ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2ichhicl can‘ only Ilbe iuterpreted;erpretedTaw as aat;on=3.107: we can exclude the alternative identification as aat 2=0.339. because in this case. we would have also detected the llinc.," which can only be interpreted as at $z=3.107$; we can exclude the alternative identification as at $z=0.339$, because in this case, we would have also detected the line."3 At:ie[Dcoutzibnte107. the lline may senificautlv to the A baud flux. but object cannot be a reflection nebula. as eudssion is also detected in the Ro baud.which is free ofstrong ciission lines.," At $z=3.107$, the line may contribute significantly to the $K-$ band flux, but object cannot be a reflection nebula, as emission is also detected in the $R-$ band,which is free ofstrong emission lines."4 Object therefore appears to be a companion, Object therefore appears to be a companion5and therefore the atmospheric circulation for this planet is unconstrained at this point in (ime.,and therefore the atmospheric circulation for this planet is unconstrained at this point in time.6 Clouds would further complicate the appearance of the planets Gansmission spectrum bv efficiently scattering starlight at short wavelengths., Clouds would further complicate the appearance of the planet's transmission spectrum by efficiently scattering starlight at short wavelengths.7 At longer wavelengths in the mid-IR. the spectrum of GJ 1214b should remain mostly unaffected by clouds.," At longer wavelengths in the mid-IR, the spectrum of GJ 1214b should remain mostly unaffected by clouds."8 Qualitativelv. in the optical and near-Lt. clouds can flatten the planets transmission spectrum by scattering lieht ab higher altitudes than where spectral features in transmission are expected (o originale.," Qualitatively, in the optical and near-IR, clouds can flatten the planet's transmission spectrum by scattering light at higher altitudes than where spectral features in transmission are expected to originate."9 For GJ 1214b. we have previously found Chat clouds at pressures greater (han 200 mbar can explain the observations of a flat. transmission spectrum [rom 780 ιο 1000 nm by ?..," For GJ 1214b, we have previously found that clouds at pressures greater than 200 mbar can explain the observations of a flat transmission spectrum from 780 to 1000 nm by \citet{bea10}."10 This value was determined by cutting olf transmission al different heights in the planets abmosphere (o simulate the effects of an optically thick grav. cloud. deck., This value was determined by cutting off transmission at different heights in the planet's atmosphere to simulate the effects of an optically thick gray cloud deck.11 Clouds. deeper in the atmosphere than 200 mbar would have only a minimal effect on the Uiransnission spectrum at the wavelengths of the ? observations., Clouds deeper in the atmosphere than 200 mbar would have only a minimal effect on the transmission spectrum at the wavelengths of the \citet{bea10} observations.12 Η clouds are present. the exact shape of (he transmission spectrum at short wavelengths is determined by whether the scattering is occurring within (he Ravleieh or Mie regime. which will produce different power law slopes for the scattering opacity.," If clouds are present, the exact shape of the transmission spectrum at short wavelengths is determined by whether the scattering is occurring within the Rayleigh or Mie regime, which will produce different power law slopes for the scattering opacity."13 Unfortunately. sell-consistentlv modeling the cloud opacity requires knowledge of the cloud particle size and heieht distributions. which are currently. unknown for GJ 1214b.," Unfortunately, self-consistently modeling the cloud opacity requires knowledge of the cloud particle size and height distributions, which are currently unknown for GJ 1214b."14 Here we offer up some suggestions For what the cloud composition could be., Here we offer up some suggestions for what the cloud composition could be.15 Clouds are formed by condensation processes. which will occur if the partial pressure of a species surpasses its vapor or condensation pressure.," Clouds are formed by condensation processes, which will occur if the partial pressure of a species surpasses its vapor or condensation pressure."16 To determine whether cloud formation will occur in the atmosphere of GJ 1214b. we compare the planets T-P profile against the condensation curves of various molecules that are predicted to condense in hot planet and cool star atmospheres from ?..," To determine whether cloud formation will occur in the atmosphere of GJ 1214b, we compare the planet's T-P profile against the condensation curves of various molecules that are predicted to condense in hot planet and cool star atmospheres from \citet{lod06}."17 The only molecules (hat we find whose condensation curves intersect the predicted T-P profile of GJ 1214b are ACT and Zn5. as shown in Figure 7.. although we caution that the T-P profile of GJ 1214b is unconstrained by observations. so ils exact shape is somewhat uncertain.," The only molecules that we find whose condensation curves intersect the predicted T-P profile of GJ 1214b are KCl and ZnS, as shown in Figure \ref{f7}, although we caution that the T-P profile of GJ 1214b is unconstrained by observations, so its exact shape is somewhat uncertain."18 If (he T-P profile from Figure 7 is correct. (hen both KC and Zus should condense at pressures of ~500 mbar in GJ 1214b's aüimosphere at solar composition.," If the T-P profile from Figure \ref{f7} is correct, then both KCl and ZnS should condense at pressures of $\sim$ 500 mbar in GJ 1214b's atmosphere at solar composition."19 For hieher metallicities a wmuber of effects come into play which can shift the condensation to either higher or lower pressure in GJ 1214b's atmosphere., For higher metallicities a number of effects come into play which can shift the condensation to either higher or lower pressure in GJ 1214b's atmosphere.20 These effects are (1) the abunelaces of condensate materials tend to be higher at higher Z. (2) (the condensation curves for condensate species tend to shift to hisher temperature Le. to the right on Figure due to the increased vapor pressure of (he heavy elements in (he eas phase. ancl (3) the T-P profile tends to shift up aud to risht on Figure 7 due to the increased opacities from higher," These effects are (1) the abundaces of condensate materials tend to be higher at higher Z, (2) the condensation curves for condensate species tend to shift to higher temperature i.e. to the right on Figure \ref{f7} due to the increased vapor pressure of the heavy elements in the gas phase, and (3) the T-P profile tends to shift up and to right on Figure \ref{f7} due to the increased opacities from higher"21The velocity pattern is evolved in time by introducing changes to the spectral cocficicuts based ou two processes - the advection by the axisviunuetric flows (cliffereutial rotation aud meridional flow) and raudoni processes that lead to the finite lifetimes of the cells.,The velocity pattern is evolved in time by introducing changes to the spectral coefficients based on two processes - the advection by the axisymmetric flows (differential rotation and meridional flow) and random processes that lead to the finite lifetimes of the cells.22 The advection is governed by an advection equation where wis a velocity component. C(0)=rsindQ) eives the differcutial rotation profile and (0) eives the meridional flow velocity profile.," The advection is governed by an advection equation where $w$ is a velocity component, $U(\theta) = r \sin \theta \Omega(\theta)$ gives the differential rotation profile and $V(\theta)$ gives the meridional flow velocity profile."23 Representing was a series of spherical harmonie componcuts (Eqs., Representing $w$ as a series of spherical harmonic components (Eqs.24 1-3) aud projecting this advection equation outo a single spherical harmonic gives a series of coupled equations for the evolution of the spectral coefficients. (Appendix Aj)., 1-3) and projecting this advection equation onto a single spherical harmonic gives a series of coupled equations for the evolution of the spectral coefficients (Appendix A).25 Solid. body. rotation siauplv introduces a constantly mereasing phase for cach coefficient., Solid body rotation simply introduces a constantly increasing phase for each coefficient.26 Differential rotation couples the phase chauge iu one spectral cocfiicicut to spectral coefficients with svaveuunbers (+2 aud (+| for differential rotation of the form while a simple but reasonable meridional flow profile with couples one spectral coefficient to spectral coefficieuts with wavemmubers (2. (, Differential rotation couples the phase change in one spectral coefficient to spectral coefficients with wavenumbers $\ell \pm 2$ and $\ell \pm 4$ for differential rotation of the form while a simple but reasonable meridional flow profile with couples one spectral coefficient to spectral coefficients with wavenumbers $\ell \pm 2$. (27Spherical harimonies have fixed latitudinal structure.,Spherical harmonics have fixed latitudinal structure.28 Spectral power niust pass frou one spherical harmonic component to another in order to move a feature in latitudo.), Spectral power must pass from one spherical harmonic component to another in order to move a feature in latitude.)29 These cellular flows are embedded iu the Suus surface shear laver., These cellular flows are embedded in the Sun's surface shear layer.30 We approximate the chauee in the rotation rate in the outermost of the Sun as reported by Ioweetal.(2007) with where and the latitude dependence is given by Asstuning that the cells extend to depths similar to their horizoutal dimeusious. aud that they are advected at flow rates represcutative of that depth. Eq.," We approximate the change in the rotation rate in the outermost of the Sun as reported by \citet{Howe07} with where and the latitude dependence is given by Assuming that the cells extend to depths similar to their horizontal dimensions, and that they are advected at flow rates representative of that depth, Eq."31 9 is transformed into a fiction of ( with This shear laver profile is illustrated in Fig., 9 is transformed into a function of $\ell$ with This shear layer profile is illustrated in Fig.32 2 along with the eradieuts expected from theoretical argueimoeuts for flows that conserve augular momenta., 2 along with the gradients expected from theoretical arguements for flows that conserve angular momentum.33 We assunie a meridional flow which is coustaut with depth across this laver aud has a latitude dependence characterized by which eives a peak iieridional How velocity of Ίδης Lat 15? latitude., We assume a meridional flow which is constant with depth across this layer and has a latitude dependence characterized by which gives a peak meridional flow velocity of $15 \ \rm m \ s^{-1}$ at $45\degr$ latitude.34 The finite lifetimes for the cells are simulated bv introducing raudom perturbations to the spectral coefficient phases., The finite lifetimes for the cells are simulated by introducing random perturbations to the spectral coefficient phases.35 The size of these perturbations increaseswith wavenumber to give shorter lifetimes to smaller cells with where δρ) is the chauge in phase for a complex spectral cocficient of deeree 6 auc order i. Af is the time interval between simulated Doppler nuages. aud r(() is proportional to the lifetime or a spectral component of degree f.," The size of these perturbations increaseswith wavenumber to give shorter lifetimes to smaller cells with where $\delta\Phi_\ell^m$ is the change in phase for a complex spectral coefficient of degree $\ell$ and order $m$, $\Delta t$ is the time interval between simulated Doppler images, and $\tau(\ell)$ is proportional to the lifetime for a spectral component of degree $\ell$."36 Lifetimes are well approximated by a tfuur-over time for urbulent convective flows., Lifetimes are well approximated by a turn-over time for turbulent convective flows.37 The cellular flow velocities are roughly proportional to ( while heir diameters are inversely proportional to f., The cellular flow velocities are roughly proportional to $\ell$ while their diameters are inversely proportional to $\ell$.38 The turn-over times should then be inversely . 2 qvo ≻↥⋅≺∏⋯↥⋅⊓∪∐⋜↧↕↑∪↙−∙↖, The turn-over times should then be inversely proportional to $\ell^2$ .39↖↸∖∏∐≼↧⋜↕↥⋅↸∖⋜↧↴∖↴∪∐⋜∏⋝↕↸∖∏↑↑∪p ⋅ he data using, We find a reasonable fit to the data using40"The data cube is obtained from the sky brightness temperature 3D map T4,(@,6,v) by applying the frequency or wavelength dependent instrument response R(u,v,2).","The data cube is obtained from the sky brightness temperature 3D map $T_{sky}(\alpha, \delta, \nu)$ by applying the frequency or wavelength dependent instrument response ${\cal R}(u,v,\lambda)$."41" We have considered the simple case where the instrument response is constant throughout the survey area, or independent of the sky direction."," We have considered the simple case where the instrument response is constant throughout the survey area, or independent of the sky direction."42" For each frequency v; or wavelength A,—c/v;: The LSS signal extraction depends indeed on the white noise level.", For each frequency $\nu_k$ or wavelength $\lambda_k=c/\nu_k$: The LSS signal extraction depends indeed on the white noise level.43" The results shown here correspond to the (a) instrument configuration, a packed array of 11x=121 dishes (5 meter diameter), with a white noise level corresponding to 0.25mK per 3x3arcmin?500 kHz cell."," The results shown here correspond to the (a) instrument configuration, a packed array of $11 \times 11 = 121$ dishes (5 meter diameter), with a white noise level corresponding to $\sigma_{noise} = 0.25 \mathrm{mK}$ per $3 \times 3 \mathrm{arcmin^2} \times 500$ kHz cell."44 A brief description of the simple component separation procedure that we have applied is given here:, A brief description of the simple component separation procedure that we have applied is given here:45There is a minor discrepancy at early times (t«8Gyr) in the cooled mass generated by the two modelling techniques.,There is a minor discrepancy at early times $t<8$ Gyr) in the cooled mass generated by the two modelling techniques.46 'This is unlikely to be due to differences in cooling from the hot halo: given the similar density distributions (Fig. [4)), This is unlikely to be due to differences in cooling from the hot halo: given the similar density distributions (Fig. \ref{halogas}) )47" and cooling function, the two models should yield similar amounts of cooled gas, all else being equal."," and cooling function, the two models should yield similar amounts of cooled gas, all else being equal."48 'The discrepancy is also not due to a difference in the time of development of a hot gas halo., The discrepancy is also not due to a difference in the time of development of a hot gas halo.49 The top panel of Fig., The top panel of Fig.50" 4 shows that accreted gas in the model transitions from unshocked, cold gas to shocked, hot gas at an age of about 2 Gyr, while the bottom panel shows that this time is also when the model begins to develop a hot gas halo."," 4 shows that accreted gas in the model transitions from unshocked, cold gas to shocked, hot gas at an age of about 2 Gyr, while the bottom panel shows that this time is also when the model begins to develop a hot gas halo."51 This demonstrates that the adopted analytic separation of unshocked and shocked gas (free fall limited regime versus cooling limited regime) is an excellent analog to the transition between cold gas accretion and shocked gas accretion seen in simulations as a galaxy crosses the threshold mass capable of developing a hot halo., This demonstrates that the adopted analytic separation of unshocked and shocked gas (free fall limited regime versus cooling limited regime) is an excellent analog to the transition between cold gas accretion and shocked gas accretion seen in simulations as a galaxy crosses the threshold mass capable of developing a hot halo.52" It is important to note that this transition has always been included in analytic models of galaxy formation, and thus cold gas accretion at low galaxy mass does not alter the standard picture of galaxy formation."," It is important to note that this transition has always been included in analytic models of galaxy formation, and thus cold gas accretion at low galaxy mass does not alter the standard picture of galaxy formation."53 The discrepancy in cooled mass arises after the development of this hot halo., The discrepancy in cooled mass arises after the development of this hot halo.54 The simulated galaxy continues to accrete cold gas via filaments that penetrate within the hot gas halo (see Fig., The simulated galaxy continues to accrete cold gas via filaments that penetrate within the hot gas halo (see Fig.55" here, figure 5 of and also OcvirketB|al.(2008),, Agertzetal. and Dekeletal. (2009))), while cold gas accretion ends in the analytic model."," \ref{accretion} here, figure 5 of \scite{Brooks09} and also \scite{Ocvirk08}, \scite{Agertz09} and \scite{Dekel09}) ), while cold gas accretion ends in the analytic model."56" Brooksetal.(2009) demonstrated that the inclusion of cold gas accretion along filaments leads to an earlier phase of star formation than predicted if all gas was initially shock heated, due to the shorter cooling times onto the central galaxy of the cold gas."," \scite{Brooks09} demonstrated that the inclusion of cold gas accretion along filaments leads to an earlier phase of star formation than predicted if all gas was initially shock heated, due to the shorter cooling times onto the central galaxy of the cold gas."57 Fig., Fig.58" 12 shows that the simulated galaxy does indeed form stars earlier than the analytic model, though the overall discrepancy is never more than a factor of two."," 12 shows that the simulated galaxy does indeed form stars earlier than the analytic model, though the overall discrepancy is never more than a factor of two."59 In an attempt to adapt the simulations to include similar physics as theanalytic," In an attempt to adapt the to include similar physics as the model, Fig."60" model, Fig. ?? shows the effect on the stellar growth in the simulations if all of the cold gas had instead been shocked.", \ref{DelayedGrowth} shows the effect on the stellar growth in the simulations if all of the cold gas had instead been shocked.61 The hot gas has cooling times several Gyr longer than the cold gas., The hot gas has cooling times several Gyr longer than the cold gas.62" This is quantified, and a delay has been added to the formation time of the stars spawned from the cold accreted gas (Brooksetal.2009)."," This is quantified, and a delay has been added to the formation time of the stars spawned from the cold accreted gas \cite{Brooks09}."63". As seen in Fig. ??,,"," As seen in Fig. \ref{DelayedGrowth},"64 this delay leads to a slower build of up stellar mass in the simulations., this delay leads to a slower build of up stellar mass in the simulations.65" Comparison with shows this to be in even better agreement with the stellar growth of the analytic model, which neglects this cold gas accretion along filaments."," Comparison with \ref{baryons} shows this to be in even better agreement with the stellar growth of the analytic model, which neglects this cold gas accretion along filaments."66" In order to represent the same physical assumptions as this particular simulation, the semi-analytic code had to be significantly modified from the version which has been used most recently to study the collective properties of galaxy samples (Boweretal.2006;Stringer2009)."," In order to represent the same physical assumptions as this particular simulation, the semi-analytic code had to be significantly modified from the version which has been used most recently to study the collective properties of galaxy samples \cite{Bower06,Stringer09}."67". There are three very significant differences between this version of and the simulation studied here, all of which are manifest in the comparison of the history of the simulation and the Boweretal.(2006) model (Fig. ??))."," There are three very significant differences between this version of and the simulation studied here, all of which are manifest in the comparison of the history of the simulation and the \scite{Bower06} model (Fig. \ref{Bower}) )."68" When there are instabilities refDiskStability)) or merger events in this model which trigger disk collapse, of the available disk gas is assumed to accrete onto a central black hole."," When there are instabilities \\ref{DiskStability}) ) or merger events in this model which trigger disk collapse, of the available disk gas is assumed to accrete onto a central black hole."69" If the following criteria are satisfied, it is assumed that no hot halo gas will be able to cool onto the disk."," If the following criteria are satisfied, it is assumed that no hot halo gas will be able to cool onto the disk."70 This effect is visible in Fig., This effect is visible in Fig.71 ?? as a period of rapidly decreasing cold gas mass; during such phases it is no longer being replenished by gas cooling in from the halo., \ref{Bower} as a period of rapidly decreasing cold gas mass; during such phases it is no longer being replenished by gas cooling in from the halo.72" This is assumed to be extremely strong in the Boweretal.(2006) model, the justification being that a moremodest conversion of supernova energy to gas outflow would allow the formation of too many low-mass galaxies. ("," This is assumed to be extremely strong in the \scite{Bower06} model, the justification being that a moremodest conversion of supernova energy to gas outflow would allow the formation of too many low-mass galaxies. ("73"Indeed, it","Indeed, it"74programs. such as that at the UMRAO (Alleretal.1985.1999) which has tracked the integrated flux and polarization evolution of scores of AGN for decades at weekly or bi-weekly intervals.,"programs, such as that at the UMRAO \citep{AALH85,AAHL99} which has tracked the integrated flux and polarization evolution of scores of AGN for decades at weekly or bi-weekly intervals."75 With the VLBA it is now possible to monitor a large number of parsec scale jets at closely spaced. regular intervals. and here we present the first analysis of data of this type for flux and polarization variability.," With the VLBA it is now possible to monitor a large number of parsec scale jets at closely spaced, regular intervals, and here we present the first analysis of data of this type for flux and polarization variability."76 In this paper we focus on the overall variability properties of our sample to find common trends in the flux and polarization evolution of core regions and jet features., In this paper we focus on the overall variability properties of our sample to find common trends in the flux and polarization evolution of core regions and jet features.77 Section describes our sample. data reduction. and model-fitting procedures.," Section describes our sample, data reduction, and model-fitting procedures."78 Statistical methods used in analyzing the variability properties of our VLBI observations are discussed in$3., Statistical methods used in analyzing the variability properties of our VLBI observations are discussed in.79. We present and discuss our results in and summarize them in35., We present and discuss our results in and summarize them in.80. The Appendix explores a by-produet of our variability analysis — specifically. empirical estimates of the uncertainties in. the measurement of VLBI component properties.," The Appendix explores a by-product of our variability analysis -- specifically, empirical estimates of the uncertainties in the measurement of VLBI component properties."81 In all calculations presented here. we assume a universe with Oy20.3. Q420.7 and Hy=70 km s! Mpe!.," In all calculations presented here, we assume a universe with $\Omega_M=0.3$, $\Omega_\Lambda=0.7$ and $H_{0}=70$ km $^{-1}$ $^{-1}$ ."82" For spectral index we follow the convention. S,,«vt""."," For spectral index we follow the convention, $S_\nu \propto \nu^{+\alpha}$."83 We used the VLBA to conduct a series of six observations. each of 24 hour duration. at close to two month intervals during the year 1996.," We used the VLBA to conduct a series of six observations, each of 24 hour duration, at close to two month intervals during the year 1996."84 The observations were made at 15 GHz (42.0 em. U-band) and 22 GHz (A1.3 em. K-band).," The observations were made at 15 GHz $\lambda$ 2.0 cm, U-band) and 22 GHz $\lambda$ 1.3 cm, K-band)."85 We observed 11 target sources for six epochs and one (J12244-21) for only the last five epochs., We observed 11 target sources for six epochs and one (J1224+21) for only the last five epochs.86 These sources are listed in table 1.., These sources are listed in table \ref{t:Sources}.87 The epochs of observation during 1996 were the following: January 19th (1996.05). March 22nd (1996.23). May 27th (1996.41). July 27th (1996.57). September 27th (1996.74). and December 6th (1996.93).," The epochs of observation during 1996 were the following: January 19th (1996.05), March 22nd (1996.23), May 27th (1996.41), July 27th (1996.57), September 27th (1996.74), and December 6th (1996.93)."88 The sources were chosen from those regularly monitored by the University of Michigan Radio Astronomy Observatory (UMRAO) in total intensity and polarization at 4.8. 8.0. and 14.5 GHz.," The sources were chosen from those regularly monitored by the University of Michigan Radio Astronomy Observatory (UMRAO) in total intensity and polarization at $4.8$, $8.0$, and $14.5$ GHz."89 They were selected according to the following criteria. (, They were selected according to the following criteria. (901) High total intensity: The weakest sources are about I Jy. the most powerful as much as 22 Jy. (,"1) High total intensity: The weakest sources are about 1 Jy, the most powerful as much as 22 Jy. ("912) High polarized flux: Typically over 50 mJy. (,2) High polarized flux: Typically over 50 mJy. (923) Violently variable: In both total and polarized intensity.,3) Violently variable: In both total and polarized intensity.93 Such sources are likely to be under-sampled by annual VLBI. (, Such sources are likely to be under-sampled by annual VLBI. (944) Well distributed in right ascension: This allowed us to make an optimal observing schedule.,4) Well distributed in right ascension: This allowed us to make an optimal observing schedule.95 Most of the UMRAO sources meet the first three of the above criteria., Most of the UMRAO sources meet the first three of the above criteria.96 The 12 actually selected were the strongest. most violently variable sources. subject to the fourth eriteria.," The 12 actually selected were the strongest, most violently variable sources, subject to the fourth criteria."97" Clearly these sources do not comprise a “complete sample"" in any sense.", Clearly these sources do not comprise a “complete sample” in any sense.98 The frequency agility and high slew speeds of the VLBA antennas were used to schedule our observations to generate maximal (u.v)-coverage.," The frequency agility and high slew speeds of the VLBA antennas were used to schedule our observations to generate maximal (u,v)-coverage."99 Scan lengths were kept short (13 minutes for the first two epochs and 5.5 minutes for the last four). with à switch in frequency at the end of each scan.," Scan lengths were kept short (13 minutes for the first two epochs and 5.5 minutes for the last four), with a switch in frequency at the end of each scan."100 In addition. scans of neighboring sources were heavily interleaved at the cost of some additional slew time.," In addition, scans of neighboring sources were heavily interleaved at the cost of some additional slew time."101 Each source. was observed for approximately 45 minutes per frequency at each epoch., Each source was observed for approximately 45 minutes per frequency at each epoch.102 The data were correlated on the VLBA correlator in Socorro. NM.," The data were correlated on the VLBA correlator in Socorro, NM."103 After correlation. the data were distributed on DAT tape to Brandeis University where they were loaded into NRAO'sAstronomical Imaging Processing System (AIPS) (Bridle&Greisen1994;1988) and calibrated using standard techniques for VLBI polarization observations. e.g.. (Cotton1993;Roberts.Wardle&Brown1994).," After correlation, the data were distributed on DAT tape to Brandeis University where they were loaded into NRAO'sAstronomical Imaging Processing System (AIPS) \citep{BG94,G88} and calibrated using standard techniques for VLBI polarization observations, e.g., \citep{C93,RWB94}."104. For a detailed description of our calibration steps see Paper IIL., For a detailed description of our calibration steps see Paper III.105 One point that bears mentioning here is our calibration of the polarization position angle (also called the Electric Vector Position Angle or EVPA)., One point that bears mentioning here is our calibration of the polarization position angle (also called the Electric Vector Position Angle or EVPA).106 Our EVPAs were set at each epoch and at both 15 and 22 GHz by aligning the strong jet component. Ul (ΚΙ. in 2279 to an angle of 67.," Our EVPAs were set at each epoch and at both 15 and 22 GHz by aligning the strong jet component, U1 (K1), in 279 to an angle of $67^\circ$."107 This orientation is roughly parallel with the structural position angle for this component and is within 5° of the independently calibrated observations of Leppiinnen.Zensus&Diamond(1995).. Taylor(1998).. and Homan&Wardle(2000) whose epochs of observation bracket our own.," This orientation is roughly parallel with the structural position angle for this component and is within $5^\circ$ of the independently calibrated observations of \citet{LZD95}, \citet{T98}, and \citet{HW00} whose epochs of observation bracket our own."108 By examining the other sources in our sample. we see no evidence that this component in 2279 has significant Faraday rotation at these frequencies or varies in EVPA during our observations.," By examining the other sources in our sample, we see no evidence that this component in 279 has significant Faraday rotation at these frequencies or varies in EVPA during our observations."109 As a result of this EVPA calibration procedure. our internal consistency between epochs is very good with uncertainties z2—3 degrees on the most robust jet features (see the Appendix).," As a result of this EVPA calibration procedure, our internal consistency between epochs is very good with uncertainties $\approx 2-3$ degrees on the most robust jet features (see the Appendix)."110 Figure 1. compares our 15 GHz VLBA observations of JOS30+13 (PKS 0528+134) and J1751+09 (OT O81) to the single dish monitoring done by the UMRAO at 14.5 GHz., Figure \ref{f:compare} compares our 15 GHz VLBA observations of $+$ 13 (PKS $+$ 134) and $+$ 09 (OT 081) to the single dish monitoring done by the UMRAO at 14.5 GHz.111 The total fluxes and polarizations from our CLEAN maps agree quite well with the independent UMRAO results in all six of the VLBI epochs., The total fluxes and polarizations from our CLEAN maps agree quite well with the independent UMRAO results in all six of the VLBI epochs.112 The two sources plotted in figure 1. are quite compact. and the VLBA observations account for nearly all of the single dish flux.," The two sources plotted in figure \ref{f:compare} are quite compact, and the VLBA observations account for nearly all of the single dish flux."113 Although a detailed comparison ts difficult. on the more extended sources. such as 1120 and 2273. we see a nearly constant offset between the VLBA and single dish monitoring. and the VLBI core and jet seem to account for essentially all of the observed variability in the single dish monitoring.," Although a detailed comparison is difficult, on the more extended sources, such as 120 and 273, we see a nearly constant offset between the VLBA and single dish monitoring, and the VLBI core and jet seem to account for essentially all of the observed variability in the single dish monitoring."114 Given this. it may be possible to use frequent single dish monitoring to help interpolate between the more widely spaced VLBI epochs to follow the evolution of parsec-scale core and jet features.," Given this, it may be possible to use frequent single dish monitoring to help interpolate between the more widely spaced VLBI epochs to follow the evolution of parsec-scale core and jet features."115 To parameterize our data for quantitative analysis. we used the model fitting capabilities of the DIFMAP software package (Shepherd.Pearson&Taylor1994.1995). to fit the sources with a number of discrete Gaussian components.," To parameterize our data for quantitative analysis, we used the model fitting capabilities of the DIFMAP software package \citep{SPT94,SPT95} to fit the sources with a number of discrete Gaussian components."116 The fitting was done directly on the final. self-calibrated visibility data (1.e.. i1 the (u.v)-plane).," The fitting was done directly on the final, self-calibrated visibility data (i.e., in the (u,v)-plane)."117 Our procedures for fitting in total intensity (Stokes /) were described in Paper I. We fit the polarization in Stokes Q anc U by fixing the locations (and sizes) of the / components and allowing the fluxes to vary., Our procedures for fitting in total intensity (Stokes $I$ ) were described in Paper I. We fit the polarization in Stokes $Q$ and $U$ by fixing the locations (and sizes) of the $I$ components and allowing the fluxes to vary.118 This procedure for fitting the polarization forces coincidence with the 7 components anc does not account for cases where the polarization may be displaced from the total intensity., This procedure for fitting the polarization forces coincidence with the $I$ components and does not account for cases where the polarization may be displaced from the total intensity.119 While a close inspectior of the CLEAN images showed a number of cases with small displacements between total intensity and polarization peaks. our fitting procedure seemed insensitive to these and. in general. produced good agreement with the polarized fluxes andposition angles observed in our CLEAN images.," While a close inspection of the CLEAN images showed a number of cases with small displacements between total intensity and polarization peaks, our fitting procedure seemed insensitive to these and, in general, produced good agreement with the polarized fluxes andposition angles observed in our CLEAN images."120 Our full model-fits for each source will appear in Paper III., Our full model-fits for each source will appear in Paper III.121" As discussed in 83.. obtaining good estimates of the real ""1"," As discussed in , obtaining good estimates of the real “1"122"Now, assuming that the sum of gas mass and star mass is constant in the typical galaxy, the gas-mass fraction is simply given by Thus, given the cosmic history of the star-formation-rate density, one could compute j4(z) by backwards de-evolving the present-day Milky-Way gas mass fraction, µΜνν.","Now, assuming that the sum of gas mass and star mass is constant in the typical galaxy, the gas-mass fraction is simply given by Thus, given the cosmic history of the star-formation-rate density, one could compute $\mu(z)$ by backwards de-evolving the present-day Milky-Way gas mass fraction, $\mu_{\rm MW}$."123" The assumption of a total baryonic mass of galaxies staying constant in time is not necessarily realistic, as star formation ispartly fueled by newly accreted gas (Prodanovié&Fields 2008)."," The assumption of a total baryonic mass of galaxies staying constant in time is not necessarily realistic, as star formation ispartly fueled by newly accreted gas \citep{Prodanovic2008}."124". However, the overall effect of the details of the gas fraction evolution is relatively small (~factor of two, PF02)."," However, the overall effect of the details of the gas fraction evolution is relatively small $\sim$ factor of two, PF02)."125" A more realistic modeling of the evolving gas fraction, including the effects of infall, will be addressed in an upcoming publication."," A more realistic modeling of the evolving gas fraction, including the effects of infall, will be addressed in an upcoming publication."126" For the present study, we adopt a model given by Hopkins&Beacom(2006) for the global star-formation-rate density as a function of redshift, p.(z)."," For the present study, we adopt a model given by \citet{Hopkins2006}127 for the global star-formation-rate density as a function of redshift, $\dot \rho_\ast (z)$ ."128" For the Milky-Way parameters, following PF02 and references therein, we use ww= yr! and umw=0.14."," For the Milky-Way parameters, following PF02 and references therein, we use $\psi_{\rm MW} = 3.2 M_{\sun}$ $^{-1}$ and $\mu_{\rm MW} = 0.14$."129" Lastly, we parametrize the 3.2MoeMilky-Way y-ray luminosity as Lymw(E)=1.36x10°°(E/600MeV)"" s! MeV, where κ.=1.5 for E<600 MeV and κ=2.7 for E>600 MeV. This parametrization comes from a broken power-law fit to the ""GALPROP conventional"" (Strongetal.2004) model of the energy spectrum of the diffuse Milky-Way 4-ray emission (which is compatible with no GeV We set the normalization by requiring that the energy integral of L+,mw above 100 MeV is 2.85x1045photonss~ (see PF02 and references therein)."," Lastly, we parametrize the Milky-Way $\gamma$ -ray luminosity as $L_{\gamma, {\rm MW}}(E) = 1.36 \times 10^{39}130(E/600~\mathrm{MeV})^{-\kappa}$ $^{-1}$ $^{-1}$, where $\kappa =1311.5$ for $E \le 600$ MeV and $\kappa = 2.7$ for $E > 600$ MeV. This parametrization comes from a broken power-law fit to the “GALPROP conventional” \citep{Strong2004} model of the energy spectrum of the diffuse Milky-Way $\gamma$ -ray emission (which is compatible with no GeV We set the normalization by requiring that the energy integral of $L_{\gamma,\rm MW}$ above 100 MeV is $2.85\times 10^{42} {\rm \,132photons \,\, s^{-1}}$ (see PF02 and references therein)."133" In Fig. 1,,"," In Fig. \ref{fig:spectrum},"134" we plot, with the solid line, the y-ray intensity E?I(E) from normal galaxies, compared with the Sreekumar et ((1998) determination of the CGB from EGRET data."," we plot, with the solid line, the $\gamma$ -ray intensity $E^2135I(E)$ from normal galaxies, compared with the Sreekumar et (1998) determination of the CGB from EGRET data."136" The galaxy contribution appears to be important in particular for energies between 50 MeV and 1 GeV. We point out that due to the shift of the spectral break in the Milky- diffuse emission spectrum from 850 MeV (which was the location of the break in EGRET data which suffered from the GeV excess) to 600 MeV (the location of the break in GALPROP conventional), the peak of the normal galaxy contribution correspondingly shifted from ~500 MeV in PF02 to ~250 MeV in Fig."," The galaxy contribution appears to be important in particular for energies between 50 MeV and 1 GeV. We point out that due to the shift of the spectral break in the Milky-Way diffuse emission spectrum from 850 MeV (which was the location of the break in EGRET data which suffered from the GeV excess) to 600 MeV (the location of the break in GALPROP conventional), the peak of the normal galaxy contribution correspondingly shifted from $\sim$ 500 MeV in PF02 to $\sim$ 250 MeV in Fig."137 1 in this work., \ref{fig:spectrum} in this work.138" Additionally, the contribution of normal galaxies to the CGB declines with energy above 1 GeV faster than it did in PF02, as the high-energy slope of the Milky Way spectrum adopted here (2.7) is steeper than the value implied by EGRET data (2.4) and adopted by ΡΕΟΖ."," Additionally, the contribution of normal galaxies to the CGB declines with energy above 1 GeV faster than it did in PF02, as the high-energy slope of the Milky Way spectrum adopted here (2.7) is steeper than the value implied by EGRET data (2.4) and adopted by PF02."139" It is worth noting that a preliminary analysis ofFermi data indicates that the slope of the CGB spectrum at high energies may be substantially steeper (consistent with ~E~?4°, see M.Ackermann for the LAT Colaboration*)) than the EGRET measurement."," It is worth noting that a preliminary analysis of data indicates that the slope of the CGB spectrum at high energies may be substantially steeper (consistent with $\sim E^{-2.45}$, see M.Ackermann for the LAT ) than the EGRET measurement."140" 'To illustrate this point, in Fig. 1,,"," To illustrate this point, in Fig. \ref{fig:spectrum},"141 we also plot the preliminaryFermi CGB results., we also plot the preliminary CGB results.142" In Fig. 2,,"," In Fig. \ref{fig:z_dist},"143" we plot, with the solid line, the integrand of Eq. (1))"," we plot, with the solid line, the integrand of Eq. \ref{iofe}) )"144 in units of the integral as a function of redshift at E=300 MeV; this quantity represents the contribution to the mean CGB intensity at a given energy from galaxies in a specific redshift range., in units of the integral as a function of redshift at $E = 300$ MeV; this quantity represents the contribution to the mean CGB intensity at a given energy from galaxies in a specific redshift range.145" Following the evolution of the cosmic star-formation rate, it peaks at z~1 and declines for higher redshifts."," Following the evolution of the cosmic star-formation rate, it peaks at $z \simeq 1$ and declines for higher redshifts."146" The angular auto-power spectrum of the CGB map dueto normal galaxies is given by where r is the comoving distance and Pyai(k,z) is the galaxy power spectrum at comoving wave number k and redshift z (e.g.,Andoetal. 