features are quite different. the full width to zero power (FWZP) linewidthsmight be similar (AVo ~ ss! ).," While the FWHP linewidths of the two features are quite different, the full width to zero power (FWZP) linewidths be similar $\Delta V_0$ $\sim$ $^{-1}$ )."669 Nevertheless. it is not possible to convincingly disentangle a potentially broader systemic component from the dominant narrow one.," Nevertheless, it is not possible to convincingly disentangle a potentially broader systemic component from the dominant narrow one."670" For the first observations. taken in February 2006. our amplitude calibration yielded a 6.7GGHz continuum flux density of S, = (275441)mmJy."," For the first observations, taken in February 2006, our amplitude calibration yielded a GHz continuum flux density of $S_{\rm c}$ = $\pm$ mJy."671" No suitable. flux-density calibrator was observed in March. 2007. and S, = (318447) mmJy was obtained in the following November."," No suitable flux-density calibrator was observed in March 2007, and $S_{\rm c}$ = $\pm$ mJy was obtained in the following November."672 For comparison. we obtain 260 and mmJy by extrapolating the GGHz flux densities of Gregory et al. (," For comparison, we obtain 260 and mJy by extrapolating the GHz flux densities of Gregory et al. ("6731991) and Mangum et al. (,1991) and Mangum et al. (674"2008) with a spectral index of a = —0.7 (S.x v"").","2008) with a spectral index of $\alpha$ = –0.7 $S675\propto \nu^{\alpha}$ )."676 These agree within the uncertainities with the measured fluxes and do not provide any evidence of continuum variability., These agree within the uncertainities with the measured fluxes and do not provide any evidence of continuum variability.677 Observations of emission and absorption lines are complementary., Observations of emission and absorption lines are complementary.678 Emission commonly traces extended regions that show an excitation that 1s. significantly above the temperature of the cosmic microwave background., Emission commonly traces extended regions that show an excitation that is significantly above the temperature of the cosmic microwave background.679 To achieve this collisional excitation requires that the density approximately matches or surpasses the critical density of the line., To achieve this collisional excitation requires that the density approximately matches or surpasses the critical density of the line.680 Absorption lines have the advantage that extremely tenuous gas can also be studied (7. ~ KK). that the effective beam size is confined to the sometimes extremely compact background continuum source(s). and that optical depths can be obtained directly byà comparison of line and continuum flux densities.," Absorption lines have the advantage that extremely tenuous gas can also be studied $T_{\rm ex}$ $\sim$ K), that the effective beam size is confined to the sometimes extremely compact background continuum source(s), and that optical depths can be obtained directly bya comparison of line and continuum flux densities."681 For the line profile shown in refspectrum and the line parameters given in Table 2 we calculate the optical depth. τ. using = 5.’).," For the line profile shown in \\ref{spectrum} and the line parameters given in Table \ref{table2} we calculate the optical depth, $\tau$ , using $$ = )."6823oth elfects tend to allow soft photons to leak through the absorber. and we found we could. not. distinguish. between these effects at the spectral resolution ofC.,"Both effects tend to allow soft photons to leak through the absorber, and we found we could not distinguish between these effects at the spectral resolution of."683. To allow for absorption in our complex model we followed the example of ? and allowed the absorber to be partially ionised., To allow for absorption in our complex model we followed the example of \scite{do97} and allowed the absorber to be partially ionised.684 To do this we cmplovecl the model in XSPEC (?:?)..," To do this we employed the model in \cite{done92,zdziarskiabsori}."685 We fitted the model with two free parameters: the column clensity of the absorbing medium. and the ionisation parameter £=Lnd. where L is the integrated source luminosity between ουδ) and kkeV. n is the density of the material. and £ is the distance of the material from the illuminating source (the temperature of the absorber was fixed at 5« LOtWKIN in all cases).," We fitted the model with two free parameters: the column density of the absorbing medium, and the ionisation parameter $\xi=L/nR^2$, where $L$ is the integrated source luminosity between eV and keV, $n$ is the density of the material, and $R$ is the distance of the material from the illuminating source (the temperature of the absorber was fixed at $5\times10^{4}$ K in all cases)."686 For svstems with interstellar absorption densities known precisely [rom non X-ray methods (listed in reftable:done)) we also included neutral absorption fixed at this value., For systems with interstellar absorption densities known precisely from non X-ray methods (listed in \\ref{table:done}) ) we also included neutral absorption fixed at this value.687 tesicluals around the iron lines reffige:poorfit)) tend. to be a sign of I[luorescence. [rom cold material (X-ray rellection) and/or an inadequate representation of the temperature structure of the spectrum., Residuals around the iron lines \\ref{fig:poorfit}) ) tend to be a sign of fluorescence from cold material (X-ray reflection) and/or an inadequate representation of the temperature structure of the spectrum.688 With onlv one free temperature the fitting process tends to find a best fit to the continuum (which contributes to all cata points) and to allow a poor fit to the emission lines (which. contribute only to a limited number of data points)., With only one free temperature the fitting process tends to find a best fit to the continuum (which contributes to all data points) and to allow a poor fit to the emission lines (which contribute only to a limited number of data points).689 In à cataclysmic variable we expect emission from a range of temperatures as the shock-heatecl gas cools to settle onto the surface of the white να (e.g.ὃν?:?)..," In a cataclysmic variable we expect emission from a range of temperatures as the shock-heated gas cools to settle onto the surface of the white dwarf \egcite{wheatley96a,do97,Mukai03}."690 The temperature distribution. can also elfect. the fit at ow energies. particularly around the iron. L-shell complex (~LkkeWV).," The temperature distribution can also effect the fit at low energies, particularly around the iron L-shell complex $\sim$ keV)."691 To allow for a range of temperatures we emploved hececmkt model inο which is a niulti-tompcrature lasma emission. model based. on themoekat model.," To allow for a range of temperatures we employed the model in, which is a multi-temperature plasma emission model based on the model."692 The emission. measure follows a power-law in. temperature. woportional to CL/Tuu)'.," The emission measure follows a power-law in temperature, proportional to $(T/T_{\rm max})^\alpha$."693 We chose this model because it allowed us to fit the full range of outburst and quicscent spectra with a single simple model., We chose this model because it allowed us to fit the full range of outburst and quiescent spectra with a single simple model.694 Cooling Low mocdels are often a good representation of quiescentspectra (ee.7). but not outburst spectra., Cooling flow models are often a good representation of quiescentspectra \egcite{Mukai03} but not outburst spectra.695 (e.g.77)..," \citep[e.g.][]{urryPadovani95,jackson99}."696 plav a role in the standard AGN picture. complicating investigations of orientation measures.," play a role in the standard AGN picture, complicating investigations of orientation measures."697 The “holy erail” of evidence for the unification paradigm would be au observational parameter that is understood to correlate directly with orientation angle.," The “holy grail"" of evidence for the unification paradigm would be an observational parameter that is understood to correlate directly with orientation angle."698 Owing to its variety and colplenity. quasar radio morphology is often considered to hold the kev to unlocking the orieutation iuvsterv.," Owing to its variety and complexity, quasar radio morphology is often considered to hold the key to unlocking the orientation mystery."699 Statistical studies of radio emission fom extragalactic sources have recently eutered a new era. thanks to the availability of large skvy-area high-resolution radio contiuununi surveys that are sensitive to iuJv flux density levels. such as the Faint huages of the Radio Sky at Twenty cu (FIRST:7) survey.," Statistical studies of radio emission from extragalactic sources have recently entered a new era, thanks to the availability of large sky-area high-resolution radio continuum surveys that are sensitive to mJy flux density levels, such as the Faint Images of the Radio Sky at Twenty cm \citep[FIRST;][]{first} survey."700 Iu this paper. we present a sample of 1711 radio quasars. spectroscopically-confirmed by the Sloan Digital Sky Survey (SDSS:7). aud with robust visual classifications of radio imorpholoey from FIRST nuages.," In this paper, we present a sample of 4714 radio quasars, spectroscopically-confirmed by the Sloan Digital Sky Survey \citep[SDSS;][]{york} and with robust visual classifications of radio morphology from FIRST images."701 This is the largest sample of visually morphologically-classitied radio quasars to date., This is the largest sample of visually morphologically-classified radio quasars to date.702 We use the radio quasar saunple to investigate the relationship between radio morphology, We use the radio quasar sample to investigate the relationship between radio morphology703result is shown in the right panel of Figure 1..,result is shown in the right panel of Figure \ref{chirpgal}.704 One can note that these distribution could also be obtained analvtically by multiplving the distributions of Figure 1. bv the volume xM7 and normalizing it., One can note that these distribution could also be obtained analytically by multiplying the distributions of Figure \ref{chirpgal} by the volume $\propto \chirp^{5/2}$ and normalizing it.705 In this plot the DII-DII svstems are now the dominant contribution of the distribution., In this plot the BH-BH systems are now the dominant contribution of the distribution.706 This is due to the fact that the seunpling volume lor the DII-DII binaries more than 100 limes larger Chat that for the NS-NS systems. which easily compensates for the lower merger rate of the DII-DII binaries.," This is due to the fact that the sampling volume for the BH-BH binaries more than 100 times larger that that for the NS-NS systems, which easily compensates for the lower merger rate of the BH-BH binaries."707 Let us now address (he following questions: are the distributions of observed chirp masses expected in the framework of alternative models different?, Let us now address the following questions: are the distributions of observed chirp masses expected in the framework of alternative models different?708 If so. are these differences significant?," If so, are these differences significant?"709 We simulate the distributions of chirp masses in the expected observations with the binary populations obtained from the set of models of Table 1 similarily as we have done above for the model A. We present the results in Figure 2.., We simulate the distributions of chirp masses in the expected observations with the binary populations obtained from the set of models of Table 1 similarily as we have done above for the model A. We present the results in Figure \ref{chidist}.710 Different stellar evolution models lead to drastically dillerent distributions of the chirp masses in the expected observations., Different stellar evolution models lead to drastically different distributions of the chirp masses in the expected observations.711 Various parameters describing stellar evolution affect the distribution of observed chirp Masses in several wavs., Various parameters describing stellar evolution affect the distribution of observed chirp masses in several ways.712 Changing the kick velocity distribution (models B) alters the ratio, Changing the kick velocity distribution (models B) alters the ratio713age indicator al best for a varielv of reasons.,age indicator at best for a variety of reasons.714 The lack of detailed abundance intormation. including the possible spread in He within a given GC. has important implications for IB morphology.," The lack of detailed abundance information, including the possible spread in He within a given GC, has important implications for HB morphology."715 The effect of a spread in (he total Le content on WB morphology cdilferent GCs has been explored by many authors (see.e.g...Catelan&deFreitasDemaoarque.&Zinn1994) as well as a spread in Ie single GCs (see.Caloi2003).," The effect of a spread in the total He content on HB morphology different GCs has been explored by many authors \citep[see, e.g., ][]{ca93,ldz94} as well as a spread in He single GCs \citep[see, e.g., ][]{dc08}."716. Another important [actor in matching GC IB morphology to model predictions is statistical (Iuctuations., Another important factor in matching GC HB morphology to model predictions is statistical fluctuations.717 The ACS GC Treasury project photometric database contains GCs with anvwhere [from ~20 to several hundred IB stars. leading to uncertainty in the median color of the IIB of up to in the sparsest GC (Dotteretal.2010.Table1)..," The ACS GC Treasury project photometric database contains GCs with anywhere from $\sim20$ to several hundred HB stars, leading to uncertainty in the median color of the HB of up to in the sparsest GC \citep[][Table 1]{do10}."718 Addressing the question of which parameters most stronglv influence HB morphology using full CMDs for laree samples of GC's. Dotterοἱal.(2010) and Grattonοἱal.(2010) reached (he same conclusion: (hat age is the second parameter influencing IB morphology.," Addressing the question of which parameters most strongly influence HB morphology using full CMDs for large samples of GCs, \citet{do10} and \citet{gr10} reached the same conclusion: that age is the second parameter influencing HB morphology."719 The results presented in (his paper lend further support to this conclusion., The results presented in this paper lend further support to this conclusion.720 Ht is important to note that the term ‘second parameter used here applies specifically to the variation ol IIB morphology different GCs. the context in which the term was originally used in the 1960's (e.e..vandenBerel1967;Sandage&Wildey1967).," It is important to note that the term `second parameter' used here applies specifically to the variation of HB morphology different GCs, the context in which the term was originally used in the 1960's \citep[e.g., ][]{vdb67,sa67}."721. Second parameter’ is not intended to apply to the spread in HB stars within a single GC. for which the same term is often employed. nor does (his paper seek (to address that important issue.," `Second parameter' is not intended to apply to the spread in HB stars within a single GC, for which the same term is often employed, nor does this paper seek to address that important issue."722 and Grattonetal.(2010). both found evidence for at least a third parameter as well. suggesting that. age and metallicity alone are not sufficient to fully characterize HB morphology.," \citet{do10} and \citet{gr10} both found evidence for at least a third parameter as well, suggesting that age and metallicity alone are not sufficient to fully characterize HB morphology."723 Fieure 11. shows the IIB morpholoevmetallicity diagram of the full sample of 68 GCs., Figure \ref{HB} shows the HB morphology-metallicity diagram of the full sample of 68 GCs.724 The left panel considers IB morphology as the median color difference between the HB anc RGB (Dotterοἱal.2010). and the right panel instead uses the (DB—I)/(D4-V) metric ol Lee(1989) as compiled by Alackey&vandenDergh (2005).., The left panel considers HB morphology as the median color difference between the HB and RGB \citep{do10} and the right panel instead uses the $-$ R)/(B+V+R) metric of \citet{le89} as compiled by \citet{ma05}. .725 Dotteretal.(2010) demonstrated (hat these (wo HB morphology metrics are strongly correlated. wilh (he main difference being that ACY—I) does not saturate as (B-—R)/(B+V+R) does at 41.," \citet{do10} demonstrated that these two HB morphology metrics are strongly correlated, with the main difference being that $\dvi$ does not saturate as $-$ R)/(B+V+R) does at $\pm1$."726 In this context. it is clear (hat age is the second parameter influencing HD morphology as concluded by Dotteretal.(2010) ancl Grattonetal.(2010).," In this context, it is clear that age is the second parameter influencing HB morphology as concluded by \citet{do10} and \citet{gr10}."727. While Figure 11. is not well samplecl over the full range of metallicity. it can still be seen that the transition from a red HD to a blue one happens over S0.5 dex in |Fe/1l] for a fixed age. or S2 Gyr at fixed [Fe/II].," While Figure \ref{HB} is not well sampled over the full range of metallicity, it can still be seen that the transition from a red HB to a blue one happens over $\la 0.5$ dex in [Fe/H] for a fixed age, or $\la 2$ Gyr at fixed [Fe/H]."728 It is interesting to consider the ensemble in (his manner. despite the fact that age uncertainties remain at or near the level.," It is interesting to consider the ensemble in this manner, despite the fact that age uncertainties remain at or near the level."729 It is a fortunate coincidence (hat we observe these GC's al a time when the HB diagram is rich with information., It is a fortunate coincidence that we observe these GCs at a time when the HB morphology-metallicity diagram is rich with information.730 Turn the clock back ~2 Gyr and the IB morphologyvanetallicity diagram: would have been populated only on the red sideas. for," Turn the clock back $\sim2$ Gyr and the HB morphology-metallicity diagram would have been populated only on the red side—as, for"731"Zamorani (1996) to predict the evolution of the aand UV luminosity densities in a ""model uuiverse with a kuown star formation history.",Zamorani (1996) to predict the evolution of the and UV luminosity densities in a “model universe” with a known star formation history.732 The key steps in our approach are (1) calculate the evolution of the actual SFR cleusity defined by the j»arameters elven in the model: (2) combine auc the model universe to predict the evolving uninosity densities: (3) use to calibrate the SFR in terms of luminosity density using he methods comiuouly applied to observations. aud (1) combine the calibration aud the predicte uminosity ceusity evolution to deduce the SER history for comparison with step (1).," The key steps in our approach are (1) calculate the evolution of the actual SFR density defined by the parameters given in the model; (2) combine and the model universe to predict the evolving luminosity densities; (3) use to calibrate the SFR in terms of luminosity density using the methods commonly applied to observations, and (4) combine the calibration and the predicted luminosity density evolution to deduce the SFR history for comparison with step (1)."733 Pozzettiefal.(19096). explored pure luminosity evolution (PLE) moclels based on a iix of our galaxy types. E/50. Sab-Sbe. Sed-5di and very Blue (vB).," \citet{Poz96} explored pure luminosity evolution (PLE) models based on a mix of four galaxy types, E/S0, Sab-Sbc, Scd-Sdm and very Blue (vB)."734 The different types are denotec iereinafter by the parameter A., The different types are denoted hereinafter by the parameter $k$.735" The local luminosity function $,(L) of each type in each selectec waveband is parametrised by the local space density 97. characteristic luminosity L7. aud faint-euc slope ay."," The local luminosity function $\Phi_k(L)$ of each type in each selected waveband is parametrised by the local space density $\Phi_k^{\ast}$, characteristic luminosity $L^{\ast}_k$, and faint-end slope $\alpha_k$."736 Each type also has a characteristic INF Vj(ÀA) and star formation rate history. pi(/).," Each type also has a characteristic IMF $\Psi_k(M)$ and star formation rate history, $\dot{\rho}_k(t)$."737" A Scalo-type IMF is used for the E/50 aud Sab-Sbe types. hereinafter called ""early. while a IME is used for the Sed-Scin aud vB types. hereinafter called “late”."," A Scalo-type IMF is used for the E/S0 and Sab-Sbc types, hereinafter called “early”, while a Salpeter-type IMF is used for the Scd-Sdm and vB types, hereinafter called “late”."738 For the E/50 galaxies. Pozzetti ccousider two mocels distinguished by different e-folcling tinies (741.