ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 In relation to the present study. tidal ellects like orbital circularisation inject internal energy into the planet. aud herefore delay its contraction.," In relation to the present study, tidal effects like orbital circularisation inject internal energy into the planet, and therefore delay its contraction."3 7 have estimated. the amount of tidal energy absorbed by the planet curing orbital circularisation. and show that it is large enough to alfect the rylanctary raclius.," \citet{jac08} have estimated the amount of tidal energy absorbed by the planet during orbital circularisation, and show that it is large enough to affect the planetary radius."4 We repeat our analysis of tical scales. identifying aancts with anomalously large. radii. by comparison of heir observed. position in the mass-racius ciagrams with heoretical mocels from. ?..," We repeat our analysis of tidal scales, identifying planets with anomalously large radii, by comparison of their observed position in the mass-radius diagrams with theoretical models from \citet{bar08}."5 Phe result is shown in bie. 4..," The result is shown in Fig. \ref{bloat},"6 on the same plane as Fig. 2.., on the same plane as Fig. \ref{tides}.7 Η tidal elfects. were related. το radius excess. some correlation would be expected between the strength of tidal forces and the excess radius.," If tidal effects were related to radius excess, some correlation would be expected between the strength of tidal forces and the excess radius."8 Correlation does not. prove, Correlation does not prove9"where g(p.rg)=ara|rp)21/2""|. and ro=FfC (0.1) where R. is the distance of blob to the center.","where $g(\mu,r_0)=\left[\left(1-r_0^2+r_0^2\mu^2\right)^{1/2}-r_0\mu\right]^{-2}$, and $r_0=R_{\gam}/\rblr \in (0,1)$ , where $R_{\gam}$ is the distance of blob to the center."10 Figure 2 shows the augular distribution in blob comoving frame., Figure 2 shows the angular distribution in blob comoving frame.11 It can be secu that the geometry effect of reflecting mirror isotropizes the radiation at some degrees. but the beamine effect still dominates.," It can be seen that the geometry effect of reflecting mirror isotropizes the radiation at some degrees, but the beaming effect still dominates."12 It is still a good approxination that the radiation is beamed with a cone of solid angle z/I?., It is still a good approximation that the radiation is beamed with a cone of solid angle $\pi/\Gam^2$.13 Thus the pair opacity cau be written as (Could Schrédder 1967) where e.=2/(1gle. and the photon-photou cross section σ.. reads where 2! is the speed of the electron and positron iu the center momentum frame 3={lL2/e;e.(1li., Thus the pair opacity can be written as (Gould Schrédder 1967) where $\eps_c=2/(1-\mu)\epsg$ and the photon-photon cross section $\siggg$ reads where $\beta$ is the speed of the electron and positron in the center of momentum frame $\beta=\left[1-2/\epsg \eps_s(1-\mu)\right]^{1/2}$.14" Performing ofthe integral we have where A(q) reads with ly (ye)nFGdo,οηνis the. integral of. μι) andover the eutire broad line region. which can be evaluated as with oq=7/2I). 0»=arcoosflyAy. and Oy=aresinv1pe."," Performing the integral we have where $A(q)$ reads with and $A_1(\mu)=\int_0^1f(\mu,r_0)dr_0$ is the integral of $f(\mu,r_0)$ over the entire broad line region, which can be evaluated as with $\phi_1=\pi/2-\theta_0$, $\phi_2=\arccos \sqrt{1-\mu^2}-\theta_0$, and $\theta_0=\arcsin \sqrt{1-\mu^2}$."15 The function fy) is plotted in Fig 3., The function $A(q)$ is plotted in Fig 3.16 Since the beamed radiation field reduces the effective cross section of plioton-plioton interaction by a factor 1/(2D)7. it would be couvenieut to check our approximation by the quantity (2D?Atq).," Since the beamed radiation field reduces the effective cross section of photon-photon interaction by a factor $1/(2\Gam)^2$, it would be convenient to check our approximation by the quantity $(2\Gam)^2A(q)$."17 We can easilv fud that it is close to 0.30.1 when q~1.7. sugeesting our approximation is accurate chough.," We can easily find that it is close to $\sim$ 0.4 when $q \sim 1.7$, suggesting our approximation is accurate enough."18 It should be pointed out that the prescut treatincuts of reflected. svuchrotrou radiation cau be couvenicutly extended to the inclusion ofthe radiation from the secondary electrons if we further study the pair cascade im the future., It should be pointed out that the present treatments of reflected synchrotron radiation can be conveniently extended to the inclusion of the radiation from the secondary electrons if we further study the pair cascade in the future.19 The last two subsections are devoted to theinfernal absorption of TeV photons. the developments of pair cascade due to the present mechanisua will be treated In a preparing paper (Wane. Zhou Cheng 2000).," The last two subsections are devoted to the absorption of TeV photons, the developments of pair cascade due to the present mechanism will be treated in a preparing paper (Wang, Zhou Cheng 2000)."20 However it would be useful to compare the dimensions aud radiation of the pair cloud due to theinterne? absorption and the pair halo sugeested by Abaronian. Coppi. Voolk (1991). who argue the formation of pair halo due to the interaction of TeV photons from ACNs with infrared photous of cosmological background. radiation.," However it would be useful to compare the dimensions and radiation of the pair cloud due to the absorption and the pair halo suggested by Aharonian, Coppi, Veolk (1994), who argue the formation of pair halo due to the interaction of TeV photons from AGNs with infrared photons of cosmological background radiation."21 Thisο absorption produces pairs. which are quickly isotropized by an ambicut random magnetic field. forming a extended halo of pairs with typical dimension of (2>1Mpc).," This absorption produces pairs, which are quickly isotropized by an ambient random magnetic field, forming a extended halo of pairs with typical dimension of $R>1$ Mpc)."22 Without specific mechanisin we know that the time scale of halo formation is of about 109 vr., Without specific mechanism we know that the time scale of halo formation is of about $10^6$ yr.23 Usually this absorption is regarded as the main mechanism of deficiency of TeV emissiou from ECRET-loud blazars (Stecker de Jager 1998)., Usually this absorption is regarded as the main mechanism of deficiency of TeV emission from -loud blazars (Stecker de Jager 1998).24 Let us simply estimate the scale of pair halo before it is isotropized by the aimbicut maguetic field., Let us simply estimate the scale of pair halo before it is isotropized by the ambient magnetic field.25 Asstuning the intergalactic magnetic field B=1Ὁ Gauss. then the mean free path of pair electrous im halo reacls The initial halo is of such a dimension. which is much larger than that of absorption case.," Assuming the intergalactic magnetic field $B=10^{-9}$ Gauss, then the mean free path of pair electrons in halo reads The initial halo is of such a dimension, which is much larger than that of absorption case."26 Abarouian. Coppi. Volk (1991) have suggested. some signatures of such an exteuded halo. especially for the light curves iu ligh euergv bands (Coppi Aharonian 1990).," Aharonian, Coppi, Volk (1994) have suggested some signatures of such an extended halo, especially for the light curves in high energy bands (Coppi Aharonian 1999)."27 Auvway this is much larger than that of the present pair cloud., Anyway this is much larger than that of the present pair cloud.28" Thus it is easier to distinguish the two cases,", Thus it is easier to distinguish the two cases.29 We have set a new constraint on the very high enerev Cluission iu terii of observable quantities., We have set a new constraint on the very high energy emission in term of observable quantities.30 As the applications of the present model. we would like to address sole properties of very high cnerey from blazars.," As the applications of the present model, we would like to address some properties of very high energy from blazars."31 The broadbaud contimmiun of blazars show attractive features which indicate the different processes powering the objects., The broadband continuum of blazars show attractive features which indicate the different processes powering the objects.32" The ratio L./L,, of >-ray huuiuositv to optical in flat spectrum radio quasars (FSRQs) is quite different frou that in BL Lacs (Doudi Chiscllini 1995).", The ratio $L_{\gam}/L_{\rm op}$ of $\gam$ -ray luminosity to optical in flat spectrum radio quasars (FSRQs) is quite different from that in BL Lacs (Dondi Ghisellini 1995).33" Comastzi et al (1997) confirmed this result in a lore larger samples and found this mean ratio is roushlv of unity iu DL Lacs aud £./£L.,,%30. uamely hasc0.03 in FSROs."," Comastri et al (1997) confirmed this result in a more larger samples and found this mean ratio is roughly of unity in BL Lacs and $L_{\gam}/L_{\rm op}\approx 30$, namely $l_{\rm rsc}\approx 0.03$ in FSRQs."34" Chisellini et al (1993).using the classical limut of SSC model. show that there is a svstemiatical difference i Doppler factors D between BL Lacs and corc-dominated quasars, (dlogD;=0.12 for BL Lacs aud dogD)=ΟΤΙ for core-domiunatec quasars."," Ghisellini et al (1993),using the classical limit of SSC model, show that there is a systematical difference in Doppler factors $\cd$ between BL Lacs and core-dominated quasars, $\langle \log \cd \rangle=0.12$ for BL Lacs and $\langle \log \cd \rangle=0.74$ for core-dominated quasars."35 These differences have Όσοι. confirmed by Cuuijosa Daly (1996) who assiune that the particles aud magnetic field are in equipartition., These differences have been confirmed by Güiijosa Daly (1996) who assume that the particles and magnetic field are in equipartition.36 This differeuce would lead to more prominent difference of reflected svuchrotron plotou energv deusitv. sugeesting a differcut mechanisui in these objects.," This difference would lead to more prominent difference of reflected synchrotron photon energy density, suggesting a different mechanism in these objects."37" The two systematically differcut features m 7A, and Doppler factor 2 strongly sueecst that the different mechaisiu of 5-ray radiation may operate in these objects.", The two systematically different features in $\lrsc$ and Doppler factor $\cd$ strongly suggest that the different mechanism of$\gam$ -ray radiation may operate in these objects.38 From eq.(15) it is believed that the deficiency of TeV Cluission im radio-loud quasars may be due to the present mechanism., From eq.(15) it is believed that the deficiency of TeV emission in radio-loud quasars may be due to the present mechanism.39"lu this section we preseut some analytical calculations which clearly demoustrate what Kind of combinations vetween amplitudes aud phases of the CMD signal in the V.OW bands aud phases of foregrounds are represented iu the dA, estimator.","In this section we present some analytical calculations which clearly demonstrate what kind of combinations between amplitudes and phases of the CMB signal in the V, W bands and phases of foregrounds are represented in the $d^{\Delta}_{\l,m}$ estimator."40 As was mentioned in Section 1. lis cstimator is desigued as a luear cstimator of the oase difference εςνε. if the phase difference is s«nuall.," As was mentioned in Section 1, this estimator is designed as a linear estimator of the phase difference $\Phi_{\l+\Delta,m}-\Phi_{\l,m}$, if the phase difference is small."41" Let us introduce the model of the signal at each baud Dm[2]=cs|F,Γη]v where ο ds. frequencyd independent. CMD sigual. aud F, Di.is the sui over all kinds. of foregrouuds for cach baud j (svuchrotron. frec-frec. dust endssion etc.)."," Let us introduce the model of the signal at each band $a^{(j)}_{\l,m}=c_{\l,m}+F^{(j)}_{\l,m}$, where $c_{\l,m}$ is frequency independent CMB signal and $F^{(j)}_{\l,m}$ is the sum over all kinds of foregrounds for each band $j$ (synchrotron, free-free, dust emission etc.)."42" According to the investigation above ou the foreground models. it ix realized that without the ILC signal the d, estimation of the foregrounds. especially for V aud W bauds. correspoucds to the signal the power of which is significantly simaller then that of the CAIB Iu terms of moduli aud phases of the foreerouuds at cach frequency baud where δι aud εν are the phases of foreground. aud the CAIB. respectively,"," According to the investigation above on the foreground models, it is realized that without the ILC signal the $d^{\Delta}_{\l,m}$ estimation of the foregrounds, especially for V and W bands, corresponds to the signal the power of which is significantly smaller then that of the CMB In terms of moduli and phases of the foregrounds at each frequency band where $\Phi_{\l,m}$ and $\xi_{\l,m}$ are the phases of foreground and the CMB, respectively."43" Aud from Eq.(31)) we eet aud practically speaking. we have $,,,—&Aim"," And from \ref{dd0}) ) we get and practically speaking, we have $\Phi_{\l,m}=\Phi_{\l+\Delta,m}$."44 Thus taking the le correlation iuto account. we can conclude that it reflects directly the high correlation of the phases of the foregrounds. determined by the GF.," Thus, taking the $4n$ correlation into account, we can conclude that it reflects directly the high correlation of the phases of the foregrounds, determined by the GF."45 Moreover. if any foreground cleaned CAIB maps derived from) different imethods display the ly correlation of phases. if would be evident that foreground residuals still determine the statistical properties of the derived signal.," Moreover, if any foreground cleaned CMB maps derived from different methods display the $4n$ correlation of phases, it would be evident that foreground residuals still determine the statistical properties of the derived signal."46" One of the basic ideas for comparison of phases of two sjenals is to define the following trigonometric moments for the phases $, aud Wy, as: where («€(0, "," One of the basic ideas for comparison of phases of two signals is to define the following trigonometric moments for the phases $\xi_{\l^{'},m}$ and $\Psi_{\l,m}$ as: where $\l \le \l^{'}$."47We appv these trigonometric moments to investigate the pliase correlations for ΤΟΠ FCM and WEM., We apply these trigonometric moments to investigate the phase correlations for TOH FCM and WFM.48" For that we simpy substitute (= in Eq.(33)). and define €),, as the pvase of FOCAL and V, as that of WEN."," For that we simply substitute $\l= \l^{'}$ in \ref{def2}) ), and define $\xi_{\l,m}$ as the phase of FCM and $\Psi_{\l,m}$ as that of WFM."49 The result of he caleulatiouns is preseuted iu Fie.13.., The result of the calculations is presented in \ref{comp}.50 From Fig.13 it can be clearly ποσα that the PCM has strong Af=| correlations starting from (.~10 which rapidly increase for 6>LO. while for WEM these correlations are significautlv damped. especially at low iultipole rauge 6<10.," From \ref{comp} it can be clearly seen that the FCM has strong $\Delta \l=4$ correlations starting from $\l\simeq 40$ which rapidly increase for $\l > 40$, while for WFM these correlations are significantly damped, especially at low multipole range $\l \le 40$."51 ITowever. the dA estimator allow us to clarify the properties of pliase. correlations for low multipole rauge.," However, the $d^{\Delta}_{\l,m}$ estimator allow us to clarify the properties of phase correlations for low multipole range."52 The idea is to apply dA estimator to FCM and WEAL and to compare the power spectra of the signals obtained before and after that.," The idea is to apply $d^{\Delta}_{\l,m}$ estimator to FCM and WFM, and to compare the power spectra of the signals obtained before and after that."53 According to the definition of dA estimator. the power spoectru of the sienalis given by Eq.(28)). which now has the form," According to the definition of $d^{\Delta}_{\l,m}$ estimator, the power spectrum of the signal is given by \ref{pp1}) ), which now has the form"54(2001).. Fanetal.(2003)..and Whiteetal.(2003) (Table 3)).,", \citet{Fan03},and \citet{White03} (Table \ref{tab:transmissiondata}) )."55 Note that we did not include the J1044-0125 (2=5.74) data in Table 3. because it is already incorporated into the compilation of SongailaandCowie(2002)., Note that we did not include the J1044-0125 $z=5.74$) data in Table \ref{tab:transmissiondata} because it is already incorporated into the compilation of \citet{SC2002}.56. In order to combine (hese data. we must take into account the fact that at redshifts 2S5.6. the uncertainties in the transmission data are dominated by intrinsic scatter. while ab higher5 redshifts. (he uncertainties ave dominated by measurement errors.," In order to combine these data, we must take into account the fact that at redshifts $z\lesssim 5.6$, the uncertainties in the transmission data are dominated by intrinsic scatter, while at higher redshifts, the uncertainties are dominated by measurement errors."57 Since our model predicts the transmission. our likelihood. function must properly account Lor both nmeasurenient error as well as the scatter.," Since our model predicts the transmission, our likelihood function must properly account for both measurement error as well as the scatter."58 For a compilation of transmissions. such as that by SongailaandCowie(2002).. the contribution of the data D.=[(z;.T;)] to the likelihood is simply The contribution to the likelihood from the compiled data is estimated (his wav.," For a compilation of transmissions, such as that by \citet{SC2002}, the contribution of the data $D_c = \{(z_j, {\cal T}_j)\}$ to the likelihood is simply The contribution to the likelihood from the compiled data is estimated this way."59" For the individual transmission data. especially in the case where both measurement error and scatter are important. the simplest wav (o do Chis is to estimate scatter 9,444 aul acd in e(quadrature wilh the measurement error ey, to obtain the total uncertainty in the mean for each data point."," For the individual transmission data, especially in the case where both measurement error and scatter are important, the simplest way to do this is to estimate scatter $\sigma_{\rm scatter}$ and add in quadrature with the measurement error $\sigma_{\rm meas}$ to obtain the total uncertainty in the mean for each data point."60" In particular. for individual transmission data D;=σι7;)] with known (Gaussian) errors Tyea, ALC o,uos probabilitv of a mean transmission as a function ol redshift7. is Note that if the measurement error is negligible. (hen Equation 22 reduces (ο Equation (21))."," In particular, for individual transmission data $D_i = \{(z_j,T_j)\}$ with known (Gaussian) errors $\sigma_{\rm meas}$ and $\sigma_{\rm scatter}$, probability of a mean transmission as a function of redshift${\cal T}_z$ is Note that if the measurement error is negligible, then Equation \ref{eq:likelihoodindividual} reduces to Equation \ref{eq:likelihoodcompiled}) )."61" To estimate e,45. we use (he SongailaandCowie(2002) compilation [ουςS5.6 (interpolated). and use the data themselves (binned) to determine o,,,,, al higher redshilis."," To estimate $\sigma_{\rm scatter}$, we use the \citet{SC2002}62 compilation for $z\lesssim 5.6$ (interpolated), and use the data themselves (binned) to determine $\sigma_{\rm scatter}$ at higher redshifts."63 These results are also labluatecl in Table 3.., These results are also tabluated in Table \ref{tab:transmissiondata}.64 The total likelihood function. Z. then is given by the product of the two separate likelihoods.," The total likelihood function, $\cal L$, then is given by the product of the two separate likelihoods."65 For this initial comparison. we fix the other cosmological parameters to their best fit values: n= 0.99. O45?= 0.024. and /= 0.72.," For this initial comparison, we fix the other cosmological parameters to their WMAP-only best fit values: $n=0.99$ , $\Omega_b h^2=0.024$ , and $h=0.72$ ."66 We use the WALAP-only results, We use the WMAP-only results67The low surface brightness of the nebulositv. and the presence of faint [field stars superimposed upon it and nearby. combine to make a morphological interpretation dillicult.,"The low surface brightness of the nebulosity, and the presence of faint field stars superimposed upon it and nearby, combine to make a morphological interpretation difficult."68 Phe image of taken from the ESO data shows the nebulosity clearly but it is unclear whether some of the brighter patehes are stars or enhanced nebular emission., The image of taken from the ESO data shows the nebulosity clearly but it is unclear whether some of the brighter patches are stars or enhanced nebular emission.69 However. because the filter bandpass is ellectively à subset of the broader I. filter. the stellar continuum emission present in the images can be largely removed using an Ro band image.," However, because the filter bandpass is effectively a subset of the broader R filter, the stellar continuum emission present in the images can be largely removed using an R band image."70 The final result shows that the emission is smoother than would appear from the image alone. though two slightly brighter features are weakly visible to the SSW.," The final result shows that the emission is smoother than would appear from the image alone, though two slightly brighter features are weakly visible to the SSW."71 Initial analyses of the nebula used CCD imaging from the SAAO 1.0m provided the ‘first look’., Initial analyses of the nebula used CCD imaging from the SAAO 1.0m provided the 'first look'.72 Though images were obtained in all filters. only the image shows nebulosity.," Though images were obtained in all filters, only the image shows nebulosity."73 Though emission is present (Lable 2)). it is apparently too weak to register in the image. due both to the Large amount of continuum also transmitted. and to the poor response of the CCD in the blue.," Though emission is present (Table \ref{tab:nebulalinelist}) ), it is apparently too weak to register in the image, due both to the large amount of continuum also transmitted and to the poor response of the CCD in the blue."74 llowever these cata were to some extent superseded by the archival images from the ESO 2.2m telescope due to their superior depth and. resolution., However these data were to some extent superseded by the archival images from the ESO 2.2m telescope due to their superior depth and resolution.75 Images in//o.. continuum. OLI] and SH]. were dearchived.. but again only clearly clisplaved nebulosity (Figure. 8))," Images in, continuum, [OIII] and [SII] were dearchived, but again only clearly displayed nebulosity (Figure \ref{fig:xtej0111halpha}) )."76 Continua were removed for both the SL] anc OLLI] images., Continua were removed for both the [SII] and [OIII] images.77 Unfortunately only continuum images were available to model the continuum component: this was not a problem with SH] (at AGTIT.G?31 ο," Unfortunately only continuum images were available to model the continuum component; this was not a problem with [SII] (at $\lambda$ 6717,6731 c.f."78 at. AG563) because of the minimal spectral separation. but the OLLI] A5007 continuum was not adequately represented. by the continuiun image. thus leaving significant stellar images and preventing the detection of the small OLLI] nebula (Section 3.3.4)).," at $\lambda6563$ ) because of the minimal spectral separation, but the [OIII] $\lambda5007$ continuum was not adequately represented by the continuum image, thus leaving significant stellar images and preventing the detection of the small [OIII] nebula (Section \ref{section:linedistribution}) )."79 The ENIM. of was measured both in the un-subtracted ancl continuume-subtracted. OLLI] images and found to be consistent with the other field stars. , The FWHM of was measured both in the un-subtracted and continuum-subtracted [OIII] images and found to be consistent with the other field stars. [80SLL] appears to show extremely weak emission coincicent withdla.,SII] appears to show extremely weak emission coincident with.81 Thus analyses of the structure of the nebula in the light of these species were undertaken spectroscopically (see below).Using the maximum diameter D of ata distance of 63.1pc one arrives at à diameter of 6.1pc for the nebulosity., Thus analyses of the structure of the nebula in the light of these species were undertaken spectroscopically (see below).Using the maximum diameter $D$ of at a distance of 63.1pc one arrives at a diameter of 6.1pc for the nebulosity.82"We begin our study of velocity asymmetries by evaluating the effects of using different values forN, the number of particles used to define the mean velocity of the core in equations (3) to (5).","We begin our study of velocity asymmetries by evaluating the effects of using different values for$N$, the number of particles used to define the mean velocity of the core in equations (3) to (5)."83 Large values of N result in less measurement noise but an overly large effective core for low-mass halos., Large values of $N$ result in less measurement noise but an overly large effective core for low-mass halos.84 Some compromise is thus required for these systems., Some compromise is thus required for these systems.85 In Fig., In Fig.86 2 we show cumulative distributions for our estimates of the square of the velocity offset between the core and the bulk of the main subhalo in each of our objects (equation (3) with Voun taken to be Vinain)-, \ref{fig:fig2} we show cumulative distributions for our estimates of the square of the velocity offset between the core and the bulk of the main subhalo in each of our objects (equation (3) with $\vec{V}_{\rm bulk}$ taken to be $\vec{V}_{\rm main}$ ).87 The four panels refer to our four different halo mass ranges and the four curves in each panel refer to different values of Ν., The four panels refer to our four different halo mass ranges and the four curves in each panel refer to different values of $N$.88 Here and below we divide the estimate for each halo by Ven.=GMa200/r2o0 in order to make it easier to compare results for the different mass ranges., Here and below we divide the estimate for each halo by $V_{200}^2 = G M_{200}/r_{200}$ in order to make it easier to compare results for the different mass ranges.89" In the two bottom panels and for the three lowest N values in the upper right panel, the curves coincide within the noise for all but thesmallest velocity offsets."," In the two bottom panels and for the three lowest $N$ values in the upper right panel, the curves coincide within the noise for all but thesmallest velocity offsets."90 This shows that for these N the central region for which the core velocity is estimated is small enough to be considered to move as a unit., This shows that for these $N$ the central region for which the core velocity is estimated is small enough to be considered to move as a unit.91 In the upper left panel and for the N=1000 curve in the upper right panel a trend towards less extreme offsets for larger N is visible., In the upper left panel and for the $N=1000$ curve in the upper right panel a trend towards less extreme offsets for larger $N$ is visible.92 This is because these halos have small enough masses (~3000 particles on average in the upper left panel) that increasing N washes out a significant part of the core motion., This is because these halos have small enough masses $\sim 3000$ particles on average in the upper left panel) that increasing $N$ washes out a significant part of the core motion.93" On the other hand, differences between the curves at small velocity offset clearly show the effects of small-N noise in our estimates of core velocity."," On the other hand, differences between the curves at small velocity offset clearly show the effects of $N$ noise in our estimates of core velocity."94" These are significant for N=100 but appear acceptably small for N>200, at least as judged from the curvesfor higher mass halos which appear converged at large velocity offset."," These are significant for $N=100$ but appear acceptably small for $N\ge 200$, at least as judged from the curvesfor higher mass halos which appear converged at large velocity offset."95 In the following we adopt N=200 as the best compromise between these competing effects., In the following we adopt $N=200$ as the best compromise between these competing effects.96" In the left panel of Fig. 3,,"," In the left panel of Fig. \ref{fig:fig3},"97 we replot the N=200 curves of Fig., we replot the $N=200$ curves of Fig.98 2 on top of each other for easier comparison., \ref{fig:fig2} on top of each other for easier comparison.99" There is a clear systematic trend for more massive halos to have larger velocity asymmetries, in direct analogy to the trend found above for position asymmetries."," There is a clear systematic trend for more massive halos to have larger velocity asymmetries, in direct analogy to the trend found above for position asymmetries."100" More than a quarter of all cluster halos have core velocities which differ from the mean halo value by at least of V200 (i.e. by velocities greater than about 300 km/s), whereas only a few percent of Milky Way halos have such a large offset."," More than a quarter of all cluster halos have core velocities which differ from the mean halo value by at least of $V_{200}$ (i.e. by velocities greater than about 300 km/s), whereas only a few percent of Milky Way halos have such a large offset."101 The typical offset for low mass halos is small and only about of them have offsets exceeding 0.2V200 (i.e. greater than about 40 km/s)., The typical offset for low mass halos is small and only about of them have offsets exceeding $0.2 V_{200}$ (i.e. greater than about 40 km/s).102 The right panel of Fig., The right panel of Fig.103" 3 shows identical curves, except that the offset is now calculated with respect to the barycentric motion of the halo."," \ref{fig:fig3} shows identical curves, except that the offset is now calculated with respect to the barycentric motion of the halo."104" The resulting distributions are almost indistinguishable from those in the left panel, showing that effects due to substructures and to the definition of the halo boundary are too small to be significant for these statistics."," The resulting distributions are almost indistinguishable from those in the left panel, showing that effects due to substructures and to the definition of the halo boundary are too small to be significant for these statistics."105 An interesting question is whether the relative motions we measure are due to non-equilibrium effects in the outer part of the halos or whether they also reflect significant motions of the core with respect to intermediate halo regions., An interesting question is whether the relative motions we measure are due to non-equilibrium effects in the outer part of the halos or whether they also reflect significant motions of the core with respect to intermediate halo regions.106 Presumably motions of the latter type are more likely to relate to observable galaxy distortions such as warps or lopsidedness., Presumably motions of the latter type are more likely to relate to observable galaxy distortions such as warps or lopsidedness.107" In Fig. 4,,"," In Fig. \ref{fig:fig4},"108 we address this question by measuring velocity offsets of the core relative to different regions of the halo., we address this question by measuring velocity offsets of the core relative to different regions of the halo.109 The four panels here refer to halos in each of our four mass ranges., The four panels here refer to halos in each of our four mass ranges.110" The three curves in each panel give the cumulative offset distributions for core velocities calculated relative to all particles within rooo, relative to all particles within 0.5rooo, and relative to all particles within 0.25r200."," The three curves in each panel give the cumulative offset distributions for core velocities calculated relative to all particles within $r_{200}$ , relative to all particles within $0.5111r_{200}$ , and relative to all particles within $0.25 r_{200}$ ."112" As expected, typical offsets go down in all cases as the"," As expected, typical offsets go down in all cases as the"113Examination of the MOS spectra for X1 also show the same absorption.,Examination of the MOS spectra for X1 also show the same absorption.114" The absorption feature cannot be explained by a neutron star atmosphere model alone, but perhaps may be indicative of metals present on the surface of the neutron star due to active accretion (Rutledgeetal."," The absorption feature cannot be explained by a neutron star atmosphere model alone, but perhaps may be indicative of metals present on the surface of the neutron star due to active accretion \citep{Rutledge02}."115" However, further observations are necessary to 2002)..determine whether the source of the absorption is inherent to the source and any possible physical significance it may have."," However, further observations are necessary to determine whether the source of the absorption is inherent to the source and any possible physical significance it may have."116" X1 is well separated from the other X-ray objects in Figure 6,, lying within the area for population I, X-ray transient and qLMXB, objects."," X1 is well separated from the other X-ray objects in Figure \ref{xcmd}, lying within the area for population I, X-ray transient and qLMXB, objects."117 There is a possible UV counterpart for X1 located 1/445 (1.30) from the X-ray position., There is a possible UV counterpart for X1 located 45 $\sigma$ ) from the X-ray position.118" The UV source is located in the region blue-ward of the main sequence in Figure 5bb, also known as the UV-excess region."," The UV source is located in the region blue-ward of the main sequence in Figure \ref{cmds}b b, also known as the UV-excess region."119" This region is primarily dominated by objects with accretion disk emission (Dieball and is a plausible location in a UV CMD for a qLMXB2007),, counterpart."," This region is primarily dominated by objects with accretion disk emission \citep{Dieball07}, and is a plausible location in a UV CMD for a qLMXB counterpart."120" Although this is also the location in a UV CMD where CV populations are found, we note that the lack of coherent periodicity as well as the absence of a hard component to the X-ray spectrum makes it highly unlikely that X1 is an intermediate polar CV, so we tentatively classify X1 as acandidate qLMXB."," Although this is also the location in a UV CMD where CV populations are found, we note that the lack of coherent periodicity as well as the absence of a hard component to the X-ray spectrum makes it highly unlikely that X1 is an intermediate polar CV, so we tentatively classify X1 as acandidate qLMXB."121" The nearest optical source has V= 16.4, B—V=1.5 and is located 1556 away from ΧΙ (Figure 3)).", The nearest optical source has $V=16.4$ $B - V=1.5$ and is located 56 away from X1 (Figure \ref{findingcharts}) ).122" The UV counterpart and nearby optical source are separated by 0/334, which is a —2c separation given the UV and optical source position errors, making the association of the two rather unlikely."," The UV counterpart and nearby optical source are separated by 34, which is a $\sim$ $\sigma$ separation given the UV and optical source position errors, making the association of the two rather unlikely."123" In addition, the optical source is far from the main sequence of NGC 6819, indicating that it is not a cluster member, and its red color is difficult to reconcile with UV emission."," In addition, the optical source is far from the main sequence of NGC 6819, indicating that it is not a cluster member, and its red color is difficult to reconcile with UV emission."124 The most plausible scenario is that the UV source is associated with X1 (separated by 1.30) and the optical source is an unrelated field star., The most plausible scenario is that the UV source is associated with X1 (separated by $\sigma$ ) and the optical source is an unrelated field star.125" This nearby bright star makes detection of the true optical counterpart difficult, and it is likely that the true optical counterpart to X1 is hidden in the glare from this bright source."," This nearby bright star makes detection of the true optical counterpart difficult, and it is likely that the true optical counterpart to X1 is hidden in the glare from this bright source."126" Although we do not detect an optical counterpart, the X-ray to optical luminosity limit for X1 also shows it to be in the range of X-ray transient objects (Figure 7))."," Although we do not detect an optical counterpart, the X-ray to optical luminosity limit for X1 also shows it to be in the range of X-ray transient objects (Figure \ref{xopt}) )."127" We note that the lack of an optical counterpart is not surprising as qLMXBs can be extremely optically faint (Heinkeetal.2003),, with the added complication of a nearby bright source making detection of an optical counterpart very difficult."," We note that the lack of an optical counterpart is not surprising as qLMXBs can be extremely optically faint \citep{Heinke03}, with the added complication of a nearby bright source making detection of an optical counterpart very difficult."128" The X-ray spectrum, X-ray color, and limit of the X-ray to optical luminosity ratio all point to X1 as a candidate quiescent low mass X-ray binary."," The X-ray spectrum, X-ray color, and limit of the X-ray to optical luminosity ratio all point to X1 as a candidate quiescent low mass X-ray binary."129" In addition, the absence of a hard component to the X-ray spectrum makes it highly unlikely that X1 is a dwarf nova or intermediate polar CV."," In addition, the absence of a hard component to the X-ray spectrum makes it highly unlikely that X1 is a dwarf nova or intermediate polar CV."130" With this candidate qLMXB classification, X1 may be the first system of its kind found in an open cluster environment."," With this candidate qLMXB classification, X1 may be the first system of its kind found in an open cluster environment."131 Higher spatial resolution X-ray and optical data are needed to confirm the counterpart identification and source classification., Higher spatial resolution X-ray and optical data are needed to confirm the counterpart identification and source classification.132 We note that vandenBergetal.(2004) discovered a highly variable and soft X-ray source in M67 (CX 2)., We note that \citet{vandenBerg04} discovered a highly variable and soft X-ray source in M67 (CX 2).133" 'They lack a confident classification due to the variable nature of the source, but detect system parameters that fall between expected values for a black hole qLMXB and a neutron star qLMXB."," They lack a confident classification due to the variable nature of the source, but detect system parameters that fall between expected values for a black hole qLMXB and a neutron star qLMXB."134" However, vandenBergetal. emphasize the need for more information before final classification."," However, \citeauthor{vandenBerg04} emphasize the need for more information before final classification."135" Source X2 has a confident UV source counterpart at Q""779 (0.74c) and a possible optical counterpart at a distance of 17224 (1.150).", Source X2 has a confident UV source counterpart at 79 $\sigma$ ) and a possible optical counterpart at a distance of 24 $1.15\sigma$ ).136" The UV counterpart to X2 is located in the blue UV-excess region of Figure 5bb, an area dominated by objects with accretion disk emission such as CVs (Dieballetal.2007)."," The UV counterpart to X2 is located in the blue UV-excess region of Figure \ref{cmds}b b, an area dominated by objects with accretion disk emission such as CVs \citep{Dieball07}."137". The possible optical counterpart is located in the “gap” region between the main-sequence and white dwarf cooling sequence (Figure 5aa), an area also dominated by CV systems."," The possible optical counterpart is located in the “gap” region between the main-sequence and white dwarf cooling sequence (Figure \ref{cmds}a a), an area also dominated by CV systems."138" Based on the X-ray color and luminosity of X2 (see Figure 6)) it lies on the boundary between population I and II objects, indicating the possibility that this object is a CV candidate or qLMXB."," Based on the X-ray color and luminosity of X2 (see Figure \ref{xcmd}) ) it lies on the boundary between population I and II objects, indicating the possibility that this object is a CV candidate or qLMXB."139" Its X-ray to optical luminosity ratio (Figure 7)) is more indicative of a CV than an LMXB, therefore we classify X2 as a CV candidate."," Its X-ray to optical luminosity ratio (Figure \ref{xopt}) ) is more indicative of a CV than an LMXB, therefore we classify X2 as a CV candidate."140" We fit the X-ray spectrum of X2 with an APEC thermal plasma model with an absorption component from the neutral hydrogen column density to the cluster, resulting in a best fit temperature of kT —6.224 keV, in good agreement with expected dwarf novae temperatures (Bycklingetal.2010;Fertigetal. 