ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Identifications were made using likelihood ratio tests aud by comparing optical aud near-IR nuages with the morphology of the N-rav source., Identifications were made using likelihood ratio tests and by comparing optical and near-IR images with the morphology of the X-ray source.3 27 of the stars were identified morphologically or through positional aligmiment of an N-ray source with a bright star., 27 of the stars were identified morphologically or through positional alignment of an X-ray source with a bright star.4 A further 21 stellar identifications were made by fitting multi-waveleusthi photometry to the spectral energy. distributions (SEDs) of templates taken from ?).. while the remaining 13 were identified spectroscopically frou dedicated COSMOS spectroscopic campaigns (see Section 2.2. for more details).," A further 21 stellar identifications were made by fitting multi-wavelength photometry to the spectral energy distributions (SEDs) of templates taken from \citet{salv09}, while the remaining 13 were identified spectroscopically from dedicated COSMOS spectroscopic campaigns (see Section \ref{s-spectra} for more details)."5" In many cases these sources were identified as stars by multiple methods (ο,ο, photometrically identified and then coufirmmed spectroscopicallv).", In many cases these sources were identified as stars by multiple methods (e.g. photometrically identified and then confirmed spectroscopically).6 The majority of the remaining Chandra-COSMOS sources were identified as galaxies based on the above methods. with oulv 11 sources reaming unidenti&ed bv ?7): 2 of these have uo ideuti&able counterpart aud 9 either have imultiple possible counterparts or are either associated with fait optical sources in close augular proximity to bright stars or galaxies. such that their properties cannot be studied.," The majority of the remaining -COSMOS sources were identified as galaxies based on the above methods, with only 11 sources remaining unidentified by \citet{civa10}: 2 of these have no identifiable counterpart and 9 either have multiple possible counterparts or are either associated with faint optical sources in close angular proximity to bright stars or galaxies, such that their properties cannot be studied."7 Statistically. based ou the 1750 ideutificatious iade. of which only are stars. the 11 nnideutified sources are likely to be ealaxies.," Statistically, based on the 1750 identifications made, of which only are stars, the 11 unidentified sources are likely to be galaxies."8 Since the extraction and characterization of COSAIOS sources performed by tle survey collaboration has been conducted on the basis that they are extragalactic sources (which have different morphological and spectral properties to stellar sources) we have re-analyzed the observations of the stellar sources assuiuing that they are stellar., Since the extraction and characterization of COSMOS sources performed by the survey collaboration has been conducted on the basis that they are extragalactic sources (which have different morphological and spectral properties to stellar sources) we have re-analyzed the observations of the stellar sources assuming that they are stellar.9 Thiswas done using 1.2 (2).. CALDB 1.2.2. aud the ACIS code (AE.7) usine the method outlined in ?)..," Thiswas done using 4.2 \citep{frus06}, CALDB 4.2.2, and the ACIS code \citep[AE,][]{broo02} using the method outlined in \citet{wrig09a}."10 To stuumarize. AE uses a variety of point spread fictions (PSFs) appropriate for the off-axis anele of cach observation of cach source to extract photons m a set fraction of the PSF (typically 90543).," To summarize, AE uses a variety of point spread functions (PSFs) appropriate for the off-axis angle of each observation of each source to extract photons in a set fraction of the PSF (typically )."11 The backeround is estimated from a region surroundius this PSF that excludes tlhe PSFs of other sources., The background is estimated from a region surrounding this PSF that excludes the PSFs of other sources.12" From these extractions. AE calculates a source significance aud the Poisson probability. D,,4. hat the source counts are a superposition of backeround ohotous."," From these extractions, AE calculates a source significance and the Poisson probability, $P_{not}$, that the source counts are a superposition of background photons."13 At this point all sources were inspected visually and compared to the position of their designated optical counterpart to confini their association., At this point all sources were inspected visually and compared to the position of their designated optical counterpart to confirm their association.14" We then applied a cut to the sample. discarding auv sources that had a ugher probability of being a false source than of being a real source (Le. D,,;20.5). which resulted in oue source vcing discarded aud reduced our sample to GO sources."," We then applied a cut to the sample, discarding any sources that had a higher probability of being a false source than of being a real source (i.e. $P_{not} > 0.5$ ), which resulted in one source being discarded and reduced our sample to 60 sources."15 This rather liberal cut level was chosen to maintain a Hel level of completeness with respect to the existingChandra COSMOS catalog., This rather liberal cut level was chosen to maintain a high level of completeness with respect to the existing COSMOS catalog.16" Spectral fitting was performed for the 27 sources with 220 net counts using version 12.6.0 91,", Spectral fitting was performed for the 27 sources with $>20$ net counts using version 12.6.0 \citep{arna96}.17 The spectra were compared to (7) spectra corresponding to sinele-temperature thermal plasma nodels (7) in collisional ionization equilibrium aud absorbed by a hydrogen column density using the model (2)., The spectra were compared to \citep{smit01} spectra corresponding to single-temperature thermal plasma models \citep{raym77} in collisional ionization equilibrium and absorbed by a hydrogen column density using the model \citep{balu92}.18. Due to the low Galactic extinetion iu he COSMOS sieht-line the hydrogen column density was allowed to vary ouly up to the maxiuun value for the field of ~2«1029 2 (?2).. while the thermal plasma cluperature was allowed to vary freely.," Due to the low Galactic extinction in the COSMOS sight-line the hydrogen column density was allowed to vary only up to the maximum value for the field of $\sim 2 \times 10^{20}$ $^{-2}$ \citep{kalb05}, while the thermal plasma temperature was allowed to vary freely."19 A exid of initial hermal plasma temperatures covering AL=0.7—2.6 was used to prevent fitting local minima and the model with the lowest C-statistic (?) was then used for each source., A grid of initial thermal plasma temperatures covering $kT = 0.7-2.6$ was used to prevent fitting local minima and the model with the lowest C-statistic \citep{cash79} was then used for each source.20 Two-temperature thermal plasma models were also tested for these sources. but only the brisehtest source. 516. had sufficient couuts to produce a joticeably better fit using a two-component model.," Two-temperature thermal plasma models were also tested for these sources, but only the brightest source, 546, had sufficient counts to produce a noticeably better fit using a two-component model."21 For he 33 sources with less than 20 net counts we used he method outlined iu 7?) to calculate N-rav. fluxes roni count rates and median photon energies, For the 33 sources with less than 20 net counts we used the method outlined in \citet{getm10} to calculate X-ray fluxes from count rates and median photon energies.22" Since he hydrogen colui density in our field of view (FoV) is neelieible. we use apparent X-ray fluxes as intrinsic Ηχος,"," Since the hydrogen column density in our field of view (FoV) is negligible, we use apparent X-ray fluxes as intrinsic fluxes."23" Uncertainties on these fluxes are not specified individually, but were determüued statistically bv. 2).."," Uncertainties on these fluxes are not specified individually, but were determined statistically by \citet{getm10}."24 They are an approxinate function of the net counts of he source and range from for sources with ~20 net counts to >TO% forsources with «5 net counts., They are an approximate function of the net counts of the source and range from for sources with $\sim$ 20 net counts to $> 70$ forsources with $< 5$ net counts.25 The X-ray properties of the 60 retained sources are isted iu Table 1.., The X-ray properties of the 60 retained sources are listed in Table \ref{xstars_cosmos}.26 With the exception of a single very xieht source (CID 516). the majority of sources have count rates of 107—7. appropriate for a sample owed on observations of 100-200. ks and a source detectiono procedure that has extracted sources down/ to ~3 net counts.," With the exception of a single very bright source (CID 546), the majority of sources have count rates of $10^{-5} - 10^{-3}$, appropriate for a sample based on observations of 100-200 ks and a source detection procedure that has extracted sources down to $\sim$ 3 net counts."27 Optical aud ucar-IR photometry was taken from the COSMOS optical that include data from the Sloan Digital Sky Survey (SDSS. ?).. the Subaru photometric catalog (?).. aud the CFUT*//Meeacam catalog (?)..," Optical and near-IR photometry was taken from the COSMOS optical that include data from the Sloan Digital Sky Survey \citep[SDSS,][]{york00}, , the Subaru photometric catalog \citep{capa07}, , and the /Megacam catalog \citep{mccr10}. ."28 For the brightest sources that saturate im the deep COSMOS catalogs we complemented this data, For the brightest sources that saturate in the deep COSMOS catalogs we complemented this data29predictions of the unmodified SCM prior to turnaround ὃ«5.6.,predictions of the unmodified SCM prior to turnaround $\bar{\delta} < 5.6$.30" We found a best fit value of Ryir/Rta=0.5896, which is fairly close to the value of 0.5 that is generally used in the spherical collapse model, despite the fact that we did not constrained it to be so."," We found a best fit value of $R_{vir}/R_{ta} = 0.5896$, which is fairly close to the value of $0.5$ that is generally used in the spherical collapse model, despite the fact that we did not constrained it to be so."31" For comparison, the improved spherical collapsedeveloped by Engineeretal. gave Ryir/Rta©0.65, and N-body simulations(2000) have been found to support Roir/Rta70.56 (Hamiltonetal."," For comparison, the improved spherical collapsedeveloped by \citet{Engineer:2000} gave $R_{vir}/R_{ta} \approx 0.65$, and N-body simulations have been found to support $R_{vir}/R_{ta} \approx 0.56$ \citep{Hamilton:1991}."32 Our value of Ryir/Rta is therefore a better approximation1991).. to the value found from simulations than that generally used in the unmodified SCM and that found in the model developed by Engineeretal.(2000)., Our value of $R_{vir}/R_{ta}$ is therefore a better approximation to the value found from simulations than that generally used in the unmodified SCM and that found in the model developed by \citet{Engineer:2000}.33". In our improved SCM the linear density contrast is given by: When ój;,=1.6865, which corresponds to the instant of collapse in the unmodified SCM, we find 6=54.65 rather than the SCM’s value of 178."," In our improved SCM the linear density contrast is given by: When $\delta_{lin} = 1.6865$, which corresponds to the instant of collapse in the unmodified SCM, we find $\bar{\delta} = 54.65$ rather than the SCM's value of $178$."34 We find that 6=200 corresponds to 6jin=2.286., We find that $\bar{\delta} = 200$ corresponds to $\delta_{lin} = 2.286$.35" We compare the form of found in our model to that predicted by the unmodifiedO(dum) SCM model, with virialisation put in by hand, in FIG. 3.."," We compare the form of $\bar{\delta}(\bar{\delta}_{lin})$ found in our model to that predicted by the unmodified SCM model, with virialisation put in by hand, in FIG. \ref{fig3}."36" We also show the divergent behaviour of 6(duin) in the standard SCM without virialisation, and the asymptotic behaviour of if Ria=1.8Ryir as suggested by simulations (Hamiltonó(0j;4)etal. 1991).."," We also show the divergent behaviour of $\bar{\delta}(\bar{\delta}_{lin})$ in the standard SCM without virialisation, and the asymptotic behaviour of $\bar{\delta}(\bar{\delta}_{lin})$ if $R_{ta} = 1.8 R_{vir}$ as suggested by simulations \citep{Hamilton:1991}. ."37 The two major advantages of our improved SCM over the unmodified version are clearly visible in this plot:, The two major advantages of our improved SCM over the unmodified version are clearly visible in this plot:38540.,.395. The contours of wo and wa are plotted in Fig. 1((, The contours of $w_0$ and $w_a$ are plotted in Fig. \ref{u2cont}( (40"a), andthe contours of Q, and £2; are plotted in Fig. 4((","a), andthe contours of $\Omega_m$ and $\Omega_k$ are plotted in Fig. \ref{u2omkcont}( ("41b).,b).42" For the flat CPL model, Om(z) becomes where Cpz(z) is defined in equation (27)) with Q,=0."," For the flat CPL model, $Om(z)$ becomes where $\Omega_{DE}(z)$ is defined in equation \ref{cplde}) ) with $\Omega_k=0$."43" By fitting the combined data to the flat CPL model, we get the marginalized 1σ constraints, Qm=0,26Τ 10013, wo= —1.05*0-17, and wa=0.077032 with x?=541.1."," By fitting the combined data to the flat CPL model, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.267^{+0.019}_{-0.01}$ , $w_0=-1.05^{+0.17}_{-0.1}$ , and $w_a=0.07^{+0.32}_{-0.88}$ with $\chi^2=541.1$."44" Using this result, we reconstruct Om(z) with equation (28)) and the result is shown in Fig. 2(("," Using this result, we reconstruct $Om(z)$ with equation \ref{cplomz}) ) and the result is shown in Fig. \ref{u2omz}( ("45a).,a).46" For the Jassal-Bagla-Padmanabhan (JBP) parametrization (Jassal,Bagla&Padmanabhan 2005),, the equation of state parameter is so w(z=0)wo and w(z)~wo when z>1."," For the Jassal-Bagla-Padmanabhan (JBP) parametrization \citep{jbp}, the equation of state parameter is so $w(z=0)=w_0$ and $w(z)\sim w_0$ when $z\gg 1$."47" In this model, the parameter wo determines the property of the equation of state parameter w(z) at both low and high redshifts."," In this model, the parameter $w_0$ determines the property of the equation of state parameter $w(z)$ at both low and high redshifts."48" The corresponding dimensionless dark energy density is then where Q,=1—O4, Ωμ.", The corresponding dimensionless dark energy density is then where $\Omega_x=1-\Omega_{m}-\Omega_r-\Omega_{k}$ .49" In thismodel, we also have four parameters p=(Qm,Qe,Wo, Wa)."," In thismodel, we also have four parameters $\mathbf{p}=(\Omega_{m},\ \Omega_{k}, \ w_0, \ w_a)$ ."50" Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and H(z) data, we get the marginalized 1c constraints, (2,=0651001, Qu,=0.004+ 0.006, wo= —1.21*075. and wa=1.297533 with x?=540.6."," Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.263^{+0.02}_{-0.01}$, $\Omega_k=0.004\pm 0.006$ , $w_0=-1.21^{+0.32}_{-0.18}$ , and $w_a=1.29^{+1.35}_{-2.33}$ with $\chi^2=540.6$."51" The contours of Ωμ, and CQ; are plotted in Fig. 4((", The contours of $\Omega_m$ and $\Omega_k$ are plotted in Fig. \ref{u2omkcont}( (52"c), and the contours of wo and wa are plotted in Fig. 1((","c), and the contours of $w_0$ and $w_a$ are plotted in Fig. \ref{u2cont}( ("53b).,b).54" For the flat JBP model, Om(z) becomes where Qpg(z) is defined in equation (30)) with 0."," For the flat JBP model, $Om(z)$ becomes where $\Omega_{DE}(z)$ is defined in equation \ref{jbpde}) ) with $\Omega_k=0$ ."55" By fitting the combined data to the flat JBP model, we get the marginalized 1c constraints, Qm=0.26570017. wo= 1.087376, and wa=0.32*12 with x?=541.0."," By fitting the combined data to the flat JBP model, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.265^{+0.019}_{-0.011}$, $w_0=-1.08^{+0.24}_{-0.19}$ , and $w_a=0.32^{+1.01}_{-1.72}$ with $\chi^2=541.0$."56" Using this result, we reconstruct Om(z) with equation (31)) and the result is shown in Fig. 2(("," Using this result, we reconstruct $Om(z)$ with equation \ref{jbpomz}) ) and the result is shown in Fig. \ref{u2omz}( ("57b).,b).58" Now we consider the parametrization proposed by Wetterich (2004)., For this model, w(z=0)wo and w(z)~0 when z> 1, so the behaviour of w(z) at high redshift is limited."," Now we consider the parametrization proposed by \cite{wetterich}, For this model, $w(z=0)=w_0$ and $w(z)\sim 0$ when $z\gg 1$ , so the behaviour of $w(z)$ at high redshift is limited."59" The dark energy density is In thismodel, the model parameters are p=(Qu,Qk,Wo, Wa)."," The dark energy density is In thismodel, the model parameters are $\mathbf{p}=(\Omega_{m},\ \Omega_{k}, \ w_0, \ w_a)$ ."60" Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and H(z) data, we get the marginalized lo constraints, Qn=0.264+0.013, Q,=0.00910005, wo=—117*025, and wa=0.327946 with x?=540.4."," Fitting the model to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.264\pm 0.013$, $\Omega_k=0.009^{+0.014}_{-0.005}$, $w_0=-1.17^{+0.09}_{-0.23}$, and $w_a=0.32^{+0.46}_{-0.16}$ with $\chi^2=540.4$."61 The contours of wo and we are plotted in Fig. 1((, The contours of $w_0$ and $w_a$ are plotted in Fig. \ref{u2cont}( (62"c), and the contours of Qm and €), are plotted in Fig. 4((","c), and the contours of $\Omega_m$ and $\Omega_k$ are plotted in Fig. \ref{u2omkcont}( ("63d).,d).64" For the flat Wetterich model, Om(z) becomes where Qpz(z) is defined in equation (33)) with Q,=0."," For the flat Wetterich model, $Om(z)$ becomes where $\Omega_{DE}(z)$ is defined in equation \ref{wetde}) ) with $\Omega_k=0$."65" By fitting the combined data to the flat Wetterich model, we get the marginalized 1σ constraints, Qn=0.26675015, wo= —1.05*005, and wa=0.14+0.1 with X?=541.1."," By fitting the combined data to the flat Wetterich model, we get the marginalized $1\sigma$ constraints, $\Omega_m=0.266^{+0.01}_{-0.015}$, $w_0=-1.05^{+0.02}_{-0.16}$ , and $w_a=0.14\pm 0.1$ with $\chi^2=541.1$."66" Using this result, we reconstruct Om(z) with equation (34)) and the result is shown in Fig. 2(("," Using this result, we reconstruct $Om(z)$ with equation \ref{wetomz}) ) and the result is shown in Fig. \ref{u2omz}( ("67c).,c).68" Finally, we consider a more model-independent parametrization of w(z), the piecewise parametrization of w(z)."," Finally, we consider a more model-independent parametrization of $w(z)$, the piecewise parametrization of $w(z)$."69" In this parametrization, the equation of state parameter is a constant, w(z)=wi; for the redshift in the range z;-1«z<zi."," In this parametrization, the equation of state parameter is a constant, $w(z)=w_i$ for the redshift in the range $z_{i-1}<z<z_i$."70" For convenience, we choose 2ο=0."," For convenience, we choose $z_0=0$."71 Wealso assume that —1. a, Wealso assume that $w(z>1.8)=-1$ .72" Forflat Universe, if zi4€z< zi, Again, the four parameters w; are correlated and we follow Huterer&Cooray(2005) to transform these parameters to decorrelated parameters W;."," For a flat Universe, if $z_{i-1}\le z<z_i$ , Again, the four parameters $w_i$ are correlated and we follow \cite{huterer05} to transform these parameters to decorrelated parameters$\mathcal{W}_i$ ."73" By fitting themodel to the combined SN Ia, Bao2, Baoz, WMAP7 and Hí(z) data, we get the error estimations of W; and the results are shown inFig. 5.."," By fitting themodel to the combined SN Ia, Bao2, Baoz, WMAP7 and $H(z)$ data, we get the error estimations of $\mathcal{W}_i$ and the results are shown inFig. \ref{wzunc}. ."74 We summarize all the results in Table 1 and some results are shown in Figs. 1--5.., We summarize all the results in Table 1 and some results are shown in Figs. \ref{u2cont}- \ref{wzunc}. .75" By parametrizing the deceleration parameter q(z),we find verystrong evidence for the current acceleration."," By parametrizing the deceleration parameter $q(z)$,we find verystrong evidence for the current acceleration."76" For the piecewise parametrization of q(z), we find that q(z)<0 in the redshift range 0<zS; 0.6, and q(z)>O in the redshift range"," For the piecewise parametrization of $q(z)$ , we find that $q(z)<0$ in the redshift range $0\le z\la 0.6$ , and $q(z)>0$ in the redshift range"77The realization that X-ray binaries are. 100-1000. times overabundant in Galactic elobular clusters relative to the rest of the \lilky Way. (Clark1975:Katz1975). was crucial in understanding that intimate and Gehtly coupled relationships exist between stellar evolution and stellar dynamics.,"The realization that X-ray binaries are 100-1000 times overabundant in Galactic globular clusters relative to the rest of the Milky Way \citep{cla75,kat75} was crucial in understanding that intimate and tightly coupled relationships exist between stellar evolution and stellar dynamics."78 Among the predictions of this theory is (he expectation that many white chwarl/red cwarf binaries should form via two-body tidal capture (Fabian1975). and/or three-body exchange captures (Int1983:Hut.&Paczvuski1984).," Among the predictions of this theory is the expectation that many white dwarf/red dwarf binaries should form via two-body tidal capture \citep{fab75} and/or three-body exchange captures \citep{hut83,hut84}."79. some of these binary svstems will be in very. close orbits. such that the red dwarl fills its Roche lobe.," Some of these binary systems will be in very close orbits, such that the red dwarf fills its Roche lobe."80 This leads to the transfer of mass. via an aceretion disk. from the red dwarl to the white dwarf component in other words. to cataclvsmic variables (CVs).," This leads to the transfer of mass, via an accretion disk, from the red dwarf to the white dwarf component – in other words, to cataclysmic variables (CVs)."81 Yel searclies for the many dozens of expected erupting CVs have tvpically found zero to (vo cwarf novae in clusters searched [rom the ground (Sharaοἱal.1994:ÓTuairisg2003). and with," Yet searches for the many dozens of expected erupting CVs have typically found zero to two dwarf novae in clusters searched from the ground \citep{sha94,tua03} and with"82It is important to note a new result evident in Fig. 3::15.,It is important to note a new result evident in Fig. \ref{fig:delta}:.83 This is true regardless of the strength of the UVB., This is true regardless of the strength of the UVB.84 We will< examine this interesting result furtherin §4.., We will examine this interesting result furtherin \ref{sec:pos}.85" Next, we investigate how the combination of transient UV heating and a persistent LW background impact star formation."," Next, we investigate how the combination of transient UV heating and a persistent LW background impact star formation."86" This is a more physically-relevant scenario, since a LW background is likely established before a large fraction of the Universe has been reionized (?).."," This is a more physically-relevant scenario, since a LW background is likely established before a large fraction of the Universe has been reionized \citep{HAR00}."87" Photons in the LW band dissociate H2 molecules; thus by definition they provide additional negative feedback, undercutting some of the enhancement in the Hz abundances in relic HII regions."," Photons in the LW band dissociate $_2$ molecules; thus by definition they provide additional negative feedback, undercutting some of the enhancement in the $_2$ abundances in relic HII regions."88 Negative feedback from a LW background kicks in when the He dissociation timescale becomes shorter than the Ἡο formation timescale., Negative feedback from a LW background kicks in when the $_2$ dissociation timescale becomes shorter than the $_2$ formation timescale.89" Since the formation timescale is inversely proportional to gas density, whereas the dissociation timescale is independent of density, the density decrease caused by UV heating should make halos more susceptible to the negative feedback of a LW background (?)?.."," Since the formation timescale is inversely proportional to gas density, whereas the dissociation timescale is independent of density, the density decrease caused by UV heating should make halos more susceptible to the negative feedback of a LW background \citep{OH03} ."90 We investigate these processes further below., We investigate these processes further below.91" Specifically, in Fig. 4,,"," Specifically, in Fig. \ref{fig:LW_delta},"92" we plot values of dy7,ca(z) panel) and ów,ca(z) panel) for our runs including a LW background.", we plot values of $\delM$ ) and $\delN$ ) for our runs including a LW background.93 The LW background turns on at z—24.62 and remains on., The LW background turns on at $z=24.62$ and remains on.94" At the simplest level, we can see the suppression of molecular hydrogen (and hence cooling)due to the LW background by the more negative values of both daz,ca(z) and 6n,ca(z) at fixed redshift."," At the simplest level, we can see the suppression of molecular hydrogen (and hence cooling)due to the LW background by the more negative values of both $\delM$ and $\delN$ at fixed redshift."95 Does this panel show evidence for theadditional negative impact of the transient UVB discussed above?, Does this panel show evidence for the negative impact of the transient UVB discussed above?96" Without UV heating, a LW background with a specific intensity of Ji]=0.01 is needed for notable negative feedback (see the blue empty triangles at z<14 in the lower panel)."," Without UV heating, a LW background with a specific intensity of $\Jlwb=0.01$ is needed for notable negative feedback (see the blue empty triangles at $z\leq14$ in the lower panel)."97" This value is similar to the one found in MBHO06, where we showed that by equating H5-cooling and H»5-photodissociation one expects this critical LW background to scale as JI""xngfua/T.* When the UV heating is added, this critical value of ή. causing negative feedback decreases by a factor of ~10 to Jay”1073 (see the green solid circles in lower panel at z< 14)."," This value is similar to the one found in MBH06, where we showed that by equating ${\rm H_2}$ –cooling and ${\rm H_2}$ –photodissociation one expects this critical LW background to scale as $\Jlwb \propto n_g f_{\rm H2}/T$ When the UV heating is added, this critical value of $\Jlwb$ causing negative feedback decreases by a factor of $\sim10$ to $\Jlwb\sim10^{-3}$ (see the green solid circles in lower panel at $z\leq14$ )."98 This decrease seems to confirm the above arguments., This decrease seems to confirm the above arguments.99" However, such an interpretation is too simplistic and the negative impact of the LWB can be ameliorated by positive feedback inside the HII region at lower redshifts, as we shall see in §4.."," However, such an interpretation is too simplistic and the negative impact of the LWB can be ameliorated by positive feedback inside the HII region at lower redshifts, as we shall see in \ref{sec:pos}."100 From Fig., From Fig.101" 4 one can also note that a value of JI""~10”5-- 107? separates feedback regimes dominated by a LW background from those dominated by our transient UVB.", \ref{fig:LW_delta} one can also note that a value of $\Jlwb\sim 10^{-3}$ $10^{-2}$ separates feedback regimes dominated by a LW background from those dominated by our transient UVB.102" This can be seen by the fact that the amount of suppression differs between the NoUVB and Heat0.8 cases at low values of the LW background (Le. for JI""< 1073), while at large values of JL"", the amount of suppression is independent of the UVB."," This can be seen by the fact that the amount of suppression differs between the NoUVB and Heat0.8 cases at low values of the LW background (i.e. for $\Jlwb < 10^{-3}$ ), while at large values of $\Jlwb$ , the amount of suppression is independent of the UVB."103" Near the threshold value of JI?"" , negative feedback transitions from being UV heating"," Near the threshold value of $\Jlwb$ , negative feedback transitions from being UV heating"104superdisks must be drawn mostly. [rom closer objects for which radio maps with adequate resolution ancl dynamic range are available. and for which the actual conditions are often more similar to those of the ICM at lower redshifts.,"superdisks must be drawn mostly from closer objects for which radio maps with adequate resolution and dynamic range are available, and for which the actual conditions are often more similar to those of the ICM at lower redshifts."105 Under those circumstances the typical sizes for wind inllated xibbles would be compressed to a few kpe., Under those circumstances the typical sizes for wind inflated bubbles would be compressed to a few kpc.106 We now summarize some salient features of our moclel. (, We now summarize some salient features of our model. (1071) Superdisks (at. least the wider ones) markgian! λαας conduits along which the AGN's non-relativistic wind is able to escape preferentiallv. ic. in directions roughly »rpendicular to the radio axis along which svnachrotron asma is transported.,"1) Superdisks (at least the wider ones) mark planar conduits along which the AGN's non-relativistic wind is able to escape preferentially, i.e., in directions roughly perpendicular to the radio axis along which synchrotron plasma is transported."108 We suggest that the surface. of dvnamical interaction between the wind bubble and the radio lobe pair can offen give rise to well-defined. planar »oundaries between the two media. which we identify asinferfaces and which may be manifested. in. the ts as central emission gaps or superdisks. (," We suggest that the surface of dynamical interaction between the wind bubble and the radio lobe pair can often give rise to well-defined, planar boundaries between the two media, which we identify as and which may be manifested in the RGs as central emission gaps or superdisks. ("109In most RCs. rowever. the viewing angle would. work against the sharp edges. Le. a superdisk morphology. being observed).,"In most RGs, however, the viewing angle would work against the sharp edges, i.e., a superdisk morphology, being observed)."110 The metal enriched. gas swept out of the host galaxy is thus ransported to great. distances. not only by being dragged along bv the jets. but in the perpendicular. direction. as well (through the superdisk).," The metal enriched gas swept out of the host galaxy is thus transported to great distances, not only by being dragged along by the jets, but in the perpendicular direction as well (through the superdisk)."111 Phus. the AGN activity would end to isotropize the metal enrichment process. as is indeed iound Crom measurements (de Grandi et 22004). ," Thus, the AGN activity would tend to isotropize the metal enrichment process, as is indeed found from measurements (de Grandi et 2004). ("112"E) Phis scenario provokes us to revisit the question radsed three decades ago by Jenkins Seheuer (1976): ""what docks the tails of radio source components?""","2) This scenario provokes us to revisit the question raised three decades ago by Jenkins Scheuer (1976): “what docks the tails of radio source components?"""113 They concluded that the cause is other than svnchrotron Losses., They concluded that the cause is other than synchrotron losses.114 Later. an explanation was proposed in terms of blocking of the radio lobe plasma by the LSAL of the host galaxy (e.g. Leahy Williams 1984).," Later, an explanation was proposed in terms of blocking of the radio lobe plasma by the ISM of the host galaxy (e.g., Leahy Williams 1984)."115 In our picture. on the other hand. the sharp ancl straight edges of the strip-like central gaps in the radio bridge signify where the thermal wind outflowing from the AGN is actually countered and redirected. by. the lobe overpressure assisted. by. the dynamic pressure of the back-owing relativistic plasma inside the radio lobes.," In our picture, on the other hand, the sharp and straight edges of the strip-like central gaps in the radio bridge signify where the thermal wind outflowing from the AGN is actually countered and redirected by the lobe overpressure assisted by the dynamic pressure of the back-flowing relativistic plasma inside the radio lobes."116 Eventually. when the pressure of this back-Llow has declined sulliciently. it could even mix with and be dragged: along the thermal wind. escaping in the perpendicular direction. (," Eventually, when the pressure of this back-flow has declined sufficiently, it could even mix with and be dragged along the thermal wind escaping in the perpendicular direction. ("117"3) J£ indeed the “wind” outflow precedes the radio jet ejection. the pancake or superdisk resulting from the Iobe-wind interaction can become ""frozen"" in space quite early in the active phase of the galaxy.","3) If indeed the “wind"" outflow precedes the radio jet ejection, the pancake or superdisk resulting from the lobe-wind interaction can become “frozen"" in space quite early in the active phase of the galaxy."118 Now. if the galaxy has a large enough component of motion normal to the superclisk (sav. 500 km 1 or more). LE. may even move out of the Latter into. the lobe during its active lifetime.," Now, if the galaxy has a large enough component of motion normal to the superdisk (say, 500 km $^{-1}$ or more), it may even move out of the latter into the lobe during its active lifetime."119 Two RCs exemplifving such a situation are 3€ 16 and 3€ 19. where the host galaxy is seen the radio gap (Llarvanck Llarcdeastle 1998: Leahy Perley 19901: Gilbert et 22004).," Two RGs exemplifying such a situation are 3C 16 and 3C 19, where the host galaxy is seen the radio gap (Harvanek Hardcastle 1998; Leahy Perley 1991; Gilbert et 2004)."120 While such a morphology is expected only in extreme cases. it is quite conceivable in our picture but hard to understand within the usual interpretation of the radio gaps invoking a buovaney led outward squeezing of the radio lobes by the denser LSAL of the parent galaxy. (," While such a morphology is expected only in extreme cases, it is quite conceivable in our picture but hard to understand within the usual interpretation of the radio gaps invoking a buoyancy led outward squeezing of the radio lobes by the denser ISM of the parent galaxy. ("1214) Notwithstanding the sharp. quasi-planar boundaries of the radio gap. the present model does allow for some fainter radio emission seen within the gap (being remnant of the carly phase when the radio jets were still boring their wav through the bubble).,"4) Notwithstanding the sharp, quasi-planar boundaries of the radio gap, the present model does allow for some fainter radio emission seen within the gap (being remnant of the early phase when the radio jets were still boring their way through the bubble)."122 Examples of this can be found in the radio sources J11371613 (Lara οἱ 22001) and J1628| 3932 (de Dreuck οἱ 2004)., Examples of this can be found in the radio sources $+$ 613 (Lara et 2001) and $+$ 3932 (de Breuck et 2004).123 Otherpossible manifestations of this situation are 3€ 63 (Llarvanek Llarcleastle 1998). 3€ 136.1 (Leahy Williams. 1984). and 3€ 300 (Leahy Williams. 1984: Llardeastle et 11997).," Otherpossible manifestations of this situation are 3C 63 (Harvanek Hardcastle 1998), 3C 136.1 (Leahy Williams 1984), and 3C 300 (Leahy Williams 1984; Hardcastle et 1997)."124 However. such remnant emission usually will be cillicult to see without high dvnamic range observations and will not last. very long compared. to the total lifetime of the radio source.," However, such remnant emission usually will be difficult to see without high dynamic range observations and will not last very long compared to the total lifetime of the radio source."125 This is because this inner racio emitting plasma will be cut olf [rom a continued supply of the baekllow from the lobes and. will be mixed. up and dispersed with the the thermal outflow through the chimney (i.e... superclisk).," This is because this inner radio emitting plasma will be cut off from a continued supply of the backflow from the lobes and will be mixed up and dispersed with the the thermal outflow through the chimney (i.e., superdisk)."126" Finally. although the scenario. sketehed here has been quantified in a highly simplified. analytical form. the possibility. of the. sharp-ccged radio gaps being wind-lobe interfaces. Le. ""active surfaces of dynamical interaction between the thermal anc nonthermal outllows. may have other interesting observational ancl theoretical consequences."," Finally, although the scenario sketched here has been quantified in a highly simplified analytical form, the possibility of the sharp-edged radio gaps being wind-lobe interfaces, i.e., “active"" surfaces of dynamical interaction between the thermal and nonthermal outflows, may have other interesting observational and theoretical consequences."127 dence. this general picture needs. to. be explored further.," Hence, this general picture needs to be explored further."128 Full hyelrodyvnamic simulations of this situation are worth pursuing., Full hydrodynamic simulations of this situation are worth pursuing.129 On the observational side. detailed radio imaging of high= radio galaxies would provide useful input and constraints on the basic moclel presented here.," On the observational side, detailed radio imaging of $-z$ radio galaxies would provide useful input and constraints on the basic model presented here."130 We thank the referee. Martin. Hardcastle. for criticisms which significantly focussed. the arguments of this paper.," We thank the referee, Martin Hardcastle, for criticisms which significantly focussed the arguments of this paper."131 This research— has mace use of the NASA/IPAC Extragalactic Database (NIED) which is operated by the Jet Propulsion Laboratory. under contract with the National Acronautics and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, under contract with the National Aeronautics and Space Administration."132 iis erateful [or continuing hospitality at. the Princeton University Department of Astrophysical Sciences. and acknowledges support from a sub-contract to GSU from National Science. Foundation. grant. AST-0507529 to the University of Washington., is grateful for continuing hospitality at the Princeton University Department of Astrophysical Sciences and acknowledges support from a sub-contract to GSU from National Science Foundation grant AST-0507529 to the University of Washington.133,.134 Tudeed. Sclavineger(1919) followed this path in deriving an analytic expression for the svuchrotron chussivity.," Indeed, \citet{schwinger49} followed this path in deriving an analytic expression for the synchrotron emissivity."135 Tlowever. because the integrands are oscillatory. it is instead preferable to group them together.," However, because the integrands are oscillatory, it is instead preferable to group them together."136 Transforming the integration variable from 7 to the phase-lag g defined iu (13)). iu the case of the first τν in (10)). aud as g=wr(l|3(f)) iu the case of the second tei. leads to Eu |.," Transforming the integration variable from $\tau$ to the phase-lag $g$ defined in \ref{phaselagdef}) ), in the case of the first term in \ref{firstorderint}) ), and as $g=\omega\tau(1+\beta(t))$ in the case of the second term, leads to ,t) = ] ]."137 where cTA(t.7)/|r|(52) As required. P vanishes to zeroth order in the deviations from a ballistic orbit. (299). (313) and. (33)).," where - - As required, $P$ vanishes to zeroth order in the deviations from a ballistic orbit, \ref{devposition}) ), \ref{devvelocity}) ) and \ref{devdisplacement}) )."138" The erouping of the terms in Equation (51)) in this manner Is especially portant at high frequencies. where the higher order terms in P? aud P, are simall."," The grouping of the terms in Equation \ref{instpower}) ) in this manner is especially important at high frequencies, where the higher order terms in $P_1$ and $P_2$ are small."139 Iu this laut. the two terms cau be expressed as = and cancel exactly whensuuuned.," In this limit, the two terms can be expressed as = and cancel exactly whensummed."140 In a mmucrical evaluation. a small error remains. which erows linearly with w.," In a numerical evaluation, a small error remains, which grows linearly with $\omega$."141 Grouping the terms together prevents the erowtli of this error., Grouping the terms together prevents the growth of this error.142 Under the assuniptious that the clectromaguetic fields varyslowly ou the timescale of a photonformatio- leugth. aud that linear acceleration cussion (e.g.Sclwinecr1919) ds unimüportant. we demonstrate 1- appendix A that (51)) reduces to a local ciissivity.," Under the assumptions that the electromagnetic fields varyslowly on the timescale of a photonformation length, and that linear acceleration emission \citep[e.g.][]{schwinger49} is unimportant, we demonstrate in appendix \ref{appendix_synchrotron} that \ref{instpower}) ) reduces to a local emissivity."143 This is au obvious ecucralization of standard svuchrotrou Cluission. Which takes account of acceleration iu both magnetic and electric fields by forumlating it iu ters of the local curvature of the trajectory: where woc—oujf2(51) aud the curvature & is defined. locally in terms of the particle velocityaud acceleration 3 aud 3: -- A perturbative approach thatincludes linear acceleration cluission as a first order— correction— to (56))has been preseuted by Melrose(1978).," This is an obvious generalization of standard synchrotron emission, which takes account of acceleration in both magnetic and electric fields by formulating it in terms of the local curvature of the trajectory: ,t) = (x) where /2 and the curvature $\kappa$ is defined locally in terms of the particle velocityand acceleration $\bm{\beta}$ and $\dot{\bm{\beta}}$ : = A perturbative approach thatincludes linear acceleration emission as a first order correction to \ref{instsyncheq}) )has been presented by \citet{melrose78}."144. To perform the imteeration in (51)) ποαν. we first split it at the points where sing= 0. Le.