ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Por NGC 1399. 25/554 clusters are brighter: for the NGC 3379 DII source. 15/61 are brighter: for NGC 44723. 92/928 are brighter.," For NGC 1399A, 25/554 clusters are brighter; for the NGC 3379 BH source, 15/61 are brighter; for NGC 4472B, 92/928 are brighter."3 The other wo clusters. NGC 1399DB and NGC 44724. are not covered » the LIST cluster catalogs.," The other two clusters, NGC 1399B and NGC 4472A, are not covered by the HST cluster catalogs."4 For these two clusters. we determine where their magnitudes fall in the LIST catalogs. rather than comparing with the ground-based catalogs.," For these two clusters, we determine where their magnitudes fall in the HST catalogs, rather than comparing with the ground-based catalogs."5 The ground-based catalog of NGC 1399 from Dirsch et al. (, The ground-based catalog of NGC 1399 from Dirsch et al. (62004) is especially biased in luminosity. since it represents a spectroscopically selected sample of clusters.,"2004) is especially biased in luminosity, since it represents a spectroscopically selected sample of clusters."7 This sample is in C ancl A. so we use the metallicitv-color conversions from Smits et al.," This sample is in $C$ and $R$, so we use the metallicity-color conversions from Smits et al."8 to convert from. Z2 to f. so that the magnitude can be compared with the LIST catalog for NCC 1399.," to convert from $R$ to $I$, so that the magnitude can be compared with the HST catalog for NGC 1399."9 We thus obtain an estimate of £=21.3 for NGC 1399D. brighter than all but 89/554 clusters in the LIST catalog.," We thus obtain an estimate of $I=21.3$ for NGC 1399B, brighter than all but 89/554 clusters in the HST catalog."10 Phe NGC 4472 brightness is directly comparable to the existing LUST catalog. and. the cluster is brighter than all but 25/928 ol the NGC 4472 clusters.," The NGC 4472 brightness is directly comparable to the existing HST catalog, and, the cluster is brighter than all but 25/928 of the NGC 4472 clusters."11 Xpplving the same sort of INS test as was done for color. a null hypothesis probability results that the clusters are more luminous than the cluster »opulation as a whole.," Applying the same sort of KS test as was done for color, a null hypothesis probability results that the clusters are more luminous than the cluster population as a whole."12 There may be a slight bias in favor of this hypothesis. given that spectroscopic confirmation was obtained for most of these clusters before papers were published. and that in several cases. the spectra were already existing in the archives.," There may be a slight bias in favor of this hypothesis, given that spectroscopic confirmation was obtained for most of these clusters before papers were published, and that in several cases, the spectra were already existing in the archives."13 Both of the M 31 clusters suspected o contain black holes are also considerably. more massive han the mean for M 31., Both of the M 31 clusters suspected to contain black holes are also considerably more massive than the mean for M 31.14 lt has already. been well established that the clusters containing X-ray sources in general are more massive (Verbunt LOST) and redder than a randomly selected sample of clusters would be (see e.g. Silk Arons 1975 for the first suggestion of this cllect: Bellazzini ct al., It has already been well established that the clusters containing X-ray sources in general are more massive (Verbunt 1987) and redder than a randomly selected sample of clusters would be (see e.g. Silk Arons 1975 for the first suggestion of this effect; Bellazzini et al.15 1995 and Wundu ct al., 1995 and Kundu et al.16 2002 for the first strong observational evidence for it)., 2002 for the first strong observational evidence for it).17 In recent. vears. it has become clear that clusters with higher. collision rates are more likely to have bright X-rav sources. even alter. accounting for the fact that such clusters are also more massive (e.g. Jordánn et al.," In recent years, it has become clear that clusters with higher collision rates are more likely to have bright X-ray sources, even after accounting for the fact that such clusters are also more massive (e.g. Jordánn et al."18 2007: Peacock et al., 2007; Peacock et al.19 2009. 2010b).," 2009, 2010b)."20 At the present time. there are not vet. high enough quality cata from. LIST to estimate Wing moclel parameters for these clusters. but obtaining such data would be of great interest.," At the present time, there are not yet high enough quality data from HST to estimate King model parameters for these clusters, but obtaining such data would be of great interest."21 The same recent theoretical work that demonstrates that many. elobular clusters will retain substantial [fractions of their stellar mass black holes also shows that the core radii of clusters with black holes can be enlarged (Alackey et al., The same recent theoretical work that demonstrates that many globular clusters will retain substantial fractions of their stellar mass black holes also shows that the core radii of clusters with black holes can be enlarged (Mackey et al.22 2007)., 2007).23 We have reported the detection of a new globular cluster black hole candidate. confirmed to be a black hole rather than a collection of neutron stars by its. strong variability.," We have reported the detection of a new globular cluster black hole candidate, confirmed to be a black hole rather than a collection of neutron stars by its strong variability."24 Lhe source is the fifth object with this type of convincing evidence of its black hole nature., The source is the fifth object with this type of convincing evidence of its black hole nature.25 Even with this small population of objects. it now seems Likely. but not conclusively demonstrable. that the formation of X-ray sources with black hole accretors is favored in red. clusters. and it is clear that luminous globular clusters are more likely to host black hole accretors.," Even with this small population of objects, it now seems likely, but not conclusively demonstrable, that the formation of X-ray sources with black hole accretors is favored in red clusters, and it is clear that luminous globular clusters are more likely to host black hole accretors."26 Given the suggestions that black holes should have strong ellects on the dvnamical evolution of globular clusters. estimation of the Wing mocel parameters of these clusters would be especially valuable.," Given the suggestions that black holes should have strong effects on the dynamical evolution of globular clusters, estimation of the King model parameters of these clusters would be especially valuable."27 TJAL thanks the European Union for support under EI? erant 215212: Black l!lole Universe., TJM thanks the European Union for support under FP7 grant 215212: Black Hole Universe.28 Aly thanks NASA for support under Chandra grant. COO-LIILIA and LIST archival program LIS'T-AR-11264., AK thanks NASA for support under Chandra grant GO0-11111A and HST archival program HST-AR-11264.29 SEZ thanks NASA. for support under grants NNAOSAJGOG ancl Chandra: CO0-11105X., SEZ thanks NASA for support under grants NNX08AJ60G and Chandra GO0-11105X.30 This research is supported in part by an NSE Faculty Early Career Development (CAREER) award CAS'T-0847109) to KLR., This research is supported in part by an NSF Faculty Early Career Development (CAREER) award (AST-0847109) to KLR.31acemuulates close the central accretor (e.g. Lawley οἱ al.,accumulates close the central accretor (e.g. Hawley et al.32 1984a.b.: Clarke et al.," 1984a,b,; Clarke et al."33 1985: Chen et al 1997: PDO3a: Janiuk & Proga 2007)., 1985; Chen et al 1997; PB03a; Janiuk $\&$ Proga 2007).34 The simulations presented by PBO3a illustrate a eeneral flow pattern with an inflow in the polar funnel. ancl an equatorial outflow (Fig.," The simulations presented by PB03a illustrate a general flow pattern with an inflow in the polar funnel, and an equatorial outflow (Fig."35 1 there)., 1 there).36 Such flow pattern is induced by the angular momentum distribution simply because rolaling gas tend (o converge toward the equator., Such flow pattern is induced by the angular momentum distribution simply because rotating gas tend to converge toward the equator.37 If / is hieh. the gas forms a subsonic very dvnamic torus with gas flowing out.," If $l$ is high, the gas forms a subsonic very dynamic torus with gas flowing out."38 The mass accretion rate can be significantly smaller compared to corresponding the Dondi rate., The mass accretion rate can be significantly smaller compared to corresponding the Bondi rate.39 In (his work. we address the problem how the properties of the accretion flow presented in δα. change when different micro-phvsical properties of the flow are assumed.," In this work, we address the problem how the properties of the accretion flow presented in PB03a, change when different micro-physical properties of the flow are assumed."40 In parüeular. we explore effects of changing 5 in the polvtvopic equation of state.," In particular, we explore effects of changing $\gamma$ in the polytropic equation of state."41 In reality. accretion flows with different 5 s. max. correspond. to different (wpes of objects or different phases of activity.," In reality, accretion flows with different $\gamma$ 's, may correspond to different types of objects or different phases of activity."42 For example. in the weakly active galaxies like e.g. Ser ΑἘν 5 is usually considered to be around 5/3. because these flows are believed to be racdiatively inefficient and eas pressure dominated.," For example, in the weakly active galaxies like e.g. Sgr A*, $\gamma$ is usually considered to be around 5/3, because these flows are believed to be radiatively inefficient and gas pressure dominated."43 On the other hand. (he large energetic output observed in GRBs indicates that an accretion [low must be radiation pressure dominated (e.g.. Meszaros 2006) andl a relativistie equation of state is required with 54/3.," On the other hand, the large energetic output observed in GRBs indicates that an accretion flow must be radiation pressure dominated (e.g., Meszaros 2006) and a relativistic equation of state is required with $\gamma$ =4/3."44 Another example are protogalactie disks. which are sometimes considered as being formed by isothermal accretion flow (521: e.g.. Mo οἱ al.," Another example are protogalactic disks, which are sometimes considered as being formed by isothermal accretion flow $\gamma\approx 1$; e.g., Mo et al."45 1998)., 1998).46 Also. the so-called ‘high’ and ‘low’ accretion states in the X-ray binary svslenms. nav reflect physical proprieGies changing in time (lor a review see Done et al.," Also, the so-called `high' and `low' accretion states in the X-ray binary systems, may reflect physical proprieties changing in time (for a review see Done et al."47 2007)., 2007).48 Our work is a straightIorward extension of PDO3a's work. who showed results [or 5 —5/3.," Our work is a straightforward extension of PB03a's work, who showed results for $\gamma$ =5/3."49 We extend (heir models by considering the flows. for > ranging between 1 and 5/3.," We extend their models by considering the flows, for $\gamma$ ranging between 1 and 5/3."50 We also perform additional caleulations with sound speed at infinity ος much smaller (han that considered by PBO3a allowing us to model flows with the Bondi radius as large as that estimated in real svstems. for example in Sev A*.," We also perform additional calculations with sound speed at infinity $c_{s,\infty}$ much smaller than that considered by PB03a allowing us to model flows with the Bondi radius as large as that estimated in real systems, for example in Sgr A*."51 Taking advantage of faster computers. we perform sinulations with higher resolution in (he @ direction. anc with much larger computational domain in comparison to PB03a.," Taking advantage of faster computers, we perform simulations with higher resolution in the $\theta$ direction, and with much larger computational domain in comparison to PB03a."52 We keep other model parameters such as angular momentum distribution as in PBO3a., We keep other model parameters such as angular momentum distribution as in PB03a.53 For 5=5/3. our new simulations are consistent wilh those presented by PBO3a.," For $\gamma=5/3$, our new simulations are consistent with those presented by PB03a."54" However. we find that AZ,. the flow structure. defined by the gas density and angular momentum distribution. and the sonic surlace topology depend on 5."," However, we find that $\MDOT_a$, the flow structure, defined by the gas density and angular momentum distribution, and the sonic surface topology depend on $\gamma$."55" D particular.for ο”=5/3. AM, is nearly constant whereas [or 5=4/3. AL, shows stochastic. large-amplilicle lime-variability."," In particular,for $\gamma=5/3$, $\MDOT_a$ is nearly constant whereas for $\gamma=4/3$, $\MDOT_a$ shows stochastic, large-amplitude time-variability."56" For +=101. M, shows small-amplitude periodic changes."," For $\gamma=1.01$, $\MDOT_a$ shows small-amplitude periodic changes."57 In Sec.2. we describe a general set-up of our simulations.," In Sec.2, we describe a general set-up of our simulations."58 li Sec.3. we present our results.," In Sec.3, we present our results."59 In (he last section. we discuss the results. and relate them to results found in previous studies.," In the last section, we discuss the results, and relate them to results found in previous studies."60the values contributiug to each pixel carefully weighted iu order to niaxinize their significance: and in the latter as a display of suuple values comprising a “density plot”.,the values contributing to each pixel carefully weighted in order to maximize their significance; and in the latter as a display of sample values comprising a “density plot”.61" Tn the first feure. the values coutributing to a pixel were weighted according the square of their S/N valuesafter taking care to estimate the PA error according to the procedure given in Rankin Rathnasree (1997: see footnote 11): whereas in the latter the PA values ave given as “dots” corresponding to all data samples for which the οπου in the PA. 64 (= o,,/L) was less than 307."," In the first figure, the values contributing to a pixel were weighted according the square of their S/N values---after taking care to estimate the PA error according to the procedure given in Rankin Rathnasree (1997; see footnote 11); whereas in the latter the PA values are given as “dots” corresponding to all data samples for which the error in the PA, $\sigma_\chi$ $= \sigma_{\rm on}/L$ ) was less than $\deg$."62" The on- noise level σον was estimated as oug(£as|£)/Lj where τν, is the total power corresponding to the svstem temperature and a4 is the standard deviation of the inse in Stokes parameter Fowell away frou the pulse window. ("," The on-pulse noise level $\sigma_{\rm on}$ was estimated as $\sigma_{\rm off}(I_{\rm sys}+L)/I_{\rm sys}$, where $I_{\rm sys}$ is the total power corresponding to the system temperature and $\sigma_{\rm off}$ is the standard deviation of the noise in Stokes parameter $I$ well away from the pulse window. ("63Clearly. στων=(27Ar)2. whore Av is the total bandwidth aud 7 the effective integration time.).,"Clearly, $\sigma_{\rm off}/I_{\rm sys} = (2\tau \Delta\nu)^{-{1 64\over 2}}$, where $\Delta\nu$ is the total bandwidth and $\tau$ the effective integration time.)."65 Finally. the bottom panel of Fig.," Finally, the bottom panel of Fig."66 1. eives the density of the fractional linear polarization. also as a erev scalewhere," \ref{fig:0809-328} gives the density of the fractional linear polarization, also as a grey scale—where"675) Contrary to the usual interpretation. we rule out any particular relation between the a Fe] break position in the ofFe]-Fe/H] plane and the onset of SN la explosions.,"5) Contrary to the usual interpretation, we rule out any particular relation between the $\alpha$ /Fe] break position in the $\alpha$ /Fe]-[Fe/H] plane and the onset of SN Ia explosions."68" Alethocls intended to determine fy, in this way might. be incorrect.", Methods intended to determine $t_{\rm Ia}$ in this way might be incorrect.69 6) In agreement with observations. our models develop initially moderate metallicity. gradients which become weaker and weaker as the galaxy. evolves.," 6) In agreement with observations, our models develop initially moderate metallicity gradients which become weaker and weaker as the galaxy evolves."70 7) Finally. the above results are slightly. dependent on the particular star formation history adopted.," 7) Finally, the above results are slightly dependent on the particular star formation history adopted."71" We thank the referee, Leticia C'arigi.. whose comments greatly improved the presentation of the paper."," We thank the referee, Leticia Carigi, whose comments greatly improved the presentation of the paper."72 We are very erateful to M. Bellazzini for giving us the data used in our Fig. S.., We are very grateful to M. Bellazzini for giving us the data used in our Fig. \ref{fig:zstellenosni}.73 We are also indebted to CG. Lanfranchi and E. Matteucci to sent. us some simulations in advance of publication to compare with our models., We are also indebted to G. Lanfranchi and F. Matteucci to sent us some simulations in advance of publication to compare with our models.74 Many thanks also to L. Mayer ancl all the above friends for useful suggestions and: discussions which greatly. improved. the final version., Many thanks also to L. Mayer and all the above friends for useful suggestions and discussions which greatly improved the final version.75 We acknowledge financial support from National Institute for Astrophysics (INA)., We acknowledge financial support from National Institute for Astrophysics (INAF).76 “Phe simulations were run at the CINIZCA Supercomputing Centre with CPU time provided by a grant of the National institute for Astrophysics (INE)., The simulations were run at the CINECA Supercomputing Centre with CPU time provided by a grant of the National institute for Astrophysics (INAF).77 Slt. acknowledges financial support from. the Deutsche lorschungsgemeinschaft (DEC) under grant VIE 5115 A SNK expanding in a homogeneous uniform. medium evolves initially following |the Sedov solution during which radiative losses can be neglected., S.R. acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG) under grant TH 511/8 A SNR expanding in a homogeneous uniform medium evolves initially following the Sedov solution during which radiative losses can be neglected.78 With time. however. such losses eventually cause the formation of a dense shell. and the high pressure of the hot interior pushes this shell (the snowplow phase).," With time, however, such losses eventually cause the formation of a dense shell, and the high pressure of the hot interior pushes this shell (the snowplow phase)."79 Assuming an explosion energv of 1075 org. the time at which the Sedov phase ends is given by ? lo=1.49↓∪⊔∩∣↳12LfDI : : ∙∖⇁↓⋅⊳∖∖⊽↓⊔⋅↓⋅⋖⊾⊔⊔↓≱∖↥↓↥⋖⋅∠⇂⋖⋅⊔≱∖⊔∙∖⇁∪⇂ the ambient medium and ¢ is the ISM metal abundance in solar units.," Assuming an explosion energy of $^{51}$ erg, the time at which the Sedov phase ends is given by \citet{cioffi1991} $t_0=1.49\times 8010^4n_0^{-4/7}\zeta^{-5/14}$ yr, where $n_0$ is the density of the ambient medium and $\zeta$ is the ISM metal abundance in solar units."81" The SNR stalls when its expansion velocity drops to the the local sound speed co: the stalling radius is eiven by ?. Roy=59n,""Tq1vovDia pe. in terms of the pressure of the ambient medium P,=2/Cey«105em*K) (where Ap is the Doltzman constant). after a time ἐν=138007D,‘De279 ANTvr"," The SNR stalls when its expansion velocity drops to the the local sound speed $c_0$; the stalling radius is given by \citet{cioffi1991} $R_{\rm st}=59n_0^{-6/35}P_4^{-1/5}\zeta ^{-2/35}$ pc, in terms of the pressure of the ambient medium $P_4=P/(k_{\rm 82B}\times 10^4\;{\rm cm^{-3}\;\rm K})$ (where $k_{\rm B}$ is the Boltzman constant), after a time $t_{\rm st}=1.38n_0^{0.33}P_4^{-7/10} 83\zeta ^{-2/35}$ Myr."84 Eventually. the SNR cavity. is refilled by the ISAT on a timescale of the order of fey.," Eventually, the SNR cavity is refilled by the ISM on a timescale of the order of $t_{\rm fill}=R_{\rm st}/c_0$ ."85 lt is known that a single SNR does not contribute significantly to the LSAT energization: at the end. of its evolution only a few percent of the explosion energy has been Fed into the surrounding gas. while the rest has been raciated away (e.g.7).," It is known that a single SNR does not contribute significantly to the ISM energization; at the end of its evolution only a few percent of the explosion energy has been fed into the surrounding gas, while the rest has been radiated away \citep[e.g.][]{bradamante1998}."86 However. when many SNe explode with a rate per unit volume S high enough. their combined. effect may leac to the thermalization of a very high fraction (close to 100%)) of the explosion energy.," However, when many SNe explode with a rate per unit volume $S$ high enough, their combined effect may lead to the thermalization of a very high fraction (close to ) of the explosion energy."87 In fact. if many SNRs collide with each other the shells fragment and the hot eas of their interior merges forming a dilute medium.," In fact, if many SNRs collide with each other the shells fragment and the hot gas of their interior merges forming a dilute medium."88 Repeatec supernova explosions are especially elfective in reheating this medium because the SNR cooling time is relatively long in a low density region., Repeated supernova explosions are especially effective in reheating this medium because the SNR cooling time is relatively long in a low density region.89 A considerable fraction of gas may hus be driven out of the galaxy., A considerable fraction of gas may thus be driven out of the galaxy.90 To understand when this is elfectivelv the case. one has to caleulate the collision time fan.," To understand when this is effectively the case, one has to calculate the collision time $t_{\rm int}$."91 This time can be defined as the time required for SNIts orming at the rate ο to fill up the volume of space., This time can be defined as the time required for SNRs forming at the rate $S$ to fill up the volume of space.92 Lf the expansion law of a remnant is given by Ro=P (cl.22) (?)..," If the expansion law of a remnant is given by $R_{\rm 93s}=At^{\alpha}$ \citep[cf.][] 94{larson1974, melioli2004} \citep{cioffi1991}."95"where C, is the FUV intensity relative to the Solar neighborhood. and σι is the dust cross section per H atom to UV photons.","where $G_0'$ is the FUV intensity relative to the Solar neighborhood, and $\sigma_{\rm d}$ is the dust cross section per H atom to UV photons."96" Here. we assume that the C4,=Lando, =1.107! 7."," Here, we assume that the $G_0' = 1$ and $\sigma_d =971\times10^{-21}$ $^{-2}$."98 Test models in which we scale Cy by the star formation rate density compared to that found in the solar neighbourhood have similar results to those presented in this work. and are presented in the Appendix.," Test models in which we scale $G_0$ by the star formation rate density compared to that found in the solar neighbourhood have similar results to those presented in this work, and are presented in the Appendix."99 The cosmic ray heating rate is given by: where c' is the cosmic rayionisation rate (here. assumed to be2 .10οσης ty and qoi is the thermal energy increase per cosmic ray ionisation.," The cosmic ray heating rate is given by: where $\zeta'$ is the cosmic rayionisation rate (here, assumed to be 2 $\times 10^{-17} Z' {\rm s}^{-1}$ ), and $q_{\rm CR}$ is the thermal energy increase per cosmic ray ionisation."100 ForHe. {οιe12.25 eV2011). and for HI. gon=6.5 eV1972).. We utilise a constant cosmic ray heating rate for all simulations.," For, $q_{\rm CR}101\approx 12.25$ eV, and for HI, $q_{\rm CR} = 6.5$ eV. We utilise a constant cosmic ray heating rate for all simulations."102 Some models suggest that there may be enhanced cosmic ray fluxes during starbursts which would increase the ggas temperature2010).. and further enhance the effects found in our Results section.," Some models suggest that there may be enhanced cosmic ray fluxes during starbursts which would increase the gas temperature, and further enhance the effects found in our Results section."103 Finally. in a subset of models we have explored the potential effects of turbulent heating on molecular clouds.," Finally, in a subset of models we have explored the potential effects of turbulent heating on molecular clouds."104 In unresolved GMCs we can estimate this heating rate basedon numerical experiments on the rate of turbulent dissipation: Pianzm1.5ao?/ Ro where His the GMC radius2007).," In unresolved GMCs we can estimate this heating rate basedon numerical experiments on the rate of turbulent dissipation: $\Gamma_{\rm turb} \approx 1.5 \times105\sigma^3/R$ , where $R$ is the GMC radius."106. For resolved GMCs. we can measure the turbulent heating rate directly from the code.," For resolved GMCs, we can measure the turbulent heating rate directly from the code."107 Bulk turbulent motions can be converted to heat through two pathways: adiabatic compression and viscous dissipation., Bulk turbulent motions can be converted to heat through two pathways: adiabatic compression and viscous dissipation.108 The compressive heating rate per unit mass Is Liu;=D(N| v)/p. and we can evaluate this directly from the density and velocity fields output by Gadget.," The compressive heating rate per unit mass is $\Gamma_{\rm comp} = P109(\nabla \cdot \mathbf{v})/\rho$ , and we can evaluate this directly from the density and velocity fields output by Gadget."110 The viscous dissipation rate per unit mass is Voie=(tisecV)ovp. where guo ds the viscous stress tensor.," The viscous dissipation rate per unit mass is $\Gamma_{\rm visc} =111(\mathbf{\pi}_{\rm visc} \cdot \nabla) \cdot \mathbf{v} / \rho$, where $\mathbf{\pi}_{\rm visc}$ is the viscous stress tensor."112 The code relies on implicit dissipation rather than an explicit viscosity. but we can estimate the viscous heating rate produced by that implicit dissipation by noting that the Reynolds number must be ~1 on the resolution scale of the code2009).," The code relies on implicit dissipation rather than an explicit viscosity, but we can estimate the viscous heating rate produced by that implicit dissipation by noting that the Reynolds number must be $\sim 1$ on the resolution scale of the code."113. This implies that the dynamic viscosity is ηcpeh. where h is the SPH smoothing scale.," This implies that the dynamic viscosity is $\eta \approx \rho v h$, where $h$ is the SPH smoothing scale."114" Given this approximation. the components of the viscous stress tensor are Ripeee=OVfOr,|Ovὃς αμ which we can again evaluate directly from the density and velocity fields output by Gadget."," Given this approximation, the components of the viscous stress tensor are $\pi_{ij,\rm visc} = \eta [\partial115 v_i/\partial x_j + \partial v_j/\partial x_i - (2/3) \partial116 v_i/\partial x_j \delta_{ij}]$, and which we can again evaluate directly from the density and velocity fields output by Gadget."117 We tind that the effects of turbulent heating are modest in both the resolved and unresolved cases., We find that the effects of turbulent heating are modest in both the resolved and unresolved cases.118 In our tiducial merger including viscous dissipation reduces bby ~30%. while the the fiducial dise it reduces bby less than a few percent.," In our fiducial merger including viscous dissipation reduces by $\sim 30\%$, while the the fiducial disc it reduces by less than a few percent."119 Hereafter we neglect this heating term. though we note that including it would only enhance the results we present below.," Hereafter we neglect this heating term, though we note that including it would only enhance the results we present below."120 The line cooling is assumed to occur via either CII or CO emission., The line cooling is assumed to occur via either CII or CO emission.121 The fraction of hydrogen for which the carbon is mostly in the form of CO is well-approximated by the following result from both semi-analytic and numerical work: When this fraction is above50%.. we assume the cooling happens predominantly via CO line cooling: else. the cooling occurs via ΟΠ emission.," The fraction of hydrogen for which the carbon is mostly in the form of CO is well-approximated by the following result from both semi-analytic and numerical work: When this fraction is above, we assume the cooling happens predominantly via CO line cooling; else, the cooling occurs via CII emission."122 The cooling rate is calculated via an escape probability formalism utilising the public code of(2007)., The cooling rate is calculated via an escape probability formalism utilising the public code of.123 We describe the equations for the line radiative transfer (both within clouds. as is pertinent to caleulating the cooling rates. and across the model galaxy. in 2.49).," We describe the equations for the line radiative transfer (both within clouds, as is pertinent to calculating the cooling rates, and across the model galaxy, in \ref{section:turtlebeach}) )."124 The dust cooling rate is: We assume the bulk of the dust heating happens via IR radiation as TR radiation likely dominates the heating over UV flux in the optically thick centres of GMCs., The dust cooling rate is: We assume the bulk of the dust heating happens via IR radiation as IR radiation likely dominates the heating over UV flux in the optically thick centres of GMCs.125 The IR radiation field is known from ddust radiative transfer calculations (which will be described in 2.3))., The IR radiation field is known from dust radiative transfer calculations (which will be described in \ref{section:sunrise}) ).126" Finally. the dust and gas exchange energy via: where the thermal gas-dust exchange rate is Quq=3.2""Z'emem? τή ΓΗ... andes =1510ni“Zerg em? 77 for HI2001)."," Finally, the dust and gas exchange energy via: where the thermal gas-dust exchange rate is $\alpha_{\rm gd} = 3.2127\times 10^{-34} Z'$ erg $^3$ $^{-3/2}$ for, and $\alpha_{\rm128 gd } = 1 \times 10^{-33} Z'$ erg $^{3}$ $^{-3/2}$ for HI."129 In order to calculate the background radiation field from stars and the dust temperature. we perform dust radiative transfer calculations with the publicly available codeSUNRISE.," In order to calculate the background radiation field from stars and the dust temperature, we perform dust radiative transfer calculations with the publicly available code."130.. A full description of the algorithms can be found in(2010). and(2010).," A full description of the algorithms can be found in, and."131. Here. we summarise the aspects of the simulations most relevant to this study.," Here, we summarise the aspects of the simulations most relevant to this study."132 The sources of radiation in the model galaxies are stellar clusters and accreting black holes., The sources of radiation in the model galaxies are stellar clusters and accreting black holes.133 The stellar clusters emit a template spectrum derived from cealeulations. with the metallicities. masses and ages known from the ssimulations.," The stellar clusters emit a template spectrum derived from calculations, with the metallicities, masses and ages known from the simulations."134 The AGN emits a spectrum based on observations of unreddened quasars2007b).. though has little effect in the calculations here (see the Appendix).," The AGN emits a spectrum based on observations of unreddened quasars, though has little effect in the calculations here (see the Appendix)."135 The substructure of the ISM on scales below the smoothing length of the SPH simulations is unresolved., The substructure of the ISM on scales below the smoothing length of the SPH simulations is unresolved.136 We assume that star clusters with ages «LQ Myr reside in natal. birthelouds. and modulate their SED accordingly.," We assume that star clusters with ages $< 10$ Myr reside in natal birthclouds, and modulate their SED accordingly."137 These birthelouds contain HII regions and photodissociation regions (PDRs) whose SEDs are calculated utilising ID pphotoionisation models 2010)., These birthclouds contain HII regions and photodissociation regions (PDRs) whose SEDs are calculated utilising 1D photoionisation models .138. The time-averagec PDR covering fraction is a free-parameter., The time-averaged PDR covering fraction is a free-parameter.139 We assume a constan fraction of fpi=0.3. corresponding to a covering lifetime of ~2.3 Myr2008).," We assume a constant fraction of $f_{\rm PDR} = 0.3$, corresponding to a covering lifetime of $\sim 2-3$ Myr."140. This value is motivatec in part by simulations by which showed covering fractions comparable to these result in synthetic SEDs of dise galaxies comparable to the SINGS sample2003)., This value is motivated in part by simulations by which showed covering fractions comparable to these result in synthetic SEDs of disc galaxies comparable to the SINGS sample.141. Changing this parameter has minimal effects on the fina results of this paper: we quantify this and other potential effects of the subresolution modeling in the Appendix., Changing this parameter has minimal effects on the final results of this paper: we quantify this and other potential effects of the subresolution modeling in the Appendix.142 When radiation leaves either the naked stellar cluster (with age —LO Myr). or the HIT region/PDR (for younger clusters). it is allowed to interact with the diffuse ISM.," When radiation leaves either the naked stellar cluster (with age $>14310$ Myr), or the HII region/PDR (for younger clusters), it is allowed to interact with the diffuse ISM."144 We assume the remaining cold molecular phase has an negligible cross-section for interaction. though test the effects of this assumption in the Appendix.," We assume the remaining cold molecular phase has an negligible cross-section for interaction, though test the effects of this assumption in the Appendix."145 The dust mass in the diffuse ISM is calculated assuming a constant dust to metals ratio of 0.42008).. where the metallicity distribution is known from the SPH calculations.," The dust mass in the diffuse ISM is calculated assuming a constant dust to metals ratio of 0.4, where the metallicity distribution is known from the SPH calculations."146 We use the dust model with /?=elyfleeyv 3.105. as updated by (2007).," We use the dust model with $R \equiv A_V/E_{B-V} = 3.15$ , as updated by ."147. The dust and radiation field are assumed to be in radiative equilibrium. utilising the methodology of for calculating the converged radiation field.," The dust and radiation field are assumed to be in radiative equilibrium, utilising the methodology of for calculating the converged radiation field."148 When the radiation, When the radiation149where we have dropped the irrelevant arbitrary constant (hat initializes time.,where we have dropped the irrelevant arbitrary constant that initializes time.150" The integral to be evaluated is now⋅⋅ divide the⋅↽ integral into⋅ two⋅↽− contributions Vy⊏↓⊐ and(2j V; .(d where V, =σιI.doWe(2) Vj; =σιJe,odo−where (he (ime parameter⋅ σι is chosen⋅ {ο be large and negative (recalland we chose g=0 at closest approach). and to satisfy the following inequalities (1/v0,)|x,|."," The integral to be evaluated is We now divide the integral into two contributions $\Psi_a^{(1)}$ and $\Psi_a^{(2)}$ , where $\Psi_a^{(1)} = \int_{\sigma_e}^{\sigma_1} \dots151d\sigma$ and $\Psi_a^{(2)} = \int_{\sigma_1}^{\sigma_r} \dots d\sigma$ where the time parameter $\sigma_1$ is chosen to be large and negative (recall we chose $\sigma = 0$ at closest approach), and to satisfy the following inequalities $|{\bf x}_a| \ll |\sigma_1| \ll (1/v_a)|{\bf x}_a|$ ."152 Since vy«I. an appropriate value of σι clearly exists.," Since $v_a \ll 1$, an appropriate value of $\sigma_1$ clearly exists."153" Then in evaluating ο.uj we can expand the integrand in powers of 1/o. since jo]>>|x,| everywhere. and integrate ∣↽≻⋡∖↽↕↽≻"," Then in evaluating $\Psi_a^{(1)}$ , we can expand the integrand in powers of $1/\sigma$, since $|\sigma|154\gg |{\bf x}_a|$ everywhere, and integrate by parts."155≀↕↴↕⋅↥⋟∖⊽⋅∐⊔↲∖↽≀↧↴↥∏≀↧↴⊔∐≸≟∖↕∣↙∣⋅⋟∖⊽↕∐≺∢≼↲⊔∐↲∐∐≼↲≸≟↕⋅≀↧↴⊔∪∐↕⋟∖⊽≀↧↴↥∖∖⇁≀↕∶∖↽⋟∖⊽∖∖⇁↕⊔∐∐⊔∐↲∐↲≀↕↴↕⋅∠∪∐≼↲⋅∖∖⇁≼↲≺∢≀↧↴∐− ⊏⇉⊐⋅ ⋅ ⋅⋅ ⋅⋅ expand the variables of the bodies about their values at the coordinate time corresponding to closest approach in a slow-molion expansion.," In evaluating $\Psi_a^{(2)}$, since the integration is always within the near zone, we can expand the variables of the bodies about their values at the coordinate time corresponding to closest approach in a slow-motion expansion."156 We will work only (o first order in e., We will work only to first order in $v_a$.157 Each integral will depend on the arbitrarily chosen value of σι., Each integral will depend on the arbitrarily chosen value of $\sigma_1$.158 We then match the integrals by expanding (he relevant terms in We) in a slow-motion expansion. and the relevant terms in Vin powers of L/o4.," We then match the integrals by expanding the relevant terms in $\Psi_a^{(1)}$ in a slow-motion expansion, and the relevant terms in $\Psi_a^{(2)}$ in powers of $1/\sigma_1$ ."159 We will see that all dependenceon σι cancels to the order considered. as it must.," We will see that all dependenceon $\sigma_1$ cancels to the order considered, as it must."160 We first evaluate VI., We first evaluate $\Psi_a^{(2)}$.161" We re-initialize the parameter u lor body α so that it is zero al the time of closest approach ancl expand (he variables of body à about that point. so that x,(4)=(0)4-v,(0)u+Oleu)."," We re-initialize the parameter $u$ for body $a$ so that it is zero at the time of closest approach and expand the variables of body $a$ about that point, so that ${\bf x}_a(u) = {\bf x}_a(0) + {\bf v}_a(0) u +162O(\epsilon u)$."163" When evaluated at that value of 4 equal to retarded time s,. we gel an analogous result x,(¢@=s,)x,(0)+v,(0)s,Oles,)."," When evaluated at that value of $u$ equal to retarded time $s_a$, we get an analogous result ${\bf x}_a(u=s_a) = {\bf x}_a(0) + {\bf v}_a(0) s_a+164O(\epsilon s_a) $."165" Also. v,(0)+ Ofet70,)."," Also, ${\bf v}_a(u=s_a) = {\bf v}_a(0) +166O(\epsilon^{1/2} v_a)$ ."167" Note that x,(0) and v,(0) are evaluated al uw=0.", Note that ${\bf x}_a(0)$ and ${\bf v}_a(0)$ are evaluated at $u=0$.168" By defining the vector d,(s,)=£,— x,(s,). which points from the body at retarded time to the point of closest approach. we can wrile rj(c.5,)=ko+d,(s,)."," By defining the vector ${\bf d}_a(s_a) \equiv {\bf \xi}_a - {\bf x}_a(s_a)$ , which points from the body at retarded time to the point of closest approach, we can write ${\bf r}_a(\sigma,s_a) = {\bf k} \sigma + {\bf d}_a(s_a)$."169 We note that. to the necessary order. the denominator in Eq. (19))," We note that, to the necessary order, the denominator in Eq. \ref{psiintegral}) )"170" can be written r(0.54)—VelSe)Lolo.ο)ο=[Di+O0ler,). where The term in square brackets in Eq. (20))"," can be written $r_a(\sigma,s_a) - {\bf v}_a(s_a) \cdot {\bf171r}_a(\sigma,s_a)/c_g = |{\bf D}| + O(\epsilon r_a)$, where The term in square brackets in Eq.