2011)."," We fit the X-ray spectrum of X2 with an APEC thermal plasma model with an absorption component from the neutral hydrogen column density to the cluster, resulting in a best fit temperature of kT $=6.2^{+2.1}_{-1.0}$ keV, in good agreement with expected dwarf novae temperatures \citep{Byckling10, Fertig11}."141". The pn spectrum and best-fit model with residuals for X2 is shown in Figure 10,, binned to 15 counts perbin for plotting purposes only."," The pn spectrum and best-fit model with residuals for X2 is shown in Figure \ref{X2spec}, binned to 15 counts perbin for plotting purposes only."142 The error and residual calculations are the same as in Figure 9.., The error and residual calculations are the same as in Figure \ref{X1spec}.143" The background-subtracted light curve for X2, with 500s bins, is shown in Figure 11.."," The background-subtracted light curve for X2, with 500s bins, is shown in Figure \ref{X2lc}."144 The appropriately scaled background light curve is shown in grey., The appropriately scaled background light curve is shown in grey.145 Errors are calculated using the same method as in Figure 11.., Errors are calculated using the same method as in Figure \ref{X2lc}.146" 'The average number of counts per bin is 5.8, or a rate of 0.012 counts s~!, shown with the dashed line."," The average number of counts per bin is 5.8, or a rate of 0.012 counts $^{-1}$ , shown with the dashed line."147" We find a bin with 13 counts,or a rate of 0.026 counts s~, as can be seen at ~10500ss. The probability of finding a bin"," We find a bin with 13 counts,or a rate of 0.026 counts $^{-1}$ , as can be seen at $\sim$ s. The probability of finding a bin"148ins ?7?7.. m which we also compare our abundances will literature results.,"in \ref{sec:abundances}, in which we also compare our abundances with literature results."149 In section we analvze the scatter in the N/O plateau., In section \ref{sec:analysis} we analyze the scatter in the N/O plateau.150 Finally. section ?? gives à stummary of our work.," Finally, section \ref{sec:conclusion} gives a summary of our work."151 In a companion paper to (his one (Henry et al., In a companion paper to this one (Henry et al.152 2006). chemical evolution models are combined with Monte Carlo techniques to further interpret the plateau morphology.," 2006), chemical evolution models are combined with Monte Carlo techniques to further interpret the plateau morphology."153 The N and O ionic abundances for our sample of low metallicity svstems were determined directly. [rom published optical emission-lines using the general expression: where the fraction on the left is the number density ratio of the N or O ion relative to IL. the first fraction on the right is the line flux ratio of a nebular [orbidden feature of ion X! relative to the strength. of 112. is the electron densitv 7). is the electron temperature of the region where the relevant ion is emitting (Ix). a4i is the effective recombination coefficient of IL3 which includes radiative and three-body processes (cm? 1). V ds the fraction of ions N! with an electron in the upper level of the transition of interest. Af is the corresponding spontaneous de-excitation rate coefficient 1). and the last term is the wavelength ratio of the line of interest and Ilo (A).," The N and O ionic abundances for our sample of low metallicity systems were determined directly from published optical emission-lines using the general expression: where the fraction on the left is the number density ratio of the N or O ion relative to $^+$, the first fraction on the right is the line flux ratio of a nebular forbidden feature of ion $^i$ relative to the strength of $\beta$, is the electron density $^{-3}$ ), is the electron temperature of the region where the relevant ion is emitting (K), $\alpha^{eff}_{H\beta}$ is the effective recombination coefficient of $\beta$ which includes radiative and three-body processes $^3$ $^{-1}$ ), $\chi^u$ is the fraction of ions $^i$ with an electron in the upper level of the transition of interest, $^u_l$ is the corresponding spontaneous de-excitation rate coefficient $^{-1}$ ), and the last term is the wavelength ratio of the line of interest and $\beta$ )."154 Note that equation (1)) is based on the assumption that IL? arises [rom recombination., Note that equation \ref{eq:ionabun}) ) is based on the assumption that $\beta$ arises from recombination.155 The contribution to II lines from collisional excitation was neglected because the excitation potentials of II levels are much veher (han (he average thermal equilibrium temperature that characterizes II 1 regions (Osterbrock.D.E.&Ferland.G.J.2006)., The contribution to H lines from collisional excitation was neglected because the excitation potentials of H levels are much higher than the average thermal equilibrium temperature that characterizes H II regions \citep{osterbrock06}.156. In addition. equation (1)) assumes that nebular orbidden lines originate from collisionally excited levels.," In addition, equation \ref{eq:ionabun}) ) assumes that nebular forbidden lines originate from collisionally excited levels."157 Collisional excitation is significant in this case because the low-lving energy levels of the relevant ions are of the order of ATT. However. according to Rubin(1986).. recombinations of 7 can excite the nebular doublet AA3126.3129. used to compute.," Collisional excitation is significant in this case because the low-lying energy levels of the relevant ions are of the order of T. However, according to \cite{rubin86}, recombinations of $^{+2}$ can excite the nebular doublet $\lambda\lambda3726, 3729$, used to compute."158. The effect of this process will be analvzed in the future., The effect of this process will be analyzed in the future.159 Although the presence of the nebular He II 4686 emission-line in the spectra of several metal-poor svstems implies the presence of unobserved ΤΗ . the contribution of this ion to the total oxveen abundance amounts to only a few percent according to our photoionization models.," Although the presence of the nebular He II 4686 emission-line in the spectra of several metal-poor systems implies the presence of unobserved $^{+3}$ $^+$, the contribution of this ion to the total oxygen abundance amounts to only a few percent according to our photoionization models."160 Therefore. we obtained the oxvgen abundance by assuming that," Therefore, we obtained the oxygen abundance by assuming that"161The recent release of Kepler data reporting more than 1200 planet eaudidates transiting (heir host star confirms (hat the core accretion scenario for forming planets is ubiquitous.,The recent release of Kepler data reporting more than 1200 planet candidates transiting their host star confirms that the core accretion scenario for forming planets is ubiquitous.162 Indeed.," Indeed,"163were taken [rom the experimental compilation in the NIST database.,were taken from the experimental compilation in the NIST database.164 For the remainder. the theoretical values of Agearwal Wkeenan were adopted.," For the remainder, the theoretical values of Aggarwal Keenan were adopted."165 Test) calculations inelucling higher-Iving levels. such as those arising from the 3s ?3p4s configuration. were found to have a negligible elfeet on the theoretical line ratios considered in this paper.," Test calculations including higher-lying levels, such as those arising from the $^{2}$ $^{4}$ 4s configuration, were found to have a negligible effect on the theoretical line ratios considered in this paper."166 The electron impact excitation cross sections employed in the present paper are those calculated using the fully relativistic Dirac code by Aggarwal lIxeenan (2005)., The electron impact excitation cross sections employed in the present paper are those calculated using the fully relativistic Dirac code by Aggarwal Keenan (2005).167" For Einstein A-coellicicnts. Agegarwal Keenan (2004) cmplovecl the fully relativistic code to generate results for all transitions among the 54 fine-structure levels of⋅ the ⋅⊐⋅ "" 3873p. i383p"". VEN Le3d. and. MM3d configurations⋅. ofFex."," For Einstein A-coefficients, Aggarwal Keenan (2004) employed the fully relativistic code to generate results for all transitions among the 54 fine-structure levels of the $^{2}$ $^{5}$ , $^{6}$, $^{2}$ $^{4}$ 3d and $^{5}$ 3d configurations of."168. Subsequently. Aegearwal Ixeenan (2005) extended this work to include the additional 36 levels arising from," Subsequently, Aggarwal Keenan (2005) extended this work to include the additional 36 levels arising from"169using new calibrations to improve the accuracy.,using new calibrations to improve the accuracy.170 This position. listed in Table 7.. excludes the ROSAT source ax a possible counterpart. and thus confirms that ASCA iudecd detected a source in the cluster.," This position, listed in Table \ref{tabpos}, excludes the ROSAT source as a possible counterpart, and thus confirms that ASCA indeed detected a source in the cluster."171" Tu the three low-reddened clustersCeu. 66397 aud 66752 we have detected a total of 17 dim N-rav sources, of which 5 are well outside the core."," In the three low-reddened clusters, 6397 and 6752 we have detected a total of 17 dim X-ray sources, of which 5 are well outside the core."172 The N-ray huninosities of these sources are listed in reftxhuu.. and plotted in roffxlun..," The X-ray luminosities of these sources are listed in \\ref{txlum}, and plotted in \\ref{fxlum}."173 The interpretation of roffixhun iuust be made with some care., The interpretation of \\ref{fxlum} must be made with some care.174 First. sources outside the core may not belong to the cluster: the faiutest core source in niuav be a fore- or background source.," First, sources outside the core may not belong to the cluster; the faintest core source in may be a fore- or background source."175 Second. the conversion of observed countrate to huninositv depends ou the assumed spectimm. aud. frour PSPC observations we know that different sources have different spectral paranueters (Johnston et 11991).," Second, the conversion of observed countrate to luminosity depends on the assumed spectrum, and from PSPC observations we know that different sources have different spectral parameters (Johnston et 1994)."176 For exaniple. the kkeV. black body spectra used for he sources iu eoives a ihigher fux for the same countrate than an assumed κο bronasstrahluueOo spectra would Ooeive.," For example, the keV black body spectrum used for the sources in gives a higher flux for the same countrate than an assumed keV bremsstrahlung spectrum would give."177 The wenistrahluung spectrum is used for the three other clusters., The bremsstrahlung spectrum is used for the three other clusters.178 Third. the detection limuts iu 66397. 66752 aud are higher iu the cores. where the »oiut spread fictions of sources overlap. than outside the core.," Third, the detection limits in 6397, 6752 and are higher in the cores, where the point spread functions of sources overlap, than outside the core."179 Such a difference is not presen oereCon., Such a difference is not present in.180 Fourth. we show the average bhuuinositv. and several sources are shown to be variable.," Fourth, we show the average luminosity, and several sources are known to be variable."181 With these poiuts in mind. we note from roffxhun that im all clusters except possibly the most huuimous sources appear be in the cluster core.," With these points in mind, we note from \\ref{fxlum} that in all clusters except possibly the most luminous sources appear to be in the cluster core."182 The main difference between aand the other clusters is that the collision frequency in lis so low that oue expects no low-1nass X-ray. binaries iu it. and that most cataclvsiiic variables in it will be evolved roni primordial binaries (Verbuut ADMevlan 1988. Davies 1997).," The main difference between and the other clusters is that the collision frequency in is so low that one expects no low-mass X-ray binaries in it, and that most cataclysmic variables in it will be evolved from primordial binaries (Verbunt Meylan 1988, Davies 1997)."183 Iu addition. the lius segregation iu this cluster is very low.," In addition, the mass segregation in this cluster is very low."184 Thus in there is no marked difference between the core aud the regions outside the core., Thus in there is no marked difference between the core and the regions outside the core.185 Iu cach cluster we detect sources down to the detection nuit: this sugesests---- hat Wore scusitive observations will detect more sources., In each cluster we detect sources down to the detection limit; this suggests that more sensitive observations will detect more sources.186 Iu the πο... of 66397 and 66752. the ctection of nore source will also require better imagine. so that the [αι sources cau be detected against the brighter ones.," In the cores of 6397 and 6752 the detection of more source will also require better imaging, so that the faint sources can be detected against the brighter ones."187 We do not detect a difference between he hunuinosities of sources in the collapsed elobular cluster 66397. aud the much less concentrated elobular cluster 66752., We do not detect a difference between the luminosities of sources in the collapsed globular cluster 6397 and the much less concentrated globular cluster 6752.188 On the other haud. the hieghlv concentrated cluster [7 Tuc contaius three sources which are an order of magnitude brighter than the brightest sources iun 66397 and 66752.," On the other hand, the highly concentrated cluster 47 Tuc contains three sources which are an order of magnitude brighter than the brightest sources in 6397 and 6752."189Thus external constraints on expansion velocity evolution. wip (oz =1.7 trom the SNAP spectrograph. will be needed (o assess the efficacy of using photometric redshifts from the 5Ne Ia themselves for cosmology.,"Thus external constraints on expansion velocity evolution, up to $z=1.7$ from the SNAP spectrograph, will be needed to assess the efficacy of using photometric redshifts from the SNe Ia themselves for cosmology."190 As described above. calibrated photometric redshifts from the host galaxies are sulficient Lo satislv the bias limit lor the recshilt range z>1.7.," As described above, calibrated photometric redshifts from the host galaxies are sufficient to satisfy the bias limit for the redshift range $z>1.7$."191 Independently determined photometric redshifts from the SN lighteurves could then play a role in resolving remaining ambieuities., Independently determined photometric redshifts from the SN lightcurves could then play a role in resolving remaining ambiguities.192 The accuracy of (he photometric redshifts is certainly sullicient for triggering targeted programs. uusing JWST.," The accuracy of the photometric redshifts is certainly sufficient for triggering targeted follow-up programs, using JWST."193 Categorizing the supernovae into (vpes is an essential element of supernova. astrophysical. and cosmological studies.," Categorizing the supernovae into types is an essential element of supernova, astrophysical, and cosmological studies."194 Photometric seeregation of supernovae can be performed wilh some success based on lighteurve and color evolution., Photometric segregation of supernovae can be performed with some success based on lightcurve and color evolution.195 Early variations of this approach have been presented in Poznanskietal.(2002);Gal-Yam(2004):RiessοἱTonry (2004).," Early variations of this approach have been presented in \citet{poznanski02,galyam04,riess04,barris04}."196. In general. when restirame UV data are available Type II SNe are seen {ο be UV-bright whereas opacity [vom iron-group elements in SNe Ia suppresses the UV brightness.," In general, when restframe UV data are available Type II SNe are seen to be UV-bright whereas opacity from iron-group elements in SNe Ia suppresses the UV brightness."197 In addition. the lighteurves of SNe IP are quite distinct lom those of other SN twpes.," In addition, the lightcurves of SNe IIP are quite distinct from those of other SN types."198 Using a Monte Carlo lighteurve simulation appropriate to the color coverage. cadence. and depth ol SNAP we confirm that for the S/N achievable for SNe la at 2=3 the shape of the D-band lighteurve distinguishes between Type Ia and Type LIP 5Ne.," Using a Monte Carlo lightcurve simulation appropriate to the color coverage, cadence, and depth of SNAP we confirm that for the $S/N$ achievable for SNe Ia at $z=3$ the shape of the B-band lightcurve distinguishes between Type Ia and Type IIP SNe."199 Disünguishing Types Ib and Ie from Type Ia is more difficult. especially in the [ace of an uncertain redshift and dust exGuelion.," Distinguishing Types Ib and Ic from Type Ia is more difficult, especially in the face of an uncertain redshift and dust extinction."200 SNe Ib/c are generally redder (han SNe Ia (wilh resUrame B-V color about 0.5 magnitudes redder (Poznauskietal. 2002)))., SNe Ib/c are generally redder than SNe Ia (with restframe B-V color about 0.5 magnitudes redder \citep{poznanski02}) ).201 The color evolution is different as well: Type Ib/c have similar pre- ancl post-iaxinmumn colors while Type Ia become τοον after (heir maximum brightness is reached., The color evolution is different as well: Type Ib/c have similar pre- and post-maximum colors while Type Ia become redder after their maximum brightness is reached.202 The colors ancl magnitude can be used to largely break (he degeneracy between dust reddening and SN (wpe once a full lighteurve is obtained., The colors and magnitude can be used to largely break the degeneracy between dust reddening and SN type once a full lightcurve is obtained.203 The precise multi-band. photometry afforded by SNAP can greatly improve (he power of such techuiiques., The precise multi-band photometry afforded by SNAP can greatly improve the power of such techniques.204 The largest and most complete sample on which this technique has been tested to date is (he Supernova Legacy Survey., The largest and most complete sample on which this technique has been tested to date is the Supernova Legacy Survey.205 Sullivanetal.(200Ga) use 4-color lighteurve photometry to reject all ten SNe II while rejecting only one SN Ia in a sample of 85 spectroscopically- high-redshift SNe., \citet{sullivan06} use 4-color lightcurve photometry to reject all ten SNe II while rejecting only one SN Ia in a sample of 85 spectroscopically-classified high-redshift SNe.206 ILowever. Sullivanetal.(200G6a) do not demonstrate their ability to reject SNe Ib/c and they do not comment on whether or not all the SNe II were HP. or might have included SNe IL.," However, \citet{sullivan06} do not demonstrate their ability to reject SNe Ib/c and they do not comment on whether or not all the SNe II were IIP, or might have included SNe IIL."207whereas the lower density material is hotter and produces ligh ionization enuission.,whereas the lower density material is hotter and produces high ionization emission.208the value that gives the best results on the following discussion of the cosmological parameters.,the value that gives the best results on the following discussion of the cosmological parameters.209 The initial guess for the cosmological weight function wl!) is not very important for the determination of the shear. because a wrong choice would only lead to an increase of the errors (at least in the weak lensing limit: see comment after Eq. (C4))).," The initial guess for the cosmological weight function $w^{[0]}$ is not very important for the determination of the shear, because a wrong choice would only lead to an increase of the errors (at least in the weak lensing limit; see comment after Eq. \ref{K}) ))."210 This behavior ts well verified in the simulations., This behavior is well verified in the simulations.211" At the end of the first inner iteration. the mass density obtained. 5/4], does not differ significantly from the determinations obtained at the end of the following cycles. wl! (except for a factor arising from the global sealing invariance)."," At the end of the first inner iteration, the mass density obtained, $\kappa^{[0,I]}$, does not differ significantly from the determinations obtained at the end of the following cycles, $\kappa^{[j, I]}$ (except for a factor arising from the global scaling invariance)."212 After the first inner cycle. the mass and the shear maps are close to the best ones that we can hope to have.," After the first inner cycle, the mass and the shear maps are close to the best ones that we can hope to have."213 This suggests that the number of inner iterations 7 could decrease after the first cycle., This suggests that the number of inner iterations $I$ could decrease after the first cycle.214 Thus we could start with J=5 for j= 0. and then let /=3 or even [=2 for j>0.," Thus we could start with $I=5$ for $j=0$ , and then let $I=3$ or even $I=2$ for $j > 0$."215 The reduction of 7 can lead to a significant reduction of machine-time., The reduction of $I$ can lead to a significant reduction of machine-time.216 The following step ts the determination of the cosmological weight., The following step is the determination of the cosmological weight.217 Simulations show that the number of outer iterations needed to obtain a good estimation of the cosmological weight is very low. say .7=3. because the method ts able to give the correct shear map after the first inner loop.," Simulations show that the number of outer iterations needed to obtain a good estimation of the cosmological weight is very low, say $J = 3$, because the method is able to give the correct shear map after the first inner loop."218 Simulations also show that this property. strictly expected only in the weak lensing limit. is in fact valid (at least approximately) in the general case. provided the lens is not too “strong.”," Simulations also show that this property, strictly expected only in the weak lensing limit, is in fact valid (at least approximately) in the general case, provided the lens is not too “strong.”"219 The estimated cosmological weight w(:) (solid lines in Fig., The estimated cosmological weight $\hat w(z)$ (solid lines in Fig.220 4) is smooth on the characteristic scale of IW.(+.<7) (see Eq. (C7))):," 4) is smooth on the characteristic scale of $W_z(z, z')$ (see Eq. \ref{<w>}) ));"221 because of this. 1t remains at a finite value atτα.," because of this, it remains at a finite value at $z222= z_\mathrm d$."223 Moreover. as expected. the error on the cosmological weight increases slightly for + near στ and more for high values of :. where the number of galaxies decreases (see Fig.," Moreover, as expected, the error on the cosmological weight increases slightly for $z$ near $z_\mathrm d$ and more for high values of $z$, where the number of galaxies decreases (see Fig."224 3)., 3).225 In particular. the smoothing of the cosmological weight is very important near the cluster. at +— tq. Where the true cosmological weight vanishes abruptly.," In particular, the smoothing of the cosmological weight is very important near the cluster, at $z \simeq z_\mathrm d$ , where the true cosmological weight vanishes abruptly."226 This clearly indicates that neither the limit (OL)> lfor:>x nor the limit for 5.>» can be used to break the global scaling invariance., This clearly indicates that neither the limit $w(z) \rightarrow 1$ for $z \rightarrow \infty$ nor the limit for $z\rightarrow z_\mathrm d^+$ can be used to break the global scaling invariance.227 Figure 4+ shows the reconstruction of the cosmological weight in the case of an Einstein-de Sitter universe: different choices for € and O4 lead to similar results., Figure 4 shows the reconstruction of the cosmological weight in the case of an Einstein-de Sitter universe; different choices for $\Omega$ and $\Omega_{\Lambda}$ lead to similar results.228 Figure 4 should be compared with Fig., Figure 4 should be compared with Fig.229 3 which shows the expected mean value (w(:) and the related error for an Einstein-de Sitter universe with NN—.—10000 galaxies.," 3 which shows the expected mean value $\langle w \rangle (z)$ and the related error for an Einstein-de Sitter universe with $N = 10\, 000$ galaxies."230 Figure 3 clarifies the general properties discussed above and. in more detail. in Appendix D. for the expected error on «w(:) and suggests that our method should be able to constrain significantly the cosmological parameters.," Figure 3 clarifies the general properties discussed above and, in more detail, in Appendix D, for the expected error on $w(z)$ and suggests that our method should be able to constrain significantly the cosmological parameters."231 In fact. the error or w(2) for:c2 is sufficiently small to distinguish different consmological models even if the measured weight are affected by the global scaling invariance.," In fact, the error on $w(z)$ for $z \simeq 2$ is sufficiently small to distinguish different consmological models even if the measured weight are affected by the global scaling invariance."232 From the estimation w(:) of the cosmological weight we can obtain information on the cosmological parameters as explained in Appendix D. For a description of the results. we plot the contours of the (» function of Eq. (D6))," From the estimation $\hat w(z)$ of the cosmological weight we can obtain information on the cosmological parameters as explained in Appendix D. For a description of the results, we plot the contours of the $\ell_2$ function of Eq. \ref{ell2}) )"233 in a square domain |0.1]«10.1 of the O-O4 plane.," in a square domain $[0,1] \times234[0, 1]$ of the $\Omega$ $\Omega_\Lambda$ plane."235 Figures 5 and 6 show the confidence regions obtained for various confidence levels CL in different cosmological models and with different numbers of source galaxies., Figures 5 and 6 show the confidence regions obtained for various confidence levels $\CL$ in different cosmological models and with different numbers of source galaxies.236 From diagrams of this type we argue that 510000 can be considered as a lower bound for the applicability of our method.," From diagrams of this type we argue that $N = 10\,000$ can be considered as a lower bound for the applicability of our method."237 These figures also show that. unless an exceedingly high number of source galaxies is available. point estimation 15 notvery meaningful.," These figures also show that, unless an exceedingly high number of source galaxies is available, point estimation is notvery meaningful."238 In fact. these examples show that the minimum of the4? function can occur quite far from the true values of the cosmological parameters.," In fact, these examples show that the minimum of the$\chi^2$ function can occur quite far from the true values of the cosmological parameters."239 On the other hand.," On the other hand,"240maeuitucde listed tu Table 2:: the effective surface brielituess is then clefinecl as the average surface brightuess within the Reg elliptical aperture.,magnitude listed in Table \ref{tab:results}; the effective surface brightness is then defined as the average surface brightness within the $_{\rm eff}$ elliptical aperture.241 We note that while these values are model iudepencdent. they can be sensitive to systematic errors introduced by shallow imaging observations since tle radii are defined based ou the observed apparent iuagnitucdes.," We note that while these values are model independent, they can be sensitive to systematic errors introduced by shallow imaging observations since the half-light radii are defined based on the observed apparent magnitudes."242 Several of the galaxies tn this sample have surface photometry reported in the literature., Several of the galaxies in this sample have surface photometry reported in the literature.243 Recent observations with partially overlapping samples include. VCC 513. 917. 1036. 1261. anne 1308 reported in Gehaetal.(2003):: VCC 965. 1036. 1122. and 1308 reported in Pieriui(2002):: VCC 1036 aud 1261 reported in Barazzaetal.(2003): aud VCC 513 aud 1713 reported in (1997).," Recent observations with partially overlapping samples include VCC 543, 917, 1036, 1261, and 1308 reported in \citet{GGvM03}; VCC 965, 1036, 1122, and 1308 reported in \citet{P02}; VCC 1036 and 1261 reported in \citet{BBJ03}; and VCC 543 and 1743 reported in \citet{D97}."244. In egeneral. there is reasouable agreement[we between the literature values and those reporte iere. particularly given the variety of filters aud telescopes used by these studies.," In general, there is reasonable agreement between the literature values and those reported here, particularly given the variety of filters and telescopes used by these studies."245 However. there are iotable differeuces between the values reported lere aud the magnitudes aud effective racii liste in Celiaetal.(2003).," However, there are notable differences between the values reported here and the magnitudes and effective radii listed in \citet{GGvM03}."246. With the exception of VCC 1261. it is likely that many of these differeuces can be attributed to dillering image deptlis aud to incomplete surface photometry as a result of the restricted field-otCview of HST unagiug observatious.," With the exception of VCC 1261, it is likely that many of these differences can be attributed to differing image depths and to incomplete surface photometry as a result of the restricted field-of-view of HST imaging observations."247 For VCC 1261. the large discrepaucy between he effective radius reported here aud that reported in Gelaetal.(2003) (inore than a factor of 2) cannot be reconciled by mere observatioual differences: the present. value agrees with the surface shotometry of VCC 1261 reported in Barazzaetal.(2003)..," For VCC 1261, the large discrepancy between the effective radius reported here and that reported in \citet{GGvM03} (more than a factor of 2) cannot be reconciled by mere observational differences; the present value agrees with the surface photometry of VCC 1261 reported in \citet{BBJ03}."248" To enable comparison with galaxies of other morphological types. the outer isophotes (r > 10"")) of the B-band surface brightness profiles were fit to an exponential model: where μή) is the observed surface brightness at semi-major axis r. ji! is the extrapolated centra surlace brightuess. aud a is the exponential scale leneth."," To enable comparison with galaxies of other morphological types, the outer isophotes (r $>$ ) of the B-band surface brightness profiles were fit to an exponential model: where $\mu(r)$ is the observed surface brightness at semi-major axis $r$, $\mu^0$ is the extrapolated central surface brightness, and $\alpha$ is the exponential scale length."249 The face-on central surface brightuess. TM was calculated by applying a Galactic extinction correction aud a line-of-sight correction ol —2.5log(cos7). where 7 is the inclination derived [rom the observed axial ratios and a this disk approximation.," The face–on central surface brightness, $\mu_B^{0,c}$, was calculated by applying a Galactic extinction correction and a line–of–sight correction of $-2.5~{\rm log~(cos}~i)$, where $i$ is the inclination derived from the observed axial ratios and a thin disk approximation."250 While au exponential distribution does uot necessarily imply a clisk-like stellar cistributiou. the simplicity of this fuuctioual form permits a robust analysis of the light distributioi of the outer regious of a galaxy. regardless of the actual shape of the galaxy. (disk or spherokl).," While an exponential distribution does not necessarily imply a disk-like stellar distribution, the simplicity of this functional form permits a robust analysis of the light distribution of the outer regions of a galaxy, regardless of the actual shape of the galaxy (disk or spheroid)."251 The exponeutial fitsenable a direct. comparison between the structural parameters of dE aud dl galaxies (Figure 2))., The exponential fitsenable a direct comparison between the structural parameters of dE and dI galaxies (Figure \ref{fig:struct}) ).252 The top pauel of Figure 2. slows the scale leneth as a fuuctiou of absolute umaguitude while the bottom panel shows the face-ou central surface brightness as a fuuction of absolute magnitude.," The top panel of Figure \ref{fig:struct}253 shows the scale length as a function of absolute magnitude while the bottom panel shows the face–on central surface brightness as a function of absolute magnitude."254 For comparison. the structural parameters for dwarf irregular galaxies frou vanZee(2000) are also shown.," For comparison, the structural parameters for dwarf irregular galaxies from \citet{vZ00} are also shown."255 Despite the fact that this comparisou sample may uot be ideal. since the dls were selected to be isolated galaxies and the dEs are cluster members. these figures confirm that the structural parameters of cls ancl dEs are quite similar 1983)..," Despite the fact that this comparison sample may not be ideal, since the dIs were selected to be isolated galaxies and the dEs are cluster members, these figures confirm that the structural parameters of dIs and dEs are quite similar \citep[as first discussed in][]{LF83}. ."256 In particular. both the dE aud dE samples contain low sur(ace brightuess galaxies," In particular, both the dI and dE samples contain low surface brightness galaxies"257"the cluster core, because low-mass stars have small radii and therefore smaller cross sections for collisions.","the cluster core, because low-mass stars have small radii and therefore smaller cross sections for collisions."258 Fig., Fig.259 4 depicts the number of stellar collisions in the unsegregated cluster models., \ref{fig:coll} depicts the number of stellar collisions in the unsegregated cluster models.260" In clusters less concentrated than r;,z 0.1 pc hardly any collisions occur.", In clusters less concentrated than $r_h \approx$ 0.1 pc hardly any collisions occur.261 The reason is the low stellar density of these models in combination with the large inspiral times of the massive stars., The reason is the low stellar density of these models in combination with the large inspiral times of the massive stars.262" In clusters with half-mass radii larger than τη=0.1 pc, the inspiral times are larger than a few 0.1 Myr, meaning that massive stars do not have time to accumulate in the center while still in the accretion phase."," In clusters with half-mass radii larger than $r_h = 0.1$ pc, the inspiral times are larger than a few 0.1 Myr, meaning that massive stars do not have time to accumulate in the center while still in the accretion phase."263" Instead, they reach the center only after a few Myr, at which point they have arrived already on the main-sequence and have much smaller radii and collision cross sections."," Instead, they reach the center only after a few Myr, at which point they have arrived already on the main-sequence and have much smaller radii and collision cross sections."264" However, even in the most massive and concentrated cluster with N—104 starsand initial half-mass radius Τη=0.033 pc only 41 stars collide with each other."," However, even in the most massive and concentrated cluster with $N=10^4$ starsand initial half-mass radius $r_h=0.033$ pc only 41 stars collide with each other."265" For a Kroupa mass function with stars up to 100 Mo, 90 collisions between 10 Mo stars are necessary to create the missing stars if the initial mass function only extends up to 15 Μο."," For a Kroupa mass function with stars up to 100 $_\odot$, 90 collisions between 10 $_\odot$ stars are necessary to create the missing stars if the initial mass function only extends up to 15 $_\odot$."266" The number of collisions in the unsegregated models are therefore too small compared to the required number of collisions, especially for clusters which have final half-light radii compatible with observed clusters, i.e. clusters starting with rj>0.1 pc."," The number of collisions in the unsegregated models are therefore too small compared to the required number of collisions, especially for clusters which have final half-light radii compatible with observed clusters, i.e. clusters starting with $r_h > 0.1$ pc."267" We note that in the unsegregated runs most collisions happen after massive stars have reached their final mass, in the N=1031 stars, ry=0.033 pc run for example only 3 collisions happen in the pre-MS phase while roughly half of the collisions happen after 1 Myr, i.e. by the time the cluster has already become gas free and collisions would possibly be observable through their collision products or flashes of bright emission."," We note that in the unsegregated runs most collisions happen after massive stars have reached their final mass, in the $N=10^4$ stars, $r_h=0.033$ pc run for example only 3 collisions happen in the pre-MS phase while roughly half of the collisions happen after 1 Myr, i.e. by the time the cluster has already become gas free and collisions would possibly be observable through their collision products or flashes of bright emission."268 We next discuss the evolution of the mass-segregated clusters., We next discuss the evolution of the mass-segregated clusters.269 In the segregated clusters energy and final mass of stars were correlated such that proto-stellar cores which will become the highest mass stars have the lowest energies., In the segregated clusters energy and final mass of stars were correlated such that proto-stellar cores which will become the highest mass stars have the lowest energies.270 The high mass stars therefore form in the cluster center and do not have to spiral into the center by dynamical friction., The high mass stars therefore form in the cluster center and do not have to spiral into the center by dynamical friction.271" Furthermore, the cluster core contracts during the accretion process due to mass increase, further facilitating stellar collisions."," Furthermore, the cluster core contracts during the accretion process due to mass increase, further facilitating stellar collisions."272 Table 1 and Fig., Table 1 and Fig.273 5 show the number of collisions in the segregated models., \ref{fig:collmseg} show the number of collisions in the segregated models.274 It can be seen that the number of collisions which occur in the runs are now about a factor 10 higher than in the unsegregated models., It can be seen that the number of collisions which occur in the runs are now about a factor 10 higher than in the unsegregated models.275" In particular in the most concentrated models starting with τη=0.033 pc, the number of collisions is now sufficiently high to build up a main-sequence of high-mass stars."," In particular in the most concentrated models starting with $r_h=0.033$ pc, the number of collisions is now sufficiently high to build up a main-sequence of high-mass stars."276" A closer look at the data also shows that in the mass segregated models the collisions happen at earlier times on average, for the star cluster with N=104 and τι=0.033 pc cluster, for example, roughly half of all collisions happen in the pre-MS stage."," A closer look at the data also shows that in the mass segregated models the collisions happen at earlier times on average, for the star cluster with $N=10^4$ and $r_h=0.033$ pc cluster, for example, roughly half of all collisions happen in the pre-MS stage."277" We note that these results are not in contradiction to results obtained by Ardietal. (2008),, who found that primordial mass segregation does not lead to a significant"," We note that these results are not in contradiction to results obtained by \citet{ardietal2008}, , who found that primordial mass segregation does not lead to a significant"278mass (again. the flow has a narrow accretion column. since it is almost isothermal).,"mass (again, the flow has a narrow accretion column, since it is almost isothermal)."279 The eravilational attraction of the more massive star is stronger on the accretion line. and most of the mass flows toward (he massive companion.," The gravitational attraction of the more massive star is stronger on the accretion line, and most of the mass flows toward the massive companion."280 | treat the more massive companion. a treatment holds for equal mass components as well.," I treat the more massive companion, a treatment holds for equal mass components as well."281" The angular momentum of mass element residing near the center of mass relative to the center of the accreting star is Ja,Εμ where wyο7/e1y is the angular velocity of the binary svstem."," The angular momentum of mass element residing near the center of mass relative to the center of the accreting star is $j_{\rm cm}=\omega_{12} a_1^2$, where $\omega_{12}=[G (M_{12})]^{1/2}/a_{12}^{3/2}$ is the angular velocity of the binary system."282" For an aceretion disk to form. (his should be larger than the specilie angular momentum on the equator of the accreting star jj=(GM,)!."," For an accretion disk to form, this should be larger than the specific angular momentum on the equator of the accreting star $j_1=(G M_{b1} R_1)^{1/2}$."283 The condition Τους This condition can be met by a large fraction of binary svstems with mass ratio of q~1., The condition reads This condition can be met by a large fraction of binary systems with mass ratio of $q \simeq 1$.284 For q=Ll. a main sequence accretor. with Ry2R.. requires ay21048... and there are many binary svstems with LOR.Say1AU.," For $q=1$, a main sequence accretor, with $R_1 \simeq R_\odot$, requires $a_{12} \gtrsim 10 R_\odot$, and there are many binary systems with $10 R_\odot \lesssim a_{12} \lesssim 1 \AU$."285 However. for ¢=0.5. and q=0.3. the condition reads (yo> 54424. and ay>2071484. respectively.," However, for $q=0.5$, and $q=0.3$, the condition reads $a_{12} > 54 {R_1}$ , and $a_{12} > 271 {R_1}$, respectively."286 For q<1 the condition reads diy>qRy., For $q \ll 1$ the condition reads $a_{12} > q^{-4} {R_1}$.287 Therefore. for ¢<0.5 only a small number of svstems with accreting main sequence stars are expected to form accretion disks.," Therefore, for $ q \lesssim 0.5$ only a small number of systems with accreting main sequence stars are expected to form accretion disks."288 For accreting WDs. the mass ratio can be as small as q0.1.," For accreting WDs, the mass ratio can be as small as $ q \sim 0.1$."289 IHlowever. such svstems are rare and live for a short (ime. since a WD mass is ον0.5.U.. and a companion e10 times as massive. will evolve [ast off the main sequence.," However, such systems are rare and live for a short time, since a WD mass is $\sim 0.5 M_\odot$, and a companion $\sim 10$ times as massive, will evolve fast off the main sequence."290 Overall. (he formation of an accretion disk requires (hat the mass ratio in most systems be g20.3 (note that q<1 by definition).," Overall, the formation of an accretion disk requires that the mass ratio in most systems be $q \gtrsim 0.3$ (note that $q \leq 1$ by definition)."291 If the mass is accreted directly from the center of mass of the accreting binary svstem. the accretion disk will be in the binary-orbital plane. i.e.. perpendicular to the orbital plane wilh (he mass-losing star.," If the mass is accreted directly from the center of mass of the accreting binary system, the accretion disk will be in the binary-orbital plane, i.e., perpendicular to the orbital plane with the mass-losing star."292 Some inclination is expected. though. since mass will start flowing toward the accreting star before reaching the center of mass.," Some inclination is expected, though, since mass will start flowing toward the accreting star before reaching the center of mass."293 In any case. jets. if blown. will be in the orbital plane of the triple-star svsten. or close to it.," In any case, jets, if blown, will be in the orbital plane of the triple-star system, or close to it."294 In this case. each of the two stars in (he accreting binary svstem accretes mass in (urn. when it reaches (he accretion column up-stream side.," In this case, each of the two stars in the accreting binary system accretes mass in turn, when it reaches the accretion column up-stream side."295 The star in(urn. sav star Mg. “cleans”," The star inturn, say star $M_{b1}$ , “cleans”"296“species” of Π.