ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 In this paper we target 36 extremely wide binaries. chosen to cover the mass and separation range outlined by the ? limits.," In this paper we target 36 extremely wide binaries, chosen to cover the mass and separation range outlined by the \citet{Reid2001} limits."3 Using Keck Laser Guide Star Adaptive Optics (LGS-AO: ?)) and Palomar natural guide star adaptive optics (?).. we searched each target system for companions at separations ranging from 4 to 100 AU. and at contrast ratios sufficient to detect brown dwarf companions.," Using Keck Laser Guide Star Adaptive Optics (LGS-AO; \citealt{Wizinowich2006}) ) and Palomar natural guide star adaptive optics \citep{Troy2000}, we searched each target system for companions at separations ranging from 4 to 100 AU, and at contrast ratios sufficient to detect brown dwarf companions."4 We detail the construction of the new sample of extremely wide M-dwarf binaries in Section 2.., We detail the construction of the new sample of extremely wide M-dwarf binaries in Section \ref{sample}. .5 The observations and data reductions are described in Section 3.., The observations and data reductions are described in Section \ref{obs}.6 Sections 4. and 5 detail and discuss the survey results. and we conclude in Section 6..," Sections \ref{results} and \ref{discussion} detail and discuss the survey results, and we conclude in Section \ref{conclusions}."7 The targets were selected from a preliminary. version. of the SLoWPoKES catalog. a sample of wide (> 500 AU). low-mass (mid-K-mid-M) common proper motion (CPM) binary systems in the SDSS Data Release 7 (DR7:?)..," The targets were selected from a preliminary version of the SLoWPoKES catalog, a sample of wide $>$ 500 AU), low-mass (mid-K–mid-M) common proper motion (CPM) binary systems in the SDSS Data Release 7 \citep[DR7;][]{Abazajian2009}."8 We briefly describe the selection algorithm here: the full selection process is detailed in ?.., We briefly describe the selection algorithm here; the full selection process is detailed in \citet{Dhital2010}.9 The SDSS DR7 photometric catalog has more than 180 million stellar sources. of which ~109 million are low-mass mid-K-late-M dwarfs: many sources also have measured proper motions in the SDSS/USNO-B matched catalog (22)..," The SDSS DR7 photometric catalog has more than 180 million stellar sources, of which $\sim$ 109 million are low-mass mid-K–late-M dwarfs; many sources also have measured proper motions in the SDSS/USNO-B matched catalog \citep{Munn2004, Munn2008}."10 To identify CPM pairs from this large database ? used a relatively high proper motion sample Ge> 40 mas yr!) to avoid high field contamination., To identify CPM pairs from this large database \citet{Dhital2010} used a relatively high proper motion sample $\mu\geq$ 40 mas $^{-1}$ ) to avoid high field contamination.11 Candidate binaries were identified at angular separations of 7-180”. very conservatively requiring photometric distances and component proper motions to individually mateh within. [-σ [0.3-0.4 magnitudes (?) in photometric distance modulus. and ~2.5-5 mas yr! in proper motion (??)]].," Candidate binaries were identified at angular separations of $\arcsec$, very conservatively requiring photometric distances and component proper motions to individually match within $\sigma$ [0.3–0.4 magnitudes \citep{Bochanski2010} in photometric distance modulus, and $\sim$ 2.5–5 mas $^{-1}$ in proper motion \citep{Munn2004, Munn2008}] ]."12 A detailed galactic model was used to quantify theprobability of a random alignment. and only pairs with à <5% chance alignment probability were accepted.," A detailed galactic model was used to quantify theprobability of a random alignment, and only pairs with a $<5\%$ chance alignment probability were accepted."13 The final SLoWPoKES, The final SLoWPoKES14"by the frequency independent target beam FWHM-30' for the GSM simulations (left), 36’ for Model-II (right).","by the frequency independent target beam FWHM=30' for the GSM simulations (left), 36' for Model-II (right)."15" This orange/yellow curve shows the damping effect due to the finite instrument size at small scales (kz0.14Mpc!,0x 1?)"," This orange/yellow curve shows the damping effect due to the finite instrument size at small scales $k \gtrsim 0.1 \, h \, \mathrm{Mpc^{-1}}, \theta \lesssim 1^\circ$ )."16" The recovered power spectrum suffers also significant damping at large scales k<0.05AMpc!, due to poor interferometer response at large angles (0=4?— 5°), as well as to the filtering of radial or longitudinal Fourier modes along the frequency or redshift direction (kj) by the component separation algorithm."," The recovered power spectrum suffers also significant damping at large scales $k \lesssim 0.05 \, h \, \mathrm{Mpc^{-1}}, $ due to poor interferometer response at large angles $ \theta \gtrsim 4^\circ-5^\circ$ ), as well as to the filtering of radial or longitudinal Fourier modes along the frequency or redshift direction $k_\parallel$ ) by the component separation algorithm."17" The red curve shows the ratio of P(k) computed on the recovered or extracted 21 cm LSS signal, tothe original LSS temperature cube P»(k)/P21(k) and corresponds to the transfer function T(k) defined above, for z=0.6 and instrument setup (a)."," The red curve shows the ratio of $P(k)$ computed on the recovered or extracted 21 cm LSS signal, tothe original LSS temperature cube $P_{21}^{rec}(k)/P_{21}(k)$ and corresponds to the transfer function $\TrF(k)$ defined above, for $z=0.6$ and instrument setup (a)."18 The black (thin line) curve shows the ratio of recovered to the smoothed power spectrum ΡΟΟ()/ Pyroothed(q)., The black (thin line) curve shows the ratio of recovered to the smoothed power spectrum $P_{21}^{rec}(k)/P_{21}^{smoothed}(k)$ .19" This latter ratio (black curve) exceeds one for k=0.2, which is due to the noise or system temperature."," This latter ratio (black curve) exceeds one for $k \gtrsim 0.2$, which is due to the noise or system temperature."20" It should be stressed that the simulations presented in this section were focused on the study of the radio foreground effects and have been carried intently with a very low instrumental noise level of 0.25 mK per pixel, corresponding to several years of continuous observations 10 hours per 3’x pixel)."," It should be stressed that the simulations presented in this section were focused on the study of the radio foreground effects and have been carried intently with a very low instrumental noise level of $0.25$ mK per pixel, corresponding to several years of continuous observations $\sim 10$ hours per $3' \times 3'$ pixel)."21" This transfer function is well represented by the analytical form: We have performed simulation of observations and radio foreground subtraction using the procedure described here for different redshifts and instrument configurations, in particular for the (e) configuration with 400 five-meter dishes."," This transfer function is well represented by the analytical form: We have performed simulation of observations and radio foreground subtraction using the procedure described here for different redshifts and instrument configurations, in particular for the (e) configuration with 400 five-meter dishes."22" As the synchrotron and radio source strength increases quickly with decreasing frequency, we have seen that recovering the 21 cm LSS signal becomes difficult for larger redshifts, in particular for z>2."," As the synchrotron and radio source strength increases quickly with decreasing frequency, we have seen that recovering the 21 cm LSS signal becomes difficult for larger redshifts, in particular for $z \gtrsim 2$."23 We have determined the transfer function parameters of eq., We have determined the transfer function parameters of eq.24" 36 k4,.kp,kc for setup (e) for three redshifts, z=0.5,1,1.5, and then extrapolated the value of the parameters for redshift z= 2,2.5."," \ref{eq:tfanalytique} $k_A, k_B, k_C$ for setup (e) for three redshifts, $z=0.5, 1 , 1.5$, and then extrapolated the value of the parameters for redshift $z=2, 2.5$ ."25 The value of the parameters are grouped in table 5 and the smoothed transfer functions are shown on figure 13.., The value of the parameters are grouped in table \ref{tab:paramtfk} and the smoothed transfer functions are shown on figure \ref{tfpkz0525}.26 The impact of the various telescope configurations on the sensitivity for 21 cm power spectrum measurement has been discussed in section 3.., The impact of the various telescope configurations on the sensitivity for 21 cm power spectrum measurement has been discussed in section \ref{pkmessens}. .27 Fig., Fig.28" 6 shows thenoise power spectra, and allows us to rank visuallythe configurations in terms"," \ref{figpnoisea2g} shows thenoise power spectra, and allows us to rank visuallythe configurations in terms"29abundances of Li and C for all CEMP-no stars (see Meynet et al.,abundances of Li and $^{13}$ C for all CEMP-no stars (see Meynet et al.30 2010)., 2010).31" The case of the only CEMP-r star for which we have the abundances of C, N, and O (represented by a filled triangle in Figs."," The case of the only CEMP-r star for which we have the abundances of C, N, and O (represented by a filled triangle in Figs."32 2 and 6) is rather similar to the other discussed above., 2 and 6) is rather similar to the other CEMP-no discussed above.33 In Fig., In Fig.34 3 the predictions of models C and D (both models assume a standard IMF - see table 1) are shown., \ref{fig2} the predictions of models C and D (both models assume a standard IMF – see table 1) are shown.35" The results are similar to the ones of models A and B. This suggests that it is not necessary to consider top-heavy IMF to explain the chemical abundances of CNO at low metallicity, once the contribution of fast rotators is taken into account."," The results are similar to the ones of models A and B. This suggests that it is not necessary to consider top-heavy IMF to explain the chemical abundances of CNO at low metallicity, once the contribution of fast rotators is taken into account."36" However, models A and B, with a top-heavy IMF, do overcome the problem of producing a significative number of zero metallicity stars (still living) which have not been observed up to now."," However, models A and B, with a top-heavy IMF, do overcome the problem of producing a significative number of zero metallicity stars (still living) which have not been observed up to now."37" In addition, models A and B produce slightly more massive stars than models C and D, as is barely visible when comparing Figs."," In addition, models A and B produce slightly more massive stars than models C and D, as is barely visible when comparing Figs."38 2 and 3.., \ref{fig1} and \ref{fig2}.39 This can be seen more clearly in Fig. 4.., This can be seen more clearly in Fig. \ref{fig8}.40" This figure shows the distribution of the simulated stars with respect to the C/O, for the models A, B, C, and D. To better disentangle the differences at low metallicity we split the resulting stars in two ranges: loge(O)«5.5 in the upper panel, 5.5«loge(O)6.5 in the lower panel."," This figure shows the distribution of the simulated stars with respect to the C/O, for the models A, B, C, and D. To better disentangle the differences at low metallicity we split the resulting stars in two ranges: $\log\epsilon(\mathrm{O}) < 5.5$ in the upper panel, $ 5.5 <\log\epsilon(\mathrm{O}) < 6.5$ in the lower panel."41" In the upper panels, both models B (on the left) and D (on the right) show a peak at log(C/O)~0."," In the upper panels, both models B (on the left) and D (on the right) show a peak at $\log\mathrm{(C/O)}\sim 0$."42" On the right of this peak, there is another lower peak."," On the right of this peak, there is another lower peak."43" This secondary peak is produced by stars formed in a volume where the ISM was enriched by the stellar winds of fast rotators, before fast rotators of lower mass have had time to eject their products via the supernovae phase."," This secondary peak is produced by stars formed in a volume where the ISM was enriched by the stellar winds of fast rotators, before fast rotators of lower mass have had time to eject their products via the supernovae phase."44" As the stellar winds of fast rotators are richer in C compared to what is ejected by the SN explosion, these volumes will produce stars with higher C/O. Most of the stars will in fact originate in a gas where the contamination of less massive stars dominated (i.e. which polluted the ISM with their total yields upon the explosion of the SN)."," As the stellar winds of fast rotators are richer in C compared to what is ejected by the SN explosion, these volumes will produce stars with higher C/O. Most of the stars will in fact originate in a gas where the contamination of less massive stars dominated (i.e. which polluted the ISM with their total yields upon the explosion of the SN)."45" The second peak for model B is slightly higher than the one of model D because of the different IMF used (see Table 1)), creating more massive stars."," The second peak for model B is slightly higher than the one of model D because of the different IMF used (see Table \ref{models}) ), creating more massive stars."46" In the lower panels we compare the results of our models in a range of metallicity slightly broader, with the distribution of the observed stars in the same range (we do not show the distribution of the observed stars in the upper panel because we only have the UMP star HE 0107—5240)."," In the lower panels we compare the results of our models in a range of metallicity slightly broader, with the distribution of the observed stars in the same range (we do not show the distribution of the observed stars in the upper panel because we only have the UMP star HE $-$ 5240)."47" For C, in this metallicity range, the agreement between the observed distribution and what is predicted by model B is remarkable."," For C, in this metallicity range, the agreement between the observed distribution and what is predicted by model B is remarkable."48" In fact, our predictions agree not only with the peak value but also with the observed spread."," In fact, our predictions agree not only with the peak value but also with the observed spread."49 We underline that the number of stars observed in this range is very low (15) and larger statistics are needed to better constrain our models., We underline that the number of stars observed in this range is very low (15) and larger statistics are needed to better constrain our models.50" Model A reproduces the peak value too, but this model does not predict the observed spread; in particular, it does not"," Model A reproduces the peak value too, but this model does not predict the observed spread; in particular, it does not"51from the O5V to AOV range.,from the O5V to A0V range.52" The best fit to the data, with a X2,4—1.5, results from the elliptical + O5V + B8V model."," The best fit to the data, with a $\chi^2_{\rm red}$ =1.5, results from the elliptical + O5V + B8V model."53" The bottom panel of reffig:fit.ontinuumshowsthemodeloverplottedontheopticalS E Do febdBOE, axedl.wel dilancntériardi "," The bottom panel of \\ref{fig:fit_continuum} shows the model overplotted on the optical SED of the BCG, and the relative contributions of each component."54"The difference in X2,4 between these two models results from the poor fit to the Balmer absorption lines.", The difference in $\chi^2_{\rm red}$ between these two models results from the poor fit to the Balmer absorption lines.55 The observed SED contains strong emission lines so we are unable to fit any absorption lines to the data., The observed SED contains strong emission lines so we are unable to fit any absorption lines to the data.56" The B3V stellar template has stronger absorption lines than the 3-component model and thus results in a larger 2,3.", The B3V stellar template has stronger absorption lines than the 3-component model and thus results in a larger $\chi^2_{\rm red}$.57" We therefore cannot distinguish which model is more plausible from the x2,4.", We therefore cannot distinguish which model is more plausible from the $\chi^2_{\rm red}$.58" In Table 5 we list the relative flux contributions from the 2 and 3 component fits, and the number of ionizing stars (stellar types 05V and B3V) that lie in the BCG."," In Table \ref{tab:stellarpop} we list the relative flux contributions from the 2 and 3 component fits, and the number of ionizing stars (stellar types 05V and B3V) that lie in the BCG."59" The monochromatic lluminosities of an O5V and B3V star are 1.1x10?4 and 4.8x10?? !, respectively (?).."," The monochromatic luminosities of an O5V and B3V star are $1.1 \times10^{34}$ and $4.8 \times10^{32}$ $^{-1}$, respectively \citep{Kurucz1993}."60 B8V and later stellar types that compose the elliptical galaxy template emit negligible amounts of ionizing photons., B8V and later stellar types that compose the elliptical galaxy template emit negligible amounts of ionizing photons.61 For both models approximately of the light at ccomes from the young stellar population and only comes from the elliptical galaxy., For both models approximately of the light at comes from the young stellar population and only comes from the elliptical galaxy.62" However, at longer wavelengths the light from the old stellar population dominates, whilst at tthe young population emits ~90% of the galaxy's luminosity."," However, at longer wavelengths the light from the old stellar population dominates, whilst at the young population emits $\sim90$ of the galaxy's luminosity."63" The Ha luminosity resulting from stellar photoionization is calculated from eq.11 in ?, using the ? ionizing fluxes and assuming unity covering fraction."," The $\alpha$ luminosity resulting from stellar photoionization is calculated from 1 in \citet{Allen95}, using the \citet{Panagia1973} ionizing fluxes and assuming unity covering fraction."64" The Ha luminosity expected for the 2- and 3-component models is 6x101? and 3.4x10? 1, respectively."," The $\alpha$ luminosity expected for the 2- and 3-component models is $\times10^{40}$ and $\times10^{43}$ $^{-1}$, respectively."65" The total extinction-corrected Ha luminosity of the BCG nebula is 3.4x10?? !, therefore between of the Ha emitted by the galaxy is ionized by the young stellar population."," The total extinction-corrected $\alpha$ luminosity of the BCG nebula is $\times10^{43}$ $^{-1}$, therefore between of the $\alpha$ emitted by the galaxy is ionized by the young stellar population."66 The 3-component fit gives an upper limit to the amount of ionizing photons emitted by the young stellar population because it is forced to contain the largest possible number of O5V stars and a covering fraction of unity is asumed., The 3-component fit gives an upper limit to the amount of ionizing photons emitted by the young stellar population because it is forced to contain the largest possible number of O5V stars and a covering fraction of unity is asumed.67 Therefore the Ho luminosity from this model is also an upper limit., Therefore the $\alpha$ luminosity from this model is also an upper limit.68" So whilst it is possible that all the observed Ha results from stellar photoionization, there is ample room for additional sources to contribute to the ionization of the nebula."," So whilst it is possible that all the observed $\alpha$ results from stellar photoionization, there is ample room for additional sources to contribute to the ionization of the nebula."69 reffig:ifucontinuumaadisplaysanunsh," \\ref{fig:ifu_continuum}a a displays an unsharp-mask image of the BCG and B2, created by subtracting a smoothed image from the VIMOS $R-$ band image."70arp," The galaxy is not smooth, but contains a bright filament that traverses the prominent nuclear region and extends NE to SW across the galaxy."71"The IFU data is used to visualize the same R-band continuum without any emission line contamination from the Ηβ, [Ou] and [Ni] emission lines (Fig. reffig:ifucontinuumbb)."," The IFU data is used to visualize the same R-band continuum without any emission line contamination from the $\beta$, ] and ] emission lines \\ref{fig:ifu_continuum}b b)."72T f romthisimageand ba, The centre of the BCG is estimated from this image and marked by a cross.73ndpass, The red continuum is centrally concentrated in an elliptical shape and there are no bright filaments extending southwest and northeast.74band., Therefore the large filament must be due to the line emission that falls within the R-band passband.75"ThenearbygalaxyB2isalsovisibleatposition(- 20,0)."," The nearby galaxy B2 is also visible at position $-20,0$ )."76" Fig. reffig:ifucontinuumccshowsthe —4030A)), whichintherest — frameoftheclusteris--3190— 3310A,, falling approximately in the U-band."," \\ref{fig:ifu_continuum}c c shows the BCG as seen in the shortest wavelength emission measured in the IFU spectra ), which in the rest-frame of the cluster is $\sim$, falling approximately in the U-band."77 This wavelength range does not include any bright emission lines so the light is emitted from the young stellar population., This wavelength range does not include any bright emission lines so the light is emitted from the young stellar population.78" hi9 proofiewdcém pineeitue continuum image, implying they are the locations of the recent star formation."," Both NE and SW filaments are prominent in the blue continuum image, implying they are the locations of the recent star formation."79 reffig:ifucontinuumddmaps(in|Ou]))theemissionlinenebulathatsurroundsth We , \\ref{fig:ifu_continuum}d d maps (in ) the emission line nebula that surrounds the BCG and shows that both the NE and SW filaments are clearly visible.80highli," The brightest region is the galaxy nucleus, and the general shape of the nebula follows the blue continuum."81"ght the differences between the blue and red continuum emission with Figs.5ee and f which display the rest-frame B—R continuum, and the strength of the bbreak, D4000."," We highlight the differences between the blue and red continuum emission with \ref{fig:ifu_continuum}e e and f which display the rest-frame $B-R$ continuum, and the strength of the break, D4000."82" reffig:ifucontinuumeeshowsthattheB C Ggenerallyhasbluecolours, butthenuc rat"," \\ref{fig:ifu_continuum}e e shows that the BCG generally has blue colours, but the nucleus and SW filament are clearly bluer than the rest of the galaxy."83ios , We note that the colour variations cannot all result from the applied extinction correction.84"were observed in the nuclear region (see the E(B —V) map in reffig:ebv)), which translates into a large extinction correction."," The highest $\alpha$ $\beta$ ratios were observed in the nuclear region (see the $E$ $B-V$ ) map in \\ref{fig:ebv}) ), which translates into a large extinction correction."85" Therefore the enhanced blue colours from the nucleus may result from an excessive extinction correction, however, the dust is patchy and did not extend along the SW filament."," Therefore the enhanced blue colours from the nucleus may result from an excessive extinction correction, however, the dust is patchy and did not extend along the SW filament."86 'The variation in D4000 across the BCG is shown in reffig:ifucontinuumf f.D4000isgreaterthan1.5intheeasternregionofthegala: b," The variation in D4000 across the BCG is shown in \\ref{fig:ifu_continuum}f f. D4000 is greater than 1.5 in the eastern region of the galaxy, although the region with ${\rm D4000}>1.7$ at (-20,0) is the continuum from the nearby galaxy B2."87"breakwithD4000;1.3, muchlowerthanobservedinelliptical galaxies."," The central and southwest region of the galaxy has a shallow break with ${\rm D4000}<1.3$, much lower than observed in elliptical galaxies."88" D4000isl 1.1) and decreases smoothly down the SW filament of young stars to the western tip of the emission line nebula, kkpc away."," D4000 is low in the nuclear region $\sim1.1$ ) and decreases smoothly down the SW filament of young stars to the western tip of the emission line nebula, kpc away."89" D4000 is low in these regions, independent of the extinction correction, supporting the above finding that the central and SW parts of the galaxy host the young stars."," D4000 is low in these regions, independent of the extinction correction, supporting the above finding that the central and SW parts of the galaxy host the young stars."90" In summary, the old stellar population of the BCG lies"," In summary, the old stellar population of the BCG lies"91Figure 6 compares the dust temperature maps made by the best-fit case of our study with those by SED93.,Figure 6 compares the dust temperature maps made by the best-fit case of our study with those by SFD98.92 The dust temperature distribution of the present study shows spatial variation that is not apparent in the map by SED983., The dust temperature distribution of the present study shows small-scale spatial variation that is not apparent in the map by SFD98.93 The maximum and the standard deviation of (he temperature difference between the (vo maps are 5 Ix and 0.5 Ix. respectively.," The maximum and the standard deviation of the temperature difference between the two maps are 5 K and 0.5 K, respectively."94" Figure 7 shows the A, distribution of this area.", Figure 7 shows the $A_{V}$ distribution of this area.95 The fluctuation of both the maps seems to have similar angular scales., The fluctuation of both the maps seems to have similar angular scales.96" ILowever. the d, values of both the maps differ from each other."," However, the $A_{V}$ values of both the maps differ from each other."97 To analyze the reason for these differences. the differences in temperature and Ἐν are shown in Figure 8.," To analyze the reason for these differences, the differences in temperature and $A_{V}$ are shown in Figure 8."98 The sign of the left panel of Figure 8 is reversed compared to that of the rght panel so as to visually check the dependence because Ay has a negative dependence on temperature., The sign of the left panel of Figure 8 is reversed compared to that of the right panel so as to visually check the dependence because $A_{V}$ has a negative dependence on temperature.99 It can be seen that the two maps resemble each other remarkably. which means that the difference in Ay originates from the dillerence in the derived temperature.," It can be seen that the two maps resemble each other remarkably, which means that the difference in $A_{V}$ originates from the difference in the derived temperature."100 The methods using the best-fit anc steep cases are considered (o be more precise than the SED98 method because of the following reason., The methods using the best-fit and steep cases are considered to be more precise than the SFD98 method because of the following reason.101 As described in Section 3. (he «Ἐν map derived by the best-fit differs from that by SFD98. and the difference can be ascribed to the fact that the present temperature map has higher spatial resolution compared with that ol SFD9s.," As described in Section 3, the $A_{V}$ map derived by the best-fit differs from that by SFD98, and the difference can be ascribed to the fact that the present temperature map has higher spatial resolution compared with that of SFD98."102 Figure 9 shows the result of comparison between (he 24) values of the best-fit case and SED9s., Figure 9 shows the result of comparison between the $A_{V}$ values of the best-fit case and SFD98.103 The difference. (4). (best) — Ay (SED93))/-A (best). scatters by 21% in 1 sigma.," The difference, $A_{V}$ (best) $-$ $A_{V}$ $A_{V}$ (best), scatters by 21 in 1 sigma."104 SFD98 emploved the/RAS 100jam intensity to caleulate the extinction., SFD98 employed the $100\ \mu m$ intensity to calculate the extinction.105 They removed point sources from the7/45 100yon map to smoothen the map with a FEWIIM = 3.27 Gaussian profile., They removed point sources from the $100\ \mu m$ map to smoothen the map with a FWHM = $'$ Gaussian profile.106 The difference in the LOOsam intensity between our map and that of SEDO9S is 9% (1 sigma) in the Cvenus region., The difference in the $100\ \mu m$ intensity between our map and that of SFD98 is 9 (1 sigma) in the Cygnus region.107 This difference can also account for the αν difference between (he present study aid SFDOS (see Equations (9) aud (10) ) in addition to the difference between spatial resolution of dust temperature: (he scatter seen in Figure 9 is allected by this difference., This difference can also account for the $A_{V}$ difference between the present study and SFD98 (see Equations (9) and (10) ) in addition to the difference between spatial resolution of dust temperature; the scatter seen in Figure 9 is affected by this difference.108" The dust temperature difference in the 1, difference is estimated as 19 by Equation (11): Aly(Ty). ANM Golal).and aM(£100q0n)) is the dust temperature difference at the"," The dust temperature difference in the $A_{V}$ difference is estimated as 19 by Equation (11); $\Delta A_{V}(T_{d})$, $\Delta A_{V}(total)$ ,and $\Delta A_{V}(I (100\ \mu m))$ is the dust temperature difference at the"109indicates the trausieuts are not plaving a role iu cooline: however. it does mean that the true “initial state” of the core region (1.0. the density aud temperature profiles after the transicuts die out) is slightlv different from our given initial profiles.,"indicates the transients are not playing a role in cooling; however, it does mean that the true ""initial state"" of the core region (i.e. the density and temperature profiles after the transients die out) is slightly different from our given initial profiles."110 This is inevitable in the seuse that the initial (observed) profiles are not in lvdrostatic equilibrium., This is inevitable in the sense that the initial (observed) profiles are not in hydrostatic equilibrium.111 To test the general robustuess of our results. we have also experimented with slightly differeut sets of NEW parameters for the dark matter and find that the eas properties at the outskirts are shebtly differeut with different NFW parameters. but the cooling Sow evolution in the core region is not affected.," To test the general robustness of our results, we have also experimented with slightly different sets of NFW parameters for the dark matter and find that the gas properties at the outskirts are slightly different with different NFW parameters, but the cooling flow evolution in the core region is not affected."112 Tu many galaxy clusters. there is an offset between the X-ray cinission center and the BCG. although the offset tends to be sinaller in CC clusters (0.8.Sandersonoetal. 20093.," In many galaxy clusters, there is an offset between the X-ray emission center and the BCG, although the offset tends to be smaller in CC clusters \citep[e.g.][]{Sanderson09}."113. To see if the offset would significantly chanec the results. we have performed one simulation with au initial offset of 20 Ipc between the center of the eas and the eravitational potential.," To see if the offset would significantly change the results, we have performed one simulation with an initial offset of 20 kpc between the center of the gas and the gravitational potential."114 We fud that the cluster eas settles down and re-ceuters on the BCC before the cooling catastrophe happens., We find that the cluster gas settles down and re-centers on the BCG before the cooling catastrophe happens.115" This is consistent with the fact that tooo)2fq, nmütiallv. aud the cluster relaxes before cooling starts. aud therefore the results do not differ from the simulations without the offset."," This is consistent with the fact that $t_{\rm cool} > t_{\rm dyn}$ initially, and the cluster relaxes before cooling starts, and therefore the results do not differ from the simulations without the offset."116 To test the effect of other chauges in our initial conditions. we performed one simulation without the initial raucom velocities.," To test the effect of other changes in our initial conditions, we performed one simulation without the initial random velocities."117 We find that changing the initial random velocity docs not have a significant Hupact on the evolution of the cool core because the initial random velocity is damped before the cooling catastroplic happens., We find that changing the initial random velocity does not have a significant impact on the evolution of the cool core because the initial random velocity is damped before the cooling catastrophe happens.118 Since velocity perturbations do not directly perturb eas cutropy. to further confirm that small scale rturbatious do not erow outside the trausition radius in our simulation. we performed a run with initial deusity orturbatious instead of velocity perturbations.," Since velocity perturbations do not directly perturb gas entropy, to further confirm that small scale perturbations do not grow outside the transition radius in our simulation, we performed a run with initial density perturbations instead of velocity perturbations."119 To do lis. we multiplied the deusitv in cach cell in the initial conditions by a Caussian factor with a mean of uty aud a standard deviation of1054.," To do this, we multiplied the density in each cell in the initial conditions by a Gaussian factor with a mean of unity and a standard deviation of."120.. Again. we do not sec he growth of auv local instabilities.," Again, we do not see the growth of any local instabilities."121 This is in agreement with Jouus.Bryan&Putman(2011).. who found that orturbatious iu a hydrostatie atinosphere did not cool uuless the perturbation was sufficieutlv. non-linear that he cooling time in the perturbation dropped below the ine for the chunp to accelerate to the local sound speed (roughly the dynamical tine).," This is in agreement with \citet{Joung11}, who found that perturbations in a hydrostatic atmosphere did not cool unless the perturbation was sufficiently non-linear that the cooling time in the perturbation dropped below the time for the clump to accelerate to the local sound speed (roughly the dynamical time)."122 We also performed a simulation without initial rotation., We also performed a simulation without initial rotation.123 The eas in the very center in this run still eventually becomes rotationally supported because the vaudom initial velocities eveutually are amplified due to the conservation of angular monientuni aud a eas disk forms., The gas in the very center in this run still eventually becomes rotationally supported because the random initial velocities eventually are amplified due to the conservation of angular momentum and a gas disk forms.124 In fact. even in our standard run. a sinaller disk along the x-axis forms inside the major disk along z-axis. Which can be seen in Figure 9..," In fact, even in our standard run, a smaller disk along the x-axis forms inside the major disk along z-axis, which can be seen in Figure \ref{fig_project2}."125 The size of the disk iu the run without initial rotation is smaller at early times. aud when the cooling catastrophe first occurs iu that run. the eas in the very ceuter has vot to become rotationally supported: however. the required inflow velocity to balance cooling has already. exceeded the sound speed. aud so the flow passes through a sonic point (in the run with iuitial rotation. rotational support occurs before a sonic point develops).," The size of the disk in the run without initial rotation is smaller at early times, and when the cooling catastrophe first occurs in that run, the gas in the very center has yet to become rotationally supported; however, the required inflow velocity to balance cooling has already exceeded the sound speed, and so the flow passes through a sonic point (in the run with initial rotation, rotational support occurs before a sonic point develops)."126 As noted ewulier. the gravitational poteutial docs play an mportaut role iu the cooling catastrophe aud ruus without a BCC producedsiguiicautlv. different. results (see section 77. for more cletails).," As noted earlier, the gravitational potential does play an important role in the cooling catastrophe and runs without a BCG producedsignificantly different results (see section \ref{sec:results_catastrophe} for more details)."127 Finally. we carry out one simulation with a nou CC configuration. where we use the same NEW dark matter profile for Perseus but set the initial temperature to be isothermal aud compute the initial gas deusity assuiiug hydrostatic equilibrium.," Finally, we carry out one simulation with a non CC configuration, where we use the same NFW dark matter profile for Perseus but set the initial temperature to be isothermal and compute the initial gas density assuming hydrostatic equilibrium."128 The initial £4; iu the center is about 2 Cr., The initial $t_{\rm cool}$ in the center is about 2 Gyr.129 Our simulation shows that after about 2 Cor. the cooling starts to run away aud a cooling flow develops i a wav which is quite similar to what we see in the simulations with initial CC configurations.," Our simulation shows that after about 2 Gyr, the cooling starts to run away and a cooling flow develops in a way which is quite similar to what we see in the simulations with initial CC configurations."130 The temperature plateau is ποτ] differeut. which we thiuk has to do with the difference iu the initial gas to dark matter ratio.," The temperature plateau is slightly different, which we think has to do with the difference in the initial gas to dark matter ratio."131 We will return to this point iu a later paper., We will return to this point in a later paper.132 Iu this section. we try to place these results iu context. first making a link to steady-state cooling flow solutious. and then comparing to other (primarily simulation) work which looked specifically at only the developing cooling How. and did uot include feedback.," In this section, we try to place these results in context, first making a link to steady-state cooling flow solutions, and then comparing to other (primarily simulation) work which looked specifically at only the developing cooling flow, and did not include feedback."133 The classic cooling flow model (Fabian1991) predicts a “cooling flow” of 1005 ντ for rich clusters. assuming hat in a steady state. without other heating sources. he gas flows inwards at a constaut rate to replace the ceutral gas that has cooled down aud formed stars.," The classic cooling flow model \citep{Fabian94} predicts a “cooling flow” of $100s$ $_{\odot}/$ yr for rich clusters, assuming that in a steady state, without other heating sources, the gas flows inwards at a constant rate to replace the central gas that has cooled down and formed stars."134 The nass drop-out occurs over the ceutral cooling-flow region. and was οποια] assumed to cool aud coudeuse out in sanall chumps via a local cooling instability.," The mass drop-out occurs over the central cooling-flow region, and was originally assumed to cool and condense out in small clumps via a local cooling instability."135 This picture as been known to be in disagreement with observations which usually iudicate a star formation rate at least au order of magnitude lower than predicted by the steady state cooling flow model Cliuuuraetal.2001:O'Deaetal2008:Re]RattertyMcNamara&Nulsen 2008).," This picture has been known to be in disagreement with observations which usually indicate a star formation rate at least an order of magnitude lower than predicted by the steady state cooling flow model \citep{Tam01, ODea08, Rafferty08}."136.. Our simulations show that a steady state is uot reached before the ACN feedback is potentially strong cuough to balance cooling. and therefore we argue that this solution is not relevant.," Our simulations show that a steady state is not reached before the AGN feedback is potentially strong enough to balance cooling, and therefore we argue that this solution is not relevant."137 Towever. it is interesting fo see if we recover the steady-state result if we run the simulation for long enough.," However, it is interesting to see if we recover the steady-state result if we run the simulation for long enough."138 Iu Figure 13 we plot the eas inflow for a simulation with Ny.=Ol that runs much urther than our major runs., In Figure \ref{fig_classic} we plot the gas inflow for a simulation with $N_{\rm root} = 64$ that runs much further than our major runs.139 We find that after less than a hundred Myr. without any heating mechanism. the system approaches a steady state with roughly coustaut nass flow of AL~300 i /vriu the cluster core (e«100 spe). consistent with the classic cooling flow prediction.," We find that after less than a hundred Myr, without any heating mechanism, the system approaches a steady state with roughly constant mass flow of $\dot{M} \sim 300$ $_{\odot}/$ yr in the cluster core $r < 100$ kpc), consistent with the classic cooling flow prediction."140 Most previous simulation work on cool core clusters has 'ocused ou the heating process. especially ACN feedback. mt they do usually include a pure cooling flow simulation in which heating is turned off (e.g.Crotonetal.," Most previous simulation work on cool core clusters has focused on the heating process, especially AGN feedback, but they do usually include a pure cooling flow simulation in which heating is turned off \citep[e.g.][]{Croton}."1412006).. Qur results are consistent with these results inasiuucli as there is overlap., Our results are consistent with these results inasmuch as there is overlap.142 For example. Brigheuti&Mathews(2006) examined two dimensional models which also ound that a cooliug-oulv model results i a relatively flat eniperature profile (falling only by a factor of 2-3 over a range of 100 in radius).," For example, \citet{BM06} examined two dimensional models which also found that a cooling-only model results in a relatively flat temperature profile (falling only by a factor of 2-3 over a range of 100 in radius)."143 However. these simulations did rot have the resolution (—1 kpc) to follow the cooling catastrophe in detail. aud instead used a parameterized nass drop-out terii iu the mass-couservation equation.," However, these simulations did not have the resolution $\sim 1$ kpc) to follow the cooling catastrophe in detail, and instead used a parameterized mass drop-out term in the mass-conservation equation."144 Sinilur results were fouud for a ouc-dimensional cooling How in Mathews&Brighenti (2003)..., Similar results were found for a one-dimensional cooling flow in \citet{MB03}. .145 Ow results are also consistent with previous heoretical work. for cxample. Bertschinger(1989) ," Our results are also consistent with previous theoretical work, for example, \citet{Bertschinger89} "146effects of jets from a central compact remnant iu the contest of a failed supernova explosion of a 2091. progenitor star.,effects of jets from a central compact remnant in the context of a failed supernova explosion of a $25 \msun$ progenitor star.147 They studied the interaction by varving the jet paramcters., They studied the interaction by varying the jet parameters.148" Ποπονοα, ucither of the above hivdrodyiuianuical studies computed uuclosvutliesis."," However, neither of the above hydrodynamical studies computed nuclosynthesis."149 Ou the other laud. Nagataki (2000) and Maceda et al (," On the other hand, Nagataki (2000) and Maeda et al. ("1502002) examined nucleosvuthesis in aspherical supernova/Livpernova explosions. using aspherical cucrey inputs at the center of stars with Αννα=20 aud LOAL.. respectively.,"2002) examined nucleosynthesis in aspherical supernova/hypernova explosions, using aspherical energy inputs at the center of stars with $M_{\rm ZAMS} = 20$ and $40\msun$, respectively."151 In their studies. however. the energy injection by the jets was simplified as compared to that of Khokhlov et al. (," In their studies, however, the energy injection by the jets was simplified as compared to that of Khokhlov et al. ("1521999) ancl MacFadyeu et al. (,1999) and MacFadyen et al. (1532001). as their moclels represcuted asplerical prompt explosions which apply ouly to the case where the time scale of the enerev generation is mich shorter than the bydvodvuamical tine scale.,"2001), as their models represented aspherical prompt explosions which apply only to the case where the time scale of the energy generation is much shorter than the hydrodynamical time scale."154 There are two possible sites for nucleosvuthesis associated with jet-driven supernova explosions: the stellar materials heated by the jets and the materials iu the jets theiselves., There are two possible sites for nucleosynthesis associated with jet-driven supernova explosions: the stellar materials heated by the jets and the materials in the jets themselves.155 As stellar materials falls onto a central remnant. they cool via photodisiutceration and neutrino cussions to form: an accretion disk.," As stellar materials falls onto a central remnant, they cool via photodisintegration and neutrino emissions to form an accretion disk."156 A fraction of the accreted materials is likely ejected from the accretion disk. rather than is accreted outo the ceutral remmant (Naravan. Piran. and Iun 2001).," A fraction of the accreted materials is likely ejected from the accretion disk, rather than is accreted onto the central remnant (Narayan, Piran, and Kumar 2001)."157 This accretion disk wind Likely escapes from the central region aloug the rotational axis and shows collimation. 