source,target 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." 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." 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}. . The observations and data reductions are described in Section 3.., The observations and data reductions are described in Section \ref{obs}. 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}." 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}." 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}. 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}." 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. 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}] ]." 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." The final SLoWPoKES, The final SLoWPoKES "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)." " 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 $k \gtrsim 0.1 \, h \, \mathrm{Mpc^{-1}}, \theta \lesssim 1^\circ$ )." " 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." " 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)." 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 $P_{21}^{rec}(k)/P_{21}^{smoothed}(k)$ . " 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." " 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)." " 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." " 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 $z \gtrsim 2$." We have determined the transfer function parameters of eq., We have determined the transfer function parameters of eq. " 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 $z=2, 2.5$ ." 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}. 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}. . Fig., Fig. " 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" abundances 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. 2010)., 2010). " 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." 2 and 6) is rather similar to the other discussed above., 2 and 6) is rather similar to the other CEMP-no discussed above. In Fig., In Fig. 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. " 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." " 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." " 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." 2 and 3.., \ref{fig1} and \ref{fig2}. This can be seen more clearly in Fig. 4.., This can be seen more clearly in Fig. \ref{fig8}. " 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." " 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 $\log\mathrm{(C/O)}\sim 0$." " On the right of this peak, there is another lower peak."," On the right of this peak, there is another lower peak." " 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." " 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)." " 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." " 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)." " 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." " 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." 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. " 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" from the O5V to AOV range.,from the O5V to A0V range. " 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." " 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." "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. 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. " 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 $\chi^2_{\rm red}$. " We therefore cannot distinguish which model is more plausible from the x2,4.", We therefore cannot distinguish which model is more plausible from the $\chi^2_{\rm red}$. " 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." " 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}." 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. 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. " 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." " 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." " 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." " 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." 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. Therefore the Ho luminosity from this model is also an upper limit., Therefore the $\alpha$ luminosity from this model is also an upper limit. " 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." 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." arp," The galaxy is not smooth, but contains a bright filament that traverses the prominent nuclear region and extends NE to SW across the galaxy." "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)." T f romthisimageand ba, The centre of the BCG is estimated from this image and marked by a cross. ndpass, The red continuum is centrally concentrated in an elliptical shape and there are no bright filaments extending southwest and northeast. band., Therefore the large filament must be due to the line emission that falls within the R-band passband. "ThenearbygalaxyB2isalsovisibleatposition(- 20,0)."," The nearby galaxy B2 is also visible at position $-20,0$ )." " 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." 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. " 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." 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. highli," The brightest region is the galaxy nucleus, and the general shape of the nebula follows the blue continuum." "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." " 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." ios , We note that the colour variations cannot all result from the applied extinction correction. "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." " 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." '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." "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." " 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." " 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." " In summary, the old stellar population of the BCG lies"," In summary, the old stellar population of the BCG lies" Figure 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. 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. 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." " Figure 7 shows the A, distribution of this area.", Figure 7 shows the $A_{V}$ distribution of this area. The fluctuation of both the maps seems to have similar angular scales., The fluctuation of both the maps seems to have similar angular scales. " 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." 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." 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. 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." 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. 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." 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. 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." SFD98 emploved the/RAS 100jam intensity to caleulate the extinction., SFD98 employed the $100\ \mu m$ intensity to calculate the extinction. 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. 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. 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. " 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" indicates 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." 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. 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." 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}." . 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." 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. " 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." 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." 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. 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." 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." .. Again. we do not sec he growth of auv local instabilities.," Again, we do not see the growth of any local instabilities." 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)." We also performed a simulation without initial rotation., We also performed a simulation without initial rotation. 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. 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}." 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)." 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)." 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." The initial £4; iu the center is about 2 Cr., The initial $t_{\rm cool}$ in the center is about 2 Gyr. 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." 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." We will return to this point iu a later paper., We will return to this point in a later paper. 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." 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." 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." 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}." .. 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." 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." 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. 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." 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}." 2006).. Qur results are consistent with these results inasiuucli as there is overlap., Our results are consistent with these results inasmuch as there is overlap. 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)." 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." 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}. . 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} " effects 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. They studied the interaction by varving the jet paramcters., They studied the interaction by varying the jet parameters. " Ποπονοα, ucither of the above hivdrodyiuianuical studies computed uuclosvutliesis."," However, neither of the above hydrodynamical studies computed nuclosynthesis." Ou the other laud. Nagataki (2000) and Maceda et al (," On the other hand, Nagataki (2000) and Maeda et al. (" 2002) 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." 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. (" 1999) ancl MacFadyeu et al. (,1999) and MacFadyen et al. ( 2001). 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." 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. 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." 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)." 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." 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. 2001)., 2001). 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). Uufortuuatelv. both are rather uncertain.," Unfortunately, both are rather uncertain." 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." 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 $M_{\rm ZAMS} \gsim 25\msun$. 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." 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." 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." 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. In reality. the jets could be [umighly variable.," In reality, the jets could be highly variable." 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." 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." " 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." 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." 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)." 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." 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." Results are shown in Section 3. which is divided iuto three subsections.," Results are shown in Section 3, which is divided into three subsections." 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." Section 3.2 focuses ou the production of °° Ni., Section 3.2 focuses on the production of $^{56}$ Ni. 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." 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." Section 5 closes this paper with conclusions and discussion., Section 5 closes this paper with conclusions and discussion. 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. " 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." 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)." " 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 $\theta_{\rm jet}$. 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)." 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. 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." 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." Thus the jets are imomentuu-diveu., Thus the jets are 'momentum-driven'. 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." " 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)." Equation (1) leads to the following explicit expression for the jet propertics:, Equation (1) leads to the following explicit expression for the jet properties: Sevlert 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. 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). 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. 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." ‘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. 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)." 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). 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)." 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. 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 $\lambda 6087$, $\lambda 6374$ (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)." 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." 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)." 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." 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. 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. 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." 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." 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). 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." 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. 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. 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. 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)." 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. 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. “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). 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. 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. The good exposure time is about 21 ks for cach detector., The good exposure time is about 21 ks for each detector. 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. Response matrices for the SIS were generated by SESRALCG version 1.1., Response matrices for the SIS were generated by SISRMG version 1.1. 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. 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. 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." 1 in their paper)., 1 in their paper). Since the, Since the of (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." 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)." 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}. . 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." 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." 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." In Fig., In Fig. 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)." 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}. . The resulting spectra are shown in Fig., The resulting spectra are shown in Fig. 32. for LES 0229-200. and in Fig.," \ref{fig:0229} for 1ES 0229+200, and in Fig." 4 [or, \ref{fig:3c66a} for in 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." " It is imμα, in equation 12 that the (dark) density p is entirely composed of imiui-halos with masses in the range My0$ and $e>0$ is to stretch or shrink the ingress/egress duration by a factor $\tau/\tau_0$." 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 $\mathcal{I}_0 = \mathcal{I} (\tau_0/\tau)$." 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 $m\geq 2$." 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 $P$." 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." 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." 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" ]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." " 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.” " 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." " 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}) ). 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." 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 likelihood In 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}." . 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." " 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 $\epsilon_H \approx 6 \cdot 10^{18}$ erg/g, the bolometric luminosity of such systems are in the $ 10^{37}-10^{38} \ \mathrm{erg \ s^{-1}} $ range, potentially making them bright X-ray sources." 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}." 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}. . 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." 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}. . 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. 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. This quantity cannot be measured unambiguously for several reasons., This quantity cannot be measured unambiguously for several reasons. 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)." 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." 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." 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." 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. . 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." 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." 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." 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." 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. 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." The paper is structured as follows: in Sect., The paper is structured as follows: in Sect. 2 we describe the sample selection. the data preparation. and its analysis.," 2 we describe the sample selection, the data preparation, and its analysis." We identify and remove gas-rich galaxies from the sample in Sect., We identify and remove gas-rich galaxies from the sample in Sect. 3., 3. The obtained X/K ratios are presented and discussed in Sect., The obtained X/K ratios are presented and discussed in Sect. 4., 4. Our results are summarized in Sect., Our results are summarized in Sect. 5., 5. 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. 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}} $. 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}) )." 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." 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." in Mehlert. οἱ al. (,in Mehlert et al. ( "1998) was followed to achieve a uniform focus with wavelength. when necessary,","1998) was followed to achieve a uniform focus with wavelength, when necessary." 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." 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." The uncertainties in the correction are £20.1A., The uncertainties in the correction are $\approx 0.1$. 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." 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." 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. 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." Fig., Fig. 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." 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." 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)." 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." 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." 1999)., 1999). 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." 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." Fie., Fig. 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)." 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. ( in preparation).,in preparation). 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. 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" MIASTO! 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)." These parameters. however. do not change curing the fare.," These parameters, however, do not change during the flare." 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)." 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." 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." " 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)." 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." 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)." 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)." 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). Therefore we predict significantly lieher flare rates than that reported previously., Therefore we predict significantly higher flare rates than that reported previously. 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." 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, Preibisch1997, Costa2000, Ozawa2000, Tsujimoto2001}." x 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." 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." 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." 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." 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)." 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}." .. 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}. ." 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)." 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" We 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)." " 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, \mu, \mu_a$." " 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 \gamma^2/\gamma_r^2 \rightarrow 2$." 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 $u \rightarrow 1$." 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}) )" " 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." 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." 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}. ." Looking at Eq., Looking at Eq. 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$." Passing through this singularity will fix the iudex s., Passing through this singularity will fix the index $s$ . 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." 1. E obtain, \ref{main} I obtain Based 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." 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)." 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." 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." 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. in 2”-cliameter random apertures., in $2^{\prime\prime}$ -diameter random apertures. For background. [uetuations. we estimated the median sky level r.m.s.," For background fluctuations, we estimated the median sky level r.m.s." 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." " 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~ \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." 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." 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. cosmology 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. 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. 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)$. 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}. . 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$: 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." 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." 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. 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. 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)." At the late stage of evolution (when A) , At the late stage of evolution (when $R(t)$ measured syste parameters. in particular the inclination.,"measured system parameters, in particular the inclination." 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." 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. 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. 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." 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." . 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." 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$." .. 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." 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." 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}) )." 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$." 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}." . 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}." . 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. 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." 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." 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." 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." 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$. 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." 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}." . 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. 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." 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." 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." 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." 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." e 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$ ." 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." For a pure Te atinosphere he distance is ereater., For a pure He atmosphere the distance is greater. 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." 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." We thank Alike Nowak. Fred. Lau," We thank Mike Nowak, Fred Lamb" radi.,radii. “Pwo densities of cach cloud distribution were also considered., Two densities of each cloud distribution were also considered. 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." 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." 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)." 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)." 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). 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." 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. 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." 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." 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." 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. 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. 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." 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. There are wee paths (indicated bv the lines across the upper-right, There are three paths (indicated by the lines across the upper-right """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}$." 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." 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)$." 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." We close this section with a comment about locality., We close this section with a comment about locality. 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. For a detailed discussion of (his issue see for instance [2].., For a detailed discussion of this issue see for instance \cite{observables}. 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$." 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." 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. " 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}$." 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." 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. 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." 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}. ." 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. They are covariant. have," They are covariant, have" he 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)." 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$." Only Ίσα.temperatures. (, Only Eq. ( 3) 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)." 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$." 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." For 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." " 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." In 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." 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 l(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." 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. 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." " 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." 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. (" 1).,1). 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." 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." 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." 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." 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. (" 5).,5). 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$ :" deep 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. 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}." . We also analyse public UST data of the host., We also analyse public HST data of the host. 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. " 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." 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$. 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. The ealaxv spectra were flus-calibrated using spectroscopic standard stars., The galaxy spectra were flux-calibrated using spectroscopic standard stars. 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." " 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)." 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. 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. 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. 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}. . 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." The final VLT spectrum is shown in , The final VLT spectrum is shown in 1. Figuell. 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. 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)." The line can thus only be due to AAAA.., The line can thus only be due to $\lambda\lambda$. " 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." 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$. " 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." 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}." " 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." 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." 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." 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" 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. ??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}." For hydrogen. the situation is particularly poor.," For hydrogen, the situation is particularly poor." 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. 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." 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." 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." 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}." 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. 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}." 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." 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)." Details of the calculations can be found in that paper., Details of the calculations can be found in that paper. 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. 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." 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." 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}." " 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." ? 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. 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" in Table AS aud Fie.,in Table \ref{tab:ld} and Fig. 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." . 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. 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." 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$ 5and lyingwithin$m_*$ $m_*$ +2.5] to determine the slope." 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." 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." correlations 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}) )." 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." 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}. Whenever any of the constraints of Sect., Whenever any of the constraints of Sect. 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." 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." We find the best solution using a Monte Carlo method., We find the best solution using a Monte Carlo method. 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." Solutions with y larger than a threshold are discarded., Solutions with $\chi^2$ larger than a threshold are discarded. 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." 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$." 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." 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." 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." 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." 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}) ); the deficit sets on below 80Α., the deficit sets on below 80. . 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." 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. For HZ 43A we first consider the homogeneous models., For HZ 43A we first consider the homogeneous models. ? 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." The nominal equivalent width of this line derived by Barstow et al., The nominal equivalent width of this line derived by Barstow et al. 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." 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\times 10^{-7}$ for the He/H ratio." 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}$. 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$." 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." 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. 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. 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}$ . 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}. ." On the other hand. if the hydrogen layer mass," On the other hand, if the hydrogen layer mass" With 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." 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." 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. 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." 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} 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." In this paper we concentrate on the shear from associated structures., In this paper we concentrate on the shear from associated structures. The relative importance of tides and ellipticity has been considered by KKS., The relative importance of tides and ellipticity has been considered by KKS. 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." In the present paper we take a different tack to estimate the expected tidal shear due to nearby structures.," \nocite{keeton97} In the present paper we take a different tack to estimate the expected tidal shear due to nearby structures." We use the GIF Project recipe (Kauffmann et al., We use the GIF Project recipe (Kauffmann et al. 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." 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." 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." 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. " 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." 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. 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." 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}." . 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." 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." . 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}." . 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. " 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, \Gamma=0.21$ ." 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 a everything outside of this region constitutes the PCFOV.,everything outside of this region constitutes the PCFOV. " 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)." 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. " 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}." " 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." " 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." " Similarly for completeness we also estimated the 65%, 95% and 99% PSLA."," Similarly for completeness we also estimated the $65\%$, $95\%$ and $99\%$ PSLA." " 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}." 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. " 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." 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. " 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$." " 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." 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}. " 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." 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. " 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." most 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}." . 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} = 10^5 r_{\rm g}$." 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." " 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." 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}. 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." 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}. 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." 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$ ." The 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} (> 340 r_{\rm g})$ from the XIS data." 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." 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. Thus. only free parameters are D. Pow. aud the normalization.," Thus, only free parameters are $\Gamma$, $E_{\rm cut}$, and the normalization." 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." 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. 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}." 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." 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." 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." 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." 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}. 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." 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." 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." 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}$." 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." " 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." 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." 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." 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." 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." 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}$ ." " 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}: : ligure 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." 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}) )." 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." 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." 1995). can be easily generalized to fp models.," 1995), can be easily generalized to $f_{\rm NL}$ models." 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." 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." 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. For example. Berry (1973). Jones (1996) and Barreivo et al. (," For example, Berry (1973), Jones (1996) and Barreiro et al. (" 1998). 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." 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." 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_1 \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)." Note that ie and A must be evaluated numerically., Note that $w$ and $\lambda$ must be evaluated numerically. 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." 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$." 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." 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." 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." 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." 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." 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." 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." 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)." 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." 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." 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." The, The 2.5in,2.5in central regious of LO galaxies.,central regions of 10 galaxies. 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. 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}." .. 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." The RSR is a dual polarization and dual beam instruneut., The RSR is a dual polarization and dual beam instrument. The four broadbaud receivers cover instautancously the frequency range 71-111 Cz., The four broadband receivers cover instantaneously the frequency range 74-111 GHz. 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." 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." 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." 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. 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." 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." 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." 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." 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." 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. 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." 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." 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. 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." 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." 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." 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). 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. 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." 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." 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. 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." . 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. 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. Both NGC 6210 and Arp 220 are ultra huninous infrared galaxies (ULIRGS)., Both NGC 6240 and Arp 220 are ultra luminous infrared galaxies (ULIRGS). 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}." . 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}." . 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}. . 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). 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}. . 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." 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." 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. The reference beam is oulv offset bv 1.31 arcnün in azimuuth., The reference beam is only offset by 4.34 arcmin in azimuth. 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." 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}." . 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}. ." 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 by The 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. 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." " 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. 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. The SBO7 algoritim is based on light moments., The SB07 algorithm is based on light moments. 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. Then. for each cell. an ellipticity vector is calculated using light moments.," Then, for each cell, an ellipticity vector is calculated using light moments." 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." Candidates are accepted if they conform to specified parameters., Candidates are accepted if they conform to specified parameters. 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$." 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$." 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." 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." This holds also for the WFPC? images of the XBACS sample., This holds also for the WFPC2 images of the XBACS sample. 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." 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." 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." 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." 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." " 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. 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." 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." 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. " 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." 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. 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." 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." !!! 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." 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). The ares span a magnitude of range20«m24 and a//w ratio range of 8 29.," The arcs span a magnitude range of $20 < m < 24$ and a $l/w$ ratio range of $8-29$ ." As, As second one.,second one. " 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. 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." 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. 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. 2003) of the IBIS instiuneut onboardI, 2003) of the IBIS instrument onboard. "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. 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." 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). Details ou. the whole procedure can be found iu Bird et al. (, Details on the whole procedure can be found in Bird et al. ( 2007).,2007). 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. ( 2006. 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." 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. 1 aud Sect., 1 and Sect. " 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." 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. 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." This setup gave a dispersion of 2.3 fpix., This setup gave a dispersion of 2.3 /pix. 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." 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." 1992. 1991).," 1992, 1994)." 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. 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. 2007)., 2007). Usine the data of NRT obs., Using the data of XRT obs. 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." 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. 2006 for details}., 2006 for details). " 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). This position is filly consistent with the one (sce Fig., This position is fully consistent with the one (see Fig. 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." 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." " 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." The inspection of the optical spectrmu of this objec (reported in Fig., The inspection of the optical spectrum of this object (reported in Fig. 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." 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." 1985)., 1985). A telluric absorption feature is moreover detecte at GSTOΑ., A telluric absorption feature is moreover detected at 6870. ". 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." 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." " 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." Usus the (Cuni Stryker 1983) aud. (Jacoby et al., Using the (Gunn Stryker 1983) and (Jacoby et al. 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." 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." Thus. we classify C0G600_220227091 as a star of spectral type M2TITI.," Thus, we classify 20227091 as a star of spectral type III." we 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)." 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." 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." 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." 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." 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." 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." 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." 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. 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." 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. 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." 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$ ." 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). 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." 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. 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" Stellar Li abundances are at once. very informative and dillieult to interpret.,Stellar Li abundances are at once very informative and difficult to interpret. 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." 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." 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}." . 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. 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}." . 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." 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." 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." 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}," .. emploving a larger sample. agreed. with his conclusion.," employing a larger sample, agreed with his conclusion." 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}." . 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." 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." Most. recently. “Takedaetal.(2007a) measured. Li in LIS nearby solar analogs.," Most recently, \citet{tak07} measured Li in 118 nearby solar analogs." 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." 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. 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}) )." 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." We employ similar methods in the present study., We employ similar methods in the present study. 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. 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. We also examine vsini and the fig activity index in SWPs., We also examine vsini and the $R^{'}_{\rm HK}$ activity index in SWPs. We discuss our findings within the, We discuss our findings within the from 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. 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." 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." 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. 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}. 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." 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)." 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." 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. " 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)." 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." 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." 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." 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$." " 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." 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." " 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." 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." 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 ). 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." 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.”" 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." 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}. ( Since 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.)" 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." " 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. z_{\rm hor}$, where $(1+z_{\rm hor})=(32/27)\times(1+z)$." This gives a natural maximal horizon distance for Lyian à piping., This gives a natural maximal horizon distance for Lyman $\alpha$ pumping. 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." 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." 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." 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." " 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}) )." 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}) )." " 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}) )." The brightucss temperature is a nonlinear but local function of αμ., The brightness temperature is a nonlinear but local function of $n_\alpha$. 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." 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." Accordingly. we have generated realizations of the brightness temperature field.," Accordingly, we have generated realizations of the brightness temperature field." 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}. ." 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}) )." 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$." Figure LE illustrates the brightness temperature power spectrum., Figure \ref{pumpfig} illustrates the brightness temperature power spectrum. 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." The shape of the power spectrin. is therefore simple to calculate., The shape of the power spectrum is therefore simple to calculate. 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." " 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$. 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$ ." The brightness temperature contrast therefore erows rapidly in time., The brightness temperature contrast therefore grows rapidly in time. 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}$ ." " 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" "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)." '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. 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}. " 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." 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}. 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. 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}. " 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." " 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." 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. " 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." 300À.. A fitting value of == 1424+11kms1} wwas obtained., A best-fitting value of = 14.2 $\pm$ 1.1 was obtained. 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}." " 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}." " 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." " 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." " 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$ ." Instead we use V/€aand, Instead we use and Figure 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. " 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." " 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}) )." " 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." " 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." " 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)." " 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} T_{\parallel p})/(T_{\perp p} T_{\parallel \alpha})$, plotted as a function of the relative ion differential speed and the normalized wave power." " 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 \le 0.4$, the temperature anisotropy of the alpha particles, $T_{\perp \alpha}/T_{\parallel \alpha}$, is higher than the anisotropy of the protons, $T_{\perp p}/T_{\parallel p}$." " 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_{\alpha p} /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} /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)." " 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." 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. " 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$ )." 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. " 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." 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. 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. " 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}$ ." "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$. These results confirm the basic features of the analvtic model., These results confirm the basic features of the analytic model. 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. Larger break radii. ~ 110 km. are possible in more massive nebulae.," Larger break radii, $\sim$ 1–10 km, are possible in more massive nebulae." 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. 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." 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. 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." 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. The planetesimals lie in 32 annuli ad 40.75 AU., The planetesimals lie in 32 annuli at 40–75 AU. Models with Neptune have an exira annulus αἱ 30 AU., Models with Neptune have an extra annulus at 30 AU. 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." 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." 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." " 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}$." 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." " 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." " 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$." 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." " 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." 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. 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. 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}." . Small planetesimals with r;S 1 km first grow slowly., Small planetesimals with $r_i \lesssim$ 1 km first grow slowly. Collisonal damping brakes the smallest objects., Collisonal damping brakes the smallest objects. Dynamical friction brakes the largest objects and stirs up the smallest objects., Dynamical friction brakes the largest objects and stirs up the smallest objects. Gravitational focusing factorsincrease. and runaway growth begins.," Gravitational focusing factorsincrease, and runaway growth begins." At 4050 AU. it takes ~ 1 Myr to produce," At 40–50 AU, it takes $\sim$ 1 Myr to produce" In 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)." 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." 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." 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." 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$." 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)." The training set therefore consists of 3825 unique inputs., The training set therefore consists of 3825 unique inputs. 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)." 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. 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." 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." 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." 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)." 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." We set these as the weights of each training vector., We set these as the weights of each training vector. 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])}$." 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." In total. each training vector contains 14 elements.," In total, each training vector contains 14 elements." 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)." 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." 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." 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." 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})$." 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." 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$." 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." 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." 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. 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." 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(\Delta z)=0.03$ after rejecting $\sim$ $>$$3\sigma$ outliers." 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." " 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$ )." This accuracy is comparable to. or rivals. that which can be achieved with traditional spectral template titting techniques.," This accuracy is comparable to, or rivals, that which can be achieved with traditional spectral template fitting techniques." Pertinent to this data-set. Mobasher et (2007) achieved a(A:)=0.031 with a template fitting technique to 16 photometric bands in the COSMOS field.," Pertinent to this data-set, Mobasher et (2007) achieved $\sigma(\Delta z)=0.031$ with a template fitting technique to 16 photometric bands in the COSMOS field." This was found to be in good agreement with photo-zs derived from the independent codes Le Phare (Arnouts et 11999). BPZ 22000) and ZEBRA (Feldmann et 22006).," This was found to be in good agreement with s derived from the independent codes Le Phare (Arnouts et 1999), BPZ 2000) and ZEBRA (Feldmann et 2006)." Several of these methods use Bayesian inference to derive photometric redshifts., Several of these methods use Bayesian inference to derive photometric redshifts. It should be noted that more recently Ilbert et ((2009) achieved much higher photometric redshift accuracies (στ)«0.01) in the COSMOS field using the Le Phare code (S. Arnouts O. Ibert) with 30 broad-. medium- and narrow-bands for template fitting.," It should be noted that more recently Ilbert et (2009) achieved much higher photometric redshift accuracies $(\sigma(\Delta z)<0.01)$ in the COSMOS field using the Le Phare code (S. Arnouts O. Ilbert) with 30 broad-, medium- and narrow-bands for template fitting." Given the improvement seen in the SOMphoto-z technique when more photometric bands are introduced. we would anticipate an improvement in our reported accuracy if we re-trained the SOM with a similar large number of bands.," Given the improvement seen in the SOM technique when more photometric bands are introduced, we would anticipate an improvement in our reported accuracy if we re-trained the SOM with a similar large number of bands." One of the mainbenefits of the SOM technique. aside from the non-reliance on assumptions of spectral properties. is the speed at which photometric redshifts can be calculated once training has," One of the mainbenefits of the SOM technique, aside from the non-reliance on assumptions of spectral properties, is the speed at which photometric redshifts can be calculated once training has" explosion energies than figures ba and 5e.,explosion energies than figures 5a and 5c. " At late times the ""affects of οποίον series of models have verv simular densitv and velocity profiles in comparison to the ""affects of massseries of models.", At late times the “affects of energy” series of models have very similar density and velocity profiles in comparison to the “affects of mass”series of models. The similarity in velocity and density profiles accounts for the similarity in the LC tails in ligure Ta., The similarity in velocity and density profiles accounts for the similarity in the LC tails in figure 7a. " The important result here is (hat given. a certain E/M it does. nol necessarily mean varving E or M,,,. will result in the same LC A comparison between changes in E or Mj, also affects the photospherie temperature of the light curve.", The important result here is that given a certain E/M it does not necessarily mean varying E or $_{env}$ will result in the same LC A comparison between changes in E or $_{env}$ also affects the photospheric temperature of the light curve. The photospheric temperature (fis., The photospheric temperature (fig. Th) shows a much slower response to a variation in energv than the photospheric temperature when varving the mass (fig., 7b) shows a much slower response to a variation in energy than the photospheric temperature when varying the mass (fig. tb)., 4b). A comparison in the Gime difference of when the photospheric temperature drops to 4500 Ix between varving (he energv and varving (he mass shows this., A comparison in the time difference of when the photospheric temperature drops to 4500 K between varying the energy and varying the mass shows this. When the energv is tripled (he time dillerence is only 27 days as opposed to when the mass is just halved the difference is 57 days., When the energy is tripled the time difference is only 27 days as opposed to when the mass is just halved the difference is 57 days. Thus the temperature of the photosphere is much more sensitive to a change in mass rather then a change in The visual LC (fig., Thus the temperature of the photosphere is much more sensitive to a change in mass rather then a change in The visual LC (fig. το) shows very little or no change in (he LC shape between dillerences in models when compared to figure la. except for the initial peak becoming part of the plateau.," 7c) shows very little or no change in the LC shape between differences in models when compared to figure 1a, except for the initial peak becoming part of the plateau." The photospheric velocity for all models is relatively the same until (he photosphere enters (he Ile core region where the velocities separate., The photospheric velocity for all models is relatively the same until the photosphere enters the He core region where the velocities separate. The models with the highest energy show that thev reach the He core the fastest and thus start to move into the slower moving malerial earlier., The models with the highest energy show that they reach the He core the fastest and thus start to move into the slower moving material earlier. The huminositv profiles figure 8d show that for the least energetic model (long dashed lines) the affect of the gamma-ray heating wave is pushed to later times., The luminosity profiles figure 8d show that for the least energetic model (long dashed lines) the affect of the gamma-ray heating wave is pushed to later times. The more energetic models have already. passed through that stage by the same time period., The more energetic models have already passed through that stage by the same time period. By { = 190 days the proliles are exactly (he same (solid lines) indicating that the difference in energies hasn't changed the deposition of gamma ravs., By t = 190 days the profiles are exactly the same (solid lines) indicating that the difference in energies hasn't changed the deposition of gamma rays. At 0 = 379 davs the differences in the deposition can start to be seen as the Iuminositv. profiles start (ο separate slightly for ihe different Figure 9a shows that a smaller the ejected mass results is a smaller clifference in the early LC and a steeper fall of the tail., At t = 379 days the differences in the deposition can start to be seen as the luminosity profiles start to separate slightly for the different Figure 9a shows that a smaller the ejected mass results is a smaller difference in the early LC and a steeper fall of the tail. This is understandable since the smaller the II envelope the faster (he recombination wave and the faster the release of internal energy deposited by the shock., This is understandable since the smaller the H envelope the faster the recombination wave and the faster the release of internal energy deposited by the shock. At late times the steeper tail can be explained by a higher overall velocity profile than ligure Gb., At late times the steeper tail can be explained by a higher overall velocity profile than figure 6b. This is due to the lowered II mass. auc progressively more ganmia ravs escape with increasing explosion Figure 9b shows that when Ni mixing is changed (o < 0.3 M. the early LC is exactly (he same as in fig Ia.," This is due to the lowered H mass, and progressively more gamma rays escape with increasing explosion Figure 9b shows that when Ni mixing is changed to $<$ 0.3 $_\odot$ the early LC is exactly the same as in fig 1a." Bul the plateau and secondary peak are systematically affected more., But the plateau and secondary peak are systematically affected more. we do not follow the detailed cosmological evolution. of a distribution. of ionizeck bubbles. we model the spin temperature of HE I at a fixed redshift as: where Joan is the CMD temperature at that redshift (210 in our cases unless otherwise specified) and 75» is the gas kinetic temperature (which is a function of distance from the source).,"we do not follow the detailed cosmological evolution of a distribution of ionized bubbles, we model the spin temperature of H I at a fixed redshift as: where $T_{\rm CMB}$ is the CMB temperature at that redshift $z=10$ in our cases unless otherwise specified) and $T_k$ is the gas kinetic temperature (which is a function of distance from the source)." The y-coellicicnts are. related to the coupling arising from Lye photons (y.) and from collisions (5j)., The $y$ -coefficients are related to the coupling arising from $\alpha$ photons $y_\alpha$ ) and from collisions $y_c$ ). " The cocllicient jy, is taken from ? and ?..", The coefficient $y_c$ is taken from \citet{chen08} and \citet{kuhlen06}. The coellicient n is the Lvo coupling term arising from the Wouthyvsen-Field ellect., The coefficient $y_\alpha$ is the $\alpha$ coupling term arising from the Wouthysen-Field effect. " Weuse the expressions for yy, [rom ?.. 7.. and ?.. with additional parameters from ?.."," Weuse the expressions for $y_\alpha$ from \citet{chen08}, \citet{zaldarriaga04}, and \citet{pritchard07}, with additional parameters from \citet{hirata06}." In the cases considered here. Lye coupling dominates over other terms such as collisional coupling.," In the cases considered here, $\alpha$ coupling dominates over other terms such as collisional coupling." We specifically include the Lya photons from the stars and/or QSO emission in our models. as well as the auxiliary Lye photons arising from X-ray ionization (??7)..," We specifically include the $\alpha$ photons from the stars and/or QSO emission in our models, as well as the auxiliary $\alpha$ photons arising from X-ray ionization \citep{chen08, Venkatesan:01, shull85}." This leads to a brightness temperature (measured as a differential from the background CAIB temperature at that epoch) given by: When this caleulated brightness temperature. 925. lies above he CAIB temperature at that epoch. the ionized region will »e seen in emission against the CMD.," This leads to a brightness temperature (measured as a differential from the background CMB temperature at that epoch) given by: When this calculated brightness temperature, $\delta T_b$, lies above the CMB temperature at that epoch, the ionized region will be seen in emission against the CMB." Conversely. regions »vond the L-front that lic below the CMD temperature will »e seen in absorption against the CALB.," Conversely, regions beyond the I-front that lie below the CMB temperature will be seen in absorption against the CMB." In Figures S- 13. we show the temperature. profiles with radius for the spin temperature and gas kinetic emperature relative to the CAIB temperature which is constant at a fixed. redshift.," In Figures \ref{fig:radiostd}- – \ref{fig:radiostars}, we show the temperature profiles with radius for the spin temperature and gas kinetic temperature relative to the CMB temperature which is constant at a fixed redshift." \We also show the 21 cm rightness temperature profile and include the full spectrum. case (CN-ravs anc UV. photons) ancl N-ravsconlv. cases. [or each set of curves., We also show the 21 cm brightness temperature profile and include the full spectrum case (X-rays and UV photons) and X-rays-only cases for each set of curves. “These scenarios span most of the cases cliscussecl in Section 3.1 involving a combination of starburst and QSO/DII masses (most of which are at z=10. with two Cases al 2= 20).," These scenarios span most of the cases discussed in Section 3.1 involving a combination of starburst and QSO/BH masses (most of which are at $z=10$, with two cases at $z=20$ )." Some broac conclusions that are common to all the cases whose 21 em signatures are shown are as follows., Some broad conclusions that are common to all the cases whose 21 cm signatures are shown are as follows. First. the curves for the spin temperature are characteristically peaked around the location of the stalled L-front.," First, the curves for the spin temperature are characteristically peaked around the location of the stalled I-front." The transition from fully ionized within (with zero 875) to the neutral LGAL eas occurs bevond the I-front in each case. with peak values for Ty reaching 107. 107 Ix in our cases. and peak values for the 975 emission signal around 3040 milly. Negative 075 values. corresponding to an absorption signal relative to the CMD. occur on scales between 0.1 and 1 Alpe at.=10 in our models and have low net values of ~ 0 to a few mix. and larger values of ~ 2060 mlx on scales of 0.010.1 Alpe at z=20.," The transition from fully ionized within (with zero $\delta T_b$ ) to the neutral IGM gas occurs beyond the I-front in each case, with peak values for $T_s$ reaching $\sim$ $^4$ $^5$ K in our cases, and peak values for the $\delta T_b$ emission signal around 30–40 mK. Negative $\delta T_b$ values, corresponding to an absorption signal relative to the CMB, occur on scales between 0.1 and 1 Mpc at $z=10$ in our models and have low net values of $\sim$ 0 to a few mK, and larger values of $\sim$ 20–60 mK on scales of 0.01–0.1 Mpc at $z=20$." We discuss this further below., We discuss this further below. Second. the curves in cach case corresponding to the X- only case for each starburst/DII scenario consistentlyfag the curves for the corresponding full spectrum case.," Second, the curves in each case corresponding to the X-rays only case for each starburst/BH scenario consistently the curves for the corresponding full spectrum case." This is most cramatically seen in the stars-only case (Figure 13)). a LO? solar-mass starburst with no QSO/DII. where the X-rav production is low.," This is most dramatically seen in the stars-only case (Figure \ref{fig:radiostars}) ), a $10^6$ solar-mass starburst with no QSO/BH), where the X-ray production is low." " Here. the maxiniumn values of 67), occur between 1: and LO kpe for N-ravs only and at about 50 kpe for the full spectrum."," Here, the maximum values of $\delta T_b$ occur between 1 and 10 kpc for X-rays only and at about 50 kpc for the full spectrum." " This case also reveals the inherently ""fuzzy ionization fronts associated with X-rays. relative to the sharp I-fronts of UV radiation - note the eradual transition in spin temperatures for the N-ravs-only case spanning nearly two orders of magnitude in scale."," This case also reveals the inherently “fuzzy"" ionization fronts associated with X-rays, relative to the sharp I-fronts of UV radiation - note the gradual transition in spin temperatures for the X-rays-only case spanning nearly two orders of magnitude in scale." In contrast. the case of the 107 solar-niass starburst with 107 solar-mass OSO/BL (Figure 12)) reveals that the cases with ancl without N-ravs barely. diller in the location ancl peas values of 7) and 925 (emission in the latter).," In contrast, the case of the $10^5$ solar-mass starburst with $10^8$ solar-mass QSO/BH (Figure \ref{fig:radiobigBH}) ) reveals that the cases with and without X-rays barely differ in the location and peak values of $T_s$ and $\delta T_b$ (emission in the latter)." This arises directly in the strong contribution of N-ravs to the overall ionization budget in this scenario., This arises directly in the strong contribution of X-rays to the overall ionization budget in this scenario. Ironicallv. it seems that he greater the X-ray production of a source. the less likely it is have a N-rav-related signature at 21 cm.," Ironically, it seems that the greater the X-ray production of a source, the less likely it is have a X-ray-related signature at 21 cm." These results reveal one of the Κον goals of this paper: he difference in the topology of reionization between N-rav and UV ionization scenarios. and their impact on 21 em oedietions.," These results reveal one of the key goals of this paper: the difference in the topology of reionization between X-ray and UV ionization scenarios, and their impact on 21 cm predictions." Although X-rays do penetrate deeper into the IGM than do UV. photons (leading to the moderate gains in ionization and temperature mentioned earlier). their 7I-ronts trail the UV L-fronts and therefore the UV-associated 2] em signal.," Although X-rays do penetrate deeper into the IGM than do UV photons (leading to the moderate gains in ionization and temperature mentioned earlier), their ``I-front""s trail the UV I-fronts and therefore the UV-associated 21 cm signal." " This could therefore ""blur the signatures of he growth of ionized bubbles around first-light sources. and alter predictions for observing the percolation of reionization (sce the semi-numerical simulations of 2. on this point)."," This could therefore “blur"" the signatures of the growth of ionized bubbles around first-light sources, and alter predictions for observing the percolation of reionization (see the semi-numerical simulations of \citealt{warszawski09} on this point)." We note that a cosmological scenario in which X-ravs alone are eenerated is not well-motivated. physically., We note that a cosmological scenario in which X-rays alone are generated is not well-motivated physically. Rather. the igures in this section show that the dillering scale-dependent ionization [rom N-ravs and UV photons lead cirectly to 21 cm signals that can be distinguished from each other.," Rather, the figures in this section show that the differing scale-dependent ionization from X-rays and UV photons lead directly to 21 cm signals that can be distinguished from each other." " We consider time evolution in two cases for the same source of a LO” solar-mass starburst with a LO"" solar-mass QSO/DII: at z=10 for times of 1. Myr ancl 10 Myr alter the burst/QSO turn on (Figure S and Figure. 9)). and at >=20 for times of 0.1 Myr and 1: Myr (Figure 10. and Figure. 11))."," We consider time evolution in two cases for the same source of a $10^5$ solar-mass starburst with a $10^6$ solar-mass QSO/BH: at $z = 10$ for times of 1 Myr and 10 Myr after the burst/QSO turn on (Figure \ref{fig:radiostd} and Figure \ref{fig:radiostd10Myr}) ), and at $z=20$ for times of 0.1 Myr and 1 Myr (Figure \ref{fig:radiostdz20} and Figure \ref{fig:radiostdz20-1Myr}) )." The main cllects of the advancing I-front with time on the 21 em signal are the following: a similar advancing of the spin temperature curves peak. and therefore that of 975. from a few tens of kpe to about 100 kpe. and. adecreased peak value in 2.," The main effects of the advancing I-front with time on the 21 cm signal are the following: a similar advancing of the spin temperature curve's peak, and therefore that of $\delta T_b$, from a few tens of kpc to about 100 kpc, and, a peak value in $T_s$." This is mostly due to the rapid. falloff in the Lye [lux at increasing radii (going as r. 7). which leads to a decreased coupling between the eas HE E and the source radiation.," This is mostly due to the rapid falloff in the $\alpha$ flux at increasing radii (going as $r^{-2}$ ), which leads to a decreased coupling between the gas H I and the source radiation." " The important. role of this Lye photon coupling is manifested also through the slight increase in the positive values (emission signal) of 975, and the increased values of 915 (absorption signal at 21 cm) at 2=20 relative to z=10. arising from the ‘loser location of the I-fronts to the source with increasing redshift."," The important role of this $\alpha$ photon coupling is manifested also through the slight increase in the positive values (emission signal) of $\delta T_b$ and the increased values of $\delta T_b$ (absorption signal at 21 cm) at $z=20$ relative to $z=10$, arising from the closer location of the I-fronts to the source with increasing redshift." These effects are discussed in more detail in the Dext section., These effects are discussed in more detail in the next section. llere. we compare our results and model assumptions with those from papers in the recent. Literature addressing X- and/or helium ionization. and the resulting 21 cm signals.," Here, we compare our results and model assumptions with those from papers in the recent literature addressing X-ray and/or helium ionization, and the resulting 21 cm signals." We find that our results are. for the most. part. in agreement with the findings of other groups when we make similar model assumptions.," We find that our results are, for the most part, in agreement with the findings of other groups when we make similar model assumptions." We also comment on the theoretical assumption of passive X-ray production tied to star formation at high recshilts., We also comment on the theoretical assumption of passive X-ray production tied to star formation at high redshifts. In ? and ?.. the emergent spectrum djs. based: on a radiative transfer calculation starting. with a stellar," In \citet{chen04} and \citet{chen08}, , the emergent spectrum is based on a radiative transfer calculation starting with a stellar" which has been made contemporaneously. which is what we attempt next.,"which has been made contemporaneously, which is what we attempt next." In order to be considered. the X-ray and optical spectroscopic measurements had to be made within one day of each other. except at quiescent levels at which we assumed a more or less stable level had been reached (quiescent variability can reach factors of several. but this not very significant for these logarithmic plots).," In order to be considered, the X-ray and optical spectroscopic measurements had to be made within one day of each other, except at quiescent levels at which we assumed a more or less stable level had been reached (quiescent variability can reach factors of several, but this not very significant for these logarithmic plots)." In Fig + we plot Ha EW as a function of Zx for the sample of objects discussed previously (except for ΝΟ Cyg for which we do not have contemporaneous X-ray measurements). plus the more unusual object GX 339-4.," In Fig 4 we plot $\alpha$ EW as a function of $L_X$ for the sample of objects discussed previously (except for V404 Cyg for which we do not have contemporaneous X-ray measurements), plus the more unusual object GX 339-4." None of the individual sources show a Statistically significant rank tanti-)correlation (see Table 2)., None of the individual sources show a statistically significant rank (anti-)correlation (see Table 2). In Fig 5 we plot the ensemble of data points. plus a small amount of additional data from the sources V404 Cyg. GRO 11655-40. 4U 1937411. GS 2000425. ΝΤΕ J1650-500 and XTE J1859+226 (see Table | for references).," In Fig 5 we plot the ensemble of data points, plus a small amount of additional data from the sources V404 Cyg, GRO J1655-40, 4U 1957+11, GS 2000+25, XTE J1650-500 and XTE J1859+226 (see Table 1 for references)." " A Spearman rank correlation test for the complete sample plotted in Fig 5 results in a Spearman rank correlation coefficient ofr,=OAS ία ~3.9 result)."," A Spearman rank correlation test for the complete sample plotted in Fig 5 results in a Spearman rank correlation coefficient of $r_s = -0.48$ (a $\sim 3.9\sigma$ result)." This supports the conclusion of section 2.1., This supports the conclusion of section 2.1. A single power-law fit to the data presented in Fig 5 gives This is close to. but steeper than. the EW xLU estimated in section 2.1. and indicates a mean X-ray decay e-folding time less than the 30 days given in Chen et al. (," A single power-law fit to the data presented in Fig 5 gives This is close to, but steeper than, the EW $\propto L_X^{-0.1}$ estimated in section 2.1, and indicates a mean X-ray decay e-folding time less than the 30 days given in Chen et al. (" 1997).,1997). The apparent anti-correlation seems to be dominated by the difference between measurements at Ly<107 erg + where all sources are in the hard X-ray spectral state. and those at higher luminosities. where transitions between different spectral states can occur (see e.g. Nowak 1995: Homan Belloni 2005: Remillard MeClintock 2006 for a discussion of these states).," The apparent anti-correlation seems to be dominated by the difference between measurements at $L_X \leq 10^{36}$ erg $^{-1}$, where all sources are in the hard X-ray spectral state, and those at higher luminosities, where transitions between different spectral states can occur (see e.g. Nowak 1995; Homan Belloni 2005; Remillard McClintock 2006 for a discussion of these states)." It is somewhat puzzling that the anti-correlation stands out much more clearly in the first analysis (Figs 2 and 3) than in the second (Figs 4 and 5). which implies that there may not be a simple one-to-one relation between X-ray luminosity and Ha EW.," It is somewhat puzzling that the anti-correlation stands out much more clearly in the first analysis (Figs 2 and 3) than in the second (Figs 4 and 5), which implies that there may not be a simple one-to-one relation between X-ray luminosity and $\alpha$ EW." In this context it is interesting to note that the low-frequency QPOs in some hard state black hole candidates show similar monotonic behaviour with time which is not so simple when compared to flux (e.g. XTE J11184480 in Wood et al., In this context it is interesting to note that the low-frequency QPOs in some hard state black hole candidates show similar monotonic behaviour with time which is not so simple when compared to X-ray flux (e.g. XTE J1118+480 in Wood et al. 2001)., 2001). In any case. the anti-correlation. whether simple or not. is clearly there.," In any case, the anti-correlation, whether simple or not, is clearly there." Far fewer results were available in the literature for neutron star systems: the details and references are provided in Table |., Far fewer results were available in the literature for neutron star systems; the details and references are provided in Table 1. In Fig 6 we plot the neutron star data alongside the black hole data presented in Fig 5., In Fig 6 we plot the neutron star data alongside the black hole data presented in Fig 5. What we see is approximately similar behaviour. in that there is a suggestion of a similar trend. with a similar (or slightly lower) normalisation.," What we see is approximately similar behaviour, in that there is a suggestion of a similar trend, with a similar (or slightly lower) normalisation." In fact a Spearman rank correlation test indicates that the sample of seven neutron star measurements are anticorrelated at the 2.70 level (o;= 0.548)., In fact a Spearman rank correlation test indicates that the sample of seven neutron star measurements are anticorrelated at the $2.7 \sigma$ level $r_s = -0.84$ ). So the neutron star data are consistent with. but do not independently establish. the anti-correlation found for the BHXBs.," So the neutron star data are consistent with, but do not independently establish, the anti-correlation found for the BHXBs." Adding the BHXB and neutron star samples results in a Spearman rank correlation coefficient. of ry=0.58. corresponding to an anticorrelation at the 5.10 level.," Adding the BHXB and neutron star samples results in a Spearman rank correlation coefficient of $r_s = -0.58$, corresponding to an anticorrelation at the $5.1 \sigma$ level." In summary. although the individual simultaneous £x and EW measurements do not confirm the anti-correlation further. the effect is significant when considering the ensemble of all data points. moreso when combining neutron star data with the black hole sample.," In summary, although the individual simultaneous $L_X$ and EW measurements do not confirm the anti-correlation further, the effect is significant when considering the ensemble of all data points, moreso when combining neutron star data with the black hole sample." " The upper x-axes of Figs 5 and 6 also indicate a rough estimate of the optical-infrared luminosities. Lou:=vl, based on the relations presented in. Russell et al. ("," The upper x-axes of Figs 5 and 6 also indicate a rough estimate of the optical–infrared luminosities, $L_{\rm OIR} = \nu L_{\nu}$ based on the relations presented in Russell et al. (" 2006). and repeated in the figure captions (without statistical uncertainties).,"2006), and repeated in the figure captions (without statistical uncertainties)." Note that the relations are slightly different for black holes and neutron stars (Lou is larger for black holes at any given X-ray luminosity)., Note that the relations are slightly different for black holes and neutron stars $L_{\rm OIR}$ is larger for black holes at any given X-ray luminosity). This allows us to get a better idea of how the EW varies as a function of the optical continuum., This allows us to get a better idea of how the EW varies as a function of the optical continuum. = 12pt Asupernova (SN) is the brilliant death of a star.,= 12pt A supernova (SN) is the brilliant death of a star. Due to the thermonuclear explosion of à CO whie cbvarl (SN La) or to the core-collapse of a massive star (SN LL/Ib/Ic). supernovae (SNe) alter he of the progenitor object. impulsively new isot(opes.composi," Due to the thermonuclear explosion of a CO white dwarf (SN Ia) or to the core-collapse of a massive star (SN II/Ib/Ic), supernovae (SNe) alter the composition of the progenitor object, impulsively synthesizing new isotopes." tion Le was recognized in the 1960s that the decaysv nthesizingof radionuclei was required to explain the light curves of supernovae (Colgate et al., It was recognized in the 1960s that the decay of radionuclei was required to explain the light curves of supernovae (Colgate et al. 1966. Truran οἱ al.," 1966, Truran et al." 1967. Bodansky et al.," 1967, Bodansky et al." 1968)., 1968). " The principal radionuclei studied have been ""Ni and its daughter product n ""Co.‘ but ο ""Co. SLi. rps DPR ""Να and ""Cogu have also been sugeested to contribute to the optical light (Woosley. Pinto Hartmann 1989)."," The principal radionuclei studied have been $^{56}$ Ni and its daughter product $^{56}$ Co, but $^{57}$ Co, $^{44}$ Ti, $^{22}$ Na and $^{60}$ Co have also been suggested to contribute to the optical light (Woosley, Pinto Hartmann 1989)." Phe study of SN nucleosynthesis has branched into three principle explosive nucleosvnthesis. radiation transport. and ealactic chemical calegories:evolution.," The study of SN nucleosynthesis has branched into three principle categories; explosive nucleosynthesis, radiation transport, and galactic chemical evolution." The first category of studs concentrates upon applying nuclear and magneto-hyvdrodynamies to simulate the evolution of the physiesobject(s) up to and through explosive nucleosynthesis., The first category of study concentrates upon applying nuclear physics and magneto-hydrodynamics to simulate the evolution of the progenitor object(s) up to and through explosive nucleosynthesis. The results from progenitorthese studies are: a) the determination of whether (or for what range of parameters) a given explosion scenario successfully vields a SN and b) the composition ancl kinematic structure of the ejecta of explosion.successful especially the vields of radionuclei.," The results from these studies are; a) the determination of whether (or for what range of parameters) a given explosion scenario successfully yields a SN explosion, and b) the composition and kinematic structure of the ejecta of successful explosions, especially the yields of radionuclei." Phe second category of study explosions.accepts the outputs of the first. group (SN. models) and seeks to derive further constraints upon SNe through comparisons with observations., The second category of study accepts the outputs of the first group (SN models) and seeks to derive further constraints upon SNe through comparisons with observations. The key involved with these are the transport of the decay physicsproducts of the various racdionucletinvestigations (+ /x- photons ancl positrons) ancl the subsequent diffusion and emission of UV/OPT/LR., The key physics involved with these investigations are the transport of the decay products of the various radionuclei $\gamma$ /x-ray photons and positrons) and the subsequent diffusion and emission of UV/OPT/IR photons. The third ofstudy attempts to the local. and photons. categoryabundances of all isotopes.," The third category of study attempts to reproduce the local, galactic and extra-galactic abundances of all isotopes." Thereproduce information critical to the galacticthird study is the extra-galacticexact nucleosvnthesis contribution fron SNe as a function of time and location., The information critical to the third study is the exact nucleosynthesis contribution from SNe as a function of time and galaxy location. The study. of line galaxyemission is an excellent. diagnostic of SNe which can contribute to gamma-rayall three, The study of gamma-ray line emission is an excellent diagnostic of SNe which can contribute to all three investigations. In the three sections. we discuss the science derived [rom investigations.eamma-ray line Followingobservations.," In the following three sections, we discuss the science derived from gamma-ray line observations." In the first section. we discuss the physics of nuclear and. the of gamma-ray In.," In the first section, we discuss the physics of nuclear decays and the escape of gamma-ray photons." the second. section. we decaysdescribe the escapespecifications of an advanced photons.Compton telescope (ACE). particularly the version at the Naval Besearch Lab (NRL).," In the second section, we describe the specifications of an advanced Compton telescope (ACT), particularly the version being investigated at the Naval Research Lab (NRL)." In the third section. we beingdiscuss the investigatedscience that could be performed with an ACT.," In the third section, we discuss the science that could be performed with an ACT." We conclude with an assessment of what we consider to be the priorities of SN science with an ACT., We conclude with an assessment of what we consider to be the priorities of SN science with an ACT. ltacdionuclei in SNe to stable nuclei on various time-scales. generating ganuna- pro," Radionuclei produced in SNe decay to stable nuclei on various time-scales, generating gamma- and x-ray photons, electrons and positrons." ducedand x-ray ," These decay products either deposit their energy in the ejecta (at early times helping to lift the ejecta, at later times driving the UV/OPT/IR light curves) or they escape, leading to potentially detectable $\gamma$ /x-ray emission." decay elect, Shown in Figure 1 are the decay curves for the principal radionuclides of two SN The left panel shows the decay rates of the SN Ia model W7 (Nomoto et al. , 1984). rons , The right panel shows the decay rates for the SN II model W10HMM (Pinto Woosley 1988). ancl , Evident in this figure is the cascade from the early-time dominance of short-lived radioactivities to the later dominance of long-lived radioactivities. positrons.," Assuming that a large fraction of these photons escape, short-lived radioactivities give rise to intense, but brief emission, while long-lived radioactivities give rise to faint, but persistent emission." These decay produ," For the purposes of this work, the gamma emission is categorized as prompt, supernova remnant (SNR), or diffuse." cts either deposi, This categorization is based upon both the physics of the gamma-ray emission (the opacity and the angular size of the emitting region) and upon the instruments employed to detect the emission. t their photons.energy in ," Initially, the SN density is so large that all $\gamma$ /x -ray photons are scattered and no high-energy emission emerges." the cjecta (at early.," As the SN expands, the ejecta thins and the $\gamma$ /x -ray photons begin to escape." times helping to ," Thus, the $\gamma$ /x -ray line flux from a SN depends upon the overlying mass and the ejecta kinematics." lift the ejecta., This makes the evolution of the fluxes of the various gamma-ray lines a probe of the SN ejecta. at later times dri," The optical absorption and emission lines from SNe also probe these quantities, but not as early, nor as directly as do the gamma-ray lines." ving the UV/OLI'T/LIR. lig, The epoch is characterized by the lowering of the gamma-ray line opacity to negligible values. ht curves) or escape. to detectable 5 emiss, The early onset of gamma-ray escape would make prompt emission detectable to large distances. ion. Shown in Figurethey 1 are the lea," Although plausible SNe Ia and SNe II/Ib/Ic explosion scenarios exhibit a range of characteristics, the timescale of prompt emission is on the order of a year." dingdecay curves for potent," Two different approaches have been employed to detect SN gamma rays; wide-FoV instruments, and pointed, target of opportunity (ToO) instruments." iallythe principal ra," For a wide-FoV detector, the temporal and sky-coverage are large enough that the desired detection rate is achieved through low sensitivity and long-duration observations." dionuclides/x, This search discovers SNe independent of optical SN searches and is capable of detecting any escaping emission from the moment of explosion. -ray of SN t, This approach was employed by the SMM/GRS which detected 847/1238 keV emission from SN 1987A (Matz et al. woss pro, Narrow FoV detectors rely upon triggers (optical detections) to observe ToO SNe. mptsmodels., These instruments are engineered to have maximal sensitivity as a trade-off for the narrower FoV. The critical element in this approach is the time delay between the optical SN detection (and SN type identification) and the re-orientation of the gamma-ray instrument to observe the SN. Quasars are amongst the most luminous sources in the universe.,Quasars are amongst the most luminous sources in the universe. At cosmological distances. their relatively small size ensures the regions responsible for producing the various spectral ine components remains effectively unresolved with modern elescopes.," At cosmological distances, their relatively small size ensures the regions responsible for producing the various spectral line components remains effectively unresolved with modern telescopes." Gravitational microlensing. however. can significantly magnify the inner regions. providing clues to the various scales of structure located at the heart of quasars. giving some of the best estimates of the scale of the central continuum emitting region (e.g.Jaroszynski.Wambsganss.&Paezynski1992:Yonehara1999:Wyithe.Webster.Turner.&Mortlock 2000)... as well as offering he possibility of probing the nature of other quasar small scale structure (Belle&Lewis2000:WyitheLoeb2002).," Gravitational microlensing, however, can significantly magnify the inner regions, providing clues to the various scales of structure located at the heart of quasars, giving some of the best estimates of the scale of the central continuum emitting region \citep[e.g.][]{1992ApJ...396L..65J,1999ApJ...519L..31Y,2000MNRAS.315...62W}, as well as offering the possibility of probing the nature of other quasar small scale structure \citep{2000PASP..112..320B,2002ApJ...577..615W}." The degree of microlensing magnitication is dependent upon he scale size of the source. with smaller sources being more susceptible to large magnifications (e.g.Wambsganss&Paezyn-ski 1991).," The degree of microlensing magnification is dependent upon the scale size of the source, with smaller sources being more susceptible to large magnifications \citep[e.g.][]{1991AJ....102..864W}." While the continuum emitting region of a quasar is small enough to undergo significant magnification. the more extensive line emitting regions. specifically the BLR with a scale length of O.l-a few pe. were considered to be too large to suffer substantial magnitication.," While the continuum emitting region of a quasar is small enough to undergo significant magnification, the more extensive line emitting regions, specifically the BLR with a scale length of 0.1-a few pc, were considered to be too large to suffer substantial magnification." Nemiroff(1988). undertook a study to determine the degree of microlensing of various models of the BLR. examining the influence of a single microlensing mass in front of the emission region.," \citet{1988ApJ...335..593N} undertook a study to determine the degree of microlensing of various models of the BLR, examining the influence of a single microlensing mass in front of the emission region." When considering microlensing in multiply imaged quasars. however. many stars are expected to influence the light beam of a distant source. and these combine in a very non-linear fashion and the single star approximation is a poor one (e.g.Wambsganssetal.1990)..," When considering microlensing in multiply imaged quasars, however, many stars are expected to influence the light beam of a distant source, and these combine in a very non-linear fashion and the single star approximation is a poor one \citep[e.g.][]{1990ApJ...352..407W}." Schneider&Wambsganss(1990) considered the microlensing of a BLR at substantial optical depth., \citet{1990A&A...237...42S} considered the microlensing of a BLR at substantial optical depth. These studies found that while gravitational microlensing did result in the moditication of the BLR emission line profiles. the overall magnitication of the region was small. typically less than30%.," These studies found that while gravitational microlensing did result in the modification of the BLR emission line profiles, the overall magnification of the region was small, typically less than." These microlensing studies employed estimates of the size of the quasar BLR based upon simple ionization models [see Davidson&Netzer (1979)]]., These microlensing studies employed estimates of the size of the quasar BLR based upon simple ionization models [see \citet{1979RvMP...51..715D}] ]. Reverberation mapping. however. provides a more direct measure of the geometry of the BLR and early studies suggested these simple ionization models had over estimated the scale of the BLR by roughly an order of magnitude (e.g.Petersonetal.1985).. prompting a revision of BLR physics (Rees.Netzer.&Ferland1989).," Reverberation mapping, however, provides a more direct measure of the geometry of the BLR and early studies suggested these simple ionization models had over estimated the scale of the BLR by roughly an order of magnitude \citep[e.g.][]{1985ApJ...292..164P}, prompting a revision of BLR physics \citep{1989ApJ...347..640R}." ". More recent reverberation measurements have refined the size of the BLRs in active galaxies. finding it to be ~10. !pe in low luminosity AGN. up to —10.! pe in luminous quasars. with the size of the BLR scaling with the luminosity of the quasar. such that ρεxL""* (Wandel.Peter-son.&Malkan1999:Kaspietal. 2000).."," More recent reverberation measurements have refined the size of the BLRs in active galaxies, finding it to be $\sim10^{-4}$ pc in low luminosity AGN, up to $\sim10^{-1}$ pc in luminous quasars, with the size of the BLR scaling with the luminosity of the quasar, such that $R_{BLR} \propto L^{0.7}$ \citep{1999ApJ...526..579W,2000ApJ...533..631K}." Furthermore. these results demonstrate the BLR possesses a stratified. structure. with high ionization lines being an order of magnitude smaller than lower ionization lines.," Furthermore, these results demonstrate the BLR possesses a stratified structure, with high ionization lines being an order of magnitude smaller than lower ionization lines." Following this discovery. Abajasetal.(2002) reexamined the question of the microlensing of the BLR region in light of this revised scale.," Following this discovery, \citet{2002ApJ...576..640A} reexamined the question of the microlensing of the BLR region in light of this revised scale." Undertaking an analysis similar to Nemiroff(1988).. they considered the influence of a single microlensing mass located in the BLR. finding that significant modification of the BLR line protile results.," Undertaking an analysis similar to \citet{1988ApJ...335..593N}, they considered the influence of a single microlensing mass located in the BLR, finding that significant modification of the BLR line profile results." The discovery of supernova 1998bw (Galama et al. 1998)), The discovery of supernova 1998bw (Galama et al. \cite{galama98}) ) within the 8 areminute radius of the BepppoSAX WFC error circle for GRB 980425 (Soffitta et al. 1998)), within the 8 arcminute radius of the BepppoSAX WFC error circle for GRB 980425 (Soffitta et al. \cite{soffitta98}) ) has led to the hypothesis that some GRB sources are Type Ib-le SNe., has led to the hypothesis that some GRB sources are Type Ib-Ic SNe. There are some serious difficulties with this interpretation of the data for GRB 980425/SN 1998bw: the supernova occurred outside the NFI error circle of a fading X-ray source (Pian et al. 1998a..1998b.. 1999;," There are some serious difficulties with this interpretation of the data for GRB 980425/SN 1998bw: the supernova occurred outside the NFI error circle of a fading X-ray source (Pian et al. \cite{pian98a}, \cite{pian98b}, , \cite{pian99} ;" Piro et 1998))., Piro et \cite{piro98}) ). This source had a temporal decay consistent with a power-law index of ~1.2 (Pian et al. 1998b)).," This source had a temporal decay consistent with a power-law index of $\sim 1.2$ (Pian et al. \cite{pian98b}) )," which resembles the temporal behavior of X-ray afterglows seen in almost every other GRB followed up with the SAX NFL, which resembles the temporal behavior of X-ray afterglows seen in almost every other GRB followed up with the SAX NFI. It must therefore be viewed as a strong candidate to be the X-ray afterglow of GRB 980425., It must therefore be viewed as a strong candidate to be the X-ray afterglow of GRB 980425. Moreover. 1f the association between GRB 980425 and SN 1998bw were true. the luminosity of this burst would be ~10! ere | and its energy would be ~10/* erg.," Moreover, if the association between GRB 980425 and SN 1998bw were true, the luminosity of this burst would be $\sim 10^{46}$ erg $^{-1}$ and its energy would be $\sim 10^{47}$ erg." Each would therefore be five orders of magnitude less than that of other bursts. and the behavior of the X-ray and optical afterelow would be very different from those of the other BeppoSAX bursts. yet the burst itself is indistinguishable from other BeppoSAX and BATSE GRBs with respect to duration. time history. spectral shape. peak flux. and and fluence (Galama et al. 1998)).," Each would therefore be five orders of magnitude less than that of other bursts, and the behavior of the X-ray and optical afterglow would be very different from those of the other BeppoSAX bursts, yet the burst itself is indistinguishable from other BeppoSAX and BATSE GRBs with respect to duration, time history, spectral shape, peak flux, and and fluence (Galama et al. \cite{galama98}) )." In view of these difficulties. the safest procedure is to regard the association às a hypothesis that 1s to be tested by searching for correlations between SNe and GRB in catalogs of SNe and GRBs. excluding SN 1998bw and GRB 980425.," In view of these difficulties, the safest procedure is to regard the association as a hypothesis that is to be tested by searching for correlations between SNe and GRB in catalogs of SNe and GRBs, excluding SN 1998bw and GRB 980425." Wang Wheeler (19983:: see also Wang Wheeler 1998b)) have correlated BATSE GRB with Type Ia and with Type Ib-Ic Sne., Wang Wheeler \cite{wang98a}; see also Wang Wheeler \cite{wang98b}) ) have correlated BATSE GRB with Type Ia and with Type Ib-Ic Sne. They found that the data was “consistent” with the assumption of an association between GRB and Type Ib-Ic SNe., They found that the data was “consistent” with the assumption of an association between GRB and Type Ib-Ic SNe. In the present work we improve upon the Wang Wheeler correlative study by introducing an analysis method based on Bayesian inference. and therefore using the likelihood function. that incorporates information about the BATSE position errors in à non-arbitrary way and that is free of the ambiguities of statistics.," In the present work we improve upon the Wang Wheeler correlative study by introducing an analysis method based on Bayesian inference, and therefore using the likelihood function, that incorporates information about the BATSE position errors in a non-arbitrary way and that is free of the ambiguities of statistics." The method also accounts the fact that the BATSE temporal exposure ts less than unity., The method also accounts the fact that the BATSE temporal exposure is less than unity. We use the BATSE 4B GRB Catalog (Meegan et al. 1998)).," We use the BATSE 4B GRB Catalog (Meegan et al. \cite{meegan98}) )," and BATSE bursts that occurred subsequent to the 4B catalog but before | May 1998., and BATSE bursts that occurred subsequent to the 4B catalog but before 1 May 1998. We also use the Ulysses supplement to the BATSE 4B catalog. which contains 219 BATSE bursts for which 3rd IPN annuli have been determined (Hurley et al. 1998)).," We also use the Ulysses supplement to the BATSE 4B catalog, which contains 219 BATSE bursts for which 3rd IPN annuli have been determined (Hurley et al. \cite{hurley98}) )." Hurley (private communication. 1998) has kindly made available at our request 3rd IPN annuli for an additional 9 BATSE bursts that occurred subsequent to the period of the BATSE 4B catalog but before 1 May 1998.," Hurley (private communication, 1998) has kindly made available at our request 3rd IPN annuli for an additional 9 BATSE bursts that occurred subsequent to the period of the BATSE 4B catalog but before 1 May 1998." We have compiled three Type I SNe samples., We have compiled three Type I SNe samples. The first is a sample of 37 Type la SNe at low redshift (2.< 0.1) from the CfA SN Search Team (Riess 1998. private communication).," The first is a sample of 37 Type Ia SNe at low redshift $z < 0.1$ ) from the CfA SN Search Team (Riess 1998, private communication)." " The second is a sample of 46 moderate redshift (0.1.— 0,830) Type Ia SNe from the Supernova Cosmology Project (Perlmutter 1998. private communication)."," The second is a sample of 46 moderate redshift $0.1 < z < 0.830$ ) Type Ia SNe from the Supernova Cosmology Project (Perlmutter 1998, private communication)." The third sample consists of 20 Type Ib. Ib/c. and Ile SNe compiled from [AU Cireulars and various Se catalogs.," The third sample consists of 20 Type Ib, Ib/c, and Ic SNe compiled from IAU Circulars and various SNe catalogs." We compare three hypotheses: ZI: The association between SNe and GRBs is real., We compare three hypotheses: $H_1$: The association between SNe and GRBs is real. If a SN is observed. there 1s a chance e that BATSE sees the associated GRB. where e is the average BATSE temporal exposure.," If a SN is observed, there is a chance $\epsilon$ that BATSE sees the associated GRB, where $\epsilon$ is the average BATSE temporal exposure." While e varieswith Declination. the variation is modest and we," While $\epsilon$ varieswith Declination, the variation is modest and we" "identification, it is natural to investigate whether the merging AGNS look different from the isolated peaked AGNs double-peakedin terms of their pprofiles.","identification, it is natural to investigate whether the merging double-peaked AGNs look different from the isolated double-peaked AGNs in terms of their profiles." " Because our sample was compiled from three different groups, we re-modeled the emission lines to the measurements."," Because our sample was compiled from three different groups, we re-modeled the emission lines to homogenize the measurements." " We the ,A5007 line homogenizewith either two Gaussians or decomposedLorentzian profiles, whichever gives the lower X?."," We decomposed the $\lambda5007$ line with either two Gaussians or Lorentzian profiles, whichever gives the lower $\chi^2$." We found that the merging and isolated double-peaked AGNs show indistinguishable pprofiles and velocity splittings (Fig. 3))., We found that the merging and isolated double-peaked AGNs show indistinguishable profiles and velocity splittings (Fig. \ref{fig:resolve}) ). " Wangetal.(2009) found an anti-correlation between flux ratio and velocity shift ratio of the ccomponents, which they interpreted as an indication of the orbital motion of binary AGNs."," \citet{Wang09} found an anti-correlation between flux ratio and velocity shift ratio of the components, which they interpreted as an indication of the orbital motion of binary AGNs." " Such an anti-correlation is expected if (1) the lluminosities correlate with the black hole masses, and (2) the black hole masses correlates with the masses (the Magorrian relation)."," Such an anti-correlation is expected if (1) the luminosities correlate with the black hole masses, and (2) the black hole masses correlates with the bulge masses (the Magorrian relation)." " For the former statement bulgeto hold, they had to assume identical bolometric corrections and Eddington ratios for both components in each binary system."," For the former statement to hold, they had to assume identical bolometric corrections and Eddington ratios for both components in each binary system." " For the where redshifts could be measured from stellar subsampleabsorption lines systemic(compiled from Wangetal.2009;Liuetal.2010b;Smith 2010)), we found that both merging and isolated double-peaked AGNs fall on the same anti-correlation with similar dispersions (Fig. 5))."," For the subsample where systemic redshifts could be measured from stellar absorption lines (compiled from \citealt{Wang09,Liu10a,Smith10}) ), we found that both merging and isolated double-peaked AGNs fall on the same anti-correlation with similar dispersions (Fig. \ref{fig:virial}) )." " Because the isolated double-peaked AGNs cannot be kpc-scale binary AGNS, these results show that other mechanisms, such as jet-driven outflows, extended emission-line nebulae, and peculiar kinematics in the narrow line regions, can produce the same double-peaked line profilesand the apparent virial relation of Wangetal.(2009)."," Because the isolated double-peaked AGNs cannot be kpc-scale binary AGNs, these results show that other mechanisms, such as jet-driven outflows, extended emission-line nebulae, and peculiar kinematics in the narrow line regions, can produce the same double-peaked line profiles the apparent virial relation of \citet{Wang09}." ". Jet-cloud interactions are an important mechanism in producing double-peaked llines (e.g.,Stocktonetal.2007;Rosario2010)."," Jet-cloud interactions are an important mechanism in producing double-peaked lines \citep[e.g.,][]{Stockton07,Rosario10}." ". Although the radio-detected fraction of type-2 double-peaked AGNS is similar to that of the general type-2 AGN population (73595;Liuetal.2010b), Smithetal.(2010) found that radio sources are three times over-represented in type-1 double-peaked AGNs than in the general type-1 AGN population."," Although the radio-detected fraction of type-2 double-peaked AGNs is similar to that of the general type-2 AGN population \citep[$\sim$35\%;][]{Liu10a}, \citet{Smith10} found that radio sources are three times over-represented in type-1 double-peaked AGNs than in the general type-1 AGN population." Are radio-detected type-1 AGNs also over-represented in those that are undergoing mergers?, Are radio-detected type-1 AGNs also over-represented in those that are undergoing mergers? " To include objects with complex radio morphologies, we obtained 1.4 GHz radio continuum images of the double-peaked AGNs from the FIRST survey (Beckeretal.1995).."," To include objects with complex radio morphologies, we obtained 1.4 GHz radio continuum images of the double-peaked AGNs from the FIRST survey \citep{Becker95}." " For broad-line double-peaked AGNs as a whole, the radio detected fraction is (14/41)."," For broad-line double-peaked AGNs as a whole, the radio detected fraction is (14/41)." The fraction is slightly higher (47%)) for the 17 broad-line double-peaked AGNs with AO-corrected images., The fraction is slightly higher ) for the 17 broad-line double-peaked AGNs with AO-corrected images. " For the 8 sources that appear to be mergers, the fraction is (3/8)."," For the 8 sources that appear to be mergers, the fraction is (3/8)." " Although radio detections are less common in mergers (38%)) compared to isolated AGNs (56%)), the radio-detected fraction remains three times (after correcting for the bias in the AO sample) higher than that of the overall broad-line AGN population (~10%at0.270%)) of these binary AGN candidates are isolated AGNs., Our analyses demonstrate clearly that a large percentage $>$ ) of these binary AGN candidates are isolated AGNs. " Their double Iline profiles peakedcould be explained by several other processes, as discussed in ??.."," Their double peaked line profiles could be explained by several other processes, as discussed in \ref{sec:id_bAGN}." " Because only§ ~1% of the SDSS AGNs show double- line profiles, the ~30% merger fraction thus indicates a peakedkpc-scale binary AGN of «0.396, which is comparable to the fraction of AGN pairs with >10 kpc transverse separations (~0.1%))."," Because only $\sim$ of the SDSS AGNs show double-peaked line profiles, the $\sim$ merger fraction thus indicates a kpc-scale binary AGN of $<$, which is comparable to the fraction of AGN pairs with $>$ 10 kpc transverse separations $\sim$ )." There are several factors that make this binary fraction just an order of magnitude estimate., There are several factors that make this binary fraction just an order of magnitude estimate. " Firstly, it is possible that one of the merging components is actually inactive and the double-peaked line profile is produced by a single galaxy."," Firstly, it is possible that one of the merging components is actually inactive and the double-peaked line profile is produced by a single galaxy." " In a forthcoming paper, we will present spatially resolved spectroscopy of these AGN mergers to securely identify binary AGNs."," In a forthcoming paper, we will present spatially resolved spectroscopy of these AGN mergers to securely identify binary AGNs." " Secondly,"," Secondly," "critical €& is numerically determined from equation (78)) as £,— L217.",critical $\xi_c$ is numerically determined from equation \ref{diverge}) ) as $\xi_c=1.217$ . "= We. choose η=1 as a limiting.PI and the two explicit D> solutions from equation (73)) ale We stress here that Y7* anc Yi. do not. correspond to gy, and yo solutions. respectively. in a simple manner. because signs of coellicicnts vary with £."," We choose $\eta=1$ as a limiting and the two explicit $D_s^2$ solutions from equation \ref{spiralEta1}) ) are We stress here that $Y_1^A$ and $Y_1^B$ do not correspond to $y_1$ and $y_2$ solutions, respectively, in a simple manner, because signs of coefficients vary with $\xi$." For instance in Fig., For instance in Fig. d. we displav yi in solid line ancl yo in dashed line.," 4, we display $y_1$ in solid line and $y_2$ in dashed line." Across £.. solution structures changes abruptly.," Across $\xi_c$, solution structures changes abruptly." For physically reasonable marginal stability curves. we only need the portions above jy=0.," For physically reasonable marginal stability curves, we only need the portions above $y=0$." The two unstable regimes shown in Fie., The two unstable regimes shown in Fig. 4 are the ring fragmentation regime where a composite disc system rotates too fast to be stable and the collapse regime where a composite clisc svstem rotates too slowly to be stable against large-scale Jeans collapse (Lemos ct al., 4 are the ring fragmentation regime where a composite disc system rotates too fast to be stable and the collapse regime where a composite disc system rotates too slowly to be stable against large-scale Jeans collapse (Lemos et al. 1991: Sver ‘Tremaine 1996: Shu et al., 1991; Syer Tremaine 1996; Shu et al. 2000: Lou 2002: Lou Fan 2002: Lou Shen 2003: Lou Zou 2004)., 2000; Lou 2002; Lou Fan 2002; Lou Shen 2003; Lou Zou 2004). ‘These marginal stability curves can also be derived. [rom he time-dependent. ΑΝ.) analysis by imposing the scale-ree disc conditions (Shen Lou 2003). with the more straightforward 2. criterion equivalent to the effective (2 xwameters presented by Ibmegreen (1995) and Jose (1996).," These marginal stability curves can also be derived from the time-dependent WKBJ analysis by imposing the scale-free disc conditions (Shen Lou 2003), with the more straightforward $D_s-$ criterion equivalent to the effective $Q$ parameters presented by Elmegreen (1995) and Jog (1996)." By varving the sound speed. ratio η and disc density. ratio ὃν we obtain similar marginal stability curves in Fig.," By varying the sound speed ratio $\eta$ and disc density ratio $\delta$, we obtain similar marginal stability curves in Fig." 5., 5. The rends are qualitatively the same as the isothermal «7=0 case (Lou Shen 2003: Shen Lou 2003)., The trends are qualitatively the same as the isothermal $\beta=0$ case (Lou Shen 2003; Shen Lou 2003). In other νους. a composite disc system is less stable as compared. with a single cise svstem for overall axisvmumetric instabilities but becomes more dillicult for large-scale collapses (Lou Shen 2003: Shen Lou 2003).," In other words, a composite disc system is less stable as compared with a single disc system for overall axisymmetric instabilities but becomes more difficult for large-scale collapses (Lou Shen 2003; Shen Lou 2003)." Next. we consider the case of 3=1/4.," Next, we consider the case of $\beta=1/4$." The divergent point now becomes £.—3.159., The divergent point now becomes $\xi_c=3.159$. For qualitative results. we again start [roni the special case of y=1 with the two ος solutions of stationary dispersion. relation. (71)) explicitly eiven by The corresponding mareinal stability curves are displaved in Fig.," For qualitative results, we again start from the special case of $\eta=1$ with the two $D_s^2$ solutions of stationary dispersion relation \ref{spiral}) ) explicitly given by The corresponding marginal stability curves are displayed in Fig." 6., 6. We further explored. variations of the mareinal stability curves for dillerent sets of parameters in lig., We further explored variations of the marginal stability curves for different sets of parameters in Fig. 7., 7. There exists a critical 23. above whieh the collapse regime cdisappears even for the +=1 (single disc) case when the collapse region is largest., There exists a critical $\beta_c$ above which the collapse regime disappears even for the $\eta=1$ (single disc) case when the collapse region is largest. “Vhis critical ;2.=OA8G6 is determined by the condition of zero collapsed regime for the maximum of the lower-Icft branch. namely 1n order to see this clearly. we take 3=0.45 and obtain mareinal stability curves for a=1 as shown in Fig.," This critical $\beta_c=0.436$ is determined by the condition of zero collapsed regime for the maximum of the lower-left branch, namely In order to see this clearly, we take $\beta=0.45$ and obtain marginal stability curves for $\eta=1$ as shown in Fig." S where no collapse regime appears., 8 where no collapse regime appears. This result is consistent. with that of Sver Tremaine (1996) as can be seen from their fie., This result is consistent with that of Syer Tremaine (1996) as can be seen from their fig. 2 for the marginal axisvmmetric stable curve in terms of their w=1/(1|2307] as noted earlier near the end of subsection 2.2 for notational correspondences., 2 for the marginal axisymmetric stable curve in terms of their $w=1/[(1+2\beta)D_s^2]$ as noted earlier near the end of subsection 2.2 for notational correspondences. With the analysis technique developed by Shen Lou (2003). we can perform time-dependent WIND analysis for a composite svstem of two coupled scale-free disces described in Section 2.," With the analysis technique developed by Shen Lou (2003), we can perform time-dependent WKBJ analysis for a composite system of two coupled scale-free discs described in Section 2." For the above three cases with s;=18. 