Ι) .,“species” of $_2$ $^+$.297" This approximation is expected to be valid at temperatures of 10 to 20 Ix. since E, is LOL Is for the first excited state of o-H3D. ."," This approximation is expected to be valid at temperatures of 10 to 20 K, since $_{\rm u}$ is 104 K for the first excited state of $o$ $_2$ $^+$."298" The o-H3D partition functiou is caleulated from where the cegeneracies. g, aud gr. are equal to 3."," The $o$ $_2$ $^+$ partition function is calculated from where the degeneracies, $g_u$ and $g_l$, are equal to 3."299" Assumiug LTE (Equation 1). excitation temperatures iu the range 10 to 20 Ix aud the partition [uuction appropriate for these temperatures. N(o-H5D .) limits are calculated [rom the observed upper limit on the HeD J—14,05-14,4 liue flix."," Assuming LTE (Equation 1), excitation temperatures in the range 10 to 20 K and the partition function appropriate for these temperatures, $o$ $_2$ $^+$ ) limits are calculated from the observed upper limit on the $_2$ $^+$ $_{\rm1,0}$ $_{\rm1,1}$ line flux."300 As shown in Figure 3a. the limits on the disk average N(o-HoD ) range from 1.3—2.7x10P em? (with the highest value corresponding to the lowest temperature).," As shown in Figure 3a, the limits on the disk average $o$ $_2$ $^+$ ) range from $1.3-2.7\times10^{12}$ $^{-2}$ (with the highest value corresponding to the lowest temperature)."301 The limit ou the total N(HeD ). Le. o—p. depends on the o-HeD colt density aud the temperature dependent o/p ratio.," The limit on the total $_2$ $^+$ ), i.e. $o + p$, depends on the $o$ $_2$ $^+$ column density and the temperature dependent $o/p$ ratio."302 This ratio has been modeled by Sipilaetal.(2010) [rom Lto 20 Ix for a molecular hydrogene cdeusity of 10° ? aud au interstellar eerain distribution., This ratio has been modeled by \citet{Sipila10} from 4 to 20 K for a molecular hydrogen density of $^6$ $^{-3}$ and an interstellar grain distribution.303 The derived o/p1 ratio is 0.5—0.1 for temperatures of 10-20 Ix. with the lowest ratio at 13-17 Ix. While the assume erain size distribution aud deusity are more appropriate for dense clouds thau disk midplaues. the erain size cdistributiou mainly affects the temperature profile. and Sipilaetal.(2010). [iud that the Ha3D o/pis nearly constant with increasingD> density.," The derived $o/p$ ratio is 0.5–0.1 for temperatures of 10–20 K, with the lowest ratio at 13–17 K. While the assumed grain size distribution and density are more appropriate for dense clouds than disk midplanes, the grain size distribution mainly affects the temperature profile, and \citet{Sipila10} find that the $_2$ $^+$ $o/p$ is nearly constant with increasing density."304 Thus we expect the values calculated with these asstunptious sliould be valid for cisk iuidplaue couditious., Thus we expect the values calculated with these assumptions should be valid for disk midplane conditions.305 Figure 3b shows the result of applying the literature o/p ratios to the previously calculated o-HeD colt density limits to obtain limits on N(H2D ) as a functiou of temperature., Figure 3b shows the result of applying the literature $o/p$ ratios to the previously calculated $o$ $_2$ $^+$ column density limits to obtain limits on $_2$ $^+$ ) as a function of temperature.306 These ⋅⋅ e ⋅ ∐∐↕∐⊳∖↓⋅⋜↕∐∩≺↵↥⋅∩⋯⊓∩−≻↥≍∐≻∟∢∙⋯−⋅⊺∐≺↵↽∐⋅≺↵⊳∖≺, These limits range from $4$ to $21\times10^{12}$ $^{-2}$.307"↵∐∢∙≺↵∩↥⋜↕↽≻≺↲⋜↕↕⊆∖⇁⋜↕↥⋯↵⋜↕↕↥∙⋝⊾↓⊳∖⋜⊔⇂∐⋅≺↵∢∙↕∢∙∩∐⊳∖≺↲≺↽⋯↵∐∢∙≺↵o,2 2 . ye - ⋅ of the [act that the limit on N(o-H3D ) decreases with temperature. while the o/p ratio has a minununm at 13-17 Is. The limit on the total columu density of ious in the midplaue. ΝΟ Ha. D, ). depeuds ou N(H3D } aud the ratio of N(H2D ) to N(OS7 Hy ,D, )."," The presence of a peak value at 13 K is a direct consequence of the fact that the limit on $o$ $_2$ $^+$ ) decreases with temperature, while the $o/p$ ratio has a minimum at 13–17 K. The limit on the total column density of ions in the midplane, $\sum$ $_{3-x}$ $_x^+$ ), depends on $_2$ $^+$ ) and the ratio of $_2$ $^+$ ) to $\sum$ $_{3-x}$ $_x^+$ )."308 Like the o/p ratio. this ratio is expected to vary with deusity and temperature. as well as other euviroumental properties such as grain size (Floweretal.2001:Ceccarelli&Dominik2005:Sipilà2010).," Like the $o/p$ ratio, this ratio is expected to vary with density and temperature, as well as other environmental properties such as grain size \citep{Flower04,Ceccarelli05,Sipila10}."309. This ratio will also depend ou whether or uot CO aud Ne are frozen out. completely. or if low abundauces of these species can be maintained in the gas-phase through non-thermal clesorption (AseusioRamosetal.," This ratio will also depend on whether or not CO and $_2$ are frozen out completely, or if low abundances of these species can be maintained in the gas-phase through non-thermal desorption \citep{AsensioRamos07}."310"2007).. Casellietal.(2008) modeled the ratios of all deuterated Η., isotopologues for molecular hydrogen density 10? ? aud interstellar erains as a [tection of temperature.", \citet{Caselli08} modeled the ratios of all deuterated $_3^+$ isotopologues for molecular hydrogen density $^5$ $^{-3}$ and interstellar grains as a function of temperature.311 As mentioned previously. the," As mentioned previously, the"312or YSOs.,or YSOs.313 The median OCLE-UI color of these blue stars i (V.PDσ0. nae., The median OGLE-III color of these blue stars is $(V-I)\simeq0.1$ mag.314δέ. These are stars with red spectra sometimes showing molecular absorption bauds., These are stars with red spectra sometimes showing molecular absorption bands.315" We identified 68 red sources, where SIMDAD classifies Las infrared. sources (one YSO from and three 211255 sources). d as a PN. 1 as a YSO. 1 as an asvinptotic eiut branch star. and 1 asa galaxy."," We identified 68 red sources, where SIMBAD classifies 4 as infrared sources (one YSO from and three 2mass sources), 1 as a PN, 1 as a YSO, 1 as an asymptotic giant branch star, and 1 as a galaxy."316 The median III color of these sources is (VD)z1.1 nae., The median OGLE-III color of these sources is $(V-I)\simeq1.1$ mag.317 The vield of our survey is determined by a combination of contamination and depth. where it is dificult to fully characterize the effects of depth because of the large variation in integration time created by the weather.," The yield of our survey is determined by a combination of contamination and depth, where it is difficult to fully characterize the effects of depth because of the large variation in integration time created by the weather."318 For diseussion. we simply combine the four fields (Table 2)).," For discussion, we simply combine the four fields (Table \ref{tab:selectionresults}) )."319 We know from the surface density of candidates compared to quasars 9011... 2006)). shown in Figure 8.. that the level of contanunation is high. but much of this is bv desigu jecause of the large απο of available fibers.," We know from the surface density of candidates compared to quasars , ), shown in Figure \ref{fig:cumul}, that the level of contamination is high, but much of this is by design because of the large number of available fibers."320 Tn Figure d aud Table 2.. we preseut our vields frou his observing run. divided by the selection method.," In Figure \ref{fig:VennCand} and Table \ref{tab:selectionresults}, we present our yields from this observing run, divided by the selection method."321 The wid-IR-sclected sources were divided iuto several classes (QSO-Aa. QSO-Ab. ete:," The mid-IR-selected sources were divided into several classes (QSO-Aa, QSO-Ab, etc.;"322 see Section 2.1))., see Section \ref{sec:mIRsel}) ).323 As expected he purest class. QSO-Aa. has the highest coufiiinationrate. atδ," As expected the purest class, QSO-Aa, has the highest confirmationrate, at."324"ν, Next. the two classes QSO-Àb aud QSO- had coufinnation rates of and respectively."," Next, the two classes QSO-Ab and QSO-Ba had confirmation rates of and , respectively."325— 7.7masxX5.7mas. ad a position angle (PA) of —31 for 1.6 Εν. and 3.6masx3.0mos al a PA of —13° for 4.9 Gllz.,"= $7.7~mas\times5.7~mas$, at a position angle (PA) of $-31\degr$ for 1.6 GHz, and $3.6~mas\times3.0~mas$ at a PA of $-13\degr$ for 4.9 GHz."326 We have detected. (wo distinct radio components al 1.6 Gllz (marked 1 and 2 in Figure 1))., We have detected two distinct radio components at 1.6 GHz (marked 1 and 2 in Figure \ref{fig:vlbi}) ).327 There is a suggestion of a weak third component to the north of component 1., There is a suggestion of a weak third component to the north of component 1.328 New sensitive radio observations are required to confirm this feature., New sensitive radio observations are required to confirm this feature.329" The source position is ~0.58"" away [rom the listed optical host galaxy position of R.A. 19h 081m 16.3708. decl."," The source position is $\sim0.58\arcsec$ away from the listed optical host galaxy position of R.A. 19h 08m 16.370s, decl."330 50d 55m 59.588 (7)., 50d 55m 59.58s \citep{Clements81}.331 We identify components l. 2 and 3 to be the core. the jet. aud apossible counterjet. respectively.," We identify components 1, 2 and 3 to be the core, the jet, and a counterjet, respectively."332" The ""core-jet structure extends to 70.3 parsec. αἱ a DA, ol ~25""."," The “core-jet” structure extends to $\sim$ 0.8 parsec, at a P.A. of $\sim25\degr$."333" The peak surlace brightness of the core. and the total radio flux densitv of the ""core-jet structure are 0.46 mJv + and 0.80 mJy. respectively."," The peak surface brightness of the core, and the total radio flux density of the “core-jet” structure are 0.46 mJy $^{-1}$ and 0.80 mJy, respectively."334 The peak intensities and positions of the radio components. estimated using AIPS tasks JAIFIT and IMDIST. are listed in Table 1..," The peak intensities and positions of the radio components, estimated using AIPS tasks JMFIT and IMDIST, are listed in Table \ref{tabparam}."335 In order to test the credibility of component 3. we estimated a surface densitv of spurious noise peaks in the image by dividing the number of noise peaks having a signal-to-noise ratio (S/N) similar to component 3 (£e. S/N 22.6). bv (he entire image.," In order to test the credibility of component 3, we estimated a surface density of spurious noise peaks in the image by dividing the number of noise peaks having a signal-to-noise ratio (S/N) similar to component 3 $i.e.,$ S/N $>$ 2.6), by the entire image."336" We found around. 230 noise peaks in an image of size 0.4""x0.4"". resulting in a noise peak surface density of ~1370 peaks 7."," We found around 230 noise peaks in an image of size $0.4\arcsec\times0.4\arcsec$, resulting in a noise peak surface density of $\sim1370$ peaks $^{-2}$."337 Considering then a region of size (15masx15 mas). centered around the peak source enission. as (he region where a noise peak could be mistaken [or source emission (the core-]et distance being ~5 mes). we estimated thal 0.3 noise peaks could be expected in this region.," Considering then a region of size $15~mas\times15~mas$ ), centered around the peak source emission, as the region where a noise peak could be mistaken for source emission (the core-jet distance being $\sim5~mas$ ), we estimated that 0.3 noise peaks could be expected in this region."338 Therefore. there is a chance that component 3 is a noise peak.," Therefore, there is a chance that component 3 is a noise peak."339" The 1.4 GHz peak flux density of the VLA A-array core (size ~ 1.5"") is ~14 mJv (?)..", The 1.4 GHz peak flux density of the VLA A-array core (size $\sim1.5\arcsec$ ) is $\sim14$ mJy \citep{HotaSaikia06}.340 This implies that only about of the VLA flux density is detected by the VLBA., This implies that only about of the VLA flux density is detected by the VLBA.341 This is similar to what is observed in the Sevlert galaxy NGC 4151 (28%:??)..," This is similar to what is observed in the Seyfert galaxy NGC 4151 \citep[$\sim$8\%;][]{Pedlar93,Ulvestad98}."342 We believe. however. that had self-calibration worked in NGC 6764. its [raction of VLBA to VLA αν density would have been higher.," We believe, however, that had self-calibration worked in NGC 6764, its fraction of VLBA to VLA flux density would have been higher."343 Nevertheless. it appears that there is either a lot of diffuse emission on scales of tens or hundreds of parsecs which are not visible to the VLBA. or the VLBA is nol sensitive to the diffuse radio emission on parsec scales (this appears to be less likely in the case of NGC 6764 considering the large fraction of missing flux). or a combination ol both (see Orienti Prieto 2010 for a discussion on (he missing diffuse emission in VLBI observations).," Nevertheless, it appears that there is either a lot of diffuse emission on scales of tens or hundreds of parsecs which are not visible to the VLBA, or the VLBA is not sensitive to the diffuse radio emission on parsec scales (this appears to be less likely in the case of NGC 6764 considering the large fraction of missing flux), or a combination of both (see Orienti Prieto 2010 for a discussion on the missing diffuse emission in VLBI observations)."344 There appears to be a tentative detection of components 1 and 2 at 4.9 GlIz., There appears to be a tentative detection of components 1 and 2 at 4.9 GHz.345 However. (his detection is also in need of new confirmatory observations. as (he radio peak in components," However, this detection is also in need of new confirmatory observations, as the radio peak in components"346"the loss of opacity leading to smaller NLTE corrections. the opposite being true for $,»B,.","the loss of opacity leading to smaller NLTE corrections, the opposite being true for $S^l_\nu > B_\nu$."347" We see that for the lower level of the weaker line considered in the figure has J.>B,.. whilst STsB,. which leads to overionization of that level and greater departures than the stronger line and greater NLTE abundance corrections,"," We see that for the lower level of the weaker line considered in the figure has $\bar J_{\nu} > B_{\nu}$ , whilst $S^l_\nu \approx B_\nu$, which leads to overionization of that level and greater departures than the stronger line and greater NLTE abundance corrections."348 The effect of H collisions ts in general to reduce the spread of departure coefficients and drive populations towards LTE values., The effect of H collisions is in general to reduce the spread of departure coefficients and drive populations towards LTE values.349 This reduction in the spread of departure coefhcients comes from the coupling of bound states., This reduction in the spread of departure coefficients comes from the coupling of bound states.350 The increase of H collisions gradually reduces the departures from LTE through the atmosphere as shown in Fig. 1: , The increase of H collisions gradually reduces the departures from LTE through the atmosphere as shown in Fig. \ref{fig:departplots}; ;351with an increasing Sy the slope in the departure coefficient profile becomes shallower., with an increasing $\rm S_{H}$ the slope in the departure coefficient profile becomes shallower.352 In Fig., In Fig.353 | it is interesting to see that the rise i b; at around τει3—2.5 for the levels below 1.83 eV becomes smaller with increasing Sy., \ref{fig:departplots} it is interesting to see that the rise in $b_{i}$ at around $\tau_{\rm 5000} \approx -2.5$ for the levels below 1.83 eV becomes smaller with increasing $S_{\rm H}$.354 This could in fact mean an increase in NLTE departures for some levels for increasing Sy. rather than H collidions driving conditions towards LTE which is normally the case.," This could in fact mean an increase in NLTE departures for some levels for increasing $S_{\rm H}$, rather than H collidions driving conditions towards LTE which is normally the case."355 This rise is most likely caused by increased recombination in the upper (infrared) levels followed by a cascade of electrons down to lower levels., This rise is most likely caused by increased recombination in the upper (infrared) levels followed by a cascade of electrons down to lower levels.356 Exactly how this is affected by the increase in Sy is not yet knowr and requires further study., Exactly how this is affected by the increase in $\rm S_{H}$ is not yet known and requires further study.357 The decrease in level population at 73000.< ] causes a drop in opacity for all lines., The decrease in level population at $\tau_{\rm 5000} <$ 1 causes a drop in opacity for all lines.358 As a result of this. the lines form deeper in the atmosphere than in LTE.," As a result of this, the lines form deeper in the atmosphere than in LTE."359 In Fig. 3.. ," In Fig. \ref{fig:depthform}, ,"360"we clearly see this effect. where we show the continuum optical depth 73666 at which the line optical depth r, = 2/3."," we clearly see this effect, where we show the continuum optical depth $\tau_{\rm 5000}$ at which the line optical depth $\tau_{\nu}$ = 2/3."361" We also see that there is an increasingly large logarithmic optical depth difference. Alogrsooo(7,=2/3). between the formation of weak lines in NLTE and LTE. up to = 50mA.. after which the difference becomes constant."," We also see that there is an increasingly large logarithmic optical depth difference, $\Delta\log{\tau_{\mathrm{5000}}(\tau_\nu=2/3)}$, between the formation of weak lines in NLTE and LTE, up to $\approx$ 50, after which the difference becomes constant."362 With a decrease in opacity compared. to LTE. there needs to be an increase of abundance to match the equivalent width of a given line in NLTE.," With a decrease in opacity compared to LTE, there needs to be an increase of abundance to match the equivalent width of a given line in NLTE."363 Opacity is not the only variable affected by NLTE. the source function can also be affected.," Opacity is not the only variable affected by NLTE, the source function can also be affected."364 However. it is the dominant force in driving the NLTE departures within the Fe atom.," However, it is the dominant force in driving the NLTE departures within the Fe atom."365 In Fig. 4..," In Fig. \ref{fig:Chi-WEQHD140283},"366 we plot the abundance correction versus equivalent width for the star HD140283., we plot the abundance correction versus equivalent width for the star HD140283.367 We see that there is a positive correction for the different values of Su., We see that there is a positive correction for the different values of $\rm S_{H}$ .368 There ts a clear trend with equivalent width., There is a clear trend with equivalent width.369 It is how this translates to trends with excitation energy y that will affect Tay: if the abundance corrections only shifted the mean abundance without depending on y then the derived Το would not change., It is how this translates to trends with excitation energy $\chi$ that will affect $T_{\rm eff}$ : if the abundance corrections only shifted the mean abundance without depending on $\chi$ then the derived $T_{\rm eff}$ would not change.370 Through Fig., Through Fig.371 | to Fig., \ref{fig:departplots} to Fig.372 4. the general effects of NLTE on line formation can be seen., \ref{fig:Chi-WEQHD140283} the general effects of NLTE on line formation can be seen.373 The depletion of level populations (Fig. 1) , The depletion of level populations (Fig. \ref{fig:departplots}) )374leads to a lower opacity and shiftsthe depth of formation to deeper levels (Fig. 3))., leads to a lower opacity and shiftsthe depth of formation to deeper levels (Fig. \ref{fig:depthform}) ).375 This also means that a higher abundance is needed within NLTE. leading to positive abundance corrections (Fig. 4)).," This also means that a higher abundance is needed within NLTE, leading to positive abundance corrections (Fig. \ref{fig:Chi-WEQHD140283}) )."376 However. there is a competing effect in some cases where the source function deviates from the Planck function (Fig. 2).," However, there is a competing effect in some cases where the source function deviates from the Planck function (Fig. \ref{fig:sjbplots}) ),"377 which. in the case of the strong lines. compensates for the level depletion and decreases the abundance correction. as is seen in Fig. 4..," which, in the case of the strong lines, compensates for the level depletion and decreases the abundance correction, as is seen in Fig. \ref{fig:Chi-WEQHD140283}. ."378 In order to determine a new Zr for a star. we first need to calculate NLTE corrections for the LTE abundances derived in Paper 1. Abundance corrections of the form ΑνΜα - ApriMuri] are caleulated and applied to the LTE abundances from Paper I to generate NLTE abundances on the same scale as that paper. rather than using solely the new NLTE analysis.," In order to determine a new $T_{\rm eff}$ for a star, we first need to calculate NLTE corrections for the LTE abundances derived in Paper I. Abundance corrections of the form $A_{\rm NLTE,{\sc MULTI}}$ $-$ $A_{\rm LTE,{\sc MULTI}}$ are calculated and applied to the LTE abundances from Paper I to generate NLTE abundances on the same scale as that paper, rather than using solely the new NLTE analysis."379 This procedure is used so as to tie this work to the previous results. thus allowing the limitations of the LTE assumptions in that work to be seen.," This procedure is used so as to tie this work to the previous results, thus allowing the limitations of the LTE assumptions in that work to be seen."380 To do this. a grid of results for a range of abundances is created with increments of 0.02 dex.," To do this, a grid of results for a range of abundances is created with increments of 0.02 dex."381 The abundance values covered by this grid depend on the spread of abundances from individual lines in each star., The abundance values covered by this grid depend on the spread of abundances from individual lines in each star.382 gives an LTE and NLTE equivalent width for each abundance in this σης., gives an LTE and NLTE equivalent width for each abundance in this grid.383 A first step is to determine what WL; from the grid corresponds to the LTE abundance derived in Paper I (?).., A first step is to determine what $W_{\rm LTE}$ from the grid corresponds to the LTE abundance derived in Paper I \citep{Hosfordetal2009}.384 This is done for all Fe lines that are measured in the star., This is done for all Fe lines that are measured in the star.385" The NLTE abundance inferred for a line is the abundance that corresponds to this W, within the grid of NLTE results.", The NLTE abundance inferred for a line is the abundance that corresponds to this $W_{\lambda}$ within the grid of NLTE results.386 The correction is then calculated as AA(Fe) = A(Fednyy — A(Fe)ngi., The correction is then calculated as $\Delta A(\rm Fe)$ = $A(\rm Fe)_{NLTE}$ $-$ $A(\rm Fe)_{LTE}$.387 Fig., Fig.388 5 shows the corrections for the star HD140283 calculated for the three different Sy values: Sy = 0. 0.001 and I.," \ref{Fig:abnd-chi/ew-HD140283} shows the corrections for the star HD140283 calculated for the three different $\rm S_{H}$ values: $\rm S_{H}$ = 0, 0.001 and 1."389 We see a trend in the abundance correction with y. where we have values. from least square fits. of: The non-zero coefficient of y implies that a 7. correction is needed.," We see a trend in the abundance correction with $\chi$, where we have values, from least square fits, of: The non-zero coefficient of $\chi$ implies that a $T_{\rm eff}$ correction is needed."390 The values for Sy = 0 and Sy = 0.001 are very similar and imply that 7. corrections for these two values will be very similar., The values for $\rm S_{H}$ = 0 and $\rm S_{H}$ = 0.001 are very similar and imply that $T_{\rm eff}$ corrections for these two values will be very similar.391 We therefore decided that corrections for only Su = 0 and 1 would be calculated. Sy = 0 representing the maximal NLTE corrections and Sy = | representing the full Drawinian magnitude of neutral H collisions.," We therefore decided that corrections for only $\rm S_{H}$ = 0 and 1 would be calculated, $\rm S_{H}$ = 0 representing the maximal NLTE corrections and $\rm S_{H}$ = 1 representing the full Drawinian magnitude of neutral H collisions."392" To test the corrections. we compared synthetic profiles from the NLTE abundance with the observed profile. and compared measured Wy's with NLTE W,’s fromMULTI. obtained from an abundance given by Ap; + ΔΑ."," To test the corrections, we compared synthetic profiles from the NLTE abundance with the observed profile, and compared measured $W_{\lambda}$ 's with NLTE $W_{\lambda}$ 's from, obtained from an abundance given by $A_{\rm LTE}$ + $\Delta A$."393 The synthetic profiles are convolved with a Gaussian whose width is allowed to vary from line to line., The synthetic profiles are convolved with a Gaussian whose width is allowed to vary from line to line.394 This represents the macroturbulent and instrumental broadening. the latter calculated by fittingσι Gaussian profiles to ThAr lines in IRAF and found to be é 100mA.," This represents the macroturbulent and instrumental broadening, the latter calculated by fitting Gaussian profiles to ThAr lines in IRAF and found to be $\sim$ 100."395. We found that the profiles match the observed line reasonably well. and that measured and calculated W's are comparable. with a standard deviation of 2.3mA.," We found that the profiles match the observed line reasonably well, and that measured and calculated $W_{\lambda}$ 's are comparable, with a standard deviation of 2.3."396. This gives us confidence that the corrections are realistic within the framework of the atomic model used., This gives us confidence that the corrections are realistic within the framework of the atomic model used.397 These corrections were then applied to theWIDTH6LTE abundances used in Paper [ andnew plots of y versus A(Fe) were plotted., These corrections were then applied to theWIDTH6LTE abundances used in Paper I andnew plots of $\chi$ versus$A$ (Fe) were plotted.398 We then nulledtrends in this plot to constrain Z4;NLTE) by recalculating the LTE abundances using the radiative transfer program WIDTH6 (Kurucz Furenlid 1978) exactly as in ? and reapplying the NLTE corrections.derived here from for the original LTEparameters.," We then nulledtrends in this plot to constrain $T_{\rm eff}$ (NLTE) by recalculating the LTE abundances using the radiative transfer program WIDTH6 (Kurucz Furenlid 1978) exactly as in \citet{Hosfordetal2009} and reapplying the NLTE corrections,derived here from for the original LTEparameters."399infalling masses are self-similar.,infalling masses are self-similar.400" Therefore, when the abundance ratios and gas fraction are examined (Figs."," Therefore, when the abundance ratios and gas fraction are examined (Figs."401" and 6)), the three series of models (M8, M9, and M10) are overlapping."," \ref{Fig:nowdOFeH} and \ref{Fig:nowdmuY}) ), the three series of models (M8, M9, and M10) are overlapping."402 In Fig., In Fig.403 7 we plot the mass-metallicity relations predicted by models without wind., \ref{Fig:nowdMsZ} we plot the mass-metallicity relations predicted by models without wind.404" We run models for three different infall masses (105, 109, 10'!°Mo))."," We run models for three different infall masses $10^{8}$, $10^{9}$, $10^{10}$ )."405" The effects of different numbers of bursts (n=1,3, 7), different durations (d= 0.03,0.1,0.3) and different SFEs (e=0.2,0.5,1.0, 2.0) as functions of galactic mass are shown."," The effects of different numbers of bursts $n=1, 3, 7$ ), different durations $d=0.03, 0.1, 0.3$ ) and different SFEs $\epsilon=0.2, 0.5, 1.0,4062.0$ ) as functions of galactic mass are shown."407 It is evident from Fig., It is evident from Fig.408" 7 that our models can very well reproduce the M-Z relation even without galactic wind but just assuming an increase of the number, or duration of bursts, or the efficiency of SF."," \ref{Fig:nowdMsZ} that our models can very well reproduce the M-Z relation even without galactic wind but just assuming an increase of the number, or duration of bursts, or the efficiency of SF."409" If the galactic wind has the same chemical composition as the well-mixed ISM, i.e. w;—1 for all the elements, we call it “normal wind""."," If the galactic wind has the same chemical composition as the well-mixed ISM, i.e. $w_i=1$ for all the elements, we call it “normal wind”."410" In Fig. 8,"," In Fig. \ref{Fig:wdZmuY},"411" we show the the evolutionary tracks predicted by models with normal wind; abundance ratios of log(C/O) vs. 12+log(O/H) and [O/Fe] vs. [Fe/H] are on the left side, while u,—Z and Y—Z relations on the right side."," we show the the evolutionary tracks predicted by models with normal wind; abundance ratios of log(C/O) vs. 12+log(O/H) and [O/Fe] vs. [Fe/H] are on the left side, while $\mu-Z$ and $Y-Z$ relations on the right side."412" The models have the same total infall mass (Ming=10? M5)) and same bursts sequence (t=1/3/5/7/9/11/13 Gyr, with d—0.1 Gyr for each burst), but different wind efficiencies (Aw=0,0.2,0.5,1.0)."," The models have the same total infall mass $M_{inf}=10^9$ ) and same bursts sequence $t=1/3/5/7/9/11/13$ Gyr, with $d=0.1$ Gyr for each burst), but different wind efficiencies $\lambda_w=0, 0.2, 0.5, 1.0$ )."413" Oxygen is produced by massive stars, therefore no oxygen will be ejected into the ISM after star formation ceases."," Oxygen is produced by massive stars, therefore no oxygen will be ejected into the ISM after star formation ceases."414" On the other hand, elements, such as C and N produced by low- and intermediate-mass stars, and Fe mainly produced by SN Ia explosion, are continuously polluting the ISM after the star formation stops, owing to their long lifetime."," On the other hand, elements, such as C and N produced by low- and intermediate-mass stars, and Fe mainly produced by SN Ia explosion, are continuously polluting the ISM after the star formation stops, owing to their long lifetime."415" Therefore, the decrease of the mass of gas (i.e., H and He) and the o-elements lost with the wind will result in a dramatic increasing of the abundance of the “time-delayed? elements."," Therefore, the decrease of the mass of gas (i.e., H and He) and the $\alpha$ -elements lost with the wind will result in a dramatic increasing of the abundance of the ``time-delayed'' elements."416" The stronger the wind, the higher the abundance of C or Fe relative to O predicted by the models."," The stronger the wind, the higher the abundance of C or Fe relative to O predicted by the models."417" 'The main effect of normal winds is to decrease the gas fraction with a smaller effect on the O/H abundance, as we can see from the 12+log(O/H)-y relation (upper right panel of Fig. 8))."," The main effect of normal winds is to decrease the gas fraction with a smaller effect on the O/H abundance, as we can see from the $\mu$ relation (upper right panel of Fig. \ref{Fig:wdZmuY}) )."418 This means that models with normal wind cannot explain the whole spread in O/H observed at a given µ for these galaxies., This means that models with normal wind cannot explain the whole spread in O/H observed at a given $\mu$ for these galaxies.419 There are two possible reasons for that., There are two possible reasons for that.420" One is the same wind efficiency (i.e., wiAw) for both oxygen and hydrogen in the normal wind, so that both O and H decrease at the same time."," One is the same wind efficiency (i.e., $w_i\lambda_w$ ) for both oxygen and hydrogen in the normal wind, so that both O and H decrease at the same time."421 The other one is the short infall time scale assumed (τ1 Gyr)., The other one is the short infall time scale assumed $\tau=1$ Gyr).422" In this case, no primordial gas falls into the galaxies to dilute the ISM at late evolutionary times."," In this case, no primordial gas falls into the galaxies to dilute the ISM at late evolutionary times."423" Therefore, we also developed a model with long infall time scale (r—10 Gyr, magenta dotted lines in Fig. 8))."," Therefore, we also developed a model with long infall time scale $\tau=10$ Gyr, magenta dotted lines in Fig. \ref{Fig:wdZmuY}) )."424 It is clear that in this model the metallicity decreases in the interburst time., It is clear that in this model the metallicity decreases in the interburst time.425" Actually, the infall of primordial gas (i.e., H and He) results in a lower mass loss rate of H and He than metals, similar to the metal-enhanced wind case which will be further discussed in the next section."," Actually, the infall of primordial gas (i.e., H and He) results in a lower mass loss rate of H and He than metals, similar to the metal-enhanced wind case which will be further discussed in the next section."426" A very strong normal wind (e.g. A,> 0.5) seems unlikely in late-type dwarf galaxies since it would lose a large amount of gas, and hence it would predict a too low gas fraction, as it is evident in Fig. 8.."," A very strong normal wind (e.g. $\lambda_w>0.5$ ) seems unlikely in late-type dwarf galaxies since it would lose a large amount of gas, and hence it would predict a too low gas fraction, as it is evident in Fig. \ref{Fig:wdZmuY}."427" In the lower right panel of Fig. 8,,"," In the lower right panel of Fig. \ref{Fig:wdZmuY},"428" the predicted Y vs. (O/H) relation is shown and it is consistent with the observational data at the low metallicity, because the wind does not develop yet when the galaxy is still very metal poor."," the predicted Y vs. (O/H) relation is shown and it is consistent with the observational data at the low metallicity, because the wind does not develop yet when the galaxy is still very metal poor."429" However, after the wind, an increase of the helium abundance as well as of the abundances of elements produced on long timescale occurs, especially in the case of a strong wind which produces a very small final gas fraction."," However, after the wind, an increase of the helium abundance as well as of the abundances of elements produced on long timescale occurs, especially in the case of a strong wind which produces a very small final gas fraction."430is defined as those objects blue-wards (in both plots) of the lines in Figure 11..,is defined as those objects blue-wards (in both plots) of the lines in Figure \ref{samcut}.431 The lines eut the top of the white dwarf locus at (13) but allow slightly redder objects with higher RPMs into the sample., The lines cut the top of the white dwarf locus at $(B_{\rm J}-R)\sim1.2$ but allow slightly redder objects with higher RPMs into the sample.432 The white dwarf locus is unambiguous wards of (£3)H)-12., The white dwarf locus is unambiguous blue-wards of $(B_{\rm J}-R)\sim1.2$.433 Every object in the sample must appear in at least 15 stacks in each passhanc., Every object in the sample must appear in at least 15 stacks in each passband.434 Phe positional data as a function of time have been scrutinised lor every object selected as a white dwarf candidate. and those with dubious motions rejected.," The positional data as a function of time have been scrutinised for every object selected as a white dwarf candidate, and those with dubious motions rejected."435 While such a process may seem rather arbitrary. il was necessary (0 incorporate this screening stage in the sample extraction. because simple automated rejection algorithms such as the 30 rejection routine used here cannot be guaranteed. to eliminate spurious motions.," While such a process may seem rather arbitrary, it was necessary to incorporate this screening stage in the sample extraction because simple automated rejection algorithms such as the $\rm 3\sigma$ rejection routine used here cannot be guaranteed to eliminate spurious motions."436 Some examples are shown in Figures 12. and. 13.., Some examples are shown in Figures \ref{Rexamples} and \ref{Bexamples}.437 All three objects shown successfully satisfied: all the survey criteria., All three objects shown successfully satisfied all the survey criteria.438 Phe object plotted at the top of Figures 12 and 13. (IXN27) shows a clear. genuine motion in both x and v in both passbands anc was included. in the final sample without hesitation.," The object plotted at the top of Figures \ref{Rexamples} and \ref{Bexamples} (KX27) shows a clear, genuine motion in both x and y in both passbands and was included in the final sample without hesitation."439 The middle object (IRX18) has arger positional uncertainties and a smaller overall motion. out still shows consistent. smooth motions and was also included.," The middle object (KX18) has larger positional uncertainties and a smaller overall motion, but still shows consistent, smooth motions and was also included."440 “Phe final object shows evidence of large non-linear deviations in the last four epochs of the x measures. in roth passbands., The final object shows evidence of large non-linear deviations in the last four epochs of the x measures in both passbands.441 Although the bad-point rejection algorithm vas removed at least one datum [rom each x plot (as shown bv the multiple straight line fits). this object shows no evidence of proper motion based on the first. 16 data »oints and certainly cannot be considered a reliable proper motion object candidate.," Although the bad-point rejection algorithm has removed at least one datum from each x plot (as shown by the multiple straight line fits), this object shows no evidence of proper motion based on the first 16 data points and certainly cannot be considered a reliable proper motion object candidate."442 This object. along with 9 others. were rejected. from. the final WD. sample.," This object, along with 9 others, were rejected from the final WD sample."443 These rejected objects tended either to have large olfsets from a positional distribution otherwise consistent with zero motion at either the first or last few epochs. as is the case with the rejected object. described above: or the positional measures had an unusually laree scatter around the mean position. indicating the error in position was larger than the objects magnitude," These rejected objects tended either to have large offsets from a positional distribution otherwise consistent with zero motion at either the first or last few epochs, as is the case with the rejected object described above; or the positional measures had an unusually large scatter around the mean position, indicating the error in position was larger than the objects magnitude"444"as ""background"" and treated in LTE.",as “background” and treated in LTE.445 The statistical equilibrium equations in the RH-code are solved under the assumption of LTE populations within a single vibrational level since it would be time-consuming to solve them for each individual vibrational-rotational level (as we have to deal with more than 2000 transitions simultaneously)., The statistical equilibrium equations in the RH-code are solved under the assumption of LTE populations within a single vibrational level since it would be time-consuming to solve them for each individual vibrational-rotational level (as we have to deal with more than 2000 transitions simultaneously).446 Such an approximation is commonly used in NLTE molecular calculations (cf.mann1989:Uitenbroek 2000).. because oscillator strengths of pure rotational radiative transitions are negligibly small and radiative processes can contribute to the rotational population balance only via two-step processes (Raman seattering for the ground electronic state and emission followed by absorption for the exited state).," Such an approximation is commonly used in NLTE molecular calculations \citep[cf.][]{thompson1973, mountlinsky1974, ayreswiedemann1989, uitenbroek2000}, because oscillator strengths of pure rotational radiative transitions are negligibly small and radiative processes can contribute to the rotational population balance only via two-step processes (Raman scattering for the ground electronic state and emission followed by absorption for the exited state)."447" We have included calculations of electronic-vibrational molecular transitions with the fine structure into the RH-code in order to use it for the CN violet system computation,", We have included calculations of electronic-vibrational molecular transitions with the fine structure into the RH-code in order to use it for the CN violet system computation.448 Although the modified code can be used for a more general case. for the CN violet system we consider only diagonal vibrational bands as the Franck-Condon factors of the non-diagonal bands are much lower than those of the diagonal.," Although the modified code can be used for a more general case, for the CN violet system we consider only diagonal vibrational bands as the Franck-Condon factors of the non-diagonal bands are much lower than those of the diagonal."449 With the RH-code we compute the opacities and intensity. neglecting polarization.," With the RH-code we compute the opacities and intensity, neglecting polarization."450 Then. we use these as the input for the second code (hereafter POLY-code) written by Fluri&Stenflo(2003) and Flurietal.