1.0. a jetted wind.," This accretion disk wind likely escapes from the central region along the rotational axis and shows collimation, i.e., a jetted wind."158 Wow anuch fraction of the accreting eas is ejected depends on the accretion rate aud the typical radius where the accretion disk forms (Naravan ct al., How much fraction of the accreting gas is ejected depends on the accretion rate and the typical radius where the accretion disk forms (Narayan et al.159 2001)., 2001).160 They are physically related to the angular momentum distribution and the viscosity in the progenitor star (AlacFadven 2003)., They are physically related to the angular momentum distribution and the viscosity in the progenitor star (MacFadyen 2003).161 Uufortuuatelv. both are rather uncertain.," Unfortunately, both are rather uncertain."162 Iu the prescut study. we assiuue that only a small fraction of the accreting eas is ejected as the jets from the central reeion (10 or 50%: denoted as ji iu section 2). so that nucleosvuthesis in the heated stellar materials is wore prouunent than im the jet (wind) materials themselves.," In the present study, we assume that only a small fraction of the accreting gas is ejected as the jets from the central region $10$ or $50 \%$: denoted as $\mu$ in section 2), so that nucleosynthesis in the heated stellar materials is more prominent than in the jet (wind) materials themselves."163 The purpose of this paper is first to investigate in more detail the outcome (κοςσπαλος and imcleosvutliesis) of supernova explosions driven by bipolar jets for such uassive stars as Azayis2254L.., The purpose of this paper is first to investigate in more detail the outcome (hydrodynamics and nucleosynthesis) of supernova explosions driven by bipolar jets for such massive stars as $M_{\rm ZAMS} \gsim 25\msun$.164 We model the jet xoperties in terms of the accretion rate. which itself is affected by the jet properties through the bydrodvuamical interaction.," We model the jet properties in terms of the accretion rate, which itself is affected by the jet properties through the hydrodynamical interaction."165 This approach makes it possible to calculate he selfregulated interaction. and investigate how the jet properties affect the outcome by modeling the interaction with varving parameters.," This approach makes it possible to calculate the self-regulated interaction, and investigate how the jet properties affect the outcome by modeling the interaction with varying parameters."166 With the detailed micleosvutesis vields. we discuss their possible iuflueuce ou the early Galactic chemical evolution.," With the detailed nucleosynthesis yields, we discuss their possible influence on the early Galactic chemical evolution."167 We note the two main assumptions in the prescut study: 1ο paraneterized constant jet properties and the simall -ass of the jet materials., We note the two main assumptions in the present study: the parameterized constant jet properties and the small mass of the jet materials.168 In reality. the jets could be [umighly variable.," In reality, the jets could be highly variable."169 The variability will affect the detailed structive in the jet materials (e.g... Alov et al.," The variability will affect the detailed structure in the jet materials (e.g., Aloy et al."170 2000). rough we believe that the constant jet properties express je typical behavior and are adequate for the purpose of us paper.," 2000), though we believe that the constant jet properties express the typical behavior and are adequate for the purpose of this paper."171" The assuuptiou that only a simall fraction of 1ο accreting σας is ejected as the jets (νο, the Να] mass of the jets) puts more important limitation."," The assumption that only a small fraction of the accreting gas is ejected as the jets (i.e., the small mass of the jets) puts more important limitation."172 Changius the uass of the jets will change the evolution of the mass of the central remnant. may chauee the bydrodvuamic interaction between the jets aud the stellar materials.," Changing the mass of the jets will change the evolution of the mass of the central remnant, may change the hydrodynamic interaction between the jets and the stellar materials."173 Moreover. in the case of very massive jets. if they are realized. nucleosyuthesis products iu the jets will become prominent than those in the heated stellar materials (Pruct. Woosley. Wofftuan 2003: MacFadyeu 2003).," Moreover, in the case of very massive jets, if they are realized, nucleosynthesis products in the jets will become prominent than those in the heated stellar materials (Pruet, Woosley, Hoffman 2003: MacFadyen 2003)."174 This Is an interesting possibility. while we postpone to study such a very massive jets to future works.," This is an interesting possibility, while we postpone to study such a very massive jets to future works."175 Tn Section 2. we describe our models of bipolar supernova explosions im detail.," In Section 2, we describe our models of bipolar supernova explosions in detail."176 Results are shown in Section 3. which is divided iuto three subsections.," Results are shown in Section 3, which is divided into three subsections."177 Section 3.1 gives the results of hvdrodsynusiuies. discussing how he outcome (e.g... the deeree of asphericity aud the final uass of the central compact remnant) depends on the jet sropertics.," Section 3.1 gives the results of hydrodynamics, discussing how the outcome (e.g., the degree of asphericity and the final mass of the central compact remnant) depends on the jet properties."178 Section 3.2 focuses ou the production of °° Ni., Section 3.2 focuses on the production of $^{56}$ Ni.179 Section 3.3 shows the results of detailed uucleosvuthliesis. where we put ciphasis on the difference between our nodels aud previous vields.," Section 3.3 shows the results of detailed nucleosynthesis, where we put emphasis on the difference between our models and previous yields."180 Ii Section [. we examine their coutributiou to the early Calactic chemical evolution bv conrpariue our vields with abundances in extremely mctal 2001 stars.," In Section 4, we examine their contribution to the early Galactic chemical evolution by comparing our yields with abundances in extremely metal poor stars."181 Section 5 closes this paper with conclusions and discussion., Section 5 closes this paper with conclusions and discussion.182 The iain ingredient of our models is a pair of jets uetratiug into a stellar mautle., The main ingredient of our models is a pair of jets penetrating into a stellar mantle.183" At the leeginuine of cach calculation. the ceutral part (M,xMpggywo) of a progenitor star is displaced bv a point nass with rausnuütted boundary condition at the iuterface."," At the beginning of each calculation, the central part $M_r \leq M_{\rm REM 0}$ ) of a progenitor star is displaced by a point mass with transmitted boundary condition at the interface."184 Without detailed knowledge of how the central object. ecucrates energv. we take μεν as a parameter which expresses he mass of the ceutral roemimanut when it begius to produce he jets (strictly speaking. when the jets αμασο out of the coutral region).," Without detailed knowledge of how the central object generates energy, we take $M_{\rm REM 0}$ as a parameter which expresses the mass of the central remnant when it begins to produce the jets (strictly speaking, when the jets emerge out of the central region)."185" The jets are injected at the inner boundary aloug the c-axis with the opening halt-augle 6,4.", The jets are injected at the inner boundary along the $z$ -axis with the opening half-angle $\theta_{\rm jet}$.186 For the property of the jets. we adopt the formalisua simular to MacFadveu et al ((2001).," For the property of the jets, we adopt the formalism similar to MacFadyen et al (2001)."187 We inst specify two thermodynamical variables and one lvdrodvuamucal variable to deteriiuue the property of the jets at their cimeregcuce., We must specify two thermodynamical variables and one hydrodynamical variable to determine the property of the jets at their emergence.188 For these. we take the deusitv. the momentum. aud the ratio f of the internal cucrev to the total energy in the jets.," For these, we take the density, the momentum, and the ratio $f$ of the internal energy to the total energy in the jets."189 We set f=0.01. so that the internal energv in the jets is negligible.," We set $f = 0.01$, so that the internal energy in the jets is negligible."190 Thus the jets are imomentuu-diveu., Thus the jets are 'momentum-driven'.191 To connect the jet properties consistently to the flow around the central region. we asstune that the energv aud mass fluxes of the jets are proportional to the mass accretion rate.," To connect the jet properties consistently to the flow around the central region, we assume that the energy and mass fluxes of the jets are proportional to the mass accretion rate."192" In this formalisui. the jet propertics are expressed as follows: Here ely d8 the area where the jets enierge. Le. Aye=ΙπΠΩ(Ιcogs(0,4)) with Ry the radius of the inner boundary (typically ~ 10560)."," In this formalism, the jet properties are expressed as follows: Here $A_{\rm jet}$ is the area where the jets emerge, i.e., $A_{\rm jet} = 4 \pi R_0^2 (1-\cos(\theta_{\rm jet}))$ with $R_0$ the radius of the inner boundary (typically $\sim 10^8$ cm)."193 Equation (1) leads to the following explicit expression for the jet propertics:, Equation (1) leads to the following explicit expression for the jet properties:194Sevlert 1 anc QSO nuclei or an alternative mechanism is responsible is an important. issue.,Seyfert 1 and QSO nuclei or an alternative mechanism is responsible is an important issue.195 Such low luminosity active galactic nuclei (dwarl AGN) end to show weak X-ray. variability compared. with the ueher luminosity Sevfert 1 galaxies investigated by Nandra et al (1997)., Such low luminosity active galactic nuclei (dwarf AGN) tend to show weak X-ray variability compared with the higher luminosity Seyfert 1 galaxies investigated by Nandra et al (1997).196 Ptak et al (1998) interpreted this as evidence or ADAFs operating at low accretion rate in dwarl AGN., Ptak et al (1998) interpreted this as evidence for ADAFs operating at low accretion rate in dwarf AGN.197 NGC4395 hosts one of the cwarl Sevfert nuclei in the llo et al (1997a.b) sample. and the least luminous ACN known.," NGC4395 hosts one of the dwarf Seyfert nuclei in the Ho et al (1997a,b) sample, and the least luminous AGN known."198 ‘This chwarl galaxy is a late-tvpe spiral of low surface rightness with no significant bulge., This dwarf galaxy is a late-type spiral of low surface brightness with no significant bulge.199 AX study of stellar kinematics indicates à shallow gravitational potential of the small bulge (8101A... Fili»penko ο 2000) and hence he central black hole (e.g. Magorrian et al 1998).," A study of stellar kinematics indicates a shallow gravitational potential of the small bulge $<8\times 10^4$, Filippenko Ho 2000) and hence the central black hole (e.g., Magorrian et al 1998)."200 Similarly small black hole masses (7107 )) have been estimate rom optical investigations of the active nucleus (Lira et a 1999: Ixraemoer et al 1999)., Similarly small black hole masses $\sim 10^5$ ) have been estimated from optical investigations of the active nucleus (Lira et al 1999; Kraemer et al 1999).201 A point-like optical nucleus located. in the centre of he galaxy shows emission-line properties more resembling a Sevfert 1: nucleus than a LINER: (Filippenko Sargen 1989: Filippenko. Ilo Sargent 1993).," A point-like optical nucleus located in the centre of the galaxy shows emission-line properties more resembling a Seyfert 1 nucleus than a LINER (Filippenko Sargent 1989; Filippenko, Ho Sargent 1993)."202 Ho et al (1997a). classified NGC4395 as à Sevfert LS on account of the presence of broac permitted. line emission (FWZl(IIa)~5000km ‘yy αι high excitation condition., Ho et al (1997a) classified NGC4395 as a Seyfert 1.8 on account of the presence of broad permitted line emission $\alpha)\sim 5000$ ) and high excitation condition.203 A number of coronal lines like IJAGOST. FeN]A6374 (e.g... Ho et al 1997b: Ixraemer e al 1999) are detected: ancl the broad. Balmer emission. was [found to be variable (Lira et al 1999).," A number of coronal lines like $\lambda 6087$, $\lambda2046374$ (e.g., Ho et al 1997b; Kraemer et al 1999) are detected and the broad Balmer emission was found to be variable (Lira et al 1999)."205 The contribution of stellar light to the nuclear spectrum appears to be minima as no significant absorption lines are seen in the LST UV spectrum (Filippenko. llo Sargent. 1993). although weak Cally absorption was found bv Lira et al (1999) who estimate the stellar light. contribution to be about 10 per cent in the blue band.," The contribution of stellar light to the nuclear spectrum appears to be minimal as no significant absorption lines are seen in the HST UV spectrum (Filippenko, Ho Sargent 1993), although weak CaIIK absorption was found by Lira et al (1999) who estimate the stellar light contribution to be about 10 per cent in the blue band."206 The apparent deficit. of ionizing photons relative to the observed. L2. luminosity. (ο... Moran ct al 1999). similar to some Sevlert 2 nuclei. indicates that the UV. continuum source is attenuated. by some obscuration in the line of sight. while the narrow-line region (NLR) seems to be little obscured apart. from Galactic extinction (ED.V)=0.017. Ixraemoer et al 1999).," The apparent deficit of ionizing photons relative to the observed $\beta$ luminosity (e.g., Moran et al 1999), similar to some Seyfert 2 nuclei, indicates that the UV continuum source is attenuated by some obscuration in the line of sight, while the narrow-line region (NLR) seems to be little obscured apart from Galactic extinction $E(B-V)=0.017$, Kraemer et al 1999)."207 Electron scattering is suggestedn as an origin of the optical continuum polarisation (6.7 per cent) reported. by Barth. Filippenko Moran (1999). but the result is also consistent with transmission through aligned dust.," Electron scattering is suggested as an origin of the optical continuum polarisation (6.7 per cent) reported by Barth, Filippenko Moran (1999), but the result is also consistent with transmission through aligned dust."208 Νάς905 has been observed in X-rays with the ROSATLT PSPC and URL., NGC4395 has been observed in X-rays with the ROSAT PSPC and HRI.209 Lira et al (1999) and. Moran et al (1999) independently analyzed the data and found the nuclear pav source to vary by a factor of ~2 in two weeks., Lira et al (1999) and Moran et al (1999) independently analyzed the data and found the nuclear X-ray source to vary by a factor of $\sim 2$ in two weeks.210 The soft X-ray Luminosity is estimated to be 1)ere1... which led them to interpret the nuclear source as N-ray quiet compared with its wide band spectral energy. clistribution.," The soft X-ray luminosity is estimated to be $10^{38}$, which led them to interpret the nuclear source as X-ray quiet compared with its wide band spectral energy distribution."211 We observed NCGC€4395 in the higher energy X-ray band with ASCA and find that the soft. X-ray emission observed with ROSAT is faint due to absorption and the primary X-ray source has a luminosity one order of magnitude above the ROSATL estimate. when corrected. for the absorption.," We observed NGC4395 in the higher energy X-ray band with ASCA and find that the soft X-ray emission observed with ROSAT is faint due to absorption and the primary X-ray source has a luminosity one order of magnitude above the ROSAT estimate, when corrected for the absorption."212 We also find the X-ray source to be extremely variable unlike the other cwarl AGN studied by Ptak et al (1998)., We also find the X-ray source to be extremely variable unlike the other dwarf AGN studied by Ptak et al (1998).213 The properties of the absorber and the central source. assuming an intermediate mass black hole. are discussed on the basis of the X-ray results.," The properties of the absorber and the central source, assuming an intermediate mass black hole, are discussed on the basis of the X-ray results."214 Νάς905 was observed with ASCA on 1998 λίαν 2425 for a half dav., NGC4395 was observed with ASCA on 1998 May 24–25 for a half day.215 The two Solid state Imaging Spectometers (SIS: SO and SL) were operating in LOCD Faint mode throughout the observation., The two Solid state Imaging Spectometers (SIS; S0 and S1) were operating in 1CCD Faint mode throughout the observation.216 The best calibrated CCD chip on each cletectetor (SOCL and SIC3) was used., The best calibrated CCD chip on each detectetor (S0C1 and S1C3) was used.217 The field in the vieinity of NGC4895 is remarkably crowded with bright. X-ray sources (c.g. sce the ROSAT PSPC image by Racdecke 1997).," The field in the vicinity of NGC4395 is remarkably crowded with bright X-ray sources (e.g., see the ROSAT PSPC image by Radecke 1997)."218 The 1CC€D moce observation restricted the SIS field of view to a ll.11 aremin box which covers the nucleus of NO€C4395 and. four other soft. N-ray. sources detected with the ROSAT PSPC., The 1CCD mode observation restricted the SIS field of view to a $11\times 11$ arcmin box which covers the nucleus of NGC4395 and four other soft X-ray sources detected with the ROSAT PSPC.219 The Gas Imaging Spectrometer (CIS: €2 and 3) has a Larger feld of view (~40 arcmin in diameter) in which at least four more X-ray sources are significantly detected., The Gas Imaging Spectrometer (GIS; G2 and G3) has a larger field of view $\sim 40$ arcmin in diameter) in which at least four more X-ray sources are significantly detected.220 “Phese sources all have soft X-ray counterparts detected with the PSPC (Itadecke 1997)., These sources all have soft X-ray counterparts detected with the PSPC (Radecke 1997).221 The data reduction was carried out. using E'PTOOLS version 4.2 and standard calibration provided by the ASCA Guest. Observer Facility (GOR) at Goddard Space blight Center., The data reduction was carried out using FTOOLS version 4.2 and standard calibration provided by the ASCA Guest Observer Facility (GOF) at Goddard Space Flight Center.222 The pointing error of the ASCA satellite induced by the distortion of the base plate of the star tracker has been corrected so that the pointing accuracy in the ASCA images presented in this paper is the order of LO arcesec., The pointing error of the ASCA satellite induced by the distortion of the base plate of the star tracker has been corrected so that the pointing accuracy in the ASCA images presented in this paper is the order of 10 arcsec.223 The good exposure time is about 21 ks for cach detector., The good exposure time is about 21 ks for each detector.224 The mean count rates of NGC4395 obtained from the four detectors are summarised in Table 1., The mean count rates of NGC4395 obtained from the four detectors are summarised in Table 1.225 Response matrices for the SIS were generated by SESRALCG version 1.1., Response matrices for the SIS were generated by SISRMG version 1.1.226 Version 4.0 of the redistribution matrices provided by the CALS team are used. for the GIS., Version 4.0 of the redistribution matrices provided by the GIS team are used for the GIS.227 The effective areas of the source spectra were computed with ASCAARE version 2.73., The effective areas of the source spectra were computed with ASCAARF version 2.73.228 Five sources have been detected within 3 arcmin from the nucleus of. Νέας205 in the ROSAT PSPC image (Moran et al 1999). and we use the same naming convention (A. D. €. D and LE) for the five N-rav sources as used by Aloran et al (1999. see Fig.," Five sources have been detected within 3 arcmin from the nucleus of NGC4395 in the ROSAT PSPC image (Moran et al 1999), and we use the same naming convention (A, B, C, D and E) for the five X-ray sources as used by Moran et al (1999, see Fig."229 1 in their paper)., 1 in their paper).230 Since the, Since the231of (hese (wo radiation components wilh a single emission seems difficult to achieve. for the assumed redshift z-0.444.,"of these two radiation components with a single emission seems difficult to achieve, for the assumed redshift z=0.444."232 To study the impact of EBL on the VUE spectra. we corrected the reported 5-rav spectra for intergalactic absorption using (vo versions of the EBL model by (2008): (1) as in the original paper (F1.0) and (ii) sealed up by a factor of 1.6 (E1.6).," To study the impact of EBL on the VHE spectra, we corrected the reported $\gamma$ -ray spectra for intergalactic absorption using two versions of the EBL model by \citet{franceschini08}: (i) as in the original paper (F1.0) and (ii) scaled up by a factor of 1.6 (F1.6)."233 The latter case was considerecl in order (o satisfv the lower limits claimed by (2008)., The latter case was considered in order to satisfy the lower limits claimed by \citet{levenson08}.234. This simple treatment of the EBL and the related calculations οἱ intergalactic absorption allows us to ignore many details of different EBL mocdels. aud focus on the main objective of this paper. namely the explanation of hard intrinsic 5-rav spectra in blazars.," This simple treatment of the EBL and the related calculations of intergalactic absorption allows us to ignore many details of different EBL models, and focus on the main objective of this paper, namely the explanation of hard intrinsic $\gamma$ -ray spectra in blazars."235 Note that the (wo EBL templates used here cover a broad range of different realizations of the EBL described bv recent theoretical or phenomenological models. at least as long as il concerns (he calculated optical depths.," Note that the two EBL templates used here cover a broad range of different realizations of the EBL described by recent theoretical or phenomenological models, at least as long as it concerns the calculated optical depths."236 The opticaldepth for a high energv photon ££. traveling through the intergalactic medium from a source at redshift z to the observer. taking into account the cosmological distance and the EBL evolution. is where at is the cosmological line element: 1=—cos@ is the angle between the inleracting photons: ης is the number density of the EBL as a function of redshilt and soft-photon energy: and σ.. is the pair production cross section.," The opticaldepth for a high energy photon $E_{\gamma}$ traveling through the intergalactic medium from a source at redshift $z$ to the observer, taking into account the cosmological distance and the EBL evolution, is where $\frac{dl}{dz'}$ is the cosmological line element; $x=1-\cos\theta$ is the angle between the interacting photons; $n_{\gamma}$ is the number density of the EBL as a function of redshift and soft-photon energy; and $\sigma_{\gamma\gamma}$ is the pair production cross section."237 In Fig., In Fig.238 2. the VIE 5-rav optical depts (left panel) and attenuation factors (right panel) for the two blazars are shown. for the two EBL levels: E1.0 (solid lines) and F1.6 (dashed lines).," \ref{fig:tau} the VHE $\gamma$ -ray optical depths (left panel) and attenuation factors (right panel) for the two blazars are shown, for the two EBL levels: F1.0 (solid lines) and F1.6 (dashed lines)."239 The calculated allenuation was used to reconstruct the initial spectra from the observed data by ILE.S.8. on LES 0229-200 (Aharonianetal.2007) and by VERITAS on ὃς 66A 2011).., The calculated attenuation was used to reconstruct the initial spectra from the observed data by H.E.S.S. on 1ES 0229+200 \citep{aharonian07} and by VERITAS on 3C 66A \citep{lat66a}. .240 The resulting spectra are shown in Fig., The resulting spectra are shown in Fig.241 32. for LES 0229-200. and in Fig.," \ref{fig:0229} for 1ES 0229+200, and in Fig."242 4 [or, \ref{fig:3c66a} for243in equation 12. but we have not vet specified the range LV.Mo| over which it applies.,"in equation 12, but we have not yet specified the range $[M_1, M_2]$ over which it applies."244" It is imμα, in equation 12 that the (dark) density p is entirely composed of imiui-halos with masses in the range My<AMExAN.", It is implicit in equation 12 that the (dark) density $\rho$ is entirely composed of mini-halos with masses in the range $M_1<M<M_2$.245 The appropriate value o iva is difficult to estimate., The appropriate value of $M_1$ is difficult to estimate.246" To form a stable cluster there should be a aree nuuber of clouds in cach iini-halo. although the choice of what constitutes a huge umber is somewhat arbitrary: we have chosen AL,=VIAL.~107AL."," To form a stable cluster there should be a large number of clouds in each mini-halo, although the choice of what constitutes a large number is somewhat arbitrary; we have chosen $M_1=0.1\;{\rm M_\odot}\sim10^3 M_o$."247 The wpper limit is easier to estimate: Mo should be chosen such that there is a chance of finding a more massive halo within the field-ofwiew., The upper limit is easier to estimate: $M_2$ should be chosen such that there is a chance of finding a more massive halo within the field-of-view.248" If the total mass of the dark halo of our Galaxy is A4jo¢. which we take to be 2«1072AL, (Zavitsky 1999). then it follows that and solving vields A5~1.1«109MI. for AQ=(klx."," If the total mass of the dark halo of our Galaxy is $M_{tot}$, which we take to be $2\times10^{12}\;{\rm M_\odot}$ (Zaritsky 1999), then it follows that and solving yields $M_2\simeq1.4\times10^9\;{\rm M_\odot}$ for $\Delta\Omega=0.1\;{\rm sr}$."249 Fortunately our final results are not very sensitive to the particularvalues of Mio adopted. as they euter principally through the factor Ίουο(ολ)z23. and secondarily the lanits of⋅⋅ tegration ⋅το1/3 XA5).through ," Fortunately our final results are not very sensitive to the particularvalues of $M_{1,2}$ adopted, as they enter principally through the factor $\log_e(M_2/M_1)\simeq23$, and secondarily through the limits of integration $z_{1,2}\propto M_{1,2}^{1/3}$ )."250With the above muunerical estimates. aud the power-spectium formulations derived in $22.3. we are now in a position to quantifv the temperature anisotroples ex»ected iu the preseut model.," With the above numerical estimates, and the power-spectrum formulations derived in 2,3, we are now in a position to quantify the temperature anisotropies expected in the present model."251 The results are eraphed i ifieure L. showi both the uini-halo coutribition. which leads the peak at /~50. aud the nch larger peak at [oSos105 ds the Poisson rose frou incdividial clouds.," The results are graphed in figure 4, showing both the mini-halo contribution, which leads to the peak at $l\sim50$, and the much larger peak at $l\sim3\times10^8$ is the Poisson noise from individual clouds."252 Recalling. from 822.2. tha the mean sky brightness is approximately 30μ]ν. iu οιr model. we see that the niüui-halos 1itroduce fluctuations which are small iuo comparise1 with t16 Ica intensity. while the reverse is rue for the fhctuations due to the individual clouds.," Recalling, from 2.2, that the mean sky brightness is approximately $30\;{\rm \mu K}$, in our model, we see that the mini-halos introduce fluctuations which are small in comparison with the mean intensity, while the reverse is true for the fluctuations due to the individual clouds."253 This difference siuplv reflects the fact that f1ο nuni-lalos are suffüicientlv large that thev cover the entire sky several times over. whereas he imdividual clouds cover onlv a tiny fraction of the sky aud the root-nieanrsquare intensity is consequently ucl greater fiui the mean.," This difference simply reflects the fact that the mini-halos are sufficiently large that they cover the entire sky several times over, whereas the individual clouds cover only a tiny fraction of the sky and the root-mean-square intensity is consequently much greater than the mean."254 It is worth empinsislus that σαςi of these contributions is computecl under the asstuption that of the dark matter, It is worth emphasising that each of these contributions is computed under the assumption that of the dark matter255fromHST imaging is comprised of ggalaxies.,from imaging is comprised of galaxies.256a description).,a description).257 Full details of how we identified: variable sources will be given elsewhere., Full details of how we identified variable sources will be given elsewhere.258 Sullice to say. we identified a strongly variable object which was modulated on a period of ~20 min with an amplitude of 0.3 mag.," Suffice to say, we identified a strongly variable object which was modulated on a period of $\sim$ 20 min with an amplitude of 0.3 mag."259 The light curve and the corresponding power spectrum are shown in Figure 1., The light curve and the corresponding power spectrum are shown in Figure 1.260 While the dominant. period is at 19.7 min there are also prominent peaks at 715.5 and ~9.2 min., While the dominant period is at 19.7 min there are also prominent peaks at $\sim$ 15.5 and $\sim$ 9.2 min.261 We pre-whitenec the light curve on a period of 19.7 min period. and. found that the peaks at 15.5 ancl 9.2 min were still present.," We pre-whitened the light curve on a period of 19.7 min period, and found that the peaks at 15.5 and 9.2 min were still present."262 We therefore co not. believe these peaks are related. to. the window function., We therefore do not believe these peaks are related to the window function.263 We phased the data on all three periods and find that they are not strictly periodic. rather they are quasi-periodic oscillations (QPOs).," We phased the data on all three periods and find that they are not strictly periodic, rather they are quasi-periodic oscillations (QPOs)."264 lo determine the sky co-ordinates of this variable source. we identified objects in the field which were in the 2MLASS catalogue.," To determine the sky co-ordinates of this variable source, we identified objects in the field which were in the 2MASS catalogue."265 We then usedastrom (Wallace Cray 2002) to obtain the astrometric solution for the field., We then used (Wallace Gray 2002) to obtain the astrometric solution for the field.266" The the variable source is αξιο 53"" 2727. b= lw 59 positionof(2000) and the residuals on the positions are 0."," The position of the variable source is $\alpha$ $^{h}$ $^{m}$ $^{s}$, $\delta$ = $^{o}$ $^{'}$ $^{''}$ (2000) and the residuals on the positions are $^{''}$."2674 This places it 13.3. distant (equating to 1.5 the cluster tidal radius) from the globular cluster M71., This places it $^{'}$ distant (equating to 1.5 $\times$ the cluster tidal radius) from the globular cluster M71.268 We therefore consider it unlikely that the variable source is associated with the cluster., We therefore consider it unlikely that the variable source is associated with the cluster.269 We show the finding chart in Figure 2.., We show the finding chart in Figure \ref{chart}.270 We took DV images prior to the sequence of white light exposures., We took $BVI$ images prior to the sequence of white light exposures.271 Although we clic not obtain images of photometric standard fields we were able to place our filter data on the standard system by matching up objects which were in the catalogue of Gellert Alaintz (2000) who obtained photometry of stars in the field of MTI., Although we did not obtain images of photometric standard fields we were able to place our filter data on the standard system by matching up objects which were in the catalogue of Geffert Maintz (2000) who obtained photometry of stars in the field of M71.272 Our variable source was V~20-4 and (21)~0.2 at the time of our observations (we note that our BV data was not simultaneous)., Our variable source was $V\sim$ 20.4 and $(B-V)\sim$ 0.2 at the time of our observations (we note that our $BV$ data was not simultaneous).273 Compared with other stars in the same field. our variable source is clearly bluc.," Compared with other stars in the same field, our variable source is clearly blue."274 We obtained further photometry of RAT J1953|1859 using the 2.5m Nordie Optical Telescope (NOT) sited on La Palma on 28th Sept 2008 using ALEOSC., We obtained further photometry of RAT J1953+1859 using the 2.5m Nordic Optical Telescope (NOT) sited on La Palma on 28th Sept 2008 using ALFOSC.275 Lt was immeciately clear that RAV J1953|1859 was much brighter than in the discovery data (the right hand panel of Figure 2))., It was immediately clear that RAT J1953+1859 was much brighter than in the discovery data (the right hand panel of Figure \ref{chart}) ).276 We did not obtain any filtered data of the field. but comparison with our INP white light images suggest that was |16.5. or ~4 mag brighter than our INT discovery data.," We did not obtain any filtered data of the field, but comparison with our INT white light images suggest that was $V\sim$ 16.5, or $\sim$ 4 mag brighter than our INT discovery data."277 We proceeded to obtain a sequence of 15 sec exposures in white light which lasted. for 140 min., We proceeded to obtain a sequence of 15 sec exposures in white light which lasted for 140 min.278 The chip was windowed to reduce readout time to 5 see., The chip was windowed to reduce readout time to 5 sec.279 We show the ull light curve in the top left hand panel of Figure 3.., We show the full light curve in the top left hand panel of Figure \ref{not}.280 There is some evidence that the light curve repeats itself after ~90 mins with an amplitude of —0.4 mag. although we note that he observation length was 140 mins.," There is some evidence that the light curve repeats itself after $\sim$ 90 mins with an amplitude of $\sim$ 0.4 mag, although we note that the observation length was 140 mins."281 The second highest »ak in the power spectrum is at ~46 mins (lower left hand xiundel of Figure 3))., The second highest peak in the power spectrum is at $\sim$ 46 mins (lower left hand panel of Figure \ref{not}) ).282" We removed the ~90 min trend. ancl he resulting ""residual light curve is shown in the top right mine panel of Figure 3..", We removed the $\sim$ 90 min trend and the resulting `residual' light curve is shown in the top right hand panel of Figure \ref{not}.283 1t is clear even by seve’ that low amplitude (~0.02 mag) quasi-periodic behaviour is seen in he first half of the light curve., It is clear even by `eye' that low amplitude $\sim$ 0.02 mag) quasi-periodic behaviour is seen in the first half of the light curve.284 The power spectrum of this residual light curve is shown in the lower right hand panel of Figure 3. and shows peaks near 5.7. 10.2 ancl 12.7 mins.," The power spectrum of this residual light curve is shown in the lower right hand panel of Figure \ref{not} and shows peaks near 5.7, 10.2 and 12.7 mins."285 one of these peaks coincides with the peaks seen in the power spectra of the data taken using the INT., None of these peaks coincides with the peaks seen in the power spectra of the data taken using the INT.286" We obtained. spectra of WAL J1953|1859 using the 4.2m William Llersehel Telescope (IEE) and the Intermediate dispersion Spectrograph and Imaging System (18185) on La ""alma at three separate epochs (Table 1).", We obtained spectra of RAT J1953+1859 using the 4.2m William Herschel Telescope (WHT) and the Intermediate dispersion Spectrograph and Imaging System (ISIS) on La Palma at three separate epochs (Table 1).287 All the data were jas subtracted and the spectra were created using optimal extraction., All the data were bias subtracted and the spectra were created using optimal extraction.288 Since we only took one are lamp observation at he start and. end of cach sequence we cross-correlated the skv spectra ancl applied this small correction (less than 1 jxixel) to the spectra., Since we only took one arc lamp observation at the start and end of each sequence we cross-correlated the sky spectra and applied this small correction (less than 1 pixel) to the spectra.289 Our first set of spectra. which had. exposures ranging rom 120 sec to 420 sec and were taken when the source was in quiescence. shows emission lines of Ho. Ley and L7 decreasing in prominence (Figure 4)).," Our first set of spectra, which had exposures ranging from 120 sec to 420 sec and were taken when the source was in quiescence, shows emission lines of $\alpha$, $\beta$ and $\gamma$ decreasing in prominence (Figure \ref{spec-low-high}) )."290 The Balmer lines are also split. (most. clearly in Hla) and broad (a ENIM. of 40A... corresponding to velocities of 1800 km/s) indicating the presence of an accretion disk.," The Balmer lines are also split (most clearly in $\alpha$ ) and broad (a FWHM of $\sim$, corresponding to velocities of 1800 km/s) indicating the presence of an accretion disk."291 We also note the presence ofa Le L emission line at 5876 and 6678 but the absence, We also note the presence of a He I emission line at 5876 and 6678 but the absence292(1995) it would appear that the receding torus modcl cannot apply similarly to radio-quiet and racio-Ioud AGN requiring some ad-hoc explanation. for example a cilfercnt geometry for the obscuring material (1.0. a smaller scale height). due to a dillerence in black hole mass. environment and/or angular momentun.,"(1995) it would appear that the receding torus model cannot apply similarly to radio-quiet and radio-loud AGN requiring some ad-hoc explanation, for example a different geometry for the obscuring material (i.e. a smaller scale height), due to a difference in black hole mass, environment and/or angular momentum."293" We can make a crude association of the putative second x»pulation of radio sources with all sources with narrow emission line luminosities log),(Leow/W)<35.1.", We can make a crude association of the putative second population of radio sources with all sources with narrow emission line luminosities $\log_{10} (L_{\rm [OII]} / {\rm W}) < 35.1$.294 Due to he scatter in the radiooptical correlation. it is not expected hat this would. [lead to a clean division between the two »»pulations at a particular OL] Iuminositv. and if the data were available. a classification based on line ratios. and hence excitation. might well prove cleaner.," Due to the scatter in the radio–optical correlation, it is not expected that this would lead to a clean division between the two populations at a particular [OII] luminosity, and if the data were available, a classification based on line ratios, and hence excitation, might well prove cleaner."295 However. subject to this imitation. the change in quasar fraction with redshift of a combination of the two populations (seen on the left plot of Fig. 1))," However, subject to this limitation, the change in quasar fraction with redshift of a combination of the two populations (seen on the left plot of Fig. \ref{fig:qf1}) )"296 is then naturally explained by the less rapid cosmic evolution of the low-luminosity population (ee. Urry Padovani 1995) than the high-luminosity population (shown on the right plot of Fig. 19)., is then naturally explained by the less rapid cosmic evolution of the low-luminosity population (e.g. Urry Padovani 1995) than the high-luminosity population (shown on the right plot of Fig. \ref{fig:qf1}) ).297 Hence at. high-redshift. the contribution of the Iow-Iuminosity. population is negligible and the quasar fraction of 0.4. is just that of the hieh-uminositv population.," Hence at high-redshift, the contribution of the low-luminosity population is negligible and the quasar fraction of 0.4 is just that of the high-luminosity population."298 Dual population mioclelling of the ow-frequeney racio Luniinosity function is consistent. with just such a scheme (Jackson Wall 1999: Willott et al., Dual population modelling of the low-frequency radio luminosity function is consistent with just such a scheme (Jackson Wall 1999; Willott et al.299 in »ep.)., in prep.).300 Also. Laing et al. (," Also, Laing et al. ("3011994) and Larcdeastle et al. (,1994) and Hardcastle et al. (3021998) ind that low-excitation radio galaxies have linear size and core prominence distributions consistent with an isotropic »opulation.,1998) find that low-excitation radio galaxies have linear size and core prominence distributions consistent with an isotropic population.303 There are two residual concerns with the two population model., There are two residual concerns with the two population model.304 First. many of the. low-luminosity objects have emission lines. so their excitation and the correlation otween Luminosity ancl ionization parameter (Saunders et al.," First, many of the low-luminosity objects have emission lines, so their excitation and the correlation between luminosity and ionization parameter (Saunders et al."305 1989: Tadhunter et al., 1989; Tadhunter et al.306 1998). need. some explanation., 1998) need some explanation.307 Second. it must explain why radio galaxies and (quasars ie clillerent narrow line luminosity distributions at intermediate luminosities (Jackson Browne 1990) but similar distributions at. high. luminosities (Jackson tawlines 1997).," Second, it must explain why radio galaxies and quasars have different narrow line luminosity distributions at intermediate luminosities (Jackson Browne 1990) but similar distributions at high luminosities (Jackson Rawlings 1997)."308 The first concern can be addressed. by simple analogy with MS: the absence ofa broacd-line quasar nucleus does not mean an absence of a photoionising source: or example Dopita et al. (, The first concern can be addressed by simple analogy with M87: the absence of a broad-line quasar nucleus does not mean an absence of a photoionising source; for example Dopita et al. (3091997) favour radiative shocks as a source ofthe excitation for the Ho lines in the nuclear disc of AIST. and shock models in which ionization parameter correlates with line luminosity are easily envisaged. (c.g. Dopita Sutherland 1995).,"1997) favour radiative shocks as a sourceof the excitation for the $\alpha$ lines in the nuclear disc of M87, and shock models in which ionization parameter correlates with line luminosity are easily envisaged (e.g. Dopita Sutherland 1995)."310 Phe second concern is probably also easily. dealt. with., The second concern is probably also easily dealt with.311 Considering first the 3CItUIU sample. the dual-population model is consistent with the drop in quasar fraction at low luminosities because a low luminosity BCR source is necessarily at low recishift where there is clearly a mixture. of both populations: at high recshifts only the high-luminosity population is observed.," Considering first the 3CRR sample, the dual-population model is consistent with the drop in quasar fraction at low luminosities because a low luminosity 3CRR source is necessarily at low redshift where there is clearly a mixture of both populations; at high redshifts only the high-luminosity population is observed."312 Thus any comparative narrow emission line study of quasars and racio galaxies which is based on bright radio samples (Jackson Browne 1990: Jackson Rawlings 1997) should vield different line luminosity cistributions at low recdshift. and similar clistributions at high redshift. which is just as observed.," Thus any comparative narrow emission line study of quasars and radio galaxies which is based on bright radio samples (Jackson Browne 1990; Jackson Rawlings 1997) should yield different line luminosity distributions at low redshift, and similar distributions at high redshift, which is just as observed."313 Llowever. a small dilference in the clistributions of the OU) line. luminosities of intermediate: Luminosity quasars and radio galaxies is also observed in the 7€ sample (Willott et al.," However, a small difference in the distributions of the [OII] line luminosities of intermediate luminosity quasars and radio galaxies is also observed in the 7C sample (Willott et al."314.. 