1/4 and 0.45. we displav contours of frequency o7 in terms of the elfective radial wavenumber £=NK[η and the rotation parzumeter 22 in the same figure of exact stationary »rturbation configurations in Fig.," For the above three cases with $\beta=-1/8$, $1/4$ and $0.45$, we display contours of frequency $\omega^2$ in terms of the effective radial wavenumber $\xi\equiv K\equiv|k|r$ and the rotation parameter $D_s^2$ in the same figure of exact stationary perturbation configurations in Fig." 9 for the y=1 case corresponding to the single disc case., 9 for the $\eta=1$ case corresponding to the single disc case. The zero-frequencey ines (Le. marginal stability curves) for both precise ancl WABI approximation accord well with cach other for large racial wavenumber when the WIXDJ approximation is valid: or small racial wavenumber. the WIxXDJ. approximation wreaks down and the two regimes diller significantly as expected.," The zero-frequency lines (i.e., marginal stability curves) for both precise and WKBJ approximation accord well with each other for large radial wavenumber when the WKBJ approximation is valid; for small radial wavenumber, the WKBJ approximation breaks down and the two regimes differ significantly as expected." In iis context. we note the axisvnunetric stability analysis by Lemos ct al. (," In this context, we note the axisymmetric stability analysis by Lemos et al. (" 1991) in à single-disc system.,1991) in a single-disc system. Lemos et al (, Lemos et al. ( 1991) derived the same axisvnimetric background equilibrium state) for a. single disc.,1991) derived the same axisymmetric background equilibrium state for a single disc. For perturbations. they imposedadiabatie approximation with the adiabatic index 5 greater than 1 and. independent: of the barotropic index n» used for the equilibrium state. which Is ilferent. from Syer ‘Tremaine (1996) ancl our present analysis.," For perturbations, they imposedadiabatic approximation with the adiabatic index $\gamma$ greater than 1 and independent of the barotropic index $n$ used for the equilibrium state, which is different from Syer Tremaine (1996) and our present analysis." In the global analysis on axisymmetric η=0 , In the global analysis on axisymmetric $m=0$ cluster MMpce) than is twpical for these,cluster Mpc) than is typical for these (V— 16.1. :z2.9) coutinuun source. previously observed by theFUSE. heck. aud VET spectrograplis ο study intergalactic aabsorptiou iu both aand n.,"$V = 16.1$ , $z \approx 2.9$ ) continuum source, previously observed by the, Keck, and VLT spectrographs to study intergalactic absorption in both and ." HE 1312 is the first of three AGN areets scheduled for COS enarantecd-time observations of the ircionization epoch., HE $-$ 4342 is the first of three AGN targets scheduled for COS guaranteed-time observations of the reionization epoch. The data were acquired with both he mmoderate-resolution C130NI erating (518.000. A=1135τις Aj) and the low-resolution ClLOL erating (Rx1500. A=LO802000 AJ).," The data were acquired with both the moderate-resolution G130M grating $R \approx 18,000$, $\lambda = 1135-1440$ ) and the low-resolution G140L grating $R \approx 1500$, $\lambda = 1030-2000$ )." In the 303.78 ine ofLL. these wavelength bauds allow us to probe redshifts down to τμ=2.735 (CL30A0) and pp42.39 (CALLOL).," In the 303.78 line of, these wavelength bands allow us to probe redshifts down to $z_{\rm HeII} = 2.735$ (G130M) and $z_{\rm HeII} \approx 2.39$ (G140L)." The COS data enable many improvements compared to previous studies., The COS data enable many improvements compared to previous studies. First. the high far-UV throughput of the COS/CI30M. erating provides higher signal-to-noise (S/N) aud better photometric accuracy.," First, the high far-UV throughput of the COS/G130M grating provides higher signal-to-noise (S/N) and better photometric accuracy." Second. the low backeround of the COS detectors allows us to detect very weak flux-transuiission through the ICM. characterize low fiux levels in aabsorptiou troughs. and probe regions of high optical depth. thou25.," Second, the low background of the COS detectors allows us to detect very weak flux-transmission through the IGM, characterize low flux levels in absorption troughs, and probe regions of high optical depth, $\tau_{\rm HeII} \ga 5$." Finally. low-resolution ClLoL spectra (1000-2000 3) allow us to study the recovery of the ooptical depth at 2<2.7 and characterize the continui longward of the codec.," Finally, low-resolution G140L spectra (1000-2000 ) allow us to study the recovery of the optical depth at $z < 2.7$ and characterize the continuum longward of the edge." Iu 822 we discuss the observations and data reduction techniques for both CI30M. aud CalLoL exatiugs., In 2 we discuss the observations and data reduction techniques for both G130M and G140L gratings. " Iu. 833 we display the fitted quasar coutinmmun. ByxA.Ube, which we use to extrapolate below the eedee at 1186.2A."," In 3 we display the fitted quasar continuum, $F_{\lambda} \propto \lambda^{-3.0 \pm 0.1}$, which we use to extrapolate below the edge at $1186.2$." . From this coutimuun and the ransiuitted fluxes. we derive ooptical depths iu the forest and analyze the fluctuating absorption.," From this continuum and the transmitted fluxes, we derive optical depths in the forest and analyze the fluctuating absorption." We observe minimal effects of local photoionization expected roni proxiuitv to this very huuinous QSO., We observe minimal effects of local photoionization expected from proximity to this very luminous QSO. In the forest at 2.160$ kpc in radius), both based on lower resolution ROSAT data." Iu ICG 16. oue of the first such groups well studied aud much discussed in the literature. gas was unauubieuouslv detected oulv recently with NADλωνίον2003).. at a level of ~101TM," In HCG 16, one of the first such groups well studied and much discussed in the literature, gas was unambiguously detected only recently with XMM-Newton, at a level of $\sim 10^{41}$." TCG 16 is in many respectsvery simular to Satis composed of £ luminous late type galaxies in a LareaEEiekson92. weithecideitsigusofactieityiitheirnuclei andae aus +.," HCG 16 is in many respectsvery similar to: it is composed of 4 luminous late type galaxies in a small area, with evident signs of activity in their nuclei, and a velocity dispersion of $\sim 100$ km $^{-1}$." The N-rav properties appear also very similar: all [ galaxies are detected as individual sources (both due to the AGN aud starburstactivity)already.by. theROSATsatellite1999).. while thediffuse (οreceutlvcharacterised withNMM-Neowtouliasacomparableluminositybut slieltlyhigherbestfit temperature than SCCO018-155L.," The X-ray properties appear also very similar: all 4 galaxies are detected as individual sources (both due to the AGN and starburstactivity)alreadyby theROSATsatellite, while thediffuse emissionrecentlycharacterised withXMM-Newtonhasacomparableluminositybut slightlyhigherbestfit temperature than ." . Oulv. two othersystems. with a," Only two othersystems, with a" the different run of interstellar extinelion towards then... In fact. NGCa 7789 is located 5.4 degrees below the formal Galactic plane. while Trumpler 20 is al 2.2 degrees above the To make this comparison more quantitative and useful. in the rightmost panel of Fig.,"the different run of interstellar extinction towards them.. In fact, NGC 7789 is located 5.4 degrees below the formal Galactic plane, while Trumpler 20 is at 2.2 degrees above the To make this comparison more quantitative and useful, in the rightmost panel of Fig." 6 we have considered only stars located inside the core radius of Trumpler 20. and over-plotted the ridge line for NGC! {ee7789.," 6 we have considered only stars located inside the core radius of Trumpler 20, and over-plotted the ridge line for NGC 7789." This latter has been shifted by Al=—02 mag and A(W—J)=—0.05 mag., This latter has been shifted by $\Delta V = -0.2$ mag and $\Delta (V-I) = -0.05$ mag. Given that the comparison is quite convincing. we can (hen assume - as a working hvpothesis- (hat Trumpler 20 has the same metal content as NGC! 7789. neunely solar (Gim οἱ al.," Given that the comparison is quite convincing, we can then assume - as a working hypothesis- that Trumpler 20 has the same metal content as NGC 7789, namely solar (Gim et al." 1998)., 1998). Under this assumption. it turis out that the apparent distance modulus of Trumpler 20 is 0.2 mag larger than that of NGC 7789. and that it is slightly more reddened.," Under this assumption, it turns out that the apparent distance modulus of Trumpler 20 is 0.2 mag larger than that of NGC 7789, and that it is slightly more reddened." The reddening of NGC {un7789 is E(V—£)=0.365 (Cim οἱ al., The reddening of NGC 7789 is $E(V-I)=0.365$ (Gim et al. 1998). and its apparent distance modulus is (V—M)=12.2 mae. which therefore gives LE(V—1)4040 amd (V—M)12.4 mae lor Trumpler 20.," 1998), and its apparent distance modulus is $(V-M_V)=12.2$ mag, which therefore gives $E(V-I)\sim 0.40$ and $(V-M_V)\sim12.4$ mag for Trumpler 20." These values imply. a distance of ~3 kpe from the Sun for the latter., These values imply a distance of $\sim 3$ kpc from the Sun for the latter. While the T'O's are well matched. the red clamp of Trunpler 20 is shehtly fainter and redder. which might imply a lower age.," While the TO's are well matched, the red clump of Trumpler 20 is slightly fainter and redder, which might imply a lower age." We recall that the age of NGC 7789 is around 1.6 Gyr., We recall that the age of NGC 7789 is around 1.6 Gyr. We shall (av (o derive the age of Trumpler 20 in Sect., We shall try to derive the age of Trumpler 20 in Sect. 8., 8. Additional insights on (he reddening and metallicity of Trimpler 20 can be obtained [rom the two-color diagram (TCD). shown in Fig.," Additional insights on the reddening and metallicity of Trumpler 20 can be obtained from the two-color diagram (TCD), shown in Fig." 7., 7. Again. we consider only stars within the cluster core. and with photometric errors lower (han 0.09 mag in both colors.," Again, we consider only stars within the cluster core, and with photometric errors lower than 0.09 mag in both colors." The solid line plotted is an empirical Zero Age Main Sequence (ZAMS) fron Sehimidt-INaler (1982). along which we indicate a lew relevant spectral tvpes.," The solid line plotted is an empirical Zero Age Main Sequence (ZAMS) from Schmidt-Kaler (1982), along which we indicate a few relevant spectral types." The dashed sequence is this, The dashed sequence is this a volume in the disk. that is sufficiently narrow to keep the regular maguetic field coustant inside the volune. but extends alone the line of sight through the disk.,"a volume in the disk, that is sufficiently narrow to keep the regular magnetic field constant inside the volume, but extends along the line of sight through the disk." This is a reasonable approximation except for τον high inclinations *2SU7. where the azimuthal feld must change along the line of sight. but only if the line of sieht is near the major axis.," This is a reasonable approximation except for very high inclinations $i \gtrsim 80\degr$, where the azimuthal field must change along the line of sight, but only if the line of sight is near the major axis." Equation 1 includes the effect of decreased xhudzation because of the presence/ of a random conrponeut of the magnetic field iu the plane of he sky, Equation \ref{P0-eq} includes the effect of decreased polarization because of the presence of a random component of the magnetic field in the plane of the sky. Sokoloffetal.(1998) referred to this as waveleneth-independent depolarization., \citet{sokoloff1998} referred to this as wavelength-independent depolarization. The terii beam depolarization is sometimes used im this situation. mt this term ds used also im case of wavelenetl-dependent Faraday effects;," The term beam depolarization is sometimes used in this situation, but this term is used also in case of wavelength-dependent Faraday effects." The plane of polarization is xrpeudieular to the component of the regular maguetic fell projected on the plane of the sky., The plane of polarization is perpendicular to the component of the regular magnetic field projected on the plane of the sky. The observed polarization (CP? differs from (Py; jocause the polarized svuchrotron emission eeuerated iu astnall volume clement iu the disk is Faraday rotated as it travels through the disk to the observer., The observed polarization $\langle {\mathcal P} \rangle$ differs from $\langle {\mathcal P_0} \rangle$ because the polarized synchrotron emission generated in a small volume element in the disk is Faraday rotated as it travels through the disk to the observer. The effects of Faraday rotation can be written as a waveleneth-dependent factor in the complex. polarization. that includes an iutegral along the line of sight.," The effects of Faraday rotation can be written as a wavelength-dependent factor in the complex polarization, that includes an integral along the line of sight." Burn(1966) and Sokoloffetal.(1998) evaluated this inteeral analytically for a muiform slab., \citet{burn1966} and \citet{sokoloff1998} evaluated this integral analytically for a uniform slab. The observed polarized intensity from a small part of the disk is where $=2Alae2jATR is a complex umber that includes rotation measure fluctuations og in the real part and the Faraday depth R. in the imaginary part., The observed polarized intensity from a small part of the disk is where $S = 2 \lambda^4 \sigma_{\rm RM}^2 -2 j \lambda^2 {\mathcal R}$ is a complex number that includes rotation measure fluctuations $\sigma_{\rm RM}$ in the real part and the Faraday depth $\mathcal R$ in the imaginary part. The real part of S contains fiuctuatious iu rotation measure along the Line of sight through the factor Arp. Which represents the rus amplitude of rotation measure fluctuations after integration along the line of sieht.," The real part of $S$ contains fluctuations in rotation measure along the line of sight through the factor $\sigma_{\rm RM}$, which represents the rms amplitude of rotation measure fluctuations after integration along the line of sight." The plane of polarization makes a random walk because of fluctuations in density aud magnetic feld., The plane of polarization makes a random walk because of fluctuations in density and magnetic field. When polarized enuüssiou is inteerated over different lines of sight. or different depths inside the source. depolarization of the enüssion results.," When polarized emission is integrated over different lines of sight, or different depths inside the source, depolarization of the emission results." This process is called internal Faraday dispersiou., This process is called internal Faraday dispersion. " Evaluation of apa, requires assuniptious about the correlation scale of fluctuations iu density and magnetic field streneth.", Evaluation of $\sigma_{\rm RM}$ requires assumptions about the correlation scale of fluctuations in density and magnetic field strength. Sokoloffetal.(1998) discuss the difficulties estimating a correlation scale length. aud assume that the scale lenetl is the same for fluctuations m density. magnetic field. aud rotation measure.," \citet{sokoloff1998} discuss the difficulties estimating a correlation scale length, and assume that the scale length is the same for fluctuations in density, magnetic field, and rotation measure." " The streneth of the magnetic Ποια, in a turbulent cell defined by the correlation leneth is op.", The strength of the magnetic field in a turbulent cell defined by the correlation length is $\sigma_{\rm B}$. Rotation measure fluctuations also depend on the path leugth £ through the disk with thickness 25h. observed at inclination /. given by L=2h/cos/.," Rotation measure fluctuations also depend on the path length $L$ through the disk with thickness $2 h$, observed at inclination $i$, given by $L = 2h / \cos i$." The line-ofseht fillme factor of the Faracay-rotating medium is fF;, The line-of-sight filling factor of the Faraday-rotating medium is $f_i$. Rotation measure fluctuations are then calculated following Sokoloffctal.(1998) The imaginary part of ο describes rotation of the ane of polarization by the line-of-sight commpoucut of he regulu maeuctic field.," Rotation measure fluctuations are then calculated following \citet{sokoloff1998} The imaginary part of $S$ describes rotation of the plane of polarization by the line-of-sight component of the regular magnetic field." " The Faraday depth R=HefiBy2hfcosi is the product of the mean electron density. (o.f;) where s, is the electron deusitv in a urbuleut cell. By the line-oFsight component of the regular mmaenetic field. aud 7 the path leusth through he disk."," The Faraday depth $\mathcal{R} = n_e f_i B_\| 2h/\cos i $ is the product of the mean electron density $n_e f_i$ ), where $n_e$ is the electron density in a turbulent cell, $B_\|$ the line-of-sight component of the regular magnetic field, and $h$ the path length through the disk." Rotation of the plane of polarization also depolarizes cussion iutegrated along the line of sight as chuission from different depths of the source is rotated w odiffereut amounts., Rotation of the plane of polarization also depolarizes emission integrated along the line of sight as emission from different depths of the source is rotated by different amounts. This mechanisi for depolarization is called differential Faraday rotation., This mechanism for depolarization is called differential Faraday rotation. It is sometimes called depth depolarization. but it should be uuderstood hat there is a differeut depoluiziug effect iu the form of Faraday dispersion that is also the result of iuteeratiug cluission aloug the line of sight.," It is sometimes called depth depolarization, but it should be understood that there is a different depolarizing effect in the form of Faraday dispersion that is also the result of integrating emission along the line of sight." " Equation 2. provides the complex polarized itcusity CP) for every line of sight. frou, which we obtain the local Stokes Q aud C intensities. normalized by the local total iuteusitv that is presumed uniform m the current models."," Equation \ref{P-eq} provides the complex polarized intensity $\langle{\mathcal P} \rangle$ for every line of sight, from which we obtain the local Stokes $Q$ and $U$ intensities, normalized by the local total intensity that is presumed uniform in the current models." The model Stokes Q aud C intensities can be inteerated over the disk to predict the model polarized flux density. fractional polarization Wy. aud the angele Op of an unresolved spiral galaxy.," The model Stokes $Q$ and $U$ intensities can be integrated over the disk to predict the model polarized flux density, fractional polarization $\Pi_0$, and the angle $\thetaB$ of an unresolved spiral galaxy." The inteeration over the disk reduces to a one-dimensional uunerical iuteeration over aziuuthal auele for the syauinuetrie models under consideration., The integration over the disk reduces to a one-dimensional numerical integration over azimuthal angle for the symmetric models under consideration. Asstuuing values for the various model parameters. the integration over the disk can be performed as a function of inclination.," Assuming values for the various model parameters, the integration over the disk can be performed as a function of inclination." The integrated polarization Is inore sensitive to certain model parameters. ancl the influence of model paramcters can chauge with meinclination.," The integrated polarization is more sensitive to certain model parameters, and the influence of model parameters can change with inclination." The relative importance of the parameters in our model was investigated through a Monte Carlo sxperiueut., The relative importance of the parameters in our model was investigated through a Monte Carlo experiment. Each parameter was varied separately. aud the resulting range of the integrated polarization was ivided by the range obtained when all parameters were varicd indepeudeutle at the same time.," Each parameter was varied separately, and the resulting range of the integrated polarization was divided by the range obtained when all parameters were varied independently at the same time." The spread in iufegrated fractional polarization was taken as the ifference between the upper quartile aud the lower quartile., The spread in integrated fractional polarization was taken as the difference between the upper quartile and the lower quartile. As the underlvius distributions are stronelv, As the underlying distributions are strongly the aperture correctious themselves are about 0.1 maenituce larger than the values obtained by Whitimore et al.,the aperture corrections themselves are about 0.1 magnitude larger than the values obtained by Whitmore et al. This is most likely due to the resampling of the PSF that is done by when aligning the images., This is most likely due to the resampling of the PSF that is done by when aligning the images. As a check. we also carried out photometry on a combined subset of 2 images In each filter where no shifts were required: iu this case we found aperture correctious in very good agreement with those of Whitmore et al.," As a check, we also carried out photometry on a combined subset of 2 images in each filter where no shifts were required; in this case we found aperture corrections in very good agreement with those of Whitmore et al." However. we are uot golug to refer to absolute uagnitudes in this letter but ouly to colors. aud we will use the photometry based on [combined images because of the better noise characteristics aud superior CR rejection.," However, we are not going to refer to absolute magnitudes in this letter but only to colors, and we will use the photometry based on 4 combined images because of the better noise characteristics and superior CR rejection." We checked our results by performing an ALLSTAR PSF-fittiug reduction of the data., We checked our results by performing an ALLSTAR PSF–fitting reduction of the data. There is an insignificant affect on the location of the V—I peaks (at the level of 0.01 mae..," There is an insignificant affect on the location of the $V-I$ peaks (at the level of 0.01 mag.," well withiu our estimated uncertainties) and no subsequent couclusious are affected by choosing aperture rather hau PSF photometry., well within our estimated uncertainties) and no subsequent conclusions are affected by choosing aperture rather than PSF photometry. Figure 2. upper pauel. is the reddeuiug-corrected color-maguitude diagram of all objects in the Wide Field camera chips.," Figure 2, upper panel, is the reddening–corrected color–magnitude diagram of all objects in the Wide Field camera chips." " An extinction correclion of Ey 720.13 (from Ey,(920.079. Ay=0.2 L. Schlegel et al."," An extinction correction of $_{V-I}$ =0.13 (from $_{B-V}$ =0.079, $_V$ =0.24, Schlegel et al." 1998) has beenapplied., 1998) has beenapplied. Note tiat Seckeretal.(1995) used Eyy=0.015 from BursteinαμαHeiles(LOS1).. correspoucing to Ey ;=0.072. Le. there is a systematic difference of 0.05 mae.," Note that \citet{sec95} used $_{B-V}$ =0.045 from \citet{bur84}, corresponding to $_{V-I}$ =0.072, i.e. there is a systematic difference of 0.05 mag." " in Ey, between our colors aud the corresponding colors quoted by Secker et al.", in $_{V-I}$ between our colors and the corresponding colors quoted by Secker et al. Although it is in the right seuse. this dillerence is not ne:uly sufficient to account for the disagreement.," Although it is in the right sense, this difference is not nearly sufficient to account for the disagreement." Globular cluster candidates were selected [rom within the range 0.6 «V—£ 1.1.," Globular cluster candidates were selected from within the range 0.6 $< V-I <$ 1.4." There are 1971 candidates with V.«26 and 882 with V< 25., There are 1971 candidates with $V<26$ and 882 with $V<25$ . A IXMM test (Ashman. finds peaks at V—J=0.91 and 1.09 [or the maguitucde interval 2299.9% coufideuce level., Peaks are found at $V-I$ = 0.87 and 1.09 for the interval $22$ confidence level. Changing the magnitudes thus vields consistent. values for the V.—4 yeaks and we estimate that the peak colors are accurate to about 0.03 magnitudes., Changing the magnitudes thus yields consistent values for the $V-I$ peaks and we estimate that the peak colors are accurate to about 0.03 magnitudes. About half of he clusters beloug to the blue population and half to the red., About half of the clusters belong to the blue population and half to the red. The lower panel iu figure 2 shows a color histogram for the [n]globular clusters down toa maguituce limit of V=25., The lower panel in figure 2 shows a color histogram for the globular clusters down to a magnitude limit of V=25. Overplotted are the wo best-fitting Ciaussius from the WMIM analysis as well as their stun., Overplotted are the two best–fitting Gaussians from the KMM analysis as well as their sum. DIP statistics (GebhardtaudIxissler-Patig1999) tudicate the probability that the distribution is not iiumodal., DIP statistics \citep{geb99} indicate the probability that the distribution is not unimodal. For the magnitude interval 222.5L_{\rm b}$, where the critical luminosity is given by \citep[c.f.][]{kmck92}. ." "]lere Py,=BfGOOSs em7 WY. where 2) is the midplane pressure. and & is the Boltzman’s constant."," Here $P_{0,4}=P_0/(10^4\kappa$ $^{-3}$ K), where $P_0$ is the midplane pressure, and $\kappa$ is the Boltzman's constant." eis=co/(10. cmi 1). where eo represents the sound. speed. in the midplane: actually. as the temperature varies somewhat within the range 0«zLay. we adopt the mean value of c in Eq. 7..," $c_{0,6}=c_0/(10^6$ cm $^{-1}$ ), where $c_0$ represents the sound speed in the midplane; actually, as the temperature varies somewhat within the range $0$ ) between galaxies and quasars, indicating that the majority of galaxies and quasars are associated with different radio source The anti-correlation found between the projected linear size and the peak frequency \citep{odea97,bicknell97,snellen00} implies that the sources with the spectral peak occurring above a few GHz should represent the population of the smallest radio sources whose radio emission has recently turned on." Samples of high-frequency peaking objects have been selected bv choosing sources with an inverted radio spectrum. up to 5 Cllz2009).. Le. the highest. observing frequeney where a laree area survey is presently available.," Samples of high-frequency peaking objects have been selected by choosing sources with an inverted radio spectrum up to 5 GHz, i.e. the highest observing frequency where a large area survey is presently available." Llowever. due to the selection criteria these samples have been found to comprise both voung radio sources and Haring Uat-speetrum objects selected during particular phases of their spectral variability. for example when their radio enission is dominated by a knot in the jet.," However, due to the selection criteria these samples have been found to comprise both young radio sources and flaring flat-spectrum objects selected during particular phases of their spectral variability, for example when their radio emission is dominated by a knot in the jet." The study of Hux density and. spectral variability based: on repeatec simultaneous multi-[requency. observations has proved. to be an ideal tool in discriminating the cilferent nature of the sources., The study of flux density and spectral variability based on repeated simultaneous multi-frequency observations has proved to be an ideal tool in discriminating the different nature of the sources. Le was found that in samples of bright objects. where there is a high incidence of sources optically identifie with quasars. Uat-spectrum blazar objects represent. the dominant population (e.g.Torniainenetal.2007:Orientiotal.2007:Jaunceyet 2003).," It was found that in samples of bright objects, where there is a high incidence of sources optically identified with quasars, flat-spectrum blazar objects represent the dominant population \citep[e.g.][]{torniainen07,mo07,jauncey03}." . A higher incidence of senuinelv voung radio sources is expected in samples of [aint objects where the majority of radio sources should be hosted in galaxies ancl boosting elfects are supposed to play a minor The optical identification of the sources studied in this paper bv means of the SDSS DR7 indicates that of objects are hosted. in galaxies. i.c. similar to the fraction of galaxies in the bright ΕΤ sample.," A higher incidence of genuinely young radio sources is expected in samples of faint objects where the majority of radio sources should be hosted in galaxies and boosting effects are supposed to play a minor The optical identification of the sources studied in this paper by means of the SDSS DR7 indicates that of objects are hosted in galaxies, i.e. similar to the fraction of galaxies in the bright HFP sample." However. in the fain sample. another of objects lack optical identification and thus a reliable comparison between the two samples cannot be done.," However, in the faint sample, another of objects lack optical identification and thus a reliable comparison between the two samples cannot be done." The analvsis of the optical images of the galaxies hosting HET pointed. out the presence. of companions around 6 LEP candidates. indicating tha voung radio galaxies. like powerful extended. radio sources. are in groups. as previously suggested: by Stanghellinietal. (1993).. indicating a continuity between compac voung objects and the population of classical radio galaxies (οDoaοἱal.1996).," The analysis of the optical images of the galaxies hosting HFP pointed out the presence of companions around 6 HFP candidates, indicating that young radio galaxies, like powerful extended radio sources, are in groups, as previously suggested by \citet{cs93}, indicating a continuity between compact young objects and the population of classical radio galaxies \citep{odea96}." . Although in 4 galaxies the presence of companions is sugeested by photometric information onlv. in 1530|2705 and 1602|2646 the association is made by spectroscopic redshift.," Although in 4 galaxies the presence of companions is suggested by photometric information only, in J1530+2705 and J1602+2646 the association is made by spectroscopic redshift." The companion galaxies are located within a projected. distance. of about 150 200 kpc from the target which usually is hosted in the brightest. elliptica at the group centre., The companion galaxies are located within a projected distance of about 150 - 200 kpc from the target which usually is hosted in the brightest elliptical at the group centre. X. peculiar case. is. represented. by J1109|3831. whose parent galaxy seems to be à spiral tha is interacting with an elliptical.," A peculiar case is represented by J1109+3831, whose parent galaxy seems to be a spiral that is interacting with an elliptical." Young radio sources are normally associated with ellipticals., Young radio sources are normally associated with ellipticals. The case representec by J1109|3831 may be explained by the possible interaction between the hosting spiral ancl the companion that may have triggered the radio emission., The case represented by J1109+3831 may be explained by the possible interaction between the hosting spiral and the companion that may have triggered the radio emission. The small redshift) of 915002705. enabled. us το identify the morphology of its brightest companions that turned: out to be. barrec spirals., The small redshift of J1530+2705 enabled us to identify the morphology of its brightest companions that turned out to be barred spirals. " ""This group resembles that of the bright ΤΗ 0655|4100. (Orientictal.2006b).. and in both cases he HEP is hosted. by the central elliptical galaxy a he group centre."," This group resembles that of the bright HFP J0655+4100 \citep{mo06b}, and in both cases the HFP is hosted by the central elliptical galaxy at the group centre." The presence of companion galaxics in he environment of galaxies hosting voung radio sources sugeests that the onset of. the radio emission. may be rigeered by merger or interaction events that occurred. not ong ago., The presence of companion galaxies in the environment of galaxies hosting young radio sources suggests that the onset of the radio emission may be triggered by merger or interaction events that occurred not long ago. This scenario is supported by the proximity of the companions in JOSO4|5431 and in J1109|3831. although observations to establish a physical interaction are needed o unambiguously verily this idea.," This scenario is supported by the proximity of the companions in J0804+5431 and in J1109+3831, although observations to establish a physical interaction are needed to unambiguously verify this idea." Several. regions. in. the Perseus.; molecular complex. clisplay. a strong continuum. microwave. emissionD. in. the frequency. range 10-60 CGllz that is correlated. with dust. thermal emission (Watson et al.,Several regions in the Perseus molecular complex display a strong continuum microwave emission in the frequency range 10-60 GHz that is correlated with dust thermal emission (Watson et al. 2005. Tibbs et al.," 2005, Tibbs et al." 2010)., 2010). The spectral dependence of this emission cannot be explained by synchrotron. free-free or thermal dust. radiation. processes and represents one of the best known examples of the so-called anomalous microwave emission (Ixogut. ct al.," The spectral dependence of this emission cannot be explained by synchrotron, free-free or thermal dust radiation processes and represents one of the best known examples of the so-called anomalous microwave emission (Kogut et al." 1996. Leiteh et al.," 1996, Leitch et al." 1997. de Oliveira et al.," 1997, de Oliveira et al." 1999. 2002).," 1999, 2002)." This kind of ⋅⊀microwave emission ⊀∢⊀is also detected in. other molecular clouds (Casassus ο al., This kind of microwave emission is also detected in other molecular clouds (Casassus et al. 2006) ancl there is increasing statistical evidence supporting its existence at high Galactic latitudes (Llildebrandt ct al., 2006) and there is increasing statistical evidence supporting its existence at high Galactic latitudes (Hildebrandt et al. 2007)., 2007). " Draine anc Lazarian (1998)"" suggested: a possible. explanation. for⋅ this. emissionD. based. on electric. dipole radiation. from. rapidly spinning carbon based molecules (see also Lelosias-CGroth 2005. 2006)."," Draine and Lazarian (1998) suggested a possible explanation for this emission based on electric dipole radiation from rapidly spinning carbon based molecules (see also Iglesias-Groth 2005, 2006)." Polveyelie aromatic hydrocarbons (PALS) proposed as the sources of interstellar mic-intrared emission (Puget Léeeer 1989. Allamanclola. Vielens Barker 1989) and cdiluse interstellar bands. (Puget. Leéeecr 1959. Allanmaneclola. Tielens Barker 1989) are also potential carriers for the anomalous microwave emission.," Polycyclic aromatic hydrocarbons (PAHs) proposed as the sources of interstellar mid-infrared emission (Puget Légger 1989, Allamandola, Tielens Barker 1989) and diffuse interstellar bands (Puget Légger 1989, Allamandola, Tielens Barker 1989) are also potential carriers for the anomalous microwave emission." It is likely that anomalous microwave emission surveys reveal interstellar regions of enhanced. PALL abundance and. therefore further stuclies of these regions may facilitate the identification of individual DALIs., It is likely that anomalous microwave emission surveys reveal interstellar regions of enhanced PAH abundance and therefore further studies of these regions may facilitate the identification of individual PAHs. Recent progress in the laboratory measurements of optical and near infrared bands of the most simple PALLs and, Recent progress in the laboratory measurements of optical and near infrared bands of the most simple PAHs and the plane of the sky so we need to find the cross section of our cdisc model in this plane.,the plane of the sky so we need to find the cross section of our disc model in this plane. Our solution is in coordinates (r.g.2) in the frame of the black hole and the outer disc Les in the wes plane., Our solution is in coordinates $x$ $y$ $z$ ) in the frame of the black hole and the outer disc lies in the $x$ $z$ plane. We initially take this to be aligned. with the coordinates Graia. zon) which are the coordinates that we take the disc section in the μι zip plane.," We initially take this to be aligned with the coordinates $x_{\rm bh}$ $y_{\rm bh}$ $z_{\rm bh}$ ) which are the coordinates that we take the disc section in the $x_{\rm bh}$ $z_{\rm bh}$ plane." We rotate the coordinates μμ.) about the σι axis hy an angle ὡς., We rotate the coordinates $x$ $y$ $z$ ) about the $z_{\rm bh}$ axis by an angle $-\phi_{\rm c}$. Phe shape of the disce in the riy zy plane is eiven by where Όμως=arg(lV) and we have the negative sign so that our model has the same orientation as the maser data and in the positive wry direction.," The shape of the disc in the $x_{\rm bh}$ $z_{\rm bh}$ plane is given by where $\phi_{\rm max}=\arg (W)$ and we have the negative sign so that our model has the same orientation as the maser data and in the positive $x_{\rm bh}$ direction." " We are assuming that the disc is symmetric so the side of the disc with negative wri, can be found by rotating this shape bv. 180 about the yin axis.", We are assuming that the disc is symmetric so the side of the disc with negative $x_{\rm bh}$ can be found by rotating this shape by $180^\circ$ about the $y_{\rm bh}$ axis. If ὁς= Owe see the largest warp possible for à given disc because we are taking a disc section in the plane which contains both the black hole and the outer disc. angular momentum., If $\phi_{\rm c}=0$ we see the largest warp possible for a given disc because we are taking a disc section in the plane which contains both the black hole and the outer disc angular momentum. Conversely. if Oo.=x/2 then we see the least warping in our clisc section.," Conversely, if $\phi_{\rm c}=\pi/2$ then we see the least warping in our disc section." We next consider the disc section when the black hole is not in the plane of the sky but inclined at angle fine to it., We next consider the disc section when the black hole is not in the plane of the sky but inclined at angle $i_{\rm inc}$ to it. We rotate the (Gr. jg. 2) coordinates about the ην axis through an angle fine.," We rotate the $x$, $y$, $z$ ) coordinates about the $x_{\rm bh}$ axis through an angle $-i_{\rm inc}$." For small fing the shape of our disc becomes and ain remains the same., For small $i_{\rm inc}$ the shape of our disc becomes and $x_{\rm bh}$ remains the same. Wo the plane of the sky contains the black hole spin then fine=0., If the plane of the sky contains the black hole spin then $i_{\rm inc}=0$. We can use this small angle approximation because if the angle fine were big then we wouldn't see the masers because they are only seen when there is no gradient in the bulk line of sight. velocity., We can use this small angle approximation because if the angle $i_{\rm inc}$ were big then we wouldn't see the masers because they are only seen when there is no gradient in the bulk line of sight velocity. This only happens when the disc is close to edge on., This only happens when the disc is close to edge on. We sketch the plane of the sky coordinates Grin. cnn) and the coordinate svstem for the disc Gr. y. 2) in FigureL..," We sketch the plane of the sky coordinates $x_{\rm bh}$, $z_{\rm bh}$ ) and the coordinate system for the disc $x$, $y$, $z$ ) in Figure\ref{fig}." We show the plane of the sky. P. in which we find thedisc section.," We show the plane of the sky, $P$, in which we find thedisc section." Lt contains the dashed lines., It contains the dashed lines. The normal. n. to the plane P? is the line of sight.," The normal, $\bm{n}$, to the plane $P$ is the line of sight." The disc section is in coordinates dup and zun., The disc section is in coordinates $x_{\rm bh}$ and $z_{\rm bh}$. " In the case where fin=0 and Oo=0. we find the inclination of the disc at radius A? to the plane of the sky to be The observations of the svstemic masers. predict that. at R=39mas. the disc has inclination £i,=8.4."," In the case where $i_{\rm inc}=0$ and $\phi_{\rm c}=0$, we find the inclination of the disc at radius $R$ to the plane of the sky to be The observations of the systemic masers predict that, at $R=3.9\,\rm mas$, the disc has inclination $\zeta_{\rm in}=8.4^\circ$." For our models with fine=0 and ὡς= Owe find the inclination of our disc at /?=3.9mas and compare this to the observed value.," For our models with $i_{\rm inc}=0$ and $\phi_{\rm c}=0$ we find the inclination of our disc at $R=3.9\,\rm mas$ and compare this to the observed value." The inner radius of the masing disc corresponds to 2.8mas and the outer edge to Row=S2mas.," The inner radius of the masing disc corresponds to $R_{\rm in}=2.8\,\rm mas$ and the outer edge to $R_{\rm out}=8.2\,\rm mas$." examine the svstemic masers in the cirection perpenclicular to the axis of the disc., examine the systemic masers in the direction perpendicular to the axis of the disc. Fhev observe that the vertical thickness of the disc has a limit //<0.005mas.," They observe that the vertical thickness of the disc has a limit $H<0.005\,\rm mas$." Because the svstemic masers are at 2=3.9mas we see there is an observed. upper limit on 7/4 such that We use a canonical value of 44/14?=0.001 in the following calculations.," Because the systemic masers are at $R=3.9\,\rm mas$ we see there is an observed upper limit on $H/R$ such that We use a canonical value of $H/R=0.001$ in the following calculations." " The warp radius is where the Bardeen-Petterson elect. is balanced by the viscous evolution of the disce and is given by (Scheuer&Feiler1996:Martin.PringleTout 2007).. where a,= ων]."," The warp radius is where the Bardeen-Petterson effect is balanced by the viscous evolution of the disc and is given by \citep{SF,MPT07}, , where $\omega_{\rm p}=|\bm{\omega}_{\rm p}|$ ." Using equation. (24)) and the form of equation (9)) for the second. viscosity we find, Using equation \ref{omegap}) ) and the form of equation \ref{visc1}) ) for the second viscosity we find "quasar light, while J0852 appears to be in a small interacting group where the immediate neighbor to the lower-right has a SDSS photometric redshift consistent with the quasar redshift.","quasar light, while J0852 appears to be in a small interacting group where the immediate neighbor to the lower-right has a SDSS photometric redshift consistent with the quasar redshift." " Sluse ((2007) reported a serendipitously discovered AAL system in the gravitationally lensed quasar RXS J1131-1231, which also shows evidence of interactions and disturbed morphology in the reconstructed host (Claeskensetal. 2006)."," Sluse (2007) reported a serendipitously discovered AAL system in the gravitationally lensed quasar RXS J1131-1231, which also shows evidence of interactions and disturbed morphology in the reconstructed host image \citep{Claeskens_etal_2006}." ". Thus the frequency of disturbed imagemorphologies and close companions of AAL quasars is much higher than evolved quasars (e.g.,Bahcalletal.1997;Dunlop2003;Veilleuxetal. 2009),, and is more in line with the results for heavily dust-reddened quasars (e.g.,Urrutiaetal.2008)."," Thus the frequency of disturbed morphologies and close companions of AAL quasars is much higher than evolved quasars \citep[e.g.,][]{Bahcall_etal_1997,Dunlop_etal_2003,Veilleux_etal_2009}, and is more in line with the results for heavily dust-reddened quasars \citep[e.g.,][]{Urrutia_etal_2008}." ". This is fully consistent with our evolutionary scenario, but more data are needed to draw firm conclusions."," This is fully consistent with our evolutionary scenario, but more data are needed to draw firm conclusions." We defer a detailed analysis of theHST data and follow-up studies of these systems to future work., We defer a detailed analysis of the data and follow-up studies of these systems to future work. " Even though our results suggest an intrinsic origin for the bulk of the AALs, this is a statistical statement and there are still cases where the AALs are of external origins."," Even though our results suggest an intrinsic origin for the bulk of the AALs, this is a statistical statement and there are still cases where the AALs are of external origins." " Moreover, the nature of these intrinsic AALs is still unknown."," Moreover, the nature of these intrinsic AALs is still unknown." " Nevertheless, they provide a unique window to probe the conditions and during the physicalevolution of quasars and their dynamicalmassive hosts, processesand deserve in-depth studies, either in a statistical manner or for individual systems."," Nevertheless, they provide a unique window to probe the physical conditions and dynamical processes during the evolution of quasars and their massive hosts, and deserve in-depth studies, either in a statistical manner or for individual systems." " More than half of these associated absorbers show blueshifted velocity, among which some could be feedback (either stellar- or quasar-driven) at work, and possibly leading to a suppression of the host star formation."," More than half of these associated absorbers show blueshifted velocity, among which some could be feedback (either stellar- or quasar-driven) at work, and possibly leading to a suppression of the host star formation." " The typical velocity of these absorbers (ie., a few hundred kms!) is much smaller than those seen in BALs and intrinsic high velocity narrow absorption lines (NALs), hence these AAL absorbers are likely to be on scales much larger than nuclearscales?,, and thus are more likely to impact the host "," The typical velocity of these absorbers (i.e., a few hundred ${\rm km\,s^{-1}}$ ) is much smaller than those seen in BALs and intrinsic high velocity narrow absorption lines (NALs), hence these AAL absorbers are likely to be on scales much larger than nuclear, and thus are more likely to impact the host galaxy." "Gravitational inflows may also be present during thegalaxy. early stage of quasar and host formation, either in the form of accreted gas or as part of an infalling galaxy companion."," Gravitational inflows may also be present during the early stage of quasar and host formation, either in the form of accreted gas or as part of an infalling galaxy companion." " While intrinsic absorbers with infalling velocities greater than several hundred kms""! are likely to be in the vicinity of the BH, the nature of the more slowly moving absorbers needs to be explored."," While intrinsic absorbers with infalling velocities greater than several hundred ${\rm km\,s^{-1}}$ are likely to be in the vicinity of the BH, the nature of the more slowly moving absorbers needs to be explored." " In particular, infalling absorbers are expected in galaxy formation models (e.g.,Kere$etal.2005;Dekel2009) but almost never seen in galaxy spectra (Steidel et al."," In particular, infalling absorbers are expected in galaxy formation models \citep[e.g.,][]{Keres_etal_2005,Dekel_etal_2009} but almost never seen in galaxy spectra (Steidel et al." 2010)., 2010). The possibility that some of these infalling absorbers might be associated with cold flows will be explored in future work., The possibility that some of these infalling absorbers might be associated with cold flows will be explored in future work. We thank the anonymous referee for suggestions that led to of the , We thank the anonymous referee for suggestions that led to improvement of the manuscript. "We also thank Michael Strauss, Tim improvementHeckman, Gordon manuscript.Richards, Norm Murray, Martin Elvis, and Yuval Birnboim for useful discussions."," We also thank Michael Strauss, Tim Heckman, Gordon Richards, Norm Murray, Martin Elvis, and Yuval Birnboim for useful discussions." YS acknowledges support from the Smithsonian Astrophysical Observatory (SAO) through a Clay Postdoctoral Fellowship., YS acknowledges support from the Smithsonian Astrophysical Observatory (SAO) through a Clay Postdoctoral Fellowship. " Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of"," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of" Now. by using (35)). the epicycle frequency ean be cast as where 5=an.,"Now, by using \ref{velr2n}) ), the epicycle frequency can be cast as where ${\widetilde \kappa} = a\kappa$." So. as the epicycle frequency is completely determined by the set of constants «οι. which are fixed by the numerical fit ofthe rotation curve data. there are not free parameters hat can be adjusted by requiring radial stability.," So, as the epicycle frequency is completely determined by the set of constants $A_{2l}$, which are fixed by the numerical fit of the rotation curve data, there are not free parameters that can be adjusted by requiring radial stability." However. relation (44)) can be used as a consistency criterion to the numerical fit of he circular velocity with the observed data of the rotation curve.," However, relation \ref{kapr2n}) ) can be used as a consistency criterion to the numerical fit of the circular velocity with the observed data of the rotation curve." So. if the frequency it is not positive everywhere at the interval Oepicyclex:#<1 for a given set of constants. it is possible o make a new numerical tit by considering a different model. with another value of n. in order to ensure the positiveness of the epicycle frequency.," So, if the epicycle frequency it is not positive everywhere at the interval $0 \leq {\widetilde R} \leq 1$ for a given set of constants, it is possible to make a new numerical fit by considering a different model, with another value of $n$, in order to ensure the positiveness of the epicycle frequency." Accordingly. we seek for a balance between he best numerical tit and the numerical fit that agrees with the »ositiveness of the epicycle frequency.," Accordingly, we seek for a balance between the best numerical fit and the numerical fit that agrees with the positiveness of the epicycle frequency." Also. by using the Poisson equation (90). the expression (27)) or the halo density and the expression (35)) for the circular velocity. the vertical frequency can be written as where 7=av and So. as 27 must be positive everywhereat the interval 0 linorder to have vertically stable models. expression (453) detines a lower bound for the halo mass. that combined with (38)) gives also an upper bound for the dise mass M.," Also, by using the Poisson equation \ref{posec}) ), the expression \ref{denh}) ) for the halo density and the expression \ref{velr2n}) ) for the circular velocity, the vertical frequency can be written as where ${\widetilde \nu} = a \nu$ and So, as ${\widetilde \nu}^2$ must be positive everywhereat the interval $0 \leq {\widetilde R} \leq 1$ in order to have vertically stable models, expression \ref{nur2n}) ) defines a lower bound for the halo mass, that combined with \ref{lineara2n}) ) gives also an upper bound for the disc mass ${\mathcal M}_d$." We also need to consider the behavior of the surface mass density. as given by expression C15). that can be written in terms of the constants 21»; as where. for the model with »=4. and for any other value of » the explicit expression of fun can be easily obtained from (159). (323). (33)) and (369).," We also need to consider the behavior of the surface mass density, as given by expression \ref{density}) ), that can be written in terms of the constants $A_{2l}$ as where, for the model with $n = 4$, and for any other value of $n$ the explicit expression of $f_2 ({\widetilde R})$ can be easily obtained from \ref{density}) ), \ref{c2til}) ), \ref{c2ltil}) ) and \ref{relation}) )." Accordingly. in order that the surface mass density be positive everywhere on the disc. expression (48)) defines an upper bound for the halo mass. that combined with (383) gives also a lower bound for the dise mass μι ," Accordingly, in order that the surface mass density be positive everywhere on the disc, expression \ref{dena2n}) ) defines an upper bound for the halo mass, that combined with \ref{lineara2n}) ) gives also a lower bound for the disc mass ${\mathcal M}_d$." However. in order that the models make sense. we must have that which should be checked for every set of constants corresponding to any particular model.," However, in order that the models make sense, we must have that which should be checked for every set of constants corresponding to any particular model." In order to check the applicability of the previous model to describe real galaxies. we analyse a set data taken from the recent paper by Verheijen&Sancici(2001). in which are reported the results of an extensive 21 em-line synthesis imaging survey of 43 galaxies in the nearby Ursa Major cluster using the Westerbork Synthesis Radio Telescope.," In order to check the applicability of the previous model to describe real galaxies, we analyse a set data taken from the recent paper by \cite{VS}, in which are reported the results of an extensive 21 cm-line synthesis imaging survey of 43 galaxies in the nearby Ursa Major cluster using the Westerbork Synthesis Radio Telescope." For each rotation curve data. we take the value of a. the radius of the galactic disc. as given by the last tabulated value of the radius.," For each rotation curve data, we take the value of $a$, the radius of the galactic disc, as given by the last tabulated value of the radius." Accordingly. we are assuming that the radius of the galaxies is defined by the farthest observed data.," Accordingly, we are assuming that the radius of the galaxies is defined by the farthest observed data." Now. although this assumption about the galactic radius do not agrees with the accepted standard about the edge of the stellar disc (Binneyrifield. 1998). we will make it since we are assuming that all the stars moving in circular orbits at the galactic plane are inside the dise and that there are no stars moving outside the disc.," Now, although this assumption about the galactic radius do not agrees with the accepted standard about the edge of the stellar disc \citeauthor{BM} \citeyear{BM}) ), we will make it since we are assuming that all the stars moving in circular orbits at the galactic plane are inside the disc and that there are no stars moving outside the disc." So. by taking the radius normalized in units of e. we make a non-linear least square fit of the data with the general relation (359) for all the galaxies reported by Verheijen&Sancici(2001).. seeking for a balance between the best numerical fit and the fit that agrees with the positiveness of the epicycle frequency by using the consistency criterion (1) over the constants ;1»;.," So, by taking the radius normalized in units of $a$, we make a non-linear least square fit of the data with the general relation \ref{velr2n}) ) for all the galaxies reported by \cite{VS}, seeking for a balance between the best numerical fit and the fit that agrees with the positiveness of the epicycle frequency by using the consistency criterion \ref{kapr2n}) ) over the constants $A_{2l}$." By selecting between all the galaxies only those that fulfill with the consistency criterion. then we proceed to determine the lower and upper bounds over the halo mass by using expressions (47)) and (9000).," By selecting between all the galaxies only those that fulfill with the consistency criterion, then we proceed to determine the lower and upper bounds over the halo mass by using expressions \ref{mhmin}) ) and \ref{mhmax}) )." Finally. we check that this two values of the halo mass are in agreement with the condition (5 11) in order that the models make sense.," Finally, we check that this two values of the halo mass are in agreement with the condition \ref{mascon}) ) in order that the models make sense." " However. when we check the consistency of the adjust. we found that only the fit of the data for the galaxies NGC4389 and UGC6969 it agrees with this conditions. whereas that for all the other galaxies we found that .Vf,,«−©!no "," However, when we check the consistency of the adjust, we found that only the fit of the data for the galaxies NGC4389 and UGC6969 it agrees with this conditions, whereas that for all the other galaxies we found that ${\mathcal M}_n^+ < {\mathcal M}_n^-$." In Table | we present the values of the galactic radius e and the constants 24s; obtained by the numerical adjust with the rotation curve data for galaxies NGC4389 and UGC6969 by taking a model with »= +., In Table \ref{tab:a2l} we present the values of the galactic radius $a$ and the constants $A_{2l}$ obtained by the numerical adjust with the rotation curve data for galaxies NGC4389 and UGC6969 by taking a model with $n = 4$ . With this values for the constants. we obtain for the galaxy NGC4389 the relationship and for the galaxy UGC6969 the relationship," With this values for the constants, we obtain for the galaxy NGC4389 the relationship and for the galaxy UGC6969 the relationship" ealaxy colours and add: simulated measurement errors. as randomly extracted: steps from the interval ὃς 19). with à=0.01.0.03.0.05.,"galaxy colours and add simulated measurement errors, as randomly extracted steps from the interval $- \delta$ $+ \delta$ ), with $\delta = 0.01, 0.03, 0.05$." We apply our fitting procedure. searching for the best model in our svuthetic library. which reprocduces the colours of each of the simulated. galaxies ancl then compare the output. parameter estimates to the input nmiocdel values.," We apply our fitting procedure, searching for the best model in our synthetic library, which reproduces the colours of each of the simulated galaxies and then compare the output parameter estimates to the input model values." We perform the fit (1) using only the optical SDSS bands ugriz and (2) adding NUR photometry €J. Lf and Avs: Jarrettetal. 2003)) and (3) ultraviolet photometry (NUV and FUY: Martinetal. 2005)).," We perform the fit (1) using only the optical SDSS bands $ugriz$ and (2) adding NIR photometry $J$, $H$ and $Ks$; \citealt{Jarrett+03}) ) and (3) ultraviolet photometry (NUV and FUV; \citealt{Martin+05}) )." " We define the median error in the eraclients as ACN)=Xii Nine where Y; and Nir are the input and fitted gradients with No=Vx,. Vis and Vy. which we show in Tables 1. and 2.."," We define the median error in the gradients as $\Delta(X)=X_{\rm fit}-X_{\rm in}$ , where $X_{\rm in}$ and $X_{\rm fit}$ are the input and fitted gradients with $X = \gML$, $\gage$ and $\gZ$, which we show in Tables \ref{tab:tab1} and \ref{tab:tab1bis}." Starting from the purely. random: case shown in Table 1l. we have found that. αστας the NUR or UV. cata. both the vvalues ancl their gradients are perfectly recovered. with a very little scatter.," Starting from the purely random case shown in Table \ref{tab:tab1}, we have found that, adding the NIR or UV data, both the values and their gradients are perfectly recovered with a very little scatter." " With optical data only. the uncertainties are doubled: (around 0.1 in A(W+,)) and there is a small systematic shift in the gradients (of logVy,0.010.02 or the worst. case analyzed). but. the. results. are fairly well recovered. with no spurious trends expected."," With optical data only, the uncertainties are doubled (around 0.1 in $\Delta(\gML)$ ) and there is a small systematic shift in the gradients (of $\log \gML \sim 0.01-0.02$ for the worst case analyzed), but the results are fairly well recovered with no spurious trends expected." We notice hat the median results are quite independent of the range adopted for the input νους and only slight dillerences in the scatter are found.," We notice that the median results are quite independent of the range adopted for the input $\Yst_{2}$, and only slight differences in the scatter are found." Although we will be mainly interested in he trends of wwith mass anc velocity dispersion. we have also checked he systematics in age and metallicity gradients.," Although we will be mainly interested in the trends of with mass and velocity dispersion, we have also checked the systematics in age and metallicity gradients." We find similar results to the case of cleliscussecl above. but sliehthy larger shifts in the median and lareer scatters (0.2 in the worst cases) when only the optical is used.," We find similar results to the case of discussed above, but slightly larger shifts in the median and larger scatters $\sim 0.2$ in the worst cases) when only the optical is used." In. Table 2.. caleulating the sample averages. we start with the input values V4.=0 and Vz= 0.," In Table \ref{tab:tab1bis}, calculating the sample averages, we start with the input values $\gage \neq 0$ and $\gZ \neq 0$ ." Here the median errors and the scatters increase. but the conclusions discussed above are qualitatively confirmed.," Here the median errors and the scatters increase, but the conclusions discussed above are qualitatively confirmed." When optical data are used. for high Ty. we have the worst discrepancies in the estimated. eeradicnts amounting to ~(0.05. 0.07.," When optical data are used, for high $\Yst_{2}$ we have the worst discrepancies in the estimated gradients amounting to $\sim -0.05$, $-0.07$." For age and metallicity gradients. we could underestimate (overestimate) the age (metallicity) gradients of ~0.1. which is reduced to 0.02 when near-H or UN are included.," For age and metallicity gradients, we could underestimate (overestimate) the age (metallicity) gradients of $\sim 0.1$, which is reduced to $\sim 0.02$ when near-IR or UV are included." ‘Thus. in many cases we have found that the median errors are acceptable and within the typical sample scatter and the uncertainties due to the adopted stellar population prescription.," Thus, in many cases we have found that the median errors are acceptable and within the typical sample scatter and the uncertainties due to the adopted stellar population prescription." We will consider these results as qualitative indications of the ellects on estimated. eradients caused. by systenmaties., We will consider these results as qualitative indications of the effects on estimated gradients caused by systematics. 1n this section we cliscuss first the e&eracients in terms of colour. age and metallicity gradients and then as a function. of stellar mass ancl velocity dispersion. paving attention to the role of central age in the observed correlations.," In this section we discuss first the gradients in terms of colour, age and metallicity gradients and then as a function of stellar mass and velocity dispersion, paying attention to the role of central age in the observed correlations." We start by plotting in Fig., We start by plotting in Fig. 2 the eeradients as à function of gor colour gradient. (Way) for EPCs anc Ες., \ref{fig:fig2} the gradients as a function of $g-r$ colour gradient $\ggr$ ) for ETGs and LTGs. The two quantities are. strongly and. positively correlated: and no statistically significant difference between the morphological types is found., The two quantities are strongly and positively correlated and no statistically significant difference between the morphological types is found. While such a correlation is not surprising owing to the well correlations between colours and ((BelL&deJong2001: DO3). whieh should apply to all racii thus producing the relationship between aandQ2 there are important details to consider.," While such a correlation is not surprising owing to the well known-correlations between colours and \citealt{BdJ01}; B03), which should apply to all radii thus producing the relationship between and, there are important details to consider." Dell& have adopted. dillerent. evolution models for ΕΝ to establish some linear correlations between integrated total colours and the corresponding determining some best [it relations between these two uantities. which have been proven to work for EPCs as well Bellοἱal. 20032).," \cite{BdJ01} have adopted different evolution models for LTGs to establish some linear correlations between integrated total colours and the corresponding determining some best fit relations between these two quantities, which have been proven to work for ETGs as well \citealt{Bell+03}) )." XAdopting the solar mictallicity models in Dell&deJong(2001) we have found à good agreement with Druzual&Charlot(2003) or Maraston(2005). svnthetic »escriptions in IZECGs with highAZ/L.. while at low citelcJOl overestimates the (see Tortoraetal.(2009). for further details).," Adopting the solar metallicity models in \cite{BdJ01} we have found a good agreement with \cite{BC03} or \cite{Maraston05} synthetic prescriptions in ETGs with high, while at low \\cite{BdJ01} overestimates the (see \cite{Tortora2009} for further details)." In the left xiuel of Fig., In the left panel of Fig. 2. we compare our trenels with the ones (solid and dashed Lines) derived from he D03 best fitted relations. finding a good agreement.," \ref{fig:fig2} we compare our trends with the ones (solid and dashed lines) derived from the B03 best fitted relations, finding a good agreement." The Mack and green lines plotted in Fig., The black and green lines plotted in Fig. 2. are derived by the relations between the g-band aand the colours (6.ο gore gf and g2) from Bos.," \ref{fig:fig2} are derived by the relations between the g-band and the colours $u-g$, $g-r$, $g-i$ and $g-z$ ) from B03." We insert in these relations the measured. colour for cach galaxy in our sample. deriving the correspondingAL/L.," We insert in these relations the measured colour for each galaxy in our sample, deriving the corresponding." . Phis operation is macle for both the radii #y and fo. thus we can calculate the eeradients.," This operation is made for both the radii $R_{1}$ and $R_{2}$, thus we can calculate the gradients." Finally. the plotted lines are. obtained. Éfürst calculating medians of ün bins of aand then fitting a straight line.," Finally, the plotted lines are obtained, first calculating medians of in bins of and then fitting a straight line." We see that the best fitted relations depend on the colours adopted in the rrelations from D|03 to derive the eeracients., We see that the best fitted relations depend on the colours adopted in the relations from B+03 to derive the gradients. For instance. we observe a Hlattening of the rrelation when using colours probing redcder wavelengths. iie. g Pandg z. but a shallower trend is obtained when ὁ is adopted.," For instance, we observe a flattening of the relation when using colours probing redder wavelengths, i.e. $g-i$ and $g-z$, but a shallower trend is obtained when $u-g$ is adopted." The agreement is quite good for moderate colour eracients. while for very steep positive or negative gradients some cepartiures are observed.," The agreement is quite good for moderate colour gradients, while for very steep positive or negative gradients some departures are observed." Despite the good. agreement. the very simplified approach in Dell&deJong(2001) anc D03 has some strong limitations.," Despite the good agreement, the very simplified approach in \cite{BdJ01} and B03 has some strong limitations." In fact. a) the DOS relations hold. for integrated: quantities. thus the radial variation of the AlyL can be derived if one assumes that the same relations apply al different apertures and in general. the zero-point and the slope of these fitted. Linear relations would depend. on the racius adopted and b) these relationsdo not take into account the stellar parameters (e.g. age ancl metallicity at each radius) thus they do not allow to cateh the full physics behind these correlations.," In fact, a) the B03 relations hold for integrated quantities, thus the radial variation of the $M/L$ can be derived if one assumes that the same relations apply at different apertures and in general, the zero-point and the slope of these fitted linear relations would depend on the radius adopted and b) these relationsdo not take into account the stellar parameters (e.g. age and metallicity at each radius) thus they do not allow to catch the full physics behind these correlations." ποσο shortcomings are overcome by our multi-colour direct stellar population analysis which connects the eeradients sell-consistentlv {ο 1ο underlving stellar, These shortcomings are overcome by our multi-colour direct stellar population analysis which connects the gradients self-consistently to the underlying stellar "In order to test the accuracy of the method for calculating the (DV) for a particularabsorber""... we obtained estimates for the amounts of dust in a subsample of qquasar spectra with no identified absorbers from. our quasar sample (Fig. 3)).","In order to test the accuracy of the method for calculating the $E(B-V)$ for a particular, we obtained estimates for the amounts of dust in a subsample of quasar spectra with no identified absorbers from our quasar sample (Fig. \ref{cap:uncertainty}) )." For the non-absorber quasar sample we create a sipiulated: set of absorbers with. zar. ando za&/zq2) distributions which are consistent with the corresponding redshift distributions in the absorber sample., For the non-absorber quasar sample we create a simulated set of absorbers with $z_{\mathrm{abs}}$ and $z_{\mathrm{abs}}/z_{\mathrm{qso}}$ distributions which are consistent with the corresponding redshift distributions in the absorber sample. We then obtain (D.V) estimates for this sample using the prescription in Section ??.., We then obtain $E(B-V)$ estimates for this sample using the prescription in Section \ref{sub:Determining-E(B-V)}. . " Phe distribution is centred. on ἐκV)-00 indicating no detectable svstematic bias in the determination of £(BV). with an encouraginely small uncertainty. ogg.v,00.025. in the 0V) estimates for individualquasars”."," The distribution is centred on $E(B-V)=0.0$ indicating no detectable systematic bias in the determination of $E(B-V)$, with an encouragingly small uncertainty, $\sigma_{E(B-V)} \sim 0.025$, in the $E(B-V)$ estimates for individual." .. Phe spread arises from intrinsic quasar-to-quasar SEED variations., The spread arises from intrinsic quasar-to-quasar SED variations. Notwithstanding the use of an individual. control spectrum for each quasar. quasars with intrinsically. unusual SEDs lead to flux ratio spectra still dominate by the variation among quasar SEDs.," Notwithstanding the use of an individual control spectrum for each quasar, quasars with intrinsically unusual SEDs lead to flux ratio spectra still dominated by the variation among quasar SEDs." The presence of such variations in turn leads to poor determinations of E(DVO., The presence of such variations in turn leads to poor determinations of $E(B-V)$. We have estimated the quality of fit of each absorbers [lux ratio with an extinction curve by using a Ixolmogorov-Smirnoll-Dike. statistic., We have estimated the quality of fit of each absorber's flux ratio with an extinction curve by using a Kolmogorov-Smirnoff-like statistic. Our test. uses the cumulative cüllerence between the ποιακος best-Li extinction curve and. normalised absorber's [lux ratio. to identify a svstenmiatic shape difference and. thus poor-fit.," Our test uses the cumulative difference between the normalised best-fit extinction curve and normalised absorber's flux ratio, to identify a systematic shape difference and thus poor-fit." The maximum cumulative cillerence. of Diyas. is obtainec for cach absorbers SAIC. LAIC and MW. extinction curve fit.," The maximum cumulative difference, or $D_{\mathrm{max}}$ , is obtained for each absorber's SMC, LMC and MW extinction curve fit." The Ds distributions appear to show no evidence of significant bias as a function of absorber redshift. (2V). EW ancl quasar magnitude (rig. 4)).," The $D_{\mathrm{max}}$ distributions appear to show no evidence of significant bias as a function of absorber redshift, $E(B-V)$ , EW and quasar magnitude (Fig. \ref{cap:ks}) )." Visual inspection of quasar spectra with large values of Dias reveals a mixture of quasars showing i) strong emission. ii) very blue continua or iii) red. but Tat’. spectra without the curvature expected due to conventional extinction. curves.," Visual inspection of quasar spectra with large values of $D_{\mathrm{max}}$ reveals a mixture of quasars showing i) strong emission, ii) very blue continua or iii) red, but 'flat', spectra without the curvature expected due to conventional extinction curves." “Phe number of such quasars is small. consistent with the tails of the distribution evident in Fig. 3..," The number of such quasars is small, consistent with the tails of the distribution evident in Fig. \ref{cap:uncertainty}," due to the small fraction of quasars with unusual intrinsic SEDs (unrelated. to any signature due to intervening absorbers)., due to the small fraction of quasars with unusual intrinsic SEDs (unrelated to any signature due to intervening absorbers). The 20 uncertainty in (21) resultingS from quasar-ito-quasar SED variations corresponds to an E(D12 dilference of 0.050 mag (Fig. 3))., The $\sigma$ uncertainty in $E(B-V)$ resulting from quasar-to-quasar SED variations corresponds to an $E(B-V)$ difference of 0.050 mag (Fig. \ref{cap:uncertainty}) ). " Such a dillerence produces à value of Dyn =0.04 and we therefore define spectrum Ilux ratio fits with 4,420.04 as possessing a poor fit to the SMC extinction curve.", Such a difference produces a value of $D_{\mathrm{max}}$ =0.04 and we therefore define spectrum flux ratio fits with $D_{\mathrm{max}}$$>$ 0.04 as possessing a poor fit to the SMC extinction curve. The number of such spectra 329)) represent an extremely small fraction of the total (0.2 per cent)., The number of such spectra ) represent an extremely small fraction of the total (0.2 per cent). We exclude such objects from further analysis until we consider the detailed shape of the aabsorber extinction Curves in Section ??.., We exclude such objects from further analysis until we consider the detailed shape of the absorber extinction curves in Section \ref{dusttype}. The ellectiveness of the Dus statistic is verified by noting that the Hux ratio spectra with multiple (22) absorption svstems exhibit svstematically larger. values of Duas than spectra with single or double absorbers., The effectiveness of the $D_{\mathrm{max}}$ statistic is verified by noting that the flux ratio spectra with multiple $>2$ ) absorption systems exhibit systematically larger values of $D_{\mathrm{max}}$ than spectra with single or double absorbers. The differences are clue to the presence of multiple extinction signatures at cilferent recshifts. providing justification for the use of single and. double absorber lines of sight. only (Section ??))," The differences are due to the presence of multiple extinction signatures at different redshifts, providing justification for the use of single and double absorber lines of sight only (Section \ref{mgsample}) )." Extinction of quasar light due to the presence of dust in intervening absorbers. leads to objects being Lost. [rom magnitucde-limitecl quasar surveys (?7?)..," Extinction of quasar light due to the presence of dust in intervening absorbers, leads to objects being lost from magnitude-limited quasar surveys \citep{1993ApJ...402..479F, 2006MNRAS.367..211W}." ‘To illustrate the οσοι of extinction by intervening dust on our sample. the left-hand panel of Fig.," To illustrate the effect of extinction by intervening dust on our sample, the left-hand panel of Fig." 5. shows the observed extinction at (the effective wavelength of the SDSS ;-band)., \ref{cap:biascalc} shows the observed extinction at (the effective wavelength of the SDSS $i$ -band). Aclelitionally. extinction due to an intervening absorber leacks to a degredation of the spectrum S/N and hence additional absorbers are lost from the sample.as their S/N falls below theTa aabsorberdetection threshold (Section ??))," Additionally, extinction due to an intervening absorber leads to a degredation of the spectrum S/N and hence additional absorbers are lost from the sample,as their S/N falls below the$7\sigma$ absorberdetection threshold (Section \ref{mgsample}) )." We have used the magnitude and redshift distribution of the quasars in the quasar sample (Section ??)) to obtain, We have used the magnitude and redshift distribution of the quasars in the quasar sample (Section \ref{mgsample}) ) to obtain particular. logyy&=—0.5 aud the UV emission caused by the low energy exteusiou of the 10 keV bremisstralhluug. Mijas2300 whereas for an ACN-like UV spectrum. ie. a power law with the energy iudex equal to 1. MsS000 CT. Wallan private conuuunication).,"particular, $\log_{10} \xi= -0.5$ and the UV emission caused by the low energy extension of the 10 keV bremsstrahlung, $M_{\rm max}\approx 300$ whereas for an AGN-like UV spectrum, i.e., a power law with the energy index equal to 1, $M_{\rm max}\approx 8000$ (T. Kallman private communication)." For comparison. eqs.," For comparison, eqs." 12 and 13 vicld Micz3100 also for logyy¢=—0.5., 12 and 13 yield $M_{\rm max}\approx 3400$ also for $\log_{10} \xi= -0.5$. A detail investigation of these aud other depeudoeucies is bevoud the scope of this study but it is inportaut to carry out such a study in the future., A detail investigation of these and other dependencies is beyond the scope of this study but it is important to carry out such a study in the future. To calculate the photoionization paramcter needed iu eqs., To calculate the photoionization parameter needed in eqs. " 12 and 13 and in evaluation of the net radiative cooling.we use the formula: where Fy is the local X-ray flux. ο is the ΕΟΤ density of the gas (=pfGnyp). where ii, is tho proton mass. and fis the mean molecular weight)."," 12 and 13 and in evaluation of the net radiative cooling,we use the formula: where ${\cal F}_{\rm X}$ is the local X-ray flux, $n$ is the number density of the gas $={\rho}/({m_p \mu })$, where $m_p$ is the proton mass, and $\mu$ is the mean molecular weight)." We consider models with Bo—d., We consider models with $\mu=1$. The local N-vay flux is corrected for the optical depth effects: where τς is the N-vav optical depth., The local X-ray flux is corrected for the optical depth effects: where $\tau_{\rm X}$ is the X-ray optical depth. We estimate τς between the central source and a point in a flow from: where αν is the absorption cocficicut. aud r ijs the distance from the central source.," We estimate $\tau_{\rm X}$ between the central source and a point in a flow from: where $\kappa_{\rm X}$ is the absorption coefficient, and $r$ is the distance from the central source." The flow physical concitions and consequently the lue force depeud not ouly ou £., The flow physical conditions and consequently the line force depend not only on $\xi$. In particular. the gas teiuperature and ionization state can be affected by adiabatic heatiug or cooliug.," In particular, the gas temperature and ionization state can be affected by adiabatic heating or cooling." For example. the line force can be neglected even iu the region of low © if this region is hot due to adiabatic compression.," For example, the line force can be neglected even in the region of low $\xi$ if this region is hot due to adiabatic compression." Therefore. we first conrpute the line force parameters based on € and then correct the paraicters for the eas temperature effects.," Therefore, we first compute the line force parameters based on $\xi$ and then correct the parameters for the gas temperature effects." " Specifically, we compute the parameter A usine the expression We adopt this value of & if it is smaller than the one obtained by using expression 12."," Specifically, we compute the parameter $k$ using the expression We adopt this value of $k$ if it is smaller than the one obtained by using expression $12$." Expression 17 is based ou detailed pliotoionizatiou caleulatious performed usius the NSTAR code CF. Παια private commumication)., Expression $17$ is based on detailed photoionization calculations performed using the XSTAR code (T. Kallman private communication). " These expressious for the paramcters of the force multiplier predict that AZ,444 increases eradually frou ~2000 to 5000 as © increases from 0 to ~3 aud then drops to OL at &=1000.", These expressions for the parameters of the force multiplier predict that $M_{\rm max}$ increases gradually from $\sim 2000$ to $5000$ as $\xi$ increases from 0 to $\sim 3$ and then drops to $\sim 0.1$ at $\xi=1000$. The line force becomes neelieible for &£100 because then Mas~d., The line force becomes negligible for $\xi \simgreat 100$ because then $M_{\rm max} \sim 1$. The Hue force becomes also negligible i£ T>10? Ws for any &., The line force becomes also negligible if $T>10^5$ K for any $\xi$. To caleulate the gas temperature we also follow PSIsx. who assuned that the gas is optically thin to its own cooling radiation.," To calculate the gas temperature we also follow PSK, who assumed that the gas is optically thin to its own cooling radiation." The net cooling rate depeuds on the density. p. the temperature. T. the ionization parameter &£. and the characteristic temperature of the N-ray radiation Ty.," The net cooling rate depends on the density, $\rho$, the temperature, $T$, the ionization parameter $\xi$, and the characteristic temperature of the X-ray radiation $T_{\rm X}$." We refer a reader to PSIS aud Proga lIkallinan (2001) for more details., We refer a reader to PSK and Proga Kallman (2004) for more details. We calculate the evolution of the internal energv and therefore we specify the initial aud outer boundary conditions for e., We calculate the evolution of the internal energy and therefore we specify the initial and outer boundary conditions for $e$. We do this iu the following wav: we specify the gas temperature at the outer boundary (n the last erid zone in the racial direction). ων bv setting it to the Compton temperature. Te=0.25Tx.," We do this in the following way: we specify the gas temperature at the outer boundary (in the last grid zone in the radial direction), $T_{\rm 0}$, by setting it to the Compton temperature, $T_{\rm C}=0.25~T_{\rm X}$." Then we calculate the internal energy from Wo asune the amass of the non-rotating DIT. Mou=105AL. aud the disk inmuer radius. !ι=BsnEN10 cm throughout) this paper.," Then we calculate the internal energy from We assume the mass of the non-rotating BH, $M_{\rm BH}~=~10^8~\rm \MSUN$ and the disk inner radius, $r_\ast=~3~r_{\rm S}~=~8.8~\times~10^{13}$ cm throughout this paper." We consider the rest mass couversion efficiency j—0.0833., We consider the rest mass conversion efficiency $\eta=~0.0833$. " We set M, to be 1029&«1 (21,6 Myr 1).", We set $\MDOT_{\rm a}$ to be $10^{26}~{\rm g~s^{-1}}$ (=1.6 $\MSUNYR$ ). These system paramcters vield the accretion Iunünositv. L=75<.tocresi22.107? L.).," These system parameters yield the accretion luminosity, $L = 7.5\times10^{45}~{\rm erg~s^{-1}}(=2\times10^{12}~\LSUN$ )." This Iuninositv corresponds to the Eddington uuuber. D.=0.6.," This luminosity corresponds to the Eddington number, $\Gamma=0.6$." We define the Eddinetou munuber as £ in units of the Eddington luuinosity for the Schwiuzschild DII. Lea=lacGMyufo. lic. P.—L/Lear=(aMyj/(Srers)|.," We define the Eddington number as $L$ in units of the Eddington luminosity for the Schwarzschild BH, $L_{\rm Edd}= 4 \pi c G M_{\rm BH}/\sigma_e$ [i.e., $\Gamma\equiv L/L_{\rm Edd}= (\sigma_e \MDOT_{\rm a})/(8\pi c r_{\rm S}$ )]." To determine the radiatiou field. we specify also fry aud fx.," To determine the radiation field, we specify also $f_{\rm UV}$ and $f_{\rm X}$." " We note that we fix Af, during our simulations. ic. AL, does not depend ou the mass flax through the iuner boundary. μη). (see eq."," We note that we fix $\MDOT_{\rm a}$ during our simulations, i.e. $\MDOT_{\rm a}$ does not depend on the mass flux through the inner boundary, $\MDOT_{\rm in}(r_{\rm i})$ (see eq." 20 for the formal definition of ALA) and 8L for discussion of this aspect of the calculations)., 20 for the formal definition of $\MDOT_{\rm in}(r_{\rm i})$ and 4 for discussion of this aspect of the calculations). The paraueters fry and fx (aud also fp and f) specifviue the radiation field are our free parameters which we focus on exploring the most in this paper., The parameters $f_{\rm UV}$ and $f_{\rm X}$ (and also $f_{\rm D}$ and $f_\ast$ ) specifying the radiation field are our free parameters which we focus on exploring the most in this paper. We consider three cases: case. A with fry=0.5 and fx=0.5. case D with fry=0.8 and fy=0.2. aud case € with fry=0.95 and fx=0.05 (see Table 1 for sunmnuiuv of our runs).," We consider three cases: case A with $f_{\rm UV}=0.5$ and $f_{\rm X}=0.5$, case B with $f_{\rm UV}=0.8$ and $f_{\rm X}=0.2$, and case C with $f_{\rm UV}=0.95$ and $f_{\rm X}=0.05$ (see Table 1 for summary of our runs)." The spectral energy distribution of the ionizing radiation is not well known.our choice of values for fry and fx is guided by the observational results from Zhene et al. (," The spectral energy distribution of the ionizing radiation is not well known,our choice of values for $f_{\rm UV}$ and $f_{\rm X}$ is guided by the observational results from Zheng et al. (" 1997) aud Laor et al. (,1997) and Laor et al. ( 1997).,1997). To calculate the eas teniperature. we assume the temperature of the N-vay radiation. Tx=8<10° K (ee. Sazonov. Ostriker Sunvaev 2005 aud references therein) and the line cooling paramcter à=1 (see Bloudiu 199 and PSI).," To calculate the gas temperature, we assume the temperature of the X-ray radiation, $T_{\rm X}=8\times10^7$ K (e.g., Sazonov, Ostriker Sunyaev 2005 and references therein) and the line cooling parameter $\delta=1$ (see Blondin 1994 and PSK)." The force multiplier depends ouly formally ou the thermal speed. ery.," The force multiplier depends only formally on the thermal speed, $v_{\rm th}$." Therefore to compute f. we set to 20 hans tie. the thermal speed of a lydrogen atom a the temperature of 25000 Ix for which the parameters of the force multiplier were computed (Stevens Tallman 1990).," Therefore to compute $t$, we set to 20 ${\rm km~s^{-1}}$, i.e., the thermal speed of a hydrogen atom at the temperature of 25000 K for which the parameters of the force multiplier were computed (Stevens Kallman 1990)." Finally. the attennationof the N-ravs is calculates using sx=O.L@joan? for all & ," Finally, the attenuationof the X-rays is calculated using $\kappa_{\rm X}= 0.4~{\rm g^{-1}~cm^2}$ for all $\xi$ ." The resulting optica depth corresponds to the Thomson optical depth., The resulting optical depth corresponds to the Thomson optical depth. " For our parameters. both the so-called Compton radius. Πο=GAlpuypun,(kT = SAIOEF on = 9&10!s iux the Dondi radius; Rp=GALex—La.lo cm = 5.5«10!r; (Bondi 1952) are inside our conmputationa domain."," For our parameters, both the so-called Compton radius, $R_{\rm C}\equiv G M_{\rm BH} \mu m_p/k T_{\rm C}$ = $\times10^{18}$ cm = $9\times10^4~r_\ast$ and the Bondi radius, $R_{\rm B}=G M_{\rm BH}/c_\infty^2= 4.8 \times 10^{18}$ cm = $5.5 \times 10^4~r_\ast$ (Bondi 1952) are inside our computational domain." We assumed here that the gas teniperature at iufuitv T4=Te2«107 K so that the sound speed at infinity. ος=(ση1οpinu) 2= [.10* cans land Ré= Rp.," We assumed here that the gas temperature at infinity $T_\infty=T_{\rm C}=2\times10^7$ K so that the sound speed at infinity, $c_\infty=(\gamma k T_{\rm C}/\mu m_p)^{1/2}$ = $\times10^7$ cm $\rm s^{-1}$ and $R_{\rm C}=\gamma R_{\rm B}$ ." " For the isothermal flow. the Boudi accretion rate is An,=3.3<10%es t= 0.52 M.vr iL,"," For the isothermal flow, the Bondi accretion rate is $\MDOT_{\rm B}=3.3\times10^{25}{\rm g~s^{-1}}$ = 0.52 $\MSUNYR$ ." We note that the, We note that the lifetimes of radio sources are short compared to cosmologica timescales. this can only mean that the slope of their luminosity functions are dillerent. if GPS sources are to evolve into large size racio sources.,"lifetimes of radio sources are short compared to cosmological timescales, this can only mean that the slope of their luminosity functions are different, if GPS sources are to evolve into large size radio sources." I is shown that tha the slope of a luminosity function. is strongly. dependen on the evolution of radio power of the individual sources., It is shown that that the slope of a luminosity function is strongly dependent on the evolution of radio power of the individual sources. " A new method is introduced to constrain the luminosity evolution of radio sources using the luminosity functions of νομος and ""old! objects.", A new method is introduced to constrain the luminosity evolution of radio sources using the luminosity functions of `young' and `old' objects. Ht ds shown that if GPS sources are increasing in radio power with time. it would result in à relatively Latter slope of their Luminosity function compare to that of large size radio sources which decrease in raclio power.," It is shown that if GPS sources are increasing in radio power with time, it would result in a relatively flatter slope of their luminosity function compared to that of large size radio sources which decrease in radio power." A simple model was developed in which a radio source. embedded in a Ixing profile medium. evolves in a self similar wav under the equipartition energy assumption.," A simple model was developed in which a radio source, embedded in a King profile medium, evolves in a self similar way under the equipartition energy assumption." This mocel indeed results in the suggested: increase in luminosity [or voung radio sources. and decrease in luminosity. [or old. extended: objects.," This model indeed results in the suggested increase in luminosity for young radio sources, and decrease in luminosity for old, extended objects." The. calculatect luminosity. function. for arge size radio sources shows a break and slopes at [ow and high luminosity comparable to that derived by Dunlop Peacock 1900) [or steep spectrum: sources., The calculated luminosity function for large size radio sources shows a break and slopes at low and high luminosity comparable to that derived by Dunlop Peacock (1990) for steep spectrum sources. The loca uminositv function (LLE) of GPS sources can not. be measured directly since so [few GPS sources are found a ow redshift., The local luminosity function (LLF) of GPS sources can not be measured directly since so few GPS sources are found at low redshift. Therefore. the knowledge of the cosmologica evolution of the luminosity function of steep spectrum sources. as derived by Dunlop Peacock (1990). is used. so hat the LLE can be derived. from the complete samples of xieht and faint GPS sources.," Therefore, the knowledge of the cosmological evolution of the luminosity function of steep spectrum sources, as derived by Dunlop Peacock (1990), is used, so that the LLF can be derived from the complete samples of bright and faint GPS sources." Lt is shown that this LLE is as expected for radio sources which increase in Luminosity with ime. which is confirmed by simulations of the voung racio source population.," It is shown that this LLF is as expected for radio sources which increase in luminosity with time, which is confirmed by simulations of the young radio source population." Note however. that the bright and faint GPS samples are constructed in very dilferent ways and that herefore large corrections had to be made.," Note however, that the bright and faint GPS samples are constructed in very different ways and that therefore large corrections had to be made." Uncertainties ave still very large and ideally large samples of GPS sources should be constructed whieh are uniformly. selected at. low and high Lux densities., Uncertainties are still very large and ideally large samples of GPS sources should be constructed which are uniformly selected at low and high flux densities. photometric supernova (SN) classification are in high demand in the astronomical community.,Novel approaches to photometric supernova (SN) classification are in high demand in the astronomical community. " The next generation of survey telescopes, such as the Dark Energy Survey (DES; ?)) and the Large Synoptic Survey Telescope (LSST; ?)), are expected to observe light curves for a few hundred thousand supernovae (SNe), far surpassing the resources available to spectroscopically confirm the type of each."," The next generation of survey telescopes, such as the Dark Energy Survey (DES; \citealt{des}) ) and the Large Synoptic Survey Telescope (LSST; \citealt{ivez2008}) ), are expected to observe light curves for a few hundred thousand supernovae (SNe), far surpassing the resources available to spectroscopically confirm the type of each." " To fully exploit these large samples, it is necessary to develop methods that can accurately and automatically classify large samples of SNe based only on their photometric light curves."," To fully exploit these large samples, it is necessary to develop methods that can accurately and automatically classify large samples of SNe based only on their photometric light curves." " In order to use Type Ia supernovae as cosmological probes, it is imperative that pure and efficient Type Ia samples are constructed."," In order to use Type Ia supernovae as cosmological probes, it is imperative that pure and efficient Type Ia samples are constructed." " Yet, classifying SNe from their light curves is a challenging problem."," Yet, classifying SNe from their light curves is a challenging problem." " The light flux measurements are often noisy, nonuniform in time, and incomplete."," The light flux measurements are often noisy, nonuniform in time, and incomplete." " In particular, it is difficult to discern the light curves of Type Ia SNe from those of Type Ib or Ic supernovae, explosive"," In particular, it is difficult to discern the light curves of Type Ia SNe from those of Type Ib or Ic supernovae, explosive" Intergalactic globular clusters (IGC's) are not bound to any particular galaxy. but move freely in (he potential wells of galaxy clusters.,Intergalactic globular clusters (IGCs) are not bound to any particular galaxy but move freely in the potential wells of galaxy clusters. Table 1 will help the reader with the notation used in this paper., Table 1 will help the reader with the notation used in this paper. The existence of IGCs has been considered by a number of authors., The existence of IGCs has been considered by a number of authors. The first cliseussion about them was by vandenBerel(1956).. who measured the distance to the Abell No.," The first discussion about them was by \citet{B56}, who measured the distance to the Abell No." 4 globular cluster (GC)., 4 globular cluster (GC). Obtaining a distance modulus of 20.8. he concluded that it is (herefore antramp.," Obtaining a distance modulus of 20.8, he concluded that it is therefore an." Van den Berel (1953) estimated (hat the number of IGCs within the Local Group is one third of the total number of GCs., Van den Bergh (1958) estimated that the number of IGCs within the Local Group is one third of the total number of GCs. But the first real quantitative studies of IGCs in galaxy. clusters were done by Forte.Martinez.&Muzzio(1982) and Muzzio(1987)., But the first real quantitative studies of IGCs in galaxy clusters were done by \citet{F82} and \citet{M87}. . Muzzio(1987) suggested that galaxies in galaxy clusters suffer. several dvnamical ellects owing to encounters with neighboring galaxies and to the action of the general galaxy cluster field: as a result. galaxies lose some GCs.," \citet{M87} suggested that galaxies in galaxy clusters suffer several dynamical effects owing to encounters with neighboring galaxies and to the action of the general galaxy cluster field; as a result, galaxies lose some GCs." Since (hese processes are very sensitive {ο the distribution of the total mass of the galaxy. cluster. the study of IGCs maa help us to solve (he problem of how (he massis distributed.," Since these processes are very sensitive to the distribution of the total mass of the galaxy cluster, the study of IGCs may help us to solve the problem of how the is distributed." In (Bis scenario. the number density ol lost IGCs should follow the total mass distribution: hence. thev might be concentrated toward the center of the galaxy cluster.," In this scenario, the number density of lost IGCs should follow the total mass distribution; hence, they might be concentrated toward the center of the galaxy cluster." In (he same context. White(1987). suggested that cD envelopes ancl the diffuse lisht in Coma have (he same origin: thev are composed of stars lidally stripped [rom galaxies during Conma's collapse.," In the same context, \citet{W87} suggested that cD envelopes and the diffuse light in Coma have the same origin: they are composed of stars tidally stripped from galaxies during Coma's collapse." 50 GCs might have been stripped as well. creating an LGC population.," So GCs might have been stripped as well, creating an IGC population." Alternatively. if IGCs do exist in galaxy clusters. they may. have been formed in situ in scenarios such as biased GC formation.," Alternatively, if IGCs do exist in galaxy clusters, they may have been formed in situ in scenarios such as biased GC formation." West(1993). argued that the number density of GC's in biased formation scenarios is extremely sensitive lo (he presence and amplitude, \citet{W93} argued that the number density of GCs in biased formation scenarios is extremely sensitive to the presence and amplitude "it unlikely that any of our low-mass brown dwarf candidates are extragalactie background sources,",it unlikely that any of our low-mass brown dwarf candidates are extragalactic background sources. Presumably. the latter are shielded [rom the observed field by dust in the Galactic disk.," Presumably, the latter are shielded from the observed field by dust in the Galactic disk." " Is it possible that we have underestimated the background comlamination due to the fact that background sources in the ""cloud"" region are much more heavily reddened (han those in the ""exterior region?"," Is it possible that we have underestimated the background contamination due to the fact that background sources in the “cloud"" region are much more heavily reddened than those in the “exterior"" region?" For example. do highly reddened AGN resemble brown dwarls when viewed (hrough the cloud?," For example, do highly reddened AGN resemble brown dwarfs when viewed through the cloud?" " To test this. we have simulated the effect of viewing the ""exterior"" region through a dense dust cloud ancl have repeated our temperature fits using (he artificially reddened data,"," To test this, we have simulated the effect of viewing the “exterior"" region through a dense dust cloud and have repeated our temperature fits using the artificially reddened data." We found that no value of applied 24\- could produce a significant population of brown dwarf false-positives. and therefore conclude that the majority of our brown cdwarf candidates in the “cloud” region cannot be attributed to reddened background objects.," We found that no value of applied $A_V$ could produce a significant population of brown dwarf false-positives, and therefore conclude that the majority of our brown dwarf candidates in the “cloud"" region cannot be attributed to reddened background objects." llaving excluded (he various classes of possible background objects on the above basis. we are left with a total of 165 candidate cluster members in the entire observed [ield. of which 92 are brown clwarl candidates.," Having excluded the various classes of possible background objects on the above basis, we are left with a total of 165 candidate cluster members in the entire observed field, of which 92 are brown dwarf candidates." These 165 objects represent the sum of the number of objects in the cloud region (139). exterior region (18). aud the gap between (hose (wo regions (8).," These 165 objects represent the sum of the number of objects in the cloud region (139), exterior region (18), and the gap between those two regions (8)." The photometric results for the candidate cluster members are presented in Table 1.. and the locations of all detected sources (observed in at least + bands) are plotted in Figure 5..," The photometric results for the candidate cluster members are presented in Table \ref{tbl-1}, and the locations of all detected sources (observed in at least 4 bands) are plotted in Figure \ref{fig5}." In the latter. red and green svmbols denote candidate cluster members aud background stars. respectively.," In the latter, red and green symbols denote candidate cluster members and background stars, respectively." Also shown for comparison on the plot are our estimated contours of visual absorption. Ay: these were obtained by dividing the field of view into square cells of size 2!x2’. (inding the maximum value of Ay: for all stars falling into a given cell. and interpolating using a Gaussian convolution kernel.," Also shown for comparison on the plot are our estimated contours of visual absorption, $A_V$; these were obtained by dividing the field of view into square cells of size $2'\times2'$, finding the maximum value of $A_V$ for all stars falling into a given cell, and interpolating using a Gaussian convolution kernel." The fact that the background source density in Figure 5. is highest (bv far) in the oll-cloud region provides validation of our classification criterion lor background stars., The fact that the background source density in Figure \ref{fig5} is highest (by far) in the off-cloud region provides validation of our classification criterion for background stars. , 2 describes the 2-epoch ACS data set used ancl the analysis performed.,2 describes the 2-epoch ACS data set used and the analysis performed. Section 3 gives the results of (he analysis., Section 3 gives the results of the analysis. Section 4 discusses the (vpes of variable stars these are most likely (o be. aud 85Hr) summarizes the conclusions.," Section 4 discusses the types of variable stars these are most likely to be, and 5 summarizes the conclusions." The data used for this project were originally obtained as part of a program to find the optical counterparts for X-ray novae in M31. (Williamsetal.2005)., The data used for this project were originally obtained as part of a program to find the optical counterparts for X-ray novae in M31 \citep{williams2005}. . I obtained. two sels ofLST ACS data. one observed at UT 21:35 on 03-Dec-2003 ancl one observed at UT 16:38 on Ol-\ar-2004.," I obtained two sets of ACS data, one observed at UT 21:35 on 03-Dec-2003 and one observed at UT 16:38 on 01-Mar-2004." Each of these were pointed at R.A.=00:44:07. Dee.=41:12:19.5.," Each of these were pointed at R.A.=00:44:07, Dec.=41:12:19.5." " The observations had orientations of 71.75 deg and 32.73 deg respectively,", The observations had orientations of 71.75 deg and 32.73 deg respectively. Both observations were taken using (he standard ACS box 4-point dither pattern to allow the final data to be drizzled to recover the highest possible spatial resolution., Both observations were taken using the standard ACS box 4-point dither pattern to allow the final data to be drizzled to recover the highest possible spatial resolution. All exposures were taken through the F435W filter., All exposures were taken through the F435W filter. The total exposure times were 2200 seconds for each data set., The total exposure times were 2200 seconds for each data set. The 9.275 arcmin? overlapping region of the two ACS images is outlined on a wide-field IIa. image of AI31 in Figure 1.., The 9.275 $^2$ overlapping region of the two ACS images is outlined on a wide-field $\alpha$ image of M31 in Figure \ref{survey}. " I aligned and drizzled each set of 4 images into high-resolution (0.025"" +) images using the task which has been optimized to process ACS imaging data.", I aligned and drizzled each set of 4 images into high-resolution $''$ $^{-1}$ ) images using the task which has been optimized to process ACS imaging data. The task removes the cosmic ray events and geometric distortions. and it drizzles the dithered Irames together into one final photometric image wilh pixel values in units of counts per second.," The task removes the cosmic ray events and geometric distortions, and it drizzles the dithered frames together into one final photometric image with pixel values in units of counts per second." I aligned the final photometric ACS images with the coordinate svstem of the Local Group Survey (LGS: Masseyetal. 2001)) by applving the taskeemap to the centroids of stars and globular clusters common to the ACS and LGS images., I aligned the final photometric ACS images with the coordinate system of the Local Group Survey (LGS; \citealp{massey2001}) ) by applying the task to the centroids of stars and globular clusters common to the ACS and LGS images. " The LGS images have an assignedJ2000 (FINS) world eoordinate svstem accurate to 70.25"". and they provided the"," The LGS images have an assignedJ2000 (FK5) world coordinate system accurate to $\sim$ $''$ , and they provided the" "The kinetic temperature 7);,, can be estimated according to ∖∖⊽∐≼↲↕⋅≼↲∁⊽⋜⋝∃⋅⊋⇢∃⋅⊥⇄⋝≀⋯≼∏↴⊔⋅∃⇢⊥⋅⊔≀⋯↲⊔∐↲↕⋅≀↧↴∥↲⋝∖⊽∪↓≯≺∢∪∐↕⊳∖⊽↕∪∐≀↧↴↥∏⋅≀↧↴∐⊳∖⇁∐↥∪∐∣↽≻≼↲↥∖∖⊽≼↲≼↲∐⊔∐↲ levels (2.2).(2.1) and (1.1) (Walmsley&Ungerechts1933:Danbyetal. 1988).","The kinetic temperature $T_{kin}$ can be estimated according towhere $C(2,2\rightarrow2,1)$ and $C(2,2\rightarrow1,1)$ are the rates of collisional transition between the levels (2,2),(2,1) and (1,1) \citep{Walmsley83, Danby88}. ." ". The excitation temperature 7), is determined following where Z5(1.1.1) is the brightness temperature of the main component of the NII;CI.1) line."," The excitation temperature $T_{ex}$ is determined following where $T_B(1,1,m)$ is the brightness temperature of the main component of the $_3$ (1,1) line." Then the gas density n(//5) can be caleulatecl according to where -l and C are the Einstein A coefficient and (he collision rate. respectively 1983).," Then the gas density $n(H_2)$ can be calculated according to where $A$ and $C$ are the Einstein $A$ coefficient and the collision rate, respectively \citep{Ho83}." . The results derived [rom the ammonia emission are listed in Table 2.., The results derived from the ammonia emission are listed in Table \ref{table2}. The derived mean rotation temperature 26 Ik is a little higher than (hat of 18 Ix. derived by Sridharanetal. (2002).. ancl themean kinetic temperature 36 Ix is approximately equal {ο the dust temperature (Sridharanetal.2002).," The derived mean rotation temperature 26 K is a little higher than that of 18 K derived by \citet{Sridharan02}, , and themean kinetic temperature 36 K is approximately equal to the dust temperature \citep{Sridharan02}." . In Fie. 8.. ," In Fig. \ref{nh3}, ," there are peaks in NIL4CI.1) aud (2.2) approximately coincident (he mam continuum peaks.," there are peaks in $_3$ (1,1) and (2,2) approximately coincident the mm continuum peaks." It seems that NII3(1.1) and (2.2) lines (race a more extended envelope (han the mm continuum.," It seems that $_3$ (1,1) and (2,2) lines trace a more extended envelope than the mm continuum." The derived gas density is col20.6x10? and the intrinsic line width (FWILM) is ~2.5 !, The derived gas density is $\sim1.4\pm0.6\times10^5$ $^{-3}$ and the intrinsic line width (FWHM) is ${\sim}2.5$ $^{-1}$. In 113264. the SiO emission reveals (wo quasi-perpenclicular molecular outflows emanating from the western mm peak.," In I18264, the SiO emission reveals two quasi-perpendicular molecular outflows emanating from the western mm peak." The mass estimated [rom the mm continuum is as high as 570 Af. and 7300 AL. respectively for the near and far distances even wilh a fraction of the [Iux being filtered out by the interferometer., The mass estimated from the mm continuum is as high as 570 $M_{\odot}$ and 7300 $M_{\odot}$ respectively for the near and far distances even with a fraction of the flux being filtered out by the interferometer. Since (he western peak is much stronger (han the eastern one. most of the mass is attributed to the western peak.," Since the western peak is much stronger than the eastern one, most of the mass is attributed to the western peak." To check (he missing short spacings. the convolved PdBI SiO data have been compared with the single-dish SiO data observed with the IRLAM 30m telescope (Beuther. priv com.).," To check the missing short spacings, the convolved PdBI SiO data have been compared with the single-dish SiO data observed with the IRAM 30m telescope (Beuther, priv com.)." We lind that at channels around the svstemic velocity 43.6 !. less thanof the SiO flux is filtered out bythe interferometer.," We find that at channels around the systemic velocity 43.6 $^{-1}$ , less thanof the SiO flux is filtered out bythe interferometer." " While at channels above eyo, of 50 +. no missing shortspacing problem"," While at channels above $v_{LSR}$ of 50 $^{-1}$ , no missing shortspacing problem" RS is very grateful to Axel D. Sehwope for. generously providing help and software for the evelotron spectroscopy.,RS is very grateful to Axel D. Schwope for generously providing help and software for the cyclotron spectroscopy. We thank IH. Steinle for assisting the observation on Oct. 1. 1992. JJ. Schmoll for that on Alay 28. 1997 and P. Ixroll and R. Lutharet for help at the Sonnebere Observatory equipment.," We thank H. Steinle for assisting the observation on Oct. 1, 1992, J. Schmoll for that on May 28, 1997 and P. Kroll and R. Luthardt for help at the Sonneberg Observatory equipment." We also greatly acknowledge the collaboration with V. Burwitz on the 1995 ROSAT III observation., We also greatly acknowledge the collaboration with V. Burwitz on the 1995 ROSAT HRI observation. JG and. RS were supported by the Deutsche Agentur füur ltaumfahrtangelegenheiten (DARA) ΠΗΡΕ under contract PAZ 50 QQ 9602 3 and 50 OR 9206 8. respectively and WW under contract numbers 05 28 0525 and 05 55 0414.," JG and RS were supported by the Deutsche Agentur fürr Raumfahrtangelegenheiten (DARA) GmbH under contract FKZ 50 QQ 9602 3 and 50 OR 9206 8, respectively and WW under contract numbers 05 2S 0525 and 05 5S 0414." The project is supported. by. the German ssterrium ftir Dildung. Wissenschaft. Forschung und ‘Technologic (BAIBF/DARA) and the Max-Planck-Society.," The project is supported by the German rium fürr Bildung, Wissenschaft, Forschung und Technologie (BMBF/DARA) and the Max-Planck-Society." This research has mace use of the BSimbad database. operated at CDS. Strasbourg. France.," This research has made use of the Simbad database, operated at CDS, Strasbourg, France." We performed multi-epoch water and 6.7 GHz methanol maser VLBI observations towards the well known high-mass protostar20126+4104.,We performed multi-epoch water and 6.7 GHz methanol maser VLBI observations towards the well known high-mass protostar. . The mmaser data are used to measure the annual parallax of the source and thus obtain an accurate distance of 1.64+0.05 kpe., The maser data are used to measure the annual parallax of the source and thus obtain an accurate distance of $1.64\pm0.05$ kpc. This is consistent with the value adopted so far in the literature (1.7 kpe) and confirms that iis the best example of an early B-type protostar associated with a Keplerian disk and bipolar jet., This is consistent with the value adopted so far in the literature (1.7 kpc) and confirms that is the best example of an early B-type protostar associated with a Keplerian disk and bipolar jet. We also derived the absolute proper motions of the mmasers. which gives the 3D velocity of the disk+star system.," We also derived the absolute proper motions of the masers, which gives the 3D velocity of the disk+star system." This can be used to correct the mmaser velocities given by Moseadelli et al. (20055) , This can be used to correct the maser velocities given by Moscadelli et al. \cite{mosca05}) ) and optimize their model fit., and optimize their model fit. The best-fit parameters are qualitatively consistent with those obtained by Moscadelli et al. (2005)).," The best-fit parameters are qualitatively consistent with those obtained by Moscadelli et al. \cite{mosca05}) )," confirming that the jet lies very close to the plane of the sky and is roughly perpendicular to the disk., confirming that the jet lies very close to the plane of the sky and is roughly perpendicular to the disk. By referring the proper motions of the mmasers to a feature lying in the disk plane and analysing their distribution and kinematics. we identify two groups of maser features: one associated with the disk. the other possibly tracing the disk at the interface with the bipolar jet.," By referring the proper motions of the masers to a feature lying in the disk plane and analysing their distribution and kinematics, we identify two groups of maser features: one associated with the disk, the other possibly tracing the disk at the interface with the bipolar jet." We speculate that class II mmasers are an ideal tracer to investigate the dense molecular gas entrained at the basis of the jet., We speculate that class II masers are an ideal tracer to investigate the dense molecular gas entrained at the basis of the jet. HCN. aand CO». in high-resolution spectra from the Spitzer Space Telescope InfraRed Spectrograph (IRS). as well as of vibrational lines with the Iseck Near Tutrared Spectrograph (NIRSPEC).,"HCN, and $_2$ in high-resolution spectra from the Spitzer Space Telescope InfraRed Spectrograph (IRS), as well as of vibrational lines with the Keck Near Infrared Spectrograph (NIRSPEC)." Based on cimittine temperatures. fluxcs and line shapes. these lines appeared to originate iu the disk atmospheres at terrestrial-planet-forniue radii.," Based on emitting temperatures, fluxes and line shapes, these lines appeared to originate in the disk atmospheres at terrestrial-planet-forming radii." Additionally. when preseut. the mid-IR water lines likely dominate the cooling of the iuner disk surtace laver (Poutoppidauctal.2010b).," Additionally, when present, the mid-IR water lines likely dominate the cooling of the inner disk surface layer \citep{Pontoppidan10}." . The frequent detections of water and other molecules in the inner regions of protoplanetary disks. made possible largely by optimized high dynamic range observing strategies aud data reduction routines (Carr&Najita 2008). mark a turing point in our ability to study chemical evolution aud molecular transport iu the ΠΙΟ: solar system.," The frequent detections of water and other molecules in the inner regions of protoplanetary disks, made possible largely by optimized high dynamic range observing strategies and data reduction routines \citep{Carr08}, mark a turning point in our ability to study chemical evolution and molecular transport in the inner solar system." Because chemistry aud line excitation are luxed to disk plwsics. molecular enussion can be used to study disk structure aud physics.," Because chemistry and line excitation are linked to disk physics, molecular emission can be used to study disk structure and physics." For example. water is destroved by plotodissociation aud by high levels of ionization (e.g.Bereinetal.2003:Glasseold2009).. but is capable of sclfshiclding iu certain conditions (Bethell&Berein2009).. and so water abundances may reflect the disk iradiatiou cuviromment.," For example, water is destroyed by photodissociation and by high levels of ionization \citep[e.g.][]{Bergin03, Glassgold09}, but is capable of self-shielding in certain conditions \citep{Bethell09}, and so water abundances may reflect the disk irradiation environment." Because water condenses at relatively siall radii iu the disk midplane (~ a few AU for solav-imass stars). water vapor lay be driven outward by vapor pressure differences. while water ice is carried duwards by planctesimals.," Because water condenses at relatively small radii in the disk midplane $\sim$ a few AU for solar-mass stars), water vapor may be driven outward by vapor pressure differences, while water ice is carried inwards by planetesimals." Ieucc. water abundances nav also reflect radial transport aud planet formation timescales.," Hence, water abundances may also reflect radial transport and planet formation timescales." Water abundances may sinularly depeud on vertical transport. which. when coupled with midplane condcusation. could deplete water even well inside the canonical snow line (Moijerinkctal. 2009).," Water abundances may similarly depend on vertical transport, which, when coupled with midplane condensation, could deplete water even well inside the canonical snow line \citep{Meijerink09}." . Finally. the streneth of molectlar enission lines depends upon the disk structure as a whole. iucludiug he eas temperature structure and the degree of dust settlingferain growth.," Finally, the strength of molecular emission lines depends upon the disk structure as a whole, including the gas temperature structure and the degree of dust settling/grain growth." One wav to diseutauele the many factors that affect uolecular abundances aud line streueths is to observe a large sample of disks. aud look for trends predicted * the processes deseribed above.," One way to disentangle the many factors that affect molecular abundances and line strengths is to observe a large sample of disks, and look for trends predicted by the processes described above." Tere we report characteristics of a sample of disks observed with the Spitzer Space Telescope Tnfrared Spectrograph (IRS). first described auc presented in Ponutoppidinctal.(2010b) (hereafter Paper D.," Here we report characteristics of a sample of disks observed with the Spitzer Space Telescope Infrared Spectrograph (IRS), first described and presented in \citet{Pontoppidan10} (hereafter Paper I)." In Paper L we preseuted the overall characteristics of the spectra. includiug molecular detection rates. and reported a strong dependence of molecular cussion on spectral type.," In Paper I, we presented the overall characteristics of the spectra, including molecular detection rates, and reported a strong dependence of molecular emission on spectral type." Iu this paper. we analyze the IRS spectra iu more detail. reporting correlations of line streneths aud detections with svstemi paralucters. as well as molecular ratios calculated frou LTE slab models.," In this paper, we analyze the IRS spectra in more detail, reporting correlations of line strengths and detections with system parameters, as well as molecular ratios calculated from LTE slab models." Iu addition. we use observations of CO rovibrational enmuüssiou at 5 san (COA. Blake ot al.," In addition, we use observations of CO rovibrational emission at 5 $\mu$ m (G.A. Blake et al.," in prep). to estimate molecular ratios with respect to CO.," in prep), to estimate molecular ratios with respect to CO." As oue of the nost abundant aud easib-detected uolecules in disks. CO is a tracer of the bulk of the disk gas. and xovides a good baseline. for conrpariue molecular abulances.," As one of the most abundant and easily-detected molecules in disks, CO is a tracer of the bulk of the disk gas, and provides a good baseline for comparing molecular abundances." M-baud (~5 pan) CO rovibrational lines have simular excitation energies aud collisional rates as the rotaional lines observed with the IBS. making these transitions particularly suited for colmparison with the IRS observations.," M-band $\sim$ $\mu$ m) CO rovibrational lines have similar excitation energies and collisional rates as the rotational lines observed with the IRS, making these transitions particularly suited for comparison with the IRS observations." The uud-IR data in this study were all obtained with the Spitzer Infrared Spectrograph URS) iu its lieh-resolution mode., The mid-IR data in this study were all obtained with the Spitzer Infrared Spectrograph (IRS) in its high-resolution mode. " The observed sample derives from a hnieh S/N program designed for the detection of water and other molecular emission. (PID 50611: PI J. Carr). as well as from a few programs in the Spitzer archive. and is described in detail iu Paper 1. A description of the observations. including program IDs. integration times and Astronomical Observation Request (AOR) ΙΟΣ, can also be found in Paper I. A brief explanation of the data reduction procedure is as follows."," The observed sample derives from a high S/N program designed for the detection of water and other molecular emission (PID 50641; PI J. Carr), as well as from a few programs in the Spitzer archive, and is described in detail in Paper I. A description of the observations, including program IDs, integration times and Astronomical Observation Request (AOR) numbers, can also be found in Paper I. A brief explanation of the data reduction procedure is as follows." All data were reduced with our own IDL routines. along with the IRSERINGE package (Lalinisetal.2007).. uxiug a procedure similar to that described i Carr&Najita(2008).," All data were reduced with our own IDL routines, along with the IRSFRINGE package \citep{Lahuis07}, using a procedure similar to that described in \citet{Carr08}." . We began with IRS droop-corrected. nou-flat-fielded basic calibrated data (BCD) roni the Spitzer Science. Ceuter IRS pipeline.," We began with IRS droop-corrected, non-flat-fielded basic calibrated data (BCD) from the Spitzer Science Center IRS pipeline." In order o reduce noise caused by edegce-effects. pipeline fat-fields were first divided bv a low-order polvuonmual fit iu the spectral and spatial directions.," In order to reduce noise caused by edge-effects, pipeline flat-fields were first divided by a low-order polynomial fit in the spectral and spatial directions." Au off-frame was subtracted. data were flat-Belded. aud uoisy aud bad jXxels removed.," An off-frame was subtracted, data were flat-fielded, and noisy and bad pixels removed." Spectra were divided by an average of at cast five standard stars. aud münmuiallv processed with he IRSFRINGE package.," Spectra were divided by an average of at least five standard stars, and minimally processed with the IRSFRINGE package." A ore complete description of the reduction procedure can be found ii Paper I. As reported in Paper L the observed IRS spectra contain a forest of molecular emission lines fromITO... ΟΠ. IICN. Cos and CO».," A more complete description of the reduction procedure can be found in Paper I. As reported in Paper I, the observed IRS spectra contain a forest of molecular emission lines from, OH, HCN, $_2$ $_2$ and $_2$." For the analyses in Paper I and this work. positive detections require a 3.50 peak (at two line locations for aand ΟΠ). with some Hue detections inclided or excluded through individual by-eye examination.," For the analyses in Paper I and this work, positive detections require a $\sigma$ peak (at two line locations for and OH), with some line detections included or excluded through individual by-eye examination." Fluxes are calculated by defining aud subtracting a linear fit to the local contiuuunm. then stuunine over the expected width of the line. except for the water enüssion lines. which are ft with Caussians. as described in Paper 1. Waveleneth regions used are as follows: OID (23.00923.308 and 27.30827.761 pau). ICN (13.83711.075 pau). Πο (13.55313.761 pan) and COs 1δι15.0141 jou).," Fluxes are calculated by defining and subtracting a linear fit to the local continuum, then summing over the expected width of the line, except for the water emission lines, which are fit with Gaussians, as described in Paper I. Wavelength regions used are as follows: OH (23.009--23.308 and 27.308–27.764 $\mu$ m), HCN (13.837–14.075 $\mu$ m), $_2$ $_2$ (13.553–13.764 $\mu$ m) and $_2$ (14.847–15.014 $\mu$ m)." All features overlap to some extent with ecluission. with flux coutributious from water as lieh as ~[0 in the Πο aud Πο regions. and even higher near the COs O-brauch.," All features overlap to some extent with emission, with flux contributions from water as high as $\sim40$ in the HCN and $_2$ $_2$ regions, and even higher near the $_2$ Q-branch." Thus. au eemissiou model (described in 812) was subtracted before molecular line fixes were computed.," Thus, an emission model (described in \ref{sec:lte}) ) was subtracted before molecular line fluxes were computed." Nevertheless. this subtraction does not have a significant effect ou the statistical analyses we present.," Nevertheless, this subtraction does not have a significant effect on the statistical analyses we present." Statistical crrors ou imdividual poiuts in the spectra are calculated as σενN. where N is the number of frames used to caleulate the flux. aud 0 is the standard deviation of the values iu that pixel.," Statistical errors on individual points in the spectrum are calculated as $\sigma/\sqrt{N}$, where $N$ is the number of frames used to calculate the flux, and $\sigma$ is the standard deviation of the values in that pixel." It No<3. then the error is taken to be the standard deviation computed using three ucieliborimg pixels iu the dispersion direction.," If $N<3$, then the error is taken to be the standard deviation computed using three neighboring pixels in the dispersion direction." Systematic nucertaitics are undoubtedly larger. expecially for fines without dedicated background. observations. but can be difficult to characterize.," Systematic uncertainties are undoubtedly larger, especially for frames without dedicated background observations, but can be difficult to characterize." Line fiux errors are taken to be the root squared sui of errors on individual points over the wavelength rauge used to compute the line fiux., Line flux errors are taken to be the root squared sum of errors on individual points over the wavelength range used to compute the line flux. Upper Inuits are calculated asstuneg a 3.50 line height (see Paper I for a discussion of this choice). aud a feature shape defined by an LTE," Upper limits are calculated assuming a $\sigma$ line height (see Paper I for a discussion of this choice), and a feature shape defined by an LTE" In the present paper. we observed 3C 286.,"In the present paper, we observed 3C 286." " This source ts. for most purposes at em wavelengths. the ""gold standard"" polarization calibrator."," This source is, for most purposes at cm wavelengths, the “gold standard” polarization calibrator." Specifically. the fractional polarization and polarization position angle of 3C 286 have been stable over four decades of observations across a wide range of frequencies above ~ 1400 MHz (Tabara Inouye 1950: B. Gaensler 2009 priv.," Specifically, the fractional polarization and polarization position angle of 3C 286 have been stable over four decades of observations across a wide range of frequencies above $\sim$ 1400 MHz (Tabara Inouye 1980; B. Gaensler 2009 priv." comm.)., comm.). While these properties have not been established at lower frequencies. the dominance of the large-scale jet at these frequencies argue against any time variations of these quantities at 840 MHz.," While these properties have not been established at lower frequencies, the dominance of the large-scale jet at these frequencies argue against any time variations of these quantities at 840 MHz." Hence we had the fortunate circumstance of observing a source that also happens to be an excellent polarization standard., Hence we had the fortunate circumstance of observing a source that also happens to be an excellent polarization standard. For about half of our observing days. we had enough PA coverage to derive the Mueller matrix from our observed data for that particular day; thus. we could use our observed astronomical data to also determine the Mueller matrix elements—a form of “self calibration”.," For about half of our observing days, we had enough $PA$ coverage to derive the Mueller matrix from our observed data for that particular day; thus, we could use our observed astronomical data to also determine the Mueller matrix elements—a form of “self calibration”." The derived corrections were closely the same from one day to another. although there were small differences.," The derived corrections were closely the same from one day to another, although there were small differences." For any particular day’s observations. we used the matrix that was closest in time to that day: for about half the days. this matrix was obtained on that very day.," For any particular day's observations, we used the matrix that was closest in time to that day; for about half the days, this matrix was obtained on that very day." " This gives us great confidence in our polarization calibration,", This gives us great confidence in our polarization calibration. Normally. one determines a single Mueller matrix for the observed band by averaging over the whole band.," Normally, one determines a single Mueller matrix for the observed band by averaging over the whole band." " This leads to small calibration errors that change with frequency across the band. which in turn leads to small ""baseline curvature” in the three polarization spectra."," This leads to small calibration errors that change with frequency across the band, which in turn leads to small “baseline curvature” in the three polarization spectra." The latter are the fractional polarization pv). polarization position angle y(v). and Stokes V parameter V(v); one normally fits a smooth baseline to these spectra and applies them as an correction.," The latter are the fractional polarization $p(v)$, polarization position angle $\chi(v)$, and Stokes $V$ parameter $V(v)$; one normally fits a smooth baseline to these spectra and applies them as an correction." Here. we took a different approach.," Here, we took a different approach." 