Ίσα g=nz. (n—0.1. x2...). and write it as an infinite sui wt)= |," To perform the integration in \ref{instpower}) ) numerically, we first split it at the points where $\sin g=0$ , i.e., $g=n\pi$ , $(n=0,\pm1,\pm2\dots)$ , and write it as an infinite sum ,t) = ] ]."145majority of satellites reionize later than the mean.,majority of satellites reionize later than the mean.146" In practice, the difference between the patchy and instantaneous case in Fig."," In practice, the difference between the patchy and instantaneous case in Fig."147" 7 is due to a combination of two effects: that the global mean is not necessarily the best instantaneous redshift to choose for a given halo, as well as not capturing the spread in reionization times."," \ref{fig:sat_cand} is due to a combination of two effects: that the global mean is not necessarily the best instantaneous redshift to choose for a given halo, as well as not capturing the spread in reionization times."148" However, we do not find that using e.g. the host halo reionization redshift, or the median satellite reionization redshift, leads to better agreement in each case."," However, we do not find that using e.g. the host halo reionization redshift, or the median satellite reionization redshift, leads to better agreement in each case."149" While we could recover the number of satellites in each case by tuning the instantaneous reionization redshift, the value of such an exercise is limited: the only way to determine that appropriate redshift would be to already know the result from the patchy model."," While we could recover the number of satellites in each case by tuning the instantaneous reionization redshift, the value of such an exercise is limited: the only way to determine that appropriate redshift would be to already know the result from the patchy model."150" As such, this illustrates the main problem with using instantaneous spatially homogeneous reionization models."," As such, this illustrates the main problem with using instantaneous and/or spatially homogeneous reionization models."151" Depending and/oron the application, the fact that there is a distribution of satellite reionization redshifts may be important to the results — and this distribution cannot be captured in a homogeneous model, nor can the appropriate instantaneous approximation be recovered without knowing the patchy result."," Depending on the application, the fact that there is a distribution of satellite reionization redshifts may be important to the results – and this distribution cannot be captured in a homogeneous model, nor can the appropriate instantaneous approximation be recovered without knowing the patchy result."152some of the differences in interpretation of UV spectra of VW νὰ in quiescence.,some of the differences in interpretation of UV spectra of VW Hyi in quiescence.153 The first component has a photospheric temperature of 23.000. a rotation rate of 400 kins | and chemical abundances (hat are reasonably consistent wilh previous HIST FOS. GIIRS and OTIS results.," The first component has a photospheric temperature of 23,000K, a rotation rate of 400 km $^{-1}$ and chemical abundances that are reasonably consistent with previous HST FOS, GHRS and STIS results."154 This seems to indicate a cooling of the WD 11 days after a normal 3 cay outburst., This seems to indicate a cooling of the WD 11 days after a normal 3 day outburst.155 The second component has an effective temperature higher than that of the WD. and a featureless (rather flat) spectrum.," The second component has an effective temperature higher than that of the WD, and a featureless (rather flat) spectrum."156 Our numerical modeling is unable to account in detail for some of the features such as: (1) large discrepancies between our theoretical spectrum and (he present FUSE data around 925 and 1100À: (2) the aceretion belt model does not account for the upturn in flux at the Lyiman limit. where (he variability. is strongest. which is also (he region of the spectrum where the WD does not contribute to the flux. and consequently. neither the WD nor the accretion belt model can possibly be the source of the variabili: (3) the OVI emission lines in theFUSE spectrum indicate the possible presence of an optically (hin source in the svslenm.," Our numerical modeling is unable to account in detail for some of the features such as: (1) large discrepancies between our theoretical spectrum and the present FUSE data around 925 and 1100; (2) the accretion belt model does not account for the upturn in flux at the Lyman limit, where the variability is strongest, which is also the region of the spectrum where the WD does not contribute to the flux, and consequently, neither the WD nor the accretion belt model can possibly be the source of the variability; (3) the OVI emission lines in the spectrum indicate the possible presence of an optically thin source in the system."157 Therefore. (he exact nature of the second component is still relatively uncertain. due to the lack of better models for spectra of the inner disk in a quiescent. dwarf nova.," Therefore, the exact nature of the second component is still relatively uncertain, due to the lack of better models for spectra of the inner disk in a quiescent dwarf nova."158 As we mentioned in 81 the possible candidates for a second component (1) an accretion belt. ie. a fast rotating heated laver of the surface of the WD. possibly created in the outburst and which remains hot primarily because of the effective viscosity of ihe WD. (," As we mentioned in 1 the possible candidates for a second component (1) an accretion belt, i.e. a fast rotating heated layer of the surface of the WD, possibly created in the outburst and which remains hot primarily because of the effective viscosity of the WD. ("1592) the boundary laver. i.e. the region between the inner edge of the disk and the stellar surface where the remaining kinetic energy of (he accreting flow is released.,"2) the boundary layer, i.e. the region between the inner edge of the disk and the stellar surface where the remaining kinetic energy of the accreting flow is released."160" This optically (hin reeion rellects the instantaneous accretion rate ancl is expected to emit X-ray, ", This optically thin region reflects the instantaneous accretion rate and is expected to emit X-ray. (1613) an optically thick disk. however physically. unjustified in the accretion disk limit evcle nodel (Cannizzo1993).. is what we are numerically able to moclel. (,"3) an optically thick disk, however physically unjustified in the accretion disk limit cycle model \citep{can93}, is what we are numerically able to model. ("1624) ox a corona/chromosphere above a cool disk.,4) or a corona/chromosphere above a cool disk.163 Ai the present time. only the optically thick accretion belt ancl accretion disk can be nunerically modeled. while no detailed modeling exists lor the optically thin components spectra).," At the present time, only the optically thick accretion belt and accretion disk can be numerically modeled, while no detailed modeling exists for the optically thin components (spectra)."164 The results we obtained here indicate that the [ast rotating belt is the best candidate for the source of the second FUY component., The results we obtained here indicate that the fast rotating belt is the best candidate for the source of the second FUV component.165of the seismic QBO alone cannot be extracted.,of the seismic QBO alone cannot be extracted.166 To determine the latitudinal dependence of the seismic QBO we must look at solar minimum., To determine the latitudinal dependence of the seismic QBO we must look at solar minimum.167" However, as we have shown, at this time the signal is not strong enough to constrain the / dependence."," However, as we have shown, at this time the signal is not strong enough to constrain the $l$ dependence."168 The amplitude of the QBO in the low-frequency-range /=3 residuals is noticeably larger than for the other / (see Fig., The amplitude of the QBO in the low-frequency-range $l=3$ residuals is noticeably larger than for the other $l$ (see Fig.169 3 and Table 1))., \ref{figure[residuals]} and Table \ref{table[abs dev]}) ).170" This could be a genuine effect: As noted in the previous section, there is a well-known dependence on in the size of the 11-yr solar cycle frequency shifts."," This could be a genuine effect: As noted in the previous section, there is a well-known dependence on $l$ in the size of the 11-yr solar cycle frequency shifts."171" However, we note/ that the estimates of the /=3 mode frequencies are more noisy than the frequencies estimated for the other /."," However, we note that the estimates of the $l=3$ mode frequencies are more noisy than the frequencies estimated for the other $l$."172" Furthermore, estimates of the /=3 mode frequencies are also influenced by the nearby, much stronger, /21 modes."," Furthermore, estimates of the $l=3$ mode frequencies are also influenced by the nearby, much stronger, $l=1$ modes."173 This is partially reflected in the size of the error bars associated with the fitted frequencies (see also Figs., This is partially reflected in the size of the error bars associated with the fitted frequencies (see also Figs.174" 1 and 3)), but, as seen in Section ?? it is still possible that the uncertainties are underestimated."," \ref{figure[freq shifts]} and \ref{figure[residuals]}) ), but, as seen in Section \ref{subsection[significance of QBO]} it is still possible that the uncertainties are underestimated."175 Fig., Fig.176" 3 shows that the seismic QBO is more evident at high frequencies and it could be argued that the ""signal"" in the low-frequency range is just noise."," \ref{figure[residuals]}177 shows that the seismic QBO is more evident at high frequencies and it could be argued that the “signal” in the low-frequency range is just noise."178 This implies that the seismic QBO signal shows some frequency dependence., This implies that the seismic QBO signal shows some frequency dependence.179 We have used the 182.5dd frequencies to determine the frequency at which the seismic QBO stops being significant., We have used the d frequencies to determine the frequency at which the seismic QBO stops being significant.180" To do this the weighted average frequency shifts were generated for each subset in time, in the manner described in Section ??.."," To do this the weighted average frequency shifts were generated for each subset in time, in the manner described in Section \ref{section[data]}."181" However, here we averaged the frequency shifts of the modes over four overtones only."," However, here we averaged the frequency shifts of the modes over four overtones only."182" The lowest frequency range for which the mean shifts were calculated was mmHz, i.e. the lower limit of the frequency ranges described -in Section ??.."," The lowest frequency range for which the mean shifts were calculated was mHz, i.e. the lower limit of the frequency ranges described in Section \ref{section[data]}."183 The next frequency range was positioned so that it overlapped this range by 3 overtones i.e. mmHz., The next frequency range was positioned so that it overlapped this range by 3 overtones i.e. mHz.184 This process was repeated until the upper limit on the frequency ranges described in Section ?? was reached., This process was repeated until the upper limit on the frequency ranges described in Section \ref{section[data]} was reached.185 In total the mean frequency shift was determined for 11 frequency ranges., In total the mean frequency shift was determined for 11 frequency ranges.186" We have considered the /=2 frequency shifts only, because over the entire epoch considered here, the seismic QBO is strongest in the /=2 frequencies (see Fig. 2))."," We have considered the $l=2$ frequency shifts only, because over the entire epoch considered here, the seismic QBO is strongest in the $l=2$ frequencies (see Fig. \ref{figure[periodograms]}) )."187 A periodogram of the /=2 frequency shifts was then determined in the manner described in Section ??.., A periodogram of the $l=2$ frequency shifts was then determined in the manner described in Section \ref{subsection[significance of QBO]}.188 We found that the lowest frequency band at which the seismic QBO was still significant at a pper cent false alarm level was mmHz., We found that the lowest frequency band at which the seismic QBO was still significant at a per cent false alarm level was mHz.189 Residuals of the /=2 frequency shifts were then determined for the frequency bands in which the seismic QBO was significant., Residuals of the $l=2$ frequency shifts were then determined for the frequency bands in which the seismic QBO was significant.190 The maximum absolute deviations of the residuals at times of high- and low-surface activity are shown in Fig. 5..," The maximum absolute deviations of the residuals at times of high- and low-surface activity are shown in Fig. \ref{figure[frequency191dependence]}."192" For comparison purposes the maximum absolute deviation of the raw frequency shifts was also calculated, as this reflects the amplitude of the seismic 11-yr solar cycle."," For comparison purposes the maximum absolute deviation of the raw frequency shifts was also calculated, as this reflects the amplitude of the seismic 11-yr solar cycle."193 Fig., Fig.194 5 shows that the frequency dependence of the seismic QBO is weaker than the frequency dependence of the 11-yr solar cycle., \ref{figure[frequency dependence]} shows that the frequency dependence of the seismic QBO is weaker than the frequency dependence of the 11-yr solar cycle.195 Although the 11-yr solar cycle magnetic flux is believed to be generated at the base of the convection zone the main influence of the 11-yr signal on the p-mode frequencies occurs in the upper few kkm of the convection zone., Although the 11-yr solar cycle magnetic flux is believed to be generated at the base of the convection zone the main influence of the 11-yr signal on the p-mode frequencies occurs in the upper few km of the convection zone.196 This is above the upper turning point of the lowest frequency modes examined here and so explains the, This is above the upper turning point of the lowest frequency modes examined here and so explains the197convection zone: an interlace dvnamo. in which all the action is concentrated at the base of the convection zone ancl in the tachocline: and a {lis transport dynamo. which might be envisaged as having an w-ellect arising from the velocity shear in the tachocline and an a-ellect located close to the solar surlace. with the two linked by some large-scale flow.,"convection zone; an interface dynamo, in which all the action is concentrated at the base of the convection zone and in the tachocline; and a flux transport dynamo, which might be envisaged as having an $\omega$ -effect arising from the velocity shear in the tachocline and an $\alpha$ -effect located close to the solar surface, with the two linked by some large-scale flow."198 There are certainly problems with all three types of dvnamo., There are certainly problems with all three types of dynamo.199 A distributed dvnamo relies on a coherent a-effect throughout the convection zone: (his is not supported by theoretical argumentis (Cattaneo&Hughes2009) or numerical simulations (Brinetal.2004)., A distributed dynamo relies on a coherent $\alpha$ -effect throughout the convection zone; this is not supported by theoretical arguments \citep{CH09} or numerical simulations \citep{BMT04}.200.. A [Iux transport dvnamo relies crucially on the migration of surface magnetic features and a large-scale flow to return the field to the base of the convection zone. essentially ignoring all the turbulent. dynamics of the convection zone.," A flux transport dynamo relies crucially on the migration of surface magnetic features and a large-scale flow to return the field to the base of the convection zone, essentially ignoring all the turbulent dynamics of the convection zone."201 An interlace dvnamo is more appealing in (hat the different aspects of the dvnanmo process are nol widely spatially separated., An interface dynamo is more appealing in that the different aspects of the dynamo process are not widely spatially separated.202 Toroidal field would be amplified from the poloidal component bv the differential rotation in the tachocline: the diflicully though is in closing the dvnamo evele., Toroidal field would be amplified from the poloidal component by the differential rotation in the tachocline; the difficulty though is in closing the dynamo cycle.203 One possibility is from helical overshooting convection. though this would then still rely on the traditional a-ellect working at hieh magnetic Revnolds numbers.," One possibility is from helical overshooting convection, though this would then still rely on the traditional $\alpha$ -effect working at high magnetic Reynolds numbers."204 An emf resulting from magnetic buovancy instability provides a natural possible alternative solution to this problem., An emf resulting from magnetic buoyancy instability provides a natural possible alternative solution to this problem.205 Clearly. further. more involved. investigations are needed in order (o examine the viability of Chis idea.," Clearly, further, more involved, investigations are needed in order to examine the viability of this idea."206 wwas supported by a studentship Irom (the Science and Technologies Facilities Council., was supported by a studentship from the Science and Technologies Facilities Council.207 wwas supported by STFC and by a Roval Society Leverhulme Trust senior Research Fellowship., was supported by STFC and by a Royal Society Leverhulme Trust Senior Research Fellowship.208 in the measured ionization potential of 153.1 eV. We found. that this charge is Z=3.3544., in the measured ionization potential of 153.1 eV. We found that this charge is $Z=3.3544$.209 We then repeated the calculation of the plasma οσο on the bound states assuming this charge., We then repeated the calculation of the plasma effect on the bound states assuming this charge.210 The results are shown in fig. 2.., The results are shown in fig. \ref{fig:hi12-diff}.211 We then used the new values for the ionization potential in the Saha equation to find the revised f; ον, We then used the new values for the ionization potential in the Saha equation to find the revised $f_{1}$ $f_{2}$.212 The comparison between the values used with and without the plasma correction are shown in fig. 23..," The comparison between the values used with and without the plasma correction are shown in fig. \ref{fig:Be7-sun},"213 where the actual run of the occupation numbers in the Sun is given., where the actual run of the occupation numbers in the Sun is given.214 lt ijs surprising that (the dillerences in the ionization come out to be quite small., It is surprising that the differences in the ionization come out to be quite small.215 The particular results for the binding energy (calculated for a DIL potential) as a function. of the density are shown again in figure 4. along with the run of the ratios RofRelZ=4) and Grof/Rel(Z=4)., The particular results for the binding energy (calculated for a DH potential) as a function of the density are shown again in figure \ref{fig:Be-Debye} along with the run of the ratios $R_{D}/R_{B}(Z=4)$ and $\langle r_{s} \rangle /R_{B}(Z=4)$.216 The Debve radius and the mean interparticle distance are caleulated assuming N=034.Y—0.68 and Z=0.02. a composition which is close to the one at the solar core today.," The Debye radius and the mean interparticle distance are calculated assuming $X=0.34, Y=0.68$ and $Z=0.02$, a composition which is close to the one at the solar core today."217 We notice that when the density approaches the density in the solar core. namely abou 150οem (a) the Debve radius becomes of the order of the mean interparticle distance and hence the approximation of a smooth Dehve screened. potential loses its validity. emphasizing once more the conclusion reached in section 2.. (," We notice that when the density approaches the density in the solar core, namely about $150~{\rm g~cm^{-3}}$, (a) the Debye radius becomes of the order of the mean interparticle distance and hence the approximation of a smooth Debye screened potential loses its validity, emphasizing once more the conclusion reached in section \ref{sec:whatp}. ("218b) In the solar core. we find that Ry=Re(Z—4) and therefore the probability for complete ionization of the De is very high.,"b) In the solar core, we find that $R_{D} \approx R_{B}(Z=4)$ and therefore the probability for complete ionization of the ${\rm Be}$ is very high."219 Llowever. the more important question here is the ratio of the mean interparticle distance to the Bohr radius since we are interested in the possibility that the ions of Bervlium still have bound electrons.," However, the more important question here is the ratio of the mean interparticle distance to the Bohr radius since we are interested in the possibility that the ions of Beryllium still have bound electrons."220 Fig. 4..," Fig. \ref{fig:Be-Debye},"221 which depicts a graph for the value of £r;. indicates that this value at the center of rw Sun it is close to Z?g(Z=4).," which depicts a graph for the value of $\langle r_{s} \rangle $, indicates that this value at the center of the Sun it is close to $R_{B}(Z=4)$."222 Therefore. it is a delicate question whether the Bervilium ions possess any bound electrons.," Therefore, it is a delicate question whether the Beryllium ions possess any bound electrons."223 Finally. we point out that Ge). which is depicted in the figure. is the mean interparticle distance irrespective of their type.," Finally, we point out that $\langle r_{s} \rangle$, which is depicted in the figure, is the mean interparticle distance irrespective of their type."224 As we shall show. it is an underestimate in the case of a Bervilium ion embedded in Livedrogen and Helium ions.," As we shall show, it is an underestimate in the case of a Beryllium ion embedded in Hydrogen and Helium ions."225Dark Encrey has challenged our knowledge οἱ fundamental plysics since the direct evidence for its existence was discovered using Type Ia supernovae (Riessetal.1998:Perhuutteret 1999)..,"Dark Energy has challenged our knowledge of fundamental physics since the direct evidence for its existence was discovered using Type Ia supernovae \citep{Riess98AJ, Perlmutter99ApJ}."226 Because there are currently no compcling theoretical expanatious for Darl Eucrex. the correct cluplasis. as poiuted outby the Darl Encrev Task Force (DETF.Albrechtettal.2006).. is on refining our observations of the accecrated expansion of the universe.," Because there are currently no compelling theoretical explanations for Dark Energy, the correct emphasis, as pointed out by the Dark Energy Task Force \citep[DETF,][]{Albrecht06}, is on refining our observations of the accelerated expansion of the universe."227 Decornmendatiou V from the DETF Report (Albrechtμιαςetal.2006) calls for an exploration of the ο effects that could iupair the needed observational refinemieuts., Recommendation V from the DETF Report \citep{Albrecht06} calls for an exploration of the systematic effects that could impair the needed observational refinements.228 Acouple of recent studies (Il&Greene2006:Coorav&Caldwell200€j) point out that the redshift every armi ueeded to accurately measure the uuiversa expansion requires the use of a local sample. but that coherent large-scale local 0.2) peculiar velocities add additional uncertaüutv to the Iblde diagran ae rence to the derived cosmological parameters.," Acouple of recent studies \citep{Hui06PhRvD, Cooray06PhRvD} point out that the redshift lever arm needed to accurately measure the universal expansion requires the use of a local sample, but that coherent large-scale local $z < 0.2$ ) peculiar velocities add additional uncertainty to the Hubble diagram and hence to the derived cosmological parameters."229 Current analyses (6.8e.Astieretal.2006:RiesseHal.2007:Wood-Vascyvct2007) of the cosmological waralucters do not attempt to correct for the effec 6X local peculiar. velocities.," Current analyses \citep[e.g.,][]{Astier06A&A,Riess07ApJ,Wood-Vasey07astroph} of the cosmological parameters do not attempt to correct for the effect of local peculiar velocities."230 As briefly noted bv and Coorav&Calelwell(2006).. it is possible to use local data to measure the local veoocitv fied aud hence liit the impact ou the derived COsinologic:d parameters.," As briefly noted by and \citet{Cooray06PhRvD}, it is possible to use local data to measure the local velocity field and hence limit the impact on the derived cosmological parameters."231 Moeasurenienuts of the local veoocitv fieId have improved to the point where there Is consiste1CY ÓdLOlg νους and methods (IIndson 06)...," Measurements of the local velocity field have improved to the point where there is consistency among surveys and methods \citep{Hud03,232HudSmiLuc04, Radburn04MNRAS, PikHud05, Sarkar06}."233 Type Ia SI)uova peculiar velocities have been sucdied recently by Radburn-Sinithetal.(2001):Pike&IIudsou(2005):FeclaE and others.," Type Ia supernova peculiar velocities have been studied recently by \cite{Radburn04MNRAS,234PikHud05, JhaRieKir06, HauHanTho06,Watkins07astroph} and others."235 Their cnls ceiuonstrate thiHi the local flows derived froin SNe are in agreement wih those derived from other distauce 1xdicators. such as the Tullv-Fisher relation aud the Fuidaimental Plane.," Their results demonstrate that the local flows derived from SNe are in agreement with those derived from other distance indicators, such as the Tully-Fisher relation and the Fundamental Plane."236 Οιr alui ds to use the current kuowkdee of the loca pcculiar notions to correct locul SNeaxc. together with a i0niogeneous set of distaun SNe. fit for cosmologica paralucters and measure the effect o tfie corrections on the cosmological fits.," Our aim is to use the current knowledge of the local peculiar motions to correct local SNe and, together with a homogeneous set of distant SNe, fit for cosmological parameters and measure the effect of the corrections on the cosmological fits."237" To produce this 1ieasureiment. we analyze the local anc distant SN Ia sample used in the firs-vear cosmology results from the Supernova Legacy 8rvey (SNLS.Αμα Αθ, "," To produce this measurement, we analyze the local and distant SN Ia sample used in the first-year cosmology results from the Supernova Legacy Survey \citep[SNLS,][hence A06]{Astier06A&A}. ."238This sampl ds οςxuposed of 1 local SNe(AOG.Table8:Wamuctal.1996Riesset are," This sample is composed of 44 local SNe \citep[A06, Table~8:][]{Hamuy96AJ, Riess99AJ, Krisciunas01AJ,239Jha02PhDT, Strolger02AJ, Altavilla04MNRAS, Krisciunas04AJa,240Krisciunas04AJb} and"241 Ou June 30th. 1908. something exploded over Tuneuska. in central Siheria.," On June 30th, 1908, something exploded over Tunguska, in central Siberia."242 Over the last nineotv vears this catastrophic event has inspired a plethora of scieutific investigations., Over the last ninety years this catastrophic event has inspired a plethora of scientific investigations.243 Despite many interesting findiugs. there are still substantial open questions and. iuconsistencies zione the theories aud the available data (for a review see Vasilvey 1998)).," Despite many interesting findings, there are still substantial open questions and inconsistencies among the theories and the available data (for a review see Vasilyev \cite{VASILYEV}) )."244 Among many different effects. the Tuuguska explosion produced shock waves. which were recorded by seiunographns at several sites.," Among many different effects, the Tunguska explosion produced shock waves, which were recorded by seismographs at several sites."245 DenMonah (1975)) made a cletailed analysis of these seismic records aid derived. an explosive energv of 12.5+2.5 AMtou., Ben–Menahem \cite{MENAHEM}) ) made a detailed analysis of these seismic records and derived an explosive energy of $12.5\pm 2.5$ Mton.246 Πο also concluded: tha the data ou the energv source are consistent with an airburst at a height of about 8.5 kin., He also concluded that the data on the energy source are consistent with an airburst at a height of about 8.5 km.247 Tn a previous etter (1998)). we have shown that seine data can be used to characterize the very bright 1993 Lugo bolide. obtaining a good match between the derived solution aud the observations.," In a previous letter \cite{FOSCHINI}) ), we have shown that seismic data can be used to characterize the very bright 1993 Lugo bolide, obtaining a good match between the derived solution and the observations."248 Tere the Sale methodology is applied to analyze the Tuuguska eveut. musing BenMenalieurs analysis as a starting point.," Here the same methodology is applied to analyze the Tunguska event, using Ben–Menahem's analysis as a starting point."249 Several different models have been developed in order to fit all the available data on the Tuneuska event (0.5. Chyba et al. 1993.. ," Several different models have been developed in order to fit all the available data on the Tunguska event (e.g. Chyba et al. \cite{CHYBA}, ,"250Grigorian 1998.. ills Coda 1993.. Lyne et al. 1996)).," Grigorian \cite{GRIGORIAN}, Hills Goda \cite{HILLS}, Lyne et al. \cite{LYNE}) )."251 All these models have contributed significantly to a general nuprovenient dn. our understanding of the atimospheric disruptiou of meteoroils., All these models have contributed significantly to a general improvement in our understanding of the atmospheric disruption of meteoroids.252 They usually assunie that the fraeiieutation process starts when the acrodvuaic pressure is equal to the mechanical strength S of the cosmic body., They usually assume that the fragmentation process starts when the aerodynamic pressure is equal to the mechanical strength $S$ of the cosmic body.253 Relating air deusitv to aimburst height. this allows oue to derive the 1neteoroid speed(V): where py is the atinospherie deusity at sea level. fis the height of first fragmentation and Π is the atmospheric scale height (about 8 kia).," Relating air density to airburst height, this allows one to derive the meteoroid speed$V$ ): where $\rho_{\mathrm{sl}}$ is the atmospheric density at sea level, $h$ is the height of first fragmentation and $H$ is the atmospheric scale height (about 8 km)."254 From BenMenalieimis analysis we infer that there was a single fragmentation eveut: there is no evidence of multiple explosions. as it should occur diving iuultiple fragmentation events (DenMoenalieia 1975)).," From Ben–Menahem's analysis we infer that there was a single fragmentation event; there is no evidence of multiple explosions, as it should occur during multiple fragmentation events (Ben–Menahem \cite{MENAHEM}) )."255 Thus Eq. (1 )), Thus Eq. \ref{e:velo}) )256 can be used to derive V. provided one assumes that the first fragmentation coimcided with the zirburst occurred at f=8.5 kan.," can be used to derive $V$, provided one assumes that the first fragmentation coincided with the airburst occurred at $h257= 8.5$ km."258 For different types of cosunic body. correspoucding to clifferenut assuinied values for ο (taken from Ilills Cocla. 1993)). we obtain the results listed in Table 1..," For different types of cosmic body, corresponding to different assumed values for $S$ (taken from Hills Goda, \cite{HILLS}) ), we obtain the results listed in Table \ref{speed-actual}."259 Now. sncee before exploding large meteoroids undergo a limited mass loss diame their atmospheric path. the preexplosion speed must be close to the (gcoceutric) orbital speed. aud thus must be greater than the Earth's escape velocity (11.2 kms).," Now, since before exploding large meteoroids undergo a limited mass loss during their atmospheric path, the pre--explosion speed must be close to the (geocentric) orbital speed, and thus must be greater than the Earth's escape velocity $11.2$ km/s)."260 Therefore. according to the results derived from Eq. (," Therefore, according to the results derived from Eq. ("2611). the most plausible solution would be that of an iron body.,"1), the most plausible solution would be that of an iron body."262" However. the iron body hypothesis is not consistent with the recent onsite recovery of nücroreninants frou, a stouv object (Longo et al. 199 L.. "," However, the iron body hypothesis is not consistent with the recent on–site recovery of microremnants from a stony object (Longo et al. \cite{LONGO}, ,"263Serra et al. 1991)., Serra et al. \cite{SERRA}) ).264 Actually. taking iuto account the wncertainty in the valueof $ aud the different measurement errors," Actually, taking into account the uncertainty in the valueof $S$ and the different measurement errors"265Alodeling the observed properties of the Galactic population of radio pulsars. with the purpose of inferring their intrinsic properties. has been the subject of extensive investigation for several decades (c.g. Gunn Ostriker 1970: Phinney Dlandford 1981: Lyne et al.,"Modeling the observed properties of the Galactic population of radio pulsars, with the purpose of inferring their intrinsic properties, has been the subject of extensive investigation for several decades (e.g. Gunn Ostriker 1970; Phinney Blandford 1981; Lyne et al."266 1985: Stollman LOST: Emunering Chevalier 1980: Naravan Ostriker 1990: Lorimer et al., 1985; Stollman 1987; Emmering Chevalier 1989; Narayan Ostriker 1990; Lorimer et al.267 1993: Hartman et al., 1993; Hartman et al.268 1997: Cordes Chernoll 1998: Arzoumanian. Cordes Chernoll 2002: Vranesevic ct al 2004: Faucher-Ciguere. Ixaspi: 2006: Ferrario Wickramasinghe 2006).," 1997; Cordes Chernoff 1998; Arzoumanian, Cordes Chernoff 2002; Vranesevic et al 2004; Faucher-Giguere Kaspi 2006; Ferrario Wickramasinghe 2006)."269 Since the fraction of »ulsars that can be detected elose to their birth constitutes a negligible fraction. of the total sample. these. studies eencrally use thedey observed. properties of pulsars (namely their period. P ancl period derivative P). together with some assumptions about their time evolution. to reconstruct the birth distribution of periods and magnetic ields for the pulsar population.," Since the fraction of pulsars that can be detected close to their birth constitutes a negligible fraction of the total sample, these studies generally use the observed properties of pulsars (namely their period $P$ and period derivative $\dot{P}$ ), together with some assumptions about their time evolution, to reconstruct the birth distribution of periods and magnetic fields for the pulsar population."270 These analyses also need o make assumptions about pulsar properties ancl their evolution (such as. for example. the exact shape of the radio beam and its dependence on the period). as well as overcome a number of selection. effects.," These analyses also need to make assumptions about pulsar properties and their evolution (such as, for example, the exact shape of the radio beam and its dependence on the period), as well as overcome a number of selection effects."271 Results from various investigations have often been conflicting. with some studies favoring initial periods in the millisecond range (e.g. Arzoumanian et al.," Results from various investigations have often been conflicting, with some studies favoring initial periods in the millisecond range (e.g. Arzoumanian et al."272 2002). and others instead finding more ikely periods in the range of several tens to several hundreds of milliseconds (c.g. Faucher-Giguere Ixaspi 2006).," 2002), and others instead finding more likely periods in the range of several tens to several hundreds of milliseconds (e.g. Faucher-Giguere Kaspi 2006)."273 The ellorts put over the vears into this area of research stem from he fact that the birth properties of neutron stars (NSs) are intimately related to the physical processes occurring during he supernova (SN) explosion and in the proto-neutron star., The efforts put over the years into this area of research stem from the fact that the birth properties of neutron stars (NSs) are intimately related to the physical processes occurring during the supernova (SN) explosion and in the proto-neutron star.274 As such. they bear crucial information on the physics of core-collapse SNe. in which most are thought to be formed.," As such, they bear crucial information on the physics of core-collapse SNe, in which most are thought to be formed."275 Besides the inferences on the birth parameters. from the radio population discussed. above. we show here that constraints can be derived. also from the X-rays.," Besides the inferences on the birth parameters from the radio population discussed above, we show here that constraints can be derived also from the X-rays."276 Young. fast rotating neutron stars are indeed expected to be very bright in the NX-ravs.," Young, fast rotating neutron stars are indeed expected to be very bright in the X-rays."277" In fact. observationally there appears to be a correlation between the rotational energy. loss of the star. Ey. and its X-ray luminosity. £,."," In fact, observationally there appears to be a correlation between the rotational energy loss of the star, $\dot{E}_{\rm rot}$, and its X-ray luminosity, $L_x$."278 Phis correlation was noticed by Verbunt et al. (, This correlation was noticed by Verbunt et al. (2791996). Becker Trumper (1997). Seward Wane (1988). Saito (1998) for a small saniple of objects. and later studied by Possentiet al. (,"1996), Becker Trumper (1997), Seward Wang (1988), Saito (1998) for a small sample of objects, and later studied by Possenti et al. ("2802002: P02 in the following) for the largest sample of pulsars known to date.,2002; P02 in the following) for the largest sample of pulsars known to date.281" ο.‘Combining the birth parameters derived from the radio (which determine the birth distribution. of Ly, for the pulsars). with the empirical L,ο correlation. the distribution of X-ray luminosity can be predicted. for a sample of pulsars with a certain age distribution."," Combining the birth parameters derived from the radio (which determine the birth distribution of $\dot{E}_{\rm rot}$ for the pulsars), with the empirical $L_x - \dot{E}_{\rm rot}$ correlation, the distribution of X-ray luminosity can be predicted for a sample of pulsars with a certain age distribution."282 The above calculation was »erformed by Perna Stella (2004)., The above calculation was performed by Perna Stella (2004).283 They foune that the ρε parameters derived by Arzoumanian et al. (, They found that the birth parameters derived by Arzoumanian et al. (284"2002). oecther with the L,La correlation","2002), together with the $L_x - \dot{E}_{\rm285rot}$ correlation"286stellar contributions were included in the SEDs.,stellar contributions were included in the SEDs.287 Nebular emission lines have been shown to be important in the first 10 yr (AndersFritze-v.Alvensleben2003) and should be considered when studying unresolved stellar populations (see $55.3)., Nebular emission lines have been shown to be important in the first $10^7$ yr \citep{and03} and should be considered when studying unresolved stellar populations (see 5.3).288 Figure | plots the V) (UB) colour-colour diagram., Figure 1 plots the $-$ V) $-$ B) colour-colour diagram.289 The black curves are our SB99 models with solar abundances and varying V)., The black curves are our SB99 models with solar abundances and varying $-$ V).290 From the bottom to the top. V)20.0. 0.5. 1.0. and. 1.5 mags.," From the bottom to the top, $-$ V)=0.0, 0.5, 1.0, and 1.5 mags."291 The filled squares are the observed colours of the standard set of open clusters in the WEBDA sample., The filled squares are the observed colours of the standard set of open clusters in the WEBDA sample.292 For each curve. age increases to the right from | Myr to 20 Gyr.," For each curve, age increases to the right from 1 Myr to 20 Gyr."293 Note that we have assumed the maximum uncertainty in colour for each OC., Note that we have assumed the maximum uncertainty in colour for each OC.294 This study is not intended as a test of the SB99 model's ability to reproduce the colours of young clusters., This study is not intended as a test of the SB99 model's ability to reproduce the colours of young clusters.295 This has already been demonstrated (see for e.g.. Vázquez&Leitherer 2005)).," This has already been demonstrated (see for e.g., \citealp{vaz05}) )."296 We intend to test how well various colours and initial model assumptions ean recover the ages of well studied Galactie open clusters., We intend to test how well various colours and initial model assumptions can recover the ages of well studied Galactic open clusters.297 In addition to using the observed colours to estimate ages. we compared the published colours with the model colours calculated assuming the published ages to look for evidence of stochastic sampling effects.," In addition to using the observed colours to estimate ages, we compared the published colours with the model colours calculated assuming the published ages to look for evidence of stochastic sampling effects."298 To determine the model predicted ages of the OCs we compared the observed integrated colours to each of the reddened (and unreddened) SB99 model colours. for a single assumed metallicity.," To determine the model predicted ages of the OCs we compared the observed integrated colours to each of the reddened (and unreddened) SB99 model colours, for a single assumed metallicity."299 We used a 47 minimization calculation (e.g.. Pasquali.deGrijs.&Gallagher2003:Grijsetal. 