\ref{dvector}) )"172 vanishes (ο the necessary. order., vanishes to the necessary order.173" Noticethat ο, has cancelled out.", Noticethat $c_g$ has cancelled out.174" Defining the vectorz(o)=ko+ d,(0). with k-d,(0)=0 (κ and d, are orthogonal at the momentofclosest approach to body à). we can write D=σσ)— v,(0)o. and thus"," Defining the vector${\bf z}(\sigma) = {\bf k}\sigma + {\bf d}_a(0)$ , with ${\bf k} \cdot {\bf d}_a(0) = 0$ $\bf k$ and ${\bf d}_a$ are orthogonal at the momentofclosest approach to body $a$ ), we can write ${\bf D} = {\bf z}(\sigma) - {\bf v}_a(0)\sigma$ , and thus"175physical. sciences. in. general aud in. astronomy in.,physical sciences in general and in astronomy in.176parliculer?.. From our perspective.. (his. is. indeed. a problem. and one worth continuing attention from the community. for the following reasons: Significant provements in womens career advancement have been achieved in (he recent vears. Wilh astronomy clearly aleacl of the curve among other physical sciences.," From our perspective, this is indeed a problem, and one worth continuing attention from the community, for the following reasons: Significant improvements in women's career advancement have been achieved in the recent years, with astronomy clearly ahead of the curve among other physical sciences."177 Indeed. representation of women among faculty members is higher in astronomy than averaged over all of phvsies in astronomy vs in physics as a whole*)) and has been on the rise in the recent vears.," Indeed, representation of women among faculty members is higher in astronomy than averaged over all of physics in astronomy vs in physics as a ) and has been on the rise in the recent years."178 The difference is even more dramatic among the vounger generation of assistant professors in. astronomv are women. compared with in phvsies).," The difference is even more dramatic among the younger generation of assistant professors in astronomy are women, compared with in physics)."179 H6 is clear that somehow astronomy. departments have created a significantly more women-friendly environment than departments in other physical disciplines., It is clear that somehow astronomy departments have created a significantly more women-friendly environment than departments in other physical disciplines.180 One possibility is that. astronomy is benefiting from (he historically higher representation of women. and the availability of role models leads to higher retention rates for voung female scientists.," One possibility is that astronomy is benefiting from the historically higher representation of women, and the availability of role models leads to higher retention rates for young female scientists."181 On top of that. the astrononmical community. benelits from being educated on the issue of gender biases (e.g.. through (the work done by the American Astronomical Societv). and many prolessionals have been involved in programs designed (o improve participadion of women — and (hese programs are working.," On top of that, the astronomical community benefits from being educated on the issue of gender biases (e.g., through the work done by the American Astronomical Society), and many professionals have been involved in programs designed to improve participation of women – and these programs are working."182 While these are encouraging trends. many problems remain.," While these are encouraging trends, many problems remain."183 Ii particular. progress is significantly slower at top-ranked. departments (among the top 20 physics departments. only of assistant [acultv ave women. compared with the for the field as a whole!)).," In particular, progress is significantly slower at top-ranked departments (among the top 20 physics departments, only of assistant faculty are women, compared with the for the field as a )."184 Very few full. professors are female in physics and in astronomy).f," Very few full professors are female in physics and in astronomy).,"185aculties’... which is a very serious problem considering (hat many astronomers start by receiving (heir undergraduate education in physics., which is a very serious problem considering that many astronomers start by receiving their undergraduate education in physics.186 Furthermore. many astvoplvsicists are employed by physics deparlinents not only in small colleges. but also in major PhD eranting institutions.," Furthermore, many astrophysicists are employed by physics departments not only in small colleges, but also in major PhD granting institutions."187 Therefore. the statistics for astronomy deparinents," Therefore, the statistics for astronomy departments"188The left-hancl side of this equation is a coordinate scalar with Vοη an element of proper volume.,"The left-hand side of this equation is a coordinate scalar with $\sqrt{g}\, {\mathrm d}^4 x$ an element of proper volume."189 Expanding (79)): From this we can derive an inteerodilferential equation for 1., Expanding \ref{eq:econ1}) ): From this we can derive an integrodifferential equation for $T^{00}$.190" ""Phe resulting equation is most simply written in terms of νι)=Invio(eV)nat."," The resulting equation is most simply written in terms of $A_{\mathrm{M}} (\eta) = R^4 (\eta) T^4 (\eta) \,\mathrm{(eV)^4 \cdot m^4}$."191 A similar cquantity was introduced in section 10.. but there it could be treated simplv as à constant.," A similar quantity was introduced in section \ref{sec:mass_1}, but there it could be treated simply as a constant."192 Here we calculate its variation with time: Note that because of the appearance of the function pty). this equation by itself is not sullicient to calculate shy.," Here we calculate its variation with time: Note that because of the appearance of the function $p(\eta )$, this equation by itself is not sufficient to calculate $A_{\mathrm{M}}$."193 We obtain an independent. equation. connecting these. two functions in the next section., We obtain an independent equation connecting these two functions in the next section.194 We will now obtain an equation for the ratio pOy) analogous to (61)). but based. on the asvmptotic form. (76)) for the tail of the vector. potential.," We will now obtain an equation for the ratio $p (\eta)$ analogous to \ref{eq:p_exp_1}) ), but based on the asymptotic form \ref{eq:A2asymptotic_2}) ) for the tail of the vector potential."195 In. our. previous calculation. where the tail of cls reached a constant asvmptotic value. we could be sure that p would rise monotonically: the only question was whether there would be factors of ely; that would make the increase far too fast or lar too slow. (," In our previous calculation, where the tail of $A_2$ reached a constant asymptotic value, we could be sure that $p$ would rise monotonically; the only question was whether there would be factors of $A_{\mathrm{M}}$ that would make the increase far too fast or far too slow. ("196This is just what happens. for example. if we use quadrupole rather than dipole potentials.),"This is just what happens, for example, if we use quadrupole rather than dipole potentials.)"197 In this second. caleulation. we can anticipate that there will not be any unwanted factors of Ayr but only a detailed. ealeulation. will show whether p continues Lo rise with η.," In this second calculation, we can anticipate that there will not be any unwanted factors of $A_{\mathrm{M}}$, but only a detailed calculation will show whether $p$ continues to rise with $\eta$."198" The analog of (56)) is To get the contribution to 215 at jj, from the particles in the shell. we multiply (83)) by ASONCn )]. with elo(a.v.g) given by (76))."," The analog of \ref{eq:numshell}) ) is To get the contribution to $A_2^2$ at $\eta_{\mathrm{p}}$ from the particles in the shell, we multiply \ref{eq:numshell_2}) ) by $A_2^2 [ \sigma, \chi, (\eta_{\mathrm{p}} - \eta_{\mathrm{s}} )]$ , with $A_2 ( \sigma, \chi, \eta )$ given by \ref{eq:A2asymptotic_2}) )."199" Proceeding as before we get the analog of (59)): with £i, given by (77)).", Proceeding as before we get the analog of \ref{exp:A2both}) ): with $F_0$ given by \ref{eq:Fasymptotic_2}) ).200 The collision time. 7. will be given by We can now get an expression for p by using (85)) in (84)) and dividing by Z7(1): with £ given hy (77)).," The collision time, $\tau$, will be given by We can now get an expression for $p$ by using \ref{eq:tau_est_2}) ) in \ref{exp:A2both_2}) ) and dividing by $T^2 (\eta_{\mathrm{p}})$: with $F$ given by \ref{eq:Fasymptotic_2}) )."201 As before. we set [In.X=10 for definiteness.," As before, we set $\ln \Lambda = 10$ for definiteness."202 Simultaneous numerical solution of (81)) and (86)) is straightforward. but we need a starting value for zd.," Simultaneous numerical solution of \ref{eq:econ6}) ) and \ref{eq:pinteqn_2}) ) is straightforward, but we need a starting value for $A_{\mathrm{M}}$."203" We choose ely,=2.5107eV!ant."," We choose $A_{\mathrm{M}} = 2.5 \times 10^{74}\, \mathrm{eV^4 \cdot m^4}$ ."204 This is approximately equal to the observed value today., This is approximately equal to the observed value today.205 p becomes equal to unity around tow=480., $p$ becomes equal to unity around $\eta_{\mathrm{cw}} = 480$.206 This value of jos is significantly larger than the previous value of 11 when &=0. but is still within a Lew orders of magnitude of unity.," This value of $\eta_{\mathrm{cw}}$ is significantly larger than the previous value of $11$ when $\sigma = 0$, but is still within a few orders of magnitude of unity."207 Phe most important feature of this calculation is that it shows pli) does continue to rise. even when ez0.," The most important feature of this calculation is that it shows $p(\eta)$ does continue to rise, even when $\sigma \ne 0$."208 In a series of papers (see ο and references given there). Mannheim has developed a cosmology based on conformal eravitv.," In a series of papers (see \citet{mann6} and references given there), Mannheim has developed a cosmology based on conformal gravity."209 The underlving geometry is a FRW space with negative curvature., The underlying geometry is a FRW space with negative curvature.210 The expansion. parameter. (η). has a minimum. non-zero value: we will assume this represents the initial size of the bubble.," The expansion parameter, $R(\eta)$, has a minimum, non-zero value; we will assume this represents the initial size of the bubble."211 A distinguishing aspect of this theory is that it contains no intrinsic mass scale. unlike conventional cosmology where the Planck mass provides a funcamoental scale.," A distinguishing aspect of this theory is that it contains no intrinsic mass scale, unlike conventional cosmology where the Planck mass provides a fundamental scale."212 I is therefore natural to ask whether. in Mannheim model. the steady increase in the ratio p could eventually.s trigger a phase change that would. generate particle masses.," It is therefore natural to ask whether, in Mannheim's model, the steady increase in the ratio $p$ could eventually trigger a phase change that would generate particle masses."213 We are no advocating the Mannheim model in this paper: it must stil meet some serious challenges before it can be regarded as a serious rival to the conventional model., We are not advocating the Mannheim model in this paper; it must still meet some serious challenges before it can be regarded as a serious rival to the conventional model.214 We are simply using it as an exaniple of the way the non-thermal component of the ellective mass can play a crucial role., We are simply using it as an example of the way the non-thermal component of the effective mass can play a crucial role.215 The mechanism we have in mind is the Coleman-Weinberg (CW) transition (72)... as discussed in the contex of cosmology in ?..," The mechanism we have in mind is the Coleman-Weinberg (CW) transition \citep{cole1}, as discussed in the context of cosmology in \citet{nar2}."216 Figure 10. shows the ellective potential. Var. for a tvpical field theory at finite temperature. (," Figure \ref{fig:Veff} shows the effective potential, $V_{\mathrm{eff}}$, for a typical field theory at finite temperature. ("217Lhe formulae used are taken from. 2)).,The formulae used are taken from \citet{nar2}) ).218" Initially. Vor is describe bv the upper curve. but as the ellective mass of the fick quanta increases. the second minimum will move lower. anc eventually, when pzz1. it will cross the horizontal axis."," Initially, $V_{\mathrm{eff}}$ is described by the upper curve, but as the effective mass of the field quanta increases, the second minimum will move lower, and eventually, when $p \approx 1$, it will cross the horizontal axis."219 A this point a CW transition can take place and normal masses will appear., At this point a CW transition can take place and normal masses will appear.220 These will have magnitude m?z(ATi., These will have magnitude $m^2 \approx \langle {\mathbf A}^2 \rangle_{\mathrm{nt}}$.221 By adjusting the parameters of the model we can arrange for sullicient conformal time to clapse from. the formation of the bubble to the CW transition. assumed to occur at the weak interaction scale.," By adjusting the parameters of the model we can arrange for sufficient conformal time to elapse from the formation of the bubble to the CW transition, assumed to occur at the weak interaction scale."222 Phe initial temperature of the bubble. νι is then found to be very high. and we have to look for an explanation of why particle masses are so very small compared to this temperature. (," The initial temperature of the bubble, $T_{\mathrm{max}}$, is then found to be very high, and we have to look for an explanation of why particle masses are so very small compared to this temperature. ("223Phis problem is analogous tothe hierarchy problem in ordinary. cosmology. where the Planck mass is so much greater than particle masses.},"This problem is analogous tothe hierarchy problem in ordinary cosmology, where the Planck mass is so much greater than particle masses.)"224 In the Mannheim model. the explanation is straightforward.," In the Mannheim model, the explanation is straightforward."225 The temperature of the CW transition— is found to depend exponentially on the conformal time. so a," The temperature of the CW transition is found to depend exponentially on the conformal time, so a"226"GeV gamma-ray emission. other six GCs have been identified as gamma-ray emillers(el,","GeV gamma-ray emission, other six GCs have been identified as gamma-ray emitters(cf."227 Abdo et al., Abdo et al.228 2010a: Abdo et al., 2010a; Abdo et al.229" 20100),", 2010b).230 It is generally believed that the gamma-ray emission from GCs either comes from maegnetospheres of MSPs or produced by inverse Compton scattering between electrons accelerated in the relativistie pulsar wind aud background soft photons., It is generally believed that the gamma-ray emission from GCs either comes from magnetospheres of MSPs or produced by inverse Compton scattering between electrons accelerated in the relativistic pulsar wind and background soft photons.231 In [act before the detection of gamma-ravs from GCs. Wang et al. (," In fact before the detection of gamma-rays from GCs, Wang et al. ("2322005) have shown that the curvature radiation spectrum caleulated from the outergap model of Zhang Cheng (1997) produced from unresolved MSPs in the galactic center can result in a simple power law with an exponential eut-off energv al ~3 GeV. They used the observed distribution functions of MSPs from the field. [rom the GCs and the combination of these (wo distributions. and they found that the model spectrum was quite consistent with the diffuse gamma-ray spectrum detected by EGRET in the direction of the galactic center.,"2005) have shown that the curvature radiation spectrum calculated from the outergap model of Zhang Cheng (1997) produced from unresolved MSPs in the galactic center can result in a simple power law with an exponential cut-off energy at $\sim 3$ GeV. They used the observed distribution functions of MSPs from the field, from the GCs and the combination of these two distributions, and they found that the model spectrum was quite consistent with the diffuse gamma-ray spectrum detected by EGRET in the direction of the galactic center."233 However it is important to note that the total gamuna-ray spectra calculated from these three different distributions (cL., However it is important to note that the total gamma-ray spectra calculated from these three different distributions (cf.234 Fig., Fig.235 4 of Wang et al., 4 of Wang et al.236 2005) are actually very. similar., 2005) are actually very similar.237 Therefore it is very clilficult to constraint the models by using average spectrum., Therefore it is very difficult to constraint the models by using average spectrum.238 Recently Venter de Jager (2008) ancl Venter et al. (, Recently Venter de Jager (2008) and Venter et al. (2392009) calculated the expected fIux of eamma-rays produced by the curvature radiation of electrons in pulsar magnetospheres.,2009) calculated the expected flux of gamma-rays produced by the curvature radiation of electrons in pulsar magnetospheres.240 Venter de Jager (2008) first calculated the expected GeV flix from 47 Tucanae (47 Tuc) by using an unscreened (pair-starved polar cap) electric [ied (see e.g. Harding. Usov. Muslimov 2005) for 12 out of the 13 MSPs they considered. and the screened field for only 1 MSP. with a relatively high spincown power based on the approximation of a screened electric fied by Dyks Iudak (2000).," Venter de Jager (2008) first calculated the expected GeV flux from 47 Tucanae (47 Tuc) by using an unscreened (pair-starved polar cap) electric field (see e.g. Harding, Usov, Muslimov 2005) for 12 out of the 13 MSPs they considered, and the screened field for only 1 MSP with a relatively high spindown power based on the approximation of a screened electric field by Dyks Rudak (2000)."241 Venter et al. (, Venter et al. (2422009) extended the model to include the inverse Compton component. which can produce TeV photons.,"2009) extended the model to include the inverse Compton component, which can produce TeV photons."243 Their model predictions are consistent. with the later reported results bv Fermi (Abdo οἱ al., Their model predictions are consistent with the later reported results by Fermi (Abdo et al.244 2009) but the predicted TeV flix seems to be higher than the observed upper limits for 47 Tuc (Abaronian et al., 2009) but the predicted TeV flux seems to be higher than the observed upper limits for 47 Tuc (Aharonian et al.245 2009)., 2009).246 On the other hand the total number of millisecond pulsar is unclear and it is süll possible that by adjusting the model parameters both GeV, On the other hand the total number of millisecond pulsar is unclear and it is still possible that by adjusting the model parameters both GeV247IE1161348—5055 (hereafter 16133) was discovered with the satellite (Tuohy&Garmire1980) close to the geometrical centre of the young supernova remnant (SNR) (age ~2 kyr: Carter.Dickel&Bomans 1997)).,161348–5055 (hereafter ) was discovered with the satellite \citep{tuohy80} close to the geometrical centre of the young supernova remnant (SNR) (age $\sim$ 2 kyr; \citealt*{carter97}) ).248 It was proposed as the first example of a radio-quiet (possibly owing to an unfavourable radio beaming). isolated. cooling neutron star &Garmire1980:Tuohyetal. 1983:: 1997).," It was proposed as the first example of a radio-quiet (possibly owing to an unfavourable radio beaming), isolated, cooling neutron star \citealt{tuohy80,tuohy83}; \citealt*{gph97}) )."249" At present. there is little doubt that iindeed is a neutron star (DeLucaetal.2006). and the source is traditionally included in the class of the ""central compact objects? (CCOs: see DeLuca2008. for a review)."," At present, there is little doubt that indeed is a neutron star \citep{deluca06} and the source is traditionally included in the class of the `central compact objects' (CCOs; see \citealt{deluca08} for a review)."250 CCOs are a small group of young and seemingly isolated X-ray-emitting neutron stars (with thermal-like spectra). observed close to the centre of non-plerionic SNRs and without obvious counterparts in. other wavebands.," CCOs are a small group of young and seemingly isolated X-ray-emitting neutron stars (with thermal-like spectra), observed close to the centre of non-plerionic SNRs and without obvious counterparts in other wavebands."251 However. its peculiar temporal behaviour distinguishes ffrom the other CCOs (actually. it singles this source out as a unique object in general).," However, its peculiar temporal behaviour distinguishes from the other CCOs (actually, it singles this source out as a unique object in general)."252 The first peculiarity of the source is its orders-of-magnitude X-ray flux variability on a few months/vears time-scale (Gotthelf.Petre&Vasisht1999:: Garmireetal.2000:Sanwal2002:Becker&Aschenbach 20027).," The first peculiarity of the source is its orders-of-magnitude X-ray flux variability on a few months/years time-scale \citealt*{gotthelf99}; \citealt{garmire00,sanwal02,becker02}) )."253 Moreover. the first oobservation of iin a low state hinted at a possible periodicity at ~6 hours (Garmire2000) that was not contirmed by subsequent observations of the source in bright states.," Moreover, the first observation of in a low state hinted at a possible periodicity at $\sim$ 6 hours \citep{gpg00} that was not confirmed by subsequent observations of the source in bright states."254 A long (90 Ks) observation withNewton.. performed in 2005. caught iin a low state and yielded unambiguous evidence for a strong. nearly sinusoidal modulation at 6.67+=0.03 hours (24.0+0.1 ks: DeLucaetal. 2006)).," A long (90 ks) observation with, performed in 2005, caught in a low state and yielded unambiguous evidence for a strong, nearly sinusoidal modulation at $6.67\pm0.03$ hours $24.0\pm0.1$ ks; \citealt{deluca06}) )."255 The same periodicity was then recognised also in the olderdata-sets. albeit with a very different pulse shape. including two narrow dips per period.," The same periodicity was then recognised also in the olderdata-sets, albeit with a very different pulse shape, including two narrow dips per period."256 No faster pulsations are seen in citepdelucade.., No faster pulsations are seen in \\citep{deluca06}.257 Large flux variations. similar to those observed in1613.. are common among magnetars (e.g. Rea&Esposito 20113). but these pulsars. whose emission is believed to be powered mainly by the magnetic crfield. are characterised: by rotational; periods. .in the narrow range 2-12 s. On the other hand. CCOs are steady sources. and their periods —when known- are in the 0.1—0.5 s range al. 2000:: Gotthelf.Halpern&Seward2005: 20095).," Large flux variations, similar to those observed in, are common among magnetars (e.g. \citealt{rea11}) ), but these pulsars, whose emission is believed to be powered mainly by the magnetic field, are characterised by rotational periods in the narrow range 2–12 s. On the other hand, CCOs are steady sources, and their periods –when known– are in the 0.1–0.5 s range \citealt{zavlin00}; \citealt*{ghs05,gotthelf09}) )."258 If iis indeed a magnetar. it must have been slowed down by some unusual mechanisms. perhaps by a propeller interaction. with a debris disk (DeLucaetal.2006:Li 2007)..," If is indeed a magnetar, it must have been slowed down by some unusual mechanisms, perhaps by a propeller interaction with a debris disk \citep{deluca06,li07}. ."259 A different possibility is that, A different possibility is that260total observing time on each source was 7 hr.,total observing time on each source was 7 hr.261 The observations emploved nodding-stvle phase referencing with a evele time of 3.5 minutes., The observations employed nodding-style phase referencing with a cycle time of 3.5 minutes.262 The phase calibrators of J1053—0016. J1235—00023. and J09132-5919. were J1048+0055. J1232—0224 . and J0921-4-6215. respectively.," The phase calibrators of $-$ 0016, $-$ 0003, and $+$ 5919, were $+$ 0055, $-$ 0224, and $+$ 6215, respectively."263 Phase-referencing observations allow the determination of (he absolute position of (he target source and its components. if anv. from the position of the calibrator (Walker1999).," Phase-referencing observations allow the determination of the absolute position of the target source and its components, if any, from the position of the calibrator \citep {WAL99}."264. In applving the phase-referencing technique. the accuracy. of the calibrator position is important.," In applying the phase-referencing technique, the accuracy of the calibrator position is important."265 The positions of our phase-reference sources are obtained [from the VLBA Calibrator Survey 2002).. ancl are accurate to about 1 mas.," The positions of our phase-reference sources are obtained from the VLBA Calibrator Survey \citep{BEA02}, and are accurate to about 1 mas."266 Two adjacent 8 MIIz baseband channel pairs were used in the observations of each source. both with right and left-hand circular polarizations. saapled al (wo bits.," Two adjacent 8 MHz baseband channel pairs were used in the observations of each source, both with right and left-hand circular polarizations, sampled at two bits."267 The data were correlated at the VLBA correlator in Socorro. NM. with 2 s correlator integration time.," The data were correlated at the VLBA correlator in Socorro, NM, with 2 s correlator integration time."268 Data reduction and analvsis were performed using NRAO's Astronomical Image Processing System (AIPS)., Data reduction and analysis were performed using NRAO's Astronomical Image Processing System (AIPS).269 After applvingpriori flageing. amplitude calibration was performed using measurements of (he antenna gain and the svstem temperature of each station.," After applying flagging, amplitude calibration was performed using measurements of the antenna gain and the system temperature of each station."270" lonospheric corrections were applied using the AIPS task ""TECOR"".", Ionospheric corrections were applied using the AIPS task “TECOR”.271 The phase calibrators were sell-calibrated in both phase and amplitude. ancl imaged in an iterative cvcle.," The phase calibrators were self-calibrated in both phase and amplitude, and imaged in an iterative cycle."272 The sell-calibration solutions of the phase calibrators were applied to the respective target sources., The self-calibration solutions of the phase calibrators were applied to the respective target sources.273 To further improve the signal-to-noise ratio of the images. we sell calibrated the target sources themselves.," To further improve the signal-to-noise ratio of the images, we self calibrated the target sources themselves."274 Figures 1. 2. and 3. are the VLBA images of J1053—0016. J1235—0003.. and," Figures 1, 2, and 3, are the VLBA images of $-$ 0016, $-$ 0003, and"275deeply embedded: sources.,deeply embedded sources.276 Some weak continuum. emission mav also be associated with AGL 437N. Commez et al. (, Some weak continuum emission may also be associated with AFGL 437N. Gómmez et al. (2771992) suggested. an interpretation for the molecular outllow in terms of motions of gas along the wall of a cavity opened in the molecular cloud by the massive stars in the cluster.,1992) suggested an interpretation for the molecular outflow in terms of motions of gas along the wall of a cavity opened in the molecular cloud by the massive stars in the cluster.278 With this anisotropic distribution of molecular gas. even if the stellar winds are isotropic. the outllow. could appear as bipolar. ancl of low collimation. to the observer.," With this anisotropic distribution of molecular gas, even if the stellar winds are isotropic, the outflow could appear as bipolar, and of low collimation, to the observer."279" Our NIL; observations were specifically designed to test whether this ""alternative"" interpretation for the outflow is valid. or this is a more “classical” bipolar outllow. where there is intrinsic collimation in the mass-Ioss process. probably driven. by source. WIx 34."," Our $_3$ observations were specifically designed to test whether this “alternative” interpretation for the outflow is valid, or this is a more “classical” bipolar outflow, where there is intrinsic collimation in the mass-loss process, probably driven by source WK 34."280 There are several kev, There are several key281Despite decades: of study. type la supernovac (Ρα) continue to be an active topic for astrophysical research.,"Despite decades of study, type Ia supernovae (SNIa) continue to be an active topic for astrophysical research."282 The aceepted physical mechanism. for these events. that hey are the result of thermonuclear explosions of degenerate material (Llovle Fowler 1960) in white cwarl stars. is very well established but owing to the considerable complexity of his process many aspects of these spectacular events remain »oorIv. understood.," The accepted physical mechanism for these events, that they are the result of thermonuclear explosions of degenerate material (Hoyle Fowler 1960) in white dwarf stars, is very well established but owing to the considerable complexity of this process many aspects of these spectacular events remain poorly understood."283 Observationallv. it is clear that all SNla are not the sanie there ijs. significant diversity. in. both brightness and decay timescale (Phillips 1993).," Observationally, it is clear that all SNIa are not the same – there is significant diversity in both brightness and decay timescale (Phillips 1993)."284 Aside from its cirect relevance to the study of SNla themselves. understanding this diversity has important implications to other branches ofastrophysics in particular to cosmology where inferences about the properties of distant. SNla play an importan role in probing the rate of expansion of the Universe.," Aside from its direct relevance to the study of SNIa themselves, understanding this diversity has important implications to other branches of astrophysics – in particular to cosmology where inferences about the properties of distant SNIa play an important role in probing the rate of expansion of the Universe."285 Some correlations between supernova properties are alreacky wel established from observations of nearby SNla (e.g.In hillips 1993)., Some correlations between supernova properties are already well established from observations of nearby SNIa (e.g. Phillips 1993).286 Llowever. it. is becoming clear that the observec diversity is not adequately. described by a single parameter ( Denettiet al.," However, it is becoming clear that the observed diversity is not adequately described by a single parameter (Benetti et al."287 2004. 2005r) and that unraveling this diversity relies on a combination of careful observational study are sophisticated theoretical modelling.," 2004, 2005) and that unraveling this diversity relies on a combination of careful observational study and sophisticated theoretical modelling."288 In recent vears. there has been rapid development in the sophistication of numerical modelling of the hydrodynamics of SNla explosions.," In recent years, there has been rapid development in the sophistication of numerical modelling of the hydrodynamics of SNIa explosions."289 In. particular. while in earlier. work supernovae explosions were modelled. using first (1D) computer codes (c.g. Nomoto. Phiclemann Yokoi 1984: Hófllich. Wheeler Thielemann 1998) and later two-dimensions (e.g. Mülller Arnett 1986: Niemever. Millebrandt. Woosley 1996). the most up-o-clate simulations ave fully three-dimensional (3D. e.g. Reinecke. Hillebrancdt Niemever 2002: CGamezo οἱ al.," In particular, while in earlier work supernovae explosions were modelled using first (1D) computer codes (e.g. Nomoto, Thielemann Yokoi 1984; Höfflich, Wheeler Thielemann 1998) and later two-dimensions (e.g. Mülller Arnett 1986; Niemeyer, Hillebrandt, Woosley 1996), the most up-to-date simulations are fully three-dimensional (3D, e.g. Reinecke, Hillebrandt Niemeyer 2002; Gamezo et al."290 2003: ltóppke 2005:r ltóppke et al., 2003; Röppke 2005; Röppke et al.291 2006)., 2006).292 Vhese multi-dimensional models. are crucial for the understanding of realistic flame propagation and hence nucleosvnthesis in. SNla explosions and have clearly cleomonstrated that the earliest D models greatly unclerestimate the likely complexity of real SNla., These multi-dimensional models are crucial for the understanding of realistic flame propagation and hence nucleosynthesis in SNIa explosions and have clearly demonstrated that the earliest 1D models greatly underestimate the likely complexity of real SNIa.293 This naturally. raises the question of whether and to what exten this multi-dimensional complexity may be responsible for the observed diversity of explosions., This naturally raises the question of whether and to what extent this multi-dimensional complexity may be responsible for the observed diversity of explosions.294 ‘To connect hvdrodynamical explosion. models anc observations of real SNla light curves or spectra requires modelling of radiation. transport in the supernova., To connect hydrodynamical explosion models and observations of real SNIa light curves or spectra requires modelling of radiation transport in the supernova.295 The majority of the light escaping from a supernova explosion a around optical maximum originates from energy. depositec in the ejecta by the absorption and Compton scattering of 5-ravs emitted. by radioactive isotopes., The majority of the light escaping from a supernova explosion at around optical maximum originates from energy deposited in the ejecta by the absorption and Compton scattering of $\gamma$ -rays emitted by radioactive isotopes.296 Given that al SNla explosion. models are significantly optically thick a the earliest times (Cl dav). the emission. transport ane deposition of radiation need only be followed for times after most of the complex dynamics have ceased and the ejecta is in near-homologous expansion: this greatly simplifies the radiation transport calculation and allows it to be decoupled from the hvdrodynamical simulation.," Given that all SNIa explosion models are significantly optically thick at the earliest times $\leq2971$ day), the emission, transport and deposition of radiation need only be followed for times after most of the complex dynamics have ceased and the ejecta is in near-homologous expansion; this greatly simplifies the radiation transport calculation and allows it to be decoupled from the hydrodynamical simulation."298 The level of sophistication of modern radiation, The level of sophistication of modern radiation299Irwin. Athev. and. Bregman (2003) found that the integrated. emission from low-mass N-rav binaries (which dominate the point source emission over most of (he region in our analvsis) has a universal spectrum (hat can be fit with a power-law distribution with a slope ID=1.56.,"Irwin, Athey, and Bregman (2003) found that the integrated emission from low-mass X-ray binaries (which dominate the point source emission over most of the region in our analysis) has a universal spectrum that can be fit with a power-law distribution with a slope $\Gamma = 1.56$."300 Using this slope and accounting lor absorption. we find that each unit of 2-6 keV emission corresponds to 1.7 units of 0.6-2 keV emission.," Using this slope and accounting for absorption, we find that each unit of 2-6 keV emission corresponds to 1.7 units of 0.6-2 keV emission."301 We scaled the 2-6 keV galactic emission bv a [actor of 1.7 and subtracted this from the 0.6-2 keV emission to remove the point source contribution., We scaled the 2-6 keV galactic emission by a factor of 1.7 and subtracted this from the 0.6-2 keV emission to remove the point source contribution.302 We stopped the unresolved point source removal alter reaching the average background. 2-6 keV surface brightness for each observation: this occurred. at 32 kpe lor observation 10528. 30 kpe lor observation 10529. and 25 kpe lor observation 10531 (observation 10530 has the galaxy 50 kpe off the edge of the detector. so there is no contribution [rom ealactic point sources.," We stopped the unresolved point source removal after reaching the average background 2-6 keV surface brightness for each observation; this occurred at 32 kpc for observation 10528, 30 kpc for observation 10529, and 25 kpc for observation 10531 (observation 10530 has the galaxy 50 kpc off the edge of the detector, so there is no contribution from galactic point sources."303 The total amount of emission due to unresolved point sources was z1.5x10 eres I. about. of the total emission.," The total amount of emission due to unresolved point sources was $\approx 1.5 \times 10^{40}$ erg $^{-1}$, about of the total emission."304 We attempted to verily Chis result by assuming the six point sources detected. with WAVDETECT represent a complete sample down to 3x10 erg !., We attempted to verify this result by assuming the six point sources detected with WAVDETECT represent a complete sample down to $3\times10^{38}$ erg $^{-1}$.305 Using the point source number counts of Nim et al. (, Using the point source number counts of Kim et al. (3062007). we expect 0.6 background. point sources above our [lux limit in (he (50 arcsecond radius) aperture. so one of (hese six sources is likely actually an unrelated background object (and one is the central low-luninositvw AGN).,"2007), we expect 0.6 background point sources above our flux limit in the (50 arcsecond radius) aperture, so one of these six sources is likely actually an unrelated background object (and one is the central low-luminosity AGN)."307 We applied (he luminosity function of Grimm. Gilfanov. and Sunvaev (2002). which was calibrated using Galactic LAINBs and HAINBs. to the five non-nuclear point sources.," We applied the luminosity function of Grimm, Gilfanov, and Sunyaev (2002), which was calibrated using Galactic LMXBs and HMXBs, to the five non-nuclear point sources."308 We adopted a power-law function for V(>L) with a slope of a=—0.3., We adopted a power-law function for $N(>L)$ with a slope of $\alpha = -0.3$.309" The ratio of the totalhuninosity (with a lower-Iuminosity cut-off at 10 erg | to the luminosity above 3x107 eres tis 5.0. and the total 0.6-2 keV luminosity of our five point sources is 7.0xLO"" ere 1to κο we expect a point source luminosity of 3.5x107"" erg +."," The ratio of the totalluminosity (with a lower-luminosity cut-off at $10^{36}$ erg $^{-1}$ to the luminosity above $3\times10^{38}$ erg $^{-1}$ is 5.0, and the total 0.6-2 keV luminosity of our five point sources is $7.0 \times10^{39}$ erg $^{-1}$, so we expect a point source luminosity of $3.5\times10^{40}$ erg $^{-1}$."310 This figure is about twice as high as the point source Iuminositw we inler from (he 2-6 keV [Iux. although the likely presence of a backeround point source is probably causing us to overestimate (he background using this method.," This figure is about twice as high as the point source luminosity we infer from the 2-6 keV flux, although the likely presence of a background point source is probably causing us to overestimate the background using this method."311 If we assume (hat all [ive detected non-nuclear point sources within 50 areseconds (13 kpc) are associated with the galaxy. then our method of scaling [rom the hish-energy emission corresponds (o a flat power-law slope of a=—0.15 lor .N€»L).," If we assume that all five detected non-nuclear point sources within 50 arcseconds (13 kpc) are associated with the galaxy, then our method of scaling from the high-energy emission corresponds to a flat power-law slope of $\alpha = -0.15$ for $N(>L)$."312 This slope is l.4o away from (he best-fit slope to the LAINB luminosity fiction in Grimm. Gillanov. and Sunyvaev (2002).," This slope is $1.4\sigma$ away from the best-fit slope to the LMXB luminosity function in Grimm, Gilfanov, and Sunyaev (2002)."313 It does seem more likely lor NGC 1961 to have a different point source Iuminositv. function than the Milky Way instead of a different X-ray. spectrum lor its point sources., It does seem more likely for NGC 1961 to have a different point source luminosity function than the Milky Way instead of a different X-ray spectrum for its point sources.314 Supporting this result. a flattening of the point source luminosity function below a [ew x10? erg | is also observed in Centaurus À (Voss et al.," Supporting this result, a flattening of the point source luminosity function below a few $\times 10^{37}$ erg $^{-1}$ is also observed in Centaurus A (Voss et al."315 2009)., 2009).316 We also included a correction for X-ray. emission [rom stars ab a level fainter then 107 erg Ll., We also included a correction for X-ray emission from stars at a level fainter then $10^{36}$ erg $^{-1}$ .317 This emission seems to scale with total stellar mass (nferred. [rom the K-band, This emission seems to scale with total stellar mass (inferred from the K-band318theta) where & is the deflection angle. simply the dillerence between the angular position of the source and image.,") where $\vec\alpha$ is the deflection angle, simply the difference between the angular position of the source and image."319 The simplest. geometric lens we consider is a triaxial Gaussian electron density cistribution., The simplest geometric lens we consider is a triaxial Gaussian electron density distribution.320 This is an extension of 7.. where we consider the limit that the axis ratios are very lavge. corresponding to thin sheets.," This is an extension of \citet{1987Natur.328..324R}, where we consider the limit that the axis ratios are very large, corresponding to thin sheets."321 Phe Romani et al picture was further quantified by 2.., The Romani et al picture was further quantified by \cite{1998ApJ...496..253C}.322 Phe main qualitative difference in our new analysis is to consider the convergent case. which solves several key problems.," The main qualitative difference in our new analysis is to consider the convergent case, which solves several key problems."323 μα projection. sheets are. highly elongated. two dimensional Gaussian surface densities.," In projection, sheets are highly elongated two dimensional Gaussian surface densities."324 The lensing physics is thus two-dimensional with £ chosen to be aligned with the short axis. with the deflection potential c (the projection of the 3-D Newtonian potential) given by: where the gradient of the potential. Vàoc. gives the dellection angle.," The lensing physics is thus two-dimensional with $\xi$ chosen to be aligned with the short axis, with the deflection potential $\psi$ (the projection of the 3-D Newtonian potential) given by: _0, where the gradient of the potential, $\nabla_{\theta}\,\psi$, gives the deflection angle."325 For a convergent lens. my«0.," For a convergent lens, $\kappa_0<0$."326" The phase velocity and group velocity of radio waves in a plasma are and where with electron number density n. electron. charge and mass e and m, respectively. and eo being the permittivity of [ree space."," The phase velocity and group velocity of radio waves in a plasma are and where with electron number density $n_{e}$, electron charge and mass $e$ and $m_{e}$ respectively, and $\epsilon_{0}$ being the permittivity of free space."327" Note that eine,=c.", Note that $c_{\rm ph}c_{\rm g}=c^2$.328 In the ISM. typical plasma [requencies are kilohertz. so the frequencies of relevance are much larger than the plasma frequency. a>oy.," In the ISM, typical plasma frequencies are kilohertz, so the frequencies of relevance are much larger than the plasma frequency, $\omega\gg\omega_{\rm p}$."329 The ellective refractive index of the plasma and. the potential are related through n=1.2/02=efeyn. and thus the intrinsic component of path (or phase) delay. due to passage through the plasma is frequency-dependent ezu= dz.," The effective refractive index of the plasma and the potential are related through $n =1-2\Phi/c^2 = c/c_{\rm ph}$, and thus the intrinsic component of path (or phase) delay, due to passage through the plasma is frequency-dependent $c \,\tau_{\rm grav}=\int \left(n(\omega)-1\right)\,{\rm d}z$ ."330 This refractive delay is the analogy to the eravitational Shapiro clelay., This refractive delay is the analogy to the gravitational Shapiro delay.331 In