1999)., 1999).315 The lower radio Hux limit of this sample means that these intermediate Luminosity sources are at high. redshift. where there are few low emission ine luminosity objects. so the dillerence is not due to he mixing of the two populations.," The lower radio flux limit of this sample means that these intermediate luminosity sources are at high redshift, where there are few low emission line luminosity objects, so the difference is not due to the mixing of the two populations."316 This is most likely he result. of small but. inevitable biases pointed. out. by tawlings Saunders (1991). ancl quantified in the context of the receding torus model by Simpson (1998): a positive correlation between quasar luminosity and opening angle. coupled with inevitable scatter in quasar luminosity at à fixed radio Luminosity. means that objects viewed within the opening angle are biased towards the more luminous objects within the scatter.," This is most likely the result of small but inevitable biases pointed out by Rawlings Saunders (1991), and quantified in the context of the receding torus model by Simpson (1998): a positive correlation between quasar luminosity and opening angle, coupled with inevitable scatter in quasar luminosity at a fixed radio luminosity, means that objects viewed within the opening angle are biased towards the more luminous objects within the scatter."317 There is vet one more possible cause of the drop in quasar fraction at low luminosities: svstematic dillerences in the time variability of objects with luminosity., There is yet one more possible cause of the drop in quasar fraction at low luminosities: systematic differences in the time variability of objects with luminosity.318 In Willott et al. (, In Willott et al. (3191999) we used the narrow. emission lineradio correlation to suggest that the most luminous objects are. probably accreting at rates close το the Edcington limit. but lower luminosity sources are sub-Eddington acereters.,"1999) we used the narrow emission line–radio correlation to suggest that the most luminous objects are probably accreting at rates close to the Eddington limit, but lower luminosity sources are sub-Eddington accreters."320 Lt therefore seems. plausible that the ower Luminosity sources have more scope for variability. since an object accreting at the Lcldington rate should nave a ready fuel supply which is accreted at a fairly steady rate [limited by radiation pressure.," It therefore seems plausible that the lower luminosity sources have more scope for variability, since an object accreting at the Eddington rate should have a ready fuel supply which is accreted at a fairly steady rate limited by radiation pressure."321 In contrast. sub-Idington aceretion suggests there is not a ready supply of uel available and hence Ductuations in accretion rate may be more likely.," In contrast, sub-Eddington accretion suggests there is not a ready supply of fuel available and hence fluctuations in accretion rate may be more likely."322 Indeed observations of radio-quiet quasars show hat the lower luminosity quasars are more highly opticallyvariable than higher luminosity quasars over timescales of a ew vears (e.g. Vérron Hawkins 1995: Cristiani et al., Indeed observations of radio-quiet quasars show that the lower luminosity quasars are more highly optically-variable than higher luminosity quasars over timescales of a few years (e.g. Vérron Hawkins 1995; Cristiani et al.323 1996: 'ltani Courvoisier LOOT). although it should. be noted hat some authors attribute at least some of this variability ο gravitational microlensing (e.g. Hawkins Taylor 1997).," 1996; Paltani Courvoisier 1997), although it should be noted that some authors attribute at least some of this variability to gravitational microlensing (e.g. Hawkins Taylor 1997)."324 The small quasar fraction at low luminosities could be explained by these objects spending a significant fraction of their active lifetimes in a “quiet” state whereas the more luminous objects are continuously active over their entire lifetime., The small quasar fraction at low luminosities could be explained by these objects spending a significant fraction of their active lifetimes in a `quiet' state whereas the more luminous objects are continuously active over their entire lifetime.325" Due to light travel time effects. dilferent. emission regions of quasars have cilferent variability timescales: BLH — months NLR —107 vro radio lobes ~10"" vr."," Due to light travel time effects, different emission regions of quasars have different variability timescales: BLR $\sim$ months; NLR $\sim 10^{4}$ yr; radio lobes $\sim 10^{6}$ yr."326 lteverberation mapping of quasars has shown that the broad line Iluxes follow the nuclear continuum fux with just such a time lag (see Peterson 1993 for a review)., Reverberation mapping of quasars has shown that the broad line fluxes follow the nuclear continuum flux with just such a time lag (see Peterson 1993 for a review).327 Lf a quasar undergoes high-amplituce variability over a timescale ~100 vr. then only the continuum and BL Uuxes would be observed to undergo this strone variability. and the NLR and extended radio emission would simply rellect the time-averaged output of the central engine.," If a quasar undergoes high-amplitude variability over a timescale $\sim 100$ yr, then only the continuum and BLR fluxes would be observed to undergo this strong variability, and the NLR and extended radio emission would simply reflect the time-averaged output of the central engine."328 Note that a quasar undergoing a in luminosity of this sort. of timescale may then appear as a low-excitation radio galaxy., Note that a quasar undergoing a in luminosity of this sort of timescale may then appear as a low-excitation radio galaxy.329emission. whose ) is 35.1 eV. indicates that. only low-excitation species are present in these regions.,"emission, whose $^{+}$ ) is 35.1 eV, indicates that only low-excitation species are present in these regions."330 Since no emission from these blobs is detected in the HUC 5.8 pim. image. it seems unlikely that PALL bands or dust continu produce the emission detected in the LRAC δ jum image. although we concede that the levels of dust continuum and PALL emission in the IRAC 5.8 jm may be lower than in the IRAC S jam band.," Since no emission from these blobs is detected in the IRAC 5.8 $\mu$ m image, it seems unlikely that PAH bands or dust continuum produce the emission detected in the IRAC 8 $\mu$ m image, although we concede that the levels of dust continuum and PAH emission in the IRAC 5.8 $\mu$ m may be lower than in the IRAC 8 $\mu$ m band."331 Given the previous dilliculties for ionic. PALL or continuum emission and that near-LR HI» 0 S(1) emission is detected. we favor the HS 0 5) AS.0251 [am emission line as the responsible for the emission from these blobs in the LAC! S jum image.," Given the previous difficulties for ionic, PAH or continuum emission and that near-IR $_2$ $-$ 0 S(1) emission is detected, we favor the $_2$ $-$ 0 S(4) $\lambda$ 8.0251 $\mu$ m emission line as the responsible for the emission from these blobs in the IRAC 8 $\mu$ m image."332 Figure 7. displavs the individual Lla anc NU] position-velocity (PV) maps of 66369. obtained. [rom the five slits positions illustrated in Fig. 4.., Figure \ref{PV.img} displays the individual $\alpha$ and [N ] position-velocity (PV) maps of 6369 obtained from the five slits positions illustrated in Fig. \ref{slits.img}.333 Overall. the Hào and ΑΝ 11] ines show similar kinematical features. but these are best seen in N i1] given that its thermal broadening is smaller wan that of the Ho line.," Overall, the $\alpha$ and [N ] lines show similar kinematical features, but these are best seen in [N ] given that its thermal broadening is smaller than that of the $\alpha$ line."334 Phe radial velocity of the source with respect to the Local Standard of Rest was determined o have a value VanSNO.5+LOKkni ss based. on le mean expansion velocity at the position of the central star.," The radial velocity of the source with respect to the Local Standard of Rest was determined to have a value $V_{\rm LSR}=-89.5\pm1.0$ $^{-1}$, based on the mean expansion velocity at the position of the central star."335" This result is in excellent agreement with the value of Vise&9046.5 "" reported by", This result is in excellent agreement with the value of $V_{\rm LSR}\simeq-90\pm6.5$ $^{-1}$ reported by.336 The line shapes of the echellogram at slit position which cuts the nebula along the cast and west extensions. is closely similar to that presented by(2006): 1ο east and. west extensions are detected as red- ancl blue-shifted. loops. respectively. and their shape is typical of the emission in bipolar outflows.," The line shapes of the echellogram at slit position 2, which cuts the nebula along the east and west extensions, is closely similar to that presented by: the east and west extensions are detected as red- and blue-shifted loops, respectively, and their shape is typical of the emission in bipolar outflows."337 The structure of the La line may give the false impression that the inner shell is a closed. ellipsoid. but the sharper view ollercel by the Ν 1] line reveals that the loops of the east ancl west extensions emanate from gaps at the tips of the inner shell.," The structure of the $\alpha$ line may give the false impression that the inner shell is a closed ellipsoid, but the sharper view offered by the [N ] line reveals that the loops of the east and west extensions emanate from gaps at the tips of the inner shell."338 The eastern extension is mapped in more detail by the slits at positions #633. 444. and #655.," The eastern extension is mapped in more detail by the slits at positions 3, 4, and 5."339 In the echellogerams at positions #44 and 3é55. this extension is detected: as," In the echellograms at positions 4 and 5, this extension is detected as"340of bolometric surface intensity.,of bolometric surface intensity.341 The reconstructed images are only of the full solar disk in radius., The reconstructed images are only of the full solar disk in radius.342" The units of pixel values are W-m~? , and they are normalized to unit total area."," The units of pixel values are $\cdot$ $^{-2}$, and they are normalized to unit total area."343" For this study, we used the 37-class reconstruction, which provides a slightly better match to the TSI, although this improvement is not important for our purpose."," For this study, we used the 37-class reconstruction, which provides a slightly better match to the TSI, although this improvement is not important for our purpose."344" discuss the ""ring effect"" in the reconstructed TSI maps, which manifests itself as a kind of diffraction ring surrounding high-contrast, compact features, especially dark spots."," \citet{ulr} discuss the ""ring effect"" in the reconstructed TSI maps, which manifests itself as a kind of diffraction ring surrounding high-contrast, compact features, especially dark spots."345" The spatial scale of these artefacts is small, and the impact on the estimated magnetic jitter is negligible."," The spatial scale of these artefacts is small, and the impact on the estimated magnetic jitter is negligible."346 The processing of the TSI maps was straightforward., The processing of the TSI maps was straightforward.347" Each of the 2881 images was integrated in first moment with respect to a fixed pixel row, e.g., ΣΣ yi). and similarly for Ay."," Each of the 2881 images was integrated in first moment with respect to a fixed pixel row, e.g., x= ), and similarly for $\Delta y$."348" The x axis is aligned with the solar equator, and the y axis with the rotation axis."," The $x$ axis is aligned with the solar equator, and the $y$ axis with the rotation axis."349 The derived offsets were brought to zero mean and converted to LAU., The derived offsets were brought to zero mean and converted to $\mu$ AU.350" Since the TSI images are based on the observed distributions of magnetic strength and the ratio of two monochromatic intensities, they are almost devoid of the limb darkening effects."," Since the TSI images are based on the observed distributions of magnetic strength and the ratio of two monochromatic intensities, they are almost devoid of the limb darkening effects."351" Therefore, we do not apply any limb darkening corrections as the counter-acting effects of the broad-band intensity reduction toward the limb and the increasing contrast of faculae with respect to the local photosphere (Foukaletal.2004) have been balanced in the images by construction."," Therefore, we do not apply any limb darkening corrections as the counter-acting effects of the broad-band intensity reduction toward the limb and the increasing contrast of faculae with respect to the local photosphere \citep{fouk} have been balanced in the images by construction."352 The main results of this study are shown in Fig. 1.., The main results of this study are shown in Fig. \ref{xy.fig}.353" The top panel displaying the integrated TSI is shown only for reference, because the TSI images were constructed to match the space-based TSI measurements as close as possible, thus, the plot does not contain any new information."," The top panel displaying the integrated TSI is shown only for reference, because the TSI images were constructed to match the space-based TSI measurements as close as possible, thus, the plot does not contain any new information."354" The middle and bottom panels show the daily photocenter offsets of the solar disk over some 11 years in the equatorial and axial dimensions, respectively."," The middle and bottom panels show the daily photocenter offsets of the solar disk over some 11 years in the equatorial and axial dimensions, respectively."355" The TSI has been for some time known to vary systematically with the solar cycle (Willsonetal.1981), but the exact contribution of the opposing effects (faculae and spots) to this process is still somewhat controversial."," The TSI has been for some time known to vary systematically with the solar cycle \citep{wil}, but the exact contribution of the opposing effects (faculae and spots) to this process is still somewhat controversial."356" The Sun is brighter when its level of magnetic activity is elevated, while younger and more active stars tend to display the opposite correlation 1998).."," The Sun is brighter when its level of magnetic activity is elevated, while younger and more active stars tend to display the opposite correlation \citep{rad}."357" The peak-to-peak variation of TSI is approximately 2 W-m?, or0.15%.."," The peak-to-peak variation of TSI is approximately 2 $\cdot$ $^{-2}$, or."358 The maximum of activity in 2000-2002 is marked with a brighter average and a much larger dispersion of TSI., The maximum of activity in 2000–2002 is marked with a brighter average and a much larger dispersion of TSI.359 A running average standard deviation over 3 months varies between 0.14 , A running average standard deviation over 3 months varies between $0.14$ 360Compared to a standard: coronagraphic imaging system. one with adaptive optics (AO) gives much higher spatial resolution and a high cdvnamic range allowing the environments of bright objects to be studied closer in than ever before (Alalbet1996),"Compared to a standard coronagraphic imaging system, one with adaptive optics (AO) gives much higher spatial resolution and a high dynamic range allowing the environments of bright objects to be studied closer in than ever before \citep{mal96}."361 Additional instrumentation used in combination with a coronagraph allows other new areas of research to be pursued., Additional instrumentation used in combination with a coronagraph allows other new areas of research to be pursued.362 There are few coronagraphs that have this facility. e.g. CLXO on Subaru. which has a choice of linear polarimeters (Murakawa2003) and. OSCA on the WILD. which has a spectroscopic capability (with the OASIS integral field unit).," There are few coronagraphs that have this facility, e.g. CIAO on Subaru, which has a choice of linear polarimeters \citep{mur03} and OSCA on the WHT, which has a spectroscopic capability (with the OASIS integral field unit)."363 The adaptive optics svstem at. the WIPE. NAOSMI. consists of a single Shack-LHlartmann wavelront sensor normally using SNS sub-apertures and a 76-clement segmented mirror.," The adaptive optics system at the WHT, NAOMI, consists of a single Shack-Hartmann wavefront sensor normally using $8\times8$ sub-apertures and a 76-element segmented mirror."364 ‘This is a reasonably high-order AO andcan oller partial correction for wavelengths down to mMandT00nm., This is a reasonably high-order AO system and can offer partial correction for wavelengths down to 700nm.365 NAOAIL has been at the telescope since. 2000 n carly 2003 was moved to à new environment-controlled laboratory at. the opposite Nasmvth platform., NAOMI has been at the telescope since 2000 and during early 2003 was moved to a new environment-controlled laboratory at the opposite Nasmyth platform.366 This provides a more clust-free and. thermally stable environment ancl so should improve the performance of the system (Myers2003)., This provides a more dust-free and thermally stable environment and so should improve the performance of the system \citep{mye03}.367. OSCA is a fully deplovable instrument which when in use leaves the focus of the NAOAIL beam unchanged., OSCA is a fully deployable instrument which when in use leaves the focus of the NAOMI beam unchanged.368 This enables OSCA to be used in conjunction with a number of instruments that have already been commissioned. at the WIIT (Fig., This enables OSCA to be used in conjunction with a number of instruments that have already been commissioned at the WHT (Fig.369 , 1).370The main imaging camera used with OSCA is the Isaac Newton Group Red Imaging. Device (INGRID): a 1024024 clement {1οςαTe cooled near-Lh detector at the NAOAIL focus., The main imaging camera used with OSCA is the Isaac Newton Group Red Imaging Device (INGRID); a $1024 \times 1024$ element HgCdTe cooled near-IR detector at the NAOMI focus.371 Ehe pixel scale when used with NAOAIL is ~¢).04 aresee/pixel. hence Nvquist sampling is only obtained clown L-band (1 μαι).," The pixel scale when used with NAOMI is $\sim$ 0.04 arcsec/pixel, hence Nyquist sampling is only obtained down to H-band $1.6 \mu$ m)."372" Prior to the detector but within the camera ervo-chamboer are a set οἱ 3 wheels containing broadband filters A). narrowband filters ancl a choice of pupil stops respectively,"," Prior to the detector but within the camera cryo-chamber are a set of 3 wheels containing broadband filters ), narrowband filters and a choice of pupil stops respectively."373 OSCA also has the option of being usec in conjunction with an integral field spectrograph (OASIS) for imaging ancl spectral analysis at visible wavelengths., OSCA also has the option of being used in conjunction with an integral field spectrograph (OASIS) for imaging and spectral analysis at visible wavelengths.374 An important criterion in creating a high contrast imaging system is keeping scattered light to a minimum., An important criterion in creating a high contrast imaging system is keeping scattered light to a minimum.375 Compared to other AO coronagraphs. the svstem at the WIP allows the insertion of an occulting mask in a focal plane before the AO system as well as those in the focal plane within the AQ.," Compared to other AO coronagraphs, the system at the WHT allows the insertion of an occulting mask in a focal plane before the AO system as well as those in the focal plane within the AO."376 Ideally this pre-XO mask would be made of a dichroie material that is transparent to the wavelengths used for wavelront sensing and opaque to the sciencefobservation wavelength., Ideally this `pre-AO' mask would be made of a dichroic material that is transparent to the wavelengths used for wavefront sensing and opaque to the science/observation wavelength.377 The many square segments in the NAOALL adaptive mirror contribute more scattered light than a similar sized continuous face-sheet. mirror and the gaps between the segments also have a higher emissivity, The many square segments in the NAOMI adaptive mirror contribute more scattered light than a similar sized continuous face-sheet mirror and the gaps between the segments also have a higher emissivity378curvature and thus would produce the maximum. error in our numerical integrations. which employ linear. plece-wise approximations.,"curvature and thus would produce the maximum error in our numerical integrations, which employ linear piece-wise approximations."379 The last of these is due to a cliscontinuous function and the former two are cue to curvatures within continuous functions., The last of these is due to a discontinuous function and the former two are due to curvatures within continuous functions.380" We will treat these two Ποσο sources of ""curvature separately. although from the arguments mace earlier. we expect the last of these cllects to be the largest source of numerical error."," We will treat these two different sources of `curvature' separately, although from the arguments made earlier, we expect the last of these effects to be the largest source of numerical error."381 The transit lighteurve has a depth ancl an ingress duration T., The transit lightcurve has a depth $\delta$ and an ingress duration $\tau$.382 For most of the ingress. the curvature is close to zero and. essentially minies a linear slope.," For most of the ingress, the curvature is close to zero and essentially mimics a linear slope."383 However. near the contact points. the sloο rapidlv changes to a flat line of zero gradient.," However, near the contact points, the slope rapidly changes to a flat line of zero gradient."384 Thereore. near the contact points. the ingress/eeress morpholον causes large amounts of curvature.," Therefore, near the contact points, the ingress/egress morphology causes large amounts of curvature."385 Phese points will exhibit the largest numerical errors in using a technique Like Simpson's composite rule., These points will exhibit the largest numerical errors in using a technique like Simpson's composite rule.386 A suitable choice of resolution can be made by increasing ;N until epusσιobs Le. our calculation should. produce a Bux which has à maximum systematic error. which is less than the observational uncertainty.," A suitable choice of resolution can be made by increasing $N$ until $\sigma_{\tilde{F}}|_{\mathrm{max}} \leq \sigma_{\tilde{F},\mathrm{obs}}$, i.e. our calculation should produce a flux which has a maximum systematic error which is less than the observational uncertainty."387 We will set. our resolution to a point where it. provides satisfactory accuracy even at the point of highest numerical error. Le. within the ingress/egress near the contact points.," We will set our resolution to a point where it provides satisfactory accuracy even at the point of highest numerical error, i.e. within the ingress/egress near the contact points."388 Another approach would be to use an aclaptive Composite Simpson's rule. for example like that proposed by Melxeeman (1962).," Another approach would be to use an adaptive composite Simpson's rule, for example like that proposed by McKeeman (1962)."389 However. our. preference. here is to avoid using adaptive routines since they would. require a new adaption for every single data point and fitting trial. which would be time consuming.," However, our preference here is to avoid using adaptive routines since they would require a new adaption for every single data point and fitting trial, which would be time consuming."390 The costs versus benefits of using such à method could warrant further investigation in the future., The costs versus benefits of using such a method could warrant further investigation in the future.391 Instead. we choose to use Che adaption required for the most troublesome points. which we have already identified.," Instead, we choose to use the adaption required for the most troublesome points, which we have already identified."392 “Phe required interval size in each clement of the Simpson's composition should be decreased until we reach: Where Sta.1) is Süimpson's rule evaluated: over. the interval a to 2.," The required interval size in each element of the Simpson's composition should be decreased until we reach: Where $S(\alpha,\beta)$ is Simpson's rule evaluated over the interval $\alpha$ to $\beta$."393" In our case. the integral is over time and a=tf, and b—f,|(Zofor). where 2m is the number of subintervals we split the integral into and 2m=NL where Nis the required factor by which the number of calls to the ALAQ2 code increases by."," In our case, the integral is over time and $a=t_I$ and $b=t_I + (\mathcal{I}_0/m)$, where $2m$ is the number of subintervals we split the integral into and $2m = N-1$ where $N$ is the required factor by which the number of calls to the MA02 code increases by."394 The reason for the subscript of 0 by the Z term will be explained shortly., The reason for the subscript of $0$ by the $\mathcal{I}$ term will be explained shortly.395 Our requirement mav be written as: In order to continue. we need to evaluate £4) in a closed-form. which cannot be achieved due to Ixepler's equation.," Our requirement may be written as: In order to continue, we need to evaluate $F(t)$ in a closed-form, which cannot be achieved due to Kepler's equation."396 Lowever. there exists a special case where Kepler's equation does vield an cxact closed-form: solution ane this occurs for circular orbits since AL=lef.," However, there exists a special case where Kepler's equation does yield an exact closed-form solution and this occurs for circular orbits since $M = E = f$."397 In such a case. WO Lay write: The ingress/egress morphology is dominated: by the expressions pertaining to a uniform source.," In such a case, we may write: The ingress/egress morphology is dominated by the expressions pertaining to a uniform source."398 Limb darkening does allect the ingress/egress curvature but. this is much less than the amplitude of the uniform source transit signal., Limb darkening does affect the ingress/egress curvature but this is much less than the amplitude of the uniform source transit signal.399 1n the small-planet. limit. NLXO2. provided. the following approximation for the ingress/egress IHux: Where we have defined z=1|c and it understood that psorx for the ingress/egress.," In the small-planet limit, MA02 provided the following approximation for the ingress/egress flux: Where we have defined $z=1+x$ and it understood that $-p < x < p$ for the ingress/egress."400 For the purposes of the evaluating the maximum error. we know that. &p and thus we may expand the cosine term into second order using a Tavlor series.," For the purposes of the evaluating the maximum error, we know that $x \simeq p$ and thus we may expand the cosine term into second order using a Taylor series."401 Let us assume we have the simple case of 6=0 which means that ;—7/2., Let us assume we have the simple case of $b=0$ which means that $i = \pi/2$.402 We make further simall-angle approximations to simplify the resultant. expression [or the error. which is justified since 2x4;tP.," We make further small-angle approximations to simplify the resultant expression for the error, which is justified since $2\pi t_I \ll P$."403Cphe other adjustment we need to account for is that so we have approximated b=0 and e=0., The other adjustment we need to account for is that so we have approximated $b=0$ and $e=0$.404 To generalize the result. we consider that the elfeet of b0 and cezO is to stretch or shrink the ingress/egress duration by a [factor T/T).," To generalize the result, we consider that the effect of $b>0$ and $e>0$ is to stretch or shrink the ingress/egress duration by a factor $\tau/\tau_0$."405 Vherefore our expressions here are actually for Zo. which mav be written as Zyστιτ).," Therefore our expressions here are actually for $\mathcal{I}_0$, which may be written as $\mathcal{I}_0 = \mathcal{I} (\tau_0/\tau)$."406 We may now rewrite equation (24) as: Where we have used: Due to the approximations mace. we find that this equation is only stable for m&2.," We may now rewrite equation (24) as: Where we have used: Due to the approximations made, we find that this equation is only stable for $m\geq 2$."407 For any. given data set. we simply need to solve equation. (28) for m. with some sensible estimates of p. b. ew. αμ and P.," For any given data set, we simply need to solve equation (28) for $m$ with some sensible estimates of $p$, $b$, $e$, $\omega$, $a_R$ and $P$."408 As an example. for Ixepler-5b. taking the quoted. parameters from the Kochetal.(2000). paper. we find that even using m—2 provides an error of 0. 1ppm. which is well below the typical measurement uncertainty of 130ppam.," As an example, for Kepler-5b, taking the quoted parameters from the \citet{koc10} paper, we find that even using $m=2$ provides an error of $0.1$ ppm, which is well below the typical measurement uncertainty of $130$ ppm."409 Another part of the lighteurve where we have significant curvature. and. thus expect the maximum numerical integration errors. is the limb-darkened. lightcurve. trough.," Another part of the lightcurve where we have significant curvature, and thus expect the maximum numerical integration errors, is the limb-darkened lightcurve trough."410 llowever. the peak-to-peak size of the changes in [lux induced by the limb. darkening are much lower than the," However, the peak-to-peak size of the changes in flux induced by the limb darkening are much lower than the"411]uininosiies [or mass segregated groups of objects. some or all of which are incividually uudetectect.,"luminosities for mass segregated groups of objects, some or all of which are individually undetected."412" The inetod measures the flux of a ""composite"" source by suumiug HRC photons detected at the optical petions of individualy uudetected objects comprising the ""composite.""", The method measures the flux of a “composite” source by summing HRC photons detected at the optical positions of individually undetected objects comprising the “composite.”413" Fim ""I .lows the loga‘ithin of average Ly. both [or the whole reference and for uneetected objecs lu several mass bius."," Figure \ref{fig:BD} shows the logarithm of average $L_X$, both for the whole reference and for undetected objects in several mass bins."414" The height of tle boxes reflect the uncertainty in the count-rae to [his cotverslou actors for the ""composite"" source (see Appexlix A)).", The height of the boxes reflect the uncertainty in the count-rate to flux conversion factors for the “composite” source (see Appendix \ref{app:nodet}) ).415 The number of suiued objects i1 each njass biu is reported in the upper part of the igure. and [or reference. the median Ly fi1i Figu‘e | is also shown.," The number of summed objects in each mass bin is reported in the upper part of the figure, and for reference, the median $L_X$ from Figure \ref{fig:LXvsMb} is also shown."416 As a “sanity check” we compared the aveage Ly COLiputed with tje metluxl described in Appendix A or the whole reference sample of cetected and undetected ojects with the average Ly computed from the maximum likelihood, As a “sanity check” we compared the average $L_X$ computed with the method described in Appendix \ref{app:nodet} for the whole reference sample of detected and undetected objects with the average $L_X$ computed from the maximum likelihood417In the framework of the singe-degenerate scenario (Whelan.&Iben.1973).. white dwarfs (WDs) accreting from a donor star in a binary system and steadily burning the acereted material on their surface are believed to be a likely path to the Type Ia supernova (Hillebrandt&Niemeyer.2000:Livio. 2000).,"In the framework of the singe-degenerate scenario \citep{whelan}, white dwarfs (WDs) accreting from a donor star in a binary system and steadily burning the accreted material on their surface are believed to be a likely path to the Type Ia supernova \citep{hillebrandt,livio}."418. Nuclear burning is only stable (required for the WD to grow in mass) if the mass accretion rate is high enough. M.~—M. 107/yr.," Nuclear burning is only stable (required for the WD to grow in mass) if the mass accretion rate is high enough, $\dot{M}\sim 10^{-7}-10^{-6} M_\odot$ /yr."419" Given that the nuclear-burning efficiency for hydrogen is ej,=6-1015 erg/e. the bolometric luminosity of such systems are in the 10—1075ergs! range. potentially making them bright X-ray sources."," Given that the nuclear-burning efficiency for hydrogen is $\epsilon_H 420\approx 6 \cdot 10^{18}$ erg/g, the bolometric luminosity of such systems are in the $ 10^{37}-10^{38} \ \mathrm{erg421\ s^{-1}} $ range, potentially making them bright X-ray sources."422 Their emission. however. has a rather low effective temperature. Tayx50—100 eV so Is prone to absorption by cold ISM (Gilfanov&Bogdan. 2009).," Their emission, however, has a rather low effective temperature, $T_{\mathrm{eff}}\lesssim 50-100$ eV so is prone to absorption by cold ISM \citep{nature}."423 The brightest and hardest sources of this type are indeed observed as supersoft sources in the Milky Way and nearby galaxies (Greiner.2000)., The brightest and hardest sources of this type are indeed observed as supersoft sources in the Milky Way and nearby galaxies \citep{greiner}.424. The rest of the population. however. remains unresolved — weakened by absorption and blended with other types of faint X-ray sources — thus makes its contribution to the unresolved X-ray emission from galaxies.," The rest of the population, however, remains unresolved – weakened by absorption and blended with other types of faint X-ray sources – thus makes its contribution to the unresolved X-ray emission from galaxies."425 We have recently proposed that the combined energy output of acereting WDs can be used to measure the rate at which WDs increase their mass in galaxies (Gilfanov&Bogdan. 2009)., We have recently proposed that the combined energy output of accreting WDs can be used to measure the rate at which WDs increase their mass in galaxies \citep{nature}.426. This allowed us to severely constrain the contribution of the single-degenerate scenario to the observed Type la supernova rate in early-type galaxies., This allowed us to severely constrain the contribution of the single-degenerate scenario to the observed Type Ia supernova rate in early-type galaxies.427 The critical quantity in our argument is the X-ray to K-band luminosity ratio of the population of accreting white dwarfs., The critical quantity in our argument is the X-ray to K-band luminosity ratio of the population of accreting white dwarfs.428 This quantity cannot be measured unambiguously for several reasons., This quantity cannot be measured unambiguously for several reasons.429 First. galaxies have large populations of bright compact X-ray sources. — accreting neutron stars and black holes in binary systems (Gilfanov. 2004).," First, galaxies have large populations of bright compact X-ray sources, -- accreting neutron stars and black holes in binary systems (Gilfanov, 2004)."430 Although their spectra are relatively hard. these sources make a significant contribution to X/K ratios. even in the soft band.," Although their spectra are relatively hard, these sources make a significant contribution to X/K ratios, even in the soft band."431 Unless their contribution 1s removed. the obtained. X/K ratios are rendered. useless.," Unless their contribution is removed, the obtained X/K ratios are rendered useless."432 This requires adequate sensitivity and angular resolution. a combination of qualities that currently can only be delivered by observatory.," This requires adequate sensitivity and angular resolution, a combination of qualities that currently can only be delivered by observatory."433 Another source of contamination is the hot ionized gas present in some of galaxies2003)., Another source of contamination is the hot ionized gas present in some of galaxies.434. Although there is a general correlation between the gas luminosity and the mass of the galaxy. the large dispersion precludes an accurate subtraction of the gas contribution based on. for example. optical properties of galaxies.," Although there is a general correlation between the gas luminosity and the mass of the galaxy, the large dispersion precludes an accurate subtraction of the gas contribution based on, for example, optical properties of galaxies."435 The gas contribution may increase the X/K ratio by ~1—2 orders of magnitude. therefore gas-rich galaxies need to be identified and excluded from the sample.," The gas contribution may increase the X/K ratio by $\sim 1-2$ orders of magnitude, therefore gas-rich galaxies need to be identified and excluded from the sample."436 Finally. other types of faint sources do exist and contribute to the unresolved X-ray emission.," Finally, other types of faint sources do exist and contribute to the unresolved X-ray emission."437 Only upper limits on the luminosity of WDs can be obtained. because different components in the unresolved emission cannot be separated.," Only upper limits on the luminosity of WDs can be obtained, because different components in the unresolved emission cannot be separated."438 The aim of this paper is to measure Ly/Ly ratios in the 0.3—0.7 keV band for a sample of nearby gas-poor galaxies., The aim of this paper is to measure $L_X/L_K$ ratios in the $0.3 - 0.7 $ keV band for a sample of nearby gas-poor galaxies.439 The energy range has been optimized to detect emission from nuclear-burning white dwarfs. considering the range of effective temperatures. absorption column densities. and the effective area curve of detectors.," The energy range has been optimized to detect emission from nuclear-burning white dwarfs, considering the range of effective temperatures, absorption column densities, and the effective area curve of detectors."440 The paper is structured as follows: in Sect., The paper is structured as follows: in Sect.441 2 we describe the sample selection. the data preparation. and its analysis.," 2 we describe the sample selection, the data preparation, and its analysis."442 We identify and remove gas-rich galaxies from the sample in Sect., We identify and remove gas-rich galaxies from the sample in Sect.443 3., 3.444 The obtained X/K ratios are presented and discussed in Sect., The obtained X/K ratios are presented and discussed in Sect.445 4., 4.446 Our results are summarized in Sect., Our results are summarized in Sect.447 5., 5.448 The superb angular resolution combined with the low and stable instrumental background of observatory makes the satellite perfectly suitable for the present study., The superb angular resolution combined with the low and stable instrumental background of observatory makes the satellite perfectly suitable for the present study.449 We searched the archive for observations in the science category “Normal Galaxies” and selected a sample of early-type galaxies with point source detection sensitivity better than 1077ergs7!., We searched the archive for observations in the science category “Normal Galaxies” and selected a sample of early-type galaxies with point source detection sensitivity better than $ 10^{37} \ \mathrm{erg \ s^{-1}} $.450 This threshold was chosen to minimize the contribution of unresolved low-mass X-ray binaries (LMXBs). and its particular value is explained later in this paper (Sect. 4.2)).," This threshold was chosen to minimize the contribution of unresolved low-mass X-ray binaries (LMXBs), and its particular value is explained later in this paper (Sect. \ref{sec:xtokvalues}) )."451 The sample was further extended to include the bulge of M31. which has similar stellar population and gas and dust content to elliptical galaxies.," The sample was further extended to include the bulge of M31, which has similar stellar population and gas and dust content to elliptical galaxies."452 To explore young elliptical galaxies we also added NGC3377 and NGC3585. which would otherwise not pass our selection criteria because of the high point source detection sensitivity.," To explore young elliptical galaxies we also added NGC3377 and NGC3585, which would otherwise not pass our selection criteria because of the high point source detection sensitivity."453in Mehlert. οἱ al. (,in Mehlert et al. (454"1998) was followed to achieve a uniform focus with wavelength. when necessary,","1998) was followed to achieve a uniform focus with wavelength, when necessary."455 A correction for the broadening of the lines due to the internal kinematics of the galaxies was applied to scale (he indices to the instrumental resolution. using a Ix-tvpe stellar template.," A correction for the broadening of the lines due to the internal kinematics of the galaxies was applied to scale the indices to the instrumental resolution, using a K-type stellar template."456 As discussed by COL. this correction is spectral type dependent and therefore somewhat uncertain: it is small (X59)) for the CaT and CaT* indices. but as large as ab o£2300 km/s for the PaT index.," As discussed by C01, this correction is spectral type dependent and therefore somewhat uncertain; it is small $\le 5$ ) for the CaT and $^*$ indices, but as large as at $\sigma\approx 300$ km/s for the PaT index."457 The uncertainties in the correction are £20.1A., The uncertainties in the correction are $\approx 0.1$.458 Finally. since the COL svstem is based on stellar spectra taken with 22 km/s resolution. nearly a [actor 4 higher than the present observations. (he dataset was calibrated on this svstem by comparing (he values of the indices for the template stars in common and applving linear corrections to the CaT and PaT indices.," Finally, since the C01 system is based on stellar spectra taken with 22 km/s resolution, nearly a factor 4 higher than the present observations, the dataset was calibrated on this system by comparing the values of the indices for the template stars in common and applying linear corrections to the CaT and PaT indices."459 Central values of the velocity dispersion σ and of the indices were derived by averaging the profiles within 2./8 (with fi. taken trom E89). Iuninositv-weighting the datapoints.," Central values of the velocity dispersion $\sigma$ and of the indices were derived by averaging the profiles within $R_e/8$ (with $R_e$ taken from F89), luminosity-weighting the datapoints."460 The typical statistical errors on the central indices are smaller than 0.1A., The typical statistical errors on the central indices are smaller than 0.1.461 The rms of the differences of the central values of the galaxy repeats is 0.2A. having applied a 0.3 ccorrection to one of the runs.," The rms of the differences of the central values of the galaxy repeats is 0.2, having applied a 0.3 correction to one of the runs."462 Fig., Fig.463 1 shows the relation between the T. PaT and CaT indices as a function of the central velocity dispersion.," \ref{figcatsig} shows the relation between the $^*$, PaT and CaT indices as a function of the central velocity dispersion."464 As already noted by Cohen (1979). Faber and French (1980) and Terlevich. Diaz Terlevich (1990). elliptical galaxies have very similar central values of Calcium triplet index.," As already noted by Cohen (1979), Faber and French (1980) and Terlevich, Diaz Terlevich (1990), elliptical galaxies have very similar central values of Calcium triplet index."465 Averagecl over the galaxy sample. the CaT* has a mean of aand rms 0.33ye)À. or zz5%... just above the measurement errors (statistical. svslematic and due to calibration).," Averaged over the galaxy sample, the $^*$ has a mean of and rms 0.33, or $\approx 5$, just above the measurement errors (statistical, systematic and due to calibration)."466 Within the derived errors. (he Ca index does not depend on o. while a mild anticorrelation is observed for both PaT and CaT. driven by the slightly larger PaT ab lower sigmas.," Within the derived errors, the $^*$ index does not depend on $\sigma$, while a mild anticorrelation is observed for both PaT and CaT, driven by the slightly larger PaT at lower sigmas."467 This contrasts with the behaviour of the Mes» ancl Me line indices. known to correlate strongly with σ in elliptical galaxies (Bender. Burstein Faber 1993. Colless et al.," This contrasts with the behaviour of the $_2$ and $b$ line indices, known to correlate strongly with $\sigma$ in elliptical galaxies (Bender, Burstein Faber 1993, Colless et al."468 1999)., 1999).469 These indices (race the a-element magnesium (Tripieco Bell 1995. Maraston et al.," These indices trace the $\alpha$ -element magnesium (Tripicco Bell 1995, Maraston et al."470 2002). and if the Call triplet indices were to trace the calcium abundance. also an a-element. a correlation wilh σ could have been expected.," 2002), and if the CaII triplet indices were to trace the calcium abundance, also an $\alpha$ -element, a correlation with $\sigma$ could have been expected."471 Fie., Fig.472 2 shows stellar population models of the CaT*. PaT and CaT indices constructed using the FF subroutines of C02 and the updated code of Maraston (1998. M93).," \ref{figssp} shows stellar population models of the $^*$, PaT and CaT indices constructed using the FF subroutines of C02 and the updated code of Maraston (1998, M98)."473 A detailed description of the models considered here will be given in Maraston et al. (, A detailed description of the models considered here will be given in Maraston et al. (474in preparation).,in preparation).475 The black lines show simple stellar population (SSP) models with the Salpeter IMIF as a function of age and metallicity., The black lines show simple stellar population (SSP) models with the Salpeter IMF as a function of age and metallicity.476 These models reproduce well the tight metallicity-CaT correlation observed for elobular clusters (open blue squares. [rom Armandrolf and. Zinn," These models reproduce well the tight metallicity-CaT correlation observed for globular clusters (open blue squares, from Armandroff and Zinn"477MIASTO! cm7. ~2 times sinaller than that of the quiescent phase (obs CI) of 41072 7. and the abundances increase by a factor of 330 from) quiescent (Z = 0.0L0.1 Z.) to the eiaut flare (0.260.29).,"$\sim$$\times$ $^{21}$ $^{-2}$, $\sim$ 2 times smaller than that of the quiescent phase (obs C1) of $\times$ $^{22}$ $^{-2}$, and the abundances increase by a factor of 3–30 from quiescent (Z = 0.01–0.1 $_{\odot}$ ) to the giant flare (0.26–0.29)."478 These parameters. however. do not change curing the fare.," These parameters, however, do not change during the flare."479 We have detected six (DoAr 21). three (ROXs 21) aud two (RONs 31) flares under our flare criterion (see 8323.2).," We have detected six (DoAr 21), three (ROXs 21) and two (ROXs 31) flares under our flare criterion (see 3.2)."480 The total exposure time of the four observations is ~7 davs. hence the flare rate is one por 1.2. 