2007b)."," The angular auto-power spectrum of the CGB map dueto normal galaxies is given by where $r$ is the comoving distance and $P_{\rm gal} (k, z)$ is the galaxy power spectrum at comoving wave number $k$ and redshift $z$ \citep[e.g.,][]{Ando2007b}."147. The multipole £ corresponds roughly to the angular scale of 0=180? /£., The multipole $\ell$ corresponds roughly to the angular scale of $\theta = 180\degr / \ell$ .148 Note, Note149mass of 0.35A4..,mass of $\sim 0.35M_{\odot}$.150 Ehe rates are lower where the trajectory is aligned. with the A-B axis., The rates are lower where the trajectory is aligned with the A-B axis.151 This elfect is larger than the lowering of the event rate that is produced. by. the introduction of smooth matter., This effect is larger than the lowering of the event rate that is produced by the introduction of smooth matter.152 In addition. the predicted event rate is dependent on the photometric error assumed.," In addition, the predicted event rate is dependent on the photometric error assumed."153 This dependence comes from the svstematic uncertainty that the assumption introduces into the determination of the ellective transverse velocity., This dependence comes from the systematic uncertainty that the assumption introduces into the determination of the effective transverse velocity.154 The microlensing parameter distributions were calculated from an ensemble of 5000. simulations of the observed. data for cach image. ancl for cach assumption of trajectory direction. photometric error. and smooth matter content.," The microlensing parameter distributions were calculated from an ensemble of 5000 simulations of the observed data for each image, and for each assumption of trajectory direction, photometric error, and smooth matter content."155 The 5000 simulations were spread over 100075. of simulated. light curves., The 5000 simulations were spread over $\eta_{o}$ of simulated light curves.156 If the error in the average rate is assumed to be due to Poison noise then it is less than 1%., If the error in the average rate is assumed to be due to Poison noise then it is less than $\sim 1\%$.157 The errors in the modelling statistics are therefore not important in determining the probability. distributions for the average HIEMIS rate., The errors in the modelling statistics are therefore not important in determining the probability distributions for the average HME rate.158" Fiewes L. 2..3 and d display the. functions Pn. py,Gua). hxCN) and fy,(Nor) obtained. for the microlensing models. considered."," Figures \ref{0smooth_images}, \ref{0smooth_tot}, , \ref{50smooth_images} and \ref{50smooth_tot} display the functions $p_{\bar{R}}(\bar{R})$, $p_{\bar{R}_{tot}}(\bar{R}_{tot})$, $h_{N}\left(N\right)$ and $h_{N_{tot}}\left(N_{tot}\right)$ obtained for the microlensing models considered."159 Both the rates. for the individual imagesas well as the combined rates are, Both the rates for the individual imagesas well as the combined rates are160Consider small disturbances to uniform shear flow with shear sy.,Consider small disturbances to uniform shear flow with shear $s_K$.161 The dispersion relation for disturbances of the form exp(57+{μέ} is mτα2Blyn|ESug)D 1 where yy=(a/c)?sy.," The dispersion relation for disturbances of the form $\exp(\gamma\tau+i\kappa\xi)$ is ^2(1+2B|y_K|+3y_K^2) - ^4, where $y_K\equiv (a/c)^{1/2}s_K$."162 There is instability if 5>0 for some . which occurs if," There is instability if $\gamma>0$ for some $\kappa$, which occurs if."163 If (his instability is present. (he stress as à function of shear g(s) is triple-valued: (here are (three roots s.«sy<s tothe equation g(s)=g(sy).," If this instability is present, the stress as a function of shear $g(s)$ is triple-valued: there are three roots $s_-<s_K<s_+$ to the equation $g(s)=g(s_K)$."164 The root sy has ο(δι)<0 and hence is unstable. while g/(s_)>0 so the roots s— are stable.," The root $s_K$ has $g'(s_K)<0$ and hence is unstable, while $g'(s_\pm)>0$ so the roots $s_\pm$ are stable."165 Almost all of the steady-state solutions of equation (38)) are bounded and periodic. and can be expressed analvtically in terms of Jacobian elliptic functions (1984).," Almost all of the steady-state solutions of equation \ref{eq:chb}) ) are bounded and periodic, and can be expressed analytically in terms of Jacobian elliptic functions \citet{ncs84}."166. ILowever. these are the final state of the svstem: it turns out that all of the periodic solutions are unstable (CarrGurtin&Slemrod1984).," However, these are the final state of the system: it turns out that all of the periodic solutions are unstable \citep{car84}."167. The only stable. stationary solution is the “kink” solution. 25). where the two + signs are independent and we require that Bκ—3/V2.," The only stable, stationary solution is the “kink” solution, ], where the two $\pm$ signs are independent and we require that $B<-3/\sqrt{2}$."168 Of course. this solution does not satisfv our periodic boundary conditions.," Of course, this solution does not satisfy our periodic boundary conditions."169 Numerical integration of the partial differential equation (38)) for a unstable initial state shows that the svstem evolves to a state in which the shear is almost always nearly equal to either s. or s. just like the solutions of the simpler equation (20)).," Numerical integration of the partial differential equation \ref{eq:chb}) ) for a unstable initial state shows that the system evolves to a state in which the shear is almost always nearly equal to either $s_-$ or $s_+$, just like the solutions of the simpler equation \ref{eq:ch}) )."170 Moreover. the interfaces between high- and low-shear domains gradually drift. so that high-shear and domains eventually coalesce.," Moreover, the interfaces between high- and low-shear domains gradually drift, so that high-shear and low-shear domains eventually coalesce."171 Once the distance between interfaces is large compared, Once the distance between interfaces is large compared172that most of the ambiguities are removed.,that most of the ambiguities are removed.173 In ? and ? I investigated the influence of the spectral lines on the parameters retrieved by the inversion., In \citet{beckthesis2006} and \citet{beck+etal2006d} I investigated the influence of the spectral lines on the parameters retrieved by the inversion.174 | found that e.g. field strength is restricted by the splitting of the 1564.8 nm line within a limit of around +100 G. Most average quantities of the field topology (field strength. field orientation) are more or less uniquely restricted by the spectra: the main source of error are actually the spectra themselves: spatial resolution. signal-to-noise ratio. polarimetric sensitivity. and the polarimetric calibration.," I found that e.g. field strength is restricted by the splitting of the 1564.8 nm line within a limit of around $\pm 100$ G. Most average quantities of the field topology (field strength, field orientation) are more or less uniquely restricted by the spectra; the main source of error are actually the spectra themselves: spatial resolution, signal-to-noise ratio, polarimetric sensitivity, and the polarimetric calibration."175 The question that however remains open ts the 3-D organization of the magnetic fields., The question that however remains open is the 3-D organization of the magnetic fields.176 The present inversion yields field strength and orientation inside the formation height of the spectral lines. but is not able to differentiate between a vertical or horizontal interweavement of field lines.," The present inversion yields field strength and orientation inside the formation height of the spectral lines, but is not able to differentiate between a vertical or horizontal interweavement of field lines."177 The approach of the integration of the field inclination assumes coherent structures from one pixel to the next in the radial direction. which ts in my opinion highly probable. but need not be the case.," The approach of the integration of the field inclination assumes coherent structures from one pixel to the next in the radial direction, which is in my opinion highly probable, but need not be the case."178 The most prominent spectral feature inside the penumbra. the Evershed effect. is not present in the gappy model.," The most prominent spectral feature inside the penumbra, the Evershed effect, is not present in the gappy model."179 | remark that all velocities derived here (besides the line core velocity of Til) always refer to velocities magnetic fields., I remark that all velocities derived here (besides the line core velocity of ) always refer to velocities magnetic fields.180 To create the multi-lobed profiles in the neutral line of Stokes V. two components of magnetic fields with different orientation and bulk velocities are needed.," To create the multi-lobed profiles in the neutral line of Stokes V, two components of magnetic fields with different orientation and bulk velocities are needed."181 Η the gappy model solves the penumbral heat transport problems. still an explanation for the Evershed flow is needed.," If the gappy model solves the penumbral heat transport problems, still an explanation for the Evershed flow is needed."182" The inclination of the bg fielc shows an azimuthal variation that leads to a ""gappy"" structure (cf.", The inclination of the bg field shows an azimuthal variation that leads to a “gappy” structure (cf.183 Figs., Figs.184 11. and B2))., \ref{penumbralgrains} and \ref{integ2}) ).185 However. the spatial scale of the variation is larger than that predicted by ?..," However, the spatial scale of the variation is larger than that predicted by \citet{scharmer+spruit2006}."186 If the integratec curves are taken at face value. this also happens in layers far below the surface layer of 7 = 1.," If the integrated curves are taken at face value, this also happens in layers far below the surface layer of $\tau$ = 1."187 Another argument in favor of the gappy model is that the spatial resolution of the observations | used may not be sufficient to detect the signatures of the structuring suggestec by Scharmer Spruit., Another argument in favor of the gappy model is that the spatial resolution of the observations I used may not be sufficient to detect the signatures of the structuring suggested by Scharmer Spruit.188" In the other direction. it shoulc be possible to construct a sunspot model based on their suggestions. calculate the resulting spectra in the 1.5 pm and 630 nm lines. reduce the spatial resolution to. arounc 1"". and then invert the spectra with two depth-independent magnetic components."," In the other direction, it should be possible to construct a sunspot model based on their suggestions, calculate the resulting spectra in the 1.5 $\mu$ m and 630 nm lines, reduce the spatial resolution to around $^{\prime\prime}$, and then invert the spectra with two depth-independent magnetic components."189 The results for the be component coulc be compared with the present inversion results., The results for the bg component could be compared with the present inversion results.190" Contrary to the regrettable sentence of ? that significance"". [think it necessary to show that their model successfully reproduces spectroscopic or spectropolarimetric observations to support its validity."," Contrary to the regrettable sentence of \citet{scharmer+spruit2006} that ”, I think it necessary to show that their model successfully reproduces spectroscopic or spectropolarimetric observations to support its validity."191" The long lifetimes (on the order of ] hr) for filaments (e.g.?). and the lack of submerging flow channels led ? to the conclusion that interchange convection by rising hot flow channels is mechanism"" for the penumbra."," The long lifetimes (on the order of 1 hr) for filaments \citep[e.g.][]{langhans+etal2005}, and the lack of submerging flow channels led \citet{schliche+solanki2003} to the conclusion that interchange convection by rising hot flow channels is ” for the penumbra."192" This claim has been renewed recently by ? and ?.. who criticize the ""paradigm"" of embedded flow channels and suggest that the penumbral fine-structure can be explained by a model of field-free gaps reaching almost up to the solar surface."," This claim has been renewed recently by \citet{spruit+scharmer2006} and \citet{scharmer+spruit2006}, who criticize the ” of embedded flow channels and suggest that the penumbral fine-structure can be explained by a model of field-free gaps reaching almost up to the solar surface."193 The energy transport in their model is then effected by convection in the field-free plasma below the sunspot., The energy transport in their model is then effected by convection in the field-free plasma below the sunspot.194 On the one hand. the findings of Sect.," On the one hand, the findings of Sect."195 6 support the static behavior of the sunspot fields: the shape of the umbral-penumbral boundary and some especially dark patches inside the penumbra stay the same during around | hour., \ref{tempevol} support the static behavior of the sunspot fields: the shape of the umbral-penumbral boundary and some especially dark patches inside the penumbra stay the same during around 1 hour.196 On the other hand. the intensity pattern of. e.g.. the penumbral grains ts completely changed after less than half an hour (cf.," On the other hand, the intensity pattern of, e.g., the penumbral grains is completely changed after less than half an hour (cf."197 Appendix AppendixC:))., Appendix \ref{appb}) ).198 The time scales in the MTM model are of a comparable order., The time scales in the MTM model are of a comparable order.199 The snapshot shown in Fig., The snapshot shown in Fig.200 14 was taken at 1 1/2 hour after the start of the simulation. but reflects the final steady-state solution.," \ref{geomcomp} was taken at 1 1/2 hour after the start of the simulation, but reflects the final steady-state solution."201 The flow channel in the MTM evolves rapidly in the beginning. and spans around half of the penumbra after 30 min (?)..," The flow channel in the MTM evolves rapidly in the beginning, and spans around half of the penumbra after 30 min \citep{schliche+jahn+schmidt1998}."202 ? used LOS magnetograms of the center side penumbra., \citet{langhans+etal2005} used LOS magnetograms of the center side penumbra.203 These LOS magnetograms are not suitable to trace the dynamic evolution of the penumbra., These LOS magnetograms are not suitable to trace the dynamic evolution of the penumbra.204 On the center side. the field of the background component is parallel to the line-of-sight. whereas the dynamic flow channels are strongly inclined to it.," On the center side, the field of the background component is parallel to the line-of-sight, whereas the dynamic flow channels are strongly inclined to it."205 Thus. the life times measured there reflect the slow evolution of the background component.," Thus, the life times measured there reflect the slow evolution of the background component."206 The same applies to the findings of Sect. 6: , The same applies to the findings of Sect. \ref{tempevol}: :207the stronger field component will dominate the topology. and thus. the small amount of change in the geometry seen in Fig.," the stronger field component will dominate the topology, and thus, the small amount of change in the geometry seen in Fig."208 12. implies that the does evolve only slowly., \ref{teempevol} implies that the does evolve only slowly.209 The conclusion on the impossibility of interchange convection due to the lack of submerging flow channels needs some more explanations., The conclusion on the impossibility of interchange convection due to the lack of submerging flow channels needs some more explanations.210 To be convinced by the argumentation. one would have to agree on the fact that the penumbra is deep (some Mm). that flow channels originate from flux located initially on the boundary layer between the sunspot and its surroundings. and that this flux can become buoyant by heat input from the fully convective surroundings outside thespot.," To be convinced by the argumentation, one would have to agree on the fact that the penumbra is deep (some Mm), that flow channels originate from flux located initially on the boundary layer between the sunspot and its surroundings, and that this flux can become buoyant by heat input from the fully convective surroundings outside the."211. The first point is suggested by the observations. while the latter two are mainly based on the MTM.," The first point is suggested by the observations, while the latter two are mainly based on the MTM."212 If one can agree on the ingredients above. I believe the penumbral heat transport can be effected by hot rising flux tubes in full agreement with the observations.," If one can agree on the ingredients above, I believe the penumbral heat transport can be effected by hot rising flux tubes in full agreement with the observations."213 If flux becomes buoyant at the outer sunspot boundary due to heating. this necessarily is a process.," If flux becomes buoyant at the outer sunspot boundary due to heating, this necessarily is a process."214 As soon as the hot flux bundle has risen from the boundary layer. new different flux will form the boundary layer.," As soon as the hot flux bundle has risen from the boundary layer, new different flux will form the boundary layer."215 This new flux would come from -- in the terminology used throughout this paper — the background component., This new flux would come from – in the terminology used throughout this paper – the background component.216 After a time span on the order of 30 min it would also have to become buoyant. and follow the previously risen flux upwards.," After a time span on the order of 30 min it would also have to become buoyant, and follow the previously risen flux upwards."217 Due to the depth of the penumbra. several flow channels could be stacked on top of each other at the same time.," Due to the depth of the penumbra, several flow channels could be stacked on top of each other at the same time."218 The inversion results along a single column (cf., The inversion results along a single column (cf.219 Sect., Sect.220 4.4 and Appendix B.1.)) suggest exactly this configuration: two flow channels are seen along a radial cut at the same time at different locations in the penumbra., \ref{hotupfl} and Appendix \ref{appa1}) ) suggest exactly this configuration: two flow channels are seen along a radial cut at the same time at different locations in the penumbra.221 The question of penumbralheating then changes to the question if the penumbral energy losses can be replenished by, The question of penumbralheating then changes to the question if the penumbral energy losses can be replenished by222It has been suggested that the difference stems from the fact that full relativistic calculations shift the bounce spectrum to lower frequencies in comparison to the ones using an effective gravitational potential (Dimmelmeier (2007))),It has been suggested that the difference stems from the fact that full relativistic calculations shift the bounce spectrum to lower frequencies in comparison to the ones using an effective gravitational potential \citet{Dimmelmeier:2007}) ).223 After this first and predominantly axisymmetric stage of GW-emission. the occurrence of a low 7/|W|-instability revives the gravitational wave signal again around = 20ms post-bounce (Saijoetal.(2003):Watts(2005):Ottetal. (2007))).," After this first and predominantly axisymmetric stage of GW-emission, the occurrence of a low $T/|W|$ -instability revives the gravitational wave signal again around $\approx 20$ ms post-bounce \citet{ 2003ApJ...595..352S,2005ApJ...618L..37W,2005ApJ...625L.119O,2006AIPC..861..728S,2006ApJ...651.1068O,2007CQGra..24..139O}) )."224" Low 7/|W| dynamical instabilities are triggered in differentially rotating systems such as neutron stars in situations where the patten speed c,=«c/m of an unstable mode #7 matches the local angular velocity at a point in the star (see Fig. 7))."," Low $T/|W|$ dynamical instabilities are triggered in differentially rotating systems such as neutron stars in situations where the patten speed $\sigma_{p}=\sigma/m$ of an unstable mode $m$ matches the local angular velocity at a point in the star (see Fig. \ref{fig7.eps}) ),"225 commonly called (the modes are. as in. Wattsetal.(2005).. assumed to behave harmonically as exp[—i(ot—mó)]. where c 1s the mode's eigenfrequency).," commonly called (the modes are, as in \citet{2005ApJ...618L..37W}, assumed to behave harmonically as $\exp[-i(\sigma t -m\phi)]$, where $\sigma$ is the mode's eigenfrequency)."226 It permits the azimuthal fluid modes to amplify., It permits the azimuthal fluid modes to amplify.227 This non-axisymmetric process yields a quasi-periodic GW signal with à rather constant time-variation. leading to a narrow-band emission at 905 Hz which lasts until the end of our simulation. as one can see particularly in the upper panels of Fig.," This non-axisymmetric process yields a quasi-periodic GW signal with a rather constant time-variation, leading to a narrow-band emission at $905$ Hz which lasts until the end of our simulation, as one can see particularly in the upper panels of Fig."228 3. for times t >20 ms., \ref{fig3.eps} for times t $>20$ ms.229 The analysis method we use to observe the growth of nonaxisymmetric structures decomposes the density at a fixed radius and constant z--component into its azimuthal Fourier components as done before e.g. in ref. (Ou&Tohline2006:Ottetal. 2007)))," The analysis method we use to observe the growth of nonaxisymmetric structures decomposes the density at a fixed radius and constant -component into its azimuthal Fourier components as done before e.g. in ref. \citep{2006ApJ...651.1068O,2007CQGra..24..139O}) ):"230 where the Hi—L—e2complex Fourier. amplitudes. are defined by In Fig., where the complex Fourier amplitudes are defined by In Fig.231" 6. the normalized mode amplitudes A,,=|C,|/Co are monitored to measure the growth of unstable modes.", \ref{fig6.eps} the normalized mode amplitudes $A_{m}=|C_{m}|/C_{0}$ are monitored to measure the growth of unstable modes.232 In our model s15g we find i= {1.2.3}-modes being triggered. with the so-called η=2 bar-mode growing fastest.," In our model s15g we find $m=\{1,2,3\}$ -modes being triggered, with the so-called $m=2$ bar-mode growing fastest."233 Further. we state that the 7;=11.2.3] modes all possess the same pattern speed.," Further, we state that the $m=\{1,2,3\}$ modes all possess the same pattern speed."234 The close relation between the m=2 bar-mode instability and the emission of gravitational waves can be seen in the following features: First. the sudden onset of GW emission along the pole. which must be completely due to nonaxisymmetric dynamics. coincides with the amplitude of the ;=3 mode reaching approximately the absolute amplitude of the η=4 mode caused by the grid.," The close relation between the $m=2$ bar-mode instability and the emission of gravitational waves can be seen in the following features: First, the sudden onset of GW emission along the pole, which must be completely due to nonaxisymmetric dynamics, coincides with the amplitude of the $m=2$ mode reaching approximately the absolute amplitude of the $m=4$ mode caused by the grid."235 Secondly. the dominant frequency of emission corresponds perfectly to the eigenfrequency of the #= 2-mode.," Secondly, the dominant frequency of emission corresponds perfectly to the eigenfrequency of the $m=2$ -mode."236 Finally. the two GW-polarisations + and x are phase shifted by 7/2. as one would expect of a perfect. monochromatic GW-source such as a rotating bar.," Finally, the two GW-polarisations $+$ and $\times$ are phase shifted by $\pi/2$, as one would expect of a perfect, monochromatic GW-source such as a rotating bar."237 These findings in the context of the low T/\|W| instability and supernova dynamics stand in remarkable agreement with the recent ones of Ottetal.(2007).., These findings in the context of the low $T/|W|$ instability and supernova dynamics stand in remarkable agreement with the recent ones of \citet{2007CQGra..24..139O}.238 For low p-unstable models similar to 155. they found narrow-band GW emission at =920-930 Hz.," For low $\beta$ -unstable models similar to s15g, they found narrow-band GW emission at $\approx 920-930$ Hz."239 The main difference to our calculations is the point that the dominant mode which was found in those computations was the #7= ]-mode., The main difference to our calculations is the point that the dominant mode which was found in those computations was the $m=1$ -mode.240 As a closing remark to model s15g we state that the time evolution of the energy emitted by gravitational radiation (see Fig.5)) fits the behaviour of the waves., As a closing remark to model s15g we state that the time evolution of the energy emitted by gravitational radiation (see \ref{fig5.eps}) ) fits the behaviour of the waves.241 It demonstrates a large peak around bounce at 1.3x10°! erg/s followed by a ringdown and an oscillating renaissance at about 1011—10? erg/s for times t>20 ms., It demonstrates a large peak around bounce at $1.3\times10^{51}$ erg/s followed by a ringdown and an oscillating renaissance at about $10^{47}-10^{48}$ erg/s for times $t>20$ ms.242 The slow-rotating model sI5h undergoes a quasi-spherically symmetric. core collapse. consequently showing fairly weak," The slow-rotating model s15h undergoes a quasi-spherically symmetric core collapse, consequently showing fairly weak"243 Ha emission. (e.g.. Rutledgeetal.2000:West2004:Berger 2006)). Zeeman broadening of FeH molecular lines in Stokes / (Reiners&Basri 2007).. and. time-resolved spectropolarimetry in Stokes V. (Zeeman-Doppler imaging: Donatietal.2008:Morin 2008)).," $\alpha$ emission (e.g., \citealt{rbm+00,whw+04,ber06}) ), Zeeman broadening of FeH molecular lines in Stokes $I$ \citep{rb07}, , and time-resolved spectropolarimetry in Stokes $V$ (Zeeman-Doppler imaging; \citealt{dmp+08,mdp+08}) )."244 Each of these techniques Is sensitive to specific properties of the magnetic field., Each of these techniques is sensitive to specific properties of the magnetic field.245 Zeeman broadening provides a measure of thefntegrated surface magnetic flux. Bf (Reiners& 2006).. where B is the magnetic field strength and f£ is the field covering fraction.," Zeeman broadening provides a measure of the surface magnetic flux, $Bf$ \citep{rb06}, where $B$ is the magnetic field strength and $f$ is the field covering fraction."246 Zeeman-Doppler imaging (ZDD. on the other hand. only allows for a reconstruction of the large- (multipole number of (= few) surface field. but it also provides information on the field (Donatietal.Morinetal. 2008).," Zeeman-Doppler imaging (ZDI), on the other hand, only allows for a reconstruction of the large-scale (multipole number of $\ell\lesssim247{\rm few}$ ) surface field, but it also provides information on the field \citep{dmp+08,mdp+08}."248. The ZDI technique has led to à characterization of surface fields in several M dwarfs. revealing a transition from mainly toroidal and non-axisymmetric fields in MO-M3 objects to predominantly poloidal axisymmetric fields in mid-M dwarfs (Donatietal.2008:Morin2008).," The ZDI technique has led to a characterization of surface fields in several M dwarfs, revealing a transition from mainly toroidal and non-axisymmetric fields in M0-M3 objects to predominantly poloidal axisymmetric fields in mid-M dwarfs \citep{dmp+08,mdp+08}."249. The apparent shift in field geometrycoincides with the transition to full convection. and may reflect a change in dynamo mechanism.," The apparent shift in field geometrycoincides with the transition to full convection, and may reflect a change in dynamo mechanism."250 The field, The field251In the last 30 vears. many studies have been devoted to the evolution of the CNO isotopic ratios (c.g.. Aucouze. Lequeux Vigroux 1975: Vieroux. Audouze Lequeux 1976: Dearborn. ‘Vinsley Schramm: LOTS: Tosi 1982: D'Antona Matteucci 1991: Matteucci D'Xntona 1991: Prantzos. Aubert Xudouze 1996: see also ‘Losi 2000 for a recent reappraisal of the problem).,"In the last 30 years, many studies have been devoted to the evolution of the CNO isotopic ratios (e.g., Audouze, Lequeux Vigroux 1975; Vigroux, Audouze Lequeux 1976; Dearborn, Tinsley Schramm 1978; Tosi 1982; D'Antona Matteucci 1991; Matteucci D'Antona 1991; Prantzos, Aubert Audouze 1996; see also Tosi 2000 for a recent reappraisal of the problem)."252 Isotopic ratios are generally not lected by physicochemical fractionation elfects. (but. see. e.g.. Sheller. Lamrer beeorman 2002).," Isotopic ratios are generally not affected by physicochemical fractionation effects (but see, e.g., Sheffer, Lambert Federman 2002)."253 Therefore. they rellee rather Laitiullv. the relevan6 production. processes which occurred in stars of «cilleren masses and Liletines.," Therefore, they reflect rather faithfully the relevant production processes which occurred in stars of different masses and lifetimes."254 Llowever. despite he considerable. |orogress in the theories of stelar evolution and nucleosvnthesis. important (tlestions relate cto the vielis and the xocducion sites of some of the CNO isotopes stil remain open.," However, despite the considerable progress in the theories of stellar evolution and nucleosynthesis, important questions related to the yields and the production sites of some of the CNO isotopes still remain open."255 In this context. chemical evoluion models can be regarded as a powerful tool in order to discriminate among cdillerent ses of stellar vields and," In this context, chemical evolution models can be regarded as a powerful tool in order to discriminate among different sets of stellar yields and"256A somewhat cdillerent. treatment of. hydrodynamics and magnetic fields is realised within the MPL parallel -body/SPIL code (δυο (?.. 27.0 7)).,"A somewhat different treatment of hydrodynamics and magnetic fields is realised within the MPI parallel -body/SPH code $\textsc{Gadget}$ \citealp{SpringelGadget1}, , \citealp{SpringelGadget}, \citealp{GadgetMHD}) )."257 Phere are. two significant dillerences in the implementation relevant. even for non-radiative simulations: First. VINE follows a classical implementation which is integrating the internal energy. whereas GADGET utilises what is generally called the entropy conserving formulation.," There are two significant differences in the implementation relevant even for non-radiative simulations: First, $\textsc{Vine}$ follows a classical implementation which is integrating the internal energy, whereas $\textsc{Gadget}$ utilises what is generally called the entropy conserving formulation."258 The important cillerence thereby. is not. the fact that GADGET integrates the entropy. instead of the internal energy., The important difference thereby is not the fact that $\textsc{Gadget}$ integrates the entropy instead of the internal energy.259 The crucial dillerences are rather the wav in which he smoothing length h; is defined (in CADGET. h; is defined xwsed on the mass within the kernel instead of the number of xuticles) and the inclusion of correction terms arising from he varving smoothing length.," The crucial differences are rather the way in which the smoothing length $h_i$ is defined (in $\textsc{Gadget}$, $h_i$ is defined based on the mass within the kernel instead of the number of particles) and the inclusion of correction terms arising from the varying smoothing length."260 Also. the entropy conserving ormulation uses à way of svmmetrizing the kernel given hy he derivation of the SPILL equations. which in sum leads to conservation of energy and entropy at the same time (?)).," Also, the entropy conserving formulation uses a way of symmetrizing the kernel given by the derivation of the SPH equations, which in sum leads to conservation of energy and entropy at the same time \citealp{Springel&Hernquist2002}) )."261 The second. clillerence originates in an alternative ormulation of the artificial viscosity., The second difference originates in an alternative formulation of the artificial viscosity.262 In. GADGET. artificial viscosity is based on the signal velocity instead of sound speed (7)) and apt to incorporate magnetic waves in à natural wav (7)).," In $\textsc{Gadget}$, artificial viscosity is based on the signal velocity instead of sound speed \citealp{Monaghan1997}) ) and apt to incorporate magnetic waves in a natural way \citealp{Price&Monaghan2004SPMHDI}) )."263 This cillerent implementation was shown to bring measurable improvements specially for MILD applications (7)). but. should. not make too much of a clilference for passive magnetic fields.," This different implementation was shown to bring measurable improvements specially for MHD applications \citealp{GadgetMHD}) ), but should not make too much of a difference for passive magnetic fields."264 Phe implementation of the induction equation and the Euler potentials formalism is the same in both codes., The implementation of the induction equation and the Euler potentials formalism is the same in both codes.265 The integration in GADGET is also performed. using the leaplroe integration. scheme. but CLADGET. utilises a kiek-clrift-kick-scheme whereas VINE uses a scheme.," The integration in $\textsc{Gadget}$ is also performed using the leapfrog integration scheme, but $\textsc{Gadget}$ utilises a kick-drift-kick-scheme whereas $\textsc{Vine}$ uses a drift-kick-drift-scheme."266 The timestep is given by where 5 translates to the accuracy parameter Tyce in eq., The timestep is given by where $\eta$ translates to the accuracy parameter $\tau_\mathrm{acc}$ in eq.267 26 via n=2g., \ref{ts1} via $\tau_\mathrm{acc}=\sqrt{2\eta}$.268 For SPIE particles. also a C'ourant-like condition in the form is applied. where f; is the SPL softening length for gas particle # and the signal velocity between particles 7 and j as defined (77in ? with the maximum taken over all neighboring particles j of particle ἐς," For SPH particles, also a Courant-like condition in the form is applied, where $h_i$ is the SPH softening length for gas particle $i$ and $v_{ij}^\mathrm{sig}$ the signal velocity between particles $i$ and $j$ as defined in \cite{Price&Monaghan2004SPMHDI} with the maximum taken over all neighboring particles $j$ of particle $i$."269" μμ is an accuracy parameter which does not translate one-to-one to τοι, in ed.", $C_\mathrm{cour}$ is an accuracy parameter which does not translate one-to-one to $\tau_\mathrm{CFL}$ in eq.270 29 due to the different definition of the Courant. criterion., \ref{ts4} due to the different definition of the Courant criterion.271 We commonly use values of η=0.02 and Cus=0.15 to ensure that the timestep Af in CLADGIET does not get too large compared to VINE., We commonly use values of $\eta=0.02$ and $C_\mathrm{cour}=0.15$ to ensure that the timestep $\Delta t$ in $\textsc{Gadget}$ does not get too large compared to $\textsc{Vine}$.272 However. changing the accuracy parameters by a factor of two does not allect the overall evolution and amplification of the magnetic field in the simulated svstems (not shown).," However, changing the accuracy parameters by a factor of two does not affect the overall evolution and amplification of the magnetic field in the simulated systems (not shown)."273 Beside that. the codes diller in details of the tree construction for calculating gravitational forces.," Beside that, the codes differ in details of the tree construction for calculating gravitational forces."274 For more details we refer the reader to the code papers for VINE (?.. 7)) and δυο (7.. 7))," For more details we refer the reader to the code papers for $\textsc{Vine}$ \citealp{VINEI}, \citealp{VINEII}) ) and $\textsc{Gadget}$ \citealp{SpringelGadget}, \citealp{GadgetMHD}) )."275 The initial conditions for our δν Way like galaxy are realised. using the method described by 2? which is based on ?. (see also 2))., The initial conditions for our Milky Way like galaxy are realised using the method described by \citet{Springel2005} which is based on \citet{Hernquist1993} (see also \citealp{Johansson2009}) ).276 The galaxy. consists of an exponential stellar clise and a Lat extended: gas disc. a stellar bulge and a dark matter halo of collisionless particles.," The galaxy consists of an exponential stellar disc and a flat extended gas disc, a stellar bulge and a dark matter halo of collisionless particles."277 The gas is represented: by SPIEL particles adopting an isothermal equation of state with a fixed sound speed of e;z15 km Ll. which. corresponds to a temperature of Z7z2-101 Ix for a molecular weight of 1.4/1.1*myroten.," The gas is represented by SPH particles adopting an isothermal equation of state with a fixed sound speed of $c_s\approx 15$ km $^{-1}$ , which corresponds to a temperature of $T\approx2\cdot10^4$ K for a molecular weight of $1.4/1.1\cdot m_\mathrm{proton}$."278 We brielly note that by using an isothermal equation of state only one component of the ISM is modeled. typically this is a reasonably good approximation for the warm. eas phase in disc galaxies (e.g. 7.. ?2.. 7)).," We briefly note that by using an isothermal equation of state only one component of the ISM is modeled, typically this is a reasonably good approximation for the warm gas phase in disc galaxies (e.g. \citealp{Barnes2002}, \citealp{Li2005}, \citealp{Naab&Jesseit2006}) )."279 Assuming an isothermal equation of state implies that additional heat. created in shocks by adiabatic compression. and feedback. processes (e.g. by SNIED is radiated away immediately., Assuming an isothermal equation of state implies that additional heat created in shocks by adiabatic compression and feedback processes (e.g. by SNII) is radiated away immediately.280 In. addition. substantial heating processes prevent the gas [rom cooling below its effective. temperature. predefined. by its sound speed.," In addition, substantial heating processes prevent the gas from cooling below its effective temperature predefined by its sound speed."281 The parameters describing the initial conditions can be found in ‘Table 1.., The parameters describing the initial conditions can be found in Table \ref{tab1}.282 The particle numbers and. the eravitational and SPILL softening lengths used in the cilferent runs can be found in Table 2.., The particle numbers and the gravitational and SPH softening lengths used in the different runs can be found in Table \ref{tab2}.283 AXofore we include magnetic fields we allow the galaxy to evolve for approximately three half mass rotation periods., Before we include magnetic fields we allow the galaxy to evolve for approximately three half mass rotation periods.284 For simplicity we choose an initial magnetic field in the .r direction., For simplicity we choose an initial magnetic field in the $x$ direction.285 Its value. By=LO? €. corresponds to the typical value of intergalactic magnetic fields (2)).," Its value, $B_0=10^{-9}$ G, corresponds to the typical value of intergalactic magnetic fields \citealp{KronbergLesch&Hopp1999}) )."286 To set up the corresponding I5uler potentials. we choose We have checked. the stability of our discs in independent. simulations without magnetic fields.," To set up the corresponding Euler potentials, we choose We have checked the stability of our discs in independent simulations without magnetic fields."287 Figs., Figs.288 2 and 3 show the surface densities Mua. of the extended gascous disces and “Moja. of the exponential stellar disces. respectively. as a function of radius for /=0.5 Gar (red). ic. the time at which the magnetic field. is switched. on. and /=2.0 vr (black).," \ref{sigma_gas} and \ref{sigma_disc} show the surface densities $\Sigma_\mathrm{gas}$ of the extended gaseous discs and $\Sigma_\mathrm{stars}$ of the exponential stellar discs, respectively, as a function of radius for $t=0.5$ Gyr (red), i.e. the time at which the magnetic field is switched on, and $t=2.0$ Gyr (black)."289 Fig., Fig.290 4 shows the circular velocitycurves of the simulated galaxies at the same times., \ref{vrot} shows the circular velocitycurves of the simulated galaxies at the same times.291 The disces simulated with VINE (dottedline) and CrAber (solid line), The discs simulated with $\textsc{Vine}$ (dottedline) and $\textsc{Gadget}$ (solid line)292where £? is the Ricci scalar associated with the metric ον.,where $R$ is the Ricci scalar associated with the metric $g_{\mu\nu}$.293 Variations of the action with respect to the metric (which involve not only variations of the total Lagrangian density but also variations of the space-time measure) leads to Einstein's equations (see for instance ?)), Variations of the action with respect to the metric (which involve not only variations of the total Lagrangian density but also variations of the space-time measure) leads to Einstein's equations (see for instance \citealt{anderssoncomer-07}) ).294 The relativistic momenta of the nucleons can be expressed in a form similar to Eq. (26)), The relativistic momenta of the nucleons can be expressed in a form similar to Eq. \ref{eq.3pi}) )295 as The non-diagonalS components of the svmametric relativistic mobility matrix AA. are equali to those of the non-relativistic matrix A. while the diagonal elements are given by The relativistic momenta of the leptons take a very simple form If the constituents are all co-moving with the 4-velocity a. the 4-momoenta reduce to With the momenta specified. we can obtain the generalized. pressure V. from. σα. (6)).," as The non-diagonal components of the symmetric relativistic mobility matrix $\widetilde{\cal K}^{q q^\prime}$, are equal to those of the non-relativistic matrix ${\cal K}^{qq^\prime}$, while the diagonal elements are given by The relativistic momenta of the leptons take a very simple form If the constituents are all co-moving with the 4-velocity $u^\mu$, the 4-momenta reduce to With the momenta specified, we can obtain the generalized pressure $\Psi$ from Eq. \ref{eq.general_pressure}) )."296 As for the non-relativistic case. V can be decomposed into an ordinary “static” part given by Eq. (31))," As for the non-relativistic case, $\Psi$ can be decomposed into an ordinary “static” part given by Eq. \ref{eq.psi.static}) )"297 and an extra contribution V due to entrainment which can be expressed as where the entraüinment energy density is now delined by AXofore concluding this section. let us remark that the relativistic Lagrangian density can be written in the very concise form where the coellicients Ay and Àj are given by and adopting the following notations Equationi (51)) is consistent with the expansion of the Lagrangian>o density in powers of Crtnp). suggestedoo bv ?..," and an extra contribution $\Psi_{\rm ent}$ due to entrainment which can be expressed as where the entrainment energy density is now defined by Before concluding this section, let us remark that the relativistic Lagrangian density can be written in the very concise form where the coefficients $\lambda_0$ and $\lambda_1$ are given by and adopting the following notations Equation \ref{eq.lambda.rel2}) ) is consistent with the expansion of the Lagrangian density in powers of $(x^2 - n p)$, suggested by \citet*{andersson-02}."298 Lt can be clearly seen on Eq. (51)).," It can be clearly seen on Eq. \ref{eq.lambda.rel2}) ),"299 that in the absence of entrainment (i.e. Ay= 0) or in the case of co-moving Huis. the Lagrangian density reduces to the opposite of the internal energy. density.," that in the absence of entrainment (i.e. $\lambda_1=0$ ) or in the case of co-moving fluids, the Lagrangian density reduces to the opposite of the internal energy density."300" Ifthe nucleons were not interacting with each other. the mobility matrix introduced in Section 3. would be diagonal and we would simply have AU""=mn, and APP=min,"," If the nucleons were not interacting with each other, the mobility matrix introduced in Section \ref{sect.non-rel.hydro} would be diagonal and we would simply have ${\cal K}^{nn}=m/n_n$ and ${\cal K}^{pp}=m/n_p$."301 OF course we know that nucleons are strongly interacting., Of course we know that nucleons are strongly interacting.302" This means that the matrix A"". does not have such a simple structure.", This means that the matrix ${\cal K}^{qq^\prime}$ does not have such a simple structure.303 I is convenient to define neutron and. proton dynamical elective masses: by respectively., It is convenient to define neutron and proton dynamical effective masses by respectively.304 The deviations of m7 from the bare barvon mass m therefore arise entirely from. the nucleon-nucleon interactions., The deviations of $m_\star^q$ from the bare baryon mass $m$ therefore arise entirely from the nucleon-nucleon interactions.305 Let us point out that these effective masses depend on the nucleon densities and therefore vary with depth inside the neutron star., Let us point out that these effective masses depend on the nucleon densities and therefore vary with depth inside the neutron star.306 As a result of I5q. (191). ," As a result of Eq. \ref{eq.gal.inv}) ),"307the non-diagonal coellicients of the mobility matrix can be expressed as, the non-diagonal coefficients of the mobility matrix can be expressed as308except oy and 7 are inscusitive to this width.,except $\sigma_8$ and $\tau$ are insensitive to this width.309 The results for the basic flat tilted ACDM . parameters are shown in Table 1L., The results for the basic flat tilted $\Lambda$ CDM parameters are shown in Table \ref{tab:basic}.310 The confidence limits are obtained * nnrginaliiug the unilti-dimensioual liselihoods down o one dimension., The confidence limits are obtained by marginalizing the multi-dimensional likelihoods down to one dimension.311 The median value is obtained by finding e πορτα] of the resulting likelihood function while 1e lower aud upper error liauits are obtained by fudiug 1ο and inteerals respectively., The median value is obtained by finding the integral of the resulting likelihood function while the lower and upper error limits are obtained by finding the and integrals respectively.312 The CA\IBall data olubination iucludes: the ACBAR results preseuted here: 1ο WMAP 3 year TT. TE. and EE spectra. with the EE rot included at higher ( as iu ?:: the CBI extended mosaic results (7) and polarization results (77).. combined iu 1ο manner described iu Ίο the DASI two year results (?): the DASI EE aud TE baudpowers (7): the VSÀ final results (?):: the ATANTATA 1998 füeht results (2): and the TT. TE. and EE results from the BOOMERANC: 2003 flight (?2?2?)