the limit a>>ων. omπα der.," In the limit $\omega\gg \omega_{\rm p}$, $\Phi\approx \omega_{\rm p}^2c^2/4\omega^2$ ."332 We use the notation of gravitational lensing. mapping the time delay as the projected potential ," We use the notation of gravitational lensing, mapping the time delay as the projected potential = ]."333where the first term accounts for the geometrical delay due to the olfset in source and iniage positions., where the first term accounts for the geometrical delay due to the offset in source and image positions.334 Two possibilities exist: electron overdensities result in à faster phase velocity. corresponding to a concave (divergent) optical lens.," Two possibilities exist: electron overdensities result in a faster phase velocity, corresponding to a concave (divergent) optical lens."335 TFhis case was considered by 2.. which results in Jj sets of caustics. which are not consistent with the observed properties of IESEs.," This case was considered by \cite{1987Natur.328..324R}, which results in 4 sets of caustics, which are not consistent with the observed properties of ESEs."336 At the center of one of these events. only one image exists. with [lux x1/A7. while observed events have only order unity [ux reduction.," At the center of one of these events, only one image exists, with flux $\propto 1/\lambda^2$, while observed events have only order unity flux reduction."337 Physically. electron overdensities can also lead to cooling instabilities. and. are difficult to pressure confine.," Physically, electron overdensities can also lead to cooling instabilities, and are difficult to pressure confine."338 Electron underdensities are convergent. lenses., Electron underdensities are convergent lenses.339 These are generic consequences of heating processes. for example magnetic reconnection events.," These are generic consequences of heating processes, for example magnetic reconnection events."340 At the centre of these lenses. as we will demonstrate. three images can be seen: a faint central image and two brighter ones on each side of the lens.," At the centre of these lenses, as we will demonstrate, three images can be seen: a faint central image and two brighter ones on each side of the lens."341 The convergence of the lens is related to the Laplacian of the dellection potential. Le. &=07/2 and the components of the shear for a sheet with the short axis on the plane of the sky are 54= 8.52=0.," The convergence of the lens is related to the laplacian of the deflection potential, i.e. $\kappa=\psi''/2$ and the components of the shear for a sheet with the short axis on the plane of the sky are $\gamma_{1}=\kappa$, $\gamma_{2}=0$."342 Thus the magnification sp=l/(l 25) , Thus the magnification $\mu=1/(1-2\kappa)$ .343The convergence is à dimensionless measure of the distance to the lens in units of its focal lens., The convergence is a dimensionless measure of the distance to the lens in units of its focal lens.344 When the convergence is small. the lensing is weak. and only one image is formed.," When the convergence is small, the lensing is weak, and only one image is formed."345 The eritical points in the lens plane occur when 1/j/= 0.The previous treatment by 2 neglected the fact that the source plane position and the lensplane positions cilfer.," The critical points in the lens plane occur when $1/\mu=0$ .The previous treatment by \cite{1986ApJ...310..737C} neglected the fact that the source plane position and the lensplane positions differ,"346Eulerian hydrodynamics simulations.,Eulerian hydrodynamics simulations.347" They found that significant quantities of hydrogen would be unbound from the companion star in each case of the envelope for main-sequence and subgiant cases,(15% and of the red giant envelope), in conflict with observational upper limits on the amount of hydrogen inferred from SN Ia spectra (??).."," They found that significant quantities of hydrogen would be unbound from the companion star in each case of the envelope for main-sequence and subgiant cases, and of the red giant envelope), in conflict with observational upper limits on the amount of hydrogen inferred from SN Ia spectra \citep{Mattila:2005p1442,Leonard:2007p102}."348 A more recent hydrodynamical study by ? reexamined the main-sequence simulation of ? using a three-dimensional smoothed particle hydrodynamics (SPH) simulation., A more recent hydrodynamical study by \cite{Pakmor:2008p139} reexamined the main-sequence simulation of \cite{Marietta:2000p112} using a three-dimensional smoothed particle hydrodynamics (SPH) simulation.349" In contrast to Marietta et al,"," In contrast to Marietta et al.,"350" Pakmor et aadopted the structure for the companion star based on the binary evolutionary models of ?,, which yielded more compact main-sequence-like companions."," Pakmor et adopted the structure for the companion star based on the binary evolutionary models of \cite{Ivanova:2004p123}, which yielded more compact main-sequence-like companions."351" As a consequence, Pakmor et ffound a tenfold reduction in the amount of unbound mass compared with Marietta et al.,"," As a consequence, Pakmor et found a tenfold reduction in the amount of unbound mass compared with Marietta et al.,"352 bringing the prediction of the amount of unbound hydrogen-rich material into agreement with the observational upper limits., bringing the prediction of the amount of unbound hydrogen-rich material into agreement with the observational upper limits.353" In à complementary analytical study, ? investigated the radiation emitted by the collision of SN Ia ejecta with a red giant, finding that the light curve should depend on the viewing angle."," In a complementary analytical study, \cite{Kasen:2009p2965} investigated the radiation emitted by the collision of SN Ia ejecta with a red giant, finding that the light curve should depend on the viewing angle."354 This result was attributed to the fact that the gas is more transparent in the region shadowed by the companion star., This result was attributed to the fact that the gas is more transparent in the region shadowed by the companion star.355 This suggests the possibility that the secondary star may be detectable in future observational studies., This suggests the possibility that the secondary star may be detectable in future observational studies.356" 'These previous simulations of the effect of a supernova impact on a companion star have been carried out only for models applicable to the long-delay-time population of SN Ia. In contrast, ?? suggest a progenitor binary model based upon a helium-star channel for the short-delay-time population."," These previous simulations of the effect of a supernova impact on a companion star have been carried out only for models applicable to the long-delay-time population of SN Ia. In contrast, \cite{Wang:2009p3601, Wang:2009p3585} suggest a progenitor binary model based upon a helium-star channel for the short-delay-time population."357" Using a binary evolution model, for this channel they find a SN Ia birthrate 1074 yr-! and a corresponding delay time of ~4.5107 yr to ~1.4x105 yr (?).."," Using a binary evolution model, for this channel they find a SN Ia birthrate $\sim 3 \times 10^{-4}$ $^{-1}$ and a corresponding delay time of $\sim 4.5 \times 10^7$ yr to $\sim 1.4 \times 10^8$ yr \citep{Wang:2009p3598}. ."358" The latter delay time is consistent with that estimated from observations for the short-delay-time population by ?,, ?,, and ?.."," The latter delay time is consistent with that estimated from observations for the short-delay-time population by \cite{Scannapieco:2005p2469}, \cite{Mannucci:2006p2431}, and \cite{Aubourg:2008p2503}."359 In this paper we report the results of Eulerian hydrodynamics simulations of the impact of SN Ia ejecta on companion stars for the single-degenerate helium-star channel., In this paper we report the results of Eulerian hydrodynamics simulations of the impact of SN Ia ejecta on companion stars for the single-degenerate helium-star channel.360" In the next section, the assumptions underlying our study, the construction of the initial model, and the numerical method are described."," In the next section, the assumptions underlying our study, the construction of the initial model, and the numerical method are described."361 Our numerical results for a range of helium-star models and orbital separations are reported in 3 and their implications are discussed in 4., Our numerical results for a range of helium-star models and orbital separations are reported in 3 and their implications are discussed in 4.362" In the final section, we summarize our results and make some concluding remarks."," In the final section, we summarize our results and make some concluding remarks."363 For our hydrodynamical simulations we used FLASH version 3 (??)..," For our hydrodynamical simulations we used FLASH version 3 \citep{Fryxell:2000p109,dubey_introduction_2008}."364" FLASH is a parallel, multi-dimensional hydrodynamics code based on block-structured adaptive mesh refinement (AMR)."," FLASH is a parallel, multi-dimensional hydrodynamics code based on block-structured adaptive mesh refinement (AMR)."365" To solve the Euler equations on the AMR grid, we used the piecewise parabolic method (?) with modifications to handle nonideal equations of state "," To solve the Euler equations on the AMR grid, we used the piecewise parabolic method \citep{Colella:1984p25} with modifications to handle nonideal equations of state \citep{Colella:1985p66}."366The equation of state used is interpolated from a precomputed(?).. table of the Helmholtz free energy., The equation of state used is interpolated from a precomputed table of the Helmholtz free energy.367" It includes contributions from radiation, completely ionized nuclei, and degenerate electrons and positrons (?) for an optically thick mixture of gas and radiation in local thermodynamic equilibrium."," It includes contributions from radiation, completely ionized nuclei, and degenerate electrons and positrons \citep{Timmes:2000p1} for an optically thick mixture of gas and radiation in local thermodynamic equilibrium."368 'The helium-star models used in our simulations were generated using a one-dimensional stellar evolution code (???).," The helium-star models used in our simulations were generated using a one-dimensional stellar evolution code \citep{Eggleton:1971p89,Eggleton:1972p114,Eggleton:1973p3453}."369" We simulated four helium-star models with initial masses equal to 1.25, 1.35, 1.4, and 1.8Mo."," We simulated four helium-star models with initial masses equal to 1.25, 1.35, 1.4, and $1.8\ M_\sun$."370" To evolve the helium-star models to the onset of the supernova explosion, an artificial constant mass loss rate was adopted such that the evolution time and final helium star masses were consistent with the detailed binary evolutionary models of ?.."," To evolve the helium-star models to the onset of the supernova explosion, an artificial constant mass loss rate was adopted such that the evolution time and final helium star masses were consistent with the detailed binary evolutionary models of \cite{Wang:2009p3585}. ."371 The resulting models are summarized in Table [I]., The resulting models are summarized in Table \ref{tab1}.372 The density profiles of the helium-star models at the onset of the supernova explosion are illustrated in Figure [I]. , The density profiles of the helium-star models at the onset of the supernova explosion are illustrated in Figure \ref{dens}. .373It can be seen that the more massive models are characterized by larger radii and less compact cores., It can be seen that the more massive models are characterized by larger radii and less compact cores.374" Since the speed of the ejecta in a SN Ia (S104 km s!) is much higher than the orbital speed of the helium star (<10? km s-1) in a binary system, we ignore the orbital motion in the first approximation and consider a 2D axisymmetric geometry."," Since the speed of the ejecta in a SN Ia $\lesssim 10^4$ km $^{-1}$ ) is much higher than the orbital speed of the helium star $\lesssim 10^3$ km $^{-1}$ ) in a binary system, we ignore the orbital motion in the first approximation and consider a 2D axisymmetric geometry."375" The simulation domain is described using cylindrical coordinates (r, z), with the z- defined as the direction along the line connecting the centers of the white dwarf and the helium star."," The simulation domain is described using cylindrical coordinates $r, z$ ), with the $z$ -axis defined as the direction along the line connecting the centers of the white dwarf and the helium star."376 We consider a simulation domain with a size equal to fifteen times the radius of the helium star (Ege) in the radial direction and 30Rye in the axial direction., We consider a simulation domain with a size equal to fifteen times the radius of the helium star $R_{\rm He}$ ) in the radial direction and $30\ R_{\rm He}$ in the axial direction.377" For convenience, the helium star is located at the origin of the coordinate grid."," For convenience, the helium star is located at the origin of the coordinate grid."378" 'To simplify the problem, the composition of the one-dimensional helium-star model was taken to be a uniform distribution of 98% helium and 2% carbon by mass when used in FLASH."," To simplify the problem, the composition of the one-dimensional helium-star model was taken to be a uniform distribution of $98\%$ helium and $2\%$ carbon by mass when used in FLASH."379 This simplification leads to an error of S in the composition and < in the radius for the lowest-mass helium-star model., This simplification leads to an error of $\lesssim$ in the composition and $\lesssim$ in the radius for the lowest-mass helium-star model.380" To initialize the two-dimensional FLASH simulations, we first interpolated the one-dimensional model onto the FLASHgrid using up to twelve levels of refinement based on the magnitudes of the secondderivatives of gas density and pressure."," To initialize the two-dimensional FLASH simulations, we first interpolated the one-dimensional model onto the FLASHgrid using up to twelve levels of refinement based on the magnitudes of the secondderivatives of gas density and pressure."381" With eachblock containing 8x16 zones, the equivalent uniform-grid resolution is thus 16,384x 32,768."," With eachblock containing $8\times 16$ zones, the equivalent uniform-grid resolution is thus $16,384 \times 32,768$ ."382" For model He-WDc, the minimum zone spacing at this level"," For model He-WDc, the minimum zone spacing at this level"383might be considered biased star formation with a high-mass IME.,might be considered biased star formation with a high-mass IMF.384 Clusters of galaxies were used in this study because they represent à closed box” piece of (he universe.," Clusters of galaxies were used in this study because they represent a ""closed box"" piece of the universe."385 The situation in clusters is likely to be representative of (he universe as a whole. in which case. most of the heavy. elements in (he universe were produced outside of galaxies bv an early population of supernovae.," The situation in clusters is likely to be representative of the universe as a whole, in which case, most of the heavy elements in the universe were produced outside of galaxies by an early population of supernovae."386 If. correct. this represents a fundamental change in our understanding for the origin of the elements.," If correct, this represents a fundamental change in our understanding for the origin of the elements."387 This moderately enriched material (0.1-0.4 solar) would fall into galaxies. producing a disk with lew low-metallicity stars (à previously proposed solution to the G-cwarl problem).," This moderately enriched material (0.1-0.4 solar) would fall into galaxies, producing a disk with few low-metallicity stars (a previously proposed solution to the G-dwarf problem)."388 The increase of the metallicity within galaxies is of course due (o star formation. mass loss ancl supernovae within the galaxy.," The increase of the metallicity within galaxies is of course due to star formation, mass loss and supernovae within the galaxy."389 In addition to the above issues. some additional evidence supports our model.," In addition to the above issues, some additional evidence supports our model."390 analvzed cluster metallicity profiles from z= 0.14 to z = 0.89 and from the lack of evolution. they conclude that the metallicity distribution was established at high redshift.," \citet{ehle09} analyzed cluster metallicity profiles from z = 0.14 to z = 0.89 and from the lack of evolution, they conclude that the metallicity distribution was established at high redshift."391 David&Nilsen(2008) note that Fe is more extended than the light of stars. which could imply Chat the galaxies ancl (he metals are not closely coupled (Lhev suggest an alternative model where AGN heating is responsible).," \citet{david08} note that Fe is more extended than the light of stars, which could imply that the galaxies and the metals are not closely coupled (they suggest an alternative model where AGN heating is responsible)."392 Sommer-Larsen&Fynbo(2003) find that αἱ z~ 3. less than of the oxveen is associated with galaxies. which is also consistent wilh most of the metals being produced outside of galaxies.," \citet {somm08} find that at z $\sim$ 3, less than of the oxygen is associated with galaxies, which is also consistent with most of the metals being produced outside of galaxies."393 If there was a predominantly high-mass population of stars outside ealaxies. (he initial mass function of these stars could be constrained by the ICL. provided one could separate the ICL trom galaxv-galaxy interactions with that from the high-mass stars.," If there was a predominantly high-mass population of stars outside galaxies, the initial mass function of these stars could be constrained by the ICL, provided one could separate the ICL from galaxy-galaxy interactions with that from the high-mass stars."394 The present values of the ICL must provide a limit to the slope of that IME. but future work may be able to constrain it more directly.," The present values of the ICL must provide a limit to the slope of that IMF, but future work may be able to constrain it more directly."395 Another constraint on the nature of the metal production has been (he variation of the elemental ratios with radius (Dupke&White2000:Daungartneretal.2005;Rasmussen&Ponman 2009).," Another constraint on the nature of the metal production has been the variation of the elemental ratios with radius \citep{dupke00,baum05,rasm09}."396. In groups. the Si/EFe ratio increases with distance awav from the central galaxy. indicating that Type Ia are less important at lareer radii (Rasmussen&Ponman2009).," In groups, the Si/Fe ratio increases with distance away from the central galaxy, indicating that Type Ia are less important at larger radii \citep{rasm09}."397. There is significant room for improvement in these twpes of studies. bv using more elements. aud especially lor the hot clusters.," There is significant room for improvement in these types of studies, by using more elements, and especially for the hot clusters."398 In obtaining this result. only a dozen clusters were used. a shortcoming that can be rectified in fiture work.," In obtaining this result, only a dozen clusters were used, a shortcoming that can be rectified in future work."399" Rich clusters are. well-represented and the number of such objects can be increased. with straightforward archival work of X-ray data: these tend to have low values of M, ΑΕ.", Rich clusters are well-represented and the number of such objects can be increased with straightforward archival work of X-ray data; these tend to have low values of $_*$ $_{bary}$.400 The greater weakness is (he number of galaxy clusters with high values of AL. /Mp;4., The greater weakness is the number of galaxy clusters with high values of $_*$ $_{bary}$.401 These tend to be of lower mass. relatively gas-poor and cooler systems. so the emission is weaker. making metallicity determinations from X-ray data more challenging.," These tend to be of lower mass, relatively gas-poor and cooler systems, so the X-ray emission is weaker, making metallicity determinations from X-ray data more challenging."402 Additional X-ray data will be needed to make progress here., Additional X-ray data will be needed to make progress here.403" Finally. more accurate values of AL, can be determined with deep imagine. as tvpically only (vo dozen galaxies define L, in a cluster."," Finally, more accurate values of $_*$ can be determined with deep imaging, as typically only two dozen galaxies define $_*$ in a cluster."404 While these are the the brightest galaxies. (he fainter end of the luminosity [function," While these are the the brightest galaxies, the fainter end of the luminosity function"405"boundary of the foreground galaxy region was then defined by the points within the same density level / (e.g., 1= 0.2).","boundary of the foreground galaxy region was then defined by the points within the same density level $l$ (e.g., $l=0.2$ )."406" Such region was converted to a polygon using the package in R, that also allows to select for a given catalog those sources whose colors lie inside or outside the polygon."," Such region was converted to a polygon using the package in R, that also allows to select for a given catalog those sources whose colors lie inside or outside the polygon."407" A comparison with the model colors obtained in ZEBRA from the convolution of the spectral templates with filter transmission curves, shows that colors inside the area selected in such way are consistent with those expected for galaxies at redshift « 0.2."," A comparison with the model colors obtained in ZEBRA from the convolution of the spectral templates with filter transmission curves, shows that colors inside the area selected in such way are consistent with those expected for galaxies at redshift $<$ 0.2."408 Galaxies classified as foreground in such way were therefore excluded from the weak lensing analysis., Galaxies classified as foreground in such way were therefore excluded from the weak lensing analysis.409" We finally used photometric redshifts (d), both for the selection of background galaxies, defined as those with 21«R<26 mag, 0.3<zy,3, and to compute the average value of B: we obtain in such way f(z,)=0.74, in good agreement with the value obtained from the COSMOS catalog with the same magnitude and redshift selection, B(z,)=0.73."," We finally used photometric redshifts ), both for the selection of background galaxies, defined as those with $21 < R < 26$ mag, $0.3 < z_{\rm ph} < 3$, and to compute the average value of $\beta$: we obtain in such way $\beta(z_s) = 0.74$, in good agreement with the value obtained from the COSMOS catalog with the same magnitude and redshift selection, $\beta(z_s)=0.73$."410" The effect of the different selections on the residual presence of cluster galaxies is displayed in Fig. 11,,"," The effect of the different selections on the residual presence of cluster galaxies is displayed in Fig. \ref{fig:rdens},"411" showing the density of background galaxies computed in different annuli around the cluster: a clear increase of the density in the inner regions is visible in casea, which indicates that magnitude selection alone does not allow to completely remove the contamination by cluster galaxies."," showing the density of background galaxies computed in different annuli around the cluster: a clear increase of the density in the inner regions is visible in case, which indicates that magnitude selection alone does not allow to completely remove the contamination by cluster galaxies."412" Such contamination is greatly reduced by color selection, and the optimal result is given by photometric redshifts, as expected."," Such contamination is greatly reduced by color selection, and the optimal result is given by photometric redshifts, as expected."413" As a further check, we also found for each method that the tangential shear signals of the rejected ’foreground/cluster’ galaxies average out."," As a further check, we also found for each method that the tangential shear signals of the rejected 'foreground/cluster' galaxies average out."414" In the following discussion, we take as reference the results from cased, which is very close to in terms of uncertainties on fitted parameters, density of background galaxies and residuals in the radial component of the shear."," In the following discussion, we take as reference the results from case, which is very close to in terms of uncertainties on fitted parameters, density of background galaxies and residuals in the radial component of the shear."415" It was pointed out in ? and ? that large-scale structures along the line of sight provide a source of uncertainty on cluster masses derived by weak lensing, which is usually ignored and increases as a larger radius (max) is used in the fitting."," It was pointed out in \citet{Hoekstra03} and \citet{Hoekstra10} that large-scale structures along the line of sight provide a source of uncertainty on cluster masses derived by weak lensing, which is usually ignored and increases as a larger radius $\theta_{\rm max}$ ) is used in the fitting."416" The uncertainty introduced by such component on the mass estimate can be ~ for a cluster with M=10M; at z~0.2, Omax=10 arcmin as in our case (see Fig."," The uncertainty introduced by such component on the mass estimate can be $\sim$ for a cluster with $M=10^{15} M_\odot$ at $z \sim 0.2$, $\theta_{\rm max} = 10$ arcmin as in our case (see Fig."417" 6 and 7 in ?)), which is comparable to the uncertainties derived in the fitting."," 6 and 7 in \citet{Hoekstra03}) ), which is comparable to the uncertainties derived in the fitting."418"The arcsecond-scale flux of Sgr A* on 95 and 96 is the same to within uncertaintiesdensity in the flux daysscale, but on day 97 the flux density of Sgr A* was ~17% higher.","The arcsecond-scale flux density of Sgr A* on days 95 and 96 is the same to within uncertainties in the flux scale, but on day 97 the flux density of Sgr A* was $\sim17$ higher."419 This brightening is accompanied by changes on VLBI scales as well., This brightening is accompanied by changes on VLBI scales as well.420" First, the SC/CD and SD/CD flux density ratios are higher on day 97 than on days 95 and 96 (Figure 2))."," First, the SC/CD and SD/CD flux density ratios are higher on day 97 than on days 95 and 96 (Figure \ref{fig-sgra-scans}) )."421" Second, there are more Hawaii-California detections during day 97, and the apparent flux densities on these baselines are on average higher than on day 96."," Second, there are more Hawaii-California detections during day 97, and the apparent flux densities on these baselines are on average higher than on day 96."422" Third, the flux densities on the SJ baseline are also larger on day 97."," Third, the flux densities on the SJ baseline are also larger on day 97."423 These differences are consistent with an episode of variability in Sgr A* during which the small-scale structure increased in flux density between days 96 and 97., These differences are consistent with an episode of variability in Sgr A* during which the small-scale structure increased in flux density between days 96 and 97.424" Though our data are better calibrated than in the previous epoch (Doelemanetal.2008), the structure of Sgr A* is poorly constrained because millimeter VLBI detections of Sgr A* remain limited in terms of baseline length and orientation."," Though our data are better calibrated than in the previous epoch \citep{doeleman2008}, the structure of Sgr A* is poorly constrained because millimeter VLBI detections of Sgr A* remain limited in terms of baseline length and orientation."425" As a result, many models can be made to fit the data: extended double sources, large rings, combinations of large- and small-scale components, etc."," As a result, many models can be made to fit the data: extended double sources, large rings, combinations of large- and small-scale components, etc."426" Nevertheless, with the caveat that this small dataset should not be it is instructive to the two classes of models overinterpreted,originally considered by investigateDoelemanetal.(2008) to fit the 1.3 mm VLBI data obtained in 2007: circular Gaussians and rings."," Nevertheless, with the caveat that this small dataset should not be overinterpreted, it is instructive to investigate the two classes of models originally considered by \citet{doeleman2008} to fit the 1.3 mm VLBI data obtained in 2007: circular Gaussians and rings."427 All of the 2007 data points could be fitted by a single Gaussian component., All of the 2007 data points could be fitted by a single Gaussian component.428" In contrast, we note a loss of ~1 Jy of correlated flux density between the connected-element (CD) and SC/SD baselines (Figure 3))."," In contrast, we note a loss of $\sim1$ Jy of correlated flux density between the connected-element (CD) and SC/SD baselines (Figure \ref{fig-corr}) )."429" In the context of Gaussian models of emission on Rs, scales, this suggests the existence of additional variable structure on scales between those probed by the SC/SD (a few hundred microarcseconds) and the CD (a few arcseconds) baselines."," In the context of Gaussian models of emission on $R_\mathrm{Sch}$ scales, this suggests the existence of additional variable structure on scales between those probed by the SC/SD (a few hundred microarcseconds) and the CD (a few arcseconds) baselines."430 We adopt this assumption to estimate the size of the inner accretion flow in Sgr A*., We adopt this assumption to estimate the size of the inner accretion flow in Sgr A*.431" Effectively, this reduces to fitting all of the VLBI data excluding the CD data points."," Effectively, this reduces to fitting all of the VLBI data excluding the CD data points."432" For the Gaussian model, the best fits imply a flux density of 2.07013 Jy and a size of 41.324 µας (FWHM; errors are 3c) on day 95 and Jy and 44.473) µας on day 96 (Figure 3 and Table 2)). 2.0701"," For the Gaussian model, the best fits imply a flux density of $2.07^{+0.14}_{-0.15}$ Jy and a size of $41.3^{+5.4}_{-4.3}~\mu$ as (FWHM; errors are $3\sigma$ ) on day 95 and $2.07^{+0.19}_{-0.19}$ Jy and $44.4^{+3.0}_{-3.0}~\mu$ as on day 96 (Figure \ref{fig-corr} and Table \ref{table-fits}) )."433"5These values are consistent with the single compact component Gaussian fit of Doelemanetal. (2008),, who estimated a flux density of 2.40.5 Jy and a size of 43*1 µας (before deconvolution of the expected interstellar 37 µας unscattered) for the 230 GHz emission."," These values are consistent with the single compact component Gaussian fit of \citet{doeleman2008}, who estimated a flux density of $2.4 \pm 0.5$ Jy and a size of $43^{+14}_{-8}~\mu$ as (before deconvolution of the expected interstellar scattering; $37~\mu$ as unscattered) for the 230 GHz emission."434" On day 97, scattering;the best fit model has a much higher flux density of 2.857022 Jy but a similar FWHM of 42.621 suas."," On day 97, the best fit model has a much higher flux density of $2.85^{+0.29}_{-0.28}$ Jy but a similar FWHM of $42.6^{+3.1}_{-2.9}~\mu$ as."435" Despite the increase in flux density observed on day 97, the diameter of the fitted component in Sgr A* on that day is identical (to within the compacterrors) to the values for the size obtained on days 95 and 96."," Despite the increase in flux density observed on day 97, the diameter of the fitted compact component in Sgr A* on that day is identical (to within the errors) to the values for the size obtained on days 95 and 96."436" Ring models with three parameters (inner radius, outer radius, and flux density) can also fit the VLBI data (Figure and Table 2))"," Ring models with three parameters (inner radius, outer radius, and flux density) can also fit the VLBI data (Figure \ref{fig-corr} and Table \ref{table-fits}) )."437" However, no single set of ring model parameters consistently fits the data on all three days, which"," However, no single set of ring model parameters consistently fits the data on all three days, which"438Thought to be driven by horizontal branch evolution. these pulsation period. changes are typically monotonic ancl of order 1 d per 0.1 GY? (Wehlauetal1992).,"Thought to be driven by horizontal branch evolution, these pulsation period changes are typically monotonic and of order 1 d per 0.1 GYr \cite{weh}."439. However there are cases in which the variation is more chaotic and on a faster timescale (Jursciketal2001).. so we must address this mechanism.," However there are cases in which the variation is more chaotic and on a faster timescale \cite{jur}, so we must address this mechanism."440 The fact that such pulsations have never been detected in the donor o£ SAIC X-1. given the high sensitivity of searches for such behaviour. leads us to stronely doubt 10 existence of pulsations at all.," The fact that such pulsations have never been detected in the donor of SMC X-1, given the high sensitivity of searches for such behaviour, leads us to strongly doubt the existence of pulsations at all."441 Furthermore. we expect companion star pulsations to produce large changes in bulk mass transfer rate from donor to accretion disk. manifesting themselves as large. changes in the magnitude. or even lirection (see. c.g: Nelson et al.," Furthermore, we expect companion star pulsations to produce large changes in bulk mass transfer rate from donor to accretion disk, manifesting themselves as large changes in the magnitude, or even direction (see, e.g: Nelson et al."442 1997) of spin of the neutron star., 1997) of spin of the neutron star.443" As noted by Wojdowski et al (1998). however. the ""hanges in neutron star spin rate are always in the same sense."," As noted by Wojdowski et al (1998), however, the changes in neutron star spin rate are always in the same sense."444 Alore gentle variation in mass transfer rate can be brought about if the ARB is part. of. an. hierarchical triple., More gentle variation in mass transfer rate can be brought about if the XRB is part of an hierarchical triple.445 The third. bods causes the inner SRB to undergo nodal precession. leading to mass transfer variations on a timescale determined. by the orbital periods of the binary and hierarchical third body (Chou&CGrindlay2001).," The third body causes the inner XRB to undergo nodal precession, leading to mass transfer variations on a timescale determined by the orbital periods of the binary and hierarchical third body \cite{chg}."446.. This mechanism could. give rise to both the superorbital period and the longer period ofits variation. with the orbit of the third bods the superorbital period and its variation period that of the nodal. precession.," This mechanism could give rise to both the superorbital period and the longer period of its variation, with the orbit of the third body the superorbital period and its variation period that of the nodal precession."447 Such a mechanism can be γιος out for SAIC Χα however. by consideration. of the orbit of the centre of mass of the inner NIB. about the system centre of mass. and the variation in pulse arrival time this would. produce.," Such a mechanism can be ruled out for SMC X-1, however, by consideration of the orbit of the centre of mass of the inner XRB about the system centre of mass, and the variation in pulse arrival time this would produce."448 Measured. discrepancies between pulse arrival delavs and those. predicted. from. a two-bocdy system amount to less than  I0ms in IUNTIE PCA data (Wojdowskictal1998)., Measured discrepancies between pulse arrival delays and those predicted from a two-body system amount to less than $\sim$ 10ms in RXTE PCA data \cite{woj}.449". To produce such a small variation in pulse arrival time. the third body would have to orbit the inner XRB with the normal vector of the orbit. pointing < 2""[rom the line of sight. for any stellar third. body."," To produce such a small variation in pulse arrival time, the third body would have to orbit the inner XRB with the normal vector of the orbit pointing $<$ from the line of sight, for any stellar third body."450 Thus a third bods scenario requires an extraordinary degree of fine-tuning to reproduce the observed results. especially when we consider that SAIC NX-1 itself is an eclipsing binary and thus would have high orbital inclination with respect to the orbit of the third body.," Thus a third body scenario requires an extraordinary degree of fine-tuning to reproduce the observed results, especially when we consider that SMC X-1 itself is an eclipsing binary and thus would have high orbital inclination with respect to the orbit of the third body."451 This leaves us with precession ofa warped accretion disk as the mechanism responsible for the superorbital period., This leaves us with precession of a warped accretion disk as the mechanism responsible for the superorbital period.452 Such systems are usually thought to have as their primary observational effect a change in absorption. which has been pulecd out for this system.," Such systems are usually thought to have as their primary observational effect a change in absorption, which has been ruled out for this system."453 What is not ruled. out. is a variation in uncovered emitting area. as suggested for Hor X-1 (Gerend Boynton 1976).," What is not ruled out is a variation in uncovered emitting area, as suggested for Her X-1 (Gerend Boynton 1976)."454 Also not ruled out is variable deposition of energy at the boundary [aver. brought on by the quasisteady nature of the precession.," Also not ruled out is variable deposition of energy at the boundary layer, brought on by the quasi-steady nature of the precession."455 This is not in conllict with the spin-up of the neutron star. as there are deviations from a purely monotonic increase. (Mojdowskietabl 19983).," This is not in conflict with the spin-up of the neutron star, as there are deviations from a purely monotonic increase \cite{woj}."456.. Indeed. if one looks at the residuals in the quadratic fit to the pulse period (Wojclowskietal1998).. the resicluals show variation of similar shape ancl timescale to the variations of the superorbital X-ray. period!," Indeed if one looks at the residuals in the quadratic fit to the pulse period \cite{woj}, the residuals show variation of similar shape and timescale to the variations of the superorbital X-ray period!"457 Lt is currently uncertain if this is à real effect or a statistically insignificant artifact., It is currently uncertain if this is a real effect or a statistically insignificant artifact.458 Η statistically significant. this would provide direct evidence linking the variation in third period to variation in accretion How onto the neutron star.," If statistically significant, this would provide direct evidence linking the variation in third period to variation in accretion flow onto the neutron star."459 There is a third wav in which a warped. precessing accretion clisk might manifest itself in the X-ray lighteurves examined here.," There is a third way in which a warped, precessing accretion disk might manifest itself in the X-ray lightcurves examined here."460 Studies of CVs have shown that local values of mass transfer in accretion disks can cramatically exceed the mass transfer rate from donor to acceptor. as shown in CW's with prominent bright spots such as LX Ser (Rutten.vanParadijs&Tinbergen 1992).," Studies of CVs have shown that local values of mass transfer in accretion disks can dramatically exceed the mass transfer rate from donor to acceptor, as shown in CV's with prominent bright spots such as LX Ser \cite{rvp}."461 In the case of SAIC X-1. the quasi-steady decrease. in spin period. noted. by Wojdowski ct al (1998) suggests that mass transfer from the donor star is also quasi-steady. either in a Roche Lobe stream or collimatec wind. allowing such a bright spot to exist.," In the case of SMC X-1, the quasi-steady decrease in spin period noted by Wojdowski et al (1998) suggests that mass transfer from the donor star is also quasi-steady, either in a Roche Lobe stream or collimated wind, allowing such a bright spot to exist."462 SAIC N-1 is expected. to have a small accretion disk given its LAINB nature. which. if warped. might allow the mass transfer stream to reach close enough to the neutron star that the resulting bright. spot. becomes. an important component in the N-rav emission of the svstem. as sugeested by Warner (2002. private communication).," SMC X-1 is expected to have a small accretion disk given its HMXB nature, which, if warped, might allow the mass transfer stream to reach close enough to the neutron star that the resulting bright spot becomes an important component in the X-ray emission of the system, as suggested by Warner (2002, private communication)."463 As he warp precesses. the intersection point moves raclially hrough the disk. thus varving the brightness ancl spectral iucdness of emission - as seen in figure 4..," As the warp precesses, the intersection point moves radially through the disk, thus varying the brightness and spectral hardness of emission - as seen in figure \ref{fig:fold_hrat}."464 Furthermore. as the mass transfer stream: would be varying its position on the precession period. the intersection point would drive he warp further.," Furthermore, as the mass transfer stream would be varying its position on the precession period, the intersection point would drive the warp further."465 Such à mechanism is deserving of further heoretical investigation., Such a mechanism is deserving of further theoretical investigation.466 The warped. precessing accretion disk has one clear advantage over the other mechanisms considered here: it can support variations in superorbital period.," The warped, precessing accretion disk has one clear advantage over the other mechanisms considered here: it can support variations in superorbital period."467 To show this. we summarise first the properties of warped accretion clisks.," To show this, we summarise first the properties of warped accretion disks."468 The hypothesis that warped. precessine accretion clisks might be responsible for superorbital periods in NRB gained acceptance through the canonical precessing disk svstcnis ller X-1. SS 433 and LMC N-4 (Petterson1977).," The hypothesis that warped, precessing accretion disks might be responsible for superorbital periods in XRB gained acceptance through the canonical precessing disk systems Her X-1, SS 433 and LMC X-4 \cite{jp}."469.. The measured. 