3C 286 is such a strongly polarized source that. for any one day. we could easily determine the seven receiver system parameters on a channel-by-channel basis.," 3C 286 is such a strongly polarized source that, for any one day, we could easily determine the seven receiver system parameters on a channel-by-channel basis." We then fit their frequency dependencies by performing à minimum-absolute-residual-sum (MARS) 3rd-degree polynomialfit?., We then fit their frequency dependencies by performing a minimum-absolute-residual-sum (MARS) 3rd-degree polynomial. . We used these fit coefficients to derive the Mueller matrix independently for each channel., We used these fit coefficients to derive the Mueller matrix independently for each channel. With this. the polarization calibration is very accurate for each channel independently. so that any features in the polarized spectra are real. characterizing the sky instead of the system.," With this, the polarization calibration is very accurate for each channel independently, so that any features in the polarized spectra are real, characterizing the sky instead of the system." In particular. it is neither appropriate nor necessary to subtract off an baseline in any of the polarized spectra.," In particular, it is neither appropriate nor necessary to subtract off an baseline in any of the polarized spectra." It is these accurately-calibrated spectra that we use and plot in this paper., It is these accurately-calibrated spectra that we use and plot in this paper. Even with this self-calibration of each channel independently. there remain small residual inaccuracies. which result from applying Mueller matrices obtained on one day to data obtained on another day: this is probably responsible for the small spectral effects in the Stokes V spectrum in Figure 1..," Even with this self-calibration of each channel independently, there remain small residual inaccuracies, which result from applying Mueller matrices obtained on one day to data obtained on another day; this is probably responsible for the small spectral effects in the Stokes $V$ spectrum in Figure \ref{newStokes}." First. we fixed the above-mentioned software bug.," First, we fixed the above-mentioned software bug." Then we reanalyzed the data., Then we reanalyzed the data. We used the same software as before and determined the Mueller matrices in the usual way (see Heiles etal. 22001). as we did before.," We used the same software as before and determined the Mueller matrices in the usual way (see Heiles et 2001), as we did before." We applied the Mueller matrix corrections and the phase difference correction of equation 5 as we did before., We applied the Mueller matrix corrections and the phase difference correction of equation \ref{phieqn} as we did before. We did three things differently: Figure | shows a four-panel plot of the data (black curves). now reduced properly.," We did three things differently: Figure \ref{newStokes} shows a four-panel plot of the data (black curves), now reduced properly." No “baseline corrections” have been subtracted or applied., No “baseline corrections” have been subtracted or applied. The data consists of 12.6 hrs of on-source integration obtained in 2007., The data consists of 12.6 hrs of on-source integration obtained in 2007. The orange curves are least squares fits to the data., The orange curves are least squares fits to the data. The top panel shows Stokes Ta/P (where / is the off-line continuum intensity. which is independent of velocity v). which has an absorption line with a fractional absorption of about5%.," The top panel shows Stokes $I(v)/I$ (where $I$ is the off-line continuum intensity, which is independent of velocity $v$ ), which has an absorption line with a fractional absorption of about." . The frequency centroid determined by the fit to the Stokes I spectrum is 839.408348 + 0.000046 MHz and its location is depicted by the vertical dot-dashed line., The frequency centroid determined by the fit to the Stokes I spectrum is 839.408348 $\pm$ 0.000046 MHz and its location is depicted by the vertical dot-dashed line. The corresponding redshift z20.692151094-0.00000009., The corresponding redshift $z$ $\pm$ 0.00000009. The second panel shows the percent polarization. pv)=/(U(Qv)ΕΟΤ. and the third panel shows the position angle \(v) (zero point is arbitrary).," The second panel shows the percent polarization, $p(v)={\sqrt{(U(v)^{2}+Q(v)^{2})}}/I$, and the third panel shows the position angle $\chi(v)$ (zero point is arbitrary)." The linearly polarized p(y) line also appears in absorption tthe percent polarization goes down in the line) and its fractional polarized absorption is close to that for Stokes 7., The linearly polarized $p(v)$ line also appears in absorption the percent polarization goes down in the line) and its fractional polarized absorption is close to that for Stokes $I$. Itscenter differs from the Stokes / line center by 5.030.25 kHz., Its differs from the Stokes $I$ line center by $5.0 \pm 0.25$ kHz. This 206. difference has high statistical significance.," This $20 \sigma$ difference has high statistical significance." Taken together. these two results are consistent with the absorbing gas covering both nonpolarized and polarized portions of the continuum source image. and the velocity of the part that covers the polarized portion differing from that covering the unpolarized portion by 5.0 KHz (which is about 1.8 km/s)’.The third panel shows that the line changes the position angle by about 1.5 degrees at line center. which ts consistent," Taken together, these two results are consistent with the absorbing gas covering both nonpolarized and polarized portions of the continuum source image, and the velocity of the part that covers the polarized portion differing from that covering the unpolarized portion by 5.0 kHz (which is about 1.8 .The third panel shows that the line changes the position angle by about 1.5 degrees at line center, which is consistent" "an important item to quantity, together with the overall clistribution of shear estimators.","an important item to quantify, together with the overall distribution of shear estimators." A histogram showing the clistribution of the shear estimators for the golcl and. silver radio sets are shown in Ligure 2.. toecther with the distribution of the optical shear estimators.," A histogram showing the distribution of the shear estimators for the gold and silver radio sets are shown in Figure \ref{fig:shearhists}, together with the distribution of the optical shear estimators." We see that the bin size is necessarily large for the gold set. on account of the small number of objects: nevertheless. we can immeciatelvy see that the variance of both radio sets and. the optical set are Comparable.," We see that the bin size is necessarily large for the gold set, on account of the small number of objects; nevertheless, we can immediately see that the variance of both radio sets and the optical set are comparable." Focussing on the silver ancl optical sets where there is more detail. we can see qualitatively that the distributions are similar in shape. with a peak ancl wings deviating from Gaussian form.," Focussing on the silver and optical sets where there is more detail, we can see qualitatively that the distributions are similar in shape, with a peak and wings deviating from Gaussian form." " Alore quantitatively. for the radio samples we find that jo0.2940.03.02,=0.30+0.03 for the gold set. and E0.02.0.4=O.4140.02 for the silver set."," More quantitatively, for the radio samples we find that $\sigma_{\gamma_{1}}=0.29\pm0.03, \sigma_{\gamma_{2}}=0.30\pm0.03$ for the gold set, and $\sigma_{\gamma_{1}}=0.35\pm0.02, \sigma_{\gamma_{2}}=0.41\pm0.02$ for the silver set." " This can »' compared with o,=0.326+0.004.0.0.3280.004 or the optical objects."," This can be compared with $\sigma_{\gamma_{1}}=0.326\pm0.004, \sigma_{\gamma_{2}}= 0.328\pm0.004$ for the optical objects." ‘This is encouraging:oὃν it shows that radio shear estimators are not much more noisy than optical shear estimators at his Hux limit., This is encouraging; it shows that radio shear estimators are not much more noisy than optical shear estimators at this flux limit. Phe combined. ellects of intrinsic ellipticity and measurement noise give comparable shear variance in »»h parts of the spectrum., The combined effects of intrinsic ellipticity and measurement noise give comparable shear variance in both parts of the spectrum. " In Figure 3. we show how the quantity a, varies with lux in the radio case (top panel) and with the z-band magnitude in the optical case (lower panel).", In Figure \ref{fig:sig} we show how the quantity $\sigma_{\gamma_{1}}$ varies with flux in the radio case (top panel) and with the $z$ -band magnitude in the optical case (lower panel). For both the sold and silver objects. we find that the Lainter objects iive a larger scatter compared to the brighter ones. due to he reduced signal-to-noise. and the greater noise associated with deconvolution for small objects.," For both the gold and silver objects, we find that the fainter objects have a larger scatter compared to the brighter ones, due to the reduced signal-to-noise, and the greater noise associated with deconvolution for small objects." The optical objects show a less pronounced trend. with bright objects having à ittle less scatter than the fainter ones.," The optical objects show a less pronounced trend, with bright objects having a little less scatter than the fainter ones." We now wish to quantify the level of systematics present in the processed. radio shear data., We now wish to quantify the level of systematics present in the processed radio shear data. This paper seeks to assess the level of the problem. and to take a straightforward first step towards its amelioration in section 6..," This paper seeks to assess the level of the problem, and to take a straightforward first step towards its amelioration in section \ref{cross}." Firstly. we caleulate the average shear for the entire catalogues.," Firstly, we calculate the average shear for the entire catalogues." For the gold radio set. we find (51)=0.035+0.040 and £525=0.007+0.040. consistent with no overall systematic ollset.," For the gold radio set, we find $\langle\gamma_{1}\rangle=0.035\pm0.040$ and $\langle\gamma_{2}\rangle=-0.007\pm0.040$, consistent with no overall systematic offset." For the silver set. we find £515=0.072+0.021 and (555=0.015+0.025. indicating a systematic elfect alllicting the estimators at. this lower signal-to-noise.," For the silver set, we find $\langle\gamma_{1}\rangle=0.072\pm0.021$ and $\langle\gamma_{2}\rangle=0.015\pm0.025$, indicating a systematic effect afflicting the estimators at this lower signal-to-noise." For the optical estimators we find $513=0.014+0.006 and DE0.006. again showing an uncorrected small svstematic clue to the basic PSE correction. and/or a cosmic shear signal.," For the optical estimators we find $\langle\gamma_{1}\rangle=-0.014\pm0.006$ and $\langle\gamma_{2}\rangle=-0.003\pm0.006$, again showing an uncorrected small systematic due to the basic PSF correction, and/or a cosmic shear signal." As a more detailed test. we median averaged our shear estimates in 1 areminute bins in we and y position on the image (Figure 4)).," As a more detailed test, we median averaged our shear estimates in 1 arcminute bins in $x$ and $y$ position on the image (Figure \ref{fig:gbarpos}) )." For the gold radio objects (top panel) we see that 54 and 5» are consistent with zero in ther clirection.," For the gold radio objects (top panel) we see that $\gamma_{1}$ and $\gamma_{2}$ are consistent with zero in the $x$ direction," Tn this papepaper. we have| confronted tle DeschSolarAnse Nebulaqe to the planetary migratioua eas⋅," In this paper, we have confronted the \citet{Desch2007} Solar Nebula to the planetary migration issue." has↴⋅⋅ a⋅ hieh eas density. a↴ high Saturn is of . . . . unchauged for 10 iillioü vears.," This disk has a high gas density, a high density slope, and this profile remains almost unchanged for 10 million years." Therefore. the question⋅ of. the plauetarv uueration. should no ο eluded.," Therefore, the question of the planetary migration should not be eluded." The 2D1D version of FARGO is uwtieularlv suited to such a study., The 2D1D version of FARGO is particularly suited to such a study. The plivsica ≻⋜∐⋅⋜↧⋯↸∖↸∖↥⋅↴∖↴∪↕≯↑∐↸∖≼∐∖↴↘↽⋜∐⋅↸∖∐⊼↸∖≼↧∙↴⋝∏↑⋜↧↴⋝↥⋅∪⋜∥ range of nuuerical parameters have been studie (resolution.. energv equation.: fate. of. the plauets hat reach the inner. edge of. the .2D eid).. as we as the influence. of. the aspect ratio.," The physical parameters of the disk are fixed, but a broad range of numerical parameters have been studied (resolution, energy equation, fate of the planets that reach the inner edge of the 2D grid), as well as the influence of the aspect ratio." : The high. density∙ slope gives. a negative. nou horual horseshoe torque. that accelerates even nore the iuwrds type I nuieration of Uranus and Neptune.," The high density slope gives a negative non thermal horseshoe torque, that accelerates even more the inwards type I migration of Uranus and Neptune." The ligh deusitv permits type III uieration of massive plaucts., The high density permits type III migration of massive planets. In particular. we cau iot avoid an extremely fast nsvards migration of Jupiter.," In particular, we can not avoid an extremely fast inwards migration of Jupiter." " In spite of several attempts. to prevent a loss of all the eiaut planets; im: less"" thanan 2.'10Layee years."," In spite of several attempts, to prevent a loss of all the giant planets in less than $2\times 10^4$ years,." Taking iuto account the enerev equation with a cooling compatible with the assumed temperature structure of the disk does not change the result., Taking into account the energy equation with a cooling compatible with the assumed temperature structure of the disk does not change the result. Preventing the uueration of the eiaut plaucts requires interactions between the planes., Preventing the migration of the giant planets requires interactions between the planets. " However, as this disk is a massive. decretiou disk. the Masset&Sucllerove(2001) mechanisin to prevent Jupiter and Saturn frou mierating awards cau not be applied."," However, as this disk is a massive, decretion disk, the \citet{MS01} mechanism to prevent Jupiter and Saturn from migrating inwards can not be applied." Shortly said. we conclude that the Desch(2007) nebula is incompatible with our prescut knowledge of planetary migration.," Shortly said, we conclude that the \citet{Desch2007} nebula is incompatible with our present knowledge of planetary migration." So. we are faciug a problem.," So, we are facing a problem." Either this new AIMSN gmakes the planetary mueration in the Solar System an even iore critical issue and makes obsolete the former solutions to preveut nueration of the elant planets (Morbidelli&Crida2007:Morbidellietal. 2007).. or the existence of planetary nigration makes this MMSN questionable (iu particular the appareutly unavoidable typo IIT migration of Jupiter).," Either this new MMSN makes the planetary migration in the Solar System an even more critical issue and makes obsolete the former solutions to prevent migration of the giant planets \citep{MC07,Morby-etal-2007}, or the existence of planetary migration makes this MMSN questionable (in particular the apparently unavoidable type III migration of Jupiter)." A possible solution las boen laid out iu section 6..., A possible solution has been laid out in section \ref{sec:Hayashi}. If one believes that the Nice model is fruc. if is clear that the outer plaucts should have euded the disk phase in a more compact configuration than the present one.," If one believes that the Nice model is true, it is clear that the outer planets should have ended the disk phase in a more compact configuration than the present one." " Ποπονο,"," However," is typically what is expected. (van Paraclijs AleClintock 1994).,is typically what is expected (van Paradijs McClintock 1994). We note that this is similar to the dillerence of the mean absolute magnitudes. derived. for persistent LAINBs and CVs (c.g. nova-likes: see van Paraclijs Verbunt 1984)., We note that this is similar to the difference of the mean absolute magnitudes derived for persistent LMXBs and CVs (e.g. nova-likes; see van Paradijs Verbunt 1984). This difference in brightness has a natural explanation in that aceretion discs of SAPS in outburst ancl persistent LAINBs are dominated by X-ray. irradiation. whereas the dises in CVs are not (see e.g. van Paraclijs Verbunt 1984 and van Paraclijs MeClintock. 199M).," This difference in brightness has a natural explanation in that accretion discs of SXTs in outburst and persistent LMXBs are dominated by X-ray irradiation, whereas the discs in CVs are not (see e.g. van Paradijs Verbunt 1984 and van Paradijs McClintock 1994)." However. it should be noted that the orbital separation of the SNTs. (most of which are black holes) are probably a factor 2 larger at a given period. therefore disc area is 4 times larger than in the dwarf novae.," However, it should be noted that the orbital separation of the SXTs, (most of which are black holes) are probably a factor 2 larger at a given period, therefore disc area is 4 times larger than in the dwarf novae." This combined with the fact that the accretion rate of a SXT dise in outhurst is an order of magnitucle higher than in a dwarf nova at a given period may partly explain the dillerence in accretion disc magnitudes., This combined with the fact that the accretion rate of a SXT disc in outburst is an order of magnitude higher than in a dwarf nova at a given period may partly explain the difference in accretion disc magnitudes. We can now use equation (5) along with the clistance modulus equation to obtain an expression for the clistance to the X-ray transients {η}& 12) as a function of orbital period: where {η is the distance in kpe and cl. is the reddening., We can now use equation (5) along with the distance modulus equation to obtain an expression for the distance to the X-ray transients $P_{orb}(h)\ltsimeq$ 12) as a function of orbital period: where $D_{kpc}$ is the distance in kpc and $A_{v}$ is the reddening. In Table 2 we estimate the distances for 7 transicnts using this relation (we have assumed. f=1.0. so the distance estimates are lower limits).," In Table 2 we estimate the distances for 7 transients using this relation (we have assumed $f$ =1.0, so the distance estimates are lower limits)." As one can see for most of the systems our estimates agree quite well with the values in the literature (see Table. 1)., As one can see for most of the systems our estimates agree quite well with the values in the literature (see Table 1). We note. however. that the main uncertainty in determining the distance is the value used for the recddening.," We note, however, that the main uncertainty in determining the distance is the value used for the reddening." By fitting the outburst amplitudes for S N-rav. transients we determine an empirical relation that can be used to predict the orbital period of an N-rav. transient., By fitting the outburst amplitudes for 8 X-ray transients we determine an empirical relation that can be used to predict the orbital period of an X-ray transient. Also. for periods below less than 12 hrs we determine a relation for the absolute magnitude of the accretion dise during outburst. which allows us to estimate the cistances to the sources.," Also, for periods below less than 12 hrs we determine a relation for the absolute magnitude of the accretion disc during outburst, which allows us to estimate the distances to the sources." We would like to thank Phil Charles for valuable discussions and the referee. Xndrew Wing for his careful reading of the manuscript.," We would like to thank Phil Charles for valuable discussions and the referee, Andrew King for his careful reading of the manuscript." The figure was plotted. using the ark software on the Oxford Starlink node., The figure was plotted using the $\sc ark$ software on the Oxford Starlink node. (CCORALS) Survey.W,"CORALS) Survey.," all?.. Peter Shaver? It is widely recognised that DLAs represent oue of the most promising methods of probing the high redshift ealaxy population., Peter $^{5}$ } It is widely recognised that DLAs represent one of the most promising methods of probing the high redshift galaxy population. However. it is similarly acknowledged that the presence of dust iu these galaxies could impose a significant bias on our curent database of DLAs. which are mostly drawn from optically bright QSO samples.," However, it is similarly acknowledged that the presence of dust in these galaxies could impose a significant bias on our current database of DLAs, which are mostly drawn from optically bright QSO samples." " Observational evidence for such a concern comes. for example. from statistically steeper continuum slopes iu QSOs with DLAs [0] aud lack of metallicity evolution in DLAs from 0.5 0.25$ Jy) sample of $z_{em} \geq 2.2$ QSOs was culled from the Parkes Catalogue." Optical counterparts have been identified for every target. resulting iu a sample of 66 radio-sclected QSOs with uo optical magnitude limit.," Optical counterparts have been identified for every target, resulting in a sample of 66 radio-selected QSOs with no optical magnitude limit." Follow-up spectroscopy revealed 22 1.56.5 with sufficient radio fux deusity to detect HIT 2lem absorption by. the ICM using the SKA.," For the most optimistic model (flat comoving number density evolution), the analysis of section 4 showed that there should be about 3 sources $^{-2}$ at $z > 6.5$ with sufficient radio flux density to detect HI 21cm absorption by the IGM using the SKA." The redshift cut-off model based ou Iuniuous QSO evolution leads to 0.05 sources 7., The redshift cut-off model based on luminous QSO evolution leads to 0.05 sources $^{-2}$. The couuts of celestial sources with Syjoy21 Jy have been determined by a umuber of eroups. and all values are cousixtent with: NC»Syjy)=(0.010+0.002)Siri 2. with the 1400 MIIz 8ux density. 8109. in iidy (Cruppioni et al.," The counts of celestial sources with $_{1400} \ge 1$ mJy have been determined by a number of groups, and all values are consistent with: $\rm N(>S_{1400}) = (0.010\pm0.002)~ S_{1400}^{-1.0\pm0.15}$ $^{-2}$, with the 1400 MHz flux density, $_{1400}$, in mJy (Gruppioni et al." 1999: White ct al., 1999; White et al. 1997: Windhorst et al., 1997; Windhorst et al. 1985)., 1985). At the relevant flux deusity limits (Syiy)~0.5 Jy). the surface deusity of all celestial radio sources is then about 72 sources 2.," At the relevant flux density limits $_{1400} \sim 0.5$ mJy), the surface density of all celestial radio sources is then about 72 sources $^{-2}$." The implied ratio of sources bevond the epoch of rcionization to foreground sources is then about i in the flat evolution model aud m in the QSO cut-off iuodel., The implied ratio of sources beyond the epoch of reionization to foreground sources is then about $1\over{25}$ in the flat evolution model and $1\over{1400}$ in the QSO cut-off model. Tn either case it appears to be a tractable sitting problem., In either case it appears to be a tractable sifting problem. It is portant to eniphasize that the structures eiviug rise to ITE 210i absorption prior to the epoch of relonization are qualitatively different thanthose seen after the universe reionizes., It is important to emphasize that the structures giving rise to HI 21cm absorption prior to the epoch of reionization are qualitatively different than those seen after the universe reionizes. After reionization the II 2tem lines arise only in rare density peaks (ὁ>100) correspouding to (protoJealaxies. ic.," After reionization the HI 21cm lines arise only in rare density peaks $\delta > 100$ ) corresponding to (proto)galaxies, ie." the damped Ly a systems., the damped Ly $\alpha$ systems. Prior to the epoch of fast reionization the bulk of the ICM is neutral with a measurable opacity in the IIT 2lem Lue., Prior to the epoch of fast reionization the bulk of the IGM is neutral with a measurable opacity in the HI 21cm line. The absorption secu iu Figure 2 arises in the ubiquitous cosmüc web. as delincated after reionization by the Ly à forest {Boud. ofan. Pogosau 1996).," The absorption seen in Figure 2 arises in the ubiquitous 'cosmic web', as delineated after reionization by the Ly $\alpha$ forest (Bond, Kofman, Pogosian 1996)." The point is siuplv that the Ly à forest as seen after the epoch of recionization corresponds to structures with neutral hydrogen colum densities of order LOY ? to 107 7. and neutral fractions of order 105 to LO? (Weinberg et al.," The point is simply that the Ly $\alpha$ forest as seen after the epoch of reionization corresponds to structures with neutral hydrogen column densities of order $10^{13}$ $^{-2}$ to $10^{15}$ $^{-2}$ , and neutral fractions of order $10^{-6}$ to $^{-4}$ (Weinberg et al." 1997)., 1997). Before reionization these same structures will then have neutral hwdrosen column deusities of order 1019 7 to 1079 7. and hence may he detectable in HT 21011 absorption.," Before reionization these same structures will then have neutral hydrogen column densities of order $10^{19}$ $^{-2}$ to $10^{20}$ $^{-2}$, and hence may be detectable in HI 21cm absorption." We conclude by emphlasiziug a few of the iniportaut differences between studving the neutral ICAL via III 21011 absorption against discrete radio sources versus via HII σσ enüssion (or absorption against the uicrowave backeround)., We conclude by emphasizing a few of the important differences between studying the neutral IGM via HI 21cm absorption against discrete radio sources versus via HI 21cm emission (or absorption against the microwave background). The structures probed by absorption extend down to galaxy scales. as opposed o the strictly large (ic.," The structures probed by absorption extend down to galaxy scales, as opposed to the strictly large (ie." cluster) scale structures bee xobed iu cussion., cluster) scale structures being probed in emission. Also. absorption features can » mutch narrower in frequency than is expected for he ceniission signal (a few kIlz vs. L00's of kIlz. respectively).," Also, absorption features can be much narrower in frequency than is expected for the emission signal (a few kHz vs. 100's of kHz, respectively)." Narrow lues are ich easier to detect in the presence of broad spectral baseline errors. as uight arise frou bandpass calibration errors or from contusion due to the frequency depeudent sidelobes roni the plethora of cosiuic sources at low frequeucy.," Narrow lines are much easier to detect in the presence of broad spectral baseline errors, as might arise from bandpass calibration errors or from confusion due to the frequency dependent sidelobes from the plethora of cosmic sources at low frequency." The sidelobe confusion problems is exacerbated by the act that euissiou studies ust be doue at arciuiuute resolution in order to have enoush iaterial in the jun to male a detection. while absorption studies are preferably done at high augular resolution.," The sidelobe confusion problem is exacerbated by the fact that emission studies must be done at arcminute resolution in order to have enough material in the beam to make a detection, while absorption studies are preferably done at high angular resolution." Ou he down-side. absorption studies ouly probe isolated ines-ofsight. or at best a few lines of site iu the case of an extended background source. audthe derivation of coliuun density is iiodulo the spin temperature.," On the down-side, absorption studies only probe isolated lines-of-sight, or at best a few lines of site in the case of an extended background source, and the derivation of column density is modulo the spin temperature." The analysis in section 2 suggests that judicious comparison of the observed absorption spectra with models of reionization will provide siguificaut insight iuto the physics of cosmic structure formation cing the gray age., The analysis in section 2 suggests that judicious comparison of the observed absorption spectra with models of reionization will provide significant insight into the physics of cosmic structure formation during the gray age. We will address this Ίππο in more detail ina future paper., We will address this issue in more detail in a future paper. (2trucin The National Radio Astronomy Observatory (NRÀO) isoperated by Associated Universities. Inc. uuder," 0.2truein The National Radio Astronomy Observatory (NRAO) isoperated by Associated Universities, Inc. under" previous case where all the ejected mass. left the binary system.,previous case where all the ejected mass left the binary system. Llowever. for the largest. mass ratios the period increases Compared to the previous model.," However, for the largest mass ratios the period increases compared to the previous model." Aneular momentum is lost from the binary system because of frietional angular momentum losses as the binary moves through the common. envelope created by. the ejected material (e.g.MacDonald.1950.1986:Sharactal.Livioetal. 1990).," Angular momentum is lost from the binary system because of frictional angular momentum losses as the binary moves through the common envelope created by the ejected material \citep[e.g.][]{macdonald80,macdonald86,shara86,livio90}." . This causes the separation of the system to decrease and so the period decreases too., This causes the separation of the system to decrease and so the period decreases too. Ehoey found that the separation change given in equation (11)) becomes (Sharaetal.1986)... where «=V2 fora very slow nova and ow=1 for à fast nova.," They found that the separation change given in equation \ref{mass}) ) becomes \citep{shara86}, where $x=\sqrt{2}$ for a very slow nova and $x=1$ for a fast nova." We note that Livio.Govarie&titter(1901). suggest that assumptions mace in deriving his mean that is is valid only for novae with longer orbital »eriods., We note that \cite{livio91} suggest that assumptions made in deriving this mean that is is valid only for novae with longer orbital periods. Again. we can find the period change for this mocel with equation (8)).," Again, we can find the period change for this model with equation \ref{dp}) )." In Fig., In Fig. 1 we plot oT as a Function of he mass ratio for this model for a slow nova (short-dashed ine).," \ref{dadm} we plot $\frac{\Delta P/P}{\Delta m_1/M}$ as a function of the mass ratio for this model for a slow nova (short-dashed line)." Phe separation change (and hence period change) here is. às expected. less than that for the previous case without he frictional angularὃν momentum losses.," The separation change (and hence period change) here is, as expected, less than that for the previous case without the frictional angular momentum losses." There are also two mechanisms that remove angular momentum from the svstem between outbursts that we consider briellv here., There are also two mechanisms that remove angular momentum from the system between outbursts that we consider briefly here. For systems with relatively long orbital periods (2= 3hr). magnetic braking provides the largest continual loss of angular momentum from the svstem.," For systems with relatively long orbital periods $P \gtrsim 3\,\rm hr$ ), magnetic braking provides the largest continual loss of angular momentum from the system." The rate of loss of angular momentum is given roughly by (Rappaport.Verbunt&Joss1983)., The rate of loss of angular momentum is given roughly by \citep{rappaport83}. . For. reasonable parameters this gives a timescale of arouncl a few billion vears (ee.Martin&“Tout2005)., For reasonable parameters this gives a timescale of around a few billion years \citep[e.g.][]{martin05}. . For the closest systems (P Shr). gravitational radiation is the dominate cause of angular momentum loss from the binary svstem between outbursts.," For the closest systems $P \lesssim 3\,\rm hr$ ), gravitational radiation is the dominate cause of angular momentum loss from the binary system between outbursts." The rate of loss of angular momentum from two point masses in a circular orbit is (Landau&Lifshitz1951)., The rate of loss of angular momentum from two point masses in a circular orbit is \citep{landau51}. . This gives a timescale of order several million. vears except for. the very closest of svstems., This gives a timescale of order several million years except for the very closest of systems. Neither gravitational radiation nor magnetic braking will have any cllect on a system on an observable timescale., Neither gravitational radiation nor magnetic braking will have any effect on a system on an observable timescale. In this Section we consider an entirely new mechanism that can change the orbital period during a nova outburst., In this Section we consider an entirely new mechanism that can change the orbital period during a nova outburst. Suppose ejected material that moves within a critical radius (that depends on the magnetic field strength) of the secondary star couples to its magnetic field and so is forced to corotate with the binary orbit., Suppose ejected material that moves within a critical radius (that depends on the magnetic field strength) of the secondary star couples to its magnetic field and so is forced to corotate with the binary orbit. The transfer of angular momentum. between the ejected material anc the binary orbit causes a change to the orbital period of the system., The transfer of angular momentum between the ejected material and the binary orbit causes a change to the orbital period of the system. The magnitude of the dipole magnetic field of the secondary is where ji is the dipole moment and 7? is the distance to the secondary star., The magnitude of the dipole magnetic field of the secondary is where $\mu$ is the dipole moment and $R$ is the distance to the secondary star. Phe magnetic field energy. density is The kinetic energy. density of the ejected matter is where p is the density of the cjected material., The magnetic field energy density is The kinetic energy density of the ejected matter is where $\rho$ is the density of the ejected material. The ejection velocity. 2. is in the range 3003000kms.+ (Sharaetal. 1986).," The ejection velocity, $u$, is in the range $300 - 3000\,\rm km\,s^{-1}$ \citep{shara86}." . From the continuity equation. close the the secondary star. we approximately. have where AZ is the mass ejection rate from the primary white dwarf star.," From the continuity equation, close the the secondary star, we approximately have where $\dot M$ is the mass ejection rate from the primary white dwarf star." We approximate the average mass-loss rate with, We approximate the average mass-loss rate with to the object of interest.,to the object of interest. The FoM is defined im au unbiased mamuner based ou the 21 san prior catalog by where R; is the ratio of the 21 jnu fux of the prior object to the 21 jin fluxes of other nearby objects within the radius (9.17) of SPIRE 2250 jan beau frou the prior and d; is the distance from the prior object to the corresponding nearby objects., The FoM is defined in an unbiased manner based on the 24 $\micron$ prior catalog by where $_i$ is the ratio of the 24 $\micron$ flux of the prior object to the 24 $\micron$ fluxes of other nearby objects within the radius (9.1”) of SPIRE 250 $\micron$ beam from the prior and $d_i$ is the distance from the prior object to the corresponding nearby objects. Tlic 250 pau bean is chosen for this criteria because it is the baud at which most of our ECDFES aud IIDEN salples are etected., The 250 $\micron$ beam is chosen for this criteria because it is the band at which most of our ECDFS and HDFN samples are detected. The norimalizations for R; aud d; are chosen such that the FoM increases rapidly if other sources that ave expected to be in the beam could be in within the same SPIRE pixel (6°) or could have comparable SPIRE fluxes to the object at the prior position., The normalizations for $_i$ and $d_i$ are chosen such that the FoM increases rapidly if other sources that are expected to be in the beam could be in within the same SPIRE pixel (6”) or could have comparable SPIRE fluxes to the object at the prior position. The R; normalization value is determined by inspecting the variation of the ratios of 21 aud.250 jin fluxes for SED templates in the Rickeetal.io(2009) library. which gives a 1s variation.," The $_i$ normalization value is determined by inspecting the variation of the ratios of 24 and 250 $\micron$ fluxes for SED templates in the \citet{Rieke09} library, which gives a $\sim$ $\times$ variation." That is. if the 21 pam fux of a nearby object is less than —1/1 that ofthe object. it is unlikely that its 250 jin flux will be comparable to the prior (aud hence cause a bleudiug problemi) at redshift 02.8. asstunine the SED shape.," That is, if the 24 $\micron$ flux of a nearby object is less than $\sim 1/4$ that of the prior object, it is unlikely that its 250 $\micron$ flux will be comparable to the prior (and hence cause a blending problem) at redshift $0 - 2.8$, assuming the \citet{Rieke09} SED shape." We emphasize that the exchision docs not depend scusitively ou the nonualizatious iu the FoAL aud we have adopted a conservative rejection threshold bv excludiug objects with FoM >5 from the final catalog. rejecting ouly the most likely blended objects.," We emphasize that the exclusion does not depend sensitively on the normalizations in the FoM, and we have adopted a conservative rejection threshold by excluding objects with FoM $> 5$ from the final catalog, rejecting only the most likely blended objects." The top righthand plot of Figure 5 presents the values of mg that give the best fit for each value of ag.,The top righthand plot of Figure \ref{fig5} presents the values of $m_B$ that give the best fit for each value of $a_B$. " As expected, when the components are more separated, the mass of the binary increases to produce same magnitude in radial velocity."," As expected, when the components are more separated, the mass of the binary increases to produce same magnitude in radial velocity." The lower lefthand plot gives the binary eccentricity eg., The lower lefthand plot gives the binary eccentricity $e_B$. Larger semimajor axes are accompanied by more elliptic orbits., Larger semimajor axes are accompanied by more elliptic orbits. " The curves show a rough resemblance to the locus of constant pericentric distance pg, here drawn for one particular orbital solution."," The curves show a rough resemblance to the locus of constant pericentric distance $p_B$, here drawn for one particular orbital solution." " Since most of the RV data points are located near the pericenter of the binary's orbit (see Figure 4)), the value of pg is much better defined than either ag or eg."," Since most of the RV data points are located near the pericenter of the binary's orbit (see Figure \ref{fig4}) ), the value of $p_B$ is much better defined than either $a_B$ or $e_B$." " Finally, the lower-right panel shows that the offset from the CfA data varies significantly as a function of the semimajor axis of binary."," Finally, the lower-right panel shows that the offset from the CfA data varies significantly as a function of the semimajor axis of binary." " This behavior is not noted for the other offsets, which remain almost constant."," This behavior is not noted for the other offsets, which remain almost constant." All the best fit solutions showed almost no variation in the longitude of pericenter nor in the time of passage through the periastron., All the best fit solutions showed almost no variation in the longitude of pericenter nor in the time of passage through the periastron. " Table 2 summarizes the minimum/maximum possible values of mg, ag, and eg leading to orbital fits with residuals x2 within the 1c confidence level."," Table \ref{table2} summarizes the minimum/maximum possible values of $m_B$ , $a_B$, and $e_B$ leading to orbital fits with residuals $\chi_\nu^2$ within the $1 \sigma$ confidence level." It is important to stress that statistically all are equally compatible with the observational data., It is important to stress that statistically all are equally compatible with the observational data. " In the next section we attempt to elucidate whether these uncertainties are important to the dynamics of small planetesimals orbiting the primary star and, consequently, whether they could have an effect on the planetary formation process."," In the next section we attempt to elucidate whether these uncertainties are important to the dynamics of small planetesimals orbiting the primary star and, consequently, whether they could have an effect on the planetary formation process." " Planetary accretion requires low relative velocities which, in turn, implies similar orbits between colliding bodies."," Planetary accretion requires low relative velocities which, in turn, implies similar orbits between colliding bodies." This condition may be satisfied if the orbital eccentricities are: (1) very small or (ii) very similar and the orbits are aligned., This condition may be satisfied if the orbital eccentricities are: (i) very small or (ii) very similar and the orbits are aligned. " For small planetesimals where mutual perturbations are not crucial, the orbital eccentricities are determined by a complex interplay between several phenomena, including gas drag, collisional history, and the gravitational effects of the secondary star (e.g. Marzari and Scholl 2000, Thébbault et al."," For small planetesimals where mutual perturbations are not crucial, the orbital eccentricities are determined by a complex interplay between several phenomena, including gas drag, collisional history, and the gravitational effects of the secondary star (e.g. Marzari and Scholl 2000, Thébbault et al." " 2006, 2008)."," 2006, 2008)." " In the secular approximation, these effects appear through the magnitude of the forced eccentricity ey."," In the secular approximation, these effects appear through the magnitude of the forced eccentricity $e_f$." " Thus, one way to study planetary accretion under different orbital solutions for y-Cephei would be to analyze the sensitivity of ey to the set (m4,mg,ag,eg) compatible with the RV data."," Thus, one way to study planetary accretion under different orbital solutions for $\gamma$ -Cephei would be to analyze the sensitivity of $e_f$ to the set $(m_A,m_B,a_B,e_B)$ compatible with the RV data." Results are presented in Figure 6 for two values of m4., Results are presented in Figure \ref{fig6} for two values of $m_A$. " Each panel shows level curves of constant forced eccentricity, as a function of the semimajor axis a of the planetesimal (abscissa), and for different semimajor axes ap for the binary pair (ordinate)."," Each panel shows level curves of constant forced eccentricity, as a function of the semimajor axis $a$ of the planetesimal (abscissa), and for different semimajor axes $a_B$ for the binary pair (ordinate)." " Contrary to our expectations, the range of eccentricities appears insensitive to the binary configuration."," Contrary to our expectations, the range of eccentricities appears insensitive to the binary configuration." In all cases the values of e; extend from ~0.03 for the small semimajor axis to ~0.077 for a~4 AU., In all cases the values of $e_f$ extend from $\sim 0.03$ for the small semimajor axis to $\sim 0.077$ for $a \simeq 4$ AU. " Adopting a lower value of ma seems to cause a slight reduction in the interval, but the change is not very significant."," Adopting a lower value of $m_A$ seems to cause a slight reduction in the interval, but the change is not very significant." " Consequently, and at least from this preliminary analysis, there appears to be no indication that different configurations for y-Cephei could cause major changes in the secular dynamics of small bodies and, therefore, on the accretional possibilities of a planetesimal swarm."," Consequently, and at least from this preliminary analysis, there appears to be no indication that different configurations for $\gamma$ -Cephei could cause major changes in the secular dynamics of small bodies and, therefore, on the accretional possibilities of a planetesimal swarm." " With hindsight, perhaps this result is not at all unexpected."," With hindsight, perhaps this result is not at all unexpected." " Since all orbital solutions for y-Cephei lead to practically the same amplitude in the RV signal, it is understandable that different values for the set (m4,mp,ag,eg) should also generate similar perturbative effects on other hypothetical bodies in the system; e.g. small planetesimals orbiting ma."," Since all orbital solutions for $\gamma$ -Cephei lead to practically the same amplitude in the RV signal, it is understandable that different values for the set $(m_A,m_B,a_B,e_B)$ should also generate similar perturbative effects on other hypothetical bodies in the system; e.g. small planetesimals orbiting $m_A$." A better test for the effects of different orbital fits on the secular dynamics is to compare the evolution of small planetesimals under the effects of a nonlinear drag force from a circumstellar gas disk centered on m4., A better test for the effects of different orbital fits on the secular dynamics is to compare the evolution of small planetesimals under the effects of a nonlinear drag force from a circumstellar gas disk centered on $m_A$ . We employ the same expression for the dissipative force as discussed in Beaugé et al. (, We employ the same expression for the dissipative force as discussed in Beaugé et al. ( 2010).,2010). " For the gaseousdisk we assume a linear surface density profile with a total mass of 3 Jupiter masses, and anouter edge located at"," For the gaseousdisk we assume a linear surface density profile with a total mass of $3$ Jupiter masses, and anouter edge located at" Section 5.. where we discuss the implications of the relatively long period and of its proximity to the stellar rotation period.,"Section \ref{concl}, where we discuss the implications of the relatively long period and of its proximity to the stellar rotation period." A further detection. CoRoT-Exo-3b. will be presented in ?.Paper VL.," A further detection, CoRoT-Exo-3b, will be presented in \citet[][Paper VI]{dha+08}." " Like the previously published CoRoT planets. CoRoT-Exo-4b was first detected during near real-time analysis of raw data. the ""alarm mode’ (which is described in Papers I and Il). triggering the ground-based follow-up described in Paper V. which included ground-based photometry in- and out-of-transit. at higher spatial resolution than CoRoT’s own. to identify which of the stars falling in the CoRoT aperture was being eclipsed. and multiple radial velocity measurements to derive the companion mass."," Like the previously published CoRoT planets, CoRoT-Exo-4b was first detected during near real-time analysis of raw data, the `alarm mode' (which is described in Papers I and II), triggering the ground-based follow-up described in Paper V, which included ground-based photometry in- and out-of-transit, at higher spatial resolution than CoRoT's own, to identify which of the stars falling in the CoRoT aperture was being eclipsed, and multiple radial velocity measurements to derive the companion mass." Once the planetary nature of the companion was confirmed. a high resolution. high signal-to-noise spectrum of the host star was obtained to derive accurate stellar parameters.," Once the planetary nature of the companion was confirmed, a high resolution, high signal-to-noise spectrum of the host star was obtained to derive accurate stellar parameters." " CoRoT-Exo-4 (GSC designation 0480002187). whose coordinates and magnitude are given in Table 1.. was observed as part of CoRoT’s initial run. during which ~12000 stars with magnitude 122.,at $z\magcir 2$ and their follow–up observations with X–ray telescopes of the next generation will contribute to fill the gap between $z\mincir 1$ studies of the thermo- and chemo-dynamics of the ICM and the study of the IGM at $z>2$. We thank the referee. Brant Robertson. for insightful comments which helped us to improve the presentation of the results.," We thank the referee, Brant Robertson, for insightful comments which helped us to improve the presentation of the results." We are indebted to Volker Springel for having provided us with the non—public version ofGADGET-2., We are indebted to Volker Springel for having provided us with the non--public version of. . We thank F. Fontanot. P. Monaco. R. Overzier. P. Rosati. L. Silva. and P. Tozzi for useful discussions and comments on the paper.," We thank F. Fontanot, P. Monaco, R. Overzier, P. Rosati, L. Silva, and P. Tozzi for useful discussions and comments on the paper." " The simulations used in this study have been carried out at the ""Centro Interuniversitario del Nord-Est per il Calcolo Elettronico"" (CINECA. Bologna). with CPU time assigned through an INAF-CINECA grant."," The simulations used in this study have been carried out at the “Centro Interuniversitario del Nord-Est per il Calcolo Elettronico” (CINECA, Bologna), with CPU time assigned through an INAF–CINECA grant." This work has been partially supported by the INFN PD-531 grant. by the INAF-PRINOO Grant and by the ASI-COFIS Theory grant.," This work has been partially supported by the INFN PD-51 grant, by the INAF-PRIN06 Grant and by the ASI-COFIS Theory grant." angular momentum. from the binary. we have performed evolution calculations for DILXDs containing a donor star of mass in the range from 3 to 5 M. with an initial orbital period of 1 d and 3 d. The calculations show that the evolution of DIILNIND is sensitive to 9.,"angular momentum from the binary, we have performed evolution calculations for BHXBs containing a donor star of mass in the range from 3 to 5 $M_{\odot}$ with an initial orbital period of 1 d and 3 d. The calculations show that the evolution of BHIMXB is sensitive to $\delta$." Generally a larger 9 is required for a wider initial orbit since the mass transfer itself during the evolution always causes orbital expansion., Generally a larger $\delta$ is required for a wider initial orbit since the mass transfer itself during the evolution always causes orbital expansion. The results indicate that the orbits of BIINBs would show secular shrinkage when the values of 6 lie in he rangee of a [ow 10το10.!., The results indicate that the orbits of BHXBs would show secular shrinkage when the values of $\delta$ lie in the range of a few $10^{-3}- 10^{-1}$. Thus our CD disc scenario suggests à new evolutionary channel for the formation of BILLAINBs from BULAINDs., Thus our CB disc scenario suggests a new evolutionary channel for the formation of BHLMXBs from BHIMXBs. llowever. our results encounter the similar. cillicult. as in Justham.Rappaport&Docdsiadlowski (2006).. that the calealated effective temperatures Z;4r are not consistent with those of the observed donor stars in BIILAINBs.," However, our results encounter the similar difficulty as in \citet{just06}, , that the calculated effective temperatures $T_{\rm eff}$ are not consistent with those of the observed donor stars in BHLMXBs." " We compare the calculated: results of both BII-LAINBs and IAINBs with the observations in the Zip - Lo, cliagrani in Vie.", We compare the calculated results of both BH-LMXBs and IMXBs with the observations in the $T_{\rm eff}$ - $P_{\rm orb}$ diagram in Fig. 5., 5. One can see that the observed. results seem to » more consistent. with the evolutionary tracks of original DIILMXDs., One can see that the observed results seem to be more consistent with the evolutionary tracks of original BHLMXBs. Justham.Rappaport&Poclsiaclowski(2006) rave already. pointed out that this tempreature discrepancy seems to be a generic dillieulty with any formation scenario hat invokes primorcially intermecdiate-mass donor stars., \citet{just06} have already pointed out that this tempreature discrepancy seems to be a generic difficulty with any formation scenario that invokes primordially intermediate-mass donor stars. Lf his elective temperat problem can be solved. the CB disc mechanism may ure.provide a plausible solution to the BULAING formation problem. without requiring anomalous magnetic fields in the donor stars.," If this effective temperature problem can be solved, the CB disc mechanism may provide a plausible solution to the BHLMXB formation problem, without requiring anomalous magnetic fields in the donor stars." The mechanism [feeding the CD disc is still unclear., The mechanism feeding the CB disc is still unclear. lt has been argued. that during mass exchange in binary systems. some of the lost matter which possesses high orbital angular momentum mav form a disc surrounding the binary system rather than leave the binary system (vandenEHeuvel 1994).," It has been argued that during mass exchange in binary systems, some of the lost matter which possesses high orbital angular momentum may form a disc surrounding the binary system rather than leave the binary system \citep{heu94}." . This part of matter may come from the stellar wind from the donor star. wind and/or outllow from the acerction disc. or mass lost. from the outer Lagrangian point.," This part of matter may come from the stellar wind from the donor star, wind and/or outflow from the accretion disc, or mass lost from the outer Lagrangian point." The values of ὁ adopted here sccm to rule out stellar wine as the origin of the CB dise. which requires a unreasonably high wind mass loss rate in intermediate- and low-mass stars.," The values of $\delta$ adopted here seem to rule out stellar wind as the origin of the CB disc, which requires a unreasonably high wind mass loss rate in intermediate- and low-mass stars." We speculate that the cise wind/outllow may play a more important role in feeding the CD disc. as the X-ray irradiation on the accretion dise in DIINDs may evaporate 1e disc much more elliciently than in CVs.," We speculate that the disc wind/outflow may play a more important role in feeding the CB disc, as the X-ray irradiation on the accretion disc in BHXBs may evaporate the disc much more efficiently than in CVs." This may explain why the values of 6 are about 2.3 orders of magnitude larger wn those for CV evolution (Spruit&Taam2001)., This may explain why the values of $\delta$ are about $2-3$ orders of magnitude larger than those for CV evolution \citep{spru01}. . Dubus.Jam&Spruit(2002) investigated the structure anc evolution of a &eometrically thin CB disc ο calculate its spectral energy. distributions. and ciscussect 16 prospects for the detection of such disces in the infrared and. submillimeter wavelength regions.," \citet{dubu02} investigated the structure and evolution of a geometrically thin CB disc to calculate its spectral energy distributions, and discussed the prospects for the detection of such discs in the infrared and submillimeter wavelength regions." Dubusetal.(2004) searched. [or excess mid-infrared. emission due to CB disc material in CVs., \citet{dubu04} searched for excess mid-infrared emission due to CB disc material in CVs. But clireet detection of the CD discs in CVs by infrare continuum studies has so far been elusive. partly because of the lack of accurate. disc atmosphere moclels.," But direct detection of the CB discs in CVs by infrared continuum studies has so far been elusive, partly because of the lack of accurate disc atmosphere models." Recently. Muno&Alauerhan(2006) studied. the blackbody spectrum of DIILMNDs A 0620-00. anc NTE JIIIS|480. zux found that the inferred excess mic-infrared emitting areas are ~2 times larger than the binary orbital separations.," Recently, \citet{muno06} studied the blackbody spectrum of BHLMXBs A 0620-00 and XTE J1118+480, and found that the inferred excess mid-infrared emitting areas are $\sim 2$ times larger than the binary orbital separations." Fherefore. the detection of excess mid-infrared emission from these BIILAINBs provides evidence ol the existence of CB disc around some BIILNMUNDs.," Therefore, the detection of excess mid-infrared emission from these BHLMXBs provides evidence of the existence of CB disc around some BHLMXBs." These observations may set useful constraints on the evolution of the €D cliscss., These observations may set useful constraints on the evolution of the CB discs. The masses of the model. CB disc. are significantly larecr than those (~1037.) estimated bv Aluno&Mauerhan(2006).," The masses of the model CB disc are significantly larger than those $\sim 10^{-9}M_{\odot}$ ) estimated by \citet{muno06}." . Combined with the non-detection of discs in €Vs by Dubusetal.(2004). this fact suggests that t10 presence of the CD disc may not always accompany the RLOE processes.," Combined with the non-detection of discs in CVs by \citet{dubu04}, this fact suggests that the presence of the CB disc may not always accompany the RLOF processes." For example. (X-ray) nova bursts may desrov the CB dise before it has developed to be massive enotwh.," For example, (X-ray) nova bursts may destroy the CB disc before it has developed to be massive enough." Or perhaps 9 only needs to be high for a short time. wile normal magnetic braking takes over the CD disc curing he majority of the evolution.," Or perhaps $\delta$ only needs to be high for a short time, while normal magnetic braking takes over the CB disc during the majority of the evolution." Ehe latter may partly account or the discrepancy between the lifetimes of BULAINBs in Eie, The latter may partly account for the discrepancy between the lifetimes of BHLMXBs in Fig. " 36 051510"" vr) and those expected for observed BILLAINBs (~1010"" vr)."," 3 $\sim 0.5-1.5\times 10^{6}$ yr) and those expected for observed BHLMXBs $\sim 10^{8}-10^9$ yr)." Since the CD disc can promote nmass transfer very. clliciently. DIILMXDs are more Likely to be observed when the value of 0 becomes extremely small.," Since the CB disc can promote mass transfer very efficiently, BHLMXBs are more likely to be observed when the value of $\delta$ becomes extremely small." We thank theanonvnmous referee for his/her helpful comments that significantly improved the manuscript., We thank theanonymous referee for his/her helpful comments that significantly improved the manuscript. This work was supported by the Nrational Science Foundation of China (NSEC)) under erant. 10573010., This work was supported by the National Science Foundation of China (NSFC) under grant 10573010. In Eq.,In Eq. 1 we assume that energy losses allow the svstem to reach stationarity (Of/0f=0)., \ref{eq:transport} we assume that energy losses allow the system to reach stationarity $\partial f/\partial t=0$ ). In the test-particle regime. (here is no precursor. therefore as usual dudar=(ue—uy)dlr). and the wv axis is oriented [rom upstream (—2€xxe0) to downstream (0zex+20).," In the test-particle regime, there is no precursor, therefore as usual $du/dx=(u_2-u_1)\delta(x)$ , and the $x$ axis is oriented from upstream $-\infty\leq x\leq 0$ ) to downstream $0\leq x\leq +\infty$ )." For our purposes it is useful to introduce the function NGr.p)=4Axpfp). so that the transport equation reads: The solution can be found by requiring the continuity of the distribution function and by satislving the boundary condition at the shock. which is easily found by integrating the full transport equation in a narrow region around the shock.," For our purposes it is useful to introduce the function $N(x,p)=4\pi p^2 f(x,p)$, so that the transport equation reads: The solution can be found by requiring the continuity of the distribution function and by satisfying the boundary condition at the shock, which is easily found by integrating the full transport equation in a narrow region around the shock." " We will return to this point later,", We will return to this point later. We now focus our attention on solving Eq., We now focus our attention on solving Eq. Ὁ in the downstream and upstream Lhicls separately., \ref{eq:transportN} in the downstream and upstream fluids separately. For this purpose. following Webb&Fritz(1990).. we uniuliply Eq.," For this purpose, following \cite{webbfritz}, we multiply Eq." " 3. bv an arbitrary finetion Gor.por’.p) and integrate both terms for rySec» and p,€ppo. where the extremes of integration will be defined later in a suitable way."," \ref{eq:transportN} by an arbitrary function $\cG(x,p;x',p')$ and integrate both terms for $x_1\leq x\leq x_2$ and $p_1\leq p\leq p_2$, where the extremes of integration will be defined later in a suitable way." This results in the following where (he injection term is not present as long as we concentrate on (he regions upstream and downstream of the shock and we assume that the injection occurs exactly al the shock surlace., This results in the following where the injection term is not present as long as we concentrate on the regions upstream and downstream of the shock and we assume that the injection occurs exactly at the shock surface. llere we also made use of the identity We recall now that the function GCGr.por’.p) was chosen to be an arbitrary fiction of ils arguments.," Here we also made use of the identity We recall now that the function $\cG(x,p;x',p')$ was chosen to be an arbitrary function of its arguments." We have therefore the freeclom to choose it in the wav that is most useful for our purposes., We have therefore the freedom to choose it in the way that is most useful for our purposes. " We choosethe functionG as the solution of the equation Inthe downstream fluid we choose ry=0 and ry= —2€. while in the upstream Παπά,"," We choosethe function $\cG$ as the solution of the equation Inthe downstream fluid we choose $x_1=0$ and $x_2=+\infty$ , while in the upstream fluid," In a MlIC-scenario. most of the main characteristics of the inverse Compton component are quite insensitive to (he origin of the seed photons and are mstead (the result of the scaltering process itself.,"In a MIC-scenario, most of the main characteristics of the inverse Compton component are quite insensitive to the origin of the seed photons and are instead the result of the scattering process itself." An example is the expected spectral correlations between the part determined by a (ie. mainlv X-ray) and (he spectral range where (he emission occurs in the IxXlein-Nishina limit (i.e.. mainly gamma-ray).," An example is the expected spectral correlations between the part determined by $\alpha$ (i.e., mainly X-ray) and the spectral range where the emission occurs in the Klein-Nishina limit (i.e., mainly gamma-ray)." These spectral correlations can be expressed in terms of the spectral breaks that occur at [requencies above the X-ray regime (see DAOO0)., These spectral correlations can be expressed in terms of the spectral breaks that occur at frequencies above the X-ray regime (see BA00). There will be one or two breaks depending on the value of a., There will be one or two breaks depending on the value of $\alpha$ . For a>(p—1)/2. the X-ray spectrum is determined by ος and extends (o hyzzmc).," For $\alpha > (p-1)/2$, the X-ray spectrum is determined by $\gamma_{\rm c}$ and extends to $h\nu \approx \gamma_{\rm c} mc^2$." Above this frequency. cooling is important and the spectral index is given by p—11970):: hence. the magnitude of this spectral break is Aa=p—1—20.," Above this frequency, cooling is important and the spectral index is given by $p-1$; hence, the magnitude of this spectral break is $\Delta \alpha = p-1-\alpha$." This isalso the frequeney where the value of vyf(v) peaks., This isalso the frequency where the value of $\nu f(\nu)$ peaks. For a<(p—1)/2. this single break splits into (wo.," For $\alpha < (p-1)/2$, this single break splits into two." The X-ray spectrum is now determined bv μι and extends to ij2μέ., The X-ray spectrum is now determined by $\gamma_{\rm min}$ and extends to $h\nu \approx \gamma_{\rm min} mc^2$. Above this [requency. emission occurs in the IxXlein-Nishina limit implving that the emitted frequency is proportional to electron energy.," Above this frequency, emission occurs in the Klein-Nishina limit implying that the emitted frequency is proportional to electron energy." " Since the electrons lose only a fraction of their enerey (x 5""). the spectral index is given by p—l—a. which corresponds to a spectral break of magnitude Aa,=p—1—2a."," Since the electrons lose only a fraction of their energy $\propto \gamma^{\alpha}$ ), the spectral index is given by $p-1-\alpha$, which corresponds to a spectral break of magnitude $\Delta \alpha_{\rm 1} = p-1-2 \alpha$." A second. cooling break at irz50nc? has magnitude Ange =a.," A second, cooling break at $h\nu \approx \gamma_{\rm c} mc^2$ has magnitude $\Delta \alpha_{\rm 2} = \alpha$ ." The peak in prf(r) occurs at the first break when ap—2: the latter requires p«3., The peak in $\nu f(\nu)$ occurs at the first break when $\alpha < p-2$ and at the second break when $\alpha > p-2$; the latter requires $p<3$. The (wo breaks merge again into one Lor cXua , The two breaks merge again into one for $\gamma_{\rm c} < \gamma_{\rm min}$. These spectral properties are summarized in relfigl.. which shows schematically how the inverse Compton scattered part of the spectrum changes as the column density of electrons (1.e.. το) increases.," These spectral properties are summarized in \\ref{fig1}, which shows schematically how the inverse Compton scattered part of the spectrum changes as the column density of electrons (i.e., $\tau_{\rm o}$ ) increases." H max be noticed that of the iree possible frequency ranges with different spectral indices only the one at the highest frequencies is determined exclusively bv. (he energy. distribution of the injected electrons (i.e.. p).," It may be noticed that of the three possible frequency ranges with different spectral indices only the one at the highest frequencies is determined exclusively by the energy distribution of the injected electrons (i.e., $p$ )." The other (wo spectral indices can vary continuously without any chanee in p., The other two spectral indices can vary continuously without any change in $p$. " Such ral""wlalions are instead caused by changes in (he electron density. ancl are correlated through je. value of a.", Such variations are instead caused by changes in the electron density and are correlated through the value of $\alpha$. The source properties of blazars deduced [rom observations in a MlIC-scenario differ m isonme crucial aspects [rom those in a single scattering scenario: however. several remain the same.," The source properties of blazars deduced from observations in a MIC-scenario differ in some crucial aspects from those in a single scattering scenario; however, several remain the same." " In a MIC-scenario. the value of 5,4, should be small to assure a smooth inverse Compton spectrum: from BAOO this implies 5,4,5S10."," In a MIC-scenario, the value of $\gamma_{\rm min}$ should be small to assure a smooth inverse Compton spectrum; from BA00 this implies $\gamma_{\rm min} \lesssim 10$." Similar values are also suggested [or V.ingle scattering of photons from the broad line region. since (he X-ray spectra measured by Swift-BAT is on average somewhat too soft to be due to the cooling5 tailof higher5 οποιον5. electrons 2009b).," Similar values are also suggested for single scattering of photons from the broad line region, since the X-ray spectra measured by -BAT is on average somewhat too soft to be due to the cooling tailof higher energy electrons ." ". For the most likely site of the emission region in asingle scattering scenario. cooling on external photons leads to 5,107 in"," For the most likely site of the emission region in asingle scattering scenario, cooling on external photons leads to $\gamma_{\rm c} \lesssim 10^2$ in" "For a 25. 1000 keV fluence of 10tereen:7 and a redshift z=0.707. the isotropic enerev of this burst would have been 1.3xI0*ere: for a peak flux of ~I0ergem7s in (he same energy range. the isotropic peak Luminosity would have been 1.3xLOerestf. These estimates assume Q=0.2.AO.andIL,65kms!Alpe|.","For a 25 – 1000 keV fluence of $\rm 10^{-4}\, erg\, cm^{-2}$ and a redshift z=0.707, the isotropic energy of this burst would have been $\rm 1.3 \times 10^{53} erg$; for a peak flux of $\rm \sim 10^{-5}\, erg\, cm^{-2}\, s^{-1}$ in the same energy range, the isotropic peak luminosity would have been $\rm 1.3 \times 10^{52} erg\, s^{-1}$ These estimates assume $\rm \Omega=0.2, \Lambda=0, and \, H_0=65 \, km\, s^{-1}\, Mpc^{-1}$." Rhoads (1997) has pointed out that one signature of beaming is a steep decay in the afterglow light curve. x19.," Rhoads (1997) has pointed out that one signature of beaming is a steep decay in the afterglow light curve, $\propto t^{-2}$." As the initial optical light eurve for GRB991208 indeed appears to decay this steeply. {he emission may well be beamed. reducing these estimates.," As the initial optical light curve for GRB991208 indeed appears to decay this steeply, the emission may well be beamed, reducing these estimates." The current. IPN now consists of Ulysses and NEAR. in interplanetary space. and nunmerous near-Earth spacecralt such as Wand.. BeppoS.AX.. and the Compton Gamina-Ray Observatory.," The current IPN now consists of Ulysses and NEAR in interplanetary space, and numerous near-Earth spacecraft such as Wind, BeppoSAX, and the Compton Gamma-Ray Observatory." . The Mars Surveyor 2001 Orbiter will join the network in mid-2001., The Mars Surveyor 2001 Orbiter will join the network in mid-2001. The IPN currently observes ~ 1... 2 GRBs per week ancl is localizing many of them rapidly to small error boxes., The IPN currently observes $\sim$ 1 – 2 GRBs per week and is localizing many of them rapidly to small error boxes. These events tend to be the brighter ones. but apart [rom this. (here is no bias towards any particular event duration: indeed. the IPN generally obtains its smallest error boxes for the short bursts.," These events tend to be the brighter ones, but apart from this, there is no bias towards any particular event duration; indeed, the IPN generally obtains its smallest error boxes for the short bursts." Neither is there any sun-angle restriction for the event locations. which means that bursts will be detected whose locations are close to (he Sun. as (Bis one was. making prompt radio observations of these positions important.," Neither is there any sun-angle restriction for the event locations, which means that bursts will be detected whose locations are close to the Sun, as this one was, making prompt radio observations of these positions important." The other advantages of radio observations over optical are the longer lifetime of the radio aftereglow. (he immunity rom weather. aud the Ireedom (o operate at any part of the diurial cycle.," The other advantages of radio observations over optical are the longer lifetime of the radio afterglow, the immunity from weather, and the freedom to operate at any part of the diurnal cycle." " This should increase the rate of counterpart detections substantially over the next several venis,", This should increase the rate of counterpart detections substantially over the next several years. WIL acknowledges support for Ulysses operations under JPL Contract 958056. [or IPN operations under NASA LTSA erant. NAG5-3500. and for NEAR operations under the NEAR. Participating Scientist program.," KH acknowledges support for Ulysses operations under JPL Contract 958056, for IPN operations under NASA LTSA grant NAG5-3500, and for NEAR operations under the NEAR Participating Scientist program." On the Russian side. this work was partially supported by RFBR erant 99-02-17031.," On the Russian side, this work was partially supported by RFBR grant 99-02-17031." We are grateful to R. Gold and BR.MeNutt for, We are grateful to R. Gold and R.McNutt for (i.e.. protostars) ancl detected munerous FIR CO rotational lines.,"(i.e., protostars) and detected numerous FIR CO rotational lines." For example. emission lines [rom jo=14—26 were observed in the Class 0 object L1448-mun (Nisinietal.1999). jo=14-31 in the Class E object IC 1396N. jo=I4—16 in the Class I object W28 A2. jo=14—20 in the Class IL object B. CraA (Saracenoetal.1999).. and jo=14—25 in T Tauri (5pinoglioetal.1999).," For example, emission lines from $j_2=14-26$ were observed in the Class 0 object L1448-mm \citep{nis99}, $j_2=14-31$ in the Class I object IC 1396N, $j_2=14-16$ in the Class I object W28 A2, $j_2=14-20$ in the Class II object R CrA \citep{sar99}, and $j_2=14-25$ in T Tauri \citep{spi99}." . Non-LTE analvses of these pre-main sequence objects suggested multiple components wilh various excitation conditions., Non-LTE analyses of these pre-main sequence objects suggested multiple components with various excitation conditions. Future studies of these protostars. the infrared sources discussed above. and future FIR. and submillimeter observations withHerschel aad ALAIA ean benefit [rom the CO-II» quenching rate coefficients presented here.," Future studies of these protostars, the infrared sources discussed above, and future FIR and submillimeter observations with and ALMA can benefit from the $_2$ quenching rate coefficients presented here." Rotational quenching of CO due to para- ancl ortho-1 collisions has been studied using an explicit quantum-mechanical close-coupling approach and the coupled-states approximation on the potential surface. Vo;. of Jankowski," Rotational quenching of CO due to para- and $_2$ collisions has been studied using an explicit quantum-mechanical close-coupling approach and the coupled-states approximation on the potential surface, $_{04}$, of \citet{jankow05}." &Szalewiez(2005).. state quenching rate coefficients for initial rotational levels jo —1. 2. +--+. 40 of CO are obtained over a wide temperature range and available in tables formatted [or astrophvsical applications.," State-to-state quenching rate coefficients for initial rotational levels $j_2=$ 1, 2, $\cdots$, 40 of CO are obtained over a wide temperature range and available in tables formatted for astrophysical applications." Resonances result in undulations in the temperature dependence of the rate coefficients with the amplitudes of the undulations (vpically decreasing with js., Resonances result in undulations in the temperature dependence of the rate coefficients with the amplitudes of the undulations typically decreasing with $j_2$. " For temperatures less than ~50 Ix. the current state-to-state rotational quenching rate coellicients obtained with Vy, are found to depart from the results of Flower(2001) obtained with the earlier Vox PES."," For temperatures less than $\sim$ 50 K, the current state-to-state rotational quenching rate coefficients obtained with $_{04}$ are found to depart from the results of \citet{flower01} obtained with the earlier $_{98}$ PES." The ciserepanices are likely related to the differences in the well depth ancl anisotropy of the (wo potentials., The discrepanices are likely related to the differences in the well depth and anisotropy of the two potentials. inertial [frames are dragged along by the star. is determined by the initially unknown stellar properties like mass and rotational Irequency (Weber1999)..,"inertial frames are dragged along by the star, is determined by the initially unknown stellar properties like mass and rotational frequency \citep{Weber:1999a}." llere we outline briefly the equations solved by the ANS code., Here we outline briefly the equations solved by the $RNS$ code. The coordinates of the stationary. axial svinnmetric space-time used (o model a (rapidly) rotating neutron star are defined through a generalization ofDardeen's metric (Stergioulas2003): where the metric potentials 5. p. o0. and the angular velocity of the stellar fluid relative to the local inertial frame. w. are functions of the quasi-isolropic radial coordinates. r. and (he polar angle 9 only.," The coordinates of the stationary, axial symmetric space-time used to model a (rapidly) rotating neutron star are defined through a generalization ofBardeen's metric \citep{Stergioulas:2003yp}: where the metric potentials $\gamma$, $\rho$, $\alpha$, and the angular velocity of the stellar fluid relative to the local inertial frame, $\omega$, are functions of the quasi-isotropic radial coordinates, $r$, and the polar angle $\theta$ only." The matter inside a rigidly rotating star is approximated as a perlect. fluid (Stergioulas2003).. whose energv momentum tensor is given bv Eq. (2)).," The matter inside a rigidly rotating star is approximated as a perfect fluid \citep{Stergioulas:2003yp}, whose energy momentum tensor is given by Eq. \ref{eq.2}) )." " The proper velocity of matter. c. relative to the local Zero Angular Momentum. Observer (ZAMO) (Ouved2002). is defined as with Q=uw/u"" the angular velocity of a fIuid element."," The proper velocity of matter, $\upsilon$, relative to the local Zero Angular Momentum Observer (ZAMO) \citep{2002A&A...382..939O} is defined as with $\Omega=u^3/u^0$ the angular velocity of a fluid element." The four-velocitv is given by In the above equation the function (5+p)/2 represents the relativistic generalization of the Newtonian gravitational potential. while exp[(5+p)/2] is a time dilation factor between an observer moving with angular velocity w and one al infinitv.," The four-velocity is given by In the above equation the function $(\gamma+\rho)/2$ represents the relativistic generalization of the Newtonian gravitational potential, while $\exp[(\gamma+\rho)/2]$ is a time dilation factor between an observer moving with angular velocity $\omega$ and one at infinity." Substitution of Eq. (13)), Substitution of Eq. \ref{eq.13}) ) into Einstein's fields equations projected onto the ZAMO reference frame gives three elliptic partial differential equations for the metric potentials 5. p. and a. and two linear ordinary differential equations lor the metric potential o.," into Einstein's fields equations projected onto the ZAMO reference frame gives three elliptic partial differential equations for the metric potentials $\gamma$, $\rho$, and $\omega$, and two linear ordinary differential equations for the metric potential $\alpha$." Technically. (he elliptic differential equations for the metric functions are converted into integral equations which are then solved iteratively applving Green's function approach (IXomatsuetal.1989:Stergioulas2002)..," Technically, the elliptic differential equations for the metric functions are converted into integral equations which are then solved iteratively applying Green's function approach \citep{1989MNRAS.237..355K,Stergioulas:2003yp}." " From the relativistic equations of motion. the equations of hvedrostatic equilibrium for a barotropic [Iuid may be obtained as (Stergioulas2003:Ouved 2002): with (12) the specilic enthalpy. 2, the re-scaled pressure. , the specific enthalpy at the pole. αρ and p, the values of the metric potentialsat the pole. O,= r.O. and A a rotational"," From the relativistic equations of motion, the equations of hydrostatic equilibrium for a barotropic fluid may be obtained as \citep{Stergioulas:2003yp,2002A&A...382..939O}: : with $h(P)$ the specific enthalpy, $P_p$ the re-scaled pressure, $h_p$ the specific enthalpy at the pole, $\gamma_p$ and $\rho_p$ the values of the metric potentialsat the pole, $\Omega_c=r_e\Omega$ , and $A$ a rotational" To resolve the differences iu the surface brightness profiles. we selected the elliptical NGC 1107 for detailed inspection.,"To resolve the differences in the surface brightness profiles, we selected the elliptical NGC 1407 for detailed inspection." NCC 1107 is an excellent test particle for its isophotes are nearly. circular (axial ratio of 0.93 from 2MLASS. 0.95 from our study) aud its envelope is [ree of any foreground stars or distortions.," NGC 1407 is an excellent test particle for its isophotes are nearly circular (axial ratio of 0.93 from 2MASS, 0.95 from our study) and its envelope is free of any foreground stars or distortions." Recent pointed observations (Finkbeiner et al.,Recent pointed observations (Finkbeiner et al. 2002. 2004: Casassus et al.," 2002, 2004; Casassus et al." 2004. 2006: Watson ct al.," 2004, 2006; Watson et al." 2005: Scaife ct al., 2005; Scaife et al. 2007: Dickinson et al., 2007; Dickinson et al. 2007) have provided some evidence for the anomalous microwave emission commonly ascribed to spinning dust (Drain Lazarian 1998a.b).," 2007) have provided some evidence for the anomalous microwave emission commonly ascribed to spinning dust (Drain Lazarian 1998a,b)." Although this emission was originally seen as a large scale phenomenon in CAIB observations (see e.g. Ixogut et al., Although this emission was originally seen as a large scale phenomenon in CMB observations (see e.g. Kogut et al. 1996) it has been suggested that the emission occurs in a number of distinct astronomical objects. such as dark. clouds. and. and photo-dissociation regions.," 1996) it has been suggested that the emission occurs in a number of distinct astronomical objects, such as dark clouds, and and photo-dissociation regions." Lt often appears to be correlated with thermal dust. emission as supported. by the. pointed observations mentioned. previously but. it must. be stated that this is not always the case. see for example C'asassus et al. (," It often appears to be correlated with thermal dust emission as supported by the pointed observations mentioned previously but it must be stated that this is not always the case, see for example Casassus et al. (" 2008).,2008). ln. spite of these. predictions the evidence [ου anomalous microwave emission in compact objects is often contradictory., In spite of these predictions the evidence for anomalous microwave emission in compact objects is often contradictory. Early observations below GCGllz of the molecular cloud LPILO96 (Finkbeiner ct al., Early observations below GHz of the molecular cloud 96 (Finkbeiner et al. 2002). which showed a rising spectrum were later contracicted by observations at 31 and δις which found. emission consistent with an optically thin free spectrum extrapolated from. lower frequencies (Dickinson ct al.," 2002), which showed a rising spectrum were later contradicted by observations at 31 and GHz which found emission consistent with an optically thin free–free spectrum extrapolated from lower frequencies (Dickinson et al." 2006: Seaile et al., 2006; Scaife et al. 2007)., 2007). Although some evidence lor an excess was found in a sample of Southern regions (Dickinson ct al., Although some evidence for an excess was found in a sample of Southern regions (Dickinson et al. 2007) and more significantly in ROWI175 (Dickinson ct al., 2007) and more significantly in RCW175 (Dickinson et al. 20038). no emission inconsistent with free.[ree was found in a sample of Northern regions (Scaife et al.," 2008), no emission inconsistent with free–free was found in a sample of Northern regions (Scaife et al." 2008)., 2008). C'asassus et al. (, Casassus et al. ( 2004) proposed a flux density of approximately 12JJy from the Lelix planetary nebula at CGlIlIz to be in excess of a free[ree spectrum extrapolated [rom lower frequencies.,2004) proposed a flux density of approximately Jy from the Helix planetary nebula at GHz to be in excess of a free–free spectrum extrapolated from lower frequencies. Llowever. based on Hux densities from the literature at 1.4. 2.7. GCGLIz CEhman. Dixon. Ixraus 1970: LHiges 1971: Wall. Wright. Bolton 1976) and the recent WNALADP 5-vear densities at ΟΕ (Wright et al.," However, based on flux densities from the literature at 1.4, 2.7, GHz (Ehman, Dixon, Kraus 1970; Higgs 1971; Wall, Wright, Bolton 1976) and the recent WMAP 5-year densities at GHz (Wright et al." 2008). which are all also x LJJ. we suggest that there is no evidence for this reported excess in the fux density spectrum. although the nebula may be anomalous in other wavs.," 2008), which are all also $\approx 1$ Jy, we suggest that there is no evidence for this reported excess in the flux density spectrum, although the nebula may be anomalous in other ways." In this letter we present observations of the Lvnds dark nebula 11111. taken from the AMI sample of compact Galactic star formation regions (Scaile et al..," In this letter we present observations of the Lynds' dark nebula 1111, taken from the AMI sample of compact Galactic star formation regions (Scaife et al.," in prep)., in prep). This sample was selected. from the SCUBA sample of compact Lynds clouds (Visser. Richer Chandler 2001).," This sample was selected from the SCUBA sample of compact Lynds' clouds (Visser, Richer Chandler 2001)." The spectra of dark clouds at gigahertz frequencies is poorly documented in all but a few cases (Finkbeiner et al 2004: Casassus et al., The spectra of dark clouds at gigahertz frequencies is poorly documented in all but a few cases (Finkbeiner et al 2004; Casassus et al. 2006: Casassus et al., 2006; Casassus et al. 2008)., 2008). 1n those cases where em-wave data is available (Casassus et al., In those cases where cm-wave data is available (Casassus et al. 2006: Casassus et al., 2006; Casassus et al. 2008) the behaviour of these objects has been found to be anomalous in a number of wavs ane in the case, 2008) the behaviour of these objects has been found to be anomalous in a number of ways and in the case when stars evolve towards the B supergiant regime.,when stars evolve towards the B supergiant regime. This M jump is referred to as the bi-stability jump., This $\dot{M}$ jump is referred to as the bi-stability jump. The mass-loss behaviour is depicted as the dotted line in Fig. 2.., The mass-loss behaviour is depicted as the dotted line in Fig. \ref{fig:brott}. Recent stellar models with rotation of Brott et al. (, Recent stellar models with rotation of Brott et al. ( 2010) that include this Vink et al.,2010) that include this Vink et al. " mass-loss jump show a dramatic braking (see solid line), which we refer to as(BSB)."," mass-loss jump show a dramatic braking (see solid line), which we refer to as." BSB might explain the general slow rotation of B supergiants., BSB might explain the general slow rotation of B supergiants. An alternative explanation for the slow rotation of B supergiants might involve a core He-burning nature for B supergiants (see Vink et al., An alternative explanation for the slow rotation of B supergiants might involve a core He-burning nature for B supergiants (see Vink et al. 2010 for a detailed discussion)., 2010 for a detailed discussion). The cause of the mass-loss bi-stability jump is that the most important line driving element Fe recombines from Fe to Feri at 25 000 K and that suddenly the Fe lines become much more effective as they fall in the wavelength range where the flux distribution is maximal., The cause of the mass-loss bi-stability jump is that the most important line driving element Fe recombines from Fe to Fe at 25 000 K and that suddenly the Fe lines become much more effective as they fall in the wavelength range where the flux distribution is maximal. The result is an increase in M and a drop in terminal velocity., The result is an increase in $\dot{M}$ and a drop in terminal velocity. The latter has been confirmed in observed data-sets (e.g. Lamers et al., The latter has been confirmed in observed data-sets (e.g. Lamers et al. " 1995), but the jump in mass-loss rate is still controversial (e.g. Crowther et al."," 1995), but the jump in mass-loss rate is still controversial (e.g. Crowther et al." " 2006, Benaglia 2007, Markova Puls 2008)."," 2006, Benaglia 2007, Markova Puls 2008)." " The relevance for stellar evolution is that when massive stars evolve to lower aafter the O star main sequence phase, they are expected to cross the bi-stability jump."," The relevance for stellar evolution is that when massive stars evolve to lower after the O star main sequence phase, they are expected to cross the bi-stability jump." " Interestingly, LBVs brighter than log (L/ Lo) =5.8 (see Fig. 3))."," Interestingly, LBVs brighter than log $L/\lsun$ ) $= 5.8$ (see Fig. \ref{fig:hrd}) )." " are expected to encounter it continuously - on timescales of their photometric variability, which we discuss in the next section."," are expected to encounter it continuously - on timescales of their photometric variability, which we discuss in the next section." " In the previous section, we discussed the physics of the bi-stability jump in the context of normal OB supergiants."," In the previous section, we discussed the physics of the bi-stability jump in the context of normal OB supergiants." " The jump might also play a role in the mass-loss behaviour of LBVs, in particular with reference to the normal “S Doradus” type variations where the stars change their effective temperatures from values as high as 30 kK (where they are identified as B supergiants) to approximately 10 kK (where they are identified as F supergiants)."," The jump might also play a role in the mass-loss behaviour of LBVs, in particular with reference to the normal “S Doradus” type variations where the stars change their effective temperatures from values as high as 30 kK (where they are identified as B supergiants) to approximately 10 kK (where they are identified as F supergiants)." " During these S Dor excursions, the stars keep crossing the temperature range of the bi-stability jump (see Fig.3)), thereby likely inducing variable mass loss."," During these S Dor excursions, the stars keep crossing the temperature range of the bi-stability jump (see \ref{fig:hrd}) ), thereby likely inducing variable mass loss." " Such variable mass loss is in turn understood to be responsible for a non-uniform circumstellar medium, which could show up in the lightcurves and spectra of core-collapse SNe — if LBVs were in an advanced enough evolutionary state."," Such variable mass loss is in turn understood to be responsible for a non-uniform circumstellar medium, which could show up in the lightcurves and spectra of core-collapse SNe – if LBVs were in an advanced enough evolutionary state." Current wisdom is that LBVs are not evolved enough (e.g. Langer et al., Current wisdom is that LBVs are not evolved enough (e.g. Langer et al. 1994) and that the LBV phase of evolution is the stage in which most, 1994) and that the LBV phase of evolution is the stage in which most is no justification for considering nonsynchronized solutions.,is no justification for considering nonsynchronized solutions. A phase shift can thus be attributed to an atmosphere alone., A phase shift can thus be attributed to an atmosphere alone. This point will have to be stressed more carefully for cooler planets. which are less subject to tidal forces. and which need to be observed by future direct detection techniques.," This point will have to be stressed more carefully for cooler planets, which are less subject to tidal forces, and which need to be observed by future direct detection techniques." If no photometric variations are seen despite accurate photometric measurements. we may be able to infer that the planet has a dense atmosphere. as attempted on bb by Seager and Deming (?)..," If no photometric variations are seen despite accurate photometric measurements, we may be able to infer that the planet has a dense atmosphere, as attempted on b by Seager and Deming \citeyearpar{Seager2009}." The absence of modulation can also be due to an inclination close to 0°. but in some cases inclinations lower than a given value can be rejected.," The absence of modulation can also be due to an inclination close to $^{\circ}$, but in some cases inclinations lower than a given value can be rejected." This can be done using the measurement of the projected rotation of the star and assuming that planetary orbits remain close to the stellar equator (known to be wrong for many hot Jupiters). but also using dynamical constraints. which was done for the systems GJ876 (?) and GJ581 (?)..," This can be done using the measurement of the projected rotation of the star and assuming that planetary orbits remain close to the stellar equator (known to be wrong for many hot Jupiters), but also using dynamical constraints, which was done for the systems GJ876 \citep{Correia2010} and GJ581 \citep{Mayor2009a}." A lack of modulation can also be come from an extremely high albedo. which may be checked at short wavelengths.," A lack of modulation can also be come from an extremely high albedo, which may be checked at short wavelengths." The ability to constrain R. A. and ; from spectral phase variation comes from the simplicity of the model that assumes an isotropic. distribution of the thermal emission. uniform surface properties. and an emissivity independent of the wavelength and equal to 1.," The ability to constrain $R$, $A$, and $i$ from spectral phase variation comes from the simplicity of the model that assumes an isotropic distribution of the thermal emission, uniform surface properties, and an emissivity independent of the wavelength and equal to 1." We now discuss the validity of these assumptions., We now discuss the validity of these assumptions. " An emissivity value € lower than | but independent of 2 would only mean that the “effective albedo"" we infer is in fact equal to (A+€—1)/e and does not affect the radius and inclination retrieval.", An emissivity value $\epsilon$ lower than 1 but independent of $\lambda$ would only mean that the “effective albedo” we infer is in fact equal to $(A+\epsilon -1)/\epsilon$ and does not affect the radius and inclination retrieval. Variation in the emissivity with wavelength (for instance from the 10 jm silicate band). if significant enough to affect the planetary emission in an observable way. would be seen in the variation spectrum just as an absorption. feature due to an atmosphere (see Selsis et al.," Variation in the emissivity with wavelength (for instance from the 10 $\mu$ m silicate band), if significant enough to affect the planetary emission in an observable way, would be seen in the variation spectrum just as an absorption feature due to an atmosphere (see Selsis et al." 2011)., 2011). A correction could thus be done a posteriori (probably yielding larger uncertainties on the retrieval)., A correction could thus be done a posteriori (probably yielding larger uncertainties on the retrieval). The variation in the surface albedo with wavelength influences our model only in terms of emissivity as our model is only sensitive to the bolometric surface albedo (the fraction. of reflected energy integrated over the whole spectrum)., The variation in the surface albedo with wavelength influences our model only in terms of emissivity as our model is only sensitive to the bolometric surface albedo (the fraction of reflected energy integrated over the whole spectrum). We tested our retrieval algorithm that assumes a uniform albedo on phase curves computed with a nonuniform albedo., We tested our retrieval algorithm that assumes a uniform albedo on phase curves computed with a nonuniform albedo. To each individual cell of the surface. we gave a random albedo using a normal distribution.," To each individual cell of the surface, we gave a random albedo using a normal distribution." We did the test for a mean albedo of 0.1. 0.3.....0.9 with a standard deviation of 0.1.," We did the test for a mean albedo of 0.1, 0.3,...,0.9 with a standard deviation of 0.1." Error bars on the retrieved albedo are centered on the mean value of the normal distribution. and the error bars are twice as broad as with a uniform albedo. but there is no noticeable effect on the inclination and radius retrieval.," Error bars on the retrieved albedo are centered on the mean value of the normal distribution, and the error bars are twice as broad as with a uniform albedo, but there is no noticeable effect on the inclination and radius retrieval." We did not test the effect of having large regions with different albedos., We did not test the effect of having large regions with different albedos. An interesting case to be addressed in the future is to consider a surface composition (and thus a surface albedo) changing at à given temperature (and thus incidence angle)., An interesting case to be addressed in the future is to consider a surface composition (and thus a surface albedo) changing at a given temperature (and thus incidence angle). This could be relevant for very hot planets like Corot 7b or Kepler IOb. which have à strong temperature gradient and which may have substellar lava-oceans covering a 0«845° area (?)..," This could be relevant for very hot planets like Corot 7b or Kepler 10b, which have a strong temperature gradient and which may have substellar lava-oceans covering a $0<\theta<45^{\circ}$ area \citep{Leger2011}." Because of its very low thermal inertia and the length of its solar day (~27 days). the temperature distribution on the day side of the Moon is similar to that of a synchronized planet. and brightness temperatures on the day side of the Moon follow the cos(#)1 law. where & is the incidence angle (?)..," Because of its very low thermal inertia and the length of its solar day $\sim 27$ days), the temperature distribution on the day side of the Moon is similar to that of a synchronized planet, and brightness temperatures on the day side of the Moon follow the $\cos(\theta)^{\frac{1}{4}}$ law, where $\theta$ is the incidence angle \citep{Lawson2000}." This means that the isotropic assumption for the emission 1s a good approximation (with no significant effect of roughness and craters). but also that variations on albedo with location are small enough.," This means that the isotropic assumption for the emission is a good approximation (with no significant effect of roughness and craters), but also that variations on albedo with location are small enough." Light reflected by the moon does not. however. follow a Lambertian distribution (the reason the full Moon seems so “flat” to us).," Light reflected by the moon does not, however, follow a Lambertian distribution (the reason the full Moon seems so “flat” to us)." As other rough planetary surfaces with a low albedo. the diffuse reflection is described better by the Lommel-Seeliger law (?).," As other rough planetary surfaces with a low albedo, the diffuse reflection is described better by the Lommel-Seeliger law \citep{Fairbairn2005}." Because of the non-Lambertian behavior of the reflected light (which. can also include a specular component for high albedo). we restricted our work to wavelengths (1>Spm) where the reflected component is orders of magnitude lower than the emission.," Because of the non-Lambertian behavior of the reflected light (which can also include a specular component for high albedo), we restricted our work to wavelengths $\lambda > 5\mu$ m) where the reflected component is orders of magnitude lower than the emission." However. the temperature distribution. and thus the thermal emission. can be affected by the dependence of the surface albedo on the incidence angle 8 found in the Lommel-Seeliger phase function.," However, the temperature distribution, and thus the thermal emission, can be affected by the dependence of the surface albedo on the incidence angle $\theta$ found in the Lommel-Seeliger phase function." We tested the impact of this effect on the thermal phase curve and found it to be insignificant on the phase curve., We tested the impact of this effect on the thermal phase curve and found it to be insignificant on the phase curve. The reason ts that surface temperature is affected only at high incidence angle. near the terminator where the temperature is too low to contribute significantly to the disk-integrated emission.," The reason is that surface temperature is affected only at high incidence angle, near the terminator where the temperature is too low to contribute significantly to the disk-integrated emission." Small departures from an isotropic behavior of the thermal emission do exist on the Moon and other planetary surfaces (due for instance to roughness and craters) but we neglect these effect in this study., Small departures from an isotropic behavior of the thermal emission do exist on the Moon and other planetary surfaces (due for instance to roughness and craters) but we neglect these effect in this study. Knowing that the retrieval of R. A. and i is feasible. it will become necessary to address this question in further works.," Knowing that the retrieval of $R$, $A$, and $i$ is feasible, it will become necessary to address this question in further works." Among the published planets detected by radial velocity and at the time of writing. at least seven are potentially terrestrial objects with characteristics allowing a measurement of the phase variations with JWST orEChO!:: aminimum mass below 20 Ms. an orbital distance within 0.05 AU. and membership in a system closer than 15 pe.," Among the published planets detected by radial velocity and at the time of writing, at least seven are potentially terrestrial objects with characteristics allowing a measurement of the phase variations with JWST or: aminimum mass below 20 $_{\oplus}$, an orbital distance within 0.05 AU, and membership in a system closer than 15 pc." According to estimates (?).. more such planets remain to be found.," According to estimates \citep{Mayor2011}, more such planets remain to be found." Expected detections with 15 pe critically depend on the occurrence of planets around M stars. which is yet poorly constrained7.," Expected detections with 15 pc critically depend on the occurrence of planets around M stars, which is yet poorly constrained." . The occurrence rate as inferred from Kepler candidates (2). shows no decrease (or even a slight increase) from K to MO dwarfs., The occurrence rate as inferred from Kepler candidates \citep{Howard2011} shows no decrease (or even a slight increase) from K to M0 dwarfs. Assuming the same frequency of exoplanets for M and K stars yields hundreds of candidates within 15 pe., Assuming the same frequency of exoplanets for M and K stars yields hundreds of candidates within 15 pc. Within the current sample of seven. three have zero eccentricity (at the precision of the measurements): GJS81 ee and b (?).. and bb," Within the current sample of seven, three have zero eccentricity (at the precision of the measurements): GJ581 e and b \citep{Mayor2009a}, , and b" "215. συ= 4,28) and FSRQs (ay=2.3. oy=049).",", $\sigma_0 = 0.28$ ) and FSRQs $\alpha_0 = 2.3$, $\sigma_0 = 0.19$ )." Thev aIso found that the flaring and quiesceut blazar popula10115 are spectrally cousisteut., They also found that the flaring and quiescent blazar populations are spectrally consistent. Iu PVOs. he shapes of the unresolved exiission were calculaed for the collective blazar population aud BL Lac objects and FSROs.," In PV08, the shapes of the unresolved emission were calculated for the collective blazar population and BL Lac objects and FSRQs." In the cases of the collective popula lonaxl FSROs. the curvatures of the shapes were not euxmel to allow the populations to explain all of the ECRD. though iu the case of BL Lac objects the curvatire was enough to. in principle. allow BL Lac objects to explain the EGRB.," In the cases of the collective population and FSRQs, the curvatures of the shapes were not enough to allow the populations to explain all of the EGRB, though in the case of BL Lac objects, the curvature was enough to, in principle, allow BL Lac objects to explain the EGRB." Uowever. in al CHSCR. the normatlizations of the emission were not deteriined. aud tl| nncertaüiuties in the shapes resulting from the unucertaiuties in the likelihood analvsis are considerable.," However, in all cases, the normalizations of the emission were not determined, and the uncertainties in the shapes resulting from the uncertainties in the likelihood analysis are considerable." Tt sheld be noted that since the PLE aud LDDE GLE inodels do not distinguish between the subpopulatious of blazars. for the purposes of self-cousisteucy. we also do not distinguish between them with regards to their SIDs.," It should be noted that since the PLE and LDDE GLF models do not distinguish between the subpopulations of blazars, for the purposes of self-consistency, we also do not distinguish between them with regards to their SIDs." Thus. for the purposes of this analvsis. we include only the collective blazar population ISID of VPOT(correcting for biases iutroduced in sample a fux-Iiuited catalog).," Thus, for the purposes of this analysis, we include only the collective blazar population ISID of VP07(correcting for biases introduced in sampling a flux-limited catalog)." Notably. has already. provied evidence that BL Lac objects and FSROs are spectrally distinct (Abdo et al.," Notably, has already provided evidence that BL Lac objects and FSRQs are spectrally distinct (Abdo et al." 2009)., 2009). Towever. since the blazar catalog is not vet complete. it is currently premature to construct huninosity functions (especially frose that distinguish betwee1 BE Lac objects and FSRQs) from data.," However, since the blazar catalog is not yet complete, it is currently premature to construct luminosity functions (especially those that distinguish between BL Lac objects and FSRQs) from data." Iu recognizing the importance of correctly treating spectral cistinetious along subpopulations of blazars. we will return o this issue in a future publication.," In recognizing the importance of correctly treating spectral distinctions among subpopulations of blazars, we will return to this issue in a future publication." The lazir contributions to the ECRB as calculated assuis two separate models of the blazar CLF aud several models of the EBL are plotted in Figure 1., The blazar contributions to the EGRB as calculated assuming two separate models of the blazar GLF and several models of the EBL are plotted in Figure 1. The dack lines represent contributions determined assuming he LDDE uodel ofthe blazar GLE. while the οταν lines represent contributions determined assuming the PLE uodel of tie blazar GLE.," The black lines represent contributions determined assuming the LDDE model of the blazar GLF, while the gray lines represent contributions determined assuming the PLE model of the blazar GLF." For comparison. the blazar contributions assuming no absorption (solid lines) aud he Strong et al. (," For comparison, the blazar contributions assuming no absorption (solid lines) and the Strong et al. (" 2001) determination of the EGRET ECGRD (data poiuts with statistical eror bars) are also Xotted.,2004) determination of the EGRET EGRB (data points with statistical error bars) are also plotted. Since the QLEs used. include the iiaxiuimia-ikelibood xuineters determined by NTOG. the blazar contributions comprise ~50% of the overall," Since the GLFs used include the maximum-likelihood parameters determined by NT06, the blazar contributions comprise $\sim 50$ of the overall." s As demonstrated in SS9G aud PVOs. there is considerable curvature in the unresolved blazar emission due to the spread in the blazar SID indicating the Increasing portance of blazars with harder spectral incices at higher.," As demonstrated in SS96 and PV08, there is considerable curvature in the unresolved blazar emission due to the spread in the blazar SID indicating the increasing importance of blazars with harder spectral indices at higher." . The most sviking feature in Fieure 1 is that of the suppression at hieh energies due to the considerable aiuount of absorption bv pair production iuteractions with EBL photous., The most striking feature in Figure 1 is that of the suppression at high energies due to the considerable amount of absorption by pair production interactions with EBL photons. Certain EBL ποσο] are quite distinewishable from he others., Certain EBL models are quite distinguishable from the others. Most notably. the Ixuciske et al. (," Most notably, the Kneiske et al. (" 20013 high: UV inodcel aud the Stecker et al. (,2004) high UV model and the Stecker et al. ( 200€ji) iiodel predict a greater degree of absorption thau the other three uodels.,2006) model predict a greater degree of absorption than the other three models. This is due to the fact that the Isneiske high UV model aud the Stecker model predict a higher amount of UW background radiation than the others., This is due to the fact that the Kneiske high UV model and the Stecker model predict a higher amount of UV background radiation than the others. " Since he pair production cross section asa fuuction of the center-ofinass οσον peaks at the elecron lnass, one would expect that gauuna-rav pliotous of energv ~ tens of GeW are most likely to interact wih UV backeround photons."," Since the pair production cross section as a function of the center-of-mass energy peaks at the electron mass, one would expect that gamma-ray photons of energy $\sim$ tens of GeV are most likely to interact with UV background photons." Thus. uusurxidunglv. mcls with high UV backerounds will result 1n more suppression at high energies.," Thus, unsurprisingly, models with high UV backgrounds will result in more suppression at high energies." Anotlier striking observation frou Figure is that the hiel-energv suppressious for the PLE nodel are consistently steeper than those of the LDDE model., Another striking observation from Figure 1 is that the high-energy suppressions for the PLE model are consistently steeper than those of the LDDE model. The cüffereut appearaices of the features can be explained by considering that the blazar GLF is the distribution of blazirs in hpuuimositv aud redshift space., The different appearances of the features can be explained by considering that the blazar GLF is the distribution of blazars in luminosity and redshift space. Since the PLE model siIppressious are steeper than those of the LDDE model. «mie would couclide that high-redshift blazars," Since the PLE model suppressions are steeper than those of the LDDE model, one would conclude that high-redshift blazars" The ll vear solar magnetic evele is. driven. bv a hvdromagnetic dynamo.,The 11 year solar magnetic cycle is driven by a hydromagnetic dynamo. Llowever. the exact nature of this dynamo mechanism is still not. fully understood. and there are several scenarios that seek to explain the observed behaviour.," However, the exact nature of this dynamo mechanism is still not fully understood, and there are several scenarios that seek to explain the observed behaviour." The well-known “interface” dvnamo model (Parker1993)... is based on the idea that the dvnamo operates in a region that stracelles the base of the solar convection zone and the stably stratified: region that lies beneath (forsomerecentreviewsseeOssendri- 2008).," The well-known “interface” dynamo model \citep{Parker}, is based on the idea that the dynamo operates in a region that straddles the base of the solar convection zone and the stably stratified region that lies beneath \citep[for some recent reviews see][]{Ossendrijver, mp06, Dormy, silvers08}." . Although this is a conceptually appealing moclel for the solar dynamo. the only numerical investigations of the interface dynamo have been. based: upon mean-field dvnamo theory (see.forexample.Charbonneau&Alac-Liao.Schubert2004:Bushby 2006).," Although this is a conceptually appealing model for the solar dynamo, the only numerical investigations of the interface dynamo have been based upon mean-field dynamo theory \citep[see, for example,][]{Char,Chan,Zhang,Bushby}." .. In. mean-ficled theory. several aspects of the dynamo model (particularly the effects of turbulent convection) are. parametrised.," In mean-field theory, several aspects of the dynamo model (particularly the effects of turbulent convection) are parametrised." However. the resulting cocllicicnts are poorly determined by both theory and observations.," However, the resulting coefficients are poorly determined by both theory and observations." Due to the computational costs involved. it has not vet. been. possible to demonstrate the operation of the interface dynamo by carrving out. three-dimensional simulations of compressible magnetohvdrodynamies.," Due to the computational costs involved, it has not yet been possible to demonstrate the operation of the interface dynamo by carrying out three-dimensional simulations of compressible magnetohydrodynamics." Given these computational constraints. it makes sense to investigate dillerent components of the interface dvnamo in isolation.," Given these computational constraints, it makes sense to investigate different components of the interface dynamo in isolation." An important feature. of the region below the solar convection zone is the solar tachocline (seeSpiegel&Zahnences therein).. which takes the form of an intense racial eradient of the solar cdillerential rotation.," An important feature of the region below the solar convection zone is the solar tachocline \citep[see][and references therein]{SZ,CT}, which takes the form of an intense radial gradient of the solar differential rotation." At the heart of the interlace dyvnamo scenario is the idea that weak ;xoloidal magnetic fields can be amplified by the intense shears in the tachocline. leading to the production of strong oroidal (azmümuthal) magnetic fields.," At the heart of the interface dynamo scenario is the idea that weak poloidal magnetic fields can be amplified by the intense shears in the tachocline, leading to the production of strong toroidal (azmimuthal) magnetic fields." In the standard interface dynamo model. these poloidal magnetic fields are owoduced in the convection zone. and are pumped. down into the tachocline by the [uid motions (TobiasοἱaL.1998. 2001).," In the standard interface dynamo model, these poloidal magnetic fields are produced in the convection zone, and are pumped down into the tachocline by the fluid motions \citep{TBCT1,TBC2}." . In. flux transport dvnamo models. these poloidal ields are transported from the surface (to the tachocline region) bv a meridional circulation. (see.e.g..Dikpati&Gilman 2009).," In flux transport dynamo models, these poloidal fields are transported from the surface (to the tachocline region) by a meridional circulation \citep[see, e.g.,][]{DG09}." . Wherever the poloidal field is generated. a mechanism is needed to produce Εαν structures that. rise through the convection zone to the surface. where they," Wherever the poloidal field is generated, a mechanism is needed to produce flux structures that rise through the convection zone to the surface, where they" "is in excellent agreement with our spectroscopic value of 470.0+ 2.7km/s. As an additional test of the photometric parameters, we measured the rotational broadening of the donor star Vyot following the method detailed in ?..","is in excellent agreement with our spectroscopic value of $470.0 \pm 2.7$ km/s. As an additional test of the photometric parameters, we measured the rotational broadening of the donor star $V_{rot}$ following the method detailed in \citet{Marsh94}." " Using the model fit detailed in Section 3.1,, we applied an offset to each spectrum to remove the orbital variation and then averaged the spectra."," Using the model fit detailed in Section \ref{sec:nir}, we applied an offset to each spectrum to remove the orbital variation and then averaged the spectra." " We then applied an artificial rotational broadening to the spectrum of a template star, and subtracted the result, multiplied by a constant representing the fraction of flux in the donor star, from the averaged OY Car spectrum."," We then applied an artificial rotational broadening to the spectrum of a template star, and subtracted the result, multiplied by a constant representing the fraction of flux in the donor star, from the averaged OY Car spectrum." " The constant was varied to optimise the subtraction, and the x? difference between the residual spectrum and a smoothed version of itself is computed."," The constant was varied to optimise the subtraction, and the $\chi^2$ difference between the residual spectrum and a smoothed version of itself is computed." This process was repeated for a range of rotational broadenings., This process was repeated for a range of rotational broadenings. By comparing our spectra with the spectroscopic sequence presented in ? we identify the donor in OY Car to be a late M-dwarf (M8/M9) or possibly an early T-dwarf., By comparing our spectra with the spectroscopic sequence presented in \citet{Cushing05} we identify the donor in OY Car to be a late M-dwarf (M8/M9) or possibly an early T-dwarf. " We rule out an earlier type M-dwarf since in these stars the K features are weaker, and there are a number of Fe absorption lines of comparable strength around the AA 11690, 11772 ddoublet which we do not observe in our OY Car spectra."," We rule out an earlier type M-dwarf since in these stars the K features are weaker, and there are a number of Fe absorption lines of comparable strength around the $\lambda \lambda$ $11690$, $11772$ doublet which we do not observe in our OY Car spectra." " We therefore used used LHS 2021 and LHS 2065 as our template stars, which are of spectral type M8 and M9 respectively."," We therefore used used LHS 2021 and LHS 2065 as our template stars, which are of spectral type M8 and M9 respectively." An additional input parameter is the limb darkening coefficient for the donor star., An additional input parameter is the limb darkening coefficient for the donor star. " ? listed limb darkening coefficients for low massstars, and from these tables we find a value of t»c0.6 — 0.7 is an appropriate J-band coefficient for the donor."," \citet{Claret98} listed limb darkening coefficients for low massstars, and from these tables we find a value of $u_{2} \sim 0.6$ – $0.7$ is an appropriate $J$ -band coefficient for the donor." We plot in Figure 4 the resulting x? curves for uo 0.6., We plot in Figure \ref{fig:broaden} the resulting $\chi^2$ curves for $u_2 = 0.6$ . The minima of these curves give our preferred values of, The minima of these curves give our preferred values of experiments.,experiments. Extrapolation to the hieh Revnolds numbers of protoplanetary clisks implies concentration of chondrules by [actors of wp to LO? (Cuzzefal.2001)., Extrapolation to the high Reynolds numbers of protoplanetary disks implies concentration of chondrules by factors of up to $10^5$ \citep{cuz01}. . However. (hese estimates do not take into account the redispersal of the concentrated pockets of solids if the turbulent edcdies are intermittent and do not maintain fixed centers. (," However, these estimates do not take into account the redispersal of the concentrated pockets of solids if the turbulent eddies are intermittent and do not maintain fixed centers. (" 2) Similarly. disk vortices could concentrate chondrules as well. but they are more effective for meter sized bodies (delaFuenteMarcos&Barge2001).,"2) Similarly, disk vortices could concentrate chondrules as well, but they are more effective for meter sized bodies \citep{fmb01}." . There also remains the issue whether vortices will rise spontaneously in protoplanetary disks if there are no natural stirring mechanisms. (, There also remains the issue whether vortices will rise spontaneously in protoplanetary disks if there are no natural stirring mechanisms. ( 3) secular instabiliGes associated with gas drag might concentrate particulates. even without sell-gravitv (Goodman&Pindor2000).,"3) Secular instabilities associated with gas drag might concentrate particulates, even without self-gravity \citep{gp00}." ". Goodman and Pindor assumed that gas crag acts collectively on a particulate ""sheet. a valid approximation when turbulent. wakes overlap."," Goodman and Pindor assumed that gas drag acts collectively on a particulate “sheet”, a valid approximation when turbulent wakes overlap." Unfortunately. wake overlap seems unlikely unless (he particles are [aivly closely packed. in which case GI would already. be effective.," Unfortunately, wake overlap seems unlikely unless the particles are fairly closely packed, in which case GI would already be effective." In a related context. Ward(1976). has shown in an underappreciated study that viscous drag modilies the standard GI criterion through the introduction of an addiGonal instability that can occur at values of GQ>>1.," In a related context, \citet{war76} has shown in an underappreciated study that viscous drag modifies the standard GI criterion through the introduction of an additional instability that can occur at values of $Q \gg 1$." However. this additional instability. being secular in nature. has a much smaller growth rate than the usual Goldreich-Ward mechanism. (," However, this additional instability, being secular in nature, has a much smaller growth rate than the usual Goldreich-Ward mechanism. (" 4) In relsecidiilft.. we develop the simplest concentration mechanism for particulates: radial migration due to gas drag.,"4) In \\ref{sec:drift}, we develop the simplest concentration mechanism for particulates: radial migration due to gas drag." The fundamental assumptions required lor the results of this paper are (he existence. al some epoch of the disk's evolution. of (1) relatively quiescence in (he midplane regions. even (hough the surface lavers may be undergoing active accretion (Gamunie1996).. and (2) compact solids with chondrule-like properties (hat are well. but not perlectly. coupled to the eas (hrough mutual drag.," The fundamental assumptions required for the results of this paper are the existence, at some epoch of the disk's evolution, of (1) relatively quiescence in the midplane regions, even though the surface layers may be undergoing active accretion \citep{gam96}, and (2) compact solids with chondrule-like properties that are well, but not perfectly, coupled to the gas through mutual drag." " Under these conditions. we argue (1) that vertical shear can only induce a level of nidplane turbulence that has limited ability to stir solids. with the critical value of the surface density of solids being given roughly by X,~rp; and (2) that gas drag alone can ead to a globalradial redistribution of solids so that the local surface density ο solids. X. can exceed the critical value. ©)..."," Under these conditions, we argue (1) that vertical shear can only induce a level of midplane turbulence that has limited ability to stir solids, with the critical value of the surface density of solids being given roughly by $\Sigma_{\rm p,c} \sim \eta r \rho_{\rm g}$; and (2) that gas drag alone can lead to a global redistribution of solids so that the local surface density of solids, $\Sigma_{\rm p}$, can exceed the critical value, $\Sigma_{\rm p,c}$." Therelore. whether a recycling of solids occus by the N-wind nechanism or a racial redistribution of solids occurs by simple gas drag. we conclude that the planet-Iorming zones of (he primitive solar svstem can achieve (he requisite conditions for the ormation of planetesimals on a time scale comparable to the typical lifetime. ~3x10° vr. that has been inferred for the disks of T Tauri stars (Halsch.Lada.&Lada2001).," Therefore, whether a recycling of solids occurs by the X-wind mechanism or a radial redistribution of solids occurs by simple gas drag, we conclude that the planet-forming zones of the primitive solar system can achieve the requisite conditions for the formation of planetesimals on a time scale comparable to the typical lifetime, $\sim 3\times 10^6$ yr, that has been inferred for the disks of T Tauri stars \citep{hll01}." . ILowever. the margin for success is not large. ancl it could be that planet formation is a less universal phenomenon than it has been widely touted to be. aud that it has a much greater diversity of outcomes (including a complete failure to form any. planets) than suspected prior to the discovery of extrasolar planets (Alavor and Queloz 1996. Marey. and Butler 1998).," However, the margin for success is not large, and it could be that planet formation is a less universal phenomenon than it has been widely touted to be, and that it has a much greater diversity of outcomes (including a complete failure to form any planets) than suspected prior to the discovery of extrasolar planets (Mayor and Queloz 1996, Marcy and Butler 1998)." Indeed.," Indeed," cosmological halos we would exr and so jx(£7.,cosmological halos we would $v\propto r$ and so $j \propto r^2$. " As such. since rr, the second term in the above will be negligible ancl non-circular orbits. the problem. becomes more complicated."," As such, since $r\ll r^\prime$, the second term in the above will be negligible and For non-circular orbits, the problem becomes more complicated." Por The maximum energy changes depends onthe value of \ al which apocentee and pericentre occur. and on the of the orbit.," The maximum energy changes depends onthe value of $\chi$ at which apocentre and pericentre occur, and on the shape of the orbit." Experiments Using elliptical orbits ol eecentshapenetty c show that using (he ο axis in place ofr and is. à reasonable approximation. (better than 20%))EE for OS., Experiments using elliptical orbits of eccentricity $e$ show that using the semi-major axis in place of $r$ and is a reasonable approximation (better than ) for $e<0.8$. Applicationto the. more complex orbits found. in. tvpicaltreatment darkis matter halos is deferred to a future paper., Application to the more complex orbits found in typical dark matter halos is deferred to a future paper. As such. we will ignore any dependence of h1(£) on orbital shape A3 Final work.," As such, we will ignore any dependence of $h_1(\xi)$ on orbital shape in this work." " s ⋅ rotating frame. the ⊀particle experiences an CoriolisAbe 2 orce(5) aclelitic to ththe tidalidal force.for which canc: |x of4 whereTUE :h,(£) additioncomparable.arable magnitude."," In the rotating frame, the particle experiences a Coriolis force in addition to the tidal force, which can be of comparable magnitude." "AON]* ""DhisΕις resultsres in sip:à torque,. For circular orbits rev=0. so Note that vector Q is normal tor’."," This results in a torque For circular orbits ${\bf r}\cdot{\bf v}=0$, so Note that vector $\mathbf{\Omega}$ is normal to ${\bf r}^\prime$." Defining angle as a measure of the rotation of the normal to the orbital plane around r with 7=0 corresponding to the plane containing r/ and Q we have The changeὃν in angularo momentum cue to the Coriolis force is then Projecting this onto our basis vectors we find where we have used 6=jofr and Q= vr., Defining angle $\gamma$ as a measure of the rotation of the normal to the orbital plane around ${\bf r}^\prime$ with $\gamma=0$ corresponding to the plane containing ${\bf r}^\prime$ and $\mathbf{\Omega}$ we have The change in angular momentum due to the Coriolis force is then Projecting this onto our basis vectors we find where we have used $v=j_0/r$ and $\Omega = v^\prime/r^\prime$ . Alternatively. Note that. for cosmological halos. we expect characteristic properties of halos of different masses to obey bxr.," Alternatively, Note that, for cosmological halos, we expect characteristic properties of halos of different masses to obey $v\propto r$." As such. we Lind guiax(7£r).," As such, we find $g_{\rm tidal} \propto (r^\prime/r)^4$." H can then be seen that the change in angular momentum due to the tidal force and the Coriolis force are of comparable magnitude., It can then be seen that the change in angular momentum due to the tidal force and the Coriolis force are of comparable magnitude. " We can compute the functions /,(£) and h»(£) when the Coriolis torque is included. by averaging over angle 5."," We can compute the functions $h_1(\xi)$ and $h_2(\xi)$ when the Coriolis torque is included, by averaging over angle $\gamma$." The results for hí1(£) is shown as a dashed line in Fig. Al, The results for $h_1(\xi)$ is shown as a dashed line in Fig. \ref{fig:hxi}. We find that the inclusion of the Coriolis torque significantIv alters Ai() (by up to a factor of around. 