..," The CMBall data combination includes: the ACBAR results presented here; the WMAP 3 year TT, TE, and EE spectra, with the EE not included at higher $\ell$ as in \citet{hinshaw06}; ; the CBI extended mosaic results \citep{readhead04} and polarization results \citep{Readhead04b,Sievers05}, combined in the manner described in \citet{Sievers05}; the DASI two year results \citep{halverson02}; the DASI EE and TE bandpowers \citep{Leitch04}; ; the VSA final results \citep{dickinson04}; the MAXIMA 1998 flight results \citep{hanany00}; ; and the TT, TE, and EE results from the BOOMERANG 2003 flight \citep{jones06, piacentini06, montroy06}."313 Only (>350baudpowers are included or BOOMERANG because of overlap with WALAP3 (although inclusion of the lower (6 results leaves the xumalneter results essentially uuchiaueced)., Only $\ell > 350$bandpowers are included for BOOMERANG because of overlap with WMAP3 (although inclusion of the lower $\ell$ results leaves the parameter results essentially unchanged).314 While ACDAR and BOOMERANG are both calibrated through WALAP. his is a snuadl contribution to the total wucertainty iu he ACBAR calibration. and we treat the calibration uucertaimtics as independent m our parameter analysis.," While ACBAR and BOOMERANG are both calibrated through WMAP, this is a small contribution to the total uncertainty in the ACBAR calibration and we treat the calibration uncertainties as independent in our parameter analysis."315 Although the DAS CBI and BOOMERANG 2003 EE and TE results for high ( polarization are included. they have little impact on the values of the parameters we 6tan.," Although the DASI, CBI and BOOMERANG 2003 EE and TE results for high $\ell$ polarization are included, they have little impact on the values of the parameters we obtain."316 Iu all our runs we have used the updated WALAP3 likehhoodσα code (http:/flambda.estc.uasa.ecovs) which includes an updated poiut-source correction 7 ancl foreground mareinalization on large aneular scales., In all our runs we have used the updated WMAP3 likelihood code (http://lambda.gsfc.nasa.gov/) which includes an updated point-source correction \citet{huffenberger06} and foreground marginalization on large angular scales.317" These updates resultin a smallincrease in the Q,, aud os values compared to those reported in 2..", These updates result in a small increase in the $\Omega_m$ and $\sigma_8$ values compared to those reported in \citet{spergel06}.318 The results for the basic model paramcter set with various conibiuationus of data are sununarzed in Fie. 5.., The results for the basic model parameter set with various combinations of data are summarized in Fig. \ref{fig:basic}.319 The most striking feature of the results is that the solutions determined from WALAP3 aloue are quite compatible with the extension by ACBAR (aud that of the other data) to higher (., The most striking feature of the results is that the solutions determined from WMAP3 alone are quite compatible with the extension by ACBAR (and that of the other data) to higher $\ell$.320 This consistency means that the additional CAIB data(includiug ACBAR) have little iupact on the cosmological parameters deterimuned by WMADP2S., This consistency means that the additional CMB data (including ACBAR) have little impact on the cosmological parameters determined by WMAP3.321 We have tested the effect of a sienificautl sinaller ACBAR calibration error. such as we auticipate for the final ACBAR release.," We have tested the effect of a significantly smaller ACBAR calibration error, such as we anticipate for the final ACBAR release."322 Wefind a much lareer impact ou the parameter values and errors: the values are simular to those fouud for CMDall|LSS., Wefind a much larger impact on the parameter values and errors; the values are similar to those found for CMBall+LSS.323" With the original ? WALAPS likelihood code. there was a shift ins and @,, to higher values when additional data was included."," With the original \citet{spergel06} WMAP3 likelihood code, there was a shift in $\sigma_8$ and $\Omega_m$ to higher values when additional data was included."324 However. with the updated WALAP3 likelihood code. the addition of the ACBAR and CMDall baudpowers leads to essentially uo shift m σς aud ο): however. includius the LSS data docs still result in a slight iucrease in these parameters.," However, with the updated WMAP3 likelihood code, the addition of the ACBAR and CMBall bandpowers leads to essentially no shift in $\sigma_8$ and $\Omega_m$; however, including the LSS data does still result in a slight increase in these parameters."325" The new likelihood code corrects the lower power in the third acoustic peak which was leading to low values for ox aud ©,,,h7 ", The new likelihood code corrects the lower power in the third acoustic peak which was leading to low values for $\sigma_8$ and $\Omega_m h^2$ .326The comoving damping scale. determined as a derived cosinological parameter using oulv the ACDAR and WMAP3 data is Rp=10.5+0.2\Mpe|.," The comoving damping scale, determined as a derived cosmological parameter using only the ACBAR and WMAP3 data is $R_D=32710.5 \pm 0.2 \, {\rm Mpc}^{-1}$ ."328 The corresponding angular scale is fp=1355/2., The corresponding angular scale is $\ell_D= 1355 ^{+5}_{-5}$.329 These values for Ry and (5 are in excellent aerecment with values obtained usine earlier datasets (7).., These values for $R_D$ and $\ell_D$ are in excellent agreement with values obtained using earlier datasets \citep{BCP03}.330 We also fud the comoving sound crossing distance is Re⋅B . with a corresponding augular scale ἐς--LOO0)=95.9!n in aerecment with the value for 0 in Table 1," We also find the comoving sound crossing distance is $R_s= 147.8^{+2.3}_{-2.3} \, {\rm331Mpc}^{-1}$ , with a corresponding angular scale $\ell_s= 100/\theta =33295.9^{+1.0}_{-0.2}$ , in agreement with the value for $\theta$ in Table \ref{tab:basic}."333 Tuchision of lensing iu our standard parameter runs increases the best-fit model likelihoods iu all cases., Inclusion of lensing in our standard parameter runs increases the best-fit model likelihoods in all cases.334 The difference between the log likelihoods of the lensed aud uonlensed models for the WMADP2 run is AluL=0.86, The difference between the log likelihoods of the lensed and non–lensed models for the WMAP3 run is $\Delta \ln L=0.86$.335 The log likelihood difference increases to 1.7 with ACBAR iucluded. 2.16 with CATBall. and 3.69 for the CMDall|LSS data combination.," The log likelihood difference increases to 1.7 with ACBAR included, 2.46 with CMBall, and 3.69 for the CMBall+LSS data combination."336 The mean values of the paraimecters do uot shift sienificautlv with the inclusion of leusine: for example. σς increases from 0.7758 to 0.788 for the CMDall data set and from 0.801 to 0.8125 for CMDall|LSS.," The mean values of the parameters do not shift significantly with the inclusion of lensing; for example, $\sigma_8$ increases from 0.778 to 0.788 for the CMBall data set and from 0.804 to 0.813 for CMBall+LSS."337 The best-fit D;'« for the lens aud no-leus cases look quite simular. but the subtle smoothing of the peaks aud troughs by lensing results iu a better fit to the the data for each combination of experiments.," The best-fit ${\cal D}_\ell$ 's for the lens and no-lens cases look quite similar, but the subtle smoothing of the peaks and troughs by lensing results in a better fit to the the data for each combination of experiments."338 The first release of WALAP data showed evidence for ruuniune of the CAIB power spectrum spectral iudex. utieubulw when combined with measurements of LSS (?)..," The first release of WMAP data showed evidence for running of the CMB power spectrum spectral index, particularly when combined with measurements of LSS \citep{spergel03}."339" Extending the basicmodel to allow for ruunius of he spectral index around the pivot point &,=(.05Mpe. ! vields ηναι)0.053toos for WMAP3 only."," Extending the basicmodel to allow for running of the spectral index around the pivot point $k_\star=0.05$ $^{-1}$ yields $dn_s/d\ln k340(k_\star)=-0.053^{+0.031}_{-0.029}$ for WMAP3 only."341 The tendeney for negative— ruuniug indices is due mostly o the low f£ eud. where the multipoles are lower than the standard ACDAL model.," The tendency for negative running indices is due mostly to the low $\ell$ end, where the multipoles are lower than the standard $\Lambda$ CDM model."342 The contribution from the hieh f cud is less significant., The contribution from the high $\ell$ end is less significant.343 Since the WALAPS results extend o reasonably high f. the addition of the ACBAR results shifts the constraints only marginally d»o./dluk(k.)=0.015nost .," Since the WMAP3 results extend to reasonably high $\ell$, the addition of the ACBAR results shifts the constraints only marginally $dn_s/d\ln k (k_\star)=344-0.045^{+0.026}_{-0.026}$ ."345 The effect of adding the ACDAR data ca- © SCCLL clearly in Fig., The effect of adding the ACBAR data can be seen most clearly in Fig.346 7 which shows the correlation vetween vy aud εςοἱια..., \ref{fig:nrun} which shows the correlation between $n_s$ and $dn_s/d\ln k$.347 The central value is simular. mt the errors are further reduced with the CNIDall | LSS conibiuation. «νεΠιο}=0017i. S," The central value is similar, but the errors are further reduced with the CMBall + LSS combination, $dn_s/d\ln k (k_\star)= -0.047^{+0.021}_{-0.021}$."348oStnular to tle results from WAITAPL and carlicr versions the CMDaLB data set (27).. à uceative running is still favored at about the 2-7 level by each of the data combinations considered.," Similar to the results from WMAP1 and earlier versions of the CMBall data set \citep{BCP03,mactavish05}, a negative running is still favored at about the $\sigma$ level by each of the data combinations considered."349 The models including running favor siguificautlv owe values of the scalar spectral index. nv.=0.903pointroe," The models including running favor significantly lower values of the scalar spectral index, $n_s=0.903^{+0.029}_{-0.028}$."350 However this result depends on the choice of pivot Ay: a sinallervalue would vield a higher result while a higher one would givean even lower result., However this result depends on the choice of pivot point $k_\star$ : a smallervalue would yield a higher result while a higher one would givean even lower result.351 As described in Section 6.2... fluctuations from the thermal Suuvaev-Zeldovich (SZ) effect are expected to dominate over the damped primordialcontributions to the CMD anisotropy atmultipolesbevoud (~ 2500.," As described in Section \ref{sec:excess}, , fluctuations from the thermal Sunyaev-Zel'dovich (SZ) effect are expected to dominate over the damped primordialcontributions to the CMB anisotropy atmultipolesbeyond $\ell \sim 2500$ ."352 The magnitude oftheSZ signal depends strongly on, The magnitude oftheSZ signal depends strongly on353"Circumstellar disks of gas and dust, a natural result of the conservation of angular momentum, are a common outcome of the star formation process.","Circumstellar disks of gas and dust, a natural result of the conservation of angular momentum, are a common outcome of the star formation process."354" find that over half the low mass (« 2 Mo) pre-main-sequence T Tauri stars in the Taurus-Auriga star formation region have more infrared emission than expected from a normal stellar photosphere, indicating the presence of a dusty circumstellar disk heated by the parent star as well as active accretion."," find that over half the low mass $<$ 2 $_{\odot}$ ) pre–main-sequence T Tauri stars in the Taurus-Auriga star formation region have more infrared emission than expected from a normal stellar photosphere, indicating the presence of a dusty circumstellar disk heated by the parent star as well as active accretion."355" T Tauri stars fall into two categories: Weak-Line T Tauri Stars (WTTSs), characterized by low Ha equivalent widths, and Classical T Tauri Stars (CTTSs), with higher Ho equivalent widths indicative of ongoing gas accretion."," T Tauri stars fall into two categories: Weak-Line T Tauri Stars (WTTSs), characterized by low $\alpha$ equivalent widths, and Classical T Tauri Stars (CTTSs), with higher $\alpha$ equivalent widths indicative of ongoing gas accretion."356" These circumstellar disks generally have the following properties al.|2009):: mass surface densities U(r)οςr°%19, surface temperatures T(r)οςr9*99-8 (depending ondisk flaring), and Keplerian rotational velocitiesV(r)ος r9."," These circumstellar disks generally have the following properties : mass surface densities $\Sigma(r)\propto r^{0\,\mathrm{to}\,-1.0}$, surface temperatures $T(r)\propto r^{0\,\mathrm{to}\,-0.6}$ (depending ondisk flaring), and Keplerian rotational velocities$V(r)\propto r^{0.5}$ ."357"result from this double Caussian fitting test should be taken seriously, We are presenting a result frou this test in order to see if we find the same kind of the dependency of fitted paraicters on the fitting method which we find int 16 Bahuer lues as a way to support our asstuuption that the Paschen line profiles are similar to the Bahuer line profiles.","result from this double Gaussian fitting test should be taken seriously, We are presenting a result from this test in order to see if we find the same kind of the dependency of fitted parameters on the fitting method which we find in the Balmer lines as a way to support our assumption that the Paschen line profiles are similar to the Balmer line profiles."358" lu iuost Case, he fitted values from the double componen fit agree with those frou the single componen fit (without the additional correction factor). where the FWIIA and flux values from the double componen fittines aro in average larger and sxnaller than he sinele component fitting results respectively."," In most case, the fitted values from the double component fit agree with those from the single component fit (without the additional correction factor), where the FWHM and flux values from the double component fittings are in average larger and smaller than the single component fitting results respectively."359 This agrees well with the treu we fiud from our analysis of the Bahuer lines using single. double. aud multiple component Gaussian fittings (see above).," This agrees well with the trend we find from our analysis of the Balmer lines using single, double, and multiple component Gaussian fittings (see above)."360 One exception is | 002310.5. whose FWIIM changed by about., One exception is $+$ 002340.8 whose FWHM changed by about.361 Distiuguishiug the narrow aud the broad compoucuts is difficult for this object. therefore the mean value between the parameters roni the two different methods was adopted as the best-fit value. with the half of the difference as its error.," Distinguishing the narrow and the broad components is difficult for this object, therefore the mean value between the parameters from the two different methods was adopted as the best-fit value, with the half of the difference as its error."362" We rote that the double compoucut fit improved thereduced. \? values VAienificantlv. >OF 3) for only three objects. where the oeuprovenient cane from fitting of xoad extended wines which did uot affect the derived fing parameter values rather than through the chanec ft the ΕΛΗΝ values (except for | 0023hay,"," We note that the double component fit improved thereduced $\chi^{2}$ values significantly $> 0.3$ ) for only three objects, where the improvement came from fitting of broad extended wings which did not affect the derived fitting parameter values rather than through the change of the FWHM values (except for $+$ 002340.8)."363" Finally. the aeasured FWIAIs were corrected for the instrumental resolution aud the fitting methodology (anultiple component fit versus singele conrponeut fit). are the fluxes were coiverted to the ununositv assunmiues a standard ACDAL cosinology of 7270 kan secI d. Q,,, 20.3 aud O4204 (ee. hu et al."," Finally, the measured FWHMs were corrected for the instrumental resolution and the fitting methodology (multiple component fit versus single component fit), and the fluxes were converted to the luminosity assuming a standard $\Lambda$ CDM cosmology of $H_{0}$ =70 km $^{-1}$ $^{-1}$, $\Omega_{m}$ =0.3 and $\Omega_{\Lambda}$ =0.7 (e.g., Im et al."364 1997)., 1997).365 The LLOASTILCC lue hunuinosities. fluxes. aud FWIIMSs are preseuted iu Table 1..," The measured line luminosities, fluxes, and FWHMs are presented in Table \ref{tbl1}."366 LOS preseut the results of their line analvsis. base ou the NIR specra that were taken with the Spex spectrograph (Ravueretal.2003) ou the Iufrar« Telescope Facility (RTF) at an average spectra resolutiou of 1 XusLl.," L08 present the results of their line analysis, based on the NIR spectra that were taken with the Spex spectrograph \citep{rayner03} on the Infrared Telescope Facility (IRTF) at an average spectral resolution of 400 $\mathrm{km~s^{-1}}$."367 For the LOS sample. we use the line fluxes iux FWIIMS derived by them aud preseutec in them Tahle 2. after correcting ΕΠΑΕvalues for the instimental resolution.," For the L08 sample, we use the line fluxes and FWHMs derived by them and presented in their Table \ref{tbl2}, after correcting FWHMvalues for the instrumental resolution."368 We also applied the correction facOr οf ue; Leiqrbroad 50.9 and Loau/L singiebroud=l.08 which corrects for the difference in the line-fitting methods (LOS versus Greene Πο 2005) Oo cevive the line. parameters which are simular to the correction factors we derived for the fitting xocess of the G6 spectra., We also applied the correction factor of $_{multi}$ $_{single broad}$ =0.9 and $L_{multi}$ $L_{single broad}$ =1.08 which corrects for the difference in the line-fitting methods (L08 versus Greene Ho 2005) to derive the line parameters which are similar to the correction factors we derived for the fitting process of the G06 spectra.369 As for the accuracy of the LOS measurements. LOX quote a typical error of of ess.," As for the accuracy of the L08 measurements, L08 quote a typical error of of less."370" Therefore. we adopt a couscrvative value of for he measurement error of the fiuxes and the EWIIMSs ILOSCILed in Los,"," Therefore, we adopt a conservative value of for the measurement error of the fluxes and the FWHMs presented in L08."371 We note that contamination from the jost galaxy light o these measurements is negligible., We note that contamination from the host galaxy light to these measurements is negligible.372 The contamination ofthe ine flux due to the host galaxy is )ossible. but the (06 data were taken with a narrow slit to niunuize the 1ost ealaxy light to less than8%.," The contamination of the line flux due to the host galaxy is possible, but the G06 data were taken with a narrow slit to minimize the host galaxy light to less than."373. We expect that the SOC sateineut holds true for the LOS sample whose data were taken with a narrow slit for AGNs at z«0.1 which are located much closer to us than the C06 sample., We expect that the same statement holds true for the L08 sample whose data were taken with a narrow slit for AGNs at $z < 0.1$ which are located much closer to us than the G06 sample.374 Before constructing mass estimators based on the Paschen lines. we show here that how well the propertics of the Paschen lines correlate with the Balmer lines.," Before constructing mass estimators based on the Paschen lines, we show here that how well the properties of the Paschen lines correlate with the Balmer lines."375 A ight correlation between the two lines would imply that he Paschen lines originate from the broad line regious siular to the Balmer lines. thus serving as a strong justification for the use of the Pascheu lines as a mass estimator.," A tight correlation between the two lines would imply that the Paschen lines originate from the broad line regions similar to the Balmer lines, thus serving as a strong justification for the use of the Paschen lines as a mass estimator."376 Good correlations between the FWIAL values of the broad Bahuer lues aud the broad. Paschen lines were shown in Lüs., Good correlations between the FWHM values of the broad Balmer lines and the broad Paschen lines were shown in L08.377 Here. we extend the analysis to the ine flux ratios. aud add quasars from the G06 sample to he LOS sample to strenethen the eooduess of the FWIAL correlation.," Here, we extend the analysis to the line flux ratios, and add quasars from the G06 sample to the L08 sample to strengthen the goodness of the FWHM correlation."378 Furthermore. we also derive equations that relate the properties of the Daliner aud the Paschenu lines.," Furthermore, we also derive equations that relate the properties of the Balmer and the Paschen lines."379 Figure 5 shows the correlation between EWIIM values of the Bahuer and the Paschen broad Ines. while Figure 6 shows a correlation of line Iuuinosities of the broad Imes.," Figure 5 shows the correlation between FWHM values of the Balmer and the Paschen broad lines, while Figure 6 shows a correlation of line luminosities of the broad lines."380 To derive the correlations between the two quantities. we performed a linear bisector fit using the equations below.," To derive the correlations between the two quantities, we performed a linear bisector fit using the equations below."381 lere. X aud Y are line ideutifiors. iud A aud D are the correlation cocficicuts iu the fit for FWHAL aud C and D are the coefiicients for the line ποστ ratio fit.," Here, X and Y are line identifiers, and A and B are the correlation coefficients in the fit for FWHM, and C and D are the coefficients for the line luminosity ratio fit."382 The results of the fitting are suuuarized in Table 2., The results of the fitting are summarized in Table 2.383 The table also lists the rius scatter of the data poiuts with respect to the best-fit lines., The table also lists the rms scatter of the data points with respect to the best-fit lines.384 These results show that the Pascheu line buuinosities and PWHAs correlate well with those of the Baluer lines., These results show that the Paschen line luminosities and FWHMs correlate well with those of the Balmer lines.385 The iis scatters iu the line Iuninositv correlation are ~O.12-0.11 dex against Ha. and ~0.16-0.19 dex against IL.," The rms scatters in the line luminosity correlation are $\sim$ 0.12-0.14 dex against $\alpha$, and $\sim$ 0.16-0.19 dex against $\beta$."386 For the FWOAL values. the rms scatters are 0.015-0.06 dex against Ta. aud 0.05-0.06 dex agaist IL.," For the FWHM values, the rms scatters are 0.045-0.06 dex against $\alpha$, and 0.05-0.06 dex against $\beta$."387 The slightly larger scatters aud a notable offset im FWIIM. values of I} against Pascheu lines suggest the conplexities in ACN spectra around I> line noted iu LOS. an excess. broad compoucut in the red part of the IT? ne caused bv an unclear origin (c.g.. Mevers Peterson 1985: Vórron et al.," The slightly larger scatters and a notable offset in FWHM values of $\beta$ against Paschen lines suggest the complexities in AGN spectra around $\beta$ line noted in L08, an excess, broad component in the red part of the $\beta$ line caused by an unclear origin (e.g., Meyers Peterson 1985; Vérron et al."388 2002)., 2002).389 We also poiut out that the line widths of Balmer lunes are systematically larecr than those of the Pascheu lines. aud that the trend is stronger as the wavelength decreases.," We also point out that the line widths of Balmer lines are systematically larger than those of the Paschen lines, and that the trend is stronger as the wavelength decreases."390 This suggests that the Paschen broad Hines and the Baluer broad lues originate from a simular BLR. but with Baluer lines originating from the iuner region of the BER thau Paschen limes.," This suggests that the Paschen broad lines and the Balmer broad lines originate from a similar BLR, but with Balmer lines originating from the inner region of the BLR than Paschen lines."391" Siuilarh. we also examine correlations between (Lo, J aud Lp,a."," Similarly, we also examine correlations between $L_{5100\mathrm{\AA{}}}$ ) and $L_{\mathrm{P\alpha,\beta}}$ ."392 Ποια values are derived frou. L(5100) using Equation (1) of (Caeene&Πο 2005).., $R_{\mathrm{BLR}}$ values are derived from $L(5100)$ using Equation (4) of \citep{greene05}. .393 Fiewe 7 shows the correlation between Πριν aud Paschen line huninositics. aud Equations (1) aud (5) are the best-fit results.," Figure 7 shows the correlation between $R_{BLR}$ and Paschen line luminosities, and Equations (4) and (5) are the best-fit results."394significant reddening. we make no reddening correction of the line ratios.,"significant reddening, we make no reddening correction of the line ratios."395 To investigate the physical conditions implied. by both the low jonisation and high ionisation species. the photoionisation model code (Ferlandetal.1998) was used to create single slab photoionisation models for the emission lines of Q1131|16.," To investigate the physical conditions implied by both the low ionisation and high ionisation species, the photoionisation model code \citep{ferland} was used to create single slab photoionisation models for the emission lines of Q1131+16."396 Phe ionisation parameter was varied over the range -3.0 x log x 0. in steps of logU]-0.5. and the hydrogen density U]was varied over the range 3.0 x log(ng em 7) S.0 in steps of log(ng 7) =0.5.," The ionisation parameter was varied over the range -3.0 $\leq$ log[U] $\leq$ 0, in steps of log[U]=0.5, and the hydrogen density was varied over the range 3.0 $\leq$ $n_H$ $^{-3}$ ) $\leq$ 8.0 in steps of $n_H$ $^{-3}$ ) =0.5."397 Phe rest of the properties of the model were, The rest of the properties of the model were398mass loss) become stronger with decreasing energy. a behavior similar to the (vpical (vpes of shock formation (e.g.. see Lu et al.,"mass loss) become stronger with decreasing energy, a behavior similar to the typical types of shock formation (e.g., see Lu et al."399 1997 for adiabatic shocks: Lu Yuan 1998. Fukumura Tsuruta 2004 for isothermal shocks).," 1997 for adiabatic shocks; Lu Yuan 1998, Fukumura Tsuruta 2004 for isothermal shocks)."400 To exclusively illustrate the black hole spin dependence α of the mass loss efficiency. {νι we fix all other parameters (£4.À. raj) except lor a.," To exclusively illustrate the black hole spin dependence $a$ of the mass loss efficiency $f_{\dot{M}}$ we fix all other parameters $E_1, \lambda, r_{\rm sh}$ ) except for $a$ ."401" Figure 7 shows Jy, against e and fr for A=3.45 and ryfr=30."," Figure \ref{fig:spin}402 shows $f_{\dot{M}}$ against $a$ and $f_E$ for $\lambda=3.45$ and $r_{\rm sh}/m=30$."403" As seen in the earlier results. black hole rotation alone can clearly enhance the efficiency of mass outflows fy, from ~3% (for a/m= 0) up to ~95% (Lor a/m= 0.35)."," As seen in the earlier results, black hole rotation alone can clearly enhance the efficiency of mass outflows $f_{\dot{M}}$ from $\sim 3\%$ (for $a/m=0$ ) up to $\sim 95\%$ (for $a/m=0.35$ )."404 On the other hand. the corresponding energy loss efficiency. fj remains as low as e0.02—0.1%.," On the other hand, the corresponding energy loss efficiency $f_E$ remains as low as $\sim 0.02 - 0.1\%$."405 Note here that A would have to be properly adjusted in order to obtain Cie solutions for higher black hole spin a., Note here that $\lambda$ would have to be properly adjusted in order to obtain the solutions for higher black hole spin $a$.406 We have chosen above some representative values for the flow energv lor parametric purpose., We have chosen above some representative values for the flow energy for parametric purpose.407 Weakly viscous/invisckl accretion in general is a good model for some limited specilic cases. like our Galactic center. for example.," Weakly viscous/inviscid accretion in general is a good model for some limited specific cases, like our Galactic center, for example."408 For such specific cases. the realistic ‘hoice of enerey should be very small.," For such specific cases, the realistic choice of energy should be very small."409 From (his perspective we examine {οsee whether low pFyergy flows can still produce shock-driven outflows., From this perspective we examine tosee whether low energy flows can still produce shock-driven outflows.410" Figure 8. shows mass loss efliciency {ή iS a function of ry, for em.=0.", Figure \ref{fig:low-E} shows mass loss efficiency $f_{\dot{M}}$ as a function of $r_{\rm sh}$ for $a/m=0$.411 We set νι=1.000001 and A=3.73., We set $E_1=1.000001$ and $\lambda=3.73$.412 Mass outflows can poendeed be produced with f; ranging from ~1'4 up to ~65%.," Mass outflows can indeed be produced with $f_{\dot{M}}$ ranging from $\sim 1\%$ up to $\sim41365\%$."414 Both unstable and stable 10cks are present as in (he earlier cases but not continuously connected (no shock regions between the (wo)., Both unstable and stable shocks are present as in the earlier cases but not continuously connected (no shock regions between the two).415 The range of shock location is much narrower in radius in (liis case. over which the mass loss efficiency can significantly change as mentioned above.," The range of shock location is much narrower in radius in this case, over which the mass loss efficiency can significantly change as mentioned above."416 We will discuss is more in (he Discussion section., We will discuss this more in the Discussion section.417 Themajor correlations we [find among (he primary parameters are summarized in Table 1.., Themajor correlations we find among the primary parameters are summarized in Table \ref{tab:tbl-1}. .418 Table 2. shows various correlations with shock strength., Table \ref{tab:tbl-2} shows various correlations with shock strength.419 Compression ratio ns/n4 , Compression ratio $n_2/n_1$ 420Can pre-enriched gas produce a good fit to the observations?,Can pre-enriched gas produce a good fit to the observations?421 We tried a model with2o delaved increase in SE. elliciency and gas inllow. but. which is mace from pre-enriched gas 17 Gyr ago. such as might be expected from à very top heavy IME from which there is a high level of feedback to enrich the ISM. and very little material is left. trapped: in. stars.," We tried a model with delayed increase in SF efficiency and gas inflow, but which is made from pre-enriched gas 17 Gyr ago, such as might be expected from a very top heavy IMF from which there is a high level of feedback to enrich the ISM and very little material is left trapped in stars."422 We assumed Co=0.7 (thought to be typical for ellipticals FOO. although mocels with carly galactic winds require much higher values of C).," We assumed $C=0.7$ (thought to be typical for ellipticals – FG94, although models with early galactic winds require much higher values of $C$ )."423 For those galaxies with very old starbursts (t:=2 or less). apre-enriched. single burst model can give comparable fits to the data (as those in table 5).," For those galaxies with very old starbursts $*=2$ or less), a, single burst model can give comparable fits to the data (as those in table 5)."424 The pre-enriched gas required for these fits starts olf with metallicity Z 0.5 to 0.75 solar., The pre-enriched gas required for these fits starts off with metallicity $Z\sim$ 0.5 to 0.75 solar.425 This confirms our earlier suggestion that the stars dominating the light at the current epoch have to be made from. enriched material., This confirms our earlier suggestion that the stars dominating the light at the current epoch have to be made from enriched material.426 Llowever. for other galaxies the observed strength of LL? rules out an entirely old stellar population.," However, for other galaxies the observed strength of $\beta$ rules out an entirely old stellar population."427 These are the galaxies which required an intermediate (NGC 5831. NGC 2329) or voung (NGC 221) starburst in our delaved burst models (table 5).," These are the galaxies which required an intermediate (NGC 5831, NGC 2329) or young (NGC 221) starburst in our delayed burst models (table 5)."428 Worthey (1996). suggested. that a model of. elliptical formation with several episodes of star formation corresponding to mergers and/or interactions can Lit some of the observational [acts (e.g. presence of kinematic sub-structures. evidence for voung stars).," Worthey (1996) suggested that a model of elliptical formation with several episodes of star formation corresponding to mergers and/or interactions can fit some of the observational facts (e.g. presence of kinematic sub-structures, evidence for young stars)."429" ""Therefore. a future extension to the current models is to try including more starbursts.", Therefore a future extension to the current models is to try including more starbursts.430 However this introduces many more free parameters and the latest burst. will remain important ini terms of iis relative luminosity., However this introduces many more free parameters and the latest burst will remain important in terms of its relative luminosity.431 Worthey (1996) suggested that more bursts at earlier times may explain the observations of earlv-twpe. galaxies., Worthey (1996) suggested that more bursts at earlier times may explain the observations of early-type galaxies.432 Since we can already produce strong enough. lines with a single delayed: burst. more bursts will still not get round the problem of non-solar ratios. which contributes to the poor fits of current models to observations of some ellipticals.," Since we can already produce strong enough lines with a single delayed burst, more bursts will still not get round the problem of non-solar ratios, which contributes to the poor fits of current models to observations of some ellipticals."433 V96 showed that no single IME. constant in time. can generate the observed. line-streneths in a closed box mocel with a single SER constant.," V96 showed that no single IMF, constant in time, can generate the observed line-strengths in a closed box model with a single SFR constant."434 The elfects of a changing LME with time are explored by V96., The effects of a changing IMF with time are explored by V96.435 They find that a shallow LM at early times (followed bv a normal IME like that inferred for local stars) can produce stellar populations with lines as strong as those seen in earlv-tvpe galaxies., They find that a shallow IMF at early times (followed by a normal IMF like that inferred for local stars) can produce stellar populations with lines as strong as those seen in early-type galaxies.436 So. primordial ellipticals with a single EME are still ruled out for clillerent assumptions about the slope of the IME. but changing the IME with time. from shallow to steep. can produce strong lines.," So 'primordial' ellipticals with a single IMF are still ruled out for different assumptions about the slope of the IMF, but changing the IMF with time, from shallow to steep, can produce strong lines."437 We showed above that an early LATIF of massive stars (pre-enriching the ISM prior to normal SE) can fit the data for some galaxies as well as our merger model., We showed above that an early IMF of massive stars (pre-enriching the ISM prior to normal SF) can fit the data for some galaxies as well as our merger model.438 However. we note that strong interactions and mergers. accompanied bv highly increased. SE and rapid gas inflow are.observced to occur and that both observations and simulations tell us that such events can produce earlv-tvpe galaxies.," However, we note that strong interactions and mergers, accompanied by highly increased SF and rapid gas inflow are to occur and that both observations and simulations tell us that such events can produce early-type galaxies."439 On the other hand evidence for a variable ΠΟ is not so definite ucher Fahlman 1996)., On the other hand evidence for a variable IMF is not so definite (Richer Fahlman 1996).440 In fact Pacloan. Nordlund Jones (1997) recently. argued. for a universal IME. arising [rom 1 statistics of random. supersonic [lows which simulate conditions during star formation.," In fact Padoan, Nordlund Jones (1997) recently argued for a universal IMF, arising from the statistics of random supersonic flows which simulate conditions during star formation."441 So there is no need for v variable LAL to. produce the observed. line-strengths in ellipticals., So there is no need for a variable IMF to produce the observed line-strengths in ellipticals.442 Non-solar light-to-heavy metal ratios seem. required by the data for most earlv-tvpe galaxies (e.g. Fig., Non-solar light-to-heavy metal ratios seem required by the data for most early-type galaxies (e.g. Fig.443 6)., 6).444 Fits to the observed Mg» index are improved for models withofd stars if the Ales calibrations for dillerent Mg/Ee ratios from Barbuy (1994) are used., Fits to the observed $_2$ index are improved for models with stars if the $_2$ calibrations for different Mg/Fe ratios from Barbuy (1994) are used.445 Fig., Fig.446 7 compares a fit to the data for NGC 4472. and shows how the Mg» index is better fitted when non-solar Alefle is accounted for in these old stars.," 7 compares a fit to the data for NGC 4472, and shows how the $_2$ index is better fitted when non-solar Mg/Fe is accounted for in these old stars."447 We also tried modelling Mg» and «Eez (mean of Fe5270 and. Le5335) features. using SSPs from Weiss. Peleticr Alatteucci (1995) (from the top half of their table 4).," We also tried modelling $_2$ and $<$ $>$ (mean of Fe5270 and Fe5335) features, using SSPs from Weiss, Peletier Matteucci (1995) (from the top half of their table 4)."448 Weiss et aallowed. for enhanced. a-element compositions and published values for Mg» and «LEFez indices for old (12 to Ls Gyr). metal rich (CZ> Z.) SSPs with Mg/Fez solar.," Weiss et allowed for enhanced $\alpha$ -element compositions and published values for $_2$ and $<$ $>$ indices for old (12 to 18 Gyr), metal rich $Z\ge$ $_{\odot}$ ) SSPs with $\ge$ solar."449 Fig., Fig.450 S shows the predictions of some of our models with delayed, 8 shows the predictions of some of our models with delayed451eiven by (Allen&Romano1999.equation3.75) llere ο) is the ‘overlap reduction funcüon. which accounts for the separation and relative orientation of the detectors (Flanagan1993).. and πι) and 2>(f) are the noise power spectral densities of the detectors. and 1 is the integration time.,"given by \citep[][equation 3.75]{SNR}452 Here $\gamma (f)$ is the `overlap reduction function', which accounts for the separation and relative orientation of the detectors \citep{gammaf}, , and $P_1(f)$ and $P_2(f)$ are the noise power spectral densities of the detectors, and $T$ is the integration time."453 As the optimal filter depends on GOcC/). a range of filler fanctious based. on theoretical expectations of this [function will need to be used.," As the optimal filter depends on $\Omega_{\rm{GW}}(f)$, a range of filter functions based on theoretical expectations of this function will need to be used."454 In this study we use data of relative positions ancl orientations for 10 independent pairs of the five advanced detectors given in Table 3 of Nishizawaetal.