το) in their SER.," For the E/S0 galaxies, Pozzetti consider two models distinguished by different e-folding times $\tau_1, \tau_2$ ) in their SFR."739 We adopt the το moclel., We adopt the $\tau_{2}$ model.740 Pozzettiefaf(1996) coustructed their model universe to match a uumber of observational constraints. including the source count. distribution iu several optical aud IR photometric bauds. the clistributiou of colours as a function of apparent maguituce. aud the distribution of redshifts as a function of maguitude.," \citet{Poz96} constructed their model universe to match a number of observational constraints, including the source count distribution in several optical and IR photometric bands, the distribution of colours as a function of apparent magnitude, and the distribution of redshifts as a function of magnitude."741 PozzettiefaL(1996) exhibit a PLE model which. iu an 2=0 Friedinauu cosinology. leads to acceptable agreement with almost all of these coustraiuts.," \citet{Poz96} exhibit a PLE model which, in an $\Omega=0$ Friedmann cosmology, leads to acceptable agreement with almost all of these constraints."742 They also deduce that PLE models in a flat (2= 1) cosmology cannot reproduce several aspects of the data. and therefore we consider only the Q=0 and Hy=50 kis + + moclel.," They also deduce that PLE models in a flat $\Omega=1$ ) cosmology cannot reproduce several aspects of the data, and therefore we consider only the $\Omega=0$ and $H_0=50$ km $^{-1}$ $^{-1}$ model."743 One coustraint not used by Pozzetti lis the observed. redshift clepeucdeuce of the luminosity deusity incertain wavebands., One constraint not used by Pozzetti is the observed redshift dependence of the luminosity density incertain wavebands.744 Figure 1 compares the UV luminosity density (Z200 — see below) of the model of Pozzetti wwitl the observations of Cowie.Songaila&Barger(1999).," Figure \ref{fig:ldens} compares the UV luminosity density ${\cal745L}^{200}$ – see below) of the model of Pozzetti with the observations of \citet{Cow99}."746. While there remain significant uncertaiuties iu the measured UV luminosity deusity (οἱ.Lillyefαἱ.1996:Cowie.Songaila&Bargervanetal. 1999).. there is satisfactory agreement between the precictiou aud recent. measurements.," While there remain significant uncertainties in the measured UV luminosity density \citep[cf.][]{Lil96,Cow99,Sul99}, there is satisfactory agreement between the prediction and recent measurements."747 The sienificaucee of this will be amplified below., The significance of this will be amplified below.748 Our application of takes place in two steps., Our application of takes place in two steps.749 First. [or galaxies of type & we compute the time-clependent spectral emission which follows the instantaneous formation of 1 ML. of stars.," First, for galaxies of type $k$ we compute the time-dependent spectral emission which follows the instantaneous formation of 1 $_\odot$ of stars."750 We use the evolutionary tracks of Bressanefal(1993) supplemented to later evolutionary phases aud to lower masses as indicated in Fioc&Rocca-Volmerauge(1997)., We use the evolutionary tracks of \citet{Bre93} supplemented to later evolutionary phases and to lower masses as indicated in \cite{Fio97}.751. We use the spectral stellar library described by Fioc&Roccea-Volinerange(1907)., We use the spectral stellar library described by \cite{Fio97}.752. We lenore extinction iu the prediction of the UV Iuminosity. aud assume the number of ionizing photons to be of the Lyman continuum photons.," We ignore extinction in the prediction of the UV luminosity, and assume the number of ionizing photons to be of the Lyman continuum photons."753 To ensure agreement with the evolutionary tracks. has au upper limit of 120 M. ," To ensure agreement with the evolutionary tracks, has an upper limit of 120 $_{\odot}$ "754The leadiug model for loug ganunua-ray bursts (CRBs) and assimmnes that they are driven bv euergv released from a disk accreting outo a black hole resulting from a massive stellar collapse.,The leading model for long gamma-ray bursts (GRBs) and assumes that they are driven by energy released from a disk accreting onto a black hole resulting from a massive stellar collapse.755 This accretion energy is converted to the explosion encrev in the GRD/hnvperuova jet either through some magnetic field miechanisi or through the anmihilation of neutrinos cuutted by the hot disk., This accretion energy is converted to the explosion energy in the GRB/hypernova jet either through some magnetic field mechanism or through the annihilation of neutrinos emitted by the hot disk.756 In this paper. we study the plysics behind the neutrino driven explosion mechanisu. deriving critical densities at which an explosion is launched.," In this paper, we study the physics behind the neutrino driven explosion mechanism, deriving critical densities at which an explosion is launched."757 For long-duration (κ 105) GRBs aud all lvpernovac. the progenitor is a παννο star that either doesut or weakly explodes via the normal supernova mechanism: aka," For long-duration $\gtrsim 10 s$ ) GRBs and all hypernovae, the progenitor is a massive star that either doesn't or weakly explodes via the normal supernova mechanism: a.k.a."758" a collapsar (MacFadven Woosley 2000. MacFadyen. Ποσο, Woosley 2001)."," a collapsar (MacFadyen Woosley 2000, MacFadyen, Heger, Woosley 2001)."759 By studving the structure of these massive stars at collapse and comparing to our critical cleusities. we cau estimate the delay between stellar collapse and the launch of the jet as well as the ultimate black hole reumant mass.," By studying the structure of these massive stars at collapse and comparing to our critical densities, we can estimate the delay between stellar collapse and the launch of the jet as well as the ultimate black hole remnant mass."760 Future observations of these delavs aud. reiinaut niasses provide constraints on the progenitor and/or jet mieclianisi for gamma-ray bursts., Future observations of these delays and remnant masses provide constraints on the progenitor and/or jet mechanism for gamma-ray bursts.761 Neutrinos enütted from black hole accretion disks push out against the iufalliug star both hrough the direct absorption aud scattering of neutrinos on iufallius matter aud through he enerey deposited in it as electrou/positvou xürs aud photons from neutrino annihilatiou., Neutrinos emitted from black hole accretion disks push out against the infalling star both through the direct absorption and scattering of neutrinos on infalling matter and through the energy deposited in it as electron/positron pairs and photons from neutrino annihilation.762 Neutrino annibhilation. which provides most of he explosion cucrey. occurs primarily above the lack hole along the rotation axis of the accretion disk.," Neutrino annihilation, which provides most of the explosion energy, occurs primarily above the black hole along the rotation axis of the accretion disk."763 Popham et al. (, Popham et al. (7641999) studied a range of isely accretion disk structures and calculated heir resultant cucrey deposition through neutrino,1999) studied a range of likely accretion disk structures and calculated their resultant energy deposition through neutrino765"side views of the halo — all the many points radiating out from the circumference of the fattest part of the ""ball",side views of the halo – all the many points radiating out from the circumference of the fattest part of the “ball.”766 However. despite its statistical unlikelihood. this geometry is still important as a limiting case. as it is the strongest lensing configuration possible for a halo of a given mass and minor axis ratio.," However, despite its statistical unlikelihood, this geometry is still important as a limiting case, as it is the strongest lensing configuration possible for a halo of a given mass and minor axis ratio."767 Thus. though halos in such orientations are uncommon. they are strongly favoured in lensing-selected samples.," Thus, though halos in such orientations are uncommon, they are strongly favoured in lensing-selected samples."768 Further. they are jxurticularly dangerous in that they show little tin the symmetric imit shown here — no) ellipticity on the sky. and so are likely to be treated as spherical if triaxial modelling is used only selectively.," Further, they are particularly dangerous in that they show little (in the symmetric limit shown here – no) ellipticity on the sky, and so are likely to be treated as spherical if triaxial modelling is used only selectively."769 In some analyses of very powerful lenses. a more complex prior. aking into account lensing efficiency in the prior distribution of axis ratios and orientation angles. may be required to capture the rue posterior distribution.," In some analyses of very powerful lenses, a more complex prior, taking into account lensing efficiency in the prior distribution of axis ratios and orientation angles, may be required to capture the true posterior distribution."770 Looking at panels 1-3 in Figure 6 uighlights this. as we see that it is low axis-ratio. low @ (close to Line of Sight). low mass solutions that give the models closest to he true lens: those that would be favoured by a strong lensing efficiency prior.," Looking at panels 1-3 in Figure \ref{fig:plot6} highlights this, as we see that it is low axis-ratio, low $\theta$ (close to Line of Sight), low mass solutions that give the models closest to the true lens: those that would be favoured by a strong lensing efficiency prior."771 Figure 8. shows the resulting contours in the completely unrealistic scenario in which the true underlying axis ratios are known. here set to be @=b0.4. while the mass. concentration. and orientation angles remain free.," Figure \ref{fig:plot8} shows the resulting contours in the completely unrealistic scenario in which the true underlying axis ratios are known, here set to be $a=b=0.4$, while the mass, concentration, and orientation angles remain free."772 The contours now contain the true model values for mass and concentration. confirming that the triaxial fitting routine behaves predictably and correctly in limits of both maximum and minimum knowledge about the underlying lens geometry.," The contours now contain the true model values for mass and concentration, confirming that the triaxial fitting routine behaves predictably and correctly in limits of both maximum and minimum knowledge about the underlying lens geometry."773 Figures 9 and 10. show the posterior probability distribution or the triaxial model under the Shaw and Mass priors. omitting 1e orientation angles for brevity.," Figures \ref{fig:plot9} and \ref{fig:plot10} show the posterior probability distribution for the triaxial model under the Shaw and Mass priors, omitting the orientation angles for brevity."774 As expected. the axis ratio distribution is significantly constrained under the Shaw prior: this eads to tighter oooC' contours that overall favour lower masses and concentrations. but are completely contained within yose obtained under the Flat prior.," As expected, the axis ratio distribution is significantly constrained under the Shaw prior; this leads to tighter $M_{200}-C$ contours that overall favour lower masses and concentrations, but are completely contained within those obtained under the Flat prior."775 This indicates that some very ow mass. low concentration models have also been lost.," This indicates that some very low mass, low concentration models have also been lost."776 Clearly. ae Shaw prior. which has very little probability in the region where us halo actually sits in parameter space. is not a good prior to impose in this case.," Clearly, the Shaw prior, which has very little probability in the region where this halo actually sits in parameter space, is not a good prior to impose in this case."777 The Mass prior. while weak. does move the contours in the direction of the true model. eliminating some higher mass cases while keeping the very low mass. low concentration cuses.," The Mass prior, while weak, does move the contours in the direction of the true model, eliminating some higher mass cases while keeping the very low mass, low concentration cases."778 This suggests that in cases in which there are reasons to suspect a particularly advantageous lensing geometry — perhaps because a studied lens is one of the strongest in our observable universe. or dynamical studies suggest elongation along the line of sight — a prior favouring lower masses may be an elegant and clear way to account for that prior belief. in place of a direct lensing efficiency prior.," This suggests that in cases in which there are reasons to suspect a particularly advantageous lensing geometry – perhaps because a studied lens is one of the strongest in our observable universe, or dynamical studies suggest elongation along the line of sight – a prior favouring lower masses may be an elegant and clear way to account for that prior belief, in place of a direct lensing efficiency prior."779 When applying this MCMC triaxial NFW fitting method tor any other method) to real lensing data from galaxy clusters. there may be some uncertainty in the exact location of the cluster centre.," When applying this MCMC triaxial NFW fitting method (or any other method) to real lensing data from galaxy clusters, there may be some uncertainty in the exact location of the cluster centre."780 This may be accounted for if necessary by including the centre position of the halo model as an unknown in the fit. increasing the number of free parameters by two for all models.," This may be accounted for if necessary by including the centre position of the halo model as an unknown in the fit, increasing the number of free parameters by two for all models."781 However. we tind that small errors in the fixed position of the cluster centre lead to only small changes in the most probable parameters recovered by our MCMC method. and that those changes are of the same scale under all priors. including at the extremes the highly triaxial Flat prior and the over-constrained Spherical prior.," However, we find that small errors in the fixed position of the cluster centre lead to only small changes in the most probable parameters recovered by our MCMC method, and that those changes are of the same scale under all priors, including at the extremes the highly triaxial Flat prior and the over-constrained Spherical prior."782 The errors induced by fixing the cluster centre are therefore no more a problem in a triaxial analysis than in any other. and we neglect them herein in our assessment of the behaviour of our new triaxial NFW fitting method.," The errors induced by fixing the cluster centre are therefore no more a problem in a triaxial analysis than in any other, and we neglect them herein in our assessment of the behaviour of our new triaxial NFW fitting method."783 We now move from looking at the behaviour of the triaxial FW fitting technique on individual. highly triaxial halos. to its behaviour across a physically-motivated population of triaxial iios.," We now move from looking at the behaviour of the triaxial NFW fitting technique on individual, highly triaxial halos, to its behaviour across a physically-motivated population of triaxial halos."784 We use a standard Monte Carlo technique to choose 100 riaxial NFW halos with Asoo=105744. and €—4 and axis ratios drawn from the distributions in Shawetal.(2006)., We use a standard Monte Carlo technique to choose 100 triaxial NFW halos with $M_{200}=10^{15}M_{\odot}$ and $C=4$ and axis ratios drawn from the distributions in \cite{shaw}.785.. The xrameter distributions of the population are shown in Appendix B:: the mean effective spherical parameters for the population are to similarthe constant triaxial values: <nisu20.99.101AL. and «C>= 3.98., The parameter distributions of the population are shown in Appendix \ref{sec:appc}; the mean effective spherical parameters for the population are similar to the constant triaxial values: $<m_{200}> = 0.99 \times 10^{15}M_{\odot}$ and $<C_{sph}> = 3.98$ .786 We randomly orient the hundred halos. lens through them as described in refsec:simulations.. and carry out MCMC fits of the triaxial NFW model under the various priors previously described.," We randomly orient the hundred halos, lens through them as described in \\ref{sec:simulations}, and carry out MCMC fits of the triaxial NFW model under the various priors previously described."787 Figure || shows the resulting most-probable triaxial parameter distributions for the population under a Flat prior and compares them witha, Figure \ref{fig:plot11} shows the resulting most-probable triaxial parameter distributions for the population under a Flat prior and compares them witha788is the adiabatic iudex.,is the adiabatic index.789" At runaway ti(yp)—te. aud cus6s between the base and a height deus) 0,25."," At runaway $t_h(y_b)=t_d$, and $v_{\rm ph}>c_s$ between the base and a height ) 0.2h."790(2) Above that location. the Aestemperature is not adequate to help initiate the detonation.," Above that location, the temperature is not adequate to help initiate the detonation."791 Of course. because of the sanall scale height compared to the racius. there is a auch sanaller temperature eracieut in the horizoutal direction. an issue we will address momentarily.," Of course, because of the small scale height compared to the radius, there is a much smaller temperature gradient in the horizontal direction, an issue we will address momentarily."792 If the initiating region calculated above is too πια]. the initial shock is unable to trigger further burning before it decays by geometrical dilution.," If the initiating region calculated above is too small, the initial shock is unable to trigger further burning before it decays by geometrical dilution."793 Direct umuerical sinulatious aud experiucnuts always fiud that to trigeer a detonation the imitiating region must be a few orders of magnitude longer than the induction leugth of the detonation Jing%ομα (see Eckettetal.2000 for a recent discussion)., Direct numerical simulations and experiments always find that to trigger a detonation the initiating region must be a few orders of magnitude longer than the induction length of the detonation $l_{\rm ind}\approx v_{CJ} t_{\rm ind}$ (see \citealt{Eckett:00} for a recent discussion).794 Tere ο is the Chapman-Jouguct velocity (see c.g... IKhokllov 1989)) aud fing ix the induction time. the time scale to complete the burning belind the shock.," Here $v_{CJ}$ is the Chapman-Jouguet velocity (see e.g., \citealt{Khokhlov:89}) ) and $t_{\rm ind}$ is the induction time, the time scale to complete the burning behind the shock."795 In the case of a spherically svuuuiectric ignition (see He&Clavin 1991)). such as in a ceutrally ignited Type Ia supernova. this nuüninmun distance is expressed iu terms of a maxumunun radius of curvature Aix (Sharpe2001:Disi&Tiuunes2006).," In the case of a spherically symmetric ignition (see \citealt{He:94}) ), such as in a centrally ignited Type Ia supernova, this minimum distance is expressed in terms of a maximum radius of curvature $\kappa_{\rm max}$ \citep{Sharpe:01, Dursi:06}."796" Disi&""Tinuues(2006) carried out direct numerical sinmlatious for carbon detonatious. aud derived a fitting functiou for Hiax(p.X32)."," \citet{Dursi:06} carried out direct numerical simulations for carbon detonations, and derived a fitting function for $\kappa_{\rm max}(\rho, X_{12})$."797" The most couservative estimate of the critical