160d. precession of the relativistic jets in 55433 have also been identified: with precession of the accretion disk. (Alargon1984)., The measured $\sim$ 160d precession of the relativistic jets in SS433 have also been identified with precession of the accretion disk \cite{mar}.470.. Vidal forces on the disk. by the companion can lead to a constant rate of precession if the disk can become tilted out of the plane (see eg: Wijers and Pringle 1999). but two issues then arise: (1) how to cause a Iluid disk to precess with uniform frequency. and (ii) how to maintain tilting out of the plane.," Tidal forces on the disk by the companion can lead to a constant rate of precession if the disk can become tilted out of the plane (see eg: Wijers and Pringle 1999), but two issues then arise: (i) how to cause a fluid disk to precess with uniform frequency, and (ii) how to maintain tilting out of the plane."471 Alodclling of disk behaviour by Wijers Pringle (1999) ancl subsequent more rigorous treatment by Ogilvie Dubus (2001: hereafter ODOL) has shown that an accretion disk is unstable to raciation-driven warping when the luminosity of the central source exceeds a critical value., Modelling of disk behaviour by Wijers Pringle \shortcite{wp} and subsequent more rigorous treatment by Ogilvie Dubus (2001: hereafter OD01) has shown that an accretion disk is unstable to radiation-driven warping when the luminosity of the central source exceeds a critical value.472 This instability provides a mechanism enabling the disk to tilt ancl to remain tilted anc so to precess with a period. that is comparable to the recorded values for superorbital periods in X-ray binaries., This instability provides a mechanism enabling the disk to tilt and to remain tilted and so to precess with a period that is comparable to the recorded values for superorbital periods in X-ray binaries.473 Furthermore the models also provide for the possibility of both retrograde and prograde motion., Furthermore the models also provide for the possibility of both retrograde and prograde motion.474 Thus all, Thus all475((Table 1)).,(Table \ref{tab:detrate}) ).476" For the three subgroups, it is ((galaxies), (AGN) and ((other)."," For the three subgroups, it is (galaxies), (AGN) and (other)."477 The large detection rate of ‘galaxies’ is consistent with their X-ray emission arising from star formation related processes., The large detection rate of `galaxies' is consistent with their X-ray emission arising from star formation related processes.478 A detailed discussion will be provided elsewhere., A detailed discussion will be provided elsewhere.479" In the following, we focus on the 224 X-ray AGN only."," In the following, we focus on the 224 X-ray AGN only."480 We use both the individual detections and stacks of nondetections derived via the stacking library of Bethermin et al. (2010))., We use both the individual detections and stacks of nondetections derived via the stacking library of Bethermin et al. \cite{bethermin10}) ).481 The 178 AGN that are individually undetected in both PACS bands are statistically well detected in the stacks at 0.79+0.08mJy (100um) and 1.46+0.16mJy (160m)., The 178 AGN that are individually undetected in both PACS bands are statistically well detected in the stacks at $\pm$ 0.08mJy $\mu$ m) and $\pm$ 0.16mJy $\mu$ m).482" These detection errors are derived from multiple stacks at random positions over the same coverage region of the PACS residual maps, and using the number of targets as the sample of interest."," These detection errors are derived from multiple stacks at random positions over the same coverage region of the PACS residual maps, and using the number of targets as the sample of interest."483" To derive far-infrared (FIR) luminosities with minimal assumptions about SED shapewe compute the rest frame 604m luminosity vL,(60um) using the detection wavelength closer to rest 60um or log-linearly interpolating for detections in both bands at 0.67«z«1.67.", To derive far-infrared (FIR) luminosities with minimal assumptions about SED shapewe compute the rest frame $\mu$ m luminosity $\nu$ $_\nu$ $\mu$ m) using the detection wavelength closer to rest $\mu$ m or log-linearly interpolating for detections in both bands at $<$ $<$ 1.67.484 We treat stacked 100um and 160um fluxes equivalently to derive the mean rest frame 60um luminosities of the individually undetected sources., We treat stacked $\mu$ m and $\mu$ m fluxes equivalently to derive the mean rest frame $\mu$ m luminosities of the individually undetected sources.485" Given the strong K-corrections for PACS fluxes over the redshift range of X-ray AGN, this requires restricted redshift ranges for the stacks, we limit to bins with Az/(1+z)«0.4 and adopt the median z of the particular sample."," Given the strong K-corrections for PACS fluxes over the redshift range of X-ray AGN, this requires restricted redshift ranges for the stacks, we limit to bins with $\Delta z/(1+z)<0.4$ and adopt the median z of the particular sample."486 Luminosities for the combined sample of detections and nondetections are obtained as averages weighted by the number of sources., Luminosities for the combined sample of detections and nondetections are obtained as averages weighted by the number of sources.487 Figure | shows the redshift distribution of all X-ray AGN in our sample., Figure \ref{fig:redshiftdist} shows the redshift distribution of all X-ray AGN in our sample.488" As expected, PACS photometry is most efficient in detecting zx2.5 AGN hosts."," As expected, PACS photometry is most efficient in detecting $\lesssim$ 2.5 AGN hosts."489" We also focus on ZX2.5 in order to probe far-infrared rest frame >45um wavelengths, beyond the mid-infrared that is more easily AGN dominated."," We also focus on $\leq$ 2.5 in order to probe far-infrared rest frame $>45\mu$ m wavelengths, beyond the mid-infrared that is more easily AGN dominated."490 Table 2 and Fig., Table \ref{tab:ztrend} and Fig.491" 2 show 60um luminosities as a function of redshift, separately for the PACS detections, stacks of nondetections and the combined sample."," \ref{fig:ztrend}492 show $\mu$ m luminosities as a function of redshift, separately for the PACS detections, stacks of nondetections and the combined sample."493 Host 60um luminosities increase with redshift., Host $\mu$ m luminosities increase with redshift.494" An increase is seen in detections, stacked nondetections, and in the averages for the combined sample."," An increase is seen in detections, stacked nondetections, and in the averages for the combined sample."495" This trend cannot be simply due to the increase of FIR detection limit with redshift, which would leave the average luminosities from the combination of detections and nondetections unchanged."," This trend cannot be simply due to the increase of FIR detection limit with redshift, which would leave the average luminosities from the combination of detections and nondetections unchanged."496 Mean fluxes for the PACS >3c detections and stacked mean for the nondetections differ by about an order of magnitude in each of the three redshift bins., Mean fluxes for the PACS $>3\sigma$ detections and stacked mean for the nondetections differ by about an order of magnitude in each of the three redshift bins.497 Such a large difference must reflect a wide intrinsic distribution of infrared luminosities., Such a large difference must reflect a wide intrinsic distribution of far-infrared luminosities.498" For the simplifying assumption of a log-normal distribution of far-infrared luminosities, the ratio of mean detections to the stacked mean as well as the 2096 ddetection rates can be reproduced with an intrinsic dispersion of about 0.5 dex for the distribution of far-infrared luminosities in each bin."," For the simplifying assumption of a log-normal distribution of far-infrared luminosities, the ratio of mean detections to the stacked mean as well as the $\sim$ detection rates can be reproduced with an intrinsic dispersion of about 0.5 dex for the distribution of far-infrared luminosities in each bin."499 The detailed shape of this distribution is not constrained but must be wide., The detailed shape of this distribution is not constrained but must be wide.500 The mean 160um flux for all the 1.4«z«2.5 AGN is 3mJy (in agreement with tentative MIPS values for ECDFS AGN by Papovich et al. 2007))., The mean $\mu$ m flux for all the $<$ $<$ 2.5 AGN is 3mJy (in agreement with tentative MIPS values for ECDFS AGN by Papovich et al. \cite{papovich07}) ).501" Given the wide distribution of FIR luminosities, the typical (median) flux must be lower, by a factor ~2 for the log-normal distribution."," Given the wide distribution of FIR luminosities, the typical (median) flux must be lower, by a factor $\sim$ 2 for the log-normal distribution."502" A considerable variety exists not only in far-infrared luminosity but also in mid-to far-infrared SED shape (Fig. 3)),"," A considerable variety exists not only in far-infrared luminosity but also in mid-to far-infrared SED shape (Fig. \ref{fig:exampleseds}) ),"503 from SEDs quite similar to those of star forming galaxies to ones that are clearly AGN dominated over a wide wavelength range., from SEDs quite similar to those of star forming galaxies to ones that are clearly AGN dominated over a wide wavelength range.504We seek to fud an upper bound of e by constructing an explicit supcr-solution of (3.3)) with suitable initial data. and comparing it with e.,"We seek to find an upper bound of $v^{\g}$ by constructing an explicit super-solution of \ref{ode-pde}) ) with suitable initial data, and comparing it with $v^{\g}$."505 For this purpose. let where ορ is equal to 07 for 5=0. aud e4 is positive constant to be precised later.," For this purpose, let where $v_{0}$ is equal to $v^{\g}$ for $\g=0$, and $c_{1}$ is positive constant to be precised later."506 We calculate: where from (3.5)). we deduce that Take οι=cLT for somefixed T.> 0.," We calculate: where from \ref{formal}) ), we deduce that Take $c_{1}=e^{LT}$ for somefixed $T>0$ ."507 Then musing (3.7)). we get ένο)cοοννο)|5 for anv τς(o.T].," Then using \ref{est_w}) ), we get $w_{t}(t,x) \geq g(w(t,x),t)+\g$ for any $t\in [0,T]$."508 ence wis a supor-solutiou of (3.3)) over 0.Τι whose initial condition Ον)—07(0..0). which finally eives: We will now show the error estimate (3.2)).," Hence $w$ is a super-solution of \ref{ode-pde}) ) over $[0,T]$ whose initial condition $w(0,x)=v^{\g}(0,x)$, which finally gives: We will now show the error estimate \ref{lambda_ext}) )."509 To this eud. we will estimate both sides of inequality. (3.8)) involving Ay aud A-.," To this end, we will estimate both sides of inequality \ref{step2}) ) involving $\l_{0}$ and $\l_{\g}$."510 Firstly. using (2.2)) aud (3.5)). we compute: We take this inequality for f—T aud c= 0. we ect Secondly. using similar arguments. and the fact that >< 1. we obtain [ο(ΤΟ(0.0ALT]<2| £. hence Combining (3.8)). (3.9)) and (3.10)). it follows that Using (3.11)). we deduce that: Since the variable Twas arbitrary chosen. let P satisfies 5T*2LT—| and therefore T> oe ," Firstly, using \ref{ergo_eq1}) ) and \ref{formal}) ), we compute: We take this inequality for $t=T$ and $x=0$ , we get Secondly, using similar arguments, and the fact that $\g<1$ , we obtain $|v^{\g}(T,0)-v^{\g}(0,0)-\l_{\g}T|\leq 2+\xi$ , hence Combining \ref{step2}) ), \ref{s1}) ) and \ref{s2}) ), it follows that Using \ref{s3}) ), we deduce that: Since the variable $T$was arbitrary chosen, let $T$ satisfies $\g T e^{2LT}=1$ and therefore $T\geq \frac{|\log \g|}{1+2L}$ ."511From(3.12)). the result directly follows.," From\ref{s4}) ), the result directly follows."512 LI An inuuediate consequence ofProposition 3.1. is the followine: Remark that estimate (3.123) is optimal in viewofExample 1.5.., $\hfill{\Box}$ An immediate consequence ofProposition \ref{prop_pert} is the following: Remark that estimate \ref{lwt3b1}) ) is optimal in viewofExample \ref{example2}. .513or present with a low signal-to-noise ratio.,or present with a low signal-to-noise ratio.514 Lhe magnitude of the star-formation rates in these objects is not large. being consistent with the pedestrian levels observed in spiral disks.," The magnitude of the star-formation rates in these objects is not large, being consistent with the pedestrian levels observed in spiral disks."515 The H2 and LL? absorption features are presumably subject to emission-filling and the object is consequently not selected in the average-Dalmer catalogue., The $\gamma$ and $\beta$ absorption features are presumably subject to emission-filling and the object is consequently not selected in the average-Balmer catalogue.516 The L9 E|A catalogue may thus contain an additional galaxy population: cust. clisk ealaxies., The $\delta$ E+A catalogue may thus contain an additional galaxy population: dusty disk galaxies.517 We also checked for inclusion of E|A galaxy catalogue members in the [ist of 2dPGB radio sources compiled by ]5.Sadler (priv., We also checked for inclusion of E+A galaxy catalogue members in the list of 2dFGRS radio sources compiled by E.Sadler (priv.518 comm.), comm.)519 after careful cross-matching of the 2dCIUS catalogue and the 1.4 Gllz NILAO VLA Sky Survey (NVSS) (Sadler et 22002)., after careful cross-matching of the 2dFGRS catalogue and the $1.4$ GHz NRAO VLA Sky Survey (NVSS) (Sadler et 2002).520 The NVSS is complete to a racio Hux-density limit of 914c6gz©3 my. corresponding to a radio luminosity Ljagusà6107 W 7 at the tvpical redshift of a 2dECIUS galaxy. z=0.1 (assuming a power-law radio spectrum Syxv °°).," The NVSS is complete to a radio flux-density limit of $S_{\rm 1.4 \, GHz} \approx 3$ mJy, corresponding to a radio luminosity $L_{\rm 1.4 \, GHz} \approx 6521\times 10^{21}$ W $^{-1}$ at the typical redshift of a 2dFGRS galaxy, $z = 0.1$ (assuming a power-law radio spectrum $S_\nu \propto522\nu^{-0.8}$ )."523 phis level of radio continuum Lux density is generated by a star-formation rate of about TM. n (using. the conversion. stated in. Sullivan]. et 22001. equation 3). therefore the Ho. emission is a probe of lower star formation rates in the present study.," This level of radio continuum flux density is generated by a star-formation rate of about $7 \, M_\odot$ $^{-1}$ (using the conversion stated in Sullivan et 2001, equation 3), therefore the $\alpha$ emission is a probe of lower star formation rates in the present study."524 In the average-Balmer (or H9) I2|A catalogue. just 1 out of 56 (2 out of 243) objects was listed as an NVSS radio detection.," In the average-Balmer (or $\delta$ ) E+A catalogue, just 1 out of 56 (2 out of 243) objects was listed as an NVSS radio detection."525 We inspected: Supercosmos Sky Survey (888) images of objects in our I2].X galaxy catalogues., We inspected Supercosmos Sky Survey (SSS) images of objects in our E+A galaxy catalogues.526 The SSS) has digitized sky survey plates taken with the Ulx Schmidt telescope. using a pixel size of 0.67. areseconds.," The SSS has digitized sky survey plates taken with the UK Schmidt telescope, using a pixel size of 0.67 arcseconds."527 “Phree dillerent. photographie colours are available (approximating D. lt and 1) and the data were accessed using the website html. An introduction to the SSS is presented bv. Llambly et. ((2001).," Three different photographic colours are available (approximating B, R and I) and the data were accessed using the website An introduction to the SSS is presented by Hambly et (2001)."528 ‘Table E. displays the results of our visual morphological Classification of our I2] galaxy samples. based on inspection of the blue SSS A)images.," Table \ref{tabmorph} displays the results of our visual morphological classification of our E+A galaxy samples, based on inspection of the blue SSS images."529 MI the galaxies in the average-Dalmoer catalogue were classified. and a comparable number (selected at. random) from the 119 sample were also classified.," All the galaxies in the average-Balmer catalogue were classified, and a comparable number (selected at random) from the $\delta$ sample were also classified."530" Galaxies were assigned one of the following broad. ""Hlubble tvpes: I. 2/80. S0. Spiral (early). Spiral (late). or Irr(egular): unless they were too distant to be sullicienthy-well resolved."," Galaxies were assigned one of the following broad `Hubble' types: E, E/S0, S0, Spiral (early), Spiral (late), or Irr(egular); unless they were too distant to be sufficiently-well resolved."531 Any evidence for tidal interactions and mergers ttidal tails. coalescing pairs. disturbed appearance) was also noted.," Any evidence for tidal interactions and mergers tidal tails, coalescing pairs, disturbed appearance) was also noted."532 As can be seen from Table. 1..catalogues.," As can be seen from Table \ref{tabmorph},."533 Average-Balmer I2].X. galaxies are predominantly. carly-tvpe spherocial ή systems., Average-Balmer E+A galaxies are predominantly early-type spherodial E/S0 systems.534 “Phere is evidence of a disk component in some objects. but this contribution is never dominant.," There is evidence of a disk component in some objects, but this contribution is never dominant."535 4n contrast. Lldé-sclected Lo|AO galaxies are preclominantly late-type spiral galaxies.," In contrast, $\delta$ -selected E+A galaxies are predominantly late-type spiral galaxies."536 This result is consistent with our analvsis of the star formation rates in Section 2.5: the 119 I2|A catalogue contains an additional population of star-forming disk systems that is not. present in the average-Dalmoer catalogue., This result is consistent with our analysis of the star formation rates in Section \ref{sechalpha}: the $\delta$ E+A catalogue contains an additional population of star-forming disk systems that is not present in the average-Balmer catalogue.537" ln this sense. the latter catalogue provides a higher-fidelitv selection of ""true IE|A galaxies."," In this sense, the latter catalogue provides a higher-fidelity selection of `true E+A galaxies'."538 Images of the eieht lowest-redshilt average-Balmer E|A galaxies are clisplaved inreffieepaabimg.. using the blue. SSS cata to match the selection. colour of the 2dkPGRS.," Images of the eight lowest-redshift average-Balmer E+A galaxies are displayed in, using the blue SSS data to match the selection colour of the 2dFGRS."539 Note that there is no morphological selection. imposed. for this Figure. only the original spectral selection together with proximity.," Note that there is no morphological selection imposed for this Figure, only the original spectral selection together with proximity."540" The plots are labelled. with the absolute magnitude of each galaxy: these nearby objects are in all cases fainter than L 5log,uh=19.66. Norberg et 22002)."," The plots are labelled with the absolute magnitude of each galaxy: these nearby objects are in all cases fainter than $L^*$ $M^*_b - 5 \, {\rm log_{10}} \, h =541-19.66$ , Norberg et 2002)."542 Our visual inspection of the SSS images also revealed that a small but significant. number of the E| galaxies possess disturbed: morphologies or tidal features indicative of a late stage of a major merger. in agreement with the findings of ZabludolT et ((1996).," Our visual inspection of the SSS images also revealed that a small but significant number of the E+A galaxies possess disturbed morphologies or tidal features indicative of a late stage of a major merger, in agreement with the findings of Zabludoff et (1996)."543" For example. in reffigepaabimg we classified images #3 and $66 as providing strong” evidence for a recent merger. ancl images ancl 68 as ""possible, candidates (see the last (wo columns of ‘Table 1))."," For example, in \\ref{figepaabimg} we classified images $\#3$ and $\#6$ as providing `strong' evidence for a recent merger, and images $\#4$, $\#7$ and $\#8$ as `possible' candidates (see the last two columns of Table \ref{tabmorph}) )."544 reffieepamerge— displays some other examples of possible mergers or interactions drawn from both catalogues: image 3Éll features a bright tidal tail extending for a physical distance of ~50 kpe., \\ref{figepamerge} displays some other examples of possible mergers or interactions drawn from both catalogues; image $\#11$ features a bright tidal tail extending for a physical distance of $\sim 50$ kpc.545 Theoretical modelling has indeed shown that major mergers can produce the characteristic ETA spectrum (Bekki et 22001). and space-basecl high-resolution imaging of I5|A galaxies (Yang et 22004) has provided further support. for this scenario.," Theoretical modelling has indeed shown that major mergers can produce the characteristic E+A spectrum (Bekki et 2001), and space-based high-resolution imaging of E+A galaxies (Yang et 2004) has provided further support for this scenario."546" We note that merger events have a relatively short duty ονοο (~107 vr) compared to the timescale of the I|A phase (~10"" vr): we expect morphological evidence for mergers to be rare.", We note that merger events have a relatively short `duty cycle' $\sim 10^8$ yr) compared to the timescale of the E+A phase $\sim 10^9$ yr): we expect morphological evidence for mergers to be rare.547 As already indicated. the Llé-selectecd I2[X galaxies displav a wider range of morphologies than the average-Balmer catalogue.," As already indicated, the $\delta$ -selected E+A galaxies display a wider range of morphologies than the average-Balmer catalogue."548 We discover. plausible merger remnants. but we also identify low-Iuminositv disk systems which display no evidence of recent or current. interactions with other galaxies.," We discover plausible merger remnants, but we also identify low-luminosity disk systems which display no evidence of recent or current interactions with other galaxies."549 Major mergers cannot. produce such. disk systems: one possible alternative formation mechanism for such an I2]A galaxy is a tidal interaction with a companion that passed by ~1 Gyr ago., Major mergers cannot produce such disk systems: one possible alternative formation mechanism for such an E+A galaxy is a tidal interaction with a companion that passed by $\sim 1$ Gyr ago.550 Dwarf galaxies are particularly susceptible to such tidal interactions. which can transform a late-tvpe spiral galaxy into a barred SO galaxy that still preserves the edge-on appearance of a disk system.," Dwarf galaxies are particularly susceptible to such tidal interactions, which can transform a late-type spiral galaxy into a barred S0 galaxy that still preserves the edge-on appearance of a disk system."551 The dvnamies of the bar drives gas to the centre of the system. trigecring a starburst. Whennicutt 1998): the rapid consumption of this eas naturally produces a characteristic LE}A spectrum.," The dynamics of the bar drives gas to the centre of the system, triggering a starburst Kennicutt 1998); the rapid consumption of this gas naturally produces a characteristic E+A spectrum."552 Lt is important to note that the angular ciameter of each fibre of the 2dE spectrograph (2 areseconds) is significantly smaller than the angular size of most of these galaxies., It is important to note that the angular diameter of each fibre of the 2dF spectrograph (2 arcseconds) is significantly smaller than the angular size of most of these galaxies.553 The I2]A galaxy selection is therefore subject to aperture ellects: we can only assert that the small portion of the galaxy sampled by the fibre. possesses an I2[X spectrum., The E+A galaxy selection is therefore subject to aperture effects: we can only assert that the small portion of the galaxy sampled by the fibre possesses an E+A spectrum.554 This obviously does not preclude ongoing star formation in other regions of the galaxy., This obviously does not preclude ongoing star formation in other regions of the galaxy.555 However. a starburst: triggered by à major galaxy. merger or interaction will tvpically reside in the centre of the system. where gas is driven by the dynamics: thus such a starburst should. co-exist with the highest optical surface brightness. where the spectrograph fibre is usually positioned.," However, a starburst triggered by a major galaxy merger or interaction will typically reside in the centre of the system, where gas is driven by the dynamics: thus such a starburst should co-exist with the highest optical surface brightness, where the spectrograph fibre is usually positioned."556We quantified the local environments of the 151A galaxy samples using a variety. of techniques:,We quantified the local environments of the E+A galaxy samples using a variety of techniques:557is assumed. to be a stable. isotropic. uid with dynamical viscosity yf.,"is assumed to be a stable, isotropic fluid with dynamical viscosity $\mu$."558 ‘The steady-state structure of the rotating radiative zone is obtained by perturbing the hyelrostatic equilibrium in the Following wav: where p is the pressure. 2 is the temperature. p is the density.9 is the gravitational potential. &=(n.p.it) is the velocity field. s is the entropy ancl & is the thermal conductivity.," The steady-state structure of the rotating radiative zone is obtained by perturbing the hydrostatic equilibrium in the following way: where $p$ is the pressure, $T$ is the temperature, $\rho$ is the density,$\Phi$ is the gravitational potential, $\bu = (\ur,\ut,\up)$ is the velocity field, $s$ is the entropy and $k$ is the thermal conductivity."559 As the system is axisvmumetric and near-uniform rotation is not assumed. there is no need to work in a rotating frame.," As the system is axisymmetric and near-uniform rotation is not assumed, there is no need to work in a rotating frame."560 Quantities denoted with sullix h are derived. [rom the non-rotating hyvdrostatie equilibrium equations. anc perturbations to that. state are. denoted with tildes.," Quantities denoted with suffix h are derived from the non-rotating hydrostatic equilibrium equations, and perturbations to that state are denoted with tildes."561" The equations are linearized. with respect to 1ο background state (e.g. p<Py. p pu). but the ""ull nonlinearity is kept in the Low and in particular in 10 advection process w-Va."," The equations are linearized with respect to the background state (e.g. $\tilde{\Phi} \ll \Phi_{\rm h}$, $\tilde{\rho} \ll \rho_{\rm h}$ ), but the full nonlinearity is kept in the flow and in particular in the advection process $\bu\cdot\grad\bu$."562" Εις approach is rigorously ""oprect. provided the star is far from breakup (that is. when 10 mean ellipticity due to rotation is much smaller than unity)."," This approach is rigorously correct provided the star is far from breakup (that is, when the mean ellipticity due to rotation is much smaller than unity)."563 The steady-state assumption is valid. provided. the lvnamical timescale of this svstem is short. compared. to 1e stellar evolution and spin-down timescales., The steady-state assumption is valid provided the dynamical timescale of this system is short compared to the stellar evolution and spin-down timescales.564 This is not always necessarily the case. so that the direct applicability of the results presented in Section 3 must. be checked. a »osterlori.," This is not always necessarily the case, so that the direct applicability of the results presented in Section 3 must be checked a posteriori."565 These equations must be. supplemented: with appropriate boundary conditions., These equations must be supplemented with appropriate boundary conditions.566 Strictly speaking. correct. boundary conditions would require a theory of the rotation and circulation in the convection zone to which the interior Bows must be matched.," Strictly speaking, correct boundary conditions would require a theory of the rotation and circulation in the convection zone to which the interior flows must be matched."567" Here. LE shall simply assume that the forces maintaining the low in the convection zone are so high that the angular velocity is unadIected by the Low in the underlving radiative zone. ancl is given by Qu.Cr.8)=Sycos""6 (where 6 is the co-latitude and ris the radial variable)."," Here, I shall simply assume that the forces maintaining the flow in the convection zone are so high that the angular velocity is unaffected by the flow in the underlying radiative zone, and is given by $\Omega_{\rm cz}(r,\theta) = \sum_{n=0}^{\infty} \Omega_n \cos^n \theta$ (where $\theta$ is the co-latitude and $r$ is the radial variable)."568 In addition. E suppose that the stresses allecting the meridional. circulation are viscous-like.," In addition, I suppose that the stresses affecting the meridional circulation are viscous-like."569" Since the cllective viscosity in the convection zone is much ereater than the viscosity in the radiative zone. it is not implausible that the continuity of stresses across the boundary imposes the constraints Q=OQ. TeocrO(uafr)ífOr|(fren,f08=O and Or is continuous (and therefore null) at the interface."," Since the effective viscosity in the convection zone is much greater than the viscosity in the radiative zone, it is not implausible that the continuity of stresses across the boundary imposes the constraints $\Omega = \Omega_{\rm cz}$, $\tau_{r,\theta} = r\ptl (\ut/r) /\ptl r + (1/r) \ptl \ur/\ptl \theta = 0$ and $\ptl \Omega/\ptl r$ is continuous (and therefore null) at the interface."570 The inner core (For r« rjj) is removed from the computational domain in order to avold singularities.," The inner core (for $r571< \rin$ ) is removed from the computational domain in order to avoid singularities."572 This core is impermeable and is assumed to rotate rigidly with angular velocity On determined in such à way as to ensure a null angular-momentum Lux through the boundary., This core is impermeable and is assumed to rotate rigidly with angular velocity $\Oin$ determined in such a way as to ensure a null angular-momentum flux through the boundary.573 Finally. the regions outside the domain of computation are assumed to satisfy Wer=O where TZ vanishes both at pr20 and when ον (since the inner core supports no Luid motion and the elective. thermal conductivitv in the convection zone is assumed to be much Larger than in the radiative zone).," Finally, the regions outside the domain of computation are assumed to satisfy $\grad^2 \tilde{T} = 0$ where $\tilde{T}$ vanishes both at $r=0$ and when $r\rightarrow574\infty$ (since the inner core supports no fluid motion and the effective thermal conductivity in the convection zone is assumed to be much larger than in the radiative zone)."575 Using the assumption of axisvmmetry. I reduce the momentum equation in (1)) to: where w=Vow is the vorticitv. €=rfr; is the new normalized radial coordinate. z is the normalized cvlindrical. coordinate that runs along the rotation axis. Lo=v ds the Ekman number (where 7= qifpy). and ο= is the ratio of the centrifugal to gravitational forces.," Using the assumption of axisymmetry, I reduce the momentum equation in \ref{eq:basic1}) ) to: where $\bomega = \curl \bu$ is the vorticity, $\xi = r/\rc$ is the new normalized radial coordinate, $z$ is the normalized cylindrical coordinate that runs along the rotation axis, $\Enu = \nu/ \rc^2\Oc$ is the Ekman number (where $\nu = \mu/\rho_{\rm h})$, and $\epsilon = \rc^2\Oc^2 (\ptl \Phi_{\rm h}/\ptl \xi)^{-1}$ is the ratio of the centrifugal to gravitational forces."576" The first of these equations simply describes angular momentum conservation. relating the advection term (LIIS) to the dillusion term(RLIS)':: the second equation is the azimuthal component. of the curl of the momenttun equation. commonly referred. to in. the ecophysical literature as the ""thermal wind equation’."," The first of these equations simply describes angular momentum conservation, relating the advection term (LHS) to the diffusion term; the second equation is the azimuthal component of the curl of the momentum equation, commonly referred to in the geophysical literature as the `thermal wind equation'."577" In all these expressions the following normalizations have been applied: 4]—n. 4]= nQ,. ]=2027.cate 1]=1k. f]= 1g/em. where re is the radius of the radiative zone and O, is the typical rotation rate of the star."," In all these expressions the following normalizations have been applied: $\left[r\right] = \rc$, $ [u]=\rc\Oc$ , $ [\tilde{\Phi}] = \rc^2578\Oc^2$, $[T] = 1K$, $[\rho] = 1$ $^3$, where $\rc$ is the radius of the radiative zone and $\Oc$ is the typical rotation rate of the star."579" Phe operator D? is delined as The energy equation. becomes. to first. order in the thermodyvnamical perturbations where m=pre,fh is the Prandtl number. and Ay, is the background buovaney Frequency."," The operator $ {\rm D}^2$ is defined as The energy equation becomes, to first order in the thermodynamical perturbations where $\sigma = \mu c_{\rm p} / k $ is the Prandtl number, and $N_{\rm580h}$ is the background buoyancy frequency."581 Finally. the equation of state can be combined. with the racial and. latitudinal components of the momentunm equation to provide an expression for fx This expression is used in the thermal wind relation in (2)) as well as in the latituclinal derivative of the Poisson equation The resulting equations (2)). (4)) and. (6))combined with the mass continuity equation are solved. for. the unknowns μιup.mou.OO06 and 1.," Finally, the equation of state can be combined with the radial and latitudinal components of the momentum equation to provide an expression for $\tilde{\rho}$ : This expression is used in the thermal wind relation in \ref{eq:basic2}) ) as well as in the latitudinal derivative of the Poisson equation The resulting equations \ref{eq:basic2}) ), \ref{eq:energy}) ) and \ref{eq:Poisson}) )combined with the mass continuity equation are solved for the unknowns $\ur,\ut,\up,\ptl \tilde{\Phi} / \ptl \theta$ and $\tilde{T}$ ."582established that accretion discs can be formed in phases of evolution when the relative radius of the mass accreting star is small enough.,established that accretion discs can be formed in phases of evolution when the relative radius of the mass accreting star is small enough.583" Classical Algols are semi-detached interacting eclipsing binary stars in which the less massive, evolved secondary component (spectral type F or later G and luminosity class of giant or sub-giant) has expanded enough to fill its Roche lobe."," Classical Algols are semi-detached interacting eclipsing binary stars in which the less massive, evolved secondary component (spectral type F or later G and luminosity class of giant or sub-giant) has expanded enough to fill its Roche lobe."584 These less massive cool secondaries are transferring material through a gas stream on to a B or A spectral-type main-sequence primary component., These less massive cool secondaries are transferring material through a gas stream on to a B or A spectral-type main-sequence primary component.585" In the long period, P> 5d, Algols the mass gaining components are small enough, relative to the binary separation, that mass transfer takes place through an accretion disc."," In the long period, $P>5\,$ d, Algols the mass gaining components are small enough, relative to the binary separation, that mass transfer takes place through an accretion disc."586 The in-falling material has too much angular momentum for the stream to directly impact on the accretor., The in-falling material has too much angular momentum for the stream to directly impact on the accretor.587 |Lubow&Shu|(1975) examined the condition for the formation of discs in semi-detached systems by modelling the stream as a ballistic flow from the inner Lagrangian point., \citet{lubow1975} examined the condition for the formation of discs in semi-detached systems by modelling the stream as a ballistic flow from the inner Lagrangian point.588 As seen in Fig., As seen in Fig.589" Bha (similartofig.4of[Lubow&Shul{1975)),, if the minimum distance of the stream from centre of the gainer acc; is smaller than the radius of detached component (Hi) the transferring material can impact directly on its surface."," \ref{figlubow}a a \citep[similar to fig.~4 of][]{lubow1975}, if the minimum distance of the stream from centre of the gainer $a\varpi_{\rm \min}$ is smaller than the radius of detached component $R_{1}$ ) the transferring material can impact directly on its surface."590 This impact leads to the formation of variable accretion structures., This impact leads to the formation of variable accretion structures.591" Otherwise, when a@min>R1, the mass flow misses the star and collides with itself at a larger radius."," Otherwise, when $a\varpi_{\rm \min}>R_{1}$, the mass flow misses the star and collides with itself at a larger radius."592 Radial motion is dissipated and the resulting ring of material spreads viscously to form a permanent accretion disc of radius ac., Radial motion is dissipated and the resulting ring of material spreads viscously to form a permanent accretion disc of radius $a\varpi_{\rm \rm d}$ .593" If the accretor has a radius between ac, and aw, a disc could exist because it could intercept the stream before it impacts the star.", If the accretor has a radius between $a\varpi_{\rm min}$ and $a\varpi_{\rm d}$ a disc could exist because it could intercept the stream before it impacts the star.594 In such a case the disc could be transient., In such a case the disc could be transient.595 If R4>awg then the stream must impact the star directly.," If $R_1 >596a\varpi_{\rm d}$ then the stream must impact the star directly."597" Expressing these distances relative to the separation a, we can predict the presence of discs in semi-detached systems."," Expressing these distances relative to the separation $a$ , we can predict the presence of discs in semi-detached systems."598" Both c1, and c are functions only of mass ratio q.", Both $\varpi_{\rm \min}$ and $\varpi_{\rm \rm d}$ are functions only of mass ratio $q$.599 The majority of Algols with P>(4—5) d are within the region (Fig.," The majority of Algols with $P > (4-5)\,$ d are within the region (Fig."600 Bbb) where we expect stars to have either a permanent or transient disc., \ref{figlubow}b b) where we expect stars to have either a permanent or transient disc.601 Indeed the presence of a disc around the gainer is easily confirmed with optical spectra of the primary star., Indeed the presence of a disc around the gainer is easily confirmed with optical spectra of the primary star.602" observed and analysed optical spectra of Algols and demonstrated that those with periods P>(4— 5)d show double-peaked Ha emission, characteristic of accretion discs, whilethose of shorter periodsshow only emission, characteristic of a mass stream structure 1999).."," \citet{richards1999} observed and analysed optical spectra of Algols and demonstrated that those with periods $P>(4-5)\,$ d show double-peaked $\alpha$ emission, characteristic of accretion discs, whilethose of shorter periodsshow only single-peaked emission, characteristic of a mass stream structure \citep[fig.~3 of][]{richards1999}. ."603satellite galaxies. such as the satellite-tvpe fraction found in the group (Weinmann 2006).. the alignment of satellite galaxies preferentially along the dominant galaxys major axis (Yangοἱal.2006:Brainercl2005:Zentneret2005).. and the rotation of satellite galaxies in the same direction as the host halo (Warnick&Ixnebe2006).,"satellite galaxies, such as the satellite-type fraction found in the group \citep{weinmann06}, the alignment of satellite galaxies preferentially along the dominant galaxy's major axis \citep{yang06,brainerd05,zentner05}, and the rotation of satellite galaxies in the same direction as the host halo \citep{warnick05}."604. The connections between (he centrally dominant galaxy in a group environment and its surrounding satellite galaxies raise the question whether there might be a more clirect kinematic connection between (hem as well., The connections between the centrally dominant galaxy in a group environment and its surrounding satellite galaxies raise the question whether there might be a more direct kinematic connection between them as well.605 Kinematic similarities between the eroup aud its brightest group member would be consistent with both cold dark matter models. suggesting the central giant and its satellite group are part of the same large-scale structure. and the hierarchical formation scenario. whereby the central giant would build up by accretion of satellites in the group.," Kinematic similarities between the group and its brightest group member would be consistent with both cold dark matter models, suggesting the central giant and its satellite group are part of the same large-scale structure, and the hierarchical formation scenario, whereby the central giant would build up by accretion of satellites in the group."606 NGC 5128 is an E/SO eiant galaxy in the positional and dynamical center of the Centaurus 5eroup of 5galaxies., NGC 5128 is an E/S0 giant galaxy in the positional and dynamical center of the Centaurus group of galaxies.607 Its remarkably close proximity Gust 4+ Mpe clistant) also provides a genuinelv rare opportunity (o study and compare the dynamics of the halo of NGC 5128 with the dynamics of the surrounding group at a level of detail that is difficult. elsewhere., Its remarkably close proximity (just 4 Mpc distant) also provides a genuinely rare opportunity to study and compare the dynamics of the halo of NGC 5128 with the dynamics of the surrounding group at a level of detail that is difficult elsewhere.608 The Centaurus group consists of 25 confirmed ealaxv members 2006).. 