(2003)... which iteratively solves the polarized radiative transfer equation. taking into aecount the Hanle effect and assuming that opacities obtained in the RH-code remain unchanged (which ts à good approximation since the degree of polarization in our calculations is always lower than )).," Then, we use these as the input for the second code (hereafter POLY-code) written by \citet{fluristenflo2003} and \citet{flurietal2003}, which iteratively solves the polarized radiative transfer equation, taking into account the Hanle effect and assuming that opacities obtained in the RH-code remain unchanged (which is a good approximation since the degree of polarization in our calculations is always lower than )."451 The POLY-code was adjusted for dealing with many blended lines as initially it was designed for treating only a few non-overlaping atomic lines. while in molecular bands even a narrow spectral region can contain several hundred lines. which have to be computed simultaneously.," The POLY-code was adjusted for dealing with many blended lines as initially it was designed for treating only a few non-overlaping atomic lines, while in molecular bands even a narrow spectral region can contain several hundred lines, which have to be computed simultaneously."452 As in most NLTE-codes. the line source function in the RH-code is calculated as a function of NLTE populations. temperature and frequency (seeUitenbroek2000).," As in most NLTE-codes, the line source function in the RH-code is calculated as a function of NLTE populations, temperature and frequency \citep[see][]{uitenbroek2000}."453. The source function deviations from the LTE are defined via population departure coefficients (the ratio between the LTE and NLTE populations)., The source function deviations from the LTE are defined via population departure coefficients (the ratio between the LTE and NLTE populations).454 Such a formalism ts sufficient for calculations of the intensity field but does not provide any direct information about the contribution of scattering processes to the line., Such a formalism is sufficient for calculations of the intensity field but does not provide any direct information about the contribution of scattering processes to the line.455 However. for polarization calculations it is important to know the exact balance between scattering and thermal processes. since polarization is produced only by scattering.," However, for polarization calculations it is important to know the exact balance between scattering and thermal processes, since polarization is produced only by scattering."456 Therefore in the POLY-code the source function is calculated as à sum of scattering and thermal parts (see Eq. (10))). (10)., Therefore in the POLY-code the source function is calculated as a sum of scattering and thermal parts (see Eq. \ref{eq:lineS}) )).457 Defining these coefficients is a standard problem for a two-level system. which is described in many textbooks (e.g.Mihalas1970).," Defining these coefficients is a standard problem for a two-level system, which is described in many textbooks \citep[e.g.][]{mihalas1970}."458. However. in the case of the CN violet system the situation becomes much more complicated as we have to consider a lot of levels. many of which are collistonally and radiatively coupled with each other.," However, in the case of the CN violet system the situation becomes much more complicated as we have to consider a lot of levels, many of which are collisionally and radiatively coupled with each other."459 To find the branching coefficients let us consider the prehistory of the photon which was emitted in the /-th line. when molecule changed from the upper to the lower state.," To find the branching coefficients let us consider the prehistory of the photon which was emitted in the -th line, when molecule changed from the upper to the lower state."460" If the excited state was collisionaly populated (it could be both the collisional excitation from a lower level or de-excitation from a higher energy level) a thermal photon. which contributes As we solve the statistical equilibrium equations only for vibrational levels. the coefficients 6), and 0, are also calculated only for vibrational levels of the excited electronic state BX (adding up all significant radiative and. collisional processes. populating the considered. vibrational level)."," If the excited state was collisionaly populated (it could be both the collisional excitation from a lower level or de-excitation from a higher energy level) a thermal photon, which contributes As we solve the statistical equilibrium equations only for vibrational levels, the coefficients $\delta_{\rm th}$ and $\delta_{\rm sc}$ are also calculated only for vibrational levels of the excited electronic state $B {}^2 \Sigma$ (adding up all significant radiative and collisional processes, populating the considered vibrational level)."461 We assume that the same fractions of thermal and scattered photons óy(v) and ON) apply to every rotational level within a given rotational band (v.v).," We assume that the same fractions of thermal and scattered photons $\delta_{\rm th}({\rm v})$ and $\delta_{\rm sc}({\rm v})$ apply to every rotational level within a given rotational band (v,v)."462 This seems to be à good approximation às the rotational energy is low in comparison with the electronic energy of the excited BE state., This seems to be a good approximation as the rotational energy is low in comparison with the electronic energy of the excited $B {}^2 \Sigma$ state.463" In the case of a two-level system the branching coethcients €"" are equal to the coefficients dy and ὃς.", In the case of a two-level system the branching coefficients $\varepsilon_{\rm th}^i$ are equal to the coefficients $\delta_{\rm th} $ and $\delta_{\rm sc} $.464 However in our case of a multi-level system this equality is not valid anc the branching coethcients depend not only on the coefficients On and o... but rather on the whole balance of populating anc depopulating rates.," However in our case of a multi-level system this equality is not valid and the branching coefficients depend not only on the coefficients $\delta_{\rm th} $ and $\delta_{\rm sc} $, but rather on the whole balance of populating and depopulating rates."465 The following algorithm was employed to compute coefficients., The following algorithm was employed to compute .466 Using the NLTE populations of the /; and, Using the NLTE populations of the $l_i$ and467]t is now generally agreed. that accretion cliscs are driven mainly by magnetic torques (Shakura Sunvaev. 1973) and that the magnetic fields in such discs are maintained by local cvnamo processes.,"It is now generally agreed that accretion discs are driven mainly by magnetic torques (Shakura Sunyaev, 1973) and that the magnetic fields in such discs are maintained by local dynamo processes."468 What is not. understood however. despite considerable theoretical clforts. is how such dvnamo processes work. and exactly where and in what form the accretion energv is released (Ixing ct al..," What is not understood however, despite considerable theoretical efforts, is how such dynamo processes work, and exactly where and in what form the accretion energy is released (King et al.,"469. 2007: Blackman. 2010).," 2007; Blackman, 2010)."470 Given the Πο of this problem. we should look for observational evidence ενwhich bears on it.," Given the difficulty of this problem, we should look for observational evidence which bears on it."471 We have unique insight into the remains of one accretion clisc the protosolar nebula., We have unique insight into the remains of one accretion disc – the protosolar nebula.472 Lt is therefore worth asking if the presentclay solar system ollers evidence which can constrain the way energy is released. in accretion disces., It is therefore worth asking if the present–day solar system offers evidence which can constrain the way energy is released in accretion discs.473 Among the oldest. solid objects in the solar svstenm ave chondrules. the round. grains present in the majority of meteorites.," Among the oldest solid objects in the solar system are chondrules, the round grains present in the majority of meteorites."474 These must have formed. as molten droplets in space before being accreted., These must have formed as molten droplets in space before being accreted.475 The need to heat them sulliciently. implies a connection with energy release in the protosolar nebula., The need to heat them sufficiently implies a connection with energy release in the protosolar nebula.476 We consider here the overall energeties required of the heating process., We consider here the overall energetics required of the heating process.477 We argue that since most of the meteoritic material has been subject to this heating. the energy. source required. must. be quite. widespread: aud substantial. and must. therefore. involve the major local source of energy. Le. disc accretion.," We argue that since most of the meteoritic material has been subject to this heating, the energy source required must be quite widespread and substantial, and must therefore involve the major local source of energy, i.e. disc accretion."478. We find that. around 10 per cent of the accretion. energy ds required., We find that around 10 per cent of the accretion energy is required.479 LL so. it is evident that the existence of chondrules: provides funclamental information about energy release in accretion clises.," If so, it is evident that the existence of chondrules provides fundamental information about energy release in accretion discs."480 This paper is organised as follows., This paper is organised as follows.481 In Section 2 we give a brief introduction to chondrules and. ideas about. their formation., In Section 2 we give a brief introduction to chondrules and ideas about their formation.482 In Section 3 we consider the elobal energeties of the heating process., In Section 3 we consider the global energetics of the heating process.483 A likely mechanism for the provision of transient. heating within the solar nebula involves strong shocks (Deschl Connolly. 2002. Connolly et ab.," A likely mechanism for the provision of transient heating within the solar nebula involves strong shocks (Deschl Connolly, 2002, Connolly et al.,"484 2006)., 2006).485 In Section 4. we brielly present. the model of chondrule formation through shock heating suggested. by Deschl Connolly (2002) but argue that their proposed. mechanism [or generating these shocks by gravitational instabilitios within the dise requires dise properties which do not sit easily with our current understanding of cise evolution.," In Section 4, we briefly present the model of chondrule formation through shock heating suggested by Deschl Connolly (2002) but argue that their proposed mechanism for generating these shocks by gravitational instabilities within the disc requires disc properties which do not sit easily with our current understanding of disc evolution."486 In Section 5 we describe the dise properties which appear likely to hold at the time of chondrule formation., In Section 5 we describe the disc properties which appear likely to hold at the time of chondrule formation.487 The need. for significant clisc dissipation in the form. of shocks. together with evidence for magnetic fields within the nebula at that time (Section. 6) lead. us to a picture of a dise dvnamo (Section 7).," The need for significant disc dissipation in the form of shocks, together with evidence for magnetic fields within the nebula at that time (Section 6) lead us to a picture of a disc dynamo (Section 7)."488 This cülfers markedly from the results of current numerical simulations., This differs markedly from the results of current numerical simulations.489 Our picture draws on the ανπαπιο model of Bagealey et al. (, Our picture draws on the dynamo model of Baggaley et al. (49020092. b) and involves thin [lux ropes and reconnection. analogous to mocels of Haring on the solar surface.,"2009a, b) and involves thin flux ropes and reconnection, analogous to models of flaring on the solar surface."491 Section S is a discussion., Section 8 is a discussion.492 Alost meteorites are chondrites (more than 75 per cent. Sears Dodd. 1988: HIutchinson 2004). and the most abundant constituent of the majority of chondritio meteorite groups are chondrules (Crossman et al..," Most meteorites are chondrites (more than 75 per cent, Sears Dodd, 1988; Hutchinson 2004), and the most abundant constituent of the majority of chondritic meteorite groups are chondrules (Grossman et al.,"493 1988)., 1988).494 Chondrules are small particles of silicate material (typically around a millimetre in size. Weishere et al.," Chondrules are small particles of silicate material (typically around a millimetre in size, Weisberg et al.,"495 2006) that experienced. melting before incorporation into chondritie meteorite parent bodies, 2006) that experienced melting before incorporation into chondritic meteorite parent bodies496We observed six of the eight members of our sample in 1999 and 2000. using the VLBA. which is described by Napieretal.(1993): the two other RQQs had been observed previously with the VLBA (Blundell&Beasley1998;Dlundellοἱal.2003).,"We observed six of the eight members of our sample in 1999 and 2000, using the VLBA, which is described by \citet{nap93}; the two other RQQs had been observed previously with the VLBA \citep{blu98,blu03}."497. J12192-0638 and J1353+6345 also were imaged by Blunclell&Beasley(1998).. but we observed them al multiple lrequencies to derive spectral inlormation useful for constraining (heir emission processes.," J1219+0638 and J1353+6345 also were imaged by \citet{blu98}, but we observed them at multiple frequencies to derive spectral information useful for constraining their emission processes."498 Table 5 summarizes the VLBA observations., Table \ref{tab:obs} summarizes the VLBA observations.499 In most cases. all 10 VLBA antennas participated successhully.," In most cases, all 10 VLBA antennas participated successfully."500 However. data and/or antennas occasionally were removed cue to snowsloris. raclio-lrequency interference. or instrumentation Lailures.," However, data and/or antennas occasionally were removed due to snowstorms, radio-frequency interference, or instrumentation failures."501 All target quasars were below the flux-densitv threshold needed to solve for instrumental and atmospheric effects. so each was pliase-relerenced (Beasley&Conway1995) (0 a nearby strong compact radio source.," All target quasars were below the flux-density threshold needed to solve for instrumental and atmospheric effects, so each was phase-referenced \citep{bea95} to a nearby strong compact radio source."502 Phase-reference cvcle limes were 45 minutes. and total times ranged Irom 1 to 4 hours per frequency. band.," Phase-reference cycle times were 4–5 minutes, and total on-source times ranged from 1 to 4 hours per frequency band."503 Charged-particle effects were corrected with global ionospheric using AIPS. the Astronomical Image Processing System (Greisen2003).," Charged-particle effects were corrected with global ionospheric using AIPS, the Astronomical Image Processing System \citep{gre03}."504. Amplitudes were calibrated using standard gain files as well as svslem lemperatures measured al 12 minute intervals. (hen checked by observations of simple strong sources.," Amplitudes were calibrated using standard gain files as well as system temperatures measured at 1–2 minute intervals, then checked by observations of simple strong sources."505 Global clock offsets were found. Irom observations of strong sources. while atmospheric aud electronic drilts were calibrated using the local phase-reference sources.," Global clock offsets were found from observations of strong sources, while atmospheric and electronic drifts were calibrated using the local phase-reference sources."506 Imaging of J13164-0051 [iled. since the distance of 87 [rom the phase-velerencing source prevented successIul atmospheric calibration.," Imaging of J1316+0051 failed, since the distance of $8^\circ$ from the phase-referencing source prevented successful atmospheric calibration."507 The other quasars had. plase+velerence sources between 1.57 and 4.57 from the target., The other quasars had phase-reference sources between $1.5^\circ$ and $4.5^\circ$ from the target.508 Although their peak flux densities initially were reduced by imperfect atmospheric calibration. all had enough signal for sell-calibration. which largely eliminated the image degradation.," Although their peak flux densities initially were reduced by imperfect atmospheric calibration, all had enough signal for self-calibration, which largely eliminated the image degradation."509 Final images were made using (wo different data weishtüngs. pure “natural” weighting which maximizes the sensitivity. aud a compromise between natural and “uniform” weighting. which provides a good combination of sensitivity and resolution.," Final images were made using two different data weightings, pure “natural” weighting which maximizes the sensitivity, and a compromise between natural and “uniform” weighting, which provides a good combination of sensitivity and resolution."510 1219-0005. J13534-6345. and J1436-4-584T were observed at multiple frequencies and are unresolved at all bands. while JQ046-2-0104. also was unresolved ab its only observed. [requencey. of 4.99 GIIz.," J1219+0638, J1353+6345, and J1436+5847 were observed at multiple frequencies and are unresolved at all bands, while J0046+0104 also was unresolved at its only observed frequency of 4.99 GHz."511 JOS044+6459 contains a core wilh weak extended emission at 4.99 Gllz. but a prominent jet al 1.67 Ην.," J0804+6459 contains a core with weak extended emission at 4.99 GHz, but a prominent jet at 1.67 GHz."512 The 4.99 GIIz VLBA images of the quasars are shown in Figure 1. and a 1.67 GlIz image also is displaved [or 0504-60-00.," The 4.99 GHz VLBA images of the quasars are shown in Figure 1, and a 1.67 GHz image also is displayed for J0804+6459."513 Table 4. lists radio positions. flux densities. powers. and brightness temperatures [or each quasar.," Table \ref{tab:tb} lists radio positions, flux densities, powers, and brightness temperatures for each quasar."514 For all except J0804-2-6459. (these results come [rom Gaussian [its to the core," For all except J0804+6459, these results come from Gaussian fits to the core"515"periods. at a significance level below:SOC. were found: Ds— 2p»: D,—23p»= 3119 aud Ds=2p.","periods, at a significance level below, were found: $\rm P_3 ~ = ~ 2 P_2$ ; $\rm P_4 ~ = ~ 2/3 P_2516~ = ~ 344^d$ ; and $\rm P_5 ~ = ~ 2 P_4$."517 The data for V Uva have several properties which cause problems for this analysis., The data for V Hya have several properties which cause problems for this analysis.518 The time interval spanned by the data is only 2.1 Py. and the uaenitude estimates in the deep stellay iunuinuuni are often poorly determuned and/or lower limits.," The time interval spanned by the data is only 2.4 $\rm P_1$, and the magnitude estimates in the deep stellar minimum are often poorly determined and/or lower limits."519 The third woblem is iat the amplitudes of the variations are cdiffereut. which oeicreases the range of the data and hence the “noise” or individual period determinations.," The third problem is that the amplitudes of the variations are different, which increases the range of the data and hence the “noise” for individual period determinations."520 We therefore refined ur estimates of the periods of V Ia as follows., We therefore refined our estimates of the periods of V Hya as follows.521 First. ENutial estimates of the amplitude. period aud phase for 1e long-terii variation (G1607) were determined from the olded. data.," First, initial estimates of the amplitude, period and phase for the long-term variation $6160^d$ ) were determined from the folded data."522 This variation was approxiuate by a sine wave aud subtracted., This variation was approximated by a sine wave and subtracted.523 The residual data were heu folded o redetermine the periods., The residual data were then folded to redetermine the periods.524 The helt curve or P» was determined. aud subtracted.," The light curve for $\rm P_2$ was determined, and subtracted."525 No significant further periods were found in the residual data., No significant further periods were found in the residual data.526 The amplitude. period and phase of πιαπα lieht for Py aud P» are given iu Table 1.," The amplitude, period and phase of maximum light for $\rm P_1$ and $\rm527P_2$ are given in Table 1."528 The resulting folded light curves. for Py=6160 with the 529.19 variation subtracted aud for Py=529.| with the 61609 variation subtracted. are shown in Fies.," The resulting folded light curves, for $\rm P_1 ~ = ~ 6160^d$ with the $\rm 529.4^d$ variation subtracted and for $\rm P_2 ~ = ~ 529.4^d$ with the $\rm 6160^d$ variation subtracted, are shown in Figs."529 3 aud L., \ref{p6160} and \ref{p529}.530 The plotted πο curves are averaged iuto 50 bins per evcle aud the evele repeated several tines., The plotted light curves are averaged into 50 bins per cycle and the cycle repeated several times.531 As discussed above. the minima are not well determined.," As discussed above, the minima are not well determined."532 Fig.lL shows a fairly typical \Mra-type light curve. to first order a sine-wave variation but with a slow rise and more rapid decline.," \ref{p529} shows a fairly typical Mira-type light curve, to first order a sine-wave variation but with a slow rise and more rapid decline."533 The loug-period variation (Fig.3)) is nof approxinatelv sinusoidal however: it resembles the light curve of an eclipsing binary star. but with a far longer period aud duration.," The long-period variation \ref{p6160}) ) is not approximately sinusoidal however; it resembles the light curve of an eclipsing binary star, but with a far longer period and duration."534 The data of Mavall (1965)) show a sinular light curve shape. aud cover five previous loue-period eveles. with P4.=620082-1008. in good agreeinent with the more recent data.," The data of Mayall \cite{mayall}) ) show a similar light curve shape, and cover five previous long-period cycles, with $\rm P_1 ~ = ~ 5356200^d \pm 400^d$, in good agreement with the more recent data."536 The long-period variation in V να thus appears to be very regular., The long-period variation in V Hya thus appears to be very regular.537" Finally, we note that the amplitude of the 17-veur variation. 3.5!"" agrees with that eiven by Ἱνμοίορον et al. ("," Finally, we note that the amplitude of the 17-year variation, $\rm 3.5^m$, agrees with that given by Kholopov et al. ("5381985) aud is naller than the amplitude of 5ο sugeested by Mavall. which is actually he total range of variation due to both periodicities.,"1985) and is smaller than the amplitude of $\rm 5^m - 6^m$ suggested by Mayall, which is actually the total range of variation due to both periodicities."539 What is the origin of the GOOQT variation of V. Ilva?, What is the origin of the $\rm 6000^d$ variation of V Hya?540 The ereat depth of the unin. arc V Tva’s large mass loss rate (Paper I). suggest obscuration by dust. analogous to the ejection of obscuring material by R CrB stars: however. the dinmuninge of R CrB stars is irregular.," The great depth of the minimum, and V Hya's large mass loss rate (Paper I), suggest obscuration by dust, analogous to the ejection of obscuring material by R CrB stars; however, the dimming of R CrB stars is irregular."541 The reeularity of V να G000' variation support. rather. a dyaiunical origin for the variation.," The regularity of V Hya's $\rm 6000^d$ variation support, rather, a dynamical origin for the variation."542 We sugeest that V να is an eclipsing binary. t that he eclipse is caused not oa stellar companion but bv cireunistellar dust.," We suggest that V Hya is an eclipsing binary, but that the eclipse is caused not by a stellar companion but by circumstellar dust."543 Siuiluw phenomena are seen in a small ummber of stars of widely different spectral types and at very different evolutionary stages., Similar phenomena are seen in a small number of stars of widely different spectral types and at very different evolutionary stages.544 One such star is the FO supergiaut € Aur. which undergoes an eclipseevery27.1 vears.," One such star is the F0 supergiant $\epsilon$ Aur, which undergoes an eclipseevery27.1 years."545 There Is no secondary eclipse. and the primary eclipse is of long duration. (22 mouths) showing that the secondary. camnot," There is no secondary eclipse, and the primary eclipse is of long duration, (22 months) showing that the secondary cannot"5461e results o£ from measurements of the X-ray. luminosity function of galaxy clusters within z«0.7.,the results of from measurements of the X-ray luminosity function of galaxy clusters within $z<0.7$.547 Figure 1. shows the redshift distribution (solid line) for clusters detected above the Spectrum-RG/eCROSLLA X-ray Hux limit with mass-weighted temperatures στου 5keV. A sky coverage. fa=0.5 ds assumed.," Figure \ref{fig:distr} shows the redshift distribution (solid line) for clusters detected above the Spectrum-RG/eROSITA X-ray flux limit with mass-weighted temperatures $kT_{2500}>5$ keV. A sky coverage, $f_{\rm sky}=0.5$ is assumed."548 Approximately 5000 clusters meet these criteria from. which. following our observing strategy. 4000 will be observed by short snapshots.," Approximately $5000$ clusters meet these criteria from which, following our observing strategy, $4000$ will be observed by short snapshots."549 Assuming that ~1/8 of these clusters will also meet the relaxation criteria based on X-ray morphology(??).. a sample of ~500 hot. N-rav luminous. dynamically relaxed clusters can be defined.," Assuming that $\sim 1/8$ of these clusters will also meet the relaxation criteria based on X-ray morphology, a sample of $\sim 500$ hot, X-ray luminous, dynamically relaxed clusters can be defined."550 Taking snapshot observations of the available ~5000 clusters instead of 4000. and assuming that 1/8 of these clusters are relaxed. we will obtain a sample of ~625 ως targets.," Taking snapshot observations of the available $\sim 5000$ clusters instead of $4000$, and assuming that $\sim 1/8$ of these clusters are relaxed, we will obtain a sample of $\sim 625$ $f_{\rm gas}$ targets."551 This allows us to either use a larger sample of clusters. assume an even more conservative ratio ol relaxed. clusters. or select a different redshift’ distribution for the faa. sample of ~500 clusters.," This allows us to either use a larger sample of clusters, assume an even more conservative ratio of relaxed clusters, or select a different redshift distribution for the $f_{\rm gas}$ sample of $\sim 500$ clusters."552 In Section 5.3... we cliscuss the latter case.," In Section \ref{redshift_distr}, we discuss the latter case."553 For comparison purposes. Figure 1. also shows (dashed curve) the redshift distribution for the case of a luminosity limit of Li73.3510-2 tinthe 0.1.2.4 band (dashed line: no temperature cut is imposed).," For comparison purposes, Figure \ref{fig:distr} also shows (dashed curve) the redshift distribution for the case of a luminosity limit of $L_{\rm i}> 3.35\times 10^{44}h_{\rm 70}^{-2}$ in the $0.1-2.4$ band (dashed line; no temperature cut is imposed)."554 Ehe effect of the X-ray flux limit on the distribution is evident. towards the highest redshifts (2~ 1.5) in this case., The effect of the X-ray flux limit on the distribution is evident towards the highest redshifts $z\sim1.5$ ) in this case.555 lt is clear from that figure that the temperature and luminosity cutslead to cilferent redshift) distributions, It is clear from that figure that the temperature and luminosity cutslead to different redshift distributions.556 In the case of the temperature cut (solid line). the redshi distribution peaks around z~0.65 and relatively [ew clusters are found at z21.5.," In the case of the temperature cut (solid line), the redshift distribution peaks around $z\sim0.65$ and relatively few clusters are found at $z>1.5$."557 For the case of the luminosity cut. (dashed. line). the distribution peaks around 2~ and has many more clusters in the redshift range 1<2<2.," For the case of the luminosity cut (dashed line), the distribution peaks around $z\sim 1$, and has many more clusters in the redshift range $1<z<2$ ."558 Lis important to note. however. that a recshi distribution. weighted towards higher redshifts does not necessarily imply tighter constraints on dark energy.," It is important to note, however, that a redshift distribution weighted towards higher redshifts does not necessarily imply tighter constraints on dark energy."559" For the DIETE FoM criterion. constraints around the pivot redshi are important: for the fas. experiment 2,~(0.25 (see Figure 5))."," For the DETF FoM criterion, constraints around the pivot redshift are important; for the $f_{\rm gas}$ experiment $z_{\rm p}\sim 0.25$ (see Figure \ref{fig:evol}) )."560 In Section 5.3. we further discuss the elfect that using dillercnt redshift distributions has on the dark energy constraints., In Section \ref{redshift_distr} we further discuss the effect that using different redshift distributions has on the dark energy constraints.561 We generate mock f; measurements for 500 clusters with the redshift distribution appropriate for the case of the temperature cut solid. curve. Figure D: in accordance with the selection criteria. used for current. fii work (?)]].," We generate mock $f_{\rm gas}$ measurements for 500 clusters with the redshift distribution appropriate for the case of the temperature cut [solid curve, Figure \ref{fig:distr}; in accordance with the selection criteria used for current $f_{\rm gas}$ work ]."562 bor each cluster. we assign à statistical error in the fii measurements of 5 per cent.," For each cluster, we assign a statistical error in the $f_{\rm gas}$ measurements of $\sim 5$ per cent."563 We have also generated a set of mock measurements for the case of 250 clusters observed with fj; measurements accurate to 3.5 per cent.," We have also generated a set of mock measurements for the case of $250$ clusters observed with $f_{\rm564 gas}$ measurements accurate to $3.5$ per cent."565 This latter data set ds used. to study the impact on the dark energy constraints in the case that the fraction of suitably relaxed clusters is less than 1/8 at high redshilts., This latter data set is used to study the impact on the dark energy constraints in the case that the fraction of suitably relaxed clusters is less than $1/8$ at high redshifts.566" We stress that the predicted redshift distribution. which peaks around z~0.65 in the case of the temperature cut. has already. been probed. at. least partially, over the luminosity and temperature range of interest. by the ALAC'S survey(2): ALACS covers the redshift range 0.3<z«0.7 to a lux limit of fia,=LOI inthe0.1 2.4keV band."," We stress that the predicted redshift distribution, which peaks around $z\sim 0.65$ in the case of the temperature cut, has already been probed, at least partially, over the luminosity and temperature range of interest, by the MACS survey; MACS covers the redshift range $0.3<z<0.7$ to a flux limit of $F_{\rm567 lim}=10^{-12}$ in the $0.1-2.4\keV$ band."568 For ALACS. approximately 1/4 clusters are found to be sullicienthy relaxed. for ως work(?).," For MACS, approximately $1/4$ clusters are found to be sufficiently relaxed for $f_{\rm gas}$ work."569. Pherefore. our asstunption that 1/8 clusters detected in a future X-ray survey and meeting the X-ray [lux and leniperature criteria will be suitably relaxed. appears reasonable.," Therefore, our assumption that $\sim 1/8$ clusters detected in a future X-ray survey and meeting the X-ray flux and temperature criteria will be suitably relaxed, appears reasonable."570 Moreover. as discussed in Section 5.1. for the case of the 250-cluster sample (i.e. assuming that only ~1/16 clusters are relaxed) and using a similar total observing time to obtain individua fons measurements to 3.5 per cent accuracy. we obtain very similar dark energv constraints (see Table 4)).," Moreover, as discussed in Section 5.1, for the case of the 250-cluster sample (i.e. assuming that only $\sim 1/16$ clusters are relaxed) and using a similar total observing time to obtain individual $f_{\rm gas}$ measurements to $\sim 3.5$ per cent accuracy, we obtain very similar dark energy constraints (see Table \ref{tab:models}) )."571 A final important. point regards contaminating poin sources: for ALACS clusters. the fraction of the measure Ol24keV X-ray flux arising from contaminating poin sources is small. twpically of order a per cent (Mantz ο al.," A final important point regards contaminating point sources: for MACS clusters, the fraction of the measured $0.1-2.4\keV$ X-ray flux arising from contaminating point sources is small, typically of order a per cent (Mantz et al."572 2008: this is also the case for the hottest. Ad.2 Ske. relaxed clusters at. lower redshifts.)," 2008; this is also the case for the hottest, $kT_{\rm e}\gsim5$ keV, relaxed clusters at lower redshifts.)"573 Therefore. we do no expect our target clusters. which have comparable X-ray temperatures ancl luminosities. to be severely. allectecl by contaminating point sources. especially at zz 1.," Therefore, we do not expect our target clusters, which have comparable X-ray temperatures and luminosities, to be severely affected by contaminating point sources, especially at $z\lesssim 1$ ."574 This alleviates the instrumental requirements on the point spread function., This alleviates the instrumental requirements on the point spread function.575 An instrument with capabilities similar to the baseline characteristics listed in Table 1 should be capable of making significant strides in dark energy. work., An instrument with capabilities similar to the baseline characteristics listed in Table 1 should be capable of making significant strides in dark energy work.576The rest-frame far-infrared (farv-UR) thermal emission from dust. grains heated. by various sources the. cilluse interstellar radiation Ποιά (SRI) in galaxies. sites of active star formation. and a central active galactic nucleus (AGN) can dominate the spectral energy. distribution (SED) of galaxies (Soifer Neugebauer. 1991: Sanders AMirabel. 1996).,"The rest-frame far-infrared (far-IR) thermal emission from dust grains heated by various sources – the diffuse interstellar radiation field (ISRF) in galaxies, sites of active star formation, and a central active galactic nucleus (AGN) – can dominate the spectral energy distribution (SED) of galaxies (Soifer Neugebauer 1991; Sanders Mirabel 1996)."577 The most luminous galaxy apparent in the Universe (APALOOS279|5255: Lewin et 11998). emits approximately GOpper cent of its bolometric Luminosity in the far-LR.o waveband. while low-redshilt: galaxies with blue optical colours that were detected. by theLRAS satellite also release about GOpper cent of their total bolometric luminosity as thermal raciation from cust (Alazzarella Balzano 1986).," The most luminous galaxy apparent in the Universe 08279+5255; Irwin et 1998) emits approximately per cent of its bolometric luminosity in the far-IR waveband, while low-redshift galaxies with blue optical colours that were detected by the satellite also release about per cent of their total bolometric luminosity as thermal radiation from dust (Mazzarella Balzano 1986)."578 Even the most quiescent spiral galaxies such as the Alilky Way emit. of order pper cent of their total luminosity [rom dust. (Reach et 11995: Alton ct 11998: Dale et 22001: Dale Llelou 2002)., Even the most quiescent spiral galaxies such as the Milky Way emit of order per cent of their total luminosity from dust (Reach et 1995; Alton et 1998; Dale et 2001; Dale Helou 2002).579 Dust emission remains important at high redshifts., Dust emission remains important at high redshifts.580 Phe most distant quasi-stellar objects (QSOs) (Benford ct 11999: Carilli ct 22001: Isaak et 22002) ancl more typical. but still very luminous galaxies detected in submillimetre(submnm) wave surveys (Blain et 22002: Smail et 22002) emit strongly ad rest-Framoe far-LR wavelengths.," The most distant quasi-stellar objects (QSOs) (Benford et 1999; Carilli et 2001; Isaak et 2002) and more typical, but still very luminous galaxies detected in submillimetre(submm) wave surveys (Blain et 2002; Smail et 2002) emit strongly at rest-frame far-IR wavelengths."581 As compared with the rich variety. of features. in the SEDs of galaxies at near-It.. optical and ultraviolet wavelengths. the far-LR SED is simple. dominated. by a smooth pseudo-thermal continuum. emission spectrum.," As compared with the rich variety of features in the SEDs of galaxies at near-IR, optical and ultraviolet wavelengths, the far-IR SED is simple, dominated by a smooth pseudo-thermal continuum emission spectrum."582 At most about pper cent of the emitted energy is associated with spectral lines from atomic fine-structure and molecular rotational transitions (Malhotra et 11997: Lubman οἱ 11998: Combes. Maoli Omont 1099: Blain οἱ 22000).," At most about per cent of the emitted energy is associated with spectral lines from atomic fine-structure and molecular rotational transitions (Malhotra et 1997; Luhman et 1998; Combes, Maoli Omont 1999; Blain et 2000)."583 The mid-Lllt spectra of galaxies [rom 10 to fam are expected. to be significantly. more complex. especially," The mid-IR spectra of galaxies from 10 to $\mu$ m are expected to be significantly more complex, especially"584random sampling with replacement from the observed light curve.,random sampling with replacement from the observed light curve.585 This analysis shows that the probability of measuring a random signal with 20.1796 amplitude at the orbital period is296., This analysis shows that the probability of measuring a random signal with $\geq$ amplitude at the orbital period is.586". Based on Figures 3 and 4 and our statistical analysis, the doppler boosting signal is likely detected in J1630."," Based on Figures 3 and 4 and our statistical analysis, the doppler boosting signal is likely detected in J1630."587" However, the boosting signal does not provide any new physical constraints on the properties of this binary."," However, the boosting signal does not provide any new physical constraints on the properties of this binary."588" Along with J0106 and J0651, J1630 is only the third detached WD binary known to have a period shorter than an hour."," Along with J0106 and J0651, J1630 is only the third detached WD binary known to have a period shorter than an hour."589 All three were discovered in the last year as part of the ELM Survey., All three were discovered in the last year as part of the ELM Survey.590" Previously, all known systems with P«1 hr were interacting AM CVn systems."," Previously, all known systems with $P<1$ hr were interacting AM CVn systems."591 We do not see any evidence of mass transfer (no emission lines and no obvious excess continuum) in the three targets mentioned above., We do not see any evidence of mass transfer (no emission lines and no obvious excess continuum) in the three targets mentioned above.592 'The primary WDs in J0106 and J0651 both show ellipsoidal variations due to their larger size and shorter orbital periods., The primary WDs in J0106 and J0651 both show ellipsoidal variations due to their larger size and shorter orbital periods.593 These variations are extremely useful for constraining the inclination angle of the systems., These variations are extremely useful for constraining the inclination angle of the systems.594" However, J1630 does not show any significant ellipsoidal variations, and we only have an upper limit on the inclination angle due to the lack of eclipses."," However, J1630 does not show any significant ellipsoidal variations, and we only have an upper limit on the inclination angle due to the lack of eclipses."595 For the companion to avoid detection in the SDSS photometry and our spectroscopy implies that it is 210x fainter than the visible WD., For the companion to avoid detection in the SDSS photometry and our spectroscopy implies that it is $\ge10\times$ fainter than the visible WD.596" For an edge on orbit, such a companion would have M=0.30Mo,, Ter<7500 K, and R«€0.021 Rociteppanei07.."," For an edge on orbit, such a companion would have $M=0.30$, $T_{\rm eff}\leq7500$ K, and $R\leq0.021$ \\citep{panei07}."597 A total eclipse would be <70% deep and last for about 1.8 minutes., A total eclipse would be $\leq$ deep and last for about 1.8 minutes.598 T'he lack of eclipses in the photometry constrain the inclination angle to i<82°., The lack of eclipses in the photometry constrain the inclination angle to $i\leq82^{\circ}$.599" Hence, J1630 is best explained by a binary system containing a 0.30 WWD with a M 20.30 WWD companion at a separation of 20.32Ro."," Hence, J1630 is best explained by a binary system containing a 0.30 WD with a $M\geq$ 0.30 WD companion at a separation of $\geq$ 0.32."600. 'The two WDs in the J1630 binary will merge in «31 Myr due to gravitational wave radiation (Landau&Lifshitz 1958)., The two WDs in the J1630 binary will merge in $\leq$ 31 Myr due to gravitational wave radiation \citep{lan58}.601". After J0651, J1630 is currently the second quickest WD merger system known."," After J0651, J1630 is currently the second quickest WD merger system known."602" When the mass transfer starts, J1630 will most likely have unstable mass transfer due to the mass ratio of its components being close to unity (Marshetal. 