conditions needed for a detonation is to then demand that the length of the spoutancously igniting region. z44. be larger than &,,1,."," The most conservative estimate of the critical conditions needed for a detonation is to then demand that the length of the spontaneously igniting region, $z_{\rm crit}$, be larger than $\kappa_{\rm max}^{-1}$."798 By equatio- (2)). this translates iuto a requirement that ij]>5. as dotted in Figure 1..," By equation \ref{eq:zcrit}) ), this translates into a requirement that $\kappa_{\rm max} h >5$, as plotted in Figure \ref{fig:X12yb}."799 Most of the data lie below this line. naking it challenging to trigger a spherical detonatio- wea vertical mitiation.," Most of the data lie below this line, making it challenging to trigger a spherical detonation by a vertical initiation."800 Building on the aremmueuts for Type Ia supernovae core detonatious. our discussion has assumed that the vertical cluperature eradieut (where the teiiperature decreases vieBOLOY over a pressure scale heisht ) plavs he critical role.," Building on the arguments for Type Ia supernovae core detonations, our discussion has assumed that the vertical temperature gradient (where the temperature decreases by $\approx 30-40\%$ over a pressure scale height $h$ ) plays the critical role."801 Wowever. the superburst occurs in a hin shell at the surface of the neutron star. aud the tour long convective phase prior to the lydrodvuamic runaway should be adequate to establish transverse cluperature eracieuts simaller than the vertical eradicut.," However, the superburst occurs in a thin shell at the surface of the neutron star, and the hour long convective phase prior to the hydrodynamic runaway should be adequate to establish transverse temperature gradients smaller than the vertical gradient."802 Onlv a nmuuerical auclastic calculation could accurately calculate such a gradient. but we think it reasonable o assume that the iitiation leneth is larecr iu the aue. potentially exceeding / at some location.," Only a numerical anelastic calculation could accurately calculate such a gradient, but we think it reasonable to assume that the initiation length is larger in the plane, potentially exceeding $h$ at some location."803 Such a cvlndzrical geometry also has the advantage of less severe ecolctrical dilution. where all analytic calculations vield a factor of two smaller value for (Leo1977:Ie&Clavin 1991).," Such a cylindrical geometry also has the advantage of less severe geometrical dilution, where all analytic calculations yield a factor of two smaller value for $\kappa_{\rm max}^{-1}$ \citep{Lee:77, He:94}."804. For this reason. we ώςplot an additional ne af |y= lin Figure 1l. represeutius our current jest guess of the constraint for detonation initiation in a planar geometry.," For this reason, we plot an additional line at $\kappa_{\rm max} h=1$ in Figure \ref{fig:X12yb}, representing our current best guess of the constraint for detonation initiation in a planar geometry."805 All the data points are above this iue. as is the explosion we are simulating in this paper (shown by the open star).," All the data points are above this line, as is the explosion we are simulating in this paper (shown by the open star)."806 Although more work clearly remains to fully assess the onset of a detonation in a dlanar geoctry after a long convective plasc. we will xoceed assume that it can happen.," Although more work clearly remains to fully assess the onset of a detonation in a planar geometry after a long convective phase, we will proceed assuming that it can happen."807" We assmne a plane parallel eeoiaetry with coustaut eravity. g=κ2.1«,10Hans27 (corresponding: toLAL... R=I0kin) and treat the detonation in oulv the vertical direction. parametrized by the column depth y uto the star Quuits of οcn7). where dy=pdr."," We assume a plane parallel geometry with constant gravity $g=2.4\times10^{14}\trm{ cm s}^{-2}$ (corresponding to, $R=10\trm{ km}$ ) and treat the detonation in only the vertical direction, parametrized by the column depth $y$ into the star (units of $\trm{g cm}^{-2}$ ), where $dy = -\rho dr$."808 Alodeliug the lateral propagation is important and left for future study (sce Ziugaleetal.2001.. who consider a laterally propagating Πο detonation in the ocean of a ueutron star).," Modeling the lateral propagation is important and left for future study (see \citealt{Zingale:01}, who consider a laterally propagating $^4$ He detonation in the ocean of a neutron star)."809 We solve the reactive fluid flow equations using a one-dimeusional. explicit. Lagrangian. finite difference scheme (see e.g. Deuz19011).," We solve the reactive fluid flow equations using a one-dimensional, explicit, Lagrangian, finite difference scheme (see e.g., \citealt{Benz:91}) )."810 We use operator splitting to couple the hvdrodwnaimics to a unclear energy eeneratioun network., We use operator splitting to couple the hydrodynamics to a nuclear energy generation network.811" The network contains 13 isotopes: HTIo. 12(5. 16(). 20N 6, 21\ To. 258i. σας. 36 Ay. IU ΕΤΗ, που, OP Fe. CONTE. and includes @-chain. heavy-iou. aud (o.pXp.5)veactions?.."," The network contains 13 isotopes: $\{^4$ He, $^{12}$ C, $^{16}$ O, $^{20}$ Ne, $^{24}$ Mg, $^{28}$ Si, $^{32}$ S, $^{36}$ Ar, $^{40}$ Ca, $^{44}$ Ti, $^{48}$ Cr, $^{52}$ Fe, $^{56}$ $\}$ , and includes $\alpha$ -chain, heavy-ion, and $(\alpha, p)(p, \gamma)$."812 We assume electrons. ious. and photons supply the pressure aud calculate the equation of state. volumetric neutrino enüssvitv. aud thermal conductivity. as in Brown(2001).," We assume electrons, ions, and photons supply the pressure and calculate the equation of state, volumetric neutrino emissivity, and thermal conductivity, as in \citet{Brown:04}."813. We model the detonation aud shocks over the colui depths 10!οeii.2 using 1000 exid points spaced uniformly in logy., We model the detonation and shocks over the column depths $10^4-10^{14}\trm{ g cm}^{-2}$ using 4000 grid points spaced uniformly in $\log y$ .814 The IC laver spaus the range ype<WOgema7., The $^{12}$ C layer spans the range $y_{\rm He} < y < y_b \sim 10^{12} \cd$ .815" The depth of the base of the freshly accreted ΠΠο laver. πιω)=ove1)~ 7. varies linearly with the phase o=f/faq, of the Type I burst evcle. whose recurrence time fgc10! 10*s, "," The depth of the base of the freshly accreted H/He layer, $y_{\rm He}(\phi) \equiv \phi y_{\rm He}(\phi = 1) \sim10^8\cd$ , varies linearly with the phase $\phi=t/t_{\rm recur}$ of the Type I burst cycle, whose recurrence time $t_{\rm recur} \sim 10^4-10^5 \trm{ s}$ ."816We asmiuue the accreted gas las a solar composition and consider local aceretiou rates per uuit area in the range s)=00150πια. where mraa is the local Eddineton accretion rate (i... roughly the range inferred from observations: Iuulkers2001)).," We assume the accreted gas has a solar composition and consider local accretion rates per unit area in the range $\dot{m}=0.05-0.3 \dot{m}_{\rm Edd}$, where $\dot{m}_{\rm Edd}$ is the local Eddington accretion rate (i.e., roughly the range inferred from observations; \citealt{Kuulkers:04}) )."817 The 12€ laver has a mass fraction 1...N4» of Fo and for JgDyp the composition is pure 9 Fe., The $^{12}$ C layer has a mass fraction $1-\trm{X}_{12}$ of $^{56}$ Fe and for $y>y_b$ the composition is pure $^{56}$ Fe.818" For a giveu gy. X4». Oo. and η, we solve for the crustal heat flux that results in unstable iguition at yw, (sce WBB) aud then calculate ueste=lop) as in Cunniaing&Bildsten (2000).."," For a given $y_b$, $X_{12}$, $\phi$, and $\dot{m}$, we solve for the crustal heat flux that results in unstable ignition at $y_b$ (see WBB) and then calculate $y_{\rm He}(\phi=1, \dot{m})$ as in \citet{Cumming:00}. ."819 The shock reaches the top of our grid (uy=10!©cni 3] ate a πιο ο10 ys after the onset of the hydrodynanie runaway., The shock reaches the top of our grid $y=10^4\cd$ ) at a time $t_{\rm top}\approx10\trm{ $ $s}$ after the onset of the hydrodynamic runaway.820—fg ," The underlying layers are adiabatically expanding at $t=t_{\rm top}$, though they remain bound to the neutron star and in plane parallel (see \ref{sec:steepening}) )."821The underly," We assume that for $t>t_{\rm top}$ the flow remains adiabatic and that after a few dynamical times (tens of $\mu\trm{s}$ ), the shocked layers settle into a new, puffed-up, hydrostatic equilibrium, with an entropy profile given by that at $t=t_{\rm top}$."822ins , This post-shock hydrostatic equilibrium sets the early-time light curve of our cooling calculations \ref{sec:lightcurves}) ).823We compute the evolution cing the convective stage (fj> fj) as in WBB., We compute the evolution during the convective stage $t_h > t_d$ ) as in WBB.824 Approximately of the PC is ined to 2!Me during the convective stage for LOYοeni7 and a pre-iguition mass fraction Ny 42. , Approximately of the $^{12}$ C is burned to $^{24}$ Mg during the convective stage for $y_b=10^{12}\cd$ and a pre-ignition mass fraction $X_{12}=0.2$ .825"We then initiate the detonation at the ouset of he dynamical runaway (fj,= ty) bv increasing theeniperature of the erid point at y, by 1%.", We then initiate the detonation at the onset of the dynamical runaway $t_h = t_d$ ) by increasing thetemperature of the grid point at $y_b$ by .826.. In Figure 2 we show the evolution of the thermal profile chiving he convective stage as Z7; rises lines) aud he hydrodynamic stage as the detonation propagates outward lines)., In Figure \ref{fig:Tyzoom} we show the evolution of the thermal profile during the convective stage as $T_b$ rises ) and the hydrodynamic stage as the detonation propagates outward ).827 The shock wave that defines the head ofthe detonation Yont is sufficicutly strong that it triggers complete °C »rnnue iu the deepest lavers., The shock wave that defines the head of the detonation front is sufficiently strong that it triggers complete $^{12}$ C burning in the deepest layers.828 However. as the shock xopagates outward into cooler. lower deusitv fuel. itfails otrigger LC Durningou the ντοναο timescale (~ qim).," However, as the shock propagates outward into cooler, lower density fuel, itfails totrigger $^{12}$ C burningon the hydrodynamic timescale $\sim\mu\trm{s}$ )."829 The shock ultimately races ahead of the burningand the detonation dies at a depth gai (see line iuFigure 2))., The shock ultimately races ahead of the burningand the detonation dies at a depth $y_{\rm det}$ (see inFigure \ref{fig:Tyzoom}) ).830 The value of yaar is approximately the deptl at which the detonation iduction leneth AZ becomes eyoater than a scale height fo=y/p (this assumes the detonation is very nearlv planar upon reaching this, The value of $y_{\rm det}$ is approximately the depth at which the detonation induction length $l_{\rm ind}$ becomes greater than a scale height $h = y/\rho$ (this assumes the detonation is very nearly planar upon reaching this831Salome aud Nemesio Rodriguez for their help wit[um the PdBI observatious and data reduction.,Salome and Nemesio Rodriguez for their help with the PdBI observations and data reduction.832 We thauk the referee for several sugecstions that improved the presentation., We thank the referee for several suggestions that improved the presentation.833 D.S.M. acknowledges support from the National Radio Astronomy Observatory which is operated by Associated Universities. Luc. under cooperative agreciuent with the National Scicuce Foundation and NSF eraut. AST-1009620.," D.S.M. acknowledges support from the National Radio Astronomy Observatory which is operated by Associated Universities, Inc., under cooperative agreement with the National Science Foundation and NSF grant AST-1009620."834 This work is n supported by NSF erants AST-0307950 aud 506169 to J.L.T., This work is also supported by NSF grants AST-0307950 and AST-0506469 to J.L.T.835"which is based on the LR source density in the field around each X-ray source position. we attempted to estimate the level of ""contamination of these counterpart. samples cluc to chance superpositions of unrelated. X-ray sources and LR clusters.","which is based on the IR source density in the field around each X-ray source position, we attempted to estimate the level of 'contamination' of these counterpart samples due to chance superpositions of unrelated X-ray sources and IR clusters."836 We expect S sources with a 1o uncertainty of of the 28 Likely counterparts to be due to. chance superpositions of unrelated. objects. and 10 with à le uncertainty of 0.4/-0.31] for the 10. possible counterparts to be chance superpositions.," We expect 8 sources with a $1\sigma$ uncertainty of of the 28 likely counterparts to be due to chance superpositions of unrelated objects, and 10 with a $1\sigma$ uncertainty of ] for the 10 possible counterparts to be chance superpositions."837 In Fig., In Fig.838 3 we plot the X-rav luminosity versus. the separation in arcseconds to the associated UR cluster counterpart., 3 we plot the X-ray luminosity versus the separation in arcseconds to the associated IR cluster counterpart.839" We also divided the N-ray. sources into three uminositv bins: Low Luminosity X-ray sources (LENs) had by <310 Cres i lligh Luminosity X-ray sources (IILN8) were between Ly of 3lU ergs s Land Po107 ODES 8+ while Ly > 1107?"" ODES twere Ultra-Luminous X-ray Sources (ULNs)."," We also divided the X-ray sources into three luminosity bins: Low Luminosity X-ray sources (LLX's) had $L_{X}$ $<$ $3\times10^{38}$ ergs $^{-1}$, High Luminosity X-ray sources (HLX's) were between $L_{X}$ of $3\times10^{38}$ ergs $^{-1}$ and $1\times10^{39}$ ergs $^{-1}$, while $L_{X}$ $>$ $1\times10^{39}$ ergs $^{-1}$ were Ultra-Luminous X-ray Sources (ULX's)."840 All luminosities were taken from able 5 of Zezasοἱal.(2006)., All luminosities were taken from table 5 of \citet{zez06}.841. Notice that there is no trend in separation from the IH. cluster counterpart. ancl N-rav uminosity., Notice that there is no trend in separation from the IR cluster counterpart and X-ray luminosity.842 This seems to indicate no preference as to where ARBs of different luminosity classes form in star clusters., This seems to indicate no preference as to where XRBs of different luminosity classes form in star clusters.843short.,short.844 For the eruption in January. 2010. there was no significant. pre-eruption rise and our (DGII. SD. JM. ML) small-telescope monitoring produced a better light curve thai ROTSE.," For the eruption in January 2010, there was no significant pre-eruption rise and our (BGH, SD, JM, ML) small-telescope monitoring produced a better light curve than ROTSE."845 A third reason for the ROTSE program was the hope that we would cateh U Seo on the rise., A third reason for the ROTSE program was the hope that we would catch U Sco on the rise.846 In all previous eruptions. U Seo has been recorded on the rise only three times. each being close to the peak. with the rise [rom quiescence apparently lasting 6-12 hours (Schaeler 2010).," In all previous eruptions, U Sco has been recorded on the rise only three times, each being close to the peak, with the rise from quiescence apparently lasting 6-12 hours (Schaefer 2010)."847 In the hours before the discovery of (he 2010 eruption. the Namibia ROTSE telescope did not look at U Sco due to a higher priority follow-up to a Ganuna-Rav Durst. the Turkey ROTSE had clouds. and the Australia ROTSE was down with equipment problems.," In the hours before the discovery of the 2010 eruption, the Namibia ROTSE telescope did not look at U Sco due to a higher priority follow-up to a Gamma-Ray Burst, the Turkey ROTSE had clouds, and the Australia ROTSE was down with equipment problems."848 With the chance lack of any. data on the rise ancl the poor photometric accuracy of the two vears of monitoring. we are not presenting anv of the ROTSE magnitudes in (his paper.," With the chance lack of any data on the rise and the poor photometric accuracy of the two years of monitoring, we are not presenting any of the ROTSE magnitudes in this paper."849 Beginning in early 2008. we (MT ancl AAILD organized a steady watch on U Seo by the many observers of the AAVSO.," Beginning in early 2008, we (MT and AAH) organized a steady watch on U Sco by the many observers of the AAVSO."850 The primary goal was to catch U Sco's eruption as quickly as possible., The primary goal was to catch U Sco's eruption as quickly as possible.851 The widespread distribution in longitude of the many AAVSO observers makes for frequent monitoring. and (this was the best chance of catching the eruption early.," The widespread distribution in longitude of the many AAVSO observers makes for frequent monitoring, and this was the best chance of catching the eruption early."852 For the half vear around opposition. U Sco was checked lor outburst up to 6.7 times per day for monthly averages.," For the half year around opposition, U Sco was checked for outburst up to 6.7 times per day for monthly averages."853 A [urther requirement for getting [ast reactions from the world's telescopes was that the discovery had to be communicated from the discoverer to the rest of the world., A further requirement for getting fast reactions from the world's telescopes was that the discovery had to be communicated from the discoverer to the rest of the world.854 For this vital need. the AAVSO IIeacdcuarters served as an around-the-cloek. everv-dav-of-the-vear communication center.," For this vital need, the AAVSO Headquarters served as an around-the-clock, every-day-of-the-year communication center."855 Observers were instructed to report their discovery electronically. then automated services would alert kev individuals who woukl test for validity and solicit [ast confirmation.," Observers were instructed to report their discovery electronically, then automated services would alert key individuals who would test for validity and solicit fast confirmation."856 Once (he eruption was discovered. we would immediately. start notifving the world through LAU. Cireulars and lone-prepared phone and email lists.," Once the eruption was discovered, we would immediately start notifying the world through IAU Circulars and long-prepared phone and email lists."857 As part of this effort. many AAVSO members made positive measures of the brightness ol U Seo during the pre-eruption phase.," As part of this effort, many AAVSO members made positive measures of the brightness of U Sco during the pre-eruption phase."858 The AAVSO database contains 412 magnitudes (from 29 observers) and 2853 limits (rom 102 observers) between the end of the 1999 eruption and the start of the 2010 eruption (JD 2451557.148 to 2455224.121)., The AAVSO database contains 412 magnitudes (from 29 observers) and 2853 limits (from 102 observers) between the end of the 1999 eruption and the start of the 2010 eruption (JD 2451557.148 to 2455224.127).859 The limits were vital αἱ the time of the observation for knowing that U Sco had not erupted. but they are not now helpful for following the aceretion rate.," The limits were vital at the time of the observation for knowing that U Sco had not erupted, but they are not now helpful for following the accretion rate."860 A further 77 magnitudes are not used here. primarily because (he photometric svstem is not standard and the meaning of the magnitude would be unclear.," A further 77 magnitudes are not used here, primarily because the photometric system is not standard and the meaning of the magnitude would be unclear."861 This leaves us with 335 positive detec(ions in the pre-eruplion (me interval., This leaves us with 335 positive detections in the pre-eruption time interval.862 Just over of these magnitudes were made with unfillered. CCD imaging. where the magnitudes were calibrated cilferentially from nearby. comparison stars using either the or B-band magnitudes.," Just over of these magnitudes were made with unfiltered CCD imaging, where the magnitudes were calibrated differentially from nearby comparison stars using either the V-band or R-band magnitudes."863 These magnitudes (designated CV or CR) will not be exactly on either the V or Ro magnitude systems. but the expected deviations (less than 0.1 mag) are alwavs small compared (o normal variations of