13 of which have radial velocity measurements used in this kinematic study: see Figure 1..," The Centaurus group consists of 25 confirmed galaxy members \citep{kar06}, 13 of which have radial velocity measurements used in this kinematic study; see Figure \ref{fig:galpos}."609 Within a projected distance of ~1 Alpe from NGC 5128 lies NGC 5236 (M83)., Within a projected distance of $\sim1$ Mpc from NGC 5128 lies NGC 5236 (M83).610 NGC 5236 is a dominant spiral galaxy. surrounded by 9 other confirmed members within the M53 group., NGC 5236 is a dominant spiral galaxy surrounded by 9 other confirmed members within the M83 group.611 Surrounding these (wo svstems are 53 smaller galaxies Chat do not have confirmed membership in either (he Centaurus group or the M33 exoup., Surrounding these two systems are 53 smaller galaxies that do not have confirmed membership in either the Centaurus group or the M83 group.612 Therefore the bounds separating these two groups are still quite uncertain. and it has been suggested (hat (lese two svslems create a dimbbell svstem. similar {ο our own Milky Way. and M31. 2006).," Therefore the bounds separating these two groups are still quite uncertain, and it has been suggested that these two systems create a dumbbell system, similar to our own Milky Way and M31 \citep{kar06}."613. Onlv one other kinematic comparison between (the halo of a dominant galaxv and iis surrounding satellite galaxies (AIST in (he Virgo cluster) has been presented in the literature (Cotéetal.2001)., Only one other kinematic comparison between the halo of a dominant galaxy and its surrounding satellite galaxies (M87 in the Virgo cluster) has been presented in the literature \citep{cote01}.614. Virgo is a much more dynamically evolved environment than the Centaurus group., Virgo is a much more dynamically evolved environment than the Centaurus group.615 The Centaurus group. therefore. provides the chance (ο carry the comparison a step further than just alignments of satellites ancl simple number statistics by looking al an environment closer to its initial structure.," The Centaurus group, therefore, provides the chance to carry the comparison a step further than just alignments of satellites and simple number statistics by looking at an environment closer to its initial structure."616 NGC 5128 has many hundreds of globular elusters (GCs) that can be used to define its halo kinematies and dynamics., NGC 5128 has many hundreds of globular clusters (GCs) that can be used to define its halo kinematics and dynamics.617 The most recent studies, The most recent studies618with optical/Xray AGN (?) that show strong evolution out 0222.5 (??)..,"with optical/Xray AGN \citep{mcc93} that show strong evolution out to $z\sim2.5$ \citep{sch68,croom09b}."619 lulio sources are stronely biased tracers of the uncerlving mass distribution of the Universe (22777)...," Radio sources are strongly biased tracers of the underlying mass distribution of the Universe \citep{ymp89,p+n91,b+w02,mag04,bra05}."620 Since he advent of deep all sky surveys (e.g. FIRST. NVSS. SUMSS. WIENSS) there have been major leaps in the ability o describe the environments of radio galaxies.," Since the advent of deep all sky surveys (e.g. FIRST, NVSS, SUMSS, WENSS) there have been major leaps in the ability to describe the environments of radio galaxies."621 These milli- surveys sample the luminosity range 1072H lo 107 WWLg at moderate redshifts. where radio sources are inc almost exclusively in LRGs.," These milli-Jansky surveys sample the luminosity range $\sim10^{23}$ to $10^{26}$ W/Hz at moderate redshifts, where radio sources are found almost exclusively in LRGs."622 LRGs are known to be a garonglv biased tracer of the matter density. ancl their bias increases with the mass/Iuminosity of the LAG.," LRGs are known to be a strongly biased tracer of the matter density, and their bias increases with the mass/luminosity of the LRG."623 Raclio sources tend to be found in the most massive elliptical galaxies and more massive galaxies are more likely to host them (??)..," Radio sources tend to be found in the most massive elliptical galaxies and more massive galaxies are more likely to host them \citep{bes05,m+s07}."624 Recent studies have compared. the justering of radio galaxies to that of racdio-quict galaxies ju have been matched in their optical properties to the racio sample., Recent studies have compared the clustering of radio galaxies to that of radio-quiet galaxies that have been matched in their optical properties to the radio sample.625 Most. find that radio galaxies are significantly more clustered than optically identical samples of quiescent galaxies (?7277).. although see ? for a counter example we will discuss later.," Most find that radio galaxies are significantly more clustered than optically identical samples of quiescent galaxies \citep{wak08a,man09,don09}, although see \citet{hic09} for a counter example we will discuss later."626 The indication is that the environment of a galaxy contributes to the probability of it hosting a racio σορός., The indication is that the environment of a galaxy contributes to the probability of it hosting a radio source.627 In this paper we are primarily concerned with how the clustering of radio sources evolves lor zz0.7., In this paper we are primarily concerned with how the clustering of radio sources evolves for $z\lesssim0.7$.628 In this redshift’ interval the clustering amplitude of LRGs is approximately constant (22)...," In this redshift interval the clustering amplitude of LRGs is approximately constant \citep{wak08b,saw09}."629 However. the clustering amplitude of quasars evolves such that. when models of gravitational collapse are assumed. the implied.ἱ dark halo mass for quasars is approximately constant (22)...," However, the clustering amplitude of quasars evolves such that, when models of gravitational collapse are assumed, the implied dark halo mass for quasars is approximately constant \citep{croom05,ros09}."630 We will evaluate the clustering amplitude of radio LRGs in a series of samples from z0.68 to 0.35 to investigate any evolution in their clustering., We will evaluate the clustering amplitude of radio LRGs in a series of samples from $z\sim0.68$ to 0.35 to investigate any evolution in their clustering.631 This will be done both for a sample of medium luminosity (L~107E* WW/LIz) radio galaxies. and a high luminosity subsaniple (L>107 WAV/LIz).," This will be done both for a sample of medium luminosity $L\sim10^{24.7}$ W/Hz) radio galaxies, and a high luminosity subsample $L>10^{26}$ W/Hz)."632 In section 2. we introduce the data that will be used in this work. section. 3. describes the algorithm we develop for identifving radio LRGs. section 4. describes the correlation analvsis to be used. section 5.r compares the clustering of racio-loud. and quiet. LRGs. section 6 then looks at the evolution of radio LRGs and in section 9 we investigate the evolution of the very brightest radio LRGs.," In section \ref{sec:data} we introduce the data that will be used in this work, section \ref{sec:rad_match} describes the algorithm we develop for identifying radio LRGs, section \ref{sec:cor_anal} describes the correlation analysis to be used, section \ref{sec:rlc} compares the clustering of radio-loud and quiet LRGs, section \ref{sec:evol} then looks at the evolution of radio LRGs and in section \ref{sec:Levol} we investigate the evolution of the very brightest radio LRGs."633" Throughout this paper we assume a flat. (Q4,,04)=(0.3.0.7). Io=TOkms+Alpe cosmology."," Throughout this paper we assume a flat $(\Omega_{\rm m},\Omega_{\Lambda})=(0.3,0.7)$, $H_{0}=70\,{\rm km\,s}^{-1}\,{\rm Mpc}^{-1}$ cosmology."634" ALL radio [lux densities and luminosities are at GCGlIz unless otherwise stated and when estimating radio luminosities throughout this paper k-corrections have been performed: assuming a continuum shape of S,xσης", All radio flux densities and luminosities are at GHz unless otherwise stated and when estimating radio luminosities throughout this paper $k$ -corrections have been performed assuming a continuum shape of $S_\nu\propto\nu^{-0.7}$.635 The LAG samples used in this paper are originally defined [rom three spectroscopic surveys: SDSS. 25LAC( and citepeisü1.can06.rosQS..," The LRG samples used in this paper are originally defined from three spectroscopic surveys: SDSS, 2SLAQ and \\citep{eis01,can06,ros08}."636 Phe LRG selection was refined. by 7 to create photometric samples from the SDSS DR5 (?7) and to cut down on stellar contamination.," The LRG selection was refined by \citet{saw09} to create photometric samples from the SDSS DR5 \citep{yor00,ald07} and to cut down on stellar contamination."637 We use LRG samples defined identically but drawn from the more recent DIU (7)., We use LRG samples defined identically but drawn from the more recent DR7 \citep{aba09}.638 To identify racio-Ioud LRGs in our sample we compare our LRG catalogues with radio source catalogues from the VSS (2?) and FIRST (2?) surveys., To identify radio-loud LRGs in our sample we compare our LRG catalogues with radio source catalogues from the NVSS \citep{con98} and FIRST \citep{bec00} surveys.639 Both surveys are carried out at GCGllIz and the high. angular resolution (~Saaresec) and faint Dux limit (lo—0.15 mmJv) of the FIRST survey combined. with the large-scale sensitivity. of he NVSS make them complementary tools for identifving radio LRGs., Both surveys are carried out at GHz and the high angular resolution $\sim$ arcsec) and faint flux limit $1\sigma\sim$ mJy) of the FIRST survey combined with the large-scale sensitivity of the NVSS make them complementary tools for identifying radio LRGs.640 Phe FIRST survey covers much of the same sky area as the SDSS north Galactic cap., The FIRST survey covers much of the same sky area as the SDSS north Galactic cap.641 In the overlap region here are 110104. 652401 ancl 799519 objects in the SDSS. PSLAQ and LLhG samples respectively.," In the overlap region there are 110104, 652401 and 799519 objects in the SDSS, 2SLAQ and LRG samples respectively."642 See 2? for the redshift distributions. expected contamination and. autocorrelation clustering properties of the LAC samples.," See \citet{saw09} for the redshift distributions, expected contamination and autocorrelation clustering properties of the LRG samples."643 Complex radio. source. morphology due to extended structures compounded. by size-cepencent response ellects due to the use of interferometers makes radio source matching more involved than simply matching sky positions., Complex radio source morphology due to extended structures compounded by size-dependent response effects due to the use of interferometers makes radio source matching more involved than simply matching sky positions.644 The most accurate ancl precise method Lor cross-matching has always been manual inspection (c.g. 2))., The most accurate and precise method for cross-matching has always been manual inspection (e.g. \citealt{sad07}) ).645 However. the size of our LRG samples forces us to define an automated cross-matching procedure that does not require visual inspection of all of the potential radio matches in the sample.," However, the size of our LRG samples forces us to define an automated cross-matching procedure that does not require visual inspection of all of the potential radio matches in the sample."646 Automated radio-matehing routines have been developed before (e.g. 27)). and even samples defined. by manual inspection use some automated procedures to define a sample of potential matches that are then visually inspected.," Automated radio-matching routines have been developed before (e.g. \citealt{bes05,k+i08}) ), and even samples defined by manual inspection use some automated procedures to define a sample of potential matches that are then visually inspected."647 7 define two samples of radio LRGs from the 25LAQ spectroscopic sample., \citet{sad07} define two samples of radio LRGs from the 2SLAQ spectroscopic sample.648 One is based on manual. inspection and the other based. on automatic cross matching to the FIRST surveys., One is based on manual inspection and the other based on automatic cross matching to the FIRST survey.649 We modified. their selection criteria to define a radio matching procedure and use their manually inspected sample to test our results., We modified their selection criteria to define a radio matching procedure and use their manually inspected sample to test our results.650 We match the LRG and FIRST catalogues within a 30aarcsec radius. and the LIC: and NWSS catalogues within a aaresec radius. retaining all radio matches within the given radius around an LRG.," We match the LRG and FIRST catalogues within a arcsec radius, and the LRG and NVSS catalogues within a arcsec radius, retaining all radio matches within the given radius around an LRG."651 In this initial cross matching we do not apply any racio Hux limits. these are applied below.," In this initial cross matching we do not apply any radio flux limits, these are applied below."652 Following ? we use the FIRST matches as our primary tool for identifving racio galaxies., Following \citet{sad07} we use the FIRST matches as our primary tool for identifying radio galaxies.653 We accept matches that meet one of three criteria: For any sources that. had NVSS matches within aaresee but not FIRST matehes we applied: a similar set of criteria based on 2? to the NVSS sources to define potential radio galaxies.," We accept matches that meet one of three criteria: For any sources that had NVSS matches within arcsec but not FIRST matches we applied a similar set of criteria based on \citet{bes05}654 to the NVSS sources to define potential radio galaxies."655 Phese are:, These are:656to unitv. the shape of the shear curve in the transition region is given approximately bv the kink solution (5)).,"to unity, the shape of the shear curve in the transition region is given approximately by the kink solution \ref{eq:kink}) )."657 Decause of the conservation law (31)). the interfaces cannot move independenilv.," Because of the conservation law \ref{eq:cons}) ), the interfaces cannot move independently."658 Their interactions can be modeled by treating each interface as a particle that exerts forces on other particles (INawasaki&Ola1982:MajumelarIIuse1995).," Their interactions can be modeled by treating each interface as a particle that exerts forces on other particles \citep{kaw82,mh95}."659. This process is known as coarsening or ripening., This process is known as coarsening or ripening.660 In an infinite svstem. (he coarsening process continues indefinitely. although at a slower and slower rate as the domain sizes grow.," In an infinite system, the coarsening process continues indefinitely, although at a slower and slower rate as the domain sizes grow."661 Thus complete thermodynamic equilibrium is never achieved., Thus complete thermodynamic equilibrium is never achieved.662 The coarsening process in the one-dimensional Cahbn-IHillimud equation exhibits scaling behavior. (hat is. the characteristic distance between (he interfaces erows indefinitely. but the correlation function retains the same shape.," The coarsening process in the one-dimensional Cahn-Hilliard equation exhibits scaling behavior, that is, the characteristic distance between the interfaces grows indefinitely but the correlation function retains the same shape."663 However. in a planetary ring (he coarsening will be halted when the clistance between interfaces becomes comparable to the tidal width ol relsec:tensile..," However, in a planetary ring the coarsening will be halted when the distance between interfaces becomes comparable to the tidal width of \\ref{sec:tensile}."664 Thus our tov model leads naturally to the conclusion that the irregular structive in Satums rings should have a characteristic size comparable to the (dal width. which we estimated could be as large as ~100km.," Thus our toy model leads naturally to the conclusion that the irregular structure in Saturn's rings should have a characteristic size comparable to the tidal width, which we estimated could be as large as $\sim 100\km$."665 Assuming that the characteristic width of the interface between solid and liquid phases is L. the parameter e is of order L?r where v is the kinematic viscosity., Assuming that the characteristic width of the interface between solid and liquid phases is $L$ the parameter $\epsilon$ is of order $L^2\nu$ where $\nu$ is the kinematic viscosity.666 It is plausible that L is comparable to the radius of large ring particles., It is plausible that $L$ is comparable to the radius of large ring particles.667 One interesting unresolved issue is whether our one-dimensional approximation is adecquate., One interesting unresolved issue is whether our one-dimensional approximation is adequate.668 Coursening in the Cahbn-Hilliard. equation is much faster for svstems with more than one dimension. where the [ree οποιον associated with the interfaces or domain walls can be reduced by reducing their radius of curvature.," Coarsening in the Cahn-Hilliard equation is much faster for systems with more than one dimension, where the free energy associated with the interfaces or domain walls can be reduced by reducing their radius of curvature."669 Is the modest curvature of annuli in the D-ring sufficient to make this an important contributor to coarsening dvnamies?, Is the modest curvature of annuli in the B-ring sufficient to make this an important contributor to coarsening dynamics?670 A second unresolved issue is (he importance of noise., A second unresolved issue is the importance of noise.671 The Cahln-IHilliard equation is a zero-tenperature model: adding thermal noise converts the equation to a finite-temperature model., The Cahn-Hilliard equation is a zero-temperature model; adding thermal noise converts the equation to a finite-temperature model.672 Is such a model more relevant lor Saturns D ring. and if so. what sets the effective temperature (impacts of small bodies?," Is such a model more relevant for Saturn's B ring, and if so, what sets the effective temperature (impacts of small bodies?"673 gravitational wakes from laree ring particles?)?, gravitational wakes from large ring particles?)?674 Are the f[Inetuations sullicient lo trigger phase separation in the metastable region of the Cahbn-IHilliard equation?, Are the fluctuations sufficient to trigger phase separation in the metastable region of the Cahn-Hilliard equation?675 We have suggested that the irregular structure in Saturis D ring arises [rom the formation of solid ring-particle assemblies. which are limited in size bv the competition between tidal forces and the tensile strength of these assemblies.," We have suggested that the irregular structure in Saturn's B ring arises from the formation of solid ring-particle assemblies, which are limited in size by the competition between tidal forces and the tensile strength of these assemblies."676" We have shown thatif the shear stress is a decreasing function of the shear.Q0X,,/0s« 0. then the ring is unstable"," We have shown thatif the shear stress is a decreasing function of the shear,$\p\Sigma_{xy}/\p s < 0$ , then the ring is unstable"677Similarly. we can ask. what is the rauge in redshift that we are probiug?,"Similarly, we can ask, what is the range in redshift that we are probing?"678 This is just which we show in Figure 6.., This is just which we show in Figure \ref{fig:zdist}.679 For larger values of the exponent (>22). relatively more events occur at ligher redshift. aud the dependence of the οἱserved strain on the maxima redshift will be stronger.," For larger values of the exponent $\gamma\gtrsim2$ ), relatively more events occur at higher redshift, and the dependence of the observed strain on the maximum redshift will be stronger."680 More specifically. we can calculate the mean redshift. Again. the iutegrals separate and we fiud that this average redshift is independent of frequency: This is iudepenudeut of the details of the MDBII population aud the normalization of the merger rate. but dependent on the merecr rate evolution aud he cosmology.," More specifically, we can calculate the mean redshift, Again, the integrals separate and we find that this average redshift is independent of frequency: This is independent of the details of the MBH population and the normalization of the merger rate, but dependent on the merger rate evolution and the cosmology."681 In Figure 7 we show the average redshift for a variety of cosiuologies aud merger histories., In Figure \ref{fig:zav} we show the average redshift for a variety of cosmologies and merger histories.682a factor 2 over the parameter range of interest. its change within the best fit contours is siguificautly less.,"a factor 2 over the parameter range of interest, its change within the best fit contours is significantly less."683" For cos;~ 0.5. 6 increases modestly with «. due to Doppler blueshiftiug. so the product of £4 aud Tig nust decrease to maintain agreenient with Z5, "," For $\cos i \sim 0.5$ , $\delta$ increases modestly with $a_*$ due to Doppler blueshifting, so the product of $f_{\rm col}$ and $\teff$ must decrease to maintain agreement with $T_{\rm obs}$."684"Since Tig ds the primary diver of variations in ως aud fi,aud Tig are positively correlated. both Tig aud. f; must decrease asd. mereases."," Since $\teff$ is the primary driver of variations in $f_{\rm col}$ , and $f_{col}$and $\teff$ are positively correlated, both $\teff$ and $f_{\rm col}$ must decrease as $a_*$ increases."685" The same argunienut applies outside the best-fit contours. but leads to a mich largervariation in ""ol:"," The same argument applies outside the best-fit contours, but leads to a much largervariation in $f_{\rm col}$."686 The confidence coutomrs in Figure 23— confini a strong auti-correlation of Af with cos/. or equivaleutly. a correlation of Af with /," The confidence contours in Figure \ref{f:inc} confirm a strong anti-correlation of $M$ with $\cos i$ or equivalently, a correlation of $M$ with $i$."687 This correlation is driveu primarily through the ¢ dependence of 6 aud jp., This correlation is driven primarily through the $i$ dependence of $\delta$ and $\mu$.688 As / increases. the projected area of the disk decreases while limb darkening shifts iutensity to lower 7.," As $i$ increases, the projected area of the disk decreases while limb darkening shifts intensity to lower $i$."689 The combined effects lead to a significant decrease in ff as / increases., The combined effects lead to a significant decrease in $\mu$ as $i$ increases.690 For higher «.. these effects are somewhat mitigated by relativistic beaming. which tends to shift iutensitv to larger /," For higher $a_*$ , these effects are somewhat mitigated by relativistic beaming, which tends to shift intensity to larger $i$."691 Iu addition. Doppler blue-shifts due to the Keplerian motion cause à to increase with /.," In addition, Doppler blue-shifts due to the Keplerian motion cause $\delta$ to increase with $i$ ."692 Both effects are present and drive a positive correlation of AL aud /. consistent with Figure 3..," Both effects are present and drive a positive correlation of $M$ and $i$, consistent with Figure \ref{f:inc}."693 The auti-correlation of / aud pe dominates at low spin. while the correlation of ó with { dominates at higher spin because rotational velocities are a laree fraction of the speedof light.," The anti-correlation of $i$ and $\mu$ dominates at low spin, while the correlation of $\delta$ with $i$ dominates at higher spin because rotational velocities are a large fraction of the speedof light."694 The effects contribute comparably for a.~0.7., The effects contribute comparably for $a_* \sim 0.7$.695 We note that found a simular correlation in their analysis of several ULN sources., We note that found a similar correlation in their analysis of several ULX sources.696 To explain their results. they attribute the correlation to Doppler shifts (ic. the dependence of à on 7). which is consistent with the fact that their best-fit models favored ligh « ," To explain their results, they attribute the correlation to Doppler shifts (i.e. the dependence of $\delta$ on $i$ ), which is consistent with the fact that their best-fit models favored high $a_*$ ."697The auti-correlation of best-fit (with A and ας follows directly from equations (2)) aud (3))., The anti-correlation of best-fit $\ell$with $M$ and $a_*$ follows directly from equations \ref{eq:tobs}) ) and \ref{eq:lobs}) ).698 As M increases. (f must decrease to keep Lop. approximately coustant. but keeping Των coustant then requiresan increase ina. (1.6. a reduction iu ry}.," As $M$ increases, $\ell$ must decrease to keep $L_{\rm obs}$ approximately constant, but keeping $T_{\rm obs}$ constant then requiresan increase in $a_*$ (i.e. a reduction in $r_{\rm in}$ )."699 This is why high AZaud low a. (and vice-versa) vield poor fits for cos/=0.5 in Figure L., This is why high $M$and low $a_*$ (and vice-versa) yield poor fits for $\cos i=0.5$ in Figure \ref{f:three}.700 With this uuderstaudius of how A. ἐν ἐν aud « correlate. it is useful to cousider what ultimately sets he 1iuuiuun allowed AL in the two data sets.," With this understanding of how $M$, $i$ , $\ell$, and $a_*$ correlate, it is useful to consider what ultimately sets the minimum allowed $M$ in the two data sets."701" The Lj, coustraint (eq. [3]])", The $L_{\rm obs}$ constraint (eq. \ref{eq:lobs}] ])702 allows AY todecrease as long as there is a corresponding Increase m µ or au increase in (., allows $M$ todecrease as long as there is a corresponding increase in $\mu$ or an increase in $\ell$.703" For fits to the NMMO data. Cis set by the T4, constraint (eq. 2|)."," For fits to the XMM2 data, $\ell$ is set by the $T_{\rm obs}$ constraint (eq. \ref{eq:tobs}] ])."704" Since (increases as M. decreases. ài, nmst increase."," Since $\ell$ increases as $M$ decreases, $r_{\rm in}$ must increase."705 Hence. the maxiuuu ( and minimum AL are obtained Or dd.=|.," Hence, the maximum $\ell$ and minimum $M$ are obtained for $a_*=-1$."706" This aygunment leads to a muüuimuun AL for any fixed / and since ids maxinimun for face on disks. the ""elobal ήπια of M occurs at /=07 aud corresponds o ( slightly less then unity."," This argument leads to a minimum $M$ for any fixed $i$ and since $\mu$ is maximum for face on disks, the `global' minimum of $M$ occurs at $i=0^\circ$ and corresponds to $\ell$ slightly less then unity."707" Ποσο, the coustraiuts that AL23000AL.. is independent the argument that («1."," Hence, the constraints that $M708\gtrsim 3000 \Msun$ is of the argument that $\ell < 1$."709 For the audChandra ofdatasets. which cousist of observations with higher Lj. this is not the case.," For the and datasets, which consist of observations with higher $L_{\rm obs}$, this is not the case."710 Our models are capped at (=1 due to incousistencies in the underlying modelassunuptious for 621., Our models are capped at $\ell=1$ due to inconsistencies in the underlying modelassumptions for $\ell \gtrsim 1$.711 For some nüunuuni AL (AL~GOOOAL.:Surf AL~LOOOAL..: Chandra). equation. (3)) cannot be satisfied for (<1. even with ;/= 07.," For some minimum $M$ $M \sim7126000 \Msun$:; $M \sim 4000 \Msun$: ), equation \ref{eq:lobs}) ) cannot be satisfied for $\ell \le 1$, even with $i=0^\circ$ ."713" This correspoucds also to a lower limit on ας since further increases d ry, cannot be offset bv decreases (iucreases) in AL (1) to keep Tii, constant.", This corresponds also to a lower limit on $a_*$ since further increases in $r_{\rm in}$ cannot be offset by decreases (increases) in $M$ $\ell$ ) to keep $T_{\rm obs}$ constant.714 If we ignored the internal iuconsistencies in thin disk assunptious aud extended our models to £6>1. we expect we would obtain reasonable fits for lower AM aud a. as equations (2)) aud (3)) could still be satisfied.," If we ignored the internal inconsistencies in thin disk assumptions and extended our models to $\ell > 1$, we expect we would obtain reasonable fits for lower $M$ and $a_*$ as equations \ref{eq:tobs}) ) and \ref{eq:lobs}) ) could still be satisfied."715 Hence. the more stringent lower luit on M. aud ας for theSwift audChandra fits is not independent of the Eddington limit.," Hence, the more stringent lower limit on $M$ and $a_*$ for the and fits is not independent of the Eddington limit."716 For the NAIAI2 data. the wminimain allowed AL is reached for amodels with (~0.7. just below the Eddingtou The assumptions uuderlviug the thin accretion diskmodel are likely to break down for (c~1 although it is difücult to precisely estimate the ( value where our spectral constraints ire πο longer reasonable.," For the XMM2 data, the minimum allowed $M$ is reached for models with $\ell \sim 0.7$, just below the Eddington The assumptions underlying the thin accretion diskmodel are likely to break down for $\ell \sim 1$ although it is difficult to precisely estimate the $\ell$ value where our spectral constraints are no longer reasonable."717 General relativistic maecuctohydrodvnamuic simulatious and slim disk models suggest that the thin disk spectral models remain reliable to (at least) (ο., General relativistic magnetohydrodynamic simulations and slim disk models suggest that the thin disk spectral models remain reliable to (at least) $\ell \lesssim 0.3$.718 Observations of Galactic Narav biuaries sugecst that there are no abrupt changes at fhis €2010).. so it is pausible that models remain basically sound even for somewhat higher f.," Observations of Galactic X-ray binaries suggest that there are no abrupt changes at this $\ell$, so it is plausible that models remain basically sound even for somewhat higher $\ell$."719 The strong correlation of 4? with P and fy. iu Fiemve (as well as a sinular one for ΑΠ) results from the failure of the BUSPEC imodel to adequately approximate the thermal cussion for AL and ας outside the confidencecontours., The strong correlation of $\chi^2$ with $\Gamma$ and $f_{\rm sc}$ in Figure \ref{f:three} (as well as a similar one for $N_{\rm H}$ ) results from the failure of the BHSPEC model to adequately approximate the thermal emission for $M$ and $a_*$ outside the confidencecontours.720 If BUSPEC is a poor match to the thermal spectrin. the ft compcusates bv adjusting Nyy or the SIMPL parameters.," If BHSPEC is a poor match to the thermal spectrum, the fit compensates by adjusting $N_{\rm H}$ or the SIMPL parameters."721 For example. at low AL aud a... the disk is too cold to match the NMM?2. data. so SIMPLE adjusts by increasing the scattering fraction aud making the power law steeper. to better fit the high cuerey tail of the thermal cuussion.," For example, at low $M$ and $a_*$, the disk is too cold to match the XMM2 data, so SIMPL adjusts by increasing the scattering fraction and making the power law steeper, to better fit the high energy tail of the thermal emission."722" To prevent au excess at lower enereies. the Nyy inereases simultaneously,"," To prevent an excess at lower energies, the $N_{\rm H}$ increases simultaneously."723 For the lower signal-to-noise Suvft andChandra data. Nyy adjusts in a simular manucr. even though the SIMPL componcut is absent.," For the lower signal-to-noise and data, $N_{\rm H}$ adjusts in a similar manner, even though the SIMPL component is absent."724 The width of the confidence contours appears to be set largely by the effectiveness of these compensation moechanisius., The width of the confidence contours appears to be set largely by the effectiveness of these compensation mechanisms.725 Hence. the extent of the confidence contours for a given / could presumably be reduced with better statistics at ligh cuereies to constrain the SIMIPL paralucters aud independent coustraiuts on Nyy.," Hence, the extent of the confidence contours for a given $i$ could presumably be reduced with better statistics at high energies to constrain the SIMPL parameters and independent constraints on $N_{\rm H}$."726 Finally. it is worth considering the degree to which our correlations could be reproduced by a uou-relativistic analvsis. but assuninug rg isequal to the ISCO radius.," Finally, it is worth considering the degree to which our correlations could be reproduced by a non-relativistic analysis, but assuming $r_{\rm in}$ isequal to the ISCO radius."727 For example. assuming coustaut fou)~l.7. ó— 1. aud ἐνονcos? in equation L. one cau recover sonie aspects of theinferred correlations of AJ with e. and ;.," For example, assuming constant $f_{\rm col} \sim 1.7$, $\delta \sim 1$ , and $\mu \sim \cos728i$ in equation \ref{eq:mass}, one can recover some aspects of theinferred correlations of $M$ with $a_*$ and$i$ ."729 The sensitivity of AL to a. would be well approximated for low-to-moderate a... but the dependence of 6. fi; aud Boon es can leadto modest discrepancies as «> l.," The sensitivity of $M$ to $a_*$ would be well approximated for low-to-moderate $a_*$, but the dependence of $\delta$ , $f_{\rm col}$ , and $\mu$ on $a_*$ can leadto modest discrepancies as $a_* \rightarrow 1$ ."730 Iu contrast. the correlation of AL with ; would only be crudely reproduced since the above prescription would suggest ALx(cos?) L7.," In contrast, the correlation of $M$ with $i$ would only be crudely reproduced since the above prescription would suggest $M \propto (\cos i)^{-1/2}$ ."731 This underestimates hesensitivity of AL to ; for low to moderate ;. but overestimates it as /> 907. where the projected area goes to zero in a non-relativistie. model.," This underestimates thesensitivity of $M$ to $i$ for low to moderate $i$ , but overestimates it as $i \rightarrow 90^\circ$ , where the projected area goes to zero in a non-relativistic model."732Since the ow to moderate range is probably more relevant for observed svstenis. the overall uncertainty of AL would veo underestimated.,"Since the low to moderate range is probably more relevant for observed systems, the overall uncertainty of $M$ would be underestimated."733 We also note that although the, We also note that although the734lowest.,lowest.735 Combined with a measurement of the distance aud apparent angular size of the neutron star. the measurement of the Eddineton flux at touchdown cau lead to uncorrelated iieasuremienuts of the neutron star mass and radius (see. e.2.. 11987: Damen et 14990: Ozzel et 22009: Coiwver ct 22010a. b).," Combined with a measurement of the distance and apparent angular size of the neutron star, the measurement of the Eddington flux at touchdown can lead to uncorrelated measurements of the neutron star mass and radius (see, e.g., 1987; Damen et 1990; Özzel et 2009; Güvver et 2010a, b)."736 Nearly continuous observations of bursting low mass XN-rav binaries over the last 15 wears with the Rossi A-rav Timing Explorer (RNTE) provided high quality data for over one thousaud N-rav bursts froii more than forty X-ray binaries (Calloway et 220084)., Nearly continuous observations of bursting low mass X-ray binaries over the last 15 years with the Rossi X-ray Timing Explorer (RXTE) provided high quality data for over one thousand X-ray bursts from more than forty X-ray binaries (Galloway et 2008a).737 This rich database of X-ray burst observations enables a study of the spectra of PRE bursts from which the Eddington lait can be measured aud anv systematic variations iu the interred spectral paralucters of the X-ray bursts can be inferred., This rich database of X-ray burst observations enables a study of the spectra of PRE bursts from which the Eddington limit can be measured and any systematic variations in the inferred spectral parameters of the X-ray bursts can be inferred.738 Such an assessment is esscutial to better establish the reliability of the lnass and radius measurements from time-resolved spectroscopic analysis of X-ray bursts., Such an assessment is essential to better establish the reliability of the mass and radius measurements from time-resolved spectroscopic analysis of X-ray bursts.739 Usine the archival RATE observations. we recently studied the systematic uncertainties prescut in the appareut radius measureimoeuts during the cooling tails of the X-ray bursts (Ciivver et 22011. hereafter Paper D.," Using the archival RXTE observations, we recently studied the systematic uncertainties present in the apparent radius measurements during the cooling tails of the X-ray bursts (Güvver et 2011, hereafter Paper I)."740 Our analysis showed that the vast majority of the N-rav spectra extracted from the cooling tails of LL? X-ray bursts are statistically consistent with Planckian functions aud the inferred spectral paraiueters for the majority of the bursts follow the expected E. X T! relatiou for most of the sources;, Our analysis showed that the vast majority of the X-ray spectra extracted from the cooling tails of 447 X-ray bursts are statistically consistent with Planckian functions and the inferred spectral parameters for the majority of the bursts follow the expected F $\propto$ $^{4}$ relation for most of the sources.741 These results enabled us to measure the appareut radii of a mmibor of neutron stars and assess the svstematic uncertainties iu these measurements., These results enabled us to measure the apparent radii of a number of neutron stars and assess the systematic uncertainties in these measurements.742 Iu this paper. we continue to analyze all of the ταν bursts observed from low mass N-rav binaries in order to determine the uucertainties related to spectroscopic iieasuremenuts of the Eddinetou μπιτ iu PRE bursts.," In this paper, we continue to analyze all of the X-ray bursts observed from low mass X-ray binaries in order to determine the uncertainties related to spectroscopic measurements of the Eddington limit in PRE bursts."743 We focus ou the measurement of the Eddington flux at the touchdown monmenuts in twelve Nav binaries from which multiple PRE events have been observed., We focus on the measurement of the Eddington flux at the touchdown moments in twelve X-ray binaries from which multiple PRE events have been observed.744 Our aiu is to determine auy systematic macertaintics in these measurements., Our aim is to determine any systematic uncertainties in these measurements.745 Iu 822. we bricfly stuumarize the observations aud data analysis techniques. which we discuss in full detail in Paper I Iu 8323. we introduce a systematic method to select the PRE eveuts from the burst archive using time resolved spectroscopic micasuremeuts.," In 2, we briefly summarize the observations and data analysis techniques, which we discuss in full detail in Paper I. In 3, we introduce a systematic method to select the PRE events from the burst archive using time resolved spectroscopic measurements."746 In ll and 5. we describe the statistical tools based ou Bayesian Gaussian mixture algorithius that we use to determine the Eddinetou limit aud associated systematic uncertainties for cach source.," In 4 and 5, we describe the statistical tools based on Bayesian Gaussian mixture algorithms that we use to determine the Eddington limit and associated systematic uncertainties for each source."747 Finally. in 866. we present our results aud discuss their duplications.," Finally, in 6, we present our results and discuss their implications."748 Galloway et (2008a) preseuted a catalog of RATE obscrvatious of N-xav. bursts from £8 low mass X-ray binaries., Galloway et (2008a) presented a catalog of RXTE observations of X-ray bursts from 48 low mass X-ray binaries.749 Following Paper L we chose 12 X-ray binaries frou this sample based on a uuuber of criteria.," Following Paper I, we chose 12 X-ray binaries from this sample based on a number of criteria."750 We included only the sources that show at least two PRE eveuts (as defined i Galloway et 220082)., We included only the sources that show at least two PRE events (as defined in Galloway et 2008a).751 We excluded all N-vay binaries that are known to be dippers. ADC sources. or lave high inclinations as well as the known millisecond pulsars.," We excluded all X-ray binaries that are known to be dippers, ADC sources, or have high inclinations as well as the known millisecond pulsars."752 Because they are likely to be affected by source confusion (Calloway et 22008a: Ίνους et 22010). we excluded observations of GRS 2853 and 2E 2929 and also a small umuber of bursts from Aq) 1. IU 3L and IU 37.," Because they are likely to be affected by source confusion (Galloway et 2008a; Keek et 2010), we excluded observations of GRS $-$ 2853 and 2E $-$ 2929 and also a small number of bursts from Aql $-$ 1, 4U $-$ 34, and 4U $-$ 37."753 Finally. since a study of the PRE events observed from EXO 218. IU 52. and LU 30 have been reported clsewhere (Ozzel et al.," Finally, since a study of the PRE events observed from EXO $-$ 248, 4U $-$ 52, and 4U $-$ 30 have been reported elsewhere (Özzel et al."754 2009: Ciüvver et 22010a. b). the results for these sources will not e repeated here.," 2009; Güvver et 2010a, b), the results for these sources will not be repeated here."755 Asin Paper L woe imposed a limit ou the persistent fiux measured prior to cach X-ray burst such that it does not excecd of the peak burst flux. io. Foo!Fraa<OL as calculated by Galloway et (20082).," As in Paper I, we imposed a limit on the persistent flux measured prior to each X-ray burst such that it does not exceed of the peak burst flux, i.e., $\gamma\equiv F_{\rm per}/F_{\rm Edd}<0.1$ as calculated by Galloway et (2008a)."756 huposiug this limit reduces the systematic uncertainties introduced by subtracting the pre-burst emission from the X-ray burst spectra., Imposing this limit reduces the systematic uncertainties introduced by subtracting the pre-burst emission from the X-ray burst spectra.757 The final list of all the A-ray binaries aud the N-ray. bursts we studied is prescuted in Table 1.., The final list of all the X-ray binaries and the X-ray bursts we studied is presented in Table \ref{sourcestable}.758 We performed the data analysis following the methods detailed iu Galloway ct (2008a) aud in Paper 1. We extracted time resolved 25.0 keV N-rav spectra from all the RNTE/PCA lavers., We performed the data analysis following the methods detailed in Galloway et (2008a) and in Paper I. We extracted time resolved $-$ 25.0 keV X-ray spectra from all the RXTE/PCA layers.759 We varied the exposure time between 0.25 s and 1 s, We varied the exposure time between 0.25 s and 1 s760these subsections have tvpical data lengths of ~30 to ~45 minutes. corresponding to between ~5 and 10 eveles of a QPO modulation.,"these subsections have typical data lengths of $\sim$ 30 to $\sim$ 45 minutes, corresponding to between $\sim$ 5 and $\sim$ 10 cycles of a QPO modulation."761 Given the incoherent nature of the QPOs and the presence of flickering on similar time-scales. QPOs are difficult to identify using standard techniques.," Given the incoherent nature of the QPOs and the presence of flickering on similar time-scales, QPOs are difficult to identify using standard techniques."762 Pherefore. we have been fairly conservative in identifying the QPOs only those that are then clearly seen in the light. curves or at least several eveles are accepted.," Therefore, we have been fairly conservative in identifying the QPOs -- only those that are then clearly seen in the light curves for at least several cycles are accepted."763 “Phere are probably other short-lived QPOs. mace dillicult to identify because of stochastic Hickering in the light curve.," There are probably other short-lived QPOs, made difficult to identify because of stochastic flickering in the light curve."764 In Paper Lwe reported hat the ~ GOO s QPOs in the February 2000 outburst of VW Livi halvecl in period. near the end of our run (see also Table 2))., In Paper I we reported that the $\sim$ 600 s QPOs in the February 2000 outburst of VW Hyi halved in period near the end of our run (see also Table \ref{dno4tab2}) ).765 This was a first hint that we should expect requeney doubling in the QPOs. as observed in the DNOs.," This was a first hint that we should expect frequency doubling in the QPOs, as observed in the DNOs."766 This has proved to be the case. and also extends to tripling of frequencies our results are shown in Fie.," This has proved to be the case, and also extends to tripling of frequencies – our results are shown in Fig."767 10. and the »eriods are listed in Table 2.., \ref{dno4fig11} and the periods are listed in Table \ref{dno4tab2}.768 From Fig., From Fig.769 LO we see that the first appearance of the irst harmonic of the QPOs is at 2 = 0.2 d. which is the same," \ref{dno4fig11} we see that the first appearance of the first harmonic of the QPOs is at $T$ = 0.2 d, which is the same"770 + —, + =0.771" In this expression (he nonzero derivatives of the δν will respect to the coordinates are 1— 7 Ff.1— 7 F,Hoc —πο HCM) -- + b,Jo, Gy derivatives of the acceleration lor 7 Zjare 2 Cm ⋅ Mue for the inverse square law. and. for the isothermal sphere model. =Gin, | Y."," In this expression the nonzero derivatives of the $S_{i,k,n}$ with respect to the coordinates are = - F^+_n, = - F^-_n, = , i, = (F^+_n + + The derivatives of the acceleration for $i\not= j$ are = ( - ), for the inverse square law, and, for the isothermal sphere model, = ( - )."772 For ¢—j the derivatives are —n, For $i=j$ the derivatives are =.773iit Equation (A)) with the nonzero terms eliminated is, Equation \ref{eq:shifts}) ) with the nonzero terms eliminated is774the 1985 outburst (Tavloretal.1989).,the 1985 outburst \citep{tay89}.775. Thus there is evidence that the bipolar emission seen here and in the radio arises Irom the same regions of the remnant. if the expansion velocities in the E-W direction are roughly constant over the first 155 claws.," Thus there is evidence that the bipolar emission seen here and in the radio arises from the same regions of the remnant, if the expansion velocities in the E-W direction are roughly constant over the first 155 days."776 Tracing (he rine-like structure of the optical remnant suggests a N-S (peak-to-peak) extent of 150425 mas., Tracing the ring-like structure of the optical remnant suggests a N-S (peak-to-peak) extent of $150 \pm 25$ mas.777 This corresponds {ο an expansion rate of 0.48+0.08 mas compared with 0.6230.0L mas d! derived in the radio for the central ring on day 13.8 (O'Brienοἱal.2006)., This corresponds to an expansion rate of $0.48 \pm 0.08$ mas $^{-1}$ compared with $0.62 \pm 0.01$ mas $^{-1}$ derived in the radio for the central ring on day 13.8 \citep{obr06}.778. As noted in O'Brienetal.