20051) to determine the best match of the observed colours to the models and hence the ages of the open clusters: where N is the number of colours (1-4) used in the analysis. obs; is the observed colour. model; is the corresponding model colour. and c; is the uncertainty in the obs; colour.," We used a $\chi^2$ minimization calculation (e.g., \citealp{pas03,deg05}) ) to determine the best match of the observed colours to the models and hence the ages of the open clusters: where N is the number of colours (1-4) used in the analysis, $_i$ is the observed colour, $_i$ is the corresponding model colour, and $\sigma_i$ is the uncertainty in the $_i$ colour."300 All ages with a fit of OX Ν were considered good fits., All ages with a fit of $\chi^2\leq$ N were considered good fits.301 For each colour set there was therefore a range of predicted ages for each OC., For each colour set there was therefore a range of predicted ages for each OC.302 The age associated with the minimum X? is taken as the best-fit age., The age associated with the minimum $\chi^2$ is taken as the best-fit age.303 To determine the uncertainties in the predicted age we find the minimum and maximum ages within a X7 defined to give a confidence level te.g.. Pressetal.19925).," To determine the uncertainties in the predicted age we find the minimum and maximum ages within a $\Delta\chi^2$ defined to give a confidence level (e.g., \citealp{pre92}) )."304 Additionally. we add the model step size to the age uncertainty.," Additionally, we add the model step size to the age uncertainty."305 We have also predicted the amount of extinction in each case., We have also predicted the amount of extinction in each case.306 The amount of extinction applied to the model associated with the best-fit age is the best-titV)., The amount of extinction applied to the model associated with the best-fit age is the best-fit.307. The uncertainty in the predicted iis determined from the minimum and maximum wwithin the same 4? mentioned above., The uncertainty in the predicted is determined from the minimum and maximum within the same $\Delta\chi^2$ mentioned above.308 Additionally. we add the model step size to the uuncertainty.," Additionally, we add the model step size to the uncertainty."309 In Table |. we list the subset of our sample that has theU.B. andV magnitudes available.," In Table 1, we list the subset of our sample that has the, and magnitudes available."310 Column one is the name of the OC. column two is the published age. column three is the predicted age determined from the (UB) and V). column four is My-. columns five and six are the reddening-corrected measured and zero reddened model (UB) colours respectively. column seven is the difference of the measured and model (UB). and columns eight. nine and ten are the same but for the — V) colour.," Column one is the name of the OC, column two is the published age, column three is the predicted age determined from the $-$ B) and $-$ V), column four is $_{V}$, columns five and six are the reddening-corrected measured and zero reddened model $-$ B) colours respectively, column seven is the difference of the measured and model $-$ B), and columns eight, nine and ten are the same but for the $-$ V) colour."311 It can be seen from Table | that for of the OCs. the (UB) differences are Z0.141. the assumed maximum measurement uncertainty in measured colour. while of the (BV) differences are =0.14.," It can be seen from Table 1 that for of the OCs, the $-$ B) differences are $\la0.14$, the assumed maximum measurement uncertainty in measured colour, while of the $-$ V) differences are $\la0.14$."312 In Figure 2. we plot the predicted ages against the published ages. if only (UB) and V) are used to estimate the ages.," In Figure 2, we plot the predicted ages against the published ages, if only $-$ B) and $-$ V) are used to estimate the ages."313 We also provide a histogram showing the distribution of the differences between the predicted and published ages. a plot of the predicted V)s against the published Vos. and a histogram showing the distribution of the differences between the predicted and published Vis.," We also provide a histogram showing the distribution of the differences between the predicted and published ages, a plot of the predicted $-$ V)s against the published $-$ V)s, and a histogram showing the distribution of the differences between the predicted and published $-$ V)s."314 In this Figure. we used the solar abundance models.," In this Figure, we used the solar abundance models."315 Plots of the predictions determined with the other colour combinations and at other assumed metallicities are similar so are not shown., Plots of the predictions determined with the other colour combinations and at other assumed metallicities are similar so are not shown.316 We see from this figure that with the combination of (UB) and V) the ages of the OCs can be predicted with reasonable accuracy., We see from this figure that with the combination of $-$ B) and $-$ V) the ages of the OCs can be predicted with reasonable accuracy.317 We present Table 2 to discuss both the accuracy and precision of various colours as age indicators., We present Table 2 to discuss both the accuracy and precision of various colours as age indicators.318 Column one is the colour combination. column two is the number of OCs in the sample with those colours available. and column three is the number of good fits for the solar. 0.2 solar and 2.5 solar models. where the number of good fits is the number of models in our grid that give Vox N. Column four is the percentage of recovered ages. which deseribes how often the predicted age uncertainties overlapped with he uncertainties in the measured ages when solar metallicity is assumed.," Column one is the colour combination, column two is the number of OCs in the sample with those colours available, and column three is the number of good fits for the solar, 0.2 solar and 2.5 solar models, where the number of good fits is the number of models in our grid that give $\chi^2\leq$ N. Column four is the percentage of recovered ages, which describes how often the predicted age uncertainties overlapped with the uncertainties in the measured ages when solar metallicity is assumed."319 The results from comparisons to models of 0.2 solar and 2.5 solar abundances are similar so are not shown., The results from comparisons to models of 0.2 solar and 2.5 solar abundances are similar so are not shown.320 Column tive lists the average uncertainty in predicted logtt) in the negative direction for all the OCs. column six lists the average uncertainty in wedicted logit) in the positive direction for all the OCs. and column seven lists the average of the positive and negative uncertainties or all the OCs.," Column five lists the average uncertainty in predicted log(t) in the negative direction for all the OCs, column six lists the average uncertainty in predicted log(t) in the positive direction for all the OCs, and column seven lists the average of the positive and negative uncertainties for all the OCs."321 It should be noted that the model ages range rom a logtt) of 6 to 10.3. therefore 2.15 is the maximum mean xositive and negative uncertainty in log(t).," It should be noted that the model ages range from a log(t) of 6 to 10.3, therefore 2.15 is the maximum mean positive and negative uncertainty in log(t)."322 Columns eight. nine.," Columns eight, nine,"323A survey of 24 circumstellar disks by Andrews&Wiliams found p~ 0.0-1.0 with an average of p~0.5. while the hydrodynamical simulations of Vorobyov&Basu(2009) found p~ 1.0-2.0 with an average around pz1.5.,"A survey of 24 circumstellar disks by \citet{andrews07} found $p\approx$ 0.0–1.0 with an average of $p\approx0.5$, while the hydrodynamical simulations of \citet{vorobyov09b} found $p\approx$ 1.0–2.0 with an average around $p\approx1.5$."324" Disk mass limits M, for p20.0. 0.5. 1.0 and 1.5. along with the more fundamental surface density limits are given in Table 2.."," Disk mass limits $M_{d}$ for $p=0.0$, 0.5, 1.0 and 1.5, along with the more fundamental surface density limits are given in Table \ref{tab:Mass-Limits}."325" We also provide the characteristic fragment mass (approximate planet mass) M, from eq. (17))", We also provide the characteristic fragment mass (approximate planet mass) $M_{f}$ from eq. \ref{eq:mass}) )326 that we would expect from the disk fragmentation mechanism., that we would expect from the disk fragmentation mechanism.327 Also note that. in order to be conservative. we are using the smallest radius found by Chiangetal.(2008) for Fomalhaut b. Using one of their better fits 1115 AU) will deerease our lower disk mass limit by a few percent. increase our upper disk mass limit by —30% (which would make fragmentation slightly easier). and increase the characteristic fragment mass by ~50%.," Also note that, in order to be conservative, we are using the smallest radius found by \citet{chiang08} for Fomalhaut b. Using one of their better fits 115 AU) will decrease our lower disk mass limit by a few percent, increase our upper disk mass limit by $\approx30\%$ (which would make fragmentation slightly easier), and increase the characteristic fragment mass by $\approx50\%$."328 We have refined the calculations of Rafikov(2005) and found cooling times over an order of magnitude shorter., We have refined the calculations of \citet{rafikov05} and found cooling times over an order of magnitude shorter.329" We have used these cooling times. along with the observed stellar parameters of Fomalhaut. HR 8799, and HL Tau. to test the viability of the disk. fragmentation mechanism."," We have used these cooling times, along with the observed stellar parameters of Fomalhaut, HR 8799, and HL Tau, to test the viability of the disk fragmentation mechanism."330 We found that in each of these systems. at least one planet could have formed as the result of fragmentation. assuming the disk mass interior to those planets fell within a particular range as indicated in Table 2..," We found that in each of these systems, at least one planet could have formed as the result of fragmentation, assuming the disk mass interior to those planets fell within a particular range as indicated in Table \ref{tab:Mass-Limits}."331 While the ranges in Table 2 only span a factor of a few. this is not by itself a significant limitation.," While the ranges in Table \ref{tab:Mass-Limits} only span a factor of a few, this is not by itself a significant limitation."332 Even if the local surface density is above the upper instability limit. fragmentation may still occur since the surface density must eventually drop through the unstable regime as the disk evolves and dissipates.," Even if the local surface density is above the upper instability limit, fragmentation may still occur since the surface density must eventually drop through the unstable regime as the disk evolves and dissipates."333 The caveat is that the surface density needs to evolve on a timescale longer than an orbital period. so that there can be sufficient time to fragment., The caveat is that the surface density needs to evolve on a timescale longer than an orbital period so that there can be sufficient time to fragment.334 Our minimum disk masses for Fomalhaut b. HR bb. and HL Tau b are about an order of magnitude larger than those inferred from observations (Andrews&Wiliams 2007).," Our minimum disk masses for Fomalhaut b, HR b, and HL Tau b are about an order of magnitude larger than those inferred from observations \citep{andrews07}."335 Note. however. that this is a problem for all planet formation models m general.," Note, however, that this is a problem for all planet formation models in general."336 Even core aceretion models require an enhanced surface density (although to a somewhat lesser extent) (Pollacketal.1996:Inaba2003).," Even core accretion models require an enhanced surface density (although to a somewhat lesser extent) \citep{pollack96,inaba03}."337. One possible mechanism for increasing the surface density is mass loading from an infalling envelope (Vorobyov&Basu2006)., One possible mechanism for increasing the surface density is mass loading from an infalling envelope \citep{vorobyov06}.338 Conversely. current estimates of disk masses may be too low because they depend on: I) the extrapolation of surface densities in. the outermost regions of the disk to the inner disk. and 2) the rather uncertain dust opacity.," Conversely, current estimates of disk masses may be too low because they depend on: 1) the extrapolation of surface densities in the outermost regions of the disk to the inner disk, and 2) the rather uncertain dust opacity."339 For example. larger dust grains would require larger disk masses to fit the observed SEDs (Andrews&Wiliams2007).," For example, larger dust grains would require larger disk masses to fit the observed SEDs \citep{andrews07}."340. As further evidence for underestimated disk masses. numerical hydrodynamical simulations by Vorobyov(2009) found disk masses much higher than those of Andrews&Wil-iams(200," As further evidence for underestimated disk masses, numerical hydrodynamical simulations by \citet{vorobyov09a} found disk masses much higher than those of \citet{andrews07}."3417 In particular. stars like Fomalhaut and HR 8799 can support )..disks as large as 0.5 M... while HL Tau could have a disk as massive as 0.1 M... all of which are within our limits for disk fragmentation.," In particular, stars like Fomalhaut and HR 8799 can support disks as large as 0.5 $M_{\sun}$, while HL Tau could have a disk as massive as 0.1 $M_{\sun}$, all of which are within our limits for disk fragmentation."342 We caution. however. that our choice of opacity model can have a major effect on our results.," We caution, however, that our choice of opacity model can have a major effect on our results."343 For example. decreasing the dust opacity raises the temperature and decreases the cooling time in the outer disk. resulting in disk fragmentation at smaller radii.," For example, decreasing the dust opacity raises the temperature and decreases the cooling time in the outer disk, resulting in disk fragmentation at smaller radii."344 On the other hand. increasing the opacity would have the opposite effect.," On the other hand, increasing the opacity would have the opposite effect."345 Regardless of the above considerations. HR 8799 c and d are too close to their parent star to have formed via fragmentation under the conditions modeled here.," Regardless of the above considerations, HR 8799 c and d are too close to their parent star to have formed via fragmentation under the conditions modeled here."346 Appealing to chronically overestimated dust opacity can only get us so, Appealing to chronically overestimated dust opacity can only get us so347{he input energy.,the input energy.348 The reprocessing optical depth is thus given by the condition To define the quantity Ly.) iis useful conceptually to divide the emergent radiation into stellar photons aud envelope photons., The reprocessing optical depth is thus given by the condition To define the quantity $L_{\rm rep}$ it is useful conceptually to divide the emergent radiation into stellar photons and envelope photons.349 In a Monte Carlo simulation. the stellar luminosity is divided into N equal energy photon packets (note that packets with different Irequencies contain a dilferent number of plvsical photons).," In a Monte Carlo simulation, the stellar luminosity is divided into $N$ equal energy photon packets (note that packets with different frequencies contain a different number of physical photons)."350" The energy per packet is given bv where L, is the stellar luminosity anc M is an arbitrary simulation time.", The energy per packet is given by where $L_\star$ is the stellar luminosity and $\Delta t$ is an arbitrary simulation time.351 Stellar photons are emitted from the star ancl (μον propagate through the envelope. where (μον may be scatlerecl or absorbed.," Stellar photons are emitted from the star and they propagate through the envelope, where they may be scattered or absorbed."352 If a stellar photon is absorbed. radiative equilibrium requires (hat il be reemittec as an envelope photon.," If a stellar photon is absorbed, radiative equilibrium requires that it be reemitted as an envelope photon."353 Note (hat scattering does not change the photon ivpe (stellar vs. envelope)., Note that scattering does not change the photon type (stellar vs. envelope).354" The fraction of the stellar Iuminositv reprocessed (absorbed) by the envelope max easily be determined by counting the number of stellar photon packets absorbed by the envelope. *absVi""."," The fraction of the stellar luminosity reprocessed (absorbed) by the envelope may easily be determined by counting the number of stellar photon packets absorbed by the envelope, $N_\star^{\rm abs}$."355" This is equivalent to counting the number of stellar photons that emerge Irom the envelope without absorption. VE""."," This is equivalent to counting the number of stellar photons that emerge from the envelope without absorption, $N_\star^{\rm em}$."356" Thus (he Iuminosity. reprocessed bv the envelope is where L7"" is the emergent stellar huninosity.", Thus the luminosity reprocessed by the envelope is where $L_\star^{\rm em}$ is the emergent stellar luminosity.357 This is the method we use to measure Lees in this paper., This is the method we use to measure $L_{\rm rep}$ in this paper.358" Note that scattering affects Ly, because a photon packet that is scattered can be absorbed subsequently.", Note that scattering affects $L_{\rm rep}$ because a photon packet that is scattered can be absorbed subsequently.359" Owing to (hese scattering effects. it is not straiehtlorwarel {ο obtain Z4, from standard radiative transfer quantities."," Owing to these scattering effects, it is not straightforward to obtain $L_{\rm rep}$ from standard radiative transfer quantities."360 The reprocessed luminosity is given bv the emergent Iuminosityv of (he envelope. so where da/dQ is the dilferential scattering cross section. which is a function of both incoming and outgoing directions (n and n. respectively). and 72 is the envelope contribution (Monte Carlo envelope photons) to the specific intensitv (this includes scattered. envelope photons but does not include scattered stellar photons).," The reprocessed luminosity is given by the emergent luminosity of the envelope, so where $d \sigma/d\Omega$ is the differential scattering cross section, which is a function of both incoming and outgoing directions $\hat{\rm{n}}^\prime$ and $\hat{\rm{n}}$, respectively), and $I_{\lambda}^{\rm{env}}$ is the envelope contribution (Monte Carlo envelope photons) to the specific intensity (this includes scattered envelope photons but does not include scattered stellar photons)."361" Energy conservation requires (hat Loveyre equals the οποιονS. absorbed in the envelope. so L..,re can also be written as"," Energy conservation requires that $L_{\rm rep}$ equals the energy absorbed in the envelope, so $L_{\rm rep}$ can also be written as"362had la‘ee lit residuas.,had large fit residuals.363 For this reason. few data are iicluded from. images with seeing worse than L.5 aresec FWHML. aud the majority of the data are fiom Πάθος with « 1l arcsec seeing.," For this reason, few data are included from images with seeing worse than 1.5 arcsec FWHM, and the majority of the data are from images with $<$ 1 arcsec seeing."364 The very best lnages include are around 0.6 arcsec. still not cuite ΕπΠρος," The very best images included are around $0.6$ arcsec, still not quite undersampled."365 When the sky was suitably. cloudless. exposures in the CBVRI filters (or sometimes only V aud J) were added to the program. together with sandard star fieds from Landolt(1992) to allow transformation to standard magnitudes.," When the sky was suitably cloudless, exposures in the $UBVRI$ filters (or sometimes only $V$ and $I$ ) were added to the program, together with standard star fields from \citet{landolt92} to allow transformation to standard magnitudes."366 Photometric exposures were obtained on at least two nights. aud the results were averaged after aualysis.," Photometric exposures were obtained on at least two nights, and the results were averaged after analysis."367 The consistency was generally better than 0.05 mae., The consistency was generally better than 0.05 mag.368 The data were reduced using staudard routines for bias subtraction aud flat field correction., The data were reduced using standard routines for bias subtraction and flat field correction.369 The flat fields were constructed from offset. mediaued images of the twilight sky.," The flat fields were constructed from offset, medianed images of the twilight sky."370 Star centers were measured with the IRAF implenentation of DAOPHOT (originally written Nw Stetson LOST)). which constructs a model »oiut-sp'ead function (PSF) from selected stars and its these to the program stars.," Star centers were measured with the IRAF implementation of DAOPHOT (originally written by \citealt{stetsondao}) ), which constructs a model point-spread function (PSF) from selected stars and fits these to the program stars."371 Because he centroid iformation is contained in the steep sides of he PSF. a small fitting radius was used. generally 0.8 arcsec.," Because the centroid information is contained in the steep sides of the PSF, a small fitting radius was used, generally 0.8 arcsec."372 For some of the later measurements. he fittiug radius was adapted to the seeing ou the Individual pictures.," For some of the later measurements, the fitting radius was adapted to the seeing on the individual pictures."373 The measurement procedure was automated as follows., The measurement procedure was automated as follows.374 First. the average of several of the yest pictues (the fiducial frame) was examined to select a set of stars to measure aud a set of suitable PSF stars.," First, the average of several of the best pictures (the `fiducial' frame) was examined to select a set of stars to measure and a set of suitable PSF stars."375 Next. lists of stars on all the piettwes frames were generated usingοι orSEvtractor (Bertin&Arnouts19060).," Next, lists of stars on all the pictures frames were generated using or \citep{bertin96}."376.. A computer program matched objects on these lists to the correspouding objects on the fiducial frame. and the matches were used to transform the program and PSF star coordinates to the system of each picture.," A computer program matched objects on these lists to the corresponding objects on the fiducial frame, and the matches were used to transform the program and PSF star coordinates to the system of each picture."377 The DAOPHOT measturements proceeded automatically., The DAOPHOT measurements proceeded automatically.378 To determiue tlie true scale aud orientation of the fiducial frame. the star images were matched to the USNO A2.0 catalog (Monetοἱal.1996).. which is aligned with the ICRS (essentially J2000).," To determine the true scale and orientation of the fiducial frame, the star images were matched to the USNO A2.0 catalog \citep{mon96}, which is aligned with the ICRS (essentially J2000)."379 In most fields several dozen stars were ma(ολους. with plate solutious typically having RMS residuals of 0.2)3. mostly from the centeringD>oO unce‘tainty ο ‘the USNO A2.0 and. proper motious since the USNO A2.0 plate epoch.," In most fields several dozen stars were matched, with plate solutions typically having RMS residuals of $0.''3$, mostly from the centering uncertainty of the USNO A2.0 and proper motions since the USNO A2.0 plate epoch."380" Civen the number of stars in the solutions aud the size of the field. the ünage scales clerivecl from these fits shotId be accurate to a few parts in 101, and the orientation should be accurate to a 0.03) degree."," Given the number of stars in the solutions and the size of the field, the image scales derived from these fits should be accurate to a few parts in $10^4$, and the orientation should be accurate to a $\sim 0.03$ degree."381 Using the scale aud orientation. the pixel coordinates of the fictucial stars were transformed to taugeu plane coordinates μα aud αμα. with the program object at the origin.," Using the scale and orientation, the pixel coordinates of the fiducial stars were transformed to tangent plane coordinates $X_{\rm fid}$ and $Y_{\rm fid}$ , with the program object at the origin."382 These coordinates correspoud closely to Aa and Adover a siuall field., These coordinates correspond closely to $\Delta \alpha$ and $\Delta \delta$over a small field.383For the eccentricities of our sample of 931 main belt asteroids. the best fit parameters are: We also fit the data to a double-Gaussian distribution. The eumulative distribution function for equation (A3)) is For the eccentricities of our sample of 931 main belt asteroids. we performed a least squares fit to equation CÀ4)) ancl obtained the following best-fit parameters: We evaluated the goodness of fit using the IxXolimogorov-Smirnov (Ix-5) test.,"For the eccentricities of our sample of 931 main belt asteroids, the best fit parameters are: We also fit the data to a double-Gaussian distribution, The cumulative distribution function for equation \ref{e:doublegaussian}) ) is For the eccentricities of our sample of 931 main belt asteroids, we performed a least squares fit to equation \ref{e:doublecdf}) ) and obtained the following best-fit parameters: We evaluated the goodness of fit using the Kolmogorov-Smirnov (K-S) test."384 The [νο test determines the probability (iat. two distributions ave (he same. or in our case how well our model distributions fit the observed data (Pressοἱal.1992).," The K-S test determines the probability that two distributions are the same, or in our case how well our model distributions fit the observed data \citep{Press:1992p1610}."385. The Ix-9 test compares the cumulative distribution of the data against the model cumulative distribution function., The K-S test compares the cumulative distribution of the data against the model cumulative distribution function.386 We found that our asteroid sample has a probability of 4.5x107 that it comes from the best fit sinele Gaussian (equation (A2))). but a probability of 0.73 that it comes from the (equation (&4))).," We found that our asteroid sample has a probability of $4.5\times10^{-2}$ that it comes from the best fit single Gaussian (equation \ref{e:cdf}) )), but a probability of $0.73$ that it comes from the double-Gaussian (equation \ref{e:doublecdf}) ))."387 Therefore. the K-S tests indieate that the double-Gaussian is a better fit to the data than the single-Gaussian.," Therefore, the K-S tests indicate that the double-Gaussian is a better fit to the data than the single-Gaussian."388 We performed Hartigan’s dip test (Ilartigan&Hartigan1985) (o test whether the observational data is consistent wilh a multi-peaked distribution., We performed Hartigan's dip test \citep{Hartigan:1985p3924} to test whether the observational data is consistent with a multi-peaked distribution.389 Hartigans dip test calculates the probability that the distribution being tested has a single peak., Hartigan's dip test calculates the probability that the distribution being tested has a single peak.390 Applving Hartigan's dip test lo a given distribution vields in a test statistic: together with the sample size. the test statistic is matelied to a p-value range in à precomputed table provided bv (1985)..," Applying Hartigan's dip test to a given distribution yields in a test statistic; together with the sample size, the test statistic is matched to a p-value range in a precomputed table provided by \cite{Hartigan:1985p3924}."391 The p-value is a measure of the probability that the distribution actually has only one peak (the null-hvpothesis. for this problem).," The p-value is a measure of the probability that the distribution actually has only one peak (the null-hypothesis, for this problem)."392 The smaller (he caleulated p-value.," The smaller the calculated p-value,"393"there is a level, deep enough in the atmosphere/interior at which the temperature is independent of latitude/longitude. (","there is a level, deep enough in the atmosphere/interior at which the temperature is independent of latitude/longitude. ("394"Note that this should be deeper, peharps considerably, than the level at which the irradiation flux has been completely absorbed).","Note that this should be deeper, peharps considerably, than the level at which the irradiation flux has been completely absorbed)."395 I hereafter turn to the derivation of the temperature profile in an atmosphere that advects heat horizontally., I hereafter turn to the derivation of the temperature profile in an atmosphere that advects heat horizontally.396" I now consider that for each atmospheric location (6,9) defined from the substellar point, mixing tables place by horizontal advection and transports heat with a flux gVT."," I now consider that for each atmospheric location $(\theta,\phi)$ defined from the substellar point, mixing tables place by horizontal advection and transports heat with a flux $\qnab$."397" The radiative equilibrium equation becomes: or, The first moment of the radiative transfer equation (eq. 4))"," The radiative equilibrium equation becomes: or, The first moment of the radiative transfer equation (eq. \ref{eq:H}) )"398" becomes by integration and hence Note that since we envision that VT—0 when m—co, this implies H(co)=στά,/(4n)."," becomes by integration and hence Note that since we envision that $\nabla T\rightarrow 0$ when $m\rightarrow\infty$, this implies $H(\infty)=\sigma\tint^4/(4\pi)$."399" Now, the equation for Hi, becomes: and by integration Hqa(0)=H(0)—H,(0) and therefore Inserting this relation into eq. (36))"," Now, the equation for $\Hth$ becomes: and by integration $\Hth(0)=H(0)-\Hv(0)$ and therefore Inserting this relation into eq. \ref{eq:Hth-q}) )"400" yields We now integrate the equation for the second moment of the radiation field: and by integrating by parts: The relation for Ji, can then be found simply from the first Eddington coefficient fxin= Kin/Jin.", yields We now integrate the equation for the second moment of the radiation field: and by integrating by parts: The relation for $\Jth$ can then be found simply from the first Eddington coefficient $\fKth=\Kth/\Jth$ .401" Then, using eq. (32))"," Then, using eq. \ref{eq:B-q}) )"402" yields We use the relations fin= Hq(0)/Jq(0), H,(0)= and H(co)=στὰ, H,(0)=μ.στῄ, to find an expression for the temperature profile at each location (τ,μ.Φ) in the atmosphere: The relation is a complex one and its resolution goes beyond the scope of the present article."," yields We use the relations $\fHth\equiv \Hth(0)/\Jth(0)$, $\Hv(0)=-\mu_*\Jv(0)$ , and $H(\infty)=\sigma\tint^4$, $\Hv(0)=\mu_*\sigma\tirr^4$ to find an expression for the temperature profile at each location $(\tau,\mu,\phi)$ in the atmosphere: The relation is a complex one and its resolution goes beyond the scope of the present article."403 We are mostly interested in the deep atmospheric temperature., We are mostly interested in the deep atmospheric temperature.404" As discussed, in the presence of an efficient-enough advection process, the temperature at deep levels should become latitudinally and longitudinally homogeneous."," As discussed, in the presence of an efficient-enough advection process, the temperature at deep levels should become latitudinally and longitudinally homogeneous."405" I therefore average over latitudes and longitudes (defined from the substellar point) to obtain a global mean temperature that depends only on depth r: For a conservative advection scheme (in particular if q does not depend on yp, ¢ or T), $qVTdw=0."," I therefore average over latitudes and longitudes (defined from the substellar point) to obtain a global mean temperature that depends only on depth $\tau$: For a conservative advection scheme (in particular if $q$ does not depend on $\mu$, $\phi$ or $T$ ), $\oint\qnab d\omega=0$."406 This leads to a great simplification of eq. (43)), This leads to a great simplification of eq. \ref{eq:T4-adv}) )407" which becomes after integration over all latitudes and longitudes isha(using µ.= 4): Note that we integrated the intrinsic flux over the entireplanet, whereas the irradiation flux is of course integrated only over the dayside hemisphere."," which becomes after integration over all latitudes and longitudes (using $\mu_*=\mu$ ): Note that we integrated the intrinsic flux over the entireplanet, whereas the irradiation flux is of course integrated only over the dayside hemisphere."408" The integral term can be rewritten or, in terms of exponential integrals E,(z)=ft""e “dt, The E, functions— have a recursive property(?)::"," The integral term can be rewritten or, in terms of exponential integrals $E_n(z)\equiv\int_1^\infty t^{-n}e^{-zt}dt$ , The $E_n$ functions have a recursive property:"409"We develop here a simple geometrical model to estimate the accretion rate onto a massive black hole in a stellar system, fueled by mass loss from stars (Quataertetal. 1999).","We develop here a simple geometrical model to estimate the accretion rate onto a massive black hole in a stellar system, fueled by mass loss from stars \citep{Quataert1999}."410". If a star is located at a distance r from the massive black hole, and if it produces an isotropic wind, with velocity Uwing, only the fraction of gas which passes within the accretion radius of the massive black hole, +¢2),(6) be accreted gravitational focusing)."," If a star is located at a distance $r$ from the massive black hole, and if it produces an isotropic wind, with velocity $v_{\rm wind}$, only the fraction of gas which passes within the accretion radius of the massive black hole, ^2+c^2_s), can be accreted (ignoring gravitational focusing)."411" Here c?scan= is (ignoringthe velocity dispersion of the stellar system at the GMetetar/(2.66r},)half-mass radius.", Here $\sigma^2=GM_{\rm stellar}/(2.66r_h)$ is the velocity dispersion of the stellar system at the half-mass radius.412" For a Hernquist profile, where the density in the inner region pοςr7!, the velocity dispersion decreases towards the center."," For a Hernquist profile, where the density in the inner region $\rho \propto r^{-1}$, the velocity dispersion decreases towards the center."413" Estimating c at the half mass radius gives a conservative lower limit to the accretion radius, and hence the accretion rate."," Estimating $\sigma$ at the half mass radius gives a conservative lower limit to the accretion radius, and hence the accretion rate."414" Following Miller&Hamilton(2002), we assume that in equation 6 the sound speed c,— 10kms~!, and, vying=50kms-!as reference values, although we study the effect that a different vwing has on our model (see Figure "," Following \cite{Miller2002}, we assume that in equation 6 the sound speed $c_s= 10 \kms$ , and, $v_{\rm wind} = 50 \kms$as reference values, although we study the effect that a different $v_{\rm wind}$ has on our model (see Figure \ref{vw}) )."415"If σ>vwinad, Race depends2)). only on the properties of the potential well of the stellar distribution, not on the wind properties."," If $\sigma \gg v_{\rm wind}$, $R_{\rm acc}$ depends only on the properties of the potential well of the stellar distribution, not on the wind properties."416" In particular, Race~ if Mstellar=10°Meu."," In particular, $R_{\rm acc} \simeq M_{\rm BH}R_{\rm417 eff}/M_{\rm stellar} \simeq 10^{-3}R_{\rm eff}$ if $M_{\rm418 stellar}=10^3 M_{BH}$."419" Note that, at fixed black hole mass, the more massive the galaxy, the smaller Race is, as the scaling of Reg with Megtellar is à power law with exponent less than one (see, e.g., equation 3)."," Note that, at fixed black hole mass, the more massive the galaxy, the smaller $R_{\rm acc}$ is, as the scaling of $R_{\rm eff}$ with $M_{\rm stellar}$ is a power law with exponent less than one (see, e.g., equation 3)."420" On the other hand, if σ<vwina, Race depends only on the wind velocity."," On the other hand, if $\sigma \ll v_{\rm421 wind}$, $R_{\rm acc}$ depends only on the wind velocity."422" These two limits are apparent in Figures 2 and 3,, and they will be discussed in the next section."," These two limits are apparent in Figures \ref{vw} and \ref{size}, and they will be discussed in the next section."423" Geometrical considerations suggest that, for r>Race: where M, is the mass loss rate from the star."," Geometrical considerations suggest that, for $r>R_{\rm424 acc}$: ], where $\dot M_*$ is the mass loss rate from the star."425" If the star lies within Racc, we consider Macc,x=M..."," If the star lies within $R_{\rm acc}$, we consider $\dot M_{{\rm acc},*}=\dot426M_*$."427 Eq. (7)), Eq. \ref{eq:geom}) )428" implicitly assumes that the stars have a spherically simmetric distribution and that their velocity field (and, as a consequence, the velocity field of the wind) is isotropic."," implicitly assumes that the stars have a spherically simmetric distribution and that their velocity field (and, as a consequence, the velocity field of the wind) is isotropic."429" In a rotating stellar system, the presence of net angular momentum of the gas can change the accretion rate onto the black hole (e.g.,Cuadraetal.2008).."," In a rotating stellar system, the presence of net angular momentum of the gas can change the accretion rate onto the black hole \citep[e.g.,][]{Cuadra2008}."430 A study of the dependence of the accretion rate on the degree of rotational support of the stellar distribution is beyond the scope of this paper., A study of the dependence of the accretion rate on the degree of rotational support of the stellar distribution is beyond the scope of this paper.431" The total contribution from all stars is found by integrating over the density profile of the stellar system:≺≺−⊮∂∁∁⊽∗∁⊈⊺⋅↿ where (m,.) is the mean stellar mass and p is given by eq. (2.1))"," The total contribution from all stars is found by integrating over the density profile of the stellar system:, where $\langle m_*\rangle$ is the mean stellar mass and $\rho$ is given by eq. \ref{eq:plummer}) )"432 and (2.1))., and \ref{eq:hernquist}) ).433 The normalization in eq. (2.2)), The normalization in eq. \ref{eq:mdot}) )434" is given by the cumulative mass loss rate of all the stars in the stellar structure, that we estimate following Ciottietal.(1991):: 13. where t, is the age of the stellar population, and Lg is the(9) total luminosity of the stellar system."," is given by the cumulative mass loss rate of all the stars in the stellar structure, that we estimate following \cite{Ciotti1991}: , where $t_*$ is the age of the stellar population, and $L_B$ is the total luminosity of the stellar system."435" We set t,=5 Gyr for dSphs and nuclear star clusters, and ἐς=12 Gyr for early type galaxies and globular clusters."," We set $t_*=5$ Gyr for dSphs and nuclear star clusters, and $t_*=12$ Gyr for early type galaxies and globular clusters."436 We derive band luminosities from stellar masses assuming a to-light ratio of 5 in the B-band., We derive B-band luminosities from stellar masses assuming a mass-to-light ratio of 5 in the B-band.437 We obtain an upper limit of the luminosity of the massive black hole by assuming that the whole Macc is indeed accreted by the massive black hole., We obtain an upper limit of the luminosity of the massive black hole by assuming that the whole $\dot M_{\rm acc}$ is indeed accreted by the massive black hole.438" Figure 2 shows the resulting accretion rate for a central massive black hole in different stellar systems, where we assume that the massive black hole mass scales with the mass of stellar component, Mpy=107?Maia; (Marconi&Hunt2003;HaringRix2004),, and we have considered vying a free parameter."," Figure \ref{vw} shows the resulting accretion rate for a central massive black hole in different stellar systems, where we assume that the massive black hole mass scales with the mass of stellar component, $M_{\rm BH}=10^{-3} M_{\rm439 stellar}$ \citep{MarconiHunt2003,Haring2004}, and we have considered $v_{\rm wind}$ a free parameter."440" We have assumed that Reg scales exactly with Maca, following the relationships discussed above."," We have assumed that $R_{\rm441 eff}$ scales exactly with $M_{\rm stellar}$ following the relationships discussed above."442" Note that for high values of the stellar masses in early-type galaxies and nuclear star clusters, the accretion rate and Race do not depend on the wind velocities."," Note that for high values of the stellar masses in early-type galaxies and nuclear star clusters, the accretion rate and $R_{\rm acc}$ do not depend on the wind velocities."443" In these cases σ>vwina, and the accretion rate depends only on the properties of the host stellar structure and on the black hole mass (see the discussion of Equation 6 above)."," In these cases $\sigma\gg v_{\rm wind}$, and the accretion rate depends only on the properties of the host stellar structure and on the black hole mass (see the discussion of Equation 6 above)."444" In Figure3 we instead fix vying, and allow for a scatter in the mass-size relationship."," In Figure \ref{size} we instead fix $v_{\rm wind}$ , and allow for a scatter in the mass-size relationship."445 For globular clusters we assume Reg=1 pc; Reg=2 pc and Reg=4 pc., For globular clusters we assume $R_{\rm eff}=1$ pc; $R_{\rm eff}=2$ pc and $R_{\rm eff}=4$ pc.446" For galaxies, the middle curve shows the best fit Reg for a given stellar mass value (Equations 1, 2 and 3), thetop curves assume that Reg is half the best fit value, and the"," For galaxies, the middle curve shows the best fit $R_{\rm eff}$ for a given stellar mass value (Equations 1, 2 and 3), thetop curves assume that $R_{\rm447 eff}$ is half the best fit value, and the"448The high angular resolution of the SALA allows us to trace the thermal emission of dust grains al physical scales of few hunedrecd astronomical (for objects in the Orion molecular cloud complex) and. therefore. is able to spatially resolve compact dust cores.,"The high angular resolution of the SMA allows us to trace the thermal emission of dust grains at physical scales of few hundred astronomical (for objects in the Orion molecular cloud complex) and, therefore, is able to spatially resolve compact dust cores."449 A detailed description of SALA is given in Hoetal.(2004)., A detailed description of SMA is given in \cite{Ho04}.450. The observations were carried oul in 2007 November 24 and December 19 with the SALA in its compact configuration., The observations were carried out in 2007 November 24 and December 19 with the SMA in its compact configuration.451 The number of antennas available for the observations were 7 and 6. respectively.," The number of antennas available for the observations were 7 and 6, respectively."452 The abmospheric opacityv al 225 Gllz was 0.11 and 0.07 for the first and second dav. respectively (values measured by the Caltech Submillimeter Observatory tau meter).," The atmospheric opacity at 225 GHz was 0.11 and 0.07 for the first and second day, respectively (values measured by the Caltech Submillimeter Observatory tau meter)."453 Observations were done in the 345 GlIIz atmospheric window. what corresponds to a wavelength of 870 jn. The SALA receivers operate in (wo sidebands separated by ~10 GlIz.," Observations were done in the 345 GHz atmospheric window, what corresponds to a wavelength of 870 $\mu$ m. The SMA receivers operate in two sidebands separated by $\sim 10$ GHz."454 The central observed frequencies for the lower and upper side bands were 336.5 Gllz and 346.5 Gllz. respectively.," The central observed frequencies for the lower and upper side bands were 336.5 GHz and 346.5 GHz, respectively."455 The SMA correlator had a bandwidth of 1.9 GIz (for each sideband) divided in 24 “chunks” of 128 channels each., The SMA correlator had a bandwidth of 1.9 GHz (for each sideband) divided in 24 “chunks” of 128 channels each.456 In total. the full-band spectrum contains 3072 channels for each sideband and a spectral resolution of 0.62 MlIIz. which corresponds (ο a velocity resolution of 0.7 km t.," In total, the full-band spectrum contains 3072 channels for each sideband and a spectral resolution of 0.62 MHz, which corresponds to a velocity resolution of 0.7 km $^{-1}$."457 SMA receivers are single linearly polarized., SMA receivers are single linearly polarized.458 By using a quarter-wave plate in front of each receiver. (he incoming radiation is converted into circular polarization (L. R).," By using a quarter-wave plate in front of each receiver, the incoming radiation is converted into circular polarization (L, R)."459 The SMA correlator combines the signal into circular polarization vectors: RR. LL. RL. LR.," The SMA correlator combines the signal into circular polarization vectors: RR, LL, RL, LR."460 In order to obtain the full four Stokes parameters for all the baselines. (he visibilities have to be averaged on a time scale of 5 minutes.," In order to obtain the full four Stokes parameters for all the baselines, the visibilities have to be averaged on a time scale of 5 minutes."461 A description of the SALA polarimeter and (he discussion of the methodology. (both hardware and software aspects)are available in Marroneetal.