2.3. and 3.5 days for DoAr 21. RONs 21 aud ROXs 31. respectively.," The total exposure time of the four observations is $\sim$ 7 days, hence the flare rate is one per 1.2, 2.3, and 3.5 days for DoAr 21, ROXs 21 and ROXs 31, respectively."481 We also confirmed the hieh flare rate of DoAr 21 in obs C2. although the data suffer frou photon pile-up.," We also confirmed the high flare rate of DoAr 21 in obs C2, although the data suffer from photon pile-up."482" Two possibilities could account for the higher rate iu DoAr 21: differences of the enerey baud (DoAr 21: 0.59.0 keV. versus RONs 21 and RONs 31: 0.5 keV iu obs AlA3) and the mean count rate (DoAr 21: 0.! counts 1, versus RONs 21 and RONs 31: 0.010.09 counts s.+ iu obs C1)."," Two possibilities could account for the higher rate in DoAr 21: differences of the energy band (DoAr 21: 0.5–9.0 keV, versus ROXs 21 and ROXs 31: 0.5--1.5 keV in obs A1–A3) and the mean count rate (DoAr 21: $\sim$ 0.4 counts $^{-1}$, versus ROXs 21 and ROXs 31: 0.04–0.09 counts $^{-1}$ in obs C1)."483 In fact. jamuitine the CIS data of DoAr 21 to 0.51.5 keV reduces the ummber of flares (under our criterion) o two (F2 in obs A2 aud F in obs A3). similar in iiuber to those of RONs 21 aud RONs 31.," In fact, limiting the GIS data of DoAr 21 to 0.5–1.5 keV reduces the number of flares (under our criterion) to two (F2 in obs A2 and F in obs A3), similar in number to those of ROXs 21 and ROXs 31."484 Also. he higher count rate of DoAr 21 results ina higher sensitivity to smaller amplitude flares that can be detected under our criterion (833.2).," Also, the higher count rate of DoAr 21 results in a higher sensitivity to smaller amplitude flares that can be detected under our criterion 3.2)."485 Indeed. both dares iu Figure laa have smaller amplitucles thaw hose in Figure 1bb aud c. Conversely. at similar sensitivities. the flare rate of RONs 21 αμα ROXs 31 may be comparable to that of DoAr 21. in spite of different ages (DoAr 21. ~10° vr: RONs 21 and RONs 31. ~ 10° vr) aud ciffercut structure (RONS 2] and RONs 31 are binaries. while DoÀr 21 may be a single star).," Indeed, both flares in Figure \ref{fig:lc_c1}a a have smaller amplitudes than those in Figure \ref{fig:lc_c1}b b and c. Conversely, at similar sensitivities, the flare rate of ROXs 21 and ROXs 31 may be comparable to that of DoAr 21, in spite of different ages (DoAr 21, $\sim$ $^5$ yr; ROXs 21 and ROXs 31, $\sim$ $^6$ yr) and different structure (ROXs 21 and ROXs 31 are binaries, while DoAr 21 may be a single star)."486 The typical flare rate of X-ray sources in the Taurus-Auriga-Perseus region (Stelzer 2000) is L/(L5) days (assuming a typical decay time scale of 1 hour)., The typical flare rate of X-ray sources in the Taurus-Auriga-Perseus region (Stelzer 2000) is 1/(4–5) days (assuming a typical decay time scale of 1 hour).487 Therefore we predict significantly lieher flare rates than that reported previously., Therefore we predict significantly higher flare rates than that reported previously.488 The higher duty ratio may be primarily due to the extended seusitivitv iu the hard N-rav baud (21.5 keV) and their brghtuess. because the flare activity (flux increase) is clearer in the harder N-rav band aud/or for brighter sources as we have already demoustrated for DoAr 21 in the previous paragraph aud in Figure 6aa. The high-quality spectra of the long ACTS exposure reveal that the 2-T models gives a better fit for overall spectra than the 1-T models for RONs 21 and ROXs 31.," The higher duty ratio may be primarily due to the extended sensitivity in the hard X-ray band $>$ 1.5 keV) and their brightness, because the flare activity (flux increase) is clearer in the harder X-ray band and/or for brighter sources as we have already demonstrated for DoAr 21 in the previous paragraph and in Figure \ref{lx_kt_abund}a a. The high-quality spectra of the long ACIS exposure reveal that the 2-T models gives a better fit for overall spectra than the 1-T models for ROXs 21 and ROXs 31."489 This supports previous 2-T model fits for some fraction of other bright TTSs (Carkuerotal.1996:Preihbisch—1997:20011.," This supports previous 2-T model fits for some fraction of other bright TTSs \citep{Carkner1996,490Preibisch1997, Costa2000, Ozawa2000, Tsujimoto2001}."491x DoÀr 21. ou the other haud. displavs a simple 1-T spectrum with ATο keV: hence it has no additional soft. component.," DoAr 21, on the other hand, displays a simple 1-T spectrum with $kT \sim$ 3 keV; hence it has no additional soft component."492 Since the age of DoAr 21 (—10 vr) is vounger than that of RONXs 21 aud ROXs 31 (109 yr) (Nürubergeral.1998).. coupled with the result of Tsujimotoetal.(2001) that 2-T spectra are found more often iu older TTSs than in vouuger protostars. we speculate that the soft component. probably a relatively steady corona. is generated eradually as the system iucreases in age. finally reaching solar-like corona.," Since the age of DoAr 21 $\sim$ $^5$ yr) is younger than that of ROXs 21 and ROXs 31 $\sim$ $^6$ yr) \citep {Nurnberger1998}, coupled with the result of \citet{Tsujimoto2001} that 2-T spectra are found more often in older TTSs than in younger protostars, we speculate that the soft component, probably a relatively steady corona, is generated gradually as the system increases in age, finally reaching solar-like corona."493 In this scenario. the hard component would be the stun of uuresolved. flares.," In this scenario, the hard component would be the sum of unresolved flares."494 The coronal abundances of the TTSs are sub-solar. consistent with the previous results.," The coronal abundances of the TTSs are sub-solar, consistent with the previous results."495 Frou Figure L. we see that both ligh-FIP (Ne aud Av) and low-FIP (Na. Mg aud Ca) elements show hieher abundances than the other elements. (the IFIP and FIP effects).," From Figure \ref{fig:abund_doar21}, we see that both high-FIP (Ne and Ar) and low-FIP (Na, Mg and Ca) elements show higher abundances than the other elements (the IFIP and FIP effects)."496 For the abundances in solu corona. the FIP-effect appears in clements with FIPs below 10 eV: these elements are collisionally ionized iu the photosphere at 60007000 I& temperature. and would be prefercutially transferred to the upper coronal region bv clectric fields (Felciuan 1992).," For the abundances in solar corona, the FIP-effect appears in elements with FIPs below 10 eV; these elements are collisionally ionized in the photosphere at 6000–7000 K temperature, and would be preferentially transferred to the upper coronal region by electric fields \citep{Feldman1992}."497.. DoAr 21 and RONs 21 are a KÜ star and a binary of Il with M2.5. respectively. aud hence have photospheric temperatures of LOOOl3X00 TN. 0.60.8 times that of the solar photosphere CNürubereeretal. 1998)...," DoAr 21 and ROXs 21 are a K0 star and a binary of K4 with M2.5, respectively, and hence have photospheric temperatures of 4000--5000 K, 0.6–0.8 times that of the solar photosphere \citep{Nurnberger1998}. ."498 Therefore the FIP- energv-luit of 10 eV should be shifted to 68S eV. which is near Mg (FIP = 7.8 eV) and Ca (6.1: 0V). but well above Na (5.1 keV).," Therefore the FIP-effect energy-limit of 10 eV should be shifted to 6–8 eV, which is near Mg (FIP = 7.8 eV) and Ca (6.1 eV), but well above Na (5.1 keV)."499 Hence. the abundance enhancements of Mg. Ca and Na provide independent evidence supporting," Hence, the abundance enhancements of Mg, Ca and Na provide independent evidence supporting"500We make here the usual assumption. that the distribution functiou depeuds upon the particle iuomentunm p as fxp in either frame (but see the Discussion for further Comments).,"We make here the usual assumption, that the distribution function depends upon the particle momentum $p$ as $f \propto p^{-s}$ in either frame (but see the Discussion for further comments)."501" From the condition of continuity of the distribution function at the shock. denotingas py aud pi, the particle's momeutum and cosine of the pitch angle in tle dowustreaim frame. we have where the irrelevant constant. of proportionality does not depeud on ρα.p.ta."," From the condition of continuity of the distribution function at the shock, denotingas $p_a$ and $\mu_a$ the particle's momentum and cosine of the pitch angle in the downstream frame, we have where the irrelevant constant of proportionality does not depend on $p, p_a,502\mu, \mu_a$."503" Using the Lorentz transformations to relate p.pa.ft.pta (6—Glatp)(CLtpfle). p—pas(Ytu). with sit. aud 7, the relative speed aud correspouding Lorentz factor between the upstream aid downstream fluids). E fiud For «4—1. it is easy to derive [rom Taub's couditions (Landau aud Lifshitz 1987) that uw,—1. and that (1—:3,)/(1—u)2257/57>2."," Using the Lorentz transformations to relate $p, p_a, \mu, \mu_a$ $\mu = (\mu_a - u_r)/(1-u_r\mu_a)$, $p = p_a \gamma_r (1-u_r \mu_a)$, with $u_r$ and $\gamma_r$ the relative speed and corresponding Lorentz factor between the upstream and downstream fluids), I find For $u \rightarrow 1$, it is easy to derive from Taub's conditions (Landau and Lifshitz 1987) that $u_r\rightarrow 1$, and that $(1-u_r)/(1-u) \approx 504\gamma^2/\gamma_r^2 \rightarrow 2$."505 This result does use a post-shock equation of state p=p/3. which is surely correct in the limit :—1.," This result does use a post–shock equation of state $p = \rho/3$, which is surely correct in the limit $u506\rightarrow 1$."507 Iu the eud. E obtaiu This equation shows why we needed to determine the pitch angle distribution. in the upstream frame. even for 1—«wz0: in fact. even though the angular distribution tu the upstream frame (Eq. 8))," In the end, I obtain This equation shows why we needed to determine the pitch angle distribution, in the upstream frame, even for $1-u \neq 0$: in fact, even though the angular distribution in the upstream frame (Eq. \ref{up}) )"508" teuds to a singularity. the downstream distribution does not (because the factor (1—9)/(1—,) has a finite. non-zero limit). and the concrete form to which it tends depends upon the departures of the upstream distribution [rom a Dirac's delta."," tends to a singularity, the downstream distribution does not (because the factor $(1-u)/(1-u_r)$ has a finite, non–zero limit), and the concrete form to which it tends depends upon the departures of the upstream distribution from a Dirac's delta."509 From now on I will drop the subscript « in jjj. since all quantities refer to downstream.," From now on I will drop the subscript $a$ in $\mu_a$, since all quantities refer to downstream."510 In order to determine s. we now appeal to a necessary regularity condition which must be obeved by the initial(56... Dor z= 0) pitch augle distribution. Eq. 1...," In order to determine $s$, we now appeal to a necessary regularity condition which must be obeyed by the initial, for $z = 0$ ) pitch angle distribution, Eq. \ref{incomplete}. ."511 Looking at Eq., Looking at Eq.512 1. specialized to the downstream case. where w=1/3 lor very fast shocks. we see that this equation has a singularity at µ=—1/3.," \ref{main} specialized to the downstream case, where $u = 1/3$ for very fast shocks, we see that this equation has a singularity at $\mu = -1/3$."513 Passing through this singularity will fix the iudex s., Passing through this singularity will fix the index $s$ .514 Ht is not convenient to use f directly: rather. E use its Laplace transform Taking Laplace trauslorms of bothsides of Eq.," It is not convenient to use $f$ directly; rather, I use its Laplace transform Taking Laplace transforms of bothsides of Eq."515 1. E obtain, \ref{main} I obtain516Based on SDSS photometry. we derived photometric equations to convert the L-band counts into g-band magnitudes.,"Based on SDSS photometry, we derived photometric equations to convert the $L$ -band counts into $g$ -band magnitudes."517 SDSS image mosaics were constructed as described in Zibetüà. Charlot Ris (2009) and high S/N. q—L color maps of these galaxies were obtained wilh (Zibetti 2009).," SDSS image mosaics were constructed as described in Zibetti, Charlot Rix (2009) and high $S/N$, $g - L$ color maps of these galaxies were obtained with (Zibetti 2009)."518 Using these maps. we estimated the median zero point and the amplitude of the color terms. which turns out to be of the order of 0.1 mag. al most.," Using these maps, we estimated the median zero point and the amplitude of the color terms, which turns out to be of the order of 0.1 mag, at most."519 There are two main limitations to the depth that can be reached in imagine low-surlace brightness features: (1) photon noise aud (1) background. fluctuations due to flat-field residual. internal reflections. ghosts. scattered lisht. ete.," There are two main limitations to the depth that can be reached in imaging low-surface brightness features: (i) photon noise and (ii) background fluctuations due to flat-field residual, internal reflections, ghosts, scattered light, etc."520 We estimate the photon noise lini as the surface brightness corresponding to 5 times r.m.s., We estimate the photon noise limit as the surface brightness corresponding to 5 times r.m.s.521 in 2”-cliameter random apertures., in $2^{\prime\prime}$ -diameter random apertures.522 For background. [uetuations. we estimated the median sky level r.m.s.," For background fluctuations, we estimated the median sky level r.m.s."523 in selected boxes. several tens to hundred. arcseconds per side. spread around the galaxies.," in selected boxes, several tens to hundred arcseconds per side, spread around the galaxies."524" We find Chat the (vpical 2""-diameter detection limit is 27.220.2mae,ogarcsec7. while the typical backeroundo Huctuations correspond to 28.5+0.5mag,arcsec>> It is worth noting that for the corresponding SDSS g-band images we measured 25 and 28.7. respectively."," We find that the typical $2^{\prime\prime}$ -diameter detection limit is $27.2\pm 0.2~\mathrm{mag}_g~\mathrm{arcsec}^{-2}$, while the typical background fluctuations correspond to $28.5\pm 0.5~525 \mathrm{mag}_g~\mathrm{arcsec}^{-2}$ It is worth noting that for the corresponding SDSS g-band images we measured 25 and 28.7, respectively."526 This shows that our images are roughly 10 times deeper than the SDSS data in terms of photon statistics and are mainly limited by svstematic background uncertainties. which are comparable to those of the SDSS data.," This shows that our images are roughly 10 times deeper than the SDSS data in terms of photon statistics and are mainly limited by systematic background uncertainties, which are comparable to those of the SDSS data."527 This implies that our images have hieh efficiency in detecting sharp or localized features but background fIuctuations hampers our ability to accurately measure smooth diffuse light., This implies that our images have high efficiency in detecting sharp or localized features but background fluctuations hampers our ability to accurately measure smooth diffuse light.528cosmology of (he section 1 because we have a Chaplvein twpe of gas to start wilh in (his case.,cosmology of the section I because we have a Chaplygin type of gas to start with in this case.529 Moreover (he isotropy of the metric dictates that p=py and so we end up with an isotropic pressure in all dimensions., Moreover the isotropy of the metric dictates that $p = p_{d}$ and so we end up with an isotropic pressure in all dimensions.530 The solutions closely resemble the earlier work of Debnath [18]. in (22)) m=0: Ποιο we eget flat extra space althoughe the total number of dimensions continues (ο be (d+4)., The solutions closely resemble the earlier work of Debnath \cite{ud} in ) $m = 0$: Here we get flat extra space although the total number of dimensions continues to be $(d+ 4)$.531 But the cosmology is exactly similar to the 4D case referred (ο earlier [L&}., But the cosmology is exactly similar to the 4D case referred to earlier \cite{ud}.532. In fact this similarity is a direct. consequence of a little known theorem of Campbell (hat anv analvtic N-dimensional Rienmnanian manilold can be locally embedded in a higher dimensional Ricci-flat manifold. [19].. GH)) d—0:, In fact this similarity is a direct consequence of a little known theorem of Campbell that any analytic N-dimensional Riemmanian manifold can be locally embedded in a higher dimensional Ricci-flat manifold \cite{tavako}. ) $d=0$:533 Here we simply recover the 4D metric aud all (he known solutions of 4D NNow with the help of equations (37) (42). we gel WWe have not been able. so far. to find a solution of equation (44) in a closed form.," Here we simply recover the 4D metric and all the known solutions of 4D Now with the help of equations (37) (42), we get We have not been able, so far, to find a solution of equation (44) in a closed form."534 Rather a Uvpereeometric series solution results given by where s=sw) and oFy is the hypergeometric EEven then. fixing the values of different parameters one can get the temporal behaviour of the seale factors as given in the adjoining figure-3.," Rather a Hypergeometric series solution results given by where $s = \frac{1}{2(1+\alpha)}$ and $_{2}F_{1}$ is the hypergeometric Even then, fixing the values of different parameters one can get the temporal behaviour of the scale factors as given in the adjoining figure-3."535 A eursory look at the figure shows that at a certain stage of evolution the cosmology starts inflating., A cursory look at the figure shows that at a certain stage of evolution the cosmology starts inflating.536 Another desirable feature is (he fact that the extra dimensions compactily al very early stage of evolution in conformity with both theoretical and observational requirements., Another desirable feature is the fact that the extra dimensions compactify at very early stage of evolution in conformity with both theoretical and observational requirements.537 NNow for small value of scale laetor. RO) CA) should be large in this situation). wwhich is verv large and corresponds to the universe dominated by an equation of state. p—(5Lp as is evident from equation (36).," Now for small value of scale factor $R(t)$ $A(t)$ should be large in this situation), which is very large and corresponds to the universe dominated by an equation of state, $p = (\gamma - 1)\rho$ as is evident from equation (36)."538 At the late stage of evolution (when A) , At the late stage of evolution (when $R(t)$ 539measured syste parameters. in particular the inclination.,"measured system parameters, in particular the inclination."540 For a flat accretion disk Lapidus&Suuvaev(1985) calculated an anisotropy factor of 2.8. depending upou the inclination auele.," For a flat accretion disk \cite{ls85} calculated an anisotropy factor of 2.8, depending upon the inclination angle."541 The precessing of a warped disk is likely to affect the proportion of reprocessed radiation observed during the burst in the same way that varving the inclination would., The precessing of a warped disk is likely to affect the proportion of reprocessed radiation observed during the burst in the same way that varying the inclination would.542 The derived anisotropy factor is more than sufficient to explain the observed modulation in the peak flux of racdius-cxpausion bursts., The derived anisotropy factor is more than sufficient to explain the observed modulation in the peak flux of radius-expansion bursts.543 Because of these uucertaimties. we can most likely adopt a relatively wide range of parameters (disk warping auele. disk albedo) which will eive rise to a modulation of at least he levelieasured iu31: thus. such auapproach would also have no ability to rule out warped disk yrecession as a 1mechlauisiu for the N-vav flux modulation.," Because of these uncertainties, we can most likely adopt a relatively wide range of parameters (disk warping angle, disk albedo) which will give rise to a modulation of at least the level measured in; thus, such an approach would also have no ability to rule out warped disk precession as a mechanism for the X-ray flux modulation."544 We note that in the archetypical precessing warped disk system Hor X-1. periodic obscuration of the neutron star w the disk gives rise to a modulation of the persistent N-ray flux of essentially. (ουςScottetal.2000)... much lareer than the ~10 neasured for34.," We note that in the archetypical precessing warped disk system Her X-1, periodic obscuration of the neutron star by the disk gives rise to a modulation of the persistent X-ray flux of essentially \cite[e.g][]{slw00}, much larger than the $\sim10$ measured for."545. Since it exhibits neither N-rav eclipses or dips. unnmst have a lower inclination (/X 857) thau Πο X- making obscuration by the disk less likely.," Since it exhibits neither X-ray eclipses or dips, must have a lower inclination $i\la85\arcdeg$ ) than Her X-1, making obscuration by the disk less likely."546 For a disk warped to the deeree iuferred for Her X-1 (207 at the miter edge). theprior? probability for obscuration iu lis ~25%.," For a disk warped to the degree inferred for Her X-1 $20\arcdeg$ at the outer edge), the probability for obscuration in is $\sim25$."547.. Even if the inclination is not sufficieutly lich to permit obscuration. X-ray reflection from the disk. coupled with the variations in the projected disk area duc to the precessing warp. nay vot be sufficient to give rise to the observed modulation.," Even if the inclination is not sufficiently high to permit obscuration, X-ray reflection from the disk, coupled with the variations in the projected disk area due to the precessing warp, may yet be sufficient to give rise to the observed modulation."548 When the svstenmiatie trends in the variation of the peak burst fluxes are removed. the residual variation is only which is comparable to the typical measurement uncertainty of," When the systematic trends in the variation of the peak burst fluxes are removed, the residual variation is only, which is comparable to the typical measurement uncertainty of."549 This las ao verv imuportant duplication. for the anisotropy of radiusexpansion bursts in21. as deseribed bv the paralcter © in equation (1)).," This has a very important implication for the anisotropy of radius-expansion bursts in, as described by the parameter $\xi$ in equation \ref{ledd}) )."550 The small residual scatter of the peak fluxes strouglv sugeests that the iutriusic variation of the peak burst flux is also small z1:," The small residual scatter of the peak fluxes strongly suggests that the intrinsic variation of the peak burst flux is also small, $\simeq1$."551 It seems unlikely that we observe the same face of the neutron star at the same orieutation ching every one of these bursts. particularly eiven the rapid rotation inferred from the burst oscillations (361Iz:Stroluuaveretal. 1996).," It seems unlikely that we observe the same face of the neutron star at the same orientation during every one of these bursts, particularly given the rapid rotation inferred from the burst oscillations \cite[364~Hz;][]{stroh96}."552. Additionally. these same oscillatious are almost never observed caring the radius expansion episode itself. even if they are present earlier or later im the burst (Munoetal.2002a).," Additionally, these same oscillations are almost never observed during the radius expansion episode itself, even if they are present earlier or later in the burst \cite[]{muno02b}."553. We conclude that the longitudinal dependence of the burst flux during the radius expansion episodes is negligible., We conclude that the longitudinal dependence of the burst flux during the radius expansion episodes is negligible.554 À latitudinal variation in flux remains plausible. particularly since the effective eravity is snaller at the neutron star equator than at the poles. and so we nieht expect a ereater degree of expansion of the atinosphiere there.," A latitudinal variation in flux remains plausible, particularly since the effective gravity is smaller at the neutron star equator than at the poles, and so we might expect a greater degree of expansion of the atmosphere there."555 However. we observe siguificaut variation iu the blackbody normalization when the peak burst flux is achieved. which suegeests that the radius expansion episodes reach different peak radii.," However, we observe significant variation in the blackbody normalization when the peak burst flux is achieved, which suggests that the radius expansion episodes reach different peak radii."556 Since we nuelt expect the degree of latitudinal anisotropy to vary with increasing radius. the effect of such a latituclinal variation of flux would be a dependence of the peal flux on the blackbody normalisation at the peak. which is not observed.," Since we might expect the degree of latitudinal anisotropy to vary with increasing radius, the effect of such a latitudinal variation of flux would be a dependence of the peak flux on the blackbody normalisation at the peak, which is not observed."557 Thus. we conclude that the degree of latitudinal fux anisotropy is most likely also liuited bv the Guferred) intrinsic variation of the peak burst fluxes.," Thus, we conclude that the degree of latitudinal flux anisotropy is most likely also limited by the (inferred) intrinsic variation of the peak burst fluxes."558 We conclude that the burst enüssioun during the radius expansion episode is isotropic to within =12%.., We conclude that the burst emission during the radius expansion episode is isotropic to within $\simeq1$.559 Note that it is stillpossible for the burst cussion at the neutron star surface to be siguificantlv anisotropic. but that this anisotropy is smoothed out through reprocessing iu the extended atinosphliere preseut caving the radius expansion episodes.," Note that it is still possible for the burst emission at the neutron star surface to be significantly anisotropic, but that this anisotropy is smoothed out through reprocessing in the extended atmosphere present during the radius expansion episodes."560 Studies such as this provide a measure of the svstematic uucertainties of the distance estimates of N-rav sources hat are based solely ou. Eddington-Imited bursts. (sec.e.g.vanParadis&White 1995j.," Studies such as this provide a measure of the systematic uncertainties of the distance estimates of X-ray sources that are based solely on Eddington-limited bursts \cite[see, e.g.,][]{vpw95}."561. We note that the standard deviation we measure is within the typical pea- ο flux uncertaiutv (215%)) measured by ERuulkerpAetal.(2002a) for the globular cluster burst sources., We note that the standard deviation we measure is within the typical peak burst flux uncertainty $\simeq15$ ) measured by \cite{kuul02} for the globular cluster burst sources.562 While he inferred Gutrinsic) isotropy of the burst radiatiou (section rofaniso)) allows us to at least eliminate that contribution Oo Wnucertainties in distance estimates. the additional systematic error contributed bv the observed scatter iu he peak burst fixes is still naller than the usual other uncertainties due to the unknown neutrou star mass aud atmospheric composition.," While the inferred (intrinsic) isotropy of the burst radiation (section \\ref{aniso}) ) allows us to at least eliminate that contribution to uncertainties in distance estimates, the additional systematic error contributed by the observed scatter in the peak burst fluxes is still smaller than the usual other uncertainties due to the unknown neutron star mass and atmospheric composition."563 Furthermore. without a detailed uunderstaudius of the degree of reprocessing occuring imn the region around the ueutron star. woe cannot at this time determine the iutriusic peak Iuninositv of the radius expansion bursts. from the broad distribution we have observed.," Furthermore, without a detailed understanding of the degree of reprocessing occurring in the region around the neutron star, we cannot at this time determine the intrinsic peak luminosity of the radius expansion bursts, from the broad distribution we have observed."564 Nevertheless. we now calculate a probable rauge for the distance to3L. eiven plausible values for the neutron star mass and atmospheric composition.," Nevertheless, we now calculate a probable range for the distance to, given plausible values for the neutron star mass and atmospheric composition."565 We identify the miuimuun peak flux of the radius expansion bursts as the best estimate of the Lxddiugtou lint: this burst will have the smallest coutribution due to reprocessed radiation. and thus will provide the best estimate of the intrinsic maxima fux.," We identify the minimum peak flux of the radius expansion bursts as the best estimate of the Eddington limit; this burst will have the smallest contribution due to reprocessed radiation, and thus will provide the best estimate of the intrinsic maximum flux."566 Since the peak fiux is typically reached near the cud of the radius coutraction. we calculate the gravitational redshift parameter at the neutron star radius Rxyy=LO kin," Since the peak flux is typically reached near the end of the radius contraction, we calculate the gravitational redshift parameter at the neutron star radius $R_{\rm NS}=10$ km."567e We also reduce our observed fluxes bv to correct for the observed systematic flux offset measured for (μου refpca)). so that the inferred Eddington flux is 6.2«10*erecm7s +.," We also reduce our observed fluxes by to correct for the observed systematic flux offset measured for (see \\ref{pca}) ), so that the inferred Eddington flux is $6.2\times10^{-8}\ \epcs$ ."568 Thus. for a 1.1(2.00 AL. neutron star with cosmic atimospheric abundance CX= 0.7). he distance is {15} kpc.," Thus, for a 1.4(2.0) $M_\sun$ neutron star with cosmic atmospheric abundance $X=0.7$ ), the distance is 4.4(4.8) kpc."569 For a pure Te atinosphere he distance is ereater., For a pure He atmosphere the distance is greater.570 These values are roughly consistent with previous estinates (vanParadij1978:Dasinskaetal.1981:Namiuker1989) and place he source within 12 pe of the Galactic plane. about [1 kpe roni the ceuter.," These values are roughly consistent with previous estimates \cite[]{vp78,bas84,kam89} and place the source within 12 pc of the Galactic plane, about 4 kpc from the center."571 This research has made use of data obtained through he Πιοι Enerey Astrophysics Science Archive Besearcli Center Ouline Service. provided bv the NASA/Coddard Space Fleht Ceuter.," This research has made use of data obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA/Goddard Space Flight Center."572 We thank Alike Nowak. Fred. Lau," We thank Mike Nowak, Fred Lamb"573radi.,radii.574 “Pwo densities of cach cloud distribution were also considered., Two densities of each cloud distribution were also considered.575 Model X possesses small clouds scattered. with a density of 391 clouds. per 100. square. Einstein radii model 1 also has small clouds. but. scattered. with a density of 40 clouds per LOO square Einstein radii;," Model A possesses small clouds scattered with a density of 391 clouds per 100 square Einstein radii, model B also has small clouds, but scattered with a density of 40 clouds per 100 square Einstein radii."576 Moclel C utilises laree clouds. with a density of 31 clouds per 100 Einstein radii ancl model D again uses large clouds with a densitv half that of model €. Figure 2) presents examples of the four cloud. distributions employed. in. this study: the erev-seale represents the distribution. of the absorbing material whereas the points are the positions of the stars.," Model C utilises large clouds, with a density of 31 clouds per 100 Einstein radii and model D again uses large clouds with a density half that of model C. Figure \ref{fig3} presents examples of the four cloud distributions employed in this study; the grey-scale represents the distribution of the absorbing material, whereas the points are the positions of the stars."577 Furthermore. the clouds were considered to be either completely opaque. absorbing all photons (absorption model A) or producing absorption (absorption moce B).," Furthermore, the clouds were considered to be either completely opaque, absorbing all photons (absorption model A) or producing absorption (absorption model B)."578 Studies of the interstellar medium. reveal that clouds ave distributed fractally. possessing structure on a range of scales (Elmegreen 1997).," Studies of the interstellar medium reveal that clouds are distributed fractally, possessing structure on a range of scales (Elmegreen 1997)."579 When sources possess a fracta distribution it is found that the scales. of structure are imprinted on the light curve as the source is microlenses (Lewis 2002)., When sources possess a fractal distribution it is found that the scales of structure are imprinted on the light curve as the source is microlensed (Lewis 2002).580 While it is expected that any fractal structure in the absorbing clouds will result in similar imprinting of a scale of structure on the microlensing light. curve. the calculations required go beyond this study and are deferred for further work.," While it is expected that any fractal structure in the absorbing clouds will result in similar imprinting of a scale of structure on the microlensing light curve, the calculations required go beyond this study and are deferred for further work."581 Figures 4 to 11. present the results of the numerical simulations detailed in the previous sections., Figures \ref{run1a} to \ref{run2d} present the results of the numerical simulations detailed in the previous sections.582 The left hand upper panel presents the microlensing magnification map without considering the inlluence of absorbing material. with dark areas corresponding to regions of magnification. while the light areas represent regions of demagnification: the sharp boundaries corresponding to caustics in the map are clearly visible.," The left hand upper panel presents the microlensing magnification map without considering the influence of absorbing material, with dark areas corresponding to regions of magnification, while the light areas represent regions of demagnification; the sharp boundaries corresponding to caustics in the map are clearly visible."583 Phe upper-right hand panel again presents a magnification map. but in this case any ravs which impinge on absorbing clouds as they pass through the microlensing screen are appropriately cenuded.," The upper-right hand panel again presents a magnification map, but in this case any rays which impinge on absorbing clouds as they pass through the microlensing screen are appropriately denuded."584 With this. the upper-left mined panel can be seen to be the magnification of continuum emission. while that in the upper-right hand panel is that in the absorption line.," With this, the upper-left hand panel can be seen to be the magnification of continuum emission, while that in the upper-right hand panel is that in the absorption line."585 The relative depth of the emission ine seen at any particular instant is the ratio of these two maps., The relative depth of the emission line seen at any particular instant is the ratio of these two maps.586 This can be simply seen if one considers a large screen of absorption that uniformly. and. completely covers 1e microlensing star field., This can be simply seen if one considers a large screen of absorption that uniformly and completely covers the microlensing star field.587 Hence. the magnification map in 1e absorption line would uniformly possess values that are fixed fraction of those in the continuum map. such that the ratio of the two would be a constant and would demonstrate ju. in this case. that there would be no absorption line Pvariability.," Hence, the magnification map in the absorption line would uniformly possess values that are a fixed fraction of those in the continuum map, such that the ratio of the two would be a constant and would demonstrate that, in this case, that there would be no absorption line variability."588 The Iower-right hand. panel presents several cuts across ) magnification map with the absorption., The lower-right hand panel presents several cuts across the magnification map with the absorption.589 There are wee paths (indicated bv the lines across the upper-right, There are three paths (indicated by the lines across the upper-right590"""vacuum"" state 0) ancl a representation © of A in the Llilbert space. such {hed But it is clear that in doing so we have simply reconstructed the Hilbert space 7£,,. the ""vacuum? state |0),,, and the algebra of the operators ὡς.","“vacuum” state $|0 \rangle$ and a representation $\phi$ of $\cal A$ in the Hilbert space, such that But it is clear that in doing so we have simply reconstructed the Hilbert space ${\cal H}_{ph}$ , the “vacuum” state $|0 \rangle_{ph}$ and the algebra of the operators $\hat\phi_{s}$."591 In other words. the content of the canonical theory of quantum gravity can be coded. in the spirit of Wightinan. in the positive linear functional W(s) over the algebra A of the spin networks.," In other words, the content of the canonical theory of quantum gravity can be coded, in the spirit of Wightman, in the positive linear functional $W(s)$ over the algebra $\cal A$ of the spin networks."592 We can (hus determine the dvnamies of the theory by giving H(s). instead of explicitly giving (he projector P. orthe Hamiltonian constraint. and reconstruct (he physical Hilbert space from VW(s).," We can thus determine the dynamics of the theory by giving $W(s)$, instead of explicitly giving the projector $P$, orthe Hamiltonian constraint, and reconstruct the physical Hilbert space from $W(s)$."593 In. particular. the main physical gauge-invariant observable. namely (he (hree-geometrv (o eeomelry (transition amplitude is simply the value of HW(5) on Che spin networks 5 formed by two disjoint components.," In particular, the main physical gauge-invariant observable, namely the three-geometry to three-geometry transition amplitude is simply the value of $W(s)$ on the spin networks $s$ formed by two disjoint components."594 We close this section with a comment about locality., We close this section with a comment about locality.595 The sense in which general relativity is a local theory is [ar more subtle that in ordinary field theory., The sense in which general relativity is a local theory is far more subtle that in ordinary field theory.596 For a detailed discussion of (his issue see for instance [2].., For a detailed discussion of this issue see for instance \cite{observables}.597 In particular. physical gauge invariant observables are independent from the spacetime coordinates cr./. and therefore they are not localized on the spacetime manifold. which is coordinatized bv £F./.," In particular, physical gauge invariant observables are independent from the spacetime coordinates $\vec x,t$, and therefore they are not localized on the spacetime manifold, which is coordinatized by $\vec x,t$."598 Nevertheless. the dvnamices of general relativity is still local in an appropriate sense.," Nevertheless, the dynamics of general relativity is still local in an appropriate sense."599 This locality should be reflected in a general property of the VW functions., This locality should be reflected in a general property of the $W$ functions.600" Roughly. we expect that if a spin network s can be cut in (wo parts (connected to each each other) 5 and γαι alid a second spin network s' can be ent in two parts (connected to each each other) 5;Ser and sus and if $,,,=s,.ead then WV(5.s) should be independent from sj."," Roughly, we expect that if a spin network $s$ can be cut in two parts (connected to each each other) $s_{ext}$ and $s_{in}$, and a second spin network $s'$ can be cut in two parts (connected to each each other) $s'_{ext}$ and $s'_{in}$, and if $s_{ext}=s'_{ext}$, then $W(s,s')$ should be independent from $s_{ext}$."601 In other words. the local evolution in apart of the spin network should be independent from what happens elsewhere on the spin network.," In other words, the local evolution in apart of the spin network should be independent from what happens elsewhere on the spin network."602 A precisely formulation of this property and its consequences deserve to be studied., A precisely formulation of this property and its consequences deserve to be studied.603 In the last few vears. intriguing developments in quantum gravity have been obtained using the spin foam [9]. formalism.," In the last few years, intriguing developments in quantum gravity have been obtained using the spin foam \cite{spinfoam} formalism."604 Recently. it has been shown that any spin foam model can be derived from an auxiliary. [ield theory.over a group manifold |11. 