(2006).. the formal error on this rad10 expansion rate is likely to be an underestimate: Rupenοἱal.(2007) also derived racliol expansion rates for the ring ~20% higher.," As noted in \cite{obr06}, the formal error on this radio expansion rate is likely to be an underestimate; \cite{rup07} also derived radio expansion rates for the ring $\sim20$ higher."779 Thus comparison of the HST and radio data tentatively suggests cleceleration in the N-5 direction. bul verification awaits further optical observations.," Thus comparison of the HST and radio data tentatively suggests deceleration in the N-S direction, but verification awaits further optical observations."780 As noted above. both aand sshow similar structure.," As noted above, both and show similar structure."781" In the ease of both lines. emission might arise either [rom regions downstream of the forward shock in the red giant wind or from a ""precursor ionised region ahead of the shock. or both (e.g.Dopita&Sutherland1996)."," In the case of both lines, emission might arise either from regions downstream of the forward shock in the red giant wind or from a “precursor” ionised region ahead of the shock, or both \citep[e.g.][]{dop96}."782. The more marginal presence of mnmaxv be a direct consequence of particular shock velocities (againseee.g.Dopita&Suther-land1996) coupled with decreasing contrast of extended emission with the central star al longer wavelengths., The more marginal presence of may be a direct consequence of particular shock velocities \citep[again see e.g.][]{dop96} coupled with decreasing contrast of extended emission with the central star at longer wavelengths.783 It is also of interest to note that the assumption [rom Spifzer observations of intrared fine structure ancl coronal lines (Evansetal.2007) of an origin ol these lines in the same remnant regions is consistent with our observations., It is also of interest to note that the assumption from $Spitzer$ observations of infrared fine structure and coronal lines \citep{eva07} of an origin of these lines in the same remnant regions is consistent with our observations.784 O'Brienetal.(2006) proposed a simple model for the radio emission comprising a bipolar structure where the evolution of the optical depth due (o Iree-[ree absorption led to (he gracual uncovering of various features. most notably (is explained the emergence of the outermost radio lobes.," \cite{obr06} proposed a simple model for the radio emission comprising a bipolar structure where the evolution of the optical depth due to free-free absorption led to the gradual uncovering of various features, most notably this explained the emergence of the outermost radio lobes."785" Here. we have modeled the optical emission seen in our IST images with a ""peanut-shaped""bipolar structure using the modeling code described in Brien(2003) (see Figure 4))."," Here, we have modeled the optical emission seen in our HST images with a “peanut-shaped”bipolar structure using the modeling code described in \cite{har03} (see Figure \ref{model}) )."786 The shell has finite thickness (0.05 aresec) and the surface brightness distribution is just determined by the line-ol-sight path length through the nebula., The shell has finite thickness $0.05$ arcsec) and the surface brightness distribution is just determined by the line-of-sight path length through the nebula.787 The axial ratio is set at 3:1. consistent will a constant velocity of expansion along the major axis and deceleration along (he “waist”. as implied by the earlier radio observations.," The axial ratio is set at 3:1, consistent with a constant velocity of expansion along the major axis and deceleration along the “waist”, as implied by the earlier radio observations."788 As can be seen [rom Figure 4.. the model reproduces the morphology of the optical emission extremely well for an inclination 7=:35. consistent with the major axis lving normal to (he plane of the binary orbit. where ;/=30°—40° was given by Dobrzveka& [rom radial velocity studies.," As can be seen from Figure \ref{model}, the model reproduces the morphology of the optical emission extremely well for an inclination $i = 35\degree$, consistent with the major axis lying normal to the plane of the binary orbit, where $i = 30\degree - 40\degree$ was given by \cite{dob94} from radial velocity studies."789 Following O'Brienetal. (2006).. we also note that the 2006 outburst occurred al approximately the same binary phase as in 1985. and," Following \cite{obr06}, , we also note that the 2006 outburst occurred at approximately the same binary phase as in 1985, and"790"Both the existence and order of the regimes forc and 7, (Table 2)) can vary based on theje strength of the turbulence»lence (a).",Both the existence and order of the regimes for$v_c$ and $H_d$ (Table \ref{RegimeOrder}) ) can vary based on the strength of the turbulence $\alpha$ ).791 For example.nmple. if1 ae=0 thenjen the(he only [ormform of e of[our ours that applies is thermal (Eq. 26)).," For example, if $\alpha=0$ then the only form of $v_c$ of ours that applies is thermal (Eq. \ref{vc0}) ),"792 ancl our derivation of Ly does not apply., and our derivation of $H_d$ does not apply.793 For 0.543U«RSAU no changes from the canonical regime ordering occur [or « 1/3., For $0.5AU<R<8AU$ no changes from the canonical regime ordering occur for $2\times 10^{-6}<\alpha<1/3$ .794 Asa drops below about 10.° our present regime ordering of Table 2 breaks down as shown below. though a new ordering (ancl possibly new regimes) could be found through a similar approach. as long as the settling tme remains short (section 3.2).," As $\alpha$ drops below about $10^{-6}$ our present regime ordering of Table 2 breaks down as shown below, though a new ordering (and possibly new regimes) could be found through a similar approach, as long as the settling time remains short (section 3.2)."795 IL αcvul. then 5«au.," If $\alpha<x_{max}^{-1}$, then $\frac{\alpha}{\Omega}<\frac{1}{\Omega x_{max}}$."796 It follows that the transition [rom ry. to Όρο will occur before (hat from v2 (to ey.," It follows that the transition from $v_{h, 1}$ to $v_{h, 2}$ will occur before that from $v_{c, 2}$ to $v_{c, 3}$."797" For large grains. a possible deviation lrom the bottom-to-top canonical ordering shown in Table 2. arises if gravitational instability is triggered before 60,4. which for 0.5.40«RSAU requires a<10 7."," For large grains, a possible deviation from the bottom-to-top canonical ordering shown in Table \ref{RegimeOrder} arises if gravitational instability is triggered before $v_{c, 3}$, which for $0.5AU<R<8 AU$ requires $\alpha \la 10^{-8}$ ."798 For small grains. possible deviations from the canonical regime ordering occurs when Lu=X (Sec.," For small grains, possible deviations from the canonical regime ordering occurs when $\frac{t_m}{x_{max}}=\frac{\sqrt{\alpha}}{\Omega}$ (Sec."799 4.3) and when equations 51.. (see appendix) hold lor 72μις.," 4.3) and when equations \ref{phi01E}, \ref{phi01S} (see appendix) hold for $\tau>{t_m}{x_{max}}$."800 In (ilis case. the weakness of the turbulence delays the transition from thermal collisions to turbulent collisions.," In this case, the weakness of the turbulence delays the transition from thermal collisions to turbulent collisions."801" We have made the approximation that “y(/?) and X,(H) are time independent and that dust erains do not migrate.", We have made the approximation that $\Sigma_d(R)$ and $\Sigma_g(R)$ are time independent and that dust grains do not migrate.802 However. while gas depleted by accretion is replenished from the outer regions of the disc or envelope. dust migration cannot be so simply ignored.," However, while gas depleted by accretion is replenished from the outer regions of the disc or envelope, dust migration cannot be so simply ignored."803 The eas in a protoplanetary disc is partially pressure supported and so rotates al a sub-keplerian velocity., The gas in a protoplanetary disc is partially pressure supported and so rotates at a sub-keplerian velocity.804 The dust grains will then feel a heaciwind and begin to spiral in towares the star (Weidenschilline(1977).. Nakagawaetal. (1986))).," The dust grains will then feel a headwind and begin to spiral in towards the star \citet{WeidenHeadWind}, \citet{Nakagawa86}) )."805 As seen in Nakagawaetal. (1986).. this sub-keplerian rotation behaves as their eq 1.9 (which omits a fraction sign): where ey is the Keplerian velocityancl parameterises the difference between the gas orbit speed and the lxepleriai speed.," As seen in \citet{Nakagawa86}, , this sub-keplerian rotation behaves as their eq 1.9 (which omits a fraction sign): where $v_K$ is the Keplerian velocityand parameterises the difference between the gas orbit speed and the Keplerian speed."806 The, The807where 7' is the temperature of the electron laver. which can be taken as à constant. since we assunie the electrons ave in (thermodynamic equilibrium with the constant temperature quark matter.,"where $T$ is the temperature of the electron layer, which can be taken as a constant, since we assume the electrons are in thermodynamic equilibrium with the constant temperature quark matter."808 In Eqs. (23))-(24)).," In Eqs. \ref{p2}) \ref{3}) ),"809 z is Che space coordinate measuring height above the quark surface. a is the fine structure constant aud inside is (he quark charge density (hequark matter.," $z$ is the space coordinate measuring height above the quark surface, $\alpha $ is the fine structure constant and }$ is the quark charge density inside thequark matter."810 The boundary conditions for Eqs. (23))-(24)), The boundary conditions for Eqs. \ref{p2}) \ref{3}) )811" are V.—V, as 2—τι and V—0 for 2— oc."," are $V\rightarrow V_{q}$ as $z\rightarrow -\infty $ and $V\rightarrow8120$ for $z\rightarrow \infty $ ."813" In the case of the zero temperature electron distribution at (he boundary 2=0 we have the condition V(0)=(3/4)V, CAlcocketal.1936).", In the case of the zero temperature electron distribution at the boundary $z=0$ we have the condition $V(0)=(3/4)V_{q}$ \citep{Al86}.814. The structure of the electrosphere ancl (he corresponding radiation processes essentially depends on the value of Vj. the electric charge density inside the quark star.," The structure of the electrosphere and the corresponding radiation processes essentially depends on the value of $V_q$, the electric charge density inside the quark star."815 When the temperature of the quark star core drops below 107 IX. the strange matter becomes superllIuid.," When the temperature of the quark star core drops below $10^{9}$ K, the strange matter becomes superfluid."816 At this temperature quarks can form colored Cooper pairs near the Fermi surface and become superconducting., At this temperature quarks can form colored Cooper pairs near the Fermi surface and become superconducting.817" From the BCS theory it follows that the critical temperature 7; al which ihe transition to the superconducting state takes place is 7,=A/1.76. where A is the pairing gap energv (Blaschkeetal.2000)."," From the BCS theory it follows that the critical temperature $T_{c}$ at which the transition to the superconducting state takes place is $T_{c}=\Delta /1.76$, where $\Delta $ is the pairing gap energy \citep{Bl}."818. An early estimation of A gave A~0.1—1 MeV BailinandLove(1984).. but some recent studies considering instamlon-incueed interactions between quarks estimated A100 MeV (Alfordetal.1993).," An early estimation of $\Delta $ gave $\Delta \sim8190.1-1$ MeV \cite{early}, but some recent studies considering instanton-induced interactions between quarks estimated $\Delta820\sim 100$ MeV \citep{all1}."821. Stange quark matter in the color-flavor locked (CFL) phase of QCD. which occurs for A~100 MeV. could be rigorously electrically neutral. despite (he unequal quark masses. even in the presence of the electron chemical potential Alfordetal.(1993).," Strange quark matter in the color-flavor locked (CFL) phase of QCD, which occurs for $\Delta \sim 100$ MeV, could be rigorously electrically neutral, despite the unequal quark masses, even in the presence of the electron chemical potential \cite{all1}."822". IIence. for the CFL state of quark matter V,=0 and no electrons are present inside the quark star."," Hence, for the CFL state of quark matter $V_q=0$ and no electrons are present inside the quark star."823" llowever. PageanclUsov(2002) pointed out that for sufficiently laree m, the low density reeime is rather expected to be in the |2-color-[avor Superconductor” phase in which only wand d quarks of (wo color are paired in single condensate while (he ones of the third color. aad s quarks of all three colors. ave unpaired."," However, \citet{PaUs02} pointed out that for sufficiently large $m_{s}$ the low density regime is rather expected to be in the ”2-color-flavor Superconductor” phase in which only $u$ and $d$ quarks of two color are paired in single condensate while the ones of the third color, and $s$ quarks of all three colors, are unpaired."824 In this phase. some electrons are still present.," In this phase, some electrons are still present."825 In other words. electrons may be absent in the core of strange stars but. present. al least. near (he surface where (he densitw is lowest.," In other words, electrons may be absent in the core of strange stars but present, at least, near the surface where the density is lowest."826 Nevertheless. (he presence of the CFL ellect can reduce the electron density at the surface ancl hence it can also significantly reduces the electromagnetic emissivity of the electrons in(the surface laver.," Nevertheless, the presence of the CFL effect can reduce the electron density at the surface and hence it can also significantly reduces the electromagnetic emissivity of the electrons inthe surface layer."827 Therefore. in order to describe the radiation properties of the electrosphere we assume that Ἐν4 0.," Therefore, in order to describe the radiation properties of the electrosphere we assume that $V_q\neq 0$ ."828 The general solution of Eq. (24)), The general solution of Eq. \ref{3}) )829 is given by (ChengandHarko2003) ," is given by \citep{ChHa03}830 "831"NIRSPEC in the low-resolution mode with the 0.38"" slit.",NIRSPEC in the low-resolution mode with the 0.38” slit.832 We emploved the four-nod script to obtain spectra at four different positions along the slit., We employed the four-nod script to obtain spectra at four different positions along the slit.833 For the {ρω spectra the erating (lt was set to cover the wavelength range 1.54 to 1.32 jmi with a dispersion of 2.91 A//pix., For the -band spectra the grating tilt was set to cover the wavelength range 1.54 to 1.83 $\mu$ m with a dispersion of 2.91 /pix.834 The A-band setup covered the wavelength range 2.00 to 2.42 pam. with a dispersion ol 4.27 A//pix.," The -band setup covered the wavelength range 2.00 to 2.42 $\mu$ m, with a dispersion of 4.27 /pix."835 Due to the strong eurvature of the spectra produced by NIRSPEC. each spectrum has a sliehtly different. wavelengt( coverage that depends on (he position οἱ the object along the slit.," Due to the strong curvature of the spectra produced by NIRSPEC, each spectrum has a slightly different wavelength coverage that depends on the position of the object along the slit."836 This effect will be apparent in some of the NIRSPEC spectral sequences presented. below., This effect will be apparent in some of the NIRSPEC spectral sequences presented below.837 The ZF-band data were obtained Irom 12:29 to 13:57 UT. covering of an orbital evele.," The -band data were obtained from 12:29 to 13:57 UT, covering of an orbital cycle."838 The A-band spectra were obtained in the interval 14:24 to 15:25 UT. and covered of an orbital period.," The -band spectra were obtained in the interval 14:24 to 15:25 UT, and covered of an orbital period."839 ΠΟ10255 was used as the tellurie παπάατα for both bandpasses., HD16358 was used as the telluric standard for both bandpasses.840 While the conditions were photometric. we found that the nodding routine did not reliably place our targets exactly on the slit during the fom-position nod. and thus we were unable to exiract photometric information [rom (hese data.," While the conditions were photometric, we found that the nodding routine did not reliably place our targets exactly on the slit during the four-position nod, and thus we were unable to extract photometric information from these data."841 We have decided to use the infrared lisht curves to produce fIux-calibrated spectra., We have decided to use the infrared light curves to produce flux-calibrated spectra.842 Three months before the Gemini observations. on 2002 September 24. we were able to obtain additional. simultaneousJi photometry of EF Eri using SQUD on the IKPNO 2.1 m. These data were reduced in the same fashion as our earlier observations (see Harrison el al.," Three months before the Gemini observations, on 2002 September 24, we were able to obtain additional, simultaneous photometry of EF Eri using SQIID on the KPNO 2.1 m. These data were reduced in the same fashion as our earlier observations (see Harrison et al."843 2003 [or full details)., 2003 for full details).844 The conditions during this run were poorer than those of our 2001 run. and the band light curve (see Fig.," The conditions during this run were poorer than those of our 2001 run, and the -band light curve (see Fig."845 1) has a lower S/N than the earlier effort., 1) has a lower S/N than the earlier effort.846 The {/- and A-band data. however. reveal identical light curves to the 2001. data set. showing no evidence for changes in either (he absolute flux levels. or in the amplitude of the variations.," The - and -band data, however, reveal identical light curves to the 2001 data set, showing no evidence for changes in either the absolute flux levels, or in the amplitude of the variations."847 llarrison et al. (, Harrison et al. (8482003) found that the phasing of EF Evi by Bailev et al. (,2003) found that the phasing of EF Eri by Bailey et al. (8491982). where phase 0 corresponded to the appearance of a sharp dip in the J-band lisht curve. appeared to be identical with binary orbital phase.,"1982), where phase 0 corresponded to the appearance of a sharp dip in the -band light curve, appeared to be identical with binary orbital phase."850 We have used the same set of ephemerides to phase the data here., We have used the same set of ephemerides to phase the data here.851 Because of EF Exis extremely short period. the spectral smearing," Because of EF Eri's extremely short period, the spectral smearing"8520.010 in C. D. V and /. As for LCO observations. we provided individual night-based johetometrie. solutions.,"0.010 in $U$ , $B$ , $V$ and $I$, As for LCO observations, we provided individual night-based photometric solutions."853 However. since the hree solutions were identical. we merged and averaged them ogether in a single johetometrie solution.," However, since the three solutions were identical, we merged and averaged them together in a single photometric solution."854 This implies a grand total of 103 measures der filter. and the solutions read: (sn|(4.902€0.010)CO.A1020).(€D) D—b|(3.1860.012)(0.3120.01)A008)-(D.V) αιο|(8.11540.007)(0.17d:0.01)011)(D.V) f=?|(42630.0110)(0.07£0.01)).012)\1) The tinal of the fitting in this case was 0.040. 0.025. 0.015. and Q.015 in C. D. V and 7. Global photometric errors were estimated using the scheme developed by Patat Carraro (2001. Appendix Al). which takes into account the errors resulting from the PSF fitting procedure (e.. from ALLSTAR/ALLFRAME). and the calibration errors (corresponding to the zero point. colour terms. and extinction errors).," This implies a grand total of 103 measures per filter, and the solutions read: $ U = u + (4.902\pm0.010) + (0.41\pm0.01) \times X + (0.129\pm0.020) \times (U-B)$ $ B = b + (3.186\pm0.012) + (0.31\pm0.01) \times X + (0.057\pm0.008) \times (B-V)$ $ V = v + (3.115\pm0.007) + (0.17\pm0.01) \times X - (0.057\pm0.011) \times (B-V)$ $ I = i + (3.426\pm0.011) + (0.07\pm0.01) \times X + (0.091\pm0.012) \times (V-I)$ The final of the fitting in this case was 0.040, 0.025, 0.015, and 0.015 in $U$, $B$, $V$ and $I$, Global photometric errors were estimated using the scheme developed by Patat Carraro (2001, Appendix A1), which takes into account the errors resulting from the PSF fitting procedure (i.e., from ALLSTAR/ALLFRAME), and the calibration errors (corresponding to the zero point, colour terms, and extinction errors)."855 In Fig., In Fig.856 2 we present our global photometric errors in ΕυVu. αἱD). and (V.1) plotted as a function of V magnitude.," 2 we present our global photometric errors in $V$ , $(B-V)$, $(U-B)$, and $(V-I)$ plotted as a function of $V$ magnitude."857 Quick inspection shows that stars brighterthan Vzm20mag have errors lower than ~0.05 mag in magnitude andlower than ——0.10 mag in (b. V)and(V— £)., Quick inspection shows that stars brighterthan $V \approx 20$mag have errors lower than $\sim0.05$ mag in magnitude andlower than $\sim0.10$ mag in $(B-V)$ and$(V-I)$ .858 Higher errors are, Higher errors are859nonlinear part of the power spectrum does not allect the relevant result much.,nonlinear part of the power spectrum does not affect the relevant result much.860 The reason why nonlincarity becomes important at lower £ for the cross-power is that with the 2PATASS-like galaxy catalog the contribution is biased to lower redshifts (compare redshift. distribution in Figs., The reason why nonlinearity becomes important at lower $\ell$ for the cross-power is that with the 2MASS-like galaxy catalog the contribution is biased to lower redshifts (compare redshift distribution in Figs.861 2 and 5)) that correspond. to larger spatial scales for. fixed angular scales (note &=(fr in the argument of galaxy power spectrum Z).," \ref{fig:z_dist} and \ref{fig:z_dist_cross}) ) that correspond to larger spatial scales for fixed angular scales (note $k = \ell / r$ in the argument of galaxy power spectrum $P_{\rm862gal}$ )."863 1n conclusion. motivated. by the fact that normal galaxies provide a guaranteed contribution to the CGB and that ferm-LAT has à good sensitivity to measure it. ve have theoretically computed. the CGB angular power spectrum due to normal galaxies.," In conclusion, motivated by the fact that normal galaxies provide a guaranteed contribution to the CGB and that -LAT has a good sensitivity to measure it, we have theoretically computed the CGB angular power spectrum due to normal galaxies."864 We have caleulated both the auto-power (C77) and the eross-power (C77) spectra. using the well measured. galaxy power spectrum: for the Cross-power. we correlated the CGB with a 2ALASS-Like ealaxy catalog.," We have calculated both the auto-power $C_\ell^{\gamma\gamma}$ ) and the cross-power $C_\ell^{\gamma g}$ ) spectra, using the well measured galaxy power spectrum; for the cross-power, we correlated the CGB with a 2MASS-like galaxy catalog."865 We found that the amplitude of (7 is smaller than that for other sources such as blazars and dark-matter annihilation., We found that the amplitude of $C_\ell^{\gamma\gamma}$ is smaller than that for other sources such as blazars and dark-matter annihilation.866 Still. Fermc-LXI can measure the significant feature of the galaxy clustering for the multipole range LOSf100 in about 5 vears.," Still, -LAT can measure the significant feature of the galaxy clustering for the multipole range $10 \lesssim \ell \lesssim867100$ in about 5 years."868" The amplitude of the cross-power spectrum CT"" is larger. and the detection prospects are better for higher-enerey photons."," The amplitude of the cross-power spectrum $C_\ell^{\gamma g}$ is larger, and the detection prospects are better for higher-energy photons."869 We also found that the redshift ranges that contribute to the power spectrum the most are cilferent from the case of mean intensity., We also found that the redshift ranges that contribute to the power spectrum the most are different from the case of mean intensity.870 This feature might be helpful in probing the 5-rav luminosity density from normal ealaxies at various recdshift ranges., This feature might be helpful in probing the $\gamma$ -ray luminosity density from normal galaxies at various redshift ranges.871 We thank John Beacom and Trov Porter for insightful comments that helped improve this paper., We thank John Beacom and Troy Porter for insightful comments that helped improve this paper.872 This work was supported. by Sherman Fairchild Foundation (SA) ancl by NASA through the GLAST Fellowship Program. NASA Cooperative Agreement: NNGOGDOOOA (VL).," This work was supported by Sherman Fairchild Foundation (SA) and by NASA through the GLAST Fellowship Program, NASA Cooperative Agreement: NNG06DO90A (VP)."873We also like to note that any type of additional linear sienal cleaniug or pre-processing step. such as those described bv Carter&Winn(2009):Wakliuaunetal. (2011).. are allowed.,"We also like to note that any type of additional linear signal cleaning or pre-processing step, such as those described by \citet{carter09,waldmann11}, are allowed."874 Linear data filtering or cleaning can be understood as iultiphiàius equation 3 from the left with a linear transformation B to ect: BX=BAS., Linear data filtering or cleaning can be understood as multiplying equation \ref{timeseries3} from the left with a linear transformation $\bf{B}$ to get: $\bf{B}\bf{X} = \bf{B}\bf{A}\bf{S}$.875 The underlying data model assumed iu lis paper is hence not affected., The underlying data model assumed in this paper is hence not affected.876 After the observed signals have successfully been whitened να we estimate the wining matrix of the whitened sigial. A. uxug the MULTI algorithiu (Tichavsk*etal.2006a).," After the observed signals have successfully been whitened $\bf{\tilde{X}}$ ), we estimate the mixing matrix of the whitened signal, $\bf{\tilde{A}}$, using the MULTI-COMBI algorithm \citep{tichavsky06}."877. MULTLCONMBI comprises two complimentary aleorithins. EFICA (Noldovskyctal.2006) aud WASODI (Yeredor2000).," MULTI-COMBI comprises two complimentary algorithms, EFICA \citep{koldovsky06} and WASOBI \citep{yeredor00}."878.. EFICA. an asvinptotically efficient variant of the FastICA algorithm (IIvvàrincu1999).. i« designed to separate non-Ciaussian. iustautaneouslv muxedd signals.," EFICA, an asymptotically efficient variant of the FastICA algorithm \citep{hyvarinen99}, is designed to separate non-Gaussian, instantaneously mixed signals."879 WASODI. ou the other hand. is au axviuptoticallv efficient version of the SOBI algorithm (Belouchranioetal.1997).. aud is geared towards separating Cassia auto-reeressive (AR) aud time-correlated componeuts.," WASOBI, on the other hand, is an asymptotically efficient version of the SOBI algorithm \citep{belouchrani97}, and is geared towards separating Gaussian auto-regressive (AR) and time-correlated components."880 It uses second-order statistics and can be understood to he siuular to principal coniponeut analysis., It uses second-order statistics and can be understood to be similar to principal component analysis.881 The use of both algorithms is necessary since a real life data set will always contain a mixture of both. nou-Gaussian and Caussian AR processes.," The use of both algorithms is necessary since a real life data set will always contain a mixture of both, non-Gaussian and Gaussian AR processes."882 For a more in-depth discussion of the algorithuus eniploved here. we like to refer the interested reader to he appendices ο ο» aud the original publications.," For a more in-depth discussion of the algorithms employed here, we like to refer the interested reader to the appendices \ref{efica} \ref{wasobi} and the original publications."883 The EFICA and WASOBI aleorithlii can be shown to be asvinptotically cfficicut. d.6. the estimators approach the Cramér-Rao lower bouud (Davison2009).," The EFICA and WASOBI algorithm can be shown to be asymptotically efficient, i.e. the estimators approach the Cramérr-Rao lower bound \citep{davison09}."884. Iu other words. the algorithiis eiiploved lere can be shown to converge to the correct solution given the original source sienals and in the hinüt of [NN>ox iterations.," In other words, the algorithms employed here can be shown to converge to the correct solution given the original source signals and in the limit of $N \rightarrow \infty$ iterations."885 lu reality the nuuber of iterations is finite aud and dnuperfect convergence results in traces of other sources to remain in the mdividual signals comprising S., In reality the number of iterations is finite and and imperfect convergence results in traces of other sources to remain in the individual signals comprising $\bf{S}$.886 We can hence state that equation becomes A ineasure of this error is the deviation of WA (or WA for the whitened case) from the nity matrix bv iuspecting the variance of its clemenuts (I&oldovsk*etal.2006:Ivvarinen&Oja.20010).," We can hence state that equation \ref{demix} becomes A measure of this error is the deviation of $\bf{WA}$ (or $\bf{\tilde{W}\tilde{A}}$ for the whitened case) from the unity matrix by inspecting the variance of its elements \citep{koldovsky06,icabook}."887 This leads to the concept of the iuterference-over-signal ratio (ISR) matrix., This leads to the concept of the interference-over-signal ratio (ISR) matrix.888 The ISR is the standard measure in signal processing of how well a eiven signal has been trausmitted or de-convolved from. a iuixture of signals., The ISR is the standard measure in signal processing of how well a given signal has been transmitted or de-convolved from a mixture of signals.889 It cau be understood as the inverse of the signal-to-noise ratio (SNR)., It can be understood as the inverse of the signal-to-noise ratio (SNR).890 The higher the ISR for à specific sigual. the less well has it been separated from the original mixture.," The higher the ISR for a specific signal, the less well has it been separated from the original mixture."891 For a real case example. A is unknown aud the ISR ueeds to be estimated.," For a real case example, $\bf{A}$ is unknown and the ISR needs to be estimated."892 An analytic approximation to the ISRs for the EFICA aud WASODI algoritluus are found in the appendices Col C.2.., An analytic approximation to the ISRs for the EFICA and WASOBI algorithms are found in the appendices \ref{efica} \ref{wasobi}. .893 Finally. we check the stability of the sigual separation x perturbing the input matrix X bv a randonm and known matrix P to give We now re-run the MULTLCONBI procedure MSIE Χο ax input and estimate PA.," Finally, we check the stability of the signal separation by perturbing the input matrix $\bf{\tilde{X}}$ by a random and known matrix $\bf{P}$ to give We now re-run the MULTI-COMBI procedure using $\bf{\tilde{X}}_{2}$ as input and estimate $\bf{P}\bf{\tilde{A}}$."894 Kuowing P we can work backwards to obtain A as we are dealing with a linear trausformation., Knowing $\bf{P}$ we can work backwards to obtain $\bf{\tilde{A}}$ as we are dealing with a linear transformation.895 This step is repeated several times to check the convergence of the algorithii by inspecting the variation ou the mean ISR values of cach separation attempt and the variations iu cousecutive estimations of A clirectly., This step is repeated several times to check the convergence of the algorithm by inspecting the variation on the mean ISR values of each separation attempt and the variations in consecutive estimations of $\bf{\tilde{A}}$ directly.896 Once the mixing matrix. A is estimated. we reed to identify which signals are astroplivsical. which ones are white and which are systematic ioise.," Once the mixing matrix, $\bf{\tilde{A}}$ is estimated, we need to identify which signals are astrophysical, which ones are white and which are systematic noise."897 This is doue m a two step process: 1) We construct the estimated signal matrix. S. and for its individual conrponeuts $1 compute he Pearsou correlatiou cocficient between $i and the first principal component of the PCA decomposition iu section 3.1..," This is done in a two step process: 1) We construct the estimated signal matrix, $\bf{\hat{S}}$, and for its individual components $\bf{\hat{s}}_{l}$ compute the Pearson correlation coefficient between $\bf{\hat{s}}_{l}$ and the first principal component of the PCA decomposition in section \ref{pca}."898 For medium signal o noise (SNR) observations. the first principal conrponeut (PC). ie.," For medium signal to noise (SNR) observations, the first principal component (PC), ie."899 the oue with the highest eigenvalue associated to it.will contain the oxedoniünaut diehteurve shape.," the one with the highest eigenvalue associated to it,will contain the predominant lightcurve shape."900 As previouslv discussed. the first PC is not perfectly separated roni the svsteniatie signals and hence caunot be used directly for further analysis but it is good," As previously discussed, the first PC is not perfectly separated from the systematic signals and hence cannot be used directly for further analysis but it is good"901parameters fron cetailed hivdrodyvianic sinmulatious.,parameters from detailed hydrodynamic simulations.902 We bracket these parameters and compute light curves for a selection of ecceuric transiting planets., We bracket these parameters and compute light curves for a selection of eccentric transiting planets.903 Our calculated ὃ yan light curves are summarized in Table 1.., Our calculated 8 $\mu$ m light curves are summarized in Table \ref{prediction_table}.904 Our principal fiudiues from this iunerical experiment are: As discussed in 6. the uivriad assumptions mace in our model will tend to cxagecrateoo the amplitude of thermal phase variations.," Our principal findings from this numerical experiment are: As discussed in 6, the myriad assumptions made in our model will tend to exaggerate the amplitude of thermal phase variations."905 This could leac. for example. to over-estimatiue the radiative time if one uses our mocdols to interxet observed. pliase variations.," This could lead, for example, to over-estimating the radiative time if one uses our models to interpret observed phase variations."906 An obvious direction for the future is to couple our sipe thermodynamic model to a 1-D radiative trauster code (c.g.Tro&Deniug2010) to produce Πιοvariade of eccentric planets rather than jus heht curves., An obvious direction for the future is to couple our simple thermodynamic model to a 1-D radiative transfer code \citep[e.g.][]{Iro_2010} to produce time-variable of eccentric planets rather than just light curves.907 Such a hvbrid solution would require far fewer computational resources than full timc-variable raclative transfer., Such a hybrid solution would require far fewer computational resources than full time-variable radiative transfer.908 N.D.C. acknowledges useful ciscussions with E. Rauscher. as well as N. Iaib for his help with orbital dvuiuics. and IAL UageardOO for his help with differential equations.," N.B.C. acknowledges useful discussions with E. Rauscher, as well as N. Kaib for his help with orbital dynamics, and H.M. Haggard for his help with differential equations."909 S.L. Uawley aud V.S. A\lcadows contributed useful comments to the manuscript., S.L. Hawley and V.S. Meadows contributed useful comments to the manuscript.910 N.D.C. was supported by the Natural Sciences and Eneinecring Research Council of Canada., N.B.C. was supported by the Natural Sciences and Engineering Research Council of Canada.911 ELA. is supported by a National Scicuce Foundation Career Grant., E.A. is supported by a National Science Foundation Career Grant.912 Support for this work was provided by NASA through an award issued by JPL/Caltech., Support for this work was provided by NASA through an award issued by JPL/Caltech.913 N.D.C. acknowledges the hospitality of the ITarvard-Siüithsouiui Ceuter for Astrophysics. and the Kavli Institute for Theoretical," N.B.C. acknowledges the hospitality of the Harvard-Smithsonian Center for Astrophysics, and the Kavli Institute for Theoretical"914"section 2, the bolometric correction factor depends on the nuclei luminosity.","section 2, the bolometric correction factor depends on the nuclei luminosity."915" By fixing a constant correction factor, the nuclear bolometric luminosity is probably underestimated at high luminosity by roughly factor of 2."," By fixing a constant correction factor, the nuclear bolometric luminosity is probably underestimated at high luminosity by roughly factor of 2."916 This causes tace to be overestimated at high luminosity by the same factor., This causes $t_{acc}$ to be overestimated at high luminosity by the same factor.917" Thus, plotting the “true” tacc versus the “true” luminosity, which