U Sco.," These magnitudes (designated CV or CR) will not be exactly on either the V or R magnitude systems, but the expected deviations (less than 0.1 mag) are always small compared to normal variations of U Sco."864 Our instrumentation is a 16-inch [/10 Schmidt-Cassegrain with a V filter located in New Smyrna Beach. Florida (BGI). an Ls-inceh Newtonian telescope without filter located in Barnesville. Maryland (JM). and a," Our instrumentation is a 16-inch f/10 Schmidt-Cassegrain with a V filter located in New Smyrna Beach, Florida (BGH), an 18-inch Newtonian telescope without filter located in Barnesville, Maryland (JM), and a"865interpretation of observations of the solar neighbourhood in which components are identified as regions of the (νο).a/Fe]) plane.,"interpretation of observations of the solar neighbourhood in which components are identified as regions of the $(\feh,\afe)$ plane."866 Thin-dise stars lic in a narrow ridge of high density between. Fe/H]~0.65 and οΗ]~0.15 hat forms part of the lower edge of the populated part of he ΜοΗ].aEe]) plane.," Thin-disc stars lie in a narrow ridge of high density between $\feh\sim-0.65$ and $\feh\sim0.15$ that forms part of the lower edge of the populated part of the $(\feh,\afe)$ plane."867 Phe metal-rich thick disc occupies a broader swath of the (Fe/I].a/EFe]) plane that runs xwallel to the downwarde-sloping ridge of the thin disc and ~0.3 in. O/TFc] higher.," The metal-rich thick disc occupies a broader swath of the $(\feh,\afe)$ plane that runs parallel to the downward-sloping ridge of the thin disc and $\sim0.3$ in $\ofe$ higher."868 Phe metal-rich thick disc extends in οΗ] from ~—0.9 to well above 0. where it merges with he thin disc.," The metal-rich thick disc extends in $\feh$ from $\sim-0.9$ to well above 0, where it merges with the thin disc."869 At its low-metallicity high-a end. the metal-rich thick disce touches the metal-poor thick disc. in which OjfFe]=0.6340.5 and Fe/L] goes at least down to —L4.," At its low-metallicity $\alpha$ end, the metal-rich thick disc touches the metal-poor thick disc, in which $\ofe\simeq0.63\pm0.5$ and $\feh$ goes at least down to $\sim-1.4$."870" There is an ""intermediate population"" of stars that in the CFef1].a/Ec]) plane lie between the thin and thick disces. but the density of such stars in the (Fe/lH].a/Ee]) plane is relatively low."," There is an “intermediate population” of stars that in the $(\feh,\afe)$ plane lie between the thin and thick discs, but the density of such stars in the $(\feh,\afe)$ plane is relatively low."871 Thus the two discs are well defined structures., Thus the two discs are well defined structures.872 'hin-disc stars are all vounger than 7€vr and are on fairly circular orbits., Thin-disc stars are all younger than $7\Gyr$ and are on fairly circular orbits.873 Their values. of Fe/H} and rotation velocity. V are. correlated. in. the sense. that higher V implies lower Fe/1l]., Their values of $\feh$ and rotation velocity $V$ are correlated in the sense that higher $V$ implies lower $\feh$.874 The stars of the metal- thick cise are nearly all older than Svr., The stars of the metal-rich thick disc are nearly all older than $8\Gyr$.875" Most. are on significantly non-circular orbits with guiding centres inside Z, and a significant number have V.<100kms", Most are on significantly non-circular orbits with guiding centres inside $R_0$ and a significant number have $V<-100\kms$.876 Specifically. the metal-rich thick disc can be considered to be a superposition of isothermal components with racial velocity dispersions between 50. and. SOKms strongly peaked around 60kms1.," Specifically, the metal-rich thick disc can be considered to be a superposition of isothermal components with radial velocity dispersions between $50$ and $80\kms$, strongly peaked around $60\kms$."877 The metal-poor thick disc consists exclusively of stars older than LOCivr., The metal-poor thick disc consists exclusively of stars older than $10\Gyr$.878 Its stars have on average more angular momentum and smaller velocity dispersions than the stars of the metal-rich thick disc., Its stars have on average more angular momentum and smaller velocity dispersions than the stars of the metal-rich thick disc.879 Among the population of strongly. a-cnhanced stars there is (cL. 4), Among the population of strongly $\alpha$ -enhanced stars there is (cf. )880) an extremely strong. negative correlation between à and V., an extremely strong negative correlation between $\alpha$ and $V$.881 Aleléndezetal.(2008) remarked that the thick disc has similar properties to the Galactic bulge., \cite{Melend08} remarked that the thick disc has similar properties to the Galactic bulge.882 This conclusion is natural in the context of our model. in which the metal-rich thick disc is mace up of stars that have migrated. to the Sun from the inner disc. where rapid. early star formation enriched the ISM to significant. metallicities before. SNla began to lower αΚΟ.," This conclusion is natural in the context of our model, in which the metal-rich thick disc is made up of stars that have migrated to the Sun from the inner disc, where rapid early star formation enriched the ISM to significant metallicities before SNIa began to lower $\afe$."883 Ht is to be expected that many of the stars that formed. alongside the thick-clise stars of the solar neighbourhood are now bulge stars., It is to be expected that many of the stars that formed alongside the thick-disc stars of the solar neighbourhood are now bulge stars.884 Perhaps the most uncertain aspect of the modelling is our assuniption that a star's probability of being “churned” to a different angular momentum is independent of the stars random. velocity., Perhaps the most uncertain aspect of the modelling is our assumption that a star's probability of being “churned” to a different angular momentum is independent of the star's random velocity.885 Since Sellwood&Binney(2002) did not investigate the dependence of churning probability on random velocity. our assumption could be significantly in error. and it is not implausible that stars with large random. velocities have low churning probabilities.," Since \cite{SellwoodB} did not investigate the dependence of churning probability on random velocity, our assumption could be significantly in error, and it is not implausible that stars with large random velocities have low churning probabilities."886 In. this case the thick cise would be less racially mixed. than our mocel predicts., In this case the thick disc would be less radially mixed than our model predicts.887 We will shortly investigate the dependence of churning probability on random velocity., We will shortly investigate the dependence of churning probability on random velocity.888 Given our model's success in svnthesising studies of the Galactic disc into a coherent picture. it is useful as it stands regardless of the theoretical considerations that motivated its construction.," Given our model's success in synthesising studies of the Galactic disc into a coherent picture, it is useful as it stands regardless of the theoretical considerations that motivated its construction."889 However. it was not made by searching an extensive parameter space for a model that would fit the studies described here.," However, it was not made by searching an extensive parameter space for a model that would fit the studies described here."890 Rather it was made by building a code that combined standard chemical evolution mocelling with a model of dynamical. evolution that rellects. the unclerstancing of how spiral structure works that Sellwood&Binney(2002). eainecl from N-body mocels and analytical dynamics., Rather it was made by building a code that combined standard chemical evolution modelling with a model of dynamical evolution that reflects the understanding of how spiral structure works that \cite{SellwoodB} gained from N-body models and analytical dynamics.891 Is two free parameters were determined [rom the mocel's fit to the metallicity gradient in the ISM and to the metallicity cüstribution of the GCS stars given in Nordstrom.etal.(2004). and LHolmboergetal., Its two free parameters were determined from the model's fit to the metallicity gradient in the ISM and to the metallicity distribution of the GCS stars given in \cite{Nordstrom04} and \cite{HolmbergNA}.892(2007).. Llence we consider he models ability to reproduce the data sets of Fulirmann(1998).. Bensbyetal.(2008.2005)... Vennetal.(2004) τονetal.(2006).. Haywoock(2008).. Juricetal.(2008) and Ivezicetal.(2008). is remarkable and suggests that it ms à sound. physical basis.," Hence we consider the model's ability to reproduce the data sets of \cite{Fuhrmann98}, \cite{Bensby03,Bensby05}, \cite{Venn04} \cite{Reddy06}, \cite{Haywood08}, \cite{Juric08} and \cite{Ivezic08} is remarkable and suggests that it has a sound physical basis."893 The Κον respect in which the model goes bevond racitional models of chemical evolution is its inclusion of racial migration by stars and inward How by gas., The key respect in which the model goes beyond traditional models of chemical evolution is its inclusion of radial migration by stars and inward flow by gas.894 Lawarel low of gas is important for the model's success. because it establishes a much steeper metallicity gradient than racitional mioclels produce., Inward flow of gas is important for the model's success because it establishes a much steeper metallicity gradient than traditional models produce.895 The radial migration of stars is absolutely kev. because it structures the thick disc.," The radial migration of stars is absolutely key, because it structures the thick disc."896 Moreover it explains the significant spread in Fe/ll] within the ocal thin disc. and the correlation that Haywood.(2008) identified between: Fe/LH] and V," Moreover it explains the significant spread in $\feh$ within the local thin disc, and the correlation that \cite{Haywood08}897 identified between $\feh$ and $V$."898 The discovery that the thick dise overlaps the thin disc in Fe/ll] presented a challenge to conventional models of chemical evolution because it implies that there are thick disc stars that have both aFe] and Fe/LH] higher than in some thin-cise stars., The discovery that the thick disc overlaps the thin disc in $\feh$ presented a challenge to conventional models of chemical evolution because it implies that there are thick disc stars that have both $\afe$ and $\feh$ higher than in some thin-disc stars.899 The lower values of a/LEFc] in the thin-disc stars imply earlier times of birth. so how come Fe/1] is lower?," The lower values of $\afe$ in the thin-disc stars imply earlier times of birth, so how come $\feh$ is lower?"900 “Phe conventional response to this challenge it to suppose that some violent event led to a suspension of star ormation in the disc. and that curing this hiatus à massive injection of metal-poor gas lowered. Fe/1l] in the 18M (Chiappinietal.1997.2001).," The conventional response to this challenge it to suppose that some violent event led to a suspension of star formation in the disc, and that during this hiatus a massive injection of metal-poor gas lowered $\feh$ in the ISM \citep{Chiappini97,Chiappini01}."901. An objection to this scenario is that many. other galaxies have thick discs with similar »operties to ours (Yoachim&Dalcanton 2006).. so thick-disc formation should not require special circumstances.," An objection to this scenario is that many other galaxies have thick discs with similar properties to ours \citep{YoachimDalcanton}, , so thick-disc formation should not require special circumstances."902 We do not press this argument but would stronely make he point that a model of chemical evolution that includes only physics and has a single. carly. maximum in he star-formation rate and a monotonically rising value of ο) at each radius automatically produces a thick disc with just the properties observed. locally.," We do not press this argument but would strongly make the point that a model of chemical evolution that includes only physics and has a single, early, maximum in the star-formation rate and a monotonically rising value of $\feh$ at each radius automatically produces a thick disc with just the properties observed locally."903 In fact an a- enhanced thick cise forms because the speed at which Fell rises declines as one moves outwards. so the value attaine by Fe/H] when SNIa start to lower aFe] increases inwards.," In fact an $\alpha$ -enhanced thick disc forms because the speed at which $\feh$ rises declines as one moves outwards, so the value attained by $\feh$ when SNIa start to lower $\afe$ increases inwards."904 Spiral structure and the Galactic bar scatter. a-enhancec stars formed at small radii onto more eccentric ancl more inclined. orbits and even scatters some of them onto orbits of sullicientlv high angular momentum that they are foun in the solar neighbourhood., Spiral structure and the Galactic bar scatter $\alpha$ -enhanced stars formed at small radii onto more eccentric and more inclined orbits and even scatters some of them onto orbits of sufficiently high angular momentum that they are found in the solar neighbourhood.905 Readers who want to believe in a violent origin of the thick dise may continue to do so., Readers who want to believe in a violent origin of the thick disc may continue to do so.906 Du they should be aware that the simplest model of the chemo- evolution of the disc that includes all relevan physics reproduces the data., But they should be aware that the simplest model of the chemo-dynamical evolution of the disc that includes all relevant physics reproduces the data.907 Hence there is absolutely. no that the thick disc has a violent origin., Hence there is absolutely no that the thick disc has a violent origin.908 RAS. acknowledges financial and material support fromMax- [rom Stiftung Maximilianeum and from Studienstiftung des Deutschen Volkes.," R.S. acknowledges financial and material support fromMax-Planck-Gesellschaft, from Stiftung Maximilianeum and from Studienstiftung des Deutschen Volkes."909star systems because the radiative feedback from the stellar core which may inhibit later fragmentation of a massive disc is absence.,star systems because the radiative feedback from the stellar core which may inhibit later fragmentation of a massive disc is absence.910 After the formation of a stellar core within the disc. dissociating gas from the inner regions of the dise falls towards the stellar core and builds a smaller dise around the stellar core.," After the formation of a stellar core within the disc, dissociating gas from the inner regions of the disc falls towards the stellar core and builds a smaller disc around the stellar core."911 This inner dise increases with radius as material with higher angular momentum falls in. and eventually merges with the inner edge of the outer disc.," This inner disc increases with radius as material with higher angular momentum falls in, and eventually merges with the inner edge of the outer disc."912 Although this inner/outer dise structure and the earlier evolution of the first core phase is similar for barotropic and radiation hydrodynamical calculations. we find that the subsequen evolution is qualitatively. different in radiation hydrodynamica calculations.," Although this inner/outer disc structure and the earlier evolution of the first core phase is similar for barotropic and radiation hydrodynamical calculations, we find that the subsequent evolution is qualitatively different in radiation hydrodynamical calculations."913 In barotropic ealeulations. the formation of the stellar core deep inside the first core (or pre-stellar dise) has no effec on the surrounding dise because the temperature of the gas is simply set by the density of the gas.," In barotropic calculations, the formation of the stellar core deep inside the first core (or pre-stellar disc) has no effect on the surrounding disc because the temperature of the gas is simply set by the density of the gas."914 However. with radiation hydrodynamics. the energy released by the formation of the stellar core within the optically thick dise is similar to the binding energy of the disce.," However, with radiation hydrodynamics, the energy released by the formation of the stellar core within the optically thick disc is similar to the binding energy of the disc."915 This heats region surrounding the stellar core and. at approximately the same time as the inner disc and outer dises merge. a shock wave forms in the merger region and propagates outwards through the disc. while a bipolar outflow is launched perpendicular to the rotation axis. dramatically decreasing the accretion rate on to the stellar core.," This heats region surrounding the stellar core and, at approximately the same time as the inner disc and outer discs merge, a shock wave forms in the merger region and propagates outwards through the disc, while a bipolar outflow is launched perpendicular to the rotation axis, dramatically decreasing the accretion rate on to the stellar core."916 The properties of the outflow do not seem to vary greatly. with the initial rotation rate of the molecular cloud core or the pre-stellar dise. but the speed of the outflow is somewhat greater for higher rotation rates and the shockwave which propagates outward through the dise reaches the outer edge of the dise more quickly for smaller disces.," The properties of the outflow do not seem to vary greatly with the initial rotation rate of the molecular cloud core or the pre-stellar disc, but the speed of the outflow is somewhat greater for higher rotation rates and the shockwave which propagates outward through the disc reaches the outer edge of the disc more quickly for smaller discs."917 It remains to be seen how the inclusion of magnetic fields alters this driven outburst., It remains to be seen how the inclusion of magnetic fields alters this thermally-driven outburst.918 MRB is grateful for the hospitality and support he received from the Monash Centre for Astrophysics while on study leave and where this paper was written up., MRB is grateful for the hospitality and support he received from the Monash Centre for Astrophysics while on study leave and where this paper was written up.919 The calculations for this paper were performed on the University of Exeter Supercomputer. a DiRAC Facility jointly funded by STFC. the Large Facilities Capital Fund of BIS. and the University of Exeter.," The calculations for this paper were performed on the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS, and the University of Exeter."920 Some figures were produced using the publicly available SPLASH visualisation software (2).., Some figures were produced using the publicly available SPLASH visualisation software \citep{Price2007}.921" This work. conducted as part of the award ""The formation of stars and planets: Radiation hydrodynamical and magnetohydrodynamical simulations” made under the European Heads of Research Councils and European Science Foundation EURYI (European Young Investigator) Awards scheme. was supported by funds from the Participating Organisations of EURYT and the EC Sixth Framework Programme."," This work, conducted as part of the award “The formation of stars and planets: Radiation hydrodynamical and magnetohydrodynamical simulations"" made under the European Heads of Research Councils and European Science Foundation EURYI (European Young Investigator) Awards scheme, was supported by funds from the Participating Organisations of EURYI and the EC Sixth Framework Programme."922 As mentioned in Section 2.2.. for the different initial conditions and equations of state discussed in this paper. most of the calculations were performed with several different numerical resolutions to check for numerical convergence of the results.," As mentioned in Section \ref{initialconditions}, for the different initial conditions and equations of state discussed in this paper, most of the calculations were performed with several different numerical resolutions to check for numerical convergence of the results."923 The numbers of SPH particles used were 1. 107.3.107. 