12]..," Recently, it has been shown that any spin foam model can be derived from an auxiliary field theoryover a group manifold \cite{dfkr,cm}. ."605 Several spin foam models defined from auxiliary theories defined over a group have been developed., Several spin foam models defined from auxiliary theories defined over a group have been developed.606 They are covariant. have," They are covariant, have"607he likelihood function: confidence intervals can be defined by treating the ikelihood function as a probability distribution in O (with nonuniform σου. i£ desired).,"the likelihood function; confidence intervals can be defined by treating the likelihood function as a probability distribution in $\Teta$ (with non–uniform prior, if desired)."608 We have implicitly been working with simple pixel values. but it should x that all follows through for differences. or any incaremphasized combination of skv fortemperature these simply transform. the covariance matrix C.," 	We have implicitly been working with simple pixel values, but it should be emphasized that all follows through for temperature, or any linear combination of sky temperatures, for these simply transform the covariance matrix $\mC$."609 Only Ίσα.temperatures. (, Only Eq. (6103) is altered: and it should be noted that in he more general case. 7;; may not be in Legendre polynomials cause. e.g.. a difference measurementexpandable breaks spherical svmmoetry. (1.6... T may depend on the orientation of the two dillerence pairs in a single cillerence scheme).,"3) is altered; and it should be noted that in the more general case, $T_{ij}$ may not be expandable in Legendre polynomials because, e.g., a difference measurement breaks spherical symmetry (i.e., $\mT$ may depend on the orientation of the two difference pairs in a single difference scheme)."611 Experimental results are usually given in ternis ofpowers. estimates of the variance of the Huctuations over a finite range of f.," 	Experimental results are usually given in terms of, estimates of the variance of the temperature fluctuations over a finite range of $l$."612 These may either be definedtemperature by the scheme emploved. during observation. or by applying a linear.dillerencing transformation to the pixel values of à ," These may either be defined by the differencing scheme employed during observation, or by applying a linear transformation to the pixel values of a map."613For an ideal with full sky. coverage. the powers map.would simply be theexperiment individual C: however. limited sky. coverage results in less resolution in / space. estimates only within finite bancdwidths.," For an ideal experiment with full sky coverage, the band--powers would simply be the individual $C_l$; however, limited sky coverage results in less resolution in $l$ –space, permitting estimates only within finite bandwidths."614" useful example is thepermitting single dillerence scheme. where one measures A—dy, with dj and do by an angle 6 on the "," A useful example is the single difference scheme, where one measures $\Delta \equiv d_1 - d_2$ with $d_1$ and $d_2$ separated by an angle $\theta$ on the sky."615In this case. the dodiagonal elements ofseparated the covariance matrix may be sky.written as where thefunelion. M1=I(cos8)]. identilies the range of/ to which the the dilference is SAPsensitive.," In this case, the diagonal elements of the covariance matrix may be written as where the, $W_l = 2|B_l|^2[1-P_l(\cos\theta)]$, identifies the range of $l$ to which the the difference is sensitive."616 The common approach is to quote apower estimate. 57. defined by DCT/(22). which leads to The banc 977. is then treated as the parameter to be estimated rom the full power.likelihood. function.," The common approach is to quote a estimate, $\delta T_f$, defined by $(\delta T_f)^2 \equiv 617l(l+1)C_l/(2\pi)$ , which leads to The band–power, $\delta T_f$, is then treated as the parameter to be estimated from the full likelihood function."618 It is this procedure which leads to the »oints and uncertainties shown in 1., It is this procedure which leads to the points and uncertainties shown in Figure 1.619 We see that it has indeed been constructed. under the assumption of Figuregaussian fluctuations. as mentioned in the Introduction.," We see that it has indeed been constructed under the assumption of gaussian fluctuations, as mentioned in the Introduction."620" Notice also that because it contains all relevant information. he likelihood function includes the uncertainty on the power estimate due o or so.called. ""cosmic. variance."," Notice also that because it contains all relevant information, the likelihood function includes the uncertainty on the power estimate due to sample, or so–called “cosmic”, variance."621 Lt is sample.convenient. and. essential for future to use xuxdpower estimates as the perhapsstarting point for constraining experiments.cosmological xuameters. instead. of vectors. as in (," 	It is convenient, and perhaps essential for future experiments, to use band–power estimates as the starting point for constraining cosmological parameters, instead of pixel vectors, as in Eq. ("6221).,1).623 Besides being the result reported in pixelthe literature. and Eq.hence easy to find. »winciple a sort of data (Bond ct al.," Besides being the principle result reported in the literature, and hence easy to find, band--powers represent a sort of data compression (Bond et al."624 1998). — there are fewer representband: than for compression ancl hence ewer calculations powers to pixelsexplore a anvgiven given experiment.," 1998) – there are fewer band–powers than pixels for any given experiment, and hence fewer calculations required to explore a given parameter space."625 If. the luctuations are required then we have lost in parameterthe space.compression.," If the fluctuations are truly gaussian, then we have lost nothing in the compression."626 Jo work in this direction.truly we gaussian.need to an easy.nothingto.use approximation o the full likelihood function for each developband: estimate. Z(977). one which requires Little information about power details.," To work in this direction, we need to develop an easy–to–use approximation to the full likelihood function for each band–power estimate, ${\cal L}(\delta T_f)$, one which hopefully requires little information about experimental details."627 With this hopefully.aim. note first that the band. shown in experimental 1 are to the variance of measured. powers (or Figuredilferences). eg. as in ooportionalEq. (," 	With this aim, note first that the band–powers shown in Figure 1 are proportional to the variance of measured temperatures (or differences), e.g., as in Eq. ("6285).,5).629 To motivate an ansatz. consider a temperaturestotally unrealistic case where the covariance matrix is strictly clagonal. including noise. ancl he noise is uniform with variance ay:," To motivate an ansatz, consider a totally unrealistic case where the covariance matrix is strictly diagonal, including noise, and the noise is uniform with variance $\sig_N^2$ :"630deep optical tnages of the burst location performed with the HIST (Iollaudctal.2000a) and the VET. (Saracco revealed an — unmae uuderlviug host ealaxy.,deep optical images of the burst location performed with the HST \citep{Holland00c} and the VLT \citep{Saracco01b} revealed an $\sim$ mag underlying host galaxy.631 Iu this letter we report on VLT observations carried out to derive the spectroscopic redshift of this host galaxy. aud which allowed us to coufirm the redshütt of 9990705 derived by Amatietal.(2000).," In this letter we report on VLT observations carried out to derive the spectroscopic redshift of this host galaxy, and which allowed us to confirm the redshift of 990705 derived by \citet{Amati00}."632. We also analyse public UST data of the host., We also analyse public HST data of the host.633 The spectroscopic observations of the 9990705 lost ealaxy were performed on 2001 December 21 aud 22 (burst | ~9900ddavs) with the FORS2 iustruneut installed on the VET. UT1/Yepuu at ESO., The spectroscopic observations of the 990705 host galaxy were performed on 2001 December 21 and 22 (burst + $\sim$ days) with the FORS2 instrument installed on the VLT UT4/Yepun at ESO.634" Spectra were obtained under moderate secing conditions (~ 1)) using a auedimm resolution evisina (600RT) in combination with a l1""-—width slit. and totalizing an integration time of hhows."," Spectra were obtained under moderate seeing conditions $\sim$ ) using a medium resolution grism (600RI) in combination with a -width slit, and totalizing an integration time of hours."635 We thus covered an effective wavelength range e 5600 with au iustrumneutal resolution ~AA.., We thus covered an effective wavelength range $\sim$ 5600 – with an instrumental resolution $\sim$.636 The slit was positioned on the sky so as to cover the outer region of the galaxy where the burst occured., The slit was positioned on the sky so as to cover the outer region of the galaxy where the burst occured.637 The ealaxv spectra were flus-calibrated using spectroscopic standard stars., The galaxy spectra were flux-calibrated using spectroscopic standard stars.638 The IIST observations of the CRB9990T05 lost were taken aud reduced by Iollaudetal.(2000a.1) as part of the “Survey of the Tost Galaxies of Camua-Rav Bursts” using the STIS camera.," The HST observations of the 990705 host were taken and reduced by \citet{Holland00c,Holland00a} as part of the “Survey of the Host Galaxies of Gamma-Ray Bursts” using the STIS camera."639" Buages were obtained with the 50CCD (clear. pivot A,AA.. hereafter CL) and F2sX50LP (one pass. pivot AyAA.. hereafter LP) apertures. respectively on 2000 July 25 and 2000 August 25 Gc. ~ LLOO davs after the burst)."," Images were obtained with the 50CCD (clear, pivot $\lambda_o$, hereafter CL) and F28X50LP (long pass, pivot $\lambda_o$, hereafter LP) apertures, respectively on 2000 July 25 and 2000 August 25 (i.e., $\sim$ 400 days after the burst)."640 The respective total exposure times were SShiss and ss iu the CL and LP apertures., The respective total exposure times were s and s in the CL and LP apertures.641 We deconvolved the images following a multi-resolution wavelet decomposition (Starcketal.1998) and the use of PSFs obtained from the conibination of foreground stars in the images., We deconvolved the images following a multi-resolution wavelet decomposition \citep{Starck98} and the use of PSFs obtained from the combination of foreground stars in the images.642 The photometry measurements were performed on the data before deconvolution to preserve reliable flux aud noise estimates., The photometry measurements were performed on the data before deconvolution to preserve reliable flux and noise estimates.643 We corrected the CL aud LP aperture data from absorptions Αει ==00.36 and Ayp ==00.28 lag αππήτο the extinction curve of Cardellietal.(1989) and the LEMC extinction (Bo W)==00.12 obtained by Dutraetal.(2001)., We corrected the CL and LP aperture data from absorptions $_{CL}$ 0.36 and $_{LP}$ 0.28 mag assuming the extinction curve of \citet{Cardelli89} and the LMC extinction $E(B-V)$ 0.12 obtained by \citet{Dutra01}.644. Moreover. we carried out a careful analysis using a multi-resolution trausftorm. method to subtract from the images the multiple LAIC foreground stars superimposed ou the plane of the galaxy.," Moreover, we carried out a careful analysis using a multi-resolution transform method to subtract from the images the multiple LMC foreground stars superimposed on the plane of the galaxy."645 The final VLT spectrum is shown in , The final VLT spectrum is shown in 1.646Figuell. Au inavegion of the spectrum where the residuals from the skv line subtraction are ueeligible., An emission feature is clearly detected at $\sim$ in a region of the spectrum where the residuals from the sky line subtraction are negligible.647 Attributing this feature respectively to Πα or Lya would πρίν redshifts Z==00.05 aud 11.66. which is inconsistent with the spiral morphology aud the angular size of the ealaxy (see section 3.2).," Attributing this feature respectively to $\alpha$ or $\alpha$ would imply redshifts 0.05 and 4.66, which is inconsistent with the spiral morphology and the angular size of the galaxy (see section 3.2)."648 The line can thus only be due to AAAA.., The line can thus only be due to $\lambda\lambda$.649" It is actually not resolved in our spectrum. but its width is iufact consistent with that of the [OT], doublet."," It is actually not resolved in our spectrum, but its width is infact consistent with that of the [OII] doublet."650 Note that the low signal to noise ratio lougward of docs not allow us to detect U6 and II., Note that the low signal to noise ratio longward of does not allow us to detect $\delta$ and $\gamma$.651" From the |OII| line, we derive a secure heliocentric redshift 00.0002. for the host ealaxy aud 9990705."," From the [OII] line, we derive a secure heliocentric redshift 0.0002 for the host galaxy and 990705."652 This is in full aerecment with the value z- OO.17 obtained bv Amatietal.(2000) from the transient feature observed in the GRB prompt cinissiou. aud also appears consistent with the redshift z==00.813 already imeutioned by Lazzatietal(2001).," This is in full agreement with the value $\sim$ 0.17 obtained by \citet{Amati00} from the transient feature observed in the GRB prompt emission, and also appears consistent with the redshift 0.843 already mentioned by \citet{Lazzati01}."653" Assuming ai standard cosmoloey with ly ==665 Jan LMMpe +. Q,, ==003 and Qy=0.7. we thus measure for the host of 9990705 a luninositv distance d; ——55.8GCGpc. aud a projected scale of 8.2 proper kpc (or 15.2 comoving kpc} per aresecond ou the sky."," Assuming a standard cosmology with $_0$ 65 km $^{-1}$ $^{-1}$, $\Omega_m$ 0.3 and $\Omega_{\lambda}\,=\,0.7$ , we thus measure for the host of 990705 a luminosity distance $_l$ Gpc, and a projected scale of 8.2 proper kpc (or 15.2 comoving kpc) per arcsecond on the sky."654 Because of the extended aud rather diffuse cinission of the galaxw (see 33.2). we did not obtain a secure estimate of the [OT] integrated fux Iviug outside of the slit. and thus we could uot derive its [OT] total huuinosity.," Because of the extended and rather diffuse emission of the galaxy (see 3.2), we did not obtain a secure estimate of the [OII] integrated flux lying outside of the slit, and thus we could not derive its [OII] total luminosity."655 We roughly measured. though with large uncertainties. au observed [OIT| equivalent width z AA. Los 2 in the rest frame.," We roughly measured, though with large uncertainties, an observed [OII] equivalent width $\approx$ , i.e., $\approx$ in the rest frame."656 cn Iu addition to the eiiissiou doublet. we tentatively detect several stellar [OTTabsorption features at a similar," .3cm In addition to the [OII] emission doublet, we tentatively detect several stellar absorption features at a similar"657Lack of accurate data for collision processes needed for reliable non-LTE line formation calculations in cool star atmospheres. especially processes involving hydrogen atom and electron impacts. poses a major source of uncertainty for stellar abundance analyses: e.g. ??2?..,"Lack of accurate data for collision processes needed for reliable non-LTE line formation calculations in cool star atmospheres, especially processes involving hydrogen atom and electron impacts, poses a major source of uncertainty for stellar abundance analyses; e.g. \citet{1993PhST...47..186L,2001NewAR..45..559K,2005ARA&A..43..481A}."658 For hydrogen. the situation is particularly poor.," For hydrogen, the situation is particularly poor."659 The possible importance of collisions with neutral hydrogen in non-LTE line formation calculations was first pointed out by ? in their study of the of the statistical equilibrium of Li in cool stars., The possible importance of collisions with neutral hydrogen in non-LTE line formation calculations was first pointed out by \citet{1984A&A...130..319S} in their study of the of the statistical equilibrium of Li in cool stars.660 Although inelastic processes due to hydrogen collisions are expected to be much less efficient than those due to electrons. the much greater abundance of hydrogen atoms may overcome this reduced efficiency: in the line forming regions of a solar-type star the abundance of hydrogen atoms is typically four orders of magnitude greater than that of electrons. even more in metal-poor stars.," Although inelastic processes due to hydrogen collisions are expected to be much less efficient than those due to electrons, the much greater abundance of hydrogen atoms may overcome this reduced efficiency: in the line forming regions of a solar-type star the abundance of hydrogen atoms is typically four orders of magnitude greater than that of electrons, even more in metal-poor stars."661 At the time of Steenbock and Holweger's study there was practically no reliable experimental or theoretical work on inelastic hydrogen collision processes: however. the situation has been improving slowly but steadily over the quarter of a century since then.," At the time of Steenbock and Holweger's study there was practically no reliable experimental or theoretical work on inelastic hydrogen collision processes; however, the situation has been improving slowly but steadily over the quarter of a century since then."662 Their work prompted an experimental study by ? of Να»+H-Na(3p) at low (15-1500 eV) energies. though due to experimental difficulties not down to near the threshold (2.1 eV for this case). which ts the relevant regime for the temperatures of interest in cool stars.," Their work prompted an experimental study by \citet{FGSSV:91} of $\mathrm{Na}(3s) + \mathrm{H} \rightarrow \mathrm{Na}(3p) + \mathrm{H}$ at low (15--1500 eV) energies, though due to experimental difficulties not down to near the threshold (2.1 eV for this case), which is the relevant regime for the temperatures of interest in cool stars."663 Revised experimental data. including results down to 10 eV. were presented in 2..," Revised experimental data, including results down to 10 eV, were presented in \citet{BGHM:99}."664 This work was followed by a number of theoretical studies involving some of the present authors., This work was followed by a number of theoretical studies involving some of the present authors.665 First. quantum scattering calculations were performed for Na(3s)+Ha(3p.45) down to the threshold (?) and found good agreement with the experimental results above 10 eV. This work on Na+H was followed by calculations for Li+H (?) based on quantum-chemical data calculated by some of us (?)..," First, quantum scattering calculations were performed for $\mathrm{Na}(3s) + \mathrm{H} \rightarrow \mathrm{Na}(3p,4s) + \mathrm{H}$ down to the threshold \citep{BGHM:99} and found good agreement with the experimental results above 10 eV. This work on Na+H was followed by calculations for Li+H \citep{2003PhRvA..68f2703B} based on quantum-chemical data calculated by some of us \citep{CDG:99a}."666 This was followed by astrophysical application (??).. where it was found that excitation collisions LiGa/)+H—Li(n’/’)Η were unimportant. yet the ion-pair production and mutual-neutralisation process Li(3s)+H=Lr+H (often referred to as charge exchange in astrophysics) was found to be rather important. resulting in changes in spectral line strengths of around in cool. metal-poor. sub-giant stars.," This was followed by astrophysical application \citep{2003A&A...409L...1B,2009A&A...503..541L}, where it was found that excitation collisions $\mathrm{Li}(nl) + \mathrm{H} \rightarrow \mathrm{Li}(n'l') + \mathrm{H}$ were unimportant, yet the ion-pair production and mutual-neutralisation process $\mathrm{Li}(3s) +\mathrm{H} \rightleftharpoons \mathrm{Li}^+ +\mathrm{H}^-$ (often referred to as charge exchange in astrophysics) was found to be rather important, resulting in changes in spectral line strengths of around in cool, metal-poor, sub-giant stars."667 In a recent paper (2) we revisited low-energy Na-H collisions. since for astrophysical non-LTE modelling of Na line formation data for transitions between all possible Na levels are needed. while the earlier experimental and theoretical studies dealt primarily with the resonance transition (which corresponds to the Na D lines).," In a recent paper \citep{2010PhRvA..81c2706B} we revisited low-energy Na+H collisions, since for astrophysical non-LTE modelling of Na line formation data for transitions between all possible Na levels are needed, while the earlier experimental and theoretical studies dealt primarily with the resonance transition (which corresponds to the Na D lines)."668 Details of the calculations can be found in that paper., Details of the calculations can be found in that paper.669 Cross-sections for transitions between all ten levels up to and including the ionic state (10n-pair production) for collision energies from threshold to 10 eV were presented., Cross-sections for transitions between all ten levels up to and including the ionic state (ion-pair production) for collision energies from threshold to 10 eV were presented.670 In fact. cross-sections were calculated up to collision energies of 100 eV: however. the results at energies higher than 10 eV are of little importance at the temperatures of interest.," In fact, cross-sections were calculated up to collision energies of 100 eV; however, the results at energies higher than 10 eV are of little importance at the temperatures of interest."671 The purpose of this research note is to present rate coefficients calculated from these cross-sections. as these rate coefficients are needed for non-LTE applications such as in cool stars.," The purpose of this research note is to present rate coefficients calculated from these cross-sections, as these rate coefficients are needed for non-LTE applications such as in cool stars."672 The rate coefficients. (v). for excitation and deexcitation processes Na(n/)+HCcls)=Natal’)HOls). and for the ion-pair production and mutual-neutralisation processes involving the ionic state Nau)+H(ls)=Na(2s-2p%H. are presented in Table |..," The rate coefficients, $\langle \sigma v \rangle$, for excitation and deexcitation processes $\mathrm{Na}(nl) + \mathrm{H(1s)} \rightleftharpoons \mathrm{Na}(n'l') + \mathrm{H(1s)}$, and for the ion-pair production and mutual-neutralisation processes involving the ionic state $\mathrm{Na}(nl) + \mathrm{H(1s)} \rightleftharpoons \mathrm{Na}^+(2s^22p^6) + \mathrm{H}^- $, are presented in Table \ref{tab:rates}."673" The coefficients have been obtained by folding the cross-sections with a Maxwellian velocity ""Sistribution from threshold to 100 eV. and are presented for temperatures in the range 500-8000 K. The 500 K data are provided since there is substantial interest in. Na lines in. low temperature astrophysical environments such as brown dwarfs and planetary atmospheres (e.g.??).. and though other perturbers such as H» and He are usually more abundant in these situations. the data may be useful."," The coefficients have been obtained by folding the cross-sections with a Maxwellian velocity distribution from threshold to 100 eV, and are presented for temperatures in the range 500–8000 K. The 500 K data are provided since there is substantial interest in Na lines in low temperature astrophysical environments such as brown dwarfs and planetary atmospheres \citep[e.g.][]{RevModPhys.73.719,2002ApJ...569L..51B}, and though other perturbers such as $_2$ and He are usually more abundant in these situations, the data may be useful."674 ? have recently calculated data for inelastic processes in Na+He collisions with application to planetary and brown dwarf atmospheres in mind., \cite{PhysRevA.78.052706} have recently calculated data for inelastic processes in Na+He collisions with application to planetary and brown dwarf atmospheres in mind.675 However. the main driver behind our study is the need for data for line formation modelling in F. G and K star atmospheres where ground state hydrogen atoms," However, the main driver behind our study is the need for data for line formation modelling in F, G and K star atmospheres where ground state hydrogen atoms"676in Table AS aud Fie.,in Table \ref{tab:ld} and Fig.677 AT where wy=eL.CD/L.() and a-0.3.0.2.0.01.," \ref{f6} where $x_0=aL_*(3)/L_*(z)$ and a=0.3,0.2,0.04."678. At lower redshifts there are fewer recolmbinations iu the diffuse ος and therefore the required flux density to keep the universe ionized Increases With ducreasing redshift., At lower redshifts there are fewer recombinations in the diffuse medium and therefore the required flux density to keep the universe ionized increases with increasing redshift.679 If the universe has finished reionizing at.. then it will be kept ionized at 25 since the required LD at 2~5 is less than that αἲ aud the observed ones are close to each other.," If the universe has finished reionizing at, then it will be kept ionized at $z\sim5$ since the required LD at $z\sim5$ is less than that at and the observed ones are close to each other."680 Iu this paper. we have reported the results of a study of a large sample of faint LBGs in the redshift interval NFooiox7.0.," In this paper, we have reported the results of a study of a large sample of faint LBGs in the redshift interval $5.7<z<7.0$."681 Working ou the five deepest.LEST fields with their most updated data. we account for the effect of photometric errors by introducing the factor f as the probability of cach galaxy to be an LBC.," Working on the five deepest fields with their most updated data, we account for the effect of photometric errors by introducing the factor f as the probability of each galaxy to be an LBG."682" We employ ταιυπο] data to keep all the oeinformation aud to avoid bias. and we develop a modified AIL process to reduce the effect of the uncertain relation between AL and ii. Our best-fitting Schechter fiction parameters of the LLF at redshift are: a=Lartoll AL,=STE20.25ER £0.23. aud o.=4L7ποτa5ο«ή1037 37. which: sugeest evolution of M.. possible steepeuiug of a. and no change of o. compared to their values at i~3."," We employ un-binned data to keep all the information and to avoid bias, and we develop a modified ML process to reduce the effect of the uncertain relation between M and m. Our best-fitting Schechter function parameters of the rest-frame LF at redshift are: $\alpha=-1.87\pm0.14$, $M_*=-20.25\pm0.23$ , and $\phi_*=1.77^{+0.62}_{-0.49}\times 10^{-3}$ $^{-3}$, which suggest evolution of $M_*$ , possible steepening of $\alpha$, and no change of $\phi_*$ compared to their values at $z\sim3$."683 Such a steep slope suggests that galaxies. especially the faint ones are possibly the main sources of ionizing photons iu the universe at redshift six (Stiavellictal.200 1).," Such a steep slope suggests that galaxies, especially the faint ones, are possibly the main sources of ionizing photons in the universe at redshift six \citep{04stiavelli}. ."684. Combining ten previous studies at with the extended Press method. we find that the most probable LF favors 20.15<M.2005 and 190<a<1.55 at the coufidence level.," Combining ten previous studies at with the extended Press method, we find that the most probable LF favors $-20.45<M_*<-20.05$ and $-1.90<\alpha<-1.55$ at the confidence level."685 The LD has beeu found not to evolve siguificautlv between ux Do5. but considerable change is detected from to ~~V.," The LD has been found not to evolve significantly between and $z\sim5$, but considerable change is detected from to $z\sim3$."6862 Tf à remains constant from to 5~3 as state bv e.g.. Bowweusetal.(2007) aud Reddy&Steide(2009).. it will be difficult to tell the intrinsically evolving paraueter. M. or o.. from faint LBCs oul. while too few bright LDGs are found due to the limited areca of current deep survers.," If $\alpha$ remains constant from to $z\sim3$ as stated by e.g., \citet{07bouwens} and \citet{09reddy}, it will be difficult to tell the intrinsically evolving parameter, $M_*$ or $\phi_*$, from faint LBGs only, while too few bright LBGs are found due to the limited area of current deep surveys."687" Crouud-based surveys such as the Subaru Deep Field (Shiniasakuetal.2005:MceLurect2009) are extremely eficicut in detecting bright LBCs ina laree field of view and nüsht clarity whether AL or o, alone is not responsible for the change of LF. while splitting the αι. iuto two separate bands may be useful to isolate the effect of a possible slope steepeuime (Slimasakuetal.2005)."," Ground-based surveys such as the Subaru Deep Field \citep{05shi,09mclure} are extremely efficient in detecting bright LBGs in a large field of view and might clarify whether $M_*$ or $\phi_*$ alone is not responsible for the change of LF, while splitting the -band into two separate bands may be useful to isolate the effect of a possible slope steepening \citep{05shi}. ."688. We look forward to iucludiug IR data from WFEC?2 on boardLST to niprove the selection of LBG candidates. aud the bright eud of the LF will be better determined when the data frou CANDELS/ERS (e.g.Bowensetal.2010b) and the BoRG survey (Treutietal.2011) are becoming available.," We look forward to including IR data from WFC3 on board to improve the selection of LBG candidates, and the bright end of the LF will be better determined when the data from CANDELS/ERS \citep[e.g.,][]{10bbouwens} and the BoRG survey \citep{11trenti} are becoming available."689 JS and AIS have been partially supported by NASA erant NAC 5-12Lis., JS and MS have been partially supported by NASA grant NAG 5-12458.690 PO is supported by NASA through IIubble Fellowship erant IIE-51275.01., PO is supported by NASA through Hubble Fellowship grant HF-51278.01.691" Support for program #110632 and #111563 was provided by NASA through a eraut from the Space Telescope Science Iustitute. which is operated bw the Association of Universities for Research in Απομών Tne... uuder NASA contract NAS 5-26555,"," Support for program 10632 and 11563 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555."692" We asstune the photometric scatter is du a Gaussian distribution. thus the probability of a galaxy arriving on the detector as mmaguitude mi but cataloged in im’ equals aud the measured LE will be where o ds the actual LE. Ίνοι, Equation (7) iu Section ?? "," We assume the photometric scatter is in a Gaussian distribution, thus the probability of a galaxy arriving on the detector as magnitude $m$ but cataloged in $m'$ equals and the measured LF will be where $\phi$ is the actual LF, i.e., Equation (7) in Section \ref{sec:v} ."693When the photometric error 0 is verv suall G takes the Init of the Dirac function aud it is always true o!=o.," When the photometric error $\sigma$ is very small, $G$ takes the limit of the Dirac function and it is always true $\phi'\equiv\phi$."694 When the survers are pushed close to the detection luit. σ is not negligible aud also far from wuiform iu the magnitude window.," When the surveys are pushed close to the detection limit, $\sigma$ is not negligible and also far from uniform in the magnitude window."695 To satisfy SYN=10 at jiSan. aud S/N= at in=an|2.5. a guess would be Simulations show that the effect of dux boosting from faiuter magnitudes outside our selection window is negligible.," To satisfy $S/N=10$ at $m=m_*$ and $S/N=5$ at $m=m_*+2.5$, a guess would be Simulations show that the effect of flux boosting from fainter magnitudes outside our selection window is negligible."696 But as shown in Table AG.. if σι) increases much faster with jb. or if lower S/N candidates are included. there will © considerable steepeniug at the faint ead due to the photometric scattering.," But as shown in Table \ref{tab:boosting}, if $\sigma(m)$ increases much faster with $m$, or if lower S/N candidates are included, there will be considerable steepening at the faint end due to the photometric scattering."697 We simulate 1000 objects according o the given LE. paraiicters. ie. nn. is fixed aud a = -1.7 in [mans |05].," We simulate 4000 objects according to the given LF parameters, i.e., $m_*$ is fixed and $\alpha$ = -1.7 in $m_*$ $m_*$ +4.5]."698 Their magnitude errors are assmued o be iu the form of 109Man75) which comes frou the real data of the ΡΕ., Their magnitude errors are assumed to be in the form of $10^{0.3(m-m_*)}$ which comes from the real data of the HUDF.699 For cach realization. the change of uaenitudes brought bv their errors will also chanee their detected S/N. We ΠΤΙchoose those with the S/N 5aud linewithin |mi«-2.5.n 2.5) to determine the slope.," For each realization, the change of magnitudes brought by their errors will also change their detected S/N. We choose those with the $>$ 5and lyingwithin$m_*$ $m_*$ +2.5] to determine the slope."700 This process repeats for differeut combinations of S/N 5. 7. 9 and a —-1.5.-L7. -1.9.," This process repeats for different combinations of $>$ 5, 7, 9 and $\alpha$ = -1.5, -1.7, -1.9."701 We can see from Table AG that ifthe S/N is kept > 5. the steepeningof the faint cud slope by the Hux boosting is less than 0.1.," We can see from Table \ref{tab:boosting} that if the S/N is kept $>$ 5, the steepeningof the faint end slope by the flux boosting is less than 0.1."702correlations between these parameters. and we have a number of constraints to be obeyed (Sect. 2.4)).,"correlations between these parameters, and we have a number of constraints to be obeyed (Sect. \ref{sect:constraints}) )."703 In summary. these constraints are: We define as usual a quantity y givenby where O; and AO; is the observed LETGS ratio and the associated uncertainty of the Sirius B to the HZ 43A spectrum. and M; is the predicted ratio based on our model.," In summary, these constraints are: We define as usual a quantity $\chi^2$ givenby where $O_i$ and $\Delta O_i$ is the observed LETGS ratio and the associated uncertainty of the Sirius B to the HZ 43A spectrum, and $M_i$ is the predicted ratio based on our model."704 We use the data points between 50-175 wwith a spacing of 5 aas derived in Sect. 2.1.., We use the data points between 50–175 with a spacing of 5 as derived in Sect. \ref{sect:letgs}.705 Whenever any of the constraints of Sect., Whenever any of the constraints of Sect.706 24x is violated. we formally add to y a large number (1000) in order to discard that solution.," \ref{sect:constraints} is violated, we formally add to $\chi^2$ a large number (1000) in order to discard that solution."707 However. as it is more likely that our constraints are near the expected value than at their extremes. we add for each of the above five constraints a nominal Ay? to (4)) corresponding to the number of standard deviations for that constraint.," However, as it is more likely that our constraints are near the expected value than at their extremes, we add for each of the above five constraints a nominal $\Delta\chi^2$ to \ref{eqn:chisq}) ) corresponding to the number of standard deviations for that constraint."708 We find the best solution using a Monte Carlo method., We find the best solution using a Monte Carlo method.709 Starting with a broad range of allowed parameters. we draw random sets of parameters within that allowed range. anc evaluate y for each set.," Starting with a broad range of allowed parameters, we draw random sets of parameters within that allowed range, and evaluate $\chi^2$ for each set."710 Solutions with y larger than a threshold are discarded., Solutions with $\chi^2$ larger than a threshold are discarded.711 After having obtained a sufficient number of solutions. we slowly decrease the y thresholc and simultaneously shrink the allowed parameter space. encompassing with some margin all solutions that up to ther have been acceptable.," After having obtained a sufficient number of solutions, we slowly decrease the $\chi^2$ threshold and simultaneously shrink the allowed parameter space, encompassing with some margin all solutions that up to then have been acceptable."712 All acceptable solutions are stored. anc after having reached the best solution with y=Uu we find the errors on the parameters by finding for each parameter the minimum and maximum value for which y«Vain+|.," All acceptable solutions are stored, and after having reached the best solution with $\chi^2=\chi^2_{\min}$ we find the errors on the parameters by finding for each parameter the minimum and maximum value for which $\chi^2<\chi^2_{\min}+1$."713 We also store each acceptable spectrum. so we can also determine for each wavelength the range of allowed flux values.," We also store each acceptable spectrum, so we can also determine for each wavelength the range of allowed flux values."714 For Sirius B we have used homogeneous models. which include à pure hydrogen atmosphere as limiting case.," For Sirius B we have used homogeneous models, which include a pure hydrogen atmosphere as limiting case."715 We have also calculated a grid. of stratified models for Sirius B. but we were not able to obtain successful fits.," We have also calculated a grid of stratified models for Sirius B, but we were not able to obtain successful fits."716 Basically. we constrained the photometric hydrogen column to the range of (1.00—1.25)x107M... around the value of 1.13x107 ffound by ? for this class of models.," Basically, we constrained the photometric hydrogen column to the range of $(1.00-1.25)\times 10^{-13}$, around the value of $1.13\times 10^{-13}$ found by \citet{holberg1998} for this class of models."717 The main reason for the failure is that the stratified models show a flux deficit of up to a factor of 2-3 around 50 aas compared to homogeneous models (see also Fig. 2)):, The main reason for the failure is that the stratified models show a flux deficit of up to a factor of 2–3 around 50 as compared to homogeneous models (see also Fig. \ref{fig:hlaag}) );718 the deficit sets on below 80Α., the deficit sets on below 80.719. As this range was at the short wavelength end of the EUVE spectrometer. ? were not able to exclude this class of models completely.," As this range was at the short wavelength end of the EUVE spectrometer, \citet{holberg1998} were not able to exclude this class of models completely."720 Thanks to the sensitivity of Chandra it is now possible to rule out this class of models., Thanks to the sensitivity of Chandra it is now possible to rule out this class of models.721 For HZ 43A we first consider the homogeneous models., For HZ 43A we first consider the homogeneous models.722 ? have put strict upper limits to the amount of He in HZ 43A. based on the limits to the 304 lline of in the EUVE spectrum.," \citet{barstow1995} have put strict upper limits to the amount of He in HZ 43A, based on the limits to the 304 line of in the EUVE spectrum."723 The nominal equivalent width of this line derived by Barstow et al., The nominal equivalent width of this line derived by Barstow et al.724 is 0.240.1 Á.. but due to possible systematic effects in the EUVE spectrum this cannot be regarded as a detection.," is $\pm$ 0.1, but due to possible systematic effects in the EUVE spectrum this cannot be regarded as a detection."725 For their mixed He/H models. they obtain an upper limit of 3x107’ for the He/H ratio.," For their mixed He/H models, they obtain an upper limit of $3\times72610^{-7}$ for the He/H ratio."727 We have calculated a grid of homogeneous models with He/H ratio’s between 0 and 107°., We have calculated a grid of homogeneous models with He/H ratio's between 0 and $10^{-5}$.728 Our models with a small ratio such as found by ? yield fluxes in the Chandra band Aj) that are 1.42.7 smaller than the fluxes for à pure H model. for the same values of Tj and g.," Our models with a small ratio such as found by \citet{barstow1995} yield fluxes in the Chandra band (10--180 ) that are 1.4–2.7 smaller than the fluxes for a pure H model, for the same values of $T_{\mathrm{eff}}$ and $g$."729 It is clear that such small differences can be easily accommodated for in à pure H model using slightly different values for 7. and ο. which are still consistent with the limits from other parts of the spectrum to these numbers.," It is clear that such small differences can be easily accommodated for in a pure H model using slightly different values for $T_{\mathrm{eff}}$ and $g$, which are still consistent with the limits from other parts of the spectrum to these numbers."730 We conclude that — at least for our calibration purposes — we can safely adopt a pure hydrogen model as far as the class of homogeneous models is concerned., We conclude that – at least for our calibration purposes – we can safely adopt a pure hydrogen model as far as the class of homogeneous models is concerned.731 The other important class of models that include He are the stratified models., The other important class of models that include He are the stratified models.732 We have made a grid of models with a hydrogen layer mass between 1077 and 107! M..., We have made a grid of models with a hydrogen layer mass between $10^{-14}$ and $10^{-10}$ .733 All models with a hydrogen layer less than 107 pproduce too deep He features in the spectrum. consistent with the findings of ?..," All models with a hydrogen layer less than $10^{-13}$ produce too deep He features in the spectrum, consistent with the findings of \citet{barstow1995}. ."734 On the other hand. if the hydrogen layer mass," On the other hand, if the hydrogen layer mass"735With the benefit of hindsight it can be argued that even the second gravitational lens discovered. PGI1154-080 (Weymann et al.,"With the benefit of hindsight it can be argued that even the second gravitational lens discovered, PG1115+080 (Weymann et al."736 1980). foreshadowed what has turned into an embarrassment of riches — a superabundance of quadruply imaged quasars.," 1980), foreshadowed what has turned into an embarrassment of riches – a superabundance of quadruply imaged quasars."737 But only with the advent of systematic lens surveys (King and Browne 1996; Rusin and Tegmark 2001) has it become clear that the high ratio of quadruple to double systems ts not an artifact of observational selection and therefore presents a genuine challenge to our understanding of lensing of galaxies., But only with the advent of systematic lens surveys (King and Browne 1996; Rusin and Tegmark 2001) has it become clear that the high ratio of quadruple to double systems is not an artifact of observational selection and therefore presents a genuine challenge to our understanding of lensing of galaxies.738 Furthermore. individual fits on a system-by-system basis often require large amplitude (0.1-0.3) external shear (HoggandBlandford1994:Schechtereta£.1997:rientos 1998).. significantly higher than values of 0.02-0.05 expected (Keeton. Kochanek and Seljak 1997; henceforth KKS) from large seale structure or nearby galaxies.," \nocite{weymann80,rusin01,king96} Furthermore, individual fits on a system-by-system basis often require large amplitude (0.1-0.3) external shear \citep{hogg94,schechter97,kneib00,fischer98}, significantly higher than values of 0.02-0.05 expected (Keeton, Kochanek and Seljak 1997; henceforth KKS) from large scale structure or nearby galaxies."739 There are three factors that will probably have some part to play in the ultimate resolution of these problems: galaxy ellipticities. shear due to random superpositions of mass along the line of sight. and shear due to structures that are associated with the lens galaxy.," \nocite{blandford87,kochanek87,turner84}740 There are three factors that will probably have some part to play in the ultimate resolution of these problems: galaxy ellipticities, shear due to random superpositions of mass along the line of sight, and shear due to structures that are associated with the lens galaxy."741 In this paper we concentrate on the shear from associated structures., In this paper we concentrate on the shear from associated structures.742 The relative importance of tides and ellipticity has been considered by KKS., The relative importance of tides and ellipticity has been considered by KKS.743 In computing the expected tidal shear they consider three contributions: a) random shear due to unassociated foreground and background structure. b) the effect of associated galaxies. through the two point correlation function. and c) the effect of clusters of galaxies. with a term proportionalto the number density of clusters.," In computing the expected tidal shear they consider three contributions: a) random shear due to unassociated foreground and background structure, b) the effect of associated galaxies, through the two point correlation function, and c) the effect of clusters of galaxies, with a term proportionalto the number density of clusters."744 In the present paper we take a different tack to estimate the expected tidal shear due to nearby structures.," \nocite{keeton97}745 In the present paper we take a different tack to estimate the expected tidal shear due to nearby structures."746 We use the GIF Project recipe (Kauffmann et al., We use the GIF Project recipe (Kauffmann et al.747 1999) for galaxy formation within a cold dark matter (CDM) simulation. to compute the shear expected along random lines of sight. in the directions of galaxies. and specifically in the directions of early-type galaxies. which appear to be the predominant type of lens galaxy.," 1999) for galaxy formation within a cold dark matter (CDM) simulation to compute the shear expected along random lines of sight, in the directions of galaxies, and specifically in the directions of early-type galaxies, which appear to be the predominant type of lens galaxy."748 In this way. the effects of correlated structure are naturally included. without artificial distinctions between different types of structures. and we can also include the clustering properties of different types of galaxies.," In this way, the effects of correlated structure are naturally included, without artificial distinctions between different types of structures, and we can also include the clustering properties of different types of galaxies."749 This is similar to recent work by White.Hernquist.andSpringel(20010. where a high resolution hydrodynamical simulation was used to find typical values of external shear at the positions of typical galaxies. rather than specifically at the positions of massive early-type galaxies.," This is similar to recent work by \citet{white01}, where a high resolution hydrodynamical simulation was used to find typical values of external shear at the positions of typical galaxies, rather than specifically at the positions of massive early-type galaxies."750 In 2 we outline our methods for using the GIF simulations to estimate the effects of correlated structure on the statistics of external shear m gravitational lens systems., In 2 we outline our methods for using the GIF simulations to estimate the effects of correlated structure on the statistics of external shear in gravitational lens systems.751" In 3 we describe two selection effects which will further increase the typical external shear measured in quadruple gravitational lens systems: high shear systems have a larger cross-section for quadruple lensing (which is partly offset by ""magnification bias”) and regions of high external shear are likely to be regions of higher convergence. due to large scale structure."," In 3 we describe two selection effects which will further increase the typical external shear measured in quadruple gravitational lens systems; high shear systems have a larger cross-section for quadruple lensing (which is partly offset by “magnification bias”) and regions of high external shear are likely to be regions of higher convergence, due to large scale structure."752 We finish with a discussion of the consequences of our calculations for various problems associated with quadruply imaged systems., We finish with a discussion of the consequences of our calculations for various problems associated with quadruply imaged systems.753 Studies of cosmic shear have noted shear of a few percent (Baconetal.32001:VanWaerbekeαἰ.20010:Wittmanefaf2000). from studies of weak distortions of background galaxies.," Studies of cosmic shear have noted shear of a few percent \citep{bacon01,vanwaerbeke01,wittman00} from studies of weak distortions of background galaxies."754 This result can not be directly applied to estimates of typical shear values for lens systems because a strong gravitational lens is not at a random position in the sky but is instead at the position of a fairly massive galaxy. typically an early-type (elliptical or SO) galaxy (Keeton.Kochanek.andFaleo 1998).," This result can not be directly applied to estimates of typical shear values for lens systems because a strong gravitational lens is not at a random position in the sky but is instead at the position of a fairly massive galaxy, typically an early-type (elliptical or S0) galaxy \citep{keeton98}."755. Such galaxies are known to be located preferentially in overdense regions. where it would also be expected that the typical shear would be higher.," Such galaxies are known to be located preferentially in overdense regions, where it would also be expected that the typical shear would be higher."756 To estimate the effects of large scale structure that 15 correlated with the lens galaxies. we used the publicly available simulations from the GIFProject!.," To estimate the effects of large scale structure that is correlated with the lens galaxies, we used the publicly available simulations from the GIF."757. The simulations provide the dark matter distribution as well as estimates of the positions. velocities. luminosities and colors of galaxies (Kauffmannefal. 