are overestimated and underestimated separately by the same factor, the points in Figure 3 should shift to the left along our observed trend."," Thus, plotting the “true” $t_{acc}$ versus the “true” luminosity, which are overestimated and underestimated separately by the same factor, the points in Figure 3 should shift to the left along our observed trend."918" Therefore, the trend in Figure 3 is robust against the uncertainties in nuclear luminosity."," Therefore, the trend in Figure 3 is robust against the uncertainties in nuclear luminosity."919 The relationship between scatter in the Mpn--σ relation and the accretion rate of the BH puts interesting constraints on how galaxies evolve in the Mau—c plane., The relationship between scatter in the $\Mbh-\sigma$ relation and the accretion rate of the BH puts interesting constraints on how galaxies evolve in the $\Mbh-\sigma$ plane.920" For example, if BH growth and host stellar spheroid growth are uncorrelated then we would expect that galaxies with rapidly accreting BHs to lie systematically off of the Mag—o relation."," For example, if BH growth and host stellar spheroid growth are uncorrelated then we would expect that galaxies with rapidly accreting BHs to lie systematically off of the $\Mbh-\sigma$ relation."921" In contrast, if BHs and spheroid coevolve, then we would expect no correlation between scatter in Mpy—c and BH activity, which is precisely what we observe."," In contrast, if BHs and spheroid coevolve, then we would expect no correlation between scatter in $\Mbh-\sigma$ and BH activity, which is precisely what we observe."922 Our results therefore favor the scenario wherein spheroid and BHs coevolve along the Maz—c relation., Our results therefore favor the scenario wherein spheroid and BHs coevolve along the $\Mbh-\sigma$ relation.923" In support of our conclusion, we also find that the dynamical time of the galaxy becomes comparable to the BH accretion timescale when the nuclear luminosity approaches the Eddington luminosity (Figure 3)."," In support of our conclusion, we also find that the dynamical time of the galaxy becomes comparable to the BH accretion timescale when the nuclear luminosity approaches the Eddington luminosity (Figure 3)."924 We can understand how galaxies populate the space in Figure 3 in light of our results., We can understand how galaxies populate the space in Figure 3 in light of our results.925" Galaxies cannot be in the upper right region of Figure 3 because otherwise the BH would grow much slower than c, resulting in a correlation between scatter and nuclear luminosity, which is not observed."," Galaxies cannot be in the upper right region of Figure 3 because otherwise the BH would grow much slower than $\sigma$, resulting in a correlation between scatter and nuclear luminosity, which is not observed."926" We can also understand why there are no galaxies in the lower left region of Figure 3: there is no limit to how long tacc can be (because the accretion rate can be arbitrarily close to zero), while there is a limit to how small tayn can be."," We can also understand why there are no galaxies in the lower left region of Figure 3: there is no limit to how long $t_{acc}$ can be (because the accretion rate can be arbitrarily close to zero), while there is a limit to how small $t_{dyn}$ can be."927 So tacc/tayn can increase at lower L/Lgqaq., So $t_{acc}/t_{dyn}$ can increase at lower $L/L_{Edd}$.928" For systems experiencing rapid growth in the BHs, the growth timescale of the BH is comparable to"," For systems experiencing rapid growth in the BHs, the growth timescale of the BH is comparable to"929"clistortecl in the small-M,, limit.",distorted in the $M_{\mathrm{a}}$ limit.930 Phirely. we solve the GradShafranov equation with the above source term to obtain the leacling-order correction to t.," Thirdly, we solve the Grad--Shafranov equation with the above source term to obtain the leading-order correction to $\psi$."931 We begin bv re-expressing the radial coordinate in terms of the fractional altitude ο” In a typical mountain. with height <107em (see Section 4.5)). one always has or&| within the mountain.," We begin by re-expressing the radial coordinate in terms of the fractional altitude $x$ In a typical mountain, with height $\lesssim 10^{5} \ \mathrm{cm}$ (see Section \ref{section_4:hydromagnetic_structure}) ), one always has $x \ll 1$ within the mountain."932" With equaions (D31)). (D3)). the Cirad.Shafranov. equation (5)) in the small-Ad,, approximation becomes The Lorentz force vanishes when the right-hand. side of equation. (B4)) is zero."," With equations \ref{approximation_1}) \ref{approximation_3}) ), the Grad–Shafranov equation \ref{gs_adiabatic}) ) in the $M_{\mathrm{a}}$ approximation becomes The Lorentz force vanishes when the right-hand side of equation \ref{gs}) ) is zero."933 Fherefore. the maximum height of the magnetic mountain as a function of latitude can be ΑΕΤΟΠ as for yessar(1pm). and [or pe<rο (ie. near the magnetic equator). (," Therefore, the maximum height of the magnetic mountain as a function of latitude can be written as for $\mu^{2} \gg x(1 - \mu^{2})$, and for $\mu \ll x/(1-x)$ (i.e. near the magnetic equator). ("934"Lt is casy to check that one has à,«I a posteriori for typical parameters.)",It is easy to check that one has $x_{m} \ll 1$ a posteriori for typical parameters.)935 Vhercefore. for adiabatie magnetic mountains. the ratio of polar to equatorial heights is Equation (D4)) can be solved by the method of Cireen's functions.," Therefore, for adiabatic magnetic mountains, the ratio of polar to equatorial heights is Equation \ref{gs}) ) can be solved by the method of Green's functions."936 From Section 3.1 in PMOA. we write roe =ming)and r« =max(r.r).," From Section 3.1 in PM04, we write with $r_{<} = \min(r, r^{\prime})$ and $r_{>} = \max(r, r^{\prime})$."937Ehe symbol Cyτεμ) denotes the ἐπ Gegenbauer polynomial., The symbol $C_{l}^{3/2}(\mu)$ denotes the th Gegenbauer polynomial.938 Phe first few are listed for reference: CuMΞ 1. C1M=n. CS3(pt)=(3/2)QA21).," The first few are listed for reference: $C_{0}^{3/2}(\mu) = 1$ , $C_{1}^{3/2}(\mu) = 3 \mu$, $C_{2}^{3/2}(\mu) = (3/2)(5 \mu^{2} - 1)$."939 SinceT we are interested.. in.. how the dipole moment is screened. at large kr. we assume r2∣⋮⋯∣⋏∙⇘⋜↧↓∖∖⊽⋜↧∙∖⇁⊳∖⊳∖∖⊽↓↕∢⊾↓⋅⋖⋅∣⋮ luax∕⋠ is the top of⋅ the mountain.," Since we are interested in how the dipole moment is screened at large $r$ , we assume $r >940r^{\prime}_{\mathrm{max}}$ always, where $r^{\prime}_{\mathrm{max}}$ is the top of the mountain."941"⋠⊳∖⋠ This simplifies the radial Cireen's function to Away from the magnetic equator. Le. 7ία.qi). equations (D1)) (D3)). (B5)) and (BS)) (DII)) combine to give δη Our goal is to calculate the dipole moment as a function of AZ, given (D14)) and (B15))."," This simplifies the radial Green's function to Away from the magnetic equator, i.e. $\mu^{\prime 2} > x^{\prime}(1-\mu^{\prime9422})$, equations \ref{approximation_1}) \ref{approximation_3}) ), \ref{max_height_pole}) ) and \ref{analytic_psi}) \ref{Q}) ) combine to give with Our goal is to calculate the dipole moment as a function of $M_{\mathrm{a}}$ given \ref{analytic_psi_even}) ) and \ref{integral_even}) )."943 In the limit +5x. the/ &1 contributions to fe vanish. and equations (12141) and (B15)) reduce to with Contows of Z6X).D). are. plotted in Fig.," In the limit $r \to944\infty$, the $l \geq 1$ contributions to $\mu$ vanish, and equations \ref{analytic_psi_even}) ) and \ref{integral_even}) ) reduce to with Contours of $I(\Lambda_{0}, \Gamma)$ are plotted in Fig."945 11 for reference.," \ref{fig:lambda_gamma}946 for reference."947 To express Qo in terms of the other variables. we substitute equations (100). (D1)). (B2)) anc (DI16)) into equation (9)) to give ∖∖⋎↓↥∢⊾↓⋅⋖⋅∣↗∶∣⊽↴∣⊽∣∆↕≻⋜↧≼⇍⋖≱↓↥≻⇂⋜↧↓↕↿↿↓⋯↿↓≻⋜⊔⋅⋜⋯↓⋖⋅⇂↓⋰↓∠∢⋅⊳∖↿↓↥∢⊾ ↓⋜⋯⊾↓⋅⋜↧↓∢⋅⇀∖∩⋅⊔∣∪⇂⋅∣↓∐⊾⋯⇍≼∼↓⋅∢⊾⇂⊲↓∪⊔≼∼∪↓," To express $Q_{0}$ in terms of the other variables, we substitute equations \ref{mass-flux}) ), \ref{approximation_1}) ), \ref{approximation_2}) ) and \ref{lambda}) ) into equation \ref{F_adiabatic}) ) to give where $b=\psi_{\ast}/\psi_{\mathrm{a}}$ is a constant that parametrizes the lateral extentofthe accretion column."948"⊔⊔↓⊔⊳∣⊲⇀⊲⊏↥⇂⇂⋜↧⇂↕⋖⋟↓↥↿∖≧↓≤⋗∣∩⋠↓≱∖ ⊔∪↿⊳∖⇂↓⋰⊔⇍⇂↓∙∖⇁⋜⋯⋖⊾⊏↥⊔⋜↧∐↿∙∖⇁∶⇂↓↕⋖⊾↕↓↥⋖⋅⋜↧↓⋅⋜↧↓↥≻⋜↧↿∠∫↰↴↿∖∣⋎⊐∶↺⊔↿∖∣⋎↴∣⋎⊐ is not an exact. solution in the small-AZ, limit (see fig.", Equation \ref{q1}) ) is not strictly an equality; the linear ansatz $F(\psi) = Q_{0}(\psi_{\ast} - \psi)$ is not an exact solution in the $M_{\mathrm{a}}$ limit (see fig.949 6 in PALO. which presents a numerical comparison).," 6 in PM04, which presents a numerical comparison)."950 Hence.," Hence,"951valagcas99.,.952 Numerical simulations of vielded. high. estimates of C~10 (40) at redshifts ο=8 (5). implving that recombinations are generally quite important.," Numerical simulations of yielded high estimates of ${\cal C}\sim 10$ (40) at redshifts $z=8$ (5), implying that recombinations are generally quite important."953 Similar values have been used in the estimate of the comoving star formation rate density needed to keep the post-reionization Universe ionized by balancing ionizations with recombinations., Similar values have been used in the estimate of the comoving star formation rate density needed to keep the post-reionization Universe ionized by balancing ionizations with recombinations.954 The inferred value. is significantlyhigher. at 2~ than some currently observationally inferred rates.," The inferred value, is significantlyhigher at $z \sim 7$ than some currently observationally inferred rates."955]bunkerl10. Current numerical simulations model reionization bv. directly. following the propagation of ionization fronts through the inhomogeneous ICM. thus in principle eliminating the need for a clumping factormecquinnOT.," Current numerical simulations model reionization by directly following the propagation of ionization fronts through the inhomogeneous IGM, thus in principle eliminating the need for a clumping factor."956tracOT. Llowever the resolution of the radiative transfer (RV) calculation is in general much coarser than that of the density Ποιά on which the sources ave identified?).. and a single clumping factor. usually derived from higher resolution small box runs. is used. to take account of the density structure below the resolution of the RV meshO07.," However the resolution of the radiative transfer (RT) calculation is in general much coarser than that of the density field on which the sources are identified, and a single clumping factor, usually derived from higher resolution small box runs, is used to take account of the density structure below the resolution of the RT mesh."957 In this letter we will show that a single value of the clumping factor is. in [act. not appropriate for estimating the recombination rate in. numerical RL reionization simulations. anc leads to a significant over estimate of the importance of recombinations.," In this letter we will show that a single value of the clumping factor is, in fact, not appropriate for estimating the recombination rate in numerical RT reionization simulations, and leads to a significant over estimate of the importance of recombinations."958 The recombination rate of Hvdrogen-onlv. eas in a volume Vds where à is the recombination cocllicient. ng the hvdrogen number densitv. C—ingi/ing the clumping factor. and. we assumed the gas to be Lully ionized ngu): the angular brackets denote a volume average.," The recombination rate of Hydrogen-only gas in a volume $V$ is where $\alpha$ is the recombination coefficient, $\nh$ the hydrogen number density, ${\cal C} \equiv \langle \nh^2\rangle/\langle \nh \rangle^2$ the clumping factor, and we assumed the gas to be fully ionized $(\nh = \nhii)$ ; the angular brackets denote a volume average."959 Alost current numerical models of reionization follow the formation of dark matter structures in a cosmological setting. compute emissivities of galaxies associated with cark matter halos. then follow how these galaxies ionize their surroundings with a radiative transfer calculation(?????).," Most current numerical models of reionization follow the formation of dark matter structures in a cosmological setting, compute emissivities of galaxies associated with dark matter halos, then follow how these galaxies ionize their surroundings with a radiative transfer calculation."960. Our method. in this letter is designed. to. reproduce. the steps taken to set up RP computational meshes in such simulations., Our method in this letter is designed to reproduce the steps taken to set up RT computational meshes in such simulations.961 We use a dark matter simulation performed. with the “Pree-PAL code Cadget-2(2)., We use a dark matter simulation performed with the Tree-PM code Gadget-2.962".. The simulation uses 1024"" cqual-mass particles in a periodic cosmological volume of size 20 bh comoving/ Alpe. assuming a Hat CDM cosmology with cosmological parameters On,Qn.OQ.boas.) = 0.25. 0.045. 0.75. 0.73. 0.9. I]."," The simulation uses $1024^3$ equal-mass particles in a periodic cosmological volume of size 20 $h^{-1}$ comoving Mpc, assuming a flat $\Lambda$ CDM cosmology with cosmological parameters $\Omega_m, \, \Omega_b, \, \Omega_\Lambda, \,963h, \, \sigma_8, \, n_s]$ = [0.25, 0.045, 0.75, 0.73, 0.9, 1]."964 Darvons are assumed to trace the dark matter. and. hence the gas density py is related to the matter density p as ps=(οΟρ.," Baryons are assumed to trace the dark matter, and hence the gas density $\rho_g$ is related to the matter density $\rho$ as $\rho_{\rm965 g}=(\Omega_b/\Omega_m)\,\rho$."966 Phe matter density p atthe position r; of particle 7 is estimated using the SPL algorithm(?7).. where m; is the particle mass. and f; its ‘resolution chosen so that it holds ~40 neighboring particles j that contribute to the sum: VW. is the smoothing. kernel.," The matter density $\rho$ atthe position ${\bf r}_i$ of particle $i$ is estimated using the SPH algorithm, where $m_i$ is the particle mass, and $h_i$ its resolution chosen so that it holds $\sim 40$ neighboring particles $j$ that contribute to the sum; $W$ is the smoothing kernel."967" The (Ilvdrosen) number density is computed as ng=(1VY)pyfm, where Y is the primordial Helium abundance by miss. andm, is the proton miss."," The (Hydrogen) number density is computed as $\nh=(1-Y)\,\rho_g/m_{\rm p}$ , where $Y$ is the primordial Helium abundance by mass, and$m_{\rm p}$ is the proton mass."968 Assigning a volume V;2m;/pi to particle 7. allows us to compute the mean clumping factor as where μαι is the number of particles in. volume V with number density lower than a given threshold. density Mor," Assigning a volume $V_i \approx m_i/ \rho_i$ to particle $i$ , allows us to compute the mean clumping factor as where $N_\mr{part}$ is the number of particles in volume $V$ with number density lower than a given threshold density $n_\mr{thr}$."969" We use mqCcasing) with Aq,=100. to exclude collapsed halos from the ICM density fieldescude3."," We use $n_\mr{thr} \equiv \Delta_\mr{thr} \langle \nh \rangle$ with $\Delta_{\rm970 thr}=100$, to exclude collapsed halos from the IGM density field."971pawlik09. Darvons in halos do not trace the dark matter but. collapse to form galaxies., Baryons in halos do not trace the dark matter but collapse to form galaxies.972 Due to their. high densities. galaxies should not be treated as general ICM. but rather as LLS and their effect on the propagation of ionizing racliation described in terms of a mean free path. as inο," Due to their high densities, galaxies should not be treated as general IGM, but rather as LLS and their effect on the propagation of ionizing radiation described in terms of a mean free path, as in."973"ν, We chose the overdensity threshold of Ay.=100 appropriate for the density at the virial radius of a halo. ancl also to allow for a direct comparison to other works Jpawlikoo."," We chose the overdensity threshold of $\Delta_\mr{thr} = 100$ appropriate for the density at the virial radius of a halo, and also to allow for a direct comparison to other works ."974 Finally. the RV calculations for large-scale reionization models are usually performed on a uniform cubic mesh. with the density at cach mesh point obtained [rom the IN-body particles using. for example. nearest &erid point interpolationJhockneyss.," Finally, the RT calculations for large-scale reionization models are usually performed on a uniform cubic mesh, with the density at each mesh point obtained from the $N$ -body particles using, for example, nearest grid point interpolation."975 We emplov several such erids in the following discussion., We employ several such grids in the following discussion.976 “Phe details of the particular simulation we use. and the way we compute densities. are not important as far as our conclusions on recombinations are concerned.," The details of the particular simulation we use, and the way we compute densities, are not important as far as our conclusions on recombinations are concerned."977 We will make a cistinction between two types of clumping [actors in the following cliscussion. both based on Iq. (4)).," We will make a distinction between two types of clumping factors in the following discussion, both based on Eq. \ref{eq:c}) )."978 The clumping Factor. Caron. is computed by summing overaff particles. as is done in ane?.," The clumping factor, ${\cal C}_\mr{global}$, is computed by summing over particles, as is done in and."979. However we can also divide the computational volume in (equal volume. non-overlapping) sub-volumes. a uniform meshl.. and evaluate C in each sub-volume (mesh cell) by summing only over particles in that sub-volume?.," However we can also divide the computational volume in (equal volume, non-overlapping) sub-volumes, a uniform , and evaluate ${\cal C}$ in each sub-volume (mesh cell) by summing only over particles in that ."980. We will call this a clumping factor. Cy.," We will call this a clumping factor, ${\cal C}_\mr{local}$ ."981 We compareCai and Cio computed on 64 equal sub-volumes of our 10245 particles. 20. 5 !Mpe: aside," We compare${\cal C}_\mr{global}$ and ${\cal C}_\mr{local}$ computed on $64^3$ equal sub-volumes of our $^3$ particles, 20 $h^{-1}$ Mpc aside"982"cathodes equipped with imultiàchaunecl plate (AICP) intensificrs auc wedge-ande-strip anodes, as used iu previous expeorinents (0,0, FAUST: Dowwer et al.","cathodes equipped with multi-channel plate (MCP) intensifiers and wedge-and-strip anodes, as used in previous experiments (e.g., FAUST: Bowyer et al."983 1993)., 1993).984 At this time we decided to name the experiment TAUVEN. for Tel Aviv UniversityUV EXpcriment.," At this time we decided to name the experiment TAUVEX, for el viv University periment."985" The science to be performed by TAUVERX, as proposed to ISA, was to survey a large fraction of the sky in the UV to depths vastly superior to those achieved by the UN szurvevs in the 1970s."," The science to be performed by TAUVEX, as proposed to ISA, was to survey a large fraction of the sky in the UV to depths vastly superior to those achieved by the UV surveys in the 1970s."986" The science goals of the TAUVEN inission were defined as xovidiung galaxy imaging im a nmunber of bands to allow studies of star formation processes, tlowing the detection and identification of ACNs bv selections based on color indices; aud collecting ""uique stellar photometry data for stellar populations and interstellar extinction studies."," The science goals of the TAUVEX mission were defined as providing galaxy imaging in a number of bands to allow studies of star formation processes, allowing the detection and identification of AGNs by selections based on color indices, and collecting unique stellar photometry data for stellar populations and interstellar extinction studies."987 These goals were discussed by e.g; Brosclh Almozuing (2007). Joshi et al. (," These goals were discussed by e.g., Brosch Almoznino (2007), Joshi et al. ("988"2007). Netzer (2007), Shastii (2007). and Mahlieswar et al. (","2007), Netzer (2007), Shastri (2007), and Maheswar et al. ("9892007).,2007).990 They were derived from the projected capabilities of TAUVEX eiven the properties listed by Brosch (1998) and subsequent modifications., They were derived from the projected capabilities of TAUVEX given the properties listed by Brosch (1998) and subsequent modifications.991 Of special iuportance for the study of ealaxies in the nearby Universe and of the stellar and. interstellar matter of the Milky Wax we mention the inclusion of two filters centered on the feature: photometric measurements hrough a wide and a narrow band filter allow the measurement of the equivalent width of this feature., Of special importance for the study of galaxies in the nearby Universe and of the stellar and interstellar matter of the Milky Way we mention the inclusion of two filters centered on the feature; photometric measurements through a wide and a narrow band filter allow the measurement of the equivalent width of this feature.992 The TAUVEX Phase A report was submitted to the scrutiny of two evaluation comunittees: one teclinical. composed of Isvacli technology experts to evaluate its feasibility. aud the other scientific. composed. of well-known international experts in the UV astronomy field to evaluate its scientific contribution and expected inunpact.," The TAUVEX Phase A report was submitted to the scrutiny of two evaluation committees: one technical, composed of Israeli technology experts to evaluate its feasibility, and the other scientific, composed of well-known international experts in the UV astronomy field to evaluate its scientific contribution and expected impact."993" The second selected proposal, submitted by the Technion, Isracl’s technological university, was evaluated at the same tine: it proposed orbiting a sinall N-ray telescope."," The second selected proposal, submitted by the Technion, Israel's technological university, was evaluated at the same time; it proposed orbiting a small X-ray telescope."994 The two evaluations proceeded iu parallel and the conclusion was that ISA selectec TAUVEXN as the pavload with the highest priority to launch., The two evaluations proceeded in parallel and the conclusion was that ISA selected TAUVEX as the payload with the highest priority to launch.995" At this point. when the development, construction and launch of TAUVEN were expected to follow :inoothlilv. ISA found that the national satellite aud launcher on which if was counting to mount TAUVIEX became unavailable."," At this point, when the development, construction and launch of TAUVEX were expected to follow smoothly, ISA found that the national satellite and launcher on which it was counting to mount TAUVEX became unavailable."996 The reason. which vecame clear ouly in 2009. was that ISA originally planned to launch TAUVEN on the qualification model (QM) of one of the OPEQ-serics satellite. the first threc-axis-stabilized Ixaeli satellites used for iuagine intelligence.," The reason, which became clear only in 2009, was that ISA originally planned to launch TAUVEX on the qualification model (QM) of one of the OFEQ-series satellite, the first three-axis-stabilized Israeli satellites used for imaging intelligence."997 The QNI would have been refurbished auc used to launch and operate TAUVEN which. as already described. was originally designed to fit the iuner volume of the satellite.," The QM would have been refurbished and used to launch and operate TAUVEX which, as already described, was originally designed to fit the inner volume of the satellite."998" However. with the loss at launch of one of the OFEQ satellites, practical necessities dictated the use of the satellite and lanucher to orbit a cdiffercut payload."," However, with the loss at launch of one of the OFEQ satellites, practical necessities dictated the use of the satellite and launcher to orbit a different payload."999" With the disappearance of the satellite aud launcher iuteuded for pure scieutifie research, ISA announced that it could only provide funding for the development of the scientific iustrmment aud that the science team should look for a platform on which TAUVEX could be flown."," With the disappearance of the satellite and launcher intended for pure scientific research, ISA announced that it could only provide funding for the development of the scientific instrument and that the science team should look for a platform on which TAUVEX could be flown."1000" With the help ofinternational colleagues, the Spectr AN-5 (SRC) spacecraft was identified as a possible carrier platform for TAUVEN."," With the help of international colleagues, the Spectrum $\gamma$ (SRG) spacecraft was identified as a possible carrier platform for TAUVEX."1001" SRO was designed as a large hiel-cucrey astrophysics platform. one of the three major observatories in the Spectrum series, together with Spectra RadioÀstron aud Spectiuu-UV."," SRG was designed as a large high-energy astrophysics platform, one of the three major observatories in the Spectrum series, together with Spectrum RadioAstron and Spectrum-UV."1002 The spacecraft was to be provided by he Soviet Union aud constructed at the Lavotchkin Space Taicustrics in Whimsy (near Moscow). with most of its scientific instruments on-board to be supplied by different Enropeaufg countries.," The spacecraft was to be provided by the Soviet Union and constructed at the Lavotchkin Space Industries in Khimky (near Moscow), with most of its scientific instruments on-board to be supplied by different European countries."1003" Originally, SRC was to be launched by a Proton rocket into a highly elliptical. four-day. Moluvia-type orbit."," Originally, SRG was to be launched by a Proton rocket into a highly elliptical, four-day Molnyia-type orbit."1004 The largest instrument on-board SRO was the Dauish-led SODART X-ray telescope with two GU-clu nested-cones concentrators for the ~0.5-L0 keV ranee (Schnopper 1990)., The largest instrument on-board SRG was the Danish-led SODART X-ray telescope with two 60-cm nested-cones concentrators for the $\sim$ 0.3-10 keV range (Schnopper 1990).1005 SODART was to provide X-rav imagine over a one degree FOV with arcmin aneular resolution and excellent sensitivity. given its larec-throughput optics.," SODART was to provide X-ray imaging over a $\sim$ one degree FOV with arcmin angular resolution and excellent sensitivity, given its large-throughput optics."1006 SRC included also soft X-ray to extreme UW imagers from Switzerland. another X-rav inagcr from the UK. a hard X-rav imager from Italy. etc.," SRG included also soft X-ray to extreme UV imagers from Switzerland, another X-ray imager from the UK, a hard X-ray imager from Italy, etc."1007 The inclusion of TAUVEX among the SRC instramentsf was intended to provide simultaneous UV information with which the X-ray observations could be correlated. nmch in the manner of NAQs Optical/UV inonitor.," The inclusion of TAUVEX among the SRG instruments was intended to provide simultaneous UV information with which the X-ray observations could be correlated, much in the manner of XMM's Optical/UV monitor."1008 Au additional task imposed on TAUVEN by the mission leaders was to aid the SRC fine guidance svstem in stabilizing the telescopes’ LOS., An additional task imposed on TAUVEX by the mission leaders was to aid the SRG fine guidance system in stabilizing the telescopes' LOS.1009 This was to be done by providing fine guidiug corrections to the SRC systeis every two seconds: these corrections were derived. frou centroiding a relatively bright star in the TAUVEN FOV and measuring displacements frou an initial position., This was to be done by providing fine guiding corrections to the SRG systems every two seconds; these corrections were derived from centroiding a relatively bright star in the TAUVEX FOV and measuring displacements from an initial position.1010" Calculations showed that with the expected sensitivity TAUVEX could provide such stabilization sienals all over the sky if it would have been used with no filter, or with a very wide bluc-eutoff filter dubbed"," Calculations showed that with the expected sensitivity TAUVEX could provide such stabilization signals all over the sky if it would have been used with no filter, or with a very wide blue-cutoff filter dubbed"1011and was in a primordial binary wilh a period of P26513vr and eccentricity e=0.73.,"and was in a primordial binary with a period of $P = 6\,513\,$ yr and eccentricity $e = 0.73$."1012 The companion star had a mass of 0.54.1. and the binary was situated just bevond the cluster half-mass radius., The companion star had a mass of $0.54 M_\odot$ and the binary was situated just beyond the cluster half-mass radius.1013 The metallicity of the stars in this simulation was Z=0.004., The metallicity of the stars in this simulation was $Z = 0.004$.1014 After 40Myr the orbital parameters of this wide binary had been reduced (ο 2=63yr and €=0.13 owing to perturbations resulting from weak gravitational encounters with nearby stars.," After $40\,$ Myr the orbital parameters of this wide binary had been reduced to $P = 63\,$ yr and $e = 0.13$ owing to perturbations resulting from weak gravitational encounters with nearby stars."1015 At Tx490 Myr the binary had drifted inside the cluster hall-mass radius aud was involved in an exchange interaction will a O.2OAL. star.," At $T \simeq 490\,$ Myr the binary had drifted inside the cluster half-mass radius and was involved in an exchange interaction with a $0.29 M_\odot$ star."1016 Subsequently the low-mass interloper was ejected from the 3-bocdy svstem leaving the original binary intact., Subsequently the low-mass interloper was ejected from the 3-body system leaving the original binary intact.1017 Following this tumultious but short-lived relationship. (he binary partners remained quietly monogamous until becoming involved in a 5-body interaction al 7=3463 Myr. by which time the binary had sunk further towards the cluster centre. through mass segregation. lving slightly outside of the core.," Following this tumultuous but short-lived relationship, the binary partners remained quietly monogamous until becoming involved in a 5-body interaction at $T = 3\,463\,$ Myr, by which time the binary had sunk further towards the cluster centre, through mass segregation, lying slightly outside of the core."1018 The other participants in this encounter were a 1.123. sinele star and a binary with component masses of 1.17 and 002141. and P?=58 vr.," The other participants in this encounter were a $1.12 M_\odot$ single star and a binary with component masses of $1.17$ and $0.32 M_\odot$ and $P = 58\,$ yr."1019 Initially the 0.54. star was ejected. cestroving the primordial binary. and a quasi-stable 4-body svstem remained.," Initially the $0.54 M_\odot$ star was ejected, destroying the primordial binary, and a quasi-stable 4-body system remained."1020 Shortly afterwards the 0.32. star was also ejected and (he 0.90. and 1.12. stars formed a binary with vr and e=0.95 in a triple svstem with the 1.17.V. star.," Shortly afterwards the $0.32 M_\odot$ star was also ejected and the $0.99 M_\odot$ and $1.12 M_\odot$ stars formed a binary with $P = 51\,$ yr and $e = 0.95$ in a triple system with the $1.17 M_\odot$ star."1021 The presence of the third body eracduallv drove (he eccentricity of the inner binary up to 0.99 at which point (7=3515 My) the two AIS stars collided to form a 2.11... DS whieh did not remain bound to the third star.," The presence of the third body gradually drove the eccentricity of the inner binary up to 0.99 at which point $T = 3\,515\,$ Myr) the two MS stars collided to form a $2.11 M_\odot$ BS which did not remain bound to the third star."1022 Figure 1. documents this interaction. aud all subsequent interactions involving (he initially 0.9917. star. in terms of the masses of the stars involved.," Figure \ref{f:fig1} documents this interaction, and all subsequent interactions involving the initially $0.99 M_\odot$ star, in terms of the masses of the stars involved."1023 We note that the 0.54. star actually escaped from the cluster. with a velocity exceeding the stellar velocity dispersion by a [actor of three. approximately 10 Myr after il was removed [rom its primordial companion - but as a direct result of the energy exchanged in that interaction.," We note that the $0.54 M_\odot$ star actually escaped from the cluster, with a velocity exceeding the stellar velocity dispersion by a factor of three, approximately $10\,$ Myr after it was removed from its primordial companion - but as a direct result of the energy exchanged in that interaction."1024 The Bs (now significantly more massive (han (he average cluster star) quickly sank inside the core of the cluster where. al Z7274000 Myr. it was involved in an exchange interaction wilh a 2.244. single star and a primordial binary.," The BS (now significantly more massive than the average cluster star) quickly sank inside the core of the cluster where, at $T \simeq 4\,000\,$ Myr, it was involved in an exchange interaction with a $2.2 M_\odot$ single star and a primordial binary."1025 The single star. itself a BS lormed via the coalescence of two AIS stars in a semi-detached binary. formed a bound pair with the original BS.," The single star, itself a BS formed via the coalescence of two MS stars in a semi-detached binary, formed a bound pair with the original BS."1026 This BS-BS binary had a period of 487vr ancl an eccentricity of 0.72.," This BS-BS binary had a period of $487\,$ yr and an eccentricity of 0.72."1027 Its orbit was perturbed by interactions wilh a 1.24. star at 7=4049 Myr and with a 0.9.M. star al P=4092 Myr which increased the eccentricity (ο 0.98.," Its orbit was perturbed by interactions with a $1.2 M_\odot$ star at $T = 4\,049\,$ Myr and with a $0.9 M_\odot$ star at $T = 4\,092\,$ Myr which increased the eccentricity to 0.98."1028 The orbit then became chaotic and at F=4162 Myr the BSs collided to form a 4.31. super-DS.," The orbit then became chaotic and at $T = 4\,162\,$ Myr the BSs collided to form a $4.31 M_\odot$ super-BS."1029 At T=4180 Myr the super-BS exchanged itself into a binary comprising a 1.11 anda 1.52... star aud left bound io the more massive of the two. also a BS.," At $T = 4\,180\,$ Myr the super-BS exchanged itself into a binary comprising a $1.11$ and a $1.52 M_\odot$ star and left bound to the more massive of the two, also a BS."1030 Then. in a final showdown. this binary formed a thody system wilh another binary and al 2=4210 Myr the 431A. super-DS ancl the 1.52.4. Bs collided to form a 5.08.M.. super-BS.," Then, in a final showdown, this binary formed a 4-body system with another binary and at $T = 4\,210\,$ Myr the $4.31 M_\odot$ super-BS and the $1.52 M_\odot$ BS collided to form a $5.78 M_\odot$ super-BS."1031 Being as massive as it was. almost five times ereater (han the MS (Curn-off mass at the time. (his promiscuous star quickly evolved off the MS and shortly afterwards lost its envelope on the asymptotic giant branch to become an," Being as massive as it was, almost five times greater than the MS turn-off mass at the time, this promiscuous star quickly evolved off the MS and shortly afterwards lost its envelope on the asymptotic giant branch to become an"1032the edge of regions (Gaume&Mutel1987).,the edge of regions \cite{Ga1987}.1033. Phe primary aim of this paper is to examine whether this prediction is supported by observation., The primary aim of this paper is to examine whether this prediction is supported by observation.1034 We have used the APCA to image the continuum emission of the regions associated with the 6.7-Cllz methanol nmiasers G318.95-0.20. CGS839.88-1.26 and NGC 19 (€1351.42|0.64).," We have used the ATCA to image the continuum emission of the regions associated with the 6.7-GHz methanol masers G318.95-0.20, G339.88-1.26 and NGC 6334F (G351.42+0.64)."1035 Our observations of NGC 022419 include three separate clusters. of masers. and so. subsequent discussions refer to a total of five. clusters. of 6.7-Cillz methanol masers.," Our observations of NGC 6334F include three separate clusters of masers, and so subsequent discussions refer to a total of five clusters of 6.7-GHz methanol masers."1036 The observations were made curing 1993 November 7 with the array in the GA configuration., The observations were made during 1993 November 7 with the array in the 6A configuration.1037 This has minimum and maximum baseline lengths of 0.33 and 5.9 km respectively., This has minimum and maximum baseline lengths of 0.33 and 5.9 km respectively.1038 The correlator was configured to record both a 128-Mllz band centred at 8.590 Cillz. and an S-MllIz band which was alternated between S.584 and 6.669 Gllz.," The correlator was configured to record both a 128-MHz band centred at 8.590 GHz, and an 8-MHz band which was alternated between 8.584 and 6.669 GHz."1039 This enabled us to make observations of the 6.7-Gllz methanol masers and the recombination line whilst simultaneously imaging the continuum emission., This enabled us to make observations of the 6.7-GHz methanol masers and the recombination line whilst simultaneously imaging the continuum emission.1040 The S-MlIz band was split into 512 channels vielding a velocity resolution of 0.84 at 6.669 Cllz., The 8-MHz band was split into 512 channels yielding a velocity resolution of 0.84 at 6.669 GHz.1041 The HPBW (hall-power beam width) of the svnthesisecl beam at 8.590 Gllz was approximately 1.2 arcsec., The HPBW (half-power beam width) of the synthesised beam at 8.590 GHz was approximately 1.2 arcsec.1042 Each program source was observed twelve times for a I6-min period over the 13-1 observing session ancl was preceded by a 4-min observatlon of a calibration source., Each program source was observed twelve times for a 16-min period over the 13-h observing session and was preceded by a 4-min observation of a calibration source.1043 The observing frequency of the S-ÀLz band was changed to the alternate frequency at the enc of each observing evele (an observation of cach program ancl calibration source)., The observing frequency of the 8-MHz band was changed to the alternate frequency at the end of each observing cycle (an observation of each program and calibration source).1044 As a result. the maser and recombination line observations consist of six 16-min scans. while the continuum observations consist of 12 scans.," As a result, the maser and recombination line observations consist of six 16-min scans, while the continuum observations consist of 12 scans."1045 The data were calibrated. ancl imaged using the AT AIPS (Astronomical Image. Processing System) which is based. on the NILAO software package of the same name.," The data were calibrated and imaged using the AT AIPS (Astronomical Image Processing System), which is based on the NRAO software package of the same name."1046 1934-638 was used as the primary lux calibrator. which we assumed to have {lux densities of 3.92 Jv ane 2.86 Jv at 6.669 CGllz and 8.590 Cllz respectively.," 1934-638 was used as the primary flux calibrator, which we assumed to have flux densities of 3.92 Jy and 2.86 Jy at 6.669 GHz and 8.590 GHz respectively."1047 1414-59. 