2)., We find that the inclusion of the Coriolis torque significantly alters $h_1(\xi)$ (by up to a factor of around 2). We therefore choose to include the Coriolis term in all calculations carried out in this work., We therefore choose to include the Coriolis term in all calculations carried out in this work. The case of non-circular orbits including Coriolis torques becomes significantly more complicated. and a full deferred⊀ to⋅⋅⋅ aMP future paper., The case of non-circular orbits including Coriolis torques becomes significantly more complicated and a full treatment is deferred to a future paper. . ο. κ. ⊀can . ⋅ ∐↥∢⊾∐⊔⋜↧↓⊳∖↿⋜⋯⊾⊔↓∢⊾⊔⇂↓⊳∖↿↓⋯↿⇂↓↥∢⊾≼⇍↓↕⋜⋯⋏∙≟∢⋅↓⊔⋖⋅⊔⋖⋅↓⋅⋏∙≟∙∖⇁∪⇂⇂↓↕∢⊾ particle be approximated. by A2 Coriolis is computed. :with the inclusion.: of the⋅for in CoriolisRN torque. term as shown in. Fig.S Αι. E, The final statement is that the change in energy of the particle can be approximated by where $h_1(\xi)$ is computed with the inclusion of the Coriolis torque term as shown in Fig. \ref{fig:hxi}. . HThus. the maximum energy of a particle relative to the satellite centre isli ]t isthis value of Zi which is used in eqn. (10)).," Thus, the maximum energy of a particle relative to the satellite centre is It isthis value of $E_{\rm max}$ which is used in eqn. \ref{eq:mloss}) )." void centres.,void (right) centres. " From bottom to top, the lines correspond to bins of (right)increasing local density; each line connects the results for samples with equal median IVD."," From bottom to top, the lines correspond to bins of increasing local density; each line connects the results for samples with equal median IVD." " The errorbars are calculated using the jacknife method, which has been shown to provide robust estimates of errors comparable to what is expected from sample variance (Padilla, Ceccarelli Lambas, 2005; all errors quoted in the remainder of this work are computed using this technique)."," The errorbars are calculated using the jacknife method, which has been shown to provide robust estimates of errors comparable to what is expected from sample variance (Padilla, Ceccarelli Lambas, 2005; all errors quoted in the remainder of this work are computed using this technique)." " As the figure shows, there is a clear dependence of the abundance of red galaxies on the large-scale environment, with different significance levels depending on the local density cut."," As the figure shows, there is a clear dependence of the abundance of red galaxies on the large-scale environment, with different significance levels depending on the local density cut." " In particular, the effect of a changing red galaxy fraction is weaker as a function of the distance to the void centres (it is significant at a 2.89c between Ry; and Ryo for the lowest local densities)."," In particular, the effect of a changing red galaxy fraction is weaker as a function of the distance to the void centres (it is significant at a $2.89\sigma$ between $R_{V1}$ and $R_{V2}$ for the lowest local densities)." " Before describing in detail these effects, we construct new galaxy samples based on a selection of host halo masses and IVDs."," Before describing in detail these effects, we construct new galaxy samples based on a selection of host halo masses and IVDs." This will help the interpretation of the variations in the red fractions with the global environment., This will help the interpretation of the variations in the red fractions with the global environment. " We measure the mass function of the host haloes of the galaxies in each sample selected to local and that as we include accordingsatellite both,galaxies, some of globalthe densityhaloes will (noticebe repeated) and new samples of taken at random from the simulation producebox so that the mass galaxiesfunctions and local IVD densities of the original samples are reproduced."," We measure the mass function of the host haloes of the galaxies in each sample selected according to both, local and global density (notice that as we include satellite galaxies, some of the haloes will be repeated) and produce new samples of galaxies taken at random from the simulation box so that the mass functions and local IVD densities of the original samples are reproduced." Notice that these new samples do not include restrictions on their environment., Notice that these new samples do not include restrictions on their global environment. " The measured mass functions are shown in global7,, and will be discussed in more detail later in this section."," The measured mass functions are shown in Figure \ref{fig:fig5}, and will be discussed in more detail later in this section." We Figureuse these random galaxy subsamples to determine what changes are to be expected in the red fraction from variations in the local density and galaxymass functions., We use these random galaxy subsamples to determine what changes are to be expected in the red galaxy fraction from variations in the local density and underlying mass functions. " We make the comparison between random and underlyingoriginal samples in Figure 5 and solid lines, "," We make the comparison between random and original samples in Figure \ref{fig:fig4} (dashed and solid lines, respectively)." "As can be seen, by comparing the (dashedadjacent dashed and solid respectively).lines, most of the large-scale modulation of red galaxy fractions (solid lines) is produced by variations in the underlying mass functions, as was suggested by Ceccarelli,Padilla&Lam-bas(2008) in their detection of this effect around voids in the SDSS."," As can be seen, by comparing the adjacent dashed and solid lines, most of the large-scale modulation of red galaxy fractions (solid lines) is produced by variations in the underlying mass functions, as was suggested by \citet{cec} in their detection of this effect around voids in the SDSS." " However, in particular for the low local density samples (lowermost sets of lines), there are some effects that cannot be completely reproduced by the random samples with matching masses and local IVD densities."," However, in particular for the low local density samples (lowermost sets of lines), there are some effects that cannot be completely reproduced by the random samples with matching masses and local IVD densities." " The detailed results from Figure 5 can be summarised as follows,"," The detailed results from Figure \ref{fig:fig4} can be summarised as follows," orbital solutions.,orbital solutions. The RV cata are given in Table 1.. while parameters of the orbital solutions are listed in Table 2..," The RV data are given in Table \ref{tab1}, while parameters of the orbital solutions are listed in Table \ref{tab2}." For most stars we used the primary eclipse predictions Irom the Cracow on-line database (Ixreinerοἱal.2001:Kreiner2004)2006.," For most stars we used the primary eclipse predictions from the Cracow on-line database \citep{kreiner2001,kreiner2004}." .. These predictions can be restored. from the observed times of conjunctions (75) and the observed. predicted deviations ο— ο as given in Table 2..," These predictions can be restored from the observed times of conjunctions $T_0$ ) and the observed predicted deviations $O-C$ , as given in Table \ref{tab2}." " ο Ant (IHIP. 46810. ILD 82610) with Vina,=6.29 is one the brightest contact binaries (his and the following estimates of Visa, were obtained from the Hipparcos magnitudes applving color dependent corrections 77,— V)."," S Ant (HIP 46810, HD 82610) with $V_{\rm max}=6.29$ is one the brightest contact binaries (this and the following estimates of $V_{\rm max}$ were obtained from the Hipparcos magnitudes \citep{hip} applying color dependent corrections $H_p - V$ )." As its name implies. it is one of the first variable stars recognized as such in the southern hemisphere.," As its name implies, it is one of the first variable stars recognized as such in the southern hemisphere." " ο Ant has been a frequent target of photometric observations. but the only previous spectroscopic observations were by Popper(1956). who saw only one component with km ! and A,=92.3z1.5 kms !."," S Ant has been a frequent target of photometric observations, but the only previous spectroscopic observations were by \citet{popper56} who saw only one component with $V_0=-1.2 \pm 1.0$ km $^{-1}$ and $K_1=92.3 \pm 1.5$ km $^{-1}$." In contrast. we could easily detect. the secondary component in the broadening functions (DES). as shown in Figure 1..," In contrast, we could easily detect the secondary component in the broadening functions (BFs), as shown in Figure \ref{fig1}." The velocity is very different from that observed previously. as are bot semi-amiplitudes dy; (Table 2)).," The center-of-mass velocity is very different from that observed previously, as are both semi-amplitudes $K_i$ (Table \ref{tab2}) )." Russoetal.(1982). encountered some cilficullies with producing a contact moclel for the binary suggesting possible problems with Popper's spectroscopic data., \citet{russo82} encountered some difficulties with producing a contact model for the binary suggesting possible problems with Popper's spectroscopic data. " They derived the mass ratio qi=0.592:0.02. which differs substantially from our ga,0200.03."," They derived the mass ratio $q_{\rm ph}=0.59 \pm 0.02$, which differs substantially from our $q_{\rm sp}=0.33 \pm 0.02$." This is not surprising for a partially eclipsing svstem wilh a leatureless light curve. for which a photometricallv derived mass ratio is notoriously unreliable.," This is not surprising for a partially eclipsing system with a featureless light curve, for which a photometrically derived mass ratio is notoriously unreliable." We note that our bootstrap errors of A; are (uite large. primarily due to the small number rather than (the low accuracy of individual observations: these uncertainty estimates are more realistic than the formal least-squares errors.," We note that our bootstrap errors of $K_i$ are quite large, primarily due to the small number – rather than the low accuracy – of individual observations; these uncertainty estimates are more realistic than the formal least-squares errors." The moment of the minimum as given in Table 2 agrees perfectly. well with the Cracow ephemerice given in reineretal.(2001) on the assumption that the trend indicated by ihe ο—C' diagram has continued and reached 0.060 day. at the time of our observations.," The moment of the minimum as given in Table \ref{tab2} agrees perfectly well with the Cracow ephemeride given in \citet{kreiner2001} on the assumption that the trend indicated by the $O-C$ diagram has continued and reached $+0.060$ day at the time of our observations." This value is uncertain and requires confirmation by photometric observations., This value is uncertain and requires confirmation by photometric observations. Judging by the light curve HromIHipparcos). the current radial velocity data ancl the shapes of the DEs. S Ant is a very typical A-type contact binary.," Judging by the light curve fromHipparcos), the current radial velocity data and the shapes of the BFs, S Ant is a very typical A-type contact binary." Hs spectral tvpe is F3V (IIDII) which agrees with 2B—WV=0.30 from Hogetal. (2000)., Its spectral type is F3V (HDH) which agrees with $B-V=0.30$ from \citet{tycho2}. . . Its orbit almost certainlydoes not have any eccentricity. so its inclusion among early-type stars with potentially e40 ," Its orbit almost certainlydoes not have any eccentricity, so its inclusion among early-type stars with potentially $e \ne 0$ " luminosity of the diffuse emission is Lx=4.5x1036 erg S.,luminosity of the diffuse emission is $L_{\rm X} = 4.5 \times 10^{36}$ erg $^{-1}$. Previous X-ray analysis of 30 Doradus was reported by ?? for a different set of observations (ObsIDs 22and 62520) totalling ~24 ks.," Previous X-ray analysis of 30 Doradus was reported by \cite{townsley1,townsley2} for a different set of observations (ObsIDs 22and 62520) totalling $\sim$ 24 ks." " By fitting the X-ray spectra of many diffuse regions across 30 Doradus, they found best-fit absorbing columns of Ny=1—6x10?! cm-?, temperatures of kTx~ 0.3-0.9 keV, and absorption-corrected luminosities (0.5-2.0 keV) of logLx= 34.2-37.0 erg s~!."," By fitting the X-ray spectra of many diffuse regions across 30 Doradus, they found best-fit absorbing columns of $N_{\rm H} = 1-6 \times 10^{21}$ $^{-2}$, temperatures of $kT_{\rm X} \sim$ 0.3–0.9 keV, and absorption-corrected luminosities (0.5–2.0 keV) of $L_{\rm X} =$ 34.2–37.0 erg $^{-1}$." " Thus, our values are fairly consistent with those of Townsley et al."," Thus, our values are fairly consistent with those of Townsley et al." " To assess how feedback varies spatially across 30 Doradus, we separate the source into 441 regions (see Figure 5))."," To assess how feedback varies spatially across 30 Doradus, we separate the source into 441 regions (see Figure \ref{fig:regions}) )." " The area of the individual regions was selected to ensure sufficient signal-to-noise across the analyzed wavebands; we chose the width of the regions (35""z« 8 pc on a side, at a distance D= 50 kpc to the to match the HST PC image of R136 so that we LMC)could use their [μοι value and not have to (?),,resolve the individual point sources in the crowded R136 cluster."," The area of the individual regions was selected to ensure sufficient signal-to-noise across the analyzed wavebands; we chose the width of the regions $\approx$ 8 pc on a side, at a distance $D =$ 50 kpc to the LMC) to match the HST PC image of R136 \citep{mal94}, so that we could use their $L_{\rm bol}$ value and not have to resolve the individual point sources in the crowded R136 cluster." The number and position of our 441 regions was determined by the field-of-view and orientation of the 3-cm radio and X-ray data., The number and position of our 441 regions was determined by the field-of-view and orientation of the 3-cm radio and X-ray data. Figure 5 shows the Η-α image with all the resulting regions overplotted., Figure \ref{fig:regions} shows the $\alpha$ image with all the resulting regions overplotted. " To ascertain the dynamical importance of the feedback processes, we compute the pressures for each region using the methods and relations described below."," To ascertain the dynamical importance of the feedback processes, we compute the pressures for each region using the methods and relations described below." " Since protostellar outflows are only important dynamically in low-mass star clusters we do not expect them to play a big role in 30 Doradus,(?),, and we will not consider them in the rest of the text."," Since protostellar outflows are only important dynamically in low-mass star clusters \citep{matzner07}, we do not expect them to play a big role in 30 Doradus, and we will not consider them in the rest of the text." The light output by stars produces a direct radiation pressure that is associated with the photons’ energy and momentum., The light output by stars produces a direct radiation pressure that is associated with the photons' energy and momentum. " The resulting radiation pressure P4;, at some position within the HII region is related to the bolometric luminosity of each star Lys; and the distance r the light traveled to reach that point: where the summation is over all the stars in the field.", The resulting radiation pressure $P_{{\rm dir}}$ at some position within the HII region is related to the bolometric luminosity of each star $L_{\rm bol}$ and the distance $r$ the light traveled to reach that point: where the summation is over all the stars in the field. " In $5.2, we describe an alternative definition of radiation pressure and compare the results from each case."," In $\S$ 5.2, we describe an alternative definition of radiation pressure and compare the results from each case." 'The above relation assumes that the stellar radiation are not attenuated by dust., The above relation assumes that the stellar radiation are not attenuated by dust. " In $ 3.2, we calculate separately the radiation pressure associated with the light absorbed by dust usingSpitzer IR. photometry."," In $\S$ \ref{sec:PIR}, , we calculate separately the radiation pressure associated with the light absorbed by dust using IR photometry." " Given that our results show that Pa;>>Pig generally (see 8 4)), the assumption that the emitted Lpoj is unattenuated seems reasonable."," Given that our results show that $P_{\rm dir} \gg P_{\rm IR}$ generally (see $\S$ \ref{sec:results}) ), the assumption that the emitted $L_{\rm bol}$ is unattenuated seems reasonable." " In order to obtain the bolometric luminosities of the massive stars in 30 Doradus, we utilize the UBV photometric data described in 82.1."," In order to obtain the bolometric luminosities of the massive stars in 30 Doradus, we utilize the UBV photometric data described in $\S$ 2.1." " To simplify the calculation, we assume the bolometric luminosity of R136 obtained by ? originates from the point in the middle of the central region marked with the red X in Fig. 5.."," To simplify the calculation, we assume the bolometric luminosity of R136 obtained by \cite{mal94} originates from the point in the middle of the central region marked with the red X in Fig. \ref{fig:regions}." " For the stars located outside R136 within a few arcminutes, the ? catalog only includes the apparent UBV magnitudes and colors."," For the stars located outside R136 within a few arcminutes, the \cite{parker1} catalog only includes the apparent UBV magnitudes and colors." " Therefore, we follow the procedure outlined by ? to obtain absolute bolometric magnitudes of the 1264 stars in the ? catalog that are not in the ? sample."," Therefore, we follow the procedure outlined by \cite{parker2} to obtain absolute bolometric magnitudes of the 1264 stars in the \cite{parker1} catalog that are not in the \cite{selman05} sample." " For the 7697 stars in the ? catalog that lie outside the field of the ? data, we use their published values for the stars’ absolute bolometric magnitudes."," For the 7697 stars in the \cite{selman05} catalog that lie outside the field of the \cite{parker1} data, we use their published values for the stars' absolute bolometric magnitudes." " Thus, in total, we calculate the bolometric luminosities Lyogj of the R136 cluster and 8961 other stars in 30 Doradus."," Thus, in total, we calculate the bolometric luminosities $L_{\rm bol}$ of the R136 cluster and 8961 other stars in 30 Doradus." " For each of the 441 regions, we sum these 8962 terms in Equation 1,, where r corresponds to the projected distance from the 8962 stars’ positions to theregion center."," For each of the 441 regions, we sum these 8962 terms in Equation \ref{eq:Pdir}, , where $r$ corresponds to the projected distance from the 8962 stars' positions to theregion center." " In this manner, we compute the radiation presure ""felt! by the 441 regions from all of the starlight in 30 Doradus."," In this manner, we compute the radiation presure 'felt' by the 441 regions from all of the starlight in 30 Doradus." thus observed in dillerent spectral/intensity states as inferred. from the hardness intensity shown in 1l.,thus observed in different spectral/intensity states as inferred from the hardness intensity diagram shown in Fig. , 1. Phe elobal trend is that in the count rate diagramregime. the spectrumFie. is soft ancl cuts olf around 0 keV. highestwhereas for the lowest count rates. the is much harder and takes a power law shape in the PCA spectrumenergy with no observable cutolls approximatelybelow ~20 keV. X paper devoted to the rangespectral analysis of the persistent emission ofthe source will be published elsewhere (Bloser et al.," The global trend is that in the highest count rate regime, the spectrum is soft and cuts off around 10 keV, whereas for the lowest count rates, the spectrum is much harder and takes approximately a power law shape in the PCA energy range with no observable cutoffs below $\sim 20$ keV. A paper devoted to the spectral analysis of the persistent emission of the source will be published elsewhere (Bloser et al." 1998)., 1998). ‘To study the ~ 100-1200 LIz variability of the N-rav emission. we used xh the 122 prs Levent mode and the so-called: (0.95558) high ime resolution PCA cata.," To study the $\sim$ 100-1200 Hz variability of the X-ray emission, we used both the 122 $\mu$ s Event mode and the so-called $\mu$ s) high time resolution PCA data." Each continuous set (bursts filtered out) was divided into segments of 4096 bins lasting 250 ys. Fast Fourier “Transform (FEE) were on cach segment., Each continuous set (bursts filtered out) was divided into segments of 4096 bins lasting 250 $\mu$ s. Fast Fourier Transform (FFT) were computed on each segment. 200 of these FET were then averaged to obtain a computed.final Power Density Spectrum (PDS)., 200 of these FFT were then averaged to obtain a final Power Density Spectrum (PDS). The analysis ws been carried out in the 5-30 keV band. where we have found that the to noise ratio of the LLEC(D'Os was maximum.," The analysis has been carried out in the 5-30 keV band, where we have found that the signal to noise ratio of the HFQPOs was maximum." signalWe have detected. above the 5m level. Os from4U1915-05 in 5 observations (see Table 1).," We have detected, above the $5\sigma$ significance level, HFQPOs from in 5 observations (see Table 1)." The significancestatistical ΕΠΟsignificance of he signals ranges from 5 to ~1θσ., The statistical significance of the signals ranges from 5 to $\sim 10\sigma$. In some observations. (e.&. September 6th. 1996). the HFQPOs could also be detected in short (~2000ο000 seconds) segments of the observation.," In some observations, (e.g. September 6th, 1996), the HFQPOs could also be detected in short $\sim 2000-3000$ seconds) segments of the observation." The three strongest ΕΟΟ signals are shown in Fie., The three strongest HFQPO signals are shown in Fig. 2., 2. Unfortunately. the weakness of the does not allow to the IMS of the as a function of signalsenergy.," Unfortunately, the weakness of the signals does not allow to study the RMS of the HFQPOs as a function of energy." Nevertheless in the studyMay 23rd observation. there HEODPOsmay be a positive correlation," Nevertheless in the May 23rd observation, there may be a positive correlation" in carbon grain formation when k1 is reduced to 0.110M (N—1).,"in carbon grain formation when k1 is reduced to $0.1\,\,10^{-10}$ (N=1)." Other parameters have moderate impact., Other parameters have moderate impact. Note that. in case N=1. the vield of CO has not diminished. and even increased somewhat. although Cll is an important factor of CO production through reaction 140 (Table 1).," Note that, in case N=1, the yield of CO has not diminished, and even increased somewhat, although CH is an important factor of CO production through reaction 140 (Table 1)." This is because other quite efficient. reactions are still at play. which compensate the blocking of that route.," This is because other quite efficient, reactions are still at play, which compensate the blocking of that route." However. the steady state is retzucded by a [actor 10.," However, the steady state is retarded by a factor 10." Other computations also showed (hat changing all initial atomi densities in (he same proportions bv a factor 2 had only marginal effects. on the final vields. but. retarded or advanced the setting of steady state.," Other computations also showed that changing all initial atom densities in the same proportions by a factor 2 had only marginal effects on the final yields, but retarded or advanced the setting of steady state." Finally. let us consider the problem of carbon grain formation.," Finally, let us consider the problem of carbon grain formation." The fraction of cosmic carbon that is available for erai formation is usually equated to the difference between photospheric (cosmic) aid ISA abundances of carbon. divided by the former.," The fraction of cosmic carbon that is available for grain formation is usually equated to the difference between photospheric (cosmic) and ISM abundances of carbon, divided by the former." In our treatinent. (his is represented by the average of neg)/ne(0) over all stars.," In our treatment, this is represented by the average of $n_{Cgr}(f)/n_{C}(0)$ over all stars." This quantity may. be deduced. with the help of Fig.," This quantity may be deduced, with the help of Fig." 5. from the measurement of the photospheric C/O ratio of," 5, from the measurement of the photospheric C/O ratio of" — 20%)) of galaxies with asymmetric profiles than in other samples such as ? and ?..,– ) of galaxies with asymmetric profiles than in other samples such as \citet{1998AJ....116.1169M} and \citet{2005A&A...438..507B}. " In this section we explore possible correlations between the asymmetry index Afjyxratio and optical properties of the rrefined subsample such as morphology, optical signs of perturbation, optical luminosity (Lg), and far-infrared luminosity (Lr;g)."," In this section we explore possible correlations between the asymmetry index $A_{flux~ratio}$ and optical properties of the refined subsample such as morphology, optical signs of perturbation, optical luminosity $L_B$ ), and far-infrared luminosity $L_{FIR}$ )." " Figure [5] shows the distribution of Afiuxratio Values for each Hubble morphological class (median, mean, and standard deviation values are indicated)."," Figure \ref{fig:afluxratiomorphologya} shows the distribution of $A_{flux~ratio}$ values for each Hubble morphological class (median, mean, and standard deviation values are indicated)." " The bins representing the majority of our sample (T(RC3) = 3 to 6, i.e. Sb to Scd) show a fairly large scatter (standard deviation o-~ 0.1)."," The bins representing the majority of our sample $T(RC3)$ = 3 to 6, i.e. Sb to Scd) show a fairly large scatter (standard deviation $\sigma$$\sim$ 0.1)." " We see a slight decreasing trend in Afiyx,4/;"" toward later-type galaxies.", We see a slight decreasing trend in $A_{flux~ratio}$ toward later-type galaxies. Studies of the relation between llopsidedness and morphological type are rare., Studies of the relation between lopsidedness and morphological type are rare. ? studied a sample of 30 moderate to low surface brightness (T=6—9) galaxies and found a higher asymmetry rate than for more luminous (and higher surface brightness) late-type spirals., \citet{1998AJ....116.1169M} studied a sample of 30 moderate to low surface brightness (T=6–9) galaxies and found a higher asymmetry rate than for more luminous (and higher surface brightness) late-type spirals. They found (for this type range) that later types were more likely to show larger asymmetries., They found (for this type range) that later types were more likely to show larger asymmetries. " In the Eridanus group the A, parameter as calculated from mmaps is larger for earlier type galaxies, suggesting that tidal interactions generate a higher lopsidedness rate in galaxies undergoing secular evolution toward earlier type (?).."," In the Eridanus group the $A_1$ parameter as calculated from maps is larger for earlier type galaxies, suggesting that tidal interactions generate a higher lopsidedness rate in galaxies undergoing secular evolution toward earlier type \citep{2006MNRAS.369.1849A}." " This result (i.e., larger asymmetries for earlier types) agrees with the general trend seen in our sample."," This result (i.e., larger asymmetries for earlier types) agrees with the general trend seen in our sample." We compared the Afjyxratio With luminosity., We compared the $A_{flux~ratio}$ with luminosity. " More luminous galaxies are slightly more asymmetric (Figure D6], left panel)."," More luminous galaxies are slightly more asymmetric (Figure \ref{fig:afluxratiomorphologyb}, left panel)." Figure (right panel) presents the cumulative distribution of Afiyxratio for the high- and low-luminosity subsamples (?).. , Figure \ref{fig:afluxratiomorphologyb} (right panel) presents the cumulative distribution of $A_{flux~ratio}$ for the high- and low-luminosity subsamples \citep{2005A&A...436..443V}. . The two distributions are different at a level of a = 0.05 using a chi square test: y7=14 and p— value=0.01., The two distributions are different at a level of $\alpha$ $=$ 0.05 using a chi square test: $\chi^2$ =14 and $p-value$ =0.01. Here we inspect a possible connection between optical signs of interaction and asymmetries in the pprofiles., Here we inspect a possible connection between optical signs of interaction and asymmetries in the profiles. ? revised the optical morphology classification for the CIG sample using POSS2/SDSS data., \citet{2006A&A...449..937S} revised the optical morphology classification for the CIG sample using POSS2/SDSS data. " Although the CIG, the starting sample of AMIGA, has been selected to minimize close neighbors to the target galaxy and thus interactions, still ?""'s revision revealed N = 193 objects with nearby companions or signs of distortion likely caused by an interaction."," Although the CIG, the starting sample of AMIGA, has been selected to minimize close neighbors to the target galaxy and thus interactions, still \citeauthor{2006A&A...449..937S}' 's revision revealed $N$ = 193 objects with nearby companions or signs of distortion likely caused by an interaction." ? flagged these galaxies as interacting in the case of a morphologically distorted system and/or almost certain interacting system or flagged as possiblyinteracting if there was any evidence of interaction/asymmetry with/without certain detection of a close companion., \citet{2006A&A...449..937S} flagged these galaxies as $interacting$ in the case of a morphologically distorted system and/or almost certain interacting system or flagged as $possibly~interacting$ if there was any evidence of interaction/asymmetry with/without certain detection of a close companion. There is no statistically significant difference in terms of pprofile asymmetry rate between galaxies that are optically classified as interacting and those without any sign of interaction., There is no statistically significant difference in terms of profile asymmetry rate between galaxies that are optically classified as interacting and those without any sign of interaction. This result is consistent with the conclusion by ? and? that optical asymmetries are not necessarily correlated with a lopsided ccomponent., This result is consistent with the conclusion by \citet{2000AJ....120..139K} and \citet{2004AJ....127.1900W} that optical asymmetries are not necessarily correlated with a lopsided component. " We compared the aasymmetry parameter with the relative spiral and bar strengths calculated as the maximal torque, or ratio of the maximum tangential force and the azimuthally averaged radial force."," We compared the asymmetry parameter with the relative spiral and bar strengths calculated as the maximal torque, or ratio of the maximum tangential force and the azimuthally averaged radial force." This has been obtained for a subsample of N = 96 CIG galaxies by ? using Fourier analysis over spiral and barcomponents separately (?).., This has been obtained for a subsample of N = 96 CIG galaxies by \citet{2009AAS...21344310D} using Fourier analysis over spiral and barcomponents separately \citep{2003AJ....126.1148B}. " Figure 27] shows the Afix,4j, parameter with respect to the relative spiral strength (Q,).", Figure \ref{fig:strengths} shows the $A_{flux~ratio}$ parameter with respect to the relative spiral strength $Q_s$ ). The overlapping sample between our rrefined subsample and the one used by ? is composed of 40 galaxies., The overlapping sample between our refined subsample and the one used by \citet{2009AAS...21344310D} is composed of 40 galaxies. " Q, seems to anti-correlate with Afiyxratio: disks with weaker spiral arms show stronger asymmetries (Figure D7)).", $Q_s$ seems to anti-correlate with $A_{flux~ratio}$: disks with weaker spiral arms show stronger asymmetries (Figure \ref{fig:strengths}) ). " There are six galaxies (CIGs 11, 33, 689, 712, 912, and 931) that are outliers to this relation in the high end of the Afiyxratio parameter."," There are six galaxies (CIGs 11, 33, 689, 712, 912, and 931) that are outliers to this relation in the high end of the $A_{flux~ratio}$ parameter." These are likely galaxies whose aasymmetry parameter is affected by instrumental effects., These are likely galaxies whose asymmetry parameter is affected by instrumental effects. On the other hand we do not find any correlation of Afiuxratio and Ον., On the other hand we do not find any correlation of $A_{flux~ratio}$ and $Q_b$. " The total strength Q, is not correlated with Afiyxratio either, not surprisingly because Q; and Q, presents a good correlation (?).."," The total strength $Q_g$ is not correlated with $A_{flux~ratio}$ either, not surprisingly because $Q_b$ and $Q_g$ presents a good correlation \citep{2009AAS...21344310D}." " The relation between Q, and Afiyxratio may originate in the observed trends in Q, versus T(RC3), because Q, would be expected to correlate with the latter."," The relation between $Q_s$ and $A_{flux~ratio}$ may originate in the observed trends in $Q_s$ versus $T(RC3)$, because $Q_s$ would be expected to correlate with the latter." " However, we did not find a clear trend between Q, and T(RC3)."," However, we did not find a clear trend between $Q_s$ and $T(RC3)$." " The correlation found between Aj;,;ratio and Οἱ suggests that other samples of galaxies characterized by lower spiral strengths will have higher aasymmetry rates.", The correlation found between $A_{flux~ratio}$ and $Q_s$ suggests that other samples of galaxies characterized by lower spiral strengths will have higher asymmetry rates. " This is consistent with the OSU sample (?),, where spiral strength is lower than for the CIG (median equal to 0.132 versus 0.161, respectively) (??),, and have a higher aasymmetry rate with respect to the rrefined subsample (seeSect.E32.and ?)."," This is consistent with the OSU sample \citep{2002ApJS..143...73E}, where spiral strength is lower than for the CIG (median equal to 0.132 versus 0.161, respectively) \citep{2005AJ....130..506B,2009AAS...21344310D}, and have a higher asymmetry rate with respect to the refined subsample \citep[see Sect.~\ref{sub:samples},and ." " Ly,g is a good tracer of the star-formation rate and is related to the environment in the sense that IR luminous galaxies (Lrpr > 10!! Lo) are usually interacting or merger systems (?)..", $L_{FIR}$ is a good tracer of the star-formation rate and is related to the environment in the sense that IR luminous galaxies $L_{FIR}$ $>$ $^{11}$ $_\odot$ ) are usually interacting or merger systems \citep{1996ARA&A..34..749S}. " Unlike other samples of galaxies, our isolated population shows low FIR measures e.g. log(Lr;g) peaks from 9.0 — 10.5 with very few (<2%)) galaxies above 10.5 (?).. "," Unlike other samples of galaxies, our isolated population shows low FIR measures e.g. $L_{FIR}$ ) peaks from 9.0 – 10.5 with very few $<$) galaxies above 10.5 \citep{2007A&A...462..507L}. ." The low Lr; values of the CIG sample support our claim that the revised CIG (AMIGA) is a sample with only isolated systems (?).. , The low $L_{FIR}$ values of the CIG sample support our claim that the revised CIG (AMIGA) is a sample with only isolated systems \citep{2007A&A...462..507L}. . Here we inspect whether the small fraction of IR-Iuminous systems in our sample corresponds to galaxies with larger aasymmetries., Here we inspect whether the small fraction of IR-luminous systems in our sample corresponds to galaxies with larger asymmetries. We find N=165 galaxies in our refined, We find $N$ =165 galaxies in our refined "of the cosmic microwave background, the local curvature may be quite different.","of the cosmic microwave background, the local curvature may be quite different." " To answer the question how big this difference actually is for realistic survey volumes, we here extend the analysis of Li&Schwarz(2007,2008),, where these effects have been estimated for the first time."," To answer the question how big this difference actually is for realistic survey volumes, we here extend the analysis of \cite{li:onset,li:scale}, where these effects have been estimated for the first time." " For the spatially flat Einstein-de Sitter (EdS) model, the averaged curvature parameter OR has been shown to deviate from zero by ~0.1 on domains at the 100 Mpc scale."," For the spatially flat Einstein-de Sitter (EdS) model, the averaged curvature parameter $\Omega_{\cal R}^{\cal D}$ has been shown to deviate from zero by $\sim 0.1$ on domains at the $100$ Mpc scale." " Here we adapt the analysis of Li&Schwarz(2008) to the case of a ACDM universe, introduce a more realistic power spectrum and use observationally interesting window functions, not restricted to full-sky measurements."," Here we adapt the analysis of \cite{li:scale} to the case of a $\Lambda$ CDM universe, introduce a more realistic power spectrum and use observationally interesting window functions, not restricted to full–sky measurements." There has been quite some confusion about the choice of gauge and the dependence of the averaged quantities on it., There has been quite some confusion about the choice of gauge and the dependence of the averaged quantities on it. " Recently it has been shown (Gasperinietal.,2010) that this is not a problem if one consistently works in one gauge and then expresses the quantity that is finally observed in this frame as well.", Recently it has been shown \citep{veneziano} that this is not a problem if one consistently works in one gauge and then expresses the quantity that is finally observed in this frame as well. " This is easier in some gauges than in others, but the result is (as expected) the same, as is also confirmed explicitly by the fact that our results are consistent with those of Clarksonetal.(2009) and Umehetal.(2010),, obtained in Newtonian gauge."," This is easier in some gauges than in others, but the result is (as expected) the same, as is also confirmed explicitly by the fact that our results are consistent with those of \cite{clarkson:pert} and \cite{clarkson:hubble}, obtained in Newtonian gauge." " The quest for simplicity explains our choice to use comoving synchronous gauge, because this is the frame that is closest to the one used by the observers."," The quest for simplicity explains our choice to use comoving synchronous gauge, because this is the frame that is closest to the one used by the observers." Fig., Fig. 1 depicts the theorist’s and the observer's view on the Universe in a schematical way., \ref{fig:theory-measurement} depicts the theorist's and the observer's view on the Universe in a schematical way. " It points out that in the end it is the average quantities that we are interested in, but that in an intermediate step, observers like to think of the objects they measure to lie in a comoving space with simple Euclidian distances."," It points out that in the end it is the average quantities that we are interested in, but that in an intermediate step, observers like to think of the objects they measure to lie in a comoving space with simple Euclidian distances." " The comoving synchronous gauge, which has a clear notion of ""today"" for a fluid observer sitting in a galaxy as we do, helps to define the things observers measure in a simple way."," The comoving synchronous gauge, which has a clear notion of ""today"" for a fluid observer sitting in a galaxy as we do, helps to define the things observers measure in a simple way." In Section 2 we establish the conceptual frameworkfor the study of effects of inhomogeneities on observable quantities.," In Section \ref{sec:Inhomogeneity-and-expansion} we establish the conceptual frameworkfor the study of effects of inhomogeneities on observable quantities." " Section 3 and 4 generalize some of the results of Li&Schwarz(2007,2008) and Li(2008) from an Einstein-de Sitter (EdS) to a ACDM background and implement a more realistic matter power spectrum."," Section \ref{sec:Var-cosmic-pars} and \ref{sec:Var-loc-cosm-par} generalize some of the results of \cite{li:onset,li:scale} and \cite{li:thesis} from an Einstein–de Sitter (EdS) to a $\Lambda$ CDM background and implement a more realistic matter power spectrum." " Section 5 investigates the effects of various window functions, again extending the analysis of Li&Schwarz(2008);Li (2008).."," Section \ref{sec:survey-geom} investigates the effects of various window functions, again extending the analysis of \cite{li:scale,li:thesis}." Section 6 concentrates on deriving the magnitude of curvature fluctuations for realistic window functions., Section \ref{sec:curv-fluct} concentrates on deriving the magnitude of curvature fluctuations for realistic window functions. " Section 7 applies the formalism to the local distance measure Dy, determined in the observation of baryonic acoustic oscillations (BAO)."," Section \ref{sec:Variances-on-BAO} applies the formalism to the local distance measure $D_{V}$, determined in the observation of baryonic acoustic oscillations (BAO)." " Section 8 is a remark on the link between the variance of averaged expansion rates at different epochs and the background evolution, before we conclude in Section 9.."," Section \ref{sec:Expansion-history} is a remark on the link between the variance of averaged expansion rates at different epochs and the background evolution, before we conclude in Section \ref{sec:Conclusion}." " We assume that the overall evolution of the Universe is described by a flat ACDM model, which we adopt as our background model throughout this work."," We assume that the overall evolution of the Universe is described by a flat $\Lambda$ CDM model, which we adopt as our background model throughout this work." Global spatial flatness does not prevent the local curvature to deviate from zero., Global spatial flatness does not prevent the local curvature to deviate from zero. The distribution of nearby galaxies indicates that the scales at which the Universe is inhomogeneous reach out to at least 100 Mpc., The distribution of nearby galaxies indicates that the scales at which the Universe is inhomogeneous reach out to at least 100 Mpc. " Above these scales it is not yet established if there is a turnover to homogeneity, as was claimed in Hoggetal. (2005)., or if the correlations in the matter distribution merely become weaker, but persist up to larger scales, as is discussed in Labini(2010).."," Above these scales it is not yet established if there is a turnover to homogeneity, as was claimed in \cite{hogg:homo}, or if the correlations in the matter distribution merely become weaker, but persist up to larger scales, as is discussed in \cite{labini:inhom}." " At least morphologically, homogeneity has not been found up to scales of about 200 Mpc (Kerscheret1998,2001;Hikageetal., 2003)."," At least morphologically, homogeneity has not been found up to scales of about 200 Mpc \citep{morph:pscz,morph:iras,morph:SDSS}." ". Consequently, we need a formalism that is applicable in the presence of inhomogeneities at least for the description of the local expansion."," Consequently, we need a formalism that is applicable in the presence of inhomogeneities at least for the description of the local expansion." " This may be accomplished considering spatial domains D and averaging over their locally inhomogeneous observables (Buchert,2000, 2001).."," This may be accomplished considering spatial domains $\cD$ and averaging over their locally inhomogeneous observables \citep{buchert:dust,buchert:fluid}. ." Technically one performs a 341 split of spacetime., Technically one performs a 3+1 split of spacetime. " Because we considered pressureless matter only, we chose a comoving foliation in which the"," Because we considered pressureless matter only, we chose a comoving foliation in which the" correct.,correct. " However, this form of the luminosity distance, without the luxury of extra free parameters, does not fit the current sample of Type la supernova as well as Equation (32)."," However, this form of the luminosity distance, without the luxury of extra free parameters, does not fit the current sample of Type Ia supernova as well as Equation (32)." " Interestingly. Equation (33) fit the data adequately at low and high redshifts, but not in between, as may be seen, ¢.g., in figure 6 of Riess et al. ("," Interestingly, Equation (33) fit the data adequately at low and high redshifts, but not in between, as may be seen, e.g., in figure 6 of Riess et al. (" 2004).,2004). " This could be an important clue, because the difficulty with interpreting the data at intermediate redshifts is made more evident through a comparison of the gold sample with other. newer compilations."," This could be an important clue, because the difficulty with interpreting the data at intermediate redshifts is made more evident through a comparison of the gold sample with other, newer compilations." " Though all of the currently available SNe la catalogs yield a consistent and robust value of Q (1.0. =0.27), they vary significantly when it comes to the inferred redshift ος at which deceleration is meant to have switched over to acceleration in the present epoc."," Though all of the currently available SNe Ia catalogs yield a consistent and robust value of $\Omega_{\rm m}$ (i.e., $\approx 0.27$ ), they vary significantly when it comes to the inferred redshift $z_{\rm acc}$ at which deceleration is meant to have switched over to acceleration in the present epoc." " For example, the gold sample gives a value πως=0.46+0.13 (Riess et al."," For example, the gold sample gives a value $z_{\rm acc}=0.46\pm 0.13$ (Riess et al." 2004)., 2004). The so-called Union? sample contains 557 events in the redshift range 0.015DS/4k=107K where k 1s Boltzmann's constant., If of ${\cal E}_{kin}$ went into heating the comet material the temperature attainable would be $T>m_pv_\odot^2/4k\approx 10^7 K$ where $k$ is Boltzmann's constant. This 15 of order the solar escape temperature since it is generated by infall of matter effectively from eo., This is of order the solar escape temperature since it is generated by infall of matter effectively from $\infty$. Flare masses ejected are of the order of 1015716 s. also comparable with those of larger impacting cometary nuclei.," Flare masses ejected are of the order of $10^{12-16}$ g, also comparable with those of larger impacting cometary nuclei." Thus a comet impact in the dense chromosphere should produce phenomena somewhat resembling a solar (magnetic) flare. though the initial comet volume is much smaller. its density much higher. and the heating rise time faster (<10 s).," Thus a comet impact in the dense chromosphere should produce phenomena somewhat resembling a solar (magnetic) flare, though the initial comet volume is much smaller, its density much higher, and the heating rise time faster $\preceq 10$ s)." Because of the initially small size scale and high density and pressure we might expect rapid initial cooling (seconds) by radiation. expansion and conduction. followed by a radiative/conductive decay phase more like that of solar flares (~1077 s) as the fireball expands outward and upward. sweeping solar plasma with it (cf.," Because of the initially small size scale and high density and pressure we might expect rapid initial cooling (seconds) by radiation, expansion and conduction, followed by a radiative/conductive decay phase more like that of solar flares $\sim 10^{2-3}$ s) as the fireball expands outward and upward, sweeping solar plasma with it (cf." the Carlson et al., the Carlson et al. 1997 study of the Jupiter impact fireball)., 1997 study of the Jupiter impact fireball). " If optically thin. the radiative output of a hot plasma of volume V depends on its temperature and its emission measure J.m4Vxcο=OSM,107PAa]105p. cm for a nucleus of mass M, when it has expanded to size a. ("," If optically thin, the radiative output of a hot plasma of volume $V$ depends on its temperature and its emission measure $EM= \int_Vn^2dV\approx a^3(M_o/\mu_c m_p)^2\approx 10^{48} (M_o/10^{12})^2/(a/10^8)^3/\mu_c$ $^{-3}$ for a nucleus of mass $M_o$ when it has expanded to size $a$. (" "Here 4, is the mean comet mass per particle in units of n).",Here $\mu_c$ is the mean comet mass per particle in units of $m_p$ ). Explosion of a nucleus occurs over a few scale heights =10° cm vertically. traversed in ~[0 s at speed Ycos&.," Explosion of a nucleus occurs over a few scale heights $\approx 10^8$ cm vertically, traversed in $\sim 10$ s at speed $v_\odot\cos \phi$." If the lateral expansion speed of the hot wake were similar then the lateral dimension of the exploding wake would also be a few seale heights., If the lateral expansion speed of the hot wake were similar then the lateral dimension of the exploding wake would also be a few scale heights. " Its optical depth for a process with absorption cross-section c would then be 7=oM,/myr=(OMATGe307/nfGr]10 P.", Its optical depth for a process with absorption cross-section $\sigma$ would then be $\tau \approx \sigma M_o/m_pa^2 = (M_o/10^{12})(\sigma/10^{-20})/\mu_c/(a/10^8)^2$ . " Thus. when a nucleus of. say. M,=102 g (d,~10* em) becomes optically thin (ag=10° em) for σ=1077? env. it would have an EM«107? em? for that emission."," Thus when a nucleus of, say, $M_o=10^{12}$ g $a_o\sim 10^4$ cm) becomes optically thin $a=10^6$ cm) for $\sigma=10^{-20}$ $^2$, it would have an $EM\approx 10^{48}$ $^{-3}$ for that emission." This EM is only for the cometary material itself. but the EM of the heated atmosphere may also be important since an atmospheric mass =ΑΜ. 1s involved in decelerating it.," This $EM$ is only for the cometary material itself, but the $EM$ of the heated atmosphere may also be important since an atmospheric mass $\succeq M_o$ is involved in decelerating it." " Since H-ἰ arcsee we may expect to see initially a source of a few aresec expanding at about O.1 aresee per sec at chromospheric altitudes and atmospheric density ~10'77!* οι depending on M,, as per Figure 4.", Since $H\sim$ 1 arcsec we may expect to see initially a source of a few arcsec expanding at about 0.1 arcsec per sec at chromospheric altitudes and atmospheric density $\simeq 10^{13-16}$ $^{-3}$ depending on $M_o$ as per Figure 4. XUV line spectra should exhibit highly non-solar abundances (eg O:H ratio) as should any matter ejected into space (cf., XUV line spectra should exhibit highly non-solar abundances (eg O:H ratio) as should any matter ejected into space (cf. Iseli et al 2002)., Iseli et al 2002). There may also be a variety of nonthermal radio and other signatures (e.g. charge exchange - e.g. Lisse et al., There may also be a variety of nonthermal radio and other signatures (e.g. charge exchange - e.g. Lisse et al. 1996 - and impact polarized spectrum lines - eg. Fletcher and Brown 1992. 1995) arising from plasma phenomena driven by the highly supersonic expansion. such as shock and/or turbulent acceleration of electrons and ions and charge separation currents as the ablated matter decelerates in the atmosphere - cf.," 1996 - and impact polarized spectrum lines - e.g. Fletcher and Brown 1992, 1995) arising from plasma phenomena driven by the highly supersonic expansion, such as shock and/or turbulent acceleration of electrons and ions and charge separation currents as the ablated matter decelerates in the atmosphere - cf." review by Péggauriérr (2007) of fusion pellet ablation physics., review by Péggauriérr (2007) of fusion pellet ablation physics. The phenomenon of flare induced sunquakes - waves in the photosphere - discovered by Kosovichev and Zharkova (1998) and now widely studied (e.g. Kosovichev. 2006) should also result from the momentum impulse delivered by à cometary impact., The phenomenon of flare induced sunquakes - waves in the photosphere - discovered by Kosovichev and Zharkova (1998) and now widely studied (e.g. Kosovichev 2006) should also result from the momentum impulse delivered by a cometary impact. All such impacts. however small the comet mass. involve a huge kinetic energy density (ram pressure) pyz2x ere/cm?.," All such impacts, however small the comet mass, involve a huge kinetic energy density (ram pressure) $\rho v_\odot^2/2\approx 10^{15}$ $^3$ ." " This is ~10!"" times the thermal energy density", This is $\sim 10^{10}$ times the thermal energy density oocedure is likely to be related to the choice of a single stellar model for each galaxy. experiments. involving the adoption of extreme models (e.g. assuming that the halos are dominated by OSPs) suggest that the derived total stellar masses are accurate to within a factor of two.,"procedure is likely to be related to the choice of a single stellar model for each galaxy, experiments involving the adoption of extreme models (e.g. assuming that the halos are dominated by OSPs) suggest that the derived total stellar masses are accurate to within a factor of two." The results lor the starburst radio e@alaxies are presented in. Table 4 and Figure 2., The results for the starburst radio galaxies are presented in Table 4 and Figure 2. They demonstrate that most starburst radio galaxies are giant elliptical galaxies in terms of their total stellar masses., They demonstrate that most starburst radio galaxies are giant elliptical galaxies in terms of their total stellar masses. Considering the galaxy mass fiinction derived by Coleetal.(2001)cosmologv.. the majority of starburst radio. galaxies are super-mi.: the mean and median stellar misses are 5.61015 M. (heme) and L7«1013 AL. (3.35 ma.," Considering the galaxy mass function derived by \citet{cole01}, the majority of starburst radio galaxies are $_{*}$: the mean and median stellar masses are $5.6\times10^{11}$ $_{\odot}$ $\times$ $_{*}$ ) and $4.7\times10^{11}$ $_{\odot}$ $\times$ $_{*}$ )." These results are consistent with those derived. for the general population of powerful radio galaxies at all redshifts. (e.g. 2010).," These results are consistent with those derived for the general population of powerful radio galaxies at all redshifts \citep[e.g.][]{dunlop03,volmerange04,seymour07,inskip10}." . For exampe. based on the near-IHt photometry measurements presente in Inskipetal. (2010).. the general population of nearby (2 0.5) 2Jx radio &ealaxies has stellar masses in the range 2104««e---2.107 M..," For example, based on the near-IR photometry measurements presented in \citet{inskip10}, the general population of nearby $z < 0.5$ ) 2Jy radio galaxies has stellar masses in the range $2\times10^{11} < M_{stellar} < 2\times10^{12}$ $_{\odot}$." However. as highlighted in Willsetal. (2008).. it is dangerous to generalise. and a minority of radio galaxies have stellar masses that are significantly lower (7m. ).," However, as highlighted in \citet{wills08}, , it is dangerous to generalise, and a minority of radio galaxies have stellar masses that are significantly lower $\sim m_{*}$ )." ligure 2 also shows a comparison between the tota stellar masses of starburst radio galaxies (lop panel). anc nearby ULIRGs from he z«0.13 complete saniple of ltodríguezZaurinetal.(2009) (bottom panel). cerivec using identical technictes.," Figure 2 also shows a comparison between the total stellar masses of starburst radio galaxies (top panel) and nearby ULIRGs from the $z < 0.13$ complete sample of \citet{zaurin09} (bottom panel), derived using identical techniques." In making this comparison i is important to recognise that the estimated total stellar masses of the ULIICs have been derived using OSP|YSP models (modellingcombinationLinltodríguezZaurineal. 2009).. whieh tend to maximise the OS? combination (and hence the total sellar masses). whereas in Lact the nuclear spectra of many of ULIRGSs can be adequately modelled by combinations of intermediate age and. voung YSDP. without any contribution from an OSP (combinationIHEinRocdefeuezZaurinctal. 2009).. similar to the case of 3€459 amongst the starburst racio galaxies. (Wills.οἱal. 2008).," In making this comparison it is important to recognise that the estimated total stellar masses of the ULIRGs have been derived using OSP+YSP models \citep[modelling combination I in][]{zaurin09}, which tend to maximise the OSP combination (and hence the total stellar masses), whereas in fact the nuclear spectra of many of ULIRGs can be adequately modelled by combinations of intermediate age and young YSP, without any contribution from an OSP \citep[combination III in][]{zaurin09}, similar to the case of 3C459 amongst the starburst radio galaxies \citep{wills08}." . Despite the fact that the masses of ULURGSs in Figure 12 may be over-estimated. most radio galaxies have total stellar masses that are. greater than those of most ULIRGs. although there is a significant overlap between the two distributions.," Despite the fact that the masses of ULIRGs in Figure 12 may be over-estimated, most radio galaxies have total stellar masses that are greater than those of most ULIRGs, although there is a significant overlap between the two distributions." Using a ντο two sample test we can reject the nullhypothesis that the two samples have the same mass distributions at the 99.54. level of significance., Using a K-S two sample test we can reject the nullhypothesis that the two samples have the same mass distributions at the $>$ level of significance. Overall.," Overall," Satellite galaxies are likely to play an important rolle in the evolution. of ‘galaxies.,Satellite galaxies are likely to play an important rôlle in the evolution of galaxies. . In recent vears the search for. representative. samples of⋅ satellite. galaxies. has gathered momentum. in. a quest to understand. their.. rolle) in. the evolution. of the. present-day galaxy population.," In recent years the search for representative samples of satellite galaxies has gathered momentum, in a quest to understand their rôlle in the evolution of the present-day galaxy population." ". 1n subsequent. papers. following⋅: the validationB: tests. presented here we will. present a study of. the luminosities.""ND spatial. distributions⊀⊀. and star. formation.. (SE)as properties: of⋅ the satellites. of⋅ nearby. bright. spiral. galaxies.. to aclelress two main. questions:. how many satellitesD do bright. field. galaxies. rave ab the current epoch. and. can such satellites. supply significant⊲⊀⋅ amounts of⋅ eas to their. central galaxies?"," In subsequent papers, following the validation tests presented here we will present a study of the luminosities, spatial distributions and star formation (SF) properties of the satellites of nearby bright spiral galaxies, to address two main questions: how many satellites do bright field galaxies have at the current epoch, and can such satellites supply significant amounts of gas to their central galaxies?" 05 These questions are motivated by the influential ierarchical. models of galaxy formation⋅. and evolution. (White&Rees1978:Frenketal.1988).. which are a central component of the lambda colddark matter CXCDAM) cosmological model.," These questions are motivated by the influential hierarchical models of galaxy formation and evolution \citep{whit78,fren88}, which are a central component of the lambda cold dark matter $\Lambda$ CDM) cosmological model." The accumulation of matter through he merger of galaxies in hierarchical ealaxy formation continues. over the ageo of the universe. H(Searle&ZinnLOTS)t and results in massive galaxies continually accreting gas. stars and dark matter," The accumulation of matter through the merger of galaxies in hierarchical galaxy formation continues over the age of the universe \citep{sear78} and results in massive galaxies continually accreting gas, stars and dark matter." Within this picture. the merging of small satellites with large central galaxies is an important process. as the gas thus supplied may provide the replenishment required for ongoing SE (Rocha-Pintoctal.2000) without cisk destruction. and may explain. the chemical. composition↔ observed in⊀ the Milkv. Wav. (Beckman>ctal..2004).," Within this picture, the merging of small satellites with large central galaxies is an important process, as the gas thus supplied may provide the replenishment required for ongoing SF \citep{roch00} without disk destruction, and may explain the chemical composition observed in the Milky Way \citep{beck04}." ".. sThe merging. of⋅ gas-rich"" satellites: either fully or ⊀∙⋅⊽∙⊽⊀by being stripped∙⊀ of ⋅⊀∙their gas could contribute: to the ongoing: star forming⋅⊀ activity.M with: or without. the disruption. of the disk⊀ (Mayerctal.onn2006)."," The merging of gas-rich satellites either fully or by being stripped of their gas could contribute to the ongoing star forming activity, with or without the disruption of the disk \citep{may06}." . Such. minor⊀∙ mergers∙∙ mav⊽ also plav⊽ a rolle» in.. producing:. ∙⊀ ⊀↼ ⇂↓⋯∼↳∠⊔⊳∖↳≼⇍∪⊔↓↓≻∪⊔∢⊾⊔⇂⊳∖↿∖∖∢⋅↓⋜↧∠⊏↥⋯⋅∠⊾∖↽∖∖⇂⊔↿⋖⋅↓≤⋗≤⋗≤∩↣∥⊔∠⇂ ⊳⇁⊀ could contribute to the growth of bulge mass (Walkerctal.⋅ 1996).," Such minor mergers may also play a rôlle in producing `thick disk' components \citep{vela99}, , and could contribute to the growth of bulge mass \citep{walk96}." . Particularlyae problematic. are the large numbers of field. spiral galaxies with little or no bulge component. and strong ongoing. SI: sspif these are being. built: up and. supplied. with: gas through mergers. the infalline∢⋅∢ galaxies. must. be small. to avoid disk disruption. and quite numerous.," Particularly problematic are the large numbers of field spiral galaxies with little or no bulge component and strong ongoing SF; if these are being built up and supplied with gas through mergers, the infalling galaxies must be small, to avoid disk disruption, and quite numerous." To aclelress these problems. and the general ‘missing satellites problem of ACDM (Ixlvpinetal.1999:Moore1999).. it is important to have large samples of true. satellites. extending. to the faintest.ον possible: Iuminosities.," To address these problems, and the general `missing satellites' problem of $\Lambda$ CDM \citep{klyp99,moor99}, it is important to have large samples of true satellites, extending to the faintest possible luminosities." ∢↔ Phe identification:.. and classificationa of satellite. galaxies. was first⋅ undertaken: using. wice-Lielcl.⋅ photographic. plates by Lolmbere(1969)., The identification and classification of satellite galaxies was first undertaken using wide-field photographic plates by \cite{hol69}. . In this study. a statistical correction was utilised for background. galaxies as redshilts were not available.," In this study, a statistical correction was utilised for background galaxies as redshifts were not available." Zaritskvctal.(1998.1900) used. multifibre spectroscopic observations to measure the redshifts and quantify the numbers of satellites of field spirals.," \cite{zar93,zar97} used multifibre spectroscopic observations to measure the redshifts and quantify the numbers of satellites of field spirals." Whether satellite galaxy mergers can provide eas replenishment ofthe, Whether satellite galaxy mergers can provide gas replenishment ofthe the lines from J=5 upwards.,the lines from $J=5$ upwards. " Note that the CO J=10-9 line is blended with the H2O 512-221 line which is expected to have some luminosity (1.8-107Lo for the model by Gonzállez-Alfonso et al.,"," Note that the CO $J=10{-}9$ line is blended with the $\HtO$ $3_{1,2}{-}2_{2,1}$ line which is expected to have some luminosity $1.8\cdot 10^7\Lsun$ for the model by Gonzállez-Alfonso et al.," " this issue), and this may account for its somewhat high flux."," this issue), and this may account for its somewhat high flux." The total luminosity measured in the CO lines up to J=13-12 is (2.8x1.1):105Lo., The total luminosity measured in the CO lines up to $J=13{-}12$ is $(2.8\pm1.1)\cdot10^8\Lsun$. Note that only 4% of the total CO line luminosity is contained in the lowest 3 transitions., Note that only $4\%$ of the total CO line luminosity is contained in the lowest 3 transitions. " For comparison, in our Milky Way this fraction is 43% (?).."," For comparison, in our Milky Way this fraction is $43\%$ \citep{Fixsenetal99}." " The approximately flat distribution of CO line luminosity with rotational level indicates that several excitation components must be present, since individual components always produce a more peaked excitation diagram."," The approximately flat distribution of CO line luminosity with rotational level indicates that several excitation components must be present, since individual components always produce a more peaked excitation diagram." " We model these components using the one dimensional PDR/XDR models of ?,, as shown in2."," We model these components using the one dimensional PDR/XDR models of \citet{Meijerinketal07}, as shown in." ". The CO lines up to J=8-7 can be produced by a combination of 2 PDRs, in qualitative agreement with the decomposition by ?.."," The CO lines up to $J=8{-}7$ can be produced by a combination of 2 PDRs, in qualitative agreement with the decomposition by \citet{Papadopoulosetal07}." " However, a challenge is presented by the highest CO lines: J=13-12 and J=12-11, arising from energy levels 503 and 461K above the ground state."," However, a challenge is presented by the highest CO lines: $J=13{-}12$ and $J=12{-}11$, arising from energy levels 503 and $461\K$ above the ground state." " As shown in2,, these lines are strongly underproduced by the PDRs dominating the emission in the lower lines, since the resulting gas temperatures are not high enough for significant population of the J>10 levels."," As shown in, these lines are strongly underproduced by the PDRs dominating the emission in the lower lines, since the resulting gas temperatures are not high enough for significant population of the $J>10$ levels." " These lines therefore require the presence of a third excitation component, which can be either an XDR or a high excitationPDR."," These lines therefore require the presence of a third excitation component, which can be either an XDR or a high excitation." . A model fit with an XDR producing the highest CO lines is shown in2., A model fit with an XDR producing the highest CO lines is shown in. ". The required X-ray illumination for this XDR can be produced by the AGN in Mrk231 (?),, out to a distance of 160pc from the nucleus, ignoring absorption."," The required X-ray illumination for this XDR can be produced by the AGN in $\Mrk{231}$ \citep{Braitoetal04}, out to a distance of $160\pc$ from the nucleus, ignoring absorption." " The ratio of radiating surfaces in the model shown in implies an extended low excitation PDR component (green curve), with a less extended and denser central XDR region (blue curve)."," The ratio of radiating surfaces in the model shown in implies an extended low excitation PDR component (green curve), with a less extended and denser central XDR region (blue curve)." " Dense clouds with a smaller surface, close to massive stars and probably embedded in the more diffuse component, account for the medium excitation component (red curve)."," Dense clouds with a smaller surface, close to massive stars and probably embedded in the more diffuse component, account for the medium excitation component (red curve)." " Alternatively, a very dense, high illumination PDR can account for the highest CO lines."," Alternatively, a very dense, high illumination PDR can account for the highest CO lines." A good fit is found with n— and Go=10° and a surface ratio from medium to high excitation of 1.0:0.03., A good fit is found with $n=10^{6.5}\pcmcub$ and $\qu{G}{0}=10^5$ and a surface ratio from medium to high excitation of $1.0:0.03$. Here the small surface area for the high excitation PDR indicates a number of small high density clumps in a very strong UV field., Here the small surface area for the high excitation PDR indicates a number of small high density clumps in a very strong UV field. " Since the radiating surface of the high excitation PDR is about 30x smaller than that of the medium excitation PDR, but its density about 30x larger, the Hz masses in these two components must be comparable."," Since the radiating surface of the high excitation PDR is about $30\times$ smaller than that of the medium excitation PDR, but its density about $30\times$ larger, the $\Ht$ masses in these two components must be comparable." " For an O5 star, the required Go=10° is reached at a radius of 0.3pc."," For an O5 star, the required $G_0=10^5$ is reached at a radius of $0.3\pc$." " For a star formation rate of 100Μοyr! and a power law initial mass function with slope —2.35 between masses of 0.3 and 120Mo, there are 7.6-10° stars of spectral type O5 or earlier in Mrk231."," For a star formation rate of $100\Msun\pyr$ and a power law initial mass function with slope $-2.35$ between masses of 0.3 and $120\Msun$, there are $7.6\cdot10^5$ stars of spectral type O5 or earlier in $\Mrk{231}$." " The total volume with Go>10° is then 8.6-104pc, while (for a 520pc radius disk with 15pc thickness, following ?)) the total volume of the gas disk ispc?."," The total volume with $G_0>10^5$ is then $8.6\cdot10^4\pun{pc}{3}$, while (for a $520\pc$ radius disk with $15\pc$ thickness, following \citet{Daviesetal04}) ) the total volume of the gas disk is." " In other words, in this scenario approximately half of the molecular mass would have to be contained in of the total volume, and located within 0.3pc from an O5 (or hotter) star."," In other words, in this scenario approximately half of the molecular mass would have to be contained in of the total volume, and located within $0.3\pc$ from an O5 (or hotter) star." Efficient UV heating by the Gy=10? radiation field would heat the dust in these clumps (in total ~50% of the total dust mass in Mrk 231) to a temperature of about 170K., Efficient UV heating by the $G_0=10^5$ radiation field would heat the dust in these clumps (in total $\sim50\%$ of the total dust mass in $\Mrk{231}$ ) to a temperature of about $170\K$. " In contrast, in the XDR model, where dust heating would be less efficient, the dust temperature would only be ~70K (?).."," In contrast, in the XDR model, where dust heating would be less efficient, the dust temperature would only be $\sim70\K$ \citep{MeijerinkSpaans05}." These predictions can be tested by analysing the infrared SED of Mrk231., These predictions can be tested by analysing the infrared SED of $\Mrk{231}$. " Gonzállez-Alfonso et ((this issue), found that the hot (T=150-400 K) component in the SED of Mrk231 accounts for about ~20% of the total infrared luminosity, but is produced by only of the total dust mass."," Gonzállez-Alfonso et (this issue), found that the hot $T=150{-}400\K$ ) component in the SED of $\Mrk{231}$ accounts for about $\sim20\%$ of the total infrared luminosity, but is produced by only of the total dust mass." This result limits the fraction of gas within 0.3pc from an O5 star in Mrk231 to much less than the ~50% required to produce the highest CO lines with a high excitationPDR., This result limits the fraction of gas within $0.3\pc$ from an O5 star in $\Mrk{231}$ to much less than the $\sim50\%$ required to produce the highest CO lines with a high excitation. ". This problem does not exist for the XDR model, which predicts most of the dust to be cooler."," This problem does not exist for the XDR model, which predicts most of the dust to be cooler." The extraordinarily luminous emission from the molecular ions H50* and OH* reveals the chemical signature of anXDR., The extraordinarily luminous emission from the molecular ions $\HtOp$ and $\OHp$ reveals the chemical signature of an. ". Assuming that the emission arises from a disk with 160pc radius (as derived above), we can derive column densities in the upper levels of the relevant transitions, whichresults in values Nyp~3.0-3.5-1019cm? for both species."," Assuming that the emission arises from a disk with $160\pc$ radius (as derived above), we can derive column densities in the upper levels of the relevant transitions, whichresults in values $\qu{N}{up}\sim3.0{-}3.5\cdot10^{13}\pun{cm}{-2}$ for both species." Modeling the nuclear molecular gas disk in Mrk231 with a radius of 520kpc and Η2 mass of 2.2-10?Mo then results in lower limits to the total OH* and H3O* abundances relative to H5 of ~2-1071? in the central 160 pc., Modeling the nuclear molecular gas disk in $\Mrk{231}$ with a radius of $520\kpc$ and $\Ht$ mass of $2.2\cdot10^9\Msun$ then results in lower limits to the total $\OHp$ and $\HtOp$ abundances relative to $\Ht$ of $\sim2\cdot10^{-10}$ in the central $160\pc$ . Given the short radiative, Given the short radiative The extinction toward the ON ts lower. Ay <3. with a peak value Ay ~6 in the direction of the Dark Bay feature.,"The extinction toward the ON is lower, $A_V\lesssim$ 3, with a peak value $A_V\sim$ 6 in the direction of the Dark Bay feature." Our findings agree with Hillenbrand(1997).. Muenchetal.(2002) and DaRioetal.(2010) who derived that the ONC members are typically extincted by Ay x3.," Our findings agree with \citet{Hill97}, \citet{Mue02} and \citet{DaRio10} who derived that the ONC members are typically extincted by $A_V\lesssim$ 3." Together with Arce&Goodman(1999) and Dobashietal. (2005).. we find that the OMC-1 extinction map proposed by SFD98 is overestimated by a factor of~3-5. especially in the optically thickest regions.," Together with \citet{Arce99} and \citet{dobashi05}, we find that the OMC-1 extinction map proposed by SFD98 is overestimated by a factor $\sim$ 3-5, especially in the optically thickest regions." Together with the comparability between our ON extinction map and the results of ODell&Yusef-Zadeh (2000).. this supports both the robustness of our statistical approach and the general validity of our results over the full spatial extent of the Orion Nebula Cluster.," Together with the comparability between our ON extinction map and the results of \citet{odell2000}, this supports both the robustness of our statistical approach and the general validity of our results over the full spatial extent of the Orion Nebula Cluster." Our derived maps for the OMC-1 and the Orion Nebula are available in electronic form as FITS files at the CDS., Our derived maps for the OMC-1 and the Orion Nebula are available in electronic form as FITS files at the CDS. To determine the completeness of the RIO photometric catalog. we use the artificial star experiment performed by R10. increasing the number of tests up to 107 per magnitude and per field.," To determine the completeness of the R10 photometric catalog, we use the artificial star experiment performed by R10, increasing the number of tests up to $^4$ per magnitude and per field." Our completeness estimation turns out to bea pprocedure as it provides the completeness sensitivity at any given position and for any given magnitude. computed within a eircle with a radius of Γή. Hower than the typical size of the nebular structure present in the [SPI images.," Our completeness estimation turns out to be a procedure as it provides the completeness sensitivity at any given position and for any given magnitude, computed within a circle with a radius of $\sim$ $\arcmin$, lower than the typical size of the nebular structure present in the ISPI images." The number of tests allows us to estimate the completeness with an error of a few[, The number of tests allows us to estimate the completeness with an error of a few. σοι According to RIO. we find that the completeness (and the oof our survey decreases with decreasing distance from the Trapezium.," According to R10, we find that the completeness (and the of our survey decreases with decreasing distance from the Trapezium." This is due to the combined effects of increasing erowding and nebular brightness close to the inner cluster., This is due to the combined effects of increasing crowding and nebular brightness close to the inner cluster. The results of our simulations are shown in FigureAl.. reporting the completeness trend for a 2117 star in the inner surveyed region.," The results of our simulations are shown in Figure, reporting the completeness trend for a 17 star in the inner surveyed region." As we stated above. we find that the sensitivity of the survey gets drastically shallower in the very inner region. decreasing from <100% down to <10% in a few areminutes.," As we stated above, we find that the sensitivity of the survey gets drastically shallower in the very inner region, decreasing from $\lesssim$ down to $<$ in a few arcminutes." where V is the receiver voltage output corresponding to the sky antenna temperature 74. Toor IS an instrumental offset and Go is the calibration factor. constant to first order.,"where $V$ is the receiver voltage output corresponding to the sky antenna temperature $T_A$, $T_{\rm offset}$ is an instrumental offset and $G_0$ is the calibration factor, constant to first order." In practice. Go can vary due to instrumental effects. e.g. amplifiers gain or thermal instabilities.," In practice, $G_0$ can vary due to instrumental effects, e.g. amplifiers gain or thermal instabilities." " For a differential measurement. as in the case of anisotropy experiments. the calibration is determined using pairs of sources: Τ. T| = Go(Vs—Vi) where T»—T,=AT, is the antenna temperature difference of sources in the sky (often a well-known bright point source and the sky background) and V»—Vj=AV is the corresponding radiometer output."," For a differential measurement, as in the case of anisotropy experiments, the calibration is determined using pairs of sources: T_2 - T_1 = G_0 (V_2-V_1), where $T_2 - T_1=\Delta T_A$ is the antenna temperature difference of sources in the sky (often a well-known bright point source and the sky background) and $V_2-V_1=\Delta V$ is the corresponding radiometer output." In order to measure the value of cosmological parameters with great precision. calibration must be performed at ~1% overall accuracy (a simple estimate of calibration requirement is shown in Appendix Appendix A:)).," In order to measure the value of cosmological parameters with great precision, calibration must be performed at $\sim 1\%$ overall accuracy (a simple estimate of calibration requirement is shown in Appendix \ref{app:requirements}) )." " The error in the determination of Go depends on the a priori uncertaintyon the calibration sources temperatures. cay,. and on the intrinsic detector noise. oy (Bersanellietal. 1997)):f in this expression σα, accounts for both the statistical error - intrinsic. detector noise - and the systematic error uncertainty on the temperatures of the calibration sources-. Eq.(3))"," The error in the determination of $G_0$ depends on the a priori uncertaintyon the calibration sources temperatures, $\sigma_{\Delta T_A}$ , and on the intrinsic detector noise, $\sigma_{\Delta V}$ \cite{oldcalib}) ):; in this expression $\sigma_{G_0}$ accounts for both the statistical error - intrinsic detector noise - and the systematic error -the uncertainty on the temperatures of the calibration sources-. \ref{eq:sigmagoverg}) )" shows that a better calibration is performed ustag higher AT4 (as long as the correspording amplitudes do not exceed the linear range of detectors)., shows that a better calibration is performed using higher ${\Delta T_A}$ (as long as the corresponding amplitudes do not exceed the linear range of detectors). Since Eq., Since Eq. 3 is an estimate of the accuracy on Go using only a pair of points in the sky. and since 11 extended surveys much more sky pixels are observed. the best value of the calibration constant is determined by fitting the distributions of AT and AV. i.e. by minimizing the one parameter y function: where the index K refers to the pixel pairs available for calibration.," \ref{eq:sigmagoverg} is an estimate of the accuracy on $G_0$ using only a pair of points in the sky, and since in extended surveys much more sky pixels are observed, the best value of the calibration constant is determined by fitting the distributions of $\Delta T_A$ and $\Delta V$, i.e. by minimizing the one parameter $\chisq$ function: _k, where the index $k$ refers to the pixel pairs available for calibration." In the following we indicate with G the value of e that minimizes von. while Ορ is the true value of the calibration factor. i.e. the value we need to recover: results will be expressed in terms of G/Go.," In the following we indicate with $G$ the value of $g$ that minimizes $\chisq(g)$ , while $G_0$ is the true value of the calibration factor, i.e. the value we need to recover; results will be expressed in terms of $G/G_0$." An observer in motion with velocity Bv/c relative to the Planckian CMB field sees a dipole pattern: an angular distribution of the temperature given by where Το is the isotropic CMB temperature and.) is the angle between the direction of observation and the direction of B. The CMB dipole has been accurately measured by the COBE-FIRAS instrument (Fixsenetal.1996)) with amplitude ATprp=ToB3.372€0.014 mK (ie. re=3714E kms) in the direction (J.b)=(264.1470.15.48.26740.15): the overall error is =0.4%.," An observer in motion with velocity $\vec{\beta}=\vec{v}/c$ relative to the Planckian CMB field sees a dipole pattern: an angular distribution of the temperature given by where $T_0$ is the isotropic CMB temperature and $\vartheta$ is the angle between the direction of observation and the direction of $\vec{\beta}.$ The CMB dipole has been accurately measured by the $COBE$ -FIRAS instrument \cite{dipole}) ) with amplitude $\Delta T_{DIP}=T_0 \beta=3.372 \pm 0.014$ mK (i.e. $\vec v = 371 \pm 1$ $^{-1}$ ) in the direction $(l,b)=(264.14^\circ \pm 0.15,48.26^\circ \pm 0.15);$ the overall error is $\simeq 0.4\%$." The dipole is an ideal calibration source for CMB anisotropy experiments covering a large sky area., The dipole is an ideal calibration source for CMB anisotropy experiments covering a large sky area. Its amplitude is adequate (not too strong to cause non-linear effects) and it allows a continuous calibration with no reduction of the observation time since it always enters the antenna’s field of view., Its amplitude is adequate (not too strong to cause non-linear effects) and it allows a continuous calibration with no reduction of the observation time since it always enters the antenna's field of view. Besides the CMB dipole. different components contribute to the radio-microwave brightness of the sky.," Besides the CMB dipole, different components contribute to the radio-microwave brightness of the sky." In. this context. we are interested in these emissions (foregrounds) as “contaminations” of the prime calibrator. the CMB ¢ipole.," In this context, we are interested in these emissions (foregrounds) as “contaminations"" of the prime calibrator, the CMB dipole." In fact. these emissions are far less precisely knowt than the dipole and so they represent a drawback for calibration. since they induce large errors in the determination of the G factor.," In fact, these emissions are far less precisely known than the dipole and so they represent a drawback for calibration, since they induce large errors in the determination of the $G$ factor." In our analysis we only considered diffuse components: Synchrotron: free free and interstellar dust emission.," In our analysis we only considered diffuse components: synchrotron, free free and interstellar dust emission." We did not include additional diffuse components. such as emission from spiining dust grains (Draine&Lazarian 1998)). since a spatial and spectral full-sky template is not yet available for such components.," We did not include additional diffuse components, such as emission from spinning dust grains \cite{grains}) ), since a spatial and spectral full-sky template is not yet available for such components." We also did not include point sources (e.g. galactic regions or supernova remnants) since they fill only à very snall fraction of the sky pixels., We also did not include point sources (e.g. galactic regions or supernova remnants) since they fill only a very small fraction of the sky pixels. To prove their low impact we considered as an example the effect of regions: results will be discussed in Sect. 6.., To prove their low impact we considered as an example the effect of regions; results will be discussed in Sect. \ref{sect:LFI-results}. Amplitude and spatial distribution of the considered components have been modeled (from available extended surveys) to produce synthetic sky maps at frequencies typical of CMB anisotropy experiments., Amplitude and spatial distribution of the considered components have been modeled (from available extended surveys) to produce synthetic sky maps at frequencies typical of CMB anisotropy experiments. " We also estimated ,uncertainties on the intensity of each sky pixel for every YQfóeground component.", We also estimated uncertainties on the intensity of each sky pixel for every foreground component. Maps are represented with the pixelization scheme (Gorskietal. 1999))., Maps are represented with the pixelization scheme \cite{healpix}) ). " In this way we are able to produce three sky maps at each frequency of interest: a “calibrator” sky. t.e. the best knowledge of the sky we can infer today from available data: 8) oc (5)an""observed"" sky. which represents a deviation from T,(yao) according to the uncertaintieson the intensity of the considered components: = ct0, Wa.) (6)and a full-sky map of errors cr.0) obtained adding in quadrature the error for each component:"," In this way we are able to produce three sky maps at each frequency of interest: a “calibrator” sky, i.e. the best knowledge of the sky we can infer today from available data: ) = , an“observed” sky, which represents a deviation from $T_{cal}(\alpha,\delta)$ according to the uncertaintieson the intensity of the considered components: ) = = + ) and a full-sky map of errors $\sigma_T(\alpha,\delta)$ obtained adding in quadrature the error for each component: ." The first stars and star clusters are responsible for the initial chemical enrichment ol the universe.,The first stars and star clusters are responsible for the initial chemical enrichment of the universe. Thev are signatures of the earliest stages of galaxy formation. and {heir remnants max provide the seeds or supermassive black holes.," They are signatures of the earliest stages of galaxy formation, and their remnants may provide the seeds for supermassive black holes." The oldest known star clusters are globular clusters (GCs)., The oldest known star clusters are globular clusters (GCs). In ihe Milkv. Was. their color distribution is bimodal (Zinn 1985: Harris 2009). possibly indicaling (wo formation channels.," In the Milky Way, their color distribution is bimodal (Zinn 1985; Harris 2009), possibly indicating two formation channels." The blue. metal-poor GC's ([Fe/Il]< —1) have a typical Fe/H]|~—1.5 and the red. metalricher ([Fe/Il]> —1]) population has a typical |Fe/1l)ce—0.5.," The blue, metal-poor GCs $\rm [Fe/H] <-1$ ) have a typical $\rm [Fe/H]\sim-1.5$ and the red, metal-richer $\rm [Fe/H] > -1]$ ) population has a typical $\rm [Fe/H]\sim -0.5$." Blue GCs (BGCs) have chemical signatures. aud racial distributions that are simiar to halo stars (e.g.. Helm 2008). while the red population is associated with the ealactic clisk and shows a clear circular velocity. component.," Blue GCs (BGCs) have chemical signatures and radial distributions that are similar to halo stars (e.g., Helmi 2008), while the red population is associated with the galactic disk and shows a clear circular velocity component." Relative age estimates show that red GCs are vounger (han DGCs. wilh an average age separation ol about 1.5 Gyr between the Galactic populations (e.g.. de Angeli et al.," Relative age estimates show that red GCs are younger than BGCs, with an average age separation of about 1.5 Gyr between the Galactic populations (e.g., de Angeli et al." 2005)., 2005). The typical GC in the Galaxy has an Mg:—7.3 (Llarris 1991) and mass Af=14x107... assuming a mass-to-light ratio Ty)=2.," The typical GC in the Galaxy has an $M_V\sim-7.3$ (Harris 1991) and mass $M=1.4\times10^{5} M_{\odot}$, assuming a mass-to-light ratio $\Upsilon_V=2$." The dark matter content of these svstenis is small. if present al all (e.g.. Moore 1996: Daunmegzudt et al.," The dark matter content of these systems is small, if present at all (e.g., Moore 1996; Baumgardt et al." 2009)., 2009). "all the neutral gas detected at substantially lower angular resolution in the CO emission(o31"" FFWIIM) by Youngοἱal.(1999).. in the CI emission (~15”"" FEWILIM) by Youngοἱal. (1997).. the HI emission (~42” FFEWIIM) by Rodriguezetal.(2002) and the IL» line emission (~4"" FEWIIM) by Specketal.(2002).","all the neutral gas detected at substantially lower angular resolution in the CO emission$\sim$ FWHM) by \cite{young99}, in the CI emission $\sim$ FWHM) by \cite{young97}, , the HI emission $\sim$ FWHM) by \cite{rodriguez02} and the $_2$ line emission $\sim$ FWHM) by \cite{speck02}." . However. all previous neutral gas studies have had insufficient resolution and sensitivity (o separate and determine the structure and number density of these neutral eas knots.," However, all previous neutral gas studies have had insufficient resolution and sensitivity to separate and determine the structure and number density of these neutral gas knots." The optical study. of the knots by provided an iniüal. lower limit for the total number of cometary. knots to be 3500 in (he entire nebula.," The optical study of the knots by \cite{odell96} provided an initial, lower limit for the total number of cometary knots to be 3500 in the entire nebula." They. base (his estimate by extrapolating the number densitv of knots they can identify in their WEDPC?2 optical images radius to the entire nebula., They base this estimate by extrapolating the number density of knots they can identify in their WFPC2 optical images radius to the entire nebula. Our II» images reveal that manv more molecular knots exist as defined by the Is emission ares than can be identified in (he optical images (Figures 2- 14))., Our $_2$ images reveal that many more molecular knots exist as defined by the $_2$ emission arcs than can be identified in the optical images (Figures \ref{nicpos1}- \ref{nicpos5}) ). For example. in the NICMOS field position 1 the number of knots that appear as [OTI] shadows are less than 10: however. the number of are-shapecl IH» emission structures is 2150.," For example, in the NICMOS field position 1 the number of knots that appear as [OIII] shadows are less than 10; however, the number of arc-shaped $_2$ emission structures is $\sim$ 150." In Table 3.. we list the number of knots. which we identilv by ares of II emission. and the FOV of the image.," In Table \ref{numdentab}, we list the number of knots, which we identify by arcs of $_2$ emission, and the FOV of the image." The number density of knots is simply the total divided by the FOV., The number density of knots is simply the total divided by the FOV. " The area filling factor of Is emission is (he percentage of the FOV that contains Ils emission structures above a la threshold intensiv (c1 2xLO"" erg “om7 ο),", The area filling factor of $_2$ emission is the percentage of the FOV that contains $_2$ emission structures above a $\sigma$ threshold intensity $\sim$ $2 \times 10^{-5}$ erg $^{-1}$ $^{-2}$ $^{-1}$ ). The total number of knots. the munber density of knots and the area filling [actors are the highest for positions 1 and 2. and decrease with arger radial distance from the star as seen in positions 4 and 5.," The total number of knots, the number density of knots and the area filling factors are the highest for positions 1 and 2, and decrease with larger radial distance from the star as seen in positions 4 and 5." Interestingly. the peak surface brightness of the knots does not decrease significantly with radial distance as we see in Figure 15. and Table 2..," Interestingly, the peak surface brightness of the knots does not decrease significantly with radial distance as we see in Figure \ref{nicprof} and Table \ref{surbrtab}." We estimate the total number of molecularknots in the Helix bv sealing the number of knots we observe in our NICMOS images to the total angular size of the Helix., We estimate the total number of molecularknots in the Helix by scaling the number of knots we observe in our NICMOS images to the total angular size of the Helix. If we look at the IH» image of Specketal.(2002) we find that our NICAIOS field positions 1 and 2 Iand in a region of average or slightly below average II» intensity., If we look at the $_2$ image of \cite{speck02} we find that our NICMOS field positions 1 and 2 land in a region of average or slightly below average $_2$ intensity. So. we base a conservative estimate of the total nmunber of knots bv using the average knot number density of positions 1 and 2. 0.041 knols/arcsec?.," So, we base a conservative estimate of the total number of knots by using the average knot number density of positions 1 and 2, 0.041 $^2$." The Hs emission region is an annulus with an inner radius of ~ aand an outer radius of ccovering a (total angular area of 5.5x10? arcsec?.., The $_2$ emission region is an annulus with an inner radius of $\sim$ and an outer radius of covering a total angular area of $5.5\times 10^5$ $^2$. Multiplving the average knot number density by the total angular area equals 223.000. molecular hydrogen knots in the IIelix nebula or a factor of 6.5 larger (han previous estimates based on optical images 1996)..," Multiplying the average knot number density by the total angular area equals $\sim$ 23,000 molecular hydrogen knots in the Helix nebula or a factor of 6.5 larger than previous estimates based on optical images \citep{odell96}. ." The estimatedmass of a single Helix knot is ~1.5x10? M. (ODell& or 1 M. (Youngetal. 1997).., The estimatedmass of a single Helix knot is $\sim$$1.5\times 10^{-5}$ $_\odot$ \citep{odell96} or $^{-4}$ $_\odot$ \citep{young97}. . ILowever. the Youngetal.(1997). CI study defined a “knot” to be the size of x iii size. which would include ~10 Il» knots if we assume the knot densities of postion 1.," However, the \cite{young97} CI study defined a “knot"" to be the size of $\times$ in size, which would include $\sim$ 10 $_2$ knots if we assume the knot densities of postion 1." turbulence becomes weak by shear stabilization(?)..,turbulence becomes weak by shear stabilization\citep{Burrell97}. " This is basically because shear advects turbulent. edcdies differenlially, elongating and distorting their shapes. (hereby rapidly eeneraling small scales which are ultimately. disrupted by molecular dissipation on small scales (see Fig. 1))."," This is basically because shear advects turbulent eddies differentially, elongating and distorting their shapes, thereby rapidly generating small scales which are ultimately disrupted by molecular dissipation on small scales (see Fig. \ref{ShearEff}) )." As a result. turbulence level as well as turbulent transport of various «quantiües can be significantly reduced compared to the case without shear (???)..," As a result, turbulence level as well as turbulent transport of various quantities can be significantly reduced compared to the case without shear \citep{Kim05,Kim06,2Shears}." In parücular. in the case when a stable shear flow is parallel to the magnetic field. a dramatic «quenching of turbulent magnetic diffusion (3-elfect) was clearly shown in a recent numerical simulation of 2D MIID (turbulence (?)..," In particular, in the case when a stable shear flow is parallel to the magnetic field, a dramatic quenching of turbulent magnetic diffusion $\beta$ -effect) was clearly shown in a recent numerical simulation of 2D MHD turbulence \citep{Newton08}." In 3D MIID turbulence. by considering a stable shear flow parallel toa uniform large-scale magnetic field. ? (ühbeoretically. predicted that the a elfect is quenched by shear as well as magnetic field.," In 3D MHD turbulence, by considering a stable shear flow parallel toa uniform large-scale magnetic field, \citet{Quenching} theoretically predicted that the $\alpha$ effect is quenched by shear as well as magnetic field." In particular. in the kinematic case (for weak magnetic field). the a effectwas shown to be reduced as flow shear A increases with the scaling A77.," In particular, in the kinematic case (for weak magnetic field), the $\alpha$ effectwas shown to be reduced as flow shear $\A$ increases with the scaling $\A^{-5/3}$." However. to understand fully the effect of shear on the dvnamo process. il remains to compute itseffect on the turbulence diffusion of magnetic field. i.e. the » effect. bv considering a non-unilorm magnetic field.," However, to understand fully the effect of shear on the dynamo process, it remains to compute itseffect on the turbulence diffusion of magnetic field, i.e. the $\beta$ effect, by considering a non-uniform magnetic field." This is what we do in ihe remainder of this letter., This is what we do in the remainder of this letter. In the kinematic limit. the backreaction of the magnetic field on the velocity is neglected.," In the kinematic limit, the backreaction of the magnetic field on the velocity is neglected." From the physical point of view. this ;:unounts to considering a very weak magnetic [field ancl ignoring the Lorentz Force on the fluid which is quadratic in the magnetic field.," From the physical point of view, this amounts to considering a very weak magnetic field and ignoring the Lorentz Force on the fluid which is quadratic in the magnetic field." For an incompressible conducting fluid. the resulüng equations of motion are: OvytV-= — VpcrANV -f.(4) Op VB=B-ΝΟ. V:V=V-Be=0.," For an incompressible conducting fluid, the resulting equations of motion are: _t + = - p + +, _t + = + , = = 0 ." For simplicity we use the shock radius given by for the relativistic case (Sarl1998:Waxman1997:Panaitescu&Mészáros1998).. while RU)x30)! for the non-relativistic case.Radiation:,"For simplicity we use the shock radius given by R(t) 4 c t/(1+z), for the relativistic case \citep{sari98,waxman97,panaitescu98}, while $R(t) \propto \beta(t) t$ for the non-relativistic case.:" Once the dvnamics abovedetermine 5(/) and R(/). we may estimate the svuchrotron spectrum as follows.," Once the dynamics abovedetermine $\gamma(t)$ and $R(t)$, we may estimate the synchrotron spectrum as follows." " The svnchrotron spectrum from relativistic electrons in a power-law distribution usually has four power-law segmentis withthree breaks at the Lrequency 1,y. the characteristic svnchrotron frequency η. and the cooling frequency v7 (Sari.Piran.&Navavan1998).."," The synchrotron spectrum from relativistic electrons in a power-law distribution usually has four power-law segments withthree breaks at the self-absorption frequency $\nu_{a,f}$, the characteristic synchrotron frequency $\nu_{m,f}$, and the cooling frequency $\nu_{c,f}$ \citep{sari98b}." If we temporarily neglect the self-absorption. the observed {lux is given by right.," If we temporarily neglect the self-absorption, the observed flux is given by ." ".. in the slow cooling case 1j,y νο. and"," in the slow cooling case $\nu_{m,f}<\nu_{c,f}$ , and" through a Fourier analysis of the length of the post-shock zone as a function of time.,through a Fourier analysis of the length of the post-shock zone as a function of time. " The temperature 7,, has been calculated from the emission measure distribution EM(7) (see Sect. 2.3))."," The temperature $T_{\rm ps}$ has been calculated from the emission measure distribution $T$ ) (see Sect. \ref{sect:X-ray_syn}) )," considering only bins with log7(K)>5., considering only bins with $\log T({\rm K})>5$. The maximum extension of the post-shock zone ranges between a factor 0.3 and 1.7 of the length estimated using Eq. 9..," The maximum extension of the post-shock zone ranges between a factor 0.3 and 1.7 of the length estimated using Eq. \ref{eqn:lslab}," whereas the post-shock temperature ranges between a factor 0.7 and 1.0 of the temperature estimated using Eq. 8.., whereas the post-shock temperature ranges between a factor 0.7 and 1.0 of the temperature estimated using Eq. \ref{eqn:posttemp}. The simulated post-shock temperatures are slightly lower than those derived from Eq., The simulated post-shock temperatures are slightly lower than those derived from Eq. 8 because the former are averaged over the whole post-shock zone. whereas the latter are estimated at the shock front. at the maximum extension of the slab.," \ref{eqn:posttemp} because the former are averaged over the whole post-shock zone, whereas the latter are estimated at the shock front, at the maximum extension of the slab." In addition. the simulated post-shock temperatures are averaged over several shock oscillations. including both the heating and the cooling phase of the evolution.," In addition, the simulated post-shock temperatures are averaged over several shock oscillations, including both the heating and the cooling phase of the evolution." During the former. the temperature is slightly higher than that derived from Eq. 8..," During the former, the temperature is slightly higher than that derived from Eq. \ref{eqn:posttemp}," " because the plasma velocity in the reference frame of the shock is higher than (64,,: the opposite is true during the cooling phase.", because the plasma velocity in the reference frame of the shock is higher than $u_{\rm acc}$; the opposite is true during the cooling phase. " The post-shock temperature depends on the accretion stream velocity. whereas both the oscillation period P4, and the length of the post-shock zone /,44 depend on the whole set of model parameters (velocity. density and metal abundance of the stream)."," The post-shock temperature depends on the accretion stream velocity, whereas both the oscillation period $P_{\rm osc}$ and the length of the post-shock zone $l_{\rm max}$ depend on the whole set of model parameters (velocity, density and metal abundance of the stream)." " Figure + and Table 1. show that P, and la, both span 5—6 orders of magnitude for the range of parameters explored here.", Figure \ref{fig:absval} and Table \ref{tab:Results} show that $P_{\rm osc}$ and $l_{\rm max}$ both span $5-6$ orders of magnitude for the range of parameters explored here. In. the complex magnetospheric accretion scenario. the mass density and velocity of the flow could vary along the accretion stream cross section (see for instance 2)).," In the complex magnetospheric accretion scenario, the mass density and velocity of the flow could vary along the accretion stream cross section (see for instance \citealt{Romanova2004ApJ}) )." Consequently. in the case ofB«I. an accretion stream cannot be described by a single 1-D model but has to be considered as a bundle of independent fibrils. each described in terms of a different 1-D model. and each independent on the others (with different instability periods and random phases of," Consequently, in the case of $\beta \ll 1$, an accretion stream cannot be described by a single 1-D model but has to be considered as a bundle of independent fibrils, each described in terms of a different 1-D model, and each independent on the others (with different instability periods and random phases of" larger than 12«101AZ.. but a large contribution of red clisks is observed below that critical mass (vanderWeletal..2009:Mastersct 2010).. in good agreement with the results by Bunelyetal.(2010). on the migration of disk galaxies to the red. sequence.,"larger than $1-2 \times 10^{11}M_\odot$, but a large contribution of red disks is observed below that critical mass \citep{arjen09, masters}, in good agreement with the results by \citet{bundy10} on the migration of disk galaxies to the red sequence." More recently. Holdenetal. report that at all redshifts 2«1 the relative fraction of disk and earlv-tvpe galaxies added to the red sequence at a given stellar mass is approximately. constant.," More recently, \citet{holden11} report that at all redshifts $z<1$ the relative fraction of disk and early-type galaxies added to the red sequence at a given stellar mass is approximately constant." Taking all these previous results together. it is clear that SE quenching in disk galaxies without the need of dramatic morphological perturbations is a valid and frequent mechanism. although not dominant to move galaxies from the blue cloud to the red. sequence.," Taking all these previous results together, it is clear that SF quenching in disk galaxies without the need of dramatic morphological perturbations is a valid and frequent mechanism –although not dominant– to move galaxies from the blue cloud to the red sequence." For this reason. red disk galaxies have drawn the attention of the extragalactic community.," For this reason, red disk galaxies have drawn the attention of the extragalactic community." In the late τς. vandenBergh(1976). reported. the existence. of passive galaxies with spiral morphology in the Virgo Cluster. ane later studies confirmed. the existence of a population of quiescent clisk galaxies in dense environments (i.c..Pogeiantietal.. 1900).," In the late 70's, \citet{vdb} reported the existence of passive galaxies with spiral morphology in the Virgo Cluster, and later studies confirmed the existence of a population of quiescent disk galaxies in dense environments \citep[i.e.,][]{poggianti}." More recently Wolfetal.(2009). show tha in intermeciatc-mass cluster environment red spiral galaxies are equivalent to the actively star-forming blue spirals. bu with lower SE and a higher fraction of dust-obscuration.," More recently \citet{wolf09} show that in intermediate-mass cluster environment red spiral galaxies are equivalent to the actively star-forming blue spirals, but with lower SF and a higher fraction of dust-obscuration." These galaxies also tend to display stronger har features than their blue counterparts (Llovleetal.2011a)., These galaxies also tend to display stronger bar features than their blue counterparts \citep{ben11a}. . A hin on the origin of these systems is provided also bv. Bamforetal.(2009) and Skibbactal.(2009).. who found by using visually classified SDSS galaxies [rom Galaxy Zoo (GZ) tha he relation between optical color and environment is more significant than the well known morphologv-density relation Dressler(1980).," A hint on the origin of these systems is provided also by \citet{bamford} and \citet{skibba09}, who found by using visually classified SDSS galaxies from Galaxy Zoo (GZ) that the relation between optical color and environment is more significant than the well known morphology-density relation \citet{dressler}." . Decades of studies have shaped a solid knowledge of the stellar populations of red-sequence galaxies., Decades of studies have shaped a solid knowledge of the stellar populations of red-sequence galaxies. These galaxies ollow several tight scaling relations linking their. stellar opulation properties to their mass and their dynamical and structural properties. such as the color-magnitude relation (Faber.1973:Gonzalezeta.1993).. the relation between absorption index strengths ancl velocity dispersion (Benderetal.1993:IxelsonaL.2006:Changal..2006) and the Fundamental Plane (Djorgovski&Davis.1987:Bernardietal.. 2003).," These galaxies follow several tight scaling relations linking their stellar population properties to their mass and their dynamical and structural properties, such as the color-magnitude relation \citep{faber73,GFW93}, the relation between absorption index strengths and velocity dispersion \citep{Bender93,Kelson06,Chang06} and the Fundamental Plane \citep{DD-FP,Bernardi03}." . Phe physical drive of these relations is an increase in all of metalliety. element abundance ratios and stellar age with galaxy mass or velocity dispersion (Trageretal..2000:2006:Tojeiro&Percival. 2010).," The physical drive of these relations is an increase in all of metallicty, element abundance ratios and stellar age with galaxy mass or velocity dispersion \citep{Trager00,kunt01,thomas05,anna06, tojeiro10}." . Indeed. stellar population properties seem to be more fundamentally: correlated. with stellar velocity. dispersion than with galaxy mass (Ciravesetal.. 2009).," Indeed, stellar population properties seem to be more fundamentally correlated with stellar velocity dispersion than with galaxy mass \citep{Graves09}." . The picture that emerges is that present-dav elliptical galaxies with deeper potential wells have reached a higher degree of chemical enrichment and have formed their gaas at earlier epochs and on shorter timescales., The picture that emerges is that present-day elliptical galaxies with deeper potential wells have reached a higher degree of chemical enrichment and have formed their stars at earlier epochs and on shorter timescales. Moreover. 1e small intrinsic scatter in the observed. scaling relations is associated primarily with variations in stellar age and. to a lesser degree. in chemical abundances. putting additional constraints on the variety of SELIs that present-day elliptical ealaxies of similar mass have undergone (e.g.Jimenezetal.2005.2007:Gallazzietal..2006:Graves 2010).," Moreover, the small intrinsic scatter in the observed scaling relations is associated primarily with variations in stellar age and, to a lesser degree, in chemical abundances, putting additional constraints on the variety of SFHs that present-day elliptical galaxies of similar mass have undergone \citep[e.g.][]{raul05,raul07,anna06,Graves10}." . An additional parameter. that. inlluences. the SEL. hence the stellar populations. of elliptical galaxies is their environment.," An additional parameter that influences the SFH, hence the stellar populations, of elliptical galaxies is their environment." While the slope of the scaling relations is independent. of the environment. small variations in their zero-point and scatter have been observed. indicating both that the fraction of galaxies with vounger stellar populations (rejuvenated) increases in low density environments (Thomasctal.2010). and that at fixed mass galaxies in denser environments tend to be older than their low-density couterparts (Cooperetal..2010:Clemens2006:Llovleetal..2011b).," While the slope of the scaling relations is independent of the environment, small variations in their zero-point and scatter have been observed, indicating both that the fraction of galaxies with younger stellar populations (“rejuvenated”) increases in low density environments \citep{Thomas10} and that at fixed mass galaxies in denser environments tend to be older than their low-density couterparts \citep{Cooper10,Clemens06, ben11}." ". On the other hand relatively few works (see e.g. SSansom 2002. ""Thomas&DDawvies 2006. Ixuntschner et al 2010. Faleon-Barroso et al 2011) have analysecl the stellar populations ancl sealing relations of dillerent/ morphological types. in particular among rec-sequence galaxies."," On the other hand relatively few works (see e.g. Sansom 2002, Davies 2006, Kuntschner et al 2010, Falcon-Barroso et al 2011) have analysed the stellar populations and scaling relations of different morphological types, in particular among red-sequence galaxies." Thomas&DDavies 2006 reanalvsed the sample of spiral bulges (from Sa. to. She) of Proctor&SSansom 2002 and found that the bulges of spiral ealaxies have similar stellar populations to elliptical galaxics ab fixed. velocity dispersion., Davies 2006 reanalysed the sample of spiral bulges (from Sa to Sbc) of Sansom 2002 and found that the bulges of spiral galaxies have similar stellar populations to elliptical galaxies at fixed velocity dispersion. Early-type spiral galaxies. also seem to follow the same Fundamental Plane as cllipticals. albeit with larger scatter (Falcon-Darroso et al 2011).," Early-type spiral galaxies also seem to follow the same Fundamental Plane as ellipticals, albeit with larger scatter (Falcon-Barroso et al 2011)." llowever these works generally do not) distinguish galaxies on the basis of their star formation activity., However these works generally do not distinguish galaxies on the basis of their star formation activity. In this work we are specifically interested. in comparing the stellar populations of galaxies that are quiescent but dliller in morphology. namely quiescent. spirals against elliptical galaxies.," In this work we are specifically interested in comparing the stellar populations of galaxies that are quiescent but differ in morphology, namely quiescent spirals against elliptical galaxies." Mastersetal.(2010). primary focus was in the characterization of red spirals and the comparison with blue spirals. but a detailed comparison of the stellar populations in quiescent spiral and. early-type galaxies could shed some ieht on the processes by which they are formed. ancl subsequently quenched.," \citet{masters} primary focus was in the characterization of red spirals and the comparison with blue spirals, but a detailed comparison of the stellar populations in quiescent spiral and early-type galaxies could shed some light on the processes by which they are formed and subsequently quenched." In particular. given the differences bound between red and blue spirals in Mastersetal.(2010).. it would be extremely important to learn whether the stars in spiral galaxies can follow an evolutionary path similar to hose in spheroidal systems even when the morphological evolution of their host. galaxies is dramatically cillerent. as hat would put constraints on the mechanisms driving the star formation histories of passive galaxies in the Universe.," In particular, given the differences found between red and blue spirals in \citet{masters}, it would be extremely important to learn whether the stars in spiral galaxies can follow an evolutionary path similar to those in spheroidal systems even when the morphological evolution of their host galaxies is dramatically different, as that would put constraints on the mechanisms driving the star formation histories of passive galaxies in the Universe." In this paper. we study the stellar populations in the central regions of a sample of truly passive spiral galaxics aonS&SOL from SDSS and compare them to those in quiescent ellipticals.," In this paper, we study the stellar populations in the central regions of a sample of truly passive spiral galaxies at $z\lesssim 0.1$ from SDSS and compare them to those in quiescent ellipticals." We choose to do so by comparing the ages. total metallicities (Z/11]) and. in particular. the a enhancement of their populations.," We choose to do so by comparing the ages, total metallicities ([Z/H]) and, in particular, the $\alpha-$ enhancement of their populations." In order to assemble a statistically significant galaxy sample we use data products from the NYU-VAC (Blantonetal.2003) ancl visua morphology estimates from the Galaxy Zoo project (Lintotetal.2008. 2011).," In order to assemble a statistically significant galaxy sample we use data products from the NYU-VAC \citep{blanton03} and visual morphology estimates from the Galaxy Zoo project \citep{lintott1,lintott2}." . We also mocel the stellar populations in SDSS DIU. quiescent galaxies. following the methoc described in Gallazzi et al. (," We also model the stellar populations in SDSS DR7 quiescent galaxies, following the method described in Gallazzi et al. (" 2005. 2006)(herealter G05 anc (060 respectively). to obtain stellar masses. r-band weightec ages. Z/II] and AMeb/ a tracer of the a-enhancement.,"2005, 2006)(hereafter G05 and G06 respectively), to obtain stellar masses, r-band weighted ages, [Z/H] and $\Delta$ $\langle$ $\rangle$ –a tracer of the $\alpha$ -enhancement." We end up with a sample of 1000 equiescent. spiral a ~1ATOO passive earlv-type galaxies., We end up with a sample of $\sim$ 1000 quiescent spiral and $\sim$ 14700 passive early-type galaxies. This paper is organized as follows: In. Section 2. we describe the sample selection and the parameters we use to characterize the stellar populations., This paper is organized as follows: In Section 2 we describe the sample selection and the parameters we use to characterize the stellar populations. In Section 3 we present our results and diseuss possible evolutionary paths., In Section 3 we present our results and discuss possible evolutionary paths. Finally. in Section 4. we present our conclusions.," Finally, in Section 4, we present our conclusions." Throughout this paper we use ος. O 4420.7 and foo =O0.7.," Throughout this paper we use $\Omega_{m0}$ =0.3, $\Omega_{\Lambda 0}$ =0.7 and $h_{100}$ =0.7." All magnitudes are in the AB photometric svstenm., All magnitudes are in the AB photometric system. in 10 several lightcurves from our time-dependent simulationsFigure for wwith different values of,in Figure \ref{f.mxb-varQ} several lightcurves from our time-dependent simulations for with different values of. " In the left panel, we keep all other parameters fixed as we Qimp..varyOjmp;; in the right panel, we adjust T; to match the first data point as we varyQimp."," In the left panel, we keep all other parameters fixed as we vary; in the right panel, we adjust $T_b$ to match the first data point as we vary." . The effect of increasing iis to delay the cooling., The effect of increasing is to delay the cooling. Qimp This can be understood in terms of the initial temperature profile at the end of the outburst., This can be understood in terms of the initial temperature profile at the end of the outburst. " When the crust has a larger impurity level, the inner crust must be hotter to be able to conduct the heat released in the crust into the core."," When the crust has a larger impurity level, the inner crust must be hotter to be able to conduct the heat released in the crust into the core." " This increase in the inner crust temperature leads to a hotter outer crust, with a shallower temperature gradient, giving a lightcurve that falls less quickly."," This increase in the inner crust temperature leads to a hotter outer crust, with a shallower temperature gradient, giving a lightcurve that falls less quickly." " As Figure 9 shows, the correlations between the fitted parameters are such that larger vvalues lead to lower values of T; Qimpand T;, i.e. to compensate for the delayed cooling due to increase in the overalltemperature scale set by T, and T; decreases."," As Figure \ref{f.qmap} shows, the correlations between the fitted parameters are such that larger values lead to lower values of $T_c$ and $T_b$, i.e. to compensate for the delayed cooling due to increase in, the overalltemperature scale set by $T_c$ and $T_b$ decreases." "Qimp,, In1731—260,, the probability distribution of hhas a peak at a similar value to1659--29., but with a long tail to small values ofQimp."," In, the probability distribution of has a peak at a similar value to, but with a long tail to small values of." ". In fact, as can be seen in Figure 11,, the fits are not sensitive to the impurity parameter for QispS1, which results in a flat probability distribution in logQiny,, reflecting the assumed prior."," In fact, as can be seen in Figure \ref{f.qmap3}, the fits are not sensitive to the impurity parameter for $\lesssim1$ , which results in a flat probability distribution in $\log$, reflecting the assumed prior." " For both sources, vvalues larger than 10 are ruled out."," For both sources, values larger than 10 are ruled out." " For1659—29,, we have used the temperatures derived by Cackett et al. ("," For, we have used the temperatures derived by Cackett et al. (" 2008) assuming a distance to the source of 10kpc.,2008) assuming a distance to the source of $10\ {\rm kpc}$. " In that paper, spectral models for different distances d=5 and 13kpc are considered, which leads to a systematic decrease or increase in the effective temperatures by 10—20%."," In that paper, spectral models for different distances $d=5$ and $13\ {\rm kpc}$ are considered, which leads to a systematic decrease or increase in the effective temperatures by $10$ $20$." ". The reason that the fitted effective temperatures depend on distance is that the peak of the thermal spectrum lies outside the X-ray band, making the fitted temperature sensitive to the overall luminosity scale."," The reason that the fitted effective temperatures depend on distance is that the peak of the thermal spectrum lies outside the X-ray band, making the fitted temperature sensitive to the overall luminosity scale." " To investigate the effect of such systematic variations, we have calculated the constraints on the models with the effective for aall decreased or increased bytemperatures20%."," To investigate the effect of such systematic variations, we have calculated the constraints on the models with the effective temperatures for all decreased or increased by." ". The effect is to change the central value of each distribution by up to50%,, with the width staying about the same."," The effect is to change the central value of each distribution by up to, with the width staying about the same." The conclusion that iis of order unity is unaffected by these systematic variations., The conclusion that is of order unity is unaffected by these systematic variations. Qimp The accretion rate M sets the overall amount of heating in the crust during the outburst., The accretion rate $\dot M$ sets the overall amount of heating in the crust during the outburst. " There are uncertainties in deriving M from the observed luminosity, and in addition, the amount of heating in the X-raycrust may differ from the 1.7MeV per nucleon that we assume in our calculation (see Appendix for details)."," There are uncertainties in deriving $\dot M$ from the observed X-ray luminosity, and in addition, the amount of heating in the crust may differ from the $1.7\nsp\MeV$ per nucleon that we assume in our calculation (see Appendix for details)." " The calculations so far have taken a fixed accretion rate M=1017gs-!.Instead, we now calculate the constraints on M assuming a uniform prior probability for M between 0 (ie. no deep heating) and 1015gs-! (ten times our fiducial rate)."," The calculations so far have taken a fixed accretion rate $\dot M=10^{17}\ {\rm g\ s^{-1}}$.Instead, we now calculate the constraints on $\dot M$ assuming a uniform prior probability for $\dot M$ between $0$ (i.e. no deep heating) and $10^{18}\nsp\grampersecond$ (ten times our fiducial rate)." " The results are shown in Figure 11,, in which we give the derived joint probability distribution for M and ffor each source."," The results are shown in Figure \ref{f.qmap3}, , in which we give the derived joint probability distribution for $\dot M$ and for each source." " The temperaturesOimp 7; and T; are not sensitive to variations in M, since theyare essentially fixed by the first and last observed values of T7. For both sources, wefind an anti-correlation between M and"," The temperatures $T_b$ and $T_c$ are not sensitive to variations in $\dot M$ , since theyare essentially fixed by the first and last observed values of $T^\infty_{\rm eff}$ For both sources, wefind an anti-correlation between $\dot M$ and" derived. by Lacey&Cole(1993) using the mass-halving times for single trajectories. although the Lacey&Cole(1993) expression contains a dependence on the shape of the dark-matter power spectrum whereas that of Sasaki(1994) does not.,"derived by \citet{lc93} using the mass-halving times for single trajectories, although the \citet{lc93} expression contains a dependence on the shape of the dark-matter power spectrum whereas that of \citet{sasaki94} does not." Llowever. for our work we are really interested in knowing the properties of gas in a halo.," However, for our work we are really interested in knowing the properties of gas in a halo." Llalos of given mass that formed earlier will be denser ancl hotter., Halos of given mass that formed earlier will be denser and hotter. In reality. the process of cluster formation is a continuous one and so it is not clear just how the formation redshift should. affect. the eas properties.," In reality, the process of cluster formation is a continuous one and so it is not clear just how the formation redshift should affect the gas properties." " In this work we will therefore consider both distributions. and also the case of 2,=τω."," In this work we will therefore consider both distributions, and also the case of $z_{\rm f}=z_{\rm o}$." Two of these »ossibilities are limiting cases., Two of these possibilities are limiting cases. " Phe case 2,= is clearly he lower limit on formation recshilt. while the distribution oposed by Lacey&Cole(1993) should give a reasonable upper limit as it is dillicult to see how the observed. gas ooperties could be determined by the physical state at any earlier time (ie. when less than hall of the final mass of he eluster is in place)."," The case $z_{\rm f} = z_{\rm o}$ is clearly the lower limit on formation redshift, while the distribution proposed by \citet{lc93} should give a reasonable upper limit as it is difficult to see how the observed gas properties could be determined by the physical state at any earlier time (i.e. when less than half of the final mass of the cluster is in place)." Our default distribution will be the Sasaki model., Our default distribution will be the Sasaki model. With ο) a Gaussian. the Press-Schechter theory oedietions diller significantly from the results of numerical simulations of structure formation (by a factor close to 2 at he characteristic mass AM)., With $P(y)$ a Gaussian the Press-Schechter theory predictions differ significantly from the results of numerical simulations of structure formation (by a factor close to 2 at the characteristic mass $M_*$ ). Several fitting formulae have »en proposed which produce a much better agreement with numerical results., Several fitting formulae have been proposed which produce a much better agreement with numerical results. We will consider two such fitting formulae. hose proposed by Sheth&Tormen(1999) and Jenkinset (hereafter ST. and J2000 respectively). which can »e described by where @=0.707 and q=0.3 for the ST formula. and cL=0.301(307). ο=0.64(0.61) and p=388682) for the 2000 formula in the . XCDAM(zCDÀM) cosmology considered in ," We will consider two such fitting formulae, those proposed by \citet{st99} and \citet{jenkins00} (hereafter ST and J2000 respectively), which can be described by where $a=0.707$ and $q=0.3$ for the ST formula and $A=0.301(307)$, $c=0.64(0.61)$ and $p=3.88(3.82)$ for the J2000 formula in the $\Lambda$ $\tau$ CDM) cosmology considered in \\ref{sec:results}." To explore non-Gaussian initial conditions we make use of the log-normal probability clistribution proposed. by Robinson.Gawiser&Silk(2000).. (y) =Ini|CyLALZALAM.with cf B. and C' as defined. by Robinson.CGawiser&Silk(2000).," To explore non-Gaussian initial conditions we make use of the log-normal probability distribution proposed by \citet{rgs}, where $x(y)=\ln(B+C y |A|/A)/|A|$, with $A$, $B$ and $C$ as defined by \citet{rgs}. ." . The degree of non-Gaussianity is fully specified by the parameter o (with ef=0 corresponding to the Ciaussian limit)., The degree of non-Gaussianity is fully specified by the parameter $A$ (with $A=0$ corresponding to the Gaussian limit). We will. however. characterize non-Gaussian mocdels by the more intuitive variable €. defined. by Robinson.Ciawiser&Silk(2000) as the number of 370 peaks in the non- distribution relative to the number in a Gaussian distribution (such that €/=1 represents the Gaussian limit).," We will, however, characterize non-Gaussian models by the more intuitive variable $G$, defined by \citet{rgs} as the number of $>3\sigma$ peaks in the non-Gaussian distribution relative to the number in a Gaussian distribution (such that $G=1$ represents the Gaussian limit)." The above calculations allow us to calculate the mean abundance of dark-matter halos as a function of their mass. ane redshifts of observation. ancl formation for any given cosmological parameters.," The above calculations allow us to calculate the mean abundance of dark-matter halos as a function of their mass, and redshifts of observation and formation for any given cosmological parameters." However. for SZ surveys covering relatively small fields. of view it is important to assess the ellects of sample variance (aka.," However, for SZ surveys covering relatively small fields of view it is important to assess the effects of sample variance (a.k.a." cosmic variance) in order to accurately determine the ability of the survey to discriminate between models., cosmic variance) in order to accurately determine the ability of the survey to discriminate between models. In fact. the sample variance is expected to be rather small (close to Poissonian) since the SZ cllect probes a wide range of redshifts such that any intrinsic correlations between clusters are clilutect (as can be estimated using analytical calculations of the cluster bias to compute their angular correlation function)," In fact, the sample variance is expected to be rather small (close to Poissonian) since the SZ effect probes a wide range of redshifts such that any intrinsic correlations between clusters are diluted (as can be estimated using analytical calculations of the cluster bias to compute their angular correlation function)." ‘To measure the sample variance we make use of the Llubhle Volume simulations which were carried out by the VIRGO Consortium and which are publically available (I2vrardctal. 