(2006) and Marrone&Rao (2003).., A description of the SMA polarimeter and the discussion of the methodology (both hardware and software aspects)are available in \citet{Marrone06} and \citet{Marrone08}. .462to roughly the same level at all radii aud for all cases. regardless of initial amplitudes.,"to roughly the same level at all radii and for all cases, regardless of initial amplitudes."463 The saturation level appears comparable to the initial field amplitudes in the 3500 case: field amplitudes in cases initially ereater than 3500 are dissipated through bydrodvuamic processes: field amplitudes in cases initially less than D500 are amplified until they reach D500 levels before leveling off., The saturation level appears comparable to the initial field amplitudes in the B500 case: field amplitudes in cases initially greater than B500 are dissipated through hydrodynamic processes; field amplitudes in cases initially less than B500 are amplified until they reach B500 levels before leveling off.464 Qur calculations sugecst no mechanism exists which cau drive field amplitudes above B500 levels. implying that we are safely modeling the upper Πιτ of sclbecuerated field streneths.," Our calculations suggest no mechanism exists which can drive field amplitudes above B500 levels, implying that we are safely modeling the upper limit of self-generated field strengths."465 Although field amplification does indeed take place in all magnetized ruus we have performed (medium and lieh resolution). it falls well short of. thermal equipartitiou so it cannot casily affect the ανασα] evolution of the star.," Although field amplification does indeed take place in all magnetized runs we have performed (medium and high resolution), it falls well short of thermal equipartition so it cannot easily affect the dynamical evolution of the star."466 This is demonstrated iu Figure 6 which shows the mass deusitv weighted average of the inverse plasmabeta (1/op) inside the star., This is demonstrated in Figure \ref{fig:betainv53} which shows the mass density weighted average of the inverse plasmabeta $1/\beta_B$ ) inside the star.467 In al cases the increase of magnetic pressure saturates at a level that is significautlv less than of the thermal pressure averaged across the star (with maxinuun peak values of about for the 62 ruus. aud forthe high resolution 96° case).," In all cases the increase of magnetic pressure saturates at a level that is significantly less than of the thermal pressure averaged across the star (with maximum peak values of about for the $64^3$ runs, and forthe high resolution $96^3$ case)."468 It appears that field saturation is cleternuned by universal behavior in the partitioning of thermal and maguctic enerev. independent of initial auplitude.," It appears that field saturation is determined by universal behavior in the partitioning of thermal and magnetic energy, independent of initial amplitude."469 This is true also for the P—2 aud 3 cases. both of which result iu mean 1/p profiles similar to the Τ=5/3 results shown in Figure 6..," This is true also for the $\Gamma=2$ and $3$ cases, both of which result in mean $1/\beta_B$ profiles similar to the $\Gamma=5/3$ results shown in Figure \ref{fig:betainv53}."470 Consequently. we do net expect eravitational waveforms to be affected appreciably by toroidal magnetic fields. as we demoustrate in Figure 7 for the D=5/3 cases. Figure δ for D=2. aud Figure 9. for TP=3.," Consequently, we do not expect gravitational waveforms to be affected appreciably by toroidal magnetic fields, as we demonstrate in Figure \ref{fig:gw53}471 for the $\Gamma=5/3$ cases, Figure \ref{fig:gw20} for $\Gamma=2$, and Figure \ref{fig:gw30} for $\Gamma=3$."472 Fiewres 7 through 9 plot the quantity rf| normalized by the scale factor (GAZ/cECy., Figures \ref{fig:gw53} through \ref{fig:gw30} plot the quantity $r h+$ normalized by the scale factor $(GM/\varpi_E c^2)^2$ .473 Figure 9 also includes results from a poloidal initial field configuration (run PCS30BLO0) for comparison., Figure \ref{fig:gw30} also includes results from a poloidal initial field configuration (run PG30B100) for comparison.474" Figure 7 (corresponding to the DP—5/3 cases) closely rescubles Figure 9 of Newetal.(2000): we match the amplitude and frequency of oscillations and find that our results are intermediate between the ""D1 aud “LI” displays in duration and pattern of the wave signal.", Figure \ref{fig:gw53} (corresponding to the $\Gamma=5/3$ cases) closely resembles Figure 9 of \citet{new00}: we match the amplitude and frequency of oscillations and find that our results are intermediate between the “D1” and “L1” displays in duration and pattern of the wave signal.475 It is uot uutil the field streneth is increased to L/opiningl with locally comparable thermal and maguctic pressures that we observe amplitude deviations of order in Figure 1," It is not until the field strength is increased to $1/\beta_{B,min} \sim 1$ with locally comparable thermal and magnetic pressures that we observe amplitude deviations of order in Figure \ref{fig:gw53}."476 The first evidence of oscillations in Figure 7?/ occurs at time f—6 which corresponds to the instant when the wm=2 mode fixst begius to dominate the spectral signal in Figure 2.., The first evidence of oscillations in Figure \ref{fig:gw53} occurs at time $t\sim6$ which corresponds to the instant when the $m=2$ mode first begins to dominate the spectral signal in Figure \ref{fig:mode53}.477 The global cuvelope shape (essentially the overall amplitude) of the gravitational wave emission tracks uicely the erowth and eventual decay of the m=2 mode curve in Figure2.., The global envelope shape (essentially the overall amplitude) of the gravitational wave emission tracks nicely the growth and eventual decay of the $m=2$ mode curve in Figure\ref{fig:mode53}. .478 Maxim peaks in both wave signals and spectral mode profiles correlate preciselv at time f£~16. ane both exhibit comparable rise and decav times.," Maximum peaks in both wave signals and spectral mode profiles correlate precisely at time $t\sim16$, and both exhibit comparable rise and decay times."479 Another point of interest iu comparing Figures 7 9 is the appareit trend for tie start of the wave signals to be delayed with Πιοσα]m adiabatic iudex D (evident also iu the spectral mole ots).," Another point of interest in comparing Figures \ref{fig:gw53} – \ref{fig:gw30}480 is the apparent trend for the start of the wave signals to be delayed with increasing adiabatic index $\Gamma$ (evident also in the spectral mode plots)."481 However. we have found that tιο onset of tie lustability is seusitive to a nuuber of uiuucrical factoTS (e.g... grid resolution. Courant factor). aid it is ciffiaIt ο lnake quantitative conclusions regmlingC» this effec," However, we have found that the onset of the instability is sensitive to a number of numerical factors (e.g., grid resolution, Courant factor), and it is difficult to make quantitative conclusions regarding this effect."482 For example. the magnetized aud παςjetized DP--Ὁ üeh-resolution cases reseiible Figure 7 but for a slig delay of about 1.5 ανασα. times. effectively a eniporal shift in the waveform.," For example, the magnetized and unmagnetized $\Gamma=5/3$ high-resolution cases resemble Figure \ref{fig:gw53} but for a slight delay of about 1.5 dynamical times, effectively a temporal shift in the waveform."483 However. other aspects of he waveforms are similar between the higher aud lower resolution cases: the magnetized results are essentially identical to the uninagnetized waveforms. aud the wave auplitudes agree nicely.," However, other aspects of the waveforms are similar between the higher and lower resolution cases: the magnetized results are essentially identical to the unmagnetized waveforms, and the wave amplitudes agree nicely."484" Even though the eravitational wave amplitudes are fairly consistent with no obvious correlation with D (approximately 0.15. 0:35.aud 0.11 for E= 5/3. 2 uud jJ. respectively). the wavelength of perturlvations betweeenr] the two biggest wave crests and the burst duratkn (between leading aud trailing wave crestswith amplitiucle larecr than 0.1) do appear to increase 1ionotouicalls ""with D."," Even though the gravitational wave amplitudes are fairly consistent with no obvious correlation with $\Gamma$ (approximately 0.45, 0.35,and 0.44 for $\Gamma=$ 5/3, 2 and 3, respectively), the wavelength of perturbations between the two biggest wave crests and the burst duration (between leading and trailing wave crestswith amplitude larger than 0.1) do appear to increase monotonically with $\Gamma$."485 Iu particular. we find wavelengths of approximatelv Af Lot and Lat for D— 5/3. 2. and 3. a fractionalincrease (in wavelength) of about between P2 aud DP2 5/3. aud abhorut betwec‘ll TC=3 and P— 5/5.," In particular, we find wavelengths of approximately $\tilde t$ , $\tilde t$ , and $\tilde t$ for $\Gamma=$ 5/3, 2, and 3, a fractionalincrease (in wavelength) of about between $\Gamma=2$ and $\Gamma=5/3$ and about between $\Gamma=3$ and $\Gamma=5/3$ ."486 Trends iu both amplitudes aud wavelengths are consistent with hose of Houser&Cen- (1996).. whofind the amplitude is independent of," Trends in both amplitudes and wavelengths are consistent with those of \citet{houser96}, , whofind the amplitude is independent of"487We note that our analysis is limited to objects in circular motion in a static uniform isothermal £&aseous medium.,We note that our analysis is limited to objects in circular motion in a static uniform isothermal gaseous medium.488 For comparison with detailed observatious. our assumptions for the backgrouud uiecdium aud the object motion may 1eed to be relaxed.," For comparison with detailed observations, our assumptions for the background medium and the object motion may need to be relaxed."489 However. tlie wake features described iu this paper may sulice to provide a zerothi order approximation of the primary features expected [rom the gravitational wakes clue to stch objects.," However, the wake features described in this paper may suffice to provide a zeroth order approximation of the primary features expected from the gravitational wakes due to such objects."490 TIe author is grateful to Ronal« E. Tan for continuous discussion on this topic through reacling the manscript. aud Oscar Morata auc Wooug-Tae iim for euncouragiug and helpful Connieus.," The author is grateful to Ronald E. Taam for continuous discussion on this topic through reading the manuscript, and Oscar Morata and Woong-Tae Kim for encouraging and helpful comments."491 The aitlior also acknowledges a stitmulating report from the anonymous referee. which iucreased the sigülicance aud potential of this work.," The author also acknowledges a stimulating report from the anonymous referee, which increased the significance and potential of this work."492 This researcl is supported by the Theoretical Institute for Advanced Resea‘cl iu Astrophysics (TIARA) in the Acaclelia Sinica Insitute of Astronomy ancl Astrophysies (ASIAA)., This research is supported by the Theoretical Institute for Advanced Research in Astrophysics (TIARA) in the Academia Sinica Institute of Astronomy and Astrophysics (ASIAA).493 The nunerical simulations preseited here are perfoined using FLASH2.0 code developed by the DOE-supported ASC/Alliauce Ceuer for Astropliysical Thermonuclear Flashes at the University of Chicago., The numerical simulations presented here are performed using FLASH3.0 code developed by the DOE-supported ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago.494should retain the triaxiality predicted by cosmological siuulatiouns.,should retain the triaxiality predicted by cosmological simulations.495 This iav help to explain the rather clongated shapes of the ultra-faint MW. satellites (? (although these cau also be attributed to tidal effects im the gravitational feld of the NW) and oddities iu the Kinematics of some dwarf spheroidal galaxies (see.c.g“Se. 7).," This may help to explain the rather elongated shapes of the ultra-faint MW satellites \citep{Martin_etal08} (although these can also be attributed to tidal effects in the gravitational field of the MW) and oddities in the kinematics of some dwarf spheroidal galaxies \citep[see, e.g.,][]{Penarrubia_etal10}."496 Many dwarf galaxies are also in the regime 5Z0.5 where they are unable to modity their surrounding halos., Many dwarf galaxies are also in the regime $\eta \simlt 0.5$ where they are unable to modify their surrounding halos.497 CGascous disks iu such galaxies should exhibit departures from axisvaiuuetry. unless the halos are either prolate or oblate aud the disk plane comcides with that where the 2D potential is axisvuuuectric.," Gaseous disks in such galaxies should exhibit departures from axisymmetry, unless the halos are either prolate or oblate and the disk plane coincides with that where the 2D potential is axisymmetric."498 This could indeed be the case in uearly oblate halos. eiven the preference of the angular moment to align with the nmünor axis (7).," This could indeed be the case in nearly oblate halos, given the preference of the angular momentum to align with the minor axis \citep{Bett_etal07}."499. However. iu nearly prolate idos (a iore conmuuon occurence according to 2V- ον siuimlations) disks whose augular moment aligus with the minor axis would feel a noun-axisviuinetric 2D gravitational potential.," However, in nearly prolate halos (a more common occurrence according to $N$ -body simulations) disks whose angular momentum aligns with the minor axis would feel a non-axisymmetric 2D gravitational potential."500 Nou-circular| motions should herefore be fairly conuuon iu the saseous disks of dwarts. aud they could iu principle be used to gauge the raxialitv of their surrounding hialos.," Non-circular motions should therefore be fairly common in the gaseous disks of dwarfs, and they could in principle be used to gauge the triaxiality of their surrounding halos."501 To first order. a gaseous disk iu the uou-axisviunietric x»teutial of a triaxial halo would behave just like gas ij a barred potential where the patteru speed of the uw ds zero.," To first order, a gaseous disk in the non-axisymmetric potential of a triaxial halo would behave just like gas in a barred potential where the pattern speed of the bar is zero."502 A subdominant disk iu a triaxial potential would thus exhibit the nou-circular ανασα. signature of a (slow) bar but with no obvious bar in the Iuminous distribution., A subdominant disk in a triaxial potential would thus exhibit the non-circular dynamical signature of a (slow) bar but with no obvious bar in the luminous distribution.503 Tutercstinely. there is one system where all these conditions are niet.," Interestingly, there is one system where all these conditions are met."504 NGC 2976 is a nearby dwarf spiral ealaxy whose barvouic disk is subdominanut. as shown iu the bottom-rielt paucl of Figure 1..," NGC 2976 is a nearby dwarf spiral galaxy whose baryonic disk is subdominant, as shown in the bottom-right panel of Figure \ref{fig1}."505 This Ποσο shows that the contribution of the barvonic component peaks at about one-half of the circular velocity at 7=2:284 and therefore 5gz0.5., This figure shows that the contribution of the baryonic component peaks at about one-half of the circular velocity at $r=2.2 R_d$ and therefore $\eta\approx 0.5$.506 2 show that the kinematics of the gaseous disk iu NGC 2976 is hniehlv complex. exlibiting large non-circular motions near the ceuter.," \citet{Simon_etal03} show that the kinematics of the gaseous disk in NGC 2976 is highly complex, exhibiting large non-circular motions near the center."507 These. according to 7.. are best understood as the characteristic kinematic asviuunuetries miposed by awa=2 bar inode in the eravitatioual potential (scealso ?)..," These, according to \citet{Spekkens_Sellwood07}, are best understood as the characteristic kinematic asymmetries imposed by an $m=2$ bar mode in the gravitational potential \citep[see also][]{Hayashi_Navarro06}. ."508 Ou the other haud. NCC 2976 has uo obvious bar. at least in the optical (butsce?).. so ascribing the origin of the nou-cireular motions to halo triaxiality is clearly tempting.," On the other hand, NGC 2976 has no obvious bar, at least in the optical \citep[but see][]{Menendez_etal07}, so ascribing the origin of the non-circular motions to halo triaxiality is clearly tempting."509 If this interpretation is correct. then it would be surprising if other galaxies with subdonüuaut barvouic conrponeuts did not also show sigus of beiug embedded in triaxial potentials.," If this interpretation is correct, then it would be surprising if other galaxies with subdominant baryonic components did not also show signs of being embedded in triaxial potentials."510 Dudeed. oue nav even argue that he absence of such signatures m a significant fraction of unbarred LSB aud chwart galaxies would be quite difücult to accommodate within the standard CDAI xwadieumi.," Indeed, one may even argue that the absence of such signatures in a significant fraction of unbarred LSB and dwarf galaxies would be quite difficult to accommodate within the standard CDM paradigm."511 Definitive conchisions ou these issues require nore sophisticated theoretical modeling of the formation of subdominant disks iu triaxial halos., Definitive conclusions on these issues require more sophisticated theoretical modeling of the formation of subdominant disks in triaxial halos.512 Note that our uodels neglect. for example. the response of the disk o the triaxial forcing of the halo. as well as a realistic accounting of the distribution of disk oricutatious relative o the principal axes of the halo.," Note that our models neglect, for example, the response of the disk to the triaxial forcing of the halo, as well as a realistic accounting of the distribution of disk orientations relative to the principal axes of the halo."513 Nevertheless. our results sugeest that a careful search for signatures of wo traniality in a statistically significant sample of dwarf and LSB ealaxies would be warranted.," Nevertheless, our results suggest that a careful search for signatures of halo triaxiality in a statistically significant sample of dwarf and LSB galaxies would be warranted."514 Steps iu hisdirection such as those taken by ? , Steps in thisdirection such as those taken by \citet{Trachternach_etal09} 515"distribution can be very well described by Equation (7)) introduced by(1996),, where Const, zo=<z>πο and f are free parameters with «z> being the first moment of the distribution and I' the Gamma function.","distribution can be very well described by Equation \ref{eqn:brainerd}) ) introduced by, where $Const$ , $z_0=<z>\frac{\Gamma (3/\beta)}{\Gamma (4/\beta)}$ and $\beta$ are free parameters with $<z>$ being the first moment of the distribution and $\Gamma$ the Gamma function."516" The best fitting values are: Const=6206, zo=0.107, and 6=0.611."," The best fitting values are: $Const=6206$, $z_0=0.107$, and $\beta=0.611$."517" Please note that if we analyse the galaxy photometric redshift histogram with a binning of Az=0.1 there are three clearly visible peaks below redshift of z=2: one at Zpnot=[0.6,0.7], one at Zpnoe=[0.9,1.0], and one at Zpnot= [1.7,1.8]. Interestingly, we also find peaks in the spectroscopic redshift histogram (see also Fig. 9))"," Please note that if we analyse the galaxy photometric redshift histogram with a binning of $\Delta z=0.1$ there are three clearly visible peaks below redshift of $z=2$: one at $z_{phot}=[0.6, 0.7]$, one at $z_{phot}=[0.9, 1.0]$, and one at $z_{phot}=[1.7, 1.8]$ Interestingly, we also find peaks in the spectroscopic redshift histogram (see also Fig. \ref{fig_tz}) )"518" with at least 10 galaxies at Zspec=[0.657,0.669], [0.672, 0.683], and Zspec=[0.926,0.941]."," with at least 10 galaxies at $z_{spec}=[0.657, 0.669]$, $z_{spec}=[0.672, 0.683]$ , and $z_{spec}=[0.926, 0.941]$."519 In this section we show the UV luminosity function (LF) at 1500 aas derived from our deep i-selected catalogue and compare it to the LFs in the FDF2004a)., In this section we show the UV luminosity function (LF) at 1500 as derived from our deep i-selected catalogue and compare it to the LFs in the FDF.520. 'To derive the absolute UV band magnitude we use the best fitting SED as determined by the photometric redshift code., To derive the absolute UV band magnitude we use the best fitting SED as determined by the photometric redshift code.521" Since the photometric redshift code works with aperture fluxes, we only need to correct to total luminosities by applying an object dependent scale factor."," Since the photometric redshift code works with aperture fluxes, we only need to correct to total luminosities by applying an object dependent scale factor."522 For this scale factor we used the ratio of the I-band aperture flux to the total flux as provided by SExtractor (MAG.AAPER and MAG.AAUTO)., For this scale factor we used the ratio of the I-band aperture flux to the total flux as provided by SExtractor APER and AUTO).523" As the SED fits all observed-frame passbands simultaneously, possible systematic errors which could be introduced by using K-corrections applied to a single observed magnitude are reduceddetails)."," As the SED fits all observed-frame passbands simultaneously, possible systematic errors which could be introduced by using K-corrections applied to a single observed magnitude are reduced."524" As an example, we plot in Fig."," As an example, we plot in Fig."525 14 the absolute UV-band magnitudes against the photometric redshifts of the objects in the COSMOS patch 06a., \ref{fig:absmag_1500} the absolute UV-band magnitudes against the photometric redshifts of the objects in the COSMOS patch 06a.526 Moreover we also show the absolute UV-band magnitudes as derived in the FDF., Moreover we also show the absolute UV-band magnitudes as derived in the FDF.527" Both fields agree very well in their magnitude distribution, although there are a few relatively bright objects in the COSMOS patch (about 5 times the area of the FDF) not seen in the FDF distribution."," Both fields agree very well in their magnitude distribution, although there are a few relatively bright objects in the COSMOS patch (about 5 times the area of the FDF) not seen in the FDF distribution."528" To check if those objects could be stars misclassified as galaxies by our star-galaxy separation criterion, we decided to use a more conservative criterion for separating stars from galaxies."," To check if those objects could be stars misclassified as galaxies by our star-galaxy separation criterion, we decided to use a more conservative criterion for separating stars from galaxies."529 We changed our criterion from 2Xstar<X2alazy to Xstar<X2alazy (see above).," We changed our criterion from $2\ \chi_{star}^2 <530\chi_{galaxy}^2$ to $\chi_{star}^2 <\chi_{galaxy}^2$ (see above)."531 As can be seen in Fig., As can be seen in Fig.532 14 even this conservative criterion does not remove a substantial fraction of these relatively bright objects., \ref{fig:absmag_1500} even this conservative criterion does not remove a substantial fraction of these relatively bright objects.533" Note that because of the larger seeing (0.95"")) compared to the FDF (0.55"")), there may be more blended objects in the catalogue."," Note that because of the larger seeing ) compared to the FDF ), there may be more blended objects in the catalogue."534 'The luminosity function is computed by dividing the number of galaxies in each magnitude bin by the volume Voin of the redshift interval., The luminosity function is computed by dividing the number of galaxies in each magnitude bin by the volume $V_\mathrm{bin}$ of the redshift interval.535" To account for the fact that some fainter galaxies are not visible in the whole survey volume, we performed a V/Vinaz correction."," To account for the fact that some fainter galaxies are not visible in the whole survey volume, we performed a $V/V_{max}$ correction."536" 'The errors of the LFs were calculated by means of Monte-Carlo simulations and include the photometric redshift error of every single galaxy, as well as the statistical error (Poissonian error)."," The errors of the LFs were calculated by means of Monte-Carlo simulations and include the photometric redshift error of every single galaxy, as well as the statistical error (Poissonian error)."537" To derive precise Schechter parameters, we limited our analysis of the LF to the magnitude bin where the V/Vmazx correction is negligible (red dots in Fig. 15))."," To derive precise Schechter parameters, we limited our analysis of the LF to the magnitude bin where the $V/V_{max}$ correction is negligible (red dots in Fig. \ref{fig:uvlf}) )."538 We also show the uncorrected LF in the various plots as open circles., We also show the uncorrected LF in the various plots as open circles.539 We did not assume any evolution of the galaxies within the single redshift bins., We did not assume any evolution of the galaxies within the single redshift bins.540" The redshift intervals are approximately the same size in In(1+2), and most of the results we are going to discuss are based on 1000 — 4000 galaxies per redshift bin and per patch."," The redshift intervals are approximately the same size in $\ln(1+z)$, and most of the results we are going to discuss are based on 1000 – 4000 galaxies per redshift bin and per patch."541 In Fig., In Fig.542 15 we present the UV luminosity functions at 1500 ((we evaluate the luminosity function in the rectangular filter at À))., \ref{fig:uvlf} we present the UV luminosity functions at 1500 (we evaluate the luminosity function in the rectangular filter at ).543 The filled (open) symbols denote the luminosity function with (without) completeness correction in the different patches., The filled (open) symbols denote the luminosity function with (without) completeness correction in the different patches.544 We also show the V/Vmaz corrected mean LFs in the COSMOS field as well as the FDF LFs2004a)., We also show the $V/V_{max}$ corrected mean LFs in the COSMOS field as well as the FDF LFs.545. The solid red lines show the Schechter function fitted to the luminosity function (we used fixed slope ofa=—1.07 as found in the FDF)., The solid red lines show the Schechter function fitted to the luminosity function (we used a fixed slope of$\alpha=-1.07$ as found in the FDF).546" The best afitting Schechter parameter, the redshift binning as well as the reduced x? are also listed."," The best fitting Schechter parameter, the redshift binning as well as the reduced $\chi^2$ are also listed."547It is obvious from the figure that there is strong,It is obvious from the figure that there is strong548nanny of the modes may contain simular information. aud this dataset may be trimmed further without sjenificaut loss of information.,"many of the modes may contain similar information, and this dataset may be trimmed further without significant loss of information."549 This is effected by a singular value decomposition of the uniou of the nodes. and modes corresponding to simall singular values are excluded.," This is effected by a singular value decomposition of the union of the modes, and modes corresponding to small singular values are excluded."550 Full details ave given in TTIT.. and an example from CODE is illustrated in Figure 1. which shows that for theconditional likclihoods at least. the data compression procedure can work extremely well.," Full details are given in \cite{TTH}, and an example from COBE is illustrated in Figure 1, which shows that for the likelihoods at least, the data compression procedure can work extremely well."551 However. this ou its own may uot be sufficieut to achieve simall mareinal errors. especially if two or more paranueters are highly correlated.," However, this on its own may not be sufficient to achieve small marginal errors, especially if two or more parameters are highly correlated."552" This is expected to be the case for high-resolution CAB experiments such as MAP. and Planck (c.e. for paraincters Qu, aud v}.", This is expected to be the case for high-resolution CMB experiments such as MAP and Planck (e.g. for parameters $Q_{\rm rms}$ and $n$ ).553 To give a more concrete example a thin ridge of likelihood. at 15? to two paraueter axes has σα]. conditional errors. but the mareiual errors can be very huge.," To give a more concrete example – a thin ridge of likelihood at $45^\circ$ to two parameter axes has small conditional errors, but the marginal errors can be very large."554 This applies whether or uot the likelihood surface cau be approximated well by a bivariate Cassia., This applies whether or not the likelihood surface can be approximated well by a bivariate Gaussian.555limit of the central density po so that (o)Z;200pcrit.,limit of the central density $\rho_0$ so that $\langle\rho\rangle \gtrsim 200 \rho_{crit}$.556" For individual substructures, both mass and volume scale as 2, keeping the average density constant."," For individual substructures, both mass and volume scale as $f_r^3$, keeping the average density constant."557 This implies that stability for one substructure level ensures stability for all other levels., This implies that stability for one substructure level ensures stability for all other levels.558" Since the halo density distribution is significantly clumpy, the velocity field for such a system is also expected to have fluctuations at all scales."," Since the halo density distribution is significantly clumpy, the velocity field for such a system is also expected to have fluctuations at all scales."559" However, due to approximate spherical symmetry of the clump distribution, the average rotation velocity over a spherical shell at radius r will still be (ve(r))& (GM,/r)!/?, where M, is the total mass within this radius."," However, due to approximate spherical symmetry of the clump distribution, the average rotation velocity over a spherical shell at radius $r$ will still be $\langle v_c(r) \rangle \approx (GM_r/r)^{1/2}$ , where $M_r$ is the total mass within this radius."560" As pointed out in subsection 2.3 using the virial stability argument, the virial velocity or, equivalently, the ""rotation"" velocity is expected to be approximately same as the local velocity dispersion."," As pointed out in subsection \ref{sec:virial} using the virial stability argument, the virial velocity or, equivalently, the “rotation” velocity is expected to be approximately same as the local velocity dispersion."561 This derived rotation curve for the fractal model is found to be NFW-like at large radial distance., This derived rotation curve for the fractal model is found to be NFW-like at large radial distance.562" At small radius, by construction, the rotation curve is obviously exactly same as that of a non-singular isothermal halo."," At small radius, by construction, the rotation curve is obviously exactly same as that of a non-singular isothermal halo."563 This is shown in Figure 2.., This is shown in Figure \ref{fig:rotcur}.564" Radial distance is scaled by Το and rotation velocity is scaled by vo, which is the rotation velocity at the maximum radius plotted."," Radial distance is scaled by $r_c$ and rotation velocity is scaled by $v_0$, which is the rotation velocity at the maximum radius plotted."565" The black curve is the predicted rotation curve for the fractal substructure model with n=35, f,=0.25, fp=1.0 and rmax=θ.0Τς and the red line is the best fit NFW profile to that."," The black curve is the predicted rotation curve for the fractal substructure model with $n=35$, $f_r=0.25$, $f_{\rho} = 1.0$ and $r_{max} = 6.0 r_c$ and the red line is the best fit NFW profile to that."566" The background density threshold pp, is assumed to be negligible in this model.", The background density threshold $\rho_{bg}$ is assumed to be negligible in this model.567 Rotation curves for non-singular isothermal sphere with and without a cutoff and blue curves respectively) as well as for NFW halo (green(magenta curve) are also shown in Figure 2 fora comparison., Rotation curves for non-singular isothermal sphere with and without a cutoff (green and blue curves respectively) as well as for NFW halo (magenta curve) are also shown in Figure \ref{fig:rotcur} for a comparison.568 The velocity scaling ensures that the total mass encompassed by the maximum radius is same for all models., The velocity scaling ensures that the total mass encompassed by the maximum radius is same for all models.569 The effect of the background density threshold is shown in Figure 3.., The effect of the background density threshold $\rho_{bg}$ is shown in Figure \ref{fig:rbgcur}.570" Here, the rotation curve is evaluatedpp, for different keeping all other parameters same as in Figure 2.."," Here, the rotation curve is evaluated for different $\rho_{bg}$ keeping all other parameters same as in Figure \ref{fig:rotcur}."571" For ppgscaling, we have used the density p(Tmaz) at the cutoff radius rma,=6.0r.."," For scaling, we have used the density $\rho(r_{max})$ at the cutoff radius $r_{max} = 6.0 r_c$."572" Different curves in Figure 3 are for pog/p(Tmax)=0.00, 0.03, 0.10 and 0.30 red, green and blue curve respectively)."," Different curves in Figure \ref{fig:rbgcur} are for $\rho_{bg}/\rho(r_{max}) = 0.00$, $0.03$, $0.10$ and $0.30$ (black, red, green and blue curve respectively)."573" The general (black,NFW-like nature of the rotation curve and the radial fluctuations remain unchanged.", The general NFW-like nature of the rotation curve and the radial fluctuations remain unchanged.574" But depending on the value of ppg, rotation curve at large radius may be rising, flat or declining."," But depending on the value of $\rho_{bg}$, rotation curve at large radius may be rising, flat or declining."575 Note that the derived rotation curves shown in Figure 3 are with the simple model of a constant , Note that the derived rotation curves shown in Figure \ref{fig:rbgcur} are with the simple model of a constant $\rho_{bg}$.576"In reality, is expected to be decreasing with ppg.increasing r, givingpy, rise to a rotation curve somewhat intermediate between the extremes shown in Figure 3.."," In reality, $\rho_{bg}$ is expected to be decreasing with increasing $r$, giving rise to a rotation curve somewhat intermediate between the extremes shown in Figure \ref{fig:rbgcur}."577 'The predicted rotation curve due to the clustering of dark matter subhalos is very similar to the observed rotation curve and the empirical NFW rotation curve., The predicted rotation curve due to the clustering of dark matter subhalos is very similar to the observed rotation curve and the empirical NFW rotation curve.578" However, unlike the NFW model with a smooth radial density distribution, the present model predicts a significant fluctuation of rotation velocity in both angular and radial directions."," However, unlike the NFW model with a smooth radial density distribution, the present model predicts a significant fluctuation of rotation velocity in both angular and radial directions."579" Since the underlying density field, which gives rise to this velocity fluctuations, is scale free, the velocity fluctuation power spectrum is expected to be a power law."," Since the underlying density field, which gives rise to this velocity fluctuations, is scale free, the velocity fluctuation power spectrum is expected to be a power law."580" Though the fractal model has many free parameters, the only relevant parameters for the index of this power law are n and f, while the rest of them will just introduce different multiplicative scaling."," Though the fractal model has many free parameters, the only relevant parameters for the index of this power law are $n$ and $f_r$ while the rest of them will just introduce different multiplicative scaling."581 'This prediction can be easily verified from high spatial and spectral resolution observation of neutral hydrogen of normal galaxies., This prediction can be easily verified from high spatial and spectral resolution observation of neutral hydrogen of normal galaxies.582 Note that part of this fluctuations will cancel out for the spherically averaged rotation curve and hence it is important to use the full velocity field to search for such scale free fluctuations., Note that part of this fluctuations will cancel out for the spherically averaged rotation curve and hence it is important to use the full velocity field to search for such scale free fluctuations.583 It is also important to note that fluctuations of the velocity field of the hydrogen gas will have contributions from the local density perturbations of the disk., It is also important to note that fluctuations of the velocity field of the hydrogen gas will have contributions from the local density perturbations of the disk.584 But the scale, But the scale585measurements without systematic effects. which are expected to be small because the wavelength calibration was derived from sky lines exposed simultaneously with the OJ 287 spectrum.,"measurements without systematic effects, which are expected to be small because the wavelength calibration was derived from sky lines exposed simultaneously with the OJ 287 spectrum."586 Figure 4. shows the position and flux density of the 26583 [NII] and Πα lines., Figure \ref{viivamuutos} shows the position and flux density of the $\lambda$ 6583 [NII] and $\alpha$ lines.587 The 46583 |NII] line is not expected to show any variations over the timescales considered here. which is also confirmed by our results: no variability larger than the error bars is observed.," The $\lambda$ 6583 [NII] line is not expected to show any variations over the timescales considered here, which is also confirmed by our results: no variability larger than the error bars is observed."588 However. the error bars of the flux densities are quite large.," However, the error bars of the flux densities are quite large."589" The broad H,, line shows no significant changes in position or flux between the two epochs it was detected.", The broad $H_{\alpha}$ line shows no significant changes in position or flux between the two epochs it was detected.590 As the upper limits show. the data are consistent with no change in the broad Πα line flux throughout the whole monitoring campaign.," As the upper limits show, the data are consistent with no change in the broad $\alpha$ line flux throughout the whole monitoring campaign."591 Thus we find no evidence of changes in the BLR in our data., Thus we find no evidence of changes in the BLR in our data.592 However. there is a big difference to the line flux observed by ?.. who reported a Ha line flux of 24κ1074 erg em sc. which is a factor of ~ 10 higher than in 2005-08.," However, there is a big difference to the line flux observed by \cite{1985PASP...97.1158S}, , who reported a $\alpha$ line flux of $2.4 \times 10^{-14}$ erg $^{-2}$ $^{-1}$, which is a factor of $\sim$ 10 higher than in 2005-08."593 The difference remains even after subtracting the summed contribution of the [NIE] and narrow Her lines. 12x107! erg em? s7!. which were unresolved by ?..," The difference remains even after subtracting the summed contribution of the [NII] and narrow $\alpha$ lines, $12 \times 10^{-16}$ erg $^{-2}$ $^{-1}$, which were unresolved by \cite{1985PASP...97.1158S}."594 The weighted average of the broad He line width is 120+14A.. which corresponds to 4200+500 km/s at the redshift of OJ 287.," The weighted average of the broad $\alpha$ line width is $120 \pm59514$, which corresponds to $4200 \pm 500$ km/s at the redshift of OJ 287."596 ? do not give the line width. but estimating from their Fig.," \cite{1985PASP...97.1158S} do not give the line width, but estimating from their Fig."597 2 itis ~ 120A.. i.e. the same as observed here.," 2 it is $\sim$ 120, i.e. the same as observed here."598 The most notable result of our monitoring is the dramatic decrease in broad Haluminosity between 1984 and 2005-08., The most notable result of our monitoring is the dramatic decrease in broad $\alpha$luminosity between 1984 and 2005-08.599 In Fig., In Fig.600 5. we show the continuum and broad Πα line flux of, \ref{kontiviiva} we show the continuum and broad $\alpha$ line flux of601The Quoreseent Kea emission line of iron is currently the best probe we have to study strong-field gravitational effects in the vicinity of black holes.,The fluorescent $\alpha$ emission line of iron is currently the best probe we have to study strong-field gravitational effects in the vicinity of black holes.602 This line. together with an associated backscattered continuum. is readilv formed when a hard N-ray continuum source irraciates the surface of a relatively cold and optically-thick slab of gas (Basko 1978: Culbert Rees 1988: Lightman White 1988: George Fabian 1901: Matt et αἱ.," This line, together with an associated backscattered continuum, is readily formed when a hard X-ray continuum source irradiates the surface of a relatively cold and optically-thick slab of gas (Basko 1978; Guilbert Rees 1988; Lightman White 1988; George Fabian 1991; Matt et al."603 1991)., 1991).604 Nowadays. the hard. X-ray source is usually identified. with thermal Comptonization from an aceretion disk. corona. and the opticallv-thick structure as the aceretion disk itself (see Itevnolds Nowak 2003 for a recent review).," Nowadays, the hard X-ray source is usually identified with thermal Comptonization from an accretion disk corona, and the optically-thick structure as the accretion disk itself (see Reynolds Nowak 2003 for a recent review)."605 The diagnostic power of these spectral features Dies in investigations of their. Doppler »oadening and gravitational redshifting (Fabian et al., The diagnostic power of these spectral features lies in investigations of their Doppler broadening and gravitational redshifting (Fabian et al.606 1989: Laor 1991)., 1989; Laor 1991).607 Phe best example to date of using these features o probe strong-field gravity is the Sevíert-1.2 galaxy MC6-30-15 Cl'anaka et al., The best example to date of using these features to probe strong-field gravity is the Seyfert-1.2 galaxy MCG--6-30-15 (Tanaka et al.608 1995: Wilms et al., 1995; Wilms et al.609 2001: Fabian et al., 2001; Fabian et al.610 2002: Revnolels et al., 2002; Reynolds et al.611 2004)., 2004).612 This object. displays a highly-xoadened and skewed iron line that is strongly suggestive of emission [from an accretion disk reaching down to near he radius of marginal stability for a rapiclhy-rotating black hole., This object displays a highly-broadened and skewed iron line that is strongly suggestive of emission from an accretion disk reaching down to near the radius of marginal stability for a rapidly-rotating black hole.613 As vet. there is no competing model that can explain. in detail. the iron line feature in MC6-30-15.," As yet, there is no competing model that can explain, in detail, the iron line feature in MCG–6-30-15."614 llowever. Ἡ is an open question whether these relativistic spectral features are. generic in the spectra of various classes of active galactic nuclei (AGN).," However, it is an open question whether these relativistic spectral features are generic in the spectra of various classes of active galactic nuclei (AGN)."615 Nandra et al. (, Nandra et al. (6161997a) used data from the observatory to conclude that relativistically-broacdened iron lines are very common features in the X-ray spectra of Sevfert-1: nuclei.,1997a) used data from the observatory to conclude that relativistically-broadened iron lines are very common features in the X-ray spectra of Seyfert-1 nuclei.617 On the other hand. found that these emission lines were often weaker and/or narrower in the X-ray spectra of low-luminosity AGN (c.g. Revnolds. Nowak Maloney 2000: ‘Torashima et al.," On the other hand, found that these emission lines were often weaker and/or narrower in the X-ray spectra of low-luminosity AGN (e.g., Reynolds, Nowak Maloney 2000; Terashima et al."618 2002). hieh-luminosity AGN (Nanera et al.," 2002), high-luminosity AGN (Nandra et al."619 1997b) ane raclio-loud ACN (Sambruna. Eracleous Alushotzky 1990).," 1997b) and radio-loud AGN (Sambruna, Eracleous Mushotzky 1999)."620 Recent results from the European Photon Imaging Camera (EPIC) on broad. the observatory have painted a more complex picture., Recent results from the European Photon Imaging Camera (EPIC) on broad the observatory have painted a more complex picture.621 While has. indeed. found uncdisputed cases of broad iron lines in the Sevlert galaxies δα6-30-15 (Wilms et al.," While has, indeed, found undisputed cases of broad iron lines in the Seyfert galaxies MCG–6-30-15 (Wilms et al."622 2001. Fabian et al.," 2001, Fabian et al."623 2002). AIC5-23-16 (Dewangan. Crilliths Schurch 2003). NGC 3516 CLurner οἱ al.," 2002), MCG–5-23-16 (Dewangan, Griffiths Schurch 2003), NGC 3516 (Turner et al."624 2002). MrR335 (CGondoin et al.," 2002), Mrk335 (Gondoin et al."625 2002). anc Mrk766 (Pounds et al.," 2002), and Mrk766 (Pounds et al."626 2003a). other Sevfert-1," 2003a), other Seyfert-1"627The paper is organized as follows.,The paper is organized as follows.628 In Section 2. the theoretical isochrones are compared to data on 47 Tuc in both the CMD and LF domains., In Section \ref{isocmd} the theoretical isochrones are compared to data on 47 Tuc in both the CMD and LF domains.629" In Section 3. we compare observed line-indices to model predictions computed rom both the original and the ""LE-corrected"" isochrones.", In Section \ref{isoobs} we compare observed line-indices to model predictions computed from both the original and the “LF-corrected” isochrones.630 Model uncertainties due to errors in the input stellar parameters are discussed in Section 4.. and our conclusions are summarized in Section 5..," Model uncertainties due to errors in the input stellar parameters are discussed in Section \ref{unc}, and our conclusions are summarized in Section \ref{conc}."631 Belore comparing the isochrone-based model spectra with the observations. we call allention to important features of the theoretical isochrones (hat are crucial to interpreting our results.," Before comparing the isochrone-based model spectra with the observations, we call attention to important features of the theoretical isochrones that are crucial to interpreting our results."632 In Figure 1. the CMD of 47 Tuc (Howell. Guhathakurta Gilliland 2000) is overlaid with isochrones from Salaris aud collaborators lor 8. 