1999).," The simulations provide the dark matter distribution as well as estimates of the positions, velocities, luminosities and colors of galaxies \citep{kauffmann99}."758. The galaxy information ts derived from à semr-analytic model of galaxy formation., The galaxy information is derived from a semi-analytic model of galaxy formation.759" The simulation box was 141.3 h Mpe (comoving) on a side. the 256? particles each had a mass of 14«10/957!M|... the gravitational softening length was 20/7! kpc. and the cosmological model was a flat universe with QO,,20.3.0420.9.520.7.D 20.21."," The simulation box was 141.3 $h^{-1}$ Mpc (comoving) on a side, the $^3$ particles each had a mass of $\times 10^{10} h^{-1} M_\odot$, the gravitational softening length was $20 h^{-1}$ kpc, and the cosmological model was a flat universe with $\Omega_m=0.3, \sigma_8=0.9,h=0.7,760\Gamma=0.21$ ."761 We made projected mass maps of the outputs at z20.42 at a, We made projected mass maps of the outputs at $z=0.42$ at a762everything outside of this region constitutes the PCFOV.,everything outside of this region constitutes the PCFOV.763" We then determine the offset as a function of detection significance in both FCFOV and PCFOV, for all objects in question, allowing us to estimate the 90% PSL confidence by adaptively binning the measured offsets in significance in order to have the same Statistics for all bins (100 measurements per bin)."," We then determine the offset as a function of detection significance in both FCFOV and PCFOV, for all objects in question, allowing us to estimate the $90\%$ PSL confidence by adaptively binning the measured offsets in significance in order to have the same statistics for all bins (100 measurements per bin)."764 Around 25000 and 75000 individual offset measurements are used in the FCFOV and PCFOV analyses respectively., Around 25000 and 75000 individual offset measurements are used in the FCFOV and PCFOV analyses respectively.765" The results are shown in Figure 1 with the solid line representing the confidence limit, whilst the dashed line shows the result from ? and the dashed-dotted line shows the theoretical PSLA as defined by ?.."," The results are shown in Figure \ref{fig:PSLA} with the solid line representing the confidence limit, whilst the dashed line shows the result from \cite{gros} and the dashed-dotted line shows the theoretical PSLA as defined by \cite{goldwurm01}."766" Note that the theoretical PSLA of ? applies only for on-axis sources, whilst the estimated 9096 PSLA from ? is derived for sources within 14 degrees of the telescope axis."," Note that the theoretical PSLA of \cite{goldwurm01} applies only for on-axis sources, whilst the estimated $90\%$ PSLA from \cite{gros} is derived for sources within 14 degrees of the telescope axis."767" In order to fit the estimated 90% PSLA we have used the form y=ax*+b (the same as used by ?)), and applied the same weights for all bins as they contain the same number of observations."," In order to fit the estimated $90\%$ PSLA we have used the form $y=ax^{c}+b$ (the same as used by \citealt{gros}) ), and applied the same weights for all bins as they contain the same number of observations."768" Similarly for completeness we also estimated the 65%, 95% and 99% PSLA."," Similarly for completeness we also estimated the $65\%$, $95\%$ and $99\%$ PSLA."769" The fit parameters for all estimated PSLA are shown in Table 1,, whilst we display only the 9096 PSLA in Figure 2.."," The fit parameters for all estimated PSLA are shown in Table \ref{all_fits}, whilst we display only the $90\%$ PSLA in Figure \ref{fig:PnF}."770 These empirical fits can now be used in order to estimate the improvement in radius and area between the previously published fit of ? and our own estimates., These empirical fits can now be used in order to estimate the improvement in radius and area between the previously published fit of \cite{gros} and our own estimates.771" To this end, Figure 2 shows once again our fits for the PSLA for the FCFOV and PCFOV and the ? result."," To this end, Figure \ref{fig:PnF} shows once again our fits for the PSLA for the FCFOV and PCFOV and the \cite{gros} result."772 To demonstrate the decrease in error radius between the ? result and our new updated PSLA we simply subtract the two fits in order to display the error radius improvement., To demonstrate the decrease in error radius between the \cite{gros} result and our new updated PSLA we simply subtract the two fits in order to display the error radius improvement.773" This is shown in Figure 3,, where it can be seen that the biggest reduction in radius occurs at approximately 10a—150."," This is shown in Figure \ref{fig:IMP1}, where it can be seen that the biggest reduction in radius occurs at approximately $10\sigma - 15\sigma$."774" The potential for reducing false matches when performing follow-up observations of such objects in other wavebands is however best shown in Figure 4,, where the percentage area improvement of the error circle is shown."," The potential for reducing false matches when performing follow-up observations of such objects in other wavebands is however best shown in Figure \ref{fig:IMP2}, where the percentage area improvement of the error circle is shown."775 This is defined to be the area subtended by our 90% PSLA as a function of significance divided by the area subtended by the 90% PSLA estimate of ?.., This is defined to be the area subtended by our $90\%$ PSLA as a function of significance divided by the area subtended by the $90\%$ PSLA estimate of \cite{gros}.776" Here the biggest reduction occurs in the range 200—250, where the area to inspect reduces by ~50% from the previous ? result."," Here the biggest reduction occurs in the range $20\sigma - 25\sigma$, where the area to inspect reduces by $\approx 50\%$ from the previous \cite{gros} result."777 This would be a typical significance for a transient detection in a single ScW of a source of ~ 250mCrab., This would be a typical significance for a transient detection in a single ScW of a source of $\sim 250$ mCrab.778" We therefore predict that these transient detections will benefit the most from this improved PSLA, where the probability of false matches for observations will be drastically reduced."," We therefore predict that these transient detections will benefit the most from this improved PSLA, where the probability of false matches for follow-up observations will be drastically reduced."779most Likely occurs in the accretion disk. we smear both reflected. continu and irou-EK cimission line by the} kerucl (Fabianetal.1989).,"most likely occurs in the accretion disk, we smear both reflected continuum and iron-K emission line by the kernel \citep{Fab89}."780. The ποιο» radius su; Is set as a free parameter by assundne an eluissivitylaw of pr. for a fixed outer radius ri=1055.," The innermost radius $r_{\rm in}$ is set as a free parameter by assuming an emissivitylaw of $r^{-3}$ for a fixed outer radius $r_{\rm out} =78110^5 r_{\rm g}$."782 When coustraimiue ry. we utilize oulv the NIS spectra around the iron-Is baud (39 keV for the NIS-FIs aud 3δ keV for the NIS-DI) aud fix all the other parameters except for the nonualization.," When constraining $r_{\rm in}$, we utilize only the XIS spectra around the iron-K band (3–9 keV for the XIS-FIs and 3–8 keV for the XIS-BI) and fix all the other parameters except for the normalization."783" Thus. the spectral fitis performed by iteration: after rg, is determined frou the AIS-oulv fit. it is then fixed when finally determining the continui parameters in the NIS|PIN fit."," Thus, the spectral fitis performed by iteration; after $r_{\rm in}$ is determined from the XIS-only fit, it is then fixed when finally determining the continuum parameters in the XIS+PIN fit."784 The results of the spectral fit to the individual spectra iu epochs 1 and 2 are sununuarzed in Table 1.., The results of the spectral fit to the individual spectra in epochs 1 and 2 are summarized in Table \ref{tab_s}.785 Figure 1. shows the XIS|PIN spectra folded by the energv responses. over which the best-fit models are plotted. with residuals iu the lower panel.," Figure \ref{F_spec} shows the XIS+PIN spectra folded by the energy responses, over which the best-fit models are plotted, with residuals in the lower panel."786 The expanded fieure of the NIS spectra between 3/9 keV in epoch 1. is plotted in Figure 5.., The expanded figure of the XIS spectra between 3–9 keV in epoch 1 is plotted in Figure \ref{Fe}.787 To eiipliasize the irou-Is line feature. the residuals when the line is excluded. from the model are shown in the lower panel of this &gure.," To emphasize the iron-K line feature, the residuals when the line is excluded from the model are shown in the lower panel of this figure."788 From epoch 1. we obtain P21.6140.05. E=80! keV. and R=0.18£ 0.0L ," From epoch 1, we obtain $\Gamma = 1.61\pm0.05$, $E_{\rm cut} = 80^{+36}_{-19}$ keV, and $R = 0.18\pm0.04$ ."789The innermost radius is constrainedM to be ry=012002031075.) from the NIS data.," The innermost radius is constrained to be $r_{\rm in} = 720 r_{\rm g}790(> 340 r_{\rm g})$ from the XIS data."791 For the analvsis of the epoch 2 spectra. we assiune the same parameters of the reflection component (ncludiug its absolute flux) as those found frou the epoch 1 data. since it is very unlikely that it varied ou such a short time scale of <10! sec.," For the analysis of the epoch 2 spectra, we assume the same parameters of the reflection component (including its absolute flux) as those found from the epoch 1 data, since it is very unlikely that it varied on such a short time scale of $< 10^4$ sec."792 The parameters of the absorption are fixed to the epoch 1 values as well., The parameters of the absorption are fixed to the epoch 1 values as well.793 Thus. only free parameters are D. Pow. aud the normalization.," Thus, only free parameters are $\Gamma$, $E_{\rm cut}$, and the normalization."794 Finally. we also perform spectral fit to the time-averaged Swift/BAT spectrums by adopting the same model.," Finally, we also perform spectral fit to the time-averaged /BAT spectrum by adopting the same model."795 The reflection strength is fixed at R=0.18 referring to the epoch 1 result., The reflection strength is fixed at $R=0.18$ referring to the epoch 1 result.796 The best-fit model is over-plotted iu Figure 2.. whose parameters are sununarized in Table 1..," The best-fit model is over-plotted in Figure \ref{bat_spec}, whose parameters are summarized in Table \ref{tab_s}."797 From the above analysis. we find no siguificaut differences iu the spectral parameters (except for the j0riualization) within the statistical errors between the epoch 1. epoch 2. aud Suift/BAT data. although here i a hint that the spectrum became slightly softer iu epoch 2.," From the above analysis, we find no significant differences in the spectral parameters (except for the normalization) within the statistical errors between the epoch 1, epoch 2, and /BAT data, although there is a hint that the spectrum became slightly softer in epoch 2."798 Thus. to best coustrain the continu xuanieters. m particular the cutoff energv. woe studv he spectra (either of the two epochs) iu the 60 keV band audSwiff spectrum in the Lt195 keV ancl smnmultaueouslbv. in all following analysis.," Thus, to best constrain the continuum parameters, in particular the cutoff energy, we study the spectra (either of the two epochs) in the 1–60 keV band and spectrum in the 14–195 keV band simultaneously, in all following analysis."799 The fiux rormalization between the (XIS-FIs) aud BAT spectra are set free. to take iuto account the time variability.," The flux normalization between the (XIS-FIs) and BAT spectra are set free, to take into account the time variability."800 In analyzing the spectra of epoch 2. we always fix the reflection componcut to that determined from the epoch 1 data.," In analyzing the spectra of epoch 2, we always fix the reflection component to that determined from the epoch 1 data."801 Table 2. sununarizes the results using the same phenomenological model (cutoff power hav) as adopted in sectiou ??.., Table \ref{tab_rfcut} summarizes the results using the same phenomenological model (cutoff power law) as adopted in section \ref{Suzaku_spec}.802 For epoch 2. we consider two extreme cases as the cause of the spectral variability frou epoch 1 that (1) oulv the continuum chauged without change of the absorber and that (2) only the absorber changed with the same continu except for its normalization.," For epoch 2, we consider two extreme cases as the cause of the spectral variability from epoch 1 that (1) only the continuum changed without change of the absorber and that (2) only the absorber changed with the same continuum except for its normalization."803 We obtain similarly good fits for the two cases. aud thus both possibilities are plausible from the spectral analysis.," We obtain similarly good fits for the two cases, and thus both possibilities are plausible from the spectral analysis."804 Iu reality. however. it mav be difficult to explain such a short time (<104 sec) variability by the absorber alone.," In reality, however, it may be difficult to explain such a short time $<10^4$ sec) variability by the absorber alone."805 If the absorber makes Kepler motion at —1000 ry. a typical location of the broad lino region in ACUNS. if moves only  py i 101 see. by assuming the black hole mass of 103AL...," If the absorber makes Kepler motion at $\sim$ 1000 $r_{\rm g}$, a typical location of the broad line region in AGNs, it moves only $\sim$ $r_{\rm g}$ in $10^4$ sec, by assuming the black hole mass of $10^{7.8}$."806 Thus. unless the cmitting region is extremely small (like < several ry). it is mulikely that crossing blobs in the liue of sight can cause the large variability as observed.," Thus, unless the emitting region is extremely small (like $<$ several $r_{\rm g}$ ), it is unlikely that crossing blobs in the line of sight can cause the large variability as observed."807" Tn this subsection. we analyze the spectra of LC 50.55 with a physically motivated model instead of the phenomenological ""cutoff power law” model. which is a dnathematical approximation of the N-vayv spectra of AGNs."," In this subsection, we analyze the spectra of 4C 50.55 with a physically motivated model instead of the phenomenological “cutoff power law” model, which is a mathematical approximation of the X-ray spectra of AGNs."808 Such analysis of ACN spectra has Όσοι very limited so far. since it requires high quality broad baud data.," Such analysis of AGN spectra has been very limited so far, since it requires high quality broad band data."809 As we will discuss in section ??.. the contribution frou the jet compoucuts is very sinall in the X-ray baud.," As we will discuss in section \ref{differ_SED}, the contribution from the jet components is very small in the X-ray band."810 Hence. we consider that the origin of the continuum cnussion is predominantly thermal Comptonization of soft (ultra-violet)photons off hot electrons in the coroua occated above the accretion disk.," Hence, we consider that the origin of the continuum emission is predominantly thermal Comptonization of soft (ultra-violet)photons off hot electrons in the corona located above the accretion disk."811 Accordingly. we adopt thermal Comptonization model. (Zvckict 1999).. for the primary continui.," Accordingly, we adopt a thermal Comptonization model, \citep{Zyc99}, , for the primary continuum."812 It has two free paralcters. the slope DP aud electrou. temperature KT...," It has two free parameters, the slope $\Gamma$ and electron temperature $kT_{\rm e}$ ."813" The electron scattering optical depth τι is related to T, and P by the following formula L9OSO}::", The electron scattering optical depth $\tau_{\rm e}$ is related to $T_{e}$ and $\Gamma$ by the following formula \citep{Sun80}: :814ligure 2.. for κι=100 and 500. when no smoothing is applied.,"Figure \ref{temperature_smart_scale_fig}, for $f_{\rm NL}=100$ and $500$, when no smoothing is applied."815 Points in the figure are averages over 200 realizations. errorbars are the le run-to-run estimates roni the simulations. and solid lines are from. equation (15)).," Points in the figure are averages over 200 realizations, errorbars are the $\sigma$ run-to-run estimates from the simulations, and solid lines are from equation \ref{one_d_pdf_fnl}) )."816 Note that. although the non-Gaussian term in (15)) is complicated. by the inclusion. of S.uti suti itself is independent of the threshold. level: this will be important or the next considerations.," Note that, although the non-Gaussian term in \ref{one_d_pdf_fnl}) ) is complicated by the inclusion of $S^{(0)}$, $S^{(0)}$ itself is independent of the threshold level; this will be important for the next considerations."817 With the one-dimensional PDF at hand. a number of well-known properties in the context of Gaussian random ields. such as the mean size and frequency of occurrence of he excursion sets above a given level (Coles Barrow 1987: Ixogut et al.," With the one-dimensional PDF at hand, a number of well-known properties in the context of Gaussian random fields, such as the mean size and frequency of occurrence of the excursion sets above a given level (Coles Barrow 1987; Kogut et al."818 1995). can be easily generalized to fp models.," 1995), can be easily generalized to $f_{\rm NL}$ models."819 We will present this analysis in a following paper. while here we focus primarily on the pixel clustering statistics.," We will present this analysis in a following paper, while here we focus primarily on the pixel clustering statistics."820 The correlation of the excursion sets above a threshold vis given by (Ixaiser 1984): where and with pj.fto.0) being the two-dimensional PDI and ie—an()0)=(up) the correlation.," The correlation of the excursion sets above a threshold $\nu$ is given by (Kaiser 1984): where and with $p(\mu_1,\mu_2,w)$ being the two-dimensional PDF and $w \equiv w (\theta) = \langle \mu_1 \mu_2 \rangle$ the correlation."821 There have been attempts in the literature to generalize equation (16)) to non-Gaussian cases., There have been attempts in the literature to generalize equation \ref{corr_smart}) ) to non-Gaussian cases.822 For example. Berry (1973). Jones (1996) and Barreivo et al. (," For example, Berry (1973), Jones (1996) and Barreiro et al. ("8231998). write prisο.0) as: so that (160) is simply given by: Expression (20)) implies that one can fully characterize the clustering statistics above (below) threshold using only the knowledge of the one-dimensional PDE (15)) and. the correlation.,"1998) write $p(\mu_1,\mu_2,w)$ as: so that \ref{corr_smart}) ) is simply given by: Expression \ref{cf_wrong_eq}) ) implies that one can fully characterize the clustering statistics above (below) threshold using only the knowledge of the one-dimensional PDF \ref{one_d_pdf_fnl}) ) and the correlation."824 Unfortunately. this tov model cannot be applied in our context: equation (20)) is valid when mw is small. which is not true in our case.," Unfortunately, this toy model cannot be applied in our context; equation \ref{cf_wrong_eq}) ) is valid when $w$ is small, which is not true in our case."825 lnstead. since we are interested in. weak non-Caussianity. we expect a bivariate IExlgeworth expansion to provide a reasonably good description at low thresholds: where A=(jypape) and Equation (21)) is the two-dimensional version of the clistribution (15)) see also Ixotz. Balakrishnan Johnson (2000) and Lam Sheth (2009).," Instead, since we are interested in weak non-Gaussianity, we expect a bivariate Edgeworth expansion to provide a reasonably good description at low thresholds: where $\lambda = \langle \mu_1^2 \mu_2 \rangle \equiv \langle \mu_1826\mu_2^2 \rangle$ and Equation \ref{2d_edge_eq}) ) is the two-dimensional version of the distribution \ref{one_d_pdf_fnl}) ) – see also Kotz, Balakrishnan Johnson (2000) and Lam Sheth (2009)."827 Note that ie and A must be evaluated numerically., Note that $w$ and $\lambda$ must be evaluated numerically.828 By inserting (15)) and (21)) into (16)). it is possible to characterize the clustering strength of pixels abovebelow threshold for weak non-Gaussianity.," By inserting \ref{one_d_pdf_fnl}) ) and \ref{2d_edge_eq}) ) into \ref{corr_smart}) ), it is possible to characterize the clustering strength of pixels above/below threshold for weak non-Gaussianity."829 When fxj=0 (ie. in the Gaussian limit) equation (21)) reduces to the usual bivariate Gaussian cistribution. since eS!=0 and A=0.," When $f_{\rm NL}=0$ (i.e. in the Gaussian limit) equation \ref{2d_edge_eq}) ) reduces to the usual bivariate Gaussian distribution, since $\sigma S^{(0)} \equiv 0$ and $\lambda \equiv 0$."830 Therefore (163) reduces to the well-known formula: where with C' is the input power spectrum. and WW;sneoelhi is the window function which includes all the additional smoothing.," Therefore \ref{corr_smart}) ) reduces to the well-known formula: where with $C_{\rm \ell}$ is the input power spectrum, and $W_{\rm \ell}^{smooth}$ is the window function which includes all the additional smoothing."831 The excursion set. statistics belongs to a more. general ‘lass of geometrical estimators. which retain information n the spatial distribution of the non-Gaussian signal.," The excursion set statistics belongs to a more general class of geometrical estimators, which retain information on the spatial distribution of the non-Gaussian signal."832 In lis respect. it is related. to many other commonly. used opological estimators.," In this respect, it is related to many other commonly used topological estimators."833 For example. since the distribution of peaks with CAB temperatures above/below a given weshold is a subset of the pixel distribution. there is a irect. correspondence between the excursion sets anc the »eak statistics.," For example, since the distribution of peaks with CMB temperatures above/below a given threshold is a subset of the pixel distribution, there is a direct correspondence between the excursion sets and the peak statistics."834 In. presence of weak non-Ciaussianitv. it is relatively straightforward to repeat the steps illustrated in 10 previous section for the peak. rather than the pixe ensemble.," In presence of weak non-Gaussianity, it is relatively straightforward to repeat the steps illustrated in the previous section for the peak, rather than the pixel ensemble."835 In fact. once the one- ancl two dimensional non-Gaussian PDEs are known (equations 15 and 21)). one only needs to impose an extra condition in order to select. loca maxima. but much of the logic remains the same.," In fact, once the one- and two dimensional non-Gaussian PDFs are known (equations \ref{one_d_pdf_fnl} and \ref{2d_edge_eq}) ), one only needs to impose an extra condition in order to select local maxima, but much of the logic remains the same."836 Hence. analytic expressions for the number density anc for the clustering strength above/below threshold can be obtainec for the peak statistics as well.," Hence, analytic expressions for the number density and for the clustering strength above/below threshold can be obtained for the peak statistics as well."837 We present a more detailec investigation of the peak clustering statistics. extended to non-Gaussian models. in a forthcoming publication: for an exhaustive treatment of the Gaussian case see instead. Bone Efstathiou (1987).," We present a more detailed investigation of the peak clustering statistics, extended to non-Gaussian models, in a forthcoming publication; for an exhaustive treatment of the Gaussian case see instead Bond Efstathiou (1987)."838 Similarly. other topological or geometrical estimators which utilize information concerning the morphology of the density structure are also. directly related to. the excursion set statistics.," Similarly, other topological or geometrical estimators which utilize information concerning the morphology of the density structure are also directly related to the excursion set statistics."839 This is for example the case of the Alinkowski funetionals (Schmalzing. Corski 1998: Winitzki Ixosowskv 1908: Bancay. Zaroubi Corski 2000: Llikage ct al.," This is for example the case of the Minkowski functionals (Schmalzing Gorski 1998; Winitzki Kosowsky 1998; Banday, Zaroubi Gorski 2000; Hikage et al."840 2006. 2008b: Matsubara 2010): the number cdensitv defined. in Section 2.3. is cllectively the first Alinkowski functional (ic. fraction of total area above the threshold). besides. some normalization. factors.," 2006, 2008b; Matsubara 2010); the number density defined in Section \ref{excursion_set_formalism} is effectively the first Minkowski functional (i.e. fraction of total area above the threshold), besides some normalization factors."841 The, The8422.5in,2.5in843central regious of LO galaxies.,central regions of 10 galaxies.844 The observations reported in this paper were obtained iu spring 2008 using the Redshift Search Receiver (RSR) ou the Five College Radio Astronomy Observatory (FCRAOQO) 1bin telescope., The observations reported in this paper were obtained in spring 2008 using the Redshift Search Receiver (RSR) on the Five College Radio Astronomy Observatory (FCRAO) 14-m telescope.845 The RSR is a sensitive. ultra-broad bandwidth receiver/spectrometer (Exicksonetal.2007) developed at the University of Massachusetts as a facility iunstruineut for the Όθ-αι diameter Large AlDllineter Telescope (Schloerb.2008).," The RSR is a sensitive, ultra-broad bandwidth receiver/spectrometer \citep{eri07} developed at the University of Massachusetts as a facility instrument for the 50-m diameter Large Millimeter Telescope \citep{sch08}."846.. This mstruneut was desigued primarily to measure the redshift of distaut. dust-obscured galaxies.," This instrument was designed primarily to measure the redshift of distant, dust-obscured galaxies."847 The RSR is a dual polarization and dual beam instruneut., The RSR is a dual polarization and dual beam instrument.848 The four broadbaud receivers cover instautancously the frequency range 71-111 Cz., The four broadband receivers cover instantaneously the frequency range 74-111 GHz.849 A high speed Faraday rotation beam switch. operating at L kilohertz. is used to overcome the1/f noise originating in the frout-end monolithic microwave integrated circuit (AIMOC) amplifiers.," A high speed Faraday rotation beam switch, operating at 1 kilohertz, is used to overcome the noise originating in the front-end monolithic microwave integrated circuit (MMIC) amplifiers."850 Following the MMIC! amplifiers. two wideband mixers couvert cach receiver band to two intermediate frequency (IF) chaunels.," Following the MMIC amplifiers, two wideband mixers convert each receiver band to two intermediate frequency (IF) channels."851 After further conversion and amplification. the IF signal is passed iuto an analog auto-correlation spectrometer.," After further conversion and amplification, the IF signal is passed into an analog auto-correlation spectrometer."852 Each analog correlator has a bandwidth of 6.5 CdIz aud there are six correlators for cach receiver polarization., Each analog correlator has a bandwidth of 6.5 GHz and there are six correlators for each receiver polarization.853 To obtain the best frequency resolution. we do not apodize the lag domain signal before transforming to the frequency domain.," To obtain the best frequency resolution, we do not apodize the lag domain signal before transforming to the frequency domain."854 Without this apodization. απ with other auto-correlation based spectrometers. a ringing effect can be seen in the baselines around strong. narrow lines.," Without this apodization, as with other auto-correlation based spectrometers, a ringing effect can be seen in the baselines around strong, narrow lines."855 The RSR has been designed to detect weak relatively broad ines. dn which case this riugius is uot a problem.," The RSR has been designed to detect weak relatively broad lines, in which case this ringing is not a problem."856 In several of the spectra preseuted here. the lue is sufficiently strong. that this ringiug adds additional baseline noise near the line.," In several of the spectra presented here, the line is sufficiently strong, that this ringing adds additional baseline noise near the line."857 The RSR has au iustautaneous bandwidth of 37 GIIz with a resolution of 31 MIIz. or a velocity resolution of approximately LOO in the 3 nuu waveleugth baud.," The RSR has an instantaneous bandwidth of 37 GHz with a resolution of 31 MHz, or a velocity resolution of approximately 100 in the 3 mm wavelength band."858 The RSR was conunissioned on the FCRAO Llau elescope in 2007 aud 2008 and used for several initial science projects., The RSR was commissioned on the FCRAO 14-m telescope in 2007 and 2008 and used for several initial science projects.859 During the time of the observations reported here. 12 of the final 21 spectrometers were available. which permitted beam switching with the ull 37 GIIz bandwidth in a single polarization.," During the time of the observations reported here, 12 of the final 24 spectrometers were available, which permitted beam switching with the full 37 GHz bandwidth in a single polarization."860 During collissiouing observations. there was a small hardware issue (which has since been diagnosed and fixed) which xoduced anomalous noise at approximately 92 CGIIz. aud a sul region around this frequeney has been blauked iu uauv of the spectra preseuted here.," During commissioning observations, there was a small hardware issue (which has since been diagnosed and fixed) which produced anomalous noise at approximately 92 GHz, and a small region around this frequency has been blanked in many of the spectra presented here."861 Observations were obtained at the positious of the LO ealaxies listed in Table 1., Observations were obtained at the positions of the 10 galaxies listed in Table 1.862 Distances in Table 1 for he nearbv galaxies. NGC 253. Matter 2. IC312 aud AIS2. are from Waracheutsey(2005). and cistauces. for he amore distant galaxies are from the NASA/TPAC Extragalactic Database.," Distances in Table 1 for the nearby galaxies, NGC 253, Maffei 2, IC342 and M82, are from \citet{kar05} and distances for the more distant galaxies are from the NASA/IPAC Extragalactic Database."863 The galaxies were selected xmuuiv because they were well studied. ando had relatively bright inolecular cussion lines. nuportaut or verifving the performauce of the RSR.," The galaxies were selected primarily because they were well studied and had relatively bright molecular emission lines, important for verifying the performance of the RSR."864 Since our observations cover the cutive 3 nua waveleneth window with uniform sensitivity. we can study the previously detected lines aud all other lines within frequency rauge of the RSR.," Since our observations cover the entire 3 mm wavelength window with uniform sensitivity, we can study the previously detected lines and all other lines within frequency range of the RSR."865 We added to the list of bright line galaxies sole additional weak-line galaxies to further test the performance of the RSR aud uiui of these additional ealaxies are known to host an active galactic uucleus CAGN)., We added to the list of bright line galaxies some additional weak-line galaxies to further test the performance of the RSR and many of these additional galaxies are known to host an active galactic nucleus (AGN).866 Also included in the table is the total integration time speut on cach galaxy., Also included in the table is the total integration time spent on each galaxy.867 The observations were taken over varying atinospheric couditions. so our broad ais were to achieve a relatively uniform seusitivitv of about 1 auk or to achieve a sigual to noise in the PCO line of 10.," The observations were taken over varying atmospheric conditions, so our broad aims were to achieve a relatively uniform sensitivity of about 1 mK or to achieve a signal to noise in the $^{13}$ CO line of 10."868 NGC 3079 and NGC 6210 did not show strong lines. so we spent additional tine on these sources to lower the noise to better than 0.5 mlx. The observatious for each galaxy were obtained over several observing sessionis and combined together.," NGC 3079 and NGC 6240 did not show strong lines, so we spent additional time on these sources to lower the noise to better than 0.5 mK. The observations for each galaxy were obtained over several observing sessions and combined together."869 The pointing and calibration was repeatedly checked by observations of the contimmiun cluission from planets and quasars., The pointing and calibration was repeatedly checked by observations of the continuum emission from planets and quasars.870 Poiutiug offsets were never more than a few arcsecouds. a siuall faction of the bea size. aud the overall fix calibration is repeatable to be better than 10%.," Pointing offsets were never more than a few arcseconds, a small fraction of the beam size, and the overall flux calibration is repeatable to be better than 10."871. Also included in Table 1 are some brief notes regarding the properties of the ceutral regions of the galaxies in our sample., Also included in Table 1 are some brief notes regarding the properties of the central regions of the galaxies in our sample.872 The molecular cussion in mauy of these galaxies is doimuünated by their nuclear starburst., The molecular emission in many of these galaxies is dominated by their nuclear starburst.873 Both NGC 6210 and Arp 220 are ultra huninous infrared galaxies (ULIRGS)., Both NGC 6240 and Arp 220 are ultra luminous infrared galaxies (ULIRGS).874 NGC 100δ. NCC 1258 aud NCC 6210 all have Seyfert 2 uuclei: however. the emission we observe iu NGC 1068is likely dominated by the surrounding nuclear starburst rine (Schinuercretal.2000).," NGC 1068, NGC 4258 and NGC 6240 all have Seyfert 2 nuclei; however, the emission we observe in NGC 1068is likely dominated by the surrounding nuclear starburst ring \citep{sch00}."875. NGC 1258 is a weak AGN. but has a pair of radio jets that iav be influencing the molecular emission (Ixrauseetal.2007).," NGC 4258 is a weak AGN, but has a pair of radio jets that may be influencing the molecular emission \citep{kra07}."876. NGC 6210 is the merger of two Sevfert 2 host ealaxies where the two ACNs are separated by less than aand the molecular chussion is concentrated i a small reeion centered on the Sevtert nuclei (Ionoetal.2007)., NGC 6240 is the merger of two Seyfert 2 host galaxies where the two AGNs are separated by less than and the molecular emission is concentrated in a small region centered on the Seyfert nuclei \citep{ion07}.877. Finally we uote that NGC 3690 is in the process of mereing with IC 691 (the system is called Arp 299 or \Ivk 171)., Finally we note that NGC 3690 is in the process of merging with IC 694 (the system is called Arp 299 or Mrk 171).878 The unelei of NGC 3690 aud IC 691 ave separated by only ν 20 arcsecouds and both nuclei have an ACN (Carcfa-Marinetal.2006)., The nuclei of NGC 3690 and IC 694 are separated by only $\backsim$ 20 arcseconds and both nuclei have an AGN \citep{gar06}.879. The aand IICUN cinission from the IC 691Ὁ nucleus is much stronger than that from the NCC 3690 nucleus (Aaltoetal. 1997):: thus. although we are centered. on NGC 3690. the emission mav have a contribution from IC 691.," The and HCN emission from the IC 694 nucleus is much stronger than that from the NGC 3690 nucleus \citep{aal97}; thus, although we are centered on NGC 3690, the emission may have a contribution from IC 694."880 Unfortunatelv. the emission. from both nuclei is at approximately the same velocity. so velocity caunot be used to separate the enissious within our telescope beau.," Unfortunately, the emission from both nuclei is at approximately the same velocity, so velocity cannot be used to separate the emissions within our telescope beam."881 One linitation of the RSR for the observations presented in this paper is the relatively simall throw of the beam switch., One limitation of the RSR for the observations presented in this paper is the relatively small throw of the beam switch.882 The reference beam is oulv offset bv 1.31 arcnün in azimuuth., The reference beam is only offset by 4.34 arcmin in azimuth.883 Thus. for the largest galaxies. such as IC 312 or NGC 253. the reference bean nav contain weak cussion from molecular clouds in the ealactic disk.," Thus, for the largest galaxies, such as IC 342 or NGC 253, the reference beam may contain weak emission from molecular clouds in the galactic disk."884 However. the cluission falls off sharply from the central reeious. aud even in the largest ealaxics. the emission in the reference bean is more than 10 times weaker than that at the center of the galaxy. (Youngetal.1995).," However, the emission falls off sharply from the central regions, and even in the largest galaxies, the emission in the reference beam is more than 10 times weaker than that at the center of the galaxy \citep{you95}."885. As a check on lue fluxes we compared the iutegrated intensity of the conussion. which of the Hues we observe has the greatest poteutial for disk contamination. iu the four galaxies (IC BIZ NGC 253. NGC 1068 aud. NGC 3079) that were ii conuuon with the study of Paelionectal. (2001)..," As a check on line fluxes we compared the integrated intensity of the emission, which of the lines we observe has the greatest potential for disk contamination, in the four galaxies (IC 342, NGC 253, NGC 1068 and NGC 3079) that were in common with the study of \citet{pag01}. ."886 Paglioueetal.