1105. and 3.10 particles. although as summarised in Table |. not all cases were performed with all resolutions.," The numbers of SPH particles used were $1\times 10^5$, $3\times 10^5$, $1\times 10^6$, and $3\times 10^6$ particles, although as summarised in Table \ref{resolutions} not all cases were performed with all resolutions."924 The only type of calculation to be performed with all four resolutions was the 97=0.005 case with radiation hydrodynamies. but the evolution of three other initial conditions performed with radiation hydrodynamics were studied with two 67=0.01 and 0.04) or three G3= 0.001) different resolutions.," The only type of calculation to be performed with all four resolutions was the $\beta=0.005$ case with radiation hydrodynamics, but the evolution of three other initial conditions performed with radiation hydrodynamics were studied with two $\beta=0.01$ and 0.04) or three $\beta=0.001$ ) different resolutions."925 In this appendix. we discuss how the results depend on numerical resolution.," In this appendix, we discuss how the results depend on numerical resolution."926 As numerical resolution was increased. all of the clouds took slightly longer to collapse.," As numerical resolution was increased, all of the clouds took slightly longer to collapse."927 However. more important for the results presented in the main sections of this paper is how the lifetime and evolution of the first core or pre-stellar dise phase depends on numerical resolution.," However, more important for the results presented in the main sections of this paper is how the lifetime and evolution of the first core or pre-stellar disc phase depends on numerical resolution."928" In Figure 16.. we plot the evolution of maximum density and temperature versus the time before stellar core formation (defined as when the maximum density reaches 10""wem "," In Figure \ref{first_core_time_convergence}, we plot the evolution of maximum density and temperature versus the time before stellar core formation (defined as when the maximum density reaches $10^{-3}$ "929"the inner regions of the disk, lifting some of the degeneracies present when these data are not considered.","the inner regions of the disk, lifting some of the degeneracies present when these data are not considered."930 The parameters of the final model are summarized in reftab:modelfit.., The parameters of the final model are summarized in \\ref{tab:modelfit}.931 Our disk model all the observables., Our disk model all the observables.932" The fits to the SED, the Spitzer spectrum, the MIDI correlated flux, the AMBER visibilities, The general slope and most features in the Spitzer spectrum are reproduced."," The fits to the SED, the Spitzer spectrum, the MIDI correlated flux, the AMBER visibilities, The general slope and most features in the Spitzer spectrum are reproduced."933" However, the observed 6.2, 7.9 and um PAH features are stronger than in our model and the predicted PAH features around 204m are not seen in the Spitzer spectrum."," However, the observed 6.2, 7.9 and $\mu$ m PAH features are stronger than in our model and the predicted PAH features around $\mu$ m are not seen in the Spitzer spectrum."934" These differences are related to the PAH chemistry, which is a much debated subject?)."," These differences are related to the PAH chemistry, which is a much debated subject."935". The N-band correlated flux obtained by MIDI has an error on the absolute calibration of approximately10%,, similar to the difference with the model output."," The N-band correlated flux obtained by MIDI has an error on the absolute calibration of approximately, similar to the difference with the model output."936 Thus our modeling of the spatial distribution of the dust grains is consistent with the MIDI result., Thus our modeling of the spatial distribution of the dust grains is consistent with the MIDI result.937" The simple flat ring+point-source model of refsec:amber actually reproduced the inclination, position angle and visibilities of the disk very well, although the inner rim radius AAU) is significantly below the AAU of our final model."," The simple flat ring+point-source model of \\ref{sec:amber} actually reproduced the inclination, position angle and visibilities of the disk very well, although the inner rim radius AU) is significantly below the AU of our final model."938 Our more physical final model gives a slightly poorer fit to the visibilities., Our more physical final model gives a slightly poorer fit to the visibilities.939 This indicates that the structure of the inner disk is more complicated than assumed., This indicates that the structure of the inner disk is more complicated than assumed.940 The exact structure is currently much debated (see refsec:model))., The exact structure is currently much debated (see \\ref{sec:model}) ).941" 'The model FWHM was obtained by making a Gaussian fit to the spatial profile after convolving the model with a Gaussian of the same width as the PSF of the VISIR 11.2,m setting.", The model FWHM was obtained by making a Gaussian fit to the spatial profile after convolving the model with a Gaussian of the same width as the PSF of the VISIR $\mu$ m setting.942" The matching continuum levels are thus a result of our method, but the increase in the FWHM at the PAH wavelengths are a confirmation of the correct modeling of the spatial distribution of theemission."," The matching continuum levels are thus a result of our method, but the increase in the FWHM at the PAH wavelengths are a confirmation of the correct modeling of the spatial distribution of the."943".  model of the Q2 image was obtained by taking the output of our model at um, just next to the artificial PAH feature."," A model of the Q2 image was obtained by taking the output of our model at $\mu$ m, just next to the artificial PAH feature."944 We convolved this model image with the VISIR PSF and we applied a PSF subtraction in analogy to the image analysis of refsec:ima.., We convolved this model image with the VISIR PSF and we applied a PSF subtraction in analogy to the image analysis of \\ref{sec:ima}.945 The by the model., The by the model.946" A likely explanation for this is the photoluminescence ofgrains,, which are not included in our model (see ?))."," A likely explanation for this is the photoluminescence of, which are not included in our model (see \citealt{2006A&A...453..969F}) )."947 Our modeling reveals that the spatial distribution of the gas and the dust in the disk around 995881 is different., Our modeling reveals that the spatial distribution of the gas and the dust in the disk around 95881 is different.948" The dust in the upper layers of the outer disk is heavily depleted, while the gas still has a large scale height."," The dust in the upper layers of the outer disk is heavily depleted, while the gas still has a large scale height."949" To reproduce the near IR flux we needed to assume a scale height, which is much larger than would be obtained from vertical hydrostatic equilibrium (V= 2.75)."," To reproduce the near IR flux we needed to assume a scale height, which is much larger than would be obtained from vertical hydrostatic equilibrium $\Psi = 2.75$ )."950" We do not have an explanation for this, but we note that the value of V is sensitive to the assumptions on the structure and composition of the material in the inner disk (seee.g. ??).."," We do not have an explanation for this, but we note that the value of $\Psi$ is sensitive to the assumptions on the structure and composition of the material in the inner disk \citep[see e.g.][]{2008A&A...483L..13I,9512008ApJ...689..513T}."952" Furthermore, our value is well within the range of scaling parameters (1.0-3.0) needed by ? to explain the near IR SED of about half of their sample of ~30 Herbig Ae/Be stars."," Furthermore, our value is well within the range of scaling parameters (1.0-3.0) needed by \cite{2009A&A...502L..17A}953 to explain the near IR SED of about half of their sample of $\sim$ 30 Herbig Ae/Be stars."954 The spatial distribution of the grain component was well constrained by the SED., The spatial distribution of the grain component was well constrained by the SED.955" The large grains could not be constrained directly, but are probably abundantly present in a settled outer disk."," The large grains could not be constrained directly, but are probably abundantly present in a settled outer disk."956 Observations of the millimeter flux will help to constrain the mass in this component as well as the size distribution., Observations of the millimeter flux will help to constrain the mass in this component as well as the size distribution.957" We can however make an estimate of the total dust mass, based on the modeled total PAH mass (5-107? MM.) and the modeled PAH abundance at the inner edge (0.25%))."," We can however make an estimate of the total dust mass, based on the modeled total PAH mass $\cdot$ $^{-9}$ $_{\odot}$ ) and the modeled PAH abundance at the inner edge )."958difference was seen on Yebes baselines after this calibration.,difference was seen on Yebes baselines after this calibration.959" The observations had not originally been designed to analyze full cross-polarizations; however, we tried to solve for the D-terms using the bright calibrator 1055+018, limiting ourselves to the European stations at the second epoch (when there were the largest number of stations)."," The observations had not originally been designed to analyze full cross-polarizations; however, we tried to solve for the D-terms using the bright calibrator 1055+018, limiting ourselves to the European stations at the second epoch (when there were the largest number of stations)."960" Reasonable solutions were found, which allowed us to study the source polarized flux."," Reasonable solutions were found, which allowed us to study the source polarized flux."961 We did not however correct for the polarization angle because of the unknown R-L phase difference at the reference antenna., We did not however correct for the polarization angle because of the unknown R-L phase difference at the reference antenna.962 The source is clearly detected at all epochs and frequencies., The source is clearly detected at all epochs and frequencies.963 Inspection of both the visibility plots and the image plane shows that the structure is dominated by a bright compact component., Inspection of both the visibility plots and the image plane shows that the structure is dominated by a bright compact component.964 The flux density is difficult to constrain to better than because of a somewhat incomplete information about the system temperature and gain curve from some stations., The flux density is difficult to constrain to better than because of a somewhat incomplete information about the system temperature and gain curve from some stations.965" It is clear however that there is a flux density of several hundreds milliJanskys revealed at all epochs, with possibly some variation."," It is clear however that there is a flux density of several hundreds milliJanskys revealed at all epochs, with possibly some variation."966" The overall non-simultaneous spectral index between 1.6 and 22 GHz is clearly inverted, with a=0.3—0.5 (S(v)« v)."," The overall non-simultaneous spectral index between 1.6 and 22 GHz is clearly inverted, with $\alpha=0.3-0.5$ $S(\nu)\propto\nu^{\alpha}$ )."967 Flux densities from visibility model fitting at all epochs are given in 77 of Table 1.., Flux densities from visibility model fitting at all epochs are given in 7 of Table \ref{t.log}.968" In Fig. 1,,"," In Fig. \ref{f.radplot},"969" we plot the visibility amplitude as a function of (u, v)-distance at the first epoch, which is the one with the longest mutual visibility on the longest baselines."," we plot the visibility amplitude as a function of $(u,v)$ -distance at the first epoch, which is the one with the longest mutual visibility on the longest baselines."970" Despite the uncertainty in the absolute flux level, the relative amplitude scales between telescopes in Europe and Australia are reliably calibrated, as shown by the consistent values across the short (u,v)-distances."," Despite the uncertainty in the absolute flux level, the relative amplitude scales between telescopes in Europe and Australia are reliably calibrated, as shown by the consistent values across the short $(u,v)$ -distances."971" We are therefore confident that the ratio of the visibility amplitudes on the longest to short baselines is reliably measured, which suggests that that some substructure is present."," We are therefore confident that the ratio of the visibility amplitudes on the longest to short baselines is reliably measured, which suggests that that some substructure is present."972 The fitting of an elliptical Gaussian model to the visibilities yields a component size of 0.205x0.055 mas at PA53.1°.," The fitting of an elliptical Gaussian model to the visibilities yields a component size of $0.205 \times 0.055\,$ mas at $53.1^\circ$."973" The minor axis corresponds to about one third of the synthesized beam; this means that the source was indeed resolved, thanks to the length of baselines in this intercontinental observation (up to kkm between Effelsberg in Europe and Hobart in Australia)."," The minor axis corresponds to about one third of the synthesized beam; this means that the source was indeed resolved, thanks to the length of baselines in this intercontinental observation (up to km between Effelsberg in Europe and Hobart in Australia)."974" Moreover, the baselines to Shanghai provide visibilities at an intermediate range (500—600 MA) in NS and EW direction."," Moreover, the baselines to Shanghai provide visibilities at an intermediate range $\sim500-600$ $\lambda$ ) in NS and EW direction."975 A smaller visibility amplitude relative to that for the longest baselines indicates that there is structure in the direction transverse to the longest baselines (PA~—45?)., A smaller visibility amplitude relative to that for the longest baselines indicates that there is structure in the direction transverse to the longest baselines $\sim-45^\circ$ ).976" In the second epoch, the Fourier transform of the visibility plane, cleaning, and self-calibration are able to more clearly constrain the total intensity structure."," In the second epoch, the Fourier transform of the visibility plane, cleaning, and self-calibration are able to more clearly constrain the total intensity structure."977 A jet component is found at 0.86 mas from the core in PA 0=35.4? (see Fig. 2)).," A jet component is found at $r=0.86\,$ mas from the core in PA $\theta=35.4^\circ$ (see Fig. \ref{f.total}) )."978" This is also consistent with the lower frequency structure, which shows a resolved jet feature in ~30—40? (Doietal.2006;Abdoetal.2009c;Foschini 2010b)."," This is also consistent with the lower frequency structure, which shows a resolved jet feature in $\sim30-40^\circ$ \citep{Doi2006,mwl,Foschini2011}."979". The brightness temperature in the source rest-frame based on the model-fit is ~3.4x10!! K for the first epoch, which is comparable to the equipartition brightness temperature (Readhead1994)."," The brightness temperature in the source rest-frame based on the model-fit is $\sim3.4\times10^{11}$ K for the first epoch, which is comparable to the equipartition brightness temperature \citep{Readhead1994}."980". Given the length of the minor axis derived by the model fit, it is conceivable that the size of the core along the major axis is not well-constrained only because of the relatively insufficient baseline lengths."," Given the length of the minor axis derived by the model fit, it is conceivable that the size of the core along the major axis is not well-constrained only because of the relatively insufficient baseline lengths."981" Therefore, the major axis of the elliptical-Gaussian model component represents only an upper limit, and the resulting brightness temperature is only a lower limit."," Therefore, the major axis of the elliptical-Gaussian model component represents only an upper limit, and the resulting brightness temperature is only a lower limit."982" This confirms that the source must be relativistically beamed, since the observed Tp exceeds the equipartition brightness temperature 2003).."," This confirms that the source must be relativistically beamed, since the observed $T_{\rm b}$ exceeds the equipartition brightness temperature \citep[see][]{Doi2006,Zhou2003}. ."983covered by our photometry and that of Cotéetal.(2002).,covered by our photometry and that of \citet{cot02}.984. The blue strageler saniples in Piottoοἱal.(2004) were not selected using uniform criteria for all clusters (F. De Angeli. priv.," The blue straggler samples in \citet{pio04} were not selected using uniform criteria for all clusters (F. De Angeli, priv."985 comm.).," comm.),"986 so we discuss (wo selections., so we discuss two selections.987 Restricting our blue straggler sample to those having V.«&20.4 (the level of the base of the giant branch) and (V—7)<0.65. we are left with 7 stars. Seiving5 FRE.2ος=1.420.8 (using≼↼≱ Poisson error estimates).," Restricting our blue straggler sample to those having $V < 20.4$ (the level of the base of the giant branch) and $(V-I) < 0.65$, we are left with 7 stars, giving $F_{BSS}^{HB} = 1.4 \pm 0.8$ (using Poisson error estimates)."988 Ouly (wo clusters (NGC GTIT and NGC 68338) in the Piotto et al., Only two clusters (NGC 6717 and NGC 6838) in the Piotto et al.989 study have higher values., study have higher values.990 These two clusters were (he faintest ones included in the Piotto et al., These two clusters were the faintest ones included in the Piotto et al.991 study. though they have central densities that are more than (wo orders of magnitude hieher.," study, though they have central densities that are more than two orders of magnitude higher."992 If. we accept all of the blue strageler candidates that are bluer than the turnoll. we have Nays=26 and FHiISS—ns»o42.5. which is higher (han any cluster value in the Piotto et al.," If we accept all of the blue straggler candidates that are bluer than the turnoff, we have $N_{BSS} = 26$ and $F_{BSS}^{HB} = 5.2 \pm 2.5$, which is higher than any cluster value in the Piotto et al."993 sample., sample.994 Piotto et al., Piotto et al.995" also examined the blue strageler population relative to the amount οἱ flix sampled. and once again (μον found a significant anticorrelation with the absolute magnitude of the cluster,"," also examined the blue straggler population relative to the amount of flux sampled, and once again they found a significant anticorrelation with the absolute magnitude of the cluster."996 When the Cotéοἱal.(2002) dataset is combined with ours. nearly the entire flux from the cluster is sampled. which gives us ΊουVy(855)=—0.65 or —0.08 depending on whether (he more restrictive sample of blue stragelers is used. (," When the \citet{cot02} dataset is combined with ours, nearly the entire flux from the cluster is sampled, which gives us $\log N_S(BSS) = -0.65$ or $-0.08$ depending on whether the more restrictive sample of blue stragglers is used. ("997For comparison. logNsCHB)= —0.80.),"For comparison, $\log N_S(HB) = -0.80$ .)"998 For the restricted sample. the logο} value places Palomar 13 among the clusters with the highest values. but for the total sample. Palomar 13 has a value second onlv to NGC 6833. à cluster that is more than 5 times brighter (M4*=—5.60: Earris 1996).," For the restricted sample, the $\log N_S(BSS)$ value places Palomar 13 among the clusters with the highest values, but for the total sample, Palomar 13 has a value second only to NGC 6838, a cluster that is more than 5 times brighter $M_V = -5.60$; Harris 1996)."999 This study makes Palomar 13 the faintest globular cluster with a thoroughly studied BSS population. covering from the cluster center out to nearly 18 core radii.," This study makes Palomar 13 the faintest globular cluster with a thoroughly studied BSS population, covering from the cluster center out to nearly 18 core radii."1000 In combination with (he results from Piottoetal.