2004)."," When the mass transfer starts, J1630 will most likely have unstable mass transfer due to the mass ratio of its components being close to unity \citep{marsh04}."603". However, the merger outcome is uncertain because of the unknown inclination angle and the companion mass."," However, the merger outcome is uncertain because of the unknown inclination angle and the companion mass."604" If the companion is another He-core WD, the merger will likely create a single He-burning subdwarf in 23-31 Myr."," If the companion is another He-core WD, the merger will likely create a single He-burning subdwarf in 23-31 Myr."605" If the companion is a more massive carbon/oxygen core WD, the system will merge in <23 Myr to form a rapidly rotating massive WD (seeKilicetal.2010,forotherpossibilites).."," If the companion is a more massive carbon/oxygen core WD, the system will merge in $\leq$ 23 Myr to form a rapidly rotating massive WD \citep[see][for other possibilites]{kilic10}."606 Short period binary WDs are important gravitational wave sources., Short period binary WDs are important gravitational wave sources.607" For example, the 12 minute orbital period binary J0651 should be detected by LISA within its first week of operation (Brownetal.2011c;Nelemans 2004)."," For example, the 12 minute orbital period binary J0651 should be detected by LISA within its first week of operation \citep{brown11c,nelemans04}."608". Similarly, the previously discovered 39 min orbital period system J0106 may be detected by LISA after 1 yr of observations."," Similarly, the previously discovered 39 min orbital period system J0106 may be detected by LISA after 1 yr of observations."609" With an orbital period similar to J0106, J1630 is also a promising candidate for detection."," With an orbital period similar to J0106, J1630 is also a promising candidate for detection."610" For an average inclination angle of 60? and model-dependent distance of 0.7 kpc, we expect the gravitational wave strain at Earth logh——22.0 at a frequency logv (Hz) — —3.08 "," For an average inclination angle of $^{\circ}$ and model-dependent distance of 0.7 kpc, we expect the gravitational wave strain at Earth $\log h = -22.0$ at a frequency $\log \nu$ (Hz) = $-3.08$ "611accreted.,accreted.612 We find that this masimaun density always mereases with ο and its functional dependence is clearly greater than linear., We find that this maximum density always increases with $a$ and its functional dependence is clearly greater than linear.613 The specific values we obtain can be found in the corresponding captions of Figs., The specific values we obtain can be found in the corresponding captions of Figs.614 1 to L., 1 to 4.615 Typical density cuhancements in the post-shock region (BL coordinates) with respect to the asvinptotic density rauge in between 1.65 (=0) aud 1.77 (0=0.99) (in logarithmic scale, Typical density enhancements in the post-shock region (BL coordinates) with respect to the asymptotic density range in between $1.65$ $a=0$ ) and $1.77$ $a=0.99$ ) (in logarithmic scale).616 Now we turn to the description of the flow morphology for different values of 5. the fluid adiabatic exponent.," Now we turn to the description of the flow morphology for different values of $\gamma$, the fluid adiabatic exponent."617 The accretion patterus for models 6 (5=1/3). Lis =5/3) and 7 (5=2) are depicted in Fig.," The accretion patterns for models 6 $\gamma=4/3$ ), 4 $\gamma=5/3$ ) and 7 $\gamma=2$ ) are depicted in Fig."618 5., 5.619 Once more. the variable we show in this figure is the logaritlin of the scaled restauass density.," Once more, the variable we show in this figure is the logarithm of the scaled rest-mass density."620 Clearly visible in this plot are the larger shock- opening angeles for the larger values of >., Clearly visible in this plot are the larger shock opening angles for the larger values of $\gamma$.621" This is explained by the eulianced values of the pressure inside the shock ""cone as 5 mereases;"," This is explained by the enhanced values of the pressure inside the shock “cone"" as $\gamma$ increases."622 We already noticed this behaviour in the non-rotating simmlatious performed in FI98a.b. Now. the larger values of 5. combined with the rapid rotation of the black hole («= 0.99). wrap the upper shock wave around the accretor.," We already noticed this behaviour in the non-rotating simulations performed in FI98a,b. Now, the larger values of $\gamma$, combined with the rapid rotation of the black hole $a=0.99$ ), wrap the upper shock wave around the accretor."623 This effect is more pronounced for the larger 5 values., This effect is more pronounced for the larger $\gamma$ values.624 We also note that the lower shock wave is less affected by the increase in 5., We also note that the lower shock wave is less affected by the increase in $\gamma$.625 While it still opens to larger angeles. the existing rotational flow counteracts the effects of the pressure force keeping its position almost unchanged.," While it still opens to larger angles, the existing rotational flow counteracts the effects of the pressure force keeping its position almost unchanged."626 The cuhancement of the pressure in the post-shock zone is responsible for the so-called “drag” force experienced by the accretor., The enhancement of the pressure in the post-shock zone is responsible for the so-called “drag” force experienced by the accretor.627 We notice here that the rotating black hole is redistributing the high pressure area. with non-trivial effects on the nature of the drag force.," We notice here that the rotating black hole is redistributing the high pressure area, with non-trivial effects on the nature of the drag force."628 Whereas in the Sclavarzschild case the drag force is alligned with the flow lines. poiutiug in the upstream direction. in the Ier case we notice a distinct asviuuetry between the co-rotating aud counterrotating side of the flow.," Whereas in the Schwarzschild case the drag force is alligned with the flow lines, pointing in the upstream direction, in the Kerr case we notice a distinct asymmetry between the co-rotating and counter-rotating side of the flow."629 The pressure cubancement is predominantly on the counterrotating side., The pressure enhancement is predominantly on the counter-rotating side.630 In Fie., In Fig.631 6 this observation is made more precise with the exaiination of the pressure profile. at the imuermost radius. for the ο=0.99 case.," 6 this observation is made more precise with the examination of the pressure profile, at the innermost radius, for the $a=0.99$ case."632 Three differcut ~ values are illustrated. showing the strong dependence of the pressure asvuuuetry on the adiabatic iudex.," Three different $\gamma$ values are illustrated, showing the strong dependence of the pressure asymmetry on the adiabatic index."633 This is particularly clear in the limiting case >=2 (dashed line)., This is particularly clear in the limiting case $\gamma=2$ (dashed line).634 We observe a pressure difference of alinost two orders of magnitude. aloug the axis normal to the asviuuptotic flow direction.," We observe a pressure difference of almost two orders of magnitude, along the axis normal to the asymptotic flow direction."635 The implication of this asviuuetry is that a rotating hole moving accross the interstellar media (or accreting from a wind). will experience. ou top of the drag force. a “litt” force. normal to its direction of motion (to the wind direction).," The implication of this asymmetry is that a rotating hole moving accross the interstellar medium (or accreting from a wind), will experience, on top of the drag force, a “lift” force, normal to its direction of motion (to the wind direction)."636" It is interesting to note that this effect bears a strong superficial reseimiblauce to the so-called ""Maeuus? effect. Ίνοι, the experience of lift forces by rotating bodies inunersed im a stream flow."," It is interesting to note that this effect bears a strong superficial resemblance to the so-called “Magnus” effect, i.e., the experience of lift forces by rotating bodies immersed in a stream flow."637 There. the lift force is due to the increased speed of the flow ou the co-rotating side (due to friction with the object). aud the Increase of pressure on the couuter-rotating side Gvhich follows inunuediatelv from the Bernoulli equation).," There, the lift force is due to the increased speed of the flow on the co-rotating side (due to friction with the object), and the increase of pressure on the counter-rotating side (which follows immediately from the Bernoulli equation)."638 We note that the direction of the lift. in relation to the scuse of rotation. agrees in both contexts.," We note that the direction of the lift, in relation to the sense of rotation, agrees in both contexts."639 We caution though that the underline causes nay be very different., We caution though that the underlying causes may be very different.640 Iu the black hole case the flow is 8upersouic aud there is no bouudary laver., In the black hole case the flow is supersonic and there is no boundary layer.641 Completing the study of the broad morphology of the dow aud its dependence on the black hole spin. we exteud the value of & above AZ. choosing. iu particular. &=LIAL GQuodel 5).," Completing the study of the broad morphology of the flow and its dependence on the black hole spin, we extend the value of $a$ above $M$, choosing, in particular, $a=1.1M$ (model 5)."642 This case correspouds to accretion onto asinyilarity. Although from the theoretical point of view such objects are believed not to exist in Nature (according to thehypothesis. allphysical singularities formed bv the gravitational collapse of nousiugular. asviuptotically flat initial data. must be hidden from the exterior world mside an event horizon) we nouctheless decided to perform such a computation. in order to assess the behaviour of the code in this regime. aud to explore the extrapolation of previous simulations.," This case corresponds to accretion onto a. Although from the theoretical point of view such objects are believed not to exist in Nature (according to the, all singularities formed by the gravitational collapse of nonsingular, asymptotically flat initial data, must be hidden from the exterior world inside an event horizon) we nonetheless decided to perform such a computation, in order to assess the behaviour of the code in this regime, and to explore the extrapolation of previous simulations."643 The resulting morphology for this simulation. using NS coordinates. is plotted in Fie.," The resulting morphology for this simulation, using KS coordinates, is plotted in Fig."644 7., 7.645 We are showing isocontours of the logarithm of the rest-imass density iu a region extending LAL in the ος and y directions from the sineularity., We are showing isocontours of the logarithm of the rest-mass density in a region extending $4M$ in the $x$ and $y$ directions from the singularity.646 Iu this situation. there is an ambiguity as to where to place the iuner boundary of the domain.," In this situation, there is an ambiguity as to where to place the inner boundary of the domain."647 The closer one gets tor=0 the «ποσο the eravity becomes (with imfuite tidal forces at the singularitv)., The closer one gets to $r=0$ the stronger the gravity becomes (with infinite tidal forces at the singularity).648 This introduces important resolution requirements on the mumierical code., This introduces important resolution requirements on the numerical code.649 For this reason we chose ων=M. iu accordance with the location of the inner boundary in the maximal case à=M.," For this reason we chose $r_{min}=M$, in accordance with the location of the inner boundary in the maximal case $a=M$."650 As can be seen from Fig., As can be seen from Fig.651" 7 the flow morphology for this uocel follows the previous treud found for lower values of à (nodels 1 to D: the shock appears slightly more wrapped (around the 7—AL circle) aud the aNd rest-mass density in the rear part of the acceretor mereases,", 7 the flow morphology for this model follows the previous trend found for lower values of $a$ (models 1 to 4): the shock appears slightly more wrapped (around the $r=M$ circle) and the maximum rest-mass density in the rear part of the accretor increases.652 We compute the accretion rates of mass. radial momentum aud angular moment.," We compute the accretion rates of mass, radial momentum and angular momentum."653 The procedure of, The procedure of6541900+500 km/s. respectively.,"$1900\pm 500$ km/s, respectively."655 The rest of the lines are not resolved and likely have smaller velocity widths., The rest of the lines are not resolved and likely have smaller velocity widths.656 We made lightcurves of the dispersed spectrum from each observation in. the 0.5-10.0 keV band., We made lightcurves of the dispersed spectrum from each observation in the 0.5–10.0 keV band.657 The lighteurves are presented in Figure 5., The lightcurves are presented in Figure 5.658 Strong variability is present in. all observations on the timescale of few«100 s. but particularly in the first and second observations.," Strong variability is present in all observations on the timescale of $few \times 100$ s, but particularly in the first and second observations."659 This variability is confirmed to also be present in the lightcurves of the simultaneousRXTE lightcurves ofH 1743-322 (see 22 and 33)., This variability is confirmed to also be present in the lightcurves of the simultaneous lightcurves of H $-$ 322 (see 2 and 3).660 A “dip” feature may be present in the third observation., A “dip” feature may be present in the third observation.661 A preliminary examination of otherRXTE observations in the publie archive revealed much stronger dipping activity typical of dipping black hole binaries viewed at high inclinations (see. e.g.. Kuulkers et 11998).," A preliminary examination of other observations in the public archive revealed much stronger dipping activity typical of dipping black hole binaries viewed at high inclinations (see, e.g., Kuulkers et 1998)."662 To explore whether the absorption lines vary within the dip. we made spectra of observation 3 from before the dip and within the dip (see Figure 5). and fit the spectrum in the manner noted above.," To explore whether the absorption lines vary within the dip, we made spectra of observation 3 from before the dip and within the dip (see Figure 5), and fit the spectrum in the manner noted above."663 Again. the only lines apparent are the Fe XXV and Fe XXV absorption lines found in the time-averaged spectrum.," Again, the only lines apparent are the Fe XXV and Fe XXVI absorption lines found in the time-averaged spectrum."664 The resultsI of fits to the spectrum prior to the dip and within the dip are given in Table 4. and the spectra are shown in Figure 6.," The results of fits to the spectrum prior to the dip and within the dip are given in Table 4, and the spectra are shown in Figure 6."665 Both absorption lines are stronger within the dip., Both absorption lines are stronger within the dip.666 While the statistical significance of the variability in the Fe XXVI line is marginal. the variability in the strength of the Fe XXV line is clearly significant.," While the statistical significance of the variability in the Fe XXVI line is marginal, the variability in the strength of the Fe XXV line is clearly significant."667 Indeed. in observation 3. the Fe XXV line is not clearly detected in the pre-dip spectrum.," Indeed, in observation 3, the Fe XXV line is not clearly detected in the pre-dip spectrum."668 Next. we investigated whether the absorption lines in observation |. and 4 vary on the few«100 s flaring variability timescale.," Next, we investigated whether the absorption lines in observation 1, and 4 vary on the $few \times 100$ s flaring variability timescale."669 We calculated the mean count rate for observations I. 2. and 4 (see 55). produced lists of time intervals for count rates above and below the mean rate. and extracted spectra from the time intervals above and below the mear rates.," We calculated the mean count rate for observations 1, 2, and 4 (see 5), produced lists of time intervals for count rates above and below the mean rate, and extracted spectra from the time intervals above and below the mean rates."670 Those spectra were also fitted in the manner described above: the spectra are shown in Figure 6., Those spectra were also fitted in the manner described above; the spectra are shown in Figure 6.671 As was the case with the time-averaged spectrum of observation 2. the count-rate selected spectra of observation. 2. show no absorptior lines.," As was the case with the time-averaged spectrum of observation 2, the count-rate selected spectra of observation 2 show no absorption lines."672 In observation 4. the strength of the lines does not vary significantly between the high rate and low rate spectra.," In observation 4, the strength of the lines does not vary significantly between the high rate and low rate spectra."673 Ii observation 1. however. the absorption lines are marginally stronger in the low rate spectra than in the high rate spectra.," In observation 1, however, the absorption lines are marginally stronger in the low rate spectra than in the high rate spectra."674 This raises the interesting possibility that the absorption may vary on a timescale of few«100 s. To establish this more clearly. we created a list of time intervals in which the source count rate was more than 5 counts/s above the mean rate. and more than 5 counts/s below the mean rate. and extracted spectra from these time intervals.," This raises the interesting possibility that the absorption may vary on a timescale of $few \times 100$ s. To establish this more clearly, we created a list of time intervals in which the source count rate was more than 5 counts/s above the mean rate, and more than 5 counts/s below the mean rate, and extracted spectra from these time intervals."675 The resultant spectra are shown in Figure 7., The resultant spectra are shown in Figure 7.676 The Fe XXV absorption line ts clearly stronger in the low count rate spectrum than in the high count rate spectrum. and the variation is statistically significant (see Table 4).," The Fe XXV absorption line is clearly stronger in the low count rate spectrum than in the high count rate spectrum, and the variation is statistically significant (see Table 4)."677 To interpret the iron absorption lines measured in the time-averaged spectra in more detail. we computed line profiles from a spherical wind with a photoionization code.," To interpret the iron absorption lines measured in the time-averaged spectra in more detail, we computed line profiles from a spherical wind with a photoionization code."678 We used the atomic physics packages from the X-ray illuminated accretion disk models of Raymond (1993)., We used the atomic physics packages from the X-ray illuminated accretion disk models of Raymond (1993).679 In this case. since the gas is optically thin. it is only necessary to consider a single slab.," In this case, since the gas is optically thin, it is only necessary to consider a single slab."680 We used the spectral parameters taken from Table 5 for each of the 4 observations and specify a density. slab thickness and distance from the central object. to model a 1-d. optically-thin wind.," We used the spectral parameters taken from Table 5 for each of the 4 observations and specify a density, slab thickness and distance from the central object, to model a 1-d, optically-thin wind."681 The code iterates to find a self-consistent temperature and ionization state. then computes equivalent widths assuming a Doppler profile with widths ranging from 100 to 2000 kms.," The code iterates to find a self-consistent temperature and ionization state, then computes equivalent widths assuming a Doppler profile with widths ranging from 100 to 2000 $\rm682km~s^{-1}$."683 It assumes 1onization equilibrium. which 15 a good approximation for the densities and dynamical times estimated below in all cases.," It assumes ionization equilibrium, which is a good approximation for the densities and dynamical times estimated below in all cases."684 From the output of the code we find the parameters that match the observed Fe XXV and Fe XXVI absorption line equivalent widths., From the output of the code we find the parameters that match the observed Fe XXV and Fe XXVI absorption line equivalent widths.685 The Fe XXV and Fe XXVI lines cannot originate in exactly the same gas. because the line widths and line shifts differ.," The Fe XXV and Fe XXVI lines cannot originate in exactly the same gas, because the line widths and line shifts differ."686 A plausible physical picture might consist of denser. slower clumps containing more Fe XXV embedded in a less dense gas where Fe XXVI dominates.," A plausible physical picture might consist of denser, slower clumps containing more Fe XXV embedded in a less dense gas where Fe XXVI dominates."687 However. a modest density contrast of order 2 (approximately) is sufficient to shift the balance between Fe XXV and Fe XXVL so an average density that produces both lines is meaningful. and we do not have enough measured parameters to justify the additional free parameters of a more complex model (the line widths are uncertain).," However, a modest density contrast of order 2 (approximately) is sufficient to shift the balance between Fe XXV and Fe XXVI, so an average density that produces both lines is meaningful, and we do not have enough measured parameters to justify the additional free parameters of a more complex model (the line widths are uncertain)."688 We therefore choose densities to match the observed equivalent widths and Doppler velocity widths intermediate between those of Fe XXV and Fe XXVI., We therefore choose densities to match the observed equivalent widths and Doppler velocity widths intermediate between those of Fe XXV and Fe XXVI.689 There is à maximum radius at which a slab can plausibly be causing the observed absorption., There is a maximum radius at which a slab can plausibly be causing the observed absorption.690 The Fe XXVI/XXV line flux ratio gives an ionization parameter (&=Ly/m7). and for any given distance from the central source r. a specific density 7118 required.," The Fe XXVI/XXV line flux ratio gives an ionization parameter $\xi = L_{X} / nr^{2}$ ), and for any given distance from the central source $r$, a specific density $n$ is required."691 A specific slab thickness. which cannot exceed r. is required to produce the measured line column densities. so that Nx:nr.," A specific slab thickness, which cannot exceed $r$, is required to produce the measured line column densities, so that $N692\leq nr$."693 Because the density that gives the tonization parameter scales as 7/7. the slab thickness scales as 777 (therefore Nj7! ). and there is a maximum radius at which a slab of thickness r can reproduce the lines observed.," Because the density that gives the ionization parameter scales as $r^{-2}$, the slab thickness scales as $r^{-2}$ (therefore $N~r^{-1}$ ), and there is a maximum radius at which a slab of thickness $r$ can reproduce the lines observed."694 We call this parameter Fray., We call this parameter $r_{max}$.695 The lines can be formed at smaller r. and if the lines are formed in a wind with ~~ density profile. the density at ως is correspondingly smaller.," The lines can be formed at smaller $r$, and if the lines are formed in a wind with $r^{-2}$ density profile, the density at $r_{max}$ is correspondingly smaller."696 Table 5 shows the derived parameters., Table 5 shows the derived parameters.697 We can also compute the mass loss rate in a wind of any velocity. because 7/77 is constant.," We can also compute the mass loss rate in a wind of any velocity, because $n r^{-2}$ is constant."698 The velocity shifts in Table 3 are generally uncertain. so We present mass loss rates for a reference wind speed of 300 kmsl.," The velocity shifts in Table 3 are generally uncertain, so we present mass loss rates for a reference wind speed of 300 $\rm km~s^{-1}$."699 The table shows that the lack of absorption lines in the second observation cannot entirely be attributed to a higher ionizing flux., The table shows that the lack of absorption lines in the second observation cannot entirely be attributed to a higher ionizing flux.700 Although the ionizing flux in this observation is about double that of the first observation. an order of magnitude lower column density of absorbing material is needed to match the upper limits to the equivalent widths.," Although the ionizing flux in this observation is about double that of the first observation, an order of magnitude lower column density of absorbing material is needed to match the upper limits to the equivalent widths."701 An interesting result in Table 5 ts the small value of ως for the 4th observation. which results primarily from the small ionizing flux.," An interesting result in Table 5 is the small value of $r_{max}$ for the 4th observation, which results primarily from the small ionizing flux."702 The lines do not show a significant Doppler shift. but they arise in a white dwarf-size region near the central source.," The lines do not show a significant Doppler shift, but they arise in a white dwarf-size region near the central source."703" In the first and third observations. the absorbing regions have a size comparable to a few solar radit, which is similar to the separation of the components m several binary black hole systems."," In the first and third observations, the absorbing regions have a size comparable to a few solar radii, which is similar to the separation of the components in several binary black hole systems."704 The second interesting aspect of the table is the indication that the observed absorption lines are formed in a wind with a mass loss rate of order 2«107?M..yr! — comparable to the inferred mass accretion rate., The second interesting aspect of the table is the indication that the observed absorption lines are formed in a wind with a mass loss rate of order $2 \times 10^{-8}~M_{\odot}~{\rm yr}^{-1}$ — comparable to the inferred mass accretion rate.705 If we assume a distance of 8.5 kpe. take the highest inferred 0.5—10.0 keV luminosity of Ly26.8\10°8eres! and assume an efficiency of in the equation Ly=aya. We obtain my.=7.6«1075es!.," If we assume a distance of 8.5 kpc, take the highest inferred 0.5–10.0 keV luminosity of $L_{X} = 6.8706\times 10^{38}~{\rm erg}~{\rm s}^{-1}$ and assume an efficiency of in the equation $L_{X} = \eta \dot{m}_{acc} c^{2}$, we obtain $\dot{m}_{acc} = 7.6 \times 10^{18}~{g}~{\rm s}^{-1}$."707 Taking the highest measured 0.5-10.0 keV luminosity to be a lower limit on the true Eddington luminosity. the highest inferred mass loss in the wind Giving=1.7«1015es ) corresponds to an outflow rate that is of the Eddington mass aceretion rate (for a unity filling factor).," Taking the highest measured 0.5–10.0 keV luminosity to be a lower limit on the true Eddington luminosity, the highest inferred mass loss in the wind $\dot{m}_{wind} = 1.7 \times 10^{18}~{\rm g}~{\rm s}^{-1}$ ) corresponds to an outflow rate that is of the Eddington mass accretion rate (for a unity filling factor)."708 Note. however. that the fraction depends crucially on the filling factor. the energy range used. and the," Note, however, that the fraction depends crucially on the filling factor, the energy range used, and the"709are comparalivelv small because of the low75.,are comparatively small because of the low.710. The dashed lime encloses the points for the same model with of the dust mass in a constant density: the scattered points are lower (there is more scattering) because there are no almost empty. paths through the nebula., The dashed line encloses the points for the same model with of the dust mass in a constant density; the scattered points are lower (there is more scattering) because there are no almost empty paths through the nebula.711 The dot-dashed and dotted lines are the boundaries of the points in Figures |. and 2.. which ave lor (e.gy.D.τι) = (0.6. 0.6. 2.6. 2).," The dot-dashed and dotted lines are the boundaries of the points in Figures \ref{fig1} and \ref{fig2}, which are for $a,\,g,\,D,\,\tau_0)$ = (0.6, 0.6, 2.6, 2)."712 The long dashed lines enclose (le very. wide boundaries for (a.g.D.τι) = (0.8. 0.35. 2.3. 4).," The long dashed lines enclose the very wide boundaries for $a,\,g,\,D,\,\tau_0)$ = (0.8, 0.85, 2.3, 4)."713observations. However. we will see that a minimun « of 70.5 is required to produce enough scattered light.," However, we will see that a minimum $a$ of $\sim$ 0.5 is required to produce enough scattered light."714 Figure 4 shows theaveraged(ru). (Teen))) values for all of the 21 different initial seeds that we tried.," Figure \ref{fig4} shows the, ) values for all of the 21 different initial seeds that we tried."715 Figure dashowspurelyhierarchicalmodels: 4b. models with of the dust in a constant distribution.," Figure \ref{fig4}$ $a$ shows purely hierarchical models; \ref{fig4}$ $b$, models with of the dust in a constant distribution."716 The parameters are (he same as in Figures | and 2: 0 = gy = 0.6. = 2.," The parameters are the same as in Figures \ref{fig1} and \ref{fig2}: $a$ = $g$ = 0.6, = 2."717 The points are as belore., The points are as before.718 The open squares are models with D = 2.3 instead of 2.6., The open squares are models with $D$ = 2.3 instead of 2.6.719 Within each panel. the D = 2.3 models are higher because the radiation. both scaltered ancl stellar. can escape more easily [rom the more stronely clamped structure.," Within each panel, the $D$ = 2.3 models are higher because the radiation, both scattered and stellar, can escape more easily from the more strongly clumped structure."720 The lines show uniform models. with albedos marked in 4a.," The lines show uniform models, with albedos marked in $a$."721 The uniform model appropriate to the actual albedo assumed in the models (α = 0.6) is just below the bottom of the figure., The uniform model appropriate to the actual albedo assumed in the models $a$ = 0.6) is just below the bottom of the figure.722 The dashed line is the uniform model with « = 0.5 and g = 0.4 instead of 0.6., The dashed line is the uniform model with $a$ = 0.5 and $g$ = 0.4 instead of 0.6.723 The differences are nol large in comparison to the effects of the other parameters., The differences are not large in comparison to the effects of the other parameters.724" The ellects on hierarchical models of changingSills, 5gg are similar.", The effects on hierarchical models of changing $g$ are similar.725 Perhaps the most striking difference between the two panels is the lower values of [for hierarchical models with of the dust in a uniform component., Perhaps the most striking difference between the two panels is the lower values of for hierarchical models with of the dust in a uniform component.726 The increase of scattering from the dust between the clumps causes the decrease in and greatly reduces the differences between models with dillerent spatial distributions of dust., The increase of scattering from the dust between the clumps causes the decrease in and greatly reduces the differences between models with different spatial distributions of dust.727 In either panel. ihe points from various viewing angles of (he (wo values of D are completely intertwined.," In either panel, the points from various viewing angles of the two values of $D$ are completely intertwined."728 Itellection nebulae are poor diagnostics of D as well as other properties of the ISM., Reflection nebulae are poor diagnostics of $D$ as well as other properties of the ISM.729 The three open circles in Figure 4 are with (μου values of the initial seed., The three open circles in Figure \ref{fig4} are with three values of the initial seed.730 Two of these values show the extrema in((74).. (744))) among the 21 initial seeds that we tested.," Two of these values show the extrema in, ) among the 21 initial seeds that we tested."731 The üghiness of the mean optical depths of the models shows the importance of hierarchical geometry. as opposed to simple Gvo-phase chuups.," The tightness of the mean optical depths of the models shows the importance of hierarchical geometry, as opposed to simple two-phase clumps."732 The of the mnocdels are similar to those of the hierarchical models with uniform dust., The of the models are similar to those of the hierarchical models with uniform dust.733 The contrast of both with purely hierarchical models illustrates the importance ofdust-Iree regions (in real space. possibly caused by extensions of hot. low-density material into the nebulae).," The contrast of both with purely hierarchical models illustrates the importance ofdust-free regions (in real space, possibly caused by extensions of hot, low-density material into the nebulae)."734" Figure 4 shows what we meant bv saving thal Figure 1 was produced by a typical hierarchical model | one with a tvpical (7,4).", Figure \ref{fig4} shows what we meant by saying that Figure \ref{fig1} was produced by a typical hierarchical model – one with a typical .735. Those with large have the star embedded within dusty material. and a relatively low central dustdensity leads to a low (Tox).," Those with large have the star embedded within dusty material, and a relatively low central dustdensity leads to a low ."736broad-band (grit) magnitudes of each individual. galaxy with one of a set of BCOS model template spectra. from which the g and i-band. k-corrections are then measured.,"broad-band $ugriz$ ) magnitudes of each individual galaxy with one of a set of BC03 model template spectra, from which the $g$ and $r$ -band k-corrections are then measured."737 We also compare with two simpler models in which the same k-corrections are assumed. for all the I2/80s: firstly. our evolving DC03 model 2 (age 12 Gyr τς1 Gyr) and secondly. the non-evolving for ellipticals from Coleman. Wu and Weedman (1980. hereafter. CYWWN).," We also compare with two simpler models in which the same k-corrections are assumed for all the E/S0s: firstly, our evolving BC03 model 2 (age 12 Gyr $\tau=1$ Gyr) and secondly, the non-evolving for ellipticals from Coleman, Wu and Weedman (1980, hereafter CWW)."738 Figure 13. shows the dilferent AyA against redshift (Table 1&22 list. the different &-corrections used in the Figure)., Figure \ref{kgkr} shows the different $k_g-k_r$ against redshift (Table 2 list the different $k$ -corrections used in the Figure).739 Firstly. note that k-corrections computed from: and magnitudes dilfer (primarily at z< 0.15) by [ess than 0.01 mag.," Firstly, note that k-corrections computed from and magnitudes differ (primarily at $z < 0.15$ ) by less than 0.01 mag."740 t z«0.15 the spectra and Blanton-Rowcis Ayare all below our DC Model 4. but the uncorrected Ay crosses all the models to reach Model 1: at z>0.3.," At $z<0.15$ the spectra and Blanton-Roweis $k_g-k_r$are all below our BC Model 4, but the uncorrected $k_g-k_r$ crosses all the models to reach Model 1 at $z>0.3$."741 1C COLTLOCCIOCC Vevp 18 ο... Ugh Lrectsht alc 16 331011OD-T00WOCLIS /i OEC LONOCD SN and 5Sive ο Leas evolution.," The corrected $k_g-k_r$ is lower at high redshift, and the Blanton-Roweis $k_g-k_r$ are lower still, and give the least evolution."742" The CWW £A,Ay is always more positive than that from the spectra. and so gives an overestimate of r) and too-blue rest-frame colours."," The CWW $k_g-k_r$ is always more positive than that from the spectra, and so gives an overestimate of $\Delta(g-r)$ and too-blue rest-frame colours."743 Neither the corrected or uncorrected Ay follow any of the BCOS models over the whole redshift range., Neither the corrected or uncorrected $k_g-k_r$ follow any of the BC03 models over the whole redshift range.744 This is to some extent because the mean luminosity increases with redshift., This is to some extent because the mean luminosity increases with redshift.745 Po examine the effect of this. Figure 14 shows mean Ay with the galaxies divided into four intervals of AL).," To examine the effect of this, Figure \ref{kgkr-fixedM} shows mean $k_g-k_g$ with the galaxies divided into four intervals of $M_r$ ."746 Ata given redshift the more luminous galaxies do tend to have a slightly more positive kyAy., At a given redshift the more luminous galaxies do tend to have a slightly more positive $k_g-k_r$.747 However. the galaxy Ay within each of the four luminosity intervals still do not closely follow any of the BCOS mocdels. tending to be lower at 0.05«z0.2. indicating systematic. dilferences al some wavelengths between the spectra and. this set of models.," However, the galaxy $k_g-k_r$ within each of the four luminosity intervals still do not closely follow any of the BC03 models, tending to be lower at $0.05<z<0.2$, indicating systematic differences at some wavelengths between the spectra and this set of models."748 We compared the spectroscopically-based. €MIS with the CAMs from photometric colours &-corrected. using only model-based or template spectra., We compared the spectroscopically-based CMRs with the CMRs from photometric colours $k$ -corrected using only model-based or template spectra.749 Phe top panel in Figure 15 shows the effect. of fitting Blanton Roweis (2007) À-corrections tofiber magnitudes. and using the observed g r.," The top panel in Figure \ref{cmr-br} shows the effect of fitting Blanton Roweis (2007) $k$ -corrections to magnitudes, and using the observed $g-r$."750 The CAIR is best-fit with The slope is very similar to that in the bottom panel ofFigure 10.. but with these rather than the spectra-based. &-the evolution is 0.092 weaker.," The CMR is best-fit with The slope is very similar to that in the bottom panel ofFigure \ref{cmr-fiber}, , but with these rather than the spectra-based $k$ -corrections,the evolution is $0.09z$ weaker."751 A similar analysis of the colour (Blanton Roweis A-corrections from, A similar analysis of the colour (Blanton Roweis $k$ -corrections from752In some applications. inclicding the present one. it is more convenient to work in terms of matter and Iuminositw densities.,"In some applications, including the present one, it is more convenient to work in terms of matter and luminosity densities."753 This is especially Cie case when thedensity. j. is known for a given band. rather than (he mass-to-light ratio.," This is especially the case when the, $j$, is known for a given band, rather than the mass-to-light ratio."754 We have which gives The luminositw densitw j for à particular band of the survey can be calculated for example from the luminosity funetion 9$(L) of galaxies in this band citealt De93)) Note that using the Relation (9)) in ((1)). we get the linear-theorv velocity measured [rom the {lux dipole as where g denotes the acceleration of the LG. in units of velocity.," We have which gives The luminosity density $j$ for a particular band of the survey can be calculated for example from the luminosity function $\Phi(L)$ of galaxies in this band \\citealt{Pe93}) ) Note that using the Relation \ref{eq:flux dipole}) ) in \ref{eq:v.and.g}) ), we get the linear-theory velocity measured from the flux dipole as where $\tilde{\bmg}$ denotes the acceleration of the LG, in units of velocity."755" The term 57,5r; is the [αν dipole moment of sources down to the zero flux over the whole skv.", The term $\sum_i S_i\hat{\bmr}_i$ is the flux dipole moment of sources down to the zero flux over the whole sky.756 The universal Iuminosity density j. measured Irom a fair sample of galaxies in the given band with known apparent Iuminosities and redshifts. is proportional to fy). which means (hat the overall result does not depend on the IIubble constant.," The universal luminosity density $j$, measured from a fair sample of galaxies in the given band with known apparent luminosities and redshifts, is proportional to $H_0$, which means that the overall result does not depend on the Hubble constant."757 Realistic galaxy catalogs will never reach down to zero flux. irrespectivelv of the used wavelength.," Realistic galaxy catalogs will never reach down to zero flux, irrespectively of the used wavelength."758 On the contrary. survevs are usually/ic-lanited.. which means that the number of observed sources. Nis finite.," On the contrary, surveys are usually, which means that the number of observed sources, $N$, is finite."759 For that reason. in the following we will denote the flux dipole of a finite sample as d: Note that the clustering dipole calculated for a finite. [Iux-limited sample may be a biased estimator of the peculiar acceleration of the Local Group. ((2)).," For that reason, in the following we will denote the flux dipole of a finite sample as $\bmd$: Note that the clustering dipole calculated for a finite, flux-limited sample may be a biased estimator of the peculiar acceleration of the Local Group, \ref{eq:g.theor}) )."760 This can be overcome by, This can be overcome by761"themselves as part of a synchrotron self-Compton (SSC) approach (see, e.g., Markoff et al.","themselves as part of a synchrotron self-Compton (SSC) approach (see, e.g., Markoff et al."762" 2001, Liu Melia 2001, Eckart et al."," 2001, Liu Melia 2001, Eckart et al."763 2004)., 2004).764" It has also been suggested that both the NIR and the X-ray components may be due to the same synchrotron process (see, e.g., Yuan et al."," It has also been suggested that both the NIR and the X-ray components may be due to the same synchrotron process (see, e.g., Yuan et al."765 2004)., 2004).766 But the analysis of several bright flares detected over the past few years has all but ruled out these earlier proposals (see Dodds-Eden et al., But the analysis of several bright flares detected over the past few years has all but ruled out these earlier proposals (see Dodds-Eden et al.767" 2009, Trap et al."," 2009, Trap et al."768 2011)., 2011).769 Single component synchrotron models (with a particle distribution dN(y)eΥ5dy) are problematic because the high-energy electrons required to generate X-ray synchrotron emission have very short cooling times (much shorter than a typical X-ray flare duration).," Single component synchrotron models (with a particle distribution $dN(\gamma)770\propto {\gamma}^{-p}\,d\gamma$ ) are problematic