(2001). also used the FCRAO 11 m telescope: however they obtained their observations by, \citet{pag01} also used the FCRAO 14 m telescope; however they obtained their observations by887The HOS arc-detection algorithm is based on application of the SExtractor (Berlin Arnouts 1996) object identification software.,The H05 arc-detection algorithm is based on application of the SExtractor (Bertin Arnouts 1996) object identification software.888 The output of repeated SExtractor calls. using different detection parameters ezich time. is filtered using some threshold of object elongation.," The output of repeated SExtractor calls, using different detection parameters each time, is filtered using some threshold of object elongation."889" T1ο tinal SExtractor call is executed on an image combined from he filtered “segmentation image"" outputs of the previous calls.", The final SExtractor call is executed on an image combined from the filtered “segmentation image” outputs of the previous calls.890 Tqe are candidates detected in tha last call are included in the final are catalogue if they meet the required detection parameters detined by the user., The arc candidates detected in that last call are included in the final arc catalogue if they meet the required detection parameters defined by the user.891 The SBO7 algoritim is based on light moments., The SB07 algorithm is based on light moments.892 Tje image is divided into small cells which are iteratively movec to their local light centres., The image is divided into small cells which are iteratively moved to their local light centres.893 Then. for each cell. an ellipticity vector is calculated using light moments.," Then, for each cell, an ellipticity vector is calculated using light moments."894 Adjacent cells with similarly oriented ellipticity vectors are joined together and considered as part of an are candidate. whose outer boundary is determined by an active contour method.," Adjacent cells with similarly oriented ellipticity vectors are joined together and considered as part of an arc candidate, whose outer boundary is determined by an active contour method."895 Candidates are accepted if they conform to specified parameters., Candidates are accepted if they conform to specified parameters.896 In the present work. we apply an acceptance criterion on are length-to-width ratio of 7w2:8.," In the present work, we apply an acceptance criterion on arc length-to-width ratio of $l/w \geq 8$."897 We also use a magnitude limit of m5.24 as another acceptance criterion which. given the exposure times of our sample. results in the detection ofares with signal-to-noise S/N=3.," We also use a magnitude limit of $m \leq 24$ as another acceptance criterion which, given the exposure times of our sample, results in the detection ofarcs with signal-to-noise $S/N \ga 3$."898 Our magnitude limit is higher than most of the magnitude limits used in previous studies. such as B98 and Zaritsky Gonzales 2003. allowing us to include fainter ares in our analysis.," Our magnitude limit is higher than most of the magnitude limits used in previous studies, such as B98 and Zaritsky Gonzales 2003, allowing us to include fainter arcs in our analysis."899 Nevertheless. our acceptance threshold for are detections is brighter than the are detection limits of all the images. with their range of exposure times and filters. thus permitting a meaningful comparison of are statisties among the various subsamples.," Nevertheless, our acceptance threshold for arc detections is brighter than the arc detection limits of all the images, with their range of exposure times and filters, thus permitting a meaningful comparison of arc statistics among the various subsamples."900 This holds also for the WFPC? images of the XBACS sample., This holds also for the WFPC2 images of the XBACS sample.901 AI1ough WFPC? was less sensitive than ACS. the WFPC? exposure times were longer. typically 7000 s. leading to similar depths.," Although WFPC2 was less sensitive than ACS, the WFPC2 exposure times were longer, typically 7000 s, leading to similar depths."902 Furthermore. the somewhat lower angular resolution of WFPC?. due to its larger pixels (01). is not important. since the ares we consider are always much larger. and all the ares we find beow in ACS images would have been detected in long WFPC? exposures as well.," Furthermore, the somewhat lower angular resolution of WFPC2, due to its larger pixels $0\farcs 1$ ), is not important, since the arcs we consider are always much larger, and all the arcs we find below in ACS images would have been detected in long WFPC2 exposures as well."903 We note that we use total-magnitude limit for ares. rather than considering surface brightness. which could also plausibly be used.," We note that we use total-magnitude limit for arcs, rather than considering surface brightness, which could also plausibly be used."904 We do this to conform with previous observationa and theoretical studies. but also because ares. especially at HST resolution. display rich structure and unresolved clumps. and hence it is not clear that mean surface brightness would be a more relevan observabe.," We do this to conform with previous observational and theoretical studies, but also because arcs, especially at HST resolution, display rich structure and unresolved clumps, and hence it is not clear that mean surface brightness would be a more relevant observable."905 Due to the varving position of the cluster centres within the FOV. the cluster coverage area varies.," Due to the varying position of the cluster centres within the FOV, the cluster coverage area varies."906" We therefore also limi our seare1 to a 60"" radius from the cluster centre.", We therefore also limit our search to a $60''$ radius from the cluster centre.907 The automated are detecion results were visually inspected in order to remove false positives such as spikes from saturated stars. galaxy spira arms. and edge-on galaxies.," The automated arc detection results were visually inspected in order to remove false positives such as spikes from saturated stars, galaxy spiral arms, and edge-on galaxies."908 While most of the ares in our sample are detected by both programs. a few unmistakable lensed arcs are picked out by only one or the other.," While most of the arcs in our sample are detected by both programs, a few unmistakable lensed arcs are picked out by only one or the other."909 The SBO7 arefinder is more sucessful than the HOS arefinder in detecting ares that are superimposed on the light of cluster galaxies., The SB07 arcfinder is more sucessful than the H05 arcfinder in detecting arcs that are superimposed on the light of cluster galaxies.910" On the other hand. the HOS arctinder produce a better ""segmentation"" compared to the SBO7 arctinder. wdich sometimes breaks ares into smaller arclets. which then do not qualify as giant ares."," On the other hand, the H05 arcfinder produce a better “segmentation” compared to the SB07 arcfinder, which sometimes breaks arcs into smaller arclets, which then do not qualify as giant arcs."911 We defer a more detailed comparison of tlese and other arctinders to a future study., We defer a more detailed comparison of these and other arcfinders to a future study.912 Figure | shows the ACS images of the clusters in which ares are detected. and Figure 2 provides zoom-ins on the individual arc features.," Figure 1 shows the ACS images of the clusters in which arcs are detected, and Figure 2 provides zoom-ins on the individual arc features."913 Table 6 lists the properties of the detected ares. which we discuss in more detail below.," Table 6 lists the properties of the detected arcs, which we discuss in more detail below."914!!! In the MACS sample we identify a total of 26 ares in 12 out of the 23 low-redshift clusters. and a total of 16 ares in 9 out of the 12 medium-redshift clusters.," In the MACS sample we identify a total of $26$ arcs in $12$ out of the $23$ low-redshift clusters, and a total of $16$ arcs in $9$ out of the $12$ medium-redshift clusters."915 All but 3 of these ares (in two clusters) have not been previously reported (see Table 6)., All but 3 of these arcs (in two clusters) have not been previously reported (see Table 6).916 The ares span a magnitude of range20«m24 and a//w ratio range of 8 29.," The arcs span a magnitude range of $20 <917m < 24$ and a $l/w$ ratio range of $8-29$ ."918 As, As919second one.,second one.920" The source background was measured within a circle with radius 95"" located far frou the source.", The source background was measured within a circle with radius $''$ located far from the source.921 The ancillary response file was generated with the task (v0.5.2) within (Blackburn 1995). and accounts for both extraction region aud PSF pile-up correction.," The ancillary response file was generated with the task (v0.5.2) within (Blackburn 1995), and accounts for both extraction region and PSF pile-up correction."922 We used the latest spectral redistribution iiriees in the Calibration (CALDB 2.3) maintained by TEASARC., We used the latest spectral redistribution matrices in the Calibration (CALDB 2.3) maintained by HEASARC.923 We also extracted the spectral and time-scrics data of this source collected with the coded-auask ISCRI detector (Lebrun et al., We also extracted the spectral and time-series data of this source collected with the coded-mask ISGRI detector (Lebrun et al.924 2003) of the IBIS instiuneut onboardI, 2003) of the IBIS instrument onboard.925"NTEGRAL, ISCRI data were processed. using the standard analysis software v5.1: Coldwur et al.", ISGRI data were processed using the standard analysis software v5.1; Goldwurm et al.926 2003): events in the band 17300 keV. conmüug from both fully-coded and partiallv-coded observations of the field of viewof IGOR 2810. were considered in the analysis.," 2003); events in the band 17–300 keV, coming from both fully-coded and partially-coded observations of the field of view of IGR $-$ 2810, were considered in the analysis."927 The time resolution for these data was that typical of IBIS science. windows (2 ks)., The time resolution for these data was that typical of IBIS science windows $\sim$ 2 ks).928 Details ou. the whole procedure can be found iu Bird et al. (, Details on the whole procedure can be found in Bird et al. (9292007).,2007).930 Tard X.rav long-term light curves aud a tinic-averaged spectrum were then obtained from the available data and using the uethod described in Bird et al. (, Hard X–ray long-term light curves and a time-averaged spectrum were then obtained from the available data and using the method described in Bird et al. (9312006. 2007). for a total of 161 ks ou-source collected in the time iuterval October 2002 - April 2006.,"2006, 2007), for a total of 461 ks on-source collected in the time interval October 2002 - April 2006."932 One imediuniresolutiou optical spectrum of the star in the XRT error box (see Fie., One medium-resolution optical spectrum of the star in the /XRT error box (see Fig.933 1 aud Sect., 1 and Sect.934" 1) was acquired starting at 19:00 UT of 22 July 2005 with the L.9-metre ""Radcliffe telescope located near Sutherland. South Africa."," 4) was acquired starting at 19:00 UT of 22 July 2005 with the 1.9-metre “Radcliffe"" telescope located near Sutherland, South Africa."935 The exposure time was 300 s. This telescope carries a spectrograph mounted at the Casscerain focus: the iustrumieut was equipped with a «266 pixel οΤο CCD., The exposure time was 300 s. This telescope carries a spectrograph mounted at the Cassegrain focus; the instrument was equipped with a $\times$ 266 pixel SITe CCD.936 Crating #77 aud a slit of 178 were used. providing a 38h07200 noninal spectral coverage.," Grating 7 and a slit of $\farcs$ 8 were used, providing a 3850–7200 nominal spectral coverage."937 This setup gave a dispersion of 2.3 fpix., This setup gave a dispersion of 2.3 /pix.938 The spectrum. after correction for flat-ficld. bias and cosmic-ray rejection. was backerouncd subtracted and optimally extracted (Ilorue 1986) usingIRAF!.," The spectrum, after correction for flat-field, bias and cosmic-ray rejection, was background subtracted and optimally extracted (Horne 1986) using."939 Waveleneth calibration was performed using Cu-Ar lamps. while flux calibration was accomplished by using the spectrophotometric standards CD /— 3279927 aud LTT 377 (Ibuuux ct al.," Wavelength calibration was performed using Cu-Ar lamps, while flux calibration was accomplished by using the spectrophotometric standards CD $-$ $^\circ$ 9927 and LTT 377 (Hamuy et al."940 1992. 1991).," 1992, 1994)."941 Wavelength calibration uncertainty was ~0.5As this was checked by using the positions of backeround nieht skv lines., Wavelength calibration uncertainty was $\sim$ 0.5; this was checked by using the positions of background night sky lines.942 Ouly one Nrav source was found in both NRT observations within the 3/5 IBIS error box of ICR 2810 (Bird et al., Only one X–ray source was found in both XRT observations within the $\farcm$ 5 IBIS error box of IGR $-$ 2810 (Bird et al.943 2007)., 2007).944 Usine the data of NRT obs., Using the data of XRT obs.945 1 (i... the deeper one). we determined the position of TGR 2810 uxiug the (v0.2.7) task.," 1 (i.e., the deeper one), we determined the position of IGR $-$ 2810 using the (v0.2.7) task."946 The correction for the uisalienent between the telescope and the satellite optical axis was taken iuto account (sce Moretti et al., The correction for the misalignment between the telescope and the satellite optical axis was taken into account (see Moretti et al.947 2006 for details}., 2006 for details).948" The coordinates we obtained for the source are the following (12000): RA = 16"" 199"" 3329: Dec = 28 077 ιο (with a confidence level error of 375 ou both coordinates).", The coordinates we obtained for the source are the following (J2000): RA = $^{\rm h}$ $^{\rm m}$ $\fs$ 29; Dec = $-$ $^\circ$ $'$ $\farcs$ 8 (with a confidence level error of $\farcs$ 5 on both coordinates).949 This position is filly consistent with the one (sce Fig., This position is fully consistent with the one (see Fig.950 l1: thus. we cau confideutlv sav that these three Xrav objects (theINTEGRAL. the aud the ones) are the same.," 1): thus, we can confidently say that these three X–ray objects (the, the and the ones) are the same."951 Ouly the brightest of the optical sources within theROSAT evor box. object USNO-A2.0 TOG00_220227091. at coordinates (J2000) RA = 165 199 332363: Dec = 28° O77 39702 (with au error of 0/2 on both coordinates: Deutsch 1999: Assafiuet al.," Only the brightest of the optical sources within the error box, object USNO-A2.0 20227091, at coordinates (J2000) RA = $^{\rm h}$ $^{\rm m}$ $\fs$ 363; Dec = $-$ $^\circ$ $'$ $\farcs$ 02 (with an error of $\farcs$ 2 on both coordinates: Deutsch 1999; Assafin et al."952" 2001). is contained in the NRT uncertaimtv circle. a 2"" froii the NRT ceutroicd."," 2001), is contained in the XRT uncertainty circle, at $''$ from the XRT centroid."953 The inspection of the optical spectrmu of this objec (reported in Fig., The inspection of the optical spectrum of this object (reported in Fig.954 2) clearly shows the typical features of a A\Ltype star (Jaschek Jaschek 1987): it is dominated by TiO absorption bands and no ciission features typical of Xray binarics. such as Balmer aud Hoe lines. are reacilv apparent.," 2) clearly shows the typical features of a M-type star (Jaschek Jaschek 1987): it is dominated by TiO absorption bands and no emission features typical of X–ray binaries, such as Balmer and He lines, are readily apparent."955 We also find. among the main spectral features. the Me absorption baud around 5170A.. the Ca line a 1226 and two atomic line blends of metal iutersvsteni lues of Fel. Ti1. Cv1. Bat. Car. Mal. Co aud Ni located at 6352 iud 6197 (see 6.8. Turushek et al.," We also find, among the main spectral features, the Mg absorption band around 5170, the Ca line at 4226 and two atomic line blends of metal intersystem lines of Fe, Ti, Cr, Ba, Ca, Mn, Co and Ni located at 6352 and 6497 (see e.g. Turnshek et al."956 1985)., 1985).957 A telluric absorption feature is moreover detecte at GSTOΑ., A telluric absorption feature is moreover detected at 6870.958". A jurow IL, lue is detected im absorption. although with possible wider emission wines (see nmsot iu Fie."," A narrow $_\alpha$ line is detected in absorption, although with possible wider emission wings (see inset in Fig."959 2). similarly to what found by Caudeuzi Polcaro (1999) in the optical spectrum of IU 1700121.," 2), similarly to what found by Gaudenzi Polcaro (1999) in the optical spectrum of 4U 1700+24."960" IIowever. eiven that the same profile is seen in the telluric feature at GSTOA.. we believe tha this is more due to au effect produced bv the stellar cutinuun shape. rather than to the actual presence of emission wines around the IL, absorption."," However, given that the same profile is seen in the telluric feature at 6870, we believe that this is more due to an effect produced by the stellar continuum shape, rather than to the actual presence of emission wings around the $_\alpha$ absorption."961 Usus the (Cuni Stryker 1983) aud. (Jacoby et al., Using the (Gunn Stryker 1983) and (Jacoby et al.962 1981) spectroscopy atlases. we then compared the spectrum) of star U(600.220227091 with those of several late-tvpe stars.," 1984) spectroscopy atlases, we then compared the spectrum of star 20227091 with those of several late-type stars."963 The best match is obtained with star BD 3271025 (of type M2IIID.. with no substantial intervening interstellar absorption.," The best match is obtained with star BD $-$ $^\circ$ 4025 (of type III), with no substantial intervening interstellar absorption."964 Thus. we classify C0G600_220227091 as a star of spectral type M2TITI.," Thus, we classify 20227091 as a star of spectral type III."965we could assess the accuracy of the result. of the inversion procedure. as shown in Figures (1) and (2).,"we could assess the accuracy of the result of the inversion procedure, as shown in Figures (1) and (2)."966 In working with real data. we require the introduction of an independen method of comparing our final result to the starting CALD. in order to check that the answer our inversion. procedure gives is a good answer.," In working with real data, we require the introduction of an independent method of comparing our final result to the starting CMD, in order to check that the answer our inversion procedure gives is a good answer."967 From our paper Lowe know tha when the stars being used in the inversion procedure were indeed. produced. from the isochrones and metallicity usec to construct the likelihood matrix. the inversion methoc gives accurate results.," From our paper I we know that when the stars being used in the inversion procedure were indeed produced from the isochrones and metallicity used to construct the likelihood matrix, the inversion method gives accurate results."968 The introduction of an independen comparison between our answer and the data is hence a wav of checking the accuracy of the input physics. usec in the inversion procedure. i.e. the IME. metallicity ane observational parameters.," The introduction of an independent comparison between our answer and the data is hence a way of checking the accuracy of the input physics used in the inversion procedure, i.e. the IMF, metallicity and observational parameters."969 The most common procedure of comparing a certain SRG) with an observed CAID is to use the S£) to generate a synthetic CALD. and compare this to the observations using a statistical test to determine the degree of similarity between the two.," The most common procedure of comparing a certain $SFR(t)$ with an observed CMD is to use the $SFR(t)$ to generate a synthetic CMD, and compare this to the observations using a statistical test to determine the degree of similarity between the two."970 The disadvantage however is that one is not comparing the STIO) with the data. but rather a particular realisation of the SER) with the cata.," The disadvantage however is that one is not comparing the $SFR(t)$ with the data, but rather a particular realisation of the $SFR(t)$ with the data."971 The. distinction. becomes arbitrary when large numbers ofstars ave found in all regions of the CMD. whieh is generally not the case.," The distinction becomes arbitrary when large numbers of stars are found in all regions of the CMD, which is generally not the case."972 Following a Davesian approach. we prefer to adopt the Wo statistic presented by Saha (1998). essentially where Bois the number of cells into which the CMD is split. and m; and s; are the numbers of points two distributions being compared. have in each cell.," Following a Bayesian approach, we prefer to adopt the $W$ statistic presented by Saha (1998), essentially where B is the number of cells into which the CMD is split, and $m_{i}$ and $s_{i}$ are the numbers of points two distributions being compared have in each cell."973 This asks [for the probability that two distinct. data sets are random realisations of the same uncderling distribution., This asks for the probability that two distinct data sets are random realisations of the same underling distribution.974 In implementing this test we first. produce a large. number (500) of random: realisations of our inferred S£720). and compute the Wo statistic between pairs in this sample of CADs.," In implementing this test we first produce a large number (500) of random realisations of our inferred $SFR(t)$, and compute the $W$ statistic between pairs in this sample of CMD's."975 This gives a distribution which is used to determine a range of values of H which are expected. to arise in random realisations of the S£A20) being tested., This gives a distribution which is used to determine a range of values of $W$ which are expected to arise in random realisations of the $SFR(t)$ being tested.976 Next the WV statistic is computed. between. the observed. data. set. and a new large number of random realisations of S4HR) (also 500). this gives a new distribution of M which can be objectively compared to the one arising from the moclel-model comparison to assess whether both data and modeled CMD's are compatible with a unique underling distribution.," Next the $W$ statistic is computed between the observed data set, and a new large number of random realisations of $SFR(t)$ (also 500), this gives a new distribution of $W$ which can be objectively compared to the one arising from the model-model comparison to assess whether both data and modeled CMD's are compatible with a unique underling distribution."977 Figure (5) shows a svnthetic CMD produced. (rom our inferred 5S4A2) For the solar neighbourhood. down to Ady= 3.15.," Figure (5) shows a synthetic CMD produced from our inferred $SFR(t)$ for the solar neighbourhood, down to $M_{V}=3.15$ ."978 This can be compared to the Hipparcos CMD complete to the same A limit of Figure (4)., This can be compared to the Hipparcos CMD complete to the same $M_{V}$ limit of Figure (4).979 A visual inspection reveals approximately equal numbers of stars in each of the distinct regions of the diagram. a more rigorous statistica comparison is also included.," A visual inspection reveals approximately equal numbers of stars in each of the distinct regions of the diagram, a more rigorous statistical comparison is also included."980 The right panel of Figure (5) shows a histogram of the values of the Wo statistic for 500 random realisations of our inferred SLR) in a modoel-mocde comparison., The right panel of Figure (5) shows a histogram of the values of the $W$ statistic for 500 random realisations of our inferred $SFR(t)$ in a model-model comparison.981 This gives the range of values of the V. statistic likely to appear in comparisons of two CMD diagrams arising [from the same underlving S/R). our inferre," This gives the range of values of the $W$ statistic likely to appear in comparisons of two CMD diagrams arising from the same underlying $SFR(t)$ , our inferred"982Stellar Li abundances are at once. very informative and dillieult to interpret.,Stellar Li abundances are at once very informative and difficult to interpret.983 This follows from the relative delicacy of Li nuclei in the shallow surface lavers of stars. where they are destroved via (p.a) reactions when they are mixed to regions with warm protons.," This follows from the relative delicacy of Li nuclei in the shallow surface layers of stars, where they are destroyed via $(p,\alpha)$ reactions when they are mixed to regions with warm protons."984 Li abundances in dwarl star photospheres are observed to correlate with effective temperature (Par). age. rotation. binarity and metallicity.," Li abundances in dwarf star photospheres are observed to correlate with effective temperature $_{\rm eff}$ ), age, rotation, binarity and metallicity."985 Llowever. even within a single coeval population (such as the open cluster M67) variations in Li abundance are observed among stars that otherwise appear identical (Ranelichetal. 2006).," However, even within a single coeval population (such as the open cluster M67) variations in Li abundance are observed among stars that otherwise appear identical \citep{rand06}."986. Some have suggested that the yrescnce Of a protoplanctary disk is the missing parameter that accounts for the observed spread in Li abundances among similar stars., Some have suggested that the presence of a protoplanetary disk is the missing parameter that accounts for the observed spread in Li abundances among similar stars.987 The the surface Li abundance ofa star could be altered via accretion of protoplanctary disk: material 1998) or via a change in its rotation (Chen&Zhao2006:Takedaetal. 2007a).," The the surface Li abundance of a star could be altered via accretion of protoplanetary disk material \citep{gg98} or via a change in its rotation \citep{chen06,tak07}."988. Phus. while Li has the potential to serve as à useful probe of stellar ancl planetary. processes. their ellects on Li abundances are cillicult to disentangle given our present level of understanding.," Thus, while Li has the potential to serve as a useful probe of stellar and planetary processes, their effects on Li abundances are difficult to disentangle given our present level of understanding."989 Nevertheless. several studies have attempted to isolate the cHeets of planets on Li abundance.," Nevertheless, several studies have attempted to isolate the effects of planets on Li abundance."990 Gonzalez&Laws(2000) first suggested. that stars with planets. (SWHDs). when corrected. for simple linear. trends with Tir. ancl age. clisplay smaller. Li abundances than field stars.," \citet{gl00} first suggested that stars with planets (SWPs), when corrected for simple linear trends with $_{\rm eff}$, and age, display smaller Li abundances than field stars."991 lixan(2000) examined the Li abundance trends more carefully. and concluded that any. possible cilferences. were not significant. Gonzalezetal.(2001).," \citet{ryan00} examined the Li abundance trends more carefully and concluded that any possible differences were not significant. \citet{gg01},"992.. emploving a larger sample. agreed. with his conclusion.," employing a larger sample, agreed with his conclusion."993 Israchianetal.(2004) revisited this topic and reported a significant depletion of Li among οἱος relative to a comparison star sample. but only in the Tir range 5600 to 5850 Ix. Takeda&Kawanomoto(2005) largely. confirmed heir findings for the Tay range 5800 to 5900 Ix. Chen&Zhao (2006).. restricting their attention to Ti= 5600 to 5900 Ix. also confirmed. the conclusions of Israclianctal. (2004).," \citet{is04} revisited this topic and reported a significant depletion of Li among SWPs relative to a comparison star sample, but only in the $_{\rm eff}$ range 5600 to 5850 K. \citet{tak05} largely confirmed their findings for the $_{\rm eff}$ range 5800 to 5900 K. \citet{chen06}, restricting their attention to $_{\rm eff} =$ 5600 to 5900 K, also confirmed the conclusions of \citet{is04}."994. Llowever. Luck&Heiter(2006).. emploving a Larger comparison star sample. did not find a significant dillerence ονους οΑς and a comparison sample.," However, \citet{luck06}, employing a larger comparison star sample, did not find a significant difference between SWPs and a comparison sample."995 They. attribute he Li abundance cillerence found by Israelianetal.(2004) ο à systematic difference in the temperature scales in their study and the study of Chenetal.(2001)... the results of which they had used to supplement their small comparison sample.," They attribute the Li abundance difference found by \citet{is04} to a systematic difference in the temperature scales in their study and the study of \citet{chen01}, the results of which they had used to supplement their small comparison sample."996 Most. recently. “Takedaetal.(2007a) measured. Li in LIS nearby solar analogs.," Most recently, \citet{tak07} measured Li in 118 nearby solar analogs."997 While they included only a few SWPs in their study. they again concluded that ολλος tend to have smaller Li abundances.," While they included only a few SWPs in their study, they again concluded that SWPs tend to have smaller Li abundances."998 The purpose of the present. study. is to resolve. the conllicting findings concerning Li abundances in SWIPs., The purpose of the present study is to resolve the conflicting findings concerning Li abundances in SWPs.999 Lt continues our series of studies on the chemical abundances of nearby SWPs (for a sumniary. of previous papers. see Gonzalez&Laws (2007)).," It continues our series of studies on the chemical abundances of nearby SWPs (for a summary of previous papers, see \citet{gl07}) )."1000 lo Gonzalez&Laws(2007) we combined the chemical abundance data from. multiple studies in à consistent way and compared the chemical abundances of SWPs and comparison stars for. several elements: we did not include Li in the comparison. because it requires a fundamentally different. analvsis.," In \citet{gl07} we combined the chemical abundance data from multiple studies in a consistent way and compared the chemical abundances of SWPs and comparison stars for several elements; we did not include Li in the comparison, because it requires a fundamentally different analysis."1001 We employ similar methods in the present study., We employ similar methods in the present study.1002 In Section 2 we present new samples of SWI's anc comparison stars formed. by combining the Li abundance results from multiple studies., In Section 2 we present new samples of SWPs and comparison stars formed by combining the Li abundance results from multiple studies.1003 In Section 3 we use these new samples to determine whether SWPsS have dillerent Li abundances than stars without detected planets;, In Section 3 we use these new samples to determine whether SWPs have different Li abundances than stars without detected planets.1004 We also examine vsini and the fig activity index in SWPs., We also examine vsini and the $R^{'}_{\rm HK}$ activity index in SWPs.1005 We discuss our findings within the, We discuss our findings within the1006from by ruining the images they analyzed through the most recent version of WSTphot and obtain mgpggow2LILzx0.19 mae.,from by running the images they analyzed through the most recent version of HSTphot and obtain $m_{\rm F606W}=24.44 \pm 0.19$ mag.1007 This is quite different from the original. published valuc. but is far more iu line with both of the mpsssy magnitudes.," This is quite different from the original, published value, but is far more in line with both of the $m_{\rm F555W}$ magnitudes."1008 AlLburall the ~V iaguitucdes for Object 7 are consistent. although: we cannot complete rule out some variability or eradual facing of the source over nearly the last two decades.," All-in-all, the $\sim V$ magnitudes for Object 7 are consistent, although we cannot complete rule out some variability or gradual fading of the source over nearly the last two decades."1009 We also obtained the STIS spectral data from theHST archive aud re-extracted the spectra using standard STSDAS routines within IRAF., We also obtained the STIS spectral data from the archive and re-extracted the spectrum using standard STSDAS routines within IRAF.1010 The portion of the spectrum including IIo is shown iu Figure 3.., The portion of the spectrum including $\alpha$ is shown in Figure \ref{figspec}.1011 Although the spectrum is nois. both a broad and a narrow component to the line are quite evident.," Although the spectrum is noisy, both a broad and a narrow component to the line are quite evident."1012 Similarly to(2011)... we analyzed the archival imud-IR data for NGC 1058. obtained usine the with both the IR Array Camera TRAC: 3.6. 15. 5.8. and 8.0 a) ancl the Multiband Band Photometer for Spitzer (MIPS: we analyzed the 21 san data onlv).," Similarly to, we analyzed the archival mid-IR data for NGC 1058, obtained using the with both the IR Array Camera (IRAC; 3.6, 4.5, 5.8, and 8.0 $\mu$ m) and the Multiband Band Photometer for (MIPS; we analyzed the 24 $\mu$ m data only)."1013 We considered the observations using both instruments from 20014 (CTO program 69: PI: C. Fazio) aud from 2007 (GO program 10619: PI: R. IKotax). aud assuming no variability for SN 1961V between these two epochs (f actually detected). we combined the data from these observatious for cach of the bands.," We considered the observations using both instruments from 2004 (GTO program 69; PI: G. Fazio) and from 2007 (GO program 40619; PI: R. Kotak), and assuming no variability for SN 1961V between these two epochs (if actually detected), we combined the data from these observations for each of the bands."1014 The data we analyzed corresponded to pipeline versions S18.7 for IRAC and 515.19 for MIPS., The data we analyzed corresponded to pipeline versions S18.7 for IRAC and S18.12 for MIPS.1015" We used the MOPEX package provided by the Science Center to mosaic the individual Basic Calibrated Data (BCDs: in fact. for TRAC we used the artifact-corrected CBCDs) to produce a single inge mosaic in cach band (for both IRAC and MIPS. we left the first frame out of cach set of observations when mosaicking. since it often has a far shorter exposure fine than the rest of the BCDs aud therefore adds mostly noise to the mosaic),"," We used the MOPEX package provided by the Science Center to mosaic the individual Basic Calibrated Data (BCDs; in fact, for IRAC we used the artifact-corrected CBCDs) to produce a single image mosaic in each band (for both IRAC and MIPS, we left the first frame out of each set of observations when mosaicking, since it often has a far shorter exposure time than the rest of the BCDs and therefore adds mostly noise to the mosaic)."1016 We also applied the array locatiou-depeudent photometric corrections to the IRAC CBCDs within MOPEX. although. given the uuber of CBCDs aud the adequate redundant coverage. this correction was not particularly portant iu the cud.," We also applied the array location-dependent photometric corrections to the IRAC CBCDs within MOPEX, although, given the number of CBCDs and the adequate redundant coverage, this correction was not particularly important in the end."1017 Although emission in all bands is detected from the environment. of SN 1961V. the emission in the resulting wosaics is diffuse.," Although emission in all bands is detected from the environment of SN 1961V, the emission in the resulting mosaics is diffuse."1018 As point out. ucither Object 7 nor any of ifs mnauuediate neighboriug sources are detected in any of the lauds.," As point out, neither Object 7 nor any of its immediate neighboring sources are detected in any of the bands."1019 Object 8. which is well separated from the SN 1961V. position. dominates the clnission from the environment at 8.0 jr.," Object 8, which is well separated from the SN 1961V position, dominates the emission from the environment at 8.0 $\mu$."1020" At 21 pan the spatial resolution is too poor to resolve which source. or sources, is the primary cutter iu the cuviromuent."," At 24 $\mu$ m the spatial resolution is too poor to resolve which source, or sources, is the primary emitter in the environment."1021 There is little point in aualvziug the relatively low-resolution. low-seusitivitv 70 jn data for the host galaxy.," There is little point in analyzing the relatively low-resolution, low-sensitivity 70 $\mu$ m data for the host galaxy."1022" We then used the routine APEX (Astronomical Poiut source EXtractor) Sinele Frame. with the ""user list™ input option. within MOPEX to perform aperture photometry at the exact position of SN 1961V. For the TRAC inosaics we used a 3.0-pixebradius aperture. with n annus for sky subtraction of radius 12.020.0 pixels. coluputing the skv background using the mode within je annulus."," We then used the routine APEX (Astronomical Point source EXtractor) Single Frame, with the “user list” input option, within MOPEX to perform aperture photometry at the exact position of SN 1961V. For the IRAC mosaics we used a 3.0-pixel-radius aperture, with an annulus for sky subtraction of radius 12.0–20.0 pixels, computing the sky background using the mode within the annulus."1023 For the MIPS 21 jnu mosaic we employed a 1.22-pixel-xadius aperture. with Ev auuulus of radius S.16.13.06 pixels.," For the MIPS 24 $\mu$ m mosaic we employed a 1.22-pixel-radius aperture, with sky annulus of radius 8.16–13.06 pixels."1024 We applied the aperture corrections for ιο IRAC bands for our aperture/auuulus coufiguration youn the online IRAC. Tustriunieut. Haudbook?))., We applied the aperture corrections for the IRAC bands for our aperture/annulus configuration from the online IRAC Instrument ).1025 Το deteriuue the correction for the MIPS aperture. we had also performed point response function (PRE) fitting photometry on the mosaic.," To determine the correction for the MIPS aperture, we had also performed point response function (PRF) fitting photometry on the mosaic."1026 We considered the PRE fixes of the two brightest stars. seen in tle mosaic well away from the body of the galaxy. as “truth.”," We considered the PRF fluxes of the two brightest stars, seen in the mosaic well away from the body of the galaxy, as “truth.”"1027 We then computed the ratio of the fluxes measured for these two stars through our apoerture/annulus configuration ancl the PRF fiuxes. i.e... LOO. and corrected the aperture flux at the SN 1961V. position by this ratio.," We then computed the ratio of the fluxes measured for these two stars through our aperture/annulus configuration and the PRF fluxes, i.e., 4.0:1.0, and corrected the aperture flux at the SN 1961V position by this ratio."1028 All of these upper limits to the detection of SN 1961V. are shown in Figure (, All of these upper limits to the detection of SN 1961V are shown in Figure \ref{figmir}. (1029Since these are ouly upper linits. we dispensed with applviug color corrections to both the TRAC aud MIPS photometry.),"Since these are only upper limits, we dispensed with applying color corrections to both the IRAC and MIPS photometry.)"1030 Our limits are comparable to. although generally higher than. those that have estimated.," Our limits are comparable to, although generally higher than, those that have estimated."1031" The pertinent values witli which to compare are those in thei Tables 2 aud 3. labelled ""SN1961V area” (particularly. their 3476-radius aperture measurements for IRAC). 1e. <0.026. <0.022. <O.079, «0.230. and «0.265 mJy (Cours) «023. <O.016. «0.069. «0.207. aud «0,226 unJv (theirs). at 3.6. 1.5. 5.8. 8.0. and 21 pan. respectively."," The pertinent values with which to compare are those in their Tables 2 and 3, labelled “SN1961V area” (particularly, their $3{\farcs}6$ -radius aperture measurements for IRAC), i.e., $<$ 0.026, $<$ 0.022, $<$ 0.079, $<$ 0.230, and $<$ 0.265 mJy (ours) $<$ 0.023, $<$ 0.016, $<$ 0.069, $<$ 0.207, and $<$ 0.226 mJy (theirs), at 3.6, 4.5, 5.8, 8.0, and 24 $\mu$ m, respectively."1032" One of the asstunptions mace by(2011).. as well as byauthors). is that the object detected in photographic alates back to the 1930s. prior to the 1960 ""S Dor-type eruption” aud the 1961 TIONS event was. in fact. the quiesceut progenitor."," One of the assumptions made by, as well as by, is that the object detected in photographic plates back to the 1930s, prior to the 1960 “S Dor-type eruption” and the 1961 luminous event was, in fact, the quiescent progenitor."1033 We are now iucreasinglv skeptical of this. and. iustead. we Bud it far more compelling to presume that the precursor star was already in a state of sustained outburst prior o the more energetic eruption in the 1960s 1999).," We are now increasingly skeptical of this, and, instead, we find it far more compelling to presume that the precursor star was already in a state of sustained outburst prior to the more energetic eruption in the 1960s ."1034. Clearly. this is difficult. if not impossible. to xove. due to the nonexisteuce of observations prior to he first available plates.," Clearly, this is difficult, if not impossible, to prove, due to the nonexistence of observations prior to the first available plates."1035 However. the BoV. color (σε0.6 mae) measured by from the 1951 Palomar Sky Survey plates is csscutially the same as he color during the outburst in 1961 and 19621965).. aud is the expected color of a LBV in an “eruptive state”1991).," However, the $B-V$ color $\simeq 0.6$ mag) measured by from the 1954 Palomar Sky Survey plates is essentially the same as the color during the outburst in 1961 and 1962, and is the expected color of a LBV in an “eruptive state”."1036. Furthermore. when the object was in its pre-outburst state at nijezmmpcml8 nae. even assunuues only Galactic foreground extinction1998).. it had Miom12.6 mag. which is well above the inodified Eddington limit. Af)=—1l mae1998)..," Furthermore, when the object was in its pre-outburst state at $m_{\rm pg} \approx m_B \simeq 18$ mag, even assuming only Galactic foreground extinction, it had $M_{\rm bol} \approx -12.6$ mag, which is well above the modified Eddington limit, $M_{\rm bol} \simeq -11$ mag."1037 The implication. therefore. is that the star was already super-Eddingtou in the decades leadiug up to theeiut. outburst.," The implication, therefore, is that the star was already super-Eddington in the decades leading up to thegiant outburst."1038 I£ Object 7 had an initial mass of 55 85M. (see below). then its preseut-dayniass would be ~25 10AZ.. aud. at its inferred preseut-day Iuninosity.," If Object 7 had an initial mass of $\sim 55$ $85\ M_{\odot}$ (see below), then its present-daymass would be $\sim\ 25$ $40\ M_{\odot}$ and, at its inferred present-day luminosity,"1039Galactic absorption. Le. f(£)=NEPeσινεμα where IL ds X-ray energy. (Ue) is photon flux given in units of photons | = ot. P is photon index. A ids the normalization factor. oj is the cross-section of photoclectric absorption given by Morrison MeCammon (1983). and Nacagis the Galactic hyvelrogen column density set equal to 5.8LF 7 (Dickey Lockman 1990).,"Galactic absorption, i.e. $f(E) = K E^{-\Gamma} e ^{ -\sigma_{\rm ph} N_{\rm H,Gal} } $, where $E$ is X-ray energy, f(E) is photon flux given in units of photons $^{-1}$ $^{-2}$ $^{-1}$, $\Gamma$ is photon index, $K$ is the normalization factor, $\sigma_{\rm ph}$ is the cross-section of photoelectric absorption given by Morrison McCammon (1983), and $N_{\rm H,Gal}$is the Galactic hydrogen column density set equal to $5.8\times10^{20}$ $^{-2}$ (Dickey Lockman 1990)."1040 Using XSPEC software (ver., Using XSPEC software (ver.1041 10.0). we performed a minimumechi-sequare fitting.," 10.0), we performed a minimum-chi-square fitting."1042 The best-fit photon-index is 0.51 vielding 7/6 = 210/32 (Figure laa)., The best-fit photon-index is 0.51 yielding $\chi^2/\nu$ = 210/32 (Figure \ref{fig:rxtespec}a a).1043 The ratio of the data to the best-fit power-law model. (Figure 1bb) clearly shows evidence.for an iron Ix emission line at ~6 keV and a Latter continuum above ~S keV. Then. we modeled the spectrum. with two power-law continua (soft and hard) plus a lino emission. as expressed by FG)QNSEV|SEPginetbyeTimee ph," The ratio of the data to the best-fit power-law model (Figure \ref{fig:rxtespec}b b) clearly shows evidencefor an iron K emission line at $\sim$ 6 keV and a flatter continuum above $\sim$ 8 keV. Then, we modeled the spectrum with two power-law continua (soft and hard) plus a line emission, as expressed by $ f(E) = ( K_s E^{-\Gamma_s} + K_h E^{-\Gamma_h} + line (K_l, E_l) )1044e ^{ -\sigma_{\rm ph} N_{\rm H,Gal} } $."1045e iron-line central energy. (£7;) and the intensity (Aj) are [ree parameters. and the line width is assumed to be zero.," The iron-line central energy $E_l$ ) and the intensity $K_l$ ) are free parameters, and the line width is assumed to be zero."1046 The litc result is shown in Figure 2. and the best-fit parameters are summarized in Table 1.," The fit result is shown in Figure \ref{fig:rxte2powfit}1047 and the best-fit parameters are summarized in Table 1."1048 Notable properties of the best-fit nmiodel ave very small photon index. ~O. of the hard. continuum. and a large equivalent. width. 