(2004).. Palomar 13 provides additional evidence that the production of blue stragglers relative to the cluster IIB stars or the cluster light may plateau for clusters with My2—6 (see Fig.," In combination with the results from \citet{pio04}, Palomar 13 provides additional evidence that the production of blue stragglers relative to the cluster HB stars or the cluster light may plateau for clusters with $M_V \gtrsim -6$ (see Fig."1001 1 of Piottoetal. (2004)))., 1 of \citet{pio04}) ).1002 On the other hand. because Palomar 13 appears {ο be a cluster in the throes of tidal disruption by the Galaxy. it is possible that the binary fraction in the cluster may have been artificially elevated. during nass segregation. affecting (he size of the straggeler population.," On the other hand, because Palomar 13 appears to be a cluster in the throes of tidal disruption by the Galaxy, it is possible that the binary fraction in the cluster may have been artificially elevated during mass segregation, affecting the size of the straggler population."1003 A characterization of the binary population in Palomar 13 can provide important inlormation about the dynamical environment and history of the cluster., A characterization of the binary population in Palomar 13 can provide important information about the dynamical environment and history of the cluster.1004 As a cluster undergoes Nass segregation as a result of internal dvnamies. ancl loses stars clue to its tidal interaction with the Galaxy. the fraction of cluster stars in multiple star svstems will increase.," As a cluster undergoes mass segregation as a result of internal dynamics, and loses stars due to its tidal interaction with the Galaxy, the fraction of cluster stars in multiple star systems will increase."1005 Siegel et al. (, Siegel et al. (10062001) noticed an apparent double subgiant branch that could be due to the presence of near equal-iass binary stars.,2001) noticed an apparent double subgiant branch that could be due to the presence of near equal-mass binary stars.1007" Their photometry only reached (he main sequence (urnoll,"," Their photometry only reached the main sequence turnoff,"1008There is no detailed: understanding of how super-massive black holes (SMIBIIS) gain their mass. except that it must be mainly through gaseous disc accretion 2002).,"There is no detailed understanding of how super-massive black holes (SMBHs) gain their mass, except that it must be mainly through gaseous disc accretion \citep{Yu02}."1009". The standard accretion cise model (Shakura&Sun-vaev.1973) shows that accretion discs must be quite massive and cold at ""large"" (sub-parsec in this context) distances from the SMDBII.", The standard accretion disc model \citep{Shakura73} shows that accretion discs must be quite massive and cold at “large” (sub-parsec in this context) distances from the SMBH.1010 Many theorists pointed out that hese clises should be unstable to scll-eravity. and thus must orm stars or giant planets by gravitational fragmentation (oc.&..Paczvski.LOTS:Ixolvkhalov&Sunvaev.1980:Shlos-Lodato.1999:Gammic. 2001).," Many theorists pointed out that these discs should be unstable to self-gravity, and thus must form stars or giant planets by gravitational fragmentation \citep[e.g.,][]{Paczynski78,Kolykhalov80,Shlosman89,Collin99,Bertin99,Gammie01}."1011. This creates a ciülenuima for he field. as star formation might be a dynamical. very [ast oocess Which may result in a complete transformation of he eas into stars.," This creates a dilemma for the field, as star formation might be a dynamical, very fast process which may result in a complete transformation of the gas into stars."1012 Phe SAIBLE would then be starved of fuel., The SMBH would then be starved of fuel.1013 Goodman(2003):Sirko&(2003) have recently demonstrated that star formation cannot be quenched. by stellar feedback. unless one is prepared. to grossly violate constraints that we have from ACN spectra.," \cite{Goodman03,Sirko03}1014 have recently demonstrated that star formation cannot be quenched by stellar feedback, unless one is prepared to grossly violate constraints that we have from AGN spectra."1015 Coocman(2003) suggested that the feeding of SAIBLIs proceeds via direct accretion of low angular momentum gas that settles in a small scale disc., \cite{Goodman03} suggested that the feeding of SMBHs proceeds via direct accretion of low angular momentum gas that settles in a small scale disc.1016 Such a dise would. be too hot to allow star formation., Such a disc would be too hot to allow star formation.1017" The size of this ""no-star-formation region"" is /?Z,0.03 pc. and is weakly. dependent on the SAIBLE mass."," The size of this ``no-star-formation region” is $R \simlt 0.03$ pc, and is weakly dependent on the SMBH mass."1018 However. one realistically expects that an even larger amount of gas settles at. larger racii where it could. collapse and formi stars. or it could accrete on the ΛΙ.," However, one realistically expects that an even larger amount of gas settles at larger radii where it could collapse and form stars, or it could accrete on the SMBH."1019 Therefore the fate of these scll-eravitating disces is still very much interesting., Therefore the fate of these self-gravitating discs is still very much interesting.1020 Current observations provide new impetus [ου theoretical work on the topic., Current observations provide new impetus for theoretical work on the topic.1021 Wehner&Llarris(2006):Ferrareseetal.(2006) have shown that many galaxies host Cextremely compact nuclei? (ECN) star clusters Iocated in the very central ~5 parsec of galaxies.," \cite{Wehner06,FerrareseEtal06} have shown that many galaxies host “extremely compact nuclei” (ECN) – star clusters located in the very central $\sim 5$ parsec of galaxies."1022 Closer to home. in the centre of our Galaxy. about a hundred massive voung stars. mostly arranged. into two stellar disces of 0.05 0.5 parsec scale (Levin.&Beloborodoy.2003:Genzeletαἱ. 2006). circle the super-massive black," Closer to home, in the centre of our Galaxy, about a hundred massive young stars, mostly arranged into two stellar discs of $\sim10230.05$ –0.5 parsec scale \citep{Levin03,Genzel03a,Paumard06}, , circle the super-massive black"1024it must be able to account for other scaling relations. such as the Faber-Jackson (Faber Jackson. 1976) and the Kormendy (1977) relations as well as the Fundamental Plane (e.g. Dressler et al.,"it must be able to account for other scaling relations, such as the Faber-Jackson (Faber Jackson, 1976) and the Kormendy (1977) relations as well as the Fundamental Plane (e.g. Dressler et al."1025 1987)., 1987).1026 At variance with the previous section. we now test the scenario in which the final galaxy is built via a series of a minor dry merger. namely adding several progenitors of either type like or B-like) to a galaxy like progenitor E until we double its mass (therefore we need roughly 200 of small building blocks).," At variance with the previous section, we now test the scenario in which the final galaxy is built via a series of a minor dry merger, namely adding several progenitors of either type (A-like or B-like) to a galaxy like progenitor E until we double its mass (therefore we need roughly 200 of small building blocks)."1027 Since the model E stars contain the right amount of a-enhancement and mean metallicity. this case will help us in assessing whether the accretion of several progenitors of either type A or B can worsen the agreement with observations.," Since the model E stars contain the right amount of $\alpha$ -enhancement and mean metallicity, this case will help us in assessing whether the accretion of several progenitors of either type A or B can worsen the agreement with observations."1028 Following the same line of reasoning of the previous sections. we first assume that we want to build the final galaxy as the sum of E and only type A+ progenitors.," Following the same line of reasoning of the previous sections, we first assume that we want to build the final galaxy as the sum of E and only type A+ progenitors."1029 We obtain the Tina for model F according to eq., We obtain the $\Upsilon_{\rm final}$ for model F according to eq.1030 | and we find that the final [«Mg/Fe >] = 0.26 1s not exceeding the observational boundaries., \ref{eq1} and we find that the final $<Mg/Fe>$ ] = 0.26 is not exceeding the observational boundaries.1031 If we assume that F is the result of a progenitor like E plus roughly two hundreds of building blocks of the type B. we predict [<Mg/Fe >] = 0.13. which ts on the lower observational boundary (see fig. 5..," If we assume that F is the result of a progenitor like E plus roughly two hundreds of building blocks of the type B, we predict $<Mg/Fe>$ ] = 0.13, which is on the lower observational boundary (see fig. \ref{fig_espl},"1032 upper panel)., upper panel).1033 The two cases presented above bracket a region of the paramenter space in which the final galaxy F can be obtained through a series of dry mergers involving a galaxy like E and progenitors like A. A+ and B in different mixtures.," The two cases presented above bracket a region of the paramenter space in which the final galaxy F can be obtained through a series of dry mergers involving a galaxy like E and progenitors like A, A+ and B in different mixtures."1034 Three main conclusions can be drawn on a scenario featuring multiple small progenitors accreted by a medium-sized ellipticals until it double its mass: 1) multiple minor dry mergers cannot be ruled out on the basis of current observations. but they are only small perturbations for a massive elliptical which formed monolithically: 11) they may explain the observed scatter in the |<Mg/Fe >] values at à given galactic mass. although it can also be explained in the framework of the revised monolithic scheme by small differences in either the star formation efficiency or the infall timescale with respect to the PMO4 best value (tuned to represent the average galaxy): in) In any case. they cannot explain the trend of [<Mg/Fe >] with c. because. even if they may lead to a modest increase in |<Mg/Fe>]. the stellar velocity dispersion does not increase (Ciotti et al..," Three main conclusions can be drawn on a scenario featuring multiple small progenitors accreted by a medium-sized ellipticals until it double its mass: i) multiple minor dry mergers cannot be ruled out on the basis of current observations, but they are only small perturbations for a massive elliptical which formed monolithically; ii) they may explain the observed scatter in the $<Mg/Fe>$ ] values at a given galactic mass, although it can also be explained in the framework of the revised monolithic scheme by small differences in either the star formation efficiency or the infall timescale with respect to the PM04 best value (tuned to represent the average galaxy); iii) in any case, they cannot explain the trend of $<Mg/Fe>$ ] with $\sigma$, because, even if they may lead to a modest increase in $<Mg/Fe>$ ], the stellar velocity dispersion does not increase (Ciotti et al.,"1035 2007)., 2007).1036 It is obvious that a few events like the ones depicted in this section can occur. for instance. in a dense environment such as à cluster of galaxy where also a residual on-going SF is detected in massive ellipticals and cD (Bildfell et al.," It is obvious that a few events like the ones depicted in this section can occur, for instance, in a dense environment such as a cluster of galaxy where also a residual on-going SF is detected in massive ellipticals and cD (Bildfell et al."1037 2008)., 2008).1038 The amount of SF inferred from UV spectra (Kavira] et al., The amount of SF inferred from UV spectra (Kaviraj et al.1039 2007) from redshift | to the present-day 2006) will lead to a modest increase (1-5 percent) in the stellar mass. even tough no SNII explosions have been detected to-date (Mannucet et al.," 2007) from redshift 1 to the present-day ) will lead to a modest increase (1-5 percent) in the stellar mass, even tough no SNII explosions have been detected to-date (Mannucci et al."1040 2007. but they might still oceur in SO. e.g.. Pastorello et al.," 2007, but they might still occur in S0, e.g., Pastorello et al."1041 2007): therefore we consider it either as an or a consequence of the environment. rather than a signature of any particular galaxy formation scenario.," 2007); therefore we consider it either as an or a consequence of the environment, rather than a signature of any particular galaxy formation scenario."1042 In fact. according to our previous calculations (Pipino Matteucci 2006). such a low intensity late SF episode cannot significantly lower the [<Mg/Fe>] ratio.," In fact, according to our previous calculations (Pipino Matteucci 2006), such a low intensity late SF episode cannot significantly lower the $<Mg/Fe>$ ] ratio."1043 Interestingly. recent observational evidences (Daddi et al.," Interestingly, recent observational evidences (Daddi et al."1044 2005. Trujillo et al.," 2005, Trujillo et al."1045 2007) favour ar increase in the size ellipticals by a factor of about 4 since redshift z=1. plausibly associated with the occurrence of dry-mergers.," 2007) favour an increase in the size ellipticals by a factor of about 4 since redshift z=1, plausibly associated with the occurrence of dry-mergers."1046 However. the simulations show that this kind of accretion occurs mainly outside one effective radius (Naab et al. 2007) and it might be due to accretion of small satellites (Daddi et al.," However, the simulations show that this kind of accretion occurs mainly outside one effective radius (Naab et al, 2007) and it might be due to accretion of small satellites (Daddi et al."1047 2005): therefore we do not expect them to affect the properties of the galactic core. Whose stars obey to the MMR and the MFMR.," 2005); therefore we do not expect them to affect the properties of the galactic core, whose stars obey to the MMR and the MFMR."1048 Again. even in the framework of the revised-monolithie scenario. these episodes are unavoidable either m a dense environment or considering the fact the massive ellitpicals are 12 Gyr old. therefore they had enough time to interact with their satellites.," Again, even in the framework of the revised-monolithic scenario, these episodes are unavoidable either in a dense environment or considering the fact the massive ellitpicals are 12 Gyr old, therefore they had enough time to interact with their satellites."1049 Finally. we want to test the feasibility of a major dry merger between two massive spheroids of the kind in order to produce the galaxyF.," Finally, we want to test the feasibility of a major dry merger between two massive spheroids of the kind in order to produce the galaxy."1050. In this case. the final elliptical will double its mass and keep a mean |«Mg/Fe >| = 0.25 dex. which does not differ much from the value expected by model Ε. Nevertheless. a problem arises from the fact that. for a pure dissipationless merger between two objects of equal mass and same velocity dispersion c. the final object will double its mass. but preserve o (Ciotti et al.," In this case, the final elliptical will double its mass and keep a mean $<Mg/Fe>$ ] = 0.25 dex, which does not differ much from the value expected by model F. Nevertheless, a problem arises from the fact that, for a pure dissipationless merger between two objects of equal mass and same velocity dispersion $\sigma$, the final object will double its mass, but preserve $\sigma$ (Ciotti et al."1051 2007)., 2007).1052 Therefore. we cannot move along the direction of the observed [<Mg/Fe »]«r relation.," Therefore, we cannot move along the direction of the observed $<Mg/Fe>$ $\sigma$ relation."1053 This seems to be the case also when the stellar central velocity dispersion is allowed to (modestly) increase due to non-homology effects (Nipoti et al..," This seems to be the case also when the stellar central velocity dispersion is allowed to (modestly) increase due to non-homology effects (Nipoti et al.,"1054 2003)., 2003).1055 We stress that this clear and straightforward consequence of the virial theorem is often neglected in works which aim at reconciling the prediction from the hierarchical clustering scenario with the evidences coming from the chemistry., We stress that this clear and straightforward consequence of the virial theorem is often neglected in works which aim at reconciling the prediction from the hierarchical clustering scenario with the evidences coming from the chemistry.1056 Nonetheless. we can exploit the [<Mg/Fe> |-mass relation to infer some constraints on the number of major dry-mergers involving massive spheroids.," Nonetheless, we can exploit the $<Mg/Fe>$ ]-mass relation to infer some constraints on the number of major dry-mergers involving massive spheroids."1057 From Thomas et al. (, From Thomas et al. (10582005). we know that |<Meg/Fe>]=—0.459+0.062/og(M.) with an intrinsic scatter of 40.05 dex.,"2005), we know that $[<Mg/Fe>]=-0.459+0.062 log(M_*)$ with an intrinsic scatter of $\pm$ 0.05 dex."1059 This means that an, This means that an1060"with S? the central surface brightness, r* the scale length, k=1,2 for exponential or functions?,, and N=1 or 2.","with $S^{0}$ the central surface brightness, $r^{s}$ the scale length, $k=1,2$ for exponential or , and $N=$ 1 or 2."1061" The fitting function was smoothed by the appropriate PSF, so the parameters we derived describe the intrinsic light distribution."," The fitting function was smoothed by the appropriate PSF, so the parameters we derived describe the intrinsic light distribution."1062" It is important to recall that our aim is to build a robust and systematic method to get at the one parameter we are searching for: the relative contribution of the core component to the total flux, and not to achieve the best representation of the full profile."," It is important to recall that our aim is to build a robust and systematic method to get at the one parameter we are searching for: the relative contribution of the core component to the total flux, and not to achieve the best representation of the full profile."1063" The use of either or exponential functions is a result of the fit, but that some of the disk profiles prefer a to an exponential must not be overinterpreted because the presence of prominent spiral arms can create a distinctive bump in the disk part of the profile that is represented by a better than by an exponential."," The use of either or exponential functions is a result of the fit, but that some of the disk profiles prefer a to an exponential must not be overinterpreted because the presence of prominent spiral arms can create a distinctive bump in the disk part of the profile that is represented by a better than by an exponential."1064 In either case we did not use the fit parameters that describe the “disk” component in the rest of the analysis., In either case we did not use the fit parameters that describe the “disk” component in the rest of the analysis.1065" The central component is almost always represented by aGaussian profile very well, with the disk component also adequately fit at the location where the core profile merges into the disk profile (see Figure 1))."," The central component is almost always represented by a profile very well, with the disk component also adequately fit at the location where the core profile merges into the disk profile (see Figure \ref{fig:prof}) )."1066 We then decomposed the luminosity of the galaxies in the following way., We then decomposed the luminosity of the galaxies in the following way.1067" The total luminosity was obtained by integrating the measured radial profile up to the background radius, the total luminosity of the core component was obtained by integrating the fitted profile of the core, and the disk luminosity is simply the difference between these two quantities."," The total luminosity was obtained by integrating the measured radial profile up to the background radius, the total luminosity of the core component was obtained by integrating the fitted profile of the core, and the disk luminosity is simply the difference between these two quantities."1068 In Table 2 we list the core components’ scalelength and contribution to the total luminosity derived from the fits., In Table \ref{tab:results} we list the core components' scalelength and contribution to the total luminosity derived from the fits.1069" In a