because the high-energy electrons required to generate X-ray synchrotron emission have very short cooling times (much shorter than a typical X-ray flare duration)."771" Thus, even a continuous injection to replenish the energetic population cannot sustain the same power-law index p at both low and high energies."," Thus, even a continuous injection to replenish the energetic population cannot sustain the same power-law index $p$ at both low and high energies."772" If instead the X-rays are submm photons inverse-Compton scattered by the electrons producing the NIR emission, the largest permissible size of the quiescent radio-producing region is about 0.27Rs (Dodds-Eden et al."," If instead the X-rays are submm photons inverse-Compton scattered by the electrons producing the NIR emission, the largest permissible size of the quiescent radio-producing region is about $0.27\,R_S$ (Dodds-Eden et al."773" 2009, Trap et al."," 2009, Trap et al."774" 2011), far smaller than the measured FWHM size (53.7R5; Doeleman et al."," 2011), far smaller than the measured FWHM size $\approx7753.7\,R_S$; Doeleman et al."776 2008) of Sgr A* at 1.3 mm., 2008) of Sgr A* at 1.3 mm.777" This uncomfortably tight restriction (see also Liu Melia 2001) is compounded by several other difficulties, but even the size issue on its own already rules out the “external” Compton scattering scenario."," This uncomfortably tight restriction (see also Liu Melia 2001) is compounded by several other difficulties, but even the size issue on its own already rules out the “external"" Compton scattering scenario."778" Attempts at fitting an SSC spectrum to the combined NIR/X-ray data are equally problematic because such a model requires low electron energies (with y~ 10-15) and unrealistically strong magnetic fields (B>1,000 G) and very large particle densities (much larger than those inferred for the quiescent emission)."," Attempts at fitting an SSC spectrum to the combined NIR/X-ray data are equally problematic because such a model requires low electron energies (with $\gamma779\sim$ 10–15) and unrealistically strong magnetic fields $B>1,000$ G) and very large particle densities (much larger than those inferred for the quiescent emission)."780 We are thus left with the following rather tightly constrained indicators., We are thus left with the following rather tightly constrained indicators.781" During a typical flare, there is little if any detectable emission at 11.88 jm, implying that the flare emission spectrum (characterized by the power density vF,) must rise from the MIR towards the NIR."," During a typical flare, there is little if any detectable emission at $11.88\;\mu$ m, implying that the flare emission spectrum (characterized by the power density $\nu F_\nu$ ) must rise from the MIR towards the NIR."782 This is consistent with the spectral index a~0.6 described above., This is consistent with the spectral index $\alpha\sim 0.6$ described above.783" It is clear, therefore, that the electron population producing the L’-band flare has a different distribution of energies than that associated with the submm bump (see, e.g., Melia 2007), so a NIR flare cannot simply be a small change in the overall properties of the steady radio-submm emitting region."," It is clear, therefore, that the electron population producing the $L^\prime$ -band flare has a different distribution of energies than that associated with the submm bump (see, e.g., Melia 2007), so a NIR flare cannot simply be a small change in the overall properties of the steady radio-submm emitting region."784" However, it is unrealistic to expect a power-law particle distribution such as this to maintain the same power-law index p at all energies."," However, it is unrealistic to expect a power-law particle distribution such as this to maintain the same power-law index $p$ at all energies."785" Synchrotron energy losses, not to mention the escape time from the acceleration region, both depend on the particle energy (see, e.g., Liu et al."," Synchrotron energy losses, not to mention the escape time from the acceleration region, both depend on the particle energy (see, e.g., Liu et al."786 2006)., 2006).787" It is well known (see, e.g., Pacholezyk 1970) that while energetic electrons are injected continuously into the system bythe acceleration process, the emitted steady-state photon spectrum has an index a=(3—p)/2 (with p the particle index) up to a “cooling break"" frequency v;, steepening to"," It is well known (see, e.g., Pacholczyk 1970) that while energetic electrons are injected continuously into the system bythe acceleration process, the emitted steady-state photon spectrum has an index $\alpha=(3-p)/2$ (with $p$ the particle index) up to a “cooling break"" frequency $\nu_b$ , steepening to"788phenomena ever discovered iu the corona.,phenomena ever discovered in the corona.789 The wave is nostly MIID. kink node propagating outwards along he thin plaza sheet., The wave is mostly MHD kink mode propagating outwards along the thin plasma sheet.790 The restoring force supporting he wavy notion is provided bv the magnetic feld of he streamer structure. which is ecucrated by the large streamer deflection upon the CALE impact.," The restoring force supporting the wavy motion is provided by the magnetic field of the streamer structure, which is generated by the large streamer deflection upon the CME impact."791 The energy received from the inipact is carried outwards by tlie wave rturbation., The energy received from the impact is carried outwards by the wave perturbation.792 Consequently. the amplitude of the wave rear the sun declines rapidly with time. aud only a few xeriods of the wave are observable.," Consequently, the amplitude of the wave near the sun declines rapidly with time, and only a few periods of the wave are observable."793 The wave period is estimated to be about 1 hour. the wavelength varies from 2to LR... the wave amplitude is a few tens of solar radii. and the plase speed is about 300 to 500 kins .," The wave period is estimated to be about 1 hour, the wavelength varies from 2 to 4 $_\odot$, the wave amplitude is a few tens of solar radii, and the phase speed is about 300 to 500 km $^{-1}$."794 There exists a general trend for the phase speed to decrease with increasing helioceutric distance., There exists a general trend for the phase speed to decrease with increasing heliocentric distance.795 Tuteractious between CAIE and παΟΠΟΥ5 are frequently observed. especially during the active phase of solu cycles.," Interactions between CME and streamers are frequently observed, especially during the active phase of solar cycles."796 Usually. such interactions result in apparent deflections of interacting streamers (Ce. Tndhausen ot al.," Usually, such interactions result in apparent deflections of interacting streamers (e.g., Hundhausen et al.,"797 1987: Sime IIuudhnauseu. 1987: Sheeley et al.," 1987; Sime Hundhausen, 1987; Sheeley et al.,"798 2000)., 2000).799 We emphasize that the streamer wavy motion. reported im the present study. is a direct consequence of a streamer deflection.," We emphasize that the streamer wavy motion, reported in the present study, is a direct consequence of a streamer deflection."800 Nevertheless. as revealed from a prelaminary overview of the long-erm LASCO observations. in onlv α ταν siall yaction of the deflection events the streamer exhibits wavelike phenomena.," Nevertheless, as revealed from a preliminary overview of the long-term LASCO observations, in only a very small fraction of the deflection events the streamer exhibits wavelike phenomena."801 In other words. most CME-diveu deflections. even very fast aud strong. are not followed κα streniner wavy motion.," In other words, most CME-driven deflections, even very fast and strong, are not followed by a streamer wavy motion."802 Therefore. there exist ain strict conditions for streamer waves to be excited| κα CAME-streamer deflection.," Therefore, there exist certain strict conditions for streamer waves to be excited by a CME-streamer deflection."803 Two observational eatures of the July 6 event can help us evaluate the relevant conditious., Two observational features of the July 6 event can help us evaluate the relevant conditions.804" Firstly. it is found that the CME ""OIree region lies ou the flank side of the closed loops colmprising the streamer. that meaus the CATE does not originate from beneath the streamer structure. aud the ejecta can collide with the streamer frou the fanuk sido."," Firstly, it is found that the CME source region lies on the flank side of the closed loops comprising the streamer, that means the CME does not originate from beneath the streamer structure, and the ejecta can collide with the streamer from the flank side."805 Secondly. the CME is a fast eruption with a speed of c1300 liu |. which has two consequences favoring he excitation of the streamer wave.," Secondly, the CME is a fast eruption with a speed of $\ge 1300$ km $^{-1}$, which has two consequences favoring the excitation of the streamer wave."806 One is that a aster eruption results iu a strouger inmupiugenieut on he nearby streamer and a consequent larger deflection of the σος structure from its equilibria position. he other is that the ejecta moves out of the corona in a relatively short time. and leaves cnough time or the streamer wave to develop.," One is that a faster eruption results in a stronger impingement on the nearby streamer and a consequent larger deflection of the streamer structure from its equilibrium position, the other is that the ejecta moves out of the corona in a relatively short time, and leaves enough time for the streamer wave to develop."807 Otherwise if the eruption is nof fast enoush. the deflected streamer nay simply moves backwards along with the cjecta. and uo wavy motions result.," Otherwise if the eruption is not fast enough, the deflected streamer may simply moves backwards along with the ejecta, and no wavy motions result."808 To observe one example of such a case. one inav check the online LASCO observations of the iuteraction eveut between a CALE and a streamer in the uortheaster quadrant dated ou July 9th. 2001.," To observe one example of such a case, one may check the online LASCO observations of the interaction event between a CME and a streamer in the northeastern quadrant dated on July 9th, 2004."809 Sheeley et al. (, Sheeley et al. (8102000) also presents LASCO exmuples of strong streamer deflection. events without accompanying apparcut streamer wavy motions.,2000) also presents LASCO examples of strong streamer deflection events without accompanying apparent streamer wavy motions.811 It should be noted that a more complete understanding of the excitation coucitious of the streamer wave cau only be obtained from observational investigations ou much more similar events and from elaborate theoretical modelling eudeavors., It should be noted that a more complete understanding of the excitation conditions of the streamer wave can only be obtained from observational investigations on much more similar events and from elaborate theoretical modelling endeavors.812 As inentioned in the introduction section. a well developed typical streamer consists of the main bocly. which is a bunch of closed field. arcades confining high density coronal plasimas. and a dense plasma sheet within which a lone thin current sheet i$ emibedded.," As mentioned in the introduction section, a well developed typical streamer consists of the main body, which is a bunch of closed field arcades confining high density coronal plasmas, and a dense plasma sheet within which a long thin current sheet is embedded."813 The intersection of the closed streamer main body and he open plasina sheet gives the streamer cusp. which is ecnerally thought to be below 2 to 2.5 R.. w(DAY close to the bottom of the LASCO ο) ΕΟΝ.," The intersection of the closed streamer main body and the open plasma sheet gives the streamer cusp, which is generally thought to be below 2 to 2.5 $R_\odot$, very close to the bottom of the LASCO C2 FOV."814 After he impact from a CAIE. the streamer deflects away roni its original equilibria position.," After the impact from a CME, the streamer deflects away from its original equilibrium position."815 The cousequeut restoring mmotion may excite the wavelike oscillations ILOweating along the plasma sheet., The consequent restoring motion may excite the wavelike oscillations propagating along the plasma sheet.816 Therefore. the σοςuetry supporting the discussed streamer wave motion can be simplified as a long slender plasiua slab extend o infinity with the lower end attaching to the streamer Cus» Which bounces back auc forth iLa quasi-periodici liamer.," Therefore, the geometry supporting the discussed streamer wave motion can be simplified as a long slender plasma slab extending to infinity with the lower end attaching to the streamer cusp which bounces back and forth in a quasi-periodic manner."817 The oscillations are observed to be genera Yaisverse to the nouinal direction of he maenetic ficd., The oscillations are observed to be generally transverse to the nominal direction of the magnetic field.818 The manifestation and the geometry of the pleLOMla are very simular to that of the well-suown sank uxxle deποσα from a sleπο. magnetic sla) except clue iu a spherical expanding 9eometrv (Roberts. 1981: Edwin Roberts. 1982).," The manifestation and the geometry of the phenomena are very similar to that of the well-known kink mode deduced from a slender magnetic slab except being in a spherical expanding geometry (Roberts, 1981; Edwin Roberts, 1982)."819" It is therefore μιeeesttCOONxL tiat the wave phenomenon discussed. ia this study rTOepreseuts the kink node. wuch Is. lu a 1uore eenera ποσο, a type of ast mnagnetosonide waves propagaimgo iu ali inhomogencous maguctized plasuia cuviromment."," It is therefore suggested that the wave phenomenon discussed in this study represents the kink mode, which is, in a more general sense, a type of fast magnetosonic waves propagating in an inhomogeneous magnetized plasma environment."820 It is interesting o notice that the morphology of the sYOOluecr wave discussed above is very similar to a raditional Chinese daice named as Colored Belt Dance? which is performed w dancers holding one cud of a long belt iu color., It is interesting to notice that the morphology of the streamer wave discussed above is very similar to a traditional Chinese dance named as 'Colored Belt Dance' which is performed by dancers holding one end of a long belt in color.821 Au important exteion to the coronal wave study is to develop diagnostic techniques of plasmas ancl magnetic fields throteh which the wave propagates. ic. to couduct the study of coronal seimnology.," An important extension to the coronal wave study is to develop diagnostic techniques of plasmas and magnetic fields through which the wave propagates, i.e., to conduct the study of coronal seismology."822 In our case. the period aud phase speed of the streamer wave which has beeu regarded as the propagating kiuk mode carried by the thin pasma sheet. if well resolved frou. observations. can be used to provide iuforiiation on magnetic properties of streamers.," In our case, the period and phase speed of the streamer wave which has been regarded as the propagating kink mode carried by the thin plasma sheet, if well resolved from observations, can be used to provide information on magnetic properties of streamers."823 Gonerallv speakiug. the phase speed for tje wave phenomenon investigated in this study is eiven by the suu of two compoucuts.," Generally speaking, the phase speed for the wave phenomenon investigated in this study is given by the sum of two components."824 The first one is the speed of the solar wind along the plasma sheet. the mediun carving the mode outwards.," The first one is the speed of the solar wind along the plasma sheet, the medium carrying the mode outwards."825 The other is of course the phase speed of the wave mode in the asma rest franc., The other is of course the phase speed of the wave mode in the plasma rest frame.826 The phase speed for the kink uxnde under thin plasma sheet econpetry cau be tentatively described with available ATID theory developed or a plasina-slab configuration In cartesia1 geonietzy (Re)berts. 1981: Edwin Roberts. 1982).," The phase speed for the kink mode under thin plasma sheet geometry can be tentatively described with available MHD theory developed for a plasma-slab configuration in cartesian geometry (Roberts, 1981; Edwin Roberts, 1982)."827" Substituting noniial parameters m the sIow-iud plasma sheet region above the streamer ctsp iuto the dispersion relation given x Edwin& Roberts (1982). we fiud that t16 phase spece of the relevaut fast kink body mode ej. Is sunaller than vet rather close to he external Alfvénn speed (y,=Boipni. where à is the proou number deusitv aid y, the protou lass."," Substituting nominal parameters in the slow-wind plasma sheet region above the streamer cusp into the dispersion relation given by Edwin Roberts (1982), we find that the phase speed of the relevant fast kink body mode $c_k$ is smaller than yet rather close to the external Alfvénn speed $v_{Ae}=B_e / \sqrt{\mu_0 n m_p}$, where $n$ is the proton number density and $m_p$ the proton mass."828 The differeice between the dediced Ch and cas is senucral voless tlm one third of ey)., The difference between the deduced $c_k$ and $v_{Ae}$ is generally less than one third of $v_{Ae}$.829" Therefore. to implement a preliminary seimnological stuv on the magnetic field sreneth D,. we take ey, to be equal to the kink mode phase spec Ch estimated frou οἱr observations."," Therefore, to implement a preliminary seismological study on the magnetic field strength $B_e$, we take $v_{Ae}$ to be equal to the kink mode phase speed $c_k$ estimated from our observations."830 Regarding the solar wind conditious in the coucerred reeion. the readers are referred. to relevant observational studies (Sheclev e al..," Regarding the solar wind conditions in the concerned region, the readers are referred to relevant observational studies (Sheeley et al.,"831 1997: Wang et al..," 1997; Wang et al.,"832 2000: Straclal, 2000; Strachan833While a more complete testing of our method will be presented in a subsequent paper. in (his section we present some resulis [rom applving our method to simulated catalogs (hat illustrate the effects of small.scale. nonlinear power and how thev are mitigated in our analvsis.,"While a more complete testing of our method will be presented in a subsequent paper, in this section we present some results from applying our method to simulated catalogs that illustrate the effects of small–scale, nonlinear power and how they are mitigated in our analysis."834 For our testing we have chosen simulated catalogs with 21000 galaxies designed to mimic the characteristics of the SET survey (claCostaefaf.1995)., For our testing we have chosen simulated catalogs with $\approx1000$ galaxies designed to mimic the characteristics of the SFI survey \citep{dacosta95}.835. The catalogs were drawn [rom a 256% Nbody PM (particle mesh) simulation with D=0.25 and 4=O'oy0.46.," The catalogs were drawn from a $256^3$ N–body PM (particle mesh) simulation with $\Gamma = 0.25$ and $\beta =836\Omega^{0.6}\sigma_8 = 0.46$."837 In these simulations. (he box size was taken to be 512 Mpc and the IInbble constant kms !Mpe.1=0.75: thus the box size in redshift space corresponds to a diameter of 38.400 kms +.," In these simulations, the box size was taken to be $512$ Mpc and the Hubble constant $h=H/100$ km $^{-1}{\rm838Mpc}^{-1}=0.75$; thus the box size in redshift space corresponds to a diameter of 38,400 km $^{-1}$."839 Galaxies were identified in (hese simulations and assigned physical properties., Galaxies were identified in these simulations and assigned physical properties.840" To duplicate the characteristics of the SEI survey. galaxies were ""observed"" bv applying the sanie selection criteria."," To duplicate the characteristics of the SFI survey, galaxies were “observed” by applying the same selection criteria."841 Realistic scatter was added (ο galaxy. properties Chat duplicates the relative error in the SFI inferred distances., Realistic scatter was added to galaxy properties that duplicates the relative error in the SFI inferred distances.842 Finally. following Freudling (1995) we applied an inhomogeneous Malhlmequist correction to our catalogs.," Finally, following Freudling (1995) we applied an inhomogeneous Malmquist correction to our catalogs."843 We perlormed the analvsis described in Sec., We performed the analysis described in Sec.844 G on these simulated catalogs., \ref{sec-anal} on these simulated catalogs.845 In Fig., In Fig.846 1 we show the window functions for selected moments calculated for a (vpical catalog in order of increasing eigenvalue. with the top plot showing the window functions for the moments with the five lowest eigenvalues. the middle showing five others associated with somewhat larger eigenvalues. aud the bottom. plot showing five more selected from the whole range ol eigenvalues.," \ref{winfun} we show the window functions for selected moments calculated for a typical catalog in order of increasing eigenvalue, with the top plot showing the window functions for the moments with the five lowest eigenvalues, the middle showing five others associated with somewhat larger eigenvalues, and the bottom plot showing five more selected from the whole range of eigenvalues."847 This demonstrates that selecting moments that are least sensitive to small scales does in [act generally result in moments that are most sensitive to large scales: window functions of moments with larger eigenvalues are successively larger on nonlinear scales as expected., This demonstrates that selecting moments that are least sensitive to small scales does in fact generally result in moments that are most sensitive to large scales; window functions of moments with larger eigenvalues are successively larger on nonlinear scales as expected.848 Thus the information contained in laree eigenvalue moments comes mostly from scales where fluctuations are nonlinear and should not be included in a linear analvsis., Thus the information contained in large eigenvalue moments comes mostly from scales where fluctuations are nonlinear and should not be included in a linear analysis.849 For our simulated catalogs. we know the “true” values of D and 2.," For our simulated catalogs, we know the “true” values of $\Gamma$ and $\beta$."850" If: we use these true values as our ""guess"" (see Sec. 6))", If we use these true values as our “guess” (see Sec. \ref{sec-anal}) )851 lo calculate the optimum moments. then the values of these moments calculated. [rom the velocities should have unit variance. since (he power spectrum model should be au excellent fit to the data.," to calculate the optimum moments, then the values of these moments calculated from the velocities should have unit variance, since the power spectrum model should be an excellent fit to the data."852 ILowever. nonlinear elfects can cause igher order moments to deviate from unit variance.," However, non–linear effects can cause higher order moments to deviate from unit variance."853 In Fig., In Fig.854 2. we show the sum of the first N moments versus moment number NV [or a (vpical catalog. where the moments are ranked in order of increasing eigenvalue.," \ref{ratio} we show the sum of the first $N$ moments versus moment number $N$ for a typical catalog, where the moments are ranked in order of increasing eigenvalue."855 Note that for small Αν the sum tracks a line with unit slope. whereas for large V the sum deviates from this line: (his is an indication that the ionlinear effects are causing the large No moments to deviate [rom unit variance.," Note that for small $N$, the sum tracks a line with unit slope, whereas for large $N$ the sum deviates from this line; this is an indication that the non–linear effects are causing the large $N$ moments to deviate from unit variance."856 In Fig., In Fig.857 3 we show the results of (he likelihood analvsis on a tvpical catalog Lor different vunber .V of moments kept., \ref{maxval} we show the results of the likelihood analysis on a typical catalog for different number $N^{\prime}$ of moments kept.858" For reference. we also give the value of A@, for each AN"" as discussed in Sec. 4.."," For reference, we also give the value of $\Delta\theta_q$ for each $N^{\prime}$ as discussed in Sec. \ref{sec-select}."859 Here the closed triangles correspond to the maximum likelihood values while the contours correspond (o 1/2. 1/10. and 1/100 of the maximum likelihood.," Here the closed triangles correspond to the maximum likelihood values while the contours correspond to $1/2$, $1/10$, and $1/100$ of the maximum likelihood."860" The asterisk svinbol corresponds to the input values used [or the simulation. the “true” values for D and ο,"," The asterisk symbol corresponds to the input values used for the simulation, the “true” values for $\Gamma$ and $\beta$."861 We see that in (his case. inclusion of all of the information leads to the location of the maximum likelihood being skewed away [from the true values (see the panel with NV’= N).," We see that in this case, inclusion of all of the information leads to the location of the maximum likelihood being skewed away from the true values (see the panel with $N^{\prime}=N$ )."862 However. when higher order moments are discarded. the location of (he maximum likelihood corresponds well with (he (rue values.," However, when higher order moments are discarded, the location of the maximum likelihood corresponds well with the true values."863" For this particular catalog. with σι,= 200km/s. the criterion of Eq. (21))"," For this particular catalog, with $\sigma_*=200$ km/s, the criterion of Eq. \ref{criterion}) )"864 would give A’~125 for the optimum number of moments to keep.," would give $N^{\prime}\simeq865125$ for the optimum number of moments to keep."866 The [act that the discarding of higher order moments leads to a much better agreement between the maximum likelihood location and the true values is a good indication that our analvsis method is effectively removing smallscale. nonlinear velocity information.," The fact that the discarding of higher order moments leads to a much better agreement between the maximum likelihood location and the true values is a good indication that our analysis method is effectively removing small–scale, nonlinear velocity information."867 thequark-cliquark cascade model with spin.We investigate thesofthadronic interactions,in the regions of $p_T < 2$ GeV/c. We analyze hyperon and anti-hyperon polarizations in868In general. (hermochemical equilibrium governs the composition of the deep atmospheres of giant planets and brown cdwarls because thev are warm enough lor chemical reactions to readily overcome energv barriers (o reaction kinetics.,"In general, thermochemical equilibrium governs the composition of the deep atmospheres of giant planets and brown dwarfs because they are warm enough for chemical reactions to readily overcome energy barriers to reaction kinetics."869 However. disequilibrium processes in substellar atmospheres are well known.," However, disequilibrium processes in substellar atmospheres are well known."870 In addition to photochemistry driven by ultraviolet irradiation. atmospheric mixing is one of the dominant mechanisms that drives the chemical composition out of equilibrium.," In addition to photochemistry driven by ultraviolet irradiation, atmospheric mixing is one of the dominant mechanisms that drives the chemical composition out of equilibrium."871 In this scenario. rapid vertical mixing may (ransport a parcel ol gas to higher. cooler altitudes before its chemical constituents have had sufficient. time to attain equilibrium via reaction chemistry a phenomenon that has been proposed to explain the overabundance of various “disequilibrium” species in the atmospheres of Jupiter. saturn. Uranus. ancl Neptune (e.g..Prinn&Owen1976:Barshavetal.2009:Visscher2010:Moses 2010).. brown cwarls 2010).. and extrasolar giant planets (e.g..Cooper&Showman2006:Fortneyetal.Mosesetal. 2011).," In this scenario, rapid vertical mixing may transport a parcel of gas to higher, cooler altitudes before its chemical constituents have had sufficient time to attain equilibrium via reaction chemistry — a phenomenon that has been proposed to explain the overabundance of various “disequilibrium” species in the atmospheres of Jupiter, Saturn, Uranus, and Neptune \citep[e.g.,][]{prinn1976,prinn1977,barshay1978,fegley1979,prinn1981jgr,prinn1984,lewis1984,fegley1985apj,fegley1986apj,fegley1988,fegley1991,fegley1994,lodders1994,lodders2002,bezard2002,taylor2004,visscher2005,fouchet2009,visscher2010icarus,moses2010}, brown dwarfs \citep[e.g.,][]{fegley1996,noll1997,griffith1999,griffith2000,saumon2000,lodders2002,golimowski2004,saumon2006,saumon2007,visscher2006,leggett2007,hubeny2007,geballe2009,king2010,yamamura2010}, and extrasolar giant planets \citep[e.g.,][]{cooper2006,fortney2006hd149,burrows2008,line2010,madhusudhan2011,stevenson2010,moses2011}."872. Prin&Barshav(1977). first developed an analvtical model to explain the observed overabundance of CO in Jupiters troposphere due (o strong vertical mixing., \citet{prinn1977} first developed an analytical model to explain the observed overabundance of CO in Jupiter's troposphere due to strong vertical mixing.873" In (his approach. a lime scale for convective mixing (7,,;.). based upon an estimated mixing length scale and vertical mixing rate. is compared to a (time scale for chemical kinetics (Τομ). based upon an assumption about which chemical pathways will be important for interconversion between atmospheric constituents."," In this approach, a time scale for convective mixing $\tau_{mix}$ ), based upon an estimated mixing length scale and vertical mixing rate, is compared to a time scale for chemical kinetics $\tau_{chem}$ ), based upon an assumption about which chemical pathways will be important for interconversion between atmospheric constituents."874 At high temperatures in the deep atmosphere. thermochemical equilibrium is maintained because reaction kinetics operate faster (han couveclive mixing Tehem< Tuis).," At high temperatures in the deep atmosphere, thermochemical equilibrium is maintained because reaction kinetics operate faster than convective mixing $\tau_{chem}<\tau_{mix}$ )."875" However. departures from. equilibrium can occur at colder. higher altitudes when convective mixing begins (o dominate over reaction kinetics(16. when Them> τε]. and (he abundance of a molecular constituent may become ""quenched al a value representative of the quench level (defined by 74,5,= τηε]."," However, departures from equilibrium can occur at colder, higher altitudes when convective mixing begins to dominate over reaction kinetics, when $\tau_{chem}>\tau_{mix}$ ), and the abundance of a molecular constituent may become “quenched” at a value representative of the quench level (defined by $\tau_{chem}=\tau_{mix}$ )."876 This level is different for each species (Feelev&Prinn1985) ancl. in principle. species that is subject to reaction chemistry and atmospheric transport will quench if the appropriate time scale for reaction kinetics becomes longer than the time scale for convective mixing (e.g... see Fig.," This level is different for each species \citep{fegley1985apj} and, in principle, species that is subject to reaction chemistry and atmospheric transport will quench if the appropriate time scale for reaction kinetics becomes longer than the time scale for convective mixing \citep[{e.g.}, , see Fig."877" 62010).Here we investigate the chemical interconversion between CO and CII,. which becomes quenched when ΤμΩω=CII;)>7,,, in a substellar atmosphere."," 6.Here we investigate the chemical interconversion between CO and $_{4}$, which becomes quenched when $\tau_{chem}(\textrm{CO}\rightleftarrows\textrm{CH}_{4})>\tau_{mix}$ in a substellar atmosphere."878Subelwarl B (scd) stars are helium core burning stars with very thin hvdrogen envelopes that [ie at the blue end. of the horizontal branch and hence are identified with the extreme horizontal branch (EIID) stars (seearecentre- 2009).,Subdwarf B (sdB) stars are helium core burning stars with very thin hydrogen envelopes that lie at the blue end of the horizontal branch and hence are identified with the extreme horizontal branch (EHB) stars \citep[see a recent review by][]{heb2009}.879. D'Cruzetal.(1996). showed. that a high mass-loss rate on the red. giant branch produces a thin hydrogen envelope and prevents the star from ascending the asymptotic giant branch., \citet{dcr1996} showed that a high mass-loss rate on the red giant branch produces a thin hydrogen envelope and prevents the star from ascending the asymptotic giant branch.880 The evolution of single 5L stars [rom zero-age to helium exhaustion may be followed on a series of tracks narrowly centred on 0.475 AZ. (Dormanetal. 1993)., The evolution of single EHB stars from zero-age to helium exhaustion may be followed on a series of tracks narrowly centred on 0.475 $M_\odot$ \citep{dor1993}.881.. After helium exhaustion these objects evolve directly onto the white chvarl sequence., After helium exhaustion these objects evolve directly onto the white dwarf sequence.882 On the other hand. following the original. proposal of Alengeletal.(1976). [or the formation of sdB stars through binary evolution. it has been found that a significant fraction of these stars reside in close binary svstenis2003).," On the other hand, following the original proposal of \citet{men1976} for the formation of sdB stars through binary evolution, it has been found that a significant fraction of these stars reside in close binary systems."883. Phe onset of a common envelope phase or Roche lobe overflow contributes to the removal of the hydrogen envelope and directs the star toward the 11112., The onset of a common envelope phase or Roche lobe overflow contributes to the removal of the hydrogen envelope and directs the star toward the EHB.884 Lanοἱal.(2002.2003). propose three formation channels for the formation of sdB stars through binary interaction. either involving common envelope (CLE) phases. episodes of Roche lobe overllow (191ΟΙ). or the merger of two helium white cwarfs.," \citet{han2002,han2003} propose three formation channels for the formation of sdB stars through binary interaction, either involving common envelope (CE) phases, episodes of Roche lobe overflow (RLOF), or the merger of two helium white dwarfs."885 Phe CI scenario involving primary stars that experience a helium Uash accompanied by a low-mass or white cwarl secondary star is expected to create short-period binaries (logP(d)=] to 1) and a linal primary mass distribution. narrowly centred: on 0.46.., The CE scenario involving primary stars that experience a helium flash accompanied by a low-mass or white dwarf secondary star is expected to create short-period binaries $\log{P(d)}\approx -1$ to 1) and a final primary mass distribution narrowly centred on $M_\odot$.886 The CLE scenario with primary stars massive enough to avoid a helium flash is expected. to achieve a much lower final mass for the primary (0.33-0.35. Alo)., The CE scenario with primary stars massive enough to avoid a helium flash is expected to achieve a much lower final mass for the primary (0.33-0.35 $M_\odot$ ).887 On the other hand. the RLOF scenario creates longer period binaries ancl a wider distribution of primary final masses.," On the other hand, the RLOF scenario creates longer period binaries and a wider distribution of primary final masses."888 Studies of the binary components. anc an estimate of the frequency of such systems are required to constrain these models ancl determine the relative contribution of these formation channels to the sdB population.," Studies of the binary components, and an estimate of the frequency of such systems are required to constrain these models and determine the relative contribution of these formation channels to the sdB population."889 In this context. we have initiated a program to identify," In this context, we have initiated a program to identify"890The final sample for cach chip was formed by using the magnitude from the long exposure image for all unsaturated stars and from the short image for those stars that are saturated on the long image.,The final sample for each chip was formed by using the magnitude from the long exposure image for all unsaturated stars and from the short image for those stars that are saturated on the long image.891 The change from long to short data is at. σετ., The change from long to short data is at $\approx$ 17.5.892 In NCC1805 we find that there is à colour shift between the chips of z0.04 mag., In NGC1805 we find that there is a colour shift between the chips of $\approx$ 0.04 mag.893 Similar shifts have been found by other groups in cluster colour magnitude diagrams (Johnsonetal.1999). and attributed to errors in CPE and aperture corrections and in zeropoints., Similar shifts have been found by other groups in cluster colour magnitude diagrams \cite{John99} and attributed to errors in CTE and aperture corrections and in zeropoints.894 Similar errors are likely causing the colour shift seen in our data., Similar errors are likely causing the colour shift seen in our data.895 The NICMOS data were combined using the WRAP task miscombine. which sums the data ancl performs cosmic rav rejection.," The NICMOS data were combined using the IRAF task mscombine, which sums the data and performs cosmic ray rejection."896 Stars were detected in the NICMOS image and aperture photometry was performed., Stars were detected in the NICMOS image and aperture photometry was performed.897 Detections near to bright stars and alone dillraction spikes were masked. as in the optical data.," Detections near to bright stars and along diffraction spikes were masked, as in the optical data."898 There are several cdillieulties with NICMOS data. fortunately none of these had a big elfect on this projecCt.," There are several difficulties with NICMOS data, fortunately none of these had a big effect on this project."899 The Ipedestal. a constant which remains after runningg the calibration pipeline and. causes an inverse Uatficld pattern to be imprinted on the image. is not a big problem for these data as we take a local background for each star.," The pedestal, a constant which remains after running the calibration pipeline and causes an inverse flatfield pattern to be imprinted on the image, is not a big problem for these data as we take a local background for each star."900 Ghosts. which appear at congruent. positions in the other quadrants when a bright star is present in one quadrant. do appear in our images. but it is possible to look carefully at. the positions where ghosts are expected to occur and eliminate false detections.," Ghosts, which appear at congruent positions in the other quadrants when a bright star is present in one quadrant, do appear in our images, but it is possible to look carefully at the positions where ghosts are expected to occur and eliminate false detections."901 An aperture correction to 0.5 aresec was calculated from bright stars in the image., An aperture correction to 0.5 arcsec was calculated from bright stars in the image.902" The cata were calibrated to magnitudes in an approximate Vega svstem Using wherePHOTENE and Pos are caleulated by STScl at the time of writing to be 2.337E-6 S/DN. and 1039.3 Jv respectively (NICMOS Data Handbook. v4. Table 5.1). and we assume ZPy4,20 (as in the CET. infrared photometry scale)."," The data were calibrated to magnitudes in an approximate Vega system using where and $_{\nu \rm{Vega}}$ are calculated by STScI at the time of writing to be 2.337E-6 $\times$ s/DN and 1039.3 Jy respectively (NICMOS Data Handbook, v4, Table 5.1), and we assume $\it{ZP}_{\rm{Vega}}$ =0 (as in the CIT infrared photometry scale)."903 The final detected. star. lists in. NICALOS FIGOW and WEPC2 F555\W were matched: using the positional information in the image headers., The final detected star lists in NICMOS F160W and WFPC2 F555W were matched using the positional information in the image headers.904" lo was found that there can be as much as 2"" offset between the RAs ancl Dees calculated for a star from the NICMOS image and. those calculated for the same star from the WEPC2 image.", It was found that there can be as much as $^{\prime\prime}$ offset between the RAs and Decs calculated for a star from the NICMOS image and those calculated for the same star from the WFPC2 image.905 According to SUScl this is due to the combined uncertainty of the guide star positions. the location of the fine guidance sensors relative to the telescope axis ancl the measured locations of the instrument apertures.," According to STScI this is due to the combined uncertainty of the guide star positions, the location of the fine guidance sensors relative to the telescope axis and the measured locations of the instrument apertures."906 Figure 3. shows the de-reddened V. vs V-L Clohnson-C'ousins magnitudes) colour-magnituce diagrams {CAIDs)) for all four chips of NGCISIS (top) and NGC1805 (bottom)., Figure \ref{fig:VIcolmag} shows the de-reddened V vs V-I (Johnson-Cousins magnitudes) colour-magnitude diagrams (CMDs) for all four chips of NGC1818 (top) and NGC1805 (bottom).907 The different chips have dillerent. svmibols., The different chips have different symbols.908 Stars marked. with bold squares are Be stars (see subsection 3.2))., Stars marked with bold squares are Be stars (see subsection \ref{subsec:Beid}) ).909 The data have been de-reddened: assuming I5(D-V)=0.075., The data have been de-reddened assuming E(B-V)=0.075.910 Tables 4 and 5 tabulate these data for Νις1515 and NGCISO5 respectively (full versions of these tables are available on the MNIUAS web site)., Tables \ref{tab:n1818dat} and \ref{tab:n1805dat} tabulate these data for NGC1818 and NGC1805 respectively (full versions of these tables are available on the MNRAS web site).911 lsochrones from Bertelli οἱ shortciteDert94.. with a range of age and metallicity values encompassing those found in the literature for these clusters. are plotted. on the CALDs.," Isochrones from Bertelli et \\shortcite{Bert94}, with a range of age and metallicity values encompassing those found in the literature for these clusters, are plotted on the CMDs."912 “Lo illustrate the effects. of age ancl metallicity the top plot in Figure 3. shows 25 40 Myr isochrones for two metallicities. Fe/1]. of -0.4 and 0 and he bottom plot shows solar metallicity isochrones for ages of 25. 