1998)., To measure the sample variance we make use of the Hubble Volume simulations which were carried out by the VIRGO Consortium and which are publically available \citep{evrard98}. . These large N-body simulations have been used to construct catalogues of dark-matter halos (listing the mass and observed. redshift) as seen along a past lightcone., These large N-body simulations have been used to construct catalogues of dark-matter halos (listing the mass and observed redshift) as seen along a past lightcone. ‘To compute the cosmic variance from these simulations we construct mock surveys of the required angular size by choosing a random line of sight. through the simulation lichtcone and assigning each cluster in the field of view the SZ tux computed from our model for a cluster of the same mass and observed: redshilt and with a formation redshift drawn at random. from the distributions described. above (note that this assumes that the spatial distribution of halos of given mass ancl observed redshift is independent of their formation redshift. which is unlikely to be correct in detail).," To compute the cosmic variance from these simulations we construct mock surveys of the required angular size by choosing a random line of sight through the simulation lightcone and assigning each cluster in the field of view the SZ flux computed from our model for a cluster of the same mass and observed redshift and with a formation redshift drawn at random from the distributions described above (note that this assumes that the spatial distribution of halos of given mass and observed redshift is independent of their formation redshift, which is unlikely to be correct in detail)." We then compute the statistic of interest. from this mock survey., We then compute the statistic of interest from this mock survey. Repeating for severalmock surveys we obtain a measure of the variance in the statistic.,Repeating for severalmock surveys we obtain a measure of the variance in the statistic. Results from these calculations will be shown in rofsecirescosmo.., Results from these calculations will be shown in \\ref{sec:rescosmo}. . to rule out one model relative to the other. the Nine model systematically fits these cluster profiles better.,"to rule out one model relative to the other, the King model systematically fits these cluster profiles better." To address the iiportauce of the background subtraction to this conclusion. we have lighlighted in the Figure the clusters for which the background is determuned to better than of the clusters central surface brightuess (au uncertaintv level below which the cluster profiles do uot appear to be erossly disturbed by incorrect background subtraction. see Figure 2)).," To address the importance of the background subtraction to this conclusion, we have highlighted in the Figure the clusters for which the background is determined to better than of the cluster's central surface brightness (an uncertainty level below which the cluster profiles do not appear to be grossly disturbed by incorrect background subtraction, see Figure \ref{fig:profile background}) )." These high quality surface xiehtuess profiles follow the mean trend., These high quality surface brightness profiles follow the mean trend. Iu the cases where the Kine model does siguificautl better than he EFF inodels aud the cluster is a rich cluster with a well determined sky brieltuess and overall profile. he difference im the models is clearly in the outermost reeious (see for examples chisters 85. 86. 96. 113. 171).," In the cases where the King model does significantly better than the EFF models and the cluster is a rich cluster with a well determined sky brightness and overall profile, the difference in the models is clearly in the outermost regions (see for examples clusters 85, 86, 96, 143, 174)." Iu other cases. the cause for the preference of the Ning uodel is more subtle aud ambiguous.," In other cases, the cause for the preference of the King model is more subtle and ambiguous." It is presumably due to a cuuulative effect iu the ft over the range )etween core aud tidal radius., It is presumably due to a cumulative effect in the fit over the range between core and tidal radius. To examine whether one particular model is favored or clusters of a particular age. for example EFF models or the vouugest clusters. we have plotted the ditfereuce iu AZ values as a function of age (ages from Rafelski& (2001))) in Figure 10. for fits where either the Ning or EFF model had 42«1.," To examine whether one particular model is favored for clusters of a particular age, for example EFF models for the youngest clusters, we have plotted the difference in $\chi_{\nu}^2$ values as a function of age (ages from \cite{rz}) ) in Figure \ref{fig:chi_age} for fits where either the King or EFF model had $\chi_\nu^2 < 1$." There is no trend evident that favors one particular mocel at a specific age., There is no trend evident that favors one particular model at a specific age. The ecneral preference. for King models (AZ.> 0) is seen at all ages., The general preference for King models $\Delta \chi_\nu^2 > 0$ ) is seen at all ages. Of course this result doesu't arene against the effectiveness of the EFF profile for some clusters. nor against the existence of some clusters that are not tidally limited.," Of course this result doesn't argue against the effectiveness of the EFF profile for some clusters, nor against the existence of some clusters that are not tidally limited." Nevertheless. the situation is clearly more coniplicated than an expectation that all voung clusters should have power-law surface brightuess profiles.," Nevertheless, the situation is clearly more complicated than an expectation that all young clusters should have power-law surface brightness profiles." Eveu those clusters that are well-fit by a ing profile are not drawn from a single parameter population., Even those clusters that are well-fit by a King profile are not drawn from a single parameter population. Although the core radius. r.. and rey are correlated at the confidence level (Spearman rauk test: see Table 3)). clusters distribute themselves over the entire rauge of rog/r. that we allow iu our fitting space eiveu the theoretical constraints described by Wivantoctal.(1985). (Figure 11)).," Although the core radius, $r_c$, and $r_{90}$ are correlated at the confidence level (Spearman rank test; see Table \ref{tab:Spearman Correlations}) ), clusters distribute themselves over the entire range of $r_{90}/r_c$ that we allow in our fitting space given the theoretical constraints described by \cite{w85} (Figure \ref{fig:c90loghist}) )." This προς that a varletv of factors influence the observed structural parameters., This implies that a variety of factors influence the observed structural parameters. Possible iufiueuces include tidal effects. age (the tuternal dvuamical evolution of the cluster). aud initial couditious (substructure. velocity anisotropics. initial stellar nmiass function. angular moment. ancl chenucal abundance).," Possible influences include tidal effects, age (the internal dynamical evolution of the cluster), and initial conditions (substructure, velocity anisotropies, initial stellar mass function, angular momentum, and chemical abundance)." These are notoriously difficult to discutanele. but the large. uniforms sample presented here offers a new opportunity to search for clues.," These are notoriously difficult to disentangle, but the large, uniform sample presented here offers a new opportunity to search for clues." We find Kine profiles to be a statistically acceptable fit to clusters that range over a factor of over LO in ο. 10 iu rog. and LO? in Ny.," We find King profiles to be a statistically acceptable fit to clusters that range over a factor of over 40 in $r_{c}$, 10 in $r_{90}$, and $10^{3}$ in $\Sigma_0$." This finding is somewhat surprising in lieht of the fact that the vast majority of clusters are inferred to be in the process of dissolution or disruption ou the basis of the cluster age distribution (Boutloukos&Lamers2003:Ratelski&Zaritsky2001) aud many have hac insufficient time to dvuamically relax.," This finding is somewhat surprising in light of the fact that the vast majority of clusters are inferred to be in the process of dissolution or disruption on the basis of the cluster age distribution \citep{bl,rz} and many have had insufficient time to dynamically relax." Therefore. the fits to some clusters are almost certaimly uot physically meaninefil. but rather are statistically allowed eiven the large observational uncertainties.," Therefore, the fits to some clusters are almost certainly not physically meaningful, but rather are statistically allowed given the large observational uncertainties." Nevertheless. even m these cases our measurements do reflect the size of the cluster aud its core.," Nevertheless, even in these cases our measurements do reflect the size of the cluster and its core." Although the Lhuge majority of SMC clusters are adequately fit by simple Ίνπιο profiles. and heuce demonstrate that measuring surtace brightness profiles alone is uot a promising avenue to ideutifviug dissolving clusters. there are several populations of clusters that merit further discussion aud iav be showing sigus of their dvuamical evolution.," Although the large majority of SMC clusters are adequately fit by simple King profiles, and hence demonstrate that measuring surface brightness profiles alone is not a promising avenue to identifying dissolving clusters, there are several populations of clusters that merit further discussion and may be showing signs of their dynamical evolution." A subset of our cluster luminosity profiles contain a sienificant bunip in the huninosity profile relative to the fitted Nine or EFF profile., A subset of our cluster luminosity profiles contain a significant bump in the luminosity profile relative to the fitted King or EFF profile. Of those. visual inspection," Of those, visual inspection" "Milesetal.(2004). found. in their study of GEMS groups. an interesting feature referred to as ""dip"" in the optical luminosity ‘unction of dim Cow velocity dispersion) X-ray groups compared to bright thigh velocity dispersion) X-ray groups interpreted as being oroduced as a result of more efficient galaxy merger in low velocity dispersion groups.","\citet{miles04} found, in their study of GEMS groups, an interesting feature referred to as “dip” in the optical luminosity function of dim (low velocity dispersion) X-ray groups compared to bright (high velocity dispersion) X-ray groups interpreted as being produced as a result of more efficient galaxy merger in low velocity dispersion groups." Similarly. the main argument behind the lack of bright galaxies in fossils is the merger of L” galaxies. but fossils are in general more X-ray luminous than the dim X-ray groups studied by (Milesetal.2004).," Similarly, the main argument behind the lack of bright galaxies in fossils is the merger of $L^\star$ galaxies, but fossils are in general more X-ray luminous than the dim X-ray groups studied by \citep{miles04}." . The velocity dispersion of galaxies in this 'ossil cluster is σzz700 km + which is consistent with the value expected from the observed cluster Ly -o (Mahdavi&Geller2001) given the X-ray luminosity of this cluster., The velocity dispersion of galaxies in this fossil cluster is $\sigma\approx 700$ km $^{-1}$ which is consistent with the value expected from the observed cluster $L_X$ $\sigma$ \citep{mahdavi01} given the X-ray luminosity of this cluster. Similarly 31552.24-2013. ies on the same x-c relation (MendesdeOliveira.CyprianoSodreJr. 2005).. though£L the scatter in the £Ly -0 relation is large.," Similarly J1552.2+2013, lies on the same $L_X$ $\sigma$ relation \citep{mendes05}, though the scatter in the $L_X$ $\sigma$ relation is large." An especially interesting feature of RX Jl416.442315 is the large size and mass of the system., An especially interesting feature of RX J1416.4+2315 is the large size and mass of the system. Dynamical friction. the key process believed to be responsible for the orbit decay which allows the major galaxies to merge within fossil groups. is much less effective at high velocities. raising the question of whether the existence of such a fossil cluster poses a problem for the whole model of fossil system formation through galaxy merging.," Dynamical friction, the key process believed to be responsible for the orbit decay which allows the major galaxies to merge within fossil groups, is much less effective at high velocities, raising the question of whether the existence of such a fossil cluster poses a problem for the whole model of fossil system formation through galaxy merging." " Jonesetal.(2000). estimated the time-scale of dynamical friction for the original fossil group. 31340.64-4018. and showed that L galaxies. initially in circular orbits at half the virial radius and. circular velocity of /26. should merge into the central galaxy in 4.5«10"" yr."," \citet{jones00} estimated the time-scale of dynamical friction for the original fossil group, J1340.6+4018, and showed that $L^\star$ galaxies, initially in circular orbits at half the virial radius and circular velocity of $\sqrt{2}\sigma$, should merge into the central galaxy in $4.5\times10^{9}$ yr." The subject of this study. 11416. is more massive and has a radial velocity dispersion. c almost twice that of J1340.64-40x," The subject of this study, J1416, is more massive and has a radial velocity dispersion, $\sigma$ almost twice that of J1340.6+4018." It also has a larger virial radius., It also has a larger virial radius. The time seale for orbital decay of a body of mass AJ by dynamical friction is proportional to E]un (Binney&Tremaine1987)... which means that a L galaxy in j.this system will require a dynamical friction time-seale larger than a Hubble time to merge.," The time scale for orbital decay of a body of mass $M$ by dynamical friction is proportional to $\frac{r^2 v_c}{M}$, \citep{binney87}, which means that a $L^\star$ galaxy in this system will require a dynamical friction time-scale larger than a Hubble time to merge." We note. however. that this estimate is based on initial conditions in which the galaxy is part of a virialised system and rotates on a cireular orbit around the centre.," We note, however, that this estimate is based on initial conditions in which the galaxy is part of a virialised system and rotates on a circular orbit around the centre." If instead. galaxies fall into the developing cluster along a filament. the loss of the angular momentum could occur in a much shorter time. due to the small pericentre radius of their orbits.," If instead, galaxies fall into the developing cluster along a filament, the loss of the angular momentum could occur in a much shorter time, due to the small pericentre radius of their orbits." The X-ray emission. and hence the dark matter distribution in 11416. is highly elongated. implying a very anisotropic velocity dispersion tensor. and supporting the idea of collapse along a dominant filament.," The X-ray emission, and hence the dark matter distribution in J1416, is highly elongated, implying a very anisotropic velocity dispersion tensor, and supporting the idea of collapse along a dominant filament." Recent simulations of the formation of fossil systems also suggest that they can be formed with high masses., Recent simulations of the formation of fossil systems also suggest that they can be formed with high masses. D'Onghiaetal.(2005). find that fossil groups have already assembled half of their final mass at ze 1. and subsequently they typically grow by minor merging only.," \citet{donghia05} find that fossil groups have already assembled half of their final mass at $\sim$ 1, and subsequently they typically grow by minor merging only." " The early assembly of fossils groups leaves sufficient time for L"" galaxies to merge into the central galaxy by dynamical friction. resulting in the large magnitude gap."," The early assembly of fossils groups leaves sufficient time for $L^\star$ galaxies to merge into the central galaxy by dynamical friction, resulting in the large magnitude gap." We would like to thank and observatory teams and the anonymous referee for helpful comments and suggestions that improved the presentation of the paper., We would like to thank and observatory teams and the anonymous referee for helpful comments and suggestions that improved the presentation of the paper. We also would like to thank John Mulchaey for his involvement in spectroscopic observations of the target and Issac-Newton group of telescopes for service observation of the target with INT., We also would like to thank John Mulchaey for his involvement in spectroscopic observations of the target and Issac-Newton group of telescopes for service observation of the target with INT. BJM is supported by NASA through Chandra Postdoctoral Fellowship Award Number PF4-50034 issued by the Chandra X-ray Observatory Center. which is operated by the Smithsonian Astrophysical Observatory for and on behalf ofNASA under contract NAS8-03060.," BJM is supported by NASA through Chandra Postdoctoral Fellowship Award Number PF4-50034 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060." The magnetic field strengths in the extended components of extragalactic radio sources cannot be inferred directly from observations of synchrotron emission. and so the energy densities and pressures in the radio-emitting components are. poorly constrained.,"The magnetic field strengths in the extended components of extragalactic radio sources cannot be inferred directly from observations of synchrotron emission, and so the energy densities and pressures in the radio-emitting components are poorly constrained." " In order to make progress it is common to estimate ""minimum energy” field strengths (Burbidge 1956). which minimise the energy density required for à given. synchrotron emissivity."," In order to make progress it is common to estimate `minimum energy' field strengths (Burbidge 1956), which minimise the energy density required for a given synchrotron emissivity." This is roughly equivalent to the assumption that that magnetic and relativistic particle energy densities are equal Cequipartition)., This is roughly equivalent to the assumption that that magnetic and relativistic particle energy densities are equal (`equipartition'). But without measurements of magnetic field strengths. these assumptions. for which there is no physical justification. may underestimate the true energy densities by arbitrary factors.," But without measurements of magnetic field strengths these assumptions, for which there is no physical justification, may underestimate the true energy densities by arbitrary factors." The magnetic field strength may be measured by observations of the “synchrotron self-Compton' (SSC) process. in. which the synchrotron-emitting electrons. inverse-Compton scatter synchrotron photons up to X-ray energies.," The magnetic field strength may be measured by observations of the `synchrotron self-Compton' (SSC) process, in which the synchrotron-emitting electrons inverse-Compton scatter synchrotron photons up to X-ray energies." Because the emissivity from this process depends on the photon number density (which is known from radio observations) and the electron number density as a function of energy. observations of SSC emission allow the electron number density to be inferred. and so determine the magnetic field strength.," Because the emissivity from this process depends on the photon number density (which is known from radio observations) and the electron number density as a function of energy, observations of SSC emission allow the electron number density to be inferred, and so determine the magnetic field strength." Such tests require observations of regions with well-measured volume and a well-defined. synchrotron spectrum with a high photon energy density: these conditions exist in the hotspots of FRII radio sources., Such tests require observations of regions with well-measured volume and a well-defined synchrotron spectrum with a high photon energy density; these conditions exist in the hotspots of FRII radio sources. Direct evidence supporting the equipartition/minimum energy assumptions in hotspots has come from only two X-ray observations., Direct evidence supporting the equipartition/minimum energy assumptions in hotspots has come from only two X-ray observations. Harris. Carilli Perley (1994) detected the hotspots of the powerful FRII Cygnus A 4405). withROSAT and showed that the X-ray emission could be interpreted as being due to the SSC process. with a magnetic field strength consistent with the equipartition model. [," Harris, Carilli Perley (1994) detected the hotspots of the powerful FRII Cygnus A 405) with and showed that the X-ray emission could be interpreted as being due to the SSC process, with a magnetic field strength consistent with the equipartition model. [" This result was recently contirmed with by Wilson. Young Shopbell (2000).],"This result was recently confirmed with by Wilson, Young Shopbell (2000).]" ROSAT was not sensitive enough to detect any other SSC hotspots. though it was used to put lower limits on the field strengths in some sources (Hardcastle. Birkinshaw Worrall 1998).," was not sensitive enough to detect any other SSC hotspots, though it was used to put lower limits on the field strengths in some sources (Hardcastle, Birkinshaw Worrall 1998)." More recently. veritication observations have detected the hotspots of 2295. another powerful radio galaxy. ata level which implies field strengths fairly close to the equipartition values if the emission process is SSC (Harris 22000).," More recently, verification observations have detected the hotspots of 295, another powerful radio galaxy, at a level which implies field strengths fairly close to the equipartition values if the emission process is SSC (Harris 2000)." Here we report a third detection. of the E hotspot of the radio galaxy 1123. based on our AOL guest observer (GO) observations.," Here we report a third detection, of the E hotspot of the radio galaxy 123, based on our AO1 guest observer (GO) observations." 1123 isa z=0.2177 radio galaxy. notable for its peculiar radio structure.," 123 is a $z = 0.2177$ radio galaxy, notable for its peculiar radio structure." Like normal classical double sources it has twin wt spots on either side of the active nucleus. but the lobes take he form of diffuse twisted plumes unlike those in any other studied object (e.g. Riley Pooley 1978: Hardeastle 11997. hereafter H97).," Like normal classical double sources it has twin hot spots on either side of the active nucleus, but the lobes take the form of diffuse twisted plumes unlike those in any other well-studied object (e.g. Riley Pooley 1978; Hardcastle 1997, hereafter H97)." Like Cygnus A and 2295. its radio uminosity is unusually high for its redshift.," Like Cygnus A and 295, its radio luminosity is unusually high for its redshift." For our purposes. its most important feature is its bright eastern double hotspot.," For our purposes, its most important feature is its bright eastern double hotspot." With a flux density of ~6 Jy at 5 GHz. it is the second brightest wtspot complex known tafter Cygnus Aj.," With a flux density of $\sim 6$ Jy at 5 GHz, it is the second brightest hotspot complex known (after Cygnus A)." The hotspots’ structure and synchrotron spectrum are well known (H97: Meisenheimer, The hotspots' structure and synchrotron spectrum are well known (H97; Meisenheimer As indicated by the error bars in the Dzlx diagram. most of the Dzlx-selected. SALGS belong to an optically fainter sample of SMCs.,"As indicated by the error bars in the BzK diagram, most of the BzK-selected SMGs belong to an optically fainter sample of SMGs." In order to emphasize this point. we show he histogram of DzA (along with £2A and JAY) of the singlv associated SALGs in Figure 2..," In order to emphasize this point, we show the histogram of $BzK$ (along with $R-K$ and $J-K$ ) of the singly associated SMGs in Figure \ref{hist}." " In these histograms. jiuched: ones indicate dy-faint (A,-21.3) racio-detected SALGs."," In these histograms, hatched ones indicate $K$ -faint $K_s > 21.3$ ) radio-detected SMGs." The distribution of DzA is clearly bimodal., The distribution of $BzK$ is clearly bimodal. This may suggest that. Bzlx-selected SMCGs have a clistinet spectral orealkk atAA. Le. the Balmer break as suggested. by Smailοἱ (2004)..," This may suggest that BzK-selected SMGs have a distinct spectral break at, i.e. the Balmer break as suggested by \cite{2004ApJ...616...71S}." We find that 14 sinely associated. SMGs out of 20 iwe A 221.3., We find that 14 singly associated SMGs out of 20 have $K_s>$ 21.3. Therefore. 9346 per cent (13/14) of the singly associated A -faint SMCGs are Bzlxs.," Therefore, $\pm$ 6 per cent (13/14) of the singly associated $K$ -faint SMGs are BzKs." “Phe LDP sample also follows the same trend., The HDF sample also follows the same trend. A high fraction of Bzlxs in /x-faint SMCGs is implied by the results of Takagietal.(2007).. using a sub-sample of the SILADIZS sources.," A high fraction of BzKs in $K$ -faint SMGs is implied by the results of \cite{2007MNRAS.381.1154T}, using a sub-sample of the SHADES sources." Also. Bertoldietal.(2007) derived à highfraction of Bzlxss in NLAMDO mmume-detected. galaxies in the COSMOS Ποιά.," Also, \cite{2007ApJS..172..132B} derived a highfraction of BzKs in MAMBO mm-detected galaxies in the COSMOS field." Γον found that 8/11 (73413 3dxs., They found that 8/11 $\pm$ BzKs. One possible dillerence between the NLAMDBO and SHADES sources could be the fraction of non-Dzlxs in the samples., One possible difference between the MAMBO and SHADES sources could be the fraction of non-BzKs in the samples. A half. of the radio counterparts of SALGs are non-Bzks. while the ALAAMIBO) counterparts include only a small fraction of non-Dzlxs. less than ~2O% (« 2/11).," A half of the radio counterparts of SMGs are non-BzKs, while the MAMBO counterparts include only a small fraction of non-BzKs, less than $\sim 20$ $<2/11$ )." Since most of the reliable NLAMDO counterparts in Bertoldietal.(2007) are faint in the dy band (2 21.3). the ciflerence between ALAAIBO ancl SLIADES sources could. be explained. by the lack of dv-hright galaxies in ALAAIBO counterparts (seealsoDannerbaueretal. 2004)..," Since most of the reliable MAMBO counterparts in \cite{2007ApJS..172..132B} are faint in the $K$ band $> 21.3$ ), the difference between MAMBO and SHADES sources could be explained by the lack of $K$ -bright galaxies in MAMBO counterparts \cite[see also][]{2004ApJ...606..664D}." This might reflect a systematic cillercnee in the redshift distribution between submm. j/i) and millimetreΑΗ) sources., This might reflect a systematic difference in the redshift distribution between submm $\mu$ m) and millimetremm) sources. This should be tested with more reliable and statistically significant (sub)mni surveys with next generation instruments., This should be tested with more reliable and statistically significant (sub)mm surveys with next generation instruments. As expected from the bimodal distribution of the DzA colours in. Figure 2.. there is a correlation between sly colours and A-band magnitudes.," As expected from the bimodal distribution of the $BzK$ colours in Figure \ref{hist}, there is a correlation between $BzK$ colours and $K$ -band magnitudes." In Figure 3.. we show this correlation along with expected colours ancl magnitudes of Arp220 and M82. well known nearby dusty galaxies.," In Figure \ref{colmag}, we show this correlation along with expected colours and magnitudes of Arp220 and M82, well known nearby dusty galaxies." In order to match the SED templates of these two galaxies to the observed trend. their bolometric luminosities are multiplied by 2 and 20. resulting in 4.1077 and 8IQ LL. for Arp220 ancl MS2. respectively.," In order to match the SED templates of these two galaxies to the observed trend, their bolometric luminosities are multiplied by 2 and 20, resulting in $4\times 10^{12}$ and $8 \times 10^{11}$ $_\odot$ for Arp220 and M82, respectively." Both SED templates are consistent with the observed. colour-magnitude relation of SAGs. indicating that the difference in A ;-band magnitudes originates mainly [rom recdshift variations.," Both SED templates are consistent with the observed colour-magnitude relation of SMGs, indicating that the difference in $K_s$ -band magnitudes originates mainly from redshift variations." According to the SID templates. A-faint. C;7 21.3). Bzly-selected SMCSs are likely to be at 2271.5.," According to the SED templates, $K$ -faint $K_s > 21.3$ ), BzK-selected SMGs are likely to be at $z\ga 1.5$." As originally claimed by Dacddial. (2004).. the colour criterion of Baldy0.2 would be useful to select galaxies having an obscured SED such as Arp220 or M82 at 214.," As originally claimed by \cite{2004ApJ...617..746D}, the colour criterion of $BzK>-0.2$ would be useful to select galaxies having an obscured SED such as Arp220 or M82 at $z\ga 1.4$." A rough correlation. between the apparent A-band magnitudes and. redshifts of SAIGSs (Serjeantet.al.2003:Smalletal.2004). also indicates that A -faint SMCs have systematically higher redshifts.," A rough correlation between the apparent $K$ -band magnitudes and redshifts of SMGs \citep{2003MNRAS.346L..51S,2004ApJ...616...71S} also indicates that $K$ -faint SMGs have systematically higher redshifts." In. Figure 4.. we show the Boy colour versus redshift for our SMGs.," In Figure \ref{colz}, we show the $BzK$ colour versus redshift for our SMGs." “Phe redshifts of the HIDE. sample are spectroscopic ones. while we adopt photometric redshifts for the SNDE sample taken [rom Clements et al. (," The redshifts of the HDF sample are spectroscopic ones, while we adopt photometric redshifts for the SXDF sample taken from Clements et al. (" 2008 from optical-to-submim bancs) and J. Furusawa et al. (,2008 – from optical-to-submm bands) and J. Furusawa et al. ( in. preparation roni optical-to-NIK. bands).,in preparation – from optical-to-NIR bands). The optical-to-NIR photometric redshifts are calculated using a widelv-used code (Bolzonellaetal. 2000)..., The optical-to-NIR photometric redshifts are calculated using a widely-used code \citep{2000A&A...363..476B}. Phis plot is remarkably similar to Figure 3.., This plot is remarkably similar to Figure \ref{colmag}. The Bed colours of SMGs indicate that the Balmer break of SAIC is strong enough to apply the Body colour criteria to select SMS at 1425252.5., The $BzK$ colours of SMGs indicate that the Balmer break of SMGs is strong enough to apply the $BzK$ colour criteria to select SMGs at $1.4\la z \la 2.5$. 1n summary. our analysis suggests that /v-faint SMCs are indeed an extreme subset of Dzlx galaxies at 1.4«2< 2.5. as originally speculatecl by Dadedietal. (2004)...," In summary, our analysis suggests that $K$ -faint SMGs are indeed an extreme subset of BzK galaxies at $1.4—1/2 and are presented for large scales in appendix B:: the full solutions are available on request or from the author'swebsite*.", Examination of equation \ref{DegenerateLineBispectrum}) ) shows that the limits on the integration are the same as for the power spectrum employed in B10: Solutions exist for all integer and half-integer $n_B\geq -1/2$ and are presented for large scales in appendix \ref{AppendixDegenerate}; the full solutions are available on request or from the author's. . These solutions complement the exact solutions for the colinear case of νε presented in CFPROO. although they included a solution at 5=—2 which due to the divergence with g=0 cannot be found for the degenerate line.," These solutions complement the exact solutions for the colinear case of $\BTrTrTr$ presented in CFPR09, although they included a solution at $n_B=-2$ which due to the divergence with $q=0$ cannot be found for the degenerate line." Solutions for 2g€—2 are of particular interest as these fields are currently the weakest constrained (22?)..," Solutions for $n_B\lesssim -2$ are of particular interest as these fields are currently the weakest constrained \citep{Kahniashvili:2010wm,Paoletti:2010rx,Yamazaki:2010nf}." If ag«—I this equation cannot be integrated: instead we sample finely along values of 6 as 6—7 to track the divergence and set (6=π)0 to impose numerical stability., If $n_B<-1$ this equation cannot be integrated; instead we sample finely along values of $\phi$ as $\phi\rightarrow\pi$ to track the divergence and set $\mathcal{B}(\phi=\pi)\equiv 0$ to impose numerical stability. Since bispectra in this configuration can be mapped onto a colinear linewe expect a very similar line. (, Since bispectra in this configuration can be mapped onto a colinear linewe expect a very similar line. ( We do not perform this mapping explicitly as our sampling in (&.7.4} will not cleanly transfer to a reasonable sampling in (korlg.,"We do not perform this mapping explicitly as our sampling in $\{k,r,\phi\}$ will not cleanly transfer to a reasonable sampling in $\{k',r',\phi'\}$." It is easier to integrate the squeezed plane directly than it is to refine the sampling to produce a suitably smooth result.), It is easier to integrate the squeezed plane directly than it is to refine the sampling to produce a suitably smooth result.) When r>| andὁ=π. the dependence on ὁ drops out and so the bispectrum becomes da.," When $r>1$ and$\phi=\pi$, the dependence on $\phib$ drops out and so the bispectrum becomes ." Consider the coordinate transformation |k—a[7= v., Consider the coordinate transformation $\left|\mathbf{k-a}\right|^2=y$ . The modulus of p+a is then, The modulus of $\mathbf{p+a}$ is then of the systematic noise or2: fitting a systematic noise model to the raw data.,of the systematic noise or: fitting a systematic noise model to the raw data. Here we apply these techniques to two primary eclipse data sets of HD 189733b and XOIb recorded by the NICMOS instrument on the Hubble Space Telescope as well as a single time-correlated time series obtained by the Kepler spacecraft., Here we apply these techniques to two primary eclipse data sets of HD 189733b and XO1b recorded by the NICMOS instrument on the Hubble Space Telescope as well as a single time-correlated time series obtained by the Kepler spacecraft. " First presented by Swainetal.(2008),, this data set of the primary eclipse of HD 189733b was recorded using HST/NICMOS in the G206 grism setting spanning five consecutive orbits."," First presented by \citet{swain08}, this data set of the primary eclipse of HD 189733b was recorded using HST/NICMOS in the G206 grism setting spanning five consecutive orbits." The HST-pipeline calibrated data were downloaded from the archive and the spectrum was extracted using both standard routines as well as a custom built routine for optimal spectral extraction., The HST-pipeline calibrated data were downloaded from the archive and the spectrum was extracted using both standard routines as well as a custom built routine for optimal spectral extraction. Both extractions are in good accord with each other but the custom built routine was found to yield a better signal to noise and was subsequently used for all further analysis., Both extractions are in good accord with each other but the custom built routine was found to yield a better signal to noise and was subsequently used for all further analysis. " A binning of 10 spectral channels (~ 0.08,4m) was used resulting in 10 light curves across the G206 grism band.", A binning of 10 spectral channels $\sim$ $\mu$ m) was used resulting in 10 light curves across the G206 grism band. Figure 10 shows the obtained time series which serve as input to the algorithm., Figure \ref{hd189rawlc} shows the obtained time series which serve as input to the algorithm. It can be seen that each time series is strongly affected by instrument systematics propagating from the blue side of the spectrum (bottom light curve) to the red with varying intensity and even sign., It can be seen that each time series is strongly affected by instrument systematics propagating from the blue side of the spectrum (bottom light curve) to the red with varying intensity and even sign. " Swainetal.(2008) showed that these systematics are correlated to instrument state vectors such as orbital phase, relative positions and angles of the spectrum on the detector, instrument temperature, etc."," \citet{swain08} showed that these systematics are correlated to instrument state vectors such as orbital phase, relative positions and angles of the spectrum on the detector, instrument temperature, etc." We can hence expect that these systematics are statistically independent from the recorded astrophysical signal (the light curve) and it should therefore be in principle possible to de-correlate the signal., We can hence expect that these systematics are statistically independent from the recorded astrophysical signal (the light curve) and it should therefore be in principle possible to de-correlate the signal. We here demonstrate the de-trending on an individual light curve at ~1.694um (8' one down in figure 13))., We here demonstrate the de-trending on an individual light curve at $\sim$ $\mu$ m $^{th}$ one down in figure \ref{hd189raw}) ). " All time series in figure 13 were taken as input to the algorithm described above to estimate the de-mixing matrix W, the astrophysical signal vectors, $4 and the systematic noise vectors, Sen."," All time series in figure \ref{hd189raw} were taken as input to the algorithm described above to estimate the de-mixing matrix $\bf{\tilde{W}}$, the astrophysical signal vectors, $\bf{\hat{S}_{a}}$ and the systematic noise vectors, $\bf{\hat{S}_{sn}}$." The interference over signal (ISR) matrix indicated the good separation of four main components figure 11 with the rest of, The interference over signal (ISR) matrix indicated the good separation of four main components figure \ref{hd189hinton} with the rest of normalization of particle distribution function f in eq.(4)) as where /j(p) is the downstream: value of /.. In this form the injection rate naturally appears as a coellicient in front of the CH. pressure in the momentum flix conservation eq.(6)) when the CR pressure is normalized to the ram pressure (see eq.|[12] in the next section).,normalization of particle distribution function f in \ref{dc1}) ) as where (p) is the downstream value of f. In this form the injection rate naturally appears as a coefficient in front of the CR pressure in the momentum flux conservation \ref{mom:c}) ) when the CR pressure is normalized to the ram pressure (see \ref{Pc:norm}{ in the next section). One aspect of (he solution shown in Figure 1 which is important here is that lor any eiven injection ratev.. (he growing maximum monent(iun ως). wil ultimately exceed a critical value. bevond which the test particle regime [ails to exist. (," One aspect of the solution shown in Figure \ref{fig:bif} which is important here is that for any given injection rate, the growing maximum momentum (t) will ultimately exceed a critical value, beyond which the test particle regime fails to exist. (" It is natural to assume that the acceleration starts at this regime where L.. point A on Figure 1)).,"It is natural to assume that the acceleration starts at this regime where 1, point A on Figure \ref{fig:bif}) )." " Formally. the svstem must then transit to à much higher A that will be still very sensitive to the current values of 0.01) and p,,,,(—10) as mav be seen [rom Figure 1. (point D)."," Formally, the system must then transit to a much higher R that will be still very sensitive to the current values of 0.01) and (=10^6) as may be seen from Figure \ref{fig:bif} (point B)." Obviously. the further development of the acceleration process will depend on how the parameters and react to this strong increase of A. One possibility is to assume that simply a constant fraction of the sub-shock plasma is injected so that (he injection rate substantially increases because (he plasma density al the sub-shock grows linearly with .. Then. the svstem must leave the critical region where the Riv) dependence is very sharp or even nonunique ancl proceed to a highly supercritical regime characterized by higher (point C).," Obviously, the further development of the acceleration process will depend on how the parameters and react to this strong increase of R. One possibility is to assume that simply a constant fraction of the sub-shock plasma is injected so that the injection rate substantially increases because the plasma density at the sub-shock grows linearly with R. Then, the system must leave the critical region where the ) dependence is very sharp or even nonunique and proceed to a highly supercritical regime characterized by higher (point C)." The curve Rv) saturates there at the level which in the most straightforward way may be deduced from the condition of the preservation. L.. (see eq.[8]]).," The curve ) saturates there at the level which in the most straightforward way may be deduced from the condition of the sub-shock preservation, 1, (see \ref{c:r}] ])." A general formula for Riv.M) with the scaling as a limiting case mav be found in (Alalkov1997)..," A general formula for ,M) with the scaling as a limiting case may be found in \citep{m97a}." This scenario was realized in many numerical models Ellison&Eichler1985:Nazanasetal. 1996)). since they normalized the injection parameter to the plasma density. al the sub-shock R.. which should clearly lead to the scaling.," This scenario was realized in many numerical models \citealt{el:eich85,kazel86,byk96}) ), since they normalized the injection parameter to the plasma density at the sub-shock R, which should clearly lead to the scaling." Obviously. the pre-compression J£? aud (hus (he acceleration efficiency. will then be insensitive (o (in deep contrast to the case v&=const. point D) since the point C is already on (he saturated part of the Riv) curve.," Obviously, the pre-compression R and thus the acceleration efficiency will then be insensitive to (in deep contrast to the case $\nu\approx=const$, point B) since the point C is already on the saturated part of the ) curve." " Often. this insensitivity is observed in numerical studies with the parameterized injection rate Berezhkoetal. 1996)). so it is tempted to conclude (hat we do not need to know the injection rateverv accurately. as soon as il exceeds the critical rate,"," Often, this insensitivity is observed in numerical studies with the parameterized injection rate \citealt{byk96}) ), so it is tempted to conclude that we do not need to know the injection ratevery accurately, as soon as it exceeds the critical rate." Although cirrently there is a general consensus in the communitv that the EBL intensity should be quite close to the robust lower limits derived [rom galaxy counts. the possibility of slehtly higher fluxes of the EBL cannot vet be excluded.,"Although currently there is a general consensus in the community that the EBL intensity should be quite close to the robust lower limits derived from galaxy counts, the possibility of slightly higher fluxes of the EBL cannot yet be excluded." " In particular. using Spitzer data and a profile fitting of the faint [ringes of galaxies. claimed a new fiducial value for the contribution of galaxies to the EBL at 3.6jm of 9.0L5nWmTar|, which exceeds by a [actor of ~1.6 the flux of the EBL suggested by Franceschinietal.(2008)."," In particular, using Spitzer data and a profile fitting of the faint fringes of galaxies, \citet{levenson08} claimed a new fiducial value for the contribution of galaxies to the EBL at $3.6\,\rm \mu m$ of $9.0^{+1.7}_ {-0.9}\,\rm nW m^{-2} sr^{-1}$, which exceeds by a factor of $\sim1.6$ the flux of the EBL suggested by \citet{franceschini08}." . Following Levenson&Wright(2003).. IXrennrichetal.(2008) indicated that for this flux of EBL the initial (absorption corrected) VILE spectra of distant blazars LES 0229+200. LES 12134-30.4 and LES 1101-232 (located at redshifts z=0.1396. 0.182 and 0.136. respectively) would have a photon index <1.3.," Following \citet{levenson08}, \citet{krennrich08} indicated that for this flux of EBL the initial (absorption corrected) VHE spectra of distant blazars 1ES 0229+200, 1ES 1218+30.4 and 1ES 1101-232 (located at redshifts $z=0.1396$ $0.182$ and $0.186$, respectively) would have a photon index $\lesssim 1.3$." This result would challenge ihe conventional models for VILE production in AGN., This result would challenge the conventional models for VHE production in AGN. Generally. the N- and 5-ray non-thermal emission of blazars is interpreted as a sum of sviiclirotron and inverse Compton (1C) components of radiation from relativistic electrons. in (he lramework of the so-called svnchrotron sell-Compton (55€) or external Compton (EC) scenarios.," Generally, the X- and $\gamma$ -ray non-thermal emission of blazars is interpreted as a sum of synchrotron and inverse Compton (IC) components of radiation from relativistic electrons, in the framework of the so-called synchrotron self-Compton (SSC) or external Compton (EC) scenarios." In the case of raciatively efficient models. i.e. assuming acooled particle distribution. the IC spectrum in the Thomson limit is expected to be sleeper than the power-law distribution with photon index 1.5.," In the case of radiatively efficient models, i.e. assuming a particle distribution, the IC spectrum in the Thomson limit is expected to be steeper than the power-law distribution with photon index $1.5$." This limit does not depend on the electron initial (injection) spectrum and can be achieved. for example. in (lie case of a mono-energetie injection.," This limit does not depend on the electron initial (injection) spectrum and can be achieved, for example, in the case of a mono-energetic injection." At higher energies. (he 5-rav. spectrum becomes steeper due to the Wlein-Nishina effect.," At higher energies, the $\gamma$ -ray spectrum becomes steeper due to the Klein-Nishina effect." We note however. that (vpically the spectra obtained in the frameworks of SSC scenario are sleeper. wilh photon indices ~2.," We note however, that typically the spectra obtained in the frameworks of SSC scenario are steeper, with photon indices $\sim2$." Therefore. the spectrum with photon index [yy=1.5 is often relerred to as the hardest spectrum. allowed by standard blazar models.," Therefore, the spectrum with photon index $\Gamma_{\rm int}=1.5$ is often referred to as the hardest spectrum allowed by standard blazar models." However. in the expense of radiation elliciency it is possible to produce harder VIIE spectra still within the SSC! framework. for example assuming a high lower-energv cutoff in the electron spectrum (Ixatarzviiskietal.2006).," However, in the expense of radiation efficiency it is possible to produce harder VHE spectra still within the SSC framework, for example assuming a high lower-energy cutoff in the electron spectrum \citep{katarzynski06}." . The postulation of such a cutoff in the electron spectrum implies very low efficiency. of radiative cooling which.," The postulation of such a cutoff in the electron spectrum implies very low efficiency of radiative cooling which," "uncertainties are less (han (he uncertainties claimed for anisotropic orbital motion ancl the statistical uncertainty in M, itsell.",uncertainties are less than the uncertainties claimed for anisotropic orbital motion and the statistical uncertainty in $M_p$ itself. " The mass component supported by rotation was calculated from (he rotational component of the Jeans Equation. where Jt), is (he outermost (racer radius in (he sample and (,,. Is the rotation amplitude. calculated in Section 2.."," The mass component supported by rotation was calculated from the rotational component of the Jeans Equation, where $R_{out}$ is the outermost tracer radius in the sample and $v_{max}$ is the rotation amplitude, calculated in Section \ref{kin}." " These Af, values are listed in Tables 2 3..", These $M_r$ values are listed in Tables \ref{tab:IGG} \ref{tab:GG}. The mass of NGC 5128 follows from its tracer population of GCs by determining the surface densitv of (he GCS and deprojecting the slope from 2-dimensions to 3-dimensions., The mass of NGC 5128 follows from its tracer population of GCs by determining the surface density of the GCS and deprojecting the slope from 2-dimensions to 3-dimensions. The surface density. distribution of the entire GCS was determined by binning the known clusters into circular annuli of equally populated bins. giving each bin the same statistical weight to minimize biases (MazApellániz&Übeda2005).. although. as noted above. the distribution may still havespeafial biases im favor of the major axis al large radii.," The surface density distribution of the entire GCS was determined by binning the known clusters into circular annuli of equally populated bins, giving each bin the same statistical weight to minimize biases \citep{maiz05}, although, as noted above, the distribution may still have biases in favor of the major axis at large radii." The prolile is shown in Figure 6.., The profile is shown in Figure \ref{fig:surden}. In the innermost region. within 5 kpc. there is incompleteness due to the observation of the dust lane and this region is therefore excluded: from the mass de(ermination.," In the innermost region, within 5 kpc, there is incompleteness due to the obscuration of the dust lane and this region is therefore excluded from the mass determination." The surface density fits well to a power law outside of 5 kpe with a slope of —2.65d:0.17 (reduced4?=0.04fromaMarquardi-Levenhergal. 1992).," The surface density fits well to a power law outside of 5 kpc with a slope of $-2.65\pm0.17$ \citep[reduced $\chi^2=0.04$ from a Marquardt-Levenberg fitting routine from][]{press92}." .. A value of 5=3.65. was then used in the mass calculations.," A value of $\gamma=3.65$, was then used in the mass calculations." The rotationally supported mass was calculated from Equation 7.. and the determined rotation amplitude in each bin shown in Table 1..," The rotationally supported mass was calculated from Equation \ref{eqn:rje}, and the determined rotation amplitude in each bin shown in Table \ref{tab:GC}." The determined masses are actually lower limits as (he inclination angle of the (rue rotation axis with the plane of the skv is nol known., The determined masses are actually lower limits as the inclination angle of the true rotation axis with the plane of the sky is not known. Peng.Ford.&Freeman(2004) argue. using planetary nebula data. that NGC 5128 is Griaxial in nature and is viewed nearly edge-on.," \cite{pff04II} argue, using planetary nebula data, that NGC 5128 is triaxial in nature and is viewed nearly edge-on." If so. the rotation measured would be a eood estimate of the (rue rotation of the svstem.," If so, the rotation measured would be a good estimate of the true rotation of the system." " In any case. M, is small compared with (he pressure component. M,"," In any case, $M_r$ is small compared with the pressure component, $M_p$." The total mass of the svstem determined within the outermost cluster in each bin is listed in Table 1.., The total mass of the system determined within the outermost cluster in each bin is listed in Table \ref{tab:GC}. . crystalline color superconducting state (Ippolitoetal. 2008)..,crystalline color superconducting state \citep{2008PhRvD..77b3004I}. The key requirement for the existence (and stability) of these objects was the observation that the nuclear equation of state must be stiff and the quark equation of state must be supplemented by a shift (bag constant) to enable the the quark and nuclear equations of state to match (Ippolitoetal.2005)., The key requirement for the existence (and stability) of these objects was the observation that the nuclear equation of state must be stiff and the quark equation of state must be supplemented by a shift (bag constant) to enable the the quark and nuclear equations of state to match \citep{2008PhRvD..77b3004I}. " In the latter study stable crystalline color superconducting stars with masse M~2Mg were obtained as ""twin"" configurations of purely nuclear counterparts.", In the latter study stable crystalline color superconducting stars with masse $M\sim 2M_{\sun}$ were obtained as “twin” configurations of purely nuclear counterparts. Subsequently. sequences of stars containing homogeneous quark matter in the 28C and CFL phases (with maximum masses <1.8Mo5) were obtained in the NJL model supplemented by a repulsive vector interaction (Pagliara&Schattner-Bielich2008:Lugonesetal. 2010)..," Subsequently, sequences of stars containing homogeneous quark matter in the 2SC and CFL phases (with maximum masses $\le 1.8 M_{\sun}$ ) were obtained in the NJL model supplemented by a repulsive vector interaction \citep{2008PhRvD..77f3004P,2010PhRvD..81h5012L}." The importance of the vector interactions in stiffening the quark equation of state has been pointed out earlier by Klühnetal.(2006).., The importance of the vector interactions in stiffening the quark equation of state has been pointed out earlier by \citet{2006PhRvC..74c5802K}. Furthermore. the emergence of twit configurations of color-superconducting stars was confirmed in complementary studies based on variations and extensions of the NLJ model (Blaschkeetal.2010a.b:Agrawal2010)..," Furthermore, the emergence of twin configurations of color-superconducting stars was confirmed in complementary studies based on variations and extensions of the NLJ model \citep{2010JPhG...37i4063B,2010PThPS.186...81B,2010PhRvD..81b3009A}." Massive hybrid configurations were also constructed withi phenomenological parameterizations of the quark matter equation of state motivated by the MIT bag model m combination with nuclear equations of state that are moderately soft; large masses require strong. quark-quark correlationsin combination with color superconductivity in the CFL phase (Alfordetal.2005:Weissenborn2011)..," Massive hybrid configurations were also constructed within phenomenological parameterizations of the quark matter equation of state motivated by the MIT bag model in combination with nuclear equations of state that are moderately soft; large masses require strong quark-quark correlationsin combination with color superconductivity in the CFL phase \citep{2005ApJ...629..969A,2011arXiv1102.2869W}." Below we shall adopt the point of view that the nuclear equation of state needs to be stiff above the saturation density in order to obtain massive hybrid stars (Ippolitoetal.2008).., Below we shall adopt the point of view that the nuclear equation of state needs to be stiff above the saturation density in order to obtain massive hybrid stars \citep{2008PhRvD..77b3004I}. With this observation as a working hypothesis we will explore the range of parameters allowing for compact stars featuring hyperonie and/or two- and three-flavor quark matter., With this observation as a working hypothesis we will explore the range of parameters allowing for compact stars featuring hyperonic and/or two- and three-flavor quark matter. We start with the low-density part of the equation of state. where the degrees of freedom are the nucleons and hyperons.," We start with the low-density part of the equation of state, where the degrees of freedom are the nucleons and hyperons." The nuclear equation of state. as is well known. can be constructed starting from a number of principles. see.e.g... Weber(1999) and Sedrakian(2007)..," The nuclear equation of state, as is well known, can be constructed starting from a number of principles, see, \citet{weber_book} and \citet{2007PrPNP..58..168S}." " Below we will work with the relativistic mean-field models. which are fitted to the bulk properties of nuclear matter and hypernuclear data to describe the baryonic octet and its interactions (Glendenning&Moszkowski1991:Lalazissisetal.1997) We adopt the following Walecka Lagrangian. which includes self-interacting o-field| where the B-sum is over the baryonic octet Bo=panA=.27°. hp are the corresponding Dirac fields. whose interactions are mediated by the « scalar. co, isoscalar-vector and po, isovector-vector meson fields."," Below we will work with the relativistic mean-field models, which are fitted to the bulk properties of nuclear matter and hypernuclear data to describe the baryonic octet and its interactions \citep{1991PhRvL..67.2414G,1997PhRvC..55..540L} We adopt the following Walecka Lagrangian, which includes self-interacting $\sigma$ -field where the $B$ -sum is over the baryonic octet $B \equiv p, n, \Lambda, \Sigma^{\pm,0}, \Xi^{-,0}$ , $\psi_B$ are the corresponding Dirac fields, whose interactions are mediated by the $\sigma$ scalar, $\omega_{\mu}$ isoscalar-vector and $\rho_{\mu}$ isovector-vector meson fields." " The meson and the baryon masses correspond to their values in the vacuum. the values of nucleon-meson couplings are g,-/7,.=3.967 fm. gon/m,=3.44 fm. gow/m,=1.157 fm for nucleons: the hyperon-meson couplings are obtained from these by multiplication by factors 0.6. 0.658. and 0.6. respectively."," The meson and the baryon masses correspond to their values in the vacuum, the values of nucleon-meson couplings are $g_{\sigma N}/m_{\sigma}= 3.967 $ fm, $g_{\omega N}/m_{\omega}= 3.244 $ fm, $g_{\rho N}/m_{\rho}= 1.157 $ fm for nucleons; the hyperon-meson couplings are obtained from these by multiplication by factors 0.6, 0.658, and 0.6, respectively." The couplings in the self-interaction terms of the c-field are given by b=0.002055 and ο=-0.002651.," The couplings in the self-interaction terms of the $\sigma$ -field are given by $b= 0.002055 $ and $c = -0.002651$." The next-to-last term in Eq. (1) , The next-to-last term in Eq. \ref{eq:L_RMF}) ) "is the Dirac Lagrangian of leptons. F,, is the energy anc momentum tensor of the electromagnetic field: we will not need the explicit from of other tensors in the Lagrangian (1))."," is the Dirac Lagrangian of leptons, $F_{\mu\nu}$ is the energy and momentum tensor of the electromagnetic field; we will not need the explicit from of other tensors in the Lagrangian \ref{eq:L_RMF}) )." The parameters above correspond to the NL3 parametrization (Lalazissisetal.1997).., The parameters above correspond to the NL3 parametrization \citep{1997PhRvC..55..540L}. Computations were made also with the GM3 parameterization (Glendenning&Moszkowski 1991).. and we will comment on the differences below.," Computations were made also with the GM3 parameterization \citep{1991PhRvL..67.2414G}, and we will comment on the differences below." The choice of this specific parametrization was made because the nucleonic matter has the stiffest equation of state compatible with the nuclear phenomenology., The choice of this specific parametrization was made because the nucleonic matter has the stiffest equation of state compatible with the nuclear phenomenology. The mean-field pressure of the (hyperynuclear matter can be obtained from Eq. (1)), The mean-field pressure of the (hyper)nuclear matter can be obtained from Eq. \ref{eq:L_RMF}) ) in the standard fashion(Weber1999).., in the standard fashion\citep{weber_book}. " The high-density quark matter is described by an NJL Lagrangian. which is extended to include the t Hooft interaction term (« A) and the vector interactions (αςGy) where the quark spinor fields Ww) carry color a=r.g.b and flavor (vw=d.d. s) indices. the matrix of quark current masses Is given by fi=diagjGn,.mg.my). A, with a=1.....8 are the Gell-Mann matrices in the color space. and Ay=(2/3)1¢."," The high-density quark matter is described by an NJL Lagrangian, which is extended to include the t' Hooft interaction term $\propto K$ ) and the vector interactions $\propto G_V$ ) where the quark spinor fields $\psi_{\alpha}^a$ carry color $a = r, g, b$ and flavor $\alpha= u, d, s$ ) indices, the matrix of quark current masses is given by $\hat m= {\rm diag}_f(m_u, m_d, m_s)$, $\lambda_a$ with $ a = 1,..., 8$ are the Gell-Mann matrices in the color space, and $\lambda_0=(2/3) {\bf 1_f}$." " The charge conjugate spinors are defined as be=CH and be=4C. where C=iy7y"" is the charge conjugation matrix."," The charge conjugate spinors are defined as $\psi_C=C\bar\psi^T$ and $\bar\psi_C=\psi^T C$, where $C=i\gamma^2\gamma^0$ is the charge conjugation matrix." The partition function of the system can be evaluated for the Lagrangian (2)) neglecting the fluctuations beyond the mean-field (Rüsteretal. 2005)..., The partition function of the system can be evaluated for the Lagrangian \ref{eq:NJL_Lagrangian}) ) neglecting the fluctuations beyond the mean-field \citep{2005PhRvD..72c4004R}. . " To do so. one linearizes the interaction term keeping the di-quark correlations Δ.xGloYuiseeusa and quark-anti-quark correlations crux Wu, "," To do so, one linearizes the interaction term keeping the di-quark correlations $\Delta_c\propto (\bar\psi_C)_{\alpha}^ai\gamma_5\epsilon^{\alpha\beta c}\epsilon_{abc}\psi_{\beta}^b$ and quark-anti-quark correlations $\sigma_{\alpha}\propto\bar\psi_{\alpha}^a\psi_{\alpha}^a$ ." At zero temperature the pressure is given by where e; are the quasiparticle spectra of quarks. wo= and @)=2GV«(QM|Iw.wQM) ," At zero temperature the pressure is given by where $\epsilon_i$ are the quasiparticle spectra of quarks, $\omega_0=G_V\langle QM \vert \psi_u^{\dagger}\psi_u+\psi_d^{\dagger}\psi_d\vert QM\rangle$ and $\phi_0=2 G_V\langle QM \vert \psi_s^{\dagger}\psi_s\vert QM\rangle$ " Unipolar induction (Ul) is a fundamental electromagnetic process.,Unipolar induction (UI) is a fundamental electromagnetic process. For astrophysical systems containing a magnetic and a non-magnetic body orbiting around a common center of gravity. a large em.E.," For astrophysical systems containing a magnetic and a non-magnetic body orbiting around a common center of gravity, a large e.m.f." is induced across the svstem by Ul when the rotation period of cach respective body. deviates from one another or from the binary orbital period., is induced across the system by UI when the rotation period of each respective body deviates from one another or from the binary orbital period. If à magnetized plasma is present in the binary environment. an electric current circuit will be set up.," If a magnetized plasma is present in the binary environment, an electric current circuit will be set up." The dissipation of the electric currents will heat the magnetic object. which may cause an observational signature.," The dissipation of the electric currents will heat the magnetic object, which may cause an observational signature." The location where the dissipation occurs depends on the conductivity of the two objects and the nature of the plasma between them: it also depends on the magnetic-field configuration of the system., The location where the dissipation occurs depends on the conductivity of the two objects and the nature of the plasma between them; it also depends on the magnetic-field configuration of the system. It the electrical conductivity of the two objects is similar. à dipolar magnetic field will lead to strong heating in regions near the field foot-points of the magnetic object. where the current density is the highest. as the electric currents are focused by the converging magnetic field Lines.," If the electrical conductivity of the two objects is similar, a dipolar magnetic field will lead to strong heating in regions near the field foot-points of the magnetic object, where the current density is the highest, as the electric currents are focused by the converging magnetic field lines." Among all astrophysical UL systems. the best. known system may be the Jovian system. (Piddington Drake 1968: Goldreich Lyaden-Dell 1969).," Among all astrophysical UI systems, the best known system may be the Jovian system (Piddington Drake 1968; Goldreich Lynden-Bell 1969)." Phe currents lowing between the Calilean moons and Jupiter cause heating on Jupiter. resulting in hot spots ancl trails on Jupiter's atmosphere. (Connerney et al.," The currents flowing between the Galilean moons and Jupiter cause heating on Jupiter, resulting in hot spots and trails on Jupiter's atmosphere (Connerney et al." 1993: Clarke et. al., 1993; Clarke et al. 1996: 2002)., 1996; 2002). In the Jovian system. the large-scale magnetic field is provided by Jupiter. while volcanism: on the moon lo may supply the plasma for the conduction of electric currents (Brown 1994).," In the Jovian system, the large-scale magnetic field is provided by Jupiter, while volcanism on the moon Io may supply the plasma for the conduction of electric currents (Brown 1994)." More recently. two very late-type stars have been found to emit radio emission which varied. in its intensity on a period of a few hours. and is polarised and hiehly variable (Berger ct al 2005. Llallinan et al.," More recently, two very late-type stars have been found to emit radio emission which varied in its intensity on a period of a few hours, and is polarised and highly variable (Berger et al 2005, Hallinan et al." 2006. 2007).," 2006, 2007)." Such properties are consistent with those predicted bv the UL moclel., Such properties are consistent with those predicted by the UI model. secondary or even a fossil flow channel (Reipurth&Olberg1991).,secondary or even a fossil flow channel \citep{Rei91}. ". Attempts to find the driving source of HH 110 have failed at optical, near infrared and radio continuum wavelengths."," Attempts to find the driving source of HH 110 have failed at optical, near infrared and radio continuum wavelengths." " A scenario that accounts for the singular morphology of HH 110 was first outlined by Reipurth,Raga&Heathcote(1996).", A scenario that accounts for the singular morphology of HH 110 was first outlined by \citet{Rei96}. . These authors proposed that HH 110 originates from the deflection (deflection angle ~ 60°) of the adjacent HH 270 jet through a grazing collision with a dense molecular clump of gas., These authors proposed that HH 110 originates from the deflection (deflection angle $\simeq 60^\circ$ ) of the adjacent HH 270 jet through a grazing collision with a dense molecular clump of gas. " The feasibility of this scenario has been further reinforced from the results of numerical simulations, which model the emission arising from the collision of a jet with a dense molecular clump (see Ragaetal.2002 and references therein)."," The feasibility of this scenario has been further reinforced from the results of numerical simulations, which model the emission arising from the collision of a jet with a dense molecular clump (see \citealp{Rag02} and references therein)." " In addition, analysis of further data are also in agreement with this scenario."," In addition, analysis of further data are also in agreement with this scenario." " First, a high-density clump of gas around the region where the HH 270 jet changes its direction to emerge as HH 110 has been detected through high-density tracer molecules (in HCO*, by Choi2001,, and in NHs, by Septilvedaetal. 2010))."," First, a high-density clump of gas around the region where the HH 270 jet changes its direction to emerge as HH 110 has been detected through high-density tracer molecules (in $^+$ , by \citealp{Cho01}, and in $_3$, by \citealp{Sep10}) )." " Second, results from proper motion determination are also consistent with the jet/cloud collision scenario (Reipurth,Raga&Heathcote1996;; Lópezetal. 2005))."," Second, results from proper motion determination are also consistent with the jet/cloud collision scenario \citealp{Rei96}; \citealp{Lop05}) )." A recent work of Hartiganetal.(2009) that included laboratory experiments has given further support to the jet/cloud collision scenario., A recent work of \citet{Har09} that included laboratory experiments has given further support to the jet/cloud collision scenario. HH 110 is a good candidate to search for the observational footprints of gas entrainment and turbulence by analysing the kinematics and the excitation conditions along and across the jet flow., HH 110 is a good candidate to search for the observational footprints of gas entrainment and turbulence by analysing the kinematics and the excitation conditions along and across the jet flow. Some works were performed in the recent past from long-slit spectroscopy and Fabry-Perot data., Some works were performed in the recent past from long-slit spectroscopy and Fabry-Perot data. " The kinematics and physical conditions, both along the outflow axis and at four positions across the jet beam, were explored from long-slit spectroscopy by al (2003a),, who found very complex structures."," The kinematics and physical conditions, both along the outflow axis and at four positions across the jet beam, were explored from long-slit spectroscopy by \citet{Rie03a}, who found very complex structures." " Rieraetal(2003b) explored the spatial distribution and the characteristic knot sizes, as well as the spatial behaviour of the velocity and line width, by performing a wavelet analysis of Fabry-Perot data, but only covering the Ha line."," \citet{Rie03b} explored the spatial distribution and the characteristic knot sizes, as well as the spatial behaviour of the velocity and line width, by performing a wavelet analysis of Fabry-Perot data, but only covering the $\alpha$ line." " Their results indicated that most of the Ha kinematics can be explained by assuming an axially peaked mean flow velocity, on which are superposed low-amplitude turbulent velocities."," Their results indicated that most of the $\alpha$ kinematics can be explained by assuming an axially peaked mean flow velocity, on which are superposed low-amplitude turbulent velocities." " In addition, their resultsare suggestive of the presence on an outer envelope that appears to be a turbulent boundary layer."," In addition, their resultsare suggestive of the presence on an outer envelope that appears to be a turbulent boundary layer." " Finally, Hartiganetal.(2009) compared images from laboratory jet experiments with numerical simulations and with long-slit, high-resolution optical spectra obtained along HH 110."," Finally, \citet{Har09} compared images from laboratory jet experiments with numerical simulations and with long-slit, high-resolution optical spectra obtained along HH 110." They found a good agreement between the shock structures observed in HH 110 and those derived from experiments of a supersonic jet deflected by a dense obstacle., They found a good agreement between the shock structures observed in HH 110 and those derived from experiments of a supersonic jet deflected by a dense obstacle. " In order to further advance on our understanding of HH 110, this object was included as a target within a program of Integral Field Spectroscopy of Herbig-Haro objects using the Potsdam Multi-Aperture Spectrophotometer (PMAS) in the wide-field IFU mode PMAS fibre PAcK (PPAK)."," In order to further advance on our understanding of HH 110, this object was included as a target within a program of Integral Field Spectroscopy of Herbig–Haro objects using the Potsdam Multi-Aperture Spectrophotometer (PMAS) in the wide-field IFU mode PMAS fibre PAcK (PPAK)." " The data obtained from this IFS HH observing program give a full spatial coverage of the HH 110 emission in several lines (Ha, aand 11])), thus allowing us to perform a more complete analysis of the kinematics and physical conditions through the whole flow than all the previous works."," The data obtained from this IFS HH observing program give a full spatial coverage of the HH 110 emission in several lines $\alpha$, and ), thus allowing us to perform a more complete analysis of the kinematics and physical conditions through the whole flow than all the previous works." The main results are given in this work., The main results are given in this work. The paper is organized as follows., The paper is organized as follows. The observations and data reduction are described in 22., The observations and data reduction are described in 2. Results are given in 33: the analysis of the physical conditions in 33.1 and the analysis of the kinematics in $3.2., Results are given in 3: the analysis of the physical conditions in 3.1 and the analysis of the kinematics in 3.2. A summary with the main conclusions is given 44., A summary with the main conclusions is given 4. Observations of HH 110 were made on 22 November 2004 with the 3.5-m telescope of the Calar Alto Observatory (CAHA)., Observations of HH 110 were made on 22 November 2004 with the 3.5-m telescope of the Calar Alto Observatory (CAHA). " Data were acquired with the Integral Field Instrument Potsdam Multi-Aperture Spectrophotometer PMAS (Rothetal.2005) using the PPAK configuration that has 331 science fibres, covering an hexagonal FOV of 74x65 arcsec? with a spatial sampling of 2.7 arcsec per fibre, and 36 additional fibres to sample the sky (see 55 in Kelzetal. 2006))."," Data were acquired with the Integral Field Instrument Potsdam Multi-Aperture Spectrophotometer PMAS \citep{Rot05} using the PPAK configuration that has 331 science fibres, covering an hexagonal FOV of $\times$ 65 $^2$ with a spatial sampling of 2.7 arcsec per fibre, and 36 additional fibres to sample the sky (see 5 in \citealt{Ke06}) )." " The 11200 grating was used, giving aneffective sampling of 0.3 ppix! (~15 km s! for Ha) and covering the wavelength range ~ 6500-7000 A,, thus including characteristic HH emission lines in this wavelength range (Ha,"," The I1200 grating was used, giving aneffective sampling of 0.3 $^{-1}$ $\sim15$ km $^{-1}$ for $\alpha$ ) and covering the wavelength range $\sim6500$ –7000 , thus including characteristic HH emission lines in this wavelength range $\alpha$ ," Mi 15 the initial cluster mass.,$M_i$ is the initial cluster mass. The time-scale f; depends on the tidal field of the environment., The time-scale $t_0$ depends on the tidal field of the environment. Lamers et al. (, Lamers et al. ( 2006) adopt ty 221.8 Myr. which is valid for a circular orbit in the Galaxy at 8.5 kpe radial distance (Baumgardt Makino 2003).,"2006) adopt $t_0=$ 21.8 Myr, which is valid for a circular orbit in the Galaxy at 8.5 kpc radial distance (Baumgardt Makino 2003)." The median galactocentric distance of the Galactic GCs plotted in Fig., The median galactocentric distance of the Galactic GCs plotted in Fig. 12. is 9.2 kpe (McLaughlin van der Marel 2005). very close to the assumed 8.5 kpc.," \ref{mass_ML_all} is 9.2 kpc (McLaughlin van der Marel 2005), very close to the assumed 8.5 kpc." "Therefore. we also adopt f, =21.8 Myr for estimating fy...","Therefore, we also adopt $t_0=$ 21.8 Myr for estimating $t_{\rm \rm diss}$ ." " Evaluating equation 4.. we obtain fyi, -δθ Gyrs for 10° Me. and tui «250 Gyrs for 10° Mo. That is.dynamical evolution should not have changed the"," Evaluating equation \ref{tdiss}, we obtain $t_{\rm \rm diss} \simeq$ 50 Gyrs for $^5$ $_{\rm \sun}$, and $t_{\rm \rm diss} \simeq$ 250 Gyrs for $^6$ $_{\rm \sun}$ That is,dynamical evolution should not have changed the" During the first oobservation. the oof SS 0Tl6--T14 amounts to 40z3% in the 0.50.75 keV and 2741% in the 310 keV (FE06).,"During the first observation, the of S5 0716+714 amounts to $40\pm3\%$ in the 0.5–0.75 keV and $27\pm1\%$ in the 3–10 keV (FE06)." Though longer duration of the second oobservation. the iis only 32.03&2.12% and 7.62d1.5% in the corresponding enerey bands.," Though longer duration of the second observation, the is only $32.03\pm2.12\%$ and $7.62\pm1.5\%$ in the corresponding energy bands." It is important to understand whether the svnchrotron or IC emissions or both are responsible for the significant. variations of $5 OF16+714 in different energy bands., It is important to understand whether the synchrotron or IC emissions or both are responsible for the significant variations of S5 0716+714 in different energy bands. It is usually argued (hat the variable high energv (ail of the svnchrotron emission is responsible for the highly variable solt X-ray emission. whereas the “stable” low energy side of the IC emission accounts for the lack of variability in the hard X-ray. band (e.g.. Giommi et al.," It is usually argued that the variable high energy tail of the synchrotron emission is responsible for the highly variable soft X-ray emission, whereas the ""stable"" low energy side of the IC emission accounts for the lack of variability in the hard X-ray band (e.g., Giommi et al." 1999: Taglialerri et al., 1999; Tagliaferri et al. 2003)., 2003). This argument is somewhat ambiguous. since the (wo oobservations clearly demonstrate that the hard X-ray fluxes are also highly variable. although (heir variability amplitudes are significantly smaller than the soft N-rav ones.," This argument is somewhat ambiguous, since the two observations clearly demonstrate that the hard X-ray fluxes are also highly variable, although their variability amplitudes are significantly smaller than the soft X-ray ones." The hard variations could be due to either the IC) or svnehrotvon variations., The hard X-ray variations could be due to either the IC or synchrotron variations. It is certain that the svnchrotron component is stronely variable on short (miescales. whereas il is unclear whether (he IC component is variable on similar limescales.," It is certain that the synchrotron component is strongly variable on short timescales, whereas it is unclear whether the IC component is variable on similar timescales." The spectral analysis by ΕΟΟ showed that the IC component might be variable on timescales of hours. which is. however. not supported by our results.," The spectral analysis by FE06 showed that the IC component might be variable on timescales of hours, which is, however, not supported by our results." Although the IC) component contributes more to the total hard X-ray. [hixes.. we still assume that the hard. X-ray variations might be controlled by the svnchrotron tail.," Although the IC component contributes more to the total hard X-ray fluxes, we still assume that the hard X-ray variations might be controlled by the synchrotron tail." With increasing energies. (he increasing dilutions of the “stable” IC component to the increasing variations of the svnchrotron Cail. might result in the observed overturn of the energv-dependent variability: amplitude for 55 07164-1714.," With increasing energies, the increasing dilutions of the ""stable"" IC component to the increasing variations of the synchrotron tail, might result in the observed overturn of the energy-dependent variability amplitude for S5 0716+714." The model-independent hardness-ratio analvsis shows that (he 0.510 keV spectra of 55 07164-7114 soften when it brightens., The model-independent hardness-ratio analysis shows that the 0.5–10 keV spectra of S5 0716+714 soften when it brightens. The phenomenon. also noticeable in the first oobservation (FEOG: Foschini et al.," The phenomenon, also noticeable in the first observation (FE06; Foschini et al." 2006). was already found in the oobservations of the source (Gionuni οἱ al.," 2006), was already found in the observations of the source (Giommi et al." 1999)., 1999). The softer-when-brishter phenomenon is interpreted in terms of the high energy. (ail of the svnchrotron emission extending more {ο higher energies when the source brightens (e.g.. Giommi οἱ al.," The softer-when-brighter phenomenon is interpreted in terms of the high energy tail of the synchrotron emission extending more to higher energies when the source brightens (e.g., Giommi et al." 1999)., 1999). Nevertheless. the soft X-ray spectra appear to harden when it brightens. though the trend is not significant.," Nevertheless, the soft X-ray spectra appear to harden when it brightens, though the trend is not significant." The variabilitv property found in the soft X-ray band of the source with ROSAT observations (Cappi el al., The variability property found in the soft X-ray band of the source with ROSAT observations (Cappi et al. 1994) is similar to what we found here., 1994) is similar to what we found here. The harder-when-brighter trend is analogous to those of IIBLs. presenting a strong evidence that the soft X-ray emission of 55 07164714 is dominated by the svnehrotron tail.," The harder-when-brighter trend is analogous to those of HBLs, presenting a strong evidence that the soft X-ray emission of S5 0716+714 is dominated by the synchrotron tail." Although the inter-band time lags and the related energy dependence have been detected in a lew X-ray bright HBLs. they have not be firmly detected in LBLs vet.," Although the inter-band time lags and the related energy dependence have been detected in a few X-ray bright HBLs, they have not be firmly detected in LBLs yet." FEOG claimed, FE06 claimed Our main finding. that the most intense y-ray flares in the IFGL light-curves occur about 70 days after the onset of a mm flare. indicates a “distant” origin scenario. with emission sites located several parsecs away from the central engine.,"Our main finding, that the most intense $\gamma$ -ray flares in the 1FGL light-curves occur about 70 days after the onset of a mm flare, indicates a ""distant"" origin scenario, with emission sites located several parsecs away from the central engine." In this scenario. corresponding to cases (11) and (i). the highest levels of y-ray emission are achieved. during. or after. the passage of the disturbance through the core (or through an outer stationaryfeature). thus compressing the moving material and enhancing substantially the energy of electrons. leading to the inverse Compton scattering of low-energy photons provided either by the jet itself or from external photon fields.," In this scenario, corresponding to cases (ii) and (iii), the highest levels of $\gamma$ -ray emission are achieved during, or after, the passage of the disturbance through the core (or through an outer stationary, thus compressing the moving material and enhancing substantially the energy of electrons, leading to the inverse Compton scattering of low-energy photons provided either by the jet itself or from external photon fields." The two-month average delay we find is most consistent with cases (1) and (it). however. for several reasons we cannot decide on whether the strongest y-ray flares occur during disturbances passing through the radio core (case (11) or if they originate from the growing shocks downstream of the radio core (case (110).," The two-month average delay we find is most consistent with cases (ii) and (iii), however, for several reasons we cannot decide on whether the strongest $\gamma$ -ray flares occur during disturbances passing through the radio core (case (ii)) or if they originate from the growing shocks downstream of the radio core (case (iii))." First. our time resolution of one month is insufficient for detailed studies of the sequence of events during the passage of the disturbance through the radio core.," First, our time resolution of one month is insufficient for detailed studies of the sequence of events during the passage of the disturbance through the radio core." Second. as can be seen in Figure 7. the spread in the lengths of the delays is not inconsiderable.," Second, as can be seen in Figure 7, the spread in the lengths of the delays is not inconsiderable." Third. we have defined the beginning of the radio flare using à simple formula (Equation 3). which obviously is an approximation.," Third, we have defined the beginning of the radio flare using a simple formula (Equation 3), which obviously is an approximation." Inspection of individual mm-flares in the Metsiihhovi monitoring program reveals that in several cases the radio flux starts to increase somewhat before or after the epoch given by Equation 3., Inspection of individual mm-flares in the Metsähhovi monitoring program reveals that in several cases the radio flux starts to increase somewhat before or after the epoch given by Equation 3. Multifrequency monitoring. preferably combined with VLBI and time-resolved y-ray light curves. is needed to achieve more accurate time determinations and studies of case (11).," Multifrequency monitoring, preferably combined with VLBI and time-resolved $\gamma$ -ray light curves, is needed to achieve more accurate time determinations and studies of case (ii)." For the strongest y-ray flares. case (1) seems to be excluded by our results. although our time resolution cannot exclude the possibility that some of the flares are produced a short distance (as compared to the distance to the central engine) upstream of the radio core.," For the strongest $\gamma$ -ray flares, case (i) seems to be excluded by our results, although our time resolution cannot exclude the possibility that some of the flares are produced a short distance (as compared to the distance to the central engine) upstream of the radio core." However. we should also remain open to the possibility that y-ray flares are generated close to the black hole due to an enhancement of the local seed photons (either from the aceretion-disk corona system or the canonical BLR). as has been suggested in other studies (e.g.22)..," However, we should also remain open to the possibility that $\gamma$ -ray flares are generated close to the black hole due to an enhancement of the local seed photons (either from the accretion-disk corona system or the canonical BLR), as has been suggested in other studies \citep[e.g.][]{marscher_2010,tavecchio_2010}." Nevertheless. y-ray flares produced in the close dissipation scenario (<] pc) should. in general. occur months before the mm-flare inception and the VLBI component ejection.," Nevertheless, $\gamma$ -ray flares produced in the close dissipation scenario $\leq 1$ pc) should, in general, occur months before the mm-flare inception and the VLBI component ejection." Whether close-dissipation y-ray flares are related to weak and/or rapid flares will be addressed in a future work by means of high-resolution y-ray light curves., Whether close-dissipation $\gamma$ -ray flares are related to weak and/or rapid flares will be addressed in a future work by means of high-resolution $\gamma$ -ray light curves. In conclusion. the results presented in this paper strongly indicate that at least for the strongest y-rays the production sites are downstream or within the radio core. well outside the BLR at distances of several parsees or even tens of parsecs from the black hole and the accretion disk.," In conclusion, the results presented in this paper strongly indicate that at least for the strongest $\gamma$ -rays the production sites are downstream or within the radio core, well outside the BLR at distances of several parsecs or even tens of parsecs from the black hole and the accretion disk." A number of papers based on data have reached similar conclusions. mainly," A number of papers based on data have reached similar conclusions, mainly" We have shown that a Large fraction of the sources in the PLES show evidence for the presence of optical svnchrotron emission. where the amount of svnchrotron emission present in the spectrum changes with wavelength.,"We have shown that a large fraction of the sources in the PHFS show evidence for the presence of optical synchrotron emission, where the amount of synchrotron emission present in the spectrum changes with wavelength." llow else can we test this model?, How else can we test this model? One of the key features of svnchrotron radiation is its hieh degree of polarisation., One of the key features of synchrotron radiation is its high degree of polarisation. LU there is significant svnchrotron emission at optical and NIR wavelengths. then one would expect to be able to detect a corresponding polarisation.," If there is significant synchrotron emission at optical and NIR wavelengths, then one would expect to be able to detect a corresponding polarisation." Indeed. this has been used. as a wav to confirm the presence of svnchrotron emission in optical jets (Daade (1956). provided. the first example of this for the jet of. MS.)," Indeed, this has been used as a way to confirm the presence of synchrotron emission in optical jets (Baade \shortcite{baade56} provided the first example of this for the jet of M87.)" 1n our combined model. the svachrotron component. is the only polarised component. as we assume that the BBB component. which is essentially emission from the accretion disk. is unpolarised (P«1% for the BBB (Antonucci 1988))).," In our combined model, the synchrotron component is the only polarised component, as we assume that the BBB component, which is essentially emission from the accretion disk, is unpolarised $P < 1\%$ for the BBB \cite{antonucci98}) )." Thus. the amount of polarisation will depend on the proportion of the total [lux that is due to the synchrotron emission.," Thus, the amount of polarisation will depend on the proportion of the total flux that is due to the synchrotron emission." Furthermore. if the relative amount of svnchrotron," Furthermore, if the relative amount of synchrotron" Table 2. presents the observing circumstances.,Table \ref{t:obs} presents the observing circumstances. The seeing was about 0.4 aresee for the first observing night and 0.6 for the second one., The seeing was about 0.4 arcsec for the first observing night and 0.6 for the second one. We obtained the long slit spectroscopy data with a 1.3 aresee slit centered on Echeclus and oriented in the motion direction (very close to the solar direction)., We obtained the long slit spectroscopy data with a 1.3 arcsec slit centered on Echeclus and oriented in the motion direction (very close to the solar direction). The spectral range covered was 345-590 nm (chosen to cover the CN and C» Swan bands wavelengths) with a spectral resolution of 600., The spectral range covered was 345-590 nm (chosen to cover the CN and $_2$ Swan bands wavelengths) with a spectral resolution of 600. One year later we managed to obtain complementary observing time with the 3.5-m New Technology Telescope (NTT) of ESO., One year later we managed to obtain complementary observing time with the 3.5-m New Technology Telescope (NTT) of ESO. These observations. conducted in service mode with the direct imaging camera SUperb-Seeing Imager (SUSI 2). consisted in imaging Echeclus in the R. B. and V-band for one hour.," These observations, conducted in service mode with the direct imaging camera SUperb-Seeing Imager (SUSI 2), consisted in imaging Echeclus in the R, B, and V-band for one hour." Table 2. also presents the observing circumstances for these observations. which we obtained. unfortunately. during a nonphotometric night.," Table \ref{t:obs} also presents the observing circumstances for these observations, which we obtained, unfortunately, during a nonphotometric night." SUSI 215 equiped with two 2kx4k CCDs providing a Χδ.5 field of view., SUSI 2 is equiped with two $\times$ 4k CCDs providing a $\times$ 5.5' field of view. Because of the very small plate scale of the instrument (0.0805 arcsec/pixel) we used the 2x2 binned mode., Because of the very small plate scale of the instrument (0.0805 arcsec/pixel) we used the $\times$ 2 binned mode. To avoid any trailing due to the proper motion of the object the exposure time was limited to 125 s. corresponding to a displacement of 0.3 aresec.," To avoid any trailing due to the proper motion of the object the exposure time was limited to 125 s, corresponding to a displacement of 0.3 arcsec." We obtained most of the images with a Bessel R filter. for which the signal-to-noise is best.," We obtained most of the images with a Bessel R filter, for which the signal-to-noise is best." First. we preprocessed all the images obtained with FORS | (subtraction of the bias and division by a master sky flat-field).," First, we preprocessed all the images obtained with FORS 1 (subtraction of the bias and division by a master sky flat-field)." We specifically processed the images corresponding to the spectra to extract ID spectra., We specifically processed the images corresponding to the spectra to extract 1D spectra. First. we calibrated in wavelength. thanks to wavelength calibration lamp images.," First, we calibrated in wavelength, thanks to wavelength calibration lamp images." Second. we extracted two different 1D spectra from each image.," Second, we extracted two different 1D spectra from each image." The first one corresponded to Echeclus itself (11 lines. corresponding to 2.2 aresee centered on Echeclus) and the second one to the center of the coma (41 lines corresponding to 8.2 aresec on the," The first one corresponded to Echeclus itself (11 lines, corresponding to 2.2 arcsec centered on Echeclus) and the second one to the center of the coma (41 lines corresponding to 8.2 arcsec on the" "J,,(0.Da is co",", all divergences are proportional to $f^2(r)-1$." mputed simply asthedifference between naive fornmla. Forthe 5»=1parüal waveil isworth mentioning (hat 1e procedure forremoving thewein," For the Gel'fand-Yaglom method the procedure consists again in removing the first order part from ^2) The functions $\tilde h^{(1)i\pm}_{n,i}(r,\nu^2)$ are again solutions of Eq. \ref{h1diagequation}) )," tegral zero modemanilests itselfbv divergence Ine?as — 0.," but with the boundary condition $\tilde h^{(1)i\pm}_{n,i}(r,\nu^2)\to 0$ as $r\to 0$." Itis this divergence whichhas tobe removed.A stra, Again the gauge field terms have to be omitted in the potential. ightforward idea isto simply subtract the pole and to compute subtraction The poleterm integral Here all numerical c," The subtracted expression is simply - ,0)- ] The classical profiles were computed using the Bais-Primack method which is described in Appendix \ref{baisprimack}." omputationsdetare performedsettingm$. =1.So. asthe exponential of the —1/2loe appearsin the (ransiüion rate. Mg.andasthe translation modeis twolold degenerate. theratewill be in units 5.3 Renormalization," We have used 2000 grid point for $x=m_W r$ in the interval $[0,30]$, the grid was not equidistant, but the interval length was chosen to increase by a factor $1.005$ between two neighbouring intervals, so as to have small intervalls at small $r$ and larger ones in the asymptotic region." As we have already mentioned thelimit A?—xof Z(0. A?) doesnot exist. Thisis duetothe divergencesmodel(heof quantum fieldtheory.," The methods of computing the fluctuation determinants has been described in the previous sections, this discussion already incorporates the numerical procedure." In thediagramspresent caseofa (wo-clmensional divergences are, We have compared the two methods for computing functional determinants analytically. just tadpole proportional to.0?and, Of course this should reflect itself in the numerical computations. © which have tobe subtracted. We describethe," The quantity to be computed and compared is $J_n(0,\Lambda^2)$ and" Ποια is almost uniform in latitude. we can argue that the angular extent of the QSL arc. however. would be expected to depend primarily on the ratio of the flux in the low-Iatitude coronal hole extension to that in the polar hole.,"field is almost uniform in latitude, we can argue that the angular extent of the QSL arc, however, would be expected to depend primarily on the ratio of the flux in the low-latitude coronal hole extension to that in the polar hole." For example. in the extreme case that the [Iuxes were equal. the corridor mapping would be expected to reach the heliospheric pole (90° [rom the HCS!).," For example, in the extreme case that the fluxes were equal, the corridor mapping would be expected to reach the heliospheric pole $90^\circ$ from the HCS!)," irrespective of the geometry of the corridor or of the coronal holes., irrespective of the geometry of the corridor or of the coronal holes. If the width of the corridor at the photosphere is small compared to (he scale οἱ (vpical motions (here. such as the supergranular flow. we expect that the whole corridor will continuously disrupt and reform at the photosphere and. consequently. closed-field plasma will be released. by reconnection all along the QSL arc in the heliosphere.," If the width of the corridor at the photosphere is small compared to the scale of typical motions there, such as the supergranular flow, we expect that the whole corridor will continuously disrupt and reform at the photosphere and, consequently, closed-field plasma will be released by reconnection all along the QSL arc in the heliosphere." Therefore. the topology of Fig.," Therefore, the topology of Fig." 2 max be able to resolve the slow wind paradox., 2 may be able to resolve the slow wind paradox. The overriding; question. however. is whether there are enough such corridors and corresponding QSL arcs in the heliosphere to account for the slow wind that is observed.," The overriding question, however, is whether there are enough such corridors and corresponding QSL arcs in the heliosphere to account for the slow wind that is observed." The flux distribution of Fie., The flux distribution of Fig. 2 produces only one such arc. which would certainly not be sufficient to reproduce the observed slow wind.," 2 produces only one such arc, which would certainly not be sufficient to reproduce the observed slow wind." There are two issues that must be addressed. the number of ares (their density and extent on the Sun ancl heliosphere). ancl (he amount of mass and energy that each arc can be expected to release.," There are two issues that must be addressed, the number of arcs (their density and extent on the Sun and heliosphere), and the amount of mass and energy that each arc can be expected to release." In (his paper we concentrate on the first issue and only briefly discuss (he second in Section 4 below. because addressing (his issue requires fully. dynamic calculations.," In this paper we concentrate on the first issue and only briefly discuss the second in Section 4 below, because addressing this issue requires fully dynamic calculations." In order to address (he issue of the number of QSL ares. we calculated (the quasi-steacly model for an observed photospheric flux distribution.," In order to address the issue of the number of QSL arcs, we calculated the quasi-steady model for an observed photospheric flux distribution." Figure 5a shows the photospheric radial field as derived [rom MDI observations on SOIIO (Scherreretal.1995). [or a time period preceding the August 1. 2008 total solar eclipse.," Figure 5a shows the photospheric radial field as derived from MDI observations on SOHO \citep{scherrer95} for a time period preceding the August 1, 2008 total solar eclipse." This caleulation was used to predict the structure of the corona prior to the eclipse. using magnetic field data measured during the period June 25July 21. 2008.," This calculation was used to predict the structure of the corona prior to the eclipse, using magnetic field data measured during the period June 25–July 21, 2008." The prediction compares very [avorably with images of the corona taken during (he eclipse in Mongolia (Rusinetal.2010)., The prediction compares very favorably with images of the corona taken during the eclipse in Mongolia \citep{rusin10}. . Note that the hieh resolution of the calculation captures the details of many small-scale bipoles in the photospheric magnetic field (IIarvey.1955)., Note that the high resolution of the calculation captures the details of many small-scale bipoles in the photospheric magnetic field \citep{harvey85}. ".. This has been incorporated into the idea of the ""magnetic carpet"" (Schrijveretal.1997).", This has been incorporated into the idea of the “magnetic carpet” \citep{schrijver97}. ". We also show the polarity inversion line D,=0 slightly above the photosphere. al r=1.054. to delineate the magnetic polarity of the structures. ("," We also show the polarity inversion line $B_r=0$ slightly above the photosphere, at $r=1.05R_\odot$ to delineate the magnetic polarity of the large-scale structures. (" The polarity inversion line in the photosphere itself shows an enormous complexity that overshaclows its usefulness to discern (he large-scale magnetic polarity.),The polarity inversion line in the photosphere itself shows an enormous complexity that overshadows its usefulness to discern the large-scale magnetic polarity.) The equasi-steady model was ealeulated by using the 3D MIID code ALAS., The quasi-steady model was calculated by using the 3D MHD code MAS. The MAS codeand its implementation are described in detail bv Mikié&Linker (1994).. Mikiéetal. (1999).," The MAS codeand its implementation are described in detail by \citet{mikic94}, , \citet{mikic99}, ," Iu principle. the general set of cumulant equations in Eq.,"In principle, the general set of cumulant equations in Eq." 10. cau be solved. with enough computational ellort., \ref{ce-eom} can be solved with enough computational effort. However. efficient. algorithms cau be developed if the uuderlyiug system exhibits further syimuuetries.," However, efficient algorithms can be developed if the underlying system exhibits further symmetries." This is typically the case for astrophiysical systems. which usually exhibit spherical or cylindrical symmetry or a corresponding trauslatioual syimauetry. in a local Cartesian domain.," This is typically the case for astrophysical systems, which usually exhibit spherical or cylindrical symmetry or a corresponding translational symmetry in a local Cartesian domain." We discuss in detail here the case of eumulants in a sphere., We discuss in detail here the case of cumulants in a sphere. For systems with au underlying spherical syinnuetry. the spectral expausiou of the clepeuceut variables discussed in section 2 often takes the form where r is spherical radius. 0 is co-latitude and © is longitude.," For systems with an underlying spherical symmetry, the spectral expansion of the dependent variables discussed in section \ref{formulation} often takes the form where $r$ is spherical radius, $\theta$ is co-latitude and $\phi$ is longitude." " Here the qu4(r) are complex functions aud the 7"" are associated Legeudre Puuctions.", Here the $q_{\ell m}(r)$ are complex functions and the $P_\ell^m$ are associated Legendre functions. Furthermore on a spherical surface the r-depeucdence is abseut and a fully spectral representation of the equation of motion (equatiou 1)) can be written as We note here that. because the scalar fields are real-valued in coordinate space. we may focus on the evolution of modes with m>0 as modes with a«0 may be obtained by complex conjugation.," Furthermore on a spherical surface the $r$ -dependence is absent and a fully spectral representation of the equation of motion (equation \ref{algebraicEOMs}) ) can be written as We note here that, because the scalar fields are real-valued in coordinate space, we may focus on the evolution of modes with $m \geq 0$ as modes with $m < 0$ may be obtained by complex conjugation." Moreover. for simplicity in the above aud iu subsequent equations tlie iudex that eucodes which state variable is beiug solved for has been substuned into the ( label.," Moreover, for simplicity in the above and in subsequent equations the index that encodes which state variable is being solved for has been subsumed into the $\ell$ label." The quadratic nonliuearities have their origin in the Jacobiaus of Eqs., The quadratic nonlinearities have their origin in the Jacobians of Eqs. 16. with coeflicients C) representing amplitudes for the scattering of two waves witli n>0: C) are for waves with nto>0 aud ii«0 to scatter., \ref{EOM} with coefficients $C^{(+)}$ representing amplitudes for the scattering of two waves with $m \geq 0$; $C^{(-)}$ are for waves with $m > 0$ and $m < 0$ to scatter. The amplitudes of these coefficients are constructed from the matrix, The amplitudes of these coefficients are constructed from the matrix future we plan to investigate hyverogen recombination in the context of cosmological recombination epoch.,future we plan to investigate hydrogen recombination in the context of cosmological recombination epoch. We (hank the anonvimous releree for helpful comments which significantly improved the presentation of (his work., We thank the anonymous referee for helpful comments which significantly improved the presentation of this work. This work was supported in part by NSF grant AST-0707704. Department of Energv. Award. Number DE-EGO2-07ERAI51T. and bv SED grant 676 [rom the DFG.," This work was supported in part by NSF grant AST-0707704, Department of Energy Award Number DE-FG02-07ER41517, and by SFB grant 676 from the DFG." This research used. resources of the National Energy Research Scientific Computing Center (NERSC). which is supported by the Ollice of Science of the U.S. Department of Energy under Contract No. DE-ACO2-05CTI11231:," This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231;" and the ILócehstleistungs Rechenzentrum Nord (HEIN)., and the Höcchstleistungs Rechenzentrum Nord (HLRN). We thank both (hese institutions for a generous allocation of computer time., We thank both these institutions for a generous allocation of computer time. not use any colour information in the classification process.,not use any colour information in the classification process. Also apparent is the clear subgroup visible in the upper right corner of the diagram., Also apparent is the clear subgroup visible in the upper right corner of the diagram. " We have visually checked several light curves of objects located in both subgroups, revealing that these two subgroups really contain different kinds of objects."," We have visually checked several light curves of objects located in both subgroups, revealing that these two subgroups really contain different kinds of objects." " Typical examples of both groups are shown in Fig. 11,,"," Typical examples of both groups are shown in Fig. \ref{rot-example}," illustrating the periodicity in the light curves., illustrating the periodicity in the light curves. " Many objects in the biggest group show very clear signs of rotational modulation in their light curves, similar to the CoRoT light curves in the training set for this class."," Many objects in the biggest group show very clear signs of rotational modulation in their light curves, similar to the CoRoT light curves in the training set for this class." " The objects in the small subgroup all exhibit clear long-term variability, with relatively large amplitudes."," The objects in the small subgroup all exhibit clear long-term variability, with relatively large amplitudes." " These are very red objects, and some of the light curves resemble those of semi-regular variables."," These are very red objects, and some of the light curves resemble those of semi-regular variables." " In Fig. 12,,"," In Fig. \ref{rot-sr}," we compare the position of these objects in the colour diagram to the regions occupied by semi-regular variables detected by the HIPPARCOS mission (?).., we compare the position of these objects in the colour diagram to the regions occupied by semi-regular variables detected by the HIPPARCOS mission \citep{HIPPARCOS}. The small rotational modulation subgroup clearly falls within the semi-regular region., The small rotational modulation subgroup clearly falls within the semi-regular region. " They are not classified as semi-regular variables with our methods, but this is due to the insufficient time-span of the current light curves."," They are not classified as semi-regular variables with our methods, but this is due to the insufficient time-span of the current light curves." Further investigation and time series of a longer time span are needed to shed more light on this group of variables., Further investigation and time series of a longer time span are needed to shed more light on this group of variables. " The inclusion of this new class clearly constitutes an improvement of our classification capabilities, since many of those variables are present, and they can now be recognized well."," The inclusion of this new class clearly constitutes an improvement of our classification capabilities, since many of those variables are present, and they can now be recognized well." " Most of our candidates are located in the cool regions of the colour diagram, where we expect to find those stars."," Most of our candidates are located in the cool regions of the colour diagram, where we expect to find those stars." " We do see some contamination of red giant stars in the sample of candidates though, suggesting that we need to tweak the classification parameters to avoid this confusion."," We do see some contamination of red giant stars in the sample of candidates though, suggesting that we need to tweak the classification parameters to avoid this confusion." " With the many good example light curves present in the data, we plan to improve the definition of this class."," With the many good example light curves present in the data, we plan to improve the definition of this class." " For the stellar activity class, we used a similar limit on the Mahalanobis distance to the class centre to select the best candidates, retaining about 1200 objects."," For the stellar activity class, we used a similar limit on the Mahalanobis distance to the class centre to select the best candidates, retaining about 1200 objects." " Note that more than 0000 objects are assigned to this class in total, not surprising given the expected abundances of active main-sequence stars in the sample."," Note that more than 000 objects are assigned to this class in total, not surprising given the expected abundances of active main-sequence stars in the sample." Figure 13 shows the position of the best candidates in 2MASS colour space., Figure \ref{act} shows the position of the best candidates in 2MASS colour space. " The ó Sct and rotational modulation candidates are shown as well, for comparison."," The $\delta$ Sct and rotational modulation candidates are shown as well, for comparison." " The activity sample occupies the same region in colour space as the rotational modulation sample, corresponding to cool main-sequence stars."," The activity sample occupies the same region in colour space as the rotational modulation sample, corresponding to cool main-sequence stars." We indeed expect to find many active stars in this region., We indeed expect to find many active stars in this region. " Note also that the activity sample is very well separated from the pulsator classes in colour space, again without using colour information in the classification process."," Note also that the activity sample is very well separated from the pulsator classes in colour space, again without using colour information in the classification process." Figure 14 shows two typical examples of light curves that ended up in the activity class., Figure \ref{act-examples} shows two typical examples of light curves that ended up in the activity class. " They show rather irregular variability (compared to the rotational modulation class) with long periods and small amplitudes, similar to the CoRoT light curves in the training set."," They show rather irregular variability (compared to the rotational modulation class) with long periods and small amplitudes, similar to the CoRoT light curves in the training set." " Some objects in the sample show stricter periodic light curves, similar to those assigned to the rotational modulation class."," Some objects in the sample show stricter periodic light curves, similar to those assigned to the rotational modulation class." The non-thermal high-energy emission from Active Galactic Nuclei (AGNs) has been widely studied in recent years at different wavelength ranges through both satellite-borne and ground-based detectors ?).,The non-thermal high-energy emission from Active Galactic Nuclei (AGNs) has been widely studied in recent years at different wavelength ranges through both satellite-borne and ground-based detectors . . Several theoretical models have been proposed to explain the electromagnetic emission of these objects., Several theoretical models have been proposed to explain the electromagnetic emission of these objects. It is commonly accepted that the high-energy radiation is emitted by particles accelerated in. the relativistic jets launched from the inner parts of an aceretion disk that surrounds the central black hole., It is commonly accepted that the high-energy radiation is emitted by particles accelerated in the relativistic jets launched from the inner parts of an accretion disk that surrounds the central black hole. In general. the high-energy spectral energy distribution (SED) of AGNs presents two characteristic bumps.," In general, the high-energy spectral energy distribution (SED) of AGNs presents two characteristic bumps." The lower energy bump. located at optical to X-ray energies. is usually explained as synchrotron emission of electrons while the origin of the high-energy peak in the SED ts still under debatereview).," The lower energy bump, located at optical to X-ray energies, is usually explained as synchrotron emission of electrons while the origin of the high-energy peak in the SED is still under debate." Leptonie models attribute this component to inverse-Compton up-scattering off synchrotron or external photons from the disk and/or radiation reprocessed in nearby clouds???)., Leptonic models attribute this component to inverse-Compton up-scattering off synchrotron or external photons from the disk and/or radiation reprocessed in nearby clouds. In hadronic models. interactions of highly relativistic protons in the jet with ambient matter and photon fields. proton-induced cascades. or synchrotron radiation. of protons. are responsible for the high-energy photons," In hadronic models, interactions of highly relativistic protons in the jet with ambient matter and photon fields, proton-induced cascades, or synchrotron radiation of protons, are responsible for the high-energy photons." There also exist models which are not based on the emission of accelerated particles in the relativistic jet and assume the production of TeV y-rays in a pulsar-like cascade mechanism in the magnetosphere of the black hole??)., There also exist models which are not based on the emission of accelerated particles in the relativistic jet and assume the production of TeV $\gamma$ -rays in a pulsar-like cascade mechanism in the magnetosphere of the black hole. . The recently reported detection by HESS of the nearby radiogalaxy AA is of great relevance since it establishes radiogalaxies as VHE y-ray emitters., The recently reported detection by HESS of the nearby radiogalaxy A is of great relevance since it establishes radiogalaxies as VHE $\gamma$ -ray emitters. AA is the second non-blazar AGN discovered at VHE. after the HEGRA detection of y-rays from 887 and the later confirmation by HESS(?).," A is the second non-blazar AGN discovered at VHE, after the HEGRA detection of $\gamma$ -rays from 87 and the later confirmation by HESS." . A great variety of leptonic and hadronic models has been already applied to this kind of sources and beyond the scope of this work., A great variety of leptonic and hadronic models has been already applied to this kind of sources and beyond the scope of this work. During the first year of operation. Fermi/LAT has detected HE emission from AA and 887(?).. providing new constraints to the models.," During the first year of operation, /LAT has detected HE emission from A and 87, providing new constraints to the models." In this work we present a lepto-hadronie model for the emission from FR I radiogalaxies., In this work we present a lepto-hadronic model for the emission from FR I radiogalaxies. Section ??. contains a brief description of observational facts on this type of sources., Section \ref{sec:sources} contains a brief description of observational facts on this type of sources. In Section ?? we present the outline of our scenario. describing its most relevant characteristics.," In Section \ref{sec:scena} we present the outline of our scenario, describing its most relevant characteristics." Section + 1s devoted to the description of the model., Section \ref{sec:model} is devoted to the description of the model. In Section ?? we present the application to CentaurusA. whereas in Section ??. the results for M87 are given.," In Section \ref{sec:AplCenA} we present the application to CentaurusA, whereas in Section \ref{sec:AplM87} the results for M87 are given." Finally. in Section ?? we discuss the model implications and perspectives.," Finally, in Section \ref{sec:concl} we discuss the model implications and perspectives." According to the unification model of AGNs FRI radiogalaxies. with their Jet axis at a large angle with the line- are the parent population of BL Lac objects whose jets are closely aligned to the line of sight.," According to the unification model of AGNs FR I radiogalaxies, with their jet axis at a large angle with the line-of-sight, are the parent population of BL Lac objects whose jets are closely aligned to the line of sight." We concentrate here on the only two of them observed until now in the VHE range., We concentrate here on the only two of them observed until now in the VHE range. AA is the closest II radiogalaxy and its proximity makes it uniquely observable among such objects. eventhough its bolometric luminosity 15 not high as compared to other AGNs.," A is the closest I radiogalaxy and its proximity makes it uniquely observable among such objects, eventhough its bolometric luminosity is not high as compared to other AGNs." It is very active at radio wavelengths presentingσι a rich jet structure., It is very active at radio wavelengths presenting a rich jet structure. We can distinguish in its structure two components: inner Jets at a kpe scale and giants lobes covering 10° in the sky., We can distinguish in its structure two components: inner jets at a kpc scale and giants lobes covering $^\circ$ in the sky. A detailed description of the radio morphology can be found in?., A detailed description of the radio morphology can be found in. ". The inner kpe jet has also been detected in X-rays with an structure of knots and diffuse emission,", The inner kpc jet has also been detected in X-rays with an structure of knots and diffuse emission. Recently reported the detection of non-thermal X-ray emission from the shock of the southwest mner radio lobe from deep observations., Recently reported the detection of non-thermal X-ray emission from the shock of the southwest inner radio lobe from deep observations. " The supermassive black hole at the center of the active galaxy has an estimated mass of about 107M, to 10°M..(22)..", The supermassive black hole at the center of the active galaxy has an estimated mass of about $10^7 M_\odot$ to $10^8 M_\odot$. The black hole host galaxy is an elliptical one 55128) with a twisted disk which obscures the central engine at optical wavelengths., The black hole host galaxy is an elliptical one 5128) with a twisted disk which obscures the central engine at optical wavelengths. AA was observed by the (CGRO) with all its instruments from MeV to, A was observed by the ) with all its instruments from MeV to spin a=0.2AM as the parameter € is varied from 0.2 to |0.2.,spin $a=0.2M$ as the parameter $\epsilon$ is varied from $-0.2$ to $+0.2$. We discussed the eimergeuce of two additional stable orbits inside the ISCO and possible consequences for astrophysical black holes., We discussed the emergence of two additional stable orbits inside the ISCO and possible consequences for astrophysical black holes. We demoustrated how this approach can be applied to QPOs observed in galactic stellar-uass black holes aud ACN focusing on two differeut models., We demonstrated how this approach can be applied to QPOs observed in galactic stellar-mass black holes and AGN focusing on two different models. " Ifa pair of QPOs is observed and identified as the fundamental g- and cAuodes, respectively, the mass; spin. aud quadrupole noment of that black hole can be measured if the nass is known from dynamical observations."," If a pair of QPOs is observed and identified as the fundamental $g$ - and $c$ -modes, respectively, the mass, spin, and quadrupole moment of that black hole can be measured if the mass is known from dynamical observations." If the QPO odr is viewed as a nonlinear resouance between the Iseplerian aud epicyclic frequencies. the parameter e cau )o ncasured together with independent measurements of he ass and spin.," If the QPO pair is viewed as a nonlinear resonance between the Keplerian and epicyclic frequencies, the parameter $\epsilon$ can be measured together with independent measurements of the mass and spin." Iu addition to galactic black holes. Ser A* is another mune target for tests of the no-hair theorem.," In addition to galactic black holes, Sgr A* is another prime target for tests of the no-hair theorem." UWieh-resolution observations of stars in close orbit arouud Ser À* for over a decade have lead to a precise mass and distance imeasuremient of Ser A* (Chez oet al, High-resolution observations of stars in close orbit around Sgr A* for over a decade have lead to a precise mass and distance measurement of Sgr A* (Ghez et al. 2008: Cüllessen et al., 2008; Gillessen et al. 2009)., 2009). Recent VLBI observatious resolved Ser A* on horizon scales (Docleman oet al., Recent VLBI observations resolved Sgr A* on horizon scales (Doeleman et al. 2008) aud poiuted the wav towards the first inage of Ser Α in the near future (Fish Doclemau 2009)., 2008) and pointed the way towards the first image of Sgr A* in the near future (Fish Doeleman 2009). In Paper IL. we showed that a rng of light will sired the image of a black hole and that its shape depends directly ou the mass. spin. quadrupole moment. and inclination of the black hole.," In Paper II, we showed that a ring of light will surround the image of a black hole and that its shape depends directly on the mass, spin, quadrupole moment, and inclination of the black hole." " In particular. we showed that the diameter depends predominantly on the mass. while the displacement aud the asvuunetry of this ring are proportional to the quantities asin’ aud οσα7 respectively, where ; is the incluation angle of the angular momentum of the black hole with respect to a distant observer."," In particular, we showed that the diameter depends predominantly on the mass, while the displacement and the asymmetry of this ring are proportional to the quantities $a\sin i$ and $\epsilon \sin^{3/2} i$, respectively, where $i$ is the inclination angle of the angular momentum of the black hole with respect to a distant observer." We noted that one additional observable is required to break the degeneracy of the displacement aud the asvuunetry with the inclination., We noted that one additional observable is required to break the degeneracy of the displacement and the asymmetry with the inclination. Tere we argue that a full test of the no-hai theorem for Ser A* miav be accomplished with a combination of VLBI nuagiug of the ring of light (or. more generally. the shadow: see Paper II) and the observation of quasi-periodic variability in the cussion from Ser A* using VLBI techniques (Docleman et al.," Here we argue that a full test of the no-hair theorem for Sgr A* may be accomplished with a combination of VLBI imaging of the ring of light (or, more generally, the shadow; see Paper II) and the observation of quasi-periodic variability in the emission from Sgr A* using VLBI techniques (Doeleman et al." 2009)., 2009). Such variability is thought to arise from deusitv fluctuations orbiting around the ceuter of mass., Such variability is thought to arise from density fluctuations orbiting around the center of mass. " The orbital frequency of these inhomogencitics is the EKeplern frequency 9,.", The orbital frequency of these inhomogeneities is the Keplerian frequency $\Omega_{\rm \phi}$. " In this oper. we showed that. for moderate values of tle spin. he dependence of O,, on the parameter € is neglieible."," In this paper, we showed that, for moderate values of the spin, the dependence of $\Omega_{\rm \phi}$ on the parameter $\epsilon$ is negligible." Consequently. if ligh-frequency VLBI observations of Ser A* (Docleman et al.," Consequently, if high-frequency VLBI observations of Sgr A* (Doeleman et al." 2009) can measure the Iepleriau requencv of an orbiting hot spot and if Ser A* is not spline rapidly. they will measure the spin of Ser A* respectively of the particular value of the parameter €.," 2009) can measure the Keplerian frequency of an orbiting hot spot and if Sgr A* is not spinning rapidly, they will measure the spin of Sgr A* irrespectively of the particular value of the parameter $\epsilon$." Therefore. measurements of the displacement aud he asvnunetrv of the ring of hieht (or the shadow) of Ser A* will uniquely determine the inclination aud the xuwanmeter e allowing us to test the mo-hair theorem.," Therefore, measurements of the displacement and the asymmetry of the ring of light (or the shadow) of Sgr A* will uniquely determine the inclination and the parameter $\epsilon$ allowing us to test the no-hair theorem." We thauk J. Schuittiman aud R. Wagoner for useful cohunents., We thank J. Schnittman and R. Wagoner for useful comments. This work was supported by the NSF CAREER award NSF 0716519., This work was supported by the NSF CAREER award NSF 0746549. "inerecdicuts we need to calculate the likelihood of the data set A(c,). using (CL) and (5).","ingredients we need to calculate the likelihood of the data set $\Lambda(e_s)$, using (4) and (5)." The relevant iuteeral is calculated mauuerically using our model distributions., The relevant integral is calculated numerically using our model distributions. " Since A(c,) is strictly proportional to the posterior probability of the model P(AL|D.D) (see The full set of calculated likelihood values for various uodels are shown in Table 3.."," Since $\Lambda(e_s)$ is strictly proportional to the posterior probability of the model $P(M|D,I)$ (see The full set of calculated likelihood values for various models are shown in Table \ref{table:lambda}. ." We note that A values arenof normalized. so their absolute values have Little uecaning.," We note that $\Lambda$ values are normalized, so their absolute values have little meaning." Ποπονο it is their comparative values that allow us to address the questions of interest to us: given he observed sample of 1ucasured DNS ecceutricities. (1) are the birth or preseut populations more likely? (," However it is their comparative values that allow us to address the questions of interest to us: given the observed sample of measured DNS eccentricities, (i) are the birth or present populations more likely? (" i) which of the teu binary evolution models considered iere more Likelw? (,ii) which of the ten binary evolution models considered here more likely? ( "0) are ""standard kick magnitudes or sunall or zero kicks more likelv?",iii) are “standard” kick magnitudes or small or zero kicks more likely? To address cach of these questions we examine the likelihood (or odds) ratios for he models relevant in each case aud compare these ratios ο unity., To address each of these questions we examine the likelihood (or ) ratios for the models relevant in each case and compare these ratios to unity. To quantitatively compare our results for the present and birth distributions we present the model odds ratios Apoesou/Minn a8 a function of the binary evolution models (Fig. 5))., To quantitatively compare our results for the present and birth distributions we present the model odds ratios $\Lambda_{\rm present}/\Lambda_{\rm birth}$ as a function of the binary evolution models (Fig. \ref{fig:oddspres}) ). It is evident that for the majority of the models. the ratios exceed munity often by factors of more than 2 or as high as 20.," It is evident that for the majority of the models, the ratios exceed unity often by factors of more than 2 or as high as 20." " We note that for wide DNS the ratio values “hover” within a factor of 2 from wuity indicating that there is little or significant evolution frou, birth to present for these wide DNS binaries (as already noted iu 33.2),", We note that for wide DNS the ratio values “hover” within a factor of 2 from unity indicating that there is little or insignificant evolution from birth to present for these wide DNS binaries (as already noted in 3.2). We conclude that the inodels for coalesciug DNS xovilde clear evidence that orbital evolution due to eravitational radiation is imaportaut., We conclude that the models for coalescing DNS provide clear evidence that orbital evolution due to gravitational radiation is important. When allowed to evolve. the roughly uniforii eccentricity distribution at àirth shifts to favor lower eccentricities at present.," When allowed to evolve, the roughly uniform eccentricity distribution at birth shifts to favor lower eccentricities at present." Four of the five coalescing DNS inhabit the lower ecceutricity xwt of the distributions. so the shift towards lower eccentricities usually raises the lkelihood of preseut uodel distributions over those at DNS birth.," Four of the five coalescing DNS inhabit the lower eccentricity part of the distributions, so the shift towards lower eccentricities usually raises the likelihood of present model distributions over those at DNS birth." " This is in full agreement with the conclisions reached by (Chaurasia&Bailes2005) based on a different analysis and arguments,", This is in full agreement with the conclusions reached by \citep{Chaur} based on a different analysis and arguments. " On the other hand the lack of strong bias in favor of the present distributions from the wide DNS models is understood. given their long orbital evolution timescales,"," On the other hand the lack of strong bias in favor of the present distributions from the wide DNS models is understood, given their long orbital evolution timescales." Two exceptions to high odds ratios in the coalescing systenis appear for models El aud L2 (these. respectively. asstune very low conumuon-euvelope efficiency and large specific augular momentum carried by inass lost from the binary iu non-conservative mass transfer phases).," Two exceptions to high odds ratios in the coalescing systems appear for models E1 and L2 (these, respectively, assume very low common-envelope efficiency and large specific angular momentum carried by mass lost from the binary in non-conservative mass transfer phases)." For model El (see Fig. 3)).," For model E1 (see Fig. \ref{fig:eprescoal}) )," the eccentricity distribution already favors low ο at birth. such that when allowed to evolve. iuuch of the DNS population possesses ο«0.05. a region where there are no observed DNS.," the eccentricity distribution already favors low $e$ at birth, such that when allowed to evolve, much of the DNS population possesses $e<0.05$, a region where there are no observed DNS." We also sce that the probability of seciug DNS at 0.2σος0.3 actually decreases. contzibutiug to lowerimg the present? likelihood.," We also see that the probability of seeing DNS at $0.2}$ ) was plotted versus $\beta$, following Kuntschner Davies." The Virgo dwarfs have ιο Fe5335 index measured., The Virgo dwarfs have no Fe5335 index measured. For them aud the NCC 1399 GCs νουςFe5270 (labeled. [MgbsFe52]). was plotted versus 1)., For them and the NGC 1399 GCs $\sqrt{{\rm Mgb} \times {\rm Fe5270}}$ (labeled $\ast$ Fe52]) was plotted versus $\beta$. Iun both panels models from Worthey (199 1)) or 17 and 8 Cyr. spanning a uictallicity range [Fe/TI roni -2.0 to 0.5 dex. are shown for reference.," In both panels models from Worthey \cite{wort}) ) for 17 and 8 Gyr, spanning a metallicity range [Fe/H] from -2.0 to 0.5 dex, are shown for reference." The large errors in our nieasurenmeut prevent a detailed comparison: age differences cannot be discriminated within a factor of 2 or 3., The large errors in our measurement prevent a detailed comparison; age differences cannot be discriminated within a factor of 2 or 3. ) Ilowever. we note that. as expected. the dwarf galaxies (except CCR 1-1) are ess nctal rich than the eiaut ellipticals and consistent with having simular ages.," However, we note that, as expected, the dwarf galaxies (except CGF 1-4) are less metal rich than the giant ellipticals and consistent with having similar ages." The comparison with the Virgo dwarf galaxies and the NGC. 1399 GCs shows that all the Fornax dwarfs Gucliding CCF 1-1) fallin ranges span by them., The comparison with the Virgo dwarf galaxies and the NGC 1399 GCs shows that all the Fornax dwarfs (including CGF 1-4) fall in ranges span by them. Towever. CGF 1-L is more metal rich than the bulee-like GCs iu NGC 1399. and could belong to the “very metal rich” eroup of GCs ford by Kissler-Patig et al. (1998)).," However, CGF 1-4 is more metal rich than the bulge-like GCs in NGC 1399, and could belong to the “very metal rich” group of GCs found by Kissler-Patig et al. \cite{kiss}) )." Tu this case. it nüght also be somewhat vouuger. which would Increase its masse-to-lieht ratio and reduce the estimated mass.," In this case, it might also be somewhat younger, which would increase its mass-to-light ratio and reduce the estimated mass." " But CGF 1-L1 and COR 5-Ireniin puzzling objects: it can not vet be decided whether they are nuclei of disrupted dwarf galaxies. CEs. or true extremely massive GCs,"," But CGF 1-4 and CGF 5-4 remain puzzling objects; it can not yet be decided whether they are nuclei of disrupted dwarf galaxies, cEs, or true extremely massive GCs." Further spectroscopic observatious with a higher signal-to-noise are needed to uncover he nature of these objects., Further spectroscopic observations with a higher signal-to-noise are needed to uncover the nature of these objects. 