10. 12 aud 14 Gyrs.," In Figure \ref{fig1}633 the CMD of 47 Tuc (Howell, Guhathakurta Gilliland 2000) is overlaid with isochrones from Salaris and collaborators for 8, 10, 12 and 14 Gyrs."634 Conversion from the theoretical plane (LiT. py) to the observational plane |V.(D VJ] was performed according to the recipe described in Paper L and adopting a distance modulus of ÀA[)y213.33. and VJ-0.04 Uxaluzny et al.," Conversion from the theoretical plane $L_{bol}$ $T_{eff}$ ) to the observational plane $V$ ] was performed according to the recipe described in Paper I, and adopting a distance modulus of $(m-M)_0$ =13.33 and =0.04 (Kaluzny et al."635 1993)., 1998).636 These isochrones are described in Vazdekis οἱ al. (, These isochrones are described in Vazdekis et al. (6372001) and were kindly provided bv M. Salaris.,2001) and were kindly provided by M. Salaris.638 They. are computed taking into consideration diffusion of heavy elements and an a-enhanced mixture (/Pe/I/j—0.7. Fej0.4).," They are computed taking into consideration diffusion of heavy elements and an $\alpha$ -enhanced mixture =–0.7, =+0.4)."639 These were the isochrones used by Vazdekis et al. (, These were the isochrones used by Vazdekis et al. (6402001) to infer a spectroscopic age of ~ 14 Gvrs lor 47 Tuc. on the basis of the measurement of the 7755-444 index (for a delinilion of that index. see Figure 16 of Paper 1).,"2001) to infer a spectroscopic age of $\sim$ 14 Gyrs for 47 Tuc, on the basis of the measurement of the $H\gamma_{\sigma<130}$ index (for a definition of that index, see Figure 16 of Paper I)."641 The age inferred [rom their fit to the CMD of the cluster is significantly vounger: ~ 10 Gvrs., The age inferred from their fit to the CMD of the cluster is significantly younger: $\sim$ 10 Gyrs.642 In spite of this discrepancy. Vazdekis et al. (," In spite of this discrepancy, Vazdekis et al. ("6432001) greatly improved over previous spectroscopic age determinations. which gave ages in excess Of 20 Gvrs (Gibson et al.,"2001) greatly improved over previous spectroscopic age determinations, which gave ages in excess of 20 Gyrs (Gibson et al."644 1999)., 1999).645 In particular. they showed that a-enhancement ancl diffusion of heavy elements cause a reduction in both the CMD ancl spectroscopic ages of 47 Tue by several Givis.," In particular, they showed that $\alpha$ -enhancement and diffusion of heavy elements cause a reduction in both the CMD and spectroscopic ages of 47 Tuc by several Gyrs."646 From Figure l it can be seen that the best match to the position of the cluster's turn-olf in the CMD is achieved [or an isochrone with age 11-12 Gvrs., From Figure \ref{fig1} it can be seen that the best match to the position of the cluster's turn-off in the CMD is achieved for an isochrone with age 11-12 Gyrs.647 This is of course dependent on the reddening assumed for the cluster., This is of course dependent on the reddening assumed for the cluster.648 An error of 0.01 mag in results in an uncertainty of ~ 1 Gvr in the age inferred [rom CAID-fitting., An error of 0.01 mag in results in an uncertainty of $\sim$ 1 Gyr in the age inferred from CMD-fitting.649 That is the reason why we infer a slightly older age than Vazdekis οἱ al..," That is the reason why we infer a slightly older age than Vazdekis et al.,"650 even though we are using (he same set of isochrones. as their adopted is 0.01 mag higher than ours.," even though we are using the same set of isochrones, as their adopted is 0.01 mag higher than ours."651 The isochrone for 11 Gvis malches verv well the color of the turn-off of the cluster., The isochrone for 11 Gyrs matches very well the color of the turn-off of the cluster.652 ILowever. it predicts a subeiant branch which is too bright by 0.05 mag.," However, it predicts a subgiant branch which is too bright by 0.05 mag."653 There also are mismatches in the color of the giant branch., There also are mismatches in the color of the giant branch.654 The model isochrone is too red by ~ 0.03 mag for giants brighter than V. ~ 14 and too blue by a comparable amount al the base of the giant branch., The model isochrone is too red by $\sim$ 0.03 mag for giants brighter than V $\sim$ 14 and too blue by a comparable amount at the base of the giant branch.655 Adopting the Alonso et al., Adopting the Alonso et al.656The rapidly oscillating Ap (roAp) stars are magnetic main sequence stars that pulsate in high radial overtone p modes with periods in the range of 5.7.21 namin.,"The rapidly oscillating Ap (roAp) stars are magnetic main sequence stars that pulsate in high radial overtone p modes with periods in the range of $5.7 - 65721$ min."658 They show broad-band photometric amplitudes less than mmag. whereas rapid radial velocity variations in rare earth. clement lines can reach several (e.g. Frevhammeretal.2009:: Wurtz 1990)).," They show broad-band photometric amplitudes less than mag, whereas rapid radial velocity variations in rare earth element lines can reach several $^{-1}$ (e.g., \citealt{Freyhammer09}; \citealt{Kurtz90}) )."659 Phe roAp stars are important targets. for the study. of the interactions among chemical anomalies. magnetic field ancl pulsations.," The roAp stars are important targets for the study of the interactions among chemical anomalies, magnetic field and pulsations."660 These stars show abnormal atmospheric structure with chemical stratification (Cowleyetal. 2001: Itvabchikovaetal. 2002))., These stars show abnormal atmospheric structure with chemical stratification \citealt{Cowley01}; \citealt{Ryab02}) ).661 The pulsations of these stars also make them: promising objects for interior model testing using asteroscismology (Aerts.Christensen-Dalseaard&Wurtz 2010))., The pulsations of these stars also make them promising objects for interior model testing using asteroseismology \citealt{Aerts10}) ).662 Phe roAp stars were discovered by Wurtz(1982):: at present more than 40 such stars are known., The roAp stars were discovered by \cite{Kurtz82}; at present more than 40 such stars are known.663 Interesting and surprising discoveries have been mace in recent vears. which give new insight in the study of pulsating Ap stars.," Interesting and surprising discoveries have been made in recent years, which give new insight in the study of pulsating Ap stars."664 New ground is being broken with p/iag precision photometric data [rom theAepler Mission., New ground is being broken with $\mu$ mag precision photometric data from the Mission.665 discovered a roAp star that pulsates in both high overtone pmuimocdes and a low- frequeney mmocde. opening up the possibility of better modelling of the interiors of these most peculiar stars.," discovered a roAp star that pulsates in both high overtone modes and a low- frequency mode, opening up the possibility of better modelling of the interiors of these most peculiar stars."666 In 2007 we started a high. resolution survey of cool chemically peculiar stars based mostly on the photometric catalogue of Martinez(1993)., In 2007 we started a high resolution survey of cool chemically peculiar stars based mostly on the photometric catalogue of \cite{Martinez93}.667. One of the goals of the survey is to select stars with high peculiarity and strong magnetic field. and to determine their fundamental. parameters to select. the most. promising candidates to be roAp stars.," One of the goals of the survey is to select stars with high peculiarity and strong magnetic field, and to determine their fundamental parameters to select the most promising candidates to be roAp stars."668 Nearly 400 stars have been observed. and many. of them are good. roAp candidates for further high time resolution spectroscopic and photometric observations., Nearly 400 stars have been observed and many of them are good roAp candidates for further high time resolution spectroscopic and photometric observations.669 For several of these stars we have obtained. such observations ancl here we present the discovery of pulsations for two objects. 669013 and 996237.," For several of these stars we have obtained such observations and here we present the discovery of pulsations for two objects, 69013 and 96237."670 Both stars were in the list. of stars with magnetically split. spectral lines found. by Freshammeretal.(2008)., Both stars were in the list of stars with magnetically split spectral lines found by \cite{Freyhammer08b}.671 669013 is à typical cool Ap star: 096237 Is more impressive with significant spectral variability., 69013 is a typical cool Ap star; 96237 is more impressive with significant spectral variability.672 Phe physical parameters Tigre and logg indicate that 660013. and 996237 are both main sequence stars. situated. in the IIR. diagram where the instability strip crosses the main sequence.," The physical parameters $T_{\rm 673eff}$ and $\log g$ indicate that 69013 and 96237 are both main sequence stars, situated in the HR diagram where the instability strip crosses the main sequence."674 For many Ap stars in this region of main sequence rapid oscillations have been detected. therefore both stars were promising objects for pulsation testing.," For many Ap stars in this region of main sequence rapid oscillations have been detected, therefore both stars were promising objects for pulsation testing."675Our stand here is that the macroscopic. uncertainties yielding such differences can. and ought to be relieved.,"Our stand here is that the macroscopic uncertainties yielding such differences can, and ought to be relieved."676 To this purpose. in 2 we present the density distributions that we duba-profiles:: these are solutions of the Jeans equation that satisfy regular inner and outer boundary conditions.," To this purpose, in 2 we present the density distributions that we dub; these are solutions of the Jeans equation that satisfy regular inner and outer boundary conditions."677 In 3 we use the a-profile suitable for the Galaxy halo as the macroscopic benchmark to evaluate the DM annihilation signal expected from the GC., In 3 we use the $\alpha$ -profile suitable for the Galaxy halo as the macroscopic benchmark to evaluate the DM annihilation signal expected from the GC.678 As for the microscopic sector. we base on a standard model for the mass. cross section and annihilation channel of the DM particles. the extension to more complex microphysics being straightforward.," As for the microscopic sector, we base on a standard model for the mass, cross section and annihilation channel of the DM particles, the extension to more complex microphysics being straightforward."679 Finally. our findings are summarized. and discussed in 4.," Finally, our findings are summarized and discussed in 4."680 Throughout this work we adopt a standard. flat cosmology with normalized matter density Ον=0.27. and Hubble constant Hyp=72 km s! Mpc.," Throughout this work we adopt a standard, flat cosmology with normalized matter density $\Omega_M = 0.27$, and Hubble constant $H_0 = 72$ km $^{-1}$ $^{-1}$."681 Galaxies are widely held to form under the drive of the gravitational instability that acts on. initial. perturbations modulating the cosmic density of the domimant cold DM component., Galaxies are widely held to form under the drive of the gravitational instability that acts on initial perturbations modulating the cosmic density of the dominant cold DM component.682 At first the instability is kept in check by the cosmic expansion. but when the local gravity prevails collapse sets in. and form a DM halo in equilibrium under self-gravity.," At first the instability is kept in check by the cosmic expansion, but when the local gravity prevails collapse sets in, and form a DM halo in equilibrium under self-gravity."683 The amplitude of more massive perturbations is smaller. so the formation Is progressive in time and hierarchical in mass. with the largest structures forming typically laterreview).," The amplitude of more massive perturbations is smaller, so the formation is progressive in time and hierarchical in mass, with the largest structures forming typically later."684. Such a formation history has been resolved to a considerable detail by many N-body simulations2006):: recently. a novel viewpoint emerged.," Such a formation history has been resolved to a considerable detail by many $N$ -body simulations; recently, a novel viewpoint emerged."685" Firstly. the halo growth has been recognized to comprise two stages: an early fast collapse including a few violent major mergers. that builds up the halo main ""body? with structure set by dynamical relaxation: and a later. quasi-equilibrium stage when the body is nearly unaffected. while the outskirts develop from the inside-out by minor mergers and smooth accretion2007)."," Firstly, the halo growth has been recognized to comprise two stages: an early fast collapse including a few violent major mergers, that builds up the halo main `body' with structure set by dynamical relaxation; and a later, quasi-equilibrium stage when the body is nearly unaffected, while the outskirts develop from the inside-out by minor mergers and smooth accretion."686. The 1s provided by the time when a DM gravitational well attains its maximal depth. re. the radial peak of the circular velocity V=GMJR attains its maximal height. along a given growth history2007).," The is provided by the time when a DM gravitational well attains its maximal depth, i.e., the radial peak of the circular velocity $v^2_c\equiv G\, M/R$ attains its maximal height, along a given growth history."687". Secondly. generic features of the ensuing equilibrium structures have been sought among powerlaw correlations of the form σρ/pr«1?: this involves the density οί) and the velocity dispersion cx""=7(1+D£).with anisotropy inserted via the standard parameter B=1-07/o7 and modulated by the index D 2007)."," Secondly, generic features of the ensuing equilibrium structures have been sought among powerlaw correlations of the form $\sigma_D^{2\epsilon/3}/\rho^{2/3}\propto r^\alpha$; this involves the density $\rho(r)$ and the velocity dispersion $\sigma_D^{2}\equiv \sigma_r^{2}\,(1+D\,\beta)$,with anisotropy inserted via the standard parameter $\beta\equiv 1-\sigma_\theta^2/\sigma_r^2$ and modulated by the index $D$ ."688. It is matter of debate which of these correlations best apply. see and(2008):: the former authors. in particular. find that the structure of different simulated halos may be described by different values of D. with linearly related values of € and « (see their Eqs.," It is matter of debate which of these correlations best apply, see and; the former authors, in particular, find that the structure of different simulated halos may be described by different values of $D$, with linearly related values of $\epsilon$ and $\alpha$ (see their Eqs."689 4 and 5)., 4 and 5).690 Here we shall focus on the specific correlation that involves solely the squared radial dispersion στι corresponding to D=0 and e=3.," Here we shall focus on the specific correlation that involves solely the squared radial dispersion $\sigma_r^2$, corresponding to $D=0$ and $\epsilon=3$."691 This is because K has not only the striking form of a DM ‘entropy’ (or rather adiabat). but also the related operational advantage of providing a expression of the radial pressure term por?=Kp’xre6? appearing in the Jeans equation for the radial equilibrium: in the latter any anisotropy is already accounted for by a separate term (see Eq.," This is because $K$ has not only the striking form of a DM `entropy' (or rather adiabat), but also the related operational advantage of providing a expression of the radial pressure term $\rho\,\sigma_r^2=K\,\rho^{5/3}\propto692r^\alpha\,\rho^{5/3}$ appearing in the Jeans equation for the radial equilibrium; in the latter any anisotropy is already accounted for by a separate term (see Eq."693 2 below)., 2 below).694 On the other hand. the correlation Kx+ with ox1.25—1.3 provides a simple yet effective fit of many simulationsothers).," On the other hand, the correlation $K\propto r^\alpha$ with $\alpha\approx 1.25-1.3$ provides a simple yet effective fit of many simulations."695. In the lower a range. Eq. (," In the lower $\alpha$ range, Eq. ("6961) has the added bonus of preserving the classic self-similar slope in the halo body (see Eq.,1) has the added bonus of preserving the classic self-similar slope in the halo body (see Eq.697 3 below)., 3 below).698 To independently probe the matter. performed a semianalytical study of the two-stage halo development. and derived (consistently with the simulations) that c Is set at the transition time via scale-free stratification of the particle orbits throughout the halo body. and thereafter remains closely constant and uniform at a value within the narrow range 1.25—1.3.," To independently probe the matter, performed a semianalytical study of the two-stage halo development, and derived (consistently with the simulations) that $\alpha$ is set at the transition time via scale-free stratification of the particle orbits throughout the halo body, and thereafter remains closely constant and uniform at a value within the narrow range $1.25 - 1.3$."699 Moreover. they found that the values of a depend though weakly on the mass of the halo. such that a=1.3 applies to galaxy clusters. while e=1.25 applies to Milky Way sized galaxies.," Moreover, they found that the values of $\alpha$ depend though weakly on the mass of the halo, such that $\alpha\approx 1.3$ applies to galaxy clusters, while $\alpha\approx 1.25$ applies to Milky Way sized galaxies."700 The halo physical profiles may be derived from the radial Jeans equation. with the radial pressure porxpen: and anisotropies described by the standard parameterB.," The halo physical profiles may be derived from the radial Jeans equation, with the radial pressure $\rho\sigma^2_r \propto701r^{\alpha}\, \rho^{5/3}$ and anisotropies described by the standard parameter $\beta$."702 Thus the Jeans equation simply writes in terms.= of the logarithmic density slope y= -dlogp/dlogr.," Thus the Jeans equation simply writes in terms of the logarithmic density slope $\gamma\equiv703-\mathrm{d}\log\rho/\mathrm{d}\log r$ ."704" As first shown by and(2005). Jeans supplemented with the mass definition M(«r)=απjyf,Hdροή)1 entering. v;4=GM(< r)/r. provides an integro-differential equation for pC). that by double differentiation reduces to a handy 2™-order differential equation for γ."," As first shown by and, Jeans supplemented with the mass definition $M(<r)\equiv7054\pi\int_0^r{\mathrm{d}r'}~r'^2\,\rho(r')$ entering $v_c^2\equiv G M(<r)/r$ , provides an integro-differential equation for $\rho(r)$, that by double differentiation reduces to a handy $2^{\mathrm{nd}}$ -order differential equation for $\gamma$."706 To set the context for the Milky Way DM distribution. we recall that the space of solutions for Eq. (," To set the context for the Milky Way DM distribution, we recall that the space of solutions for Eq. ("7072) spans the range a<1.296: the one for the upper bound and the behaviors of others ones have been analytically investigated by and (2005).,2) spans the range $\alpha\leq 1.\overline{296}$; the one for the upper bound and the behaviors of others ones have been analytically investigated by and .708. In we explicitly derive the Jeans solutions with p=0 (meaning isotropy) for the full range a=1.25-1.296 subjected to regular boundary conditions both at the center and in the outskirts. 1.e.. a," In we explicitly derive the Jeans solutions with $\beta=0$ (meaning isotropy) for the full range $\alpha\approx7091.25-1.\overline{296}$ subjected to regular boundary conditions both at the center and in the outskirts, i.e., a"710We have shown that this backsplash population is not negligible anc needs to be accounted for when interpreting the various galaxy morpholoew relationships and cecoupling the degeneraey between nature and nurture.,We have shown that this backsplash population is not negligible and needs to be accounted for when interpreting the various galaxy morphology relationships and decoupling the degeneracy between nature and nurture.711 We must also appreciate that the infalling population is not expected to be pristine., We must also appreciate that the infalling population is not expected to be pristine.712 Rather. we would expect that infall galaxies have undergone some sort of. pre-processing in groups before entering the cluster too as indicated by the sub-subhalos in2.," Rather, we would expect that infall galaxies have undergone some sort of pre-processing in groups before entering the cluster too as indicated by the sub-subhalos in."713. Our results can be summarized as follows: When translorming the last result into the observers xdane though. the velocity separation between the infalling and. backsplash population is removed.," Our results can be summarized as follows: When transforming the last result into the observers plane though, the velocity separation between the infalling and backsplash population is removed."714 Llowever. the xvksplash: population should. still be detectable as idt is responsible for a continuous rise in the distribution function owarcds low line-of-sight velocities.," However, the backsplash population should still be detectable as it is responsible for a continuous rise in the distribution function towards low line-of-sight velocities."715 Our results suggest. that we not. onky expect. the xksplash population to experience various large-scale ransformation mechanisms. but also small-scale ones. uncergoing starvation. rani pressure stripping. tidallv rigeered star formation and significant tidal stripping.," Our results suggest that we not only expect the backsplash population to experience various large-scale transformation mechanisms, but also small-scale ones, undergoing starvation, ram pressure stripping, tidally triggered star formation and significant tidal stripping."716 SPDG wishes to thank Erica Ellingson and Bernard Vollmer [or useful discussions., SPDG wishes to thank Erica Ellingson and Bernard Vollmer for useful discussions.717 The simulations presented in this paper were carried out on the Beowulf cluster at the Centre for Astrophysics Supercomputing. Swinburne University.," The simulations presented in this paper were carried out on the Beowulf cluster at the Centre for Astrophysics Supercomputing, Swinburne University."718 The financial support of the Australian Research Council is also gratefully acknowledged., The financial support of the Australian Research Council is also gratefully acknowledged.719 Finally. we wish to thank Michael Balogh for helpful correspondences.," Finally, we wish to thank Michael Balogh for helpful correspondences."7202004: Coppinetal. 2007: Stanwayetal.2008).,; \citealt{Coppin07}; ; \citealt{Stanway08}) ).721 QSOs typically have narrower linewidths than SMGs by a factor of ~2— consistent with the optically-selected QSOs being more closely inclined to the skv plane (showing its central AGN more clearly) than typical SMGs (Greveetal.2005:: Coppinetal.2008:: Carilli&Wang 2006).," QSOs typically have narrower linewidths than SMGs by a factor of $\sim2$ --3, consistent with the optically-selected QSOs being more closely inclined to the sky plane (showing its central AGN more clearly) than typical SMGs \citealt{Greve05}; \citealt{Coppin08}; \citealt{Carilli06}) )."722 Thus the CO line narrowness of JJ033229.4 (whose rest-frame UV compact morphology and strong emission indicates that it hosts an AGN: Coppinetal. 2009)) compared with other SMGs could indicate that /~107., Thus the CO line narrowness of J033229.4 (whose rest-frame UV compact morphology and strong emission indicates that it hosts an AGN; \citealt{Coppin09}) ) compared with other SMGs could indicate that $i\simeq 10^\circ$.723 Assuming that JJ033229.4 is more face-on. adopting ὁ—10. yields Mava(<2kpe)=(4.0d2.0).1014 MM...," Assuming that J033229.4 is more face-on, adopting $i\simeq 10^\circ$, yields $_\mathrm{dyn}(<2\,\mathrm{kpc})=(4.0\pm2.0)\times10^{11}$ $_\odot$."724 However. the line width differences could also indicate that JJ033229.4 is at a later stage of a merger or has a different galaxy mass or size than typical >~2 SMGs. which could be explored with high-resolution imaging of the gas distribution (e.g. Greveetal.2005: Carilli&Wang 20061).," However, the line width differences could also indicate that J033229.4 is at a later stage of a merger or has a different galaxy mass or size than typical $z\sim2$ SMGs, which could be explored with high-resolution imaging of the gas distribution (e.g. \citealt{Greve05}; \citealt{Carilli06}) )."725 If instead we assume that the gas configuration is spherical (with a uniform distibution) rather than disk-like. then the implied enclosed dynamical mass would be Μωνμίς2kpe)=(1.110 MM...," If instead we assume that the gas configuration is spherical (with a uniform distibution) rather than disk-like, then the implied enclosed dynamical mass would be $_\mathrm{dyn}(<2\,\mathrm{kpc})=(1.1\pm0.6)\times10^{10}$ $_\odot$."726 The combination of the gas and stellar mass estimates for JJ033229.4 can be used to calculate the total baryonic mass of the system., The combination of the gas and stellar mass estimates for J033229.4 can be used to calculate the total baryonic mass of the system.727 The stellar mass of the system from Coppinetal. has been recontirmed by Wardlowetal.(2010) to be 21b1017 MM... Wa, The stellar mass of the system from \citet{Coppin09} has been reconfirmed by \citet{Wardlow10} to be $\lsim 1 \times 10^{11}$ $_\odot$.728rdlowetal.(2010) has included the new HAWK-I J and A -band photometry. and adjusted the derived mass for a Salpeter(1955) IMF for compatibility with the IMF assumed in deriving the SFR in ??..," \citet{Wardlow10} has included the new HAWK-I $J$ and $K$ -band photometry, and adjusted the derived mass for a \citet{Salpeter55} IMF for compatibility with the IMF assumed in deriving the SFR in \ref{compare}."729 We caution that this quantity has an uncertainty of a factor of &5 even before considering a potential AGN contribution to the rest-frame near-infrared emission and so should be considered an approximate upper limit., We caution that this quantity has an uncertainty of a factor of $\lesssim 5$ even before considering a potential AGN contribution to the rest-frame near-infrared emission and so should be considered an approximate upper limit.730 Taken together. these estimates imply a total baryonic mass within 2kkpe of Μω MinasΜον=12ὧν100 MM.~1.101 MM.. which is consistent with the dynamical mass estimated above from the CO emission given the considerable uncertainties.," Taken together, these estimates imply a total baryonic mass within kpc of $_\mathrm{bary}$ $_\mathrm{gas}$ $_\mathrm{stars}=1.2^{+4.0}_{-0.8} \times 10^{11}$ $_{\odot}\, \simeq 1 \times 10^{11}$ $_\odot$, which is consistent with the dynamical mass estimated above from the CO emission given the considerable uncertainties."731 How representative is JJ033229.4 of the few known >~ 4-5 submillimetre-selected sources and the more abundant >~2 SMG population?, How representative is J033229.4 of the few known $z\sim4$ –5 submillimetre-selected sources and the more abundant $z\sim2$ SMG population?732" Based on the photometric constraints for JJ033229.4 which trace an SED consistent with local star formation dominated ULIRGs. Coppinetal.(2009). derive a dust mass estimate of AL,~510 MM. and a infrared luminosity of Lisc6©107 LL... implying a of c 1000MM. yyr7. close to the median luminosity of the 2o2 and >4 SMG populations (e.g. Kováesetal. 20065)."," Based on the photometric constraints for J033229.4 which trace an SED consistent with local star formation dominated ULIRGs, \citet{Coppin09} derive a dust mass estimate of $M_\mathrm{d}\sim 5 \times 10^{8}$ $_{\odot}$ and a far-infrared luminosity of $_\mathrm{IR}\simeq 6\times10^{12}$ $_\odot$, implying a of $\simeq1000$ $_\odot$ $^{-1}$, close to the median luminosity of the $z\sim2$ and $z>4$ SMG populations (e.g. \citealt{Kovacs06}) )."733 When combined with our gas mass estimate above it follows that JJ033229.4 has a star formation efficiency (SFE) of « 250LL. kkmss !ppe?) toa gas-to-dynamical mass fraction of /ZM Mas~0.3(in77/0.25). and a gas-to-dust mass ratio of ~ 30.," When combined with our gas mass estimate above it follows that J033229.4 has a star formation efficiency (SFE) of $\approx 250$ $_\odot$ $^{-1}$ $^{2})^{-1}$, a gas-to-dynamical mass fraction of $f$ $_\mathrm{gas}$ $_\mathrm{dyn}\sim0.3 (\mathrm{sin}^{2}i/0.25)$, and a gas-to-dust mass ratio of $\sim30$ ."734 Assumingthat the star formation follows the A -band light. we estimate a star formation surface density of “spur 100MM.  7. which is similar to the intense central starburst mode inferred for SMGs at 2— (e.g. Smailetal. 2003).," Assumingthat the star formation follows the $K$ -band light, we estimate a star formation surface density of $\Sigma_\mathrm{SFR}\sim100$ $_\odot$ $^{-1}$ $^{-2}$, which is similar to the intense central starburst mode inferred for SMGs at $z\sim2$ (e.g. \citealt{Smail03}) )."735" The source properties of JJ033229.4 derived from the CO line emission are very similar to those of the numerous SMGs at. o2 (MM, D38107 MM.. 1210 MM.. fc025. with SFEs of ~TOLL. + ppe)+ ond Ma Masi60: Greve Kováesetal.20062) and also the rarer emerging tail Z74 SMOs (Schinnereretal.2008: Daddietal.2009a.b))."," The source properties of J033229.4 derived from the CO line emission are very similar to those of the numerous SMGs at $z\sim2$ $<\!$ $_\mathrm{gas}\!>\sim3.0\times10^{10}$ $_\odot$, $<\!$ $_\mathrm{dyn}\!>\sim1.2 \times 10^{11}$ $_\odot$, $f\simeq0.25$, with SFEs of $\sim450\pm170$ $_\odot$ $^{-1}$ $^{2})^{-1}$ and $_\mathrm{gas}$ $_\mathrm{dust}\sim60$; \citealt{Greve05}; ; \citealt{Kovacs06}) ) and also the rarer emerging high-redshift tail $z>4$ SMGs \citealt{Schinnerer08}; \citealt{Daddi09a,Daddi09b}) )."736 Combining the samples of CO-detected 2>4 SMGs. it follows that they lie within the scatter of the Έ Γκο relation from Greveetal.(2005) Τους —2SMGs (assuming a constant line brightness ratio). with +4-5 SMGs spanning a range of Li—0.6—3 LP LL. and Li~2-6 «101 ! ppc?.," Combining the samples of CO-detected $z>4$ SMGs, it follows that they lie within the scatter of the $_\mathrm{IR}$ $'_\mathrm{CO}$ relation from \citet{Greve05} for $z\sim2$ SMGs (assuming a constant line brightness ratio), with $z\sim4$ –5 SMGs spanning a range of $_\mathrm{IR}\sim0.6$ $3\times10^{13}$ $_\odot$ and $'_\mathrm{CO}\sim2$ $6\times10^{10}$ $^{-1}$ $^{2}$."737 It thus appears that within the 2.~1-5 SMG population. πα Ίο is constant with redshift. indicating that SMGs at 2~4-5 are consistent with being higher-redshift analogues of SMGs at 2~2. forming stars with similar efficiencies.," It thus appears that within the $z\sim1$ –5 SMG population, $_\mathrm{IR}$ $'_\mathrm{CO}$ is constant with redshift, indicating that SMGs at $z\sim4$ –5 are consistent with being higher-redshift analogues of SMGs at $z\sim2$, forming stars with similar efficiencies."738" Overall this comparison suggests that SMGs at 2— and 2>d are equally evolved. have similar reservoirs of gas. similar star formation efficiencies. and similar fractions of baryons in cold gus as stars,"," Overall this comparison suggests that SMGs at $z\sim2$ and $z>4$ are equally evolved, have similar reservoirs of gas, similar star formation efficiencies, and similar fractions of baryons in cold gas as stars."739 JJ033229.4 appears to be a luminous massive starburst. forming stars at a rate of ~LOOOMM. +. with a total baryonic mass of c1.10!4 MM... with properties representative of SMGs üt ο 2—4.," J033229.4 appears to be a luminous massive starburst, forming stars at a rate of $\sim1000$ $_\odot$ $^{-1}$, with a total baryonic mass of $\simeq 1\times 10^{11}$ $_\odot$, with properties representative of SMGs at $z\sim2$ –4."740 The combination of its compact morphology and high SFR is potentially consistent with the small sizes of =:1-2 kkpe claimed for a population of massive extremely dense old quiescent 2~ galaxies (e.g. Daddietal.2005:: Toftetal.2007.2009:: Zirmetal. 2007:: Buitragoetal. 2008:: Cimattietal.20083).," The combination of its compact morphology and high SFR is potentially consistent with the small sizes of $\lsim1$ kpc claimed for a population of massive extremely dense old quiescent $z\sim2$ galaxies (e.g. \citealt{Daddi05}; \citealt{Toft07,Toft09}; \citealt{Zirm07}; \citealt{Buitrago08}; \citealt{Cimatti08}) )."741 Such compact dense galaxies at 2 have implied formation redshifts of 2~ 4-5 and are consistent with being the descendents of a population of gas-rich. highly dissipative mergers. such as 27d SMGs.," Such compact dense galaxies at $z\sim2$ have implied formation redshifts of $z\sim4$ –5 and are consistent with being the descendents of a population of gas-rich, highly dissipative mergers, such as $z>4$ SMGs."742" A critical question we can now address is whether JJ033229.4 (assumed to be representative of +4 SMOs) has the baryonic mass and gas consumption timescale necessary to be a ‘prototypical’ progenitor of the luminous ""red and dead galaxy population found at 2~3?", A critical question we can now address is whether J033229.4 (assumed to be representative of $z>4$ SMGs) has the baryonic mass and gas consumption timescale necessary to be a `prototypical' progenitor of the luminous `red and dead' galaxy population found at $z\sim3$?743 The baryonic content of JJ033229.4 is roughly equivalent to the typical stellar mass of a giant elliptical galaxy (110'4 MM. Marchesinietal. 2009)). given the large uncertainties in some of our mass estimates.," The baryonic content of J033229.4 is roughly equivalent to the typical stellar mass of a giant elliptical galaxy $1\times 10^{11}$ $_\odot$; \citealt{Marchesini09}) ), given the large uncertainties in some of our mass estimates."744 Assuming that the molecular gas reservoir is fueling the star formation within JJ033229.4. then it will have enough gas to sustain the current star formation episode for Tdopletion ~Maa/SFR~L6«1027 MM. /1000MM. vyr5— MMvr. assuming efficiency.," Assuming that the molecular gas reservoir is fueling the star formation within J033229.4, then it will have enough gas to sustain the current star formation episode for $\tau_\mathrm{depletion}\sim$ $_\mathrm{gas}$ $\sim 1.6 \times 10^{10}$ $_\odot$ $_\odot$ $^{-1}\sim 16$ Myr, assuming efficiency."745 We also compare Tilepletion with the time to form the current stellar mass of the system., We also compare $\tau_\mathrm{depletion}$ with the time to form the current stellar mass of the system.746 At the current SFR. we estimate @ Τιμ ~Meuu./SFR~1 MM. /1000MM. vyr|~LOO MMyr. which is comparable to the assumed age of the stellar population and burst inthe model used in Coppinetal.(2009).," At the current SFR, we estimate a $\tau_\mathrm{formation}\sim$ $_\mathrm{stars}$ $\sim 1\times 10^{11}$ $_\odot$ $_\odot$ $^{-1} \sim 100$ Myr, which is comparable to the assumed age of the stellar population and burst inthe model used in \citet{Coppin09}."747. Although the gas consumption timescale appears to be relatively short. it is similar to thegas depletion timescales of ~100 MMyr for SMGs (e.g. Tacconiet 2008).," Although the gas consumption timescale appears to be relatively short, it is similar to thegas depletion timescales of $\sim100$ Myr for SMGs (e.g. \citealt{Tacconi08}) )."748 It follows that we are catching this SMG approximately half way through its current star formation episode. with the majority of thegalaxy mass already in the form of stars. representative of a major stage in galaxy formation.," It follows that we are catching this SMG approximately half way through its current star formation episode, with the majority of thegalaxy mass already in the form of stars, representative of a major stage in galaxy formation."749" It thus seems plausible that JJ033229.4 would display the observed properties of being ""red and dead! by ο3 since the current stellar population would age another71 GGyr between +=4.76 and 2= 3. assuming that no further star formation occurs."," It thus seems plausible that J033229.4 would display the observed properties of being `red and dead' by $z\sim3$ since the current stellar population would age another $>1$ Gyr between $z=4.76$ and $z=3$ , assuming that no further star formation occurs."750Nucleodisruptiot has been found to be a significant producer of D and *He nuclei (?) within the standard evolution of the scale factor.,Nucleodisruption has been found to be a significant producer of D and $^3$ He nuclei \citep{Sihvola01} within the standard evolution of the scale factor.751 However. with the slow evolution of the expansion rate in the Dirac-Milne universe and the hypothesis we made about the spatial repartition of the matter and antimatter domains. this situation changes.," However, with the slow evolution of the expansion rate in the Dirac-Milne universe and the hypothesis we made about the spatial repartition of the matter and antimatter domains, this situation changes."752 Nuclet produced by nucleodisruption possess a kinetic energy ranging from a few MeV for nuclei to a few of MeV for nucleons (?).., Nuclei produced by nucleodisruption possess a kinetic energy ranging from a few MeV for nuclei to a few of MeV for nucleons \citep{Balestra88}.753 These newly produced nuclei thermalize by Coulomb scattering on ambient protons and electrons., These newly produced nuclei thermalize by Coulomb scattering on ambient protons and electrons.754 The thermalization length for D nuclei produced with an energy Ey=10MeV is presented in Fig., The thermalization length for D nuclei produced with an energy $E_0=10\;\rm{MeV}$ is presented in Fig.755 6 (blue dotted line)., \ref{diff_length} (blue dotted line).756 This distance is always much smaller than the diffusion length. implying that any D nucleus produced by nucleodisruption will finally return towards the annihilation zone and be destroyed there.," This distance is always much smaller than the diffusion length, implying that any D nucleus produced by nucleodisruption will finally return towards the annihilation zone and be destroyed there."757" A possible way to produce a higher fraction of deutertum by nucleodisruption would be to consider small domains of (antiymatter within a larger ""Somain of antimatter (matter).", A possible way to produce a higher fraction of deuterium by nucleodisruption would be to consider small domains of (anti)matter within a larger domain of antimatter (matter).758" This situation occurs continually | an emulsion. which suffers a redistribution of ""domains? when bridges in the emulsion disappear by annihilation."," This situation occurs continually in an emulsion, which suffers a redistribution of “domains"" when bridges in the emulsion disappear by annihilation."759 If the nx—imension of the larger domain is larger than the diffusion ength. then an important fraction of the D and *He produced by Seucleodisruption could survive.," If the dimension of the larger domain is larger than the diffusion length, then an important fraction of the D and $^3$ He produced by nucleodisruption could survive."760" However. precise calculations of this production require the. knowledge of the statistical properties of the spatial distribution of domains. which strongly ""Sepends of the separation mechanism."," However, precise calculations of this production require the knowledge of the statistical properties of the spatial distribution of domains, which strongly depends of the separation mechanism."761 This point should be estigated in future studies of nucleosynthesis in the Milne universe., This point should be investigated in future studies of nucleosynthesis in the Dirac-Milne universe.762 In 1998 (??).. distance measurements for type la ((SNe Ia) revealed that these objects are dimmer than expected if our Universe was correctly described by a decelerating Einstein-de Sitter model.," In 1998 \citep{Riess98, Perlmutter99}, distance measurements for type Ia (SNe Ia) revealed that these objects are dimmer than expected if our Universe was correctly described by a decelerating Einstein-de Sitter model."763 The introduction of a cosmological constant A in the field equations of general relativity. which is apt to produce an accelerating expansion. provided an impressive fit to the observational data.," The introduction of a cosmological constant $\Lambda$ in the field equations of general relativity, which is apt to produce an accelerating expansion, provided an impressive fit to the observational data."764 Today. SNe Ia are one of the nost important cosmological tests and are considered as prime evidence of an acceleration of the expansion.," Today, SNe Ia are one of the most important cosmological tests and are considered as prime evidence of an acceleration of the expansion."765 We recall however that the strong evidence of a recent transition between a decelerating phase and an accelerating phase of expansion heavily relies on the prior hypothesis of spatial flatness., We recall however that the strong evidence of a recent transition between a decelerating phase and an accelerating phase of expansion heavily relies on the prior hypothesis of spatial flatness.766 Without this hypothesis. the evidence ts less clear (?)