(2009). ancl emplov the tensor-imode functions described in their equations (33-35)., In this study we use data of relative positions and orientations for 10 independent pairs of the five advanced detectors given in Table 3 of \citet{gamma2} and employ the tensor-mode functions described in their equations (33-35).455 For ET we assume lwo detectors of triangular shape (GO° between (he (vo arms) and separated by an angle of 1207. for which the ο} has a constant value of —3/8 from 1 Iz to 1000 Hz (lowelletal.2011).," For ET we assume two detectors of triangular shape $60^{\circ}$ between the two arms) and separated by an angle of $120^{\circ}$, for which the $\gamma(f)$ has a constant value of $-3/8$ from 1 Hz to 1000 Hz \citep{Eric2010}."456. We adopt a value of SNR = 3 to indicate detection. corresponding with false alarm rate of and detection rate of (Allen&Romano1999).," We adopt a value of SNR = 3 to indicate detection, corresponding with false alarm rate of and detection rate of \citep{SNR}."457. We also assume an integration time of 3 vears lor advanced detectors and 1 vear for ET., We also assume an integration time of 3 years for advanced detectors and 1 year for ET.458 Calculating the SNRs for SGWD model (e) shown in Figure 3. we find a value of 0.14 through eross-correlation by two the Advanced LIGO detectors Il-L. For the other four models shown in Figure 3. we find variation in SNR of within 20%.," Calculating the SNRs for SGWB model (e) shown in Figure 3, we find a value of 0.14 through cross-correlation by two the Advanced LIGO detectors H-L. For the other four models shown in Figure 3, we find variation in SNR of within $20\%$."459 For ET we find SNRs of 59 and 112 assuming ET-B and ET-D sensitivities respectively for model (e). indicating that this signal will be easilv-detected by third generation detectors.," For ET we find SNRs of 59 and 112 assuming ET-B and ET-D sensitivities respectively for model (e), indicating that this signal will be easily-detected by third generation detectors."460" These results. based on average quantities. suggest that to detect the DBII background with two Advanced LIGO detectors will require a rate greater than even the higher rate estimate. ro.~0.43Mpe""Myr.|,"," These results, based on average quantities, suggest that to detect the BBH background with two Advanced LIGO detectors will require a rate greater than even the higher rate estimate, $r_{2}\,\sim 0.43\,\rm{Mpc}^{-3}\rm{Myr}^{-1}$."461 As there will exist variation in the sensitivities. locations and orientations of detectors within a worldwide detector network. it is useful to compare the performances of different detector pairs and investigate how combining the network could improve the detection prospects.," As there will exist variation in the sensitivities, locations and orientations of detectors within a worldwide detector network, it is useful to compare the performances of different detector pairs and investigate how combining the network could improve the detection prospects."462 Two approaches of combining 2N detectors to increase (he sensitivity of a stochastic background search have been proposed by Allen&Romano(1999)., Two approaches of combining 2N detectors to increase the sensitivity of a stochastic background search have been proposed by \citet{SNR}.463. We apply these two methods to a network of 4 second generation detectors., We apply these two methods to a network of 4 second generation detectors.464 In each case. (he optimal SNR can be expressed as follows. with individual detectors (1-4) indicated in parenthesis:(i) (FC) - can be performed by directly correlating the outputs of 4 detectors," In each case, the optimal SNR can be expressed as follows, with individual detectors (1-4) indicated in parenthesis:(i) (FC) - can be performed by directly correlating the outputs of 4 detectors"465ünages were compared with the i data obtained by Cotté (1995). and it appears that the emission peaks seen in our Ha image do uot have any counterparts in the / image.,"images were compared with the $i$ data obtained by Côtté (1995), and it appears that the emission peaks seen in our $\alpha $ image do not have any counterparts in the $i$ image."466 This uxdicates that they could be genuine ΠΠ regious. so they are listed as well in Table 2.," This indicates that they could be genuine HII regions, so they are listed as well in Table 2."467 None of the fIuxes given iu Table 2 have been corrected for [NIL] contamination: these dwarf galaxies have typically very low nitrogen abundances (see companion paper). so this introduces au additional ~6% {lus uncertainty.," None of the fluxes given in Table 2 have been corrected for [NII] contamination; these dwarf galaxies have typically very low nitrogen abundances (see companion paper), so this introduces an additional $\sim $ flux uncertainty."468 For derivingOm accurate positions for the HII reeious.e HST Guide Star Reference Frame scaus [rom the STScI1 Digitized.man Sky1 wwere usec. and were Compared with positious obtaiued similarly by deriving astrometric plate solutions using bright stars in the Automatic Plate Measuriug (APM) catalog vvau Zee 2000).," For deriving accurate positions for the HII regions, HST Guide Star Reference Frame scans from the STScI Digitized Sky were used, and were compared with positions obtained similarly by deriving astrometric plate solutions using bright stars in the Automatic Plate Measuring (APM) catalog van Zee 2000)."469" In each case these positions agreed to within less than2"".", In each case these positions agreed to within less than.470 The HII regions in the two faintest galaxies (SC Ls aud SC 21) were just at the limit of detectability., The HII regions in the two faintest galaxies (SC 18 and SC 24) were just at the limit of detectability.471 In both cases. coincidence with continuum sources cast doubt on whether these are true Ha sources or possible artifacts of au imperfect continuum subtraction.," In both cases, coincidence with continuum sources cast doubt on whether these are true $\alpha$ sources or possible artifacts of an imperfect continuum subtraction."472 Further inspection and experimentation led to confidence that tliese are incleecl real Ha sources., Further inspection and experimentation led to confidence that these are indeed real $\alpha$ sources.473 Nouetleless. spectroscopic observations are required for coufirination.," Nonetheless, spectroscopic observations are required for confirmation."474 For the preseut paper. we will treat these Ha sources as bona lide HII regious.," For the present paper, we will treat these $\alpha$ sources as bona fide HII regions."475 Note that iu the case of the Local Group dI DDO 210. vau Zee et ((1997) found a similar single Ha detection to show broad Baliner lines aud no forbidden lines. aud they speculate that this source may be a Iuminous blue variable star.," Note that in the case of the Local Group dI DDO 210, van Zee et (1997) found a similar single $\alpha$ detection to show broad Balmer lines and no forbidden lines, and they speculate that this source may be a luminous blue variable star."476 Miller (1996) observed. aud detected: HII regious in the Sculptor group dls UCCA [12 (= ESO 171-C06) and ESO 215-G05 (= A 113). but did not detect Ha emission from six other Sculptor group dis.," Miller (1996) observed and detected HII regions in the Sculptor group dIs UGCA 442 $=$ ESO 471-G06) and ESO 245-G05 $=$ A 143), but did not detect $\alpha$ emission from six other Sculptor group dIs."477 Note that we did re-observe any of the Sculptor group dls from Miller's sample., Note that we did re-observe any of the Sculptor group dIs from Miller's sample.478 Miller's nonu-detection of HII regious in the Sculptor Dwarf Irregular Galaxy (= SDIG. ESO 319-CG1) has been confiriued by Heisler et ((1997).," Miller's non-detection of HII regions in the Sculptor Dwarf Irregular Galaxy $=$ SDIG, ESO 349-G31) has been confirmed by Heisler et (1997)."479 van Zee (2000) lias observed DDO 6 (= UGCA 15) aud did not detect any HIE regions. but did detect a small amount of diffuse Ha emission.," van Zee (2000) has observed DDO 6 $=$ UGCA 15) and did not detect any HII regions, but did detect a small amount of diffuse $\alpha$ emission."480 van Zee (2000) also observed DDO 226 (= UGCA 9) and did detect the presence of faint HII regious., van Zee (2000) also observed DDO 226 $=$ UGCA 9) and did detect the presence of faint HII regions.481 Jerjen et ((1998) detected a [aint HID region in ESO 291-C010., Jerjen et (1998) detected a faint HII region in ESO 294-G010.482 ESO 110-C402 is au HI uou-detection. and. based ou HST imagine. Ixarachentsev et ((2000) have cletermined tliat this is a dSph galaxy.," ESO 410-G05 is an HI non-detection, and, based on HST imaging, Karachentsev et (2000) have determined that this is a dSph galaxy."483 In light of the results of the more recent deeper spectroscopy. it iniglit. be interesting to re-observe the other nou-detection by Miller (1996). Le.. LCCA [38 (= ESO ," In light of the results of the more recent deeper spectroscopy, it might be interesting to re-observe the other non-detection by Miller (1996), i.e., UGCA 438 $=$ ESO 407-G18)."484Nonetheless. tle claim by Miller (1996) that the average current star formation lor dls iu the Sculptor group is suppressed relative to other nearby groups appears to be coufirmed (see discussion iu 83).," Nonetheless, the claim by Miller (1996) that the average current star formation for dIs in the Sculptor group is suppressed relative to other nearby groups appears to be confirmed (see discussion in 3)."485a redshift shell centered on the galaxy. clusters redshift z+0.) are ideutifiecl as members.,a redshift shell centered on the galaxy cluster's redshift $z_c \pm \delta_z$ ) are identified as members.486 Because photometric redshifts have a large uncertainty. (generally a factor of teu to fifty. higher hau spectroscopic redshifts). a large recslift shell 0.0.05) is used to identify likely cluster jembers.," Because photometric redshifts have a large uncertainty (generally a factor of ten to fifty higher than spectroscopic redshifts), a large redshift shell $\delta_z487\approx 0.05$ ) is used to identify likely cluster members."488 While certainly. useful. this approach does uot provide a reliable meaus for identifviug ine-ol-sieht coutamiuatiug galaxies.," While certainly useful, this approach does not provide a reliable means for identifying line-of-sight contaminating galaxies."489 As a result. we have developed au alternative technique which relies on. the probabilistic interpretation of a photometric redshift to determine cluster membership.," As a result, we have developed an alternative technique which relies on the probabilistic interpretation of a photometric redshift to determine cluster membership."490 We define the probability ensity functiou. Pfs). for an individual galaxys redshift to be a Gaussian probability distribution uuction with mean (5) given by the estimated photometric redshift aud standard deviation (o) elined by the estimated error in the photometric recshift.," We define the probability density function, $\Phi(z)$, for an individual galaxy's redshift to be a Gaussian probability distribution function with mean $\mu$ ) given by the estimated photometric redshift and standard deviation $\sigma$ ) defined by the estimated error in the photometric redshift."491 Usine this interpretation. we can calculate the probability that a galaxy has au actual redshift within a eiven redshift interval.," Using this interpretation, we can calculate the probability that a galaxy has an actual redshift within a given redshift interval."492 where N is a suitable normalization factor. z« is the cluster redshift. Az is the width in recshift space which vou are saiupliug. the limits of integratiou are and 5 is the incomplete eamma function. (," where $N$ is a suitable normalization factor, $z_c$ is the cluster redshift, $\Delta z$ is the width in redshift space which you are sampling, the limits of integration are and $\gamma$ is the incomplete gamma function. ("493Of course. 5[2.2] is also known as the error function. erfiz)).,"Of course, $\gamma[\frac{1}{2},z]$ is also known as the error function, $erf(z)$ )."494 Within this formalism. the only. uudeclared quantity is o or. alternatively. the uncertainty iu he estimated redshilt for a given galaxy.," Within this formalism, the only undeclared quantity is $\sigma$ or, alternatively, the uncertainty in the estimated redshift for a given galaxy."495 In our framework. this value can either be determined rou the intrinsic error in our photometric redshilt relation or in a separately calculated extrinsic error.," In our framework, this value can either be determined from the intrinsic error in our photometric redshift relation or in a separately calculated extrinsic error."496 As a result. this approach is stronely depeudent on the actual technique used to estimate he photometric redshift error and corresponding redshift error.," As a result, this approach is strongly dependent on the actual technique used to estimate the photometric redshift error and corresponding redshift error."497 In this paper. we have applied this echuique using empirically derived photometric redshilis since we have a well-defined calibration dataset of spectroscopic redshifts.," In this paper, we have applied this technique using empirically derived photometric redshifts since we have a well-defined calibration dataset of spectroscopic redshifts."498 Eipirically defined photometric redshifts are much less seusitive o uncertainties in the shape aud the evolution with redshift of the spectralenergy distribution of ealaxies than competing techuiques such as template photometric redshifts (Brunner 1997).., Empirically defined photometric redshifts are much less sensitive to uncertainties in the shape and the evolution with redshift of the spectralenergy distribution of galaxies than competing techniques such as template photometric redshifts \citep{myThesis}. .499"as (he deviation of these discrepant points is larger (han would be expected Lor a transit. we reset the D(/,) value of (hat point to the mean of the data.","as the deviation of these discrepant points is larger than would be expected for a transit, we reset the $\it{D(t_i)}$ value of that point to the mean of the data."500 The consequences of this shall be discussed further when considering the application of these criteria to the 47 Tuc dataset., The consequences of this shall be discussed further when considering the application of these criteria to the 47 Tuc dataset.501 The detection process is complicated bv (the varying observational conditions tvpical ol long time series of photometric data., The detection process is complicated by the varying observational conditions typical of long time series of photometric data.502 These can produce pseudo periodic signals with an associated increase in photometric measurement errors., These can produce pseudo periodic signals with an associated increase in photometric measurement errors.503" In order to reduce these effects. the contribution of each datapoint before it was used in the ΟΕωςΤΗ) Calculation was weighted by the size of its photometric uncertainty. wilh the standard weighting scheme: where V; is the point weight and o; is the errorbar associated with the i"" point."," In order to reduce these effects, the contribution of each datapoint before it was used in the $C(P_{mod},\tau_{shift})$ calculation was weighted by the size of its photometric uncertainty, with the standard weighting scheme: where $W_{i}$ is the point weight and $\it{\sigma_i}$ is the errorbar associated with the $^{th}$ point."504" The result is that points with large errorbars are given a small weight and hence do not add significantly to the final CUP,o¢-του) lor that model."," The result is that points with large errorbars are given a small weight and hence do not add significantly to the final $\it{C(P_{mod},\tau_{shift})}$ for that model."505" By incorporating both of the (1ρω.Το) and AN, detection criteria. and incorporating the outlier removal and Ην weighting scheme. the real detections and [alse detections in the time-series were kept to acceptable levels."," By incorporating both of the $S(P_{mod},\tau_{shift})$ and $N_{p}$ detection criteria, and incorporating the outlier removal and $\it{W_{i}}$ weighting scheme, the real detections and false detections in the time-series were kept to acceptable levels."506 We now discuss the application of these criteria to the 47 Tuc dataset. and illustrate (heir effect on the final (transit candidate lists.," We now discuss the application of these criteria to the 47 Tuc dataset, and illustrate their effect on the final transit candidate lists."507 The data were split into (wo bins lor separate analvsis. distinguishing lightcurves with relatively low photometric scatter (0.02 mag). and (hose with somewhat higher scatter (0.02mssz0.04 mag).," The data were split into two bins for separate analysis, distinguishing lightcurves with relatively low photometric scatter $\le$ 0.02 mag), and those with somewhat higher scatter $\le$ $\le$ 0.04 mag)."508 We found that applying slightly different. values of the detection criteria to the two bins we could keep the detection levels high and false detection levels low., We found that applying slightly different values of the detection criteria to the two bins we could keep the detection levels high and false detection levels low.509" We perlormed Monte Carlo tests. adding model transits of various depthlis and curations Lo actual dataset lighteurves with differing photometric uncertainties to determine the maximum photonmetric scatter for which the aleorithm could reasonably detect. transits with depths as large as Dye,= 0.03 mag."," We performed Monte Carlo tests, adding model transits of various depths and durations to actual dataset lightcurves with differing photometric uncertainties to determine the maximum photometric scatter for which the algorithm could reasonably detect transits with depths as large as $\it{D_{tran}} =$ 0.03 mag."510 The expected depth of a transit is dependent. upon stellar magnitude and (his value is the expected transit depth lor stars at the lower limit of our search range. as described in Weldrakeetal.(2005).," The expected depth of a transit is dependent upon stellar magnitude and this value is the expected transit depth for stars at the lower limit of our search range, as described in \citet{Weld2005}."511. Stars with scatter greater than 0.04 mag were [found to suffer from Large false detection rates and an unacceptably low transit recoverability rate., Stars with scatter greater than 0.04 mag were found to suffer from large false detection rates and an unacceptably low transit recoverability rate.512 With this lower limit. the total number of lighteurves with rms. «0.04 mag in the 47 Tuc dataset is 21.950. allowing a statistically robust sample for analvsis.," With this lower limit, the total number of lightcurves with rms $\le$ 0.04 mag in the 47 Tuc dataset is 21,950, allowing a statistically robust sample for analysis."513"find that there exist correlations in the residuals of fits such as the Mgy—o and? relations; for example, at fixed o the residual SMBH mass scales approximately as ~Mp-™, and at fixed My the residuals scale as ~o14°,","find that there exist correlations in the residuals of fits such as the $M_{BH}-\sigma$ and relations; for example, at fixed $\sigma$ the residual SMBH mass scales approximately as $\sim M_{b}^{0.72}$, and at fixed $M_{b}$ the residuals scale as $\sim \sigma^{1.40}$."514" By marginalizing over two parameters — Μι and either σ or R, — they found a best-fit BHFP which minimized these residual correlations with the form Mpgg~ M?o1-4, both in simulations and for observed systems(??7)."," By marginalizing over two parameters – $M_{b}$ and either $\sigma$ or $R_e$ – they found a best–fit BHFP which minimized these residual correlations with the form $M_{BH}\sim M_b^{0.72}\sigma^{1.4}$ , both in simulations and for observed systems."515". This is statistically(?) indistinguishable from a correlation with the bulge binding energy proxy Myo? (Mpa~ and can be interpreted as reflecting the nature of (Myo?)97),feedback regulated SMBH growth: accretion accelerates until feedback is sufficient to unbind the local gas supply, abruptly terminating the inflow and cutting off further growth."," This is statistically indistinguishable from a correlation with the bulge binding energy proxy $M_b\sigma^2$ $M_{BH}\sim (M_b\sigma^2)^{0.7}$ ), and can be interpreted as reflecting the nature of feedback regulated SMBH growth: accretion accelerates until feedback is sufficient to unbind the local gas supply, abruptly terminating the inflow and cutting off further growth."516" Therefore it is more “fundamental” than its various projections, such as the Mepy—o and relations — a point we discuss in more detail in 5.1.."," Therefore it is more “fundamental"" than its various projections, such as the $M_{BH}-\sigma$ and relations – a point we discuss in more detail in \ref{sec:discussion_fundamental}."517" To systematically test this hypothesis, we examine the binding energy correlation — which is statistically equivalent to the BHFP - in three different modes of SMBH fueling: major mergers, minor mergers, and unstable disks (see 3 for details)."," To systematically test this hypothesis, we examine the binding energy correlation – which is statistically equivalent to the BHFP – in three different modes of SMBH fueling: major mergers, minor mergers, and unstable disks (see \ref{sec:sims} for details)."518" Figure 9 shows the binding energy correlation for major mergers (grey hexagons), the mass ratio series (left: colored points; right: black triangles), and unstable disks (right: colored points), along with the observations listed in?."," Figure \ref{fig:bhfp_all} shows the binding energy correlation for major mergers (grey hexagons), the mass ratio series (left: colored points; right: black triangles), and unstable disks (right: colored points), along with the observations listed in."519". We find that over a range of baryonic masses, gas fractions, and orbital parameters they all lie along the same relation to within the scatter, and that all reproduce the observed correlation."," We find that over a range of baryonic masses, gas fractions, and orbital parameters they all lie along the same relation to within the scatter, and that all reproduce the observed correlation."520" Inasmuch as their growth is terminated at a critical accretion rate, the final masses of SMBHs should not be determined by the available fuel supply so long as the gas reservoir is much more massive than the SMBH."," Inasmuch as their growth is terminated at a critical accretion rate, the final masses of SMBHs should not be determined by the available fuel supply so long as the gas reservoir is much more massive than the SMBH."521" While it is the case that the final SMBH mass is strongly correlated with the total gas mass of the system, this reflects the structural properties of bulges in gas-rich merger remnants: owing the effects of dissipation, a more gas rich progenitor will lead to a more compact bulge at fixed total mass, and consequently a deeper central potential φε and velocity dispersion o???).."," While it is the case that the final SMBH mass is strongly correlated with the total gas mass of the system, this reflects the structural properties of bulges in gas–rich merger remnants: owing the effects of dissipation, a more gas rich progenitor will lead to a more compact bulge at fixed total mass, and consequently a deeper central potential $\phi_c$ and velocity dispersion $\sigma$."522" As shown by for major mergers, at fixed potential the gas fraction has no effect on SMBH growth."," As shown by for major mergers, at fixed potential the gas fraction has no effect on SMBH growth."523" One method of illustrating this is presented in Figure 10,, which shows the BHFP and binding energy correlations for the mass ratio series (colored points) as compared to those derived from simulations of major mergers (grey hexagons; solid line with the dotted line indicating the scatter)."," One method of illustrating this is presented in Figure \ref{fig:bind_gas_move}, which shows the BHFP and binding energy correlations for the mass ratio series (colored points) as compared to those derived from simulations of major mergers (grey hexagons; solid line with the dotted line indicating the scatter)."524" Here we show that increasing the initial gas fraction from f,—0.4 to 0.8 for the identical interaction will drive the remnant along the BHFP and binding energy correlations, but not systematically away"," Here we show that increasing the initial gas fraction from $f_g=0.4$ to $0.8$ for the identical interaction will drive the remnant along the BHFP and binding energy correlations, but not systematically away"525right-hand side) is much larger thaw COPCτςp,right-hand side) is much larger than $\GTcore^2$.526 Asa result. changing Teoreg has only a small effect ou Typ9.," As a result, changing $\GTcore$ has only a small effect on $T_{\ND,9}$."527 Even if the direct. Urea process were to operate aud cool the core to νου«1. the temperature around neutron drip will remain high.," Even if the direct Urca process were to operate and cool the core to $\GTcore \ll 1$, the temperature around neutron drip will remain high."528 As the crust temperature increases. crust neutrino bremssrahlung and the plasina neutrino orocess become increasingly important.," As the crust temperature increases, crust neutrino bremsstrahlung and the plasma neutrino process become increasingly important."529" At the higher accretiot rate. the brighter crust neutrino uminosity balauces the nuclear heating ""on the spot.”"," At the higher accretion rate, the brighter crust neutrino luminosity balances the nuclear heating “on the spot.”"530 Figure 10 compares proper temperature panel)) aud scaled luminosity panel)). as measured yy au observer at infinite distance. or mocel aaccreting a hip (Ly=Ly242x109ergs+: and Sipe 10eres t: Une)).," Figure \ref{fig:compare-mdot}531 compares proper temperature ) and scaled luminosity ), as measured by an observer at infinite distance, for model accreting at $\dot{m}_E$ $L_A=\LAo=2.12\ee{38}\erg\second^{-1}$; ) and $5\dot{m}_E$ $L_A=5\LAo=1.06\ee{39}\erg\second^{-1}$ ; )."532 The conductivity in both cases is se by electron-ion scattering., The conductivity in both cases is set by electron-ion scattering.533 As the crust neutrio cooling increases. a sualler fraction of Ls flows outward from the op of the crust.," As the crust neutrino cooling increases, a smaller fraction of $L_N$ flows outward from the top of the crust."534 At lower accretion rates. the chauge in temperatufe over the itner crust becomes sinaller relative to tle core temperature.," At lower accretion rates, the change in temperature over the inner crust becomes smaller relative to the core temperature."535 The crust becomes 11010 1early isothermal auc len‘e Inore sensitive to tle temiperatures at its boundaries (cfMiraka-Esct«léοἱa.1990:Ztniketal. 1992). ," The crust becomes more nearly isothermal and hence more sensitive to the temperatures at its boundaries \citep[cf.~][]{miralda-escude90,zdunik92}. ."536From equation (23)). the teiiperature increase over the 1lner c‘ust ds ECOSTs ELa 0.06L4. assuiines tlat L;=La.," From equation \ref{eq:T-integrand-high}) ), the temperature increase over the inner crust is $<0.5 T_{\rm core}$ for $L_A<0.06\LAo$, assuming that $L_i=L_N$."537 Toceimonstrate this. Figure 11 «isplays. Kk al accretion uminosly £4=eres tf. the proper temperature aie ]uminosity.," To demonstrate this, Figure \ref{fig:low-mdot-sf} displays, for an accretion luminosity $L_A=0.01\LAo=2.12\ee{36}\erg\second^{-1}$ , the proper temperature and luminosity."538 The hydrostatic structure is1.1-18.. te same as in Fietre 9..," The hydrostatic structure is, the same as in Figure \ref{fig:outer-boundary}."539 The top panel is for a conductivity se by electron-ion scattering: e bottom pajel is for a coiductivity set by electron-plOIIOI) scaleriig., The top panel is for a conductivity set by electron-ion scattering; the bottom panel is for a conductivity set by electron-phonon scattering.540 Solutious for several T. ‘e shown: he range of values are reduced from those used in Figue ϱ by ο”.ο.” hich is roiely how the temperaure at the base of a hydrogen/teliuu burniug shell scaes with ‘cretion rate (Schatzetal.1999J.," Solutions for several $T_\circ$ are shown; the range of values are reduced from those used in Figure \ref{fig:outer-boundary} by $(\dot{m}/\dot{m}_E)^{2/7}=0.01^{2/7}$, which is roughly how the temperature at the base of a hydrogen/helium burning shell scales with accretion rate \citep{schatz99}."541. Of course. the hydrogeu ane 1eliunm ignition ls unsable in an envelope this cold (seeBildstetr1995.andreferences tliereiu).. a so 74 is determinec by the compressi1 of matter lu tle allic»pliere aud by the flux flowiug o he top of the crust.," Of course, the hydrogen and helium ignition is unstable in an envelope this cold \citep[see][and references542therein]{bildsten98:_nuclear}, , and so $T_\circ$ is determined by the compression of matter in the atmosphere and by the flux flowing out the top of the crust."543 As T. is reduced. LO‘e alid more of the leal geleratec in the crust flows ottwards rather than into the core.," As $T_\circ$ is reduced, more and more of the heat generated in the crust flows outwards rather than into the core."544 As fouud by Zdunikeal.(1992).. all enhlaiced Core neutriuo eulssivity will drasticaly lower the crust uperature for leWw accrellol raen.," As found by \citet{zdunik92}, an enhanced core neutrino emissivity will drastically lower the crust temperature for low accretion rates."545" To illustrate how the €""ust temperature chalges with tlie temperaure in the hydrogen,/helium Durning regiO1 (T5). E com»ute the derivaive Τομ/αΓον where Terust is the temperature at the centroid of the heat-producing reglon. p0.17MeVfin..."," To illustrate how the crust temperature changes with the temperature in the hydrogen/helium burning region $T_\circ$ ), I compute the derivative $dT_\mathrm{crust}/dT_\circ$, where $T_\mathrm{crust}$ is the temperature at the centroid of the heat-producing region, $p=0.017\MeV\fermi^{-3}$."546 Figure 12. displays doa/dI5 as a function of 1. for five cli[Terent accretio rrates: La/LA=0.01 briangles)). 0.03 friangles)). 0.1 squares)). 0.3 squares)). aud 1.0 (asterisks)).," Figure \ref{fig:sensitive} displays $dT_\mathrm{crust}/dT_\circ$ as a function of $T_\circ$ for five different accretion rates: $L_A/\LAo = 0.01$ ), 0.03 ), 0.1 ), 0.3 ), and 1.0 )."547 Whenthe coucductivity is low (electron-ion scattering:penel)). Terust Is generally less seusitive to Z7; than when scattering sets the heat trausport panel)).," Whenthe conductivity is low (electron-ion scattering;), $T_\mathrm{crust}$ is generally less sensitive to $T_\circ$ than when electron-phonon scattering sets the heat transport )."548 The derivative (at a given accretiou rate), The derivative (at a given accretion rate)549"Starting with the initial temperature profile, we can understand the evolution of the cooling layer and the resulting lightcurve by noting that at a given depth, the thermal evolution occurs on the characteristic thermal timescale associated with that depth.","Starting with the initial temperature profile, we can understand the evolution of the cooling layer and the resulting lightcurve by noting that at a given depth, the thermal evolution occurs on the characteristic thermal timescale associated with that depth."550" This is illustrated in the middle panel of Figure 5,, which shows snapshots of the profile of the crust as it cools during quiescence."," This is illustrated in the middle panel of Figure \ref{f.T-tau}, which shows snapshots of the temperature profile of the crust as it cools during quiescence."551"temperature At a given time, the temperature profile has two parts: the inner layers have not yet started to cool and still have the temperature corresponding to the initial condition (the steady state profile during outburst); the outer layers have relaxed thermally and the temperature profile there corresponds to a constant outwards flux."," At a given time, the temperature profile has two parts: the inner layers have not yet started to cool and still have the temperature profile corresponding to the initial condition (the steady state profile during outburst); the outer layers have relaxed thermally and the temperature profile there corresponds to a constant outwards flux."552 The transition occurs at a depth where the thermal time at that depth is equal to the current time., The transition occurs at a depth where the thermal time at that depth is equal to the current time.553" In the bottom panel of Figure 5,, we show the thermal time as a function of depth, where we calculate the thermal time from the surface following (1969)., where p is the density, Cp the heat, and K the thermal conductivity."," In the bottom panel of Figure \ref{f.T-tau}, we show the thermal time as a function of depth, where we calculate the thermal time from the surface following , where $\rho$ is the density, $C_{P}$ the specific heat, and $K$ the thermal conductivity."554 In the top panel of specificFigure 5 we show the temperature profiles as a function of the thermal time., In the top panel of Figure \ref{f.T-tau} we show the temperature profiles as a function of the thermal time.555 This shows directly that the deviation of each of the dashed temperature away from the initial profile occurs at a depth profileswhere the thermal time is temperatureapproximately equal to the time since cooling began., This shows directly that the deviation of each of the dashed temperature profiles away from the initial temperature profile occurs at a depth where the thermal time is approximately equal to the time since cooling began.556 The temperature of the inner crust is also affected by conduction of heat into the core., The temperature of the inner crust is also affected by conduction of heat into the core.557 We show the timescale for thermal diffusion into the core in Figure 5 line))., We show the timescale for thermal diffusion into the core in Figure \ref{f.T-tau} ).558 The two thermal times intersect at a depth (P/g~10/6 gcm) where the thermal diffusion time is x400d., The two thermal times intersect at a depth $P/g\sim 10^{16}\nsp\columnunit$ ) where the thermal diffusion time is $\approx 400\nsp\unitday$.559 After this point the temperature in the inner crust drops markedly panel))., After this point the temperature in the inner crust drops markedly ).560 This understanding suggests a simple model of the lightcurve., This understanding suggests a simple model of the lightcurve.561 We start with the initial temperature profile set by the steady-state profile at the outburst accretion rate., We start with the initial temperature profile set by the steady-state profile at the outburst accretion rate.562" Then, for each time {, we locate the depth at which τ=1."," Then, for each time $t$, we locate the depth at which $\tau=t$."563 We then find the outwards flux in a constant flux solution that has a temperature equal to the initial temperature at the depth where f=r., We then find the outwards flux in a constant flux solution that has a temperature equal to the initial temperature at the depth where $t=\tau$.564 This value of flux is the flux emerging from the surface at time f., This value of flux is the flux emerging from the surface at time $t$.565" The dotted curve in Figure 2 shows a lightcurve calculated in this way, using the same parameters Qimp, Tp, and T; as the numerical model."," The dotted curve in Figure \ref{f.mxb1659-model} shows a lightcurve calculated in this way, using the same parameters $\Qimp$, $T_b$, and $T_c$ as the numerical model."566 The simple model shows excellent agreement with the numerical model., The simple model shows excellent agreement with the numerical model.567 The origin of the broken power law nature of the lightcurve lies in the change in slope of the thermal time with depth that occurs close to neutron drip (see the lower panel of Fig. 5;;, The origin of the broken power law nature of the lightcurve lies in the change in slope of the thermal time with depth that occurs close to neutron drip (see the lower panel of Fig. \ref{f.T-tau};568 neutron drip occurs at P/g~5x10?gcm?)., neutron drip occurs at $P/g\approx 5\times 10^{15}\ {\rm g\ cm^{-2}}$ ).569" The decrease in slope is primarily due to the suppression of C, in the inner crust, shown in Figure 6.."," The decrease in slope is primarily due to the suppression of $C_{p}$ in the inner crust, shown in Figure \ref{f.k-cp}."570" The ion contribution to the specific heat line)) decreases on going to higher densities roughly as (T/Opy, where the Debye temperature Op«O0,=(h/kg) the plasma of the ions. We[4xZ2e%non/(Amu)]"," The ion contribution to the specific heat ) decreases on going to higher densities roughly as $(T/\Theta_{D})^{3}$, where the Debye temperature $\Theta_{D} \propto \Theta_p=(\hbar/\kB)\left[4\pi Z^{2}e^{2}n_{\mathrm{ion}}/(A\mb)\right]^{1/2}$, the plasma temperature of the ions."571" assume that the neutrons in the temperatureinner crust are superfluid, in which case they have a negligible contribution to the heat capacity (Fig. 6,, line))."," We assume that the neutrons in the inner crust are superfluid, in which case they have a negligible contribution to the heat capacity (Fig. \ref{f.k-cp}, )."572" The thermal time also depends on the thermal conductivity, which changes from being set by phonon scattering in the outer crust to impurity scattering in the inner crust line))."," The thermal time also depends on the thermal conductivity, which changes from being set by phonon scattering in the outer crust to impurity scattering in the inner crust )."573" Electron-electron scattering, although included in our calculations, is not a significant component of the total thermal conductivity2007),, and we do not show it in Fig. 6.."," Electron-electron scattering, although included in our calculations, is not a significant component of the total thermal conductivity, and we do not show it in Fig. \ref{f.k-cp}."574" The slight step in the ion specific heat at P/gx10?gcm""? (Fig. 6,, panel))"," The slight step in the ion specific heat at $P/g \lesssim 10^{13}\nsp\columnunit$ (Fig. \ref{f.k-cp}, )"575 is caused by the liquid-solid transition in the crust., is caused by the liquid-solid transition in the crust.576 Our code does not follow the crystallization front and hence does not include the latent heat., Our code does not follow the crystallization front and hence does not include the latent heat.577" The depth where crystallization occurs is so shallow, however, that this omission does not appreciably affect the lightcurve, unlike the case for the cooling of white dwarf starstherein)."," The depth where crystallization occurs is so shallow, however, that this omission does not appreciably affect the lightcurve, unlike the case for the cooling of white dwarf stars."578. We note that observations taken shortly (<10d) after the end of the outburst could potentially detect the effect of the latent heat; this would provide an independent constraint on the temperature in the crust and a check on the value of the plasma parameter I at which the ions crystallize (see Appendix ??))