40 and 63 Myr.," To illustrate the effects of age and metallicity the top plot in Figure \ref{fig:VIcolmag} shows 25 40 Myr isochrones for two metallicities, [Fe/H], of -0.4 and 0 and the bottom plot shows solar metallicity isochrones for ages of 25, 40 and 63 Myr."913 The two clusters have very similar CMDs. which are raceck well by the 25Mvyr solar metallicity. isochrone.," The two clusters have very similar CMDs, which are traced well by the 25Myr solar metallicity isochrone."914" The ages and metallicities of these clusters are. investigated ""urther by comparison with simulations in section 4..", The ages and metallicities of these clusters are investigated further by comparison with simulations in section \ref{sec:sim}.915 Note hat. even with the very short exposure times used here. the xieghtest stars are still saturated in the FSI4W images.," Note that, even with the very short exposure times used here, the brightest stars are still saturated in the F814W images."916 The red giant branch. of the field. population of the LAIC is apparent in the CMDs at V-Iz1. Vz 18.5.," The red giant branch of the field population of the LMC is apparent in the CMDs at $\approx$ 1, $\approx$ 18.5."917 We have not subtracted these background stars from our data as we are predominantly interested in the brighter stars x19) where the contribution from the field is negligible (see [unter et 11997. Figure)., We have not subtracted these background stars from our data as we are predominantly interested in the brighter stars $\le$ 19) where the contribution from the field is negligible (see Hunter et 1997 Figure4).918 Figure 4 show the V vs V-LI diagrams for both clusters., Figure \ref{fig:VHcolmag} show the V vs V-H diagrams for both clusters.919 Phe isochrones (Bertellietal.L994) are for 25 and 40 Myr and for solar moetallicitv., The isochrones \cite{Bert94} are for 25 and 40 Myr and for solar metallicity.920 ‘Tables G and 7 tabulate these data lor NGCTSIS and NGCISO5 respectively (full versions of these tables are available on the MNIUAS web site)., Tables \ref{tab:n1818vhdat} and \ref{tab:n1805vhdat} tabulate these data for NGC1818 and NGC1805 respectively (full versions of these tables are available on the MNRAS web site).921 Νάς1515 and NGCLSO5 have five and three red supergiants respectively., NGC1818 and NGC1805 have five and three red supergiants respectively.922 Although our having to use NIC? reduced 10 number of stars in the NICMOS data. these colour-magnitude ciagrams are still of some use as they show us that the red supergiants lic towards the red end of the isochrones.," Although our having to use NIC2 reduced the number of stars in the NICMOS data, these colour-magnitude diagrams are still of some use as they show us that the red supergiants lie towards the red end of the isochrones."923 Although the poisson errors on the magnitudes of the bright stars are small. there could well be svstematic errors of a few tenths of a magnitude due to uncertainty in the Ll calibration and the isochrones.," Although the poisson errors on the magnitudes of the bright stars are small, there could well be systematic errors of a few tenths of a magnitude due to uncertainty in the H calibration and the isochrones."924 In. λές1515 two of the red. supergiants are located. on the 25 Myr isochrone. and the other three are consistent with either the 25 or 40 Alvr isochrone.," In NGC1818 two of the red supergiants are located on the 25 Myr isochrone, and the other three are consistent with either the 25 or 40 Myr isochrone."925 ln ας1505 two of the red supergiants are located on the 40 Myr isochrone. and one which has lower limits in V is consistent with either isochrone.," In NGC1805 two of the red supergiants are located on the 40 Myr isochrone, and one which has lower limits in V is consistent with either isochrone."926 In Figure 3. there are many stars in both clusters with 15 VIT that are significantly redder than the isochrones., In Figure \ref{fig:VIcolmag} there are many stars in both clusters with $\le$ $\le$ 17 that are significantly redder than the isochrones.927 ]t was suspected that these are De stars., It was suspected that these are Be stars.928" An ellective wav to identify Be stars in clusters is to use the fact that these stars show Balmer emission anc hence will separate from non-Be stars in ία ""colour.", An effective way to identify Be stars in clusters is to use the fact that these stars show Balmer emission and hence will separate from non-Be stars in V-Ha `colour'.929 An image, An image930The signalOo component ofA is where the pixc-beam function F; is given bv Iu the flat sky limit. the theory covariance matrix is eiven bv where F;(1) is theFourier transform of F;itr).,"The signal component of$\Delta$ is where the pixel-beam function $F_i$ is given by In the flat sky limit, the theory covariance matrix is given by where ${\tilde F}_i({\bf l})$ is theFourier transform of $F_i({\bf r})$."931 To perform the iterative quadratic baud-power cstimation procedure. it is necessary to know the partial derivative of Cy with respect to cach of the band-powers q5. which according to equation(1)) is given by Note that this algorithm docs not assuue that the instrument beams stav constant duriug the observations.," To perform the iterative quadratic band-power estimation procedure, it is necessary to know the partial derivative of $C_T$ with respect to each of the band-powers $q_B$, which according to \ref{dl}) ) is given by Note that this algorithm does not assume that the instrument beams stay constant during the observations."932 As described in ?.. the ACBAR beam sizes are weak functions of the chopper position.," As described in \citet{runyan03a}, the ACBAR beam sizes are weak functions of the chopper position."933 NOL adopted a semianalytic expansion to correct for these effects to first order., K04 adopted a semi-analytic expansion to correct for these effects to first order.934 To verify that the effects due to non-uuiforii beams are sanall. we developed. two eud-to-cud pipelines.," To verify that the effects due to non-uniform beams are small, we developed two end-to-end pipelines."935" In the first pipeline. the pixebbeani functious F;(r) are calculated explicitly caving the co-adding process,"," In the first pipeline, the pixel-beam functions $F_i({\bf r})$ are calculated explicitly during the co-adding process."936 The baudpowers in Table 3. are analyzed with this aleoritlin., The bandpowers in Table \ref{tab:bands} are analyzed with this algorithm.937 Iu the secoud pipeline. au averaged beam is used for the cutire map.," In the second pipeline, an averaged beam is used for the entire map."938 The difference in the power spectra from the two pipelines is ucelieible., The difference in the power spectra from the two pipelines is negligible.939" Iu the aualvsis of οι, we assuued that the nolse is stationary in chopper position. after LAIT subtraction."," In the analysis of K04, we assumed that the noise is stationary in chopper position after LMT subtraction."940 Iu the cureut treatment. we relax this assumption and calculate the full two dimensional correlation matrix directly from the time stream data without using Fourier transforms.," In the current treatment, we relax this assumption and calculate the full two dimensional correlation matrix directly from the time stream data without using Fourier transforms."941 All the uunerical calculations are performed on the National Energy Research Scieutific Computing Center (NERSC) IDM SP RS/6000., All the numerical calculations are performed on the National Energy Research Scientific Computing Center (NERSC) IBM SP RS/6000.942 The evaluation of F;(1) and its Fourier transform are the most computationally demanding steps in this analysis., The evaluation of $F_i({\bf r})$ and its Fourier transform are the most computationally demanding steps in this analysis.943 After Cr. Ον and Crp are calculated. standard likelihood maximizing procedures are used to find the baud-powoers qp and uncertainties (?)..," After ${\bf C}_T$ , ${\bf C}_N$ and ${\bf C}_{T,B}$ are calculated, standard likelihood maximizing procedures are used to find the band-powers ${\bf q}_B$ and uncertainties \citep{bond98}."944 The results of this analysis are preseuted in Table 3 aud Figure 1.., The results of this analysis are presented in Table \ref{tab:bands} and Figure \ref{fig:acbar}.945 RCW38 is a compact UIT region in the Calactic plane at a declination simile to the ACBAR CAMB fields., RCW38 is a compact HII region in the Galactic plane at a declination similar to the ACBAR CMB fields.946 It has a large aud stable flux and serves as the primary calibrator for the ACDBAR observations., It has a large and stable flux and serves as the primary calibrator for the ACBAR observations.947 We determine the absolute flux of ΠΟΟδ usine maps from the 2003 flieht of BOOMERANG (?.. hereafter BO3). which are calibrated. relative to the WAIAP experiment with an absolute uncertaintv of LSU.," We determine the absolute flux of RCW38 using maps from the 2003 flight of BOOMERANG \cite{masi05}, hereafter B03), which are calibrated relative to the WMAP experiment with an absolute uncertainty of $1.8\%$."948 ROW3s docs not have a black-body spectrum. requiring spectral corrections for the calibration of CAIB anisotropies.," RCW38 does not have a black-body spectrum, requiring spectral corrections for the calibration of CMB anisotropies."949 However the similarity in the spectral respouses of the 150 GITz bauds iu the DOS and ACBAR experiments cusures these corrections to be sanall.," However the similarity in the spectral responses of the $150\,$ GHz bands in the B03 and ACBAR experiments ensures these corrections to be small."950 Were we outline the calibration procedure. leaving the details to Appeudix ?7..," Here we outline the calibration procedure, leaving the details to Appendix \ref{app:calib}."951 ACBAR typically observed. ROW3s before aud after cach CAIB observation., ACBAR typically observed RCW38 before and after each CMB observation.952 Comparisons between the Bos and ACBAR maps of RCW38 are used to determine the absolute calibration of the CMD fields to an unucertaiutv of6., Comparisons between the B03 and ACBAR maps of RCW38 are used to determine the absolute calibration of the CMB fields to an uncertainty of.9530%... For roughly of tlie 2002 season. we observed RCW358 with only half the 150 GIIz detectors CL out of SJ," For roughly of the 2002 season, we observed RCW38 with only half the $150\,$ GHz detectors (4 out of 8)."954 During these periods. the ROWS3s calibration was applied. to the remaiming detectors bv comparing CMD power spectra derived frou each half of the detectors.," During these periods, the RCW38 calibration was applied to the remaining detectors by comparing CMB power spectra derived from each half of the detectors."955 The calibration of the CAIB| field (observed im 2002) is extended to the overlapping CMD2 field (observed iu 2001) bv comparing power spectra frou cach field., The calibration of the CMB4 field (observed in 2002) is extended to the overlapping CMB2 field (observed in 2001) by comparing power spectra from each field.956" In the first ACBAR release. the 2001 and 2002 data sets were calibrated with au accuracy of using observations of Mags aud Veuus respectively,"," In the first ACBAR release, the 2001 and 2002 data sets were calibrated with an accuracy of using observations of Mars and Venus respectively."957 We determine the corrections o this planct-hased calibration to be 0.911-E0.072. for CAB? (2001) aud 1.1284x0.066 for CMD41-7. (2002) in CXMB temperature., We determine the corrections to this planet-based calibration to be $\pm$ 0.072 for CMB2 (2001) and $\pm$ 0.066 for CMB4-7 (2002) in CMB temperature.958 The 2002 observations dominate the final power spectra. and the final results have csseutially he same temperature calibration uucertainty as the 2002 data.," The 2002 observations dominate the final power spectra, and the final results have essentially the same temperature calibration uncertainty as the 2002 data."959 We performed a series of tests to constrain the amplitude of potential systematic errors in the power spectra. results., We performed a series of tests to constrain the amplitude of potential systematic errors in the power spectrum results.960 As described by I&01. the “first half iuinus secoud half jackkuite is a very powerful test for time clepeudcut errors. such as a chaugiug calibration. iuconsistenew in the beam or poiutiug reconstruction. and time varving sidelobe pickup.," As described by K04, the “first half minus second half"" jackknife is a very powerful test for time dependent errors, such as a changing calibration, inconsistency in the beam or pointing reconstruction, and time varying sidelobe pickup."961 Iu addition. high-f jackknife baud-powers constrain the uais-cstimation of noise.," In addition, $\ell$ jackknife band-powers constrain the mis-estimation of noise."962 We perform this test on the joint CAIB power spectrmu and find the baud-powers of the chronologically differenced maps are consistent with zero (Fig. 2))., We perform this test on the joint CMB power spectrum and find the band-powers of the chronologically differenced maps are consistent with zero (Fig. \ref{fig:sys}) ).963 Siuilarh. the data can be divided in two halves according to the direction of the chopper notion.," Similarly, the data can be divided in two halves according to the direction of the chopper motion."964 Microphouic vibrations due to the chopper turn-aromuds. erroneous trauster function corrections. or effects of wiud direction could produce a nonvanishing signal in the jackknife baud-powers.," Microphonic vibrations due to the chopper turn-arounds, erroneous transfer function corrections, or effects of wind direction could produce a nonvanishing signal in the jackknife band-powers."965 We fiud that the power spectruui of the left-right differenced maps is also consistent with ZOrO., We find that the power spectrum of the left-right differenced maps is also consistent with zero.966 To cusure that any residual chopper svuchronous offset is below the noise level. we have developed a new systematic test that the coutribution of auv such offsets relative to the CAIB.," To ensure that any residual chopper synchronous offset is below the noise level, we have developed a new systematic test that the contribution of any such offsets relative to the CMB."967 In this test. the baud-powers are derived. from an LAIT παρ. £|AL T. i which the residual svuchronous offsets (the sameiu each field) are enhanced relative to the (random) CAB fluctuations by a factor of 3 iu power Gicelecting the," In this test, the band-powers are derived from an LMT map, $L+M+T$ , in which the residual synchronous offsets (the samein each field) are enhanced relative to the (random) CMB fluctuations by a factor of 3 in power (neglecting the"968"CCs. and for the outward temperature and density declines in all clusters. is set by the underlying dominant DM distribution; specifically. such a seale is set by the peak of the DM velocity dispersion σ΄) at the position rj,2ro. that divides the ‘inner’ from the ‘outer’ cluster regions (see Figs.","CCs, and for the outward temperature and density declines in all clusters, is set by the underlying dominant DM distribution; specifically, such a scale is set by the peak of the DM velocity dispersion $\sigma^2(r)$ at the position $r_m\approx r_{-2}$, that divides the `inner' from the `outer' cluster regions (see Figs."969 | and 3 of CLFFO9)., 1 and 3 of CLFF09).970" In fact. the SM ensures that the approximation T—a7/d, [with J,=ΗμFy)kpT(ry). see CLFFO9] is to hold closely for all clusters around. |7j,. and over a wide radial range for theCCs*."," In fact, the SM ensures that the approximation $T\simeq\sigma^2/\beta_m$ [with $\beta_m\equiv \mu m_p\sigma^2(r_m)/k_BT(r_m)$, see CLFF09] is to hold closely for all clusters around $r_m$, and over a wide radial range for the."971. In the inner ICP regions. the temperature and density profiles are governed primarily by the central entropy level κ. set by events. 1.8.. energy discharged and blasts driven by major mergers or AGN outbursts: in à number of cases the latter imprint substructure on the small scale r; comparable to η.," In the inner ICP regions, the temperature and density profiles are governed primarily by the central entropy level $k_c$ set by events, i.e., energy discharged and blasts driven by major mergers or AGN outbursts; in a number of cases the latter imprint substructure on the small scale $r_f$ comparable to $r_m$."972 A novel feature ofthe SM (relative to handy isothermal or polytropie J-models where the entropy is assumed to be a functional &x11? of the density. see Cavaliere Fusco-Femiano 1976) is constituted by the radial entropy run entering Eq. (," A novel feature ofthe SM (relative to handy isothermal or polytropic $\beta$ -models where the entropy is assumed to be a functional $k\propto n^{\Gamma-5/3}$ of the density, see Cavaliere Fusco-Femiano 1976) is constituted by the radial entropy run entering Eq. ("9732).,2).974 We have collected in Table | the SM fitting parameters for all clusters in our set., We have collected in Table 1 the SM fitting parameters for all clusters in our set.975 By inspection it is apparent a correlation between the inner ICP profile type (marked by the CC/NCC tags) with the central entropy level κ... the outer entropy slope a. and the DM concentration c; high values of c and low values of a and κ. correspond to the CC class. while the opposite trend holds for NCC.," By inspection it is apparent a correlation between the inner ICP profile type (marked by the CC/NCC tags) with the central entropy level $k_c$, the outer entropy slope $a$ , and the DM concentration $c$; high values of $c$ and low values of $a$ and $k_c$ correspond to the CC class, while the opposite trend holds for NCC."976 We understand these trends in the framework of two-stage cluster formation (see 1) as follows., We understand these trends in the framework of two-stage cluster formation (see 1) as follows.977 For example. low values of & correspond to high values of bp (see Eq.," For example, low values of $a$ correspond to high values of $b_R$ (see Eq."978 4) owing to low values of Ao (see Eq., 4) owing to low values of $\Delta\phi$ (see Eq.979 3): these are related to high concentrations c=3.5(14z;) (see | and 2). which imply early transition redshifts ο. 1.e.. an old age.," 3); these are related to high concentrations $c=9803.5\,(1+z_t)$ (see 1 and 2), which imply early transition redshifts $z_t$ , i.e., an old age."981 We stress thatin the six clusters considered here the, We stress thatin the six clusters considered here the982(1998). vielding an overestimate of extinction in mocerate to high extinction regions.,"(1998), yielding an overestimate of extinction in moderate to high extinction regions."983 We estimate a calibration correction factor of for the ELI extinction values., We estimate a calibration correction factor of for the FIR extinction values.984 For the intermediate 17«|b]3° region. the relation between DIRBE/IRAS anc 2MASS extinction values departs more significantly from the identity line. as expected due to the larger contribution bv background dust.," For the intermediate $1^{\circ}<|{\it b}|<3^{\circ}$ region, the relation between DIRBE/IRAS and 2MASS extinction values departs more significantly from the identity line, as expected due to the larger contribution by background dust."985 In this region. the tvpical νομοςντι ratio is and could. be explained. by background dust. contribution and the calibration. factor allectine the Elli data.," In this region, the typical $A_{K,2MASS}/A_{K,FIR}$ ratio is and could be explained by background dust contribution and the calibration factor affecting the FIR data."986 An enhancement in the foreground. dust. with respect το the dust. model is observed in many cells in the northern strip., An enhancement in the foreground dust with respect to the dust model is observed in many cells in the northern strip.987 In the southern strip. several cells have cliourasscdpri smaller than expected. probably due to dense dust. clouds and temperature variations. currently not incorporated into our model.," In the southern strip, several cells have $A_{K,2MASS}/A_{K,FIR}$ smaller than expected, probably due to dense dust clouds and temperature variations, currently not incorporated into our model."988 For the regions very close to the Galactic Plane (|6 0.57). we have a typical value for the cliourτοςprin ratio of," For the regions very close to the Galactic Plane $|{\it b}| 989< 0.5^{\circ}$ ), we have a typical value for the $A_{K,2MASS}/A_{K,FIR}$ ratio of."990 Even considering the background. dust contribution and the calibration factor. this ratio is still smaller. than that predicted. by our. simple model. for the dust. distribution.," Even considering the background dust contribution and the calibration factor, this ratio is still smaller than that predicted by our simple model for the dust distribution."991 This fact is probably due to. the overestimation of the νι values by heated clust above that. obtained. from DIRBE temperature maps.," This fact is probably due to the overestimation of the $A_{K,FIR}$ values by heated dust above that obtained from DIRBE temperature maps."992 Another possible contribution to this dillerence is the existence of systematic clleets on the lisoaass values in high extinction regions (κοτος 2.5). where the PALASS extinction should be significantly. underestimated or even unreliable.," Another possible contribution to this difference is the existence of systematic effects on the $A_{K,2MASS}$ values in high extinction regions $A_{K,2MASS} > 2.5$ ), where the 2MASS extinction should be significantly underestimated or even unreliable."993 AX systematic asvmmetry in the values relative to the plane of the Galaxy is observed both in the 2ALASS and. DIRBE/IRAS data., A systematic asymmetry in the values relative to the plane of the Galaxy is observed both in the 2MASS and DIRBE/IRAS data.994 The behaviour and amplitude of this asymmetry with position on the sky suggest that the dominant role in creating this north-south asymmetry is a more ellective presence of foreground dust. clouds in the northern Galactic strips. such as the pe Nebula (Sect.," The behaviour and amplitude of this asymmetry with position on the sky suggest that the dominant role in creating this north-south asymmetry is a more effective presence of foreground dust clouds in the northern Galactic strips, such as the Pipe Nebula (Sect."995 2.2)., 2.2).996 X possible explanation is stellar winds and supernovae from nearby OD stellar associations xoducing dust cloud shells (Bhatt 2000)., A possible explanation is stellar winds and supernovae from nearby OB stellar associations producing dust cloud shells (Bhatt 2000).997 Phe nearby clouds »ojected towards the central parts ofthe Galaxy at positive atitudes belong to the Ophiuchus cust complex., The nearby clouds projected towards the central parts of the Galaxy at positive latitudes belong to the Ophiuchus dust complex.998 They. are oobablv related to the association Sco0D2. which is at à distance of 145 pe from the Sun (Bhatt 2000: Onishi ct al.," They are probably related to the association ScoOB2, which is at a distance of 145 pc from the Sun (Bhatt 2000; Onishi et al."999 1999)., 1999).1000 ScoO132. in turn. belongs to Upper Scorpius. which is he easternmost part of the Sco-Cen Association. as studied » means of Hipparcos (de Zeeuw οἱ al.," ScoOB2, in turn, belongs to Upper Scorpius, which is the easternmost part of the Sco-Cen Association, as studied by means of Hipparcos (de Zeeuw et al."1001 1999)., 1999).1002 In all regions. significant substructure in. the Ancarisses. dope relation is seen. with loops and. armis stretching out from the main relation.," In all regions, significant substructure in the ${\it A_{K,2MASS}} vs.$ ${\it A_{K,FIR}}$ relation is seen, with loops and arms stretching out from the main relation."1003 These structures are probably caused. by intervening dust. clouds. with cdilleren temperatures and densities for dilferent lines of sight.," These structures are probably caused by intervening dust clouds, with different temperatures and densities for different lines of sight."1004 One extremely interesting. perspective is to model the dus distribution within the Galaxy. trying to reproduce as close as possible the details of the maps currently available.," One extremely interesting perspective is to model the dust distribution within the Galaxy, trying to reproduce as close as possible the details of the maps currently available."1005 This effort. demancs models that. incorporate. on top of a smooth dust. distribution. the clleets of individual dus clouds. spiral arms. molecular rings and other structure. possibly with variable density contrasts ancl temperatures.," This effort demands models that incorporate, on top of a smooth dust distribution, the effects of individual dust clouds, spiral arms, molecular rings and other structure, possibly with variable density contrasts and temperatures."1006 This ellort is currently under way for the central region of the Galaxy., This effort is currently under way for the central region of the Galaxy.1007" This publication makes use of data products from the “Pwo Micron. All Sky Survey, which is a joint. project. of the University of Massachusetts and the Enfrared Processing and Analvsis Center/California Institute of Technology. funded by the National Acronautics and Space AXcdministration and the National Science Foundation."," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."1008 We also use the electronic form of the extinction maps provided by Schultheis et. al. (, We also use the electronic form of the extinction maps provided by Schultheis et al. (10091999) and Schlegel et al. (,1999) and Schlegel et al. (10101998).,1998).1011 We thank the anonymous referee for his/her interesting comments and suggestions., We thank the anonymous referee for his/her interesting comments and suggestions.1012 We acknowledge support from. the Brazilian institutions FAPESP and CNPq., We acknowledge support from the Brazilian institutions FAPESP and CNPq.1013 CAID acknowledges FAPIESP for a post-doe fellowship (proc., CMD acknowledges FAPESP for a post-doc fellowship (proc.1014 00/11S64-6)., 00/11864-6).1015been adequately sampled over a wide chough rauge of huninosity to observe this pattern directly.,been adequately sampled over a wide enough range of luminosity to observe this pattern directly.1016 Several more sources that vary by no more than a factor of LO in X- intensity appear to form portions of this pattern., Several more sources that vary by no more than a factor of 10 in X-ray intensity appear to form portions of this pattern.1017 IU 303 aud IU 31 in Figure 1 exhibit oulv the bottom aud diagonal portions of this pattern., 4U $-$ 303 and 4U $-$ 34 in Figure \ref{cconly} exhibit only the bottom and diagonal portions of this pattern.1018 Ser N-1 exhibits only the bottom portion. aud GS 238 ouly the top (Figure 1)).," Ser X-1 exhibits only the bottom portion, and GS $-$ 238 only the top (Figure \ref{cconly}) )."1019 The tracks from the Z sources (νο νι CON 1712. GN D. aud CX 31010 (Figure 1)) ave uuuistakablv Z-shaped. but are somewhat differeut from those of the atoll sources.," The tracks from the Z sources Cyg X-2, GX 17+2, GX $-$ 1, and GX $+$ 0 (Figure \ref{cconly}) ) are unmistakably Z-shaped, but are somewhat different from those of the atoll sources."1020 Iu general. Z sources are softer than atoll sources.," In general, Z sources are softer than atoll sources."1021 Moreover. the traditional Z sources trace out a full track on time scales as short as a dav. while atoll sources fori. their color-color diagrams on much longer time scales of 30-100 days.," Moreover, the traditional Z sources trace out a full track on time scales as short as a day, while atoll sources form their color-color diagrams on much longer time scales of 30-100 days."1022 We have highlehted using darker syiubols data spanning5 20- davs for the sources which trace their Z ou short time scales in Figure 1.. in oxder to allow an easy coniparison between the short aud long-term spectral variability.," We have highlighted using darker symbols data spanning 20 days for the sources which trace their Z on short time scales in Figure \ref{cconly}, in order to allow an easy comparison between the short and long-term spectral variability."1023 As has been previously noted. the width of the track perpendicular to the direction of motion is mach sanaller in traditional Z sources than in atoll sources whe- observed ou time scales of davs (c.¢vanderIlis.1995).," As has been previously noted, the width of the track perpendicular to the direction of motion is much smaller in traditional Z sources than in atoll sources when observed on time scales of days \cite[e.g][]{vdk95}."1024. Ou the five-vear time scales of Figure 1.. both the Z and atoll sources exhibit variations in the colors perpendicular to the direction of motion that traces the Z (o.c.Ixkuulkersetal.199L).," On the five-year time scales of Figure \ref{cconly}, both the Z and atoll sources exhibit variations in the colors perpendicular to the direction of motion that traces the Z \citep[e.g.][]{kul94}."1025. It is interesting to note that the color-color diagram of CX 1 in Figure 1 resembles that of the Z source CX 1712 more than those of the other atoll sources.," It is interesting to note that the color-color diagram of GX $+$ 1 in Figure \ref{cconly}1026 resembles that of the Z source GX $+$ 2 more than those of the other atoll sources."1027 Although CX 1311 sas classified an atoll source because it lacked. strong QPOs (Ilasiueer&vanderWlis1989).. oobservatious have revealed weak QPOs similar to those of Z sources (Tomanetal.1998)... ancl several observations have revealed sinularities between the X-ray. (Schulzetal.1989) and IR (Bandyopadhyayctal.1999). spectra of GX 1311 and other Z sources.," Although GX 13+1 was classified an atoll source because it lacked strong QPOs \citep{hv89}, observations have revealed weak QPOs similar to those of Z sources \citep{hom98}, and several observations have revealed similarities between the X-ray \citep{sht89} and IR \citep{ban99} spectra of GX 13+1 and other Z sources."1028 CX 13|L appears to exhibit both Z aud atoll properties. aud may prove important for uderstanding what causes the distinctions between the two classes of source.," GX 13+1 appears to exhibit both Z and atoll properties, and may prove important for understanding what causes the distinctions between the two classes of source."1029 We next exanunune how these colors evolve versus oeiteusity and. for the atoll sources. versus time.," We next examine how these colors evolve versus intensity and, for the atoll sources, versus time."1030 In Figure we have plotted the hard. aud soft color as a functiou of the 2I8 keV PCA count rates for the atoll source Aql N-1 aud the Z source GN 1., In Figure \ref{hid} we have plotted the hard and soft color as a function of the 2–18 keV PCA count rates for the atoll source Aql X-1 and the Z source GX $-$ 1.1031 Iu Figure 3. we lave plotted the N-raw colors and the 2-12 keV. N-rav intensity from the AASNMI from the atoll source. IU 110 over a span of 200x davs., In Figure \ref{cctime} we have plotted the X-ray colors and the 2-12 keV X-ray intensity from the ASM from the atoll source 4U $-$ 440 over a span of 200 days.1032 It is well-known that Z sources trace their colorcolor diagrams s1ioothlyv with time im less than a day (e.g.I&uulkersetal.199[:vanderWhs 1995).," It is well-known that Z sources trace their color-color diagrams smoothly with time in less than a day \citep[e.g.][]{kul94,vdk95}."1033. These data are the best-sauipled examples from the LAINBs in Table 1.., These data are the best-sampled examples from the LMXBs in Table \ref{stats}.1034 Figures 2 and 3 indicate that atoll sources also trace their Z-shaped track snoothly., Figures \ref{hid} and \ref{cctime} indicate that atoll sources also trace their Z-shaped track smoothly.1035 The horizontal portion at the top of the color-color track of the atoll sources (with a hard color of about 0.5 in Figure 1)) is traced from left to reht as the intensity increases by iiore than a factor of 10., The horizontal portion at the top of the color-color track of the atoll sources (with a hard color of about 0.8 in Figure \ref{cconly}) ) is traced from left to right as the intensity increases by more than a factor of 10.1036 For Αα X-1 and IU 1608-522. it is traced on time scales of davs to mouths as the source rises from (or decays to) below the PCA detection threshold. with a factor of 250 chanee in intensity.," For Aql X-1 and 4U 1608-522, it is traced on time scales of days to months as the source rises from (or decays to) below the PCA detection threshold, with a factor of 250 change in intensity."1037 Ou the other hand. GS 18526. 31 has relmained in a smailur faint aud hard state for the sis vears of nuuonitormue.," On the other hand, GS $-$ 34 has remained in a similar faint and hard state for the six years of monitoring."1038 The diagonal brauch is traced. ou fine scales of days. and only has been sampled well in time in a few instances (ee. Figure 3)).," The diagonal branch is traced on time scales of days, and only has been sampled well in time in a few instances (e.g. Figure \ref{cctime}) )."1039 As an atoll source moves down alone the diagonal portion of the color-color track. the cout rate usually increases by a factor of 2 (aud vice versa: see Figure 3)).," As an atoll source moves down along the diagonal portion of the color-color track, the count rate usually increases by a factor of 2 (and vice versa; see Figure \ref{cctime}) )."1040 However. during a recent uuusual outburst of the count rate decreased by a factor of 2 while," However, during a recent unusual outburst of \\citep{bai01} the count rate decreased by a factor of 2 while"1041After imposing our selection criteria we are able to compile a list of candidate zS9 star forming galaxies in the IIUDE. UDE-P34. UDE-P12 and ERS fields.,"After imposing our selection criteria we are able to compile a list of candidate $z\approx 8-9$ star forming galaxies in the HUDF, UDF-P34, UDF-P12 and ERS fields."1042 In. ‘Table 3 we list. positions and. photometry of these objects. while thumbnails of the bezzYJif images of these. candidates (where available) are presented in Figure 4..," In Table \ref{tab:objects} we list positions and photometry of these objects, while thumbnails of the $bvizYJH$ images of these candidates (where available) are presented in Figure \ref{fig:stamps}."1043 In total we find 24 Y-drop candidates (LIUDE:6. UDE-DP34:7. UDE-P12:2. ERS:9) covering a range of apparent Jig magnitudes. of 21.0.28.5.," In total we find 24 $Y$ -drop candidates (HUDF:6, UDF-P34:7, UDF-P12:2, ERS:9) covering a range of apparent $J_{AB}$ magnitudes of $27.0-28.5$."1044 In the three deep single WECS pointings. the number of cancdidates is fairly consistent from field to field. with 3. 4 and 2 Y-drops for the HUDE. UDE-I34 and fields. respectively. at Jigκ28.2.," In the three deep single WFC3 pointings, the number of candidates is fairly consistent from field to field, with 3, 4 and 2 $Y$ -drops for the HUDF, UDF-P34 and UDF-P12 fields, respectively, at $J_{AB}<28.2$."1045 There are 9 fof the 24) objects in the Y-drop list (‘Table 3)) whieh we llag as being more marginal than the other candidates as they sit at the limits of our selection. although they are plausible z28ϐ galaxies (our effective volume calculation. already corrects for. galaxies. excluded as lving just outside the selection region).," There are 9 (of the 24) objects in the $Y$ -drop list (Table \ref{tab:objects}) ) which we flag as being more marginal than the other candidates as they sit at the limits of our selection, although they are plausible $z\approx 8-9$ galaxies (our effective volume calculation already corrects for galaxies excluded as lying just outside the selection region)."1046 C'andidates ERS.YD7 and ERS.YDS in the ERS are llagged. as we only have a lower limit on the (YJ) colour (they are =lo in Y-baned).," Candidates ERS.YD7 and ERS.YD8 in the ERS are flagged, as we only have a lower limit on the $(Y-J)$ colour (they are $\lesssim\,1\,\sigma$ in $Y$ -band)."1047" Adopting the Le lower limit on the (Y—J) colour places them in or above the ""contaminant triangular region of Figure 2.. fully consistent with entering our selection area."," Adopting the $1\,\sigma$ lower limit on the $(Y-J)$ colour places them in or above the `contaminant' triangular region of Figure \ref{fig:cc_1}, fully consistent with entering our selection area."1048 Similarly. objects ERS.YD2. IS.YD5. ERS.YD9 and P34.YD7 are llagged: using a 10 lower limit on the (YJ) colour these candidates would fully meet our selection criteria (see Ligures 2. and 3)). while a more conservative 20 lower limit could. potentially locate them just. below our selection box. although with colours consistent with falling within the selection window.," Similarly, objects ERS.YD2, ERS.YD5, ERS.YD9 and P34.YD7 are flagged: using a $1\,\sigma$ lower limit on the $(Y-J)$ colour these candidates would fully meet our selection criteria (see Figures \ref{fig:cc_1} and \ref{fig:cc_2}) ), while a more conservative $2\,\sigma$ lower limit could potentially locate them just below our selection box, although with colours consistent with falling within the selection window."1049 Deeper l-band imaging is required to show unambiguously that they are not in the ‘contaminant’ region of the colour:colour space., Deeper $Y$ -band imaging is required to show unambiguously that they are not in the `contaminant' region of the colour:colour space.1050 Object P34.Y in P34 is also llagged. because it has a ~ 22a detection in D5the z-band.," Object P34.YD5 in P34 is also flagged, because it has a $\sim$ $\sigma$ detection in the $z$ -band."1051 There are no detections in vc. 7 and Y-bands. though. so it is still a likely (2> 6) object he z-band Hux might be statistical Iluctuation or perhaps a high-equivalent-width emission line within the z-band.," There are no detections in $v$ -, $i$ - and $Y$ -bands, though, so it is still a likely high-redshift $z>6$ ) object – the $z$ -band flux might be statistical fluctuation or perhaps a high-equivalent-width emission line within the $z$ -band."1052 We also llag as marginal two potential high redshift ealaxies in Ποια UDE-DP12. on the grounds that the short exposure time of the Z/-band image in this field. CFable 1)) made it impossible to measure the /Z/ig. magnitude.," We also flag as marginal two potential high redshift galaxies in field UDF-P12, on the grounds that the short exposure time of the $H$ -band image in this field (Table \ref{tab:exptimes}) ) made it impossible to measure the $H_{AB}$ magnitude."1053 The upper limits on the (/I) colours. place them. away [rom the red contaminant region with (/fl)1.5 (Figure 2)). but we require the UV. luminosity in the //-flter (uncontaminated: by the elfeets o£. Lyman-a forest absorption) to infer the absolute UV. magnitude (as described in Section 4.1)).," The upper limits on the $(J-H)$ colours place them away from the red contaminant region with $(J-H)>1.5$ (Figure \ref{fig:cc_1}) ), but we require the UV luminosity in the $H$ -filter (uncontaminated by the effects of $\alpha$ forest absorption) to infer the absolute UV magnitude (as described in Section \ref{sec:lumfunc}) )."1054 We now consider whether these single-band. cleteetions might be due to transients (such as was the case for the likely supernova in the WECS3 images of the HIUDE. object zD0 in Bunker ct 22010).," We now consider whether these single-band detections might be due to transients (such as was the case for the likely supernova in the WFC3 images of the HUDF, object zD0 in Bunker et 2010)."1055 The P12 Ποιά was observed in J-band in two observing blocks. with S freies taken on 22009 November 02. and the other 16 frames taken over 2009 November 1015.," The P12 field was observed in $J$ -band in two observing blocks, with 8 frames taken on 2009 November 02, and the other 16 frames taken over 2009 November 10–15."1056 As a check. we combined the two cillerent epochs separately with 7multidrizzle.," As a check, we combined the two different epochs separately with “multidrizzle""."1057 The magnitude of P12.YDI is consistent between the two epochs. with J=28.07£0.25 (4.30) and J=27.9540.16 (6.80) respectively.," The magnitude of P12.YD1 is consistent between the two epochs, with $J=28.07\pm 0.25$ $4.3\,\sigma$ ) and $J=27.95\pm 0.16$ $6.8\,\sigma$ ) respectively."1058 Lowever. D12.YD2 might show some variability in the J-band with J=27.36£013 (Ss.3sigma) For the first block of data and J=28.14E0.19 (5.8sigma) for the second.," However, P12.YD2 might show some variability in the $J$ -band with $J=27.36\pm 0.13$ $8.3\,sigma$ ) for the first block of data and $J=28.14\pm 0.19$ $5.8\,sigma$ ) for the second."1059 Hence it is plausible that. P12.YD2 might. be a transient rather than a high-redshift Y-drop., Hence it is plausible that P12.YD2 might be a transient rather than a high-redshift $Y$ -drop.1060 When this WECS3 program (GO-11563) is complete. the Z/-band will be much deeper on P12. allowing a further check on the robustness of the candidates in this field.," When this WFC3 program (GO-11563) is complete, the $H$ -band will be much deeper on P12, allowing a further check on the robustness of the candidates in this field."1061 Llowever. the two candidates in P12 represent less than 10 per cent of our Y-drop sample. so will not quantitively affect our conclusions: for the moment. we exclude this field from our fitting of the UV. luminosity function.," However, the two candidates in P12 represent less than 10 per cent of our $Y$ -drop sample, so will not quantitively affect our conclusions; for the moment, we exclude this field from our fitting of the UV luminosity function."1062 We now compare our new [ist of candidates within the IIUDE field with other groups! previous studies (Ocsch et 22010. Bouwens et 22010a. McLure et 22010. Yan et 22010 and Finkelstein ct al.," We now compare our new list of candidates within the HUDF field with other groups' previous studies (Oesch et 2010, Bouwens et 2010a, McLure et 2010, Yan et 2010 and Finkelstein et al."1063 2010). and particularly with our previous paper (Bunker et 22010).," 2010), and particularly with our previous paper (Bunker et 2010)."1064 A matched catalog between the Bunker et ((2010). AleLure ct ((2010) ancl Bouwens ct ((2010a) samples has already oen presented in Bunker Wilkins (2009).," A matched catalog between the Bunker et (2010), McLure et (2010) and Bouwens et (2010a) samples has already been presented in Bunker Wilkins (2009)."1065 Our refined HUDE sample. based on à new reduction of rw HUDE data. has 6 Y-band drop-outs.," Our refined HUDF sample, based on a new reduction of the HUDF data, has 6 $Y$ -band drop-outs."1066 In Bunker ct ((2010) we presented. a list of 7 Y-drop candidates within 1e HIUDE. field. the brightest. four (in. J-band) of which are reproduced with the new selection (LIUDE-YDI.2.3 4).," In Bunker et (2010) we presented a list of 7 $Y$ -drop candidates within the HUDF field, the brightest four (in $J$ -band) of which are reproduced with the new selection (HUDF-YD1,2,3 4)."1067 Of the 3 other Y-drops from Bunker et ((2010). one (YD5) has a discrepant (Y1054Jan)=00.2 colour in the new data reduction. much bluer than our selection criteria of (VionJose)0.9.," Of the 3 other $Y$ -drops from Bunker et (2010), one (YD5) has a discrepant $(Y_{105w}-J_{125w})=0.2$ colour in the new data reduction, much bluer than our selection criteria of $(Y_{105w}-J_{125w})>0.9$."1068 Phe faintest Y-drop in. Bunker et ((2010). YD7. is mareinally too faint (/=28.65) in our new reduction of the LUDE images to enter our new sample.," The faintest $Y$ -drop in Bunker et (2010), YD7, is marginally too faint $J=28.65$ ) in our new reduction of the HUDF images to enter our new sample."1069 However. applying our new colour selection criteria to the old photometry (where J=28.44) would have resulted in the selection of YD.," However, applying our new colour selection criteria to the old photometry (where $J=28.44$ ) would have resulted in the selection of YD7."1070 The remaining one (YD6) is only mareinally too blue for the Lyman-break selection in the newly-reduced data. with Oyios.Jpiesa)=0489. very close to the (Yriossγιου)20.9 cut.," The remaining one (YD6) is only marginally too blue for the Lyman-break selection in the newly-reduced data, with $(Y_{f105w}-J_{f125w})=0.89$, very close to the $(Y_{f105w}-J_{f125w})>0.9$ cut."1071 This object has slight (~ 2260) detections in the ACS bands. too. and does not meet the selection. criterion. (Yos;οτι}0.73(JonaLlisow)| 0.9. so we did not include it in our list.," This object has slight $\sim$ $\sigma$ ) detections in the ACS bands, too, and does not meet the selection criterion $(Y_{105w}-J_{125w}) > 0.73\times (J_{125w}-H_{160w})+0.9$ , so we did not include it in our list."1072 Moreover. no other group has found or listed. this object as a candidate.," Moreover, no other group has found or listed this object as a candidate."1073 Two objects in our new catalog. (IIUDE.YDs. and IHIUDE.YDO) were not found in Bunker et ((2010): our previous study of Y-drops in the ICDL used. slightly cillerent magnitude and. colour cuts (Jag<28.5 and YoJig 1.0). ancl an older reduction ancl photometric zeropoints.," Two objects in our new catalog (HUDF.YD8 and HUDF.YD9) were not found in Bunker et (2010); our previous study of $Y$ -drops in the HUDF used slightly different magnitude and colour cuts $J_{AB}<28.5$ and $(Y-J)_{AB}>1.0$ ), and an older reduction and photometric zeropoints."1074 These two objects were slightly too faint in the previous version of our HUDIE reductions (./=28.59 and J=2855. respectively) and slightly too blue (OYproseγιου.