..," Without this hypothesis, the evidence is less clear \citep{Seikel2008}."767 The Dirac-Milne universe has neither acceleration nor deceleration and is therefore equivalent to an open empty universe., The Dirac-Milne universe has neither acceleration nor deceleration and is therefore equivalent to an open empty universe.768" In terms of the usual cosmological parameters. this universe corresponds to the combination left,o0."," In terms of the usual cosmological parameters, this universe corresponds to the combination _M=0, )."769" ""EN In this context. the luminosity distance in the Dirac-Milne universe follows the simple expression(?)."," In this context, the luminosity distance in the Dirac-Milne universe follows the simple expression."770. The SNLS data consist of two distinct datasets., The SNLS data consist of two distinct datasets.771 The high-redshift sample. from the SNLS. comprises 71 SNe Ia. with redshifts between 0.2€z1.01.," The high-redshift sample, from the SNLS, comprises 71 SNe Ia with redshifts between $0.2\leq z\leq 1.01$."772 The second sample is a low-redshift set. consisting of 44 SNe Ia taken from the literature with redshifts 2<0.15.," The second sample is a low-redshift set, consisting of 44 SNe Ia taken from the literature with redshifts $z\leq 0.15$."773 These data come from different experiments and are therefore possibly subject to different sources of systematic errors., These data come from different experiments and are therefore possibly subject to different sources of systematic errors.774" Following the definition given in ?.. the distance modulus is where M is the absolute magnitude of SNe la. e and ϱ are global parameters that link the stretch s and the color c to the distance modulus. and 7, is the apparent magnitude of the supernova."," Following the definition given in \citet{Astier06}, the distance modulus is c, where $M$ is the absolute magnitude of SNe Ia, $\alpha $ and $\beta$ are global parameters that link the stretch $s$ and the color $c$ to the distance modulus, and $m^*_B$ is the apparent magnitude of the supernova."775 It should be emphasized that. in. contrast to the ACDM cosmology. there is no cosmological parameter dependence in the Dirac-Milne luminosity distance.," It should be emphasized that, in contrast to the $\Lambda$ CDM cosmology, there is no cosmological parameter dependence in the Dirac-Milne luminosity distance."776 The only degrees of freedom are the nuisance parameters. M. a. and P.," The only degrees of freedom are the nuisance parameters, $M$, $\alpha$, and $\beta$."777 Following the procedure described in 2.. we minimize the expressioni," Following the procedure described in \citet{Astier06}, , we minimize the expression."778"nt Here. c(ug) takes into account measurement errors in the apparent magnitude m,. stretch. and color parameters derived by the analysis of light curves (?).. Gig, Is the so- “intrinsic” dispersion. which is a parameter introduced to account for SNe Ia being astrophysical objects that naturally have some intrinsic dispersion in their absolute magnitude."," Here, $\sigma(\mu_B)$ takes into account measurement errors in the apparent magnitude $m_B^*$, stretch, and color parameters derived by the analysis of light curves \citep{Guy2005}, $\sigma_{\rm{int}}$ is the so-called ""intrinsic"" dispersion, which is a parameter introduced to account for SNe Ia being astrophysical objects that naturally have some intrinsic dispersion in their absolute magnitude."779" However. the valueof this parameter is unknown. and in the fitting procedure. c, 1s adjusted to ensure that the reduced squared is unity."," However, the valueof this parameter is unknown, and in the fitting procedure, $\sigma_{\rm{int}}$ is adjusted to ensure that the reduced chi-squared is unity."780 We first performed our analysis on the high-z sample without including any low-z SN Ia. Without this low-z anchoring. the analysis does not permit us to discriminate between the ACDM and the Dirac-Milne universes.," We first performed our analysis on the $z$ sample without including any low-z SN Ia. Without this $z$ anchoring, the analysis does not permit us to discriminate between the $\Lambda$ CDM and the Dirac-Milne universes."781 In this respect. we note that the three-year analysis of SNLS using their data alone (?) is consistent to a better than CL with the Dirac-Milne universe. while the Einstein-de Sitter (EdS) model is clearly excluded.," In this respect, we note that the three-year analysis of SNLS using their data alone \citep{Guy10} is consistent to a better than CL with the Dirac-Milne universe, while the Einstein-de Sitter (EdS) model is clearly excluded."782 The evidence of an expansion acceleration therefore relies on a comparison between low-z and high-z SNe la. We also present the results for the EdS model., The evidence of an expansion acceleration therefore relies on a comparison between $z$ and $z$ SNe Ia. We also present the results for the EdS model.783 The results of the analysis of the 71 SNe la are presented in Tables | and 2.., The results of the analysis of the 71 SNe Ia are presented in Tables \ref{tab:sn5} and \ref{tab:sn4}.784 In Table |.. the intrinsic dispersion ts fixed to a null value.," In Table \ref{tab:sn5}, the intrinsic dispersion is fixed to a null value."785 The analysis is therefore performed using only the measurement errors. thereby giving a stronger weight to SNe la withredshifts 0.2.€zx 0.4. which have smaller errors.," The analysis is therefore performed using only the measurement errors, thereby giving a stronger weight to SNe Ia withredshifts $0.2 \leq z\leq 0.4$ , which have smaller errors."786 (Ehe total and reduced y- of the EdS model are much larger than those of the ACDM and Dirac-Milne models. which are in," The total and reduced $\chi^2$ of the EdS model are much larger than those of the $\Lambda$ CDM and Dirac-Milne models, which are in"787the field lines (Mouschovias&Ciolek.1999).. and the second will have it along the axis. due to entrainment of the field at the shock front.,"the field lines \citep{Mo1999b}, and the second will have it along the axis, due to entrainment of the field at the shock front."788 Therefore measuring the field directions could distinguish between these two models., Therefore measuring the field directions could distinguish between these two models.789 Detailed studies (Watson.1994;Elitzur. of the polarisation properties of OH. and SiO masers have been made. but there has been relatively little investigation of the polarisation. properties of methanol masers.," Detailed studies \citep{watson_94,elitzur_96c,gray_03} of the polarisation properties of OH, and SiO masers have been made, but there has been relatively little investigation of the polarisation properties of methanol masers."790 Single dish observations of polarisation in methanol masers are all from the strongest sources: Kooetal.(1988) observed W3(OH) and NGC 6334F at 12 GHz. while Caswelletal.(1995) determined that the level of circular polarisation for a number of strong 6.7 GHz methanol maser features was less than," Single dish observations of polarisation in methanol masers are all from the strongest sources: \cite{Ko1988} observed W3(OH) and NGC 6334F at 12 GHz, while \cite{Ca1995a} determined that the level of circular polarisation for a number of strong 6.7 GHz methanol maser features was less than."791[σοι Ellingsen(2002) reported on 6.7 GHz polarisation observations with the ATCA of NGC 6334F where he found linear polarisation fractions of up to10%.," \cite{ellingsen_02} reported on 6.7 GHz polarisation observations with the ATCA of NGC 6334F, where he found linear polarisation fractions of up to."792. The first high resolution polarisation images were made with MERLIN at a resolution of 50 mas (Vlemmingsetal..2006). of W3(OH). where polarisation fractions of upto but typically were found.," The first high resolution polarisation images were made with MERLIN at a resolution of 50 mas \citep{vlemmings_06}, of W3(OH), where polarisation fractions of upto but typically were found."793 Those polarisation angles were consistent with those of the OH-masers. and furthermore lie along the methanol maser emission as expected for shock excited regions.," Those polarisation angles were consistent with those of the OH-masers, and furthermore lie along the methanol maser emission as expected for shock excited regions."794 The maser G339.88-1.26 was discovered at 12 GHz by Norrisetal. (1987).. and at 6.7 GHz by MacLeodetal.(1992).," The maser G339.88-1.26 was discovered at 12 GHz by \cite{norris_87}, and at 6.7 GHz by \cite{macleod_92}."795 Follow-up at arcsecond resolution by the Australia Telescope Compact Array (ATCA) showed strong emission with a roughly linear morphology and a monotonie velocity gradient (Norrisetal., Follow-up at arcsecond resolution by the Australia Telescope Compact Array (ATCA) showed strong emission with a roughly linear morphology and a monotonic velocity gradient \citep{norris_93}.796.1993).. Ellingsenetal.(1996) detected weak radio continuum emission which peaks at the same position as the maser emission., \cite{ellingsen_96_cont} detected weak radio continuum emission which peaks at the same position as the maser emission.797 The Mid Infra-Red (MIR) observations at 10 jm of Stecklum(1998) detected elongated emission along the same position angle as the disk inferred by the methanol masers., The Mid Infra-Red (MIR) observations at $10~\mu$ m of \cite{St1998a} detected elongated emission along the same position angle as the disk inferred by the methanol masers.798 These combined to make this one of the best candidates for the disk model for methanol masers. with the masers formed in the dusty disk hiding αἱ embedded massive. forming. star.," These combined to make this one of the best candidates for the disk model for methanol masers, with the masers formed in the dusty disk hiding an embedded massive, forming, star."799 However higher resolution. 10 and 18 jm MIR observations. at the Keck Observatory (DeBuizeretal..2002) resolved the IR source into three components.," However higher resolution, 10 and $18~\mu$ m MIR observations, at the Keck Observatory \citep{debuizer_02}800 resolved the IR source into three components."801 VLBI observations from 1996. included in the same paper. showed that the masers formed an inverted Y shape and lay between IB and IC. See Figure 2b in that paper.," VLBI observations from 1996, included in the same paper, showed that the masers formed an inverted Y shape and lay between 1B and 1C. See Figure 2b in that paper."802 That is they do not mark the disk. indeed there was no disk. nor do they have a Keplerian velocity distribution.," That is they do not mark the disk, indeed there was no disk, nor do they have a Keplerian velocity distribution."803 As a telescope tracks à source across the sky the angle of the source on the sky to that of the telescope feed changes., As a telescope tracks a source across the sky the angle of the source on the sky to that of the telescope feed changes.804 When observing with Left Circular and Right Circular Polarisations (LCP and RCP) this has the effect of introducing a phase shift between the two recorded data-streams., When observing with Left Circular and Right Circular Polarisations (LCP and RCP) this has the effect of introducing a phase shift between the two recorded data-streams.805 To post-process these data these phases need to be removed. and the feed impurities need to be solved for and included in the calibration.," To post-process these data these phases need to be removed, and the feed impurities need to be solved for and included in the calibration."806 A good summary of the steps needed to make polarisation VLBI images can be found in Aaron(1997)., A good summary of the steps needed to make polarisation VLBI images can be found in \cite{aaron_97}.807. In this study. and indeed all other sources on VLBI polarisation. the feed mounts are assumed to be Cassegrain or Equatorial.," In this study, and indeed all other sources on VLBI polarisation, the feed mounts are assumed to be Cassegrain or Equatorial."808 Different mounts rotate the feeds in different fashions on the sky as the telescope tracks a source., Different mounts rotate the feeds in different fashions on the sky as the telescope tracks a source.809 Two new mount types to those supported have been added., Two new mount types to those supported have been added.810 For VLBI observations AIPS (Greisen.1988) remains the only tool for data calibration. therefore this has been our target for the extension of mount types.," For VLBI observations AIPS \citep{aips} remains the only tool for data calibration, therefore this has been our target for the extension of mount types."811 The code to support the Nasmyth mount type and the E-W mount type have been developed., The code to support the Nasmyth mount type and the E-W mount type have been developed.812 The latter is a subset of the X-Y mount (traditionally for Low Earth Orbit satellite tracking stations) where the second axis les East-West., The latter is a subset of the X-Y mount (traditionally for Low Earth Orbit satellite tracking stations) where the second axis lies East-West.813 The only example known to the author is the Hobart telescope which is part of the Australian Long Baseline Array (LBA)., The only example known to the author is the Hobart telescope which is part of the Australian Long Baseline Array (LBA).814 The alternative configuration is the N-S mount. where the second axis lies orth-South.," The alternative configuration is the N-S mount, where the second axis lies North-South."815" The ""keyhole'. where large angular changes are required for small movements on the sky. falls on the second axis."," The `keyhole', where large angular changes are required for small movements on the sky, falls on the second axis."816 Compared the Alt-Az mount. the X-Y mounts move the keyhole from the Zenith to the horizon. where observations are not normally made.," Compared the Alt-Az mount, the X-Y mounts move the keyhole from the Zenith to the horizon, where observations are not normally made."817 The second mount type added. which is not used in the data presented here. 1s for the Nasmyth type.," The second mount type added, which is not used in the data presented here, is for the Nasmyth type."818 The asmyth mount is more normally used on optical instruments. as it allows space for very large instrumentation packages.," The Nasmyth mount is more normally used on optical instruments, as it allows space for very large instrumentation packages."819 Until now this has not been needed for Radio Telescopes. but hew quasi-optical systems allow the siting of multiple feeds for different bands at the Nasmyth foci.," Until now this has not been needed for Radio Telescopes, but new quasi-optical systems allow the siting of multiple feeds for different bands at the Nasmyth foci."820 This configuration allows the co-observing of widely separated observing bands. which is particularly useful for the calibration of mm-VLBI (Dodson&Rioja.2008).," This configuration allows the co-observing of widely separated observing bands, which is particularly useful for the calibration of mm-VLBI \citep{fpt_report}."821. The new code is for the new mm-VLBI telescope being constructed at Yebes. Spain. which will cover frequencies from GGHz to GGHz. anc also the IRAM telescope at Pico Veleta (Spain).," The new code is for the new mm-VLBI telescope being constructed at Yebes, Spain, which will cover frequencies from GHz to GHz, and also the IRAM telescope at Pico Veleta (Spain)."822 Left handed and Right handed Nasmyth foci are also included in the new AIPS code. as required for the Left or Right optical branch.," Left handed and Right handed Nasmyth foci are also included in the new AIPS code, as required for the Left or Right optical branch."823 Full details can be found in Dodson(2007).., Full details can be found in \cite{pol_report}.824 These observations with the LBA were used to test EW-mount portion of these new subroutines., These observations with the LBA were used to test EW-mount portion of these new subroutines.825 When the LBA results on G339.88-1.26 are compared to those of ATCA observations (Ellingsen. Priv.," When the LBA results on G339.88-1.26 are compared to those of ATCA observations (Ellingsen, Priv."826 Comms.).," Comms.),"827" made in Sept 1999, an excellent match in the linear polarised fluxes and angles is found. after including the absolute polarisation angle offset between the brightest polarised component (at —38.7 )."," made in Sept 1999, an excellent match in the linear polarised fluxes and angles is found, after including the absolute polarisation angle offset between the brightest polarised component (at $-38.7$ )."828 See Figure | where the position angles. linear polarised and total flux are compared for the two instruments.," See Figure \ref{fig:pa} where the position angles, linear polarised and total flux are compared for the two instruments."829 ATCA values are plotted with red closed circles. and the LBA values with blue open boxes.," ATCA values are plotted with red closed circles, and the LBA values with blue open boxes."830 The values are extracted from à sum across the Q and U images (with miriad’s imspec) which allows the comparison of these two datasets with very different resolutions., The values are extracted from a sum across the Q and U images (with miriad's ) which allows the comparison of these two datasets with very different resolutions.831 The errors are absolute errors from the confidence in the polarisation calibration. the relative errors are much less.," The errors are absolute errors from the confidence in the polarisation calibration, the relative errors are much less."832" Note that Goedhartetal.(2004) report this source as ""not significantly variable. with one component falling (-32.39 )andone rising (-33.19"," Note that \cite{goe_04} report this source as `not significantly variable', with one component falling (-32.39 ) and one rising (-33.19"833"that Ly, requires a distauce estimate to the source.",that $E_{gw}$ requires a distance estimate to the source.834 Iu practice. this may require statistical analysis on a sample of detections.," In practice, this may require statistical analysis on a sample of detections."835 The author thanks the Norean Institute for Advanced Study for their hospitality aud for hosting a very stimulating mecting., The author thanks the Korean Institute for Advanced Study for their hospitality and for hosting a very stimulating meeting.836 Te also thanks G.E. Brown. CAV. Lee and A. Leviuson for continuing couversations.," He also thanks G.E. Brown, C.W. Lee and A. Levinson for continuing conversations."837 This work is partially supported by NASA Crant No., This work is partially supported by NASA Grant No.838 5-7012 and au MIT CLE. Reed Award., 5-7012 and an MIT C.E. Reed Award.839education and advocacy.,education and advocacy.840 We also thank the Tohono O'odham National for being helpful in their choices for outdoor lighting. the International Dark Sky Association for spreading the word and surrounding governments for their continued willingness to consider the impact of their choices on the conduct of astronomy in southern Arizona.," We also thank the Tohono O'odham National for being helpful in their choices for outdoor lighting, the International Dark Sky Association for spreading the word and surrounding governments for their continued willingness to consider the impact of their choices on the conduct of astronomy in southern Arizona."841 Our study shows that these and other efforts have paid off., Our study shows that these and other efforts have paid off.842 But. constant vigilance is essential.," But, constant vigilance is essential."843 We would also like to thank Di Larmer lor her strong support and advice. Dill Binkert for helping set up the spectrograph on occasion. Jeff Hall for helping us analvze the effects of the solar evele on the night skv brightness. the Friends of Lowell Observatory [or publication costs. and the anonvmous referee for their suggestions that helped improve the paper.," We would also like to thank Di Harmer for her strong support and advice, Bill Binkert for helping set up the spectrograph on occasion, Jeff Hall for helping us analyze the effects of the solar cycle on the night sky brightness, the Friends of Lowell Observatory for publication costs, and the anonymous referee for their suggestions that helped improve the paper."844intervening e10 νου time span.,intervening $\sim10$ -year time span.845" There remains a significant discrepancy will the value Iv.=19.14x0.2 estimated by AlvesdeOliveiraοἱal.(2010).. but we suspect that the difference can be attributed to the smaller elfective beamsize (0.4—0.8"") in the latter observations. which could lead to flux underestimation for an extended source."," There remains a significant discrepancy with the value $K_s=19.14\pm0.2$ estimated by \citet{alv10}, but we suspect that the difference can be attributed to the smaller effective beamsize $0.4''-0.8''$ ) in the latter observations, which could lead to flux underestimation for an extended source."846 Object #44450 is not unique in this regardwe have found. a number of other cases in which our sources are slightly extended. aud hypothesize that we may be seeing the effects οἱ scaltering from remnant infalling dust envelopes surrounding the brown dwarl candidates.," Object 4450 is not unique in this regard—we have found a number of other cases in which our sources are slightly extended, and hypothesize that we may be seeing the effects of scattering from remnant infalling dust envelopes surrounding the brown dwarf candidates."847 It is not clear what. if any. effect such cases would have on our temperature estimates. but we note that our SED fit for 444450 vielded an effective temperature in complete agreement wilh the spectroscopic value from Marshetal.(2010).," It is not clear what, if any, effect such cases would have on our temperature estimates, but we note that our SED fit for 4450 yielded an effective temperature in complete agreement with the spectroscopic value from \citet{mar10}."848. Our conclusions are based on fits to broad-band SEDs which are subject to the uncertainties (hat we have discussed., Our conclusions are based on fits to broad-band SEDs which are subject to the uncertainties that we have discussed.849 Verification must await spectroscopic observations in order to confirm (he nature of individual objects and to better constrain (heir parameters., Verification must await spectroscopic observations in order to confirm the nature of individual objects and to better constrain their parameters.850 Nevertheless. SED fitting can play an important role in gathering statistics over wiler areas of (he sky. which is important to do because the mass function is known to vary from region to regionbetween different star-Forming clouds (Evans&Lada1991). and even within the same cloud (Barsonyetal.1997).," Nevertheless, SED fitting can play an important role in gathering statistics over wider areas of the sky, which is important to do because the mass function is known to vary from region to region—between different star-forming clouds \citep{evans91} and even within the same cloud \citep{bar97}."851. Such studies will be aided by upcoming survevs. particularly the Wide-Field Infrared Survey. Explorer (WISE) in conjunction with shorter-waveleneth data from the UIXKIRT Infrared Deep Sky Survey (ΕΝΤΟΣ) and the Visible and Infrared Survey Telescope for Astronomy (VISTA).," Such studies will be aided by upcoming surveys, particularly the Wide-Field Infrared Survey Explorer (WISE) in conjunction with shorter-wavelength data from the UKIRT Infrared Deep Sky Survey (UKIDSS) and the Visible and Infrared Survey Telescope for Astronomy (VISTA)."852" Additional complementary data. consisting of optical and [u-red photometry. will soon be available [rom the Pan-STARRS-1 and Sky-Mapper survey telescopes. and will cover a larger area of skv than UNIDSS and VISTA,"," Additional complementary data, consisting of optical and far-red photometry, will soon be available from the Pan-STARRS-1 and Sky-Mapper survey telescopes, and will cover a larger area of sky than UKIDSS and VISTA."853 We (thank (he referee for helpful comments and suggestions., We thank the referee for helpful comments and suggestions.854 We also thank Tim Thompson for making the IRAC mosaic images. and John Stauffer and Luisa. Rebull for," We also thank Tim Thompson for making the IRAC mosaic images, and John Stauffer and Luisa Rebull for"855 lt ds difficult to. clillerentiate between absorption and emission at —1.2 keV in ‘Ton 5150, It is difficult to differentiate between absorption and emission at $\sim$ 1.2 keV in Ton S180.856 A single. absorption edge at. a rest. οποιον of E=1.09+0.03 keV with an optical depth 7=0.17£0.03. vields νοfv=1072/986.," A single absorption edge at a rest energy of $=1.09\pm0.03$ keV with an optical depth $\tau=0.17\pm0.03$, yields $\chi^{2}/{\nu}=1072/986$."857 A second. edge in the spectrum (at E=1.42+0.06 keV with τξ 0.130.038) improves the fit further (\7v= 1059/985)., A second edge in the spectrum (at $=1.42\pm0.06$ keV with $\tau=0.13\pm0.03$ ) improves the fit further $\chi^{2}/{\nu}=1059/985$ ).858 ‘There is some evidence for an additional edge at ~0.73 keV (v/v= 1048/983) presumably corresponding toOvi., There is some evidence for an additional edge at $\sim$ 0.73 keV $\chi^{2}/{\nu}=1048/983$ ) presumably corresponding to.859 Llowever SIS-1 seems to underestimate the flux compared o SIS-0 below 0.8 keV. so any features in the spectrum odow 0.8 keV. need to considered with caution.," However SIS-1 seems to underestimate the flux compared to SIS-0 below 0.8 keV, so any features in the spectrum below 0.8 keV need to considered with caution."860 A significant improvement over the soft. excess [it is given when a broad Gaussian emission component is added o the model near 1 keV. The best-fit parameters are line EW=20δ eV. energy E=0.94d:0.03 keV and intrinsic width 0=0.062+0.025 keV. for whieh X7/&=the1055/985.," A significant improvement over the soft excess fit is given when a broad Gaussian emission component is added to the model near 1 keV. The best-fit parameters are line $=20\pm8$ eV, energy $=0.94\pm0.03$ keV and intrinsic width $\sigma=0.062\pm0.025$ keV, for which $\chi^{2}/{\nu}=1055/985$."861MN A model also gives an acceptable fit to vielding a plasma temperature of kP=0.89+0.11 keV (Af= 1050/986).," A model also gives an acceptable fit to the data, yielding a plasma temperature of $=0.89\pm0.11$ keV $\chi^{2}/{\nu}=1050/986$ )."862 An absorption [feature definitely gives the best. fit. in ll] 0707495, An absorption feature definitely gives the best fit in 1H 0707–495.863 A broad. absorption line improves the fit significantIy. (Xv= 404/335). as per Table 4.," A broad absorption line improves the fit significantly $\chi^{2}/{\nu}=404/335$ ), as per Table 4."864 An equally good x7 can be obtained. but for 1 additional free parameter. using twoP instead of a single Gaussian: the first edge is at 1.0020.03 keV with 7=0.632:0.27 and the second at 105-000£0.03edene keV with 7=0540.2.," An equally good $\chi^{2}$ can be obtained, but for 1 additional free parameter, using two edges instead of a single Gaussian; the first edge is at $1.09\pm0.03$ keV with $\tau=0.63\pm0.27$ and the second at $0.90\pm0.03$ keV with $\tau=0.5\pm0.2$."865 Leighlv C1997b) also find for one or more absorption features near 1 keV. Ehe addition of a Gaussian emission line in the range 63 keV. instead of an absorption feature. does not provide any improvement in the fit.," Leighly (1997b) also find evidence for one or more absorption features near 1 keV. The addition of a Gaussian emission line in the range 0.6–3 keV, instead of an absorption feature, does not provide any improvement in the fit."866 Previous investigations of the N-rav spectrum of NGC 4051 have suggested the existence. of a warm absorber., Previous investigations of the X-ray spectrum of NGC 4051 have suggested the existence of a warm absorber.867 There is no evidence for additional spectral features in the first observation (taken during the PV phase of the mission) but the second. CXO2) observation. which has much better signal/noise ratio. does show significant features in the residuals between 0.7 and 0.9 keV. In this case we have modelled this apparent warm absorber with 2 absorption edges. for the first. edge E=0.73+0.02 keV and τ0.33£0.05. for the second. edge L=0.93+0.03 keV and τς0.19+ 0.04.," There is no evidence for additional spectral features in the first observation (taken during the PV phase of the mission) but the second (AO2) observation, which has much better signal/noise ratio, does show significant features in the residuals between 0.7 and 0.9 keV. In this case we have modelled this apparent warm absorber with 2 absorption edges, for the first edge $=0.73\pm0.02$ keV and $\tau=0.33\pm0.05$ , for the second edge $0.93\pm0.03$ keV and $\tau=0.19\pm0.04$ ."868 The resulting fit statistic is yofu=2010/1842. an improvement. of Ay?⊳↘=−−77 over the model without. absorption.," The resulting fit statistic is $\chi^{2}/{\nu}=2010/1842$, an improvement of $\Delta\chi^{2}=77$ over the model without absorption."869 The results suggest a normal warn absorber in NGC 4051. with the edges probably originating from andOvi.," The results suggest a normal warm absorber in NGC 4051, with the edges probably originating from and."870 Our results are broadly consistent with those of CGuainazzi (1996). who consider the fitting of this observation in much greater detail.," Our results are broadly consistent with those of Guainazzi (1996), who consider the fitting of this observation in much greater detail."871 Emission and absorption components give comparable fits in PC 12441026., Emission and absorption components give comparable fits in PG 1244+026.872 The addition of a broad Gaussian absorption line significantlv> improves the fit (Apoc 601/532). as per Table 4.," The addition of a broad Gaussian absorption line significantly improves the fit $\chi^{2}/{\nu}=601/532$ ), as per Table 4."873 A single. edge at an. energy. of 1.18d3 keV. gives a better [it (7/6= 591/533).," A single edge at an energy of $1.18\pm0.03$ keV, gives a better fit $\chi^{2}/{\nu}=591/533$ )."874 Adding another edge further improves the fit: with two edges (at E=1.16£0.04 keV and E=0.63n keV) the fit obtained is Vp=SSBΣΙ., Adding another edge further improves the fit; with two edges (at $1.16\pm0.04$ keV and $0.63^{+0.04}_{-0.45}$ keV) the fit obtained is $\chi^{2}/{\nu}=583/531$.875 A broad. Gaussian emission. line at an enerev of E=0.97+004 keV also significantly improves the fit ονfr= 589/532). with an equivalent width of EW=36+11 eV. A slightly better fit QCvo= 586/533) is obtained. wit-— the model. with a plasma temperature of kK'T—1.040.1 keV. Fiore (1998) also find evidence for either an absorption feature at ~1.2 keV or an emission feature at 0.9 keV. Absorption components give a slightly. better fit. than emission components.," A broad Gaussian emission line at an energy of $0.97\pm0.04$ keV also significantly improves the fit $\chi^{2}/{\nu}=589/532$ ), with an equivalent width of $36\pm11$ eV. A slightly better fit $\chi^{2}/{\nu}=586/533$ ) is obtained with the model, with a plasma temperature of $1.0\pm0.1$ keV. Fiore (1998) also find evidence for either an absorption feature at $\sim$ 1.2 keV or an emission feature at 0.9 keV. Absorption components give a slightly better fit than emission components."876 The addition of a single absorption edge to the model improves the fit. significantly (4c/e= 478/424)., The addition of a single absorption edge to the model improves the fit significantly $\chi^{2}/{\nu}=478/424$ ).877 The best fit edge energy is E—1.11+0.04 keV. A second edge improves the further (x7fe= 467/422). with edge energies at 1.0ÜzE0.04 and 1.150.09 keV and optical depths of 7=0.73 and 1.15 respectively.," The best fit edge energy is $1.11\pm0.04$ keV. A second edge improves the fit further $\chi^{2}/{\nu}=467/422$ ), with edge energies at $1.00\pm0.04$ and $1.18\pm0.03$ keV and optical depths of $\tau=0.73$ and 1.15 respectively."878 This fit also, This fit also879»edieted due to the TDU. when LBB takes place the C/O ratio is expected either to decrease. as long as C is converted into N by the CN evele. or even to increase if O is ellicientlv int in favour of N bv the ON evecle (see Sect. 4.3)).,"predicted due to the TDU, when HBB takes place the C/O ratio is expected either to decrease, as long as C is converted into N by the CN cycle, or even to increase if O is efficiently burnt in favour of N by the ON cycle (see Sect. \ref{ssec_nucleos}) )."880 Variations in. CNO abundances allect the Iow-enmperature opacities essentially in two wavs. Le. i) for Zs3000 K by mocifving the equilibrium molecular pattern depending on the C/O ratio and. to a less extent. ii) for arecr temperatures by changing the contributions of the CNO atoms to both the continuum ancl line opacity.," Variations in CNO abundances affect the low-temperature opacities essentially in two ways, i.e. i) for $T\la 3\,000$ K by modifying the equilibrium molecular pattern depending on the C/O ratio and, to a less extent, ii) for larger temperatures by changing the contributions of the CNO atoms to both the continuum and line opacity."881 A detailed discussion can be found in Marigo Aringer (2009: see their section 4.2) anc Ventura Alarigo (2009)., A detailed discussion can be found in Marigo Aringer (2009; see their section 4.2) and Ventura Marigo (2009).882 The nuclear network included in the code is described in details in Ventura&D'Antona(2005a)., The nuclear network included in the code is described in details in \citet{paolo4}.883. The cross-sections of the 64 reactions considered. are taken from the NACRE compilation (Anguloctal.1999)... with the exception of HN(p.« O. taken from Formicolactal.(2004)... and. the three proton-capture reactions of the Ne-Na evele. taken from Llaleetal.(2002) for the ??Ne(p.* J Na reaction. and from Llaleetal.(2004). for the two p-captures by sodium nuclei.," The cross-sections of the 64 reactions considered are taken from the NACRE compilation \citep{angulo}, with the exception of $^{14}$ $\gamma$ $^{15}$ O, taken from \citet{luna}, and the three proton-capture reactions of the Ne-Na cycle, taken from \citet{hale1}884 for the $^{22}$ $\gamma$ $^{23}$ Na reaction, and from \citet{hale2} for the two p-captures by sodium nuclei."885 The stellar models discussed here were followed from the pre-AIS phase to almost the complete ejection of the external envelope., The stellar models discussed here were followed from the pre-MS phase to almost the complete ejection of the external envelope.886 The initial chemical composition of the gas is assigned a total metallicity (mass fraction) Z=0.001 and a degree ofa enhancement aο=10.4. with the reference solar mixture taken from Crevesse&Sauval(1998).," The initial chemical composition of the gas is assigned a total metallicity (mass fraction) $Z=0.001$ and a degree of $\alpha-$ enhancement $[\alpha/{\rm Fe}]=+0.4$, with the reference solar mixture taken from \citet{gs98}."887. ‘To investigate how much the results are allected by the the interplay between the use of the opacitics accounting for the CNO variations and the mass-loss description. we calculated 4 sets of evolutionary mociels. designated with SOGLL. SOGC. DII. and. DC. which dilfer in the adopted prescriptions as outlined in Table 1..," To investigate how much the results are affected by the the interplay between the use of the opacities accounting for the CNO variations and the mass-loss description we calculated 4 sets of evolutionary models, designated with S06H, S06C, BH, and BC, which differ in the adopted prescriptions as outlined in Table \ref{tab_mod}."888 Specifically. we consider two [ormalisms for the mass Loss. ie. Straniero et al. (," Specifically, we consider two formalisms for the mass loss, i.e. Straniero et al. ("8892006) and Bloecker (1995). and two treatments of the. low-Z* opacities. depending on whether the underlying. chemical mixture is kept fixed or accounts for changes in the CNO abundances.,"2006) and Blöccker (1995), and two treatments of the $T$ opacities, depending on whether the underlying chemical mixture is kept fixed or accounts for changes in the CNO abundances."890 In order to better disentangle the ellects of each prescription. the models cover all four combinations of the two parameters. opacity and mass loss.," In order to better disentangle the effects of each prescription, the models cover all four combinations of the two parameters, opacity and mass loss."891 The resulting physical ancl chemical. properties of the TP-AGB moclels described above are presented in Table 2.., The resulting physical and chemical properties of the TP-AGB models described above are presented in Table \ref{yields}.892" bor each stellar mass we show the number of thermal pulses experienced by the star. the final core-mass. the maximum temperature reached at the bottom of the external envelope. plus further information concerning the average content of the ejecta, namely the helium mass fraction. and the € Ν. O and Na enhancement/depletion factors. in terms of the quantities N/Ee]. ολ ολ..."," For each stellar mass we show the number of thermal pulses experienced by the star, the final core-mass, the maximum temperature reached at the bottom of the external envelope, plus further information concerning the average content of the ejecta, namely the helium mass fraction, and the C, N, O and Na enhancement/depletion factors, in terms of the quantities [X/Fe], where $\log$ $\log$ $_{\odot}$."893 The last column shows the ratio between the average CINIOabundance in the ejecta and the initial value. which is assumed to represent the chemical mixture at the epoch of the stars formation.," The last column shows the ratio between the average C+N+O abundance in the ejecta and the initial value, which is assumed to represent the chemical mixture at the epoch of the star's formation."894 We can appreciate the qualitative cllects of the dillerent descriptions of mass loss and molecular opacities from Fig. Ll.," We can appreciate the qualitative effects of the different descriptions of mass loss and molecular opacities from Fig. \ref{3msun},"895 where we show the evolution of a BAL. model calculated according to the prescriptions listed in Table 1.. to which we refer for the meaning of the various symbols.," where we show the evolution of a $_{\odot}$ model calculated according to the prescriptions listed in Table \ref{tab_mod}, to which we refer for the meaning of the various symbols."896 Core Le ancl He-burning phases are not included. in this plot. that starts from the beginning of the PP-AGB phase.," Core H- and He-burning phases are not included in this plot, that starts from the beginning of the TP-AGB phase."897 Each point marks the quiescent stage of pre-EP luminosity maximum., Each point marks the quiescent stage of pre-TP luminosity maximum.898 The solid lines are iso-mass locii. and. connect the four evolutionary sequences at the stages when the total mass of the star has been reduced to 2.9. 2.7. 