second approach, we performed 2D fitting on M81 (chosen because of the level of details available and the existence of a point-like component in the center), using theGALFIT code (Pengetal.,2002)."," In a second approach, we performed 2D fitting on M81 (chosen because of the level of details available and the existence of a point-like component in the center), using the code \citep{peng}."1070". Galactic structure (arms, bars, rings) is much more complex to represent mathematically in 2D, thus this method converges on the extraction of unresolved components."," Galactic structure (arms, bars, rings) is much more complex to represent mathematically in 2D, thus this method converges on the extraction of unresolved components."1071" This provides a cross-check to the radial profile approach since, when the central component is resolved in the profile, the 2D method should underestimate it, but both methods should agree when it is unresolved."," This provides a cross-check to the radial profile approach since, when the central component is resolved in the profile, the 2D method should underestimate it, but both methods should agree when it is unresolved."1072 This is what we observe (see below)., This is what we observe (see below).1073" In general, we observe that the same family of functions provides the best-fit models to a given galaxy, regardless of the wavelength."," In general, we observe that the same family of functions provides the best-fit models to a given galaxy, regardless of the wavelength."1074" This is mostly because the same morphological features dominate the profile of galaxies over the explored spectral domain, a fact worth noting given the quite drastic changes in the thermodynamical state and physical nature of the mid to far IR-emitting grains, from out-of-equilibrium, nearly molecular-sized grains to thermalized sub-micron grains (butseePohlenetal.,2010,foradiscussionofthefullpro-files properties).."," This is mostly because the same morphological features dominate the profile of galaxies over the explored spectral domain, a fact worth noting given the quite drastic changes in the thermodynamical state and physical nature of the mid to far IR-emitting grains, from out-of-equilibrium, nearly molecular-sized grains to thermalized sub-micron grains \citep[but see][for a discussion of the full profiles properties]{pohlen}."1075" However, the profiles already show that the relative importance of the core component is variable from one galaxy to the next (see Figure 1))."," However, the profiles already show that the relative importance of the core component is variable from one galaxy to the next (see Figure \ref{fig:prof}) )."1076 This is the closest galaxy and thus its central region is observable with a high level of detail (seeBendoet 2010b).., This is the closest galaxy and thus its central region is observable with a high level of detail \citep[see][]{bendoSI}.1077" The core is compact, possibly the IR counterpart of the Seyfert nucleus, on which a bright arc, presumably the start of one of the spiral arms, connects."," The core is compact, possibly the IR counterpart of the Seyfert nucleus, on which a bright arc, presumably the start of one of the spiral arms, connects."1078" Moving away from the center, the brightness of the arm diminishes until it increases again to form a bright,almost ring-like structure."," Moving away from the center, the brightness of the arm diminishes until it increases again to form a bright,almost ring-like structure."1079" Thus all profiles, except the"," Thus all profiles, except the"1080About a decade ago. only a few nearby low-mass stars with ages between 5 and MMvyr were known.,"About a decade ago, only a few nearby low-mass stars with ages between 5 and Myr were known."1081 Therefore. our knowledge about stellar evolution im (his pre-main-sequence (and post-T Tauri) phase depended largely on interpolating between (he wellstuclied clusters al ages <5 MMvr. tthe Orion nebula cluster (ONC). 13348. and. 22264. and benchmark zero age main sequence (ZAMS) clusters with ages between 30 and. MMvr. e.g. the Pleiades. 22391. and o PPer.," Therefore, our knowledge about stellar evolution in this pre-main-sequence (and post-T Tauri) phase depended largely on interpolating between the well-studied clusters at ages $<5$ Myr, the Orion nebula cluster (ONC), 348, and 2264, and benchmark zero age main sequence (ZAMS) clusters with ages between 30 and Myr, e.g. the Pleiades, 2391, and $\alpha$ Per."1082 In the last ten vears. however. several nearby and voung stellar associations have been discovered. which provide us with the target. samples for in-depth studies of the stellar properties in this critical age range.," In the last ten years, however, several nearby and young stellar associations have been discovered, which provide us with the target samples for in-depth studies of the stellar properties in this critical age range."1083 Most objects in these associations are spread over large areas of the skv. and have been identified primarily based on satellite all-sky survey. data from ROSAT. IRAS. or Hipparcos (e.g.etal.2000:Zuckermanοἱ 2001)..," Most objects in these associations are spread over large areas of the sky, and have been identified primarily based on satellite all-sky survey data from ROSAT, IRAS, or Hipparcos \citep[e.g.][]{1997Sci...277...67K,1999ApJ...516L..77M,1999ApJ...520L.123B,2000ApJ...535..959Z,10842000AJ....120.1410T,2001ApJ...562L..87Z}."1085 This paper concentrates on the η) Chamaeleontis cluster (hereafter 7j CCha. age MIAvr). the TW IIvdra (TWA. MMyr). 2 Pictoris Moving Group (BPAIG. MMwyr). and Tucana-Ilorologium (TIL. ~30 Αντ) associations (seeZuckerman&Song2004.forareview)...," This paper concentrates on the $\eta$ Chamaeleontis cluster (hereafter $\eta$ Cha, age Myr), the TW Hydra (TWA, Myr), $\beta$ Pictoris Moving Group (BPMG, Myr), and Tucana-Horologium (TH, $\sim 30$ Myr) associations \citep[see][for a review]{2004ARA&A..42..685Z}."1086 As (hese associations are all located within ppc of the sun. and for all of them. a significant," As these associations are all located within pc of the sun, and for all of them, a significant"1087at 8 epochs.,at 8 epochs.1088 The best-fit reduced chi-square value was 0.665. indicating that our uncertainties were assigned somewhat conservatively but not overly so.," The best-fit reduced chi-square value was 0.665, indicating that our uncertainties were assigned somewhat conservatively but not overly so."1089 Values of the fitted parameters and their formal standard errors are shown in Table 3.., Values of the fitted parameters and their formal standard errors are shown in Table \ref{tab-fit}.1090 We measure a system mass of (6.057 + 0.36). « 10 ke (roughly  Earth masses). corresponding to a fractional precision of6%.. considerably better than results from indirect techniques.," We measure a system mass of (6.057 $\pm$ 0.36) $\times$ $^{18}$ kg (roughly $^{-6}$ Earth masses), corresponding to a fractional precision of, considerably better than results from indirect techniques."1091 The IRAS Minor Planet Survey (IMPS) lists the diameter of (702) Alauda as 194.73 + 3.2 km., The IRAS Minor Planet Survey (IMPS) lists the diameter of (702) Alauda as 194.73 $\pm$ 3.2 km.1092 Combining our mass measurement with this size estimate. we compute a density with formal uncertainties of 1570 + 120 ke m.," Combining our mass measurement with this size estimate, we compute a density with formal uncertainties of 1570 $\pm$ 120 kg $^{-3}$."1093 Realistic uncertainties need to take into account the fact that there may be a bias in the asteroid size and that the shape of the asteroid may differ substantially from a sphere., Realistic uncertainties need to take into account the fact that there may be a bias in the asteroid size and that the shape of the asteroid may differ substantially from a sphere.1094 The IMPS diameter measurements have been compared with occultation results and are believed to be accurate to (2)., The IMPS diameter measurements have been compared with occultation results and are believed to be accurate to \citep{tede02}.1095". Therefore we suggest a density estimate with more realistic errors of 1570 + 500kgm "".", Therefore we suggest a density estimate with more realistic errors of 1570 $\pm$ 500 kg $^{-3}$.1096 The confounding effects of porosity must be kept in mind 1 interpreting density measurements (22)..," The confounding effects of porosity must be kept in mind in interpreting density measurements \citep{brit02,mcki08}."1097 In Fig., In Fig.1098 4 we show the range of grain densities that are compatible with our bulk density for several values of porosity., \ref{fig-porosity} we show the range of grain densities that are compatible with our bulk density for several values of porosity.1099 Because the pressure at the center of (702) Alauda is moderate (~3.3 MPa or ~33 atmospheres). this body could in principle sustain fairly large porosities.," Because the pressure at the center of (702) Alauda is moderate $\sim$ 3.3 MPa or $\sim$ 33 atmospheres), this body could in principle sustain fairly large porosities."1100 At near-zero porosities a mix of anhydrous silicates and water ice would require a fair amount of ice (roughly 3/4 by volume or 4/9 by mass) to match the density constraint., At near-zero porosities a mix of anhydrous silicates and water ice would require a fair amount of ice (roughly 3/4 by volume or 4/9 by mass) to match the density constraint.1101 Athigh porosities the asteroid could be entirely devoid of ice., At high porosities the asteroid could be entirely devoid of ice.1102 Progress in fully understanding the manifestation of porosity in small bodies will require a large sample of reliable sizes and densities. or in-situ seismic experiments.," Progress in fully understanding the manifestation of porosity in small bodies will require a large sample of reliable sizes and densities, or in-situ seismic experiments."1103 We report the discovery of a satellite to (702) Alauda. a member of an asteroid collisional family.," We report the discovery of a satellite to (702) Alauda, a member of an asteroid collisional family."1104 The satellite is small. with a ratio of primary to secondary radit of about 50.," The satellite is small, with a ratio of primary to secondary radii of about 50."1105 The secondary revolves around the primary in 4.9] days at a distance of 1.230 km. corresponding to 12.6 primary radii.," The secondary revolves around the primary in 4.91 days at a distance of 1,230 km, corresponding to 12.6 primary radii."1106 Due to tidal interactions. its spin period. is," Due to tidal interactions, its spin period is"1107The structure of the Magellanic Clouds has been a subject of study for many years.,The structure of the Magellanic Clouds has been a subject of study for many years.1108 vanderMarel&Ciont(2001) and vanderMarel(2001) determined the viewing angles of the LMC and constructed a near-IR. stàr count. map. demonstrating that the LMC is intrinsically elongated.," \citet{2001AJ....122.1807V} and \citet{2001AJ....122.1827V} determined the viewing angles of the LMC and constructed a near-IR star count map, demonstrating that the LMC is intrinsically elongated."1109 Many articles of the past decades (Bruck1980:Dottorietal.1996;Gardiner&Hatzidimitriou1992) also discuss the different area distributions of the various stellar populations in. the MCs. Maragoudakietal.(1998).. Zaritskyetal. (2000)..," Many articles of the past decades \citep{1980A&A....87...92B,1996ApJ...461..742D,1992MNRAS.257..195G} also discuss the different area distributions of the various stellar populations in the MCs. \citet{1998A&A...338L..29M}, \citet{2000ApJ...534L..53Z},"1110 and Maragoudakietal.(2001) show that. in both LMC and SMC. the spatial distribution of the stellar content tends to become more regular and ordered as its age increases.," and \citet{2001A&A...379..864M} show that, in both LMC and SMC, the spatial distribution of the stellar content tends to become more regular and ordered as its age increases."1111" Young stars are found to be results of bursts of star formation. although there is some disagreement on the reasons for the triggered star formation,"," Young stars are found to be results of bursts of star formation, although there is some disagreement on the reasons for the triggered star formation."1112 Consistent with the previous works are the results from papers based on infrared surveys., Consistent with the previous works are the results from papers based on infrared surveys.1113 Counts of objects towards the Magellanie Clouds from the DENIS near-infrared survey have been studied by Cionietal.(2000).. who used colour-magnitude diagrams (CMD) to distinguish between three groups of objects with different mean ages.," Counts of objects towards the Magellanic Clouds from the DENIS near-infrared survey have been studied by \citet{2000A&A...358L...9C}, who used colour-magnitude diagrams (CMD) to distinguish between three groups of objects with different mean ages."1114 The spatial distribution. of the three age groups is found to be quite different: the youngest stars exhibit an irregular. structure. while the older stars are smoothly and regularly distributed.," The spatial distribution of the three age groups is found to be quite different: the youngest stars exhibit an irregular structure, while the older stars are smoothly and regularly distributed."1115 Moreover. Nikolaev&Weinberg(2000) and Gonidakisetal.(2009) have investigated the spatial distribution of the LMC and SMC stellar components. respectively. from 2MASS data.," Moreover, \citet{2000ApJ...542..804N} and \citet{2009A&A...496..375G} have investigated the spatial distribution of the LMC and SMC stellar components, respectively, from 2MASS data."1116 They present morphological analysis of the MCs colour-magnitude diagram. identifying the different populations and estimating their projected spatial distributions of various stellar populations.," They present morphological analysis of the MCs colour-magnitude diagram, identifying the different populations and estimating their projected spatial distributions of various stellar populations."1117 Bicaetal.(2008) propose a scenario where the present-day. angular-averaged. large-scale structures of both Clouds appear to behave as tidally truncated systems (which is expected. since they are believed to be Milky Way satellites). characterized by well-defined core and halo substructures. even if the Clouds are not spherical systems.," \citet{2008MNRAS.389..678B} propose a scenario where the present-day, angular-averaged, large-scale structures of both Clouds appear to behave as tidally truncated systems (which is expected, since they are believed to be Milky Way satellites), characterized by well-defined core and halo substructures, even if the Clouds are not spherical systems."1118 Thus. they have undergone severe tidal perturbation when the last dynamical and hydrodynamical interaction between the Clouds took place (about 200 Myr ago. Bekki&Chiba (2007)).," Thus, they have undergone severe tidal perturbation when the last dynamical and hydrodynamical interaction between the Clouds took place (about 200 Myr ago, \citet{2007PASA...24...21B}) )."1119 The older LMC and SMC star clusters. on the other hand. appear to be distributed as an exponential disk.," The older LMC and SMC star clusters, on the other hand, appear to be distributed as an exponential disk."1120" This distribution is possibly reminiscent of the Clouds’ structure prior to the last interaction,", This distribution is possibly reminiscent of the Clouds' structure prior to the last interaction.1121 Hopefully. some of the questions regarding the Magellanic system can be answered by ESA’s cornerstone mission Gaia.," Hopefully, some of the questions regarding the Magellanic system can be answered by ESA's cornerstone mission Gaia."1122 It is primarily an astrometric mission. whose goal is to create the largest and most precise three-dimensional map of our Galaxy by providing unprecedented positional and radial velocity measurements for about one billion stars in our Galaxy and throughout the Local Group (Perrymanetal.2001)...," It is primarily an astrometric mission, whose goal is to create the largest and most precise three-dimensional map of our Galaxy by providing unprecedented positional and radial velocity measurements for about one billion stars in our Galaxy and throughout the Local Group \citep{2001A&A...369..339P}."1123 The detection of stars is expected to be complete to V=20 mag (astrometry + photometry). but the radial velocities will not be measured for stars fainter than V=17.5 mag.," The detection of stars is expected to be complete to V=20 mag (astrometry + photometry), but the radial velocities will not be measured for stars fainter than V=17.5 mag."1124 The astrometric precision should be 25 µας at V215 mag and the distances will be known with a precision better than for hundreds of millions of stars., The astrometric precision should be 25 $\mu$ as at V=15 mag and the distances will be known with a precision better than for hundreds of millions of stars.1125 Due to the spatial resolution nearby galaxies will be resolved in stars., Due to the spatial resolution nearby galaxies will be resolved in stars.1126 Thus Gaia data will improve estimation of rotational parallaxes for Local Group galaxies. kinematic separation of stellar populations. galaxy orbits. and cosmological history. all very interesting topics of our nearest galaxies.," Thus Gaia data will improve estimation of rotational parallaxes for Local Group galaxies, kinematic separation of stellar populations, galaxy orbits, and cosmological history, all very interesting topics of our nearest galaxies."1127 The galaxies that will benefit most from the Gata survey Will be the Magellanic Clouds. since they are nearest to our Galaxy. where millions of stars are expected to be detected by the Gaia instruments.," The galaxies that will benefit most from the Gaia survey will be the Magellanic Clouds, since they are nearest to our Galaxy, where millions of stars are expected to be detected by the Gaia instruments."1128 The main goal of our project is to obtain the spatial distribution of several stellar components in these galaxies. combining the available data sets of various stellar populations.," The main goal of our project is to obtain the spatial distribution of several stellar components in these galaxies, combining the available data sets of various stellar populations."1129 As the nearest neighbours of our Galaxy. the Magellanic Clouds are the most important targets with a large number of stars observed by Gaia.," As the nearest neighbours of our Galaxy, the Magellanic Clouds are the most important targets with a large number of stars observed by Gaia."1130 The results of this investigation will also be used to improve the Gaia Universe Model (Robin 2009).. a set of algorithms used by the data generators of the Gaia simulators to generate simulated data 1 the framework of Gaia data reduction preparation.," The results of this investigation will also be used to improve the Gaia Universe Model \citep{GUMoverview}, a set of algorithms used by the data generators of the Gaia simulators to generate simulated data in the framework of Gaia data reduction preparation."1131 Our contribution to the Universe Model consists in implementing a model for the galaxies. resolved in stars. as seen by Gaia.," Our contribution to the Universe Model consists in implementing a model for the galaxies, resolved in stars, as seen by Gaia."1132 In this paper we present our first results from modelling the density distribution of the Magellanie Clouds based on various available data sets that are appropriate as described in section 2., In this paper we present our first results from modelling the density distribution of the Magellanic Clouds based on various available data sets that are appropriate as described in section 2.1133 In section 3 the methodology we follow is explained. and in section 4," In section 3 the methodology we follow is explained, and in section 4"1134of 1260 reaction rates.,of 1260 reaction rates.1135" To account for neutron captures on elements heavier than arsenic we use a ""double neutron-sink"" description (Herwig.Langer.