., We note that observations taken shortly $\lesssim 10\nsp\unitday$ ) after the end of the outburst could potentially detect the effect of the latent heat; this would provide an independent constraint on the temperature in the crust and a check on the value of the plasma parameter $\Gamma$ at which the ions crystallize (see Appendix \ref{s.eos}) ).579" With some approximations, the same arguments allow us to make an analytic approximation to the lightcurve."," With some approximations, the same arguments allow us to make an analytic approximation to the lightcurve."580" The slope of the cooling curve can be written The first factor on the right hand side is the slope of the Τεῃ-- T relation, dInT3,/dInT~0.45—0.63 1))."," The slope of the cooling curve can be written The first factor on the right hand side is the slope of the $T_\mathrm{eff}$ $T$ relation, $\dif\ln\Teffinf/\dif\ln T\approx 0.45\textrm{--}0.63$ (Fig. \ref{f.teff-tb}) )."581 The second factor is the temperature gradient in the (Fig.initial model., The second factor is the temperature gradient in the initial model.582 The third factor is the dependence of thermal time with column depth., The third factor is the dependence of thermal time with column depth.583" We can obtain this analytically by noting that during the early part of the lightcurve, when the cooling wave is in the outer crust, we can approximatethe heat capacity as Cpx3kg/(Am,) the classical heat capacity of lattice, and use an approximate expression for the phonon aconductivity (see eq. [A3]]-[A4]])."," We can obtain this analytically by noting that during the early part of the lightcurve, when the cooling wave is in the outer crust, we can approximatethe heat capacity as $C_{P} \approx 3\kB/(A\mb)$ the classical heat capacity of a lattice, and use an approximate expression for the phonon conductivity (see eq. \ref{e.Wiedemann}] \ref{e.phonon-freq}] ])."584" Inserting these expressions into the expression for 7 (eq. [7]]),"," Inserting these expressions into the expression for $\tau$ (eq. \ref{e.tau}] ]),"585 we, we586used by the algorithm.,used by the algorithm.587 For this reason this result is not surprising. ancl the reconstructed correlation function is very questionable since it is based on the pixels which should have been omitted.," For this reason this result is not surprising, and the reconstructed correlation function is very questionable since it is based on the pixels which should have been omitted."588 To avoid the problem of. information transfer by smoothing the correlation function of the LLC (7vr) map is also investigated without additional smoothing., To avoid the problem of information transfer by smoothing the correlation function of the ILC (7yr) map is also investigated without additional smoothing.589 In figure 15. the corresponding correlation functions are plotted.," In figure \ref{Fig:correlation_function_ilc_KQ85_FWHM_000arcmin_nside_16}590 the corresponding correlation functions are plotted."591 The error (10)) is significantly larger now., The error \ref{Eq:error_C_theta_rec}) ) is significantly larger now.592 Without additional smoothing the dillerences between the correlation function of the reconstructed and of the full ILC (TNT) map are larger. but both agrec within the 26 οτο».," Without additional smoothing the differences between the correlation function of the reconstructed and of the full ILC (7yr) map are larger, but both agree within the $2\sigma$ errors."593 ‘This could ead to the conclusion that the reconstruction works without additional smoothing anc without a corresponding information transfer. but for 44=10.12 the errors are large compared. to the case with additional smoothing as it is shown in ligure 17..," This could lead to the conclusion that the reconstruction works without additional smoothing and without a corresponding information transfer, but for $l_{\hbox{\scriptsize max}}=10-12$ the errors are large compared to the case with additional smoothing as it is shown in figure \ref{Fig:correlation_function_ilc_KQ85_FWHM_600arcmin_nside_16}."594 For Aux15 the errors of the reconstructed correlation function are too large to allow any conclusion., For $l_{\hbox{\scriptsize max}}\gtrsim 15$ the errors of the reconstructed correlation function are too large to allow any conclusion.595 Due to these large errors the correlation function of the reconstructed LLC map also agrees on the same level with the correlation function obtained solely from the data outside the mask., Due to these large errors the correlation function of the reconstructed ILC map also agrees on the same level with the correlation function obtained solely from the data outside the mask.596 Thus. one cannot dilferentiate. between these (wo cases.," Thus, one cannot differentiate between these two cases."597 The reconstructed: correlation function shows sometimes a better agreement with the correlation function resulting from the masked ILC map and sometimes with the correlation function. of the full LLC map., The reconstructed correlation function shows sometimes a better agreement with the correlation function resulting from the masked ILC map and sometimes with the correlation function of the full ILC map.598 The quality of his agreement depends on y and A445., The quality of this agreement depends on $\vartheta$ and $l_{\hbox{\scriptsize max}}$.599 Fhus. the reconstruced correlation function favours neither the one of the maskec nor the one of the full ILC map.," Thus, the reconstructed correlation function favours neither the one of the masked nor the one of the full ILC map."600 Due to the large errors the reconstructed correlation function is uncertain by at least 100/77. and thus unsuited for the comparison with cosmological moclels., Due to the large errors the reconstructed correlation function is uncertain by at least $\mu\hbox{K}^2$ and thus unsuited for the comparison with cosmological models.601 The above discussion. puts forward arguments against he reconstruction method and favours methods which use only the data outside a given mask., The above discussion puts forward arguments against the reconstruction method and favours methods which use only the data outside a given mask.602 To provide a firm footing or the latter. the influence of the WOSS and ΙΟτὸ masks onto the ensemble average and the cosmic variance of the correlation function C'(9) is now investigated with respect o the CDM model.," To provide a firm footing for the latter, the influence of the KQ85 and KQ75 masks onto the ensemble average and the cosmic variance of the correlation function $C(\vartheta)$ is now investigated with respect to the $\Lambda$ CDM model."603 Both quantities are shown in figure 19 or an ensemble of 0000 CAIB simulations of the ΑςΔΙ model.," Both quantities are shown in figure \ref{Fig:correlation_function_100000lcdm_modelle_full_KQ85_Kq75_nside_128_s0.5}604 for an ensemble of 000 CMB simulations of the $\Lambda$ CDM model."605 Phe ensemble average and the standard. deviation is computed. from the correlation functions (9) obtained rom the data of full maps. outside the KQS5 mask and outside the Οτο mask.," The ensemble average and the standard deviation is computed from the correlation functions $C(\vartheta)$ obtained from the data of full maps, outside the KQ85 mask and outside the KQ75 mask."606 A resolution of Ας=128 and a mask threshold ον=0.5 is used., A resolution of $N_{\hbox{\scriptsize side}} = 128$ and a mask threshold $x_{\hbox{\scriptsize th}}=0.5$ is used.607 The ensemble averages are identical in all three cases., The ensemble averages are identical in all three cases.608 The standard deviation slightly increases with the size of the mask., The standard deviation slightly increases with the size of the mask.609 The smallest leo standard deviation is obtained by using no mask at all. he next larger deviation belongs to the KQS5 mask whereas he largest deviation is due to the larger WQ75 mask.," The smallest $\sigma$ standard deviation is obtained by using no mask at all, the next larger deviation belongs to the KQ85 mask whereas the largest deviation is due to the larger KQ75 mask."610 The increase of the standard. deviation. for the masked. data is. however. small compared to the uncertainty resulting rom the reconstruction method for the same mask.," The increase of the standard deviation for the masked data is, however, small compared to the uncertainty resulting from the reconstruction method for the same mask."611 This is à further argument for having more confidence in the correlation Function C'(7) computed [rom the data outside he mask than in the one obtained from a reconstructed Pull map., This is a further argument for having more confidence in the correlation function $C(\vartheta)$ computed from the data outside the mask than in the one obtained from a reconstructed full map.612 The main difference between the LLC correlation functions, The main difference between the ILC correlation functions61300J— |... a +h = ου,J = a_+ + b_- = < 0.614 In the case of a single lens. α=—20. b.=0. and |VJ|=4 on the critical curve (r= 1).," In the case of a single lens, $a_+ = -20$ , $b_-=0$, and $|\nabla J|=4$ on the critical curve $r=1$ )."615 Away from a cusp. ὁ./22044.," Away from a cusp, $\delta J \approx \delta J_1$ ."616 Near a cusp (b=0). 07 dominantly depends linearly on α-—dz amd equadratically on e=dz," Near a cusp $b=0$ ), $\delta J$ dominantly depends linearly on $u= dz_+$ and quadratically on $v = dz_-$."617" iJ =aut (Q +=) Jo? Therefore. (he critical curve (0.=0:J, 0) is parabolic near a cusp."," J = a u + (b_- + ) v^2 Therefore, the critical curve $\delta J =0; \ J_\circ = 0$ ) is parabolic near a cusp."618 u=-l— 2a{(h =)u2(24) Now we choose the cusp under consideration as the origin of the lens plane. and the eigendirection as the real axis so thal E—1(&ο=0).," u = - (b_- + ) v^2 Now we choose the cusp under consideration as the origin of the lens plane, and the eigendirection $E_+$ as the real axis so that $E_+ = 1 ~(\Leftrightarrow \varphi = 0)$."619 Then. Ka=1. and the lens equation (4)) reads as follows.," Then, $\bar\kappa_\circ = 1$, and the lens equation \ref{eqDLens}) ) reads as follows."620 The coellicients are almost real., The coefficients are almost real.621 In fact. we can ignore the imaginary component of ay. Slay)=—«a/12. when we consider only the lowest order terms.," In fact, we can ignore the imaginary component of $\alpha_3$, $\Im(\alpha_3) = - a_-/12$, when we consider only the lowest order terms."622 When there is a reflection svmmetry in (he svstem. ¢@—5.0 al the cusps on the svinnilry axis.," When there is a reflection symmetry in the system, $a_- = b_+ = 0$ at the cusps on the symmtry axis."623 That is (he case for the cusps on the lens axis of the binary lenses. as we can directly calculate from the binary equation (2)).," That is the case for the cusps on the lens axis of the binary lenses, as we can directly calculate from the binary equation \ref{eqLeq}) )."624 Without loss of generality. the real axis has been chosen to be the lens axis. ancl c.c stands for complex conjugate as usual.," Without loss of generality, the real axis has been chosen to be the lens axis, and $c.c$ stands for complex conjugate as usual."625 Then. b =0 (ο E ec) Ld teappaelleappali com deappaté cse(27)," Then, b_+ = _+ (- E_- + c.c ) = - E_- _+ ) + c.c = - i + c.c = 0."626 The last equality holds because 5075=OF is real on the real axis., The last equality holds because $\bar\kappa \partial^2\kappa = \partial^2\kappa$ is real on the real axis.627 n= |l= 1(28)TLhus. thecusps on the lens axis of the binary lenses have strong reflection svmmetries.," = _j;= 1 Thus, thecusps on the lens axis of the binary lenses have strong reflection symmetries."628Similar to HD32778.. the confidence limits in mnass-separation space for HD91204 are poorly constrained (Fig.,"Similar to HD32778, the confidence limits in mass-separation space for HD91204 are poorly constrained (Fig."629 10 middle)., \ref{contrasts} middle).630 However. since HD91204 has a larger database of velocities than HD32778. we can say to a confidence level that the companion to this star is not a close by (<0.15”) sub- or stellar secondary.," However, since HD91204 has a larger database of velocities than HD32778, we can say to a confidence level that the companion to this star is not a close by $\le$ $''$ ) sub-stellar or stellar secondary."631 The middle panel in Fig., The middle panel in Fig.632 11. shows the mass-separation parameter space for this star. reaching down onto the stars surface.," \ref{detects} shows the mass-separation parameter space for this star, reaching down onto the stars surface."633 Clearly very close-by companions can be ruled out to high levels of confidence due to the larger number of data points and the faet that this radial-velocity curve is a liner., Clearly very close-by companions can be ruled out to high levels of confidence due to the larger number of data points and the fact that this radial-velocity curve is a liner.634 This ts further highlighted by the large light region shown in the gray scale and a lack of any large contrast gradient., This is further highlighted by the large light region shown in the gray scale and a lack of any large contrast gradient.635" Objects with separations below 0.06” and masses above around 30M, can be ruled out to ~90-95% confidence and moving out to separations of 0.08"" we can still rule out objects down to around the planetary mass limit at the level of cofidence.", Objects with separations below $''$ and masses above around $_{\rm{J}}$ can be ruled out to $\sim$ confidence and moving out to separations of $''$ we can still rule out objects down to around the planetary mass limit at the level of confidence.636 Therefore. we can say that the companion to this star likely has a fairly large separation and is a faint substellar companion or. as for almost all of the imaged objects. the companion has a longer orbital period. but the melination of the system was such that when we were observing the companiot it was hidden behind the star at on-sky angular separations below 0.17.," Therefore, we can say that the companion to this star likely has a fairly large separation and is a faint substellar companion or, as for almost all of the imaged objects, the companion has a longer orbital period, but the inclination of the system was such that when we were observing the companion it was hidden behind the star at on-sky angular separations below $''$."637 In comparison to these other two stars. HD145825 has enough data points and exhibits enough curvature in. the timeseries that fairly high levels of confidence from the velocities overlap with the confidence limits from the imaging work.," In comparison to these other two stars, HD145825 has enough data points and exhibits enough curvature in the timeseries that fairly high levels of confidence from the velocities overlap with the confidence limits from the imaging work."638 The bottom panel in Fig., The bottom panel in Fig.639 10. shows that below the SDI curve we still have over confidence in ruling out close by (x0.17) objects down to low brown dwarf masses., \ref{contrasts} shows that below the SDI curve we still have over confidence in ruling out close by $\le$ $''$ ) objects down to low brown dwarf masses.640 In addition. the (27) confidence limit can rule out a lot of possible brown dwarf/stellar companions below the 0.1” angular separation limit of the SDI technique (Fig.," In addition, the $\sigma$ ) confidence limit can rule out a lot of possible brown dwarf/stellar companions below the $''$ angular separation limit of the SDI technique (Fig."641 11. bottom)., \ref{detects} bottom).642 The gray scale reveals more structure than HD32778 and HD91204 due to the significant curvature in the velocities., The gray scale reveals more structure than HD32778 and HD91204 due to the significant curvature in the velocities.643" Particularly we can see that the region around 0.2” separation is less constrained than inside and outside this separation and due to the indication of secondary curvature in the velocities. we arrive at fairly high confidence levels beyond 0.3” separation,"," Particularly we can see that the region around $''$ separation is less constrained than inside and outside this separation and due to the indication of secondary curvature in the velocities, we arrive at fairly high confidence levels beyond $''$ separation."644 From these combined constraints we can rule out to really high levels of confidence any brown dwarf/stellar companions with small separations (short period orbits)., From these combined constraints we can rule out to really high levels of confidence any brown dwarf/stellar companions with small separations (short period orbits).645" Also. at the lo level we can say that there are no objects at all below a separation of around 0.34” with masses above 40M, anc also no companions down into the giant exoplanet regime within 0.20""."," Also, at the $\sigma$ level we can say that there are no objects at all below a separation of around $''$ with masses above $_{\rm{J}}$ and also no companions down into the giant exoplanet regime within $''$."646 These combined data sets argue for the companion to HD145825 to be an extremely faint sub-stellar companion with a moderate separatio, These combined data sets argue for the companion to HD145825 to be an extremely faint sub-stellar companion with a moderate separation.647 Out of the five stars that we searched around. two possible detections were made around the stars HD25874 and HD120780.," Out of the five stars that we searched around, two possible detections were made around the stars HD25874 and HD120780."648 Both of these candidates fulfilled the requirements to be considered as bona fide candidates as they were bright sources. that had counterparts at 33° in the rolled images.," Both of these candidates fulfilled the requirements to be considered as bona fide candidates as they were bright sources, that had counterparts at $^{\circ}$ in the rolled images."649 However. after careful analysis we believe these to be artifacts of the reduction procedure and not true companion objects.," However, after careful analysis we believe these to be artifacts of the reduction procedure and not true companion objects."650 Both will be discussed here., Both will be discussed here.651 Figure 12. shows the 33° roll angle of the camera and how it projects along the image through the T3 filter (FI1CI.5754mo- l.6254um)) for HD25874., Figure \ref{annotate_hd25874} shows the $^{\circ}$ roll angle of the camera and how it projects along the image through the T3 filter $\mu$ $\mu$ m)) for HD25874.652 The detections are found at the ends of the second are along the projection with a separation from the central pixel of 0.29+0.01 and a position angle of 240°., The detections are found at the ends of the second arc along the projection with a separation from the central pixel of $\pm$ $''$ and a position angle of $^{\circ}$.653 This enhanced image highlights more of the speckles across the images in both negative and positive formats e.g. bright spot to the extreme left middle of the left panel and its counterpart in the corresponding position of the right panel., This enhanced image highlights more of the speckles across the images in both negative and positive formats e.g. bright spot to the extreme left middle of the left panel and its counterpart in the corresponding position of the right panel.654 Along the projected angle there is also another bright and dark par that could be separated by the roll angle and these are found at the ends of the inner arc., Along the projected angle there is also another bright and dark pair that could be separated by the roll angle and these are found at the ends of the inner arc.655 As these are so close and connected to the central star we believe these to be an artifact of the PSF subtraction. however worryingly since they are found projected along the same axis as the potential candidate detection they may signify that the detection is an artifact as well e.g. uncorrected residual trefoil in the image.," As these are so close and connected to the central star we believe these to be an artifact of the PSF subtraction, however worryingly since they are found projected along the same axis as the potential candidate detection they may signify that the detection is an artifact as well e.g. uncorrected residual trefoil in the image."656 As mentioned. Fig.," As mentioned, Fig."657 13 (upper) shows the contrast limits that were determined for HD25874. highlighting both the conventional AO and the SDI reduced limits.," \ref{hd25874_contrast} (upper) shows the contrast limits that were determined for HD25874, highlighting both the conventional AO and the SDI reduced limits."658" For companion candidates such as the one here it is clear that the SDI reduction performs significantly better than conventional AO e.g. gain of ~2.5 magnitudes at 0.2"".", For companion candidates such as the one here it is clear that the SDI reduction performs significantly better than conventional AO e.g. gain of $\sim$ 2.5 magnitudes at $''$.659 The confidence limits m this figure show a lot of structure at separations reaching well into the imaging phase space., The confidence limits in this figure show a lot of structure at separations reaching well into the imaging phase space.660 This is due to the large baseline (>4 yrs) of observations. even though they describe a liner system.," This is due to the large baseline $>$ 4 yrs) of observations, even though they describe a liner system."661" confidence limits are seen to rule out objects down into the planetary mass regime with angular separations below 0.14"". depending on where we place the boundary between exoplanets and brown dwarfs. and we can rule out such objects up to separations of almost 0.18” at the confidence limit."," confidence limits are seen to rule out objects down into the planetary mass regime with angular separations below $''$, depending on where we place the boundary between exoplanets and brown dwarfs, and we can rule out such objects up to separations of almost $''$ at the confidence limit."662 The lower panel better highlights the structure in detectability for this star and shows clearly that we have high levels of confidence out to the timeseries of this data set., The lower panel better highlights the structure in detectability for this star and shows clearly that we have high levels of confidence out to the timeseries of this data set.663" The gray scale shows similar structure to that of HD145825 with a large inner region that is highly constrained. a dark unconstrained region around 0.2” separation from the star and then a growing lighter constrained region out to separations of 0.3""."," The gray scale shows similar structure to that of HD145825 with a large inner region that is highly constrained, a dark unconstrained region around $''$ separation from the star and then a growing lighter constrained region out to separations of $''$."664 This time the constrained region at larger separations arises not from any curvature in the velocities but due to the overall span of velocity across the data set. showing that it is unlikely that lower mass companions at these orbital separations could give rise to this data set.," This time the constrained region at larger separations arises not from any curvature in the velocities but due to the overall span of velocity across the data set, showing that it is unlikely that lower mass companions at these orbital separations could give rise to this data set."665 By combining the imaging data with the radial-velocity data. we can say that with confidence we can rule out almost all companions to this star with separations below 0.17” (4.40 AU).," By combining the imaging data with the radial-velocity data, we can say that with confidence we can rule out almost all companions to this star with separations below $''$ (4.40 AU)."666 Again we conclude that the companion to this star is probably a widely separated. low mass (<70M)) and therefore really faint sub-stellar object.," Again we conclude that the companion to this star is probably a widely separated, low mass $<$ $_{\rm{J}}$ ) and therefore really faint sub-stellar object."667 If such is the case then there is a fairly high possibility here that the object is a brown dwarf located in the brown dwarf desert (?))., If such is the case then there is a fairly high possibility here that the object is a brown dwarf located in the brown dwarf desert \citealp{grether06}) ).668 Note that there were no other objects detected around this star out to orbital distances of ~52 AU., Note that there were no other objects detected around this star out to orbital distances of $\sim$ 52 AU.669same wavelength intervals.,same wavelength intervals.670 The masks available in the HARPS DRS pipeline are proprietary and not available outside the DRS. so they can only be used for the reduction of HARPS spectra.," The masks available in the HARPS DRS pipeline are proprietary and not available outside the DRS, so they can only be used for the reduction of HARPS spectra."671 Hence. for these calculations. we decided to create new masks using line lists for the spectral regions under study.," Hence, for these calculations, we decided to create new masks using line lists for the spectral regions under study."672" For the sake of simplicity. we used the ""extract stellar function from to retrieve a list of lines with estimated central depths expressed as a fraction of continuum flux for two generic solar-metallicity stars belonging to the two spectral types."," For the sake of simplicity, we used the “extract stellar” function from to retrieve a list of lines with estimated central depths expressed as a fraction of continuum flux for two generic solar-metallicity stars belonging to the two spectral types."673 We constructed the masks by simply overlapping a series of impulse functions centered at the wavelength of each spectral line and with amplitude proportional to the spectral line’s depth., We constructed the masks by simply overlapping a series of impulse functions centered at the wavelength of each spectral line and with amplitude proportional to the spectral line's depth.674 We were then able to cross-correlate both our thetic and our observed spectra with the same masks., We were then able to cross-correlate both our synthetic and our observed spectra with the same masks.675 The Cross-correlation was done using [DL’s function., The cross-correlation was done using 's function.676 ally. we extracted the bisectors from the resultant CCFs of thetic and observed spectra and compared them with one other.," Finally, we extracted the bisectors from the resultant CCFs of synthetic and observed spectra and compared them with one another."677 Fig., Fig.678 17. shows the CCF bisectors extracted from. the sythetic (left panel) and observed (right panel) spectra in the 6215-6275 range., \ref{fig:compbis_6215_6275_G8} shows the CCF bisectors extracted from the synthetic (left panel) and observed (right panel) spectra in the $6215$ $6275$ range.679" The CCFs were computed using the ""(Qn ""mask. that is the more closely corresponding to the Sun's spectral type."," The CCFs were computed using the “G” mask, that is the more closely corresponding to the Sun's spectral type."680 The agreement between the CCF bisectors from synthetic and observed spectra is very good: the curvature and asymmetry of the observed bisector are well reproduced by the theoretical caleulations., The agreement between the CCF bisectors from synthetic and observed spectra is very good: the curvature and asymmetry of the observed bisector are well reproduced by the theoretical calculations.681 Fig., Fig.682" 18. shows the CCF bisectors from the synthetic and observed spectra for the same wavelength interval computed using the ""K"" mask instead.", \ref{fig:compbis_6215_6275_K9} shows the CCF bisectors from the synthetic and observed spectra for the same wavelength interval computed using the “K” mask instead.683 While the curvature of the CCF bisector is more pronounced in the case of the synthetic spectrum. the overall agreement with the observed case is still good.," While the curvature of the CCF bisector is more pronounced in the case of the synthetic spectrum, the overall agreement with the observed case is still good."684 Small differences of these kind are acceptable considering. e.g.. that lines may be missing from the list used for the synthetic spectrum calculations and that elemental abundances were not adjusted to reproduce all line strengths.," Small differences of these kind are acceptable considering, e.g., that lines may be missing from the list used for the synthetic spectrum calculations and that elemental abundances were not adjusted to reproduce all line strengths."685" The correspondingCCF bisectors for the 5150—5200 interval computed for the synthetic and observed spectra with the ""G and ""K masks are shown in Fig.", The correspondingCCF bisectors for the $5150-5200$ interval computed for the synthetic and observed spectra with the “G” and “K” masks are shown in Fig.686 19 and 20.. respectively.," \ref{fig:compbis_5150_5200_G8_mgincluded} and \ref{fig:compbis_5150_5200_K9_mgincluded}, respectively."687 This region is characterized by the presence of one moderately strong and two strong lines at 5183. 5172. and 5167 which carry a significant weight in determining the overall shape of CCF bisector in this region.," This region is characterized by the presence of one moderately strong and two strong lines at $5183$, $5172$, and $5167$ which carry a significant weight in determining the overall shape of CCF bisector in this region."688 The agreement between CCF bisectors derived from synthetic and observed spectra is actually excellent for this region. implying that the modelling of these strong lines in our theoretical calculations is robust and satisfactory.," The agreement between CCF bisectors derived from synthetic and observed spectra is actually excellent for this region, implying that the modelling of these strong lines in our theoretical calculations is robust and satisfactory."689 We have shown that the well known CCF bisector parameters BIS. voor. and cp correlate well with logg and e Των.," We have shown that the well known CCF bisector parameters BIS, $v_\mathrm{bot}$, and $c_b$ correlate well with $\log g$ and $T_\mathrm{eff}$ ."690 We have constructed à new CCF bisector measure. the CBS. based," We have constructed a new CCF bisector measure, the CBS, based"691detector. aud moreover to the oft-axis position of the source in the FOV.,"detector, and moreover to the off-axis position of the source in the FOV."692 Iu contrast. the more detailed IMRT image reveals a number of X-ray sources clistributed over he ealactic disk (Fie. D).," In contrast, the more detailed HRI image reveals a number of X-ray sources distributed over the galactic disk (Fig. \ref{hrioveropt}) )."693 Iun comparison to the utmibered sources in Fie., In comparison to the numbered sources in Fig.694 1 he closer view allows to distinguish iuore details., \ref{hrifov} the closer view allows to distinguish more details.695 For example. source no.," For example, source no."696 9 in Fie., 9 in Fig.697 1 splits 1ito three ταν 4nots (labeled Aο in Fie. 3)., \ref{hrifov} splits into three X-ray spots (labeled A–C in Fig. \ref{hrisrcareas}) ).698 T10 lost MLULOUS source Ciucides with the center of NCGC (303 andl dominates ji the soft N-ravs., The most luminous source coincides with the center of NGC 4303 and dominates in the soft X-rays.699 The count rates al fluxes derived fco sources from the TRI are isted in Table Ll..., The count rates and fluxes derived for sources from the HRI are listed in Table \ref{tabhrisources}.700 The corresponding areas are plotted in Fig. ?)3, The corresponding areas are plotted in Fig. \ref{hrisrcareas}.701 «To determine the fluxes we used the euergv couversio1 factor (ECF) from tιο ROSAT doa1nenutation., To determine the fluxes we used the energy conversion factor (ECF) from the ROSAT documentation.702" The EXC""F determines the ratio betwee1 COL rates and unabsorbed source fux in the ROSAT baud OY giveu spectral pariuneters.", The ECF determines the ratio between count rates and unabsorbed source flux in the ROSAT band for given spectral parameters.703 For the disk sources AF we asse a 0.3 keV Riwvinond-Suith model (Baviuonud Suith 1977)) with an absorption column density of a7., For the disk sources A–F we assume a 0.3 keV Raymond-Smith model (Raymond Smith \cite{ray77}) ) with an absorption column density of $^{-2}$.704 For the nucleus a power law with P=2.6 iu a coli1 deusitv ofDl 22? (see Sect., For the nucleus a power law with $\Gamma$ =2.6 and a column density of $^{-2}$ (see Sect.705] 3.2.Qa and Tab: e5)) is applied as spectra model., \ref{specfit} and Table \ref{fittab}) ) is applied as spectral model.706 The contours of sources D. C. D. and F i1 Fie.," The contours of sources B, C, D, and F in Fig."707 3 are all located within the optical arii strucnre and coincide with bright Πα eiuission regions within the spiral armis (Fie. 1)., \ref{hrisrcareas} are all located within the optical arm structure and coincide with bright $\alpha$ emission regions within the spiral arms (Fig. \ref{hrioveropt}) ).708 In addition. source E is emibedded in the faint outer part of the soutliwestern spiral arm.," In addition, source E is embedded in the faint outer part of the southwestern spiral arm."709 \IR92 distinguished 79, \cite{mar92} distinguished 79710could still give Similarly. for the 55 MlIS line to be mased we require the corresponding level populations be inverted: which implies Condition is satisfied if the populations in the levels corresponding to the 1667. MlIz ancl 1720 MlIz lines are inverted while those in the levels corresponding to the 1612 MlIz and 1665 MlIS lines are not.,"could still give Similarly, for the 55 MHz line to be mased we require the corresponding level populations be inverted: which implies Condition is satisfied if the populations in the levels corresponding to the 1667 MHz and 1720 MHz lines are inverted while those in the levels corresponding to the 1612 MHz and 1665 MHz lines are not."711 Observationalv if the 1667 AMllIz and 1720 Mllz lines are miased. while the 1612 MllIz and 1665 MllIz lines are not. we could expect the 55 Mllz line levels to be inverted.," Observationaly if the 1667 MHz and 1720 MHz lines are mased, while the 1612 MHz and 1665 MHz lines are not, we could expect the 55 MHz line levels to be inverted."712 1n summary. a region where the 1720 MlIé line is mased. but the 1612 MlIz line is not. would be a promising region to look for mased emission from the 53/55 MlIS lines.," In summary, a region where the 1720 MHz line is mased, but the 1612 MHz line is not, would be a promising region to look for mased emission from the 53/55 MHz lines."713 Which of these is likely to be mased depends on whether the 1665 ΔΗΙ or 1667 Mllz line is mased., Which of these is likely to be mased depends on whether the 1665 MHz or 1667 MHz line is mased.714 Lt is interesting to note in this context that there are regions in our (Clurner1979) and in external galaxies(vanLangeveldectal.1995:Ixanekar.Chengalur&Chosh2004) where the satellite lines are conjugate. viz.," It is interesting to note in this context that there are regions in our \citep{turner}715 and in external \citep*{langevelde95,chengkan} where the satellite lines are conjugate, viz."716 where their profiles are. mirror images of one another. i.e. when one is in emission the other is in absorption. and the sum of the two profiles is consistent with noise.," where their profiles are mirror images of one another, i.e. when one is in emission the other is in absorption, and the sum of the two profiles is consistent with noise."717 Regions such as these are promising ones to search for the 53 MlIZ and 55 MIEZz OL lines., Regions such as these are promising ones to search for the 53 MHz and 55 MHz OH lines.718 H£ the hvperfine OLL 53 MllIz or 55 MlIz lines are strongly amplified. then the lines may be detectable.," If the hyperfine OH 53 MHz or 55 MHz lines are strongly amplified, then the lines may be detectable."719 Llowever. the amplification factor is a matter of speculation.," However, the amplification factor is a matter of speculation."720 Menonctal.(2005). attempted to detect the 53 MlI line. but could only place an upper limit to the amplification factor.," \citet{roshi}721 attempted to detect the 53 MHz line, but could only place an upper limit to the amplification factor."722" bor our particular observations. we have chosen the target region. Ci84.3|0.1 (a(2000)=is""59""06.75: o(2000)=LOI24 397.40) where the 1720 MIIz line is masec. while the 1612 Alllz line is in absorption."," For our particular observations, we have chosen the target region G34.3+0.1 $\alpha(2000) = 18^{h}\ 59^{m}\ 06^{s}.75$; $\delta(2000) = 723+01\degr\ 24\arcmin\ 39\arcsec.40$ ) where the 1720 MHz line is mased, while the 1612 MHz line is in absorption."724 Phe main lines are both seen in emission. although it is not clear if they are mased or not.," The main lines are both seen in emission, although it is not clear if they are mased or not."725 Phe lines all occur within the LSR. range of 56-58 kin *(Purner1979)..., The lines all occur within the LSR range of 56-58 km $^{-1}$ \citep{turner}.726 Lhe supernova remnant. ΧΑΕΕ is only 48? away [rom (54.90.1 and lies well within the 107 GMACE primary beam., The supernova remnant W44 is only 48' away from G34.3+0.1 and lies well within the $\degr$ GMRT primary beam.727 In this region the 1720 MlIZ line is mased. while the 1612 MIIz line is seen in absorption.," In this region the 1720 MHz line is mased, while the 1612 MHz line is seen in absorption."728 The main lines are also seen in absorption over a velocity range of 10 km (προς1979)..., The main lines are also seen in absorption over a velocity range of 10 km $^{-1}$ \citep{turner}.729 These lines occur over the velocity range 43-46 km +., These lines occur over the velocity range 43-46 km $^{-1}$.730 Thus both G34.3|0.1 and. W44 could eive rise to mased 53/55 MIITz lines., Thus both G34.3+0.1 and W44 could give rise to mased 53/55 MHz lines.731 Strictly speaking. the conditions described above. viz.," Strictly speaking, the conditions described above, viz."732 that the 1720 MlIz line is mased but the 1612 Mllz line is not etc., that the 1720 MHz line is mased but the 1612 MHz line is not etc.733 should be satisfied along the same line of sight inorder for the 55/53 MlIZ lines to be mased., should be satisfied along the same line of sight inorder for the 55/53 MHz lines to be mased.734 VLBI observations show that the OLL maser emission generally. comes from extremely compact (~ LOO mas) hot spots(Llolfmanetal., VLBI observations show that the OH maser emission generally comes from extremely compact $\sim$ 100 mas) hot \citep{hoffman}.7352003).. It is rare to have VLBI observations of all the four OLL 15 em transitions: hence it is dillicult at the current time to unambiguously identify a, It is rare to have VLBI observations of all the four OH 18 cm transitions: hence it is difficult at the current time to unambiguously identify a736Disks where the angular momentum is transported outwards (&« 0) tend to develop a warmer core. while the opposite trend «scours for disks where the aneular 1noiucntuni ds CALTIC( inwards (£2 0).,"Disks where the angular momentum is transported outwards $\xi<0$ ) tend to develop a warmer core, while the opposite trend occurs for disks where the angular momentum is carried inwards $\xi>0$ )."737 This is shown in Fig., This is shown in Fig.738 2 (Fig., \ref{fig:termica} (Fig.739 2 aud the following Fig. 3..," \ref{fig:termica} and the following Fig. \ref{fig:massa},"740 Fie. LL.," Fig. \ref{fig:epsilon},"741 aud Fig., and Fig.742 5 are shown in ogarithinic scale to better bring out the behavior in the 1mer parts of the disk)., \ref{fig:spessore} are shown in logarithmic scale to better bring out the behavior in the inner parts of the disk).743 Note that in the case of mnward augular monieutuu fiux ($>0) the effective thermal speed need not vanish at the imuer edec of the disk (as it does in our models) where à boundary laver is expected to be generated (see discussion at the cucl of Section 2.3))., Note that in the case of inward angular momentum flux $\xi>0$ ) the effective thermal speed need not vanish at the inner edge of the disk (as it does in our models) where a boundary layer is expected to be generated (see discussion at the end of Section \ref{chiboundary}) ).744 There are several quantities directly related to the disk density distribution iu the disk that allow us to characterize the role of the disk selt-eravity., There are several quantities directly related to the disk density distribution in the disk that allow us to characterize the role of the disk self-gravity.745 The most natural quantity to consider is the ratio of the mass of the disk to that of the ceutral object., The most natural quantity to consider is the ratio of the mass of the disk to that of the central object.746 Obviously. for our non-truucated models this quantity is nmeanineful onlv when referred to a given radius.," Obviously, for our non-truncated models this quantity is meaningful only when referred to a given radius."747 Fie., Fig.748 5 shows how rapidly iun radius the svstem becomes doiiumnated by the mass of the disk.," \ref{fig:massa}749 shows how rapidly in radius the system becomes dominated by the mass of the disk."750" Note that. iu any case. Miia)(AL, »0forr»0."," Note that, in any case, $M_{disk}(r)/M_{\star}\rightarrow 0$ for $r\rightarrow 0$."751 Iun galactic dywnuanüces tie local disk sclferavity is usually micasured in. terms of. the parameter e=gzGoτα2 rk., In galactic dynamics the local disk self-gravity is usually measured in terms of the parameter $\epsilon=\pi G\sigma/r\kappa^2$ .752 The fully sclferaviating selt-sinilar disk (with flat rotation curve) is cliaracterizec by e=1/1., The fully self-gravitating self-similar disk (with flat rotation curve) is characterized by $\epsilon=1/4$.753 The profile of this parameter (sec| Fie. 0) , The profile of this parameter (see Fig. \ref{fig:epsilon}) )754confirms that indeed. close to the ceuter. the influence of he central mass becomes stronger and strouger.," confirms that indeed, close to the center, the influence of the central mass becomes stronger and stronger."755" Caven the behavior of the xofiles AvanifA, and e(r). one nuelt conclude that the innermost disk should be treated as a standard EKepkYan accretion disk."," Given the behavior of the profiles $M_{disk}(r)/M_{\star}$ and $\epsilon(r)$, one might conclude that the innermost disk should be treated as a standard Keplerian accretion disk."756 This couclusion is contradicted bv t1e following arguineut., This conclusion is contradicted by the following argument.757 Insetting up the equatious of otr models.we have taken," Insetting up the equations of our models,we have taken"758In this note we report resulis of our investigation of (he limitations of using SDSS photometry for bright stars. and give a prescription lor setting zero points in CCD images taken through.CBVRI filters.,"In this note we report results of our investigation of the limitations of using SDSS photometry for bright stars, and give a prescription for setting zero points in CCD images taken through filters."759 We obtainedwgriz magnitudes [rom SDSS data release (DR5) for the Landolt(1992). standard stars in SDSS fields.," We obtained magnitudes from SDSS data release (DR5) \citep{abazajian05} for the \cite{landolt92}760 standard stars in SDSS fields."761 We first removed very blue and red stars outside the ranges 0.08«(r—ij)0.5 and 0.2<(ο—r)«L4., We first removed very blue and red stars outside the ranges $0.08 < (r-i) < 0.5$ and $ 0.2 < (g-r) < 1.4$ .762 We then plotted the (r—£P) vs. (g—r) color-color diagram and removed oullving points more than 2.5 stancarel deviations from the linear least squares fil., We then plotted the $(r-i)$ vs. $(g-r)$ color-color diagram and removed outlying points more than 2.5 standard deviations from the linear least squares fit.763 We derived transformation equations only [or stars with r2Id., We derived transformation equations only for stars with $r > 14$.764 A few points lving more than 2.5 standard. deviations away [rom the least-squares fils were removed., A few points lying more than 2.5 standard deviations away from the least-squares fits were removed.765 We obtained the following Gransformations: As is well known. tranformations to C are particularly problematic.," We obtained the following transformations: As is well known, tranformations to $U$ are particularly problematic."766 Since our aim is only lo give a prescription for selling CDVRI zero points rather than (to obtain transformations valid for inclividual stars for astrophivsical purposes. we determined (he transformation Lor the U filter as follows.," Since our aim is only to give a prescription for setting $UBVRI$ zero points rather than to obtain transformations valid for individual stars for astrophysical purposes, we determined the transformation for the $U$ filter as follows."767 First we removed all stars thal were more than 2.5 standard deviations from a linear fit in f[our-dimensional (u—49).(g—r).(r—i).