2.5 and 2A1..," The solid lines are iso-mass locii, and connect the four evolutionary sequences at the stages when the total mass of the star has been reduced to 2.9, 2.7, 2.5 and $_{\odot}$."899 lo all four cases considered here the 3M. models share a [ew common features. namelv: i) they experience LBL. which is usually associated to an ellect. and ii) they enter the domain of C-stars. as the surface. C/O ratio increases above unity due to the Ελ," In all four cases considered here the $_{\odot}$ models share a few common features, namely: i) they experience HBB, which is usually associated to an effect, and ii) they enter the domain of C-stars, as the surface C/O ratio increases above unity due to the TDU."900 At the same time significant dillerences arise., At the same time significant differences arise.901 The SOGLL and 806€ models experience a much weaker mass loss at the beginning. evolving at approximately constant mass for many VPs: this is at odes with the behaviour of BLE and BC models. where an cllicient mass loss determines an earlier extinction. of LBB and its overluminosity (following a rapid cooling of the envelope structure).," The S06H and S06C models experience a much weaker mass loss at the beginning, evolving at approximately constant mass for many TPs; this is at odds with the behaviour of BH and BC models, where an efficient mass loss determines an earlier extinction of HBB and its overluminosity (following a rapid cooling of the envelope structure)."902 This circumstance is seen in the maximum luminosity attained. which is 0.2 dex fainter than in SO6LL and. SOGC sequences.," This circumstance is seen in the maximum luminosity attained, which is $\sim 0.2$ dex fainter than in S06H and S06C sequences."903 The vole plaved by the opacity treatment can be understood by examining the evolution of models sharing 1e same description of mass loss. e.g. the SOGLE ancl SOGC models.," The role played by the opacity treatment can be understood by examining the evolution of models sharing the same description of mass loss, e.g. the S06H and S06C models."904 In the latter. the rapid increase in the mass loss rale as soon as the surface ο exceeds unity (clearly etectable as a jump in Al) favours an earlier. reduction of the mass of the external mantle. which again causes an earlier drop in the luminosity £ (we have à ~0.1 dex dilference in the maximum luminosity in this case).," In the latter, the rapid increase in the mass loss rate as soon as the surface C/O exceeds unity (clearly detectable as a jump in $\dot M$ ) favours an earlier reduction of the mass of the external mantle, which again causes an earlier drop in the luminosity $L$ (we have a $\sim 0.1$ dex difference in the maximum luminosity in this case)."905 The drop in L is associated to a lower temperature at the bottom of the convective envelope. Le. less favourable conditions for LBB.," The drop in $L$ is associated to a lower temperature at the bottom of the convective envelope, i.e. less favourable conditions for HBB."906 As à consequence. we may conclude that. in general. using a mass loss description only mildly dependent on the luminosity. and/or neglecting the changes in the molecular hemistryv. in the opacity computations when C/O 1," As a consequence, we may conclude that, in general, using a mass loss description only mildly dependent on the luminosity, and/or neglecting the changes in the molecular chemistry in the opacity computations when $>1$ ,"907 As à consequence. we may conclude that. in general. using a mass loss description only mildly dependent on the luminosity. and/or neglecting the changes in the molecular hemistryv. in the opacity computations when C/O 1.," As a consequence, we may conclude that, in general, using a mass loss description only mildly dependent on the luminosity, and/or neglecting the changes in the molecular chemistry in the opacity computations when $>1$ ,"908" ppc/"". Αν. Ay~10"". Ενx7’? ~1 Εαν 0.330.88. |0.31. sm. "," $^{\prime\prime}$ ${\rm A_V}$ ${\rm A_V} \sim 10^{\rm m}$ $F_\nu \propto \nu^{1/3}$ $\sim 1$ $\sim 100$ ${\rm d} F_\nu / {\rm d} 909\nu$ $-0.33$$-0.88$ $+0.31$ $\mu$ "910galaxies at the distance to the Virgo cluster.,galaxies at the distance to the Virgo cluster.911 TFhis region contains the majority of LIL deficient. A better insight into the structure of the cluster. is obtained with Fig., This region contains the majority of HI deficient A better insight into the structure of the cluster is obtained with Fig.912 5. which reports the same data as Fig.," 5, which reports the same data as Fig."913 4. but with symbols whose size decreases with increasing distance. and. whose shape refers to 7 regions of the Virgo cluster. represented. in Fig.," 4, but with symbols whose size decreases with increasing distance, and whose shape refers to 7 regions of the Virgo cluster, represented in Fig."914 6 with clotted lines. (galaxies with o«100Ams1 are omitted)., 6 with dotted lines (galaxies with $\sigma<100~km~s^{-1}$ are omitted).915"; Galaxies'. are assigned. to these regions with a criterion that combines their position on the skv with their distance ancl Distant (p,2 31.5) galaxies with Vie.71900 belong almost exclusively to the regions marked M and: W. These correspond to the. M and. Wo clouds. which thus are found o be in Hubble Distant (4, 31.5) objects with Vee,«1900 mostly xilong to the region marked D. Εις corresponds to Cluster D of Binggeli et al. ("," Galaxies are assigned to these regions with a criterion that combines their position on the sky with their distance and Distant $\mu_o>31.5$ ) galaxies with $V_{LG}>1900$ belong almost exclusively to the regions marked M and W. These correspond to the M and W clouds, which thus are found to be in Hubble Distant $\mu_o>31.5$ ) objects with $V_{LG}<1900$ mostly belong to the region marked B. This corresponds to Cluster B of Binggeli et al. ("9161993). but with a smaller extent than in the original definition.,"1993), but with a smaller extent than in the original definition."917 The mean distance moclulus [ου his structure is found to be 31.854. in good agreement with he determination by Federspiel et al. (," The mean distance modulus for this structure is found to be 31.84, in good agreement with the determination by Federspiel et al. ("9181998). (a.= 31.8).,1998) $\mu_o=31.8$ ).919" To the East of approx à=]1225'""' (ALL9) all galaxies iàve distances not cdissimülar [rom those of Cluster A (us0 343).", To the East of approx $\alpha=12^h25^m$ (M49) all galaxies have distances not dissimilar from those of Cluster A $\mu_o~\sim31$ ).920 For example 4 spiral galaxies (NGC 4519. 4332. and 4535. and IC 3521) which are assigned to Cluster D bx Bingecli et al. (," For example 4 spiral galaxies (NGC 4519, 4332, and 4535, and IC 3521) which are assigned to Cluster B by Binggeli et al. ("921"1985) are not confirmed. to lie at significantly larger distance than Cluster A. since they are ound at (4,230.2-31.3.","1985) are not confirmed to lie at significantly larger distance than Cluster A, since they are found at $\mu_o$ =30.2-31.3."922 For these objects our TE. distance determinations are in agreement with those of Yasuda et al. (, For these objects our TF distance determinations are in agreement with those of Yasuda et al. (9231997).,1997).924 Another 3 E/SO Cluster D candidates according o Binggeli et al. (, Another 3 E/S0 Cluster B candidates according to Binggeli et al. (925NGC 4472 (M49). 4526. and 4570) have fiex31.2. as determined. using the FP relation.,"NGC 4472 (M49), 4526, and 4570) have $\mu_o<31.2$, as determined using the FP relation."926 Our low distance estimate of MAO agrees with independent estimates obtained using all methods quoted above., Our low distance estimate of M49 agrees with independent estimates obtained using all methods quoted above.927 Unfortunately this is the only galaxy with independent. distance estimate among this group of carly-twpe objects., Unfortunately this is the only galaxy with independent distance estimate among this group of early-type objects.928" We propose that MA9 belongs to cloud S. Ls redshift (Vee,=1200£ms. 1) is 400 Arnos lower than the mean. but it is well within he distribution of Vie. in this region.","	 We propose that M49 belongs to cloud S. Its redshift $V_{LG}=1200~km~s^{-1}$ ) is 400 $km~s^{-1}$ lower than the mean, but it is well within the distribution of $V_{LG}$ in this region."929" The remaining galaxies have 4,<31.5.", The remaining galaxies have $\mu_o<31.5$.930 They form he main body of the cluster. indicated here with region A (AIST). N. to the NW. E. to the East and S. to the Region A coincides with Cluster A and with the X-ray ;»osition (see Fig.," They form the main body of the cluster, indicated here with region A (M87), N, to the NW, E, to the East and S, to the Region A coincides with Cluster A and with the X-ray position (see Fig."931 7 adapted from Bóhhringer et al., 7 adapted from Böhhringer et al.932 1994. reproduced. on the same scale as Fig.," 1994, reproduced on the same scale as Fig."933 6)., 6).934 As expected. most HE deficient. galaxies belong to this region (see Fig.," As expected, most HI deficient galaxies belong to this region (see Fig."935 S)., 8).936 Two exceptions are surprisingly found at the southern edge of the cluster in the region of NGC 4636. a strong and extended N-ray source (Vrinehieri et al.," Two exceptions are surprisingly found at the southern edge of the cluster in the region of NGC 4636, a strong and extended X-ray source (Trinchieri et al."937 L994)., 1994).938 We argue that a significant quantity of extended. gas must. be associated with this galaxy., We argue that a significant quantity of extended gas must be associated with this galaxy.939" The distribution of ji. in the cluster A itself is centered ab qn,=30.84 with a dispersion of 0.45 mag.", The distribution of $\mu_o$ in the cluster A itself is centered at $\mu_o=30.84$ with a dispersion of 0.45 mag.940 This is comparable to the nominal uncertainty of the. distance determination. methods (0.35 and. 0.45. mae for TE. and FP). thus the depth along the line of sight of this aggregate cannot be determined.," This is comparable to the nominal uncertainty of the distance determination methods (0.35 and 0.45 mag for TF and FP), thus the depth along the line of sight of this aggregate cannot be determined."941 One of the most interesting results of the present analysis is that. among galaxies at the main cluster distance. those belonging to clouds N anc S show a significant velocity segregation.," One of the most interesting results of the present analysis is that, among galaxies at the main cluster distance, those belonging to clouds N and S show a significant velocity segregation."942 This is illustrated in Fig., This is illustrated in Fig.943 9., 9.944 The two rightmost panels of this figure give histograms of Vics and of pi; derived from this work for the 7 considered regions., The two rightmost panels of this figure give histograms of $V_{LG}$ and of $\mu_o$ derived from this work for the 7 considered regions.945 While the distances of cluster A and. clouds S. N. and E are in agreement (μμ=30.8431.23) the only significantly more distant structures are cluster D and clouds Wand M. Clusters A and B ancl cloud E have similar velocity distributions peaked at the standard Έτ~1350Amosf.," While the distances of cluster A and clouds S, N, and E are in agreement $\mu_o=30.84-31.23$ ) the only significantly more distant structures are cluster B and clouds W and M. Clusters A and B and cloud E have similar velocity distributions peaked at the standard $V_{LG} \sim 1350~km~s^{-1}$."946 Clouds. Wane AL have instead a higher velocity., Clouds W and M have instead a higher velocity.947 Clouds S and N have significantly cillerent distributions., Clouds S and N have significantly different distributions.948 The N one contains galaxies with Έντο«1300fins+. thus. blueshifted with respect to Virgo.," The N one contains galaxies with $V_{LG}<1300~km~s^{-1}$, thus blueshifted with respect to Virgo."949 Similar evidence was pointec out by Llolfmann et al. (, Similar evidence was pointed out by Hoffmann et al. (950LOS9b) and was extensively analyzed by Tully Shava. (1984) to model the infall of galaxies on the Virgo cluster.,"1989b) and was extensively analyzed by Tully Shaya, (1984) to model the infall of galaxies on the Virgo cluster."951 On the contrary. cloud S contains mainly redshifted galaxies. with 750«Vee.2700kims+.," On the contrary, cloud S contains mainly redshifted galaxies, with $750 < V_{LG} < 2700~km~s^{-1}$."952 To check if the latter result is not due to the limited statistics of the sample used in this work. and since the velocity distribution can be derived from. a larger body of velocity measurements than the one represented in our sample of galaxies with distance estimates. we determine the velocity. distributions in the 7 studied regions using the whole VCC (which contains over 400 galaxies with redshift estimates) (see left. panel of Fig.," To check if the latter result is not due to the limited statistics of the sample used in this work, and since the velocity distribution can be derived from a larger body of velocity measurements than the one represented in our sample of galaxies with distance estimates, we determine the velocity distributions in the 7 studied regions using the whole VCC (which contains over 400 galaxies with redshift estimates) (see left panel of Fig."953 9)., 9).954 The dillerence between regions S and N. noticed in our smaller sample with distance estimates. is equally present in the larger VOC sample. ancl we conclude it represents a real ¢illerence between the two A summary of the mean velocity. velocity. dispersion. ancl distance modulus determinations for all seven regions is presented in Tab.," The difference between regions S and N, noticed in our smaller sample with distance estimates, is equally present in the larger VCC sample, and we conclude it represents a real difference between the two A summary of the mean velocity, velocity dispersion, and distance modulus determinations for all seven regions is presented in Tab."955 3. and is also shown in Fig.," 3, and is also shown in Fig."956 10. where the average velocities and distance. moduli are. plotted with error bars indicating the statistical uncertainties on the determination. of the two quantities (galaxies with a«100kms are exeluded).," 10, where the average velocities and distance moduli are plotted with error bars indicating the statistical uncertainties on the determination of the two quantities (galaxies with $\sigma<100~km~s^{-1}$ are excluded)."957 Estimates of cluster A are also given separately for earlv-tvpe. and. latc-type ealaxies. subclividecl into LL deficient anc IL normal.," Estimates of cluster A are also given separately for early-type and late-type galaxies, subdivided into HI deficient and HI normal."958 Alean quantities ancl the associatecl uncertainties were computed. using the so-called. biweight estimators (sec Beers et al., Mean quantities and the associated uncertainties were computed using the so-called biweight estimators (see Beers et al.959 1990 for details). that are known to provide a robust parameter estimation for samples covering a wide interval in size.," 1990 for details), that are known to provide a robust parameter estimation for samples covering a wide interval in size."960 Statistical uncertainties on the, Statistical uncertainties on the961ligehteurves. accounting as usal for the typical error bars in the data aud in the models.,"lightcurves, accounting as usual for the typical error bars in the data and in the models."962 We derive the distributiou of colors or both true and simulated data., We derive the distribution of colors for both true and simulated data.963 The distributious are plotted in Figure &.., The distributions are plotted in Figure \ref{fig:BmV}.964 The top pane shows the distribution for true data., The top panel shows the distribution for true data.965" There is 10 blue excess in flux iu the true color: iu fact the clistribution has a ueanofg ὃν1ὃν ἃ median ~0.002, anda staudard deviation σ0.051: statistically consistent with a raneol distribution around 0."," There is no blue excess in flux in the true color: in fact the distribution has a mean of $\mu~\sim ~-8 \times 10^{-4}$, a median $\sim 0.002$, and a standard deviation $\sigma \sim 0.054$: statistically consistent with a random distribution around 0."966 The distributions eencrated from simulated hehteurves— are shown below the= distribution for tine data in yo (M. ROG contributions RGgareTM664and9€. plotted from the top to the bottom.," The distributions generated from simulated lightcurves are shown below the distribution for true data in Figure \ref{fig:BmV}, for RG contributions $\RGf~=~ 0\%,~33\%,~ 66\%,~ \mathrm{and}~ 99\%$, plotted from the top to the bottom."967 Each distribution is generated from a factor of LOO more poiits than the true color distribution ancl is thus Ιαν joisv., Each distribution is generated from a factor of 100 more points than the true color distribution and is thus minimally noisy.968 The mean of the cistributiou Increases as we increase aud the distributions eot inercasingly asvnunetric. weighted toward positive values of (bluer color).," The mean of the distribution increases as we increase and the distributions get increasingly asymmetric, weighted toward positive values of (bluer color)."969" The svuthetic distributions generated with no RCis 43) has moments that are extremely siular to frose of the true color distribution: p2«10""7.m median ~0.001. and ac0.077."," The synthetic distributions generated with no RGs ) has moments that are extremely similar to those of the true color distribution: $\mu~\sim~2\times 10^{-3}$, median $\sim 0.001$ and $\sigma \sim 0.077$."970 Ouce/— again. this shows hat the distribution of colors iu the SNLS data is compatible with minimal Or no contributiπι of RC to progenitors. confrniug the results obtained from the IN-S tests.," Once again, this shows that the distribution of colors in the SNLS data is compatible with minimal – or no – contribution of RG to progenitors, confirming the results obtained from the K-S tests."971 The excess due to shocking of t16 SN ejecta affects the carly time domain plicXtonietrie ancl spectral behavior of the explosions., The excess due to shocking of the SN ejecta affects the early time domain photometric and spectral behavior of the explosions.972 Since in surveys such as SNLS aud SDSS are ideutified by heir early lghteurves. and thus an explosio ids followed wp spectroscopically oulv ifit is thought to be a SN explosion. au interesting question is whether this carly effect might have lead to the rejcction of plenonena that indeed wereB. but deviate from the exrected early behavior ou account of shocsine.," Since in surveys such as SNLS and SDSS are identified by their early lightcurves, and thus an explosion is followed up spectroscopically only if it is thought to be a SN explosion, an interesting question is whether this early effect might have lead to the rejection of phenomena that indeed were, but deviated from the expected early behavior on account of shocking."973 Iu Uavdenetal.(2010a).. a subset of πιοσο. is visually inspected and no such is found.," In \citet{2010sdss}, a subset of unconfirmed is visually inspected and no such effect is found."974 We 1uvestigate 905 SNLS liebhteurves with some redshift iuormation. either spectroscopic or photometric.," We investigate 905 SNLS lightcurves with some redshift information, either spectroscopic or photometric."975 We exchde likely or known ACN. variable stars. and core-collapse (CC) SNe.," We exclude likely or known AGN, variable stars, and core-collapse (CC) SNe."976 Iu order to avoid contamination frou. 1widentified SNe IL. Ib. or Ic. we aso ayply cuts in stretch aud color space.," In order to avoid contamination from unidentified SNe II, Ib, or Ic, we also apply cuts in stretch and color space."977 Iu. particular. CC SNe show a different average color than SNe Ia. ad color constraints eliminate them frou the sample.," In particular, CC SNe show a different average color than SNe Ia, and color constraints eliminate them from the sample."978 A detailed discussion of ]photometric selection of iu the SNLS data cau he found in Bazinetal.(2011)., A detailed discussion of photometric selection of in the SNLS data can be found in \citet{Bazin10}.979". We thus believe our new dataset has minimal contamination from, non events.", We thus believe our new dataset has minimal contamination from non events.980 Our new dataset contains 336 hehtcurves before our cuts are applied (see Section ??)). and 110 after.," Our new dataset contains 336 lightcurves before our cuts are applied (see Section \ref{sec:data}) ), and 110 after."981 Our iw composite liehteurves. contain 25] poiuts iu rest-frarue aud 270 in rest-frame 1- the region of iuterest: =-l7.1 to -7.1 davs to pea- (Figure 9))., Our new composite lightcurves contain 251 points in rest-frame and 270 in rest-frame in the region of interest: -17.4 to -7.4 days to peak (Figure \ref{fig:complc_uncf}) ).982 We repeat the I-5 tcts applied eurlier to the extended set aud fud theut the statistics coufinn the upper limits set to the contiibution of RCo binary svstenis to explosious (Figures 10 and 11)), We repeat the K-S tests applied earlier to the extended set and find that the statistics confirm the upper limits set to the contribution of RG binary systems to explosions (Figures \ref{fig:ks_unconf} and \ref{fig:ks_color_unconf}) ).983 The K-S test of the composite lighteurve in cach B aud V. with the respective svuthetic lighteurves is entirely consistent with the test for the spectroscopically confirmed subset.," The K-S test of the composite lightcurve in each B and V with the respective synthetic lightcurves is entirely consistent with the test for the spectroscopically confirmed subset,"984The abundances of neutron())-capture elements (atomic number Z> 30) are sensitive probes of the nucleosynthetic histories of stellar populations and the chemical evolution of the Universe (???)..,"The abundances of )-capture elements (atomic number $Z>30$ ) are sensitive probes of the nucleosynthetic histories of stellar populations and the chemical evolution of the Universe \citep{wally97, busso99, sneden08}."985 Our knowledge of the production of these elements is largely based on the interpretation of abundances derived from stellar spectroscopy (e.g..2222?.andrefer-ences therein)..," Our knowledge of the production of these elements is largely based on the interpretation of abundances derived from stellar spectroscopy \citep[e.g.,][and references therein]{smith90, busso99, travaglio04, sneden08, roederer10}."986 However. only a limited number of trans-iron elements can be detected in stellar spectra.," However, only a limited number of trans-iron elements can be detected in stellar spectra."987 Moreover. some classes of stars or stages of evolution with high mass-loss rates are very difficult to study spectroscopically due to photospheric obscuration.," Moreover, some classes of stars or stages of evolution with high mass-loss rates are very difficult to study spectroscopically due to photospheric obscuration."988" The recent detection of emission lines from. /--capture elements in a large number of planetary nebulae (PNe) (222?)., as well as other astrophysical objects including H II regions (e.g..90999999*220222222)2222222?).. starburst galaxies (2).. and active galactic nuclei (?).. has demonstrated that nebular spectroscopy is a potentially powerful tool for investigating the nucleosynthesis and chemical evolution of trans-iron species."," The recent detection of emission lines from -capture elements in a large number of planetary nebulae (PNe) \citep{sterling07, sharpee07, sterling08, sterling09}, as well as other astrophysical objects including H II regions \citep[e.g.,][]{aspin94, lumsden96, luhman98, baldwin00, puxley00, okumura01, blum08, roman-lopes09}, starburst galaxies \citep{vanzi08}, and active galactic nuclei \citep{thompson78}, has demonstrated that nebular spectroscopy is a potentially powerful tool for investigating the nucleosynthesis and chemical evolution of trans-iron species."989" The abundances of n--capture elements are of particular interest in PNe. since these species can be produced in PN progenitor stars via slow z--capture nucleosynthesis (the ""s--process"") during the asymptotic giant branch (AGB) stage of evolution."," The abundances of -capture elements are of particular interest in PNe, since these species can be produced in PN progenitor stars via slow -capture nucleosynthesis (the -process”) during the asymptotic giant branch (AGB) stage of evolution."990 Nebular spectroscopy provides access to many elements that cannot be detected in cool giant stars. such as the lightest n--capture elements (Z= 31-36) and noble gases.," Nebular spectroscopy provides access to many elements that cannot be detected in cool giant stars, such as the lightest -capture elements $Z=31$ –36) and noble gases."991 Due to the difficulty in detecting these species in stellar spectra or supernova remnants (?).. the origins of light -capture elements are based predominantly on theoretical considerations that lack empirical validation.," Due to the difficulty in detecting these species in stellar spectra or supernova remnants \citep{wally95}, the origins of light -capture elements are based predominantly on theoretical considerations that lack empirical validation."992" In. addition, nebular spectroscopy enables investigations of nucleosynthesis in classes or evolutionary stages of stars obscured by optically thick circumstellar envelopes."," In addition, nebular spectroscopy enables investigations of nucleosynthesis in classes or evolutionary stages of stars obscured by optically thick circumstellar envelopes."993 For example. intermediate-mass AGB stars (4-8 M4) experience heavy mass loss. shielding their photospheres in a cocoon of circumstellar material that hinders spectroscopic investigations in the wavelength regimes of many useful z--capture element transitions.," For example, intermediate-mass AGB stars (4–8 $_{\odot}$ ) experience heavy mass loss, shielding their photospheres in a cocoon of circumstellar material that hinders spectroscopic investigations in the wavelength regimes of many useful -capture element transitions."994 As a result. the contribution of these stars to the Galactic inventory of heavy element nuclei is poorly understood (e.g..?)..," As a result, the contribution of these stars to the Galactic inventory of heavy element nuclei is poorly understood \citep[e.g.,][]{karakas09}."995 However. these intermediate-mass stars produce PNe in which z--capture element emission lines are readily detected (??)..," However, these intermediate-mass stars produce PNe in which -capture element emission lines are readily detected \citep{sharpee07, sterling08}. ."996 Likewise. AGB stars that become carbon-rich as a result of convective dredge-up (see?) are characterized by high opacities (?) that substantially increase their mass-loss rates. and hence -process enrichments engendered by the final stages of AGB evolution are not well-constrained.," Likewise, AGB stars that become carbon-rich as a result of convective dredge-up \citep[see][]{busso99} are characterized by high opacities \citep{marigo02} that substantially increase their mass-loss rates, and hence -process enrichments engendered by the final stages of AGB evolution are not well-constrained."997 PNe are composed of material from the stellar envelope at the end of the AGB phase. and hence are useful probes of s--process enrichments during late AGB evolution.," PNe are composed of material from the stellar envelope at the end of the AGB phase, and hence are useful probes of -process enrichments during late AGB evolution."998 However. the accuracy of nebular n--capture element abundances is hindered by the poorly known atomic data for these species. thereby limiting the usefulness of nebular spectroscopy for studying the origins of these elements.," However, the accuracy of nebular -capture element abundances is hindered by the poorly known atomic data for these species, thereby limiting the usefulness of nebular spectroscopy for studying the origins of these elements."999 The reason for this is that generally only one or two tons of n-- elements have been detected in individual nebulae. and hence the abundances of unobserved tons must be estimated in order to derive elemental abundances.," The reason for this is that generally only one or two ions of -capture elements have been detected in individual nebulae, and hence the abundances of unobserved ions must be estimated in order to derive elemental abundances."1000 This ts most robustly achieved by numerically simulating the thermal and ionization structure ofnebulae with phototonization codes such as Cloudy (?).. but the reliability of these models strongly depends on the availability of accurate atomic data for processes that control the tonization balance.," This is most robustly achieved by numerically simulating the thermal and ionization structure of nebulae with photoionization codes such as Cloudy \citep{ferland98}, but the reliability of these models strongly depends on the availability of accurate atomic data for processes that control the ionization balance."1001 For photoionized nebulae such as PNe. these data include photoionization (PI) cross sections and rate coefficients for radiative recombination (RR). dielectronic recombination (DR). and charge transfer (CT).," For photoionized nebulae such as PNe, these data include photoionization (PI) cross sections and rate coefficients for radiative recombination (RR), dielectronic recombination (DR), and charge transfer (CT)."1002 Unfortunately. such data have not been determined for the vast majority of trans-iron element tons.," Unfortunately, such data have not been determined for the vast majority of trans-iron element ions."1003 To address this need. we have computed multi-configuration Breit-Pauli (MCBP) distorted-wave PI cross sections and RR and DR rate coefficients for the first six Se ions. using the atomic structure code AUTOSTRUCTURE (??)..," To address this need, we have computed multi-configuration Breit-Pauli (MCBP) distorted-wave PI cross sections and RR and DR rate coefficients for the first six Se ions, using the atomic structure code AUTOSTRUCTURE \citep{badnell86, badnell97}."1004 Along with. Kr and. Xe. Se is one of the most widely observed --capture elements in ionized nebulae (??)..," Along with Kr and Xe, Se is one of the most widely observed -capture elements in ionized nebulae \citep{sharpee07, sterling08}."1005 In fact. Se has been identified in nearly twice as many PNe às any other trans-iron element. and hence is the initial target for our study.," In fact, Se has been identified in nearly twice as many PNe as any other trans-iron element, and hence is the initial target for our study."1006 In subsequent papers. we will present similar data for low-charge Kr and Xe tons. as well as CT ratecoefficients for several --capture elements.," In subsequent papers, we will present similar data for low-charge Kr and Xe ions, as well as CT ratecoefficients for several -capture elements."1007 These data will be suitable, These data will be suitable1008"In reffig:dlogs,, all aand dderivativeP5,, terms are tied together at zero at small scales.","In \\ref{fig:dlogs}, all and derivative terms are tied together at zero at small scales."1009" This is because for each, the variance is unity in 1300/256 Mpc z ccells."," This is because for each, the variance is unity in $1300/256$ Mpc $\approx$ cells."1010" The derivative terms are generally smaller in absolute value for these power spectra, which translates into poorer parameter constraints below than for aandPj(145),, with the exception of the parameter ns."," The derivative terms are generally smaller in absolute value for these power spectra, which translates into poorer parameter constraints below than for and, with the exception of the parameter $n_s$ ."1011" Curiously, at this resolution, Dj,oz(k) is of comparable absolute magnitude for aand ffor small P5)k."," Curiously, at this resolution, $D_{\lses}(k)$ is of comparable absolute magnitude for and for small $k$."1012" Naively, one might expect all information about the amplitude to be destroyed inP5,,,, in which one divides the power spectrum by the variance in cell densities (here, of ssize, but this holds to some degree for "," Naively, one might expect all information about the amplitude to be destroyed in, in which one divides the power spectrum by the variance in grid-cell densities (here, of size, but this holds to some degree for cells)."1013"However, recall that the amplitude c2 is the ccells).variance in vvolumes in the linearly, not nonlinearly, evolved density field; the nonzero Dj, at small scales is apparently from the rise in the nonlinearoz(k) power spectrum in aandP"," However, recall that the amplitude $\sigma_8^2$ is the variance in volumes in the linearly, not nonlinearly, evolved density field; the nonzero $D_{\lses}(k)$ at small scales is apparently from the rise in the nonlinear power spectrum in and."1014"5,,.. reffig:ellipsesyplogshowserrorbarsoverthesetof aandPj(.5).."," \\ref{fig:ellipses_pplog} shows error bars over the set of five cosmological parameters, for and."1015 The effective volume for these results is (1.8 Gpc)?/2z1.1 Gpce?z.5 Gpc))?., The effective volume for these results is (1.3 $^3/2\approx 1.1$ $^3\approx .5$ $^3$.1016" The factor of two is from the sinusoidal weightings used for the covariance matrices, which effectively halve the volume."," The factor of two is from the sinusoidal weightings used for the covariance matrices, which effectively halve the volume."1017" Along the diagonal, the curves are unmarginalized error bars over single parameters, holding all else fixed."," Along the diagonal, the curves are unmarginalized error bars over single parameters, holding all else fixed."1018" Off the diagonal, we examine error bars allowing sets of two parameters to vary at a time."," Off the diagonal, we examine error bars allowing sets of two parameters to vary at a time."1019" The upper plots show how error ellipses contract as ἆγμακ increases, while the lower plots show how marginalized error bars shrink."," The upper plots show how error ellipses contract as $k_{\rm1020 max}$ increases, while the lower plots show how marginalized error bars shrink."1021" Constraints obtained analyzing aare substantially smaller than forP5,,(1..5) for all parameters, typically by a factor of 2 or 3 if the analysis is pushed to the smallest scales shown."," Constraints obtained analyzing are substantially smaller than for, for all parameters, typically by a factor of 2 or 3 if the analysis is pushed to the smallest scales shown."1022" The difference is particularly large for n,, where the error bar is reduced by a factor of 5."," The difference is particularly large for $n_s$, where the error bar is reduced by a factor of 5."1023 Another parameter whose behavior is simple to understand is Ino2., Another parameter whose behavior is simple to understand is $\lses$.1024" As discussed above, Diyo2(k) is smaller for tthan forP(1..5)P5, at all k."," As discussed above, $D_{\lses}(k)$ is smaller for than for, at all $k$."1025" Looking at the diagonal, unmarginalized plots, this is why the error bars are degraded in wwhen only Pjlinear (1,5)scales are included."," Looking at the diagonal, unmarginalized plots, this is why the error bars are degraded in when only linear scales are included."1026" However, when pushing into translinear scales, the penalty from the decreased derivative term is quickly overcome because of drastically reduced cosmic variance, resulting in tighter constraints from aat sufficiently small Py(1+5)scales."," However, when pushing into translinear scales, the penalty from the decreased derivative term is quickly overcome because of drastically reduced cosmic variance, resulting in tighter constraints from at sufficiently small scales."1027" reffig:ellipses, vpgshowsthesame figure forP aand", \\ref{fig:ellipses_pvpg} shows the same figure for and.1028" Except for the case of the stilt/> n,, the constraints Pg(sj.from aare weaker than Pas)from and often even weaker than fromP;."," Except for the case of the tilt $n_s$, the constraints from are weaker than from, and often even weaker than from."1029". This could be P,(.5),,surprising given that the covariance matrix of hhas the smallest non-GaussianPa; component, and the highest diagonality, of any of the power spectra considered here."," This could be surprising given that the covariance matrix of has the smallest non-Gaussian component, and the highest diagonality, of any of the power spectra considered here."1030" The performance of fivecosmologiiàlplsFaflieephoinóye, given the high P5,diagonality of its covariance matrix; the performance is also degraded for ccompared/o to ffor some parameters.", The performance of is also disappointing given the high diagonality of its covariance matrix; the performance is also degraded for compared to for some parameters.1031" For aandP5/,,, this behavior is Pas)from small derivative terms D(k)."," For and, this behavior is from small derivative terms $\bD(k)$."1032" As discussed above, this is largely from the unitvariance enforced in cell densities for these density fields."," As discussed above, this is largely from the unitvariance enforced in cell densities for these density fields."1033 Other analysis procedures are certainly possible., Other analysis procedures are certainly possible.1034 It would be convenient to use, It would be convenient to use1035large accretion rates at carlicy stages unexplained.,large accretion rates at earlier stages unexplained.1036" There Is no reason to expect MRI turbulence in the outer disk to ""shut off when a eapis opened. so while our observatiou of a sinall turbuleut linewidth in the TW να system is consistent with the 7T. hwpothesis. if is still surprising that the turdlent Lnewidth in WD 163296 should be sO mich larger."," There is no reason to expect MRI turbulence in the outer disk to “shut off” when a gap is opened, so while our observation of a small turbulent linewidth in the TW Hya system is consistent with the \citet{chi07} hypothesis, it is still surprising that the turbulent linewidth in HD 163296 should be so much larger."1037 Another oossibilitv wnrelatcc to the AIRT is that ΠΟ 163296 is still expericucing iufal outo the disk from a relait envelope., Another possibility unrelated to the MRI is that HD 163296 is still experiencing infall onto the disk from a remnant envelope.1038 Since he high optical depth of the CO(3-2) line iuples that most of the enüssion arises from the up]xY lavers of the disk. such a scenario could nuuc tje signature of a tfirbuleut Hnewidth that we observe: however» there is no observational evidence for anu envelope iu this system.," Since the high optical depth of the CO(3-2) line implies that most of the emission arises from the upper layers of the disk, such a scenario could mimic the signature of a turbulent linewidth that we observe; however, there is no observational evidence for an envelope in this system."1039 We plan to address this possibility more thoroughly iu a follow-up paper modeling 1nultiple lines with lower optical depths tlat probe deeper toxs the disk midplane., We plan to address this possibility more thoroughly in a follow-up paper modeling multiple lines with lower optical depths that probe deeper towards the disk midplane.1040 The presence of 3bsonic turbulence in protoplanetary accretion disks likely substautially subsonic iu the uilpluie — is consiseut with the observations xeseuted in this) study., The presence of subsonic turbulence in protoplanetary accretion disks – likely substantially subsonic in the midplane – is consistent with the observations presented in this study.1041 Susonic turbulence has inportaut iuplications for the formation aud evolution of vouug anetarv svstenis., Subsonic turbulence has important implications for the formation and evolution of young planetary systems.1042 Oue SCTICS of papers (2272) explores im detail tιο effects of turbulence oi planct-ormune disks.," One series of papers \citep{pap03,pap04,nel03,nel04} explores in detail the effects of turbulence on planet-forming disks."1043 Thei evlindrical models of urbuleut disks⋅ have au average o iu⋅ the range of 10 ⊳↽⋅≻↽7-1052a mt they demonstrae that the realistic iuplemoenutatiou of turbulence results dn differeut effects than are secu i luuinur disk siuulatious with comparable values of a incorporated as an anomalous Navicer-Sto|SOS viscosity.," Their cylindrical models of turbulent disks have an average $\alpha$ in the range of $10^{-2}$ $10^{-3}$, but they demonstrate that the realistic implementation of turbulence results in different effects than are seen in laminar disk simulations with comparable values of $\alpha$ incorporated as an anomalous Navier-Stokes viscosity."1044 They show that for massive planets. turbulence can widen and deepen the eap « Ες protoplauets; and may reduce the accretion rate oito the protoplanet.," They show that for massive planets, turbulence can widen and deepen the gap opened by massive protoplanets, and may reduce the accretion rate onto the protoplanet."1045 Εςx the case of nüerating low-niass planet cores. the picποσο of turbulence iu the disk can slow or even reversc» the uueration rate. converting the mionotonic inward uotion of the plaiet into a random walk.," For the case of migrating low-mass planet cores, the presence of turbulence in the disk can slow or even reverse the migration rate, converting the monotonic inward motion of the planet into a random walk."1046 The presence of dead zones im he racial direction may also act to walt migration axl encourage the survival and erowth of protoplancts (c.g.?7).., The presence of dead zones in the radial direction may also act to halt migration and encourage the survival and growth of protoplanets \citep[e.g.][]{mat09}.1047 Ànotlor inportant propose effect of subsonic turbulence is to aid du concenutratiuο plauetesuunals to allow them to collapse gravitation:uly (2).., Another important proposed effect of subsonic turbulence is to aid in concentrating planetesimals to allow them to collapse gravitationally \citep{joh07}.1048 AMID turbuleuce on these scales can also redice the streneth of the eravitational iustabilitv aud redice disk fragmentation (?).., MHD turbulence on these scales can also reduce the strength of the gravitational instability and reduce disk fragmentation \citep{fro05}.1049 There is also subsautial literature on the effects of turbule100 Oll dust settling and ex:un erowth (e.c.727??7)..," There is also substantial literature on the effects of turbulence on dust settling and grain growth \citep[e.g.][]{joh05,car06,1050cie07,bal09,fro09}."1051 Although it i« difheult to compare the properties of the siulations directle with our observations. the generic features of tlvese models (610. 