19 ealaxies with velocities around 33700 kin + (Fie., 19 galaxies with velocities around 33700 km $^{-1}$ (Fig. 8) were fouud., 8) were found. The velocity dispersion is about 360 kins + which is typical for poor clusters (e.g. den IHartog hatgert 1996))., The velocity dispersion is about 360 km $^{-1}$ which is typical for poor clusters (e.g. den Hartog Katgert \cite{denh}) ). The ratio of carly type (E1580) to late type (5hr) eiant galaxies is about 1.1., The ratio of early type (E+S0) to late type (S+Irr) giant galaxies is about 1.1. It is slightly lower than iu the Fornax cluster., It is slightly lower than in the Fornax cluster. The spatial distribution of the 19 ealaxics is shown in Fig., The spatial distribution of the 19 galaxies is shown in Fig. 9 (bold hexagous)., 9 (bold hexagons). Tt amatches well the density distribution of the fainter, It matches well the density distribution of the fainter measurements should recover the UVD spectral shape well for the line-of-sight considered. with the median. providing a better estimate of 5.,"measurements should recover the UVB spectral shape well for the line-of-sight considered, with the median providing a better estimate of $S$." The results of ZOLb agree very well with our analysis for a [uctuating ionization rate., The results of Z04b agree very well with our analysis for a fluctuating ionization rate. Note that the results of Z0J4b cannot be compared directly to the predictions of the ΔΕΗΗΧΟ model which assumes a spatially uniform UND., Note that the results of Z04b cannot be compared directly to the predictions of the MHR99 model which assumes a spatially uniform UVB. We have used state-of the art hverodynamical simulations to (tain improved measurements of the spectral shape of the imizing UV background from the and forest and to investigate the origin of the large spatial Ductuations observed in the to column density ratio., We have used state-of the art hydrodynamical simulations to obtain improved measurements of the spectral shape of the ionizing UV background from the and forest and to investigate the origin of the large spatial fluctuations observed in the to column density ratio. Using artificial absorption spectra we have shown that the softness parameter of the UV. background: can be accurately inferred. from the column density ratio of and. absorption lines obtained. by applying standard Voigt profile fitting routines., Using artificial absorption spectra we have shown that the softness parameter of the UV background can be accurately inferred from the column density ratio of and absorption lines obtained by applying standard Voigt profile fitting routines. Uncertainties in the identification of corresponding and absorption and errors in the determination. of the column densities contribute little to the large Iuctuations observed. in the and column density ratio. although one should be cautious of extreme values of η.," Uncertainties in the identification of corresponding and absorption and errors in the determination of the column densities contribute little to the large fluctuations observed in the and column density ratio, although one should be cautious of extreme values of $\eta$." These Huctuations must be due to genuine spatial variations in the spectral shape of the UVB., These fluctuations must be due to genuine spatial variations in the spectral shape of the UVB. X model where the ionization rate Iuctuates due to variation in the number. luminosity ancl spectral shape of a small number of QSOs reproduces the observed spatial variations of the and column density ratio. as well as the observed anti-correlation of the column density ratio with the density.," A model where the ionization rate fluctuates due to variation in the number, luminosity and spectral shape of a small number of QSOs reproduces the observed spatial variations of the and column density ratio, as well as the observed anti-correlation of the column density ratio with the density." This is in good agreement with previous suggestions that the observed. forest spectra at z723.5 probes the tail end of the reionization of iby QSOs., This is in good agreement with previous suggestions that the observed forest spectra at $z\sim 2-3.5$ probes the tail end of the reionization of by QSOs. The large fluctuations observed. in. the and column density ratio argue strongly against a significant contribution of emission by hot gas to the ionization rate at 2«&z«3., The large fluctuations observed in the and column density ratio argue strongly against a significant contribution of emission by hot gas to the ionization rate at $2σι Soa,Ol (Fev&Charlot1997).. Ojliaetal.(2006)."," $|b| > 45\arcdeg$ $S_{\mathrm{6\,cm}} \approx 1$ \citep{fc97}. \cite{ofljlk-c06}." . eenerallv carried out at nieht so that the sources had large solar elougatious., generally carried out at night so that the sources had large solar elongations. Indeed. observiug at large solar elongation was au explicit criterion iu scheduliug the observatious for the second subset.," Indeed, observing at large solar elongation was an explicit criterion in scheduling the observations for the second subset." As a result. the smallest clongation for anv source is. aud the typical elongation is approximately1307.," As a result, the smallest elongation for any source is, and the typical elongation is approximately." ". For the preseut analysis. we have used the core components models from these two obscrving oogranas,. augnieuted by measurements from the iterature."," For the present analysis, we have used the core components models from these two observing programs, augmented by measurements from the literature." All sources lave aneular diameters ueasured at at least 3 frequencies; and some sources have measured angular diameters at as nany as Y frequencies.," All sources have angular diameters measured at at least 3 frequencies, and some sources have measured angular diameters at as many as 7 frequencies." See Table 2 of Ojlaetal.(2006)., See Table 2 of \cite{ofljlk-c06}. . While the selection criteria for the wo subsets differed. the ποιαον WOYOC treated identically in the following analysis.," While the selection criteria for the two subsets differed, the sources were treated identically in the following analysis." Aneular broadening is manifested as an observed angular diameter that scales approximately as A2., Angular broadening is manifested as an observed angular diameter that scales approximately as $\lambda^2$. " We ft the measured angular diameters to the functional form where 0, aud 0; ave the scattering aud intrinsic (FWOAD diameters of t16Αν, respectively. at the fiducial frequency o: 1] CGIIz."," We fit the measured angular diameters to the functional form where $\theta_s$ and $\theta_i$ are the scattering and intrinsic (FWHM) diameters of the, respectively, at the fiducial frequency of 1 GHz." " We found the best-fitting values for 0, and @; in a iiniummn 4? sense;", We found the best-fitting values for $\theta_s$ and $\theta_i$ in a minimum $\chi^2$ sense. " We considered bo hour=0 (1e. frequency-independent iutriusic diaΠΟΤΟ, for a flat spectrin source) aud e= LG.e. frequeney scaling for a single icolhiereut svucwotron coniponent) aud selected the value of ο hat produced the lower 2Ve"," We considered both $x = 0$ (i.e., frequency-independent intrinsic diameter, for a flat spectrum source) and $x = -1$ (i.e., frequency scaling for a single incoherent synchrotron component) and selected the value of $x$ that produced the lower $\chi^2$." As a motivation for the use of equation (1)). as well as anticipatiug later| discussion. we gin by considering a crude approximation to equation (1)).," As a motivation for the use of equation \ref{eqn:fit}) ), as well as anticipating later discussion, we begin by considering a crude approximation to equation \ref{eqn:fit}) )." For the sources having uxasured augular diameters at both 133 aud 1.6 CIz. we lave assunued a simple power-law scaling for the angular diameter. 0xve. and solved for ," For the sources having measured angular diameters at both 0.33 and 1.6 GHz, we have assumed a simple power-law scaling for the angular diameter, $\theta \propto \nu^\beta$, and solved for $\beta$." Wo chose 0.33. GIIz because the frequency «lepeudence of scattering means that it will be the inost sensitive to ποσατοπιο wechose 1.G QGIIZz as the second. frequeucy as an attempt fo balance between having a sufficiently laree frequencydvuauiicrange so as to obtain a robust estimate of Jjj , We chose 0.33 GHz because the frequency dependence of scattering means that it will be the most sensitive to scattering; wechose 1.6 GHz as the second frequency as an attempt to balance between having a sufficiently large frequencydynamicrange so as to obtain a robust estimate of $\beta$ "not observe fragmentation for any of the resolutions, and the surface densities appear very similar.","not observe fragmentation for any of the resolutions, and the surface densities appear very similar." " We also find that the resulting total stresses are equivalent in the three cases (see Fig. 4)),"," We also find that the resulting total stresses are equivalent in the three cases (see Fig. \ref{figalpha}) )," and agree very well with equation (3))., and agree very well with equation \ref{eqabc}) ). We therefore conclude that we have reached numerical convergence in this case., We therefore conclude that we have reached numerical convergence in this case. " A side-effect of letting the disc evolve for 3500 orbits is that mass is redistributed over the computational domain, as the disc is trying to reach a steady state with XoxR-?/?,"," A side-effect of letting the disc evolve for 3500 orbits is that mass is redistributed over the computational domain, as the disc is trying to reach a steady state with $\Sigma \propto R^{-3/2}$." We find that 8 can be reduced to a value of 5 without seeing fragmentation for all 3 resolutions., We find that $\beta$ can be reduced to a value of $5$ without seeing fragmentation for all 3 resolutions. " From Fig. 4,,"," From Fig. \ref{figalpha}," " we see that in all cases, we find very similar total shear stresses for different resolutions, which in turn agree very well with equation (3))."," we see that in all cases, we find very similar total shear stresses for different resolutions, which in turn agree very well with equation \ref{eqabc}) )." " For 8<4, we find fragmentation for all resolutions considered."," For $\beta \lesssim 4$, we find fragmentation for all resolutions considered." The maximum stress the disc can provide to balance the cooling is Qmax& 0.1., The maximum stress the disc can provide to balance the cooling is $\alpha_\mathrm{max} \approx 0.1$ . " This is in agreement with the results of?,, who found that the maximum stress increased by approximately a factor of 2 compared to?,, who started from smooth initial conditions."," This is in agreement with the results of, who found that the maximum stress increased by approximately a factor of 2 compared to, who started from smooth initial conditions." Note that we do not attempt to determine the exact value of Bc., Note that we do not attempt to determine the exact value of $\betac$ . " Around 8=βε, other numerical effects may play a role?)."," Around $\beta=\betac$, other numerical effects may play a role." . Figure ὅ shows the fragmented disc with 6=2.5 at AR/R=0.004., Figure \ref{figdens3} shows the fragmented disc with $\beta=2.5$ at $\Delta R/R=0.004$. " Note that there are no special locations anymore: the disc fragments everywhere as long as H is resolved, which is basically the criterion of?."," Note that there are no special locations anymore: the disc fragments everywhere as long as $H$ is resolved, which is basically the criterion of." ". We also do not find any borderline cases(?),, for which the disc fragments at early times but the fragments do not survive."," We also do not find any borderline cases, for which the disc fragments at early times but the fragments do not survive." " The disc either fragments, after which the formed clumps migrate and merge, or the disc finds itself in a steady gravito-turbulent state."," The disc either fragments, after which the formed clumps migrate and merge, or the disc finds itself in a steady gravito-turbulent state." " With this setup, a single parameter, 3, determines whether the disc fragments or not."," With this setup, a single parameter, $\beta$, determines whether the disc fragments or not." We have studied the numerical convergence of simulations of self-gravitating discs using the grid-based code FARGO., We have studied the numerical convergence of simulations of self-gravitating discs using the grid-based code . " For smooth initial conditions, we find the same non-convergence as recently reported for SPH simulations(?).."," For smooth initial conditions, we find the same non-convergence as recently reported for SPH simulations." " We have argued that this non-convergence is related to the smooth initial conditions, that lead to an edge in temperature and surface density at the outer boundary of the gravito-turbulent region."," We have argued that this non-convergence is related to the smooth initial conditions, that lead to an edge in temperature and surface density at the outer boundary of the gravito-turbulent region." surface gives a global accretion rate of Al=1.6.vr+,surface gives a global accretion rate of $\dot{M}=1.6 \moyr$. Note that the peak in the accretion rate lies well beyond the peak in the Milkv Ways SER. which occurs. around R=A4kpe.," Note that the peak in the accretion rate lies well beyond the peak in the Milky Way's SFR, which occurs around $R\!=\!4\kpc$." Vhis implies the need for a redistribution of gas in the disc. the study of which is bevond the scope of the present paper (butseeforinstance??)..," This implies the need for a redistribution of gas in the disc, the study of which is beyond the scope of the present paper \citep[but see for instance][]{SchoenrichBinney09,SpitoniMatteucci11}." The top panel of Fig., The top panel of Fig. 9 shows the net How LLIL) as function of £7. obtained as the dilference between the rate at which gas arrives at à given radius and the rate at which supernovae eject gas from that radius.," \ref{accretion} shows the net flow ) as function of $R$, obtained as the difference between the rate at which gas arrives at a given radius and the rate at which supernovae eject gas from that radius." The net Dow profile differs from the accretion profile because fountain clouds do not fall back onto the disc at the same radius they are ejected from., The net flow profile differs from the accretion profile because fountain clouds do not fall back onto the disc at the same radius they are ejected from. As # increases. the orbits of fountain clouds start to get an inward component because of the interaction with the corona. thus elouds land at smaller and smaller radii.," As $R$ increases, the orbits of fountain clouds start to get an inward component because of the interaction with the corona, thus clouds land at smaller and smaller radii." Ln particular. most of the clouds ejected at 11R90kms+ (?)..," At large line-of-sight velocities the emission in the halo region of our Galaxy is dominated by the HVCs, the emission from which lies in rather isolated outlying regions of $(l,b,v)$ space delimited by $|v_{\rm DEV}|>90\kms$ \citep{vanWoerden+04}." The upper panels in Fig., The upper panels in Fig. 10. compare the emission. predicted. by our. best. mode| (loft. panel) near μα=dddkms with what is actually observed., \ref{channels} compare the emission predicted by our best model (left panel) near $v_{\rm LSR}\!=\!-144\kms$ with what is actually observed. Ln he observational data. three main islands of emission. are apparent.," In the observational data, three main islands of emission are apparent." At b30 we see Complexes A and C. which lave no real counterparts in the model.," At $b>30^\circ$ we see Complexes A and C, which have no real counterparts in the model." Similarly emission at |1501 associated with the Xnticentre High-Velocity Cloud (ACIIV) has no counterpart in the model., Similarly emission at $l\ga 180^\circ$ associated with the Anticentre High-Velocity Cloud (ACHV) has no counterpart in the model. Lt is well known ju the metallicity of most. HVCSs. in particular Complexes AX and € is much lower than that of gas in the disc. which garonely suggests that they come from outside the Galaxy (sce2)..," It is well known that the metallicity of most HVCs, in particular Complexes A and C is much lower than that of gas in the disc, which strongly suggests that they come from outside the Galaxy \citep[see][]{Wakker01}." Moreover. assuming a distance of LOkpe for both ο.‘Complexes A and € (2?) gives for these objects heights from 1e midplane of 6Skpc.," Moreover, assuming a distance of $10\kpc$ for both Complexes A and C \citep{vanWoerden+04, Thom+08} gives for these objects heights from the midplane of $6-8\kpc$." To produce emission so far from he plane. we would need a kick velocity Ay150kins," To produce emission so far from the plane, we would need a kick velocity $h_{\rm v}\gtrsim150\kms$." iX model with fy so large completely fails to reproduce the ata globally., A model with $h_{\rm v}$ so large completely fails to reproduce the data globally. In summary. ΗΝος such as Complexes A and C are almost certainly extragalactic in origin and our moclel is quite Correct not to reproduce them.," In summary, HVCs such as Complexes A and C are almost certainly extragalactic in origin and our model is quite correct not to reproduce them." The rate at which the Galaxy aceretes gas [rom infalling LIVCs is ~0.2AM.vr+ (?).. an order of magnitude lower than our estimate of the rate of accretion via the fountain | corona condensation mechanism.," The rate at which the Galaxy accretes gas from infalling HVCs is $\sim0.2\moyr$ \citep{Sancisi08}, an order of magnitude lower than our estimate of the rate of accretion via the fountain $+$ corona condensation mechanism." The main body. of emission in the upper right panel of Fie., The main body of emission in the upper right panel of Fig. IO. forms a large island that stractelles the plane.," \ref{channels} forms a large island that straddles the plane." " Hs summit [ies at (/.6)=(1207.15) and is labelled ""Outer Arn’."," Its summit lies at $(l,b)=(120^\circ,15^\circ)$ and is labelled “Outer Arm”." This feature is thought to arise from the warp of the clelise., This feature is thought to arise from the warp of the disc. Our model (elt panel) does not include a warp in the disc. so apart [from two horns of very faint emission either side of the plane. its emission is confined in a thin region around the plane.," Our model (left panel) does not include a warp in the disc, so apart from two horns of very faint emission either side of the plane, its emission is confined in a thin region around the plane." The lower panels of Fig., The lower panels of Fig. 10 show predicted: (Left) and observed. (right) emission at much lower heliocentric velocities (rispc—G6Gkms+) than the upper panel.," \ref{channels} show predicted (left) and observed (right) emission at much lower heliocentric velocities $v_{\rm LSR}\!\simeq\!-66\kms$ ) than the upper panel." At such Intermediate Velocities (λος are classically celine to be at 35kms+1."," The host SED is best fit by an obscured starburst galaxy template at $z\approx 1.9$, with a stellar of $\sim 10^{11.5}$ $_\odot$ and an inferred metallicity \citep{esp+06} of about 0.5 $_\odot$, suggesting that GRB progenitors can in fact exist at near-solar metallicity, and may occur in the most massive galaxies at $z>1$." wwas discovered by the ssatellite on 2002 Jan. 27.875 UT. with a positional accuracv of δ radius (Rickerctal.2002)..," was discovered by the satellite on 2002 Jan. 27.875 UT, with a positional accuracy of $8'$ radius \citep{gcn1229}." The burst duratiou and fluence in the 2.100 keV baud are 18 s and 2.7«10© eve 7 (Sakamotoetal. 2005). , The burst duration and fluence in the $2\!-\!400$ keV band are $18$ s and $2.7\times 10^{-6}$ erg $^{-2}$ \citep{slk+05}. . "Optical observations did not uncover au afterglow candidate, with R.f>19.5 mag at. Lt aud 8.2 hr after the burst. respectively (Lambetal.2002)... aud AR>21.5 ias atl hr over 75% of the error circle (CastroCeréuetal. 2002)."," Optical observations did not uncover an afterglow candidate, with $R,I\!>\!19.5$ mag at 4.4 and 8.2 hr after the burst, respectively \citep{gcn1230}, and $R\!>\!21.5$ mag at 3.1 hr over $75\%$ of the error circle \citep{gcn1234}." . The Galactic extinction in the direction of is low. E(DVy)0018 mag (Schlegeletal.1998).," The Galactic extinction in the direction of is low, $E(B-V)=0.048$ mag \citep{sfd98}." . We initiated two LO ks observatious with theObservatory. Lit aud 1161 d after the burst. to identify the fading X-ray afterelow.," We initiated two 10 ks observations with the, $4.14$ and $14.64$ d after the burst, to identify the fading X-ray afterglow." The data were obtained with the Advanced CCD Tagine Spectrometer (ACIS) and reduced and analyzed using the CIAO softwareharvard., The data were obtained with the Advanced CCD Imaging Spectrometer (ACIS) and reduced and analyzed using the CIAO software. edufciag.. A comparison of the two epochs reveals three fading sources not associated with bright stellar counterparts., A comparison of the two epochs reveals three fading sources not associated with bright stellar counterparts. FE Of these. only one is detected iu both epochs. and las faded with high sjenificauce. with 2.6 aud 1.0 count 10.37 keV). respectively.," Of these, only one is detected in both epochs, and has faded with high significance, with 2.6 and 1.0 count $^{-1}$ $0.3-7$ keV), respectively." Using a Galactic column of 3. A= 12000). with an uucertaiutv of about 1” in cach coordina"," The position of the X-ray afterglow candidate is $\alpha$, $\delta$ (J2000), with an uncertainty of about $1''$ in each coordinate." We observed this source with the Verv Large Array Iuc.)) at a frequency of 8.16 CGIIz on 2002 Feb. 11.20. 16.25. 21.97. aud Alar. 18.10 UT.," We observed this source with the Very Large Array ) at a frequency of 8.46 GHz on 2002 Feb. 14.20, 16.23, 21.97, and Mar. 18.10 UT." The data were processedusing AIPS., The data were processedusing AIPS. " In the first observation we detect an object with a flux of 22263 qi]. coincident with the N-vay position. at a—üsb125. A= (J2000). £0.08"" in each coordinate."," In the first observation we detect an object with a flux of $222\pm 63$ $\mu$ Jy, coincident with the X-ray position, at $\alpha$, $\delta$ (J2000), $\pm 0.03''$ in each coordinate." Subsequent observations reveal that the object has faded. with 3o limits of 150 yy (Feb. 16.23 and 21.97) aud 65 μ]ν (Na. 18.10). sugeesting that this is the radio afterglow of020127.," Subsequent observations reveal that the object has faded, with $3\sigma$ limits of 150 $\mu$ Jy (Feb. 16.23 and 21.97) and 65 $\mu$ Jy (Mar. 18.10), suggesting that this is the radio afterglow of." . Optical observations were obtained with the Large Format Camera (LEC) ou the 200-nch telescope at the Aft. Palomar Observatory ou 2002 Feb. 1.29 aud Feb. 6.31 UT for a total of 1300 s (g/). 2100 s (7). and 1800 s (77).," Optical observations were obtained with the Large Format Camera (LFC) on the 200-inch telescope at the Mt. Palomar Observatory on 2002 Feb. 4.29 and Feb. 6.34 UT for a total of 4300 s $g'$ ), 2400 s $r'$ ), and 1800 s $i'$ )." The images were bias-subtracted. flat-ficlded. aud coadded using IRAE. aud photometry was performed relative to SDSS.," The images were bias-subtracted, flat-fielded, and coadded using IRAF, and photometry was performed relative to SDSS." At the position of the N-ray and radio afterglows we detect a faint object with /=23.89£0.13 mae. Moos23423.5 mae. aud gy’25.8 mae: limits are 20 aud magnitudes are in the AB system.," At the position of the X-ray and radio afterglows we detect a faint object with $i'=23.89\pm 0.13$ mag, $r'>23.5$ mag, and $g'>25.8$ mag; limits are $2\sigma$ and magnitudes are in the AB system." We identify this object as the host galaxy ofGRBO20127., We identify this object as the host galaxy of. . Further observations were obtained with the Echellete Spectrograph aud Bhuager (ESI) on the νους II 10-1 telescope on 2002 Nur. 13.28 UT in R (1500 8) aud on 2003 Feb. 28.36 UT in 7 (600 3)., Further observations were obtained with the Echellete Spectrograph and Imager (ESI) on the Keck II 10-m telescope on 2002 Mar. 13.28 UT in $R$ (1500 s) and on 2003 Feb. 28.36 UT in $I$ (600 s). The data were reduced as described above., The data were reduced as described above. We measure I—23.56£0.10 mae aud R=21.7350.15 mae.," We measure $I=23.56\pm 0.10$ mag and $R=24.73\pm 0.15$ mag." " NIR observatious in A, aud oJ were obtained with the Near Infra-Red Camera (NIRC) on the Iseck I 10-ii telescope ou 2002 Oct. 13.63 aud Nov. 17.18 UT. respectively, for a total of 1080 s in each filter."," NIR observations in $K_s$ and $J$ were obtained with the Near Infra-Red Camera (NIRC) on the Keck I 10-m telescope on 2002 Oct. 13.63 and Nov. 17.48 UT, respectively, for a total of 1080 s in each filter." The oeidividual frames were dark-subtracted. flat-fielded. aud corrected for bad pixels and cosmic ravs using custoni IRAF routines.," The individual frames were dark-subtracted, flat-fielded, and corrected for bad pixels and cosmic rays using custom IRAF routines." Photometry was performed relative to the standard star Έσσο 16., Photometry was performed relative to the standard star Feige 16. The host galaxy has J=20.37£0.10 mag and Ay=1S.5140.05 inae., The host galaxy has $J=20.37\pm 0.10$ mag and $K_s=18.54\pm 0.05$ mag. Optical/NIR nuages of the host are shown in Figure 1.., Optical/NIR images of the host are shown in Figure \ref{fig:sed}. . Finally. on 2002 Apr. 6 UT we observed the host ealaxy with the musing the Space Telescope Inaging Spectrograph (STIS) ax part of program CO 9180 (PE I&ullkarni).," Finally, on 2002 Apr. 6 UT we observed the host galaxy with the using the Space Telescope Imaging Spectrograph (STIS) as part of program GO 9180 (PI: Kulkarni)." A total of 15868 sawere obtained with the CL filter., A total of 4868 s were obtained with the CL filter. We processed aud combined the individual exposures using the IRAF task (Fruchter&Mook2002).. with andpixscale=0.," We processed and combined the individual exposures using the IRAF task \citep{fh02}, with and." 5. At the position of the afterglow we detect an extended object with an AB maguitude of 2L840.1 mae (Έπος 1))., At the position of the afterglow we detect an extended object with an AB magnitude of $24.8\pm 0.1$ mag (Figure \ref{fig:sed}) ). We obtained optical spectra of the host galaxy using ESI on four separate occasions., We obtained optical spectra of the host galaxy using ESI on four separate occasions. The data were reduced. using custom:IRAF routines to bias-subtract. flat-field. and rectify the ten individual echelle orders.," The data were reduced using customIRAF routines to bias-subtract, flat-field, and rectify the ten individual echelle orders." Sky subtraction was performed using the method aud software described in Welson (2003).., Sky subtraction was performed using the method and software described in \citet{kel03}. . Wavelength calibration was performed using CuAr aud HeNeXe are lamps auc air-to-vacuuni and heliocentric correctionswere applied., Wavelength calibration was performed using CuAr and HgNeXe arc lamps and air-to-vacuum and heliocentric correctionswere applied. The spectra covers the range 0.39 to 1.05 μπι at a resolution of 11.5 lan s 1., The spectrum covers the range $0.39$ to $1.05$ $\mu$ m at a resolution of 11.5 km $^{-1}$ . We detect οσοαπ emission beyond 0.6 pu.," We detect continuum emission beyond 0.6 $\mu$ m," 6 x-ray (Nouveliotin (B~1027 (Duncan&Thompson1992:Iouveliotiu (Ikaspi2007:vanParadijs," $6$ $\gamma$ \citep{kouveliotou1} $B \sim 10^{15}$ \citep{duncan, kouveliotou2}. \citep{kaspi, paradijs}." etal.1995).. (2001). (1995). between the magnitude aud waiting times both for active earthquake regious and for SGR 1806-20., \citet{woods} \citet{cheng} between the magnitude and waiting times both for active earthquake regions and for SGR 1806-20. Thus. the statistical similarities between earthquakes aud SCR events argue for physically similar origins.," Thus, the statistical similarities between earthquakes and SGR events argue for physically similar origins." The Quasi-Periodic Oscillations (QPOs) observed at late-times of ejut flames of SCR 1806-20. SCR 19001114. and SCR 0525-66 (Aareehetti2008:Watts&Strolumaver2007) constitute another piece of observational evidence in favor of starquakes.," The Quasi-Periodic Oscillations (QPOs) observed at late-times of giant flares of SGR 1806-20, SGR 1900+14, and SGR 0525-66 \citep{mareghetti, watts} constitute another piece of observational evidence in favor of starquakes." These QPOs ave most likely due to seignic oscillations duced by the large crustal fractures occurnue in extremely cherectic events similar to what happeus after earthquakes., These QPOs are most likely due to seismic oscillations induced by the large crustal fractures occurring in extremely energetic events similar to what happens after earthquakes. Such oscillations could be Ἠιιητος to the crust or involve the eutire neutron star., Such oscillations could be limited to the crust or involve the entire neutron star. Crackling noise Sethnaetal.(2001). arises when a system responds to changing external conditions through discrete. nuüpulse events spanning a broad range of sizes.," Crackling noise \citet{sethna} arises when a system responds to changing external conditions through discrete, impulse events spanning a broad range of sizes." Bak. Taug. aud Wiesenteld (1988) iutroduced a connection. between dywnuanücal critical plenomena and crackling noise.," Bak, Tang, and Wiesenfeld (1988) introduced a connection between dynamical critical phenomena and crackling noise." They emphasized low svstenis nay cud up naturally at the critical point through a process of selforganized criticality., They emphasized how systems may end up naturally at the critical point through a process of self-organized criticality. Based upon this idea of the crackling noise. Noudratvey (2002) studied he statistics of magnetic noise iu neutron star crusts. and compared its intensity and statistical properties to he burst activity of SCRs.," Based upon this idea of the crackling noise, Kondratyev (2002) studied the statistics of magnetic noise in neutron star crusts, and compared its intensity and statistical properties to the burst activity of SGRs." Te then argued that the roise could originate from iiagnetic avalanches., He then argued that the noise could originate from magnetic avalanches. However. )ecause of the required iulhoimogeueous crust structure. 16 postulated the existence of iiagnetic domains withiu he neutrou-star crust for au iuterior maguctic Ποια streugth in the range ~Lote10 C. Usine the randomly jumping interacting moment (RJIM) model. it was shown that the burst intensity and waiting ine distributions are not ouly in good agreement with observations. but also are analogous with the statistical xoperties of SGRs.," However, because of the required inhomogeneous crust structure, he postulated the existence of magnetic domains within the neutron-star crust for an interior magnetic field strength in the range $\sim 10^{16} - 10^{17}$ G. Using the randomly jumping interacting moment (RJIM) model, it was shown that the burst intensity and waiting time distributions are not only in good agreement with observations, but also are analogous with the statistical properties of SGRs." Whether or not imagnetars are the source of SCRs and ANDPs. as relicsofstellar interiors. thestudyof he maguetic fields iu and around degenerate stars," Whether or not magnetars are the source of SGRs and AXPs, as relicsofstellar interiors, thestudyof the magnetic fields in and around degenerate stars" in à cloud of racdius 24 helium abundance may vary by at most NY/Y=(Vg.VaMasuada.,in a cloud of radius $R_{\rm cl}$ helium abundance may vary by at most $\Delta Y/Y=(V_{\rm He}-V_{\rm H})R_{\rm cl}/V_{\rm turb}R_{\rm turb}$. When turbulence becomes strong after helium sedimentation had some time to act unopposed. then over time the initial abundance gradient is clilutecl by a [actor ~eVineeiveLT 1.," When turbulence becomes strong after helium sedimentation had some time to act unopposed, then over time the initial abundance gradient is diluted by a factor $\sim e^{-V_{\rm turb}R_{\rm turb}t/R_{\rm cl}^2}$ ." By contrast. larec-scale turbulent motion. with opxRow. has no ellect on the small-scale abundance [uctuations.," By contrast, large-scale turbulent motion, with $R_{\rm cl}\ll R_{\rm turb}$, has no effect on the small-scale abundance fluctuations." Furthermore. if the cloud. is magnetized. the magnetic stress may be able to suppress the turbulent mixing altogether.," Furthermore, if the cloud is magnetized, the magnetic stress may be able to suppress the turbulent mixing altogether." In general there is no reason to expect strong turbulent motion in the low density gas clouds that were first to form out of cosmological density perturbation field (82 and 3)., In general there is no reason to expect strong turbulent motion in the low density gas clouds that were first to form out of cosmological density perturbation field 2 and 3). Strong turbulence may arise later. as these clouds. are accreted by larger objects and. become pressure-confined. but its length scales. amplitude and duration. are very uncertain.," Strong turbulence may arise later, as these clouds are accreted by larger objects and become pressure-confined, but its length scales, amplitude and duration are very uncertain." However. as has been pointed out by Bruston et al. (," However, as has been pointed out by Bruston et al. (" 1981). while the impact of turbulence on the abundance variation in the interstellar clouds. is hard. to. caleulate. observations suggest that it should be limited.,"1981), while the impact of turbulence on the abundance variation in the interstellar clouds is hard to calculate, observations suggest that it should be limited." In particular turbulence failed to destroy an order of magnitude variation in the abundances of dillerent isotopes of carbon (I2ncrenaz. Falearone Lucas 1975: Goldsmith Langer LOTS) and the separation between the different types of dust. grains (Carrasco. Strom Strom 1973).," In particular turbulence failed to destroy an order of magnitude variation in the abundances of different isotopes of carbon (Encrenaz, Falgarone Lucas 1975; Goldsmith Langer 1978) and the separation between the different types of dust grains (Carrasco, Strom Strom 1973)." Therefore it seems likely that the Huctuations of helium abundance may survive as well., Therefore it seems likely that the fluctuations of helium abundance may survive as well. We have shown that diffusion can significantly. increase he helium. abuncance of protostellar clouds., We have shown that diffusion can significantly increase the helium abundance of protostellar clouds. Similarly diffusion may also produce spatial variation of the deuterium (Bruston et al., Similarly diffusion may also produce spatial variation of the deuterium (Bruston et al. 1981). and. lithium abundances., 1981) and lithium abundances. The amplitude of the variation. depends on many factors (magnetic field. outside pressure. turbulence ete.)," The amplitude of the variation depends on many factors (magnetic field, outside pressure, turbulence etc.)" ane in some systems the clleet of diffusion may still. be negligible., and in some systems the effect of diffusion may still be negligible. However. as demonstrated. by our. calculations. he conservation of primordial abundances until the onse of stellar nucleosvnthesis. cannot in general be taken for erantecd.," However, as demonstrated by our calculations, the conservation of primordial abundances until the onset of stellar nucleosynthesis, cannot in general be taken for granted." ltecent observations strongly suggest that stars in a cast some elobular clusters have been formed with enhance yolium abundance (Beclin et al., Recent observations strongly suggest that stars in at least some globular clusters have been formed with enhanced helium abundance (Bedin et al. 2004: Norris 2004: Lee et al., 2004; Norris 2004; Lee et al. 2005: Piotto et al., 2005; Piotto et al. 2005)., 2005). " It has been even suggested. tha he initial abundance of helium may be the missing “scconc xwameter"" (Caloi DAntona 2005).", It has been even suggested that the initial abundance of helium may be the missing “second parameter” (Caloi D'Antona 2005). Several scenarios involving early pollution bx helium-rich but metal-poor stars rave been suggested. as an explanation., Several scenarios involving early pollution by helium-rich but metal-poor stars have been suggested as an explanation. However. Bekki Norris (2005) have shown that such pollution is very unlikely. unless the helium rich gas comes from the outside source and is kept in place by high external pressure.," However, Bekki Norris (2005) have shown that such pollution is very unlikely, unless the helium rich gas comes from the outside source and is kept in place by high external pressure." Therefore. diffusion. provides a strong alternative as an explanation to high helium abundance.," Therefore, diffusion provides a strong alternative as an explanation to high helium abundance." The author thanks Volker Dromm. Abraham. Loch. Adi Nusser ancl Marcelo Alvarez lor stimulating discussions. aud AleDonalel Observatory for the Wot. McDonald.Fellowship.," The author thanks Volker Bromm, Abraham Loeb, Adi Nusser and Marcelo Alvarez for stimulating discussions, and McDonald Observatory for the W.J. McDonaldFellowship." of specilic angular momentum and an observed one.,of specific angular momentum and an observed one. In (he present simulations. we used an initial ris Ma number of 10 and which decavs to M~3 by |~0.42Γεω whereas the observed cores by Goodman et al. (," In the present simulations, we used an initial $\it {rms}$ Ma number of $10$ and which decays to ${\cal M} \sim 3$ by $t \sim 0.42~t_{ff,cl}$ whereas the observed cores by Goodman et al. (" 1993) and Caselli et al (2002a) are samplecl from clifferent molecular cloud complexes in which the dynamical conditions (e.g.. the Mach number) are different.,"1993) and Caselli et al (2002a) are sampled from different molecular cloud complexes in which the dynamical conditions (e.g., the Mach number) are different." The most simple situation is (hat the parameters governing the dvnanmical evolution ol the molecular cloud in the models do not exactly match (the dvnamical conditions in the regions where the observed. cores are formed and (hus cores in the observations may have intrinsically more specific angular momentum than the simulated ones., The most simple situation is that the parameters governing the dynamical evolution of the molecular cloud in the models do not exactly match the dynamical conditions in the regions where the observed cores are formed and thus cores in the observations may have intrinsically more specific angular momentum than the simulated ones. The second effect may be related to the fact that the simulated cores are identified in intrinsic space whereas the observed cores are identified in position-position-velocitv cubes., The second effect may be related to the fact that the simulated cores are identified in intrinsic space whereas the observed cores are identified in position-position-velocity cubes. Although some differences in (he cores populations may arise when using the (wo methods. most of the most massive cores will be detected in the PPV method with their masses modified by a correction factor ol order unity (e.g.. Smith et al.," Although some differences in the cores populations may arise when using the two methods, most of the most massive cores will be detected in the PPV method with their masses modified by a correction factor of order unity (e.g., Smith et al." 2008)., 2008). It is therefore unlikely that a factor of ~10 difference can originate from variations from the chuup finding algorithm., It is therefore unlikely that a factor of $\sim 10$ difference can originate from variations from the clump finding algorithm. A third possibility is (hat the totally different wavs of calculating the specific angular momentum im the observations and in (he simulations may stand behind (his discrepancy., A third possibility is that the totally different ways of calculating the specific angular momentum in the observations and in the simulations may stand behind this discrepancy. In order (ο test the latter hypothesis. il is necessary (o generate svnthetic velocity maps of the cores using individual projections. such as (ο eliminate anv potential effect of blending of the cores along the lime of sight. and measure (he specific angular momentum from (he projected velocity maps following the standard observational procedure.," In order to test the latter hypothesis, it is necessary to generate synthetic velocity maps of the cores using individual projections, such as to eliminate any potential effect of blending of the cores along the line of sight, and measure the specific angular momentum from the projected velocity maps following the standard observational procedure." Unlike previous simulations. our models which have a hieh spatial resolution. ancl a large number of cores allow us to compare the entire distributions of the intrinsicallv measured specific angular momentum distributions to (hie ones derived from svnthetic observations of the cores.," Unlike previous simulations, our models which have a high spatial resolution, and a large number of cores allow us to compare the entire distributions of the intrinsically measured specific angular momentum distributions to the ones derived from synthetic observations of the cores." " We generate svnthetic velocity maps of the C160 cores in both simulations at a nearly similar epoch (Le. at /=1.152 Myis =0.417yp For simulation BL and /=1.159 Myrs =0.420!,p,4 lor simulation D2) along the three main directions of the box."," We generate synthetic velocity maps of the C160 cores in both simulations at a nearly similar epoch (i.e., at $t=1.152$ Myrs $=0.417~t_{ff,cl}$ for simulation B1 and $t=1.159$ Myrs $=0.420~t_{ff,cl}$ for simulation B2) along the three main directions of the box." As stated above. the cores ave projected individually such as to eliminate any effect of blending along the line of sight.," As stated above, the cores are projected individually such as to eliminate any effect of blending along the line of sight." The velocity in each pixel of the cores is the mean velocity in the line of sieht., The velocity in each pixel of the cores is the mean velocity in the line of sight. The velocily maps corresponding to the cores shown in Fig., The velocity maps corresponding to the cores shown in Fig. 2. and Fig., \ref{fig3} and Fig. 4 are displaved in Fig., \ref{fig4} are displayed in Fig. and Fig. 10..," \ref{fig9} and Fig. \ref{fig10}," respectively., respectively. The velocity maps exhibit a variety of features ranging Irom well ordered motions that can be assimilated to rotation. both for roundish and filamentary cores. {ο more complex dynamical configurations in which (there is no clearly verifiable velocity eradient.," The velocity maps exhibit a variety of features ranging from well ordered motions that can be assimilated to rotation, both for roundish and filamentary cores, to more complex dynamical configurations in which there is no clearly verifiable velocity gradient." In general. the velocity maps of (he cores. especially when the same cores are seen along the three different projections. do not support the idea of simple rigid-body rotation.," In general, the velocity maps of the cores, especially when the same cores are seen along the three different projections, do not support the idea of simple rigid-body rotation." It is interesting to note that recent hieh spatial ancl spectral resolution observations using the Platean de Bures interferometer by Csengeri et al. (, It is interesting to note that recent high spatial and spectral resolution observations using the Plateau de Bures interferometer by Csengeri et al. ( 2010) of five massive dense cores in Cyvenus-X show a variety. and level of complexity in (heir dynamical features similar to the,2010) of five massive dense cores in Cygnus-X show a variety and level of complexity in their dynamical features similar to the , becomes concentrated toward the equator resulting in relatively stronger alpha-vich freeze-out. which iucreases AFCUTI) to ~2«101M. (for ALCON)z007M).,"becomes concentrated toward the equator resulting in relatively stronger alpha-rich freeze-out, which increases $\Ti44$ to $\sim 2\EE{-4} \Msun$ (for $\Nii \approx 0.07 \Msun$ )." This is outside our observationallv deteriined range aud could indicate that asvnuuetryv was not extreme in SN 1987À. especially if AL¢ΗΤΗ) is close to the limit derived by Borkowski et al. (," This is outside our observationally determined range and could indicate that asymmetry was not extreme in SN 1987A, especially if $\Ti44$ is close to the limit derived by Borkowski et al. (" 1997).,1997). " We rote that a piston-driveu calculation could perhaps allow for asviuunuetry. as such models give very sniall values of M(HTi) in 1-D. A direct wav to estimate ACTI) in Supernovae is to observe the ganuua-ray cussion from the radioactive decay of Τι, T"," We note that a piston-driven calculation could perhaps allow for asymmetry, as such models give very small values of $\Ti44$ in 1-D. A direct way to estimate $\Ti44$ in supernovae is to observe the gamma-ray emission from the radioactive decay of $^{44}$ Ti." he 1.156. MeV line associated with the decay of Ti las ouly been detected in two supernova remnants (and no supernovae): Cas A (Ivudin et al., The 1.156 MeV line associated with the decay of $^{44}$ Ti has only been detected in two supernova remnants (and no supernovae): Cas A (Iyudin et al. 1991: The et al., 1994; The et al. 1996) and the newly discovered ολαταX-rav source GRO J0852-1262/RN. 0852.0-1622 (Ivuclin et al., 1996) and the newly discovered gamma-ray/X-ray source GRO J0852-4262/RX J0852.0-4622 (Iyudin et al. 1998: Ascheubach 1998)., 1998; Aschenbach 1998). While ΑΠΕTi) in the latter is not vet well-gown. M(ITi) in Cas A was L7!05LOLAL. (GOrmes et al.," While $\Ti44$ in the latter is not yet well-known, $\Ti44$ in Cas A was $1.7^{+ 0.6}_{-0.5}\EE{-4} \Msun$ (Görrres et al." 1998)., 1998). In the models of Nagataki et al. (, In the models of Nagataki et al. ( 1998). the value of AZCHTi) at the upper eud of this range would indicate that Cas A exploded asyauetricallv.,"1998), the value of $\Ti44$ at the upper end of this range would indicate that Cas A exploded asymetrically." Our estimate of AZ(HUTi) in Sect., Our estimate of $\Ti44$ in Sect. LL does not secu to indicate a high deeree of asviuinetry for SN 1987À. but au independent ioeasurement of its 1.156 MeV line may be needed to be more conclusive ou this point.," 4.1 does not seem to indicate a high degree of asymmetry for SN 1987A, but an independent measurement of its 1.156 MeV line may be needed to be more conclusive on this point." To detect this clnission frou SN 1987À. instruments like INTEGRAL (Leising 1991) are required.," To detect this emission from SN 1987A, instruments like INTEGRAL (Leising 1994) are required." The two [O ITT lines observed. (see Sect., The two [O III] lines observed (see Sect. 2.2 and Fig., 2.2 and Fig. 2) can be usec to estimate the average density of the ciittineg eas., 2) can be used to estimate the average density of the emitting gas. We have used a multi-level atom to do this. using the atomic data of Meudoza (1983). Osterbrock (1989) and Agearwal (1993).," We have used a multi-level atom to do this, using the atomic data of Mendoza (1983), Osterbrock (1989) and Aggarwal (1993)." Asstuning a temperature of 10! Ik. we obtain a mean clectrou density of 120475cm°? in the [ο ΠΠ ciitting gas.," Assuming a temperature of $10^4$ K, we obtain a mean electron density of $120 \pm 75 \cm3$ in the [O III] emitting gas." The contimuni can be fitted with a spectrum of the form FYxBADexpt7p]). where το is thedust optical depth.," The continuum can be fitted with a spectrum of the form $F_{\lambda} \propto B_{\lambda}(T) (1 - {\rm exp}(-\tau_{\rm D}))$, where $\tau_{\rm D}$ is thedust optical depth." " With a functional form of το=Tys3(0.55/AY""* (where A is in microus) we obtain a best fit with Z237 Ik. πιο20.7 Land a~0.83."," With a functional form of $\tau_{\rm D} = \tau_{0.55} (0.55 / \lambda)^{\alpha}$ (where $\lambda$ is in microns) we obtain a best fit with $T \simeq 37$ K, $\tau_{0.55} \simeq 0.74$ and $\alpha \simeq 0.83$." The fit (sce Fig., The fit (see Fig. 2) works well up to z110722. where an extra source appears to add in.," 2) works well up to $\simeq 140 \mum$, where an extra source appears to add in." This could iudicate the preseuce of cold dust., This could indicate the presence of cold dust. Asstunineg the same functional form for this eiission as for the 37 I& component. the temperature of the cold conrponeut is close to LO Is. We lave looked at SN 1987À with ISO SWS/IAVS.," Assuming the same functional form for this emission as for the $37$ K component, the temperature of the cold component is close to 10 K. We have looked at SN 1987A with ISO SWS/LWS." The supernova was nof detected iu iu of the spectra., The supernova was not detected in any of the spectra. Iu particular. we lave derived upper lanits for the fluxcs of [Fe I| 2L05jnu and [Fe TI] 25.9972. and made tine dependent caleulatious for the late line enuüssion from the supernova.," In particular, we have derived upper limits for the fluxes of [Fe I] $\mum$ and [Fe II] $\mum$, and made time dependent calculations for the late line emission from the supernova." We lave assessed various uncertainties to the models. and for a plausible line profile we then πα an upper limit ou the mass of ejected I Ti; AZ(HTi)~1.5«10.1ALL.," We have assessed various uncertainties to the models, and for a plausible line profile we then find an upper limit on the mass of ejected $^{44}$ Ti, $\Ti44 \simeq 1.5\EE{-4} \Msun$ ." Together with the preliminary results of KFE99 this brackets the ejected mass of !! Ti to the range ΑΟΤΙ)=(0515)ς101ALL. which is close to the vield of H'Ti in models of tlhe explosion by Woosley Weaver (1995). Thiclemmann ct al. (," Together with the preliminary results of KF99 this brackets the ejected mass of $^{44}$ Ti to the range $\Ti44 = (0.5 - 1.5)\EE{-4} \Msun$, which is close to the yield of $^{44}$ Ti in models of the explosion by Woosley Weaver (1995), Thielemann et al. (" 1996) and Nagatala et al. (,1996) and Nagataki et al. ( 1997).,1997). The lower limit is probably less stringeut han he upper. as indicated by the results of Borkowski ct al. (," The lower limit is probably less stringent than the upper, as indicated by the results of Borkowski et al. (" 1997).,1997). A more clirec limit ou ACT) can be made when instruments ueasurue the eamunaray line emission frou he !ITi decay will be available., A more direct limit on $\Ti44$ can be made when instruments measuring the gamma-ray line emission from the $^{44}$ Ti decay will be available. The only eiiission our ISO observations detect is from eas and dust in the direction toward the supernova., The only emission our ISO observations detect is from gas and dust in the direction toward the supernova. In articular. the 10 IT) 5l.sjau aud 10 III] lan lues indicate a eas density of 120τὸ 2m and the dust continu can be explained by a teiperature of ~37 IK. A secoud dust component with ~LO I may also be present.," In particular, the [O III] $\mum$ and [O III] $\mum$ lines indicate a gas density of $120\pm75$ $^{-3}$ , and the dust continuum can be explained by a temperature of $\sim 37$ K. A second dust component with $\sim 10$ K may also be present." et al. (,et al. ( 2009).,2009). The results of απο et al. (, The results of Griest et al. ( 2010) apply only to the Ikeck TURES instrument. but there is another instrument. the VET UVES spectrograph. that is plaviug a kev role iu the search for possible changes in the fine-structure coustant using absorption lines in high redshift QSOs.,"2010) apply only to the Keck HIRES instrument, but there is another instrument, the VLT UVES spectrograph, that is playing a key role in the search for possible changes in the fine-structure constant using absorption lines in high redshift QSOs." In this paper. we perform a similar recalibration of the standard UVES Th/Ar waveleneth calibration pipeline using the VLT iodine cell.," In this paper, we perform a similar recalibration of the standard UVES Th/Ar wavelength calibration pipeline using the VLT iodine cell." We find simular. but smaller. waveleneth calibration errors than found in IIIRES.," We find similar, but smaller, wavelength calibration errors than found in HIRES." We discuss the possible origi of these offsets. iu particular whether they arise from the UVES pipeline software or svstematic errors within the telescope and/or spectrograph.," We discuss the possible origin of these offsets, in particular whether they arise from the UVES pipeline software or systematic errors within the telescope and/or spectrograph." " We also make a first attempt at calculating whether these calibration crrors can give rise to important systematic crrors in the lneasuremeuts to date of A,", We also make a first attempt at calculating whether these calibration errors can give rise to important systematic errors in the measurements to date of $\delalpha$. Six exposures were taken of the quasar ITEOD15-111 (;=Lal Vzc l1L9uunag) with the VET-UVES spectrograph in 2003 October.," Six exposures were taken of the quasar HE0515-4414 $z=1.71$, $V\approx14.9$ mag) with the VLT-UVES spectrograph in 2003 October." In this paper. we analyze the wavelength calibration of the three exposures tha were taken with the iodine cell in place.," In this paper, we analyze the wavelength calibration of the three exposures that were taken with the iodine cell in place." We include a journal of these observations iu Table 1.., We include a journal of these observations in Table \ref{tab:journal}. " Over the wavelength rauge of interest. the median signal/noise of the spectra extracted from these exposures is around. 20 pixel+ for the upper ""w chip aud around LL pixel for the lower ""E chip."," Over the wavelength range of interest, the median signal/noise of the spectra extracted from these exposures is around 20 $^{-1}$ for the upper “u” chip and around 11 $^{-1}$ for the lower “l” chip." One pixel corresponds to abou 1.5 luus+ at the leading edee of cach echelle order aud around 0.9 kus at the trailing edge., One pixel corresponds to about 1.5 $\kms$ at the leading edge of each echelle order and around 0.9 $\kms$ at the trailing edge. We note tha ESO's specifications for UVES are that the eratiugs. after being moved. be returned to the same position to within a tolerance corresponding to 0.1 pixels (D'Odorico et al.," We note that ESO's specifications for UVES are that the gratings, after being moved, be returned to the same position to within a tolerance corresponding to 0.1 pixels (D'Odorico et al." 2000)., 2000). Thus naively we nüght expect to see au overall non-zero velocity calibration shift between the iodine and Th/Ar lines of roughlv 1l0ms1 at 5500Α., Thus naively we might expect to see an overall non-zero velocity calibration shift between the iodine and Th/Ar lines of roughly 140 $\ms$ at 5500. ", The six QSO exposures were taken diving two nights. with the first two I5 QSO exposures being taken on the first nieht aud the third Is exposure taken on the next."," The six QSO exposures were taken during two nights, with the first two $_2$ QSO exposures being taken on the first night and the third $_2$ exposure taken on the next." The first two exposures were calibrated with the same 'Th/Ar exposure: however we note that the eratines were noved after the two data exposures aud then moved back ο the same position in order to take the Tl/Ar exposure., The first two exposures were calibrated with the same Th/Ar exposure; however we note that the gratings were moved after the two data exposures and then moved back to the same position in order to take the Th/Ar exposure. " The third I; QSO exposure was followed first by a ron-l, QSO exposure (une QSO. erating setting. etc.)"," The third $_2$ QSO exposure was followed first by a $_2$ QSO exposure (same QSO, grating setting, etc.)" and then by the ΤαΔι calibration exposure., and then by the Th/Ar calibration exposure. " We had roped this scheduling would remove a possible source of error caused by erating movement. but in fact. the third QSO L exposure was part of a different ""observation dock. meaning the eratiugs were reset (moved and then returned) between the data and Th/Ar exposures."," We had hoped this scheduling would remove a possible source of error caused by grating movement, but in fact, the third QSO $_2$ exposure was part of a different “observation block”, meaning the gratings were reset (moved and then returned) between the data and Th/Ar exposures." We herefore expect overall velocity shifts between the I» aud Th/Ar wavelength scales of order 110 115.+ for all three of our QSO exposures through the I5 cell., We therefore expect overall velocity shifts between the $_2$ and Th/Ar wavelength scales of order 140 $\ms$ for all three of our QSO exposures through the $_2$ cell. We can also cstimate an overall average velocity shift having to do with the position of the QSO in the spectrograph slit., We can also estimate an overall average velocity shift having to do with the position of the QSO in the spectrograph slit. The slit width is 0.7 and our exposures were taken with sccing between 0.657 aud (85°., The slit width is 0.7” and our exposures were taken with seeing between 0.65” and 0.85”. This slitavidth projects outo the CCD with an FWIIA of about L8 kaus. 3GR~62.000).," This slit-width projects onto the CCD with an FWHM of about 4.8 $\kms$ $R \sim 62,000$ )." Therefore. ifa eiven exposure has. for example. a 0.17 positioning error. we nmiehnt expect a roughly 600 mis> overall calibration shift. substantially larecr than the error caused by the resetting of the spectrometer erating.," Therefore, if a given exposure has, for example, a 0.1” positioning error, we might expect a roughly 600 $\ms$ overall calibration shift, substantially larger than the error caused by the resetting of the spectrometer grating." Iu iore detail. we note that cach 2100 s I» exposure used only the red arm of UVES in the staudard 600 nu central wavelength setting for L5 observations.," In more detail, we note that each 2400 s $_2$ exposure used only the red arm of UVES in the standard 600 nm central wavelength setting for $_2$ observations." The red arin of UVES has a detector containing two CCD detectors covering the waveleneth ranges 196597 aud umm., The red arm of UVES has a detector containing two CCD detectors covering the wavelength ranges 496–597 and nm. No on-chip binning was used: the pixels have a width of zL3kuus5. providing 3.7 pixels per FEWIIM resolution clement.," No on-chip binning was used; the pixels have a width of $\approx1.3 \kms$, providing $\approx$ 3.7 pixels per FWHM resolution element." " A circular bate. or ""pupil stop”. is used routinely in UVES to provide a beam frou calibration lamps (e.g. Th/Ar. flat field) similar in size ο that from the telescope from an astronomical poiut source."," A circular baffle, or “pupil stop”, is used routinely in UVES to provide a beam from calibration lamps (e.g., Th/Ar, flat field) similar in size to that from the telescope from an astronomical point source." Our Is exposures were taken with an wuder-sized o»pil stop. Le. a ΠΙΟ smaller beam than usual was allowed into UVES. but our Th/Ar exposures used a slightly over-sized pupil stop.," Our $_2$ exposures were taken with an under-sized pupil stop, i.e., a slightly smaller beam than usual was allowed into UVES, but our Th/Ar exposures used a slightly over-sized pupil stop." " While these are the default settiues for I, observatious. strictly speaking our aini rere is to treat the In aud Th/Ar exposures as similarly as possible so that auy wavelength shifts between the wo are appropriate to normal QSO observations where a slelthy “oversize” pupil stop is used for both object and calibration exposures."," While these are the default settings for $_2$ observations, strictly speaking our aim here is to treat the $_2$ and Th/Ar exposures as similarly as possible so that any wavelength shifts between the two are appropriate to normal QSO observations where a slightly “oversize” pupil stop is used for both object and calibration exposures." However. we would not expect slight. circular viguettine/trmcation of the beam to affect our results here.," However, we would not expect slight, circular vignetting/truncation of the beam to affect our results here." Indeed. subsequent iocdine-cell tests with UVES have shown any effect from the undersized pupil stop to be very siuall. if preset at all: these results will be presented iu a forthcoming paper.," Indeed, subsequent iodine-cell tests with UVES have shown any effect from the under-sized pupil stop to be very small, if present at all; these results will be presented in a forthcoming paper." The QSO flux was extracted using the standard pipeline recipes., The QSO flux was extracted using the standard pipeline recipes. Five bias aud flat field exposures were median filtered to produce master bias aud Πατ Ποια corrections., Five bias and flat field exposures were median filtered to produce master bias and flat field corrections. The echelle order positions aud overall spectrograph setup were derived from short-aud-uarrow slit exposures of quartz and Th/AÀr lamps which were used to refine a physical model for the expected fiux distribution within each order., The echelle order positions and overall spectrograph setup were derived from short-and-narrow slit exposures of quartz and Th/Ar lamps which were used to refine a physical model for the expected flux distribution within each order. Ta our exposures. the QSO flux had high cnough signal/noise iu each echielle order to allow the flux distribution itself to define its spatial profile for use as object weights in the subsequent optimal extraction.," In our exposures, the QSO flux had high enough signal/noise in each echelle order to allow the flux distribution itself to define its spatial profile for use as object weights in the subsequent optimal extraction." No redispersoun of the spectra was performed after optimal extraction: each extracted echelle order retained its original wavelength dispersion as a function of pixel position., No redispersion of the spectra was performed after optimal extraction; each extracted echelle order retained its original wavelength dispersion as a function of pixel position. Rather than co-adding extracted QSO spectra. we treated cach order of cach exposure separately so that cach Tn (auc accompanying Th/Ar) exposure gives a separate measurement of the Th/Ar waveleugth calibration shifts for each order.," Rather than co-adding extracted QSO spectra, we treated each order of each exposure separately so that each $_2$ (and accompanying Th/Ar) exposure gives a separate measurement of the Th/Ar wavelength calibration shifts for each order." The UVES Couunon Pipeline Laneuaee (CPL) software package includes considerable inuprovenieuts to the waveleneth calibration process compared to previous UVES veduction pipelines., The UVES Common Pipeline Language (CPL) software package includes considerable improvements to the wavelength calibration process compared to previous UVES reduction pipelines. The Th/AÀxr line list is only a sinall subset of all known Th/Ar lines in the relevant wavelength range aud was derived via an objective line selection algorithin detailed in Murphy et al. (, The Th/Ar line list is only a small subset of all known Th/Ar lines in the relevant wavelength range and was derived via an objective line selection algorithm detailed in Murphy et al. ( 2007).,2007). An, An on vet unpublished measurements. except to take it into account in estimating the errors (see below).,"on yet unpublished measurements, except to take it into account in estimating the errors (see below)." Adopting τ=S days as the phase of these photometric data. the following relations have been applied to estimate the reddenme and the distance modulus (Riess et al.. 1996)):," Adopting $\tau = -8$ days as the phase of these photometric data, the following relations have been applied to estimate the reddening and the distance modulus (Riess et al., \cite{riess}) ):" aud We have adopted Ry(7= 8)21.259and Rpv(r—δ)=0.191 fron Table 2 of Riess et al. (1996)), and We have adopted $R_V(\tau = -8) = 1.259$ and $R_{B-V}(\tau = -8) = 0.494$ from Table 2 of Riess et al. \cite{riess}) ) and the standard value of the galactie extinction law CA/EG V)2351)., and the standard value of the galactic extinction law $A_V / E(B-V) = 3.1$ ). This last assuniptiou means that the reddening ratio in the Milkv Way can be used to describe the reddening in distant galaxies. which was also favored bv Riess et al. (1996)).," This last assumption means that the reddening ratio in the Milky Way can be used to describe the reddening in distant galaxies, which was also favored by Riess et al. \cite{riess}) )." We tried to estimate the colour excess {1VW) in two wavs., We tried to estimate the colour excess $E(B-V)$ in two ways. " First. we adopted (2BV),=0.02£0.03 (IIauzl Caton. 1998)). (BoWy0.11 (Riess et al.. 19963) "," First, we adopted $(B-V)_{obs} = 0.02 \pm 0.03$ (Hanzl Caton, \cite{hanzl}) ), $(B-V)_0 = -0.244$ (Riess et al., \cite{riess}) )" and used Eq.(1) to get E(BVj)=0.23+0.01 mag., and used Eq.(1) to get $E(B-V) = 0.23 \pm 0.04$ mag. Second. we used the COBE/IRAS ΑΙδν Reddcnine Map published very recently by Schlegel et al. (1998).," Second, we used the $COBE/IRAS$ All-Sky Reddening Map published very recently by Schlegel et al. \cite{schlegel}) )." This gives the reddening toward a specified direction based on a calibration between colour excess aud the infrared flux at 1004., This gives the reddening toward a specified direction based on a calibration between colour excess and the infrared flux at $\mu$. The query in the direction of SN 1998aq resulted in ECQBV)=0011E0.01 mae., The query in the direction of SN 1998aq resulted in $E(B-V) = 0.014 \pm 0.01$ mag. This low reddening value supports the suspicion that the observed (BW) color of SN 1998aq arouud asin was actually ducr than the oulv one published iieasurement of Tauzl (Πα Caton. 1998)).," This low reddening value supports the suspicion that the observed $(B-V)$ color of SN 1998aq around maximum was actually bluer than the only one published measurement of Hanzl (Hanzl Caton, \cite{hanzl}) )." On the other haud. the host ealaxv NGC 3982 has an active nucleus of a Sevtert 2 ype (see the next section). thus. higher dust couceutratiou within the host ealaxv ασ not be uurealistie.," On the other hand, the host galaxy NGC 3982 has an active nucleus of a Seyfert 2 type (see the next section), thus, higher dust concentration within the host galaxy might not be unrealistic." If this were the case. then the reddening of SN 1998aq would be uainlv due to dust absorption iu its host galaxy. rather han hat in the Milkv Way.," If this were the case, then the reddening of SN 1998aq would be mainly due to dust absorption in its host galaxy, rather than that in the Milky Way." Finally. we cau consider LBPy)=0.18£0.11 mag as the maveielted average of the two data above. cuphasizing the ureent need for »iblishied precise photometric mcasurements to solve this inportant and interesting problem.," Finally, we can consider $E(B-V) = 0.13 \pm 0.11$ mag as the unweighted average of the two data above, emphasizing the urgent need for published precise photometric measurements to solve this important and interesting problem." Tn order to derive the distance modulus via Eq.(2). he followiug data were adopted: Vip.=12.67£0.01 inag (Wauzl Caton. 1998)). Als=8)—8.693 (Ricss et al.. 19963) ," In order to derive the distance modulus via Eq.(2), the following data were adopted: $V_{obs}=12.67 \pm 0.01$ mag (Hanzl Caton, \cite{hanzl}) ), $M_V(\tau = -8) = -18.693$ (Riess et al., \cite{riess}) )" and RyA=0.076 imag (Crom the values above)., and $R_V \Delta = 0.076$ mag (from the values above). " The uncertainty of My and &y-A was estimated as being +0.2 and £0.01 mae. respectively, allowingga +1 day error in the epoch of the spectroscopic nicasureimoeut."," The uncertainty of $M_V$ and $R_V \Delta$ was estimated as being $\pm 0.2$ and $\pm 0.01$ mag, respectively, allowing $\pm 1$ day error in the epoch of the spectroscopic measurement." From the reddening estimated above. the total absorption is sty=31LE(BPy=O.10£0.31 with stronger probability that jc actual value is lower than this estimate.," From the reddening estimated above, the total absorption is $A_V = 3.1 E(B-V) = 0.40 \pm 0.34$ with stronger probability that the actual value is lower than this estimate." Substituting these values iuto Eq.(2). we get the extiuctiou-free. distance modulus as jg=30.89.d0.56 uag.," Substituting these values into Eq.(2), we get the extinction-free distance modulus as $\mu_0 = 30.89 \pm 0.56$ mag." The distance of the SN. corrected for interstellar absorption. isd=15.14L1 Mpc.," The distance of the SN, corrected for interstellar absorption, is $d ~=~ 15.1 \pm 4.4$ Mpc." However. it is stressed. hat this value can be considered ouly preliminary. which weed. further confirmation based ou much more extensive datasets.," However, it is stressed, that this value can be considered only preliminary, which need further confirmation based on much more extensive datasets." The relatively large uncertaiutyv of the distance reflects mainly the lack of precise photometric information on this object., The relatively large uncertainty of the distance reflects mainly the lack of precise photometric information on this object. There have been controversial evidence of hydrogen Dahuec-lines in the spectra of SNe Ia prescuted iui the literature (see Filippeuko. 1997 for review).," There have been controversial evidence of hydrogen Balmer-lines in the spectra of SNe Ia presented in the literature (see Filippenko, \cite{filip} for review)." In order to study the presence/absence of any fa feature in SN 1998aq. two consecutive spectra with higher resolution was obtained ou April 21th. about 8 davs before maxima.," In order to study the presence/absence of any $H\alpha$ feature in SN 1998aq, two consecutive spectra with higher resolution was obtained on April 21th, about 8 days before maximum." The contamination of the light of the host ealaxy was removed by fitting a parabolic function outside the profile of the SN spectrum (Fig. L.," The contamination of the light of the host galaxy was removed by fitting a parabolic function outside the profile of the SN spectrum (Fig. \ref{fig_4}," bottom panel). siuularly to Della Valle et al. (1996)).," bottom panel), similarly to Della Valle et al. \cite{della}) )." As it cam be seen iu the upper panel of Fie. L.," As it can be seen in the upper panel of Fig. \ref{fig_4}," no convincing detection of fa could be made., no convincing detection of $H\alpha$ could be made. As it has been mentioned above. the host galaxy. NGC 3982. has a Sevtert 2 type uucleus showing La and some other forbidden lines im enuüssdon (Io et al. 1997 )).," As it has been mentioned above, the host galaxy, NGC 3982, has a Seyfert 2 type nucleus showing $H\alpha$ and some other forbidden lines in emission (Ho et al., \cite{ho}) )." We have obtained one spectrum of the core region of NCC 3982 which is plotted in Fig. 5.., We have obtained one spectrum of the core region of NGC 3982 which is plotted in Fig. \ref{fig_5}. . The ciission, The emission higher redshifts z=2—3. relatively cold gas is flowing along the filaments toward the connected galactic halos.,"higher redshifts $z = 2 - 3$, relatively cold gas is flowing along the filaments toward the connected galactic halos." The cold gas streams may even reach inner galactic regions. which are closer to the center than the virial shock region.," The cold gas streams may even reach inner galactic regions, which are closer to the center than the virial shock region." These cold gas streams may supply galaxies with fuel for star formation or may influence the the galactic star formation. at least.," These cold gas streams may supply galaxies with fuel for star formation or may influence the the galactic star formation, at least." Several studies discuss in which way the existence of these cold streams is related to the galaxy mass., Several studies discuss in which way the existence of these cold streams is related to the galaxy mass. ? find that the cold gas accretion is only important for total galactic masses €10!'+Mo., \citet{Keres05} find that the cold gas accretion is only important for total galactic masses $\le 10^{11.4} M_{\sun}$. Related estimates are given in ?.., Related estimates are given in \citet{Dekel09}. If the WHIM gas ts located mainly within a network of large shock-confined filaments at z«0. then even recently a certain gas flow could be expected towards the corresponding knots of the network.," If the WHIM gas is located mainly within a network of large shock-confined filaments at $z \approx 0$, then even recently a certain gas flow could be expected towards the corresponding knots of the network." Those knots could be matter concentrations of galactic or even of galaxy cluster size., Those knots could be matter concentrations of galactic or even of galaxy cluster size. If extending our above considerations in three dimensions. multi-streaming occurs. leadingto the formation of a filament and a halo. ep.," If extending our above considerations in three dimensions, multi-streaming occurs, leadingto the formation of a well-defined filament and a halo, cp." Fig. 9.., Fig. \ref{fFilament}. Though the shape of the gas distribution is extremely idealized. it is expected to exhibit the correct density and temperature profiles depending on the initial scale length. again.," Though the shape of the gas distribution is extremely idealized, it is expected to exhibit the correct density and temperature profiles depending on the initial scale length, again." The large-scale gas velocities are determined by the gravitational potential., The large-scale gas velocities are determined by the gravitational potential. In the three-dimensional case. the velocities toward the forming filament and even more toward the halo are becoming high enough to generate shocks.," In the three-dimensional case, the velocities toward the forming filament and even more toward the halo are becoming high enough to generate shocks." Instead of a core. a relatively cold stream forms along the three-dimensional filament. propagating deep into the halo.," Instead of a core, a relatively cold stream forms along the three-dimensional filament, propagating deep into the halo." The temperature and density profiles for the three-dimensional case are much more complex even for the highly idealized geometry., The temperature and density profiles for the three-dimensional case are much more complex even for the highly idealized geometry. We are going to consider this in a forthcoming paper (Klar Müccket. in preparation).," We are going to consider this in a forthcoming paper (Klar Müccket, in preparation)." However. the existence of a natural regulation mechanism for the size and existence of a cold core for the one-dimensional case might indicate similar restrictions for the cold stream in three dimensions.," However, the existence of a natural regulation mechanism for the size and existence of a cold core for the one-dimensional case might indicate similar restrictions for the cold stream in three dimensions." The coefficients used to compute the evolution of the chemical network and the cooling and heating function are shown in Table A1.., The coefficients used to compute the evolution of the chemical network and the cooling and heating function are shown in Table \ref{tChemicalRates}. The values of the rates of the collisional processes are taken from ?.. while the photoionization and photoheating rates are taken from ?..," The values of the rates of the collisional processes are taken from \citet{Katz96}, while the photoionization and photoheating rates are taken from \citet{Black81}." In terms of these rates the chemical source term writes: The cooling function A is the sum of contributions from the collisional processes discussed above as well as collisional excitation of and and bremsstrahlung. while the heating function [is the sum of the heating rates corresponding to the photoionization: For the computation. of photoionization as well as photoheating the flux of the UV background is needed.," In terms of these rates the chemical source term writes: The cooling function $\Lambda$ is the sum of contributions from the collisional processes discussed above as well as collisional excitation of and and bremsstrahlung, while the heating function $\Gamma$ is the sum of the heating rates corresponding to the photoionization: For the computation of photoionization as well as photoheating the flux of the UV background is needed." We use a simplified model for its redshift dependence which resembles the current view in the literature. (222):," We use a simplified model for its redshift dependence which resembles the current view in the literature. \citep{Gnedin00,HaardtMadau01,Bianchi01}:" " A spectrum inversely proportional to the frequency is assumed,", A spectrum inversely proportional to the frequency is assumed. Most of the techniques used in our code are common in cosmological simulation codes., Most of the techniques used in our code are common in cosmological simulation codes. We will therefore concentrate on specific features ofevora., We will therefore concentrate on specific features of. . To preserve readability we will give one dimensional descriptions in x direction., To preserve readability we will give one dimensional descriptions in $x$ direction. The generalization to three dimensions ts straightforward., The generalization to three dimensions is straightforward. We will use X—(f+AD for a quantity x after the time step Ar and N=ΧΑ) at its beginning.," We will use $x^\prime = x(t +\Delta t)$ for a quantity $x$ after the time step $\Delta t$ and $x = x(t)$ at its beginning." The length of the time step Ar 1s given by the minimum of three different constraints., The length of the time step $\Delta t$ is given by the minimum of three different constraints. The first is the Courant-Friedrich-Levy condition implied by the the hydrodynamie solver: where « is the speed of sound., The first is the Courant-Friedrich-Levy condition implied by the the hydrodynamic solver: where $a$ is the speed of sound. Moreover. the cosmological expansion during one single time step is limited by The last constraint on the time step Is associated with thermal conduction.," Moreover, the cosmological expansion during one single time step is limited by The last constraint on the time step is associated with thermal conduction." Here. the maximal length of the time step can be computed by estimating the fraction. between the thermal energy and and its change due to the thermal conduction: Furthermore. each of these time steps 1s further restricted by a heuristic factor 0350 kin 1 are extremely uuconumiou. to argue iit the stars in the ealaxies with largest velocity dispersions niust have formicxl at sufficiently lieh redshift that eas dissipation effects are «λα,"," Indeed, Loeb Peebles (2002) have used our measurement of $\phi(\sigma)$, in particular, our finding that values of $\sigma>350$ km $^{-1}$ are extremely uncommon, to argue that the stars in the galaxies with largest velocity dispersions must have formed at sufficiently high redshift that gas dissipation effects are small." Iochanek (2001) has pointed out that combining a lensing based estimate of o(0) with tre one based on the motions of the stars. such as that presented here. xovides powerful coustraiuts ou 1iodels of galaxy formation.," Kochanek (2001) has pointed out that combining a lensing based estimate of $\phi(\sigma)$ with the one based on the motions of the stars, such as that presented here, provides powerful constraints on models of galaxy formation." By the time the SDSS survey is complete. a lensing based estimate of the velocity dispersion fiction should be »ossibloe.," By the time the SDSS survey is complete, a lensing based estimate of the velocity dispersion function should be possible." This will almost certainly measure velocity dispersions ou Luger scales than the few kpc scale probed by our measurement., This will almost certainly measure velocity dispersions on larger scales than the few kpc scale probed by our measurement. Therefore. a comparison of the wo will provide iuforiiation about the effects of dissipation aud birvouic contraction.," Therefore, a comparison of the two will provide information about the effects of dissipation and baryonic contraction." PLS evatefully acknowledges the award of a Joliu Simon CGugecuheinOO Fellowship axd the hospitality of the Institute or Advanced Study., PLS gratefully acknowledges the award of a John Simon Guggenheim Fellowship and the hospitality of the Institute for Advanced Study. Funding for the creation and distribution of the SDSS Archive has been provide by the Alfred P. Sloan Foundation. he Participating Institutions. the>National Aeronautics and Space Adiuinistration. the?National Science Foundation. he U.S. Depaxtinen of Eucrex. the Japanese Monbukagakusho. aud the Max Planck Society.," Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society." The SDSS Web site Is itp/Avwww.sdss.ore/ The SDSS is manage by the Astrophysical Research Consortimm (ARC) for the Paricipating Insitutious., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago. Fermulal. the Lustitute for AcΠω Stuv. the Japan Participation Group. The Johis Hopkins Uuniversity. Los Alamos National Laboratory. tl1ο Max-Plauck-Tustitute for Astronomy (AIPIA). the Max-PIluuck-Iustitue for Astroplivsics (AIPA). Now Mexico State Uuversity. the Universitv of Dittsbureh. Princeton Uuniversity. the Unite States Naval Observatorv. aud the Uuversitv of Washingο.," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, the University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington." "wheredj),=aj4(0.0.0) are the coellicients defined in the Galactic coordinate svstem. and Dnum(0.0.0) is the Wigner rotation matrix (Exlnonds1985)..","where$a_{lm}\equiv a_{lm}(0,0,0)$ are the coefficients defined in the Galactic coordinate system, and $D^{l}_{mm'}(\psi,\theta,\phi)$ is the Wigner rotation matrix \citep{Angular_Momentum}." Similar to Eq. (0)).," Similar to Eq. \ref{dpow}) )," we can deline (he power spectrum (Fi.0.0).," we can define the power spectrum $D(l;\psi,\theta,\phi)$." " It is easy to fine that DU:i.0.0) is independent of the angle ο, so in this paper we only consider two Euler angle q=(8.6) and set &=0."," It is easy to find that $D(l;\psi,\theta,\phi)$ is independent of the angle $\psi$, so in this paper we only consider two Euler angle $\hat{\bf q}\equiv(\theta,\phi)$ and set $\psi=0$." If we consider q as à vector. which labels (he z-axis direction in the rotated coordinate svstem. then (8.6) is the polar coordinate of this direction in the Galactic svstem !.," If we consider $\hat{\bf q}$ as a vector, which labels the $z$ -axis direction in the rotated coordinate system, then $(\theta,\phi)$ is the polar coordinate of this direction in the Galactic system ." . Now. we can define the rotationally variable parity parameter C(/:q) by replacing C(/) in Eq. (5))," Now, we can define the rotationally variable parity parameter $G(l;\hat{\bf q})$ by replacing $C(l)$ in Eq. \ref{est}) )" with D(f:q). ancl estimate the maxima and minima of G(/:q) for different Euler angles q.," with $D(l;\hat{\bf q})$, and estimate the maxima and minima of $G(l;\hat{\bf q})$ for different Euler angles $\hat{\bf q}$." Dv the definition. the parity. parameter G(/:q) depends on the coefficients αμ) as follows: where Απ)=32αρα)(P). and So the cross-terna «μεν 1s responsible for the angular dependency of the parity parameter G(F:q).," By the definition, the parity parameter $G(l;\hat{\bf q})$ depends on the coefficients $a_{l0}(\hat{\bf q})$ as follows: where $X^{\pm}(l;\hat{\bf q})\equiv\frac{1}{4\pi}\sum_{l'=2}^{l} a^2_{l'0}(\hat{\mathbf q})\Gamma^{\pm}(l')$, and So the cross-term $a_{lm}a^*_{lm'}$ is responsible for the angular dependency of the parity parameter $G(l;\hat{\mathbf q})$." We can also caleulate Che difference between G(/:q) ancl 90) by From the relation A(/)=OF). we know that X-7(/:q)«&P.(P). and E«| for f>3.," We can also calculate the difference between $G(l;\hat{\mathbf q})$ and $g(l)$ by From the relation $\Delta(\l)=O(\frac{1}{2l})$, we know that $X^{\pm}(l;\hat{\bf q})\ll P^{-}(l)$, and $\frac{G(l;\hat{\mathbf q})-g(l)}{g(l)}\ll1$ for $l>3$." 50. we conclude that G(/:q) mainly stands for the amplitude of the original parity parameter g(/).," So, we conclude that $G(l;\hat{\mathbf q})$ mainly stands for the amplitude of the original parity parameter $g(l)$." At the same time. due to the rotational variance of G(f;q). we can study the possible preferred direction. which max reveal hints on the origin of the observed parity asvmmetrv in CMD field.," At the same time, due to the rotational variance of $G(l;\hat{\mathbf q})$ , we can study the possible preferred direction, which may reveal hints on the origin of the observed parity asymmetry in CMB field." Let us show that G(/:q) map depends on the angular q., Let us show that $G(l;\hat{\mathbf q})$ map depends on the angular $\hat{\mathbf q}$ . As we have mentioned. q labels (he z-axis direction in(he rotated coordinate svstem. ancl (0.6) is just the polar coordinate of this direction in Galactic coordinate.," As we have mentioned, $\hat{\bf q}$ labels the $z$ -axis direction inthe rotated coordinate system, and $(\theta,\phi)$ is just the polar coordinate of this direction in Galactic coordinate." We plotted(he parameter C(/:q) as a function of, We plottedthe parameter $G(l;\hat{\mathbf q})$ as a function of J. Cohen: You and some previous speakers have spoken about abundance peculiarities.,J. Cohen: You and some previous speakers have spoken about abundance peculiarities. We ueed to make sure that the abundauce peculiarities are real aud not the result of the, We need to make sure that the abundance peculiarities are real and not the result of the The four largest dwarf planets in the Kuiper Belt form a distinct population of bodies with high albedos and volatile-rich surfaces (??)..,"The four largest dwarf planets in the Kuiper Belt form a distinct population of bodies with high albedos and volatile-rich surfaces \citep{Schaller2007,Stansberry2008}." " A significant history of collisions is suggested by the abundance of satellites in this group, which is much higher than expected for the Kuiper Belt as a whole (?).."," A significant history of collisions is suggested by the abundance of satellites in this group, which is much higher than expected for the Kuiper Belt as a whole \citep{Brown2006}." " Three of the four have known satellites: Pluto has three, Haumea (formerly 2003 EL¢1) has two, Eris has one, and Makemake (2005 has no substantial(2003 UB313)satellite"," Three of the four have known satellites: Pluto has three, Haumea (formerly 2003 $_{61}$ ) has two, Eris (2003 $_{313}$ ) has one, and Makemake (2005 $_9$ ) has no substantial satellite \citep{Brown2008}." The size and orbits of ΕΥ)these satellites are different from (?)..those found around smaller (100-km size) Kuiper Belt Objects (KBOs)., The size and orbits of these satellites are different from those found around smaller (100-km size) Kuiper Belt Objects (KBOs). " To date, most known satellites around smaller KBOs are thought to have formed via still-debated capture mechanism (?).."," To date, most known satellites around smaller KBOs are thought to have formed via a still-debated capture mechanism \citep{Knoll2008}." " Hence, a differenta satellite formation process is needed for the dwarf planets, and the most promising mechanism is collisions."," Hence, a different satellite formation process is needed for the dwarf planets, and the most promising mechanism is collisions." " Recently, numerical simulations support a giant collision origin for Pluto’s massive satellite, Charon (?).."," Recently, numerical simulations support a giant collision origin for Pluto's massive satellite, Charon \citep{Canup2005}." " However, the formation of the smaller satellites on the other dwarf planets has not been studied in detail."," However, the formation of the smaller satellites on the other dwarf planets has not been studied in detail." " Haumea, a ~1500 km diameter classical belt object with a semi-major axis of 43 AU, is a particularly puzzling case as it is also associated with several smaller KBOs with diameters between 70 and 365 km."," Haumea, a $\sim 1500$ km diameter classical belt object with a semi-major axis of 43 AU, is a particularly puzzling case as it is also associated with several smaller KBOs with diameters between 70 and 365 km." The smaller KBOs share similar orbits and surface properties., The smaller KBOs share similar orbits and surface properties. 'The associated KBOs have been likened to collisionally-produced dynamicallyand compositionally associated “families” that are observed in the asteroid belt (?)..," The associated KBOs have been likened to collisionally-produced dynamicallyand compositionally associated “families"" that are observed in the asteroid belt \citep{Brown2007}." " We collectively refer to Haumea, its satellites and proposed family members as the Haumea system."," We collectively refer to Haumea, its satellites and proposed family members as the Haumea system." Haumea has the only known family in the Kuiper Belt., Haumea has the only known family in the Kuiper Belt. The Haumea family members share a deep water spectral feature and neutral color (???)..," The Haumea family members share a deep water spectral feature and neutral color \citep{Brown2007,Ragozzine2007,Schaller2008}." The water feature is unique in the Kuiper Belt (7) and indicative of unusually carbon-free water ice (?).., The water feature is unique in the Kuiper Belt \citep{Brown2007} and indicative of unusually carbon-free water ice \citep{Pinilla2009}. Haumea also has the distinction of being the only known highly elongated dwarf planet though its precise shape is not known., Haumea also has the distinction of being the only known highly elongated dwarf planet though its precise shape is not known. " It has a spin period of only 3.9 hours (?),, the fastest of all the major and dwarf planets."," It has a spin period of only 3.9 hours \citep{Rabinowitz2006}, the fastest of all the major and dwarf planets." " 'The surface of Haumea is nearly homogenous with the exception of a red spot or faint red hemisphere (?7);; hence, the light curve is primarily a reflection of the non-spherical shape."," The surface of Haumea is nearly homogenous with the exception of a red spot or faint red hemisphere \citep{Lacerda2008,Lacerda2009}; hence, the light curve is primarily a reflection of the non-spherical shape." " Using the observed light curve and rotation period, ? fit a density of 2.6 g cm? assuming an equilibrium fluid body (a Jacobi ellipsoid)."," Using the observed light curve and rotation period, \citet{Rabinowitz2006} fit a density of 2.6 g $^{-3}$ assuming an equilibrium fluid body (a Jacobi ellipsoid)." " Although the dimensions of Haumea are not yet uniquely constrained (?), the observations require a tri-axial shape (see Table 2)) "," Although the dimensions of Haumea are not yet uniquely constrained \citep{Lockwood2009}, , the observations require a tri-axial shape (see Table \ref{tab:sims}) ) \citep{Rabinowitz2006}." "The derived density is greater than the average of (?)..~2g cm? for the largest KBOs (?),, although the density may be smaller with some internal friction (?).."," The derived density is greater than the average of $\sim 2$g $^{-3}$ for the largest KBOs \citep{Brown2008}, , although the density may be smaller with some internal friction \citep{Holsapple2007}. ." We have compared (he values of 7; (xine model) with the rj measured in a large sample of earlv-0tvpe galaxies by Jórrdan et al. (,We have compared the values of $r_h$ (King model) with the $r_h$ measured in a large sample of early-type galaxies by Jórrdan et al. ( 2005).,2005). " Note that these authors estimated ry, using a King rather than Wilson model.", Note that these authors estimated $r_h$ using a King rather than Wilson model. " Determining the peak of the distribution of ού) for our whole sample with a nonparametric fit ancl Epanechnikov filler (Epanechnikov 1969). aud assuming that this peak should fall at 7j,=2.35+0.3 pe. we find a distance lo NGC5128 of 3.58£0.38 Alpe."," Determining the peak of the distribution of $log(r_h)$ for our whole sample with a nonparametric fit and Epanechnikov filter (Epanechnikov 1969), and assuming that this peak should fall at $r_h= 2.85\pm 0.3$ pc, we find a distance to NGC5128 of $3.58\pm 0.3$ Mpc." The distance adopted in section 2 is within the error bars of this new distance estimate lor NGC5123., The distance adopted in section 2 is within the error bars of this new distance estimate for NGC5128. The individual groups are too small to show any clear peak in the distribution of rj., The individual groups are too small to show any clear peak in the distribution of $r_h$. " G3 is different [rom the two other groups in that it is mainly distributed in the outer regions of the galaxy (large J2,.. see Fig.3)."," G3 is different from the two other groups in that it is mainly distributed in the outer regions of the galaxy (large $R_{gc}$, see Fig.3)." Because most. GCs of G3 are of low mass and thus of faint. Iuminosity. no spectroscopy is available for them. aud (hus no age. racial velocity or spectroscopically determined metal abundance ([Z/1]).," Because most GCs of G3 are of low mass and thus of faint luminosity, no spectroscopy is available for them, and thus no age, radial velocity or spectroscopically determined metal abundance ([Z/H])." A possible consequence of this is thal G3 mieht be polluted by foreground stars. although MeLaughlin et al. (," A possible consequence of this is that G3 might be polluted by foreground stars, although McLaughlin et al. (" 2003) only mention two possible such cases (C145. C152). bv objects resembling intermecdiate-age Galactic open clusters (van den Dergh.2007). or bx backeround galaxies.,"2008) only mention two possible such cases (C145, C152), by objects resembling intermediate-age Galactic open clusters (van den Bergh,2007), or by background galaxies." The three groups have very different distributions of photometric metallicity |Fe/11]. as shown by their probability. density. functions (PDF) in Figs.," The three groups have very different distributions of photometric metallicity [Fe/H], as shown by their probability density functions (PDF) in Figs." 4 and 5., 4 and 5. The lines indicate non-parametric densitv estimates using an Epanechnikov kernel (Epanechunikov 1969)., The lines indicate non-parametric density estimates using an Epanechnikov kernel (Epanechnikov 1969). The bin width (0.2 dex for all groups) was chosen using the whole sample aud the Freedinan-Diaconis rule based on (he sample size aud the spread of the data (lor a delinilion. see “Freedman—Diaconisrule in wikipedia.," The bin width (0.2 dex for all groups) was chosen using the whole sample and the Freedman-Diaconis rule based on the sample size and the spread of the data (for a definition, see $""Freedman-Diaconis-rule""$ in wikipedia." For an explanation of the histogram as a densitv. see Freedman ancl Diaconis (1981)).," For an explanation of the histogram as a density, see Freedman and Diaconis (1981))." A peak in the metallicity distribution at [Fe/1I/|~—1 is seen in all three groups., A peak in the metallicity distribution at $[Fe/H]\sim -1$ is seen in all three groups. The PDF of G3 is clearly bimodal with a subgroup al verv low metallicity. while (he metallicity range of the (wo other groups is more limited and more in line with that of GC's in other galaxies. including our own.," The PDF of G3 is clearly bimodal with a subgroup at very low metallicity, while the metallicity range of the two other groups is more limited and more in line with that of GCs in other galaxies, including our own." "In $22. we have performed the partial correlation analysis and the regression on the sample and found that the apparent intrinsic correlation between σημ, and the black hole mass is likely to be caused by including the sub-sample 2 into the analysis.","In 2, we have performed the partial correlation analysis and the regression on the sample and found that the apparent intrinsic correlation between $\sigma _{\rm rms}^2 $ and the black hole mass is likely to be caused by including the sub-sample 2 into the analysis." Because the black hole masses of AGNs in. sub-sample 2 were estimated from their optical luminosity which in turn is positively correlated with their X-ray luminosity. an extra correlation between the black hole mass and X-ray luminosity will be introduced by the sub-sample 2.," Because the black hole masses of AGNs in sub-sample 2 were estimated from their optical luminosity which in turn is positively correlated with their X-ray luminosity, an extra correlation between the black hole mass and X-ray luminosity will be introduced by the sub-sample 2." If the X-ray luminosity is the primary quantity. then this will artificially strengthen any correlation with black hole mass.," If the X-ray luminosity is the primary quantity, then this will artificially strengthen any correlation with black hole mass." We therefore should exclude them when investigating the intrinsic correlation with oz., We therefore should exclude them when investigating the intrinsic correlation with $\sigma _{\rm rms}^2 $. " According to the results from the sub- |. we conclude that the correlation between ση, and the X-ray luminosity may be the intrinsic one. whereas the apparent correlation between c7. and the black hole mass 1s doubtful."," According to the results from the sub-sample 1, we conclude that the correlation between $\sigma _{\rm rms}^2 $ and the X-ray luminosity may be the intrinsic one, whereas the apparent correlation between $\sigma _{\rm rms}^2 $ and the black hole mass is doubtful." Our K-S tests also suggest that sub-samples | and 2 are not likely drawn from the same parent population., Our K-S tests also suggest that sub-samples 1 and 2 are not likely drawn from the same parent population. As discussed in Lu Yu (2001). several mechanisms may be responsible for the correlation between σημ. and the X-ray luminosity. such as the hot-spot model. the obscurative variability and so on.," As discussed in Lu Yu (2001), several mechanisms may be responsible for the correlation between $\sigma _{\rm rms}^2 $ and the X-ray luminosity, such as the hot-spot model, the obscurative variability and so on." " After the apparent correlation between στι,Inns and the black hole mass was discovered. some models accounting for this correlation were proposed (e.g. O Neill et al."," After the apparent correlation between $\sigma _{\rm rms}^2 $ and the black hole mass was discovered, some models accounting for this correlation were proposed (e.g. O' Neill et al." 2005. Pessah 2007).," 2005, Pessah 2007)." However. it needs to be verified whether the correlation is intrinsic.," However, it needs to be verified whether the correlation is intrinsic." Although the black hole masses of about three dozen AGNs have been determined by the reverberation mapping method. the size of our sample is still limited due to the lack of long enough and high quality observation data of these objects.," Although the black hole masses of about three dozen AGNs have been determined by the reverberation mapping method, the size of our sample is still limited due to the lack of long enough and high quality observation data of these objects." More conclusive results could be obtained when nore and higher quality data become available., More conclusive results could be obtained when more and higher quality data become available. Iu addition to the above coalescence process. we include binary agerceations.,"In addition to the above coalescence process, we include binary aggregations." So for cach DM halo with circular velocity V.owe compute the further evolution of the galaxy mass distribution in a timestep duc to binary agerceations.," So for each DM halo with circular velocity $V$, we compute the further evolution of the galaxy mass distribution in a timestep due to binary aggregations." OO This is described by the Sumioluchowski equation. which we write m terms of masses for the sake of simplicity: where FaggUn.ml.V) is the aggregation rate depending on the DM halo where the ealaxies i aud il reside.," This is described by the Smoluchowski equation, which we write in terms of masses for the sake of simplicity: where $\tau^{-1}_{agg}(m,m',V)$ is the aggregation rate depending on the DM halo where the galaxies $m$ and $m'$ reside." The first term describes the construction of ealaxies with mass m7from simaller oues with mass 75 aud inoan’. while the second represcuts the destruction of galaxies i due to their ageregationCoco with others.," The first term describes the construction of galaxies with mass $m$from smaller ones with mass $m'$ and $m- m'$, while the second represents the destruction of galaxies $m$ due to their aggregation with others." A schematic representation of the two terms eoverming thebinary ageregations is giveu in the lower part of fig., A schematic representation of the two terms governing the binary aggregations is given in the lower part of fig. 1, 1. " The ageresation rate is governed by 7,2=Viaεπ9) (see Cavaliere. Colafrancesco Meuci 1992)."," The aggregation rate is governed by $\tau^{-1}_{agg}=\Sigma\,V_{rel}/(4\pi R^3/3)$ (see Cavaliere, Colafrancesco Menci 1992)." Here Vay is the averagerelative velocity of galaxies in the DM halo whose riis value is equal to twice the halo 1-D velocity dispersion aymἘν2. and X is the cross section.," Here $V_{rel}$ is the average relative velocity of galaxies in the DM halo whose rms value is equal to twice the halo 1-D velocity dispersion $\sigma_V\approx V/\sqrt{2}$, and $\Sigma$ is the cross section." The latter is given for nearly eraziug. weakly hvperbolie encounters by Saslaw (1985). and by Cavaliere. Colafraucesco. Moeuci (1992).," The latter is given for nearly grazing, weakly hyperbolic encounters by Saslaw (1985), and by Cavaliere, Colafrancesco, Menci (1992)." It includes a geometrical teria (proportional to the area of the ealaxies). aud a focussing factor 1|(C0/V44P. that accounts for the enhancement of X in slow eucouuters with resonance between the internal aud the orbital degrees of freedom (sce also Binney Tremaine 1986).," It includes a geometrical term (proportional to the area of the galaxies), and a focussing factor $\sim 1+(v/V_{rel})^2$ that accounts for the enhancement of $\Sigma$ in slow encounters with resonance between the internal and the orbital degrees of freedom (see also Binney Tremaine 1986)." Thus. the average rate for binary agerceatious is where the average is over the relative velocities V4.," Thus, the average rate for binary aggregations is where the average is over the relative velocities $V_{rel}$." " The distribution of the encounter velocities is assumed to be Maswellian. namely Note that for encounters «l1between equal galaxies with 72 rand N(M/)=N(M)N the scaling of the agerceation rate (13) reduces to aMx""DAEoe(1ο2wD)σε)-Va)."," The distribution of the encounter velocities is assumed to be Maxwellian, namely Note that for encounters between equal galaxies with $r'=r$ and $N(M')=N(M)=N$ the scaling of the aggregation rate \ref{aggtime}) ) reduces to $\tau_{agg}^{- 1}\propto \langle r^2\,(1+v^2/V_{rel}^2)\,V_{rel}\rangle$." " Pertormung. the average over the distribution. g(V,.4) in terms of the rescaled variable y=Vi4/0 vie Tad)reee,ROTor). where the function Pir)={αμPeepgh£a?)|fdyyorplyefer) tends to a coustant when the ratio.—σεις»x."," Performing the average over the distribution $g(V_{rel})$ in terms of the rescaled variable $y\equiv V_{rel}/v$ yields $\tau_{agg}^{-1}\propto r^2\,v^4\,\sigma_V^{-3}\,R^{- 3}\,I(x)$, where the function $I(x)\equiv \int\,dy\,y^3\,exp(-y^2/x^2)+ \int\,dy\,y\,exp(-y^2/x^2)$ tends to a constant when the ratio $x\equiv \sigma_V/v\rightarrow \infty$." " Thus the ageregation rate (1)) reduces to the expression given by Makino IIut (1997) originally derived analyticallybv Miuuou (1992) αμα the τιανν,", Thus the aggregation rate \ref{aggtime}) ) reduces to the expression given by Makino Hut (1997) – originally derived analytically by Mamon (1992) – and the r.h.s. of eq. (, of eq. ( 3) becomes proportional Αι”clay?RO? (the effective rate adopted by Somerville Primack 1999) in the proper limits of large οπου(ο velocities relative to the internal galaxy velocity dispersion. and of encounters between equal galaxies.,"3) becomes proportional to $N^2\,r^2\,v^4\,\sigma_V^{-3}\,R^{-3}$ (the effective rate adopted by Somerville Primack 1999) in the proper limits of large encounter velocities relative to the internal galaxy velocity dispersion, and of encounters between equal galaxies." Finally. note that after performing the average of eq. C," Finally, note that after performing the average of eq. (" "L) over the distribution g(V,,4) oulv σι: euters the computation: in other words. we use an average description for eucounter velocities typical of the cuviromment considered.","4) over the distribution $g(V_{rel})$ only $\sigma_V$ enters the computation; in other words, we use an average description for encounter velocities typical of the environment considered." The ecometrical cross section contained iu eq. {, The geometrical cross section contained in eq. ( 1) does not properly describe single eveuts with V729e. but these are rare for our typical values of σι:/c in the range from 1 to about [.,"4) does not properly describe single events with $V_{rel}\gg v$, but these are rare for our typical values of $\sigma_V/v$ in the range from $1$ to about $4$." Tn cases with larger ratios ay:fe the effect of the ageregatious is suppressed SECO TrygX as shown above. but even iuside rich clusters the averaged cross section that we adopt is consistent witli the simulation σιresults. see Makino IIut (1997): for nmuerical computations of the role of iuteractious inside clusters see also Lauzoni (2000).," In cases with larger ratios $\sigma_V/v$ the effect of the aggregations is suppressed since $\tau_{agg}\propto \sigma_V^3$ as shown above, but even inside rich clusters the averaged cross section that we adopt is consistent with the simulation results, see Makino Hut (1997); for numerical computations of the role of interactions inside clusters see also Lanzoni (2000)." Iu sunu. our cross section provides an accurateereraye description of ageregatious in svstenis where the velocity dispersion is close to the ealaxy circular velocity and the focussing term is relevant: on the other haud. it constitutes an effective average approxinatiou for encounters in environments with laree velocity dispersion up to the scale of rich clusters. where the agerceatious are disfavoured auyway.," In sum, our cross section provides an accurate description of aggregations in systems where the velocity dispersion is close to the galaxy circular velocity and the focussing term is relevant; on the other hand, it constitutes an effective average approximation for encounters in environments with large velocity dispersion up to the scale of rich clusters, where the aggregations are disfavoured anyway." " As a final global check. we have verified that the insertion of au artificial cutoff at V5,= Lein X does not change our results."," As a final global check, we have verified that the insertion of an artificial cutoff at $V_{rel}=4\,v$ in $\Sigma$ does not change our results." " The equations (1)) aud (3)) describing the evolution of Non.M.£f) ave iuteerated nuuencallv on a grid of circular velocities and cosuic times with step At=102I7,+"," The equations \ref{dynfrict}) ) and \ref{smoluch}) ) describing the evolution of $N(m,M,t)$ are integrated numerically on a grid of circular velocities and cosmic times with step $\Delta t=10^{-2}\,H_o^{-1}$." Iu order to test our nuierical code. we first run the computation for two relevant simplecases where analytic solutions are available.," In order to test our numerical code, we first run the computation for two relevant simplecases where analytic solutions are available." " Iu the liit zy>0 (νο, when merging of the host haloes is proiiptly followed by coalescence of the galaxies within them by dynamical friction) the solution /N(e.V.£f) of eq. ("," In the limit $\tau_{df}\rightarrow 0$ (i.e., when merging of the host haloes is promptly followed by coalescence of the galaxies within them by dynamical friction) the solution $N(v,V,t)$ of eq. (" 1) when iutegrated over the circular velocity V. must vield the Press Schechter mass distribution.,1) when integrated over the circular velocity $V$ must yield the Press Schechter mass distribution. The comparison between the nuuerical and the analytic solution in this case is performed at three ditfereut times in the top panel of fe., The comparison between the numerical and the analytic solution in this case is performed at three different times in the top panel of fig. 2. which shows that the nuuerical solutions remain close to the analytic Press Schechter forma over the whole rauge of e: in fact. the relative deviation is always smaller than ," 2, which shows that the numerical solutions remain close to the analytic Press Schechter form over the whole range of $v$; in fact, the relative deviation is always smaller than ." To test the code section coucermme the Simoluchowski equation. we umunuericallv solve eq. (," To test the code section concerning the Smoluchowski equation, we numerically solve eq. (" "3) in the case of coustaut agerceationao rate Taggτα,=coust for galaxies within a host halo of given mass AL.",3) in the case of constant aggregation rate $\tau_{agg}^{-1}={\rm const}$ for galaxies within a host halo of given mass $M$ . Tn this case the exact solution (Smohichowski, In this case the exact solution (Smoluchowski stars.,stars. " The Asiago spectrum. albeit of lower S/N due to its shorter exposure. shows the presence of Hy, and [O n] 23727 at the same redshift. thus confirming the result of the Loiano observations."," The Asiago spectrum, albeit of lower S/N due to its shorter exposure, shows the presence of $_\beta$ and [O ] $\lambda$ 3727 at the same redshift, thus confirming the result of the Loiano observations." " Unfortunately. the actual useful spectral range secured by this spectrum has its rec end at 7800Az: therefore it does not cover the region containing H,."," Unfortunately, the actual useful spectral range secured by this spectrum has its red end at 7800; therefore it does not cover the region containing $_\alpha$." Table | reports the emission-line fluxes as determined from the Loiano spectrum. dereddened for Galactic absorption.," Table 1 reports the emission-line fluxes as determined from the Loiano spectrum, dereddened for Galactic absorption." Given the limited S/N and resolution of the spectrum. o correction for starlight contamination (e.g.. Ho et al.," Given the limited S/N and resolution of the spectrum, no correction for starlight contamination (e.g., Ho et al." " 1993. 1997) was attempted. but this does not strongly affect any of our conclusions,"," 1993, 1997) was attempted, but this does not strongly affect any of our conclusions." Magnitudes of the source in the Loiano images were measured through aperture photometry. since its profile is significantly larger than the image PSF (276 versus 175) and. as measured on the U-band frame. is possibly elongated in the NW-SE direction.," Magnitudes of the source in the Loiano images were measured through aperture photometry, since its profile is significantly larger than the image PSF $\farcs$ 6 versus $\farcs$ 5) and, as measured on the $U$ -band frame, is possibly elongated in the NW-SE direction." Using an aperture radius of 4.5 pixels (corresponding to 276). we found the following optical magnitudes (not corrected for Galactic absorption): U = 19.4940.08. B = 19.7840.04. V = 18.6940.03. R = 18.3340.03. and J = 17.6840.05.," Using an aperture radius of 4.5 pixels (corresponding to $\farcs$ 6), we found the following optical magnitudes (not corrected for Galactic absorption): $U$ = $\pm$ 0.08, $B$ = $\pm$ 0.04, $V$ = $\pm$ 0.03, $R$ = $\pm$ 0.03, and $I$ = $\pm$ 0.05." The broad-band spectral energy distribution (SED) of the source. constructed with data from. (X-ray). Loiano (optical). and 2MASS (NIR). is shown in Fig.," The broad-band spectral energy distribution (SED) of the source, constructed with data from (X-ray), Loiano (optical), and 2MASS (NIR), is shown in Fig." 3., 3. The optical-NIR data points were corrected. for Galactic. absorptior and converted into flux densities using the tables by Fukugita et al. (, The optical-NIR data points were corrected for Galactic absorption and converted into flux densities using the tables by Fukugita et al. ( 1995) for the optical and by Bersanelli et al. (,1995) for the optical and by Bersanelli et al. ( 1991) for the NIR.,1991) for the NIR. A systematic error was added in quadrature to account for the uncertainties in the magnitude-to-flux conversion factors (Fukugita et al., A systematic error was added in quadrature to account for the uncertainties in the magnitude-to-flux conversion factors (Fukugita et al. 1995)., 1995). No correction for any possible further absorption along the line of sight produced by the halo of NGC 4168 was included; this. however. should not be high às the source Is well detected in the U band.," No correction for any possible further absorption along the line of sight produced by the halo of NGC 4168 was included; this, however, should not be high as the source is well detected in the $U$ band." So. yet another putative ULX is found to be a background source.," So, yet another putative ULX is found to be a background source." " Assuming a cosmology with Hy = 65 km s! Μρο. Q4 = 0.7 and Q,, = 0.3. we find that the luminosity distance to this source is d; = 1.16 Gpe. and that its X-ray luminosity is 2.9x107 ere s7! in the 0.6-12 keV rest-frame energy range."," Assuming a cosmology with $H_{\rm 0}$ = 65 km $^{-1}$ $^{-1}$, $\Omega_{\Lambda}$ = 0.7 and $\Omega_{\rm m}$ = 0.3, we find that the luminosity distance to this source is $d_L$ = 1.16 Gpc, and that its X-ray luminosity is $2.9\times 10^{42}$ erg $^{-1}$ in the 0.6–12 keV rest-frame energy range." The angular size of the source translates into a linear diameter of about 30 kpe at z = 0.217., The angular size of the source translates into a linear diameter of about 30 kpc at $z$ = 0.217. " The measured value for the luminosity is ~ 100-1000 times less that of ""classical"" active galactic nuclei (AGNs).", The measured value for the luminosity is $\sim$ 100–1000 times less that of “classical” active galactic nuclei (AGNs). Indeed. visual inspection of the optical spectrum in Fig.," Indeed, visual inspection of the optical spectrum in Fig." 2 suggests that the lines are due to stellar photoionization. rather than to an AGN.," 2 suggests that the lines are due to stellar photoionization, rather than to an AGN." " The diagnostic line ratios [N n]/H,. [S u]/H,. and [O m]/H;. together with the nondetection of substantial [O 1] 46300 emission. place this source in the regime of metal-rich giant extragalactic H regions or starburst nuclei (Ho et al."," The diagnostic line ratios [N $_\alpha$, [S $_\alpha$, and [O $_\beta$, together with the nondetection of substantial [O ] $\lambda$ 6300 emission, place this source in the regime of metal-rich giant extragalactic H regions or starburst nuclei (Ho et al." 1993. 