(7-2) color space.," First we removed all stars that were more than 2.5 standard deviations from a linear fit in four-dimensional $(u-g), (g-r), (r-i), (i-z)$ color space."768 For the remaining stars with no saturation warning flags. we restricted ourselves to stars wilh 1«(u—9g)<2 and u>16.," For the remaining stars with no saturation warning flags, we restricted ourselves to stars with $1 < (u-g) < 2$ and $u769> 16$."770 For these stars we found no statistically significant dependence on the (4—g) color., For these stars we found no statistically significant dependence on the $(u-g)$ color.771 This is not surprising since. of the SDSS ugriz fillers. the passhand of the« filter agrees most closely to the Johnson-Cousins passbands.," This is not surprising since, of the SDSS $ugriz$ filters, the passband of the$u$ filter agrees most closely to the Johnson-Cousins passbands."772 The transformation for C is thus, The transformation for $U$ is thus773"Notice-. that there is. no power-law growth in"" the perturbation. energy forJ Ri.""E1/17"" consistent with the classical Richardson criterion (??)).",Notice that there is no power-law growth in the perturbation energy for ${\rm{Ri}} > 1/4$ consistent with the classical Richardson criterion \ref{RICH}) ).774 Iu our analysis the euergy decays witli time for 2a—1<0. or Ri>3/16.," In our analysis the energy decays with time for $2\alpha-1<0$, or ${\rm{Ri}} > 3/16$."775 Thus the energy of an initial isotropic set of incompressive perturbations iu a radially-stratified shearing sheet-inodel grows asymptotically (for Ri<3/16). just like the compressive sliwaves aud the incompressive sliwaves in au uustratified shearing sheet. for which the euergy is constant in time.," Thus the energy of an initial isotropic set of incompressive perturbations in a radially-stratified shearing sheet-model grows asymptotically (for ${\rm{Ri}} < 3/16$ ), just like the compressive shwaves and the incompressive shwaves in an unstratified shearing sheet, for which the energy is constant in time."776 The growth of au eusemble of incompressive sliwaves in a stratified disk is πο toa or convective type instability., The growth of an ensemble of incompressive shwaves in a stratified disk is due to a Rayleigh-Taylor or convective type instability.777 There is asyinptotie growth for 0<Bi«3/16. aud convective instability requires Ri«0.," There is asymptotic growth for $0 < {\rm{Ri}} < 3/16$, and convective instability requires ${\rm{Ri}} < 0$."778" One cau also see this by examining the asyinptotic euergy [or small values of Ηλ, such as would be expected for a Ixeplerian disk with modest radial gradients: ο 1)) Ri (EQ = 0))."," One can also see this by examining the asymptotic energy for small values of $|{\rm{Ri}}|$, such as would be expected for a Keplerian disk with modest radial gradients: E_i t 1) + E_i(t = 0)."779.(96) Evideutly for small values of Ri the near-linear growth iu time of the euergy is indepencent of the sien of Ri and therefore V7.7! We have studied the uouaxisyiuuetric linear tleory of a thin. radially-stratified disk.," Evidently for small values of Ri the near-linear growth in time of the energy is independent of the sign of Ri and therefore $N_x^2$ We have studied the nonaxisymmetric linear theory of a thin, radially-stratified disk."780" Our findings are: (1) incompressive. short-wavelenetl peru‘batious in the unstratilied shea‘jue sheet exhibit trausieut. growth auc asyiuptotie decay. bu ile enerey of an eusemble of suc1 cslwaves is constant with time (consistent. with Afshordi.Àdopadhlyay.&Narayan200 1)): (ii) short-waveleneth compressive sliwaves grow. asviuptotically in the uustratified shearing sheet. as cloes the energy of au ensemble of such shiwaves. which i ie abseuce of any otler dissipative effects (e.g..ζ radiative camping) will result in a compressive sliwave steepening into a trail of weak shocks: (ii) incompressive sliwaves in the stratiliec slearing sheet have deusity and azimutal velocity perturbations X. de,~1FH (for [Ri]<| (iv) incompressive slaves iu the stratified shearing sheet are associated. with au augular momenum flux proportional to —&,/Kky. leadim sliwaves therefore have positive angular ruomentum flux aud trailing sliwaves Lave 1egalive angular momeutum flux: (v) the euergy of au eusemble of iucompressive sliwaves in the str'atified shearim sheet behaves asymptotically as /+HH [or |Ri|<Jn1,"," Our findings are: (i) incompressive, short-wavelength perturbations in the unstratified shearing sheet exhibit transient growth and asymptotic decay, but the energy of an ensemble of such shwaves is constant with time (consistent with \citealt781{amn04}) ); (ii) short-wavelength compressive shwaves grow asymptotically in the unstratified shearing sheet, as does the energy of an ensemble of such shwaves, which in the absence of any other dissipative effects (e.g., radiative damping) will result in a compressive shwave steepening into a train of weak shocks; (iii) incompressive shwaves in the stratified shearing sheet have density and azimuthal velocity perturbations $\delta \Sigma$, $\delta v_y \sim t^{-{\rm Ri}}$ (for $|{\rm Ri}| \ll 1$ ); (iv) incompressive shwaves in the stratified shearing sheet are associated with an angular momentum flux proportional to $-\tilde{k}_x/k_y$; leading shwaves therefore have positive angular momentum flux and trailing shwaves have negative angular momentum flux; (v) the energy of an ensemble of incompressive shwaves in the stratified shearing sheet behaves asymptotically as $t^{1-4{\rm Ri}}$ for $|{\rm782Ri}| \ll 1$."783 For Ivepleriau disks with modest racial eracients. [Lil is expected to be «I. aud there will therefore be weak growth in a single sliw:ive for Ri<0 and near-Iinear growth tn the euergy of an ensemble of slawaves. iucepetrdent of the sieu of Ri.," For Keplerian disks with modest radial gradients, $|{\rm784Ri}|$ is expected to be $\ll 1$, and there will therefore be weak growth in a single shwave for ${\rm Ri} < 0$ and near-linear growth in the energy of an ensemble of shwaves, independent of the sign of Ri."785during commissioning and the first 33 davs of science operations.,during commissioning and the first 33 days of science operations.786 1.996 of the 10.000 stars have been explicitly included as a result of the dwarl/eiant discriminator while 2.272 of the ~10.000 stars have been explicitly excluded.," 1,996 of the $\sim 10,000$ stars have been explicitly included as a result of the dwarf/giant discriminator while 2,272 of the $\sim 10,000$ stars have been explicitly excluded."787 The remaining ~6.000 remain on the unclassified target list pending additional data.," The remaining $\sim 6,000$ remain on the unclassified target list pending additional data."788 The unclassified stars that were determined to be giants comprise part of the Quarter 2 Dropped Target List., The unclassified stars that were determined to be giants comprise part of the Quarter 2 Dropped Target List.789 The light curves of dropped targets are made available to the public GO days after release (Haasetal.2010)., The light curves of dropped targets are made available to the public 60 days after release \citep{haas}.790.Kepler is observing more than 150.000 stars during the first vear of mission operations. more (han 90.000 of which are G-ivpe stars on or near (he Main Sequence.," is observing more than 150,000 stars during the first year of mission operations, more than 90,000 of which are G-type stars on or near the Main Sequence."791 10.575 are G-(vpe stars brighter (han 18th magnitude.," 10,575 are G-type stars brighter than 13th magnitude."792 28.519 are brighter than 14th magnitude.," 28,519 are brighter than 14th magnitude."793 Over 90% of the target stars are selected based on detectability metrics Chat suggest a lerrestvialsize planet (22< 2H.) is detectable in 3.5 vears., Over $90\%$ of the target stars are selected based on detectability metrics that suggest a terrestrial-size planet $R < 2R_{e}$ ) is detectable in 3.5 years.794 The detectability metrics are derived [rom stellar properties in (heCatalog., The detectability metrics are derived from stellar properties in the.795 Stellar classifications (surface eravitv. effective temperature. and the inferred. stellar radius) are complete at the 80% level. independent of magnitude.," Stellar classifications (surface gravity, effective temperature, and the inferred stellar radius) are complete at the $80\%$ level, independent of magnitude."796 A photometric luminosity class discriminator is applied to 1.000 Alain Sequence ancl 1.000 Giant light curves (as indicated by KIC classifications and confirmed. in some cases. by. Hipparcos parallaxes) [rom commissioning data.," A photometric luminosity class discriminator is applied to 1,000 Main Sequence and 1,000 Giant light curves (as indicated by KIC classifications and confirmed, in some cases, by Hipparcos parallaxes) from commissioning data."797 We report agreement between the KIC and photometric discriminators >9054 of the time for stars brighter than 13th magnitude., We report agreement between the KIC and photometric discriminators $>90\%$ of the time for stars brighter than 13th magnitude.798 Priority on the target list is given to stars that can be followed up with high-precision radial velocity measurements Ilrom current ground-based facilities., Priority on the target list is given to stars that can be followed up with high-precision radial velocity measurements from current ground-based facilities.799 High priority is also assigned to the fainter (14<Ap 16) Ix and M-t0vpe cwarls that will benelit from future IR. spectrometers., High priority is also assigned to the fainter $14 \leq Kp < 16$ ) K and M-type dwarfs that will benefit from future IR spectrometers.800 Ancillary target lists are generated for special purposes (e.g. to detect planets around EBs. to extend the age-rotation relation for Main sequence stars. and (to ensure that (he closest Main Sequence stars are included).," Ancillary target lists are generated for special purposes (e.g. to detect planets around EBs, to extend the age-rotation relation for Main Sequence stars, and to ensure that the closest Main Sequence stars are included)."801 Finally, Finally802"with /?., being the photospherie radius.",with $R_*$ being the photospheric radius.803" The thermal equilibrium condition 1s where L,,, is the total luminosity output from all energy sources as described below in Sec.??.", The thermal equilibrium condition is where $L_{tot}$ is the total luminosity output from all energy sources as described below in \ref{ensources}.804. Starting with a mass A/ and an estimate for the outer radius ες. the code integrates Eqns. (??))," Starting with a mass $M$ and an estimate for the outer radius $R_*$ , the code integrates Eqns. \ref{hydro}) )"805 and (??)) outward from the center., and \ref{eqstate}) ) outward from the center.806" The total luminosity output {ο is compared to the stellar radiated luminosity, as in Eq.(??)) and the radius is adjusted until the condition of thermal equilibrium is met (a convergence of 1 in 10! is reached)."," The total luminosity output $L_{tot}$ is compared to the stellar radiated luminosity, as in \ref{thermal}) ) and the radius is adjusted until the condition of thermal equilibrium is met (a convergence of $1$ in $10^4$ is reached)."807 The first stars form inside ~LO°A/. haloes., The first stars form inside $\sim 10^6 \msun$ haloes.808" Simulations imply that DM halos have a naturally cuspy profile, but there is still some uncertainty about the exact inner slope of a DM halo: ???.."," Simulations imply that DM halos have a naturally cuspy profile, but there is still some uncertainty about the exact inner slope of a DM halo: \citet{2007ApJ...667..859D,2008MNRAS.391.1685S,2010arXiv1002.3660K}."809" Luckily, a previous paper (2) showed that a dark star results regardless of the details of the initial density profile, even for the extreme case of a cored Burkert profile (such a Burkert profile is completely unrealistic)."," Luckily, a previous paper \citep{DS3}810 showed that a dark star results regardless of the details of the initial density profile, even for the extreme case of a cored Burkert profile (such a Burkert profile is completely unrealistic)."811" In this paper, we use a Navarro, Frenk, White (NEW) profile (2) for conercteness."," In this paper, we use a Navarro, Frenk, White (NFW) profile \citep{NFW} for concreteness."812" We assume that initially both the baryons of the mass) and the DM of the mass) can be deseribed with the same NFW profile where pi is the ""central"" density and x, is the scale radius."," We assume that initially both the baryons of the mass) and the DM of the mass) can be described with the same NFW profile where $\rho_0$ is the ""central"" density and $r_s$ is the scale radius."813" Clearly at any point of the profile, baryons will only make up of the mass."," Clearly at any point of the profile, baryons will only make up of the mass."814" The density scale, pi can be re-expressed in terms of the critical density of the universe ata given redshift, p,.(2) via"," The density scale, $\rho_0$ can be re-expressed in terms of the critical density of the universe ata given redshift, $\rho_c(z)$ via"815OJ 287 in 1980-2010.,OJ 287 in 1980-2010.816 In the upper panel three outburst seasons of OJ 287 can be seen: 1982-84. 1994-95 and 2005-08.," In the upper panel three outburst seasons of OJ 287 can be seen: 1982-84, 1994-95 and 2005-08."817 The high Ha flux appeared just after the strong outbursts in. 1982-83. 290 days after the second peak.," The high $\alpha$ flux appeared just after the strong outbursts in 1982-83, 290 days after the second peak."818 Unfortunately. the sampling is too poor to draw any conclusions on the possible connection between continuum and BLR luminosity in OJ 287.," Unfortunately, the sampling is too poor to draw any conclusions on the possible connection between continuum and BLR luminosity in OJ 287."819 Such a connectiol would not even be necessarily expected because in BL Lae objects the vast majority of the continuum arises from the jet and is highly beamed by relativistic effects due to the small angle between the line of sight and the Jet axis., Such a connection would not even be necessarily expected because in BL Lac objects the vast majority of the continuum arises from the jet and is highly beamed by relativistic effects due to the small angle between the line of sight and the jet axis.820 Thus the observed continuum variations are not necessarily connected to the changes of the continuum source illuminating the Ha emitting clouds. most likely the inner parts of the accretion disk.," Thus the observed continuum variations are not necessarily connected to the changes of the continuum source illuminating the $\alpha$ emitting clouds, most likely the inner parts of the accretion disk."821 It is nevertheless an intriguing observation that the high line luminosity in 1984 was observed right after a luminous continuum outburst., It is nevertheless an intriguing observation that the high line luminosity in 1984 was observed right after a luminous continuum outburst.822 Given the weakness of the broad Ha line we are unable to study a possible connection between BLR velocity field and the suggested periastron of the secondary black hole in 2005-07 (?).., Given the weakness of the broad $\alpha$ line we are unable to study a possible connection between BLR velocity field and the suggested periastron of the secondary black hole in 2005-07 \citep{2007ApJ...659.1074V}.823 The average ime luminosities in. 2005-05. were log(L/ergs!) = 41.8. 41.1. 41.2 and 40.8 for broad Ha. narrow Ha. 46583[NII] and /46548[NII]. respectively.," The average line luminosities in 2005-08 were $\log(L/{\rm erg\824s}^{-1})$ = 41.8, 41.1, 41.2 and 40.8 for broad $\alpha$ , narrow $\alpha$, $\lambda$ 6583[NII] and $\lambda$ 6548[NII], respectively."825 The He luminosities of Seyfert galaxies and quasars are generally much higher as shown by he comparisons in Table 4+ and Fig. 6.., The $\alpha$ luminosities of Seyfert galaxies and quasars are generally much higher as shown by he comparisons in Table \ref{llumtable} and Fig. \ref{lumvertailu}.826 The quasar data were obtained from ?.. who give data of 77 429 quasars from the Fifth Data Release of the Sloan Digital Sky Survey (?)..," The quasar data were obtained from \cite{2007AJ....134..102S}, who give data of 77 429 quasars from the Fifth Data Release of the Sloan Digital Sky Survey \citep{2007ApJS..172..634A}."827 We selected quasars at the redshift interval z = 0.30—0.31 (147 quasars) and obtained the Πα line fluxes and widths from the SpecLine tables in the SDSS archive., We selected quasars at the redshift interval z = $0.30 - 0.31$ (147 quasars) and obtained the $\alpha$ line fluxes and widths from the SpecLine tables in the SDSS archive.828 Figure 6 shows only quasars with FWHM > 1000 km s! (101 quasars)., Figure \ref{lumvertailu} shows only quasars with FWHM $>$ 1000 km $^{-1}$ (101 quasars).829 In addition we plot data for 17 z = 0.36 Seyfert galaxies in. 2.., In addition we plot data for 17 z = 0.36 Seyfert galaxies in \cite{2008ApJ...673..703M}.830 As can be seen from Fig., As can be seen from Fig.831 6. the He luminosity of OJ 287 was lower than in typical quasars and Seyfert galaxies by a factor of ~ 10 in 2005-08., \ref{lumvertailu} the $\alpha$ luminosity of OJ 287 was lower than in typical quasars and Seyfert galaxies by a factor of $\sim$ 10 in 2005-08.832 In December 1984. however. the Ha luminosity was comparable to that of quasars and Seyferts.," In December 1984, however, the $\alpha$ luminosity was comparable to that of quasars and Seyferts."833 We finally note that the luminosities of the two narrow lines 6548 and 26583 |NIIJ]. however. are comparable to the narrow-line luminosities of the quasars in 9," We finally note that the luminosities of the two narrow lines $\lambda$ 6548 and $\lambda$ 6583 [NII], however, are comparable to the narrow-line luminosities of the quasars in \cite{2007AJ....134..102S}."834 We have presented high S/N spectra of the BL Lac object OJ 287 during seven epochs in. 2005-08., We have presented high S/N spectra of the BL Lac object OJ 287 during seven epochs in 2005-08.835" Our results can be summarized as follows: 1) We were able to detect five narrow emission lines. A16548.6583,NI]. 26563Ha and ;L16716.6731 [SIT] during at least one of the epochs and a broad He feature during two epochs."," Our results can be summarized as follows: 1) We were able to detect five narrow emission lines, $\lambda\lambda$ 6548,6583[NII], $\lambda6563$ $\alpha$ and $\lambda\lambda$ 6716,6731 [SII] during at least one of the epochs and a broad $\alpha$ feature during two epochs."836 The luminosities of the [NII] lines are comparable to those in quasars at the same redshift. whereas the broad Hw line is a factor of ~ 10 less luminous than the Ha line in quasars and Seyfert galaxies.," The luminosities of the [NII] lines are comparable to those in quasars at the same redshift, whereas the broad $\alpha$ line is a factor of $\sim$ 10 less luminous than the $\alpha$ line in quasars and Seyfert galaxies."837 2) The luminosity of the broad Ha line was a factor of ~ 10 lower in 2005-08 than in 1984 when itwas reported to have been detected the last time., 2) The luminosity of the broad $\alpha$ line was a factor of $\sim$ 10 lower in 2005-08 than in 1984 when itwas reported to have been detected the last time.838 3) We do not see any significant change in luminosity. position or width if the broad Ha line between the two epochs," 3) We do not see any significant change in luminosity, position or width if the broad $\alpha$ line between the two epochs"839statistics are not good enough to obtain a reliable Xταν spectrum.,statistics are not good enough to obtain a reliable X–ray spectrum.840 Iu particular. he ERO S2F1.1113 (—35 net couuts in the 0.51.5 keV baud) is detected oulv in the AIOSI while the S2E1.1193 (—21 uct counts in the 0.52 keV) and ERO 7711 (~31 uet counts in the27.5. in particular —1] uct counts in the 215 keV. plus ~20 net counts in the L57.5 keV) are detected oulv in the pu.," In particular, the ERO 443 $\sim$ 35 net counts in the 0.5–4.5 keV band) is detected only in the MOS1 while the 493 $\sim$ 24 net counts in the 0.5–2 keV) and ERO 714 $\sim$ 31 net counts in the2–7.5, in particular $\sim$ 11 net counts in the 2–4.5 keV plus $\sim$ 20 net counts in the 4.5–7.5 keV) are detected only in the pn."841 By performing a visual inspection of all the 3 EPIC cameras. we find hat. while S2E1.1193 and S2FL_7711 are ouly visible iu the image where they have Όσσα detected. S2FI_LLL8 is also barely visible iu the MOS2 imaec.," By performing a visual inspection of all the 3 EPIC cameras, we find that, while 493 and 714 are only visible in the image where they have been detected, 443 is also barely visible in the MOS2 image."842 Iu order to increase the statistics of this source we have used MOS|MOS2 data thus accumulating 50 net counts in total., In order to increase the statistics of this source we have used MOS1+MOS2 data thus accumulating $\sim$ 50 net counts in total.843 Later. we will use these statistics to derive the basic Nταν properties of S2F1.1113.," Later, we will use these statistics to derive the basic X–ray properties of 443."844 Some indications about the origin of the Xrav chussion of these 3. EROs have been derived by calculating their hardness (hereafter IR)., Some indications about the origin of the X–ray emission of these 3 EROs have been derived by calculating their hardness (hereafter HR).845" While the value of the TR (~ 0.9) derived for S2E1.1195 is not a discriminant of the Xravemiüssiou origin. both ILLS i;~ 0.3) aud 7711 (IRs, ~1) have hardness ratios typical of obscured ACNs (see Della Ceca et al. 2001)."," While the value of the HR $\sim$ –0.9) derived for 493 is not a discriminant of the X–rayemission origin, both 443 $_{443}\sim$ –0.3) and 714 $_{714}\sim$ 1) have hardness ratios typical of obscured AGNs (see Della Ceca et al. \cite{Dellaceca04}) )."846" By using a simulated spectrum at the redshift of the source and by assuming an intrinsic photon index of 1.9. we have estimated hat the intriusic cohunn deusitv uceded to reproduce the harduess ratios of [113 aud S2PL7711 ave consistent with values larecr han 1072 ? and of about 10?! 2. respectively,"," By using a simulated spectrum at the redshift of the source and by assuming an intrinsic photon index of 1.9, we have estimated that the intrinsic column density needed to reproduce the hardness ratios of 443 and 714 are consistent with values larger than $^{22}$ $^{-2}$ and of about $^{24}$ $^{-2}$, respectively."847 Although the statistics of S2F1.1I3 are not good enough to perform a complete Xταν spectral analysis. it allows us to compare the model used to reproduce the hardness ratio with the X.ταν data.," Although the statistics of 443 are not good enough to perform a complete X–ray spectral analysis, it allows us to compare the model used to reproduce the hardness ratio with the X–ray data."848 The good agrecineut betweenmodel aud data is shown iu Figure 3 where a rest- absorbed )owerlaw model (T=1.9. Ng < 107? 7) js superiuposed on the backeroundsubtracted Xταν counts. binned in order to have at least 15 total counts per cucrey channel.," The good agreement betweenmodel and data is shown in Figure 3 where a rest-frame absorbed power–law model $\Gamma$ =1.9, $_H$ $\times$ $^{22}$ $^{-2}$ ) is superimposed on the background–subtracted X–ray counts, binned in order to have at least 15 total counts per energy channel."849" From this model we derive a Galactie corrected flux of Fioqug,76. 752.1410. P? erg D 1 and. by usingB dtsH spectroscopic- redshift (1.70.05, see Table 1 and Sect."," From this model we derive a Galactic corrected flux of $_{(2-10\rm keV)}$ $\pm$ $\times$ $^{-15}$ erg $^{-2}$ $^{-1}$ and, by using its spectroscopic redshift $\pm$ 0.05, see Table 1 and Sect."850" [) we estimate am intrinsic huuinosity of Lyρω 20.6 <1 yl Cres 1 (the huuiuosity errors take uto account also he redslüft ""ucertaities). iun good aereciment with its high radio numositv (see Sect."," 4) we estimate an intrinsic luminosity of $_{(2-10\rm keV)}$ $\pm$ $\times$ $^{44}$ erg $^{-1}$ (the luminosity errors take into account also the redshift uncertainties), in good agreement with its high radio luminosity (see Sect."851 Tn order to estimate the flux and the buninosity or ERO S2F1.7711. we have calculated the vignettingcorrected count rates in the 27.5 keV band (the ERO das been detected only iu the 21.5 and 157.5 SSC xad).," In order to estimate the flux and the luminosity for ERO 714, we have calculated the vignetting--corrected count rates in the 2–7.5 keV band (the ERO has been detected only in the 2–4.5 and 4.5–7.5 SSC band)."852 Usine the measured count rates and asstuuine a oowerlawmodel with DP-—1.4 (simular to that of the uuresolved Cosme Nrav background since the source seelus to be very hard} we obtain a Galactic corrected Bux of Froque HELD S10 P ere 2s 12, Using the measured count rates and assuming a power–lawmodel with $\Gamma\sim$ 1.4 (similar to that of the unresolved Cosmic X–ray background since the source seems to be very hard) we obtain a Galactic corrected flux of $_{(2-10\rm keV)}$ $\pm$ $\times$ $^{-15}$ erg $^{-2}$ $^{-1}$.853" Takius into account the photometric redshift (1.02:0.2) and the imiriusic cohunuu deusitv derived from the WR aualvsis (Ny consistent+ with. 1074P P7. see above) we estiiate an intrinsic huninosity L,5okey DIO ore sf,"," Taking into account the photometric redshift $\pm$ 0.2) and the intrinsic column density derived from the HR analysis $_H$ consistent with $^{24}$ $^{-2}$, see above) we estimate an intrinsic luminosity $_{(2-10\rm keV)}>$ $^{44}$ erg $^{-1}$."854 Iu stumary. we find evidence that both S2FL_L113 aud S2FL771L1 are probably Xταν obscured ACNs of high huuinosity (>10!! ere 1).," In summary, we find evidence that both 443 and 714 are probably X–ray obscured AGNs of high luminosity $>10^{44}$ erg $^{-1}$ )."855 This result is also supported by the (210 keV)tooptical flux ratios of these two EROs asa function of their (2LO keV) fluxes (see Figure £., This result is also supported by the (2–10 keV)–to–optical flux ratios of these two EROs as a function of their (2–10 keV) fluxes (see Figure 4).856 The two EROs discussed here are plottec with solid circles. while the : EROs for which he presence of an obscured aud Yeh luminosity ACUNS is already indicated by the X spectral analysis (see Sec.," The two EROs discussed here are plotted with solid circles, while the 3 EROs for which the presence of an obscured and high luminosity AGNs is already indicated by the X--ray spectral analysis (see Sec."857 3.1) have been plotted with solid circles encircled by larger open circle., 3.1) have been plotted with solid circles encircled by larger open circle.858 For comparison in Figure Lowe plot also other Xrav emitting EROs taken from the literature Ge. Hollas-2NMM. Mignoli et al. 2001:," For comparison in Figure 4 we plot also other X–ray emitting EROs taken from the literature (i.e. Hellas2XMM, Mignoli et al. \cite{Mignoli};"859 Lockiman ole. Mainieri et al. 2002.. ," Lockman Hole, Mainieri et al. \cite{Mainieri}, ,"860Stevens et al. 2003: , Stevens et al. \cite{Stevens}; ; –861CDEN. Vienali et al. 2002.. ,"CDFN, Vignali et al. \cite{Vignali}, ,"862Alexander et al. 2002.. 2003..," Alexander et al. \cite{Alexander02}, \cite{Alexander03},"863 Darger et al. 2003: , Barger et al. \cite{Barger03}; –864CDES. Roche ct al. 2003..,"CDFS, Roche et al. \cite{Roche},"865 Szokolv et al. 2001: , Szokoly et al. \cite{Szokoly}; ;866ELATS. Willott et al 2003)).," ELAIS, Willott et al \cite{Willott}) )."867 Different saubols have been used to mark the differeiut EROs on the basis of the iuforinatiou available in the, Different symbols have been used to mark the different EROs on the basis of the information available in the868Tablel for G338.3-0.0 CASE 2). the current spin-down power of the pulsar is 1.65«107 ere 1. and the resulting radius of the PWN is just 2.45 pe. which is even smaller than the extension of the X-rays (~3.5 pe) assuming a distance of 10 kpe (Lemiereetal..2009).,"\ref{para} for G338.3-0.0 CASE 2), the current spin-down power of the pulsar is $1.65\times10^{37}$ erg $^{-1}$, and the resulting radius of the PWN is just 2.45 pc, which is even smaller than the extension of the X-rays $\sim3.5$ pc) assuming a distance of 10 kpc \citep[][]{Lea09}."869. A smaller jp=0.3«10.7. and the maximum energy of the particles is set to 500 TeV to reproduce the observational fluxes in the X-rays and >-rays.," A smaller $\eta_{\rm870B}=0.3\times10^{-3}$, and the maximum energy of the particles is set to 500 TeV to reproduce the observational fluxes in the X-rays and $\gamma$ -rays."871 The resulting multiband nonthermal emission is indicated in Fig.9 with soft densities of 1.0eV  and 6.0eV ° for the infrared and the optical soft photons. respectively.," The resulting multiband nonthermal emission is indicated in \ref{Figj1640b} with soft densities of 1.0 eV $^{-3}$ and 6.0 eV $^{-3}$ for the infrared and the optical soft photons, respectively."872 In this scenario. the PWN has been compressed by the reverse shock. and the resulting flux with energies below | eV is about two orders of magnitude higher than that in the CASE I.," In this scenario, the PWN has been compressed by the reverse shock, and the resulting flux with energies below 1 eV is about two orders of magnitude higher than that in the CASE 1."873 Motivated by the finding that the spectrum of the particles downstream of a relativistic shock consists of two components: arelativistic Maxwellian and a power-law high-energy tail with an index of —2.1+0.1 (Spitkovsky.2008).. we investigate the possibility of particles with this new spectrum injected in PWNe from the TS based on the studies of multiband emission from PWNe.," Motivated by the finding that the spectrum of the particles downstream of a relativistic shock consists of two components: a relativistic Maxwellian and a power-law high-energy tail with an index of $-2.4\pm0.1$ \citep[][]{Sp08}, we investigate the possibility of particles with this new spectrum injected in PWNe from the TS based on the studies of multiband emission from PWNe."874 Following the dynamical method proposed in Gelfandetal.(2009). we study the dynamical and multi-band radiative properties of the three composite SNRs GO.940.1. MSH 15-52 and G338.3-0.0.," Following the dynamical method proposed in \citet[][]{GSZ09}, we study the dynamical and multi-band radiative properties of the three composite SNRs G0.9+0.1, MSH 15-52 and G338.3-0.0."875 With appropriate parameters. we find that a typical PWN is an important 5-ray emitter during its evolution although the non-thermal radiation from the radio to the X-ray band is insignificant sometimes.," With appropriate parameters, we find that a typical PWN is an important $\gamma$ -ray emitter during its evolution although the non-thermal radiation from the radio to the X-ray band is insignificant sometimes."876 The multiband observations of the three PWNe in the remnants can be well reproduced with the new spectrum of the injected particles., The multiband observations of the three PWNe in the remnants can be well reproduced with the new spectrum of the injected particles.877 Therefore. our studies on the dynamical and multiwavelength radiative properties of PWNe provide evidence of high-energy electrons/positrons can be injected into a PWN with a Maxwellian plus a power-law high-energy tail from the TS of the PWN.," Therefore, our studies on the dynamical and multiwavelength radiative properties of PWNe provide evidence of high-energy electrons/positrons can be injected into a PWN with a Maxwellian plus a power-law high-energy tail from the TS of the PWN."878 In modeling the multiband nonthermal emission from a PWN detected in the radio. X-ray and +-ray bands. particles injected with a spectrum of a broken power-law are widely used to reproduce the observed multiwavelength emission (e.g..Venter&deJager.2006:Slane.2008:Zhangetal.. 2008).," In modeling the multiband nonthermal emission from a PWN detected in the radio, X-ray and $\gamma$ -ray bands, particles injected with a spectrum of a broken power-law are widely used to reproduce the observed multiwavelength emission \citep[e.g.,][]{Vd06,S08,ZCF08}."879. Of course. for the three PWNe discussed in this paper. the multiband observed spectra of them can also be explained if the particles are injected with a broken power-law.," Of course, for the three PWNe discussed in this paper, the multiband observed spectra of them can also be explained if the particles are injected with a broken power-law."880 However. it is unclear why the broken power-law spectrum 1s valid when using it to reproduce the multiwavlength emission from a PWN.," However, it is unclear why the broken power-law spectrum is valid when using it to reproduce the multiwavlength emission from a PWN."881" From our calculations. we have found out that the energy distribution of the electrons/positrons in the nebula can be approximated as a broken power-law with an index ~1 in the lower-energy band and an index of ~2.5 in the higher-energy part before the PWN undergos significant compression. which is most likely the physical explanation of the broad usage ""Sff a broken power law in modeling the multi-band non-thermal emission from PWNe."," From our calculations, we have found out that the energy distribution of the electrons/positrons in the nebula can be approximated as a broken power-law with an index $\sim 1$ in the lower-energy band and an index of $\sim2.5$ in the higher-energy part before the PWN undergos significant compression, which is most likely the physical explanation of the broad usage of a broken power law in modeling the multi-band non-thermal emission from PWNe."882 In this paper. high-energy electrons/positrons are injected into the PWN from the TS. and the main energy of the nebula is contained in these particles.," In this paper, high-energy electrons/positrons are injected into the PWN from the TS, and the main energy of the nebula is contained in these particles."883 These particles undergo radiative and adiabatie losses when the nebula evolves 1n the host SNR., These particles undergo radiative and adiabatic losses when the nebula evolves in the host SNR.884 Our study indicates that. for atypical PWN with the parameters similar as GO.9+0.1. the adiabatic loss of the particles in the nebula is significant after an age of ~1000 yr (see Fig.3. and Fig.4).," Our study indicates that, for atypical PWN with the parameters similar as G0.9+0.1, the adiabatic loss of the particles in the nebula is significant after an age of $\sim1000$ yr (see \ref{Epwn} and \ref{Epower}) )."885 Multiwaveband nonthermal emission from a PWN has been investigated using a simplified time-dependent injection model. in which high-energy electrons/positrons are injected into the PWN (e.g..Venter&deJager.2006:Slane.2008:Zhangetal.. 2008).," Multiwaveband nonthermal emission from a PWN has been investigated using a simplified time-dependent injection model, in which high-energy electrons/positrons are injected into the PWN \citep[e.g.,][]{Vd06,S08,ZCF08}."886. The pulsar inside the PWN transfers a part of its spin-down power to the particles with a spectrum of a broken power-law., The pulsar inside the PWN transfers a part of its spin-down power to the particles with a spectrum of a broken power-law.887 In the simplified time-dependent injection model in Zhangetal.(2008).. synchrotron loss of the particles is taken into account. whereas the adiabatic one ts ignored.," In the simplified time-dependent injection model in \citet[][]{ZCF08}, synchrotron loss of the particles is taken into account, whereas the adiabatic one is ignored."888 As a result. either a relatively smaller initial spin-down power of the pulsar or a smaller efficiency of the power to the kinetic energy of the accelerated electrons/positrons is employed in the model.," As a result, either a relatively smaller initial spin-down power of the pulsar or a smaller efficiency of the power to the kinetic energy of the accelerated electrons/positrons is employed in the model."889 Moreover. note that in Zhangetal.(2008)... an initial spin-down power of 1«1075 ere + for MSH 15-52 was used to investigate the multiband emission from the PWN. which is a factor of 15 smaller than that used in this paper.," Moreover, note that in \citet[][]{ZCF08}, an initial spin-down power of $1\times10^{38}$ erg $^{-1}$ for MSH 15-52 was used to investigate the multiband emission from the PWN, which is a factor of 15 smaller than that used in this paper."890 Besides the above reasons. the another main one ts a relatively big spin-down time scale of ~5000 vr. whichis x»Ey in the paper. used by Zhangetal. (2008).. whereas in this paper it is adopted to be 500 vr.," Besides the above reasons, the another main one is a relatively big spin-down time scale of $\sim 5000$ yr, which is $\propto \dot{E_0}^{-1}$ in the paper, used by \citet[][]{ZCF08}, , whereas in this paper it is adopted to be $500$ yr."891 The energy released by the pulsa is mainly determined by Lyή{μαςτο}. and the value in this paper is not much bigger than that in Zhangetal. (2005). ," The energy released by the pulsar is mainly determined by $E_0892\min \{T_{\rm age}, \tau_0 \}$, and the value in this paper is not much bigger than that in \citet[][]{ZCF08}. ."893Therefore. the multiband observed spectra for MSH 15-52 caαυ] be reproduced within the two scenarios even theinitial power of the pulsar ts significantly different.," Therefore, the multiband observed spectra for MSH 15-52 can be reproduced within the two scenarios even theinitial spin-down power of the pulsar is significantly different."894degeneracies between the NS magnetic configuration. viewing geometry. and compactiness make it diflieult to extract physical parameters from observations.,"degeneracies between the NS magnetic configuration, viewing geometry, and compactness make it difficult to extract physical parameters from observations."895 As an alternative. several recent works discuss the evolution of photon polarization states in NS magnetospheres. showing that. in the magnetar case. significant. linear. polarization fractions are expected. possibly containing a unique signature of the strong magnetic field per," As an alternative, several recent works discuss the evolution of photon polarization states in NS magnetospheres, showing that, in the magnetar case, significant linear polarization fractions are expected, possibly containing a unique signature of the strong magnetic field \citep[][]{HeylShaviv00a,HeylShaviv02a,Heyletal03a,LaiHo03a,vanAdelsbergLai06a,WangLai09a}."896formed for (he Crab nebula using the OSO-8 satellite (2)..," Measurements of significant X-ray polarization, at 2.6 keV and 5.2 keV, were performed for the Crab nebula using the OSO-8 satellite \citep[][]{Weisskopfetal76a}."897 These measurements confirmed an earlier detection bv a sounding rocket experiment (?).., These measurements confirmed an earlier detection by a sounding rocket experiment \citep[][]{Novicketal72a}.898 ILowever. as of (his writing. no subsequent. polarization measurements have been made [or anv object al energies [7~ keV (relevant for thermal magnetar emission).," However, as of this writing, no subsequent polarization measurements have been made for any object at energies $E\sim 0.1-10$ keV (relevant for thermal magnetar emission)."899 Recent advances in instrumentation have stimulated interest in future missions (ο perform polarimetry in the soft. X-ray banc. leading to several projects which are in active development (see???)