2-10.7. subsonic turbulence even i the upper disk lavers) are globally consistent with the derived. properties of turbulence iu the disks around ΠΟ 163296 and TW Iva. indicating that these effects are likely to play a role in dlanet formation.," Although it is difficult to compare the properties of the simulations directly with our observations, the generic features of these models $\alpha$ $10^{-2}$ $10^{-3}$, subsonic turbulence even in the upper disk layers) are globally consistent with the derived properties of turbulence in the disks around HD 163296 and TW Hya, indicating that these effects are likely to play a role in planet formation."1052 The most obvious iuprovenient to our method would be to include additional spectral lines frou different transitions or dsofcypologues of the CO molecule. iu order to provide iilependenut constraints ou the gas teiiperature., The most obvious improvement to our method would be to include additional spectral lines from different transitions or isotopologues of the CO molecule in order to provide independent constraints on the gas temperature.1053 While this would necessarily iutroduce additional parameters iuto the model G.c.. to describe the vertical distribution of temperature aud turbuence. as well as a consistent density disribution to properly account for the line opacity). the acdition of severa lies that are resoved in the spectral and spatial dowads would more fxiulv constraiu he models.," While this would necessarily introduce additional parameters into the model (i.e., to describe the vertical distribution of temperature and turbulence, as well as a consistent density distribution to properly account for the line opacity), the addition of several lines that are resolved in the spectral and spatial domains would more firmly constrain the models."1054 It might also provide direc nueasurenmentas of t1ο vertical profile of the turbuleut VC‘locity. structure., It might also provide direct measurements of the vertical profile of the turbulent velocity structure.1055 ? and ? provide exanples of sudies that use multiale molecular liles to study the verlcd structure of deusity and tempcrature in circiuustellar disks: these tecudques could be extended ο constrain the turbulent lineidti dn snuilar svstenis., \citet{dar03} and \citet{pan08} provide examples of studies that use multiple molecular lines to study the vertical structure of density and temperature in circumstellar disks; these techniques could be extended to constrain the turbulent linewidths in similar systems.1056 Another possibility is to observe 10is rather than jeutral species., Another possibility is to observe ions rather than neutral species.1057 This would clinunate colplicatious introduced by the interaction between 10is and neutrals. ancl would more cürectlv xobe the turlulent motions of he charged gas.," This would eliminate complications introduced by the interaction between ions and neutrals, and would more directly probe the turbulent motions of the charged gas."1058 Even with he curren set of observations. greater sensitivitv wolId be extremely valuable iu conustraining he turbulent luevidth. since the distinctions between urbuleut arc thermal broadening are subtle (sec Section L.1)).," Even with the current set of observations, greater sensitivity would be extremely valuable in constraining the turbulent linewidth, since the distinctions between turbulent and thermal broadening are subtle (see Section \ref{sec:degen}) )."1059 The vast improvements i seusitivitv xovided bw tιο Atacama Large Millimeter Array will vert sienificautly better inodelius of the velocity stcture of voung disks., The vast improvements in sensitivity provided by the Atacama Large Millimeter Array will permit significantly better modeling of the velocity structure of young disks.1060 Such data will also allow us to filv nle out deviations from perfect Keplerian rotation hat could complicate the derivation of turbulent linewidth., Such data will also allow us to firmly rule out deviations from perfect Keplerian rotation that could complicate the derivation of turbulent linewidth.1061 m accditiou. hieher sensitivitv combined with a ereater spatial dynamic range will allow for he investigation of radial variations 1ji the turbuleut inewidth.," In addition, higher sensitivity combined with a greater spatial dynamic range will allow for the investigation of radial variations in the turbulent linewidth."1062 We have obtaijid. the. first spatially resolved observations of molecala line emissiou from two nearby cireunistellar disks witji spectral rexution finer than the expected turinlew luewidth., We have obtained the first spatially resolved observations of molecular line emission from two nearby circumstellar disks with spectral resolution finer than the expected turbulent linewidth.1063 We ft these high spectral resoution observations of he CO(3-2) line enudsson using tWO woLtested models of circtuustelar disk structure. and derive a turbueut Lnewidth of ~ he disk around IID 163296 aud = ," We fit these high spectral resolution observations of the CO(3-2) line emission using two well-tested models of circumstellar disk structure, and derive a turbulent linewidth of $\sim$ $^{-1}$ for the disk around HD 163296 and $\lesssim$ "1064area in that energy range (see Figure 1)).,area in that energy range (see Figure \ref{spectra}) ).1065" At energies below 300 eV. we find that the PN and MOS counts numbers are smaller than expected from what we see in ACIS-S. This might be explained by statistical fluctuations. errors in. the effective area determination or energy redistribution effects in the CCD detectors (EPIC “low-energy shoulder"")."," At energies below 300 eV, we find that the PN and MOS counts numbers are smaller than expected from what we see in ACIS-S. This might be explained by statistical fluctuations, errors in the effective area determination or energy redistribution effects in the CCD detectors (EPIC ""low-energy shoulder"")."1066 Given these uncertainties for very low energies. we use only the counts (0.45-0.65 keV) of PN and MOS for our flux calculations and then extrapolate the flux to à common energy range of 11 keV for comparison.," Given these uncertainties for very low energies, we use only the counts (0.45-0.65 keV) of PN and MOS for our flux calculations and then extrapolate the flux to a common energy range of 1 keV for comparison."1067 For the other instruments. we use 0.65 keV as the upper bound of the energy range and their low-energy sensitivity limits as the lower bound (0.15 keV for ACIS-S/HRC. 0.1 keV for PSPC) and then extrapolate to the common energy range.," For the other instruments, we use 0.65 keV as the upper bound of the energy range and their low-energy sensitivity limits as the lower bound (0.15 keV for ACIS-S/HRC, 0.1 keV for PSPC) and then extrapolate to the common energy range."1068 The fluxes normalized to the 11 keV energy band and the corresponding X-ray luminosities are consistent within lo errors except for the HRC-I flux. which seems to be larger.," The fluxes normalized to the 1 keV energy band and the corresponding X-ray luminosities are consistent within $1\sigma$ errors except for the HRC-I flux, which seems to be larger."1069 The count rate measured by the HRC instrument is higher by a factor of ca., The count rate measured by the HRC instrument is higher by a factor of ca.1070 2.5 compared to the ACIS-S count rate., 2.5 compared to the ACIS-S count rate.1071 The nominal effective areas of the two instruments are very similar at low energies. with the HRC having somewhat larger effective area below 200 eV (AA=10em? or at 200 eV. at 150 eV).," The nominal effective areas of the two instruments are very similar at low energies, with the HRC having somewhat larger effective area below 200 eV $\Delta A \approx 10\ \mbox{cm$ $}$ or at 200 eV, at 150 eV)."1072 The additional counts might arise from photons at these energies. but considering the small difference in effective areas. it does not seem likely that this is the case for all excess HRC photons.," The additional counts might arise from photons at these energies, but considering the small difference in effective areas, it does not seem likely that this is the case for all excess HRC photons."1073 This mismatch is further validated by comparing ACIS-S and HRC count rates with WebPIMMS: assuming a thermal plasma with solar abundances and 7=1 MK. 8 counts in the 0.1500.65 keV energy band in ACIS-S translate into 9 expected counts in the same energy band in HRC-I. which is obviously inconsistent with the 21 recorded HRC photons only 15 minutes after the ACIS-S observation.," This mismatch is further validated by comparing ACIS-S and HRC count rates with WebPIMMS: assuming a thermal plasma with solar abundances and $T=1$ MK, 8 counts in the 0.65 keV energy band in ACIS-S translate into 9 expected counts in the same energy band in HRC-I, which is obviously inconsistent with the 21 recorded HRC photons only 15 minutes after the ACIS-S observation."1074 Thephoton count estimate changes by <20% if one assumes a plasma temperature of 0.8 or 1.25 MK. so a slightly different plasma2 temperature does not cure the substantial mismatch in the cour=a rates.," Thephoton count estimate changes by $<20\%$ if one assumes a plasma temperature of 0.8 or 1.25 MK, so a slightly different plasma temperature does not cure the substantial mismatch in the count rates."1075 Mismatches between HRC and count rates have been reported before for « Cen (??)..," Mismatches between HRC and count rates have been reported before for $\alpha$ Cen \citep{robradeschmittfavata2005, ayresjudgesaar2008}."1076 This mismatch between almost simultaneous HRC and ACIS-S count rates can be explained reasonably by two possibilities: either the effective area of the HRC at low energies is underestimated in the current calibration or the effective areas ofXMM MOS and PN (while using the thick filter) as well as S are overestimated in that energy range., This mismatch between almost simultaneous HRC and ACIS-S count rates can be explained reasonably by two possibilities: either the effective area of the HRC at low energies is underestimated in the current calibration or the effective areas of MOS and PN (while using the thick filter) as well as ACIS-S are overestimated in that energy range.1077 A detailed cross-calibration effort. preferably with a soft coronal source. could help to resolve any systematic errors in the effective areas of the instruments.," A detailed cross-calibration effort, preferably with a soft coronal source, could help to resolve any systematic errors in the effective areas of the instruments."1078 We found 51 Peg to be a rather constant. weak and soft source over the last 15 years.," We found 51 Peg to be a rather constant, weak and soft X-ray source over the last 15 years."1079 Another available activity indicator isCan., Another available long-term activity indicator is.1080 In the H and K line flux monitoring programs carried out at the Mount Wilson and Lowell Observatories (??).. 5] Peg was found to have a very low chromospheric activity level GR)=-S.01. 0.16).," In the H and K line flux monitoring programs carried out at the Mount Wilson and Lowell Observatories \citep{baliunasdonahuesoon1995, halllockwoodskiff2007}, , 51 Peg was found to have a very low chromospheric activity level $\langle R^{'}_{HK}\rangle=-5.01$, $S_{MW}\approx 0.16$ )."1081 In Figure 3. we plot the stars Mount Wilson S index measured since 1996 together with the average of older data., In Figure \ref{calcium} we plot the star's Mount Wilson S index measured since 1996 together with the average of older data.1082 Clearly. the overall chromospherte activity is low. with some variations in the older set of data which is also seen in the more recent observations.," Clearly, the overall chromospheric activity is low, with some variations in the older set of data which is also seen in the more recent observations."1083 Apart from one data point which is derived from a very small number of observations. 51 Peg's S indices are at the lower end of or even below the Sun's respective data during a solar minimum (data taken from ?)).," Apart from one data point which is derived from a very small number of observations, 51 Peg's S indices are at the lower end of or even below the Sun's respective data during a solar minimum (data taken from \cite{baliunasdonahuesoon1995}) )."1084 Other stellar properties like radius. mass. age and effective temperature are similar to the Sun's respective parameters.," Other stellar properties like radius, mass, age and effective temperature are similar to the Sun's respective parameters."1085 The steady low-activity behavior of 51 Peg's H and K line fluxes is also reflected by its X-ray properties., The steady low-activity behavior of 51 Peg's H and K line fluxes is also reflected by its X-ray properties.1086 Compared to estimates for the solar X-ray luminosity in theROSAT RASS band (0.122.4 keV) during a solar cycle (2).. 51 Peg's luminosity is also at the lower end of the Sun’s values.," Compared to estimates for the solar X-ray luminosity in the RASS band 2.4 keV) during a solar cycle \citep{judgesolomonayres2003}, 51 Peg's luminosity is also at the lower end of the Sun's values."1087 The ratio of the star’s X-ray to bolometric luminosity is also rather low with Ly/Lp.=1x1077., The ratio of the star's X-ray to bolometric luminosity is also rather low with $L_X/L_{bol}=1\times10^{-7}$.1088 The X-ray surface flux of F to M stars was shown to be constrained at the lower end by the surface flux level of a solar coronal hole: Fy¢holey*107 erg s7| em7El for theROSAT and energy band. which translates to =[099 ere sv! em? for XMM's 112 keV band (?)..," The X-ray surface flux of F to M stars was shown to be constrained at the lower end by the surface flux level of a solar coronal hole; $F_{X\,\mbox{(hole)}}\approx10^{4}$ erg $^{-1}$ $^{-2}$ for the and energy band, which translates to $\approx10^{3.8}$ erg $^{-1}$ $^{-2}$ for 's 12 keV band \citep{schmitt1997}."1089 5] Peg's surface flux. calculated from the ACIS-S data. is one of the lowest so far detected with logFy=10 erg s! em: the coronal hole surface flux seems to be a good deseription of this star’s X-ray flux. with regards to the flux level as well as the plasma temperature.," 51 Peg's surface flux, calculated from the ACIS-S data, is one of the lowest so far detected with $\log F_{X}=10^{3.7}$ erg $^{-1}$ $^{-2}$; the coronal hole surface flux seems to be a good description of this star's X-ray flux, with regards to the flux level as well as the plasma temperature."1090 There has been some discussion on how to identify a Maunder minimum (MM) star over the last years., There has been some discussion on how to identify a Maunder minimum (MM) star over the last years.1091 The original criterion of chromospheric activity levels (RWR=-5.] was derived by ?.. but relied on a stellar sample contaminated with evolved stars. which have significantly lower chromosphericactivity levels compared to main sequence stars.," The original criterion of chromospheric activity levels $\langle R^{'}_{HK}\rangle=-5.1$ was derived by \cite{henrysoderblomdonahue1996}, , but relied on a stellar sample contaminated with evolved stars, which have significantly lower chromosphericactivity levels compared to main sequence stars."1092 ? reanalyzed these data. excluding evolved stars with luminosities more," \cite{wright2004} reanalyzed these data, excluding evolved stars with luminosities more"1093the fainter side. without changing its shape.,"the fainter side, without changing its shape."1094" The black short-dashed. line included in the figure gives the observational estimate of the rest-frame V-bancl luminosity function. by Shapleyetal.(2001) with a faint-end slope of a=1.85. normalisation P=0.18.10.7h?Alpe"". and characteristic magnitude Al=2221|5logh—22.98. for h=07."," The black short-dashed line included in the figure gives the observational estimate of the rest-frame V-band luminosity function by \citet{Sha01} with a faint-end slope of $\alpha=-1.85$, normalisation $\Phi^*=0.18\times 10^{-2}1095h^3\mpc^{-3}$, and characteristic magnitude $M*=-22.21+5\log h =1096-22.98$, for $h=0.7$."1097 ‘The observational magnitude limit of Ady=20.5r is shown bv the arrows., The observational magnitude limit of $M_V= -20.5$ is shown by the arrows.1098 The most prominent feature seen in all panels is that the luminosity functions of the simulated. galaxies are all very steep. with a faint-end slope comparable toa~2. which is the slope of the dark matter halo mass function.," The most prominent feature seen in all panels is that the luminosity functions of the simulated galaxies are all very steep, with a faint-end slope comparable to $\alpha \sim -2$, which is the slope of the dark matter halo mass function."1099— “Phis suggests that the strong feedback included in the simulations has not been able to reduce the luminosities of low-mass ealaxies much more strongly than those of more massive systems: if such a cilferential elect existed. it should. have manifested. itself as a flattening of the faint-end compared to the halo mass function.," This suggests that the strong feedback included in the simulations has not been able to reduce the luminosities of low-mass galaxies much more strongly than those of more massive systems; if such a differential effect existed, it should have manifested itself as a flattening of the faint-end compared to the halo mass function."1100 t face value. however. the observational data actually support a rather steep end slope at 2=3. quite close to that of the halo mass function.," At face value, however, the observational data actually support a rather steep faint-end slope at $z=3$, quite close to that of the halo mass function."1101 One should note. however. that the observational estimate of the slope à ats=3 is very uncertain because 1ο observations can only reach down to a magnitude of Ad~20.5. even with S-meter class telescopes.," One should note, however, that the observational estimate of the slope $\alpha$ at $z=3$ is very uncertain because the observations can only reach down to a magnitude of $M_V\sim -20.5$, even with 8-meter class telescopes."1102" When compared. with the observational fit of Shapleyal. (2001)... it is clear that the ""OQr-eries. are. deficient in the brightest galaxies at the high. Iuminositv-end. of the uminositv function."," When compared with the observational fit of \citet{Sha01}, it is clear that the `Q'-series are deficient in the brightest galaxies at the high luminosity-end of the luminosity function."1103" This can be understood as a result of ye small box size (Li,=10h.+ Alpe) of these runs. which do not have large enough volume to allow a faithful sampling of rare. bright objects."," This can be understood as a result of the small box size $\Lbox = 10\,\himpc$ ) of these runs, which do not have large enough volume to allow a faithful sampling of rare, bright objects."1104" As the box size becomes larger from Ίο QU-series to the D'-series (Ling=33.75ht Alpe). and ren to the ""C-series (Li=1005.+ Alpe). this situation improves however."," As the box size becomes larger from the `Q'-series to the `D'-series $\Lbox=33.75\,\himpc$ ), and then to the `G'-series $\Lbox=100\,\himpc$ ), this situation improves however."1105 More and more of the luminous objects can then be found. and the agreement with the observation xcomes better at the bright-end of the luminosity function.," More and more of the luminous objects can then be found, and the agreement with the observation becomes better at the bright-end of the luminosity function."1106 On the other extreme of the luminosity distribution. we see that increasing the resolution from (Q3 to Q4. and hen to Q5. allows inclusion of ever. fainter objects. as expected.," On the other extreme of the luminosity distribution, we see that increasing the resolution from Q3 to Q4, and then to Q5, allows inclusion of ever fainter objects, as expected."1107" Therefore the luminosity function becomes wider owards the fainter end,", Therefore the luminosity function becomes wider towards the fainter end.1108 Note. however. that the bright-end hardly changes. suggesting good. convergence in the simulation results for the massive galaxies.," Note, however, that the bright-end hardly changes, suggesting good convergence in the simulation results for the massive galaxies."1109 The run :O. (no wind run) slightly. overpredicts the number of galaxies compared to observations. arguing for," The run `O3' (no wind run) slightly overpredicts the number of galaxies compared to observations, arguing for"1110When 5c€min- ρμ1) is determined bv electrons with 5=nine,"When $\gamma_{\rm c}<\gamma_{\rm min}$ , $U_{\rm ph}(\nu)$ is determined by electrons with $\gamma=\gamma_{\rm min}$."1111" However. in contrast with the previous case. electrons with 5=s,yin lose all the energy. ancl. hence. the factor (min/c) Is substituted by unity. which leads to Physically. Che factor (αμος) accounts lor the decrease in the column density. of electrons with 5—,4, Causecl by cooling."," However, in contrast with the previous case, electrons with $\gamma=\gamma_{\rm min}$ lose all the energy and, hence, the factor $\left(\gamma_{\rm min}/\gamma_{\rm c}\right)^{\alpha}$ is substituted by unity, which leads to Physically, the factor $\left(\gamma_{\rm min}/\gamma_{\rm c}\right)^{\alpha}$ accounts for the decrease in the column density of electrons with $\gamma = \gamma_{\rm min}$ caused by cooling."1112" The value of a describes the upper envelope connecting (he dillerent Compton orders and is determined by electrons of a given energy (1.6.. , OF 4.) ."," The value of $\alpha$ describes the upper envelope connecting the different Compton orders and is determined by electrons of a given energy (i.e., $\gamma_{\rm min}$ or $\gamma_{\rm c}$ ) ."1113" Hence. the local spectral index can deviate substantially from o. in particular. for large values of 5,44 or ον."," Hence, the local spectral index can deviate substantially from $\alpha$, in particular, for large values of $\gamma_{\rm min}$ or $\gamma_{\rm c}$."1114 However. as discussed in D.AO0. a power-law distribution of electron energies considerably smoothens the spectrum as compared to a thermal/mono-energetic distribution.," However, as discussed in BA00, a power-law distribution of electron energies considerably smoothens the spectrum as compared to a thermal/mono-energetic distribution."1115" A distinct feature of a power-law distribution is that the energy of the electrons determining the value of a changes rapidly from . to y, (or vice versa) as the value of τι goes through unity.", A distinct feature of a power-law distribution is that the energy of the electrons determining the value of $\alpha$ changes rapidly from $\gamma_{\rm c}$ to $\gamma_{\rm min}$ (or vice versa) as the value of $\tau_{\rm o}$ goes through unity.1116" Although the value of a changes smoothly in this transition. the local spectral index can change rapidly. in particular for cases will +.X44, al this instance."," Although the value of $\alpha$ changes smoothly in this transition, the local spectral index can change rapidly, in particular for cases with $\gamma_{\rm c} \gg\gamma_{\rm min}$ at this instance."1117" This change in spectral character from a bumpw to a smooth spectvim as , is replaced by5,44, as the main contributor to the inverse Compton emission is evident in the spectra presented in DAOO."," This change in spectral character from a ""bumpy"" to a smooth spectrum as $\gamma_{\rm c}$ is replaced by$\gamma_{\rm min}$ as the main contributor to the inverse Compton emission is evident in the spectra presented in BA00."1118" These expressions for a and 5, for a given value of 7, depend only on (he assumption ol cooling in the IxXlein-Nishina limit.", These expressions for $\alpha$ and $\gamma_{\rm c}$ for a given value of $\tau_{\rm o}$ depend only on the assumption of cooling in the Klein-Nishina limit.1119" In order (o relate the values for a and 5, to the source properties. the origin of the seed photons needs to be considered."," In order to relate the values for $\alpha$ and $\gamma_{\rm c}$ to the source properties, the origin of the seed photons needs to be considered."1120 Two different scenarios are usually envisaged: external photons. whose properties are unrelated to those of the relativistic electrons. and svnchrotron photons produced by the relativistic electrons themselves models).," Two different scenarios are usually envisaged; external photons, whose properties are unrelated to those of the relativistic electrons, and synchrotron photons produced by the relativistic electrons themselves (SSC-models)."1121 When the seed photons are due (ο svuchrotron radiation from the same electrons producing the inverse Compton flix. a particular simple description is possible.," When the seed photons are due to synchrotron radiation from the same electrons producing the inverse Compton flux, a particular simple description is possible."1122 This is due to the fact that svuehrotron radiation can be regarded as inverse Compton scattering of (he virtual photons associated with the magneticfield., This is due to the fact that synchrotron radiation can be regarded as inverse Compton scattering of the virtual photons associated with the magneticfield.1123" Hence. the second equation needed to obtain separatevalues for a and >, is straightforward to derive."," Hence, the second equation needed to obtain separatevalues for $\alpha$ and $\gamma_{\rm c}$ is straightforward to derive."1124 a> (p—1)/2: The expression relating the svnchrotron and inverse Compton components, $\alpha>(p-1)/2$ : The expression relating the synchrotron and inverse Compton components1125Therefore. it is difficult to make a statement on the probable cause for the changing orbital period of NTE J1710-251.,"Therefore, it is difficult to make a statement on the probable cause for the changing orbital period of XTE J1710-281."1126 We cmphasise that if magnetic evcling of the binary components is indeed a reason behind the observed epochs of orbital period. then long term monitoring of N'TIS J1710-351. is required. to determine the timescales of magnetic evcling of the secondary star.," We emphasise that if magnetic cycling of the binary components is indeed a reason behind the observed epochs of orbital period, then long term monitoring of XTE J1710-281, is required to determine the timescales of magnetic cycling of the secondary star."1127 It may also be useful to foretell the cistinet orbital period epochs of NTE JIT10-281. if any.," It may also be useful to foretell the distinct orbital period epochs of XTE J1710-281, if any."1128 Lastly. the forthcoming Inclan-satcllite. ASTROSAL with a very large area. X-ray proportional counter (Paul2009) could be a boon in determining the orbital parameters of the system.," Lastly, the forthcoming Indian-satellite, $ASTROSAT$ with a very large area X-ray proportional counter \citep{Paul09} could be a boon in determining the orbital parameters of the system."1129 This research has made use of cata obtained: from the Ligh Enerev Astrophysics Science Archive Research Center (IIEASARC). provided by NASA's Goddard Space Flight Center.," This research has made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center."1130"results in any sensible way, given the flatness of the spectrum in this short wavelength range.","results in any sensible way, given the flatness of the spectrum in this short wavelength range."1131 The LF of galaxies at any redshift z is obtained by counting the galaxies with a given absolute magnitude in each magnitude bin and dividing the final result by the total volume of the simulation and bin size (0.5 mag)., The LF of galaxies at any redshift $z$ is obtained by counting the galaxies with a given absolute magnitude in each magnitude bin and dividing the final result by the total volume of the simulation and bin size (0.5 mag).1132" We perform this procedure for the following six redshifts z=(5,6,7,8,9,10)."," We perform this procedure for the following six redshifts $z=(5, 6, 7, 8, 9, 10)$."1133 The results are shown in Fig., The results are shown in Fig.1134" 1 as solid histograms, where the error bars represent the Poisson error on the number of galaxies in each magnitude bin."," \ref{fig:LF} as solid histograms, where the error bars represent the Poisson error on the number of galaxies in each magnitude bin."1135 These theoretical LFs are then compared to the experimental ones collected from the various analyses of the HUDF., These theoretical LFs are then compared to the experimental ones collected from the various analyses of the HUDF.1136 For z—10 we show the upper limits on the LF obtained from the three available candidates identified by Bouwens et al. (, For $z=10$ we show the upper limits on the LF obtained from the three available candidates identified by Bouwens et al. (11372009).,2009).1138 Let us now analyze the results shown in Fig., Let us now analyze the results shown in Fig.1139 1 in more detail., \ref{fig:LF} in more detail.1140 It is clear that the luminosity range sampled by the observations and our predictions is only partially overlapping., It is clear that the luminosity range sampled by the observations and our predictions is only partially overlapping.1141" This is because on one hand, even the exquisite sensitivity of WFC3 is not sufficient to properly sample the faint-end of the LF (Μυνρω2 —18); on the other hand, our simulations, which are specifically designed to properly resolve the very first galactic units in a relatively small volume, lack the most massive, rare objects which comprise the bright end of the LF."," This is because on one hand, even the exquisite sensitivity of WFC3 is not sufficient to properly sample the faint-end of the LF $M_{UV}\simgt -18$ ); on the other hand, our simulations, which are specifically designed to properly resolve the very first galactic units in a relatively small volume, lack the most massive, rare objects which comprise the bright end of the LF."1142" In spite of these shortcomings, we consider it a rewarding success that the amplitudes of the theoretical and experimental LFs match almost perfectly, and at the same time, have quite similar slopes at all redshifts for which data are available."," In spite of these shortcomings, we consider it a rewarding success that the amplitudes of the theoretical and experimental LFs match almost perfectly, and at the same time, have quite similar slopes at all redshifts for which data are available."1143" This is even more striking as no attempts have been made to fit or adjust the theoretical curves to the observed LF, i.e. they have been computed directly from the simulation output with no free extra parameters."," This is even more striking as no attempts have been made to fit or adjust the theoretical curves to the observed LF, i.e. they have been computed directly from the simulation output with no free extra parameters."1144 Our results suggest two clear trends., Our results suggest two clear trends.1145" First, the LFs shift towards fainter luminosities with increasing redshift, mimicking a pure luminosity or density evolution."," First, the LFs shift towards fainter luminosities with increasing redshift, mimicking a pure luminosity or density evolution."1146" This is quite consistent with the trend of an increasing My with redshift, found in the data by several groups (see the extended discussion in Ouchi et al."," This is quite consistent with the trend of an increasing $M^*_{UV}$ with redshift, found in the data by several groups (see the extended discussion in Ouchi et al."1147" 2009), preferring a pure luminosity evolution."," 2009), preferring a pure luminosity evolution."1148" Second, the faint-end slope of the simulated LF does not vary (within errors) from z—5 to"," Second, the faint-end slope of the simulated LF does not vary (within errors) from $z=5$ to"1149distribution resenibles à noded network. with filancuts converging and cuding at vertices iu the uetwork. the filaments in the CGaussimu raudom field appear more randomly orieuted and show no apparent correlations with one another.,"distribution resembles a noded network, with filaments converging and ending at vertices in the network, the `filaments' in the Gaussian random field appear more randomly oriented and show no apparent correlations with one another."1150 Using 5 siuoothliug. the Blunent leugth distributions for the Gaussian random Held aud dark matter distribution are shown in the centre xuel of Fig. 6..," Using $5$ smoothing, the filament length distributions for the Gaussian random field and dark matter distribution are shown in the centre panel of Fig. \ref{fig:FilsGRFCompare_all}."1151 The distributions are very sinilar aud clearly exponential above a leugth of ~LOAlpe. with ΔΟΕ)~1077. sugecsting that filaments lave rot collapsed πιο aloug their longest axis since their ormation. but have chaneed their aliguiment in relation o nearby structures.," The distributions are very similar and clearly exponential above a length of $\sim 10$, with $N(L) \sim 10^{\frac{-0.1L}{\rm Mpc}}$, suggesting that filaments have not collapsed much along their longest axis since their formation, but have changed their alignment in relation to nearby structures."1152 We will define the width ofa flament clement. IH. to be he root mean squared perpendicular offset of particles within a sinoothing leugth: that is. where Ry is defined in Equation 5 aud the sum is over all of the NV particles within oue smoothing leneth of the filament element.," We will define the widthof a filament element, $W$, to be the root mean squared perpendicular offset of particles within a smoothing length; that is, where $\mathbf{R_i}$ is defined in Equation \ref{eq:PerpDisplace} and the sum is over all of the $N$ particles within one smoothing length of the filament element."1153 In the bottom pancl of Fie. 6..," In the bottom panel of Fig. \ref{fig:FilsGRFCompare_all},"1154 we plot he width distributions for the two fields. again using P=5Nope.," we plot the width distributions for the two fields, again using $l=5$."1155 The dark matter width distributions are broader aud are peaked at simaller widths. sugeesting hat the flaments have collapsed significantly along wo of their principal axes. despite having a similar eueth distribution.," The dark matter width distributions are broader and are peaked at smaller widths, suggesting that the filaments have collapsed significantly along two of their principal axes, despite having a similar length distribution."1156 As oue would expect with bottomsup structure formation. the width distribution in the Gaussian raudonm field auc dark matter distribution are nore discrepant at siialler smoothing scales (other scales rot show).," As one would expect with bottom-up structure formation, the width distribution in the Gaussian random field and dark matter distribution are more discrepant at smaller smoothing scales (other scales not shown)."1157 Tn Paper 1. we showed that on a given comoving snoothing scale. there was evidence for ai wallto-filament-to-chunp evolution with cosiic finc.," In Paper $1$, we showed that on a given comoving smoothing scale, there was evidence for a wall-to-filament-to-clump evolution with cosmic time."1158 Furthermore. we showed that the axis of structure— aligns with the filamentary backbone in two-dimensional slices frou cosmological simulations as carly απ 2—3 (sce fleure Ll in Paper 1)," Furthermore, we showed that the axis of structure aligns with the filamentary backbone in two-dimensional slices from cosmological simulations as early as $z=3$ (see figure 14 in Paper 1)."1159 Fig., Fig.1160 7 shows the filament distribution at ;= Qand:=3. now with?=157 sso as to test the largest and least-evolved structures in the simulation box.," \ref{fig:EvolveAll} shows the filament distribution at $z=0$ and $z=3$, now with $l=15$ so as to test the largest and least-evolved structures in the simulation box."1161 We used a smaller removal width. N=0.6. for the 2=3 filament distribution because the filaments are of lower contrast than at 2.=0. causing Equation 3. to overestimate their sizes.," We used a smaller removal width, $K=0.6$, for the $z=3$ filament distribution because the filaments are of lower contrast than at $z=0$, causing Equation \ref{eq:RemoveWidth} to overestimate their sizes."1162 The :=3 and :=0 filament distributious are very sinular to the eve. sugeesting that the basic flamenut framework for |=15 is almost entirely in place at 2=3 (here 15 fluctuations have CAMAyNE 0.1).," The $z=3$ and $z=0$ filament distributions are very similar to the eye, suggesting that the basic filament framework for $l=15$ is almost entirely in place at $z=3$ (where $15$ fluctuations have $\left<\left(\Delta M/M\right)^2\right>^{1/2}\sim 0.1$ )."1163 The righthaud paucl of Fig., The righthand panel of Fig.1164 7 shows the flament clement width distributions as a function of redshift., \ref{fig:EvolveAll} shows the filament element width distributions as a function of redshift.1165 As non-linear evolution proceeds. the fBluueut width distributions broaden and peak at stnaller widths.," As non-linear evolution proceeds, the filament width distributions broaden and peak at smaller widths."1166 Before we proceed to ideutifv filameuts in the SDSS data. we run the filament finder ou the mock galaxy saluples iu redshift space (see Paper 1) aud compare he resulting filaments to those identified iu the space +=0 dark matter distribution.," Before we proceed to identify filaments in the SDSS data, we run the filament finder on the mock galaxy samples in redshift space (see Paper 1) and compare the resulting filaments to those identified in the real-space $z=0$ dark matter distribution."1167 The 7!=Sh filament distribution is vorv stronglv affected we redshift distortions the contamination rates are vpicallv ~LO per cent. about double the contamination of the fllamcut samples without redshift distortions.," The $l=5$ filament distribution is very strongly affected by redshift distortions – the contamination rates are typically $\sim 40$ per cent, about double the contamination of the filament samples without redshift distortions."1168 This is due primarily to the Ππσα-οἱσος effect. which causes ealaxv clusters to extend iuto narrow. sharp flunenut-like features alone the Lue of sight.," This is due primarily to the `finger-of-god' effect, which causes galaxy clusters to extend into narrow, sharp filament-like features along the line of sight."1169 Fortunately. the filament finder is insensitive to these distortions on 107 aud lsh scales because the fingers-6-eod are typically Z inwidth.," Fortunately, the filament finder is insensitive to these distortions on $10$ and $15$ scales because the fingers-of-god are typically $\lesssim 1$ in width."1170 Nevertheless. we ean improve our results if we first remove the fingers-ofgod.," Nevertheless, we can improve our results if we first remove the fingers-of-god."1171 Fingers-ofeod from galaxy clusters are extended aloug the observers Lue of sight. while real flameutary structure have no preferred direction.," Fingers-of-god from galaxy clusters are extended along the observer's line of sight, while real filamentary structure have no preferred direction."1172 Iu order to separate the fiugers-of-god from the real filaments. we will use a fricuds-offricuds aleorithii with two linking leneths. where fis the unit vector along the observers line of sight (7)..," In order to separate the fingers-of-god from the real filaments, we will use a friends-of-friends algorithm with two linking lengths, where $\mathbf{\hat{r}}$ is the unit vector along the observer's line of sight \citep{FOF}. ."1173 With these two parameters defined. the aleorithni searches for cylindrical structures with a iamietorto-leugth ratio of bj ," With these two parameters defined, the algorithm searches for cylindrical structures with a diameter-to-length ratio of $b_\perp/b_\parallel$ ."1174"?.hereafterDOG. did an exhaustive study of this two-paranueter/bj. space and found that bj,=00.ll aud bj=0.75 gave unbiased estimates of theeroup multiplicity function. so we adopt these values in our study."," \citet[e.g.][hereafter B06]{ZClusterFind2} did an exhaustive study of this two-parameter space and found that $b_\perp=0.14$ and $b_\parallel=0.75$ gave unbiased estimates of thegroup multiplicity function, so we adopt these values in our study."1175"light curve, Fig. [I],","light curve, Fig. \ref{fig:LATGBMlight curve},"1176 consisted of a single pulse with Του of 2042 s (8-1000 keV)., consisted of a single pulse with $_{90}$ of $\pm$ 2 s (8-1000 keV).1177" The time-averaged, combined GBM/LAT spectrum from TO to T0+20.7 s, where TO is the trigger time, is best fit by a Band function (Band et al."," The time-averaged, combined GBM/LAT spectrum from T0 to T0+20.7 s, where T0 is the trigger time, is best fit by a Band function (Band et al."1178" 1993), with Eyeak = 26844 keV, a = -0.69340.009 and 8 = -2.342+0.011."," 1993), with $E_{peak}$ = $\pm$ 4 keV, $\alpha$ = $\pm0.009$ and $\beta$ = $\pm 0.011$."1179" The fluence (10 keV - 10 GeV) during this interval is (2.474-0.03)x10-7* ergs cm7?, bright enough to result in a repointing."," The fluence (10 keV - 10 GeV) during this interval is $\pm$ $\times10^{-4}$ ergs $^{-2}$, bright enough to result in a repointing."1180" In the first 300 s, LAT observed 150 and 20 photons above 100 MeV and 1 GeV, respectively."," In the first 300 s, LAT observed 150 and 20 photons above 100 MeV and 1 GeV, respectively."1181 Possible extended emission continued out to a few kilo-seconds., Possible extended emission continued out to a few kilo-seconds.1182" The highest energy photon, 19.6 GeV, was observed 26 s after the trigger."," The highest energy photon, 19.6 GeV, was observed 26 s after the trigger."1183" The LAT light curve, Fig. [I],"," The LAT light curve, Fig. \ref{fig:LATGBMlight curve},"1184 is fit by a power-law of a = -2.17+0.14., is fit by a power-law of $\alpha$ = $\pm0.14$ .1185" We fit the LAT spectrum, from 100 - 1000 s, with a power-law of 6=—1.26*025."," We fit the LAT spectrum, from 100 - 1000 s, with a power-law of $\beta = -1.26^{+0.24}_{-0.22}$."1186" XRT began observing GRB 0909264 ~46.6 ks after the trigger, in Photon Counting (PC) mode."," XRT began observing GRB 090926A $\sim$ 46.6 ks after the trigger, in Photon Counting (PC) mode."1187" The light curve, Fig."," The light curve, Fig."1188 (taken from the XRT light curve repository; Evans et al., \ref{fig:lightcurves} (taken from the XRT light curve repository; Evans et al.1189" 2|2007, Evans et al."," 2007, Evans et al."1190" 2009), shows a decaying behavior with some evidence of variability, and is fit with a single power-law, decaying with a = -1.404-0.05 confidence level)."," 2009), shows a decaying behavior with some evidence of variability, and is fit with a single power-law, decaying with $\alpha$ = $\pm$ 0.05 confidence level)."1191 The average spectrum from 46.6(90% ks — 149 ks is best fit by an absorbed power-law model with @=—1.6*03 and an absorption column density of 1.0°9°3x107+ cm? in excess of the Galactic value of 2.7x10?? cm-? (Kalberla et al., The average spectrum from 46.6 ks – 149 ks is best fit by an absorbed power-law model with $\beta = -1.6^{+0.3}_{-0.2}$ and an absorption column density of $1.0^{+0.5}_{-0.3}\times10^{21}$ $^{-2}$ in excess of the Galactic value of $\times10^{20}$ $^{-2}$ (Kalberla et al.1192 2005)., 2005).1193 The counts to observed flux conversion factor deduced from this spectrum is 3.5x107!! ergs cm? count~!., The counts to observed flux conversion factor deduced from this spectrum is $\times10^{-11}$ ergs $^{-2}$ $^{-1}$.1194 The average (unabsorbed) fluxes are 1.3(1.9)x10~! ergs cm observeds, The average observed (unabsorbed) fluxes are $\times10^{-12}$ ergs $^{-2}$ $^{-1}$.1195" UVOT began settled observations of GRB 0909264 at T0+~47 ks, and the optical afterglow was immediately detected (Gronwall et al."," UVOT began settled observations of GRB 090926A at $\sim$ 47 ks, and the optical afterglow was immediately detected (Gronwall et al."1196 , 2009).1197The resulting optical afterglow light curve is shown in 2009).Fig. 2}., The resulting optical afterglow light curve is shown in Fig. \ref{fig:lightcurves}.1198" Removing these flares, the underlying optical light curve is well fit (x2, = 0.92/82 d.o.f)"," Removing these flares, the underlying optical light curve is well fit $\chi^{2}_{red}$ = 0.92/82 d.o.f.)"1199 by a broken powerlaw., by a broken powerlaw.1200" The best fit parameters are: QOpt.1=—1.01*007, toreak=351*102, ks, GOpt2=—1."," The best fit parameters are: $\alpha_{Opt,1} = -1.01^{+0.07}_{-0.03}$, $t_{break} = 351^{+70.2}_{-141.9}$ ks, $\alpha_{Opt,2} = -1.77^{+0.21}_{-0.26}$."

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