0.79 keV. of the iron line.," Notable properties of the best-fit model are very small photon index, $\sim$ 0, of the hard continuum, and a large equivalent width, 0.79 keV, of the iron line."1049 An absorption edge structure is noticeable at TS keV in the fit residual (Eig. 2)).," An absorption edge structure is noticeable at 7–8 keV in the fit residual (Fig. \ref{fig:rxte2powfit}) ),"1050 which is most likely the iron Ix-edge., which is most likely the iron K-edge.1051 ποσο features are characteristic of the rellected X-rays from an optically thick material as has been pointed out by several authors (Dwasawa Comastri 1998: Netzer et al., These features are characteristic of the reflected X-rays from an optically thick material as has been pointed out by several authors (Iwasawa Comastri 1998; Netzer et al.1052 1998)., 1998).1053 N-ravs impinging on optically thick matter are photo-absorbed as well as Compton-scattered., X-rays impinging on optically thick matter are photo-absorbed as well as Compton-scattered.1054 These processes form a very Lat continuum around ~10 keV. together with the Ix-absorption edge and Ix. emission. line of iron.," These processes form a very flat continuum around $\sim10$ keV, together with the K-absorption edge and K emission line of iron."1055 We fit the AXE spectrum together with data in 4 with models including the Compton reflection., We fit the spectrum together with data in 4 with models including the Compton reflection.1056where p is the gas density ancl gis the average flow velocity (averaged across the channel width).,where $\rho$ is the gas density and $\bar{u}$ is the average flow velocity (averaged across the channel width).1057 Excellent agreement is observed., Excellent agreement is observed.1058 As stated above and shown in [9.12.14).. this class of deviational methods exhibit statistical uncertainties (hat scale with the local deviation from equilibrium (hus allowing the simulation of arbitrarily low deviations from ecuilibrium at a cost that is independent. of this deviation.," As stated above and shown in \cite{pof2005,lowell,thomas2}, this class of deviational methods exhibit statistical uncertainties that scale with the local deviation from equilibrium thus allowing the simulation of arbitrarily low deviations from equilibrium at a cost that is independent of this deviation."1059 llere we demonstrate this feature by studying the statistical uncertainty of (he temperature in a problem involving heat transfer., Here we demonstrate this feature by studying the statistical uncertainty of the temperature in a problem involving heat transfer.1060" Specifically. figure 3. shows the relative statistical uncertainty in ihe temperature (oy) as a function of the normalized wall temperature dillerence (71—7p)/Th in the heat (ransfer problem. discussed above. lor f=1 and Ty=273k: in evaluating op. the characteristic value for temperature was taken to be the difference 7,—Z5."," Specifically, figure \ref{fluct} shows the relative statistical uncertainty in the temperature $\sigma_T$ ) as a function of the normalized wall temperature difference $(T_1-T_0)/T_0$ in the heat transfer problem discussed above, for $k=1$ and $T_0=273$ K; in evaluating $\sigma_T$, the characteristic value for temperature was taken to be the difference $T_1-T_0$."1061 The stanclard deviation is measured from (wo computational cells in the middle of the computational domain. each containing approximately 950 particles.," The standard deviation is measured from two computational cells in the middle of the computational domain, each containing approximately 950 particles."1062 The figure shows that. lor small Tj—Zi. the relative statistical uncertainty. remains independent of this quantity in sharp contrast to. methods!..," The figure shows that, for small $T_1-T_0$, the relative statistical uncertainty remains independent of this quantity in sharp contrast to ``non-deviational'' ."1063 Moreover. the variance reduction achieved is such that significant computational savings are expected for (Tj—T5)/ToS0.1.," Moreover, the variance reduction achieved is such that significant computational savings are expected for $(T_1-T_0)/T_0\lesssim 0.1$."1064 The algorithin described above imposes no restrictions on the magnitude of f. alübough it is expected Chat the deviational approach will be significantly more efficient (han traditional," The algorithm described above imposes no restrictions on the magnitude of $f^d$, although it is expected that the deviational approach will be significantly more efficient than traditional"1065LUNAdi— const. but it is straightforward to eeucralize our results for an arbitrary ciission spectrum.,"$\nu dN/d\nu=\,$ const, but it is straightforward to generalize our results for an arbitrary emission spectrum."1066 The local Lvxuuura photon uuuber deusitv at cach poiut iu space aud redshift is then given by a convolution of the collapsed barvou deusitv with a retarded Greens function. or in Fourier space. where jg is couformal time aud jo60)=sinGe)/.e.," The local $\alpha$ photon number density at each point in space and redshift is then given by a convolution of the collapsed baryon density with a retarded Green's function, or in Fourier space, where $\eta$ is conformal time and $j_0(x)=\sin(x)/x$."1067 We can further simplify this expression by using our previous result that. ou large scales. f(R) las time dependence x(fibus9(F2.—G7£307.," We can further simplify this expression by using our previous result that, on large scales, $f_c(\bm{k})$ has time dependence $\propto\langle f_c\rangle b_{\rm eff}=\langle f_c\rangle1068-\langle v^2 f_c\rangle/\sigma^2$."1069 Theretore. we have where the sinoothing filter is Iu this expression. jg is the conformal time at redshift +. aud note that d/dij=HHdfd:.," Therefore, we have where the smoothing filter is In this expression, $\eta_0$ is the conformal time at redshift $z$, and note that $d/d\eta = -H\,d/dz$."1070 The propagation of Lyman o photous over luge distances cousiderably danps the spatial fluctuations iun Ly à intensity., The propagation of Lyman $\alpha$ photons over large distances considerably damps the spatial fluctuations in Ly $\alpha$ intensity.1071 However. our discussion so far has neglected au important effect: Lyman à pliotous can only travel a limited distance.," However, our discussion so far has neglected an important effect: Lyman $\alpha$ photons can only travel a limited distance."1072 A rest frame Lyinan o photon which participates iu pumping was enuütted at some clistance binewards of Lyiau o. redshitting as it travels.," A rest frame Lyman $\alpha$ photon which participates in pumping was emitted at some distance bluewards of Lyman $\alpha$, redshifting as it travels."1073 The higher the frequency at cussion. the longer the distance that the photon travels before redshiftiug into Lyman a.," The higher the frequency at emission, the longer the distance that the photon travels before redshifting into Lyman $\alpha$."1074 However. a photon that is emitted at a waveleneth shorter than Lyman Επ be absorbed in the neutral intergalactic medimu. aud ultimately lost to double photon decay. before it can redshift into Lyman oa.," However, a photon that is emitted at a wavelength shorter than Lyman $\beta$ will be absorbed in the neutral intergalactic medium, and ultimately lost to double photon decay, before it can redshift into Lyman $\alpha$."1075 This means that gas clouds at redshift 2 cannot be pumped by photous emitted by sources at redshift agis2thor. Where (1)n4)=(32/27)«(112).," This means that gas clouds at redshift $z$ cannot be pumped by photons emitted by sources at redshift $z_{\rm emit} > z_{\rm hor}$, where $(1+z_{\rm hor})=(32/27)\times(1+z)$."1076 This gives a natural maximal horizon distance for Lyian à piping., This gives a natural maximal horizon distance for Lyman $\alpha$ pumping.1077 Conceivably. the propagation distance could be even shorter given sufficient molecular opacity. either iu the host munmihalos or in the intergalactic medium (Ricottietal.2001).. but we disregard this possibility iu our calculations.," Conceivably, the propagation distance could be even shorter given sufficient molecular opacity, either in the host minihalos or in the intergalactic medium \citep{Ricotti01}, but we disregard this possibility in our calculations."1078 If μήνloc1. we can approximate ((21)) as This shows how the shape of the smoothing window depends on the formation history of collapsed barvonic objects and their Lyman a cussion.," If $z_{\rm hor}/z - 1 \ll 1$, we can approximate \ref{window}) ) as This shows how the shape of the smoothing window depends on the formation history of collapsed baryonic objects and their Lyman $\alpha$ emission."1079 As noted above. the shape of Wh.:) also depends on the spectrum of escaping UV enission from the first stars. which will generally be iimch more complicated than we lave assumed here.," As noted above, the shape of $W(k,z)$ also depends on the spectrum of escaping UV emission from the first stars, which will generally be much more complicated than we have assumed here."1080 Fortunately. it is entirely straightforward to compute how J changes when realistic spectra aud. opacity are used instead of the flat spectrmu aud sharp cutoff that we have adopted for simplicity.," Fortunately, it is entirely straightforward to compute how $W$ changes when realistic spectra and opacity are used instead of the flat spectrum and sharp cutoff that we have adopted for simplicity."1081" Caven this expression for the πουhing wiudow. we can compute the wmuber of Lyman ©photons per atom. 0,. using ((23)). which then eives , aud the spin temperature Zi using ((15--16))."," Given this expression for the smoothing window, we can compute the number of Lyman $\alpha$photons per atom, $n_\alpha$, using \ref{intensity}) ), which then gives $x_\alpha$ and the spin temperature $T_s$ using \ref{spintemp}- \ref{coupling}) )."1082 Caven Zi. we compute the optical depth aud brightuess temperature using ((19--20)).," Given $T_s$, we compute the optical depth and brightness temperature using \ref{tau}- \ref{contrast}) )."1083" The Lyinan-a intensity 0, is a linear function of the collapse fraction. so its power spectrum is simply the product of the f. power spectrum with the (square of the) window function. ((21))."," The $\alpha$ intensity $n_\alpha$ is a linear function of the collapse fraction, so its power spectrum is simply the product of the $f_c$ power spectrum with the (square of the) window function, \ref{window}) )."1084 The brightucss temperature is a nonlinear but local function of αμ., The brightness temperature is a nonlinear but local function of $n_\alpha$.1085 Therefore. on large scales it is a biased tracer of the intensity field. aud its power spectrum will be proportional to the Εμ power spectrum. with some proportionality cocticicut.," Therefore, on large scales it is a biased tracer of the intensity field, and its power spectrum will be proportional to the $n_\alpha$ power spectrum, with some proportionality coefficient."1086 We could write down an analytic expression for this bias cocfitcicut m terms of the N-point correlation functions of n. but it is simpler to calculate it bv simulation instead.," We could write down an analytic expression for this bias coefficient in terms of the $N$ -point correlation functions of $n_\alpha$, but it is simpler to calculate it by simulation instead."1087 Accordingly. we have generated realizations of the brightness temperature field.," Accordingly, we have generated realizations of the brightness temperature field."1088 We first generate realizations of the Gaussian random relative velocity field 0.4. which we then transform ito collapse fraction f. using ((1-2)). replacing ον>esp as described im retsec:te..," We first generate realizations of the Gaussian random relative velocity field $v_{cb}$ , which we then transform into collapse fraction $f_c$ using \ref{Mc}- \ref{eqn:fc}) ), replacing $c_s\to c_{s,{\rm eff}}$ as described in \\ref{sec:fc}. ."1089 From. the collapse fraction. we compute the Lyiman-o intensity using ((23)). which then gives the spin temperature Zi. optical depth rz and brightness temperature contrast 075 using ((15-20)).," From the collapse fraction, we compute the $\alpha$ intensity using \ref{intensity}) ), which then gives the spin temperature $T_s$, optical depth $\tau$ and brightness temperature contrast $\delta T_b$ using \ref{spintemp}- \ref{contrast}) )."1090 We ecucrate realizatious ina 2 h tCpe box of 1021? pixels at a variety of differeut redshifts. varving the nuuber of Τά photons per collapsed barvou. NV.," We generate realizations in a 2 $h^{-1}$ Gpc box of $1024^3$ pixels at a variety of different redshifts, varying the number of $\alpha$ photons per collapsed baryon, $N_\alpha$."1091 Figure LE illustrates the brightness temperature power spectrum., Figure \ref{pumpfig} illustrates the brightness temperature power spectrum.1092 As expected. the 67; power spectrum is proportional to the product of the £f. power spectrum. multiplied bv the square of the window functionVAk.2) given by ((21)). which suppresses snall-scale fluctuations iu the brightucss temperature.," As expected, the $\delta T_b$ power spectrum is proportional to the product of the $f_c$ power spectrum, multiplied by the square of the window function$W(k,z)$ given by \ref{window}) ), which suppresses small-scale fluctuations in the brightness temperature."1093 The shape of the power spectrin. is therefore simple to calculate., The shape of the power spectrum is therefore simple to calculate.1094 The power spectrum peaks ou the scale of the Lyiman- horizon. and exhibits damped but pronounced acoustic oscillations at higher wavevectors.," The power spectrum peaks on the scale of the $\alpha$ horizon, and exhibits damped but pronounced acoustic oscillations at higher wavevectors."1095" The amplitucle of the power spectrui is a nontrivial function of N,, aud 2.", The amplitude of the power spectrum is a nontrivial function of $N_\alpha$ and $z$.1096 At hieh redshift. when the collapse fraction is stnall and the πα pumping intensity μι 18 weak. the spin temperature is close to the CAIB temperature. with siuall fuctuations proportional to μι ," At high redshift, when the collapse fraction is small and the $\alpha$ pumping intensity $n_\alpha$ is weak, the spin temperature is close to the CMB temperature, with small fluctuations proportional to $n_\alpha$ ."1097The brightness temperature contrast therefore erows rapidly in time., The brightness temperature contrast therefore grows rapidly in time.1098 Eveutuallv. however. the spin temperaturebegins to saturate at the eas kinetic temperature Zh.," Eventually, however, the spin temperaturebegins to saturate at the gas kinetic temperature $T_{\rm kin}$ ."1099" Às 0», becomes very larec. the spin tempcrature beeins to approach a wuitorm value evervwhere. Ty>Tug. audso the brightuess temperature"," As $n_\alpha$ becomes very large, the spin temperature begins to approach a uniform value everywhere, $T_s \to T_{\rm kin}$, andso the brightness temperature"1100"cloud and a guiding issue caused by the close proximity of the bright Moon illumination, 26? from target).","cloud and a guiding issue caused by the close proximity of the bright Moon illumination, $^\circ$ from target)."1101 'The 16 CORALIE spectra of WASP-30 were co-added to produce a single spectrum with a typical S/N of around 70:1., The 16 CORALIE spectra of WASP-30 were co-added to produce a single spectrum with a typical S/N of around 70:1.1102 The analysis was performed using the methods given in Gillonetal.(2009).., The analysis was performed using the methods given in \citet{2009A&A...501..785G}.1103" The line was used to determine the effective temperature (T.g)), while the Na D and Mg b lines were used as surface gravity g.)) diagnostics."," The line was used to determine the effective temperature ), while the Na D and Mg b lines were used as surface gravity ) diagnostics."1104 The parameters obtained from the analysis are given in the top panel of Table 3.., The parameters obtained from the analysis are given in the top panel of Table \ref{tab:mcmc}.1105 The elemental abundances were determined from equivalent width measurements of several clean and unblended lines., The elemental abundances were determined from equivalent width measurements of several clean and unblended lines.1106 A value for microturbulence (&)) was determined from Fe using the method of Magain (1984).., A value for microturbulence ) was determined from Fe using the method of \citet{1984A&A...134..189M}.1107" The quoted error estimates include that given by the uncertainties inΤομ, and&,, as well as the scatter due to measurement and atomic data uncertainties."," The quoted error estimates include that given by the uncertainties in, and, as well as the scatter due to measurement and atomic data uncertainties."1108" Our quoted lithium abundance takes account of non local thermodynamic equilibrium corrections (Carlssonetal.1994),, with a value of == 2.95 resulting when neglecting them."," Our quoted lithium abundance takes account of non local thermodynamic equilibrium corrections \citep{1994A&A...288..860C}, with a value of = 2.95 resulting when neglecting them."1109 The projected stellar rotation velocity (vsini)) was determined by fitting the profiles of several unblended Fe1 lines., The projected stellar rotation velocity ) was determined by fitting the profiles of several unblended Fe lines.1110" A value for macroturbulence (Όμιας)) of 4.7 + 0.3 wwas assumed, based on the tabulation by Gray (2008),, and an instrumental FWHM of 0.11 + 0.01À,, determined from the telluric lines around6"," A value for macroturbulence ) of 4.7 $\pm$ 0.3 was assumed, based on the tabulation by \citet{2008oasp.book.....G}, and an instrumental FWHM of 0.11 $\pm$ 0.01, determined from the telluric lines around."1111300À.. A fitting value of == 1424+11kms1} wwas obtained., A best-fitting value of = 14.2 $\pm$ 1.1 was obtained.1112 The WASP and Euler photometry were combined with the CORALIE RV measurements in a simultaneous Markov-chain Monte Carlo (MCMC) analysis (Collier 2008)..," The WASP and Euler photometry were combined with the CORALIE RV measurements in a simultaneous Markov-chain Monte Carlo (MCMC) analysis \citep{2007MNRAS.380.1230C, 2008MNRAS.385.1576P}."1113" Our proposal parameters are: Tc, P, AF, Tis, b, Ki,Tog,[Fe/H],, aand (CollierCameronetal.2007;Enoch"," Our proposal parameters are: $T_{\rm c}$ , $P$, $\Delta F$ , $T_{14}$, $b$, $K_{\rm 1}$, and \citep{2007MNRAS.380.1230C, 2010A&A...516A..33E}."1114" Here T. is the epoch of mid-transit, P is the orbital 2010)..period, AF= is the fractional flux-deficit that would be observed R2/R2during transit in the absence of limb-darkening, Ti4 is the total transit duration (from first to fourth contact), b is the impact parameter of the BD's path across the stellar disc, K, is the semi-amplitude of the stellar reflex velocity, iis the stellar effective temperature, iis the stellar metallicity, e is the orbital [Fe/H]eccentricity and w is the argument of periastron."," Here $T_{\rm c}$ is the epoch of mid-transit, $P$ is the orbital period, $\Delta F = R_{\rm p}^2/R_*^2$ is the fractional flux-deficit that would be observed during transit in the absence of limb-darkening, $T_{14}$ is the total transit duration (from first to fourth contact), $b$ is the impact parameter of the BD's path across the stellar disc, $K_{\rm 1}$ is the semi-amplitude of the stellar reflex velocity, is the stellar effective temperature, is the stellar metallicity, $e$ is the orbital eccentricity and $\omega$ is the argument of periastron."1115" As Ford notes, it is convenient to use ecosw and esinw as (2006)MCMC jump parameters, because these two quantities are nearly orthogonal and their joint probability density function is well-behaved when the eccentricity is small and w is highly uncertain."," As \citet{2006ApJ...642..505F} notes, it is convenient to use $e\cos\omega$ and $e\sin\omega$ as MCMC jump parameters, because these two quantities are nearly orthogonal and their joint probability density function is well-behaved when the eccentricity is small and $\omega$ is highly uncertain."1116" Ford cautions, however, that theuseof aand aas jump parameters implicitly imposes a prior on the eccentricity that increases linearly with e."," Ford cautions, however, that theuseof and as jump parameters implicitly imposes a prior on the eccentricity that increases linearly with $e$ ."1117 Instead we use V/€aand, Instead we use and1118Figure B| a shows the data distribution of the normalized wave power versus the normalized ion differential speed.,Figure \ref{fig.3}~ a shows the data distribution of the normalized wave power versus the normalized ion differential speed.1119" It hardly exceeds unity, a result which is consistent with the prediction of kinetic theory for a linear plasma instability."," It hardly exceeds unity, a result which is consistent with the prediction of kinetic theory for a linear plasma instability."1120" The theory says that, whenever the ion differential speed exceeds the Alfvénn speed, the plasma should become unstable and excite magnetosonic waves (see, e.g. (2000)))."," The theory says that, whenever the ion differential speed exceeds the Alfvénn speed, the plasma should become unstable and excite magnetosonic waves (see, e.g., \cite{li2000}) )."1121" As found previously, the present study also indicates a positive correlation between the normalized ion differential speed and the normalized wave power (see the white curve, which represents the weighted mean values of the normalized wave power shown in Figure [] a. ) It is commonly believed (see, e.g., the review of (2006))) that low collisional friction would permit a relatively high differential speed to occur between the two main ion species in the solar wind."," As \citet{bourouaine2011} found previously, the present study also indicates a positive correlation between the normalized ion differential speed and the normalized wave power (see the white curve, which represents the weighted mean values of the normalized wave power shown in Figure \ref{fig.3}~ a. ) It is commonly believed (see, e.g., the review of \cite{marsch2006}) ) that low collisional friction would permit a relatively high differential speed to occur between the two main ion species in the solar wind."1122" This notion is confirmed by the results of our FigureD] b, which shows that higher values of the normalized ion differential speed correspond to lower collision ages."," This notion is confirmed by the results of our Figure \ref{fig.3}~ b, which shows that higher values of the normalized ion differential speed correspond to lower collision ages."1123" In slow solar wind, when the value of the collision age is higher than 0.2, the corresponding normalized differential speed is low (i.e., Vop/V4«0.3), but it is higher than 0.3 for comparatively low values of the collision age (as is indicated later in Figure] d)."," In slow solar wind, when the value of the collision age is higher than 0.2, the corresponding normalized differential speed is low (i.e., $V_{\alpha p} /V_A < 0.3$ ), but it is higher than 0.3 for comparatively low values of the collision age (as is indicated later in Figure \ref{fig.3}~ d)."1124" In Figure Bec the coloured pixels represent the ratio of the alpha-particle-to-proton temperature anisotropy, (T1aT\p)/(TipTia), plotted as a function of the relative ion differential speed and the normalized wave power."," In Figure \ref{fig.3}c c the coloured pixels represent the ratio of the alpha-particle-to-proton temperature anisotropy, $(T_{\perp\alpha}1125T_{\parallel p})/(T_{\perp p} T_{\parallel \alpha})$, plotted as a function of the relative ion differential speed and the normalized wave power."1126" Interestingly, this figure clearly shows that when V,,/V4x0.4, the temperature anisotropy of the alpha particles, T,/Ty, is higher than the anisotropy of the protons, T,,/Ty,."," Interestingly, this figure clearly shows that when $V_{\alpha p} /V_A \le11270.4$, the temperature anisotropy of the alpha particles, $T_{\perp1128\alpha}/T_{\parallel \alpha}$, is higher than the anisotropy of the protons, $T_{\perp p}/T_{\parallel p}$."1129" However, the ratio of the ion temperature anisotropies tends to decrease to lower values of about 0.6 when γαρ/γα>0.6, as is quantitatively shown in Figure B] d. The curve in Figure BHd, which represents the weighted mean value of the ratio of the ion temperature anisotropies (black symbols), clearly indicates that alpha particles are preferentially heated (perpendicularly to the mean magnetic field) with respect to the protons whenever Vy,/Vax 0.4, and this is true even for a relatively low wave energy (indicated by the white curve in Figure Bpa) and at high collision rates (green symbols)."," However, the ratio of the ion temperature anisotropies tends to decrease to lower values of about 0.6 when $V_{\alpha1130p} /V_\mathrm{A} > 0.6$, as is quantitatively shown in Figure \ref{fig.3}~ d. The curve in Figure \ref{fig.3}d d, which represents the weighted mean value of the ratio of the ion temperature anisotropies (black symbols), clearly indicates that alpha particles are preferentially heated (perpendicularly to the mean magnetic field) with respect to the protons whenever $V_{\alpha p}1131/V_\mathrm{A} \le 0.4$ , and this is true even for a relatively low wave energy (indicated by the white curve in Figure \ref{fig.3}a a) and at high collision rates (green symbols)."1132" One would expect that the plasma tends to thermal equilibrium, in coincidence with the lowest values of the normalized ion differential flow speed, if a relatively high collision rate."," One would expect that the plasma tends to thermal equilibrium, in coincidence with the lowest values of the normalized ion differential flow speed, if a relatively high collision rate."1133 Then the temperature ratios of the ion species should also be near unity., Then the temperature ratios of the ion species should also be near unity.1134" However, observationally it seems that preferential perpendicular heating of the alpha particles with respect to the protons can persist even in regions where collision rates are high (with V,,/V4< 0.4)."," However, observationally it seems that preferential perpendicular heating of the alpha particles with respect to the protons can persist even in regions where collision rates are high (with $V_{\alpha p} /V_A \le 0.4$ )."1135 This is possible because a wave-related local ion heating mechanism may be acting on time scales much lower than the long cumulative collision time., This is possible because a wave-related local ion heating mechanism may be acting on time scales much lower than the long cumulative collision time.1136" Such a fast wave-heating mechanism can drive the plasma far away from thermal equilibrium, and therefore may cause a significant ion temperature anisotropy, because on the other side collisions are not fast enough to enforce thermal equilibrium."," Such a fast wave-heating mechanism can drive the plasma far away from thermal equilibrium, and therefore may cause a significant ion temperature anisotropy, because on the other side collisions are not fast enough to enforce thermal equilibrium."1137 We found in our previous paper (2011))) that the helium ion abundance for this selected data set varies mainly between 0.02 and 0.04., We found in our previous paper \citet{bourouaine2011}) ) that the helium ion abundance for this selected data set varies mainly between 0.02 and 0.04.1138 The helium abundance does not show a clear dependence on the normalized differential ion speed., The helium abundance does not show a clear dependence on the normalized differential ion speed.1139" However, we showed that there is an anti-correlation between the alpha-to-proton temperature ratio and the heliumabundance at a fixed V, /VA."," However, we showed that there is an anti-correlation between the alpha-to-proton temperature ratio and the heliumabundance at a fixed $V_{\alpha p} /V_\mathrm{A}$ ."1140"Calculations for minimum mass solar nebulae show little variation of rj wilh (Q,.",Calculations for minimum mass solar nebulae show little variation of $r_b$ with $Q_b$.1141 These results confirm the basic features of the analvtic model., These results confirm the basic features of the analytic model.1142 Both models predict rj< 1l km for low mass nebulae with ~ of the mass in (he minimum mass solar nebula., Both models predict $r_b \lesssim$ 1 km for low mass nebulae with $\sim$ of the mass in the minimum mass solar nebula.1143 Larger break radii. ~ 110 km. are possible in more massive nebulae.," Larger break radii, $\sim$ 1–10 km, are possible in more massive nebulae."1144 The analytic model predicts large break radii for larger e than the numerical ealeulations., The analytic model predicts large break radii for larger $e$ than the numerical calculations.1145 In numerical calculations with € = 0.2. disruptive collisions reduce the space density considerably in ~ 100 Myr.," In numerical calculations with $e$ = 0.2, disruptive collisions reduce the space density considerably in $\sim$ 100 Myr."1146 The smaller collision rates prevent formation of a break in the size distribution al large radii., The smaller collision rates prevent formation of a break in the size distribution at large radii.1147 Thus. numerical calculations with e = 0.2 vield log rj only ~ 0.10.2 larger than caleulations with e = 0.04.," Thus, numerical calculations with $e$ = 0.2 yield log $r_b$ only $\sim$ 0.1–0.2 larger than calculations with $e$ = 0.04."1148 These calculations begin with 11000 m planetesimals in mass bins wilh 6 = 1.4 or 1.7 ancl equal mass per bin., These calculations begin with 1–1000 m planetesimals in mass bins with $\delta$ = 1.4 or 1.7 and equal mass per bin.1149 The planetesimals lie in 32 annuli ad 40.75 AU., The planetesimals lie in 32 annuli at 40–75 AU.1150 Models with Neptune have an exira annulus αἱ 30 AU., Models with Neptune have an extra annulus at 30 AU.1151 For most models. we adopt ej=10 or ey = 10 and i = e/2 for all planetesimals.," For most models, we adopt $e_0 = 10^{-4}$ or $e_0$ = $10^{-5}$ and $i$ = $e$ /2 for all planetesimals."1152 At the start of our caleulations. these initial values vield a rough balance between viscous stirring by 0.11 km objects and collisional damping of 10.100 m objects.," At the start of our calculations, these initial values yield a rough balance between viscous stirring by 0.1–1 km objects and collisional damping of 10–100 m objects."1153 The bodies have a mass censity py = 1.5- g oE . which is fixed throughout the evolution.," The bodies have a mass density $\rho_d$ = 1.5 g $^{-3}$ , which is fixed throughout the evolution."1154" We consider a range in initial surface density. with X = 0.030.3 & 7 (04/30 82,"," We consider a range in initial surface density, with $\Sigma_0$ = 0.03–0.3 g $^{-2}$ $a_0$ /30 $^{-3/2}$."1155 To measure the senusiüvitv of our results (o stochastic variations. we performed 25 calculations for each set of fragmentation parameters.," To measure the sensitivity of our results to stochastic variations, we performed 2–5 calculations for each set of fragmentation parameters."1156" For ο = 0 and a [actor of ten range in My. we considered log Q; = 1. 2. 3. 4. 5. 6. and 1: Cp = 0.15 and 1.5: and 9, = 1.25 and 2.0."," For $\beta_b$ = 0 and a factor of ten range in $\Sigma_0$, we considered log $Q_b$ = 1, 2, 3, 4, 5, 6, and 7; $C_0$ = 0.15 and 1.5; and $\beta_g$ = 1.25 and 2.0."1157" We also performed a limited set of caleulations for C; = 0.15 and 1.5. 3, = 0.5. and a small set of log Q,."," We also performed a limited set of calculations for $C_g$ = 0.15 and 1.5, $\beta_g$ = 0.5, and a small set of log $Q_b$."1158 Although stochastic variations can change the size of the largest object ab 40.50 AU. repeat calculations with identical initial conditions vield small changes in the shape of the size distribution or the location of the break radius.," Although stochastic variations can change the size of the largest object at 40–50 AU, repeat calculations with identical initial conditions yield small changes in the shape of the size distribution or the location of the break radius."1159" A few caleulations with 5,x O0 vield interesting behavior in the size distribution at 1.100 m sizes. but ry does nol change dramatically."," A few calculations with $\beta_b \neq$ 0 yield interesting behavior in the size distribution at 1–100 m sizes, but $r_b$ does not change dramatically."1160 A larger suite of ealeulations with οz 0 leads to similar conclusions., A larger suite of calculations with $\beta_v \neq$ 0 leads to similar conclusions.1161 We plan to report on these aspects of the calculations in a separate paper., We plan to report on these aspects of the calculations in a separate paper.1162 lev planet formation in (he outer solar system follows a standard pattern (seeKenvon&IXenvon&Bromley2004:Goldreich.Lithwick.Sari 2004).," Icy planet formation in the outer solar system follows a standard pattern \citep[see][]{kl99a,kb04,gol04}."1163. Small planetesimals with r;S 1 km first grow slowly., Small planetesimals with $r_i \lesssim$ 1 km first grow slowly.1164 Collisonal damping brakes the smallest objects., Collisonal damping brakes the smallest objects.1165 Dynamical friction brakes the largest objects and stirs up the smallest objects., Dynamical friction brakes the largest objects and stirs up the smallest objects.1166 Gravitational focusing factorsincrease. and runaway growth begins.," Gravitational focusing factorsincrease, and runaway growth begins."1167 At 4050 AU. it takes ~ 1 Myr to produce," At 40–50 AU, it takes $\sim$ 1 Myr to produce"1168In this demonstration. we again use the photometric data from COSMOS (Capak et 22007) and S-COSMOS (Sanders et 22007). but merge it with 8910 spectroscopic redshifts from version 3.5 of the «COSMOS (bright) sample. the ;<22.5 mmagnitude limited spectroscopic branch of the survey (Lilly et 22007).,"In this demonstration, we again use the photometric data from COSMOS (Capak et 2007) and S-COSMOS (Sanders et 2007), but merge it with 8910 spectroscopic redshifts from version 3.5 of the $z$ COSMOS (bright) sample, the $i<22.5$ magnitude limited spectroscopic branch of the survey (Lilly et 2007)."1169 The training sub-set is limited to galaxies with z<1 that are detected in each of the and [3.6]. [4.5]. [5.8]. [8.0] bands.," The training sub-set is limited to galaxies with $z\leq1$ that are detected in each of the and [3.6], [4.5], [5.8], [8.0] bands."1170 In general. missing data Hack of coverage in a particular band for a galaxy. perhaps due to masking or contamination) could be dealt with. for example. by not allowing the missing weight to contribute to the learning and/or handicapping the learning coefficient for that particular test vector.," In general, missing data lack of coverage in a particular band for a galaxy, perhaps due to masking or contamination) could be dealt with, for example, by not allowing the missing weight to contribute to the learning and/or handicapping the learning coefficient for that particular test vector."1171 Similarly. upper detection limits can be treated as equivalent to measurements at the relevant significance. but for the purposes of clarity in this demonstration. we require detection in all bands.," Similarly, upper detection limits can be treated as equivalent to measurements at the relevant significance, but for the purposes of clarity in this demonstration, we require detection in all bands."1172 The number of objects in the catalogue after enforcing these constraints is 7651. with a median redshift of 2=0.55.," The number of objects in the catalogue after enforcing these constraints is 7651, with a median redshift of $z=0.55$."1173 In order to est the predictive power of the SOM. the sample is randomly split in two. such that one half of the catalogue can be used for training. and the other for testing (where the SOM has not had an opportunity ο see those galaxies).," In order to test the predictive power of the SOM, the sample is randomly split in two, such that one half of the catalogue can be used for training, and the other for testing (where the SOM has not had an opportunity to see those galaxies)."1174 The training set therefore consists of 3825 unique inputs., The training set therefore consists of 3825 unique inputs.1175 Multiple neural networks. or ‘committees’. are often usec © increase the robustness of predictions CCollister 22004).," Multiple neural networks, or `committees', are often used to increase the robustness of predictions Collister 2004)."1176 Committees introduce an extra level of stochasticity hat provide a measure of uncertainty through an examination of he fidelity of predictions made by committee members., Committees introduce an extra level of stochasticity that provide a measure of uncertainty through an examination of the fidelity of predictions made by committee members.1177 Here we initialise ten SOMs. each with 100.-100 nodes. and set the tota number of iterations per SOM to 382500. thus over-sampling the input training set by a factor 1O for an individual map. and a factor 100 over the committee.," Here we initialise ten SOMs, each with $100$$\times$$100$ nodes, and set the total number of iterations per SOM to 382500, thus over-sampling the input training set by a factor 10 for an individual map, and a factor 100 over the committee."1178 To introduce an extra level of randomness. the initial choice of learning coefficient. £L. +) is selected from a gaussian distribution centred at unity with a scale of 0.1: this allows each SOM to learn at slightly different rates.," To introduce an extra level of randomness, the initial choice of learning coefficient $L$ 4) is selected from a gaussian distribution centred at unity with a scale of 0.1; this allows each SOM to learn at slightly different rates."1179 The final predicted value is taken to be the mean of the individual predictions from the committee members. and the standard deviation of these predictions we take to be the uncertainty in the estimate.," The final predicted value is taken to be the mean of the individual predictions from the committee members, and the standard deviation of these predictions we take to be the uncertainty in the estimate."1180 If we had used many more SOMs in the committee. it should be possible to collect the results together to form a probability density function for the parameter prediction. which might provide a better representation of the uncertainty (note that SOMs can be trained in parallel for this purpose).," If we had used many more SOMs in the committee, it should be possible to collect the results together to form a probability density function for the parameter prediction, which might provide a better representation of the uncertainty (note that SOMs can be trained in parallel for this purpose)."1181 In our example. for each training vector we have a set of broad band photometry and a spectroscopic redshift.," In our example, for each training vector we have a set of broad band photometry and a spectroscopic redshift."1182 We set these as the weights of each training vector., We set these as the weights of each training vector.1183 To reduce the parameter space. we assign the photometry as a set of colours in consecutive bands. (ur DB.(DB gq).ítgV). and so-on up to (5.5].5.0).," To reduce the parameter space, we assign the photometry as a set of colours in consecutive bands, $(u^*-B)$ , $(B-g)$, $(g-V)$, and so-on up to ${\rm ([5.8]-[8.0])}$."1184 We also include the single &/ and i magnitudes as monochromatic flux measurements. and finally the spectroscopic redshift from :COSMOS.," We also include the single $u^*$ and $r$ magnitudes as monochromatic flux measurements, and finally the spectroscopic redshift from $z$ COSMOS."1185 In total. each training vector contains 14 elements.," In total, each training vector contains 14 elements."1186 After training all SOMs in the committee. we test the predictive yower of the SOM ensemble using the halfof the catalogue that did not participate in the training. calculating the BMU for each object using sub-sets of the photometry jjust (6.—D). then adding (b. qg)(gV ).andso-on until we include all photometry weights up to the IRAC bands).," After training all SOMs in the committee, we test the predictive power of the SOM ensemble using the half of the catalogue that did not participate in the training, calculating the BMU for each object using sub-sets of the photometry just $(u^*-B)$, then adding $(B-g)$, $(g-V)$, and so-on until we include all photometry weights up to the IRAC bands)."1187 In this ease. the spectroscopie redshift component of the weight is not considered when calculating the BMU.," In this case, the spectroscopic redshift component of the weight is not considered when calculating the BMU."1188 In each trial. the redshift weight tagged to the BMUs provides the ‘photometric’ redshift. and these are averaged over the committee to give the final prediction.," In each trial, the redshift weight tagged to the BMUs provides the `photometric' redshift, and these are averaged over the committee to give the final prediction."1189 As we know what the true redshift of each test galaxy is. we ean assess the accuracy of the method.," As we know what the true redshift of each test galaxy is, we can assess the accuracy of the method."1190 We define the figure of merit for the photometric redshift accuracy in the usual way as the root mean square of the difference between the true and estimated redshift a(A+)=\/¢As?» where At=(uosπμ)|tapec).," We define the figure of merit for the photometric redshift accuracy in the usual way as the root mean square of the difference between the true and estimated redshift $\sigma(\Delta z) = \surd\left< \Delta z^2\right>$, where $\Delta z = (z_{\rm spec} - z_{\rm phot}) / (1+z_{\rm spec})$."1191 55 and 6 shows the results. where we have interrogated the committee of ten SOMs for the photometric redshift of a test galaxy with increasingly complete sub-sets the full range of photometry.," 5 and 6 shows the results, where we have interrogated the committee of ten SOMs for the photometric redshift of a test galaxy with increasingly complete sub-sets the full range of photometry."1192 There is a clear decline in e(;Nz) as more photometric information information is added. asymptoting at A>)~0.03.," There is a clear decline in $\sigma(\Delta z)$ as more photometric information information is added, asymptoting at $\sigma(\Delta z)\sim0.03$."1193 Surprising accuracy can be achieved with a rathera7 sparsely sampled input vector. however in these cases one can clearly see the bias described above that results in the overestimation of redshifts for galaxies at ><(2; and vice versa.," Surprising accuracy can be achieved with a rather sparsely sampled input vector, however in these cases one can clearly see the bias described above that results in the overestimation of redshifts for galaxies at $z<\left< z\right>$ and vice versa."1194 Where shown. the error bars are the standard deviation of redshifts recovered from the ten SOMs.," Where shown, the error bars are the standard deviation of redshifts recovered from the ten SOMs."1195 This is certainly an underestimation of the true error: one could also incorporate the formal photometric uncertainties by running the SOM interrogation several times and allowing each photometry value to randomly scatter about its mean according to its Lo measured uncertainty., This is certainly an underestimation of the true error; one could also incorporate the formal photometric uncertainties by running the SOM interrogation several times and allowing each photometry value to randomly scatter about its mean according to its $\sigma$ measured uncertainty.1196 In this example. large error bars simply reflect cases where galaxies with similar characteristics were poorly represented in the training set. and thus are scattered between dissimilar BMUs in each committee member.," In this example, large error bars simply reflect cases where galaxies with similar characteristics were poorly represented in the training set, and thus are scattered between dissimilar BMUs in each committee member."1197 Using the «ραπ to A';-band photometry. we can achieve a(A:)=0.03 after rejecting ~2% 736 outliers.," Using the $u^*$ -band to $K_s$ -band photometry, we can achieve $\sigma(\Delta1198z)=0.03$ after rejecting $\sim$ $>$$3\sigma$ outliers."1199 Including the IRAC bands does not significantly improve the accuracy. despite the fact they were included in the training: c(4Nz) no longer improves after the 9th parameter ἐς fv.) is added.," Including the IRAC bands does not significantly improve the accuracy, despite the fact they were included in the training: $\sigma(\Delta z)$ no longer improves after the 9th parameter $z-K_s$ ) is added."1200" This reflects the fact that for >< litis the A< μπι photometry that ""carries most of the information required for the photometric redshift (as expected: the aand Balmer breaks are still blueward of the -/-band at 2«1. and the [.67/m stellar bump. another good redshift discriminant is just redward of Avs)."," This reflects the fact that for $z<1$ it is the $\lambda<2$$\mu$ m photometry that `carries' most of the information required for the photometric redshift (as expected; the and Balmer breaks are still blueward of the $J$ -band at $z<1$, and the $\mu$ m stellar bump, another good redshift discriminant is just redward of $K_s$ )."

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