..," Recent advances in instrumentation have stimulated interest in future missions to perform polarimetry in the soft X-ray band, leading to several projects which are in active development \citep[see][]{Costaetal01a,Kallman04a,Costaetal06a}."900 In this paper. we explore the future role of X-ray polarimetry as a complement {ο spectroscopy in interpreting observational spectra.," In this paper, we explore the future role of X-ray polarimetry as a complement to spectroscopy in interpreting observational spectra."901 We will argue that the combination of polarimetry aid spectroscopy can constrain several eritical NS parameters. including the temperature. magnetic field strength ancl geometry. size of emission region. and ratio of highly magnetized NSs with B~107—10 G. We use the latest magnetar abmosphere models of2.. and expand on the work of ?.. ?.. νι and ?.. lo compute the phase-resolved. observed Stokes parameters from magnetars.," We will argue that the combination of polarimetry and spectroscopy can constrain several critical NS parameters, including the temperature, magnetic field strength and geometry, size of emission region, and mass-to-radius ratio of highly magnetized NSs with $B\sim 10^{12}-10^{15}$ G. We use the latest magnetar atmosphere models of\citet[][]{vanAdelsbergLai06a}, and expand on the work of \citet[][]{HeylShaviv02a}, \citet[][]{Heyletal03a}, \citet[][]{LaiHo03a}, and \citet[][]{vanAdelsbergLai06a}, to compute the phase-resolved, observed Stokes parameters from magnetars."902 We assume (hat. these NSs have dipole magnetic field strengths of B=4xLOM G5x10! G and emit [rom a region centered around (he star polar cap wilh modest opening angle., We assume that these NSs have dipole magnetic field strengths of $B = 4\times 10^{13}$ G – $5\times 10^{14}$ G and emit from a region centered around the star polar cap with modest opening angle.903 We confirm that the polarization sienal Iron a finite region on a magnetar surface retains important information about the streneth of the magnetic field. as reported in previous works.," We confirm that the polarization signal from a finite region on a magnetar surface retains important information about the strength of the magnetic field, as reported in previous works."904 We show (hat this signal has a strong dependence on (he magnetic field and viewing geometry. and a weaker dependence on (he NS EOS. emission region size. and atmosphere composition.," We show that this signal has a strong dependence on the magnetic field and viewing geometry, and a weaker dependence on the NS EOS, emission region size, and atmosphere composition."905 Finally. we argue (hat. polarization measurements can break (he degeneracy inherent in inlerring physical parameters [from spectroscopic measurements alone.," Finally, we argue that polarization measurements can break the degeneracy inherent in inferring physical parameters from spectroscopic measurements alone."906 Qur paper is organized as follows: in relsect:Physies Inputs... we discuss our assumptions and (the atmosphere models used to calculate the emitted polarization Iraction [rom the NS surface.," Our paper is organized as follows: in \\ref{sect:Physics Inputs}, we discuss our assumptions and the atmosphere models used to calculate the emitted polarization fraction from the NS surface."907 Iu refsect:Emission Model.. we describe our methods for calculating the observed polarization signal [rom an extended NS polar cap. including relativistic effects.," In \\ref{sect:Emission Model}, we describe our methods for calculating the observed polarization signal from an extended NS polar cap, including relativistic effects."908 In relsect:ltesulis.. we show the results of our calculations [or several representative cases.," In \\ref{sect:Results}, , we show the results of our calculations for several representative cases."909For at least four decades. searches have been conducted for stars with properties very similar to the Sun (see Hardorp 1978. Cayrel de Strobel et al.,"For at least four decades, searches have been conducted for stars with properties very similar to the Sun (see Hardorp 1978, Cayrel de Strobel et al."910 1981; see also the review by Cayrel de Strobel 1996. and for a recent short summary e.g. Melénndez Ramírrez 2007).," 1981; see also the review by Cayrel de Strobel 1996, and for a recent short summary e.g. Melénndez Ramírrez 2007)."911" It would be important to find a star with physical characteristies indistinguishable from those of the Sun. a ""perfect good solar twin"". as defined by Cayrel de Strobel (1996)."," It would be important to find a star with physical characteristics indistinguishable from those of the Sun, a “perfect good solar twin”, as defined by Cayrel de Strobel (1996)."912 The reasons for this importance are both physical and technical., The reasons for this importance are both physical and technical.913 Physically. the statistics of solar twins would certainly. contribute to our understanding of the uniqueness or normality of the Sun (ef.," Physically, the statistics of solar twins would certainly contribute to our understanding of the uniqueness or normality of the Sun (cf."914 Gustafssor 1998)., Gustafsson 1998).915 Technically. a solar twin would be useful in setting zero points in the calibration of effective-temperature scales. basec on stellar colours.," Technically, a solar twin would be useful in setting zero points in the calibration of effective-temperature scales, based on stellar colours."916 Another use would be in the calibration of night-time reflectance spectroscopy of solar-system bodies. where the spectral component of the Sun must be removed before an analysis of the spectroscopic features of the body itself can be performed.," Another use would be in the calibration of night-time reflectance spectroscopy of solar-system bodies, where the spectral component of the Sun must be removed before an analysis of the spectroscopic features of the body itself can be performed."917 Numerous searches and accurate analyses have resulted 11 a small sample of solar-twin candidates (Porto de Mello da Silva 1997. Melénndez et al.," Numerous searches and accurate analyses have resulted in a small sample of solar-twin candidates (Porto de Mello da Silva 1997, Melénndez et al."918 2006. Takeda et al.," 2006, Takeda et al."919 2007. Melénndez et al.," 2007, Melénndez et al."920 2009. Ramírrez et al.," 2009, Ramírrez et al."921 2009)., 2009).922 Although these stars in. general have fundamental parameters very close to solar. recent advances in high-accuracy differential abundance analyses have proven almost all of them to have chemical compositions slightly. but systematically. deviating from that of the Sun.," Although these stars in general have fundamental parameters very close to solar, recent advances in high-accuracy differential abundance analyses have proven almost all of them to have chemical compositions slightly, but systematically, deviating from that of the Sun."923 A special opportunity in the search for solar twins is offered by the old and rich open cluster M67., A special opportunity in the search for solar twins is offered by the old and rich open cluster M67.924 It has à chemical composition similar to the Sun with [Fe/H] in the range 0.04 to 0.03 on the customary logarithmic scale normalised to the Sun (Hobbs Thorburn 1991]. Tautvaisiene et al.," It has a chemical composition similar to the Sun with [Fe/H] in the range $-$ 0.04 to 0.03 on the customary logarithmic scale normalised to the Sun (Hobbs Thorburn 1991, $\check{\rm s}$ iene et al."925 2000. Yong et al.," 2000, Yong et al."926 2005. Randich et al.," 2005, Randich et al."927 2006. Pace et al.," 2006, Pace et al."928 2008. Pasquini et al.," 2008, Pasquini et al."929 2008)., 2008).930 Its age is also comparable to that of the Sun: 44.8 Gyr YYadav et al., Its age is also comparable to that of the Sun: 4.8 Gyr Yadav et al.931 2008)., 2008).932 M67 is relatively nearby (~ ppc) and is only little. affected by interstellar extinction. which allows detailed spectroscopic studies of its main-sequence stars.," M67 is relatively nearby $\sim$ pc) and is only little affected by interstellar extinction, which allows detailed spectroscopic studies of its main-sequence stars."933 The depleted Li abundance of the Sun seems rather representative of solar-twins in the Galaxtie field (Baumann et al., The depleted Li abundance of the Sun seems rather representative of solar-twins in the Galaxtic field (Baumann et al.934 2010)., 2010).935 M67 also seems to contain Li-depleted G stars (Pasquini et al., M67 also seems to contain Li-depleted G stars (Pasquini et al.936 1997)., 1997).937 M67 thus offers good possibilities of finding solar-twin candidates for further exploration., M67 thus offers good possibilities of finding solar-twin candidates for further exploration.938 Pasquini et al. (, Pasquini et al. (9392008) (followed by a paper of Biazzo et al.,2008) (followed by a paper of Biazzo et al.940 2009) recently searched the cluster for solar analogs. and listed ten promising candidates.," 2009) recently searched the cluster for solar analogs, and listed ten promising candidates."941 Here we present an analysis of (NGC 2682 YBP 1194. ES 4063. ES IV-63. FBC 2867. MMJ 5357. SAND 770. 2MASS JO8510080+41148527). a cluster. solar-twin candidate suggested by Pasquini et al. (," Here we present an analysis of (NGC 2682 YBP 1194, ES 4063, ES IV-63, FBC 2867, MMJ 5357, SAND 770, 2MASS J08510080+1148527), a cluster solar-twin candidate suggested by Pasquini et al. ("9422008).,2008).943 Our analysis is based on high-resolution observations with relatively high signal-to-noise (S/N) ratio., Our analysis is based on high-resolution observations with relatively high signal-to-noise (S/N) ratio.944 In Section 2.. we discuss the observations and some aspects of the data reduction.," In Section \ref{sec:obs}, we discuss the observations and some aspects of the data reduction."945" Section 3. deseribes the analysis method and the determination of fundamental parameters(ζωα. logg. [Fe/H] and £,)."," Section \ref{sec:analys} describes the analysis method and the determination of fundamental parameters, $\log g$ , [Fe/H] and $\xi_{t}$ )."946 In Section 4+. we present the results of a detailed analysis of a number of chemical elements. and these results are compared to those obtained for known twins in the Galactic field.," In Section \ref{sec:comp} we present the results of a detailed analysis of a number of chemical elements, and these results are compared to those obtained for known twins in the Galactic field."947 In Section 5.. we present a new age determination for M67. and in Section 6 we discuss the results.," In Section \ref{sec:age}, we present a new age determination for M67, and in Section \ref{sec:disc} we discuss the results."948 The observations of M67-1194 were carried out with the multi-object spectrometer FLAMES-UVES at ESO-VLT in Service Mode in the spring of 2009 during a period of three months (18th of January — 3rd of April)., The observations of M67-1194 were carried out with the multi-object spectrometer FLAMES-UVES at ESO-VLT in Service Mode in the spring of 2009 during a period of three months (18th of January – 3rd of April).949 The observations analysed here are part of a larger project with a main goal to study atomic diffusion m stars of M67 (082.D-0726(A))., The observations analysed here are part of a larger project with a main goal to study atomic diffusion in stars of M67 (082.D-0726(A)).950 In each observing block of the project. one fibre of the spectrograph system was positioned on M67-1194 in order to collect as many observations as possible of this faint G dwarf.," In each observing block of the project, one fibre of the spectrograph system was positioned on M67-1194 in order to collect as many observations as possible of this faint G dwarf."951 We obtained altogether I8hh in 13 observing nights (23 individual observations)., We obtained altogether h in 13 observing nights (23 individual observations).952" The spectrometer setting (RED580) was chosen to yield a resolution of R=A/AA— 447.000 (1"" fibre) and a wavelength coverage of nnm."," The spectrometer setting (RED580) was chosen to yield a resolution of $R = \lambda/\Delta\lambda =$ 47,000 $1''$ fibre) and a wavelength coverage of nm."953 The typical signal-to-noise ratio (S/N) per frame is !(as measured in theline-free region between aand, The typical signal-to-noise ratio (S/N) per frame is $^{-1}$ (as measured in theline-free region between and9544 shows the growth of fragments formed in both simulations at the overlapping times.,\ref{arepo} shows the growth of fragments formed in both simulations at the overlapping times.955 There is a similar interval in both cases between the first sink forming and the first burst of fragmentation., There is a similar interval in both cases between the first sink forming and the first burst of fragmentation.956" In both cases the same number of sinks form, although there are slight differences in the mass growth rates due to the different N- dynamics which occur in each simulation."," In both cases the same number of sinks form, although there are slight differences in the mass growth rates due to the different N-body dynamics which occur in each simulation."957" As our results are reproduced by two highly complementary numerical schemes, we are confident that we capture the true physical evolution and are not strongly influenced by numerical artefacts."," As our results are reproduced by two highly complementary numerical schemes, we are confident that we capture the true physical evolution and are not strongly influenced by numerical artefacts."958 The fact that larger sinks are used here compared to the original ? simulations mean that we are not resolving tight binaries and missing some young low-mass objects formed within this radius that may have been ejected., The fact that larger sinks are used here compared to the original \citet{Greif11} simulations mean that we are not resolving tight binaries and missing some young low-mass objects formed within this radius that may have been ejected.959 Therefore our 20 AU sinks are a conservative estimate of the level of fragmentation., Therefore our $20$ AU sinks are a conservative estimate of the level of fragmentation.960" However, at this radius we are avoiding many of the uncertainties associated with protostellar mergers."," However, at this radius we are avoiding many of the uncertainties associated with protostellar mergers."961" As our young protostars would actually be puffy extended objects with radii about 100 (?),, there will be strong tidal forces evoked during close interactions, leading to the possibility that fragments formed close to each other will merge when they interact."," As our young protostars would actually be puffy extended objects with radii about $100$ \citep{Stahler86a}, there will be strong tidal forces evoked during close interactions, leading to the possibility that fragments formed close to each other will merge when they interact."962 It is still unclear how best to treat this possibility., It is still unclear how best to treat this possibility.963" By not forming low-mass objects in close proximity to existing sinks, encounters that are close enough for the stellar radii to touch occur rarely compared to the original simulations (typically between 0-2 times in each halo) and we generally avoid this issue."," By not forming low-mass objects in close proximity to existing sinks, encounters that are close enough for the stellar radii to touch occur rarely compared to the original simulations (typically between 0-2 times in each halo) and we generally avoid this issue."964" However, despite these small differences, qualitatively the evolution of the halos is similar to that in ?,, with the main difference being that we follow the evolution for ten thousand years compared to the original thousand."," However, despite these small differences, qualitatively the evolution of the halos is similar to that in \citet{Greif11}, with the main difference being that we follow the evolution for ten thousand years compared to the original thousand."965" 5 shows the combined mass function of all the sinks formed in minihalos 1-5, one and two thousand years after the first sink formed."," \ref{mf} shows the combined mass function of all the sinks formed in minihalos 1-5, one and two thousand years after the first sink formed."966 At 2000 yr in the non-feedback case ionisation effects are becoming important within Halo 5., At 2000 yr in the non-feedback case ionisation effects are becoming important within Halo 5.967" However, for the sake of the mass function only, we run Halo 5 until this point despite the lack of ionisation in our model."," However, for the sake of the mass function only, we run Halo 5 until this point despite the lack of ionisation in our model."968 This is due to the difficulty in achieving a statistically significant number of sinks for the mass function., This is due to the difficulty in achieving a statistically significant number of sinks for the mass function.969" At these early stages the sinks represent protostars rather than finished stars, and so these masses will not be those of the final population III stars."," At these early stages the sinks represent protostars rather than finished stars, and so these masses will not be those of the final population III stars."970 Nonetheless it can already be seen that the resulting mass function will contain a range of masses rather than just being one characteristic mass., Nonetheless it can already be seen that the resulting mass function will contain a range of masses rather than just being one characteristic mass.971" The mass functions show no systemic variation between the case with feedback and the reference case, and both cases contain a similar total amount of mass in stars at each time."," The mass functions show no systemic variation between the case with feedback and the reference case, and both cases contain a similar total amount of mass in stars at each time."972 Hence the feedback has not significantly altered the fragmentation and mass growth when considering the five minihalos combined., Hence the feedback has not significantly altered the fragmentation and mass growth when considering the five minihalos combined.973 This suggests that the results of previous studies which neglected this effect (e.g.?) will still be broadly correct., This suggests that the results of previous studies which neglected this effect \citep[e.g.][]{Stacy10} will still be broadly correct.974" The mass functions appear to be flatter than the IMF’s seen in the present day universe (??),, although as yet we have only of order ~50 sinks, so this remains statistically uncertain."," The mass functions appear to be flatter than the IMF's seen in the present day universe \citep{Kroupa02,Chabrier03}, although as yet we have only of order $\sim 50$ sinks, so this remains statistically uncertain."975" Tables 2 and 3 show the number of fragments formed in each halo when the mass of the most massive protostar first reaches 10 or 15 solar masses, respectively."," Tables \ref{n10} and \ref{n15} show the number of fragments formed in each halo when the mass of the most massive protostar first reaches $10$ or $15$ solar masses, respectively."976 ? find that ionising feedback does not become effective until the star is older than its Kelvin-Helmholtz time and is contracting towards the main sequence., \citet{Tan04} find that ionising feedback does not become effective until the star is older than its Kelvin-Helmholtz time and is contracting towards the main sequence.977 For their fiducial model this equates to a mass of around for a rotating protostar., For their fiducial model this equates to a mass of around for a rotating protostar.978" However the accretion rate for the most massive object is typically only a few 107? when the protostar has reached in our minihalos, whereas in the fiducial ? models the accretion rate is 10? for a 10 protostar."," However the accretion rate for the most massive object is typically only a few $10^{-3}$ when the protostar has reached in our minihalos, whereas in the fiducial \citet{Tan04} models the accretion rate is $10^{-2}$ for a 10 protostar."979" Since the Kelvin-Helmholtz contraction stage commences earlier with a lower accretion rate, as shown in 1,, we estimate that ionisation feedback will become important for our minihalos when the most massive star is between 10—15.."," Since the Kelvin-Helmholtz contraction stage commences earlier with a lower accretion rate, as shown in \ref{radmodel}, we estimate that ionisation feedback will become important for our minihalos when the most massive star is between $10-15$."980 Hz photodissociation will also become important at this time., $_{2}$ photodissociation will also become important at this time.981" Beyond this point, the assumptions that we make for the luminosity heating model break down, so we chose to terminate the simulations here."," Beyond this point, the assumptions that we make for the luminosity heating model break down, so we chose to terminate the simulations here."982malches the energy that would be transported aud dissipatecl out of that depth by an asstuned effective viscosity: where primes denote derivatives with respect to 2 and p is the background density profile.,matches the energy that would be transported and dissipated out of that depth by an assumed effective viscosity: where primes denote derivatives with respect to $z$ and $\bar{\rho}$ is the background density profile.983" For the y dependent οὐ forcing. we would like to show that the work per unit mass done bv the forcing on the flow al each y plane: malches (he enerev (hat would be transported and dissipated out of that plane by an asstuned effective viscosity: where now primes denote derivativeswilh respect (oY. tj, and ρω are the minimal and maximal depth respectively that we want to include in the fit and .N2[7p(z)dz."," For the $y$ dependent $x$ forcing, we would like to show that the work per unit mass done by the forcing on the flow at each $y$ plane: matches the energy that would be transported and dissipated out of that plane by an assumed effective viscosity: where now primes denote derivativeswith respect to $y$, $z_{min}$ and $z_{max}$ are the minimal and maximal depth respectively that we want to include in the fit and $N\equiv\int_{z_{min}}^{z_{max}} \bar{\rho}(z)dz$."984 The reason we do not want to include the entire simulated domain is that near the boundaries the flow is stronelv. affected by the impenetrable top and bottom wallsand is (hus non-phlivsical., The reason we do not want to include the entire simulated domain is that near the boundaries the flow is strongly affected by the impenetrable top and bottom wallsand is thus non-physical.985" We find the values of AT,and AT5,5 by least squares fitting ο to WI"" in the » reise me""urbin the+ range —L,/2↽ <⋅y∕L,/2respectively.", We find the values of $K^0_{1313}$and $K^0_{1212}$ by least squares fitting of $W_{xz}^{visc}$ to $W_{xz}^{turb}$ in the range $z_{min}<z<z_{max}$ and $W_{xy}^{visc}$ to $W_{xy}^{turb}$ in the range $-L_y/2<y<L_y/2$ respectively.986" Clearly.↽∙ the presence of the turbulence will cause random (lnetuations in the velocity prolile which should average oul if we combine a large enough umimber of time steps in evaluating (he quantities C,.. C. ὃν. and 5,,."," Clearly, the presence of the turbulence will cause random fluctuations in the velocity profile which should average out if we combine a large enough number of time steps in evaluating the quantities $C_{xz}$ , $C_{xy}$ , $S_{xz}$ and $S_{xy}$ ."987 These fluctuations are highly amplified when we, These fluctuations are highly amplified when we988removed by fitting a low-order Legeudre polvinonial to the continu sections of each order «X an O-star spectrui. and then dividing the correspouding order of the spectra bv this polynomial.,"removed by fitting a low-order Legendre polynomial to the continuum sections of each order of an O-star spectrum, and then dividing the corresponding order of the spectra by this polynomial."989 The resultant. almost flat orders were then combined using he taskscomb.," The resultant, almost flat orders were then combined using the task."990 This procedure proved to be satisfactory. except when the overlapping regions fall in a specral domain with verv steep intensity eradients. as in the |ne wine of A 1686 (see Fie.2)).," This procedure proved to be satisfactory, except when the overlapping regions fall in a spectral domain with very steep intensity gradients, as in the blue wing of $\lambda$ 4686 (see \ref{f2}) )."991 The combined spectra were then subdivided iuto spectral reeious roughly corresnudius to those of the lone-slit spectra discussed above (82.2.1)., The combined spectra were then subdivided into spectral regions roughly corresponding to those of the long-slit spectra discussed above 2.2.1).992 For consistency purposes. these spectra lave been coutimmum normalized by fitting a low-order Leseudre poyhonual to the contimmun sections that selected for the loue-slit spectra.," For consistency purposes, these spectra have been continuum normalized by fitting a low-order Legendre polynomial to the continuum sections that selected for the long-slit spectra."993 The light curve of is plotted as a function of the helocentic Julian date of observation iu Figure 1.., The light curve of is plotted as a function of the heliocentric Julian date of observation in Figure \ref{f1}.994 The main feature of this light curve is the gradual increase of the stellar σοιαι flux amounting to Ac ~-- 0.09 mae beeimmne at ILJD 2.150.316. followed by its decline on about the same timescale after ILJD 2.150.350.," The main feature of this light curve is the gradual increase of the stellar continuum flux amounting to $\Delta v$ $\approx$ 0.09 mag beginning at HJD 2,450,346, followed by its decline on about the same timescale after HJD 2,450,350."995 During the last 11 nights (after ILJD. 2.150.353). only mareinal," During the last 11 nights (after HJD 2,450,353), only marginal"996"The IT, rotational lines could strouglv affect the 12 band and may explain why the 8(12)/8(25) ratio is a factor of 22.5 larecr ou the southern rim of IC03. ie. at ~ ϱ 405. 22723 (ef","The $_2$ rotational lines could strongly affect the 12 band and may explain why the S(12)/S(25) ratio is a factor of $\simeq$ 2.5 larger on the southern rim of IC443, i.e. at $\simeq$ $^h$ $^m$ $^s$ $^o$ 23' (cf."997 Fie. 1))., Fig. \ref{iras_map}) ).998 This region is a well known powerful source of IT) (1.005(1)A22.12 line cluission (Burton ct al. 1988)), This region is a well known powerful source of $_2$ 2.12 line emission (Burton et al. \cite{burton88}) )999 whose spatial distrition closely resembles the TRAS 12 contours., whose spatial distribution closely resembles the IRAS 12 contours.1000 (ποια.based observations of the (0.008(2)A112.3. rotational transition were obtained w Richter et al. (1995)), Ground–based observations of the 12.3 rotational transition were obtained by Richter et al. \cite{richter}) )1001 who measured a line flux z10 ines brighter than (1.0)8(1)A22.12., who measured a line flux $\simeq$ 10 times brighter than 2.12.1002 Assiniue a coustaut /1(A22.12) ratio over the large area mapped iu he latter transition bv Burton et al. (1988)), Assuming a constant 2.12) ratio over the large area mapped in the latter transition by Burton et al. \cite{burton88}) )1003 vields iu average line surface brightuess of aout J510* Wan? orl/3o0fthe IRAS 12 ypeak surface briehtuess.," yields an average line surface brightness of about $1.5\,10^{-7}$ W $^{-2}$ $^{-1}$ or 1/3 of the IRAS 12 peak surface brightness."1004" Considering that the I, spectrum of ICLEA is remarkably similar to that of Orion oeakl (e.g. Richter et al. 1995))", Considering that the $_2$ spectrum of IC443 is remarkably similar to that of Orion peak1 (e.g. Richter et al. \cite{richter}) )1005 one then expects similar fluxes in the (0.008(3)A99.66. aud (0.008(2)A112.3. lines (Pariar et al. 1991)), one then expects similar fluxes in the 9.66 and 12.3 lines (Parmar et al. \cite{parmar}) )1006 or. equivalently. that the two lines should account for about 2/3 of the TRAS 12 flux.," or, equivalently, that the two lines should account for about 2/3 of the IRAS 12 flux."1007 Finally. it should be noted that IRAS was virtually diu to the To(O.0jS(1jAL17.0 line (c£.," Finally, it should be noted that IRAS was virtually blind to the $_2$ 17.0 line (cf."1008 Fie. 3)), Fig. \ref{iras_filt}) )1009 while the Helly forbidden eround state transition (0.0)8(0)A228.2 is most probably too weak to significantly contaminate the 25 IRAS baud (cf., while the highly forbidden ground state transition 28.2 is most probably too weak to significantly contaminate the 25 IRAS band (cf.1010 e.g. Fig., e.g. Fig.1011 2 of Oliva ct al. 1998))., 2 of Oliva et al. \cite{rcw103_iso}) ).1012 Au ISOSWS spectiuu of ICLIS has revealed promincut ΟΠ and [Fell line cussion which. together with {STI and [OTV]. account for most of the observed IRAS fux in he 12. 25 xuids.," An ISO–SWS spectrum of IC443 has revealed prominent [NeII] and [FeII] line emission which, together with [SIII] and [OIV], account for most of the observed IRAS flux in the 12, 25 bands."1013" Simple arguments indicate that this is probably he case in other radiative SNRs and this result suggests hat the unusually blue IRAS colours of radiative SNRs siuplv reflect line contamination. rather than a large »pulatiou of sinall eraius which are otherwise required o explain the warmer ""continu endssiou."," Simple arguments indicate that this is probably the case in other radiative SNRs and this result suggests that the unusually blue IRAS colours of radiative SNRs simply reflect line contamination, rather than a large population of small grains which are otherwise required to explain the warmer “continuum” emission."1014 Available eround based data also indicate that S(2). ος} rotational ines of II» contribute to a large fraction of the IRAS 12 chussion from the southern ria of The relaive fluxes of the ionic lines detected by ISO vield a ~0.6 \ solar Fe gasphase relative abundance which is significantly lower than that found iu the much more poworul ROWL03 supernova remnant.," Available ground based data also indicate that S(2), S(3) rotational lines of $_2$ contribute to a large fraction of the IRAS 12 emission from the southern rim of The relative fluxes of the ionic lines detected by ISO yield a $\simeq$ 0.6 $\times$ solar Fe gas–phase relative abundance which is significantly lower than that found in the much more powerful RCW103 supernova remnant."1015 This max inplv tha he shock in ICLL3 is slower aud thus less effective in cestroving the Febearing ooerains., This may imply that the shock in IC443 is slower and thus less effective in destroying the Fe–bearing grains.1016 This scenario is also supported by the lower line surface brightuess aud [NGHE]/|NeII| ratio which both indicate a lower shock speed in ICE13., This scenario is also supported by the lower line surface brightness and [NeIII]/[NeII] ratio which both indicate a lower shock speed in IC443.1017"model with average Z/H predicts line ratios about nearly the same as the Τειω--40000 K and log U=-3.67 model with an abundance enhancement of about 0.5 dex, would have the very different temperatures of 6530 K and 4680 K. The important conclusion of this section is that theoretically one can explain the low-ionization color-color diagram for the non-Barnard’s Loop samples by a range of values of U,Tstar, and Z/H. A simple ratio of nebular line intensities for two different ions cannot produce an unambiguous estimate ofΤο.","model with average Z/H predicts line ratios about nearly the same as the =40000 K and log U=-3.67 model with an abundance enhancement of about 0.5 dex, would have the very different temperatures of 6530 K and 4680 K. The important conclusion of this section is that theoretically one can explain the low-ionization color-color diagram for the non-Barnard's Loop samples by a range of values of U, and Z/H. A simple ratio of nebular line intensities for two different ions cannot produce an unambiguous estimate of."1018 The reason for the designation WIM (warm ionized medium) is the fact that tthere is higher than the cold gas in the ISM., The reason for the designation WIM (warm ionized medium) is the fact that there is higher than the cold gas in the ISM.1019 The actual value for the WIM's temperature is much more uncertain than sometimes stated in the literature because there are few observations (summarized in this section) that allow a direct determination and the indirect methods (based on only the I([N II] 6583 A))/I(Ha)) ratio) commonly employed are uncertain as they assume a fixed nitrogen ionization ratio and abundance., The actual value for the WIM's temperature is much more uncertain than sometimes stated in the literature because there are few observations (summarized in this section) that allow a direct determination and the indirect methods (based on only the I([N II] 6583 ) ratio) commonly employed are uncertain as they assume a fixed nitrogen ionization ratio and abundance.1020 In this section we summarize the results for dderived by direct means., In this section we summarize the results for derived by direct means.1021" There are three direct methods of determiningT,.", There are three direct methods of determining.1022. The first is from the measurement of forbidden line intensity ratios within a single ion., The first is from the measurement of forbidden line intensity ratios within a single ion.1023 The second is from the width of emission lines from ions of very different mass., The second is from the width of emission lines from ions of very different mass.1024 The third is from the ratio of continuum to recombination line emission., The third is from the ratio of continuum to recombination line emission.1025" Observations of the low-ionizationization WIM cannot use the most widely used indicator, the [O III] auroral/nebular line ratios."," Observations of the low-ionizationization WIM cannot use the most widely used indicator, the [O III] auroral/nebular line ratios."1026" However, Reynoldsetal.(2001) were"," However, \citet{rey01} were"1027 , 1028Black holes are the vacuum solutions of Einstein's field equations in general relativity.,Black holes are the vacuum solutions of Einstein's field equations in general relativity.1029 Classically. a black hole is conceived as a singularity in space time. censored from the rest of the Universe by a mathematically detined one way surface. the event horizon.," Classically, a black hole is conceived as a singularity in space time, censored from the rest of the Universe by a mathematically defined one way surface, the event horizon."1030 In astrophysics. black holes are the end points of the gravitational collapse of massive celestial objects.," In astrophysics, black holes are the end points of the gravitational collapse of massive celestial objects."1031" ""Observed! astrophysical black holes may be broadly classified into three different categories. the stellar mass CVgg a few A. ). the intermediate mass (significantly more massive than the stellar mass black holes but far less massive than the super massive black holes) and super massive (Ade42:10""AZ. ) black 10les."," `Observed' astrophysical black holes may be broadly classified into three different categories, the stellar mass $M_{BH}{\sim}$ a few $M_{\odot}$ ), the intermediate mass (significantly more massive than the stellar mass black holes but far less massive than the super massive black holes) and super massive $M_{BH}{\ge}{10^6}M_{\odot}$ ) black holes."1032 All of the above mentioned candidates accrete matter from the surroundings. provided that the sources for such infalling material do exist.," All of the above mentioned candidates accrete matter from the surroundings, provided that the sources for such infalling material do exist."1033 Depending on the iiatrinsic angular momentum content of accreting material. either spherically symmetric (zero angular momentum flow of matter). or axisymmetric (matter flow with non-zero finite angular momentum) flow geometry may be invoked to study an accreting black hole system.," Depending on the intrinsic angular momentum content of accreting material, either spherically symmetric (zero angular momentum flow of matter), or axisymmetric (matter flow with non-zero finite angular momentum) flow geometry may be invoked to study an accreting black hole system."1034 Since he black holes manifest their presence only gravitationaly. and no spectral information can directly be obtained or these candidates. one must rely on the accretion processes to understand teir observational signature 2002). ," Since the black holes manifest their presence only gravitationally, and no spectral information can directly be obtained for these candidates, one must rely on the accretion processes to understand their observational signature \citep{pri81,kato-book,fkr02}. ."1035The local Mach number AZ of the accreting fluid can be detined as the ratio of he local dynamical flow velocity o the local velocity of ?ropagation of the acoustiο perturbation embedded inside the accreting matter., The local Mach number $M$ of the accreting fluid can be defined as the ratio of the local dynamical flow velocity to the local velocity of propagation of the acoustic perturbation embedded inside the accreting matter.1036 The flow will be locally subsonic or supersonie according to Al(r) lorI., The flow will be locally subsonic or supersonic according to $M(r) < 1$ or $ >1$.1037 Thefl(»w Is transonic if at any moment it crosses 1=1., The flow is transonic if at any moment it crosses $M=1$.1038 At a distance far away from the black hole. accreting material almost always remains subsonic (except possibly for the supersonic stellar wind fed accretion) since it possesses neσigible dynamical flow velocity.," At a distance far away from the black hole, accreting material almost always remains subsonic (except possibly for the supersonic stellar wind fed accretion) since it possesses negligible dynamical flow velocity."1039 On the other hand. the flow velocity will approach the velocity of light e while crossing the event horizon. whereas the maximum possible value of sound sneed (even for the steepest possible equation of state) would be ¢/\/3. resulting AZ>1 ckyse to the event horizon.," On the other hand, the flow velocity will approach the velocity of light $c$ while crossing the event horizon, whereas the maximum possible value of sound speed (even for the steepest possible equation of state) would be $c/\sqrt{3}$, resulting $M>1$ close to the event horizon."1040 In order to satisfy such inner boundary concition imposed by the event horizon. accretion onto black holes exhibi ransonic properties in general.," In order to satisfy such inner boundary condition imposed by the event horizon, accretion onto black holes exhibit transonic properties in general."1041 A sonic/transonie transition in black hole accretion occurs when a subsonic to supersonic or supersonic to subsonic transition takes place either continuously (usually from a subsonic to a supersonic transition) or discontinuously (usually from a supersonic oa subsonic transition)., A sonic/transonic transition in black hole accretion occurs when a subsonic to supersonic or supersonic to subsonic transition takes place either continuously (usually from a subsonic to a supersonic transition) or discontinuously (usually from a supersonic to a subsonic transition).1042 The particular value of the spatial location where such transition takes place coninuously is called a transonie point or a sonic point. and where such crossing takes place discontinuously are called shocks or discontinuities.," The particular value of the spatial location where such transition takes place continuously is called a transonic point or a sonic point, and where such crossing takes place discontinuously are called shocks or discontinuities."1043 In supersonic black hole accretion. perturbation of various Kinds may produce shocks. where some dynamical and thermodynamic accretion variables changes disconinuously as such shock surfaces are crossed.," In supersonic black hole accretion, perturbation of various kinds may produce shocks, where some dynamical and thermodynamic accretion variables changes discontinuously as such shock surfaces are crossed."1044 Cert;ain boundary conditions are to be satistied across the sqywock. and according to those conditions. shocks in black hole accretion dises are classitied into various categories.," Certain boundary conditions are to be satisfied across the shock, and according to those conditions, shocks in black hole accretion discs are classified into various categories."1045 Such shock waves are quite often generated in supersonic accretion flows having small amount o “intrinsic angular momentum. resulting the final subsonie state of tthe flow.," Such shock waves are quite often generated in supersonic accretion flows having small amount of intrinsic angular momentum, resulting the final subsonic state of the flow."1046" This is because the repulsive centrifugal potential barrier experienced by such flows is sufficiently strong to brake the infalling nx""tion and a stationary solution could be introduced only through a shock.", This is because the repulsive centrifugal potential barrier experienced by such flows is sufficiently strong to brake the infalling motion and a stationary solution could be introduced only through a shock.1047 Rotating. transonic astrophysical fluid flows are thus believed to be ‘prone’ to the shock formation phenomena.," Rotating, transonic astrophysical fluid flows are thus believed to be `prone' to the shock formation phenomena."1048 The study of steady. standing. stationary shock waves produced in black hoe accretion and related phenomena thus acquired an important status in recent years (Fukue1983.1987.2004.2:Chakrabarti1989:KafatosCzerny 2000).," The study of steady, standing, stationary shock waves produced in black hole accretion and related phenomena thus acquired an important status in recent years \citep{fuk83,fuk87,fuk04,fuk04a,c89,ky94,yk95,caditz-tsuruta,1049fukumara-suruta,takahashi,das02,dpm03,abd06,dbd07,lyyy97,lugu,nf89,nagyam08,1050nakayama,nagakura,toth,das-czerny}."1051 On the other hand. a physical transonic accretion solutions can mathemaically be realized as critical solution on the phase portrai (spanned by dynamical flow velocity/Mach number and the radial distance) of the black hole accretion.," On the other hand, a physical transonic accretion solutions can mathematically be realized as critical solution on the phase portrait (spanned by dynamical flow velocity/Mach number and the radial distance) of the black hole accretion."1052 Tus is becuuse. from analytica erspective. problems in |black hole accretion fall under the general class of nonlinear dynamics (Ray&Bhattacharjee2002:Afshordi2007:Bhattacharjeeetal. 2009).. since accretion describes the dynamics of a conipressible astrophysica fluid. governed by a set of nonlinear differential equations.," This is because, from analytical perspective, problems in black hole accretion fall under the general class of nonlinear dynamics \citep{rb02,ap03,ray03a,ray03b,rbcqg05a,rbcqg05b,crd06,rbcqg06,rbcqg07a,br07,gkrd07,jkb09}, since accretion describes the dynamics of a compressible astrophysical fluid, governed by a set of nonlinear differential equations."1053 Such non-linear equations describing the steady. inviscid axisymmetric flow can urther be tailored to construct a first order autonomous dynamical system.," Such non-linear equations describing the steady, inviscid axisymmetric flow can further be tailored to construct a first order autonomous dynamical system."1054 Physical transonie solution in such flows can be represenec mathematically as critical solutions in the velocity (or Mach number) phase plane of the flow — they are associated with the critical points (alternatively known as the fixed points or the equilibrium points. see Jordan&Smith(1999). and Chicone(2006) for further details abcnu he fixed point analysis techniques).," Physical transonic solution in such flows can be represented mathematically as critical solutions in the velocity (or Mach number) phase plane of the flow – they are associated with the critical points (alternatively known as the fixed points or the equilibrium points, see \cite{js99} and \cite{diff-eqn-book} for further details about the fixed point analysis techniques)."1055 To maintain the transonicity such critical points will perforce have to be saddle points. which will enaE a solution to pass through themselves.," To maintain the transonicity such critical points will perforce have to be saddle points, which will enable a solution to pass through themselves."1056 Hereafter. ‘multi-critical’ flow refers to the category of the accretion flow configuration which can have multiple critical points accessiMis ο the accretion flow.," Hereafter, `multi-critical' flow refers to the category of the accretion flow configuration which can have multiple critical points accessible to the accretion flow."1057 For low angular momentum axisymmetric black hole accretion. it may so happen that the critical features are exhibied more than once in the johase portrait of a stationary solution describing such flow (Liang&Thompson1980:AbramowiezZurek198etal.2006:Das2007:&Czerny 2009). and accretion becomes multi-critieal.," For low angular momentum axisymmetric black hole accretion, it may so happen that the critical features are exhibited more than once in the phase portrait of a stationary solution describing such flow \citep{lt80,az81,boz-pac,boz1,fuk83,fuk87,fuk04,fuk04a,lu85,lu86,bmc86,ak89,abram-chak,1058ky94,yk95,caditz-tsuruta,das02,bdw04,abd06,dbd07,das-czerny}, and accretion becomes multi-critical."1059 In reality. such weakly rotating sub-Keplerian flows are exhibited in various physical situations. such as detached binary systems fed by accretion from OB stellar winds Hllarionov&Sunvaevt1975):LiangNolan ¢1980))). semi-detached low-mass non-magnetic binaries €Bisikaloetal. (1998))). and black holes fed by accretion from slowly rotating central stellar clusters (IHlarionov(1988):Ho(1999) and references therein).," In reality, such weakly rotating sub-Keplerian flows are exhibited in various physical situations, such as detached binary systems fed by accretion from OB stellar winds \cite{ila-shu,liang-nolan}) ), semi-detached low-mass non-magnetic binaries (\cite{bisikalo}) ), and super-massive black holes fed by accretion from slowly rotating central stellar clusters \cite{ila,ho} and references therein)."1060 Even, Even1061"were grouped to require at least 20 counts per bin using the ftool ""erppha"" to ensure valid results using X statistical analysis.",were grouped to require at least 20 counts per bin using the ftool “grppha” to ensure valid results using $\chi^2$ statistical analysis.1062 The spectra were analyzed using XSPEC version 11.3.2ag (Arnaud1996)., The spectra were analyzed using XSPEC version 11.3.2ag \citep{a96}.1063. Fits were restricted to the 0.6-10 keV range due to calibration uncertainties at energies less than 0.6 keV. The uncertainties reported in this work are Io errors. obtained by allowing all fit parameters to vary simultaneously.," Fits were restricted to the 0.6-10 keV range due to calibration uncertainties at energies less than 0.6 keV. The uncertainties reported in this work are $1\sigma$ errors, obtained by allowing all fit parameters to vary simultaneously."1064 The observations were affected by pile-up. as the observed count rate varied from 161—331cts! (0.6-10 keV).," The observations were affected by pile-up, as the observed count rate varied from $161 - 331\,\mathrm{ct}\,\mathrm{s}^{-1}$ (0.6-10 keV)."1065 To correct for pile-up. we followed the spectral fitting method described in Romanoetal.