1997).," 1993, 1997)." Inspection of the SED of the source (Fig., Inspection of the SED of the source (Fig. 3) shows that a peak in the optical-NIR domain is present. followed by a drop across the U and B bands.," 3) shows that a peak in the optical-NIR domain is present, followed by a drop across the $U$ and $B$ bands." Given the dominance of the stellar continuum in the spectrum (Fig., Given the dominance of the stellar continuum in the spectrum (Fig. 2). most of the optical and NIR light comes from the integrated stellar emission from the galaxy.," 2), most of the optical and NIR light comes from the integrated stellar emission from the galaxy." Although the S/N of the spectrum is insufficient to place strong constraints on the age and metallicity of the stellar population. they are not inconsistent. with that of an evolved population.," Although the S/N of the spectrum is insufficient to place strong constraints on the age and metallicity of the stellar population, they are not inconsistent with that of an evolved population." The optical-NIR SED also supports this conjecture., The optical-NIR SED also supports this conjecture. The X-ray emission. by contrast. is likely to be associated with the star-forming regions that give rise to the optical line emission.," The X-ray emission, by contrast, is likely to be associated with the star-forming regions that give rise to the optical line emission." This may consist of a single starburst nucleus or multiple off-nuclear sources., This may consist of a single starburst nucleus or multiple off-nuclear sources. An X-ray luminosity of =10¥ erg s7! is high. but not unusual. for a starburst (David et al.," An X-ray luminosity of $\approx$ $^{42}$ erg $^{-1}$ is high, but not unusual, for a starburst (David et al." 1992)., 1992). The strength of the optical emission lines. afteraccounting for internal reddening. can be used to estimate the star formation rate (SFR) and metallicity.," The strength of the optical emission lines, afteraccounting for internal reddening, can be used to estimate the star formation rate (SFR) and metallicity." " Assuming an intrinsic Balmer decrement of H,/H,; = 2.86 (Osterbrock 1989) and the extinction law of Cardelli et al. (", Assuming an intrinsic Balmer decrement of $_\alpha$ $_\beta$ = 2.86 (Osterbrock 1989) and the extinction law of Cardelli et al. ( "1989). the observed H,/Hy = 5.82 implies an internal reddening of E(B—V) = 0.72 mag.","1989), the observed $_\alpha$ $_\beta$ = 5.82 implies an internal reddening of $E(B-V)$ = 0.72 mag." " Following Kennicutt (1998). we determine a SFR of 4345 M. yr! from the reddening-corrected H, luminosity of 5.5x10? erg s! "," Following Kennicutt (1998), we determine a SFR of $\pm$ 5 $M_\odot$ $^{-1}$ from the reddening-corrected $_\alpha$ luminosity of $5.5 \times 10^{42}$ erg $^{-1}$ ." Similarly. the [O u] luminosity yields a SFR," Similarly, the [O ] luminosity yields a SFR" the inclination-corrected distribution.,the inclination-corrected distribution. " The inclination correction moves galaxies to the left and downward, almost completely evacuating the high rregion of spirals and spiral/lenticulars."," The inclination correction moves galaxies to the left and downward, almost completely evacuating the high region of spirals and spiral/lenticulars." " Based on the locations of visually classified galaxies on this plane and on the shape of the joint distribution, we have drawn a boundary in the pplane to separate late-type galaxies from intermediate- and early-type galaxies, indicated by the solid line in the right panel of Figure 3.."," Based on the locations of visually classified galaxies on this plane and on the shape of the joint distribution, we have drawn a boundary in the plane to separate late-type galaxies from intermediate- and early-type galaxies, indicated by the solid line in the right panel of Figure \ref{cmdconeye}. ." " Within the intermediate- and early-type region of parameter space, there is some overlap in the distributions of the various visual classifications, although there is a clear trend for more later types at smallerChorm."," Within the intermediate- and early-type region of parameter space, there is some overlap in the distributions of the various visual classifications, although there is a clear trend for more later types at smaller." ". We tentatively place a border between intermediate- and early-type galaxies at Chorm=1.23 (indicated by the dashed line), which is the cross-over point between the intermediate and ppeaks in the hhistogram (see Figure 2))."," We tentatively place a border between intermediate- and early-type galaxies at $\cnorm=1.23$ (indicated by the dashed line), which is the cross-over point between the intermediate and peaks in the histogram (see Figure \ref{cmdcon}) )." We have further examined the distribution of visually-classified galaxies in the axis ratio-concentration (b/a-Cnorm)) plane of Paper I. There are several reasons for doing this., We have further examined the distribution of visually-classified galaxies in the axis ratio-concentration $b/a$ ) plane of Paper I. There are several reasons for doing this. " Firstly, the overlap in the distribution of visually-classified galaxies of a given type within the Intermediate and Early regions of Figure 3 may perhaps be disentangled if the populations differ in another morphological parameter."," Firstly, the overlap in the distribution of visually-classified galaxies of a given type within the Intermediate and Early regions of Figure \ref{cmdconeye} may perhaps be disentangled if the populations differ in another morphological parameter." " Secondly, we note that in Paper I, we found that flattened galaxies with high hhave more in common with intermediate-concentration galaxies than with ellipticals."," Secondly, we note that in Paper I, we found that flattened galaxies with high have more in common with intermediate-concentration galaxies than with ellipticals." " While this may suggest a problem with our inclination correction, the cause is simply statistics: the intrinsic axis ratio distribution of ellipticals drops off dramatically at low while the concentration distribution of intermediate-typesb/a, is relatively wide."," While this may suggest a problem with our inclination correction, the cause is simply statistics: the intrinsic axis ratio distribution of ellipticals drops off dramatically at low $b/a$, while the concentration distribution of intermediate-types is relatively wide." " Therefore, flattened galaxies with high aare more likely to be unusually concentrated intermediate-types than unusually flattened ellipticals."," Therefore, flattened galaxies with high are more likely to be unusually concentrated intermediate-types than unusually flattened ellipticals." " In Figure 4, we show the distribution of all SDSS galaxies as the grayscale, along with the visual classification of those galaxies that lie in the “Intermediate” and “Early” regions of Figure 3.."," In Figure \ref{bacon}, we show the distribution of all SDSS galaxies as the grayscale, along with the visual classification of those galaxies that lie in the “Intermediate” and “Early” regions of Figure \ref{cmdconeye}." " The visual classification of these galaxies varies systematically as a function of axis ratio even at a constant concentration, and the ellipticals are very concentrated in the hhigh-b/a region of parameter space."," The visual classification of these galaxies varies systematically as a function of axis ratio even at a constant concentration, and the ellipticals are very concentrated in the $b/a$ region of parameter space." We therefore use this plane to separate early-type galaxies from intermediate-type galaxies as shown., We therefore use this plane to separate early-type galaxies from intermediate-type galaxies as shown. Our final classificationis as follows:, Our final classificationis as follows: line center frequency. expansion velocity. (which is a proxy lor line width) ancl horn-to-center ralio (which characterizes the line shape).,"line center frequency, expansion velocity (which is a proxy for line width) and horn-to-center ratio (which characterizes the line shape)." All three bands display some emission features. and we have identilied (he carriers of most of these features (see labels in Figure 1. and below).," All three bands display some emission features, and we have identified the carriers of most of these features (see labels in Figure \ref{cspec} and below)." We have also measured the line strengths of all features (listed in Table 3))., We have also measured the line strengths of all features (listed in Table \ref{linefit}) ). We discuss each band individually below., We discuss each band individually below. The 241.802 GlIlz band is the simplest. as (here is only one line present.," The $241.802\,$ GHz band is the simplest, as there is only one line present." The line is the J=17—16 transition of an isotopologue of aluminum monochloride. AlCl," The line is the $J=17-16$ transition of an isotopologue of aluminum monochloride, $^{37}$ Cl." The J=12—I1l.1110 and 10—9 transitions of this molecule were previously observed in IRC-10216 (Cernicharo&Quélin1937:Cernicharoetal.2000).. but this is the first observation of the JJ=17—16 transition.," The $J=12-11, 11-10$ and $10-9$ transitions of this molecule were previously observed in IRC+10216 \citep{cer87,CGK00}, but this is the first observation of the $J=17-16$ transition." The vertical dotted lines in the spectrum indicate the position of the brightest expected methanol line in our spectrum., The vertical dotted lines in the spectrum indicate the position of the brightest expected methanol line in our spectrum. There is clearly no evidence lor any emission feature al this frequency., There is clearly no evidence for any emission feature at this frequency. The 150.498 GllIz band is more complicated than the 241.802 GIIz band. but still it is relatively simple. as it contains only three. well-separated lines.," The $150.498\,$ GHz band is more complicated than the $241.802\,$ GHz band, but still it is relatively simple, as it contains only three, well-separated lines." " We identifv (he line centered around Όρου=—26.5kms! as the 244,—ly transition of formaldehyde at 150.498 GL."," We identify the line centered around $v_{LSR}=-26.5{\rm \,km\,s^{-1}}$ as the $2_{11}-1_{10}\>$ transition of formaldehyde at $150.498\,$ GHz." " We [it this line with all four parameters (area. line center Irequency. expansion velocity and horn/center ralio) [ree to vary. and find that 0,4=18.930.2kms! for this line."," We fit this line with all four parameters (area, line center frequency, expansion velocity and horn/center ratio) free to vary, and find that $v_{exp}=13.9\pm0.2{\rm \,km\,s^{-1}}$ for this line." This value is somewhat smaller than. but still consistent with. the literature value for IRO+10216 OL Very=14.5.," This value is somewhat smaller than, but still consistent with, the literature value for IRC+10216 of $v_{exp}=14.5$." " The line at roughly 150.437 GIlz is identified as the 2s,—1j, transition of e-Colls. and the line near 150.386 GIlz is unidentified we believe the carrier of that [eature is not vet fully catalogued or perhaps still undiscovered."," The line at roughly $150.437\,$ GHz is identified as the $2_{20}-1_{11}$ transition of $_3$ $_2$, and the line near $150.386\,$ GHz is unidentified – we believe the carrier of that feature is not yet fully catalogued or perhaps still undiscovered." In later discussions we will refer to this unidentified line as U150., In later discussions we will refer to this unidentified line as U150. We note that the fit for U150 is somewhat affected by a svstematic uncertaintv stemming from a number of bad channels in our fillerbank which appear in the blueshifted wing of that line., We note that the fit for U150 is somewhat affected by a systematic uncertainty stemming from a number of bad channels in our filterbank which appear in the blueshifted wing of that line. The band around 140.840 GIHz is the most complex.," The band around $140.840\,$ GHz is the most complex." " In it. we see a blend of lines centered around tps,=—26.5kms!. the svstemic velocity of IRC--10216."," In it, we see a blend of lines centered around $v_{LSR}=-26.5{\rm \,km\,s^{-1}}$, the systemic velocity of IRC+10216." . By eve. we identify one line centered αἱ approximately 140.853 (11. a second line centered. αἱ approximately 140.840 Giz and a third line which has a poorly determined shape and central frequency but which appears in the redshifted wing of the 140.840 GIIz line.," By eye, we identify one line centered at approximately $140.853\,$ GHz, a second line centered at approximately $140.840\,$ GHz and a third line which has a poorly determined shape and central frequency but which appears in the redshifted wing of the $140.840\,$ GHz line." We identilv the line centered, We identify the line centered a large number of stars of different twpes.,a large number of stars of different types. Zf(heslarsmereevenlydistribuledovertherange 0.5«C /O«2. the fraction would be ~0.25.," $\emph {If the stars were evenly distributed over the range}$ $<$ $<$ 2, the fraction would be $\sim$ 0.25." If. furthermore. the cosmic CIL ratio is assunied to be that recommended by Snow and Witt (1995).. 2.2510. 4. then. the available number of C atoms for carbon grains becomes 55 for 105 LL atoms.," If, furthermore, the cosmic C/H ratio is assumed to be that recommended by Snow and Witt \cite{sno}, $2.25\,\,10^{-4}$ , then, the available number of C atoms for carbon grains becomes 55 for $10^{6}$ H atoms." llowever. (his must be considered a lower limit. as it is (he result of calculations with kI=110!! em?s. |. a reasonable but arbitrary value. adopted in Table 1. in the absence of experimental data.," However, this must be considered a lower limit, as it is the result of calculations with $1\,\,10^{-10}$ $^{3}$ $^{-1}$, a reasonable but arbitrary value, adopted in Table 1, in the absence of experimental data." If. on the other hand. one takes k1—6.610... as suggested bv our chemical modeling (see Appendix). ancl if. moreover. one adopts the Grevesse cosmic carbon abundance for the Sun (1991).. Le. 10.!. then the number of available C atoms rises to 144.," If, on the other hand, one takes $6.6\,\,10^{-10}$, as suggested by our chemical modeling (see Appendix), and if, moreover, one adopts the Grevesse cosmic carbon abundance for the Sun \cite{gre}, i.e. $\,\,10^{-4}$, then the number of available C atoms rises to 144." Circumstances mav be envisioned where (his upper limit mary still be raised to some extent., Circumstances may be envisioned where this upper limit may still be raised to some extent. For instance. as (he expanding gas reaches the outskirts of (he envelope. it is no longer shielded from the UV radiation of the ISM.," For instance, as the expanding gas reaches the outskirts of the envelope, it is no longer shielded from the UV radiation of the ISM." If the latter is strong enough. CO may then be dissociated. making some more free C atoms available for grain formation. as observed by Ilerpin et al.," If the latter is strong enough, CO may then be dissociated, making some more free C atoms available for grain formation, as observed by Herpin et al." (2002) in the case of post-AGD stars., \cite{her} in the case of post-AGB stars. Iu combination with the other studies our data put stringent coustraiuts on the existence of eiaut exoplaucts around IID115592 aud IIDI172555 interior aud exterior to the debris disks.,In combination with the other studies our data put stringent constraints on the existence of giant exoplanets around HD115892 and HD172555 interior and exterior to the debris disks. Although our data probe regious very close to the assumed location of the debris disks (1.6 AU). our Lypothesis that dvuamical interactions between a planet aud the debris disk could have led to a recent collision of planetesinal lacks direct observational support.," Although our data probe regions very close to the assumed location of the debris disks (4–6 AU), our hypothesis that dynamical interactions between a planet and the debris disk could have led to a recent collision of planetesimal lacks direct observational support." We note. however. that plauets (or planetary svstenis) with masses below our detection Limits are certainly able to dynamically shape debris disks aud influcuce their evolution (see.c.g...Ravinoudetal.2011).," We note, however, that planets (or planetary systems) with masses below our detection limits are certainly able to dynamically shape debris disks and influence their evolution \citep[see, e.g.,][]{raymond2011}." . Our data demonstrate that the APP opens up a new paramcter space for direct iuaging of cxoplancts by pushing the backeround limit significautl closer to the star., Our data demonstrate that the APP opens up a new parameter space for direct imaging of exoplanets by pushing the background limit significantly closer to the star. " A comparison to surveys carried out in the II band shows that Chauvinetal.(2010). and Latrenicreetal.(2007a)) typically reached a contrast of ~10 mae aud ~9.5 mag af a separation of 0.5"". respectively."," A comparison to surveys carried out in the H band shows that \citet{chauvin2010} and \citet{lafreniere2007} typically reached a contrast of $\sim$ 10 mag and $\sim$ 9.5 mag at a separation of $''$ , respectively." For HIID1158592 our contrast is ΟΤΙ mag at the same separation., For HD115892 our contrast is $\gtrsim$ 11 mag at the same separation. A similar coutrast has been reported by the NICT campaign at the Gemini observatory (Chunetal.2008) also operating iu the II baud. but a iore direct conrparisou of the contrast performance is lited due to different integration times and different tareet stars with different briehtuesses.," A similar contrast has been reported by the NICI campaign at the Gemini observatory \citep{chun2008} also operating in the H band, but a more direct comparison of the contrast performance is limited due to different integration times and different target stars with different brightnesses." Iowever. since planetary lass objects appear red in the infrared. NACO/APP has an advantage when it comes to the final detectable mass limits. because it works in the L baud aud not in the II baud.," However, since planetary mass objects appear red in the infrared, NACO/APP has an advantage when it comes to the final detectable mass limits, because it works in the L band and not in the H band." We preseuted the first observations combining NACO's Apodizing Phase Plate coronagraplh with Aneular Differential huaeiug to search for faint companions to the voung debris disk host stars ITD115892 aud ITD172555 in the NB1.05 filter., We presented the first observations combining NACO's Apodizing Phase Plate coronagraph with Angular Differential Imaging to search for faint companions to the young debris disk host stars HD115892 and HD172555 in the NB4.05 filter. Our conclusions are as follows: NACO/APP is cumeutlv a superior combination to search for planets at unprecedented small TWA in particular around bright targets., Our conclusions are as follows: NACO/APP is currently a superior combination to search for planets at unprecedented small IWA in particular around bright targets. And even when the nest generation ligh-coutrast imaging mstrumnenuts sucli as SPIIERE and CPI come online. with its unique L-baud capabilities NACO/APP can help to characterize at least a certain subset of the exoplaucts these imstriuneut will find in the near-infrared.," And even when the next generation high-contrast imaging instruments such as SPHERE and GPI come online, with its unique L-band capabilities NACO/APP can help to characterize at least a certain subset of the exoplanets these instrument will find in the near-infrared." This research has made use of the SIAIBAD database. operated at CDS. Strasboure. France.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France." We thank D. Latrenierre for kindly allowing us to adapt his LOCT source code., We thank D. Lafrenièrre for kindly allowing us to adapt his LOCI source code. We thank C. Thahuaun for his support setting up the data reduction pipeline., We thank C. Thalmann for his support setting up the data reduction pipeline. NL. Jansou aud I. Daraffe kindly provided us with the evolutionary models in the NBLOS filter., M. Janson and I. Baraffe kindly provided us with the evolutionary models in the NB4.05 filter. We are indebted to U. Welimneier and the ESO staff ou Paranal. in particular J.O'Neal. for their support during the observations.," We are indebted to U. Wehmeier and the ESO staff on Paranal, in particular J.O'Neal, for their support during the observations." "are derived. [rom ""dte IRAS samples (Sandersctal.2003:Rushctal.1993 mand these subsets at least clo. not span values of £2). from the rest of our sample.","are derived from complete IRAS samples \citep{b60,b59} and these subsets at least do not span values of $R_{ir/x}$ different from the rest of our sample." Jas is of course a potential problem with any approach such as ours. but it is comforting that we can Line some independent. verification for our simple. mocdel-independent ipproach.," Bias is of course a potential problem with any approach such as ours, but it is comforting that we can find some independent verification for our simple, model-independent approach." Estimates of the intrinsic 2-10. keV. luminosity [or Compton-thick AGN from very hard. X-rayMAN ion ) observations ((o10S3) 'Tuelleret.al.SN):MattMinediteal.(1999):nΠοetCX reveal that m intrinsic — is consistent with the group 1 AGN (in vereement with the findings of c.g. Lutzetal.(2001):Krabbeetal.(2001):LLorst(2007):Müushotzky (2008))).," Estimates of the intrinsic 2-10 keV luminosity for Compton-thick AGN from very hard X-ray (absorption independent) observations (e.g. \citet{b37,b38,b36}) ) reveal that the intrinsic luminosity ratio is consistent with the group 1 AGN (in agreement with the findings of e.g. \citet{b3,b4,b5,b71}) )." llowever. unlike Lutzetal.(2001):KrabbectLlorstetal.(2007) we have endeavoured to avoid the highly mocel-dependent. business of estimating intrinsic 2-IOkeV X-rav luminosity of group 2 AGN based on the 2-0keV observed luminosity.," However, unlike \citet{b3,b4,b5} we have endeavoured to avoid the highly model-dependent business of estimating intrinsic 2-10keV X-ray luminosity of group 2 AGN based on the 2-10keV observed luminosity." We also studied the far-LR to micl-LR luminosity ratios of the nuclei in our sample., We also studied the far-IR to mid-IR luminosity ratios of the nuclei in our sample. We found that the T0051 to 12jum Luminosity ratio CLjo04um/Lisqun~ 1) is an extremely effective separator of the group T(unobscured) and group 2 (obscured Low luminosity) populations (see Γιο)., We found that the $100\micron$ to $12\micron$ luminosity ratio $L_{100\micron}/L_{12\micron} \sim 1$ ) is an extremely effective separator of the group 1(unobscured) and group 2 (obscured low luminosity) populations (see \ref{fig:ir12v100}) ). Using archetypal AGN as a guide. this plot ranks eroup 2 AGN in order of decreasing luminosity ratio for increasing Obscuration.," Using archetypal AGN as a guide, this plot ranks group 2 AGN in order of decreasing luminosity ratio for increasing obscuration." 1n principle our approach could be applicc to intermediate mass black holes (LNMDIIS) and Galactic black hole. candidates. (CDIICS) to investigate the accretion neighbourhood around black holes on all mass. scales., In principle our approach could be applied to intermediate mass black holes (IMBHs) and Galactic black hole candidates (GBHCs) to investigate the accretion neighbourhood around black holes on all mass scales. The outstanding question is whether reprocessing material around LAIBIIs ancl GBLICs is substantially different in covering factor. structure. chemistry or reprocessing details from that around AGN.," The outstanding question is whether reprocessing material around IMBHs and GBHCs is substantially different in covering factor, structure, chemistry or reprocessing details from that around AGN." Are a Uarecl disk or dusty torus associated with a minimum mass scale. or are we looking at a basically identical. phenomenon across 1-8. orders of magnitude in mass?," Are a flared disk or dusty torus associated with a minimum mass scale, or are we looking at a basically identical phenomenon across 7-8 orders of magnitude in mass?" We gratefully acknowledge support from NASA grant. C(O6-TOSSB(BAL)., We gratefully acknowledge support from NASA grant GO6-7085B(BM). " We made extensive use of the NASA/LPAC Extragalactic Database (NED). operated. by the Jet ""propulsion Laboratory. CalTech. under contract with ASA."," We made extensive use of the NASA/IPAC Extragalactic Database (NED), operated by the Jet Propulsion Laboratory, CalTech, under contract with NASA." We gratefully acknowledge very helpful discussions with Tahir Yaqook who helped. inspire this work and with Sylvain Veilleux who provided. useful. insights into ieterogeneous samples and. samples of LR-observed ACN., We gratefully acknowledge very helpful discussions with Tahir Yaqoob who helped inspire this work and with Sylvain Veilleux who provided useful insights into heterogeneous samples and samples of IR-observed AGN. DM WESE gratefully. acknowledge the support of the Department of Astrophysics of the American Museum. of ratural Listory and PSC-CUNY erants PSC'OOC-38-99 and PSCOOC-38-98 respectively., BM KESF gratefully acknowledge the support of the Department of Astrophysics of the American Museum of Natural History and PSC-CUNY grants PSCOOC-38-99 and PSCOOC-38-98 respectively. No compelling cases for such a relationship were found.,No compelling cases for such a relationship were found. A set of cases in which something like the expected relationship seemed to be present in the data (often referred to by individuals as “tantalizing”) were collected lor further scrutiny., A set of cases in which something like the expected relationship seemed to be present in the data (often referred to by self-deluded individuals as “tantalizing”) were collected for further scrutiny. In these cases. (here seemed to be a larger average value of £? [or smaller values of |cosAl than for larger values.," In these cases, there seemed to be a larger average value of $\xi^2$ for smaller values of $|\cos A |$ than for larger values." The total number of such cases was 10. and these cases were roughly clustered in (he direction Àc407.2~607.," The total number of such cases was 10, and these cases were roughly clustered in the direction $\lambda \sim 40^{\circ}, \beta \sim 60^{\circ}$." The ease for (A=40°.9607) is shown in Figure 2.," The case for $(\lambda=40^{\circ}, \beta=60^{\circ})$ is shown in Figure 2." We do not claim Chis result. as a detection of anisotropy in the Local Cloud turbulence. but it does give an indieation of the data quality in one of the best cases for anisotropy.," We do not claim this result as a detection of anisotropy in the Local Cloud turbulence, but it does give an indication of the data quality in one of the best cases for anisotropy." An obvious feature in Figure 2 is the presence of two data points at |cosA)&0.8—0.9 with possibly anomalous values of £?., An obvious feature in Figure 2 is the presence of two data points at $| \cos A | \simeq 0.8 - 0.9$ with possibly anomalous values of $\xi^2$. These points correspond to the +2.6 km/sec radial velocity component for Alkaid (ID 120315) ancl the +13.9 km/sec radial velocity component Lor ¢ , These points correspond to the +2.6 km/sec radial velocity component for Alkaid (HD 120315) and the +13.9 km/sec radial velocity component for $\zeta$ When relativistic particles dominate the entropy. the adiabat satisfies 77xp.,"When relativistic particles dominate the entropy, the adiabat satisfies $T^3\propto \rho$." When [ree nucleons dominate the entropy. the adiabat satisfies 77xp.," When free nucleons dominate the entropy, the adiabat satisfies $T^{3/2}\propto\rho$." The evolution of the electron fraction in a convective blob is crucially sensitive to the adiabat on which the blob travels., The evolution of the electron fraction in a convective blob is crucially sensitive to the adiabat on which the blob travels. To illustrate this. consider first a disk with AZ=0.01. a=0.1.," To illustrate this, consider first a disk with $\dot M=0.01$, $\alpha=0.1$." In Fig., In Fig. 9. we show the evolution of the electron fraction in matter originating from (wo different points in this disk and for different assumptions about toy., \ref{blob1} we show the evolution of the electron fraction in matter originating from two different points in this disk and for different assumptions about $\tau_{\rm conv}$ . The upper curves in Fie., The upper curves in Fig. 9. correspond {ο material originating from r=105cem in the disk., \ref{blob1} correspond to material originating from $r=10^{6.5}\cm$ in the disk. " At this point the entropy is relatively high. s/h,~23 by the estimate in Eq. 12.. "," At this point the entropy is relatively high, $s/k_b\sim 23$ by the estimate in Eq. \ref{entropy}, ," and consequently the adiabat is closer to Txp than to 777xp., and consequently the adiabat is closer to $T^3\propto \rho$ than to $T^{3/2}\propto\rho$. The temperature decreases quite slowly relative to the density. allowing for the formation of pairs which efficiently drive n/p to equality.," The temperature decreases quite slowly relative to the density, allowing for the formation of pairs which efficiently drive $n/p$ to equality." " For laree T, (his process occurs more elliciently (han for small Τωµν.", For large $\tau_{\rm conv}$ this process occurs more efficiently than for small $\tau_{\rm conv}$. The lower curves in Fie., The lower curves in Fig. 9 correspond to matter originating from r=I0*cm in the disk., \ref{blob1} correspond to matter originating from $r=10^7\cm$ in the disk. At this point the entropy is zz17. so the adiabat is near T7?xp.," At this point the entropy is $\approx 17$, so the adiabat is near $T^{3/2}\propto \rho$." For low entropies. then. the temperature and density decrease al a comparable rate and pair formation is somewhat suppressed. keeping Y; low.," For low entropies, then, the temperature and density decrease at a comparable rate and pair formation is somewhat suppressed, keeping $Y_e$ low." For flows where the electron fraction is high enough to drive the inner disk neutron rich. the entropy is generally dominated by non-relativistic particles. ancl the adiabat again preserves alow Y.," For flows where the electron fraction is high enough to drive the inner disk neutron rich, the entropy is generally dominated by non-relativistic particles, and the adiabat again preserves a low $Y_e$." This is illustrated in Fig., This is illustrated in Fig. LO where we plot the evolution of electron fraction in an adiabatic convective bubble [for two dillerent. disks characterized by a low Y..., \ref{blob2} where we plot the evolution of electron fraction in an adiabatic convective bubble for two different disks characterized by a low $Y_e$. In this figure we only show the evolution of a fluid element [rom a single initial radius (10*em) because the entropy in these is disks never dominated by relativistic particles when Y.ds low. so that the behavior shown in Fig.," In this figure we only show the evolution of a fluid element from a single initial radius $10^7\cm$ ) because the entropy in these is disks never dominated by relativistic particles when $Y_e$ is low, so that the behavior shown in Fig." 10. is generic., \ref{blob2} is generic. " The above considerations outline the general features of how Y, evolves in material as il (travels [rom the center to the surface of the disk.", The above considerations outline the general features of how $Y_e$ evolves in material as it travels from the center to the surface of the disk. " In flows where Y, is driven small. the degeneracy of the electrons implies that [ree nucleons dominate the entropy."," In flows where $Y_e$ is driven small, the degeneracy of the electrons implies that free nucleons dominate the entropy." A low Y. (then. will remain low.," A low $Y_e$ then, will remain low." " Dv contrast. in flows where Y, is close to 1/2. the adiabat can be close enough to T7xp lor Y, to be driven to 1/2. and the neutron excess at the center of the disk is larger than the neutron excess in material finding itswav out of the disk."," By contrast, in flows where $Y_e$ is close to 1/2, the adiabat can be close enough to $T^3\propto \rho$ for $Y_e$ to be driven to 1/2, and the neutron excess at the center of the disk is larger than the neutron excess in material finding itsway out of the disk." The most obvious consequence of our caleulations is that Ni will be absent [rom the winds of hyper-accreting blackholes unless a) the accretion rate is low (0.1AL.sec. 1). and b) the disk viscosity is high. α 50.1.," The most obvious consequence of our calculations is that $^{56}$ Ni will be absent from the winds of hyper-accreting blackholes unless a) the accretion rate is low $\ltaprx 0.1\ \Msunsec$ ), and b) the disk viscosity is high, $\alpha \gtaprx 0.1$ ." Interestinglv. modern views regarding a-disks and GRB," Interestingly, modern views regarding$\alpha$ -disks and GRB" Iu fact. if the uueratineC» plauct is Movie inward. the planetesimals are not permancutly trapped iu the resonances.,"In fact, if the migrating planet is moving inward, the planetesimals are not permanently trapped in the resonances." Their semiüauajor axis remain unchauged and their eccentricities are onlv slightly lucreased., Their semi-major axis remain unchanged and their eccentricities are only slightly increased. Consequently. the decrease of the periastrou distance is too sinall to allow the volatiles to evaporate.," Consequently, the decrease of the periastron distance is too small to allow the volatiles to evaporate." Ou the contrary. if the planet is moving outward. as eiven by the results of Feruiuudoez Ip (1996) which show an expansion of the Uranus aud Neptune orbits. a fraction of bodies can be trapped in resonances.," On the contrary, if the planet is moving outward, as given by the results of Fernánndez Ip (1996) which show an expansion of the Uranus and Neptune orbits, a fraction of bodies can be trapped in resonances." Their seimianajor axis aud eccentricities iucrease siguificautlv and the net result is a decrease of their periastrou., Their semi-major axis and eccentricities increase significantly and the net result is a decrease of their periastron. If qs. gy. a; aud ay are respectively the iuitial aud final periastron distances and scuu-iajor axis of the body. we have ων(1 —y— ," If $q_i$ , $q_f$ , $a_i$ and $a_f$ are respectively the initial and final periastron distances and semi-major axis of the body, we have $q_f/q_i \sim (1-\sqrt{\ln \frac{a_f}{a_i}}) \frac{a_f}{a_i} $ ." Thus] qr/qi0.75- as soon ax —a>Ld., Thus $q_f/q_i < 0.75 $ as soon as $\frac{a_f}{a_i}> 1.1$. As soon as a body is trapped in the resonance. the ratio of the final to the initial semi-major axis is the same for the body as well as for the planet.," As soon as a body is trapped in the resonance, the ratio of the final to the initial semi-major axis is the same for the body as well as for the planet." The decrease of the periastron of the body can be significant even if the planets seni-uajor axis Is increased. by only ten percent., The decrease of the periastron of the body can be significant even if the planet's semi-major axis is increased by only ten percent. This can start the evaporation of trapped bodies., This can start the evaporation of trapped bodies. We have tested several configurationsC» of outward nueration and have evaluated the effect ou planetesinials in the zones swept bv first order resonances., We have tested several configurations of outward migration and have evaluated the effect on planetesimals in the zones swept by first order resonances. We have arbitrarily considered only one planet starting from an initial sciiinuajor axis a;=60 AU and migrating of 12 AU to a final semi-major axis ay=72 AU (aya;= 1.2)., We have arbitrarily considered only one planet starting from an initial semi-major axis $a_i=60$ AU and migrating of 12 AU to a final semi-major axis $a_f=72$ AU $a_f/a_i=1.2$ ). The velocity dispersion of the planetesimals swari is given bythe inclinatiousrandomly chosen between 0 aud 2 deerces.," The velocity dispersion of the planetesimals swarm is given bythe inclinationsrandomly chosen between 0 and 2 degrees," in 1999 as implemented in the 31Dec09 version of AIPS.,in 1999 as implemented in the 31Dec09 version of AIPS. The secondary calibrator was J1744—3116 (1 degree from the target source)., The secondary calibrator was $-$ 3116 (1 degree from the target source). " Observations were carried out in fast switching mode to reduce target-calibrator slew time, using a 3.3 s integration time."," Observations were carried out in fast switching mode to reduce target–calibrator slew time, using a 3.3 s integration time." Data calibration and imaging were carried out using standard procedures within AIPS., Data calibration and imaging were carried out using standard procedures within AIPS. The source flux density was measured by fitting an elliptical Gaussian to the source in the image plane using the AIPS task JMFIT., The source flux density was measured by fitting an elliptical Gaussian to the source in the image plane using the AIPS task JMFIT. For a journal of the observations see Table 5.., For a journal of the observations see Table \ref{vla-log}. In Figure 2 we plot the observed radio 8.46 GHz decay light curve., In Figure \ref{rlc} we plot the observed radio 8.46 GHz decay light curve. " Besides the VLA observations we use one observation obtained with the Austrialian Telescope Compact Array (ATCA) on Jan. 28, 2008 (MJD 54493) at 8.64 GHz."," Besides the VLA observations we use one observation obtained with the Austrialian Telescope Compact Array (ATCA) on Jan. 28, 2008 (MJD 54493) at 8.64 GHz." During this observation the source was not detected down to a 3 c rms upper limit of 0.15 mJy (Kalemcietal.2008b;; at 8.64 GHz)., During this observation the source was not detected down to a 3 $\sigma$ rms upper limit of 0.15 mJy \citealt{2008ATel.1378....1K}; at 8.64 GHz). This stringent ATCA upper limit shows that the radio emission reactivated close in time to the transition to the low-hard state., This stringent ATCA upper limit shows that the radio emission reactivated close in time to the transition to the low–hard state. " The solid line in Figure 2 is the best-fitting exponential decay to the blue open circles, i.e. the VLA 8.46 GHz detections when the source was in the low-hard state."," The solid line in Figure \ref{rlc} is the best–fitting exponential decay to the blue open circles, i.e. the VLA 8.46 GHz detections when the source was in the low–hard state." The exponential decay timescale is 193-2 days., The exponential decay timescale is $\pm$ 2 days. " The last radio observation yields a stringent upper limit of 0.04 mJy, which is below the extrapolation of the best—fitting exponential."," The last radio observation yields a stringent upper limit of 0.04 mJy, which is below the extrapolation of the best–fitting exponential." This might indicate that the radio decay accelerated., This might indicate that the radio decay accelerated. " The increase in source flux on Feb. 24, 2008 (MJD 54520) compared with the preceding observations on Feb. 20 and 23, 2008 (MJD 54516, 54519) is atypical since the X-ray flux decayed by a factor of 15 in the same period."," The increase in source flux on Feb. 24, 2008 (MJD 54520) compared with the preceding observations on Feb. 20 and 23, 2008 (MJD 54516, 54519) is atypical since the X–ray flux decayed by a factor of 15 in the same period." Such behaviour could have been caused by a radio flare., Such behaviour could have been caused by a radio flare. Note that the radio flare was apparently not accompanied by an X-ray flare., Note that the radio flare was apparently not accompanied by an X–ray flare. " Alternatively, the X-ray flare has been missed as the radio observation on Feb. 24, 2008 occurred 1.3 days before a oobservation and 2.5 days after the oobservation nearest in time."," Alternatively, the X–ray flare has been missed as the radio observation on Feb. 24, 2008 occurred 1.3 days before a observation and 2.5 days after the observation nearest in time." On several nights near-simultaneous radio data has been obtained at different frequencies., On several nights near–simultaneous radio data has been obtained at different frequencies. We use this data to assess the radio spectral index., We use this data to assess the radio spectral index. " Initially, the spectral index is negative, implying optically thin radio emission."," Initially, the spectral index is negative, implying optically thin radio emission." " E.g. the 1.4, 4.86 to 8.46 GHz spectral index on MJD 54486 is -0.644-0.07."," E.g. the 1.4, 4.86 to 8.46 GHz spectral index on MJD 54486 is $\pm$ 0.07." After the transition to the low-hard state the spectral index is consistent with being 0., After the transition to the low–hard state the spectral index is consistent with being 0. " To obtain a more accurate measurement of the radio spectral index, we have averaged three short 4.86 GHz and 5 8.46 GHz observations close in time (in the range MJD 54499-54505) where the radio flux was consistent with being constant."," To obtain a more accurate measurement of the radio spectral index, we have averaged three short 4.86 GHz and 5 8.46 GHz observations close in time (in the range MJD 54499–54505) where the radio flux was consistent with being constant." The 4.86-8.46 GHz radio spectral index for these averages is 0.03--0.18., The 4.86–8.46 GHz radio spectral index for these averages is $\pm$ 0.18. This is consistent with optically thick emission as has been observed in low-hard radio spectra., This is consistent with optically thick emission as has been observed in low–hard radio spectra. " However, the radio spectral index does not stay close to 0 during the decay to quiescence."," However, the radio spectral index does not stay close to 0 during the decay to quiescence." We have averaged the 1.4 GHz and 8.46 GHz data in the MJD range 54516-54526., We have averaged the 1.4 GHz and 8.46 GHz data in the MJD range 54516--54526. This data coincides with the radio flare observable at 8.46 GHz., This data coincides with the radio flare observable at 8.46 GHz. Combining the three 1.4 GHz observations does provide a detection at 0.431+0.097 mJy., Combining the three 1.4 GHz observations does provide a detection at $\pm$ 0.097 mJy. At 8.46 GHz the average flux is 0.175+0.028 mJy., At 8.46 GHz the average flux is $\pm$ 0.028 mJy. The 1.4-8.46 GHz radio spectral index is -0.50+0.15., The 1.4–8.46 GHz radio spectral index is $\pm$ 0.15. This implies optically thin radio emission late in the low-hard state., This implies optically thin radio emission late in the low–hard state. In Figure 3 we plot the observed correlation between the X-ray and 8.46 GHz radio fluxes for uusing the X-ray observations closest in time to the radio observations (see footnotes to the journals of the X-ray observations and Table 5))., In Figure \ref{rxcorr} we plot the observed correlation between the X–ray and 8.46 GHz radio fluxes for using the X–ray observations closest in time to the radio observations (see footnotes to the journals of the X–ray observations and Table \ref{vla-log}) ). The best-fitting power law with index 0.1840.01 (1 σ) is overplotted., The best–fitting power law with index $\pm$ 0.01 (1 $\sigma$ ) is overplotted. " The index is less steep than the index of a —7:0.7 as found for several sources before (S,ος v;Galloetal.2003;; Corbeletal. 2003))."," The index is less steep than the index of $\alpha=\approx$ 0.7 as found for several sources before $_\nu \propto \nu^\alpha; $ \citealt{2003MNRAS.344...60G}; \citealt{2003A&A...400.1007C}) )." There are several effects that could distort the picture., There are several effects that could distort the picture. " First, the radio and X-ray data are not strictly simultaneous (see Table 5))."," First, the radio and X–ray data are not strictly simultaneous (see Table \ref{vla-log}) )." " There is typically less than 1 day between the start of the radio and X-ray observations, however, in one case the difference in start times is as much as 1.5 days."," There is typically less than 1 day between the start of the radio and X–ray observations, however, in one case the difference in start times is as much as 1.5 days." This together with the flares apparent in the radio light curve as well as in theRXTE and XX-ray observations could result in a higher flux in either radio or X-ray which might confuse the apparent correlation., This together with the flares apparent in the radio light curve as well as in the and X–ray observations could result in a higher flux in either radio or X–ray which might confuse the apparent correlation. Short duration radio flares have been found in e.g. V404 Cyg (Miller-Jonesetal. 2008))., Short duration radio flares have been found in e.g. V404 Cyg \citealt{2008MNRAS.388.1751M}) ). " Last, since the spatial resolution of our VLA observations is several arcseconds, the observed radio flux might include emission from ballistic jet-ejection event earlier in the outburst."," Last, since the spatial resolution of our VLA observations is several arcseconds, the observed radio flux might include emission from a ballistic jet–ejection event earlier in the outburst." " Althougha the ATCA non-detection shows that the initial radio emission probably related to jet-ejection events occurring before the transition to the low-hard state faded away, shocks further down the flow can lead to rebrightenings in radio (and X-ray) at a later stage."," Although the ATCA non–detection shows that the initial radio emission probably related to jet–ejection events occurring before the transition to the low–hard state faded away, shocks further down the flow can lead to rebrightenings in radio (and X–ray) at a later stage." The fact that the radio spectral index during the epoch related to the radio flare at MJD 54520 is showing that the radio emission is optically thin strongly argues in favour of this scenario., The fact that the radio spectral index during the epoch related to the radio flare at MJD 54520 is showing that the radio emission is optically thin strongly argues in favour of this scenario. Given the low spatial resolution of our radio observations this emission can significantly contribute to the radio flux density during the subsequent measurements., Given the low spatial resolution of our radio observations this emission can significantly contribute to the radio flux density during the subsequent measurements. All-skv 5-rav observations bv SAS 2 (Fichteletal.1977:Fichtel.Simpson.&Thompson1973) and most recently by EGRET (Sreekumaretal.1993). have revealed the existence of,"All-sky $\gamma$ -ray observations by SAS 2 \citep{fichtel,fichtel2} and most recently by EGRET \citep{sreek_obs} have revealed the existence of" total observed flux Gu the 0.33.0 keV. baud) of 1.1.«101? 1,total observed flux (in the 0.3–3.0 keV band) of $1.1\times 10^{-12}$ . With the given temperature aud absorption column. the fiux of the thermal emission was calculated to be ~6x10205 tin the 2.0 keV baud.," With the given temperature and absorption column, the flux of the thermal emission was calculated to be $\sim$$6 \times 10^{-13}$ in the 0.5--2.0 keV band." This is comparable to our result., This is comparable to our result. The cuhancement of O and/or Ne abundances was reported in the works of Bomansetal(2003). aud Cooperetal.(2000., The enhancement of O and/or Ne abundances was reported in the works of \cite{bomans03} and \cite{c04}. Ou the other hand. our spectruni does not show any evidence of a significant deviation from the typical LAIC abundances. sugecsting that the hot gas mainly originates frou ISM with only slieht enrichment by SN ejecta.," On the other hand, our spectrum does not show any evidence of a significant deviation from the typical LMC abundances, suggesting that the hot gas mainly originates from ISM with only slight enrichment by SN ejecta." The N-rav spectra of the SBs NI1I aud ND1D are well reproduced bv sinele-component thin-thermal plasmas (with the models for the eroup of point sources)., The X-ray spectra of the SBs N11 and N51D are well reproduced by single-component thin-thermal plasmas (with the models for the group of point sources). Figure 11 shows the unfolded spectra of both SBs., Figure \ref{fig:unfold} shows the unfolded spectra of both SBs. The presence of additional uouthermal cussion. argued In previous works CN1l: Maddox et 22009: N51D: Cooper et 22001). is 1iuchi less evident in our detailed analyses. supporting the earlier results by Nazéctal.(2000) and Bomansetal.(2003).," The presence of additional nonthermal emission, argued in previous works (N11: Maddox et 2009; N51D: Cooper et 2004), is much less evident in our detailed analyses, supporting the earlier results by \cite{naze04} and \cite{bomans03}." . The 210 keV fiux of the diffuse component £j (— 0p) for cach SB can be calculated as where Fy. Fp. aud Fps (and σα. op. Opa) are the 210 keV fluxes (aud uncertainties) of the SRC and BCD regious and that of the point sources.," The 2–10 keV flux of the diffuse component $F_{\rm D}$ $\pm~\sigma_{\rm D}$ ) for each SB can be calculated as where $F_{\rm S}$, $F_{\rm B}$, and $F_{\rm PS}$ (and $\sigma_{\rm S}$, $\sigma_{\rm B}$, $\sigma_{\rm PS}$ ) are the 2–10 keV fluxes (and uncertainties) of the SRC and BGD regions and that of the point sources." Usine the values given in Tables 2. and 5.. we obtain 36 upper limits of the fluxes to be 3.6«LO+! aand LT«10teres for N11 and N51D. respectively.," Using the values given in Tables \ref{tab:sbn_n11} and \ref{tab:sbn_n51d}, we obtain $\sigma$ upper limits of the fluxes to be $3.6 \times 10^{-14}$ and $4.7 \times 10^{-14}$ for N11 and N51D, respectively." For Nil. Maddoxetal.(2009) claimed that the hard N-ravs. detected at energies of up to ~7 keV. required a power-law component with a photon index of P—1.7 aud au observed fix of ⋟∙340ς:10.193 inthe 0.210 keV baud)?," For N11, \cite{m09} claimed that the hard X-rays, detected at energies of up to $\sim$ 7 keV, required a power-law component with a photon index of $\Gamma \sim 1.7$ and an observed flux of $\sim$$3.0\times 10^{-13}$ (in the 0.2–10 keV $\!\!$." photon For.NSLD. eiit heVbandwercereportedtobeLthe~1.3 aud ὃν102Lo respeetivele. (Cooper," For N51D, the photon index and observed flux in the 0.3--3.0 keV band were reported to be $\Gamma \sim 1.3$ and $\sim$$3.3\times 10^{-13}$, respectively \citep{c04}." To directly conipare these values with our results. these fluxes are modified to values in the 210 keV band. giviug 2.3«10.DP ffor NIl and 7.1.10 ffor ΟΤΕ. These values are about oue order higher than the upper linits that we have obtained.," To directly compare these values with our results, these fluxes are modified to values in the 2–10 keV band, giving $2.3\times 10^{-13}$ for N11 and $7.1\times 10^{-13}$ for N51D. These values are about one order higher than the upper limits that we have obtained." The spectral models for the claimed hard N-ray cuiissious are shown in Figure LL with black- solid lines., The spectral models for the claimed hard X-ray emissions are shown in Figure \ref{fig:unfold} with black solid lines. Note that the point sources had been excluded from the EPIC spectrum of N51D (Cooperetal.2001)., Note that the point sources had been excluded from the EPIC spectrum of N51D \citep{c04}. . Nevertheless. both mocels eive fluxes clearly exceeding those given by the NIS spectrmm in which the poiut-source fluxes are contaimed.," Nevertheless, both models give fluxes clearly exceeding those given by the XIS spectrum in which the point-source fluxes are contained." Given that the poiut-source flux in N11 is ποσο] αμα (Fig. 11)).," Given that the point-source flux in N11 is negligibly small (Fig. \ref{fig:unfold}) )," the detection of hard N-ravs. claiiied in the previous report was probably due to correct backeround subtraction., the detection of hard X-rays claimed in the previous report was probably due to incorrect background subtraction. Iu fact. Maddoxetal.(2009) commented that the subtraction of Ni lines originatiug from the NND. was unsuccessful.," In fact, \cite{m09} commented that the subtraction of Ni lines originating from the NXB was unsuccessful." The NAB spectra of the NIS consists of enüssion-liue and coutiuuuuui components. and their intensities are correlated with each other (Tawaetal.2008).," The NXB spectrum of the XIS consists of emission-line and continuum components, and their intensities are correlated with each other \citep{tawa08}." . Therefore. this also caused the incomplete subtraction of the continu colmponecnt iu the previous reports.," Therefore, this also caused the incomplete subtraction of the continuum component in the previous reports." In our analyses. ou the other laud. the fluorescent NXD lunes are accurately subtracted (see Section 3.3.0)). aud hence the backeround reduction is considered to be successtul.," In our analyses, on the other hand, the fluorescent NXB lines are accurately subtracted (see Section \ref{sssec:n11_suzaku1}) ), and hence the background reduction is considered to be successful." The problem concerning N51D is analogous to the case of N11. because the residual of the Iline due to iuconiplete backeround subtraction has been reported (Cooperetal.2001).," The problem concerning N51D is analogous to the case of N11, because the residual of the line due to incomplete background subtraction has been reported \citep{c04}." . We point out that the analysis of faint extended sources. such as SBs in the LAIC. is very scusitive to the estimation of the NNB and the vignetting effect. and thus should be performed with ereat care.," We point out that the analysis of faint extended sources, such as SBs in the LMC, is very sensitive to the estimation of the NXB and the vignetting effect, and thus should be performed with great care." Nouthermal X-ray cussions have πο far Όσοι discovered frou several Galactic star-formune regions. the Arches cluster (Tsujimoto et 22007). NCC 6331 (Ezoe et 22006). ROW 38 AVols et 22002). Westerluud 1 (Muno et 22006). aud Westerluund 2 (Fujita et 22009).," Nonthermal X-ray emissions have so far been discovered from several Galactic star-forming regions, the Arches cluster (Tsujimoto et 2007), NGC 6334 (Ezoe et 2006), RCW 38 (Wolk et 2002), Westerlund 1 (Muno et 2006), and Westerlund 2 (Fujita et 2009)." Th these cases. however. the emissions are correlatedhel withid relatively compact (110-pc-scalo) indecandobseea OB association or in a molecular cloud. core.," In these cases, however, the emissions are correlated with relatively compact (1–10-pc-scale) regions around an OB association or in a molecular cloud core." 30 Dor C is another example of a star-foriung region that exhibits nouthermal (svuchrotron) N-ravs (Bahaetal.2001)., 30 Dor C is another example of a star-forming region that exhibits nonthermal (synchrotron) X-rays \citep{bamba04}. . Towever. the X-ray shell cau be imterpreted as a sinele middle-aged SNR expanding rapidly inside the SB cavity (Yamaguchietal.2009).," However, the X-ray shell can be interpreted as a single middle-aged SNR expanding rapidly inside the SB cavity \citep{yama09}." . Therefore. at preseut. there is no evidence for large-scale (100 pc) noutheriial cussion distributed eutirelv iu an SD.," Therefore, at present, there is no evidence for large-scale $\sim$ 100 pc) nonthermal emission distributed entirely in an SB." As given in Table 7.. the hunuinosities of the nouthermal N-rav cluissions iu NLL aud N51D are. if ay. less than those of 30 Dor C aud some of the other star- regions.," As given in Table \ref{tab:comparison}, the luminosities of the nonthermal X-ray emissions in N11 and N51D are, if any, less than those of 30 Dor C and some of the other star-forming regions." It is theoretically expected that efficient cosmic-ray acceleration can take place in SBs due to repeated SN shocks and/or maguetic turbulence (e.g.. Bykov Fleishman 1992: Parizot et 22001).," It is theoretically expected that efficient cosmic-ray acceleration can take place in SBs due to repeated SN shocks and/or magnetic turbulence (e.g., Bykov Fleishman 1992; Parizot et 2004)." Moreover. Butt Bykov (2008) suegeested that more than of the enerev stored in an SD can be coustautly transterred to accelerating cosmüc-cray particles at the evolutiou stage," Moreover, Butt Bykov (2008) suggested that more than of the energy stored in an SB can be constantly transferred to accelerating cosmic-ray particles at the evolution stage" JCMIT observations were perlormed in beam switelied mode with a lrequency of 111. and beam throw of 2 in azimuth.,JCMT observations were performed in beam switched mode with a frequency of Hz and beam throw of $2'$ in azimuth. The ACSIS digital antocorrelator spectrometer was used wilh a bandwidth of MMIIZz providing a resolution of ~1 MMITz., The ACSIS digital autocorrelator spectrometer was used with a bandwidth of MHz providing a resolution of $\sim1$ MHz. We have used (he receiver A3 to observe the transition al GGIIz., We have used the receiver A3 to observe the $^+$ transition at GHz. " At this frequency. the beam size of the telescope is 21"" and the main beam ellicieney 0.69."," At this frequency, the beam size of the telescope is $21''$ and the main beam efficiency 0.69." " The observations were carried towards (he nominal position o3590=00547933:1.9,304) (radiocontinuumposition.Douglasetal.1996)."," The observations were carried towards the nominal position $\alpha_{J2000}=00^{\rm h}47^{\rm m}33\fs1, \delta_{J2000}=-25^\circ17'18''$ \citep[radio continuum position,][]{Douglas96}." ". As seen in the IIC4N J=25—24 profile. most of the emission is observed from one of the velocity components ab (his position. which is due to the JCAIT observed position being 6"" and 10"" away [rom those observed with the IILAM 301mm. respectively."," As seen in the $_3$ N $J=25-24$ profile, most of the emission is observed from one of the velocity components at this position, which is due to the JCMT observed position being $\sim6''$ and $10''$ away from those observed with the IRAM m, respectively." This position is half beam away from the positions observed with the 330m. so the abundance ratios derived [ron (his observation might be affected by a lareer uncertainty of up to a factor of 2.," This position is half beam away from the positions observed with the 30m, so the abundance ratios derived from this observation might be affected by a larger uncertainty of up to a factor of 2." " However. this effect might be attenuated by the emission being extended over scales of >20""."," However, this effect might be attenuated by the emission being extended over scales of $>20''$." The 5/2—3/2F/ —-2—12and 3/2—1/2F—2-—] transitions are clearly detected above the noise level (~1.5 mink in channels).," The $^+$ $5/2- 3/2\,F=2-1$ and $3/2- 1/2\,F=2-1$ transitions are clearly detected above the noise level $\sim 1.5$ mk in channels)." Llowever. we observe its profile sienilicantly blended to that of the eroup οἱ transitions of ΟΠ=5—4.," However, we observe its profile significantly blended to that of the group of transitions of $\rm^{13}CH_3OH\, J=5-4$." This overlap was not a problem in thecase of the detection towards 382 due to the significantly lower abundance of ΟΙ towards this ealaxv (Martinetal., This overlap was not a problem in thecase of the $^+$ detection towards 82 due to the significantly lower abundance of $_3$ OH towards this galaxy \citep{Martin06a}. 2006a).. The 3/2—F—2—1 component was not detected due to its low relative intensity.," The $^+$ $3/2- 3/2\, F=2-1$ component was not detected due to its low relative intensity." We have fitted the observed profile with a single Gaussian component svntheüe spectra with radial velocity aud linewidth lixed [rom those derived from HCN. The relative intensities of the components were also fixed to those expected from optically thin emission under under local thermodynamic equilibrium conditions., We have fitted the observed profile with a single Gaussian component $^+$ synthetic spectra with radial velocity and linewidth fixed from those derived from $_3$ N. The relative intensities of the $^+$ components were also fixed to those expected from optically thin emission under under local thermodynamic equilibrium conditions. The derived line profiles parameters are presented in Table 1.., The derived line profiles parameters are presented in Table \ref{tab:gaussfit}. . Additionally. we," Additionally, we" operation between 2010-2015.,operation between 2010-2015. An examination of the lower panels in Figure 7 demonstrate that with the advent of such telescopes. the fractional deviation introduced by a planet planetary companion will be readily. identifiable. even for planets presenting only a thin crescent.," An examination of the lower panels in Figure \ref{noise} demonstrate that with the advent of such telescopes, the fractional deviation introduced by a planet planetary companion will be readily identifiable, even for planets presenting only a thin crescent." Lt must be remembered that the above discussion is for a particular set of planetary ancl microlensing parameters. such as planetary radius. albedo. caustic strength and relative velocities. and that the detectability of a planetary companion will depend on the specific values of these for the system under consideration.," It must be remembered that the above discussion is for a particular set of planetary and microlensing parameters, such as planetary radius, albedo, caustic strength and relative velocities, and that the detectability of a planetary companion will depend on the specific values of these for the system under consideration." ltecent studies have demonstrated that when a star in he Galactic Bulge or Magellanie Cloucs is magnified during a microlensing event. anv light. reflected [rom an orbiting λαοί can also be signilicantlv. magnified to observable evels.," Recent studies have demonstrated that when a star in the Galactic Bulge or Magellanic Clouds is magnified during a microlensing event, any light reflected from an orbiting planet can also be significantly magnified to observable levels." These previous works. however. have assumed a simplified model for the distribution of rellected light from he planet. namely a circularly svimmetrie disk.," These previous works, however, have assumed a simplified model for the distribution of reflected light from the planet, namely a circularly symmetric disk." Phe reflected ight from any real planet. however. will display phases akin o those seen with the moon and the inferior planets.," The reflected light from any real planet, however, will display phases akin to those seen with the moon and the inferior planets." This paper has presented a study on the effect. of planetary phase on the degree to which the light. reflected. rom a planet is magnified as it is swept bv a caustic during a eravitational microlensing event., This paper has presented a study on the effect of planetary phase on the degree to which the light reflected from a planet is magnified as it is swept by a caustic during a gravitational microlensing event. Considering simple mocels to represent. various planetary. phases. this work has demonstrated that these non-circular profiles resul in strikinely cillerent light curves that are solely dependen Upon their orientation with respect to the sweeping caustic.," Considering simple models to represent various planetary phases, this work has demonstrated that these non-circular profiles result in strikingly different light curves that are solely dependent upon their orientation with respect to the sweeping caustic." While this behaviour is cilferent. depending upon the specifies of the light distribution rellected by the planet. al the models display the same generic trends.," While this behaviour is different, depending upon the specifics of the light distribution reflected by the planet, all the models display the same generic trends." Equallyi interestinge is that the peak magnificationὃν of a light curve for a model of the planet is also. strongly dependent upon the planetary orientation with respect to the caustic., Equally interesting is that the peak magnification of a light curve for a model of the planet is also strongly dependent upon the planetary orientation with respect to the caustic. In each model. the planet was substantially more magnified if orientated at x72. than at 0 (see Figure 1)).," In each model, the planet was substantially more magnified if orientated at $\pm\pi/2$, than at 0 (see Figure \ref{planetphase}) )." " In the case of the simple ""quarter moon (model a). this resulted in up to GO per cent more magnification than when compared to planets orientated at ~0."," In the case of the simple `quarter moon' (model a), this resulted in up to $\sim60$ per cent more magnification than when compared to planets orientated at $\sim0$." Due to scaling relations. Figures 3. and 5 are insensitive to specific values of caustic strength ancl planetary. racius.," Due to scaling relations, Figures \ref{half2} and \ref{cres2} are insensitive to specific values of caustic strength and planetary radius." These trends are also seen in models (b) aad (ο) which are more crescent-like. both possessing peak magnification distributions that possess à minimum at ϐ~0. rising to πο.," These trends are also seen in models (b) and (c) which are more crescent-like, both possessing peak magnification distributions that possess a minimum at $\theta\sim0$, rising to $\pm\pi/2$." In the case of model (ο). the light. curve at 7/2 possesses a peak magnification exceeding those at 0~QO by 40 per cent.," In the case of model (c), the light curve at $-\pi/2$ possesses a peak magnification exceeding those at $\theta\sim0$ by 140 per cent." Considering. that model (a) al @=O is degenerate. with the circularly svimetric models typically emploved. in. microlensing studies. these results imply that previous results have underestimated the potential magnification in planetary microlensing events by a [actor of a few.," Considering that model (a) at $\theta=0$ is degenerate with the circularly symmetric models typically employed in microlensing studies, these results imply that previous results have underestimated the potential magnification in planetary microlensing events by a factor of a few." While these results are encouraging. the detectability of a planetary microlensing event will depend on. the amount of [lux received by an observer.," While these results are encouraging, the detectability of a planetary microlensing event will depend on the amount of flux received by an observer." As well as he magnification. this will depend also on the amoun of stellar light that is reflected. by a planet. a value hat decreases as à planct appears more crescent-Llike.," As well as the magnification, this will depend also on the amount of stellar light that is reflected by a planet, a value that decreases as a planet appears more crescent-like." Simulatecl observations presented in this paper reveal tha he microlensing of moderately. erecsent-like planets (moce jj are detectable with current. telescopes at a tempora sampling that allows the detailed recovery of the underlving wofile., Simulated observations presented in this paper reveal that the microlensing of moderately crecsent-like planets (model b) are detectable with current telescopes at a temporal sampling that allows the detailed recovery of the underlying profile. With more extreme crescents. the planetary. even he fractional ceviation of ©0.54 oceurs too quickly to be cllectively sampled. by photometric monitoring with a LO-m class telescope. although proposed. 30-m class telescopes will resolve the fluctuations.," With more extreme crescents, the planetary event the fractional deviation of ${\lta0.5\%}$ occurs too quickly to be effectively sampled by photometric monitoring with a 10-m class telescope, although proposed 30-m class telescopes will resolve the fluctuations." The exact details of the microlensing light curve deviations due to the presence of a planetary companion depend upon a number of parameters. although the results presented here and in. previous studies (μα Gaudi 2000: LI2000) suggest that this approach should successfully uncover hot Jupiters at. kiloparsec-scale distances.," The exact details of the microlensing light curve deviations due to the presence of a planetary companion depend upon a number of parameters, although the results presented here and in previous studies (Graff Gaudi 2000; LI2000) suggest that this approach should successfully uncover hot Jupiters at kiloparsec-scale distances." Due to condensed particulate matter in the atmospheres of planets. the light they reflect is expected to be polarized (Seager et al.," Due to condensed particulate matter in the atmospheres of planets, the light they reflect is expected to be polarized (Seager et al." 2000). although the degree of this polarization is extremely small (~10.7).," 2000), although the degree of this polarization is extremely small $(\sim10^{-5})$." LI2000. considered. the elfect of microlensing magnification on this polarization signature and found that it too can be boosted to detectable levels. although at a fraction of a percent. the measurement. of such polarizations still presents observational cilliculties.," LI2000 considered the effect of microlensing magnification on this polarization signature and found that it too can be boosted to detectable levels, although at a fraction of a percent, the measurement of such polarizations still presents observational difficulties." In light of the results of the study. presented in this paper. we have begun an extensive investigation into the further ellects of the microlensing of planets. especially the expected »olarization signaturese from crescent-like sources.," In light of the results of the study presented in this paper, we have begun an extensive investigation into the further effects of the microlensing of planets, especially the expected polarization signatures from crescent-like sources." Vhe anonvmous referee is thanked. for comments that improved the paper., The anonymous referee is thanked for comments that improved the paper. GEL thanks I5ric Agol for discussions that initiated this study., GFL thanks Eric Agol for discussions that initiated this study. CLEA thanks the Anelo-Australian Observatory for hospitality and support for the duration of her Ulx Student. Fellowship., CEA thanks the Anglo-Australian Observatory for hospitality and support for the duration of her UK Student Fellowship. 2009). GRBs would be excellent candidates to display effects of anisotropic lensing.,"2009), GRBs would be excellent candidates to display effects of anisotropic lensing." Since GRBs are short-livecl sources. CRB lensing would not generally result in contemporaneous multiple imaging.," Since GRBs are short-lived sources, GRB lensing would not generally result in contemporaneous multiple imaging." Rather. if à CRB goes olf behind a massive cluster. one would naively expect to see a nearly identical (modulo some magnification factor) GRB within the same instrumental error circle some months or vears later.," Rather, if a GRB goes off behind a massive cluster, one would naively expect to see a nearly identical (modulo some magnification factor) GRB within the same instrumental error circle some months or years later." We aave found. however. that there could be a small but finite oobability that one of the images could be missed. because of the angular beam separation between the light rays that orm t1e lensed images.," We have found, however, that there could be a small but finite probability that one of the images could be missed because of the angular beam separation between the light rays that form the lensed images." " As a specific exampe. M we consider a GERD abt ος=6 lensed by a massive cluster at 2=1 (1.0... 11e scenario depicted in 4)). aux its jet. opening angle is 5,4=1°. there is a probability. that the second CGRB image will not appear."," As a specific example, if we consider a GRB at $z_{\rm s} = 6$ lensed by a massive cluster at $z_{\rm l} = 1$ (i.e., the scenario depicted in ), and its jet opening angle is $\theta_{\rm jet} = 1^\circ$, there is a probability that the second GRB image will not appear." That. probaμέν doubles. if Bua.=57. and it increases to about for a lens recdshift uoc8.," That probability doubles if $\theta_{\rm jet} = 0.5^\circ$, and it increases to about for a lens redshift $z_{\rm l} = 3$." The possilέν of missing images ought to be incorporated. into staistical forecasts of GRD lensing (which have heretofore assumed. isotropic source emission: οἱ., The possibility of missing images ought to be incorporated into statistical forecasts of GRB lensing (which have heretofore assumed isotropic source emission; cf. Porciani Macau 200, Porciani Madau 2001). οher sources that have been suggested to be hig relativistic are blazars., Other sources that have been suggested to be highly relativistic are blazars. Ciannios et al. (, Giannios et al. ( "2009) SUgECS that the fast Toy variability observed. in. (vo sources c""wl be exrnlained as the result. of compact emitting regions moving towards the observer with Lorentz factors of ~100. and embedded: within à jet moving at lower speed.","2009) suggested that the fast TeV variability observed in two sources can be explained as the result of compact emitting regions moving towards the observer with Lorentz factors of $\sim 100$, and embedded within a jet moving at lower speed." In this scenario. the emission. [from cach blob is beamed. within a sub-degree scale.," In this scenario, the emission from each blob is beamed within a sub-degree scale." Depending on the angle at which the blob is moving with respect to the line of sight to the observer. there is some probability that a lensed. blazar might be missing one of the images.," Depending on the angle at which the blob is moving with respect to the line of sight to the observer, there is some probability that a lensed blazar might be missing one of the images." ΙΓ that does happen to be the case in lensing observations (o.:9. when a blazar is observed. behind a Luge cluster and the number of images appears anomalous) it would provide support for this physical picture of blazars.," If that does happen to be the case in lensing observations (e.g., when a blazar is observed behind a large cluster and the number of images appears anomalous) it would provide support for this physical picture of blazars." Anisotropy in the net flux leaving the source can also result. from inhomogeneous absorption within the source., Anisotropy in the net flux leaving the source can also result from inhomogeneous absorption within the source. ‘This is indeed the case for AGNs. in which dense clouds in the broad abosorption line region create a highly anisotropic absorbtion pattern.," This is indeed the case for AGNs, in which dense clouds in the broad abosorption line region create a highly anisotropic absorbtion pattern." The precise location ancl size of these clouds is still à controversial issue., The precise location and size of these clouds is still a controversial issue. Estimates suggest hat their size is not larger than about 1013 cm (e.g.. Baldwin et al.," Estimates suggest that their size is not larger than about $10^{14}$ cm (e.g., Baldwin et al." 1995: Elvis 2000). while their location has been placed in a range between 0.01 and 1000 pe (e.g.. de Ixool et al.," 1995; Elvis 2000), while their location has been placed in a range between 0.01 and 1000 pc (e.g., de Kool et al." 2VOL: Everett et al., 2001; Everett et al. 2002)., 2002). These scales fall in a quite interesting range for our problem., These scales fall in a quite interesting range for our problem. A cloud of size 1033 em at a distance of 1 pe would subtend an angle of about 77. which is similar to the median angular beam separation for NEW lenses with image separations A@>107.," A cloud of size $10^{14}$ cm at a distance of 1 pc would subtend an angle of about $7\arcsec$, which is similar to the median angular beam separation for NFW lenses with image separations $\Delta\theta > 10\arcsec$." ΙΓ the cloud were significantly closer to the central engine than 1 pe. it would most likely cover both of the light ravs that correspond to lensecl images. so the importance of source anisotropy would depend on whether there is significant internal structure within BAL clouds on scales smaller than 1033 em.," If the cloud were significantly closer to the central engine than 1 pc, it would most likely cover both of the light rays that correspond to lensed images, so the importance of source anisotropy would depend on whether there is significant internal structure within BAL clouds on scales smaller than $10^{14}$ cm." Conversely. if BAL clouds are significantly farther than 1 pc. the importance of source anisotropy would depend on the covering fraction of BAL clouds.," Conversely, if BAL clouds are significantly farther than 1 pc, the importance of source anisotropy would depend on the covering fraction of BAL clouds." If an AGN is strongly lensed ancl there is significant cillerential absorpion within the source. that would ellectiveIv cause diIorent lensecl images to have cilferent source [luxes. whici would in turn break the connection between observed lux ratios and lensing magnification ratios.," If an AGN is strongly lensed and there is significant differential absorption within the source, that would effectively cause different lensed images to have different source fluxes, which would in turn break the connection between observed flux ratios and lensing magnification ratios." Hf this complication is not recognized. it could Iead to errors in lens models and their interpretation.," If this complication is not recognized, it could lead to errors in lens models and their interpretation." By contrast. if the diferential source absorption is recognized. the ability Oo simultaneously obe multiple lines of sight. into the source with strong lensing would provide à new wav to xobe the structure. of the absorbing. medium. in AGN. which is still very. uncertain.," By contrast, if the differential source absorption is recognized, the ability to simultaneously probe multiple lines of sight into the source with strong lensing would provide a new way to probe the structure of the absorbing medium in AGN, which is still very uncertain." This possibility is related: to he suggestion by Chelouche (2003) anc Green (2006) that ensed quasars can be used to study. small-scale structure in quasar outllows., This possibility is related to the suggestion by Chelouche (2003) and Green (2006) that lensed quasars can be used to study small-scale structure in quasar outflows. One good would to identify. dillerential absorption would be to compare llux measurements al o. X-ray. and optical wavelengths (Green 2006)., One good would to identify differential absorption would be to compare flux measurements at both X-ray and optical wavelengths (Green 2006). Column, Column and. blended sources. turns out to be The procedure. described. above has been conducted considering only cluster stars (anc artificial stars) located inside one core radius (see Sect. 3.1)).,"and blended sources, turns out to be The procedure described above has been conducted considering only cluster stars (and artificial stars) located inside one core radius (see Sect. \ref{prof_sec}) )." " The obtained. minimum binary [fractions £,,5, for the clusters in our sample are listed in Table 2.", The obtained minimum binary fractions $\xi_{min}$ for the clusters in our sample are listed in Table 2. Phe typical error (calculated. by taking into account of the Poisson statistic and the uncertainties in the completeness corrections) is of the order of54., The typical error (calculated by taking into account of the Poisson statistic and the uncertainties in the completeness corrections) is of the order of. ".. As can be noted. the minimum binary fraction €,,;, is lareer than in all the clusters of our sample."," As can be noted, the minimum binary fraction $\xi_{min}$ is larger than in all the clusters of our sample." " The procedure described. above allowed: us to estimate the minimum binary fraction £,,;, without any (arbitrary) assumption on the distribution of mass-ratios f(q).", The procedure described above allowed us to estimate the minimum binary fraction $\xi_{min}$ without any (arbitrary) assumption on the distribution of mass-ratios $f(q)$. However. caution must be used when comparing the derived: binary fraction among the clillerent clusters of our sample.," However, caution must be used when comparing the derived binary fraction among the different clusters of our sample." In fact. the definition of the ALSsample and binarysample given in Sect.," In fact, the definition of the $MS~sample$ and $binary~sample$ given in Sect." 4.1. depends on the photometric accuracy that vary from cluster to cluster., \ref{minfrac} depends on the photometric accuracy that vary from cluster to cluster. An alternative approach consists in the assumption of a given clistribution f(q) and in the comparison between the color distribution of simulated stars and the observed. CMD., An alternative approach consists in the assumption of a given distribution $f(q)$ and in the comparison between the color distribution of simulated stars and the observed CMD. Until now there are neither theoretical arguments nor observational constraints o the shape of f(q) in stellar clusters., Until now there are neither theoretical arguments nor observational constraints to the shape of $f(q)$ in stellar clusters. Fisher ct al. (, Fisher et al. ( 2005) estimated. the mass-ratio distribution. f(q) in the binary xopulation of the local field. (at distances d«LOO pe).,2005) estimated the mass-ratio distribution $f(q)$ in the binary population of the local field (at distances $d<100~pc$ ). They found that most binary systems are formed by similar mass components (q 1)., They found that most binary systems are formed by similar mass components $q\sim 1$ ). Although this distribution is subject o significant observational uncertainties and is derived. for παν systems in a dillerent environment. it represents one of the few observational constraints to. f(q) which can be ound in literature.," Although this distribution is subject to significant observational uncertainties and is derived for binary systems in a different environment, it represents one of the few observational constraints to $f(q)$ which can be found in literature." In the following we calculate the binary [fraction € in he target clusters assuming the distribution f(q) measured ον Fisher et al. (, In the following we calculate the binary fraction $\xi$ in the target clusters assuming the distribution $f(q)$ measured by Fisher et al. ( 2005. sce Fig. 4).,"2005, see Fig. \ref{fq}) )." Jo derive this quantity. we simulated a population of ~ 100.000 artificial single. ancl binary stars (see Sect. 3.3))," To derive this quantity, we simulated a population of $\sim$ 100,000 artificial single and binary stars (see Sect. \ref{blend}) )" " and calculated the ratios c, ancl ey between the number of binarysample objects (ΔΝ) and ALSsample objects (Nays) for the simulated. population of single stars and binaries. respectively."," and calculated the ratios $\psi_{s}$ and $\psi_{b}$ between the number of $binary~sample$ objects $N_{bin}$ ) and $MS~sample$ objects $N_{MS}$ ) for the simulated population of single stars and binaries, respectively." The quantities Αν and Nays have been therefore counted in the observed. CALD and in the reference Ποιά CALD., The quantities $N_{bin}$ and $N_{MS}$ have been therefore counted in the observed CMD and in the reference field CMD. The binary fraction that allows to reproduce the observed. ratio t4; has been therefore calculated using the formula Errors have been calculated. according to the standard error propagation and assuming a Poisson statistic error on star counts (oy~VN)., The binary fraction that allows to reproduce the observed ratio $\psi_{obs}$ has been therefore calculated using the formula Errors have been calculated according to the standard error propagation and assuming a Poisson statistic error on star counts $\sigma_{N}\simeq\sqrt{N}$ ). OF course. the small fraction of stars present in the cluster cores produces uncertainties as large as10-1554.," Of course, the small fraction of stars present in the cluster cores produces uncertainties as large as." . A typical outcome of the procedure described above is showed in Fig., A typical outcome of the procedure described above is showed in Fig. 5. where a simulated. CALD of NCC2204 is compared. with the observed. one., \ref{sim} where a simulated CMD of NGC2204 is compared with the observed one. The overall shape of 16 observed. CAID turns out to be well reproduced., The overall shape of the observed CMD turns out to be well reproduced. In particular. the spread. of the MS calculated in the observed wie in the simulated CMD between 1 and 4 mag below the ‘luster turn-oll agree within 0.005 mag (see Fig. 5)).," In particular, the spread of the MS calculated in the observed and in the simulated CMD between 1 and 4 mag below the cluster turn-off agree within 0.005 mag (see Fig. \ref{sim}) )." This represents à &ood quality check to the photometric errors estimates., This represents a good quality check to the photometric errors estimates. The obtained binary fractions £p απ their corresponding errors are listed in Tableστ., The obtained binary fractions $\xi_{F}$ and their corresponding errors are listed in Table. As expected. the values of € estimated. following the assumption of a Fisher et al. (," As expected, the values of $\xi_{F}$ estimated following the assumption of a Fisher et al. (" "2005) f(q) are Larger than the minimum binary. fraction £,,5.",2005) $f(q)$ are larger than the minimum binary fraction $\xi_{min}$. Note that neither the ranking nor the relative proportions of the binary. fractions estimated among the cdillerent clusters of the sample appear to depend on the assumption of the shape of f(q)., Note that neither the ranking nor the relative proportions of the binary fractions estimated among the different clusters of the sample appear to depend on the assumption of the shape of $f(q)$. For some clusters of our sample the binary fraction were alreacly estimated. in previous works., For some clusters of our sample the binary fraction were already estimated in previous works. Anthony-TPwaroe et al. (, Anthony-Twarog et al. ( 1990). Lec. Ixang Ann (1999) Ixim ct al. (,"1990), Lee, Kang Ann (1999) Kim et al. (" 2001) and Sharma et al. (,2001) and Sharma et al. ( 2006) estimated a binary fraction 40%<£«5O'X for NGC2420 by adopting a technique similar to the one adopted. here.,"2006) estimated a binary fraction $40\% <\xi<50\% $ for NGC2420 by adopting a technique similar to the one adopted here." These values agree within the uncertainties with our estimates., These values agree within the uncertainties with our estimates. Note that part of the small (although not significant) overestimation of binaries predicted in the present work for this cluster with respect to literature values is due to the fact that we restricted our analysis to the core of the cluster where the majority of binaries are expected to be located., Note that part of the small (although not significant) overestimation of binaries predicted in the present work for this cluster with respect to literature values is due to the fact that we restricted our analysis to the core of the cluster where the majority of binaries are expected to be located. Minimum binary fractions have been also estimated for NOGC2243 (230'4.. Bonifazi et al.," Minimum binary fractions have been also estimated for NGC2243 $>$, Bonifazi et al." 1991) ancl NOGC2516(26'4.. Gonzalez Lapasset 2000:26%.. Jeflfries et al.," 1991) and NGC2516, Gonzalez Lapasset 2000;, Jeffries et al." 2001: Sune et al., 2001; Sung et al. 2002)., 2002). ALL these estimates are in agreement with the values derived in the present analysis., All these estimates are in agreement with the values derived in the present analysis. In the following section we compare the obtained binary fractions among the clusters of our sample ancl with the sample of GCs presented. in Sollima ct al. (, In the following section we compare the obtained binary fractions among the clusters of our sample and with the sample of GCs presented in Sollima et al. ( 2007) as a function of their main physical parameters.,2007) as a function of their main physical parameters. As introduced in Sect., As introduced in Sect. 1 the sample of OCS analysed. here cover à range in masses and ages still unexplored by previous analysis on GC's., \ref{intro} the sample of OCs analysed here cover a range in masses and ages still unexplored by previous analysis on GCs. Therefore. the derived binary fractions can be used to check the validity of the correlations with age and," Therefore, the derived binary fractions can be used to check the validity of the correlations with age and" A number of reliable values in the literature (Abt Levy 1974: ‘Takeda 1984: Ducquennov. Mayor Llalbwachs 1991) suggested. that the racial velocity of 9. Aur was slightly variable.,"A number of reliable values in the literature (Abt Levy 1974; Takeda 1984; Duquennoy, Mayor Halbwachs 1991) suggested that the radial velocity of 9 Aur was slightly variable." After Curlin demonstrated in early 1993 that the racial velocity of 9 Aur was indeed variable. a concentrated set of 83 data points was obtained from 1993 December 25 to 1994 January 9.," After Griffin demonstrated in early 1993 that the radial velocity of 9 Aur was indeed variable, a concentrated set of 83 data points was obtained from 1993 December 25 to 1994 January 9." These are shown in Fig., These are shown in Fig. 7., 7. Five more values were obtained from 1994 February 16 to 20. and seven more from April 29 to May. 4.," Five more values were obtained from 1994 February 16 to 20, and seven more from April 29 to May 4." The radial velocities range from 5.50d:0.61 to 15.15+£0.66 kms1., The radial velocities range from $-5.50 \pm 0.61$ to $+5.15 \pm 0.66$ km $^{-1}$. One can clearly see hour to hour and day to day variations., One can clearly see hour to hour and day to day variations. In Fig., In Fig. S we plot the power spectrum of the radial velocity data shown in Fig., 8 we plot the power spectrum of the radial velocity data shown in Fig. 7., 7. fo is clearly the dominant peak in the power spectrum., $f_2$ is clearly the dominant peak in the power spectrum. Interestingly enough. while the frequeney fy and its one day alias 1.fi are clearly present in the photometry. fj apparently does not show up in the radial velocity data.," Interestingly enough, while the frequency $f_1$ and its one day alias $1 - f_1$ are clearly present in the photometry, $f_1$ apparently does not show up in the radial velocity data." In Fig., In Fig. S there is à peaknear 1.fim 0.20 + (namely at 0.248 dt ), 8 there is a peak $1 - f_1 \approx$ 0.20 $^{-1}$ (namely at 0.248 $^{-1}$ ). The small peakear fi is not significant., The small peak $f_1$ is not significant. We do not understand howonly the one day alias of fj should appear. but not the frequeney itselt. if indeed the peak near 1fy is the one clay alias of f1.)," We do not understand how the one day alias of $f_1$ should appear, but not the frequency itself, if indeed the peak near $1 - f_1$ is the one day alias of $f_1$ .)" Ht could be that during the time most of the radial velocities were obtained (a period of only 15 davs) the frequency fi was in abevance., It could be that during the time most of the radial velocities were obtained (a period of only 15 days) the frequency $f_1$ was in abeyance. Future observations are clearly warrantect., Future observations are clearly warranted. Since high degree spherical harmonies delineate a large number of regions on the star (which are alternatinglv moving in and out or transversely). while low degree iwmonies delineate a small number regions (e.g. 2 to 4 for f = |] or 2). one would only see radial velocity variations in a μαar pulsating racially or in a low order harmonic.," Since high degree spherical harmonics delineate a large number of regions on the star (which are alternatingly moving in and out or transversely), while low degree harmonics delineate a small number regions (e.g. 2 to 4 for $\ell$ = 1 or 2), one would only see radial velocity variations in a star pulsating radially or in a low order harmonic." Le follows ju fo must be related to a low degree harmonic., It follows that $f_2$ must be related to a low degree harmonic. " Since f, apparently does not show up in the racial Pelocity data. it seems unwise to make a two frequency fit to re raclial velocity data to derive the phases ancl amplitudes."," Since $f_1$ apparently does not show up in the radial velocity data, it seems unwise to make a two frequency fit to the radial velocity data to derive the phases and amplitudes." The peak of fozz0.36£0.03 is close to fo=0.345684from 16 photometry., The peak of $f_2 \approx 0.36 \pm 0.03$ is close to $f_2 = 0.345684$from the photometry. Adopting the latter value ane using all 95 radial velocities available from the 1993/4 season. we find duas=2.00+0.27 km and μι=0.139+0.021 (which is the phase of maximum radial velocity).," Adopting the latter value and using all 95 radial velocities available from the 1993/4 season, we find $A_{RV} = 2.00 \pm 0.27$ km $^{-1}$ and $\phi_{RV} = -0.139 \pm 0.021$ (which is the phase of maximum radial velocity)." are larger (han the median hall-light radius of Galactic globular clusters.,are larger than the median half-light radius of Galactic globular clusters. " The median radius of the clusters in Table 5 is 2, = 6.8 pe. which is 2.5x larger than the Jij = 2.74 pc median radius of all Galactic globular clusters in Table 2."," The median radius of the clusters in Table 5 is $R_h$ = 6.8 pc, which is 2.5x larger than the $R_h$ = 2.74 pc median radius of all Galactic globular clusters in Table 2." OI the six globulus with A> 6.8 pe in Table 2. two are likely associated with the Sagittarius dwarf.," Of the six globulars with $R_{h} >$ 6.8 pc in Table 2, two are likely associated with the Sagittarius dwarf." This suggests that: (1) satellite clusters of disrupted dwarf companions probably provided a significant contribution to total population of large Galactic globular clusters. and (2) that only a few mergers with sSagittarius-like cwarls took place during the assembly of the Milkv. Way system.," This suggests that: (1) satellite clusters of disrupted dwarf companions probably provided a significant contribution to total population of large Galactic globular clusters, and (2) that only a few mergers with Sagittarius-like dwarfs took place during the assembly of the Milky Way system." It is a pleasure to thank Mark Peacock for a listing of projected galactocentric distances for the globular clusters in M31., It is a pleasure to thank Mark Peacock for a listing of projected galactocentric distances for the globular clusters in M31. I also thank Alan MeConnachie for reading the draft manuscript., I also thank Alan McConnachie for reading the draft manuscript. | am also indebted to Dill aud Gretchen Harris for exchanges of e-mails and to Brenda Parrish and Jason Shrivell lor technical support., I am also indebted to Bill and Gretchen Harris for exchanges of e-mails and to Brenda Parrish and Jason Shrivell for technical support. consider that results of quality factors smaller than do not provide a sufficiently precise estimation of.,consider that results of quality factors smaller than do not provide a sufficiently precise estimation of. . Figure[§] indicates the quality factor values for companions with various effective temperatures at 3 angular separations around an MO star at 10 ρε in LRS., Figure \ref{figure:quality_factor_M0_10pc} indicates the quality factor values for companions with various effective temperatures at 3 angular separations around an M0 star at 10 pc in LRS. The plot gives an overview of the evolution of the quality factor with effective temperature and angular separation., The plot gives an overview of the evolution of the quality factor with effective temperature and angular separation. " The evolution with is globally the same at each separation: the quality factor slope is very high over a small range of effective temperature, going from close to 0 to approximately80%."," The evolution with is globally the same at each separation: the quality factor slope is very high over a small range of effective temperature, going from close to 0 to approximately." ". Above this limit, the slope slowly decreases to reach an almost flat regime above95%."," Above this limit, the slope slowly decreases to reach an almost flat regime above." . The difference with angular separation is the temperature at which the level is reached: there is a large improvement in contrast between and1., The difference with angular separation is the temperature at which the level is reached: there is a large improvement in contrast between and. "5"".. At0.5"",, the level is reached for a of 700 K (contrast of 11.0 magnitudes), while at the same level is reached for a of 500 K (contrast of 13.6 magnitudes)."," At, the level is reached for a of 700 K (contrast of 11.0 magnitudes), while at the same level is reached for a of 500 K (contrast of 13.6 magnitudes)." " Results are of even higher contrast for the GO star (not plotted here), generating wider error bars, in particular for low for which the contrast is very high (15 magnitudes for a 600 K companion)."," Results are of even higher contrast for the G0 star (not plotted here), generating wider error bars, in particular for low for which the contrast is very high (15 magnitudes for a 600 K companion)." " The slope of the curves is different for each angular separation: it is steep for a separation of1.5"",, and decreases for increasing separations."," The slope of the curves is different for each angular separation: it is steep for a separation of, and decreases for increasing separations." " The curves for separations of1.5”,,1.0’’,, and reach the level at different effective temperatures of 700 K, 900 K, and 1200 K, corresponding to contrasts of 13.6, 12.2, and 10.0 magnitudes respectively."," The curves for separations of, and reach the level at different effective temperatures of 700 K, 900 K, and 1200 K, corresponding to contrasts of 13.6, 12.2, and 10.0 magnitudes respectively." This is consistent with the contrast values at which the level is reached for the MO star., This is consistent with the contrast values at which the level is reached for the M0 star. Figure D] summarizes the results of the quality factor for both MO and GO stars at 10 pc at both LRS and MRS., Figure \ref{figure:quality_summary_M0_G0_10pc} summarizes the results of the quality factor for both M0 and G0 stars at 10 pc at both LRS and MRS. It shows the effective temperature at which a value of gq=80% is reached as a function of angular separation., It shows the effective temperature at which a value of $q = 80\%$ is reached as a function of angular separation. We clearly see the difference in regime between the two stars., We clearly see the difference in regime between the two stars. " A square law was fitted to the data to provide a general idea of the overall evolution, but more points are necessary to have a clearer idea of the real dependence on angular separation."," A square law was fitted to the data to provide a general idea of the overall evolution, but more points are necessary to have a clearer idea of the real dependence on angular separation." " For the MO stars, the level is reached over a small range in (less than 200 K)."," For the M0 stars, the level is reached over a small range in (less than 200 K)." " The influence of angular separation is then quite small, especially at MRS for which the curve is almost flat."," The influence of angular separation is then quite small, especially at MRS for which the curve is almost flat." This is because at MRS we are limited by the sky level for an MO star at 10 pc., This is because at MRS we are limited by the sky level for an M0 star at 10 pc. " For GO stars, the influence of angular separation is far more significant: the range of covered to reach q=80% is more than 600 K in LRS."," For G0 stars, the influence of angular separation is far more significant: the range of covered to reach $q = 80\%$ is more than 600 K in LRS." " At MRS, the range is only ~250 K, but compared to the evolution in MO stars, this range is rather large."," At MRS, the range is only $\sim$ 250 K, but compared to the evolution in M0 stars, this range is rather large." It finally shows that good characterization of companions with of 600 K orbiting at angular separations of around an MO star at 10 pc can be achieved., It finally shows that good characterization of companions with of 600 K orbiting at angular separations of around an M0 star at 10 pc can be achieved. " For a GO star at 10 pc, the characterization of companions with a of 900 K is possible at separations of1."," For a G0 star at 10 pc, the characterization of companions with a of 900 K is possible at separations of." "0"".. We study the influence of different data analysis parameters and procedures on the quality factor.", We study the influence of different data analysis parameters and procedures on the quality factor. " To compare the different effects, we focus on the case of an MO star at 10 pc at LRS, with companions of various at an angular separation of1.0"".."," To compare the different effects, we focus on the case of an M0 star at 10 pc at LRS, with companions of various at an angular separation of." " The MRS case was not considered given the fact that only 2 sets of simulation data in J band were available, but the conclusions for LRS would be applicable to MRS, with a possible scaling factor related to the resolution difference."," The MRS case was not considered given the fact that only 2 sets of simulation data in J band were available, but the conclusions for LRS would be applicable to MRS, with a possible scaling factor related to the resolution difference." The two parameters, The two parameters The results in Section 3. as well as 4 demonstrate that the relation between PALL 8 and 24 jam emission exhibits a significant scatter on spatial scales smaller than ~2 kpc.,The results in Section \ref{s_comp_pah24} as well as \ref{s_comp_pah160} demonstrate that the relation between PAH 8 and 24 $\mu$ m emission exhibits a significant scatter on spatial scales smaller than $\sim2$ kpc. In contrast. some ISO results from. comparisons of 7 and 15 jum emission. had. implied. that the ratio of PALL to hot dust. emission should be relatively uniform across the disces of most galaxies (e.g.Rousseletal.2001).," In contrast, some ISO results from comparisons of 7 and 15 $\mu$ m emission had implied that the ratio of PAH to hot dust emission should be relatively uniform across the discs of most galaxies \citep[e.g.][]{retal01}." .. However. some ISO studies actually found significant variations in the 7 qun/15 qun ratio (Llaasetal. 2002).. and even studies that. did find uniform 7 jun/15 gm colours within. the clises of galaxies noted that the ratio might decrease within starbursts in the centres of some galaxies (Roussel 2001).," However, some ISO studies actually found significant variations in the 7 $\mu$ m/15 $\mu$ m ratio \citep{hkb02}, , and even studies that did find uniform 7 $\mu$ m/15 $\mu$ m colours within the discs of galaxies noted that the ratio might decrease within starbursts in the centres of some galaxies \citep{retal01}." . The variations in the (PALL S. //m)/24 jm ratio observed in this subsample of SINGS ealaxics are consistent with results for individual galaxies. such as for M51 (Calzettietal.2005).. MSI (Perez-Gonzalezetal.2006).. and NGC 4631 (Dendoοἱal.2006).," The variations in the (PAH 8 $\mu$ m)/24 $\mu$ m ratio observed in this subsample of SINGS galaxies are consistent with results for individual galaxies, such as for M51 \citep{cetal05}, M81 \citep{petal06}, and NGC 4631 \citep{betal06}." . Moreover. we find that 241 pm emission is more peaked in the centres of regions while the PALL S sam emission is relatively stronger outsideΗ regions. which is consistent with similar phenomena observed in NCC 300 (Llelouetal.2004). NCC 4631 etal. 2006).. ancl ALLOL (Gordonetal.2008).," Moreover, we find that 24 $\mu$ m emission is more peaked in the centres of regions while the PAH 8 $\mu$ m emission is relatively stronger outside regions, which is consistent with similar phenomena observed in NGC 300 \citep{hraetal04}, NGC 4631 \citep{betal06}, and M101 \citep{getal08}." . The variations in the (PALL S jun)/24 pmi ratio are best seen by comparing bright star-forming regions and cilfuse regions., The variations in the (PAH 8 $\mu$ m)/24 $\mu$ m ratio are best seen by comparing bright star-forming regions and diffuse regions. HE. because of the limited. sensitivity of the data. the ratio between PALL and hot dust emission is only measured in the bright regions in some galaxies. as was done bv Rousseletal.(2001).. then the ratio between PALL and hot dust emission may appear uniform.," If, because of the limited sensitivity of the data, the ratio between PAH and hot dust emission is only measured in the bright regions in some galaxies, as was done by \citet{retal01}, then the ratio between PAH and hot dust emission may appear uniform." When these bright regions are compared to dilfuse emission. however. variations mav be seen in the ratio of PAIL to hot. cust. emission.," When these bright regions are compared to diffuse emission, however, variations may be seen in the ratio of PAH to hot dust emission." This may be the primary reason why some results from 190) suggested that the ratio of PALL to hot dust. emission. was uniform in most spiral galaxies whereas variations may beseen in data., This may be the primary reason why some results from ISO suggested that the ratio of PAH to hot dust emission was uniform in most spiral galaxies whereas variations may beseen in data. Acldütionallv. cüllerences between the nature of 15 and 24 jum dust. emission. could. have also contributed. το the dillerences between the 7 j/m/15 yam relation observed.with ISO and the (PALL δ μαι){δε jim relation observed. withSpitzer.," Additionally, differences between the nature of 15 and 24 $\mu$ m dust emission could have also contributed to the differences between the 7 $\mu$ m/15 $\mu$ m relation observedwith ISO and the (PAH 8 $\mu$ m)/24 $\mu$ m relation observed with." Basecl on semi-empirical and theoretical models. the 24 yam band is expected to increase faster than the 15 pm as the illuminating radiation field increases (Daleetal.2001:Li&Draine 2007).," Based on semi-empirical and theoretical models, the 24 $\mu$ m band is expected to increase faster than the 15 $\mu$ m as the illuminating radiation field increases \citep{dhcsk01, ld01, dl07}." . Moreover. unlike the 24 jam band. a significant fraction of the 15 jum band includes PALL emission (Smithetal.2007:Draine 2007).," Moreover, unlike the 24 $\mu$ m band, a significant fraction of the 15 $\mu$ m band includes PAH emission \citep{setal07, dl07}." . Consequently. a comparison of PALL to 24 jim data should exhibit more scatter than a comparison of PALL to 15 pom data.," Consequently, a comparison of PAH to 24 $\mu$ m data should exhibit more scatter than a comparison of PAH to 15 $\mu$ m data." We also found that differences in the distribution of star-forming regions within galaxies could inlluence how the (PALL δ jm)/24 pim ratio varies with 24 jim surface brightness., We also found that differences in the distribution of star-forming regions within galaxies could influence how the (PAH 8 $\mu$ m)/24 $\mu$ m ratio varies with 24$\mu$ m surface brightness. In some galaxies. such as NGC 3351 and NGC 6046. the nucleus is the strongestsite ofstar formation.," In some galaxies, such as NGC 3351 and NGC 6946, the nucleus is the strongestsite of star formation." llence. the location expected to have the lowest (PALL S pm)/24 pam ratio will correspond to the location with 1 highest 24 yam surface brightness. so the data will show ju the (PALL δ yam)/24 jun ratio decreases as the 24 yan surface brightness increases. thus varving as expected. from many mocels of dust. emission (e.g.Daleetal.2001:Li&Draine2001:&Li 2007).," Hence, the location expected to have the lowest (PAH 8 $\mu$ m)/24 $\mu$ m ratio will correspond to the location with the highest 24 $\mu$ m surface brightness, so the data will show that the (PAH 8 $\mu$ m)/24 $\mu$ m ratio decreases as the 24 $\mu$ m surface brightness increases, thus varying as expected from many models of dust emission \citep[e.g.][]{dhcsk01, ld01, dl07}." .. In other galaxies. such as NGC 925 and NGC 2403. the nucleus is not the site of the strongest star formation activity. and many regions can be found at the periphery of the regions that were detected. at. the. 30. level in these data.," In other galaxies, such as NGC 925 and NGC 2403, the nucleus is not the site of the strongest star formation activity, and many regions can be found at the periphery of the regions that were detected at the $3\sigma$ level in these data." While point-like 24 pmi sources should correspond to regions (Prescott 2007)... dust. emission. models such as those presented by Li&Draine (2001).. Daleet (2001).. ancl Draine&Li(2007) suggest that cilfuse 24 pm dust emissionmay. still potentially originate [rom regions outside star-formüng regions with high radiation fieles.,"While point-like 24 $\mu$ m sources should correspond to regions \citep{pkbetal07, cetal07}, , dust emission models such as those presented by \citet{ld01}, , \citet{dhcsk01}, , and \citet{dl07} suggest that diffuse 24 $\mu$ m dust emissionmay still potentially originate from regions outside star-forming regions with high radiation fields." Furthermore. ionising photons may escape from," Furthermore, ionising photons may escape from" "reaching a lew hundred MeV. This exceeds the accepted upper limit (radiation-reaction limit) for photons produced via the svnchrotvon mechanism. ec(9/4)m,c?/og, (where ag=ce?/he is the fine structure constant). obtained by balancing the accelerating electric Loree on a particle e£ with the svnchrotron radiation reaction crag lovee. fatPone/@=2055?D?/8z (where 5 is the Lorentz factor of the particle. Sret/3mec! is the Thomson cross-section and 7L"" means perpendicular to the particles molion). in combination with the requirement £5D., Here we focus on the alternative possibility that electrons are indeed accelerated to very high (PeV) energies in an extended region where $E>B_\perp$. This is impossible in ideal mmagnelohvdrocdvuamies (MIID). E——vxB/e. where e«c is the bulk flow velocity. implving £«Bo (assuming that the particle moves along E).," This is impossible in ideal magnetohydrodynamics (MHD), ${\bf E = - v\times B}/c$, where $v B_{\perp}$ is satisfied naturally in a thin layer." Sulliciently energetic particles tend to be drawn into the laver. where (μον become (rapped and max be accelerated to extreme energies. as was suggested by Ixirk(2004).," Sufficiently energetic particles tend to be drawn into the layer, where they become trapped and may be accelerated to extreme energies, as was suggested by \cite{Kirk-2004}." . By explicitly demonstrating this focusing effect in the ultrarelativisc limit. in (his paper we show that a linear accelerator. utilizing the large-scale electric field. associated with a reconnection process. can explain gamma-ray flares in the Crab.," By explicitly demonstrating this focusing effect in the ultrarelativistic limit, in this paper we show that a linear accelerator, utilizing the large-scale electric field associated with a reconnection process, can explain gamma-ray flares in the Crab." We describe the mechanism in 2 and ils application to the Crab flares in 3., We describe the mechanism in 2 and its application to the Crab flares in 3. Reconnection is generally recognized as an miportant mechanism of non-thermal particle acceleration. including in relativistic pair plasmas thought to exist in the Crab Nebula," Reconnection is generally recognized as an important mechanism of non-thermal particle acceleration, including in relativistic pair plasmas thought to exist in the Crab Nebula" models. based on the growth of initially small density perturbations with gaussian statistics. this takes the general form of a power law tics a gaussian (Press Schechter 1971)): Iu this equation.