&Lugaro 2003).. and include two artificial species which are linked by the following reactions AAs(r7) eg and ee(n.L)ee. where “ge replaces “AAs. and has an initial abundance equal to the sum of solar abundances from Se to Bi."," To account for neutron captures on elements heavier than arsenic we use a “double neutron-sink” description \citep*{herwig03a}, and include two artificial species which are linked by the following reactions $n, \gamma$ g and $n,L$ g, where g replaces As, and has an initial abundance equal to the sum of solar abundances from Se to Bi."1136 The second artificial particle. L. is equivalent to counting the number of neutrons captured beyond arsenic.," The second artificial particle, $L$, is equivalent to counting the number of neutrons captured beyond arsenic."1137" The ratio (L/° is a description of the neutrons captured per seed nuclei and gg)could in principle be related to the s-process distribution,", The ratio $L$ g) is a description of the neutrons captured per seed nuclei and could in principle be related to the $s$ -process distribution.1138 Most of the 1260 reaction rates are from the 1991 updated REACLIBData Tables (Thielemann.Truran.&Arnould 1986)., Most of the 1260 reaction rates are from the 1991 updated REACLIBData Tables \citep*{thielemann86}.1139. Many of the proton. a and 1 capture-reaction rates have been updated by Lugaroetal.(2004).," Many of the proton, $\alpha$ and $n$ capture-reaction rates have been updated by \citet{lugaro04}."1140. We use the NACRE (Anguloetal.1999) rates for the NeNa and MgAI chains. and rates from Karakasetal.(2006) for the NNe +e reactions.," We use the NACRE \citep{angulo99} rates for the NeNa and MgAl chains, and rates from \citet{karakas06a} for the Ne $+ \alpha$ reactions."1141" The cross-section of the L) ""eet. reaction is à composite caleulated using heavy element distributionsee produced by the s process in low-mass AGB stars from the models of Gallinoetal.(1998)."," The cross-section of the $n,L$ g reaction is a composite calculated using heavy element distributions produced by the $s$ process in low-mass AGB stars from the models of \citet{gallino98}."1142. Test simulations show that using a different cross-section for “ee does not significantly effect the elemental abundance of Ge (or any other species) in a3M...Z=0.012 ora 2.5M... Z20.004 model.," Test simulations show that using a different cross-section for g does not significantly effect the elemental abundance of Ge (or any other species) in a $\Msun$, $Z=0.012$ or a $\Msun$, $Z = 0.004$ model."1143 We compute stellar models covering a range of initial mass and metallicity listed in the first two columns of Table I.., 		 We compute stellar models covering a range of initial mass and metallicity listed in the first two columns of Table \ref{models}. .1144 The metallicities were chosen to reflect the composition of the progenitor AGB stars which were estimated to range from 0.3Z to Z.. (Sterling&Dinerstein2005).., The metallicities were chosen to reflect the composition of the progenitor AGB stars which were estimated to range from $0.3 Z_{\odot}$ to $Z_{\odot}$ \citep{sterling05c}.1145 The Z=0.012 stellar ..models were computed with the revised solar elemental abundances from Asplund.Grevesse.&Sauval(2005) for comparison to the Z=0.02 models with abundances from Anders&Grevesse(1989)., The $Z=0.012$ stellar models were computed with the revised solar elemental abundances from \citet*{asplund05} for comparison to the $Z = 0.02$ models with abundances from \citet{anders89}.1146. Scaled-solar abundances were assumed for the Z=0.008 and 0.004 models., Scaled-solar abundances were assumed for the $Z=0.008$ and 0.004 models.1147 We use Vassiliadis&Wood(1993) mass loss on the AGB., We use \citet{vw93} mass loss on the AGB.1148 In Table 1. we include the number of TPs. the maximum temperature in the He-shell. the total mass dredged into the envelope during the AGB. the final surface C/O and ICC/UCC ratios. and envelope mass at the last computed time-step.," In Table \ref{models} we include the number of TPs, the maximum temperature in the He-shell, the total mass dredged into the envelope during the AGB, the final surface C/O and C ratios, and envelope mass at the last computed time-step."1149 All masses are in solar units and temperatures in 10°K. From Table | we see that the 3 and 6.35M.. Z= models were similar to their Z20.02 counterparts.," All masses are in solar units and temperatures in $10^{6}\,$ K. From Table \ref{models} we see that the 3 and $\Msun$, $Z=0.012$ models were similar to their $Z=0.02$ counterparts."1150 The low-mass AGB models became carbon stars. whereas those models with hot bottom burning (HBB) retained an O-rich atmospheric composition (5. 6.5M ..).," The low-mass AGB models became carbon stars, whereas those models with hot bottom burning (HBB) retained an O-rich atmospheric composition (5, $\Msun$ )."1151 There is evidence (e.g.Abia&Isern1997) that some extra-mixing takes place in ~ | to 3M.. AGB stars. resulting in lower observed ος and C/O ratios than predicted by models such as ours.," There is evidence \citep[e.g.][]{abia97} that some extra-mixing takes place in $\sim \,$ 1 to $\Msun$ AGB stars, resulting in lower observed C and C/O ratios than predicted by models such as ours."1152 The results presented in this study are subject to many model uncertainties including convection and mass loss. which affect both the structure and nucleosynthesis.," The results presented in this study are subject to many model uncertainties including convection and mass loss, which affect both the structure and nucleosynthesis."1153 We refer to Goriely&Mowlavi(2000)... Herwig(2005)... Ventura&D'Antona(2005).. and Stranieroetal.(2006). for detailed discussions on this topic.," We refer to \citet{goriely00}, \citet{herwig05}, \citet{ventura05a}, , and \citet{straniero06}1154 for detailed discussions on this topic."1155" The inclusion of a partial mixing zone (PMZ) at the deepest extent of dredge-up will mix protons from the envelope into the He-intershell. producing a ""CC pocket."," The inclusion of a partial mixing zone (PMZ) at the deepest extent of dredge-up will mix protons from the envelope into the He-intershell, producing a C pocket."1156 In the PMZ neutrons are liberated during the interpulse period by the reaction Οία) 0Ο. and are captured by Fe-seed nuclei to produce heavy elements.," In the PMZ neutrons are liberated during the interpulse period by the reaction $\alpha,n$ O, and are captured by Fe-seed nuclei to produce heavy elements."1157 Observational and theoretical evidence suggests this is the dominant neutron source in low-mass AGB stars (Smithetal.19857;Gallino1998).," Observational and theoretical evidence suggests this is the dominant neutron source in low-mass AGB stars \citep{smith87,gallino98}."1158 The details of how the pocket forms and its extent in mass in the He-intershell are still unknown although gravity waves (Denissenkov&Tout2003).. convective overshoot (Herwig2000).. induced overshoot during the TDU episodes (Cristallo et al.," The details of how the pocket forms and its extent in mass in the He-intershell are still unknown although gravity waves \citep{denissenkov03}, convective overshoot \citep{herwig00}, induced overshoot during the TDU episodes (Cristallo et al."1159 2004: Straniero. et al., 2004; Straniero et al.1160 2006). and rotationally-induced mixing (Langeretal.1999:Herwig2003) have been suggested.," 2006), and rotationally-induced mixing \citep{langer99,herwig03a} have been suggested."1161 The NNe(a.n MMg reaction produces a brief strong burst of neutrons in the convective pocket during a TP when the temperature exceeds ~300«10°K. This is probably the dominant neutron source in massive AGB stars. where the mass of the He-shell is smaller by about an order of magnitude compared to lower-mass stars. reducing the importance of the CC pocket.," The $\alpha, n$ Mg reaction produces a brief strong burst of neutrons in the convective pocket during a TP when the temperature exceeds $\sim 300 \times 10^{6}$ K. This is probably the dominant neutron source in massive AGB stars, where the mass of the He-shell is smaller by about an order of magnitude compared to lower-mass stars, reducing the importance of the C pocket."1162 As done in previous nucleosynthesis studies (Gallinoetal.1998:Goriely&Mowlavi2000;Lugaroetal.2004) we artificially include a PMZ of constant mass.," As done in previous nucleosynthesis studies \citep{gallino98,goriely00,lugaro04}1163 we artificially include a PMZ of constant mass."1164 In Table 2 we show the maximum mass of the pulse-driven convective region. M. at the last TP along with the PMZ masses used.," In Table \ref{results} we show the maximum mass of the pulse-driven convective region, $M_{\rm csh}$, at the last TP along with the PMZ masses used."1165" Note that M, is approximately equal to the He-intershell mass during the TP.", Note that $M_{\rm csh}$ is approximately equal to the He-intershell mass during the TP.1166 The PMZ mass ts estimated to be between ~5% to of the mass of the He-rich intershell. and we used PMZs of1«10™ and 3«10M... for the 3M... models.," The PMZ mass is estimated to be between $\sim 5$ to of the mass of the He-rich intershell, and we used PMZs of $1 \times 10^{-3}$ and $3 \times 10^{-3}\Msun$ for the $\Msun$ models."1167 We chose a proton profile in which the number of protons decreases exponentially with the mass depth below the base of the convective envelope in the same way as described in Lugaroetal.(2004)., We chose a proton profile in which the number of protons decreases exponentially with the mass depth below the base of the convective envelope in the same way as described in \citet{lugaro04}.1168. We also computed models with PMZ for all masses. in order to single out the effect of the NNe source.," We also computed models with PMZ for all masses, in order to single out the effect of the Ne source."1169 In Table 2. we show the surface [Ge/Fe] and [Gi/Fe] ratios after the last computed TP for each stellar model. where we use Fe as the reference element which ts justified because the surface abundance is predicted by the models to be unaltered by AGBnucleosynthesis?.," In Table \ref{results} we show the surface [Ge/Fe] and [Ga/Fe] ratios after the last computed TP for each stellar model, where we use Fe as the reference element which is justified because the surface abundance is predicted by the models to be unaltered by AGB."1170. We also provide the surface [Ge/S] and [Ge/S| ratios for the 3M... Z=0.012 model (with a PMZ 22«I07M.) for comparison.," We also provide the surface [Ge/S] and [Ge/S] ratios for the $\Msun$ , $Z = 0.012$ model (with a PMZ $= 2\times 10^{-3}\Msun$ ) for comparison."1171 There isno difference between these values and those computed usingFe as the reference element., There isno difference between these values and those computed usingFe as the reference element.1172 Sterling&Dinerstein(2003) tentatively detected Ga in one PN (SwSt 1). with the derived [Ga/S] = 1.64 — 2.87. depending on the level of depletion into dust.," \citet{sterling03} tentatively detected Ga in one PN (SwSt 1), with the derived [Ga/S] = 1.64 – 2.87, depending on the level of depletion into dust."1173 Table 2. shows that the largest predicted enhancements in terms of [Ge/Fe] were =0.56 (or a factor of ~ 3.6) for, Table \ref{results} shows that the largest predicted enhancements in terms of [Ge/Fe] were $\lesssim 0.56$ (or a factor of $\sim 3.6$ ) for1174three parallel lines correspond to fie; 1.0. 0.1 and 0.01 from left to right. respectively.,"three parallel lines correspond to $f_{DG}$ $=$ 1.0, 0.1 and 0.01 from left to right, respectively."1175" These scalings essentially represent the fraction of the measured mass that is above the 0.8 magnitude extinction threshold or equivalently above a volume density threshold of roughly n(Ilo) = 10 ""(Paper I).", These scalings essentially represent the fraction of the measured mass that is above the 0.8 magnitude extinction threshold or equivalently above a volume density threshold of roughly $_2$ ) = $^4$ (Paper I).1176 These lines also correspond to lines of constant gas depletion times of 20 Myr. 200 Myr and 2 Gyr. respectively.," These lines also correspond to lines of constant gas depletion times of 20 Myr, 200 Myr and 2 Gyr, respectively."1177 For the open svanbols on the plot. AM; = Ape; (he total mass of the molecular cloud.," For the open symbols on the plot, $M_G$ = $M_{TG}$, the total mass of the molecular cloud."1178 The interesting aspect of this plot is (hat the low extinction (total) masses also appear to follow a linear scaling law. similar to that of the high extinction (high densitv) masses.," The interesting aspect of this plot is that the low extinction (total) masses also appear to follow a linear scaling law, similar to that of the high extinction (high density) masses."1179 Indeed. a formal least-squares fit to the former data produces a slightly sub-linear index value of 0.81 zc 0.19.," Indeed, a formal least-squares fit to the former data produces a slightly sub-linear index value of 0.81 $\pm$ 0.19."1180 The total cloud masses. At6. appear to follow and scatter around the relation given by Equation 1. if fpe; = 0.1.," The total cloud masses, $M_{TG}$, appear to follow and scatter around the relation given by Equation 1, if $f_{DG}$ $=$ 0.1."1181 However the magnitude of the scatter around {his linear relation is significantly higher than that for the high extinction masses around the best-lit line given by Equation 1 (Le.. fpc; = 1 and Ado;=Moye).," However the magnitude of the scatter around this linear relation is significantly higher than that for the high extinction masses around the best-fit line given by Equation 1 (i.e., $f_{DG}$ $=$ 1 and $M_G = M_{DG}$ )."1182" Star formation occurs almost exclusively in gas characterized by high densities (n(4/5) > 104""à: Lada 1992) and the origin of the large scatter in the star formation scaling law for the total cloud masses is a direct result of the large variations in the dense gas (high extinction) fractions that are observed [or (hese clouds (Paper D).", Star formation occurs almost exclusively in gas characterized by high densities $H_2$ ) $>$ $^4$; Lada 1992) and the origin of the large scatter in the star formation scaling law for the total cloud masses is a direct result of the large variations in the dense gas (high extinction) fractions that are observed for these clouds (Paper I).1183 In contrast to classical Schmidt-Ixennicutt extragalactic scaling laws. there is no evidence lor a super-linear scaling lor the star formation law [or local clouds. even when the total masses of the clouds are considered.," In contrast to classical Schmidt-Kennicutt extragalactic scaling laws, there is no evidence for a super-linear scaling for the star formation law for local clouds, even when the total masses of the clouds are considered."1184 In order (o compare galaxies with the galactic clouds on the SFR-Aoleeular Mass diagram we use the sample of galaxies observed by Gao and Solomon (2004: herealter GS04)., In order to compare galaxies with the galactic clouds on the SFR-Molecular Mass diagram we use the sample of galaxies observed by Gao and Solomon (2004; hereafter GS04).1185 Their sample consists of normal spirals aud starburst galaxies. including Iuminous aud inlrared galaxies (1.e.. LIRGs ULIBGs).," Their sample consists of normal spirals and starburst galaxies, including luminous and ultra-luminous infrared galaxies (i.e., LIRGs ULIRGs)."1186 We selected this sample for comparison with our local cloud sample because it is (he only sample of galaxies with svstematicallv measured molecular masses using both a tracer of high density gas. HCN. and a tracer of total cloud mass. CO.," We selected this sample for comparison with our local cloud sample because it is the only sample of galaxies with systematically measured molecular masses using both a tracer of high density gas, HCN, and a tracer of total cloud mass, CO."1187 In addition. the SETBRs of the galaxies in (he sample are all derived in je same manner [from a homogeneous set of infrared observations.," In addition, the SFRs of the galaxies in the sample are all derived in the same manner from a homogeneous set of infrared observations."1188 It is a priori unclear whether (he star formation rales and/or gas masses reported for 16 GS04 galaxy. sample are directly comparable to those reported in Paper I for the local ‘loud sample., It is a priori unclear whether the star formation rates and/or gas masses reported for the GS04 galaxy sample are directly comparable to those reported in Paper I for the local cloud sample.1189 The SEHR. lor the local clouds was determined by direct. counting of nearly complete inventories of Young Stellar Objects in each cloud ancl assuming a star formation imescale of 2 Myrs. while the SFRs for the GS04 galaxies are galaxv-wide averages (hat were derived [rom conversion of a FIR fIux into a mass growth rate using stellar population," The SFR for the local clouds was determined by direct counting of nearly complete inventories of Young Stellar Objects in each cloud and assuming a star formation timescale of 2 Myrs, while the SFRs for the GS04 galaxies are galaxy-wide averages that were derived from conversion of a FIR flux into a mass growth rate using stellar population"1190erant NÀG5-3428. and by the University of Minnesota Supercomputing Institute.,"grant NAG5-8428, and by the University of Minnesota Supercomputing Institute."1191"one would. need to measure logg to better than zz0.03 dex to distinguish between AZ.=0.60A7. and M,=0.75M...","one would need to measure $\log g$ to better than $\approx 0.03$ dex to distinguish between $M_c=0.60\,M_{\odot}$ and $M_c=0.75\,M_{\odot}$."1192 We can compute the distance to the source using the results of our model fitting., We can compute the distance to the source using the results of our model fitting.1193 Once the inclination / is given. we can compute the total mass of the svstem.," Once the inclination $i$ is given, we can compute the total mass of the system."1194 The. size of the semimajor axis e is then computed from Ixepler's third law., The size of the semimajor axis $a$ is then computed from Kepler's third law.1195 We then use Egeleton's (1983) formula to compute the elfective radius of the secondary’s Roche lobe in terms of the orbital separation e: The intrinsic luminosity of the secondary star then follows from the Stelan-Boltzmann relation. where we assume Z;r=TOOOXx250 WK and a bolometric correction of 0.," We then use Eggleton's (1983) formula to compute the effective radius of the secondary's Roche lobe in terms of the orbital separation $a$: The intrinsic luminosity of the secondary star then follows from the Stefan-Boltzmann relation, where we assume $T_{\rm eff}=7000\pm 250$ K and a bolometric correction of $0$."1196 To ect the intrinsic luminosity of the entire svsten we must. add light from the accretion disc., To get the intrinsic luminosity of the entire system we must add light from the accretion disc.1197 We do not have spectroscopic observations in the Y band. available so we will interpolate between the measurements of ke ancl Ay and adopt Ay=0.30£0.05., We do not have spectroscopic observations in the $V$ band available so we will interpolate between the measurements of $k_B$ and $k_R$ and adopt $k_V=0.30\pm 0.05$.1198 Finally. the distance moclulus can be computed after we account for interstcllar extinction.," Finally, the distance modulus can be computed after we account for interstellar extinction."1199 The most complete studs of the interstellar extinction in the direction of (νο X-2 is that of AleClintock οἱ ((1984)., The most complete study of the interstellar extinction in the direction of Cyg X-2 is that of McClintock et (1984).1200 They derived. a colour excess of {01)=040+0.07 based on spectra from theEvplorer and on optical photometry ancl spectra of 38 nearby field stars., They derived a colour excess of $E(B-V)=0.40\pm 0.07$ based on spectra from the and on optical photometry and spectra of 38 nearby field stars.

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