(2006) and. Rykoffetal.(2007): using various exclusion regions centered on the source. we refit the continuum spectrum until the fit parameters did not vary significantly.," To correct for pile-up, we followed the spectral fitting method described in \citet{rcccc06}1066 and \citet{rmst07}: using various exclusion regions centered on the source, we refit the continuum spectrum until the fit parameters did not vary significantly."1067 We found that a 10 pixel exclusion region was sufficient to correct pile-up in the brightest epochs., We found that a 10 pixel exclusion region was sufficient to correct pile-up in the brightest epochs.1068 For simplicity. we use the same exclusion region for all of the observations.," For simplicity, we use the same exclusion region for all of the observations."1069 We then caleulate the conversion factor to determine the non-piled-up equivalent count rate., We then calculate the conversion factor to determine the non-piled-up equivalent count rate.1070 This is obtained from the ratio of the arf (at 1.5 keV) calculated with and without PSF correction., This is obtained from the ratio of the arf (at 1.5 keV) calculated with and without PSF correction.1071 We note that this correction is only applied when estimating the source intensity. and Is not necessary when calculating colors. which are count rate ratios.," We note that this correction is only applied when estimating the source intensity, and is not necessary when calculating colors, which are count rate ratios."1072"This trend can also be found in the work of ?,, where the MRI turbulent transport in presence of a toroidal field is investigated with more emphasis on the Pm>| regime.","This trend can also be found in the work of \cite{SH09}, where the MRI turbulent transport in presence of a toroidal field is investigated with more emphasis on the $Pm > 1$ regime."1073 Their Figs., Their Figs.1074" 6 and 7 show that, for Pm=2 and 4 at least (the only ones with enough data in the Pm>1 regime), the transport increases steadily with the Reynolds number for Re<1000 and much more weakly for Re=1000."," 6 and 7 show that, for $Pm=2$ and $4$ at least (the only ones with enough data in the $Pm > 1$ regime), the transport increases steadily with the Reynolds number for $Re \lesssim 1000$ and much more weakly for $Re \gtrsim 1000$."1075" On the contrary, the spread in Reynolds number for Pm<1 is substantial, and systematic."," On the contrary, the spread in Reynolds number for $Pm \le 1$ is substantial, and systematic."1076" Such a spread was not detected in our earlier investigation, due to the larger fluctuations in transport related to the box aspect ratio, as discussed earlier."," Such a spread was not detected in our earlier investigation, due to the larger fluctuations in transport related to the box aspect ratio, as discussed earlier."1077" In fact, this dispersion seems to be an effect of the magnetic Reynolds number."," In fact, this dispersion seems to be an effect of the magnetic Reynolds number."1078" To illustrate this point, the transport is represented on Fig."," To illustrate this point, the transport is represented on Fig."1079" 6 as a function of Rm (left panel) and Re (right panel), for Pm<1; the colors describe different field strengths (8=10? to 104 from top to bottom)."," \ref{transpReRm} as a function of $Rm$ (left panel) and $Re$ (right panel), for $Pm \le 1$; the colors describe different field strengths $\beta=10^2$ to $10^4$ from top to bottom)."1080" The statistics in the number of points at any given Re or Rm is rather low; however, it appears quite clearly that the dispersion of the points at any given Reynolds number is substantially larger in Re (with varying Rm) than in Rm (with varying Re)."," The statistics in the number of points at any given $Re$ or $Rm$ is rather low; however, it appears quite clearly that the dispersion of the points at any given Reynolds number is substantially larger in $Re$ (with varying $Rm$ ) than in $Rm$ (with varying$Re$ )."1081 The largest Reynolds number data strongly support this conclusion., The largest Reynolds number data strongly support this conclusion.1082" Furthermore, the of the transport as a function of Rm indicate the Rm dependence of the transport for Pm<1 is very similar to its Pm dependence as shown on Fig. 5.."," Furthermore, the of the transport as a function of $Rm$ indicate the $Rm$ dependence of the transport for $Pm \le 1$ is very similar to its $Pm$ dependence as shown on Fig. \ref{transp-pm}."1083 This strongly suggests that the Pm dependence observed on this figure is in fact mostly a Rm dependence for Pm<1., This strongly suggests that the $Pm$ dependence observed on this figure is in fact mostly a $Rm$ dependence for $Pm \le 1$.1084" Including the Pm=4 data destroys this correlation, which strengthens the idea that there are two regimes, depending on the Prandtl number (a feature that may be related to the existence of a transition around Pm=2 in zero net flux shearing box simulations)."," Including the $Pm=4$ data destroys this correlation, which strengthens the idea that there are two regimes, depending on the Prandtl number (a feature that may be related to the existence of a transition around $Pm=2$ in zero net flux shearing box simulations)."1085" The relevant results of ?;; although less detailed, are consistent with these findings (see their Fig."," The relevant results of \cite{SH09}; ; although less detailed, are consistent with these findings (see their Fig."1086 7)., 7).1087the circular velocity from the mass of the host halo and its redshift.,the circular velocity from the mass of the host halo and its redshift.1088" The rate at which mass is accreted scales with the Eddington rate for the SMBH, and we set either a fixed Eddington ratio of fgaa=1 (for Pop III seeds), fgaa=0.3 (for massive seeds), or an accretion rate derived from the distribution derived by Merloni&Heinz(2008) (we apply this model to massive seeds only)."," The rate at which mass is accreted scales with the Eddington rate for the SMBH, and we set either a fixed Eddington ratio of $f_{\rm Edd}=1$ (for Pop III seeds), $f_{\rm Edd}=0.3$ (for massive seeds), or an accretion rate derived from the distribution derived by \cite{Merloni08} (we apply this model to massive seeds only)."1089" The empirical distribution of Eddington ratios derived by Merloni Heinz (2008, MHO08 thereafter) is fit by a function in log(Lsa/Lgaa)."," The empirical distribution of Eddington ratios derived by Merloni Heinz (2008, MH08 thereafter) is fit by a function in $\log(L_{\rm bol}/L_{\rm Edd})$."1090" The fitting function of the Eddington ratio distribution as a function of SMBH mass and redshift, is computed in 10 redshift intervals (from z=0 to z= 5) for 4different mass bins (6<log(Mpu/Mo) <77<log(Mpu/Mo)<8 8«log(Msu/Mc)<9; 9«log(Mau/Mc)< 10), and then fit with an analytic function which is the sum of a Schechter function and a log-normal (A. Merloni, private communication)."," The fitting function of the Eddington ratio distribution as a function of SMBH mass and redshift, is computed in 10 redshift intervals (from $z=0$ to $z=5$ ) for 4different mass bins $6 < \log(M_{\rm BH}/\msun)< 7$; $7 < \log(M_{\rm BH}/\msun) < 8$; $8 < \log(M_{\rm BH}/\msun) < 9$; $9 < \log(M_{\rm BH}/\msun) < 10$ ), and then fit with an analytic function which is the sum of a Schechter function and a log-normal (A. Merloni, private communication)."1091 The Eddington ratio distributions are then normalized to unity at every given mass and redshift., The Eddington ratio distributions are then normalized to unity at every given mass and redshift.1092" We dub the three modelsPopIII-Edd, and respectively."," We dub the three models, and respectively."1093 Note that in the model names the first part refers to the type of seed and the second part refers to the kind of accretion history assumed., Note that in the model names the first part refers to the type of seed and the second part refers to the kind of accretion history assumed.1094 Therefore the modelPopIII-Edd refers to: initial sees from Pop III remnants always accreting at the Eddington rate; model refers to initial massive seeds accreting with Eddington ratios drawn from the MHOS8 distribution and the modelMassive-subEdd: initial massive seeds accreting 0.3.X Eddington at all times., Therefore the model refers to: initial sees from Pop III remnants always accreting at the Eddington rate; model refers to initial massive seeds accreting with Eddington ratios drawn from the MH08 distribution and the model: initial massive seeds accreting $0.3X$ Eddington at all times.1095 In the model the accretion rate is not limited to the Eddington rate and mildly super-Eddington accretion rates (up to faa~ 10) are possible and allowed as per MHO8., In the model the accretion rate is not limited to the Eddington rate and mildly super-Eddington accretion rates (up to $f_{\rm Edd}\sim 10$ ) are possible and allowed as per MH08.1096" For all three scenarios considered here, accretion starts after a dynamical timescale at the virial radius, tay,—108yr(Rvir/100kpc) (vvir/100kms~')~+, and lasts until the SMBH, of initial mass Min, has accreted AM."," For all three scenarios considered here, accretion starts after a dynamical timescale at the virial radius, $t_{\rm dyn}=10^8 {\rm yr}\; (R_{\rm vir}/100\, {\rm kpc})(v_{\rm vir}/100 \kms)^{-1}$ , and lasts until the SMBH, of initial mass $M_{\rm in}$, has accreted $\Delta M$."1097" The lifetime of an AGN therefore depends on how much mass it accretes during each episode: where c is the radiative efficiency (c~ 0.1), traa=0.45 Gyr and Mg,=min[(My,+AM),1.3x108(σ/200 kms~')*?4Mo)."," The lifetime of an AGN therefore depends on how much mass it accretes during each episode: where $\epsilon$ is the radiative efficiency $\epsilon \simeq 0.1$ ), $t_{\rm Edd}=0.45$ Gyr and $M_{\rm fin}=\min[(M_{\rm in}+\Delta M),1.3\times10^8\,(\sigma/200 \kms)^{4.24}\msun]$ ."1098" We further assume that, when two galaxies hosting SMBHs merge, the SMBHs themselves merge within the merger timescale of the host halos, which is a plausible assumption for SMBH binaries formed after gas-rich galaxy mergers Dottietal.(2007)."," We further assume that, when two galaxies hosting SMBHs merge, the SMBHs themselves merge within the merger timescale of the host halos, which is a plausible assumption for SMBH binaries formed after gas-rich galaxy mergers \cite{Dotti2007}."1099. We adopt the relations suggested by Taffonietal.(2003) for the merger timescale., We adopt the relations suggested by \cite{Taffoni2003} for the merger timescale.1100" Black holes are allowed to accrete during the merging process if the timescale for accretion, corresponding to the sum of the dynamical timescale and tacn, is longer than the merger timescale."," Black holes are allowed to accrete during the merging process if the timescale for accretion, corresponding to the sum of the dynamical timescale and $t_{\rm AGN}$, is longer than the merger timescale."1101" As outlined earlier, in propagating the seeds it is assumed that accretion episodes and therefore growth spurts are triggered only by major mergers."," As outlined earlier, in propagating the seeds it is assumed that accretion episodes and therefore growth spurts are triggered only by major mergers."1102 We find that in a merger-driven scenario for SMBH growth the most biased galaxies at every epoch host the most massive SMBHs that are most likely already sitting on the Mang— relation., We find that in a merger-driven scenario for SMBH growth the most biased galaxies at every epoch host the most massive SMBHs that are most likely already sitting on the $M_{\rm BH} -\sigma$ relation.1103 Lower mass SMBHs (below 109 Ma) are insteadoc off the relation at z=4 and even at z=2.," Lower mass SMBHs (below $10^6\,\msun$ ) are instead off the relation at $z = 4$ and even at $z = 2$."1104 These baseline results aremechanism., These baseline results are.1105" In the initial massive seeds scenario, most of the SMBH seeds start out the z=0 Mgu—c relation, that is, they are ‘over massive’ compared to the local relation."," In the initial massive seeds scenario, most of the SMBH seeds start out the $z=0$ $\msigma$ relation, that is, they are `over massive' compared to the local relation."1106" Seeds form only in haloes within a narrow range of velocity dispersion (c~15kms! at the earliest epochs, see eqns."," Seeds form only in haloes within a narrow range of velocity dispersion $\sigma \simeq 15\,{\rm1107km\,s}^{-1}$ at the earliest epochs, see eqns."1108 1 and 3., 1 and 3.1109" The SMBH mass corresponding to e~15kms~"", according to the local Mgu—c relation, would be ~3x10?Mc."," The SMBH mass corresponding to $\sigma \simeq 15\,{\rm km\,s}^{-1}$, according to the local $M_{\rm BH} -\sigma$ relation, would be $\sim 3\times 10^31110\msun$."1111 The MF instead peaks at 10?Mc (Lodato Natarajan 2007)., The MF instead peaks at $10^5\msun$ (Lodato Natarajan 2007).1112" As time elapses, all haloes are bound to grow in mass by mergers."," As time elapses, all haloes are bound to grow in mass by mergers."1113" The lowest mass haloes, though, experience mostly minor mergers, that do not trigger accretion episodes, and hence do not grow the SMBH."," The lowest mass haloes, though, experience mostly minor mergers, that do not trigger accretion episodes, and hence do not grow the SMBH."1114" The evolution of these systems can be described by a shift towards the right of the Mau—o relation: o increases, but Msz stays roughly constant."," The evolution of these systems can be described by a shift towards the right of the $\msigma$ relation: $\sigma$ increases, but $M_{\rm BH}$ stays roughly constant."1115" In what follows, we present a detailed comparison of the data with our three models, namely thePopIII-Edd: initial seeds from Pop III remnants with accretion assumed at all times at the Eddington rate;Massive-MH: wherein the initial massive seeds have accretion rates drawn from the distribution determined by MH08; Edd: initial massive seeds with accretion assumed at all Massive-subtimes to be at 0.3x the Eddington rate."," In what follows, we present a detailed comparison of the data with our three models, namely the: initial seeds from Pop III remnants with accretion assumed at all times at the Eddington rate;: wherein the initial massive seeds have accretion rates drawn from the distribution determined by MH08; : initial massive seeds with accretion assumed at all times to be at $0.3 \times$ the Eddington rate."1116" For all three models, we compare our derived MF of BLQSOs with that estimated"," For all three models, we compare our derived MF of BLQSOs with that estimated"1117with which Mechanisms L1 and Lb occur. was. specifically chosen in order to reproduce the observed numbers of short- and long-period BS binaries.,with which Mechanisms I and II occur was specifically chosen in order to reproduce the observed numbers of short- and long-period BS binaries.1118 The important. point to take away is that the observed. BS binary period-eccentricity distribution olfers a potential constraint on the fraction of encounters that result in different merger scenarios., The important point to take away is that the observed BS binary period-eccentricity distribution offers a potential constraint on the fraction of encounters that result in different merger scenarios.1119 Based on our results. Mechanism. LL must occur 4 times more often than Mechanism LE in order to reproduce the observed. BS period. distribution from 113 encounters (or. equivalently. 2|3 encounters involving à very wide binary and 2]|2 encounters between a short-period. binary and a lone-period binary).," Based on our results, Mechanism II must occur $\sim 4$ times more often than Mechanism I in order to reproduce the observed BS period distribution from 1+3 encounters (or, equivalently, 2+3 encounters involving a very wide binary and 2+2 encounters between a short-period binary and a long-period binary)."1120 This can be tested. by performing numerical scattering experiments of encounters involving triples., This can be tested by performing numerical scattering experiments of encounters involving triples.1121 Therefore. our results highlight the need for simulations of 113. 213 and 313 encounters to. be performed. in order to better. understand. their. expected contributions to. BS populations in open and globular clusters.," Therefore, our results highlight the need for simulations of 1+3, 2+3 and 3+3 encounters to be performed in order to better understand their expected contributions to BS populations in open and globular clusters."1122 Once a preferred. encounter. scenario has been identified for an observed. binary or triple containing one or more Bss. numerical scattering experiments can be used. to further constrain the conditions under which that scenario will occur (or to show that it cannot occur)," Once a preferred encounter scenario has been identified for an observed binary or triple containing one or more BSs, numerical scattering experiments can be used to further constrain the conditions under which that scenario will occur (or to show that it cannot occur)."1123 We have demonstrated. that a combination of observational and analytic constraints can be usec to isolate the parameter space relevant to the dynamical. formation of an observed. multiple star system (or population of star systems) containing one or more merger products., We have demonstrated that a combination of observational and analytic constraints can be used to isolate the parameter space relevant to the dynamical formation of an observed multiple star system (or population of star systems) containing one or more merger products.1124" ""This will drastically narrow the relevant. parameter space for numerical scattering experiments.", This will drastically narrow the relevant parameter space for numerical scattering experiments.1125 We have improved. upon the results of Perets&Fab-rvcky(2009). ancl Mathieu&Geller(2009) since. we have shown that dynamical encounters involving triples could not only be contributing to the lone-period DS binaries in NGC Iss. but they could also be an important formation mechanism. for short-periock BS binarics and triples containing Bss.," We have improved upon the results of \citet{perets09} and \citet{mathieu09} since we have shown that dynamical encounters involving triples could not only be contributing to the long-period BS binaries in NGC 188, but they could also be an important formation mechanism for short-period BS binaries and triples containing BSs."1126 We have not ruled. out mass transfer or Ixozai-induced: mergers in. triples (primordial or otherwise) (Mathieu&Geller2009:PeretsLFab-rvcky 2009).. or even various combinations of cillerent mechanisms. as contributing formation channels to the BS binary population in NGC 188.," We have not ruled out mass transfer or Kozai-induced mergers in triples (primordial or otherwise) \citep{mathieu09,1127 perets09}, or even various combinations of different mechanisms, as contributing formation channels to the BS binary population in NGC 188."1128 For instance. à 113 exchange interaction could. stimulate a merger. indirectly if the resulting angle of inclination between the inner and outer orbits of the triple exceeds ~39. ultimately allowing the triple to evolve via the Ixozai. mechanism so that the eccentricitv of the inner binary increases while its period remains roughly constant (Eeeleton2006).," For instance, a 1+3 exchange interaction could stimulate a merger indirectly if the resulting angle of inclination between the inner and outer orbits of the triple exceeds $\sim 39^{\circ}$, ultimately allowing the triple to evolve via the Kozai mechanism so that the eccentricity of the inner binary increases while its period remains roughly constant \citep{eggleton06}."1129. There is evidence to suggest that mass transfer. via toche lobe over Low could play a role in the formation of at least some Bss., There is evidence to suggest that mass transfer via Roche lobe over flow could play a role in the formation of at least some BSs.1130 Ht is dillicult to account for. the near zero cecentricities of some of the long-period DS rinaries without at. least one episode of mass transfer laving occurred., It is difficult to account for the near zero eccentricities of some of the long-period BS binaries without at least one episode of mass transfer having occurred.1131 This is because none of the normal MS-MS rinaries with similar periods have such small eccentricities (Mathieu&Geller2009)., This is because none of the normal MS-MS binaries with similar periods have such small eccentricities \citep{mathieu09}.1132. On the other hand. it may not » Unreasonable to expect that some collision products Left in binaries undergo mass transfer since they are expected o expand aclabatically post-collision. ancl will sooner or ater evolve to ascend the giant branch.," On the other hand, it may not be unreasonable to expect that some collision products left in binaries undergo mass transfer since they are expected to expand adiabatically post-collision, and will sooner or later evolve to ascend the giant branch."1133 As a result. of conservation of energv and angular momentum. the mass ransfer process will usually act to increase the orbital »eriods of these binaries provided it is conservativeLO91).," As a result of conservation of energy and angular momentum, the mass transfer process will usually act to increase the orbital periods of these binaries provided it is conservative."1134. Interestinglv. the cut-olf period for. Roche lobe overllow is 1000 cays for low-mass stars (Egeleton2006).. which is in rough agreement with the lone-periocd peak in the observed: period-eccentricity: distribution of the DS binary population in NGC 188.," Interestingly, the cut-off period for Roche lobe overflow is $\sim 1000$ days for low-mass stars \citep{eggleton06}, which is in rough agreement with the long-period peak in the observed period-eccentricity distribution of the BS binary population in NGC 188."1135 Therefore. mass transfer could also be contributing to the period gap observed. for the BS binaries.," Therefore, mass transfer could also be contributing to the period gap observed for the BS binaries."1136 According to the results of Gelleratal.(2009).. the number of eiant-\IS binaries with P?1000 cdavs is comparable to the number of DS binaries CX. Geller. private communication).," According to the results of \citet{geller09}, the number of giant-MS binaries with $P \lesssim11371000$ days is comparable to the number of BS binaries (A. Geller, private communication)."1138 It is unlikely that every giant-MS binary will form a BS from mass transfer. however. suggesting that at most a few of the long-period DS binaries in NGC ISS were formed via this mechanism.," It is unlikely that every giant-MS binary will form a BS from mass transfer, however, suggesting that at most a few of the long-period BS binaries in NGC 188 were formed via this mechanism."1139 Finally. if the outer companion of a triple svstem evolves to over-fill its Roche lobe it. could. transfer mass to both of the components of the close inner binary.," Finally, if the outer companion of a triple system evolves to over-fill its Roche lobe it could transfer mass to both of the components of the close inner binary."1140 This mechanism could therefore also produce two BSs in a close binary. although it predicts the presence of an orbiting triple companion.," This mechanism could therefore also produce two BSs in a close binary, although it predicts the presence of an orbiting triple companion."1141 For these reasons. a better understanding of triple evolution. as well as binary evolution in binaries containing merger products. is needed.," For these reasons, a better understanding of triple evolution, as well as binary evolution in binaries containing merger products, is needed."1142 The clissipational cllects of tides tend to convert stars bulk translational kinetic energies into internal or thermal energv within the stars. leading to an increase in the total eravitational binding energy of the stellar configuration (e.g.AleMillan.Wut&Making 1990).," The dissipational effects of tides tend to convert stars' bulk translational kinetic energies into internal or thermal energy within the stars, leading to an increase in the total gravitational binding energy of the stellar configuration \citep[e.g.][]{mcmillan90}."1143. ὃν increasing the ternis U;; in Equation 1.. the initial orbital energies of any. binarics &oing into an encounter can increase accordingly in order to conserve energy.," By increasing the terms $_{ii}$ in Equation \ref{eqn:energy-conserv}, the initial orbital energies of any binaries going into an encounter can increase accordingly in order to conserve energy."1144 A higher orbital energy. corresponds to a larger semi-major axis and hence cross section for collision., A higher orbital energy corresponds to a larger semi-major axis and hence cross section for collision.1145 ‘This suggests that the derived encounter time-scales can be taken as upper limits in the limit that tidal dissipation is negligible., This suggests that the derived encounter time-scales can be taken as upper limits in the limit that tidal dissipation is negligible.1146 We expect tides to be particularly elfective during encounters for which the total energy is very negative as à result of one or more very hard binarics being involved., We expect tides to be particularly effective during encounters for which the total energy is very negative as a result of one or more very hard binaries being involved.1147 We have argued in Section 2.2 that the average stellar miss is expected to be comparable to (but slightly less than) the mass of the MAISTO in old OCs and low-mass GC's., We have argued in Section \ref{general} that the average stellar mass is expected to be comparable to (but slightly less than) the mass of the MSTO in old OCs and low-mass GCs.1148 Me have also arguedὃν that most encounters will involve stars having masses slightly larger than the average stellar mass., We have also argued that most encounters will involve stars having masses slightly larger than the average stellar mass.1149 We might therefore expect to find that a high proportion of merger products have masses that exceed that of the AIS'TO in very clyvnamically-evolvect clusters that have lost a aree [fraction of their low-mass stars., We might therefore expect to find that a high proportion of merger products have masses that exceed that of the MSTO in very dynamically-evolved clusters that have lost a large fraction of their low-mass stars.1150 Consequently. a larger number of merger products could appear sullicienthy bright o end up in the DS region of the cluster CMD in these clusters than in their less cvnamicallv-evolved counterparts.," Consequently, a larger number of merger products could appear sufficiently bright to end up in the BS region of the cluster CMD in these clusters than in their less dynamically-evolved counterparts."1151 This is consistent with the results of Ixnigge.Leigh&Sills(2009) and Leigh.Sills&Ixnigge(2009) who found that the number of DSs in the cores of GC's scales sub-linearly with he core mass., This is consistent with the results of \citet{knigge09} and \citet{leigh09} who found that the number of BSs in the cores of GCs scales sub-linearly with the core mass.1152 In particular. since the cluster relaxation time increases with increasing cluster mass. it is the lowest mass GC's that should have lost the largest fraction of their low-mass stars.," In particular, since the cluster relaxation time increases with increasing cluster mass, it is the lowest mass GCs that should have lost the largest fraction of their low-mass stars."1153 Therefore. if à larger fraction of merger products do indeed end up more massive than the MSTO in these clusters. this could be a contributing factor to the observed sub-linear dependence on core mass.," Therefore, if a larger fraction of merger products do indeed end up more massive than the MSTO in these clusters, this could be a contributing factor to the observed sub-linear dependence on core mass."1154 It is also interesting to note that. since BSs are among the most massive cluster members and many are thought to have a binary companion. Bss should be preferentially retained in clusters as they evolve dynamically compared to low-mass ALS stars.," It is also interesting to note that, since BSs are among the most massive cluster members and many are thought to have a binary companion, BSs should be preferentially retained in clusters as they evolve dynamically compared to low-mass MS stars."1155 “Phis, This1156We have presented a new AICAIC aleorithiu for the hiel-L. low signal to noise limit of the joiut posterior Which solves the slow probabilistic couverecuce of the traditional Cübbs sampler iu this regiue.,"We have presented a new MCMC algorithm for the high-L, low signal to noise limit of the joint posterior which solves the slow probabilistic convergence of the traditional Gibbs sampler in this regime."1157 This in principle allows sampling over the joint posterior pCi.sid) over the entire range of angular scales probed by current aud future CAIB experinenuts;," This in principle allows sampling over the joint posterior $p(C_{l}, \Bs | \Bd)$ over the entire range of angular scales probed by current and future CMB experiments."1158 The Πιο coluputational burden is now cutirely in the map-malking step of Cübbs sampling. for which the cost per Cübbs iteration now scales with the expense of multiplication bv the inverse noise matrix INN[2," The limiting computational burden is now entirely in the map-making step of Gibbs sampling, for which the cost per Gibbs iteration now scales with the expense of multiplication by the inverse noise matrix $\BN^{-1}$."1159 Asstnine pixel uncorrelated (but scan weighted) noise as a good approximation at small augular scales. the cost of au NP) anultipleation is that of a forward aud inverse," Assuming pixel uncorrelated (but scan weighted) noise as a good approximation at small angular scales, the cost of an $\BN^{-1}$ multiplcation is that of a forward and inverse"1160is described in Sect.,is described in Sect.1161 5 but it is important to note here that as the starburst radius increases the dust gets colder aud the spectrum shifts to lounger wavelenetls., 5 but it is important to note here that as the starburst radius increases the dust gets colder and the spectrum shifts to longer wavelengths.1162 Starburst models with a radius of LOkpe come close to matching the coniplete spectral energv distribution but as we discuss in Sect., Starburst models with a radius of 10kpc come close to matching the complete spectral energy distribution but as we discuss in Sect.1163 6 such extended starbursts are excluded by millimetre interferometry., 6 such extended starbursts are excluded by millimetre interferometry.1164 Efstathiou. Rowan-Robinsou Siebenimoreeu (2000; rereatter ERRS) prescuted a starburst model tha conibined a simpe anodel for the evolution of eian nolecular clou stje stelay population svuthesis model of Druzual Charlot (1993) and detailed radiative trausfer hat included the effect of temperature fluctuating sinal erains with dust particle radius &<LOOA and PATIs o account for the detected infrared enmüssiou bands (Sichemmorecen Rrüesel 1992).," Efstathiou, Rowan-Robinson Siebenmorgen (2000; hereafter ERRS) presented a starburst model that combined a simple model for the evolution of giant molecular clouds, the stellar population synthesis model of Bruzual Charlot (1993) and detailed radiative transfer that included the effect of temperature fluctuating small grains with dust particle radius $a < 100$ and PAHs to account for the detected infrared emission bands (Siebenmorgen Krüggel 1992)."1165 Au important feature of ιο ERRS model is that the expansion of the IIT region cads to the formation of a narrow shell of gas and dust., An important feature of the ERRS model is that the expansion of the HII region leads to the formation of a narrow shell of gas and dust.1166 This naturally explains the fact that the near- aud micd-oeifared. spectra of starburst ealaxies are not dominated wv enmusson from hot laree (a> LOOA)) dust erains but w the PATs cussion., This naturally explains the fact that the near- and mid-infrared spectra of starburst galaxies are not dominated by emission from hot large $a>100$ ) dust grains but by the PAHs emission.1167" As in ERRS we assiune that the oeutial ον of f1ο moleculu clouds that constitue the y.arburst is SOmae but we use the erai modcl described oe1 Sect,", As in ERRS we assume that the initial $A_V$ of the molecular clouds that constitute the starburst is $50$ mag but we use the grain model described in Sect.1168 3., 3.1169" We urther assume a constant star formation rate and an age of ολο,", We further assume a constant star formation rate and an age of 5Myr.1170 The assumed starburst age is very poorly coustrained by our modeling but as we discuss oe1 section 6 a value of 5bMyr can explain the fact that the oeferred hunosities of the starburst aud cis components are coniparablo., The assumed starburst age is very poorly constrained by our modeling but as we discuss in section 6 a value of 5Myr can explain the fact that the inferred luinosities of the starburst and cirrus components are comparable.1171 Tn Fig., In Fig.1172 | we preseut fits to f1e galaxies in our sample with a colubination of starburst ando cirrus., \ref{ane.ps} we present fits to the galaxies in our sample with a combination of starburst and cirrus.1173 Wo first normalize the cirrus nodel at 850750 and then scale the starburst model so that the comΠλ of starburst aux cunrus gives the best fit to the mid-infrared spectroscopy and is consistent with the far-infrared plotometry., We first normalize the cirrus model at $\mu m$ and then scale the starburst model so that the combination of starburst and cirrus gives the best fit to the mid-infrared spectroscopy and is consistent with the far-infrared photometry.1174 As discussed in Sect., As discussed in Sect.1175 3. for tiree ofthe objects we do not nee auv starburst contriution for explaining the SED.," 3, for three of the objects we do not need any starburst contribution for explaining the SED."1176 For two of the objects we also find evidence for an ACN compoucut which we model with the tapered discs of Efstathiot Rowan-Robinson (1995)., For two of the objects we also find evidence for an AGN component which we model with the tapered discs of Efstathiou Rowan-Robinson (1995).1177 The more hDuninous of f1e wo objects (SMM. 02399-0126). has been classified as a Sevtert 2 by Simail et al. (," The more luminous of the two objects (SMM J02399-0136), has been classified as a Seyfert 2 by Smail et al. ("11782002).,2002).1179 SMIAL J02399-0136 is also he object that has been detected at 70 and 160455., SMM J02399-0136 is also the object that has been detected at 70 and $\mu m$.1180 The uninosities o the tiree coniponenuts and the associated dust niasses are give rin Table 2., The luminosities of the three components and the associated dust masses are given in Table 2.1181 Iu the ERRS mocel iu lucrease in the Iuniuositv trauslates into a Lincrease in the imiuber of molecular clouds that constitute the starburst and therefore the dust mass., In the ERRS model an increase in the luminosity translates into an increase in the number of molecular clouds that constitute the starburst and therefore the dust mass.1182 Sicbenmorecn νήσος (2007) presented a starburst model which dis an evolution of an ewrlior ος described by νήσοςOO Tutukov (1978) aud E&zrüsecl85 Siebeninoreen (1991)., Siebenmorgen Krüggel (2007) presented a starburst model which is an evolution of an earlier model described by Krüggel Tutukov (1978) and Krüggel Siebenmorgen (1994).1183 The model assumes that the stars are divided in two classes: OB stars that are surrounded by dense clouds aud constitute so-called hot spots aud other stars (old bilee stars or massive stars} that are dispersed in the diffuse medimm (see below)., The model assumes that the stars are divided in two classes: OB stars that are surrounded by dense clouds and constitute so-called hot spots and other stars (old bulge stars or massive stars) that are dispersed in the diffuse medium (see below).1184 The hot spots determine the mid infrared part of he ciission spectrun., The hot spots determine the mid infrared part of the emission spectrum.1185 The outer radius of the hot spots isi determiye by the condition of equal heating of the dust by f10 stars and the iaubieut iutersellar radiation field., The outer radius of the hot spots is determined by the condition of equal heating of the dust by the stars and the ambient interstellar radiation field.1186 Both classes of stas are represented in the οςuation of radiativei transfer bv continuously distributed source teris., Both classes of stars are represented in the equation of radiative transfer by continuously distributed source terms.1187 It is assumed that the uuuber deusitv of the hot spots aud othe other stars falls off with the radius othe starburs as wa), It is assumed that the number density of the hot spots and of the other stars falls off with the radius of the starburst as $r^{-1.5}$.1188 Iu addition to the dist in the hot spots the mode asstumes that the volue of the starburst is Ἡed by dust which is uniformly distributed aud gives rise to a tota extinction Aj from the outer radius £7 of 1ο ealactic cleus to its center., In addition to the dust in the hot spots the model assumes that the volume of the starburst is filled by dust which is uniformly distributed and gives rise to a total extinction $A_V^{'}$ from the outer radius $R$ of the galactic nucleus to its center.1189 lut Us homogeneous density mode he parameter A is (irectlv related to the dus mass Map and ouly oue of them is independent., In this homogeneous density model the parameter $A_V^{'}$ is directly related to the dust mass $M_{SB}^{'}$ and only one of them is independent.1190" The other mode πο are the toalh iinuosity Loy, aud the starburst radius R.", The other model parameters are the total luminosity $L_{SB}^{'}$ and the starburst radius $R$.1191 The OD sars are assumed to be confined to he central 350pc whereas the bulge stars fll the whole volue., The OB stars are assumed to be confined to the central 350pc whereas the bulge stars fill the whole volume.1192 Iu Fig., In Fig.1193 5 we combine starburst models computed with he method of Sicbcumoregen νήσος. (2007) with cirrus uodels and compare them with the data of he objects iu our suuple., \ref{rs.ps} we combine starburst models computed with the method of Siebenmorgen Krüggel (2007) with cirrus models and compare them with the data of the objects in our sample.1194 As iu the case of he evolutiouarv mnodcls we first normalize the cirrus mode lat 8S5üjnn., As in the case of the evolutionary models we first normalize the cirrus model at $\mu m$.1195 Tien we search in the SED library to fud asarburst mode] which. after scaling to the distance of the object but without further jormalization. best fit the 12k-iufrared specroscopy.," Then we search in the SED library to find a starburst model which, after scaling to the distance of the object but without further normalization, best fit the mid-infrared spectroscopy."1196 The starburst radius is fixed at 3kpc to be coidstent with he sizes inferred from iterteyolmetry for these galaxies (Sect., The starburst radius is fixed at 3kpc to be consistent with the sizes inferred from interferometry for these galaxies (Sect.1197 6)., 6).1198 Unless otherwise iidicated the value of ¢ is asstunecd to be 5 as before., Unless otherwise indicated the value of $\psi $ is assumed to be 5 as before.1199 Siace the original suggestionOO of ERRO3 aud Iia et al. (, Since the original suggestion of ERR03 and Kaviani et al. (12002x003) that SMCs are colder aud more extended than local ULIRGs a nuuber of studies have eiven support to this idea.,2003) that SMGs are colder and more extended than local ULIRGs a number of studies have given support to this idea.

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