= O77. 0.92 respectively) to be selected with our original criteria in Bunker et ((2010).," These two objects were slightly too faint in the previous version of our HUDF reductions $J=28.59$ and $J=28.55$, respectively) and slightly too blue $(Y_{f105w}-J_{f125w})=0.77$ , $0.92$ respectively) to be selected with our original criteria in Bunker et (2010)."1075 The new candidate HLUDE.YDs lies only Laaresee from the z-drop zD5 in Bunker et ((2010). and it is conceivable that both objects might be physically associated and might have similar redshifts at zὃν ," The new candidate HUDF.YD8 lies only arcsec from the $z$ -drop zD5 in Bunker et (2010), and it is conceivable that both objects might be physically associated and might have similar redshifts at $z\sim 8$."1076We note that no other group has identified LLUDE.YD9 as a candidate., We note that no other group has identified HUDF.YD9 as a candidate.1077 In Table 4 we show the Y -drop galaxy candidates from our LIUDE catalog which have been previously reported with their corresponding catalog names from other groups. while in Table 5. we show all the objects found by these groups," In Table \ref{tab:common} we show the $Y$ -drop galaxy candidates from our HUDF catalog which have been previously reported with their corresponding catalog names from other groups, while in Table \ref{tab:spare} we show all the objects found by these groups"1078"available unipolar potential drop across the polar cap reads The αμα energv of the electrons accelerated iu tlis potential drop is s4a(ομως=7.6104B,oRep-(P/77min) 7.","available unipolar potential drop across the polar cap reads The maximum energy of the electrons accelerated in this potential drop is $\gamma_{e,M} = e \Phi_{\rm max} / m c^2 = 7.6 \times 10^4 B_{p,9}1079{R^3_{\rm WD,8.7}} ({P}/{77~{\rm min}})^{-2}$ ."1080 The potential drop is about 2 orders of magnitudes sinaller than that in radio pulsars., The potential drop is about 2 orders of magnitude smaller than that in radio pulsars.1081 The surface laver of a white dwarf is composcel of a nou-degencrate clectron eas anc possibly an ionic lattice (Shapiro Teulolsky 1983)., The surface layer of a white dwarf is composed of a non-degenerate electron gas and possibly an ionic lattice (Shapiro Teukolsky 1983).1082" The lattice imnelting temperature is T5,~NNονLeτς(p10?CresClu1δεσ 121015, where pis the density iu the surface laver. aud Z is the atoniüc umber (Alestal Ruderman 1967)."," The lattice melting temperature is $T_m \sim 8.8 \times 10^51083~{\rm K}~ (\rho / 10^2 ~{\rm ergs ~ cm^{-3}})^{1/3} (Z/12)^{5/3}$ , where $\rho$ is the density in the surface layer, and $Z$ is the atomic number (Mestal Ruderman 1967)."1084 Given ai typical surface teiiperature 74~«10H K. we can see that eenerallv the surface is in the ionic lattice state.," Given a typical surface temperature $T_s \sim 3 \times 10^4$ K, we can see that generally the surface is in the ionic lattice state."1085 For au anti-parallel rotator. ic. O0.B« where Q and B are the vectors for the rotational and maguetic axes. the polar cap region is populated with positively charged particles.," For an anti-parallel rotator, i.e. ${\bf \Omega \cdot B} < 0$, where ${\bf1086\Omega}$ and ${\bf B}$ are the vectors for the rotational and magnetic axes, the polar cap region is populated with positively charged particles."1087 Ta a co-rotating magnetic white dwarf magnetosphere. whether or not the surface can provide a free ionic flow iuto the polar cap region depends on two factors. ic. whether theriuionic enüssion could overcome the atomic cohesive energv in the surface laver. aud whether the free atoms are adequately ionized.," In a co-rotating magnetic white dwarf magnetosphere, whether or not the surface can provide a free ionic flow into the polar cap region depends on two factors, i.e, whether thermionic emission could overcome the atomic cohesive energy in the surface layer, and whether the free atoms are adequately ionized."1088 In stroug magnetic fields. the ion cohesive cherev is eulianced aud depends on the streneth of the ficld. ic. xBY and is about several hundred eV. for B=10! © for iron (Jones 1986: Usov Melrose 1996).," In strong magnetic fields, the ion cohesive energy is enhanced and depends on the strength of the field, i.e. $\propto1089B^{0.7}$ and is about several hundred eV for $B=10^{12}$ G for iron (Jones 1986; Usov Melrose 1996)."1090 When B is lower than ~10° C. which is the general case of the white dwarf pulsar discussed here. however. the atoms are essentially uot influcucedby the magnetic field (Lai 2001). - that the atom cohesive energies are simular to the B=soM case.," When $B$ is lower than $\sim109110^9$ G, which is the general case of the white dwarf pulsar discussed here, however, the atoms are essentially not influenced by the magnetic field (Lai 2001), so that the atom cohesive energies are similar to the $B=0$ case."1092" For carbon. which is Likely the composition in the WD surface laver. the cohesive cucrey is Ae,~8 eV/atoni and the first ionization euerev of carbon is Ae;~11.3 eV. The Coldveich-Julian (1969) charge umuber deusity at the maguetic pole is a,=GuPee)=1.5105«n3D,o9(PPTOdu) ldfor GCRT J1T15-3009. which is mich lower than the wumber deusitv of carbou atomis iu the surface laver. l6. Varuncpilin,=5.0«10?!cin. Ops."," For carbon, which is likely the composition in the WD surface layer, the cohesive energy is $\Delta\epsilon_c \sim 8$ eV/atom, and the first ionization energy of carbon is $\Delta\epsilon_i \sim 11.3$ eV. The Goldreich-Julian (1969) charge number density at the magnetic pole is $n_{_{\rm1093GJ}}=(B_p/Pce)=1.5 \times 10^4 ~{\rm cm^{-3}}~ B_{p,9} (P/77~{\rm1094min})^{-1}$ for GCRT J1745-3009, which is much lower than the number density of carbon atoms in the surface layer, i.e. $n_{\rm atom} \sim \rho/Am_p = 5.0 \times 10^{24} ~{\rm1095cm^{-3}} \rho_2$ ."1096 For photoionization and thermionic ejection of the ions. even if the ionization/cejection rate decreases exponentially with temperature. the critical enperatures should be still several teus siualler than the enperature defined by the colesiveionization cucrey.," For photoionization and thermionic ejection of the ions, even if the ionization/ejection rate decreases exponentially with temperature, the critical temperatures should be still several tens smaller than the temperature defined by the cohesive/ionization energy."1097" Siuuilar to the troatinent for the neutron star surface (Ruclerman Sutherland 1975: Usov Melrose 1996). or the parameters of CCRT JT15-3009. this reductiou ‘actor ds ~oglZeplGT)?nin)Cn)B,2pDB|=logs 38."," Similar to the treatment for the neutron star surface (Ruderman Sutherland 1975; Usov Melrose 1996), for the parameters of GCRT J1745-3009, this reduction factor is $\sim \log [Z e1098\rho (kT)^{1/2} (Am_p)^{-3/2} P/B]=\log [3.8 \times 10^{16} (kT/2.61099~{\rm eV})^{1/2} (P/77 ~{\rm min}) B_{p,9}^{-1} \rho_2 (Z/6)1100(A/12)^{-3/2} \sim 38$ ."1101 As a result. the critical temperatures for ionization of 1ο carbon atom aud for thernionic ejection of the carbou tonis are ~3.2«10? I and ~2.3«10? Is. respectively. voth are «OT.~«104 K. the typical temperature of je white chwarf surface.," As a result, the critical temperatures for ionization of the carbon atom and for thermionic ejection of the carbon atoms are $\sim 3.2\times 10^3$ K and $\sim 2.3\times 10^3$ K, respectively, both are $\ll T_s \sim 3\times 10^4$ K, the typical temperature of the white dwarf surface."1102 The temperature at the magnetic vole could be cooler (simular to Sunspots). but as long as je temperature is higher than ~3«10? K. the white dwarf surface is able to provide copious ious to supply a Coldreich-Julian space charge linited flow from the xilar cap region (Arous Scharlemaun 1979: Tarding Aluslinov 1998).," The temperature at the magnetic pole could be cooler (similar to Sunspots), but as long as the temperature is higher than $\sim 3\times 10^3$ K, the white dwarf surface is able to provide copious ions to supply a Goldreich-Julian space charge limited flow from the polar cap region (Arons Scharlemann 1979; Harding Muslimov 1998)."1103 Α similay conclusion applies for other surface compositions. as well as for the case of a parallel rotator (OQ.B0) in which case an electron free flow is pplied.," A similar conclusion applies for other surface compositions, as well as for the case of a parallel rotator ${\bf1104\Omega \cdot B} > 0$ ) in which case an electron free flow is supplied."1105 Iu a space-charec-linited flow. a charge depleted region is developed in the polar cap region due to the eeucral relativistic frame draseiug effect (Muslinov Tsvean 1992) and the curvature effect of the maguetic field mes (Arous Scharlemanun 1979).," In a space-charge-limited flow, a charge depleted region is developed in the polar cap region due to the general relativistic frame dragging effect (Muslimov Tsygan 1992) and the curvature effect of the magnetic field lines (Arons Scharlemann 1979)."1106" The ratio between the potential drops developed for these two compoucuts is roushlv (ILudiug Miaslimov 1998) ~(8/0,etary. where \ ds the inclination angle between the magnetic aud the rotational axes. (,. is the opening augle of the polar cap region. &(RF). Ry is the Scluwarzschild radius. aud A. is the radius of the star (neutron star or white dwiutf)."," The ratio between the potential drops developed for these two components is roughly (Harding Muslimov 1998) $\sim (\kappa / \theta_{pc})~ 1107{\rm ctan} \chi$, where $\chi$ is the inclination angle between the magnetic and the rotational axes, $\theta_{pc}$ is the opening angle of the polar cap region, $\kappa \sim (R_g/R_*)$, $R_g$ is the Schwarzschild radius, and $R_*$ is the radius of the star (neutron star or white dwarf)."1108 For neutron star pulsars. the frame-drageine term dominates unless the inclination is near 90 degrees (Warding Abushinov 1998).," For neutron star pulsars, the frame-dragging term dominates unless the inclination is near 90 degrees (Harding Muslimov 1998)."1109" For the white dwart pulsars. with the paramcters of CCRT J1715-3009. we find that αν0,.~10 5 which means that both contributions are comparable."," For the white dwarf pulsars, with the parameters of GCRT J1745-3009, we find that $\kappa \sim \theta_{pc} \sim111010^{-3}$ , which means that both contributions are comparable."1111" The poteutial drop develops with height 7 in the form of (Ixidiug ADuslimov 1998) Oh)-—(2xD,/Pe(h/Rwpy which achieves the maxiuun potential Bas,I. essentially at Ro~Bap."," The potential drop develops with height $h$ in the form of (Harding Muslimov 1998) $\Phi (h) \sim (2 \pi B_p/Pc) R_{pc}^2 (h/R_{\rm1112WD})^2$, which achieves the maximum potential $\Phi_{\rm max}$ essentially at $R \sim R_{\rm WD}$."1113" Without pair production. clectrous iu the acceleration region could gain anu energv close to 54,44."," Without pair production, electrons in the acceleration region could gain an energy close to $\gamma_{e,M}$."1114" Below we take a typical electron Lorentz factor 5,=slot.", Below we take a typical electron Lorentz factor $\gamma_e=5\times 10^4$ .1115 Can the electron-positron. plasua needed by pulsar activity be eeuerated iu such white dwarts?, Can the electron-positron plasma needed by pulsar activity be generated in such white dwarfs?1116 This would require generation of seed eauuna photons with energies well exceeding the electron rest enerev., This would require generation of seed gamma photons with energies well exceeding the electron rest energy.1117 The dipolar field curvature radius in the wme dwarf maguectosphere is very large. Le. py=vanARR.Lbs103ein(RARwpyh?Pj 3 ," The dipolar field curvature radius in the white dwarf magnetosphere is very large, i.e. $\rho_{d}=(4/3)\sqrt{R R_{lc}}=1.4 \times 10^{11} ~{\rm1118cm} ~ (R/R_{\rm WD})^{1/2} (P/77 ~{\rm min})^{1/2}$ ."1119Near the surface. uou-dipolar magnetic fields could develop. as is tle case of the Sun (suuspots) and omeblv also the case of neutron stars (Ruderman Sutherland 1975: Arous Scharlemann 1979: Cal Altra 2001).," Near the surface, non-dipolar magnetic fields could develop, as is the case of the Sun (sunspots) and presumably also the case of neutron stars (Ruderman Sutherland 1975; Arons Scharlemann 1979; Gil Mitra 2001)."1120" However. even if we choose a much xnaller curvature radius. ess p~10? cun the typical curvature radiation energv ds i too snl. Le. eeu,=(3/2)(hepyr?=3.7ονpo well below the pair production threshold."," However, even if we choose a much smaller curvature radius, e.g. $\rho \sim 10^9$ cm, the typical curvature radiation energy is still too small, i.e. $\epsilon_{\rm CR}=(3/2)1121(\hbar c/\rho)\gamma_e^3 = 3.7 ~{\rm eV} ~ \gamma_{e,4.7}^31122\rho_9^{-1}$ , well below the pair production threshold."1123" The typical thermal photou energy is ἐν~2.8&T7.375 ον for T,~3«104 K. Given the vpical electron energv and the streneth of the local maguetic field. the resonant inverse Compton(IC) scattering is uniniportant."," The typical thermal photon energy is $\epsilon_{\rm th} \sim 2.8 k T1124= 7.3 T_{4.5}$ eV for $T_s \sim 3 \times 10^4$ K. Given the typical electron energy and the strength of the local magnetic field, the resonant inverse Compton (IC) scattering is unimportant."1125 The typical resonant IC photon energy (Zhang ct al., The typical resonant IC photon energy (Zhang et al.1126" 1997) is eft,~Se€p=D805,17Dug Κον. hich is slightly larecr than the clectrou vest eneregv ne?=511 keV. but does not mect the pair production threshold."," 1997) is $\epsilon_{\rm IC}^{R} \sim \gamma_{e} \epsilon_{\rm B} =1127580 \gamma_{e,4.7} B_{p,9}$ keV, which is slightly larger than the electron rest energy $m c^2 = 511$ keV, but does not meet the pair production threshold."1128 The most cfiicicut eamuna-ray production nechauisui ina white dwarf maguctosplere is non-resonant iuverse Compton (IC) scattering (Zhang et al., The most efficient gamma-ray production mechanism in a white dwarf magnetosphere is non-resonant inverse Compton (IC) scattering (Zhang et al.1129 1997)., 1997).1130 Thetypical eanuua-ray photon cucrey reads, Thetypical gamma-ray photon energy reads1131We have studied the spin parameter of uniformly rotating compact stars in general relativity.,We have studied the spin parameter of uniformly rotating compact stars in general relativity.1132 Our numerical results show that the behavior of the spin parameter of quark stars is quite different from that of neutron stars., Our numerical results show that the behavior of the spin parameter of quark stars is quite different from that of neutron stars.1133" In particular, the spin parameter of neutron stars is bounded above by jmax£0.7, while quark stars can have a value larger than unity."," In particular, the spin parameter of neutron stars is bounded above by $ j_{\rm max} \approx 0.7$, while quark stars can have a value larger than unity."1134" In this section, we shall discuss (in our view) the astrophysical implications of our results."," In this section, we shall discuss (in our view) the astrophysical implications of our results."1135" First, how could the spin parameter of a compact star be measured?"," First, how could the spin parameter of a compact star be measured?"1136" Unfortunately, so far there is no general technique to infer the spin parameter j of compact stars directly."," Unfortunately, so far there is no general technique to infer the spin parameter $j$ of compact stars directly."1137" As far as we are aware, the spin parameter of a compact star could be potentially measured in disk-accreting compact-star systems."," As far as we are aware, the spin parameter of a compact star could be potentially measured in disk-accreting compact-star systems."1138" In particular, the neutron stars (or quark stars) in low-mass X-ray binaries (LMXBs) provide the most natural cosmic laboratories for studying the spin parameter."," In particular, the neutron stars (or quark stars) in low-mass X-ray binaries (LMXBs) provide the most natural cosmic laboratories for studying the spin parameter."1139" In order to understand how the spin parameter might be inferred in disk-accreting systems, it should be noted that the spin parameter of the central compact star directly affects the particle motion around the star."," In order to understand how the spin parameter might be inferred in disk-accreting systems, it should be noted that the spin parameter of the central compact star directly affects the particle motion around the star."1140" For example, to first order in j, the orbital frequency of a point particle in a prograde orbit around a compact star is given by (see, e.g., vanderKlis (2006))) where is the orbital radius."," For example, to first order in $j$, the orbital frequency of a point particle in a prograde orbit around a compact star is given by (see, e.g., \citet{van_der_klis2006}) ) where $r$ is the orbital radius."1141" For infinitesimally tilted and eccentricr orbits, the disk particles will have radial (v.) and vertical (vg) epicyclic frequencies which also depend on j vanderKlis(2006) for the expressions)."," For infinitesimally tilted and eccentric orbits, the disk particles will have radial $\nu_r$ ) and vertical $\nu_\theta$ ) epicyclic frequencies which also depend on $j$ (see \citet{van_der_klis2006} for the expressions)."1142" Furthermore, (seethe combination vg—v, also gives rise to the periastron frequency of the orbit."," Furthermore, the combination $\nu_\theta - \nu_r$ also gives rise to the periastron frequency of the orbit."1143" These frequencies in general depend on M and j, and hence their observations (possibly needed to be combined with the measurement of other stellar parameters such as the mass) would in principle provide useful information on the spin parameter."," These frequencies in general depend on $M$ and $j$, and hence their observations (possibly needed to be combined with the measurement of other stellar parameters such as the mass) would in principle provide useful information on the spin parameter."1144" In fact, there are strong evidences that these frequencies have already been observed in LMXBs."," In fact, there are strong evidences that these frequencies have already been observed in LMXBs."1145" It should be noted that existing algebraic relations, such as Equation (1)) which relate various orbital frequencies to stellar parameters are in general only valid for small spin rate j~0.1."," It should be noted that existing algebraic relations, such as Equation \ref{eq:orbital_freq}) ), which relate various orbital frequencies to stellar parameters are in general only valid for small spin rate $j \sim 0.1$."1146 The difficulty of obtaining the corresponding algebraic relations for rapidly rotating stars (j~ 1) lies in the fact that there is no exact analytic representation of the vacuum spacetime outside a rapidly rotating compact star., The difficulty of obtaining the corresponding algebraic relations for rapidly rotating stars $j \sim 1$ ) lies in the fact that there is no exact analytic representation of the vacuum spacetime outside a rapidly rotating compact star.1147 Having such an analytic representation of the spacetime metric will allow one to obtain the desired algebraic relations for a rapidly rotating compact star., Having such an analytic representation of the spacetime metric will allow one to obtain the desired algebraic relations for a rapidly rotating compact star.1148 A starting point along this direction would be to take the closed-form asymptotically flat solution of the Einstein-Maxwell system obtained by Mankoetal. and study the geodesics in this spacetime., A starting point along this direction would be to take the closed-form asymptotically flat solution of the Einstein-Maxwell system obtained by \citet{manko2000} and study the geodesics in this spacetime.1149" If (2000)there is no charge and magnetic moment, this analytic solution depends only on the mass, angular momentum, and quadrupole moment of the spacetime."," If there is no charge and magnetic moment, this analytic solution depends only on the mass, angular momentum, and quadrupole moment of the spacetime."1150" Furthermore, this solution only involves rational functions, which helps to simplify the analytical study of geodesic motions."," Furthermore, this solution only involves rational functions, which helps to simplify the analytical study of geodesic motions."1151" Berti&Stergioulas(2004) have demonstrated that this analytic solution can describe the exterior spacetime of a rapidly rotating neutron star (e.g., j> 0.5) very well."," \citet{berti2004} have demonstrated that this analytic solution can describe the exterior spacetime of a rapidly rotating neutron star (e.g., $j > 0.5$ ) very well."1152" Nevertheless, further investigation is needed to check whether this analytic solution is also valid for rapidly rotating quark stars."," Nevertheless, further investigation is needed to check whether this analytic solution is also valid for rapidly rotating quark stars."1153 One of the well-observed features of LMXBs is the high-frequency (~ kHz) QPOs., One of the well-observed features of LMXBs is the high-frequency $\sim$ kHz) QPOs.1154" To date, QPOs have been observed in more than 20 LMXBs."," To date, QPOs have been observed in more than 20 LMXBs."1155 These QPOs often come in pairs with frequencies νι and νι., These QPOs often come in pairs with frequencies $\nu_u$ and $\nu_l$ .1156" In all systems in which the spin frequencies of the compact Stars Vstar have been measured, the frequency separation Av=v,—νι is approximately equal to vaa: OF Vstar/2."," In all systems in which the spin frequencies of the compact stars $\nu_{\rm star}$ have been measured, the frequency separation $\Delta \nu = \nu_u - \nu_l$ is approximately equal to $\nu_{\rm star}$ or $\nu_{\rm star}/2$."1157 We refer the reader to vanderKlis(2006) and Lamb for recent reviews., We refer the reader to \citet{van_der_klis2006} and \citet{lamb2008} for recent reviews.1158" While the physical mechanism responsible for producing the high-frequency QPOs is not known yet, most physical models involve orbital motion and disk oscillations."," While the physical mechanism responsible for producing the high-frequency QPOs is not known yet, most physical models involve orbital motion and disk oscillations."1159" Hence, the frequencies ν,, vg, and various combinations of them are often invoked v; directly or indirectly) to explain high-frequency QPOs."," Hence, the frequencies $\nu_r$, $\nu_\theta$, $\nu_\phi$ and various combinations of them are often invoked (either directly or indirectly) to explain high-frequency QPOs."1160 (eitherThis is the reason why one might hope to obtainuseful information on the spin parameter of the central compact star in an LMXB by observing, This is the reason why one might hope to obtainuseful information on the spin parameter of the central compact star in an LMXB by observing1161lines are overplotted in red on the observed spectra in black in the bottom panels.,lines are overplotted in red on the observed spectra in black in the bottom panels.1162" Our analysis has shown that the spectra of the B[e]SGs 773 and 112 display emission from the !?CO band heads (see reffig:fits)) which means that their circumstellar disk material is strongly enriched with 12Ο; hence, these stars are indeed evolved post-main sequence objects."," Our analysis has shown that the spectra of the B[e]SGs 73 and 12 display emission from the $^{13}$ CO band heads (see \\ref{fig:fits}) ) which means that their circumstellar disk material is strongly enriched with $^{13}$ C; hence, these stars are indeed evolved post-main sequence objects."1163 Our model computations have also confirmed the relatively low temperature of the CO gas as indicated by the about equal strengths of the !*CO band heads., Our model computations have also confirmed the relatively low temperature of the CO gas as indicated by the about equal strengths of the $^{12}$ CO band heads.1164" Such low temperatures are not expected within the canonical picture of B[e]SGs, which assumes that their disks are formed by enhanced mass flux from the stars’ equatorial regions."," Such low temperatures are not expected within the canonical picture of B[e]SGs, which assumes that their disks are formed by enhanced mass flux from the stars' equatorial regions."1165" If the disks of the two B[e]SGs studied here were continuously supplied, then the CO in the gaseous parts of the disk should be visible from the hottest component having temperatures close to the CO dissociation temperature of KK. In this case the observable CO band spectrum, which always reflects the hottest available CO component, would be dominated by the peaks of the higher vibrational transitions occurring at longer wavelengths, while the lowest band head (at um) would be strongly suppressed (seeKraus2009)."," If the disks of the two B[e]SGs studied here were continuously supplied, then the CO in the gaseous parts of the disk should be visible from the hottest component having temperatures close to the CO dissociation temperature of K. In this case the observable CO band spectrum, which always reflects the hottest available CO component, would be dominated by the peaks of the higher vibrational transitions occurring at longer wavelengths, while the lowest band head (at $\mu$ m) would be strongly suppressed \citep[see][]{Kraus09}."1166. The apparent deficiency in CO gas hotter that ~2800 KK therefore suggests that there is no CO gas closer to the star., The apparent deficiency in CO gas hotter that $\sim 2800$ K therefore suggests that there is no CO gas closer to the star.1167" Hence, the disks seen around 112 and 773 cannot extend down to the stellar surface."," Hence, the disks seen around 12 and 73 cannot extend down to the stellar surface."1168 Instead it would be more appropriate to assume that the stars are surrounded by a dense and coolring of material., Instead it would be more appropriate to assume that the stars are surrounded by a dense and cool of material.1169 Support for such a scenario comes from the recent detection of a detached ring in quasi-Keplerian rotation around the Small Magellanic Cloud (SMC) B[e]SG star 665 (Krausetal.2010)., Support for such a scenario comes from the recent detection of a detached ring in quasi-Keplerian rotation around the Small Magellanic Cloud (SMC) B[e]SG star 65 \citep{Kraus2010}.1170". Alternatively, gravitational darkening according to the von Zeipel theorem (vonZeipel1924) in rapidly rotating stars can lead to equatorial temperatures being sufficiently low (i.e., S3000 KK) for the hottest CO gas to not exceed ~2800 KK. In this picture, the disk still could extend from the stellar surface out to large distances, with the CO emitting gas located closest to the star within the innermost, hottest disk region."," Alternatively, gravitational darkening according to the von Zeipel theorem \citep{vonZeipel} in rapidly rotating stars can lead to equatorial temperatures being sufficiently low (i.e., $\la 3000$ K) for the hottest CO gas to not exceed $\sim 2800$ K. In this picture, the disk still could extend from the stellar surface out to large distances, with the CO emitting gas located closest to the star within the innermost, hottest disk region."1171" While this scenario is somewhat speculative (and heating of the disk through light from hotter regions of the star would have to be considered as well), we can estimate the minimum rotation speed of the stars required to achieve an equatorial surface temperature of KK. Stellar rotation leads the poles to be hottest."," While this scenario is somewhat speculative (and heating of the disk through light from hotter regions of the star would have to be considered as well), we can estimate the minimum rotation speed of the stars required to achieve an equatorial surface temperature of K. Stellar rotation leads the poles to be hottest."1172" Assuming that both stars are seen pole-on and that their effective temperatures, To, listed in reftab:parameters correspond to the polar values, requires a decrease in Τομ from polar to equatorial values by factors of 7.7 112) and 4 773)."," Assuming that both stars are seen pole-on and that their effective temperatures, $T_{\rm eff}$, listed in \\ref{tab:parameters} correspond to the polar values, requires a decrease in $T_{\rm eff}$ from polar to equatorial values by factors of 7.7 12) and 4 73)."1173" This, in turn, requires the stars to rotate with >>99% of their critical velocity (seeFig.5ofKraus2006)."," This, in turn, requires the stars to rotate with $\gg117499\%$ of their critical velocity \citep[see Fig.\,5 of][]{Kraus06}."1175". The assumed pole-on orientation only provides us withlimits of the real rotation velocity, but even in the unexpected case that both stars are seen perfectly pole-on, rotation rates close to or even at the critical limit are highly unlikely."," The assumed pole-on orientation only provides us with of the real rotation velocity, but even in the unexpected case that both stars are seen perfectly pole-on, rotation rates close to or even at the critical limit are highly unlikely."1176" For comparison, the two most rapidly rotating B[e]SGs known, the SMC stars S223 and 665, rotate with =75% of their critical velocity (Zickgraf2000;Krausetal.2008,2010)."," For comparison, the two most rapidly rotating B[e]SGs known, the SMC stars 23 and 65, rotate with $\ga 75\%$ of their critical velocity \citep{Zickgraf00, Kraus08, Kraus2010}."1177". If our program stars rotated at ~75% of their critical velocity, resulting equatorial temperatures would still be ~72% of the polar values (cf. reftab:parameters)),"," If our program stars rotated at $\sim 75\%$ of their critical velocity, resulting equatorial temperatures would still be $\sim 72\%$ of the polar values (cf. \\ref{tab:parameters}) ),"1178" i.e. much hotter than KK. The deficiency of CO gas hotter than KK is thus real, and the most plausible scenario is hence that the molecular gas is located within a detached ring of material rather than in a disk extending down to the stellar surface."," i.e. much hotter than K. The deficiency of CO gas hotter than K is thus real, and the most plausible scenario is hence that the molecular gas is located within a detached ring of material rather than in a disk extending down to the stellar surface."1179" In we include the sizes of the CO emitting regions (projected to the line of sight, Acocos i) as obtained from our"," In \\ref{tab:bestfit} we include the sizes of the CO emitting regions (projected to the line of sight, $A_{\rm CO} \cos{i}$ ) as obtained from our"1180"Gamma-Ray Bursts (GRBs) without an optical counterpart of their X-ray afterglow are usually called ""dark bursts”: a more precise definition based on their X-ray to optical spectral energy distribution (SED) has been proposed (Jakobssonetal.2004:Rol2005:vanderHorstetal. 2009).","Gamma-Ray Bursts (GRBs) without an optical counterpart of their X-ray afterglow are usually called “dark bursts”; a more precise definition based on their X-ray to optical spectral energy distribution (SED) has been proposed \citep{jakobsson04,rol05,vanderhorst09}."1181. It is clear now that in most cases extinction by dust in their host galaxies makes these afterglows optically dim (Greineretal.20101).. while cosmological Lyman drop out (high redshift) or intrinsic faintness are the exception rather than the rule (Cenkoetal.2009;Perley 2011).," It is clear now that in most cases extinction by dust in their host galaxies makes these afterglows optically dim \citep{greiner11}, while cosmological Lyman drop out (high redshift) or intrinsic faintness are the exception rather than the rule \citep[][]{cenko09,perley09,rossi11}."1182 The long-duration lis one of these truly dark GRBs., The long-duration is one of these truly dark GRBs.1183 It was detected by Swiftf/BAT on 2008 February 7 at 21:30:21 UT., It was detected by /BAT on 2008 February 7 at 21:30:21 UT.1184 Swift/XRT began observing the field 124 s after the BAT trigger and found a bright X-ray afterglow. with a positional uncertainty radius of 1744 (Racusinetal. 2008a).," /XRT began observing the field 124 s after the BAT trigger and found a bright X-ray afterglow, with a positional uncertainty radius of 4 \citep{racusin08a}."1185. No optical/near-infrared afterglow was detected for080207.. despite heroic efforts by several ground-based observatories.," No optical/near-infrared afterglow was detected for, despite heroic efforts by several ground-based observatories."1186 The deepest limit relative to the fading X-ray afterglow was achieved by the Zeiss-600 telescope at Mt.Terskol observatory which did not detect the afterglow down to Rag>20.5 at 1.69 hr after the burst (Andreevetal, The deepest limit relative to the fading X-ray afterglow was achieved by the Zeiss-600 telescope at Mt.Terskol observatory which did not detect the afterglow down to $R_{\rm AB}>20.5$ at 1.69 hr after the burst \citep{andreev08}.1187.2005). Racusinetal.(2008b.c) report that the XRT light curve between |.30hhr and hhr after the GRB start time declines monotonically with a power-law of index ay=1.85+0.10.," \citet{racusin08b,racusin08c} report that the XRT light curve between hr and hr after the GRB start time declines monotonically with a power-law of index $\alpha_X=1.85\pm0.10$."1188" Therefore. we have assumed that the optical light curve in the same time interval is also decreasing monotonically. so that its behavior is sufficiently regular that the criterion of Jakobssonetal.(2004) to define GRB ""darkness"" — based on the comparison of the X-ray and optical flux levels at hhr — can be applied to the optical upper limit Rap>20.5 measured at 1.69 hr after the trigger."," Therefore, we have assumed that the optical light curve in the same time interval is also decreasing monotonically, so that its behavior is sufficiently regular that the criterion of \citet{jakobsson04} to define GRB “darkness” – based on the comparison of the X-ray and optical flux levels at hr – can be applied to the optical upper limit $R_{\rm AB}>20.5$ measured at 1.69 hr after the trigger."1189 The X-ray flux at 1.69 hr is ~0.35 c/s (~3.1x100! eem). which. assuming the spectral index fitted by Racusin et al.," The X-ray flux at 1.69 hr is $\sim$ 0.35 c/s $\sim11903.1 \times 10^{-11}$ $^{-1}$ $^{2}$ ), which, assuming the spectral index fitted by Racusin et al."1191 to the average XRT spectrum in the above time interval.By=1440.2. corresponds to a kkeV flux of 4.2 jJy.," to the average XRT spectrum in the above time interval, $\beta_{X}=1.4\pm0.2$, corresponds to a keV flux of 4.2 $\mu$ Jy."1192 Together with thesimultaneous optical upper limit. this yields an. optical-to-X-ray index of Box<0.27. which leads to à dark GRB classification. according. to Jakobssonetal.(2004) and vanderHorstetal.(2009).," Together with thesimultaneous optical upper limit, this yields an optical-to-X-ray index of $\beta_{OX} < 0.27$, which leads to a dark GRB classification, according to \citet{jakobsson04} and \citet{vanderhorst09}."1193 In the vicinity of the XRT error circle. Rossietal.(2011) found two very faint host candidates. one better visible in VIMOS/R-band and the second brighter in Κ.," In the vicinity of the XRT error circle, \citet{rossi11} found two very faint host candidates, one better visible in $R$ -band and the second brighter in $K$."1194" However. the satellite observed the field of nnine days after the burst detection bySwiff (Racusinetal.2008a).. and was able to localize the GRB X-ray afterglow with very high accuracy of 07667 (Evans @== 113:50:02.97, 6 007:30:07.8 (J2000)."," However, the satellite observed the field of nine days after the burst detection by \citep{racusin08a}, and was able to localize the GRB X-ray afterglow with very high accuracy of 67 \citep{evans10}: $\alpha$ 13:50:02.97, $\delta$ 07:30:07.8 (J2000)."1195" This position. coincides with one of the candidates found by Rossietal.(2011)— (source ""Bk a very faint (Raz- mmag). very red [R-K26. (R-Κα~4.7] galaxy."," This position coincides with one of the candidates found by \citet{rossi11} (source “B”): a very faint $R_{\rm AB}\sim$ mag), very red $R-K\ga$ 6, $(R-K)_{\rm AB}\sim4.7$ ] galaxy."1196" The other candidate 1s bluer (dubbed""A""by.Rossietal.2011). with (R—K)ag.~2.1. and located just outside the XRT error circle. ~ 2733 northeast of the position."," The other candidate is bluer \citep[dubbed ``A'' by ][]{rossi11}, with $(R-K)_{\rm AB}\sim2.1$, and located just outside the XRT error circle, $\sim$ 3 northeast of the position."1197 Hence we associate the first source (B) with080207., Hence we associate the first source (B) with.1198. In this Letter. we present proprietary and archival optical and near-infrared (NIR) observations. combined with archival IIRAC and MIPS data of the host of080207.," In this Letter, we present proprietary and archival optical and near-infrared (NIR) observations, combined with archival IRAC and MIPS data of the host of."1199. We estimate the photometric redshift oof the host by fitting the observed SED with a vast library of GRASIL models (Silvaetal.1998:[glestas-Páramoetal.2007;Michalowski2008. 2010).," We estimate the photometric redshift of the host by fitting the observed SED with a vast library of GRASIL models \citep{silva98,iglesias07,michal08,michal10}."1200 Despite its optical faintness. because of the clear photospherie NIR bump at rest-frame .t=micron.. we are able to estimate the redshift of the host of wwith a precision of £0.3.," Despite its optical faintness, because of the clear photospheric NIR bump at rest-frame $\lambda$, we are able to estimate the redshift of the host of with a precision of $\pm$ 0.3."

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