1740-517 and 1744-312. were used. as secondary. calibrators ancl their positions and [ux densities. caleulated by comparing them. with 1934-638 are listed in Table 1..," 1414-59, 1740-517 and 1744-312 were used as secondary calibrators and their positions and flux densities, calculated by comparing them with 1934-638 are listed in Table \ref{tab:sc}."1048 After the initial calibration. the continuum emission for each source was imaged and CLEANoed using the ALPS task ALX.," After the initial calibration, the continuum emission for each source was imaged and CLEANed using the AIPS task MX."1049 ‘The spectral resolution of our 6.7-Cillz methanol maser observations is four times lower than that of Norris (1993)., The spectral resolution of our 6.7-GHz methanol maser observations is four times lower than that of Norris \shortcite{No1993}.1050. Because of this we did not try to determine the relative positions of the 6.7-CGllz methanol masers from these data. but. rather used the positions determined. by Norris," Because of this we did not try to determine the relative positions of the 6.7-GHz methanol masers from these data, but rather used the positions determined by Norris."1051 We independently imaged. only the reference. maser [oature., We independently imaged only the reference maser feature.1052 We used three dillerent. techniques to determine the ollset. between the position of the SN.5-Cllz continuum peak and the reference feature from the 6.7-Cillz methanol maser spectrum., We used three different techniques to determine the offset between the position of the 8.5-GHz continuum peak and the reference feature from the 6.7-GHz methanol maser spectrum.1053 The first and simplest technique was to measure independently the absolute positions of the continuum peak and the reference maser., The first and simplest technique was to measure independently the absolute positions of the continuum peak and the reference maser.1054 The second technique was to reference the phase of all the channels in. the 6.7-CillIz methanol maser observations to a channel containine a strong unresolved maser feature (the reference feature)., The second technique was to reference the phase of all the channels in the 6.7-GHz methanol maser observations to a channel containing a strong unresolved maser feature (the reference feature).1055 We hen formed a continuum image from the channels which cid not contain maser emission. and determined the position of he peak.," We then formed a continuum image from the channels which did not contain maser emission, and determined the position of the peak."1056 This method. works only if the radio continuum emission from the region is strong., This method works only if the radio continuum emission from the region is strong.1057 The final technique was to reference the ohase of the Ss.5-Cllz continuum channels to the 6.7-CillIz reference feature., The final technique was to reference the phase of the 8.5-GHz continuum channels to the 6.7-GHz reference feature.1058 Lowe assume that the same region of the atmosphere causes the phase errors at both 6.7 and 8.5 Cillz. hen we can correct the 8.5-Cillz phase simply by multiplving he 6.7-Gllz correction by the ratio of the [requencies.," If we assume that the same region of the atmosphere causes the phase errors at both 6.7 and 8.5 GHz, then we can correct the 8.5-GHz phase simply by multiplying the 6.7-GHz correction by the ratio of the frequencies."1059 Scaling the phase corrections causes a discontinuity if the reference phase wraps., Scaling the phase corrections causes a discontinuity if the reference phase wraps.1060 For these observations we found that after calibration the reference phase did not wrap for many of the baselines., For these observations we found that after calibration the reference phase did not wrap for many of the baselines.1061 For those where the phase did wrap. it did so only once and we Iageed these data before phase referencing the S.5-Cillz data.," For those where the phase did wrap, it did so only once and we flagged these data before phase referencing the 8.5-GHz data."1062" ""To assess the accuracy with whieh we could measure the olfset. between a reference maser feature ancl the &.5-Cllz continuum peak. we calculated the offset for NGC 025 using each of the above methods."," To assess the accuracy with which we could measure the offset between a reference maser feature and the 8.5-GHz continuum peak, we calculated the offset for NGC 6334F using each of the above methods."1063 In addition. we calculated the olfset for several datasets which had not been. fully calibrated. or contained. small deliberate errors. in the calibration.," In addition, we calculated the offset for several datasets which had not been fully calibrated, or contained small deliberate errors in the calibration."1064 In all cases the measured ollset was very similar. with the rms being 0.2 aresec.," In all cases the measured offset was very similar, with the rms being 0.2 arcsec."1065 The olfsets quoted below are the mean of the olfsets caleulated from each of the methods outlined. above (for. €1339.88-1.26 only the first. and. third methods were used)., The offsets quoted below are the mean of the offsets calculated from each of the methods outlined above (for G339.88-1.26 only the first and third methods were used).1066 We adopt 0.2 aresec as à conservative estimate of the standard. error., We adopt 0.2 arcsec as a conservative estimate of the standard error.1067 Images of the 8.5-Cllz radio continuum with the positions of the 6.7-Gllz methanol masers marked are shown in Figs 1 and 2.., Images of the 8.5-GHz radio continuum with the positions of the 6.7-GHz methanol masers marked are shown in Figs \ref{fig:g339} and \ref{fig:ngc6334f}.1068 Five separate sites of 6.7-Cillz methanol maser emission were observed in the three sources. but we detected radio continuum emission associated with only two.," Five separate sites of 6.7-GHz methanol maser emission were observed in the three sources, but we detected radio continuum emission associated with only two."1069 The observed parameters of the radio continuum emission toward each of the sites of maser emission. are summarized. in ‘Table 2.., The observed parameters of the radio continuum emission toward each of the sites of maser emission are summarized in Table \ref{tab:cont}.1070 Pwo of the sites without continuum emission lie in the NGC 6334 star formation region., Two of the sites without continuum emission lie in the NGC 6334 star formation region.1071 The upper limits on the peak Dux density we obtained for them (see Table 2)) are quite large. due to the presence of nearby strong cilluse sources. which severely limited the dvnamic range we were able to achieve for images of this region.," The upper limits on the peak flux density we obtained for them (see Table \ref{tab:cont}) ) are quite large, due to the presence of nearby strong diffuse sources, which severely limited the dynamic range we were able to achieve for images of this region."1072 The resulting upper limits are not significantly smaller than the peak Iux, The resulting upper limits are not significantly smaller than the peak flux1073relfie:peaks.. the integrands are plotted. also showing (he peak energies ancl the widths of the peaks for different energies.,", the integrands are plotted, also showing the peak energies and the widths of the peaks for different energies."1074 The shown energies are in agreement with the mean excitation energies derived by Tubbs&Ixoonin(1979)., The shown energies are in agreement with the mean excitation energies derived by \citet{tub79}.1075. In the same manner. (he cut-off energy of 25 MeV. often used for ealeulating partition functions up to Zo=LO. can be justified.," In the same manner, the cut-off energy of 25 MeV, often used for calculating partition functions up to $T_9=10$, can be justified."1076 For Ty>12. we extract a (nearly) euadratie dependence on temperature of the peak ο ο and a linear dependence of the width Dyjwii of the integrand: The integration cut-off was then set to = )) MeV. Due to the exponential increase of (he nuclear level density with excitation energy. extremely large partition functions already result at temperatures of a few MeV (temperatures eiven as energies and in 75 are related by £—15/11.6045 MeV).," For $T_9>12$, we extract a (nearly) quadratic dependence on temperature of the peak energy $E_{\rm peak}$ and a linear dependence of the width $\Gamma_\mathrm{FWHM}$ of the integrand: The integration cut-off was then set to = + ) MeV. Due to the exponential increase of the nuclear level density with excitation energy, extremely large partition functions already result at temperatures of a few MeV (temperatures given as energies and in $T_9$ are related by $E=T_9/11.6045$ MeV)."1077 However. it has been realized that a straightforward. integration over the level density might overestimate the parütion functions.," However, it has been realized that a straightforward integration over the level density might overestimate the partition functions."1078 High excitation energies of the nucleus permit (he emission of nucleons and therefore an appropriate Iraction of the level density associated. with such continuum states should be neglected in the computation of the partition function., High excitation energies of the nucleus permit the emission of nucleons and therefore an appropriate fraction of the level density associated with such continuum states should be neglected in the computation of the partition function.1079 Fowler.Engelbrecht.&Woosley(1973). introduced such high temperature corrections by truncating (he integration near the nucleon separation energy aud by subtracüng continuum scattering states (which. however. do not act below το= 100).," \citet{fow78} introduced such high temperature corrections by truncating the integration near the nucleon separation energy and by subtracting continuum scattering states (which, however, do not act below $T_9=100$ )."1080 Mazurek.Lattimer.(1979) accounted for the suppression of the partition functions by arbitrarily setting the integral cut-off to 25 MeV. In a semi-classical ealeulation. Tubbs&Ixoonin(1979). showed that Fowler.Engelbrecht.&Wooslev(1978) and Mazurek.Lattimer.&Brown(1979) largely overestimated (he suppression. that a simple truncation of the integral is incorrect. and that partition functions remain large for temperatures as high as Z4=LOO.," \citet{maz79} accounted for the suppression of the partition functions by arbitrarily setting the integral cut-off to 25 MeV. In a semi-classical calculation, \citet{tub79} showed that \citet{fow78} and \citet{maz79}1081 largely overestimated the suppression, that a simple truncation of the integral is incorrect, and that partition functions remain large for temperatures as high as $T_9=100$."1082 Thev find that the corrections are much smaller than given by truncated level density integrals and that the conventional partition lunctions (with full integration) are much closer (to their values than values obtained with anv of the truncation methods., They find that the corrections are much smaller than given by truncated level density integrals and that the conventional partition functions (with full integration) are much closer to their values than values obtained with any of the truncation methods.1083 The advantage of the description by Tubbs&Koonin(1979).. which is based on the independent particle model. is (he natural inclusion of both bound aud continuum nuclear," The advantage of the description by \citet{tub79}, which is based on the independent particle model, is the natural inclusion of both bound and continuum nuclear"1084"The observing material was gathered at the Telescope Bernard Lyot (Observatoire du Pic du Midi, France) using the NARVAL spectropolarimeter.","The observing material was gathered at the Telescope Bernard Lyot (Observatoire du Pic du Midi, France) using the NARVAL spectropolarimeter."1085" As a strict copy of ESPaDOnS (Petitetal., 2003),, NARVAL spectra provide a simultaneous coverage of the whole optical domain (from 370 nm to 1,000 nm) at high spectral resolution (R 265,000)."," As a strict copy of ESPaDOnS \citep{Pet03}, NARVAL spectra provide a simultaneous coverage of the whole optical domain (from 370 nm to 1,000 nm) at high spectral resolution $R=$ 65,000)."1086" The instrument consists of a bench-mounted spectrograph and a Cassegrain-mounted polarimeter, with an optical fiber carrying the light between the two units."," The instrument consists of a bench-mounted spectrograph and a Cassegrain-mounted polarimeter, with an optical fiber carrying the light between the two units."1087" A series of 3 Fresnel rhombs (two half-wave rhombs that can rotate about the optical axis and one fixed quarter-wave rhomb) are used in the polarimeter, followed by a Wollaston prism which splits the incident light into two beams, respectively containing light linearly polarized perpendicular/parallel to the axis of the prism."," A series of 3 Fresnel rhombs (two half-wave rhombs that can rotate about the optical axis and one fixed quarter-wave rhomb) are used in the polarimeter, followed by a Wollaston prism which splits the incident light into two beams, respectively containing light linearly polarized perpendicular/parallel to the axis of the prism."1088" Each Stokes V spectrum is obtained from a combination of four sub-exposures taken with the half-wave rhombs oriented at different azimuths (Semeletal.,1993).", Each Stokes V spectrum is obtained from a combination of four sub-exposures taken with the half-wave rhombs oriented at different azimuths \citep{Sem93}.1089". The data reduction is performed by Libre-Esprit, a dedicated, fully automated software described by Donatietal.(1997)."," The data reduction is performed by Libre-Esprit, a dedicated, fully automated software described by \citet{Do97}."1090". The data were collected during 4 consecutive nights in the summer of 2008, from July 25 to July 28, using 6 sec integration times for each sub-exposure of the Stokes V sequences (except the first two sequences of the run, for which exposure times of 15 and 10 sec were adopted)."," The data were collected during 4 consecutive nights in the summer of 2008, from July 25 to July 28, using 6 sec integration times for each sub-exposure of the Stokes V sequences (except the first two sequences of the run, for which exposure times of 15 and 10 sec were adopted)."1091" We retained the 257 Stokes V spectra with a typical peak signal-to-noise ratio (S/N hereafter) of 1,500 per 1.8 ss!, around 2=600 nm."," We retained the 257 Stokes V spectra with a typical peak signal-to-noise ratio (S/N hereafter) of 1,500 per 1.8 $^{-1}$, around $\lambda = 600$ nm."1092" For each spectrum, both Stokes I V parameters were processed using the LSD cross-correlation method1997)."," For each spectrum, both Stokes I V parameters were processed using the LSD cross-correlation method."1093". Using a line mask computed from a stellar atmospheric model with T.g-10,000 K and logg = 4.0 (Kurucz,1993),, we calculated LSD line profiles from a total of 1,200 photospheric lines."," Using a line mask computed from a stellar atmospheric model with $_{\rm eff}$ =10,000 K and $\log g$ = 4.0 \citep{Kur93}, we calculated LSD line profiles from a total of 1,200 photospheric lines."1094" The multiplex gain in the S/N from the raw spectra to the LSD mean profiles is about 30, reducing the noise level of the cross-correlation profiles to between c=3 and 7x10:51. where o is the standard deviation of the noise and J, stands for the intensity of continuum."," The multiplex gain in the S/N from the raw spectra to the LSD mean profiles is about 30, reducing the noise level of the cross-correlation profiles to between $\sigma = 3$ and $7\times 10^{-5}I_{c}$, where $\sigma$ is the standard deviation of the noise and $I_{c}$ stands for the intensity of continuum."1095" Since no signature was observed above noise level in individual Stokes V LSD profiles, we then calculated an average of the 257 profiles, where each profile is weighted by the square of its S/N. In this global profile, the noise in the Stokes V parameter is further decreased to o=2x10-61 (Fig. 1))"," Since no signature was observed above noise level in individual Stokes V LSD profiles, we then calculated an average of the 257 profiles, where each profile is weighted by the square of its S/N. In this global profile, the noise in the Stokes V parameter is further decreased to $\sigma = 2\times 10^{-6}I_{c}$ (Fig. \ref{fig:stokesv}) )"1096 and a signature is now observed in circular polarization with an amplitude of 1077. (that is 5 times the noise level)., and a signature is now observed in circular polarization with an amplitude of $10^{-5}I_{c}$ (that is $5$ times the noise level).1097" Running a Y? test on the signature (Donatietal.,1992),, we found a reduced X? of 3.5, which corresponds to a false-alarm probability of 3x107!."," Running a $\chi^2$ test on the signature \citep{Do92}, we found a reduced $\chi^2$ of 3.5, which corresponds to a false-alarm probability of $3\times 10^{-11}$."1098 Various tests have been performed to make sure that the polarization is of stellar origin and not due to an artefact of the instrument or the reduction process., Various tests have been performed to make sure that the polarization is of stellar origin and not due to an artefact of the instrument or the reduction process.1099" This is particularly important in the present case, as the amplitude of the polarized signal is the lowest detected by NARVAL to date."," This is particularly important in the present case, as the amplitude of the polarized signal is the lowest detected by NARVAL to date."1100" A strong test to discard the possibility of a spurious signal is the ""null"" profile calculated from a different combination of the four exposures constituting the polarimetric sequence (Donatial.,1997)."," A strong test to discard the possibility of a spurious signal is the ""null"" profile calculated from a different combination of the four sub-exposures constituting the polarimetric sequence \citep{Do97}."1101". As shown in Fig. 1,,"," As shown in Fig. \ref{fig:stokesv},"1102" no detectable counterpart of the Stokes V signal is seen in the ""null"" profile (note that a similar conclusion is reached by calculating another null profile (not shown here) from another possible combination of the sub-exposures)."," no detectable counterpart of the Stokes V signal is seen in the ""null"" profile (note that a similar conclusion is reached by calculating another null profile (not shown here) from another possible combination of the sub-exposures)."1103 We then checked that the signal possesses the expected properties of a stellar polarized signal., We then checked that the signal possesses the expected properties of a stellar polarized signal.1104" First, we split the whole time-series into two independent subsets, containing respectively the first and second half of the observing run, both subsets having equivalent signal-to-noise ratios."," First, we split the whole time-series into two independent subsets, containing respectively the first and second half of the observing run, both subsets having equivalent signal-to-noise ratios."1105 As can be seen in Fig., As can be seen in Fig.1106" 2aa, the polarized signal is present in both sets, the false-alarm probabilities based on the y? test being 5x107? and 6x10, respectively."," \ref{fig:2epochs}a a, the polarized signal is present in both sets, the false-alarm probabilities based on the $\chi^2$ test being $5\times 10^{-6}$ and $6\times 10^{-3}$, respectively."1107" Second, we built two line-lists from the atmospheric model, containing all spectral lines with Landé factors respectively higher and lower than ος=1.2."," Second, we built two line-lists from the atmospheric model, containing all spectral lines with Landé factors respectively higher and lower than $g_c = 1.2$."1108 The Stokes V profiles computed from the two line-lists are plotted in Fig., The Stokes V profiles computed from the two line-lists are plotted in Fig.1109" 2bb. As expected, the amplitude of the polarized signal appears higher for the high Landé factor lines than for the low Landé factor lines."," \ref{fig:2epochs}b b. As expected, the amplitude of the polarized signal appears higher for the high Landé factor lines than for the low Landé factor lines."1110 The peak-to-peak amplitudes of the polarized signals taken inside the line profile are respectively 2.8x107. and 2.0x107..," The peak-to-peak amplitudes of the polarized signals taken inside the line profile are respectively $2.81111\times 10^{-5}I_c$ and $2.0\times 10^{-5}I_c$."1112" Their difference slightly exceeds the noise level (c=6X10~°/, and 5x10~°/., respectively) and their ratio is roughly consistent with the ratio of the average Landé factors of the line-lists (gj,=1.51 and g,,=0.94 respectively), taking into account that the corresponding Stokes I LSD profiles have a similar depth, within10%.."," Their difference slightly exceeds the noise level $\sigma = 6\times 10^{-6}I_c$ and $5\times 10^{-6}I_c$, respectively) and their ratio is roughly consistent with the ratio of the average Landé factors of the line-lists $g_m=1.51$ and $g_m=0.94$ respectively), taking into account that the corresponding Stokes I LSD profiles have a similar depth, within."1113" Third, we checked that the signal was still consistently recovered when other ways of splitting our line-list were considered (low versus high excitation potential or low versus high wavelengths)."," Third, we checked that the signal was still consistently recovered when other ways of splitting our line-list were considered (low versus high excitation potential or low versus high wavelengths)."1114" Finally, we tested the effect of changing the line mask."," Finally, we tested the effect of changing the line mask."1115" Indeed, spectroscopic and interferometric studies of Vega have shown that its surface temperature is inhomogeneous, due to the gravity darkening"," Indeed, spectroscopic and interferometric studies of Vega have shown that its surface temperature is inhomogeneous, due to the gravity darkening"1116discoveries of very massive galaxies near z=6 (Mobasheretal.2005) and as new surveys probe redshifts up to z=10 (Bouwensetal.2006;IyeStark2007).,"discoveries of very massive galaxies near $z = 6$ \citep{Mobasher05} and as new surveys probe redshifts up to $z=10$ \citep{Bouwens06,Iye06,Stark07}."1117". Even at high-redshifts, narrow-band surveys of Lyman-alpha emitters (LAEs) span such a small range of redshifts that they are unaffected by the exponential change in the mass function of halos with redshift."," Even at high-redshifts, narrow-band surveys of Lyman-alpha emitters (LAEs) span such a small range of redshifts that they are unaffected by the exponential change in the mass function of halos with redshift."1118" However, the photometric selection functions (PHSFs) of the bands used in drop-out surveys of Lyman-break galaxies (LBGs) can be fairly broad in redshift space (Bouwens&Illingworth2006)."," However, the photometric selection functions (PHSFs) of the bands used in drop-out surveys of Lyman-break galaxies (LBGs) can be fairly broad in redshift space \citep{BI06}."1119". In this paper, we examine the significance of light-cone distortions on the inferred abundance and clustering properties of high-redshift galaxies in dropout surveys of LBGs."," In this paper, we examine the significance of light-cone distortions on the inferred abundance and clustering properties of high-redshift galaxies in dropout surveys of LBGs."1120" First, we describe the PHSFs used in dropout surveys in 8??.."," First, we describe the PHSFs used in dropout surveys in \ref{selection}."1121" Subsequently, we derive analytic formulae for the first and second statistical moments of the count of halos in a given survey volume (§??)) and consider the two-point correlation function of halos on the light-cone (§??))."," Subsequently, we derive analytic formulae for the first and second statistical moments of the count of halos in a given survey volume \ref{moments}) ) and consider the two-point correlation function of halos on the light-cone \ref{correlation}) )."1122" In §??,, we review a simple model for high-redshift star forming galaxies by Starketal.(2007),, that gives the luminosity of LBGs and LAEs contained in a halo of a given mass."," In \ref{model}, , we review a simple model for high-redshift star forming galaxies by \citet{SLE07}, that gives the luminosity of LBGs and LAEs contained in a halo of a given mass."1123" We then use this model to calculate the quantitative difference between our light-cone formalism and the standard snapshot approach for various survey volumes ??)), exploring the dependence on cosmological parameters."," We then use this model to calculate the quantitative difference between our light-cone formalism and the standard snapshot approach for various survey volumes \ref{results}) ), exploring the dependence on cosmological parameters."1124" Finally, we discuss the significance of our results in 8??.."," Finally, we discuss the significance of our results in \ref{discussion}."1125" Unless otherwise stated, we assume a flat, ACDM cosmology with cosmological parameters (Qm,Qa,Qs,h,08,0,T)(0.268,0.732,0.042,0.704,0.776,0.947,0.000) etal. 2007)."," Unless otherwise stated, we assume a flat, $\Lambda$ CDM cosmology with cosmological parameters $\left( \Omega_m, \Omega_{\Lambda}, \Omega_b, h, \sigma_8, \alpha, r\right) = \left( 0.268, 0.732, 0.042, 0.704, 0.776, 0.947, 0.000 \right)$ \citep{Spergel07}."1126. All distance scales are comoving., All distance scales are comoving.1127 Dropout surveys at high redshifts (z= 6) select LBGs by measuring a drop in flux shortward of the Lya wavelength (due to absorption by intergalactic hydrogen)., Dropout surveys at high redshifts $z\ga 6$ ) select LBGs by measuring a drop in flux shortward of the $\alpha$ wavelength (due to absorption by intergalactic hydrogen).1128 This requires comparing the observed flux in different photometric bands., This requires comparing the observed flux in different photometric bands.1129 The filter for each band is described by a profile that indicates how much light is transmitted at each wavelength., The filter for each band is described by a profile that indicates how much light is transmitted at each wavelength.1130 This transmission profile provides a probability distribution for the wavelength of a given photon that has passed through the filter., This transmission profile provides a probability distribution for the wavelength of a given photon that has passed through the filter.1131" Since the edge of the Lya absorption trough appears at a wavelength corresponding to the redshift of the observed galaxy, the filter profile can be expressed in redshift space as the photometric selection function (PHSF) for a given photometric band, which gives the distribution of the surveyed galaxies over redshift (Bouwens&Illingworth 2006)."," Since the edge of the $\alpha$ absorption trough appears at a wavelength corresponding to the redshift of the observed galaxy, the filter profile can be expressed in redshift space as the photometric selection function (PHSF) for a given photometric band, which gives the distribution of the surveyed galaxies over redshift \citep{BI06}."1132. The volume of the survey is an integral over this function (Steideletal.1999)., The volume of the survey is an integral over this function \citep{Steidel99}.1133". In this paper we focus on dropout selections in the i-, z-, and J- corresponding to the standard HST filters F775W, F850LP, and F110W, respectively."," In this paper we focus on dropout selections in the i-, z-, and J-bands corresponding to the standard HST filters F775W, F850LP, and F110W, respectively."1134" The PHSFs for each band depend on the specific selection criteriachosen, but are roughly approximated by Gaussians (Bouwens 2007, personal communication)."," The PHSFs for each band depend on the specific selection criteriachosen, but are roughly approximated by Gaussians (Bouwens 2007, personal communication)."1135" We take the mean redshifts of the i-, z-, and J-band PHSFs to be ju;=6.5, 7.4, and 10, respectively, and their standard deviations to be 0.5, 0.5, and 1.0."," We take the mean redshifts of the i-, z-, and J-band PHSFs to be $\mu_z = 6.5$, $7.4$, and $10$, respectively, and their standard deviations to be $\sigma_z = 0.5$ , $0.5$, and $1.0$."1136" We also ignore, for simplicity, possible interlopers at lower redshifts whose spectra mimic those of LBGs at higher redshift as a result of dust attenuation."," We also ignore, for simplicity, possible interlopers at lower redshifts whose spectra mimic those of LBGs at higher redshift as a result of dust attenuation."1137" Due to the evolution of the mass function of galaxy halos within the survey volume, the probability distribution for the redshift (RPD) of a galaxy in the survey is not the same as the PHSF."," Due to the evolution of the mass function of galaxy halos within the survey volume, the probability distribution for the redshift (RPD) of a galaxy in the survey is not the same as the PHSF."1138" Even though the contribution from galaxies in the Gaussian tail of the PHSFs is exponentially suppressed, the density of the rare halos that contain the observed galaxies is theoretically expected to be exponentially higher toward the low-redshift end of the survey."," Even though the contribution from galaxies in the Gaussian tail of the PHSFs is exponentially suppressed, the density of the rare halos that contain the observed galaxies is theoretically expected to be exponentially higher toward the low-redshift end of the survey."1139" The volume per redshift interval also changes within the survey since the area of the survey perpendicular to the line-of-sight and the comoving distance per redshift interval along the line-of-sight are both redshift dependent, but this is a small correction."," The volume per redshift interval also changes within the survey since the area of the survey perpendicular to the line-of-sight and the comoving distance per redshift interval along the line-of-sight are both redshift dependent, but this is a small correction."1140" Ignoring the variationof the survey volume per redshift interval, the RPD for LBGs with luminosity at a wavelength of 1500À that is greater than Lisoo within the volume observed in a given dropout band is given by, where juz and o; are the mean and standard deviation of the given band, n(z,M) is the mass function of halos, and Lisoo(Mnato) is a relation for the luminosity of an LBG contained in a halo of mass Mpato, which we describe in §??.."," Ignoring the variationof the survey volume per redshift interval, the RPD for LBGs with luminosity at a wavelength of $1500\,\mbox{\AA}$ that is greater than $L_{1500}$ within the volume observed in a given dropout band is given by, where $\mu_z$ and $\sigma_z$ are the mean and standard deviation of the given band, $n(z,M)$ is the mass function of halos, and $L_{1500}(M_{halo})$ is a relation for the luminosity of an LBG contained in a halo of mass $M_{halo}$ , which we describe in \ref{model}. ."1141 Figure 1 shows how the PHSF is multiplied by the mass function to generate thereal RPD for J-dropouts., Figure \ref{Nplot} shows how the PHSF is multiplied by the mass function to generate thereal RPD for J-dropouts.1142" In §??,, we calculate the moments of this true distribution."," In \ref{results}, , we calculate the moments of this true distribution."114310kms! (Berger et al 2009): the latter property is a clear departure from typical SN behavior.,$10^3 \kms$ (Berger et al 2009); the latter property is a clear departure from typical SN behavior.1144 According to Prieto οἱ al. (, According to Prieto et al. (11452009) the ILOT event that most resembles NGC 300 OT is SN 20035 (Prieto et al.,2009) the ILOT event that most resembles NGC 300 OT is SN 2008S (Prieto et al.1146 2008: Wesson et al., 2008; Wesson et al.1147 2009)., 2009).1148 Both ILOTs were the result of an energetic eruption in a dust-enshrouded 10—20M. star that survived the eruption (namely. SN 20085 was nol a SN al all).," Both ILOTs were the result of an energetic eruption in a dust-enshrouded $10-20 M_\odot$ star that survived the eruption (namely, SN 2008S was not a SN at all)."1149 Smith et al. (, Smith et al. (11502009) suggested Chat the physical mechanism which produced SN. 20088 is a super-Edeington wind. similar to the super-outbursts of massive Lunminous Blue Variables (LBVs).,"2009) suggested that the physical mechanism which produced SN 2008S is a super-Eddington wind, similar to the super-outbursts of massive Luminous Blue Variables (LBVs)."1151 Dotticella et al. (, Botticella et al. (11522009) suggested that the progenitor was an extreme (“super”) AGB star.,2009) suggested that the progenitor was an extreme (“super”) AGB star.1153 Bond et al. (, Bond et al. (11542009) suggested that both SN 20085 and NGC 300 OT originated form evolved massive stars on a blue loop (to warmer temperatures. and were subjected to increased instability due (ο prior mass loss.,"2009) suggested that both SN 2008S and NGC 300 OT originated form evolved massive stars on a blue loop to warmer temperatures, and were subjected to increased instability due to prior mass loss."1155 An asymmetric dustv environment extending a AU surrounding NGC 300 OT (Patat et al., An asymmetric dusty environment extending a $\AU$ surrounding NGC 300 OT (Patat et al.1156 2009) hints to a previous possible eruption., 2009) hints to a previous possible eruption.1157 This asvimmmetry may further hint to the presence of a companion star. although we note that up to date there has been no delinile observation proving a companionexistence.," This asymmetry may further hint to the presence of a companion star, although we note that up to date there has been no definite observation proving a companion."1158 Thompson et al. (, Thompson et al. (11592008) suggested that ILOTSs occur due to single star processes. e.g.. electron-capture SN. an explosive birth of a massive WD. or an enormous outburst of a massive star.,"2008) suggested that ILOTs occur due to single star processes, e.g., electron-capture SN, an explosive birth of a massive WD, or an enormous outburst of a massive star."1160 Ii NGC 300 OT and SN 20088 the progenitors were luminous (c4—6x1011. ) dust-enshrouded stars. ad the end of their AGB stage.," In NGC 300 OT and SN 2008S the progenitors were luminous $\sim 4 - 61161\times 10^4 L_\odot$ ) dust-enshrouded stars, at the end of their AGB stage."1162 Based on the model proposed by Soker (2004). we examine in this (Section 2)) whether an eruptive mass (ransler a companion can account for (he properties ol NGC 300 OT.," Based on the model proposed by Soker (2004), we examine in this (Section \ref{sec:companion}) ) whether an eruptive mass transfer a companion can account for the properties of NGC 300 OT."1163 In that model most of the οποιον of the outburst was gravitational enerev released by ~fewxO.LAL. accreted by a AIS B-type companion., In that model most of the energy of the outburst was gravitational energy released by $\sim {\rm few} \times 0.1 M_\odot$ accreted by a MS B-type companion.1164 The binary system survives the event., The binary system survives the event.1165 In Section 3 we suggest a physical mechanism (o account for most of the eravitationallv-powered outbursts., In Section \ref{sec:transients} we suggest a physical mechanism to account for most of the gravitationally-powered outbursts.1166 We examine a model where the source of the mass is an extreme-AGB star. while the main source of (he energy is a gravitational energy released by the mass aceretecl onto a MS companion.," We examine a model where the source of the mass is an extreme-AGB star, while the main source of the energy is a gravitational energy released by the mass accreted onto a MS companion."1167 Dased on previous papers (Berger et al., Based on previous papers (Berger et al.1168 2009: Dond et al., 2009; Bond et al.1169 2009: Gogarten et al., 2009; Gogarten et al.1170 2009: Prieto et al., 2009; Prieto et al.1171 2009) we scale the mass of the extreme-AGD star by A4~1911..., 2009) we scale the mass of the extreme-AGB star by $M_1 \simeq 15M_\odot$.1172 We also assume that the main sequence companion is not much lighter (han the primary. and scale ib with A»~8JM.. corresponding to a MS radius of Πο~3.54.2H (our model can work [or," We also assume that the main sequence companion is not much lighter than the primary, and scale it with $M_2 \simeq 8 M_\odot$, corresponding to a MS radius of $R_2 \simeq 3.5 R_\odot$ (our model can work for"1173"Positive results obtained so far ideutifv the excess of source DC flux by couparison with the ""off source” nieasureimeuts.",Positive results obtained so far identify the excess of source DC flux by comparison with the off source' measurements.1174 For example. in the TIIEMISTOCLE experiment he observation of Crab nebula gained about 1110 events ocalized within 5 nur from the Crab pulsar direction.," For example, in the THEMISTOCLE experiment the observation of Crab nebula gained about 1440 events localized within 5 mrad from the Crab pulsar direction."1175" Frou, ""off source’ observation the expected backerouud within 5Γ luraα ας estimated.", From off source' observation the expected background within 5 mrad was estimated.1176 The OXCOSS ~-- 260 eveuts are the Crab nebula DC signal., The excess $\approx$ 260 events are the Crab nebula DC signal.1177 Tιο rest of zc 1150 eveifs are imnostlv due to jadrouic EAS Using any other method of ideutifving the hadronic iature of observed eveit it would be possible ο Increase signal to noise ratio and add the streugth to he result observed so ar., The rest of $\approx$ 1180 events are mostly due to hadronic EAS Using any other method of identifying the hadronic nature of observed event it would be possible to increase signal to noise ratio and add the strength to the result observed so far.1178 We preseuted here some details of differences between EM EAS and hadronic EAS due to the presence of fast uous aud Cherenkov light produced by It is very difficult to eive a quantitative calculated prediction about the cfiicieney of this method., We presented here some details of differences between E–M EAS and hadronic EAS due to the presence of fast muons and Cherenkov light produced by It is very difficult to give a quantitative calculated prediction about the efficiency of this method.1179 There are many problems aud only some of them were addressed here., There are many problems and only some of them were addressed here.1180 We hope that examining carefully already existing experimental data oue would be able to see a muon signal and then estimate the eficieucy of the method in the specific experimental conditions., We hope that examining carefully already existing experimental data one would be able to see a muon signal and then estimate the efficiency of the method in the specific experimental conditions.1181 We would like to thank Dr. Pierre Expigat aud Dr. Claude Chesquierre for very valuable discussions., We would like to thank Dr. Pierre Espigat and Dr. Claude Ghesquièrre for very valuable discussions.1182Among many cosmological surveys. the submillimetre (submm) survey is very unique. in the sense that the expected [ux density of sources is almost. insensitive to redshift for z 1. Ss. owing to the strong negative A- (e.g.Blainetal.2002)..,"Among many cosmological surveys, the submillimetre (submm) survey is very unique, in the sense that the expected flux density of sources is almost insensitive to redshift for $z\approx $ 1 – 8, owing to the strong negative $K$ -correction \citep[e.g.][]{2002PhR...369..111B}."1183 Although the current SCnsitivity allows us to detect only the brightest infrared galaxies in the universe. it is possible to detect. massive starbursts and eas rich QSOs at extreme redshifts 2>>6 if exist (c.g.Priddeyetal.2008)..," Although the current sensitivity allows us to detect only the brightest infrared galaxies in the universe, it is possible to detect massive starbursts and gas rich QSOs at extreme redshifts $z\gg 6$ if exist \citep[e.g.][]{2008MNRAS.383..289P}."1184 However. most. of the subnim galaxies (SMS) currently. identified lie at 253.," However, most of the submm galaxies (SMGs) currently identified lie at $z\la 3$."1185" This is not because of the detection limit as noted above. but because of the ""identification limit. owing to a large oam size of current (sub)mm telescopes used. for surveys."," This is not because of the detection limit as noted above, but because of the `identification limit', owing to a large beam size of current (sub)mm telescopes used for surveys."1186 The racio emission provides a high-resolution substitute for he infrared. emission. observed. in the submam (c.g.Chap-Dannerbaueretal.2004:Ivison 2007).. ancl hence he detection limit in the racio has set the upper limits on redshifts of identified SALGs (Chapmanetal.2005)..," The radio emission provides a high-resolution substitute for the infrared emission observed in the submm \citep[e.g.][]{2001ApJ...548L.147C,2003ApJ...585...57C,11872002MNRAS.337....1I,2004MNRAS.355..485B,2004ApJ...606..664D,2007MNRAS.380..199I}, and hence the detection limit in the radio has set the upper limits on redshifts of identified SMGs \citep{2005ApJ...622..772C}."1188 The vest wav το identify optical counterparts of SMCGs is to have veh resolution submunm images with interferometers (Lonoxulerotal. 2008)...," The best way to identify optical counterparts of SMGs is to have high resolution submm images with interferometers \citep{2006ApJ...640L...1I,2007ApJ...671.1531Y,2007ApJ...670L..89W,2008ApJ...673L.127D}."1189 Although time consuming. it allows us o perform direct optical/near-infrared (NUR) identifications rom the subnmun position.," Although time consuming, it allows us to perform direct optical/near-infrared (NIR) identifications from the submm position."1190 Ilere we adopt another method. of direct optical identification using optical/NIIt. colours of galaxies around he submum source., Here we adopt another method of direct optical identification using optical/NIR colours of galaxies around the submm source.1191 The expected number of. random optical/NIlt associations within the error circle of the, The expected number of random optical/NIR associations within the error circle of the1192We thauk the anouviuous referee for very careful reading and very nice coments tha nuprove this paper.,We thank the anonymous referee for very careful reading and very nice comments that improve this paper.1193 The authors are grateful to M. Fujioto. Ix. Sorai. IX. ΟΙ. A. IN. Inoue. T. Takerchi. N. Yoshida aud D. T. Draine for helptu discussions.," The authors are grateful to M. Fujimoto, K. Sorai, K. Omukai, A. K. Inoue, T. Takeuchi, N. Yoshida and B. T. Draine for helpful discussions."1194 Numerical computations were carriec out on NEC SX-9 at the Center for Computationa Astropwsics. CHCA. of National Astronomica Observatory of Japan.," Numerical computations were carried out on NEC SX-9 at the Center for Computational Astrophysics, CfCA, of National Astronomical Observatory of Japan."1195 This work was partly SIypored bv the Craut-in-Aid for Scicutific ReSOCALl of Japan Society for the Promotion of Sciences (OSOO0TS23. Taloloos. 0310038).," This work was partly supported by the Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Sciences (08091823, 18104003, 0340038)."1196 ILIT. is SIypored by NSC eraut 99-2112-M-001-006-NIY3., H.H. is supported by NSC grant 99-2112-M-001-006-MY3.1197 T.N. aid WN are supported by World Premicr Tuternational Research Center Initiative. Next. Jaul.," T.N. and K.N are supported by World Premier International Research Center Initiative, Next, Japan."1198the east. as observed around the FUR 5 core.,"the east, as observed around the FIR 5 core."1199 In order to check if the radiation pressure can be large enough to compress the molecular gas. we have studied the distribution of the ionized eas in NGC 2024.," In order to check if the radiation pressure can be large enough to compress the molecular gas, we have studied the distribution of the ionized gas in NGC 2024."1200 For this purpose. we accessed ilie NRAO Data Archive System {ο search for centimeter emission that could reproduce this morphology.," For this purpose, we accessed the NRAO Data Archive System to search for centimeter emission that could reproduce this morphology."

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