is the mean. comoving deusitv of the Uuiverse aud 6(M.:) is the power spectrin as a function of the mass scale. M.,"models, based on the growth of initially small density perturbations with gaussian statistics, this takes the general form of a power law times a gaussian (Press Schechter \cite{PS}) ): In this equation, $<\rho>$ is the mean, comoving density of the Universe and $\sigma(M,z)$ is the power spectrum as a function of the mass scale, $M$." " The quantity is a function of the linear growth factor. Do(2:Q,.A)}. which depends on 9, and A.of the critical density needed for collapse. ὃς, which has ouly a weal dependence on Ορ aud A. aud of o,(AL). the presentday power spectrin. a function of mass oulv."," The quantity is a function of the linear growth factor, $D_{\rm g}(z;\Omo,\Lambda)$ , which depends on $\Omo$ and $\Lambda$,of the critical density needed for collapse, $\delta_c$ , which has only a weak dependence on $\Omo$ and $\Lambda$, and of $\sigma_{\rm o}(M)$, the present–day power spectrum, a function of mass only." " The appearance of D, in the exponcutial of the mass function indicates that the , dependence cau be quite strone: lence. the couunenut that even a σα uuuber of clusters at large 2 can severely constrain the density parameter."," The appearance of $D_{\rm g}$ in the exponential of the mass function indicates that the $\Omo$ dependence can be quite strong; hence, the comment that even a small number of clusters at large $z$ can severely constrain the density parameter." The key poiut is thatparameters (the power spectrum cannot be changed to alter this fact) (Oukbir Blanchard 1997))., The key point is that (the power spectrum cannot be changed to alter this fact) (Oukbir Blanchard \cite{ob}) ). The problem is that we do not measure mass directly: we need some other. more readily observable quantity which correlates well with cluster mass.," The problem is that we do not measure mass directly; we need some other, more readily observable quantity which correlates well with cluster mass." Because we believe that the hot cluster gas is heated by iufall during cluster formation. we expect that the Nray temperature should represeut the depth of the cluster potential well and. therefore. its 11ass.," Because we believe that the hot cluster gas is heated by infall during cluster formation, we expect that the X–ray temperature should represent the depth of the cluster potential well and, therefore, its mass." This las in fact been well established by various lydrodvuamical simulations (n ‘standard’ scenarios) (Evrard et al. 1996)).," This has in fact been well established by various hydrodynamical simulations (in `standard' scenarios) (Evrard et al. \cite{Tsim}) )," which also provide the exact form of the temperaturemass relation., which also provide the exact form of the temperature–mass relation. The Xrav hnuuinositv. on the other haud. is a more coniplicated animal. depending not oulv on the tempcrature of the eas. but also ou its abundance aud spatial distribution.," The X–ray luminosity, on the other hand, is a more complicated animal, depending not only on the temperature of the gas, but also on its abundance and spatial distribution." As we discuss below. observing clusters via the Sunyaev.Zeldovich effect. avoids these problems associated with the Nrav flux. while prescrving the simplicity of a straightforward flux measurement (plus other advantages).," As we discuss below, observing clusters via the Sunyaev–Zel'dovich effect avoids these problems associated with the X–ray flux, while preserving the simplicity of a straightforward flux measurement (plus other advantages)." This is nüportaut because Xray spectra demand spacebased observatious.," This is important because X–ray spectra demand time--consuming, space–based observations." " For our discussion here. we take a plenomenological poiutofview and adopt a powerlaw approximation to the power spectrum: o,=(L/b)(MAMAS)"". where bis the bias parameter aud. My is tle mass contained in a sphere of 87.1Alpe."," For our discussion here, we take a phenomenological point–of–view and adopt a power–law approximation to the power spectrum: $\sigma_{\rm o} = (1/b)(M/M_8)^{-\alpha}$, where $b$ is the bias parameter and $M_8$ is the mass contained in a sphere of $8\; h^{-1}\; {\rm Mpc}$." " We will focus ou the coniparison of two extreme models. a critical model aud an open model with Q=0.2 (fh=IL,/100kii/s/Mpce1/2 in both cases)."," We will focus on the comparison of two extreme models, a critical model and an open model with $\Omega=0.2$ $h=H_o/100\; {\rm km/s/Mpc} = 1/2$ in both cases)." The paralucters b and a for cach model are coustrained by fitting to the local Nrav temperature fiction of galaxy clusters (IHoeury Arnaud 19913). the results of which are given in the Table (Oukbir et al. 1997:," The parameters $b$ and $\alpha$ for each model are constrained by fitting to the local X–ray temperature function of galaxy clusters (Henry Arnaud \cite{ha}) ), the results of which are given in the Table (Oukbir et al. \cite{obb};" Oukhbir Blanchard 1997)., Oukbir Blanchard \cite{ob}) ). The Suuvaev-Zeldovich effect offers unique advantages for finding high redshift clusters aud quautifving their abuudance., The Sunyaev-Zel'dovich effect offers unique advantages for finding high redshift clusters and quantifying their abundance. " The surface brightuess of a cluster relative to the unperturbed CAIB is expressed as a product of a spectral function. των aud theperamcter, which is an iuteeral of the electron pressure along the lineofsight: yxfloT."," The surface brightness of a cluster relative to the unperturbed CMB is expressed as a product of a spectral function, $j_\nu$, and the, which is an integral of the electron pressure along the line–of–sight: $y\propto \int dl\; n_e T$." Integratingthe surface brightucss over solid anele vields the following functional form for the total flux density of a cluster with aneular size 0:, Integratingthe surface brightness over solid angle yields the following functional form for the total flux density of a cluster with angular size $\theta$ : correlations on scales in our metric equivalent to ~1—8 kpc (for all observers on the Solar circle).,correlations on scales in our metric equivalent to $\sim 1-8$ kpc (for all observers on the Solar circle). " Most of the models are consistent with the Milky Way data for the outer halo, r>30 kpc."," Most of the models are consistent with the Milky Way data for the outer halo, $r>30$ kpc." " For the inner halo, however, particularly at galactocentric distances smaller than 20 kpc, the simulations tend to be significantly more strongly clustered than the data."," For the inner halo, however, particularly at galactocentric distances smaller than 20 kpc, the simulations tend to be significantly more strongly clustered than the data." " One possible explanation for this is a deficiency of smoothly distributed halo stars in the models, perhaps attributable to the absence of so-called ‘in situ’ halo stars."," One possible explanation for this is a deficiency of smoothly distributed halo stars in the models, perhaps attributable to the absence of so-called `in situ' halo stars." " These stars may be scattered from the Galactic disc, or born on eccentric orbits (in streams of accreted gas or an unstable cooling flow, for example)."," These stars may be scattered from the Galactic disc, or born on eccentric orbits (in streams of accreted gas or an unstable cooling flow, for example)." Neither of these processes are included in our model of the accreted halo., Neither of these processes are included in our model of the accreted halo. " Although it seems reasonable to expect that in situ haloes are distributed with spherical or axial symmetry and have a low degree of coherence in phase space, models of such components and predictions for the fraction of stars they contain are not well constrained."," Although it seems reasonable to expect that in situ haloes are distributed with spherical or axial symmetry and have a low degree of coherence in phase space, models of such components and predictions for the fraction of stars they contain are not well constrained." Most hypotheses for in situ halo formation limit these stars to an ‘inner’ halo and predict that the accreted component (which we simulate) dominates at larger radii (e.g. Abadi 2006; Zolotoval. 2009; Font 2011)., Most hypotheses for in situ halo formation limit these stars to an `inner' halo and predict that the accreted component (which we simulate) dominates at larger radii (e.g. Abadi 2006; Zolotov 2009; Font 2011). " However, the fraction of the halo formed in situ and the boundary between 'inner' and ‘outer’ halo are highly model-dependent."," However, the fraction of the halo formed in situ and the boundary between `inner' and `outer' halo are highly model-dependent." " Detections of observable *dichotomies' in the Milky Way halo (Carollo 2007) are still debated (e.g. Schónnrich, Asplund Casagrande 2011; Beers 2011)."," Detections of observable `dichotomies' in the Milky Way halo (Carollo 2007) are still debated (e.g. Schönnrich, Asplund Casagrande 2011; Beers 2011)." " It is possible to place broad limits on the fraction of stars in a *missing' smooth component, for example by comparing the RMS variation of projected star-counts in our models (Helmi 2011b) to the Milky Way (Bell 2008)."," It is possible to place broad limits on the fraction of stars in a `missing' smooth component, for example by comparing the RMS variation of projected star-counts in our models (Helmi 2011b) to the Milky Way (Bell 2008)." " However, the uncertainties involved are substantial."," However, the uncertainties involved are substantial." Another factor in the discrepancy between the models and the data may be the absence of a baryonic (disc) contribution to the gravitational potential., Another factor in the discrepancy between the models and the data may be the absence of a baryonic (disc) contribution to the gravitational potential. " A massive disc could alter the process of satellite disruption in the inner halo and might make the potential within 30 kpc more spherical (Kazantzidis, Abadi Navarro 2010), possibly distributing more inner halo stars into the SDSS footprint (on the other hand, a more axisymmetric or spherical dark halo might also result in fewer chaotic orbits, hence more coherent streams)."," A massive disc could alter the process of satellite disruption in the inner halo and might make the potential within $30$ kpc more spherical (Kazantzidis, Abadi Navarro 2010), possibly distributing more inner halo stars into the SDSS footprint (on the other hand, a more axisymmetric or spherical dark halo might also result in fewer chaotic orbits, hence more coherent streams)." " Because of these modelling uncertainties, our application of the statistic can presently serve only as a basic test for the abundance of substructure in the simulations."," Because of these modelling uncertainties, our application of the statistic can presently serve only as a basic test for the abundance of substructure in the simulations." Several aspects of our approach could be improved., Several aspects of our approach could be improved. It seems desirable to use well-measured radial velocity data to enhance clustering signals such as our correlation function relative to those based on configuration space data alone., It seems desirable to use well-measured radial velocity data to enhance clustering signals such as our correlation function relative to those based on configuration space data alone. " However, so far, no proposal for including these velocity data is well-supported by theory."," However, so far, no proposal for including these velocity data is well-supported by theory." " Here, we have used a straightforward choice of parametrised metric to illustrate the concept of scaling radial velocity separations to ‘equivalent’ configuration space separations, and this is empirically useful in recovering a measurable signal."," Here, we have used a straightforward choice of parametrised metric to illustrate the concept of scaling radial velocity separations to `equivalent' configuration space separations, and this is empirically useful in recovering a measurable signal." " Nevertheless, we have not found any compelling or generic way to select the scaling parameter (w,)."," Nevertheless, we have not found any compelling or generic way to select the scaling parameter $w_{v}$ )." Improving either the definition of the metric itself or the means of fixing this parameter is a clear priority for extensions of this approach., Improving either the definition of the metric itself or the means of fixing this parameter is a clear priority for extensions of this approach. A similar issue affects the weighting of velocity information in clustering algorithms (e.g. Sharma 2010)., A similar issue affects the weighting of velocity information in clustering algorithms (e.g. Sharma 2010). " Finally, further comparisons between stellar halo models and observational data should also account for the selection effects such spectroscopic incompleteness and the potential bias of BHB stars as a tracer of the stellar halo (Bell 2010; Xueal. 2011)."," Finally, further comparisons between stellar halo models and observational data should also account for the selection effects such spectroscopic incompleteness and the potential bias of BHB stars as a tracer of the stellar halo (Bell 2010; Xue 2011)." " For statistical analysis, there is a pressing requirement for observational samples with well-understood selection functions, even if they do not probe the most distant halo."," For statistical analysis, there is a pressing requirement for observational samples with well-understood selection functions, even if they do not probe the most distant halo." The LAMOST Galactic survey is likely to be the first to approach this goal., The LAMOST Galactic survey is likely to be the first to approach this goal. " In summary, we have taken a first step in adapting a well- cosmological statistic, the two-point correlation function, to the study of the Milky Way halo."," In summary, we have taken a first step in adapting a well-studied cosmological statistic, the two-point correlation function, to the study of the Milky Way halo." " Our comparisons highlight the complexity of statistical analysis in the stellar halo, and the importance of interpreting observational results in the context of realistic models of halo assembly."," Our comparisons highlight the complexity of statistical analysis in the stellar halo, and the importance of interpreting observational results in the context of realistic models of halo assembly." We have compared the SDSS data with the stellar halos produced by disrupted satellites in galaxy formation models constructed from the Aquarius N- simulations of galactic dark halos in the ACDM cosmology., We have compared the SDSS data with the stellar halos produced by disrupted satellites in galaxy formation models constructed from the Aquarius N-body simulations of galactic dark halos in the $\Lambda$ CDM cosmology. " With further refinements and more data, our statistical approach to quantifying the smoothness of the halo can provide a practical and productive way to study the structure of the Milky Way halo and compare with theoreticalexpectations."," With further refinements and more data, our statistical approach to quantifying the smoothness of the halo can provide a practical and productive way to study the structure of the Milky Way halo and compare with theoreticalexpectations." sources. they are thought to have higher conversion efliciency of jet kinetic energy. (ο radio ]uminositv.,"sources, they are thought to have higher conversion efficiency of jet kinetic energy to radio luminosity." For J14274-3312. the radio lobes would be the two dominant components seen in the 1.4 Gllz VLBA results. which are separated by 174 pe.," For J1427+3312, the radio lobes would be the two dominant components seen in the 1.4 GHz VLBA results, which are separated by 174 pc." In this model. the core. which would have an inverted or flat spectzum (Tavlor.Readhbead.&Pearson1996).. would be faint and below our detection threshold.," In this model, the core, which would have an inverted or flat spectrum \citep{TRP96}, would be faint and below our detection threshold." In CsOs. anv radio component that is coincident with the central engine is comparatively weak. with flux densities of only a few percent of the total flux density. (Reaclheadetal.1996).," In CSOs, any radio component that is coincident with the central engine is comparatively weak, with flux densities of only a few percent of the total flux density \citep{RTXPWP96}." . Classifving this source as a CSO. where the radio lobes are confined by a dense ambient medium. is also consistent with its being a BALQSO (AleGreeretal.2006).," Classifying this source as a CSO, where the radio lobes are confined by a dense ambient medium, is also consistent with its being a BALQSO \citep{MCG06}." .. This is in agreement with recent X-ray observations which suggest that the presence of massive. highly ionized. and high-velocity outflows in BALQSOs may be providing significant feedback to the surrounding gas (Chartasetal.2007).," This is in agreement with recent X-ray observations which suggest that the presence of massive, highly ionized, and high-velocity outflows in BALQSOs may be providing significant feedback to the surrounding gas \citep{CH07}." . In general. the higher average gas densities expected in the earliest galaxies might lead to a higher fraction of CSO sources.," In general, the higher average gas densities expected in the earliest galaxies might lead to a higher fraction of CSO sources." Alulti-epoch and multi-frequency VLBI observations carried oul by on three CSOs have shown typical advance speeds of ~0.3c., Multi-epoch and multi-frequency VLBI observations carried out by \citet{TMPR00} on three CSOs have shown typical advance speeds of $\sim 0.3c$. Adopting this value for J1427-2-3312. and assuming equal speeds [or the two radio lobes. we derive a kinematic age of ~10? vr. indicating that the 2=6.12 QSO is a very voung radio source.," Adopting this value for J1427+3312, and assuming equal speeds for the two radio lobes, we derive a kinematic age of $\sim 10^3$ yr, indicating that the $z=6.12$ QSO is a very young radio source." With overwhelming majority of CSOs (> σος) showing HI 21 em absorption lines with optical depth levels between and and line widths ranging between about 50 and 500 km ! (Pecketal.2000).. the z=6.12 QSO J14272-3312. which is believed to be near the Epoch of Reionization. would be an excellent candidate for HI absorption experiments to detect the neutral IGM in its host galaxy. (Furlanetto&Loeb2002).," With overwhelming majority of CSOs $\geq$ ) showing HI 21 cm absorption lines with optical depth levels between and and line widths ranging between about 50 and 500 km $^{-1}$ \citep{PECK00}, the $z=6.12$ QSO J1427+3312, which is believed to be near the Epoch of Reionization, would be an excellent candidate for HI absorption experiments to detect the neutral IGM in its host galaxy \citep{FL02}." . Such a search is currently underway using the Giant Meterwave hadio Telescope (GAIRT)., Such a search is currently underway using the Giant Meterwave Radio Telescope (GMRT). Ixnowledge of source structure. as presented herein. is critical for both identilving potential candidates for III 21 em absorption searches and for subsequent interpretation of the results.," Knowledge of source structure, as presented herein, is critical for both identifying potential candidates for HI 21 cm absorption searches and for subsequent interpretation of the results." The high resolution radio imagine presented here sets constraints on the hypothesis that Jl427+3312 has undergone strong gravitational lensing resulting in multiple images., The high resolution radio imaging presented here sets constraints on the hypothesis that J1427+3312 has undergone strong gravitational lensing resulting in multiple images. The VLA 3.4 Gllz imaging rules ont multiple images separated bv >0.2 and with a flux ralio <8:Il., The VLA 8.4 GHz imaging rules out multiple images separated by $ > 0\rlap{.}^{''}2$ and with a flux ratio $< 8:1$. The VLBA 1.4 Gllz imaging sets similar constraints down to the mas scale., The VLBA 1.4 GHz imaging sets similar constraints down to the mas scale. " The expected lensing svstem for a z6 quasar is a singular isothermal ellipsoid (SIE). with image pairs having separations S1"" and flux ratios <10:1 (Turneretal.1954)."," The expected lensing system for a $z \sim 6$ quasar is a singular isothermal ellipsoid (SIE), with image pairs having separations $\lesssim 1''$ and flux ratios $< 10:1$ \citep{TOG84}." . The typical lens svstem is thus ruled out. and only a high magnification or small separation lensing event is allowed by the images obtained [rom these radio observations.," The typical lens system is thus ruled out, and only a high magnification or small separation lensing event is allowed by the images obtained from these radio observations." On the other hand. the possible lant. component in the VLBA image to the east," On the other hand, the possible faint component in the VLBA image to the east" 2006).,2006). In contrast the Dzlx galaxies studied by Dacddi et al. (, In contrast the BzK galaxies studied by Daddi et al. ( 2010) have similarly high SFRs but lower dense gas fractions.,2010) have similarly high SFRs but lower dense gas fractions. " Their hieh star formation rales appear to result from hieh global molecular gas mass fractions (ie. Myjj,/M,). as might be expected for very. voung galaxies,"," Their high star formation rates appear to result from high global molecular gas mass fractions (i.e., $_{H_2}$ $_*$ ), as might be expected for very young galaxies." " We note Chat a linear relation in the SFR-Alass plane should transform (o a linear relation in the X4,5-X, plane (provided the surface densities lor the galaxies are global averages) and we can express our star formation scaling law in (his latter plane as: where X, refers to the II» gas mass.", We note that a linear relation in the SFR-Mass plane should transform to a linear relation in the $\Sigma_{SFR}$ $\Sigma_{g}$ plane (provided the surface densities for the galaxies are global averages) and we can express our star formation scaling law in this latter plane as: where $\Sigma_{g}$ refers to the $_2$ gas mass. Moreover. the Spitzer study of Galactic clouds by Ileiderman οἱ al. (," Moreover, the Spitzer study of Galactic clouds by Heiderman et al. (" 2010) suggestedS6 a linear star formation law in the τομSLR 9 plane that holds for egas above a threshold surface density of 130 7? (hes Ay > 0.9 mag) and extrapolates smoothly to the GS04 galaxies.,"2010) suggested a linear star formation law in the $\Sigma_{SFR}$ $\Sigma_{g}$ plane that holds for gas above a threshold surface density of $\sim$ 130 $^{-2}$ (i.e., $_K$ $>$ 0.9 mag) and extrapolates smoothly to the GS04 galaxies." Our result is apparently not consistent with the standard Schmidt-Ixennicutt. linear. scaling law (Ixennieutt 19983a).," Our result is apparently not consistent with the standard Schmidt-Kennicutt, super-linear, scaling law (Kennicutt 1998a)." Both are based on valid empirical relations., Both are based on valid empirical relations. However. here we argue that the underlving scaling law for star formation is linear over all scales for all clouds ancl galaxies. provided thev are characterized by the same dense gas Iraction.," However, here we argue that the underlying scaling law for star formation is linear over all scales for all clouds and galaxies, provided they are characterized by the same dense gas fraction." Kennicutt (1998a) uses total (ILE + Is) gas mass surface densities with CO derived molecular masses and combines results lor both normal star-forming disk galaxies and starburst galaxies to derive his star formation sealing law., Kennicutt (1998a) uses total (HI $+$ $_2$ ) gas mass surface densities with CO derived molecular masses and combines results for both normal star-forming disk galaxies and starburst galaxies to derive his star formation scaling law. Note that [or these latter galaxies the total gas surface densities are dominated by the molecular component., Note that for these latter galaxies the total gas surface densities are dominated by the molecular component. " The starbursts dominate his relation for X44, > LOO 7.", The starbursts dominate his relation for $\Sigma_{gas}$ $>$ 100 $^{-2}$. It is possible that the fit of a single relation to the combined sample wilh CO determined masses is inappropriate aud skewed by (he starbursts because foc for starbursts is hieher (han that for normal star forming spirals., It is possible that the fit of a single relation to the combined sample with CO determined masses is inappropriate and skewed by the starbursts because $f_{DG}$ for starbursts is higher than that for normal star forming spirals. Iideed. Gao and Solomon (2004) showed that using the masses calculated from the CO observations produced a super-linear (n 7 1.7) scaling law (in the SFR vs Me; plane) lor a sample that included their galaxies and an additional nunber of luminous starbursts drawn form the literature.," Indeed, Gao and Solomon (2004) showed that using the masses calculated from the CO observations produced a super-linear (n $\approx$ 1.7) scaling law (in the SFR vs $_G$ plane) for a sample that included their galaxies and an additional number of luminous starbursts drawn form the literature." Using gas masses derived solely Grom HHC€N observations. however. produces a linear star formation law connecting both normal star forming galaxies and starbursts.," Using gas masses derived solely from HCN observations, however, produces a linear star formation law connecting both normal star forming galaxies and starbursts." The standard Schmidt-Ixennieutt relation may also be skewed at low mass surface densities., The standard Schmidt-Kennicutt relation may also be skewed at low mass surface densities. " For galaxies in (his portion of the diagram. the ILE surface density is a large Iraction of the total gas surface density and thus the measured total gas surface density. Xj,|yp. contains a large component of inert. non-star Forming. (HI) eas: this dilutes and lowers the SFR corresponding to a fixed mass surface density. resulting in a steepening of the slope of the Magy vs X, relation."," For galaxies in this portion of the diagram, the HI surface density is a large fraction of the total gas surface density and thus the measured total gas surface density, $\Sigma_{HI + H_2}$, contains a large component of inert, non-star forming, (HI) gas; this dilutes and lowers the SFR corresponding to a fixed mass surface density, resulting in a steepening of the slope of the $\Sigma_{SFR}$ vs $\Sigma_{gas}$ relation." These two effects. the increasing dense gas fraction for the starbursts and the dilution of," These two effects, the increasing dense gas fraction for the starbursts and the dilution of" "turbulence (e.g.Perez&Boldyrev2008,2009;Beresnyak2011).","turbulence \citep[e.g.][]{perez08,perez09,beresnyak11}." ". They can be written in Elsasser potentials (Schekochihinetal. where {A,B}=Z-(V,AxV_B), 2 is the global mean field direction, v4 is the sspeed and the Elsasser potentials are defined via óz;=du,+ób,—2xVj,6-."," They can be written in Elsasser potentials \citep{schekochihin09}: : where $\left\{A,B\right\} = \mathbf{\hat{z}}\cdot\left(\nabla_\perp A\times\nabla_\perp B\right)$, $\mathbf{\hat{z}}$ is the global mean field direction, $v_A$ is the speed and the Elsasser potentials are defined via $\delta\mathbf{z}_\perp^\pm=\delta\mathbf{u}_\perp\pm\delta\mathbf{b}_\perp=\mathbf{\hat{z}}\times\nabla_\perp\zeta^\pm$ ." " Equations (4)) contain only the perpendicular fluctuations and are, therefore, suitable for simulating tturbulence."," Equations \ref{eq:rmhd}) ) contain only the perpendicular fluctuations and are, therefore, suitable for simulating turbulence." " They are also more efficient to simulate than MHD, since they involve only two scalar fields."," They are also more efficient to simulate than MHD, since they involve only two scalar fields." " Although originally derived from MHD, it has been shown that RMHD holds for a collisionless plasma such as the solar wind and may, therefore, be more generally applicable (Schekochihinetal.2009)."," Although originally derived from MHD, it has been shown that RMHD holds for a collisionless plasma such as the solar wind and may, therefore, be more generally applicable \citep{schekochihin09}." ". The RMHD derivation assumes anisotropy (k,> Kj) and a strong mean field (Bg>>5B, ), both of which are observed at the smallest scales of the solar wind inertial range."," The RMHD derivation assumes anisotropy $k_{\perp} \gg k_{\para}$ ) and a strong mean field $B_0 \gg \delta \mathbf{B}_{\perp}$ ), both of which are observed at the smallest scales of the solar wind inertial range." The simulation reported here solves the RMHDequations in a triply periodic cube of size (2z)? with a resolution of 5123., The simulation reported here solves the RMHDequations in a triply periodic cube of size $(2\pi)^3$ with a resolution of $512^3$. The sspeed is set to v4=1 (making the ccrossing time 21)., The speed is set to $v_A=1$ (making the crossing time $2\pi$ ). " It can be seen from equations (4)) that if the sspeed is scaled by a factor R and the z coordinate, which is the mean field direction, is also scaled by R, the equations remain identical."," It can be seen from equations \ref{eq:rmhd}) ) that if the speed is scaled by a factor $R$ and the $z$ coordinate, which is the mean field direction, is also scaled by $R$, the equations remain identical." " This means that a given simulation corresponds to all values of R, and therefore all values of 5B,/Bo if the box is also stretched in the z direction."," This means that a given simulation corresponds to all values of $R$, and therefore all values of $\delta\mathbf{B}_{\perp}/B_0$ if the box is also stretched in the $z$ direction." The units of length in the perpendicular and parallel directions are independent of each other because the anisotropy is formally infinite and the fluctuation level is infinitely small under the RMHD asymptotic expansion., The units of length in the perpendicular and parallel directions are independent of each other because the anisotropy is formally infinite and the fluctuation level is infinitely small under the RMHD asymptotic expansion. " Different values of R can be chosen, setting the anisotropy and fluctuation level so that the same simulation can be compared to a variety of real world situations."," Different values of $R$ can be chosen, setting the anisotropy and fluctuation level so that the same simulation can be compared to a variety of real world situations." " The equations are solved pseudospectrally in x and y, and using a centred finite difference scheme in z."," The equations are solved pseudospectrally in $x$ and $y$, and using a centred finite difference scheme in $z$." The time step is chosen so that the Courant numbers based on both the fluctuation amplitude and the sspeed are much less than unity., The time step is chosen so that the Courant numbers based on both the fluctuation amplitude and the speed are much less than unity. With dissipation and forcing terms the equations are where v=5x107? and v;=1x107 are the viscosity coefficients and f~ is the forcing term., With dissipation and forcing terms the equations are where $\nu=5\times10^{-15}$ and $\nu_z=1\times10^{-4}$ are the viscosity coefficients and $f^\pm$ is the forcing term. " In the x and y directions, a 4th order hyperviscosity dissipation term is used, while in the z direction a very small Laplacian viscosity is added to prevent the high k, modes becoming unstable."," In the $x$ and $y$ directions, a 4th order hyperviscosity dissipation term is used, while in the $z$ direction a very small Laplacian viscosity is added to prevent the high $k_z$ modes becoming unstable." Hyperviscosity is used so that the inertial range covers a wide enough range of scales to measure accurate scalings., Hyperviscosity is used so that the inertial range covers a wide enough range of scales to measure accurate scalings. " The magnetic Prandtl number is Prm=1 and the initial conditions are straight mean field with no fluctuations: b(r,t20) Zand u(r,ta20)—0."," The magnetic Prandtl number is $\text{Pr}_\text{m}=1$ and the initial conditions are a straight mean field with no fluctuations: $\mathbf{b}(\mathbf{r},t=0)=\mathbf{\hat{z}}$ and $\mathbf{u}(\mathbf{r},t=0)=0$." " The simulation is initially forced on large scales (Κι=1,2 and k,= 1) with Gaussian white noise forcing f, i.e. the random forcing amplitude is refreshed at each time step."," The simulation is initially forced on large scales $k_\perp=1,2$ and $k_z=1$ ) with Gaussian white noise forcing $f^\pm$, i.e. the random forcing amplitude is refreshed at each time step." This means that the input power can be controlled; it is set to unity in the code units to produce strong turbulence., This means that the input power can be controlled; it is set to unity in the code units to produce strong turbulence. " We choose to force only the velocity to match possible sources of solar wind forcing, such as velocity shears or large scale wwaves, so f*=f at all times."," We choose to force only the velocity to match possible sources of solar wind forcing, such as velocity shears or large scale waves, so $f^+=f^-$ at all times." We do not force the magnetic field since there is no known mechanism of breaking magnetic flux conservation at large scales., We do not force the magnetic field since there is no known mechanism of breaking magnetic flux conservation at large scales. " After a while, the forcing is removed and the simulation is left to freely decay."," After a while, the forcing is removed and the simulation is left to freely decay." A time series of various simulation parameters is shown in Fig. 4.., A time series of various simulation parameters is shown in Fig. \ref{fig:timeseries}. " After the simulation begins, the values take a few time units to settle down, which is roughly the turnover time of the largest eddies."," After the simulation begins, the values take a few time units to settle down, which is roughly the turnover time of the largest eddies." " The transition between the forced and decaying periods of the simulation can be seen by the change in behaviour of all the quantities at t=28, marked by the dashed line."," The transition between the forced and decaying periods of the simulation can be seen by the change in behaviour of all the quantities at $t=28$, marked by the dashed line." " The top two panels show the root mean square (RMS) values of the Elsasser variables, velocity and magnetic field."," The top two panels show the root mean square (RMS) values of the Elsasser variables, velocity and magnetic field." Their values up to t=28 are determined by the forcing power and after t=28 by the decay of the turbulence., Their values up to $t=28$ are determined by the forcing power and after $t=28$ by the decay of the turbulence. " One noticeable feature is the oscillation in the velocity and magnetic field RMS values with a period =27.This is most likely due to large scale wwaves,also seen by Bigotetal. (2008), which should not significantly affect the average inertial range measurements."," One noticeable feature is the oscillation in the velocity and magnetic field RMS values with a period $\approx 2\pi$.This is most likely due to large scale waves,also seen by \citet{bigot08a}, , which should not significantly affect the average inertial range measurements." " The normalised cross helicity o; in the third panel is calculated spectrally [equation (1))], as was done for the solar wind intervals in Section 2.1,, and averaged over the range 7«Κι< 33."," The normalised cross helicity $\sigma_c$ in the third panel is calculated spectrally [equation \ref{eq:sigmac}) )], as was done for the solar wind intervals in Section \ref{sec:swintervals}, , and averaged over the range $7\leq k_\perp\leq 33$ ." are dominated. by evelic or periodic phase variations.,are dominated by cyclic or periodic phase variations. An important issue would be to determine why in some Blazhko stars the modulation is dominated by amplitude variations. while in others it is dominated by phase oscillations.," An important issue would be to determine why in some Blazhko stars the modulation is dominated by amplitude variations, while in others it is dominated by phase oscillations." Signilicantlv. dillerent. frequencies of the modulation have been derived for dillerent epochs for two Blazhko stars (V2 and V14). whieh cannot be explained. by continuous changes of the modulation period.," Significantly different frequencies of the modulation have been derived for different epochs for two Blazhko stars (V2 and V14), which cannot be explained by continuous changes of the modulation period." The ratios of the detected modulation periods are close to 2:1 and 4:3 for V2 and VI4. respectively.," The ratios of the detected modulation periods are close to 2:1 and 4:3 for V2 and V14, respectively." Another case of strong multiperiodicity of the modulation has been documented. in Sódorοἱal.(2010.CZ Lacertae).., Another case of strong multiperiodicity of the modulation has been documented in \citet[][CZ Lacertae]{czl}. Phe modulation frequencies detected in CZ Lac were very close to 3:4 and. 4:5 resonances., The modulation frequencies detected in CZ Lac were very close to 3:4 and 4:5 resonances. Rich modulation frequency patterns with multiplets of the same modulation frequency. were revealed in extended. accurate observations of some Blazhko stars (MW.LyranclV1127λαinJuresik.etal.2008a:Chacliclh 2010).," Rich modulation frequency patterns with multiplets of the same modulation frequency were revealed in extended, accurate observations of some Blazhko stars \citep[MW Lyr and V1127 Aql in][]{mwI,aql}." . In dese cases the dominant. modulation corresponded to the shortest. [requeney. component of the multiplets., In these cases the dominant modulation corresponded to the shortest frequency component of the multiplets. Lowever. 10 examples of V2. Vid and CZ Lac show that in some Blazhko stars. from time to time. cillerent components of a hidden modulation. frequency. multiplet may. emerge.," However, the examples of V2, V14 and CZ Lac show that in some Blazhko stars, from time to time, different components of a hidden modulation frequency multiplet may emerge." If these modulations correspond. to. elements. of series. of equidistant-spacing multiplets. their frequency. ratios are ‘lose to fractions of small integer numbers.," If these modulations correspond to elements of series of equidistant-spacing multiplets, their frequency ratios are close to fractions of small integer numbers." " This indicates wt the observed. mocdulation-frequeney values may. not always correspond to the ""base frequency. re. the shortest frequeney component of a multiplet."," This indicates that the observed modulation-frequency values may not always correspond to the `base frequency', i.e. the shortest frequency component of a multiplet." One must be cautious in interpreting the data., One must be cautious in interpreting the data. Using a large sample of Blazhko variables. including stars from the galactic field. elobular clusters. the ealactic bulge. the LAIC and the Sagittarius-dwarl galaxy. Jurcsikοἱal.(2005) showed that the larger the pulsation frequeney of a Blazhko star is. the larger its modulation frequency. can be.," Using a large sample of Blazhko variables, including stars from the galactic field, globular clusters, the galactic bulge, the LMC and the Sagittarius-dwarf galaxy, \cite{acta} showed that the larger the pulsation frequency of a Blazhko star is, the larger its modulation frequency can be." Phe modulation versus pulsation frequencies of the M5 Blazhko variables are plotted in Fig. 27..," The modulation versus pulsation frequencies of the M5 Blazhko variables are plotted in Fig. \ref{mod}," and it appears that a similar trend might occur in. ALS., and it appears that a similar trend might occur in M5. However. the ranges of the observed. pulsation and. modulation. frequencies are much smaller in M5 than in the sample investigated: by Juresiketal.(2005).," However, the ranges of the observed pulsation and modulation frequencies are much smaller in M5 than in the sample investigated by \cite{acta}." . Most. probably. if à relation between the pulsation and the modulation frequencies indeed exists. its actual form strongly depends on the global parameters of the stellar population studied (e.g. luminosity. chemical composition. age. etc.).," Most probably, if a relation between the pulsation and the modulation frequencies indeed exists, its actual form strongly depends on the global parameters of the stellar population studied (e.g, luminosity, chemical composition, age, etc.)." The long time-base of the observations of the M5 variables also made it possible to determine the modulation properties at different epochs for some variables., The long time-base of the observations of the M5 variables also made it possible to determine the modulation properties at different epochs for some variables. Significant changes in the modulation properties were already. detected, Significant changes in the modulation properties were already detected The source GX 339-4 is a well known stellar-mass Galactic black hole candidate.,The source GX 339-4 is a well known stellar-mass Galactic black hole candidate. This bright variable X-ray source was first observed during the survey period from October 197] to January 1973 by the MIT X-ray detector on-board the OSO-7 satellite in the energy range of 1-60 keV. GX 339-4. a transient low-mass X-ray binary (LMXB) system located at 4.9)=(338°.93.-4°.27) (Markert et al.," This bright variable X-ray source was first observed during the survey period from October 1971 to January 1973 by the MIT X-ray detector on-board the OSO-7 satellite in the energy range of 1-60 keV. GX 339-4, a transient low-mass X-ray binary (LMXB) system located at $(l,b) = (338^\circ.93,-4^\circ.27)$ (Markert et al." " 1973) with R.A.=17""02""495,36 and Dee.= —48°47'22"".8 (J2000).", 1973) with $17^h~02^m~49^s.36$ and Dec.= $-48^\circ~47'~22''.8$ (J2000). The optical spectroscopic study indicates that the mass function of the source is M = 5.8+0.5M. and the distance D = 6 kpe (Hynes et al., The optical spectroscopic study indicates that the mass function of the source is $M$ = $5.8\pm0.5~M_\odot$ and the distance $D$ = $6$ kpc (Hynes et al. 2003. 2004).," 2003, 2004)." Since its discovery. GX 339-4 has undergone several outburst’ phases. during which the source was observed in different wavebands to reveal the nature in multiple wavelengths (Liu et al.," Since its discovery, GX 339-4 has undergone several outburst phases, during which the source was observed in different wavebands to reveal the nature in multiple wavelengths (Liu et al." 2001. Homan et al.," 2001, Homan et al." 2005)., 2005). During the RXTE era (1996 onward). this source exhibited frequent X-ray outbursts (1998. 2002/2003. 2004/2005. 2006/2007) at a 2-3 years of interval with very low luminosity states in between each episode.," During the RXTE era (1996 onward), this source exhibited frequent X-ray outbursts (1998, 2002/2003, 2004/2005, 2006/2007) at a 2-3 years of interval with very low luminosity states in between each episode." The complex outburst profile in each epoch generally begins and ends in the low/hard state. which is quite common in other outburst candidate of black holes (e.g.. GRO J1655-40. ΝΤΕ J1550-564).This general behavior is understood to be caused by sudden variation of viscosity in the system (Mandal Chakrabarti. 2010). which in turn causes the accretion rate of the standard Shakura-Sunyaev (1973) disk (hereafter referred to as the Keplerian rate) to rise and possibly makes the inner edge move in.," The complex outburst profile in each epoch generally begins and ends in the low/hard state, which is quite common in other outburst candidate of black holes (e.g., GRO J1655-40, XTE This general behavior is understood to be caused by sudden variation of viscosity in the system (Mandal Chakrabarti, 2010), which in turn causes the accretion rate of the standard Shakura-Sunyaev (1973) disk (hereafter referred to as the Keplerian rate) to rise and possibly makes the inner edge move in." These transient black hole candidates show low and intermediate frequency quasi-periodic oscillations (QPOs) in their power density spectra., These transient black hole candidates show low and intermediate frequency quasi-periodic oscillations (QPOs) in their power density spectra. In general. during the rising hard state of the outburst the frequency of the QPO increases. whereas during the declining phase. the QPO frequency is gradually decreased.," In general, during the rising hard state of the outburst the frequency of the QPO increases, whereas during the declining phase, the QPO frequency is gradually decreased." The QPO evolution in these objects can be well understood through the propagating oscillatory shocks (POS: Chakrabarti et al., The QPO evolution in these objects can be well understood through the propagating oscillatory shocks (POS; Chakrabarti et al. 2008. 2009).," 2008, 2009)." Though several studies of the evolution of the temporal and spectral states of GX 339-4 during the previous outbursts were carried out (Nowak et al., Though several studies of the evolution of the temporal and spectral states of GX 339-4 during the previous outbursts were carried out (Nowak et al. " 1999, Belloni et al."," 1999, Belloni et al." 2005: Motta. Belloni Homan 2009). the underlying physical processes remained unclear.," 2005; Motta, Belloni Homan 2009), the underlying physical processes remained unclear." Our attempt here ts to see if the POS solution of our group can also explain the present outburst., Our attempt here is to see if the POS solution of our group can also explain the present outburst. Note that for the traditional soft-X-ray transients with fast rise and exponential decay (FRED) lightcurve with typically long recurrence times. there are so-called disk instability models (Cannizzo. 1993: Lasota. 1996) where matter also moves in owing to viscous processes.," Note that for the traditional soft-X-ray transients with fast rise and exponential decay (FRED) lightcurve with typically long recurrence times, there are so-called disk instability models (Cannizzo, 1993; Lasota, 1996) where matter also moves in owing to viscous processes." However these models do not address variations of QPOs., However these models do not address variations of QPOs. Recently. after remaining in the quiescent state for three long years (except for a short spell of very weak activity in 2009 as observed in SWIFT/BAT). GX 339-4 became X-ray-active again on 2010 January 03. with a first detection by MAXI/GSC onboard HETE (Yamaoka et al.," Recently, after remaining in the quiescent state for three long years (except for a short spell of very weak activity in 2009 as observed in SWIFT/BAT), GX 339-4 became X-ray-active again on 2010 January 03, with a first detection by MAXI/GSC onboard HETE (Yamaoka et al." 2010)., 2010). Immediately after the announcement of the X-ray trigger. RXTE started monitoring the source from 2010 January 12 (Tomsick. 2010).," Immediately after the announcement of the X-ray trigger, RXTE started monitoring the source from 2010 January 12 (Tomsick, 2010)." During the initial outburst phase. the source was in the low-hard state without any signature of QPO in the power density spectrum (PDS).," During the initial outburst phase, the source was in the low-hard state without any signature of QPO in the power density spectrum (PDS)." In this outburst phase we first observed the QPO at 102 mHz on 2010 March 22 (MJD 55277)., In this outburst phase we first observed the QPO at $102$ mHz on 2010 March 22 (MJD 55277). After that. the QPO frequency monotonically increased to 5.69 Hz until 2010 April 17 (MJD 55303).," After that, the QPO frequency monotonically increased to $5.69$ Hz until 2010 April 17 (MJD 55303)." Afterward. QPOs were sporadically on and off (e.g.. 5.739 Hz. 5.677 Hz and 5.913Hz on April 18. 22 and 29 respectively). always remaining at about the same value.," Afterward, QPOs were sporadically on and off (e.g., $5.739$ Hz, $5.677$ Hz and $5.913$ Hz on April 18, 22 and 29 respectively), always remaining at about the same value." These sporadically appearing QPOs in PDS were observed until 2010 May I4., These sporadically appearing QPOs in PDS were observed until 2010 May 14. " The observed QPOs in hard and hard-intermediate states (Homan Belloni. 2005) are of the ""C"" type and in soft-intermediate state are of the ""B type (van der Klis 2004. Casella et al."," The observed QPOs in hard and hard-intermediate states (Homan Belloni, 2005) are of the `C' type and in soft-intermediate state are of the `B' type (van der Klis 2004, Casella et al." 2005)., 2005). The gradual increase of the ΟΡΟ frequency 1n the rising phases of transient black hole and neutron star candidates have been known for a long time (e.g. Bellont Hasinger 1990. Belloni et al.," The gradual increase of the QPO frequency in the rising phases of transient black hole and neutron star candidates have been known for a long time (e.g., Belloni Hasinger 1990, Belloni et al." 2002. Maitra Bailyn 2004).," 2002, Maitra Bailyn 2004)." In. the present context of studying outbursting black hole candidates. evolutions of QPOs during the 2005 outburst of GRO J1655-40 (Chakrabarti. Debnath. Nandi Pal 2008. hereafter CDNPOS) and the 1998 outburst of XTE J1550-564 (Chakrabarti. Dutta Pal 2009. hereafter CDP09) showed the monotonically increasing behavior in the rising phase like the one we find here in GX 339-4.," In the present context of studying outbursting black hole candidates, evolutions of QPOs during the 2005 outburst of GRO J1655-40 (Chakrabarti, Debnath, Nandi Pal 2008, hereafter CDNP08) and the 1998 outburst of XTE J1550-564 (Chakrabarti, Dutta Pal 2009, hereafter CDP09) showed the monotonically increasing behavior in the rising phase like the one we find here in GX 339-4." However. while in GRO 1655-40 the QPO disappeared completely and then re-appeared after about six months (Debnath et al.," However, while in GRO J1655-40 the QPO disappeared completely and then re-appeared after about six months (Debnath et al." 2008) and in ΧΤΕ J1550-564. vopo Started declining immediately after reaching maximum (CDP09). in the present case. vopo began to stall at about," 2008) and in XTE J1550-564, $\nu_{QPO}$ started declining immediately after reaching maximum (CDP09), in the present case, $\nu_{QPO}$ began to stall at about" The main goal of the Araucaria project is to improve the calibration of the cosmic distance scale Trom accurate observations of (he various primary stellar distance inclicators in nearby galaxies (e.g. Gieren et al.,The main goal of the Araucaria project is to improve the calibration of the cosmic distance scale from accurate observations of the various primary stellar distance indicators in nearby galaxies (e.g. Gieren et al. 2005b)., 2005b). In the course of our project we are observing Cepheids. RIA Lyrae stars. red clump stars. blue supereiants. eclipsing binaries and (he tip of the red giant branch (TRGB) brightness in both optical and infrared (14) domains.," In the course of our project we are observing Cepheids, RR Lyrae stars, red clump stars, blue supergiants, eclipsing binaries and the tip of the red giant branch (TRGB) brightness in both optical and infrared (IR) domains." Since with IR photometry one can minimize the influence of interstellar reddening on the derived distances. aud in many cases also the population dependence of the standard candles. this part of our project is particularly important lor precise distance determinations to our target ealaxies. and therefore for a more accurate calibration of the extragalactic distance scale.," Since with IR photometry one can minimize the influence of interstellar reddening on the derived distances, and in many cases also the population dependence of the standard candles, this part of our project is particularly important for precise distance determinations to our target galaxies, and therefore for a more accurate calibration of the extragalactic distance scale." In our previous papers we already demonstrated (hat red clump stars (Pielrzvuski and Gieren 2002: Pietrzvnski. Gieren and Udalski 2003). Cepheids (e.g. Pietrzvnski οἱ al.," In our previous papers we already demonstrated that red clump stars (Pietrzynski and Gieren 2002; Pietrzynski, Gieren and Udalski 2003), Cepheids (e.g. Pietrzynski et al." 2006: Gieren el al., 2006; Gieren et al. 2005a. 2006. 2008a. 2003b: Soszvnski οἱ al.," 2005a, 2006, 2008a, 2008b; Soszynski et al." 2006). and IR. Lyrae stars (Pietrzvuski el al.," 2006), and RR Lyrae stars (Pietrzynski et al." 2008. Szewezvk et al.," 2008, Szewczyk et al." 2008) in the IE. domain are very accurate tools for distance determination to nearby galaxies., 2008) in the IR domain are very accurate tools for distance determination to nearby galaxies. In this paper we extend our near-infrared clistance work (o the TRGB method in the J aud Ix bands. starting with the two dwarl spheroidals Carina aud Fornax.," In this paper we extend our near-infrared distance work to the TRGB method in the J and K bands, starting with the two dwarf spheroidals Carina and Fornax." The success of the TRGB method as a tool for distance measurement begun in 1993 when Lee et al. (, The success of the TRGB method as a tool for distance measurement begun in 1993 when Lee et al. ( 1993) convincinglv showed that the optical I band magnitude of the TRGB,1993) convincingly showed that the optical I band magnitude of the TRGB smaller (han the observed value by a factor of 5.5.,smaller than the observed value by a factor of 5.5. Despite the existence of a 27 vr long 5-rav ephemeris of Genminga. it has not been possible to measure a (rue braking index because f is apparenilv dominated by πας noise. even apart [rom the observed elitch. which is among the smallest ever detected in a pulsar.," Despite the existence of a 27 yr long phase-connected $\gamma$ -ray ephemeris of Geminga, it has not been possible to measure a true braking index because $\ddot f$ is apparently dominated by timing noise, even apart from the observed glitch, which is among the smallest ever detected in a pulsar." More sensitive hard. X-ray observations. such as are possible withNewton. also have the potential to disentangle anv additional spectral and pulse components that may be present. such as evelotron features. hot polar cap emission. and even atomic spectral lines from the neutron star photosphere.," More sensitive hard X-ray observations, such as are possible with, also have the potential to disentangle any additional spectral and pulse components that may be present, such as cyclotron features, hot polar cap emission, and even atomic spectral lines from the neutron star photosphere." and follows A for longer waveleneths.,and follows $\lambda^{-\beta}$ for longer wavelengths. The spectral energv distributions (SEDs) of debris disks with more extensive niultióvaveleusth data are well described by this prescription. with ο= 1.1 to 0.5 (Deutetal.2000)...," The spectral energy distributions (SEDs) of debris disks with more extensive multi-wavelength data are well described by this prescription, with $\beta=$ 1.1 to 0.5 \citep{2000MNRAS.314..702D}." For this range of Jj. the GJ 803 data are fit with Z7—535.15 K. with T—10x2 K for a nominal §=(0.8. where the nucertaity is the formal lo error in the fit. (," For this range of $\beta$, the GJ 803 data are fit with $T=35-45$ K, with $T=40\pm2$ K for a nominal $\beta=0.8$ , where the uncertainty is the formal $\sigma$ error in the fit. (" Fitting a pure blackbody to the data gives 62£5 Ix.) Note that the nnon-detection at 100 iis a good match to ¢=(.8 aud rules out /21.,Fitting a pure blackbody to the data gives $62\pm5$ K.) Note that the non-detection at 100 is a good match to $\beta=0.8$ and rules out $\beta\gtrsim1$. With slightly ereater seusitivitv. sshould have detected this source.," With slightly greater sensitivity, should have detected this source." Iu addition. the mareinal detection at 150 aaerees well with the 20.5 fit.but is inconsistent with a pure blackbody.," In addition, the marginal detection at 450 agrees well with the $\beta$ =0.8 fit,but is inconsistent with a pure blackbody." The integrated fractional dust luninosity LoasafLage G.1«10.1 forthe nominal /20.8. T=lok iocdel.," The integrated fractional dust luminosity $L_{dust}/L_{star}$ is $6.1\times10^{-4}$ for the nominal $\beta=0.8$, $T=40$ K model." For GJ 182. the excess cussion at 25 aud S50 ccannot be fit with a siuele modified blackbody that also satisfies the uuonu-doetectious.," For GJ 182, the excess emission at 25 and 850 cannot be fit with a single modified blackbody that also satisfies the non-detections." Ignoring the 25 fflux for the moment. à. 10 IN.)=0.8 modified blackhody. like that which fits the C.J 803 SED. is consistent with the —X0. 100. and 850 ata CFigure )).," Ignoring the 25 flux for the moment, a 40 K, $\beta=0.8$ modified blackbody, like that which fits the GJ 803 SED, is consistent with the 60, 100, and 850 data (Figure \ref{plot-sed}) )." A higher dust temperature would violate ARAhe 60 pper luit., A higher dust temperature would violate the 60 upper limit. Of course. a lower dust tempcrature would also be cousisteut with the 850 etection.," Of course, a lower dust temperature would also be consistent with the 850 detection." Fiuuer constraints on the dust teniperatures await more seusitive IR/sub-uuu measurements., Firmer constraints on the dust temperatures await more sensitive IR/sub-mm measurements. The mid-IR SEDs are sensitive to the preseuce of war (st in the inner disk regions., The mid-IR SEDs are sensitive to the presence of warm dust in the inner disk regions. CJ 182 shows a strong 25 cexcess (but see 1.2)., GJ 182 shows a strong 25 excess (but see 4.2). " I£ sve add à 150.200 IK component which cuits as a}=0.8 modified blackbody. a dust mass of(l12)«10 lis needed to account for the 25 eexcess, or of the T=10 Ix dust component which satisfies the 850 Hux (Figure ))."," If we add a 150–200 K component which emits as a $\beta=0.8$ modified blackbody, a dust mass of $(4-12)\times10^{-5}$ is needed to account for the 25 excess, or of the T=40 K dust component which satisfies the 850 flux (Figure \ref{plot-sed}) )." For GJ 805. the large nid-IR dip indicates an absence of wart dust in the immer regious.," For GJ 803, the large mid-IR dip indicates an absence of warm dust in the inner regions." Hf we add a wirni component which cuits as ai?=0.8 modified dackbody. oulv a very πα amount of 150.200 IX dust is ρολτος. since the 225 Ὥτις is cousisteut with beine photospheric.," If we add a warm component which emits as a $\beta=0.8$ modified blackbody, only a very small amount of 150–200 K dust is permitted, since the 25 flux is consistent with being photospheric." Taking the nareinal 25 cexcess at face value eives a wari dust mass of (39)&109 AL... or of the T=10 I& dust component.," Taking the marginal 25 excess at face value gives a warm dust mass of $(3-9)\times10^{-6}$ , or of the T=40 K dust component." " For the entire sample. we compute dust masses from the S50 fluxes in the standard fashion. assuming optically thin cnhussion characterized by a single temperature: where £L is the flux deusitv. d is distance. s, Is the dust opacity at the observing frequency. and D, is the Planck fuuctiou for a dust temperature T."," For the entire sample, we compute dust masses from the 850 fluxes in the standard fashion, assuming optically thin emission characterized by a single temperature: where $F_\nu$ is the flux density, $d$ is distance, $\kappa_\nu$ is the dust opacity at the observing frequency, and $B_\nu$ is the Planck function for a dust temperature $T$." We adopt a dust opacity of LF cn?i. iu agreeiuent with past studies2003).," We adopt a dust opacity of 1.7 $^2$, in agreement with past studies." .. This value is on the upper end of the 0.11.7 cui iranse discussed by Pollacketal.(1991)., This value is on the upper end of the 0.4–1.7 $^2$ range discussed by \citet{1994ApJ...421..615P}. For detections. we use 30 upper limits on the 850 füux and assmue 7=30100 Ik. in agreement with previously detected debris disks (Deutotal.2000)..," For non-detections, we use $\sigma$ upper limits on the 850 flux and assume $T=30-100$ K, in agreement with previously detected debris disks \citep{2000MNRAS.314..702D}." For CJ 803. we adopt the 10 Is temperature from the SED fitting.," For GJ 803, we adopt the 40 K temperature from the SED fitting." The calculated dust masses are presented iu Table 1., The calculated dust masses are presented in Table 1. It is unlikely that our detections are due to backerouud ealaxies., It is unlikely that our detections are due to background galaxies. Scottetal.(2002) estimate a surface density of about 500 objects per square degree brighter than an 850 flux of 6 mv. about the 236 seusitivitv of our survey.," \citet{2002MNRAS.331..817S} estimate a surface density of about 500 objects per square degree brighter than an 850 flux of 6 mJy, about the $\sigma$ sensitivity of our survey." The probability of any background objects to be within an angular distauce 0 ofa target is 1.exp(x07X). where Mods the surface density of background objects above a specified fiux level.," The probability of any background objects to be within an angular distance $\theta$ of a target is $1-\exp(-\pi \theta^2 \Sigma)$, where $\Sigma$ is the surface density of background objects above a specified flux level." We compute the euseimible probability of detecting anv backeround objects in SCUDAs coutral bolometer for our cutive sample of 8 objects; accountius for the fact that we mapped GJ sO3.," We compute the ensemble probability of detecting any background objects in SCUBA's central bolometer for our entire sample of 8 objects, accounting for the fact that we mapped GJ 803." This gives a probability that backeround sources would produce at least oue detection dui our survey., This gives a probability that background sources would produce at least one detection in our survey. The GJ 803 system appears to have very little molecular gas., The GJ 803 system appears to have very little molecular gas. The CO 32 inteusity is £5+19 iu üntegrated over £7 aabout the stellar velocity. (, The CO 3–2 intensity is $-45 \pm 49$ mK integrated over $\pm$ 7 about the stellar velocity. ( This velocity range corresponds to the maxinmun orbital speed for a disk viewed at au inclination of wwith the inner disk edee of LF AU derived from the SED fit),This velocity range corresponds to the maximum orbital speed for a disk viewed at an inclination of with the inner disk edge of 17 AU derived from the SED fit.) " Ássuuing the eas is optically thin and in thermal equilibrimu with 10 Is dust. the 30 upper Πατ iplics a CO column density of 6.2ος1005ον,"," Assuming the gas is optically thin and in thermal equilibrium with 40 K dust, the $\sigma$ upper limit implies a CO column density of $6.2\times10^{13}$." Temperatures as wart as 2150 Ik.ees if the gas were located iu the inner few AU. would eive inferred CO column densities of a factor of 2 larger.," Temperatures as warm as $\approx$ 150 K, if the gas were located in the inner few AU, would give inferred CO column densities of a factor of 2 larger." Deteriiuiug au upper Iuuit ou the total eas mass is uncertain. since this is dominated by aand the to CO conversion is hiehly uncertiüiu.," Determining an upper limit on the total gas mass is uncertain, since this is dominated by and the to CO conversion is highly uncertain." " CO lay freeze-out onto erains. making it a poor tracer of the total disk mass,"," CO may freeze-out onto grains, making it a poor tracer of the total disk mass." Also. photoionization may affect the to CO conversion factor.," Also, photoionization may affect the to CO conversion factor." To attempt to account for photoionization by the interstellar UV field. we refer to calculations by vanDishoeck&Black(1988)... slightly extrapolated to lower CO column deusities. aud adopt an to CO abundance ratio of *(ef... normal abundance ratio of 13.," To attempt to account for photoionization by the interstellar UV field, we refer to calculations by \citet{1988ApJ...334..771V}, slightly extrapolated to lower CO column densities, and adopt an to CO abundance ratio of $^{-7}$, normal abundance ratio of $^{-4}$ )." This results in an nunass of 1.3AL)... ifwe ignore the possibility of CO freeze-," This results in an mass of 1.3, if we ignore the possibility of CO freeze-out." " Overall. the gas non-detection limits for GJ 803 are comparable to those for older solar-type stars (Deutctal.1995:Greavesetal.2000α) and rules out the possibility of GJ 803 having a eas-vich disk comparable to those detected aroundvounger stars (Zuckermanctal.1995: 20001), "," Overall, the gas non-detection limits for GJ 803 are comparable to those for older solar-type stars \citep{1995MNRAS.277L..25D, 2000MNRAS.312L...1G} and rules out the possibility of GJ 803 having a gas-rich disk comparable to those detected aroundyounger stars \citep{1995Natur.373..494Z, 2000Icar..143..155G}. ." Figure 3 sunnmnuaarizes the known debris disk mass estimates based ou sub-auni observations from) our work and the published literature., Figure \ref{agetrend} summarizes the known debris disk mass estimates based on sub-mm observations from our work and the published literature. Our SCUBA survey adds a significant nuniber of stars of 21050 Myr., Our SCUBA survey adds a significant number of stars of $\approx$ 10–50 Myr. Our raw 850 ssensitfivitv (1nediau rius of 1.9 παν) is poorer than the, Our raw 850 sensitivity (median rms of 1.9 mJy) is poorer than the it could be seen extending οί the central meridian right up to the north-east limb in EUVIAA. The prominence eruption commenced at UUT. and the CME LE could be seen αἱ 08:50 and ULT respectively in CORLAA and D FOVs.,"it could be seen extending from the central meridian right up to the north-east limb in A. The prominence eruption commenced at UT, and the CME LE could be seen at 08:50 and UT respectively in A and B FOVs." The CME LE could be seen in (he COR? FOV at UUT., The CME LE could be seen in the COR2 FOV at UT. The prominence material could also be very conspieuouslv seen in images from both the coronagraphis on the (wo spacecraft., The prominence material could also be very conspicuously seen in images from both the coronagraphs on the two spacecraft. This CME showed changes in speed and acceleration similar to the one on 2007 November 16 (Figures 11. and 7))., This CME showed changes in speed and acceleration similar to the one on 2007 November 16 (Figures \ref{F:res13apr} and \ref{F:res16nov}) ). Its speed very rapidly reached a value of 300kisbal heieht. .3.81... and during. the same time. its: acceleration: dropped fromB 60ms⋅97 to ge271897," Its speed very rapidly reached a value of $300\kmps$ at height $3.8\Rsun$, and during the same time its acceleration dropped from $60\mpss$ to $27\mpss$." The peak of the acceleration however could not be observed., The peak of the acceleration however could not be observed. Like the event of 2008 April 9. here too we find the prominence showing an increasing acceleration al least tll 41...," Like the event of 2008 April 9, here too we find the prominence showing an increasing acceleration at least till $4\Rsun$." This CME was also associated with a northern polar crown filament. as seen in Figure 6..," This CME was also associated with a northern polar crown filament, as seen in Figure \ref{F:img01aug}." The filament appeared as a hedgerow prominence in DD images. while the line-o[-sight was along the spine in EUVIAA images.," The filament appeared as a hedgerow prominence in B images, while the line-of-sight was along the spine in A images." The CME was first seen in AA FOV at ULT. and at ULT in DD FOV.," The CME was first seen in A FOV at UT, and at UT in B FOV." Due to a data eap in the COR2 observations. the CALE was seen only in a single image at. ULT in COR? A and D. This CME behavecl very. differently. Grom (he rest analysed in (this studs.," Due to a data gap in the COR2 observations, the CME was seen only in a single image at UT in COR2 A and B. This CME behaved very differently from the rest analysed in this study." Its speed was very low at the start. and it gradually reached the maximum speed of 567kms.J|. al a height of ~4.5R...," Its speed was very low at the start, and it gradually reached the maximum speed of $567\kmps$, at a height of $\sim4.5\Rsun$." At this height. the CME was still accelerating. but owing to a data eap in the CODB2 observations. its peak value couldnot be determined.," At this height, the CME was still accelerating, but owing to a data gap in the COR2 observations, its peak value couldnot be determined." The maxinum acceleration of the prominence was 40nmis7 at a height of about 1.5RB.. and then showed a steady. decrease {ο around 1018/7 at a height of 2Η...," The maximum acceleration of the prominence was $40\mpss$ at a height of about $1.5\Rsun$, and then showed a steady decrease to around $10\mpss$ at a height of $3\Rsun$ ." The CME LE accelerated verv late, The CME LE accelerated very late Now we focus on the ealeulation of relaxation time ancl bulk viscosity in (he mixed phase.,Now we focus on the calculation of relaxation time and bulk viscosity in the mixed phase. For this. we have to express the chemical imbalance (050) in the non-leptonic hyperon process as given by Eq.(17) in terms of dr from the following constraints. lere we have ὃν=0 because number densities deviate from their equilibrium. values only by internal reactions (Lindblom&Owen2002).," For this, we have to express the chemical imbalance $\delta {\mu}$ ) in the non-leptonic hyperon process as given by Eq.(17) in terms of $\delta{n_n^K}$ from the following constraints, Here we have $\delta \chi = 0$ because number densities deviate from their equilibrium values only by internal reactions \citep{Lin02}." . First two constraints follow from the conservation of barvon number and electric charge neutrality., First two constraints follow from the conservation of baryon number and electric charge neutrality. The last constrain is the result of the chemical equilibrium involving A— condensate as already shown bv Eq.(19)., The last constrain is the result of the chemical equilibrium involving $K^-$ condensate as already shown by Eq.(19). " The other constraints are due to the equality of neutron. proton and A chemical potentials in the hadronic aud condensed phases ancl we can rewrite them as We express dn, on. on. n. ón and diy in terms of dn’ using above six constraints."," The other constraints are due to the equality of neutron, proton and $\Lambda$ chemical potentials in the hadronic and condensed phases and we can rewrite them as We express $\delta n_n^h$, $\delta n_p^h$, $\delta n_{\Lambda}^h$, $\delta n_p^K$, $\delta n_{\Lambda}^K$ and $\delta n_{K^-}$ in terms of $\delta n_n^K$ using above six constraints." For this purpose. we solve a 6 x 6 matrix constructed out of above six relations ancl obtain D.. ein," For this purpose, we solve a 6 $\times$ 6 matrix constructed out of above six relations and obtain $\frac{\delta \mu}{\delta {n_n^K}}$." ilarly. we obtain x in (he mixed phase from the above constraints.," Similarly, we obtain $\frac{\delta \mu}{\delta {n_n^h}}$ in the mixed phase from the above constraints." This completes the calculation of relaxation tme and bulk viscosity in the mixed phase., This completes the calculation of relaxation time and bulk viscosity in the mixed phase. Next we calculate critical angular velocity as a function temperature and mass of a rotaling neutron star., Next we calculate critical angular velocity as a function temperature and mass of a rotating neutron star. The bulk viscosity damping timescale (75) due to the non-leptonic process involving A hvperons ancl the bulk viscosity profile as a ΠΟΙΟ of r are obtained following the Ref. (Lindblometal.1999:Lindblom&Owen2002:Navvar2006:Chatterjee&Bandvopachvay 2006).," The bulk viscosity damping timescale $\tau_B$ ) due to the non-leptonic process involving $\Lambda$ hyperons and the bulk viscosity profile as a function of $r$ are obtained following the Ref. \citep{Lin99,Lin02,Nar,DR1}. ." ".. Further we take into account. time scales associated with gravitational radiation (τομ) (Lindblometal.1998).. bulk viscosity. due to modified Urea process (τι) involving only nucleons (Sawyer1989;Andersson&IxXokkotas2001) and the shear viscosity (το) (Lindblomοἱal.1998:Andersson anddefine the overall r-mode (ime scale (7,.) as"," Further we take into account time scales associated with gravitational radiation $\tau_{GR}$ ) \citep{Lin98} , bulk viscosity due to modified Urca process $\tau_U$ ) involving only nucleons \citep{Saw,Kok} and the shear viscosity $\tau_{SV}$ ) \citep{Lin98,Kok,And06} anddefine the overall r-mode time scale $\tau_r$ ) as" "CFL-constaint. C,20.01 for the cosmological constraint. and C,.=0.9 for the thermal conduction constraint.","CFL-constaint, $C_{a} = 0.01$ for the cosmological constraint, and $C_{tc} = 0.9$ for the thermal conduction constraint." The time steps are computed in every cell. and the minimal value is used to compute the global time step.," The time steps are computed in every cell, and the minimal value is used to compute the global time step." The cooling timescale (which ts also. the chemical timescale) can be much shorter than timescales given above., The cooling timescale (which is also the chemical timescale) can be much shorter than timescales given above. Therefore. it is not used as a constraint on the global time step.," Therefore, it is not used as a constraint on the global time step." Instead we usesubeycling:: The time evolution of the number densities and the thermal energy density is computed using several shorter time steps., Instead we use: The time evolution of the number densities and the thermal energy density is computed using several shorter time steps. This ts done locally in each cell while keeping the other quantities constant (seealso?).., This is done locally in each cell while keeping the other quantities constant \citep[see also][]{Kay00}. In cosmological simulations. one often encounters flows of high velocity and low pressure.," In cosmological simulations, one often encounters flows of high velocity and low pressure." " In these situations. the numerical computation of the difference E—£,;,. needed for the computation of the pressure. might might not yield reasonable results."," In these situations, the numerical computation of the difference $E - E_{\mathrm{kin}}$, needed for the computation of the pressure, might might not yield reasonable results." This is known as theproblem., This is known as the. . To overcome this problem we implement the algorithm suggested by ?.., To overcome this problem we implement the algorithm suggested by \citet{Feng04}. " In addition the conservative quantities we also follow the evolution of a modified entropy density S= p/p"".", In addition the conservative quantities we also follow the evolution of a modified entropy density $S = p / \rho^{\gamma- 1}$ . In high Mach flows. where E=Ej;j. we use $ to compute the pressure. while elsewhere E is used.," In high Mach flows, where $E \approx E_{\mathrm{kin}}$, we use $S$ to compute the pressure, while elsewhere $E$ is used." After the pressure is computed the quantity used for the computation is recomputed using p. thus keeping both quantities synchronized.," After the pressure is computed the quantity used for the computation is recomputed using $p$, thus keeping both quantities synchronized." If we set the right-hand side of Eq., If we set the right-hand side of Eq. (1. - 4)) to zero we obtain the homogeneous Euler-equations., \ref{eRho} - \ref{eS}) ) to zero we obtain the homogeneous Euler-equations. These equations are used to compute the pure hydrodynamic evolution of the fluid., These equations are used to compute the pure hydrodynamic evolution of the fluid. This problem is solved using the MUSCL-Hancock scheme as presented in 2.., This problem is solved using the MUSCL-Hancock scheme as presented in \citet{Toro99}. To ensure the monotonicity of the solution the MINMOD slope limiter is applied., To ensure the monotonicity of the solution the MINMOD slope limiter is applied. The inter-cell fluxes are computed using a HLLC Riemann-solver., The inter-cell fluxes are computed using a HLLC Riemann-solver. " This. solver approximatesthe analytic solution of the Riemann problem by three waves separating (with velocities S5. S,. $4) four different states: the left (L) and the right (R) initial state. and regions left (xL) and right CR) of the contact discontinuity."," This solver approximatesthe analytic solution of the Riemann problem by three waves separating (with velocities $S_L$, $S_\star$, $S_R$ ) four different states: the left $L$ ) and the right $R$ ) initial state, and regions left $\star L$ ) and right $\star R$ ) of the contact discontinuity." We use the algorithm given in 2.chap.10.4and10.5 and add a prescription for the computation of the modified entropy density and. for non-IE simulations. the number densities in the central regionsxL and *R: where K= Lor K=R for the left or right states.," We use the algorithm given in \citet[chap. 10.4 and 10.5]{Toro99} and add a prescription for the computation of the modified entropy density and, for non-IE simulations, the number densities in the central regions$\star L$ and $\star R$ : where $K = L$ or $K = R$ for the left or right states." The wave speeds are computed by, The wave speeds are computed by where wr./) is a complex function with real and imaginary components given by and where eq is the speed of sound in the unperturbed medium.,"where $\omega(r,t')$ is a complex function with real and imaginary components given by and respectively, where the notation of the pioneer work of Field (1965) is used as follows where $c_0$ is the speed of sound in the unperturbed medium." " The Fiekls isobaric instability criterion (hyLO"" erg/s and ~1 source with L,210!""10 erg/s. Finally. the presence of a voung SNR (Tas< several tens of vr) surrounding the source is a fundamental ingredient of (he voung pulsar scenario."," For an optically dull galaxy with a SFR $\sim 0.2 M_\odot$ /yr, we predict that there is a $\sim 7\%$ probability of finding a source with $L_x\ga 10^{39}$ erg/s and a $\sim 0.3\%$ probability of finding a source with $L_x\ga 10^{40}$ erg/s. Correspondingly, for an active, starburst galaxy with a SFR $\sim 10 M_\odot$ /yr, we expect to find $\sim$ a few sources with $L_x\ga 10^{39}$ erg/s and $\sim 1$ source with $L_x\ga 10^{40}$ erg/s. Finally, the presence of a young SNR $T_{SNR}\la$ several tens of yr) surrounding the source is a fundamental ingredient of the young pulsar scenario." There is at least one case where the association between a ULX and a SNR has been established (Roberts et al., There is at least one case where the association between a ULX and a SNR has been established (Roberts et al. 2003)., 2003). Dinarily A large munber of stars are in binary sistems., A large number of stars are in binary sistems. Whether a binary. survives the first SN explosion will mostly depend on Che kick velocity of the NS and the mass of the companion: for high mass companions up to several (ens of percent of binaries are expected to survive (he first SN explosion (Brandt Podsiacllowski 1995; Ixalogera. 1998)., Whether a binary survives the first SN explosion will mostly depend on the kick velocity of the NS and the mass of the companion; for high mass companions up to several tens of percent of binaries are expected to survive the first SN explosion (Brandt Podsiadlowski 1995; Kalogera 1998). Therefore. a sizeable fraction of voung pulsars is expected to be in a binary svstem.," Therefore, a sizeable fraction of young pulsars is expected to be in a binary system." On the other hand. while binarily is requirecl in most models of ULXs. for the voung pulsar scenario il is not a requirement as the source of the X-ray luminosity is the rotational enerev of the star.," On the other hand, while binarity is required in most models of ULXs, for the young pulsar scenario it is not a requirement as the source of the X-ray luminosity is the rotational energy of the star." emission Young pulsars are also detected in radio and often in optical (e.g. Becker Trumper 1991 [or a review)., Young pulsars are also detected in radio and often in optical (e.g. Becker Trumper 1997 for a review). " For the Crab. the ratio Loy/L, is ~10?. while for Vela it is ~10.7,"," For the Crab, the ratio $L_{\rm opt}/L_x$ is $\sim 10^{-2}$, while for Vela it is $\sim 10^{-3}$." The statistics of optical detections i voung pulsars is too small to vield predictions about the intensity of the optical radiation as a function of (he X-ray one., The statistics of optical detections in young pulsars is too small to yield predictions about the intensity of the optical radiation as a function of the X-ray one. However. if the ratio remains of the same order as lor Crab and Vela. (hen significant optical emission is expected. although prospects for detection appear promising only for sources in relatively close by. galaxies.," However, if the ratio remains of the same order as for Crab and Vela, then significant optical emission is expected, although prospects for detection appear promising only for sources in relatively close by galaxies." The greatest majority of voung X-ray pulsars are also radio emitters., The greatest majority of young X-ray pulsars are also radio emitters. Although the radio, Although the radio barred galaxies have vines (Buta 1996). so if the Calaxy is barred then there is a high chance that it will have a ving as well,"barred galaxies have rings (Buta 1996), so if the Galaxy is barred then there is a high chance that it will have a ring as well." The prominence of the peak at /22° indicates that it is caused by an imiportaut feature in the inner Galaxy., The prominence of the peak at $l=-22^\circ$ indicates that it is caused by an important feature in the inner Galaxy. Its form indicates that it is the tangential point toa ring or spiral arii. and that its location coimcides with tangent from the 73 kpe axi seen in the CO may)5.," Its form indicates that it is the tangential point to a ring or spiral arm, and that its location coincides with tangent from the “3 kpc arm” seen in the CO maps." The 3 kpe arin is an unusual radio feature iu the plane with a radial velocity of haus bat? =0° yather thali approximately zero as for the other arius., The 3 kpc arm is an unusual radio feature in the plane with a radial velocity of $-53$ km $^{-1}$ at $l=0^\circ$ rather than approximately zero as for the other arms. Furthermore. the tanecutial poiut to the Norma ar is at about 30° vet there is no clear evidence for the arm in fhe comnts," Furthermore, the tangential point to the Norma arm is at about $l=-30^\circ$ , yet there is no clear evidence for the arm in the counts." The most likely explanation for the peak at is that it is theftangential point to a rime. or nke probably a pseudo-ariug (i.c. the ner armis are very tightly wound arouud the bar to form what is almost a ring. as iu NGC 1133).," The most likely explanation for the peak at $l=-22^\circ$ is that it is the tangential point to a ring, or more probably a pseudo-ring (i.e. the inner arms are very tightly wound around the bar to form what is almost a ring, as in NGC 1433)." Sevenster(1999) deected au excess of OIT/IR stars at |=22° and sugeested that the 3 kpc arni Was he cause., Sevenster (1999) detected an excess of OH/IR stars at $l=-22^\circ $ and suggested that the 3 kpc arm was the cause. Ile also concluded. tat this feature is ludied rinelike., He also concluded that this feature is indeed ringlike. " Ati=22"" the radio tangential point aux star-cout vealss almost colucido. whereas 2, fangenial points at yositive longitudes in radio. {--—m. there is actual va strong dip in the counts."," At $l=-22^\circ$ the radio tangential point and star-count peaks almost coincide, whereas at tangential points at positive longitudes in radio, $l=24^\circ$, there is actually a strong dip in the counts." " The peal o 72] is at |=277. hence it is probable that the tanecuial volt to the ring coincides with the eu of the 211, which produces the strong peak iu the counts seen at he Galactic Centre itself."," The closest peak to $l=24^\circ$ is at $l=27^\circ$, hence it is probable that the tangential point to the ring coincides with the end of the bar, which produces the strong peak in the counts seen at the Galactic Centre itself." The reason that the stars aud eas are somewhat separated at positive longitides whils at regative longitudes they are close together is probadv )ecause at positive longitudes the taugeutial poiut to he ring almost coincides with the end of the bar., The reason that the stars and gas are somewhat separated at positive longitudes whilst at negative longitudes they are close together is probably because at positive longitudes the tangential point to the ring almost coincides with the end of the bar. The ring isi cllipical aud. assuming that the main axis were parale o the bar. which is not necessarily the case (Saudage Dedke 1991). tje axial ratio of the ring would be 1:0.7(το ortje stars and some what higher for the eas.," The ring is elliptical and, assuming that the main axis were parallel to the bar, which is not necessarily the case (Sandage Bedke 1994), the axial ratio of the ring would be 1:0.76 for the stars and some what higher for the gas." This woulc collre with t1e lncan axial ratio for rings of 0:51 + 0.06 (Buta 1996)., This would compare with the mean axial ratio for rings of 0.81 $\pm$ 0.06 (Buta 1996). T1e diameter of the ring would be the sue astjio bar. hence 8 kpc. again very close to the tvpica values of 9 kpc foundin exterual Galaxies (Freciman L996)).," The diameter of the ring would be the same as the bar, hence 8 kpc, again very close to the typical values of 9 kpc found in external Galaxies (Freeman 1996)." Combining the results from this paper aud those prescuted in Π00 aud II91 the priuciple paraicters of the bar c“ALL be determined., Combining the results from this paper and those presented in H00 and H94 the principle parameters of the bar can be determined. The ‘ollowing features are seen in the plane in the iuner regiois of the Galaxy (QUI«, The following features are seen in the plane in the inner regions of the Galaxy $|l|<30^\circ $ ): identical set-ups for a generic hot Jupiter (see the papers for details). except for differeut :unounts ol Rayleigh drag applied as a term iu the momeutuim equation.,"identical set-ups for a generic hot Jupiter (see the papers for details), except for different amounts of Rayleigh drag applied as a term in the momentum equation." The model in has no drag applied. while the three models in. Peruaetal.(2010a) have drag streugthlis that vary with eight (stronger higher in tle atmosphere).," The model in \citet{RM10} has no drag applied, while the three models in \citet{Perna2010a} have drag strengths that vary with height (stronger higher in the atmosphere)." " Drag timescalesn range fromHJ E10*""i—10?6 seconds iu the weakest-drag model (PMBa in Table 1). aud are a factor of 10 and 100 shorter iu the inedium- aud strougest-drag models (PIRb and PMRe in Table 1)."," Drag timescales range from $10^7-10^9$ seconds in the weakest-drag model (PMRa in Table 1), and are a factor of 10 and 100 shorter in the medium- and strongest-drag models (PMRb and PMRc in Table 1)." For reference. advective timescales are ou the order of 10? secouds axd radiative timescales vary [rom 3x107 to greater than 10* seconc5 (itcreasing witli «epth).," For reference, advective timescales are on the order of $10^5$ seconds and radiative timescales vary from $\sim3\times10^3$ to greater than $10^7$ seconds (increasing with depth)." " The local specific kinetic enerey loss is calculated. [roi the prescribed drag timescales as D=(1/2)e7/7,drag", The local specific kinetic energy loss is calculated from the prescribed drag timescales as $\mathcal{D} = (1/2) v^2/\tau_{\mathrm{drag}}$. The radiative jealing Is treatec wo a Newtonian relaxation scheme. making it simple to determine the value of Grad al each poiu in the mocleled atimosphliere.," The radiative heating is treated by a Newtonian relaxation scheme, making it simple to determine the value of $q_{\mathrm{rad}}$ at each point in the modeled atmosphere." We calculate the elobal integrals of these quantities. as well as tie source terius for UPE anc APE (from Equatiois 19 ancl 20) . alid present our 'esults in Table 1.," We calculate the global integrals of these quantities, as well as the source terms for UPE and APE (from Equations \ref{eq:finalu} and \ref{eq:finala}) ), and present our results in Table 1." Note that our numerica solver does not convert the lost kitelic enerey into reheatiug (in other words. while D is uouzer in Equation 21.. qy=0 in Equations 19 aud 20)).," Note that our numerical solver does not convert the lost kinetic energy into reheating (in other words, while $\mathcal{D}$ is nonzero in Equation \ref{eq:finalke}, $q_f=0$ in Equations \ref{eq:finalu} and \ref{eq:finala}) )." " The values listed for the generatiou of UPE anc APE are (TD)qua aud (1—T]dead. respectively. wille the values istecd as ""missiug"" generatiol replace μα with gp=P to determie how mitch potential euergy should have been generated if we «did indeed include frictioua heatig in the models."," The values listed for the generation of UPE and APE are $(T_r/T)q_{\mathrm{rad}}$ and $(1-T_r/T)q_{\mathrm{rad}}$, respectively, while the values listed as “missing"" generation replace $q_{\mathrm{rad}}$ with $q_f=\mathcal{D}$ to determine how much potential energy should have been generated if we did indeed include frictional heating in the models." Belore cliscussing the resuls. We address one issue of concern with these moclels. which is tha the deepest levels (below ~10 bar) lay have not completely reached a statistically steady state by the eud of the 1150 or 500 ylane days simulated in Rauscher&Menou(2010) and (2010a).," Before discussing the results, we address one issue of concern with these models, which is that the deepest levels (below $\sim$ 10 bar) may have not completely reached a statistically steady state by the end of the 1450 or 500 planet days simulated in \citet{RM10} and \citet{Perna2010a}." . It is likely that these deep evels are still beiug accelerated through interaction witli the upper atmosphere., It is likely that these deep levels are still being accelerated through interaction with the upper atmosphere. This cotId couplicate or euergetics caleulatious aud so we have rerun ancl extended all of the ruus from those papers to miigate this issue., This could complicate our energetics calculations and so we have rerun and extended all of the runs from those papers to mitigate this issue. We calculate energy rates at. 1075. 2000. aud. 10000 planet days for the Rauscher&Menou(2010) model. aud at 5000 days for the Pernaetal.(20104). moclels.," We calculate energy rates at 4975, 5000, and 10000 planet days for the \citet{RM10} model, and at 5000 days for the \citet{Perna2010a} models." The first point. worth noting is that lor all of these moclels the global ineeral of Grad50. ueaning that the planet is not in elobal radiative equilibrium.," The first point worth noting is that for all of these models the global integral of $q_{\mathrm{rad}} \neq 0$, meaning that the planet is not in global radiative equilibrium." There are two possible resolutions o this issue., There are two possible resolutions to this issue. The first is that the atinosphiere is still being accelerated by the ieating and so has vet to reach a steady state., The first is that the atmosphere is still being accelerated by the heating and so has yet to reach a steady state. However. if this were the case. tlie value of qq for the run at 10000 cays should be less than at 2000 days. whereas the ‘eis not significant difference between them.," However, if this were the case, the value of $q_{\mathrm{rad}}$ for the \citet{RM10} run at 10000 days should be less than at 5000 days, whereas there is not significant difference between them." We lave also iuspectect the time evolution of kinetic aicL internal energies hroughout the ruus aud we see uo evidence for continued acceleration of the flow or heating of the, We have also inspected the time evolution of kinetic and internal energies throughout the runs and we see no evidence for continued acceleration of the flow or heating of the ocal FRC. bv a factor of 2Lat. =0.,"local FRC, by a factor of $2 - 4$ at $z = 0$." " Like the conrpact starbursts. puffv starbursts show little rest-iine evolution iu Loi.Εμμ except at relatively low surface deusities (X4,=05an?; Mapcm2LAL.kpe3yr bh where they become radio dim at Heh redshifts because of IC losses on CAIB photons."," Like the compact starbursts, puffy starbursts show little rest-frame evolution in $L_{\rm TIR}^{\prime}/L_{\rm radio}^{\prime}$, except at relatively low surface densities $\Sigma_g = 0.1~\gcm2$; $\Sigma_{\rm SFR} \approx 2 - 4~\Msun~\kpc^{-2}~\yr^{-1}$ ), where they become radio dim at high redshifts because of IC losses on CMB photons." Therefore. we predict that puffy starbursts which are uainlv observed at high :. have different radio properties nof caused by their redshift.," Therefore, we predict that puffy starbursts, which are mainly observed at high $z$, have different radio properties not caused by their redshift." We propose a natural explanation of this radio excess in the framework of LTO 2) , We propose a natural explanation of this radio excess in the framework of LTQ \ref{sec:Theory}) ). Iun dense starbursts. protons are efücieutlv converted ito secondary electrons and positrons through inelastic proton-proton scattering. which coutribute to the svuchrotrou chussion.," In dense starbursts, protons are efficiently converted into secondary electrons and positrons through inelastic proton-proton scattering, which contribute to the synchrotron emission." Furthermore. the νο effect increases {μεμι foy starbursts which have larger D.," Furthermore, the $\nu_C$ effect increases $L_{\rm TIR}^{\prime}/L_{\rm radio}^{\prime}$ for starbursts which have larger $B$." Compact starbursts ling ou the τ=0 FRC balance hese effects with decreased breusstralilune. ionization. and IC losses. which compete with the svuchrotron losses and suppress the excess radio bhuuinositv 2)).," Compact starbursts lying on the $z = 0$ FRC balance these effects with increased bremsstrahlung, ionization, and IC losses, which compete with the synchrotron losses and suppress the excess radio luminosity \ref{sec:Theory}) )." Iu ouffv starbursts with relatively low volume densities compared to their compact cousins at fixed however. enmisstralhlune aud ionization are not stroug X.chough to conrpensate for these effects.," In puffy starbursts with relatively low volume densities compared to their compact cousins at fixed $\Sigma_g$, however, bremsstrahlung and ionization are not strong enough to compensate for these effects." Ouly svuchrotrou aud IC osses remain. upsetting the conspiracy.," Only synchrotron and IC losses remain, upsetting the conspiracy." The radio excess xediceted bv this picture is svstematically ercater when using the NOs star-formation relation. because the IC loss rate on starlieht is smaller at fixed surface density bv a actor of 2.5 to 11 from weal: starbursts to the densest starbursts.," The radio excess predicted by this picture is systematically greater when using the K98 star-formation relation, because the IC loss rate on starlight is smaller at fixed surface density by a factor of 2.5 to 11 from weak starbursts to the densest starbursts." This freedom to vary the racdio-excess with 2 does not exist iu the standard calorimeter model. where all CR clectrou/positrou cacrey goes iuto svuchrotrou cluission. and the radio enmuüssion saturates.," This freedom to vary the radio-excess with $B$ does not exist in the standard calorimeter model, where all CR electron/positron energy goes into synchrotron emission, and the radio emission saturates." The balance between svuchrotrou aud the other forms of cooling cau be changed m starbursts to alter the normalization of the FRC. even though escape is negligible.," The balance between synchrotron and the other forms of cooling can be changed in starbursts to alter the normalization of the FRC, even though escape is negligible." There is a reason to expect our allowed DxXUT7US specifically:radiation pressure iav drive turbulence aud enhance the maeuetic feld uutil its euergv deusitv is conrparable to radiation (0.9...Thompson2008).," There is a reason to expect our allowed $B \propto \Sigma_g^{0.7-0.8}$ specifically:radiation pressure may drive turbulence and enhance the magnetic field until its energy density is comparable to radiation \citep[e.g.,][]{Thompson08}." .. If the R98 relation holds. then since the magnetic energy deusity scales as Upx Uy. Boxa and if the Bos relation holds. then Bx XU. ," If the K98 relation holds, then since the magnetic energy density scales as $U_B \propto U_{\rm ph}$ , $B \propto \Sigma_g^{0.7}$, and if the B08 relation holds, then $B \propto \Sigma_g^{0.85}$ ." This explauation is more problematic for the DOT relation and Dxyu.7—g, This explanation is more problematic for the B07 relation and $B \propto \Sigma_g^{0.7}$. ILowever. while we asstune that there is a parametrization for D that applied to both compact starbursts aud puffy starbursts. the radio excess should arise more ecuerally.," However, while we assume that there is a parametrization for $B$ that applied to both compact starbursts and puffy starbursts, the radio excess should arise more generally." " The radio excess aries simply because svuchrotrou cooling time is shorter than the breniesstrahlung and ionization cooling times iu puffy starbursts. but longer in compact starbursts at fixed Sy: at fixed γή. fususXAAS, aud tienxBVey1Xnp2Ny):"," The radio excess arises simply because synchrotron cooling time is shorter than the bremsstrahlung and ionization cooling times in puffy starbursts, but longer in compact starbursts at fixed $\Sigma_g$: at fixed $\nu^{\prime}$, $t_{\rm brems} \propto n^{-1} \propto h / \Sigma_g$ and $t_{\rm ion} \propto B^{-1/2} n^{-1} \propto h / (B^{1/2} \Sigma_g)$." We therefore expect there to be a radio excess with respect to the FRC in auy puffv starburst with a strong chough magnetic field. with the exact cuhanccment depenudiug ou naeguetic feld streneth because of the remaiming conrpetition. after ionization aud bremsstrabhme are sub-donmiuant. frou the IC losses on Qur results imply that a moderate radio excess at tle factor of ~3 level alone is not a safe indicator of the preseuce of a radio-Ioud ACN. especially at high redshifts where SAIGs are observed.," We therefore expect there to be a radio excess with respect to the FRC in any puffy starburst with a strong enough magnetic field, with the exact enhancement depending on magnetic field strength because of the remaining competition, after ionization and bremsstrahlung are sub-dominant, from the IC losses on Our results imply that a moderate radio excess at the factor of $\sim 3$ level alone is not a safe indicator of the presence of a radio-loud AGN, especially at high redshifts where SMGs are observed." " While radio excess with respect to the local FRC has been suggested as a selection criterion for radio-loud ACNs ίσιο,Yunetal.2001:Yang our models with Eub inuplv that αι&1.7.2.0 for puffv starbursts powered w star-formation alone."," While radio excess with respect to the local FRC has been suggested as a selection criterion for radio-loud AGNs \citep[e.g.,][]{Yun01,Yang07,Sajina08}, our models with $\Sigma_g^{0.7-0.8}$ imply that $q_{\rm FIR} \approx 1.7 - 2.0$ for puffy starbursts powered by star-formation alone." A radio excess is inexplicable iu our models ouly when the source is an order of maguitude xighter (qgis.S1.5) in the radio than predicted from the FIR emission., A radio excess is inexplicable in our models only when the source is an order of magnitude brighter $q_{\rm FIR} \la 1.5$ ) in the radio than predicted from the FIR emission. While SAICs are relatively rare aud may rot be a problem im small samples. we recommend that other means be used to be sure that the racio-excess is caused by an ACN. such as a flat radio spectrum. radio norpholoey. mid-IR colors. or the preseuce of strong X-rav endssion (seealsoMurphyetal.2009a).," While SMGs are relatively rare and may not be a problem in small samples, we recommend that other means be used to be sure that the radio-excess is caused by an AGN, such as a flat radio spectrum, radio morphology, mid-IR colors, or the presence of strong X-ray emission \citep[see also][]{Murphy09}." . A maeuctic field dependence of Boxp? appears to hold for Galactic molecular clouds (6.9...Crutcher1999).. and LTO found that the FIR-radio correlation was consistent with this magnetic field depeudence.," A magnetic field dependence of $B \propto \rho^{0.5}$ appears to hold for Galactic molecular clouds \citep[e.g.,][]{Crutcher99}, and LTQ found that the FIR-radio correlation was consistent with this magnetic field dependence." The existence of galaxies with different scale heights. allows us to distinguish the two possibilities for maenetic field scaling., The existence of galaxies with different scale heights allows us to distinguish the two possibilities for magnetic field scaling. If BoxX. then the maguetic field strength will be the sue for all galaxies with the same X. regardless of scale height.," If $B \propto \Sigma_g^a$, then the magnetic field strength will be the same for all galaxies with the same $\Sigma_g$, regardless of scale height." " In models with B.xp?9, by contrast. the magnetic field streneth is weaker iu putty starbursts than iu coupact starbursts with the same X,"," In models with $B \propto \rho^{0.5 - 0.6}$, by contrast, the magnetic field strength is weaker in puffy starbursts than in compact starbursts with the same $\Sigma_g$." As secu in Figure 1.panel. dotted lines). putty starbursts again form their own FRC.," As seen in Figure \ref{fig:LFIRRadioRest} , dotted lines), puffy starbursts again form their own FRC." Iu models with Dxp?95 they are radio dim couared to the zz0 FRC.," In models with $B \propto \rho^{0.5 - 0.6}$, they are radio dim compared to the $z \approx 0$ FRC." We show in Table À2. that the normalization of the FRC is radio-«din by a factor of ~152.0., We show in Table \ref{table:Models} that the normalization of the FRC is radio-dim by a factor of $\sim 1.2 - 2.0$. We can explain this iu the LTO theory of the FRC as well., We can explain this in the LTQ theory of the FRC as well. " The magnetic feld strength umst increase more slowly with pb than with X, to reproduce the :z0 FRO. because fhxX,/p is 10 times sinaller in compact starbursts thin normal galaxies aud putty starbursts."," The magnetic field strength must increase more slowly with $\rho$ than with $\Sigma_g$ to reproduce the $z \approx 0$ FRC, because $h \propto \Sigma_g / \rho$ is 10 times smaller in compact starbursts than normal galaxies and puffy starbursts." Compact starbursts are highly. compressed with respect to normal galaxies. so they have stroug magnetic fields and svuchrotrou radio enuüssion is strong chough to compete with the other losses.," Compact starbursts are highly compressed with respect to normal galaxies, so they have strong magnetic fields and synchrotron radio emission is strong enough to compete with the other losses." Puffy starbursts are not conrressed. so that their magnetic fields are weak and svuchrotron losses caunot keep up with IC losses. nor with bremisstralibuns aud ionization as 1.1 Giz eiuission traces ever lowerelectronenergies at higher magnetic field streugths.," Puffy starbursts are not compressed, so that their magnetic fields are weak and synchrotron losses cannot keep up with IC losses, nor with bremsstrahlung and ionization as 1.4 GHz emission traces ever lowerelectronenergies at higher magnetic field strengths." " Putty starbursts therefore turi out to be radio dim compared to compact starbursts on the +0 FRC. if Bxp? ""9, "," Puffy starbursts therefore turn out to be radio dim compared to compact starbursts on the $z \approx 0$ FRC, if $B \propto \rho^{0.5 - 0.6}$ ." As before. the BOT star-formation relation predicts greater IC losses aud therefore weaker," As before, the B07 star-formation relation predicts greater IC losses and therefore weaker" the wavelength dependent positions over the band(7)..,the wavelength dependent positions over the band\citep{Helminiak:2009p2198}. The weighting factor is the number of photons per wavelength which in turn is the convolution of the input spectrum with the interstellar extinction and the atmospheric and instrumental transmission numbers., The weighting factor is the number of photons per wavelength which in turn is the convolution of the input spectrum with the interstellar extinction and the atmospheric and instrumental transmission numbers. The size of the net effect grows quadratically with the bandpass used and hence narrow band filters help to suppress the atmospheric chromatic effects on the astrometry., The size of the net effect grows quadratically with the bandpass used and hence narrow band filters help to suppress the atmospheric chromatic effects on the astrometry. " Figure 5 shows the resulting effect for black body type emission compared to a fictitious object with 10? K. For young, hot stars (most of the S-stars have T'&25000 K, ??)) the K-band measured positions for typical zenith angles are altered by z20 as."," Figure \ref{f5} shows the resulting effect for black body type emission compared to a fictitious object with $10^5\,$ K. For young, hot stars (most of the S-stars have $T\approx 25000\,$ K, \cite{Ghez:2003p178,Martins:2008p177}) ) the K-band measured positions for typical zenith angles are altered by $\approx20\,\mu$ as." For stars with a temperature of 6000 the K-band shift would be ©70 as.," For stars with a temperature of $6000\,$ K the K-band shift would be $\approx70\,\mu$ as." " Below 5000 K, the approximationK as black body breaks down due to the presence of the broad CO absorption features around 2.3 um, and the shift does not get larger anymore but rather is close to 0 with a typical spread of «+20 as compared to the fictitious emitter."," Below $5000\,$ K, the approximation as black body breaks down due to the presence of the broad CO absorption features around $2.3\,\mu$ m, and the shift does not get larger anymore but rather is close to 0 with a typical spread of $<\pm20\,\mu$ as compared to the fictitious emitter." " Since our position measurements are relative to other sources in the field, the differential effect between reference stars and target sources is an error source for the positions obtained."," Since our position measurements are relative to other sources in the field, the differential effect between reference stars and target sources is an error source for the positions obtained." " The reference frame is constructed from early- and late-type stars in roughly equal numbers, such that in K-band it refers to coordinates shifted by zz10 µας compared to the fictitious object."," The reference frame is constructed from early- and late-type stars in roughly equal numbers, such that in K-band it refers to coordinates shifted by $\approx10\,\mu$ as compared to the fictitious object." Individual stars are then shifted again depending on their stellar type by & 10µμας compared to the coordinate system.," Individual stars are then shifted again depending on their stellar type by $\approx10\,\mu$ as compared to the coordinate system." Only G-type stars would experience a shift of zz50 µας; but main sequence stars of that type are by far too faint to be detected in the GC field.," Only G-type stars would experience a shift of $\approx50\,\mu$ as; but main sequence stars of that type are by far too faint to be detected in the GC field." The net effect for K-band based astrometry is thus very small., The net effect for K-band based astrometry is thus very small. For H-band data the effect is larger in the first place (figure 5)) and secondly late-type stars actually can be approximated by black bodies in H-band., For H-band data the effect is larger in the first place (figure \ref{f5}) ) and secondly late-type stars actually can be approximated by black bodies in H-band. For z—40? and a late-type star the chromatic shift can reach 400 µας compared to the 10? K emitter.," For $z=40^\circ$ and a late-type star the chromatic shift can reach $400\,\mu$ as compared to the $10^5\,$ K emitter." " For hot, young stars a more typical value is 50 µας."," For hot, young stars a more typical value is $50\,\mu$ as." The astrometric net effect will thus be z175 pas.," The astrometric net effect will thus be $\approx 175\,\mu$ as." " Of course, these values strongly depend on the actual zenith angle and the exact input spectrum."," Of course, these values strongly depend on the actual zenith angle and the exact input spectrum." " Also, this error source is correctable, given that the zenith angle is known and if the input spectrum is at least approximately known."," Also, this error source is correctable, given that the zenith angle is known and if the input spectrum is at least approximately known." More subtle is the combined effect of the patchy nature of the extinction screen towards the GC and the chromaticity of the atmosphere., More subtle is the combined effect of the patchy nature of the extinction screen towards the GC and the chromaticity of the atmosphere. " Extinction variations lead to a change in observed color for each object as it moves behind the screen, the change in color in turn leads to a positional offset."," Extinction variations lead to a change in observed color for each object as it moves behind the screen, the change in color in turn leads to a positional offset." " By looking at the scatter of the observed K-band magnitudes of some isolated, bright stars (e.g. S8, $10, 830, S65, S87 in the nomenclature of ?)) we conclude that the extinction variation AAx<0.1 for the central field of interest Opor."," By looking at the scatter of the observed K-band magnitudes of some isolated, bright stars (e.g. S8, S10, S30, S65, S87 in the nomenclature of \cite{Gillessen:2009p1117}) ) we conclude that the extinction variation $\Delta A_\mathrm{K} \lesssim 0.1$ for the central field of interest $\Theta_\mathrm{FoI}$." Figure 6 plots the positional shift per 0.1 mag extinction variation as a function of zenith angle., Figure \ref{f6} plots the positional shift per 0.1 mag extinction variation as a function of zenith angle. " For K-band data, the effect is o;X20 as, for H-band data σαS100 pas."," For K-band data, the effect is $\sigma_x\lesssim 20\,\mu$ as, for H-band data $\sigma_x\lesssim 100\,\mu$ as." " Also note that for larger regions in the GC of a few arcsecond, values of AE£z0.5 are reported (?),, which yields a correspondingly larger chromatic effect."," Also note that for larger regions in the GC of a few arcsecond, values of $\Delta E \approx 0.5$ are reported \citep{Buchholz:2009p1131}, which yields a correspondingly larger chromatic effect." " Finally, it is worth investigating the chromatic effects for Sgr A*, the MBH itself,which in the NIR is a variable source powered by the synchrotron emission of relativistic electrons and possibly changes its power law index ϐ (vS,~ v?) with flux (??7),, but see also ?.."," Finally, it is worth investigating the chromatic effects for Sgr A*, the MBH itself,which in the NIR is a variable source powered by the synchrotron emission of relativistic electrons and possibly changes its power law index $\beta$ $\nu S_\nu \sim ~\nu^\beta$ ) with flux \citep{Eisenhauer:2005p117, Gillessen:2006p160, Krabbe:2006p1515}, , but see also \cite{Hornstein:2007p1513}. ." The astrometric, The astrometric nuclei (090. Sevlert galaxes. etc).,"nuclei (QSO, Seyfert galaxes, etc)." This paper is (he first in a series of papers on the effects (hat strong gravitational fields play in formation and structure of winds driven by radiation pressure in lines., This paper is the first in a series of papers on the effects that strong gravitational fields play in formation and structure of winds driven by radiation pressure in lines. Theory of winds from O-(vpe stars is well-developed and has a good agreement with observations., Theory of winds from O-type stars is well-developed and has a good agreement with observations. In a pioneering paper of Sobolev (1960). it was recognized (hat a radiation transler in accelerated medium is simplilied drastically in comparison with that of static atmosphere.," In a pioneering paper of Sobolev (1960), it was recognized that a radiation transfer in accelerated medium is simplified drastically in comparison with that of static atmosphere." The importance of (he line opacity for the formation of winds from hot stars was pointed out in paper of Luev Solomon (1970)., The importance of the line opacity for the formation of winds from hot stars was pointed out in paper of Lucy Solomon (1970). A prominent step in this lield was made in papers of Castor. Abbott Ixlein (1975). ( hereafter CAI ).," A prominent step in this field was made in papers of Castor, Abbott Klein (1975), ( hereafter CAK )." In these papers ib was shown that absorption of (he radiation flux in lines can be an elfective mechanism of redistributing of momentum from radiation to the wind., In these papers it was shown that absorption of the radiation flux in lines can be an effective mechanism of redistributing of momentum from radiation to the wind. The presence of the velocity gracient gives additional effect on the acceleration because of the Sobolev effect., The presence of the velocity gradient gives additional effect on the acceleration because of the Sobolev effect. CAIX showed that the resultant radiation force. which is due to absorption in an ensemble of optically (hin and optically thick lines. may be several orders of magnitude greater than that due to electron scattering.," CAK showed that the resultant radiation force, which is due to absorption in an ensemble of optically thin and optically thick lines, may be several orders of magnitude greater than that due to electron scattering." The ideas aud technique of CAI were developed by Abbott (1930) and in works of many other authors., The ideas and technique of CAK were developed by Abbott (1980) and in works of many other authors. Theory of winds accelerated bv the radiation pressure in lines is usually applied to explain outflows from active galactic nuclei (AGN)., Theory of winds accelerated by the radiation pressure in lines is usually applied to explain outflows from active galactic nuclei (AGN). The many puzzling. observational characteristic features of AGNs are: the blue-shifted. relative to the emission line rest frequency. broad absorption lines (BALs) - ihe most convincing evidence of outflows with velocities as large as 0.10 NALs -narrow absorption lines seen in UV ancl X-ray spectra associated wilh eLOOOkm-s+ outflows: BELs - broad emission lines observed in UV indicate the flow with the characteristic velocity about several thousand km-s+.," The many puzzling, observational characteristic features of AGNs are: the blue-shifted, relative to the emission line rest frequency broad absorption lines (BALs) - the most convincing evidence of outflows with velocities as large as $0.1 c$; NALs -narrow absorption lines seen in UV and X-ray spectra associated with $\sim 1000 \,{\rm km\cdot s^{-1}}$ outflows; BELs - broad emission lines observed in UV indicate the flow with the characteristic velocity about several thousand ${\rm km\cdot s^{-1}}$." From the short time-scale of the X-Ray variability. (Tennantal 1981) it is concluded that the size of the emitting region is e10!cm. (, From the short time-scale of the X-Ray variability (Tennant 1981) it is concluded that the size of the emitting region is $\sim 10^{14}{\rm cm}$. ( "Although there exist an uncertainty in the estimation of the column densities. see Arav οἱ al. 2002. and references therein) Only black hole (BID) as a central object ean couple this small length scale with the total Iuminositv Lον10eer-s !, ","Although there exist an uncertainty in the estimation of the column densities, see Arav et al, 2002, and references therein) Only black hole (BH) as a central object can couple this small length scale with the total luminosity $L\sim 10^{46} {\rm egr\cdot s^{-1}}$ ." The existence of BALs together with large huninosity makes radiation driven mechanism plausible., The existence of BALs together with large luminosity makes radiation driven mechanism plausible. Line-locking. observed in spectra of some QSO gives additional evidence of (he importance of radiation in acceleration ol the wind.," Line-locking, observed in spectra of some QSO gives additional evidence of the importance of radiation in acceleration of the wind." Murray. at al. (, Murray at al. ( 1995) model the wind that originates not [ar from BIL ~10ο.,1995) model the wind that originates not far from BH $\sim 10^{16} {\rm cm}$. Simplifving assumptions allowed (o solve separately equation of moGon in radial and polar angle directions., Simplifying assumptions allowed to solve separately equation of motion in radial and polar angle directions. Two-dimensional time-dependent. hvdrocdvnamic ealeulations of radiation-«driven winds from Iuminous accretion disks were made in Proga et al. (, Two-dimensional time-dependent hydrodynamic calculations of radiation-driven winds from luminous accretion disks were made in Proga et al. ( 1993). Proga et al. (,"1998), Proga et al. (" 2000).,2000). In all papers where the radiation pressure was assumed as a main driving foree forming outflows from AGNs. authors adopted. modifications of the," In all papers where the radiation pressure was assumed as a main driving force forming outflows from AGNs, authors adopted modifications of the" dusty starburst galaxies only.,dusty starburst galaxies only. Allowing for the (1+2) frequency. folding of the Doppler effect. we estimate an overall uncertainty of σ.~0.1(1+2) with an upper bound in reclshilt uncertainty of about 0.3(1+2).," Allowing for the $1+z$ ) frequency folding of the Doppler effect, we estimate an overall uncertainty of $\sigma_z \sim 0.1 (1+z)$ with an upper bound in redshift uncertainty of about $0.3(1+z)$." In either case. this photometric redshift’ technique utilizing the racio-to-FIR. dusiv starburst SED represents a significant step forward. parlicularly at high. redshifts. when compared will existing methods.," In either case, this photometric redshift technique utilizing the radio-to-FIR dusty starburst SED represents a significant step forward, particularly at high redshifts, when compared with existing methods." The hil potential of this method will be realized when the sources identilied by several large deep. multi-frequency. surveys planned in the immediate future (e.g. SIRTF Legacy Survevs) are analvzed together (o reveal an accurate recshilt distribution of luminous dusty galaxies at high redshift.," The full potential of this method will be realized when the sources identified by several large deep, multi-frequency surveys planned in the immediate future (e.g. SIRTF Legacy Surveys) are analyzed together to reveal an accurate redshift distribution of luminous dusty galaxies at high redshift." The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities. Inc. Some of the data presented here are obtained [rom the NASA/IPAC Extragalactic Database (NED). which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautical and Space Administration.," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Some of the data presented here are obtained from the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautical and Space Administration." becoming smaller Chan the rotational frequency for €>1000.,becoming smaller than the rotational frequency for $\epsilon > 1000$. Fast magnetic Rossby waves also depend on e. their Irequency significantly decreasing when (liis parameter is increased.," Fast magnetic Rossby waves also depend on $\epsilon$, their frequency significantly decreasing when this parameter is increased." Slow magnetic Rosshy waves have almost no dependence on € as il is suggested from Eq. (13))., Slow magnetic Rossby waves have almost no dependence on $\epsilon$ as it is suggested from Eq. \ref{approx_fs_large_eps}) ). Thus increasing e. which is equivalent to reducing g. generally leads (o a decrease of the wave frequencies.," Thus increasing $\epsilon$, which is equivalent to reducing $g$, generally leads to a decrease of the wave frequencies." The numerical solution of the dispersion relation (10) shows that the frequency of the magnetic Rossby wave harmonic with v=0 becomes complex for sufficiently large ay. ie. large magnetic field.," The numerical solution of the dispersion relation (10) shows that the frequency of the magnetic Rossby wave harmonic with $\nu=0$ becomes complex for sufficiently large $\alpha_0$, i.e. large magnetic field." This may point to some kind of instabilities similar to the polar kink instability found by Cally (2003)., This may point to some kind of instabilities similar to the polar kink instability found by Cally (2003). However. the value of ay for which the frequency becomes complex is signilicantlv outside (he range for which Eq. (," However, the value of $\alpha_0$ for which the frequency becomes complex is significantly outside the range for which Eq. (" "10) is valid (note that ay should be proportional to e. £1),",10) is valid (note that $\alpha_0$ should be proportional to $\epsilon^{-1/4}$ ). Therefore. the complex solution can be spurious and may not reflect a real instability.," Therefore, the complex solution can be spurious and may not reflect a real instability." We have derived analvlical solutions ancl dispersion relations of global shallow water ΑΔΗ) waves lor the solar tachocline in a rotating spherical coordinate svstem., We have derived analytical solutions and dispersion relations of global shallow water MHD waves for the solar tachocline in a rotating spherical coordinate system. The solutions aud dispersion relations are obtained for weakly and strongly stable stratifications separately., The solutions and dispersion relations are obtained for weakly and strongly stable stratifications separately. The weakly stable stratification is valid in the upper overshoot part of tachocline. while the stronglv stable stratification is valid for the radiative part of tachocline.," The weakly stable stratification is valid in the upper overshoot part of tachocline, while the strongly stable stratification is valid for the radiative part of tachocline." The solutions include the Poincaré and Rossby waves modified by the presence of the magnetic [ield., The solutions include the Poincaré and Rossby waves modified by the presence of the magnetic field. llere we use a realistic latitudinal profile of the toroidal magnetic field. 73o0CosBsin that changes sien al the equator., Here we use a realistic latitudinal profile of the toroidal magnetic field $B_{\phi}\sim \cos{\theta} \sin{\theta}$ that changes sign at the equator. Similar to the €=0 case (Zaqarashvilietal.2001).. the magnetic field leads to the splitting of hydrodyvnamic Rossby waves into [ast ancl slow," Similar to the $\epsilon=0$ case \citep{zaq07}, the magnetic field leads to the splitting of hydrodynamic Rossby waves into fast and slow" discussion under the assumption that the major fraction of the MIR luminosity of most of our sources is due to dust emission.,discussion under the assumption that the major fraction of the MIR luminosity of most of our sources is due to dust emission. Since the 11s show little evidence for luminous dust tori and their AGNs are weak. we check whether their MIR emission — if due to dust — is powered by the AGNs or by the presumably strong interstellar radiation field (SRF) of the giant hosts.," Since the 1s show little evidence for luminous dust tori and their AGNs are weak, we check whether their MIR emission – if due to dust – is powered by the AGNs or by the presumably strong interstellar radiation field (ISRF) of the giant hosts." Starbursts might play only à minor role. as shown further below.," Starbursts might play only a minor role, as shown further below." Therefore we compare the MIR luminosity with two independent AGN luminosity measures: 1) The ratio of jm to MMHz power shows the same dependency for 11s as for 22s and quasars refmsxxxxogpiniresoadio)), Therefore we compare the MIR luminosity with two independent AGN luminosity measures: 1) The ratio of $\mu$ m to MHz power shows the same dependency for 1s as for 2s and quasars \\ref{msxxxx_fig_lmir_vs_radio}) ). " Inthe 2sandthequasarsthe MPRMe by Pn HiSRE. at, gigntriüskera", In the 2s and the quasars the MIR power is dominated by AGN heated dust emission (Haas et al. 2001), 2004). " ofthe M EBpowerwereductodust.theratioPs, would still lie within the dispersion of the distribution of a factor of ten."," Even, if for the 1s only of the MIR power were due to dust, the ratio $_{\rm 15 \mu m}$ $_{\rm 178\,MHz}$ would still lie within the dispersion of the distribution of a factor of ten." The similarity of this ratio. independent of radio power and source type. would be difficult to understand. if i1 the 11s the MIR dust emission were heated only by the ISRF without any significant AGN contribution.," The similarity of this ratio, independent of radio power and source type, would be difficult to understand, if in the 1s the MIR dust emission were heated only by the ISRF without any significant AGN contribution." " 2) We consider the luminosity of the H,, *[NII emission lines (from Zirbel Baum 1995) which refers to the central 2.5 kpe of the sources.", 2) We consider the luminosity of the $_\alpha$ +[NII] emission lines (from Zirbel Baum 1995) which refers to the central 2.5 kpc of the sources. The emission line luminosity of 11s. normalized by the absolute V magnitude of the host. lies between the high range of 22s and the low one of radio- elliptical galaxies (Fig.22 in Baum et al.," The emission line luminosity of 1s, normalized by the absolute V magnitude of the host, lies between the high range of 2s and the low one of radio-quiet elliptical galaxies 2 in Baum et al." 1995)., 1995). This argues against a pure host galaxy origin of the emission lines and favours a significant AGN contribution to the lumiosity in 22s and also in 11s., This argues against a pure host galaxy origin of the emission lines and favours a significant AGN contribution to the luminosity in 2s and also in 1s. Now considering our data. the ratio of emission line luminosity and MIR jim power is similar for all source types (range 10.! to 10. 7) and independent of radio power.," Now considering our data, the ratio of emission line luminosity and MIR $\mu$ m power is similar for all source types (range $10^{-1}$ to $10^{-3}$ ) and independent of radio power." " This would be difficult to understand if P454, were purely due to ISRF heated dust.", This would be difficult to understand if $_{\rm 15 \mu m}$ were purely due to ISRF heated dust. If the emission line luminosity were significantly driven by the AGN. the Pisas should include power from the AGN heated dust. too.," If the emission line luminosity were significantly driven by the AGN, then $_{\rm 15 \mu m}$ should include power from the AGN heated dust, too." These two results are consistent with the interpretation that also in the 11s the MIR dust emission can be powered by the AGN. but a considerable contribution from the host's interstellar radiation field cannot be excluded.," These two results are consistent with the interpretation that also in the 1s the MIR dust emission can be powered by the AGN, but a considerable contribution from the host's interstellar radiation field cannot be excluded." As mentioned above. the FIR luminosity of IIs is probably dominated by dust emission.," As mentioned above, the FIR luminosity of 1s is probably dominated by dust emission." Relative to both the MIR and the radio MMHz luminosities. the FIR luminosity of the 11 galaxies is higher than that of the quasars and many 22 galaxies refmsxxxxpigyo)fivosiir))," Relative to both the MIR and the radio MHz luminosities, the FIR luminosity of the 1 galaxies is higher than that of the quasars and many 2 galaxies \\ref{msxxxx_fig_lmir_to_lfir_vs_lir}) )." Thissuggeststhatiuthe RlLlsthe ," This suggests that in the 1s the FIR luminosity is substantially provided by another heating source than by a weak AGN, e.g. at a first glance by starbursts." FT Dhisis, But the temperature T of the dust component associated with the FIR flux peak lies between 25 K and 35 K for the 1s \\ref{msxxxx_fig_seds}) ). ccactlytherange found forradio quictellipticalgalavies(e.g Bregmanctal, This is exactly the range found for radio-quiet elliptical galaxies (e.g. Bregman et al. L998). andlowerthan forF ," 1998), and lower than for 2s and luminous starburst galaxies $>$ K)." Also. the ratio of total optical luminosity. including that from the host galaxy. to the FIR luminosity is about 50-500 times higher for 11s than for 22s and dusty starburst galaxies.," Also, the ratio of total optical luminosity, including that from the host galaxy, to the FIR luminosity is about 50-500 times higher for 1s than for 2s and dusty starburst galaxies." Therefore. we conclude that in 11s the bulk of the FIR Reward by nhe phe. mUaxy.," Therefore, we conclude that in 1s the bulk of the FIR emission is mainly powered by the ISRF of the giant host galaxy." If the dust is distributed quite homogeneously. then the ISRF may heat it to higher temperatures than those around T = 15-20 K found in spiral galaxies. where the bulk of the dust s typically concentrated in dense clumps shielding against the ISRE.," If the dust is distributed quite homogeneously, then the ISRF may heat it to higher temperatures than those around T = 15-20 K found in spiral galaxies, where the bulk of the dust is typically concentrated in dense clumps shielding against the ISRF." The AGN or starbursts. if any. play only a minor role for the FIR luminosity of Hs.," The AGN or starbursts, if any, play only a minor role for the FIR luminosity of 1s." This is consistent with the results by Heckman et al. (, This is consistent with the results by Heckman et al. ( 1986) and de Koff et al. (,1986) and de Koff et al. ( 2000) that many 22 hosts show morphological distortions and signs of interaction. which trigger starbursts and nuclear activity. while the 11 hosts are typically regular ellipticals.,"2000) that many 2 hosts show morphological distortions and signs of interaction which trigger starbursts and nuclear activity, while the 1 hosts are typically regular ellipticals." Finally. in the case of rather homogeneously distributed dust as indicated for the 11s one would expect that there is not much cold dust. which would radiate at submillimetre wavelengths and could have escaped our detection.," Finally, in the case of rather homogeneously distributed dust as indicated for the 1s one would expect that there is not much cold dust, which would radiate at submillimetre wavelengths and could have escaped our detection." In order to explain why the FRIIs do not show the powerful extended radio lobes like 22s. deceleration of the 11 jets due to entrainment of the [ISM or stellar wind material has been proposed (de Young 1993. Bicknell 1994. 1995. Bowman et al.," In order to explain why the 1s do not show the powerful extended radio lobes like 2s, deceleration of the 1 jets due to entrainment of the ISM or stellar wind material has been proposed (de Young 1993, Bicknell 1994, 1995, Bowman et al." 1996)., 1996). Also the existence of sources with hybrid morphology — 11 on one side. 22 on the other side of the core — argues againstphysical differences in the central engine. such às black hole spin (slow for 11. fast for 22.) or jet plasma composition p! for I1lI.e e! for 22). and favours an origin for the 22 dichotomy (Gopal-Krishna Wiita 2000).," Also the existence of sources with hybrid morphology – 1 on one side, 2 on the other side of the core – argues against differences in the central engine, such as black hole spin (slow for 1, fast for 2,) or jet plasma composition $^{-}$ $^{+}$ for 1, $^{-}$ $^{+}$ for 2), and favours an origin for the 2 dichotomy (Gopal-Krishna Wiita 2000)." In addition to entrainment. the pressure of the external hot X-ray emitting gas turns out to play a role in the confinement of the jets (e.g. Laing Bridle 2002).," In addition to entrainment, the pressure of the external hot X-ray emitting gas turns out to play a role in the confinement of the jets (e.g. Laing Bridle 2002)." We should make clear that the actual distribution of stars is neither a perfect single nor a perfect double exponential distribution.,We should make clear that the actual distribution of stars is neither a perfect single nor a perfect double exponential distribution. With the low-mass clusters we only see a thin distribution like a ‘peak’ and only few stars in a sort of envelope? but with low z-heights., With the low-mass clusters we only see a thin distribution like a 'peak' and only few stars in a sort of 'envelope' but with low $z$ -heights. Therefore a single exponential fits the data well., Therefore a single exponential fits the data well. For high-mass clusters we see this ‘peak’ as well together with a very extended structure (the ‘envelope’) reaching out to large z-heights., For high-mass clusters we see this 'peak' as well together with a very extended structure (the 'envelope') reaching out to large $z$ -heights. These clusters are able to spread out their stars to large radii., These clusters are able to spread out their stars to large radii. For those distributions a double exponential fits the data better., For those distributions a double exponential fits the data better. Even though none of the values from Tab., Even though none of the values from Tab. 2. come anywhere close to the values of the thin and thick dise of the MW. it is astonishing that our high-mass clusters distribute their particles automatically into a distribution which is best fitted by a double exponential. sshow the same shape as the actual distribution of MW stars.," \ref{tab:fit} come anywhere close to the values of the thin and thick disc of the MW, it is astonishing that our high-mass clusters distribute their particles automatically into a distribution which is best fitted by a double exponential, show the same shape as the actual distribution of MW stars." The low numbers can easily be understood by the fac that the MW is not made out of one single dispersed star cluster a one certain time and on one certain orbit., The low numbers can easily be understood by the fact that the MW is not made out of one single dispersed star cluster at one certain time and on one certain orbit. We rather have an overlay of star clusters forming with different masses at different times and on all radial distances., We rather have an overlay of star clusters forming with different masses at different times and on all radial distances. " Furthermore. we do not take any further effect into account which could enhance the vertical spread of the star particles. e.g. scattering with giant molecular clouds or spira arms, adiabatic heating due to the growth in mass of the MW disk."," Furthermore, we do not take any further effect into account which could enhance the vertical spread of the star particles, e.g. scattering with giant molecular clouds or spiral arms, adiabatic heating due to the growth in mass of the MW disk." To at least asses the influence a generation of star clusters would have onto the results we build our combined model by assuming an initial cluster mass function ICMF)., To at least asses the influence a generation of star clusters would have onto the results we build our combined model by assuming an initial cluster mass function (ICMF). The ICMF is a fundamental property of the process of star formation in galaxies Boily 2002)., The ICMF is a fundamental property of the process of star formation in galaxies \citep{kroup02}. It gives the number of star clusters in a certain mass interval οΛέρο which form during one event of star formation. where «2 is the spectral index of cloud mass spectrum.," It gives the number of star clusters in a certain mass interval $dM_{\rm ecl}$ which form during one event of star formation, where $\beta$ is the spectral index of cloud mass spectrum." In this work we use 7=2. because this value was measured for young star clusters in the Antennae (Whitmoreetal.1999) and generally by Weidner&Kroupa(2004).," In this work we use $\beta=2$, because this value was measured for young star clusters in the Antennae \citep{whit99} and generally by \citet{weid04}." . Because we use a particle-mesh code. where particles represent phase-space elements and not single stars. all of our model clusters have the same number of particles. irrespective of their mass.," Because we use a particle-mesh code, where particles represent phase-space elements and not single stars, all of our model clusters have the same number of particles, irrespective of their mass." We therefore are able mimie an ICMF with a power law index of 4.7=2 by co-adding our results using a power of Jj1=| only. to ensure that every particle has the correct Weight in the combined model.," We therefore are able mimic an ICMF with a power law index of $\beta=2$ by co-adding our results using a power of $\beta-1=1$ only, to ensure that every particle has the correct weight in the combined model." The density distribution of the disrupted star clusters at 10Gyr using the ICMF is shown in Fig 2.., The density distribution of the disrupted star clusters at $10~Gyr$ using the ICMF is shown in Fig \ref{fig:hist-icmf}. In this figure we consider star clusters with a SFE of 20% and where the gas expulsion happens during a crossing time., In this figure we consider star clusters with a SFE of $20\%$ and where the gas expulsion happens during a crossing time. One clearly sees that the shape of the density distribution has a similar resemblance as the thin and thick dise of the MW., One clearly sees that the shape of the density distribution has a similar resemblance as the thin and thick disc of the MW. We tit a double exponential function given by Eq., We fit a double exponential function given by Eq. 5 and obtain values for the 2 scale-heights of fyain=50 pe for the thin dise and μον=500 for the thick dise (see also last line of Tab. 29.," \ref{eq:doble} and obtain values for the $z$ scale-heights of $h_{\rm z,thin} = 50$ pc for the thin disc and $h_{\rm z,thick} = 500$ for the thick disc (see also last line of Tab. \ref{tab:fit}) )." These values are now much closer to the real values of the MW and therefore we believe that by adding also additional scattering and multiple star formation events. we may be able to account for the real disces of the MW.," These values are now much closer to the real values of the MW and therefore we believe that by adding also additional scattering and multiple star formation events, we may be able to account for the real discs of the MW." In addition to studying the shape of the z-distribution of the stars. we can also use our simulations to look at the velocity space.," In addition to studying the shape of the $z$ -distribution of the stars, we can also use our simulations to look at the velocity space." Table 3. shows the velocity dispersion obtained for all our simulations by fitting straight lines to the probability plot of VV- (velocity in z-direction). as described in Bochanskiet 2007).," Table \ref{tab:vel} shows the velocity dispersion obtained for all our simulations by fitting straight lines to the probability plot of $W$ -velocities (velocity in $z$ -direction), as described in \citet{boch07}." The probability plot is a graphical technique where we plot the cumulative probability distribution in units of the standard deviation of the distribution., The probability plot is a graphical technique where we plot the cumulative probability distribution in units of the standard deviation of the distribution. When the distribution is a Gaussian. it shows as a straight line in the probability plot with a slope corresponding to the standard deviation.," When the distribution is a Gaussian, it shows as a straight line in the probability plot with a slope corresponding to the standard deviation." The y-axis-intercept is equal to the median of the distribution., The $y$ -axis-intercept is equal to the median of the distribution. When the distribution is non-Gaussian. the plotting line deviates from a straight line.," When the distribution is non-Gaussian, the plotting line deviates from a straight line." We are therefore able to fit two separate lines to the inner and outer parts of the distribution. resembling the velocity dispersion for the thin and thick dise component of our models.," We are therefore able to fit two separate lines to the inner and outer parts of the distribution, resembling the velocity dispersion for the thin and thick disc component of our models." Again. we note that our low-mass models only contribute to the thin dise component.," Again, we note that our low-mass models only contribute to the thin disc component." As example we show the velocity distribution and. its probability plot for a high mass model in Fig. 3.., As example we show the velocity distribution and its probability plot for a high mass model in Fig. \ref{fig:vel-m06}. " It shows a star cluster with a SFE of 20 and a mass of 2.2.«10"" M.."," It shows a star cluster with a SFE of $20$ and a mass of $2.2 \times 10^{6}$ $_{\odot}$." Clearly. the velocity distribution of thestars is not a Gaussian at all.," Clearly, the velocity distribution of thestars is not a Gaussian at all." Also two Gaussians will not represent this kind of distribution fully., Also two Gaussians will not represent this kind of distribution fully. But it shows clear similarities with the velocity distribution of stars found in the MW (Bochanskietal. 2007).., But it shows clear similarities with the velocity distribution of stars found in the MW \citep{boch07}. . So even though we have an, So even though we have an Py=23 Pp↗2.8 Demo877+3°pe ~ yrs ∐∪∐∐∐⋜↧↕≼∐↴∖↻↸∖↥↴∖↕∪∐⋯↸∖⋜↧↴∖↿∐↸∖∪↕↓≺∖∙⊳⊓⊳↕⊔↻↸⊳≺↕≻↿∐∶↴∙⋜↧⋅∏∖↑E ,$P_A = 23$ $P_B = 2.8$ $87\deg \pm3\deg$ $\sim$ $\mu$ $^{-3}$ reference o solar abundances is necessary in order to convert our abundance of element X to either of the quantities [X/H] or [X/Fe]. we defer o Asplund et al. (,"reference to solar abundances is necessary in order to convert our abundance of element X to either of the quantities [X/H] or [X/Fe], we defer to Asplund et al. (" 2005).,2005). In general. many stellar lines are strong saturated lines in the solar spectrum and. therefore. a line-by-ine analysis for the stellar-solar abundance differences is precluded.," In general, many stellar lines are strong saturated lines in the solar spectrum and, therefore, a line-by-line analysis for the stellar-solar abundance differences is precluded." Carretta provided their adopted solar abundances which we use to convert their [X/Fe] to abundances log ¢(X)., Carretta provided their adopted solar abundances which we use to convert their [X/Fe] to abundances $\log\epsilon$ (X). In addition. t1ον provided a list of lines which were the basis for the line selecion made in the analysis of the red giants.," In addition, they provided a list of lines which were the basis for the line selection made in the analysis of the red giants." A statistical comparison of the g f-values for common lines suggess that zero-point differences in abundances arising from differen choices of gf-value between the RGB stars and the PAGB star are small., A statistical comparison of the $gf$ -values for common lines suggests that zero-point differences in abundances arising from different choices of $gf$ -value between the RGB stars and the PAGB star are small. 0.2 em Our abundances are presented in Table 3 for the CONSENSUS model (6300. 0.80) anc the three other models.," 0.2 cm Our abundances are presented in Table 3 for the consensus model (6300, 0.80) and the three other models." An error analysis is summarized in Table 4+ where we give tfYe abundance differences resulting from models that are variously 300 K hotter. +0.2 dex of higher gravity. and experiencing a 0.5 km different microturbulence than the consensus model.," An error analysis is summarized in Table 4 where we give the abundance differences resulting from models that are variously 300 K hotter, +0.2 dex of higher gravity, and experiencing a $\pm0.5$ km $^{-1}$ different microturbulence than the consensus model." " 0.2 cm Comments on individual elements follow: (2cm Detection of lines was sought via the 3s? P""- 3pP multiplet with lines between aand9112À.", 0.2 cm Comments on individual elements follow: 0.2 cm Detection of lines was sought via the $^3$ $^o$ $^3$ P multiplet with lines between and. . The multiplet is absent., The multiplet is absent. The upper limit to the C abundance for the consensus model is log «(Cy5.7 from the 906|44. 9062.49. and lines with the g f-values from he database.," The upper limit to the C abundance for the consensus model is $\log\epsilon$ $\leq 5.7$ from the 9061.44, 9062.49, and lines with the $gf$ -values from the database." 0.2 em The triplet at 7774 lis srong (Figure 7): an abuncance log c(O) &8.0 fits the triplet., 0.2 cm The triplet at 7774 is strong (Figure \ref{f_oxygen_synthesis}) ); an abundance $\log\epsilon$ (O) $\simeq 8.0$ fits the triplet. The 8446 ffeaure is present and. provices an abundance loge(O) =8.0 (Figure 7 »., The 8446 feature is present and provides an abundance $\log\epsilon$ (O) $\simeq 8.0$ (Figure \ref{f_oxygen_synthesis}) ). The lines at 9260.8 and 9?6ΤΑ aare absent and the upper limi log«(Q) x8.0 is obtained., The lines at 9260.8 and 9262.7 are absent and the upper limit $\log\epsilon$ (O) $\leq 8.0$ is obtained. These consistent abundances correspond to the consensus model and to adoption of the NIST ¢f-values., These consistent abundances correspond to the consensus model and to adoption of the NIST $gf$ -values. Carretta (private communication) has noted that a correction for non-LTE effects lowers the 7774 aabundance by about 0.6-0.8 dex., Carretta (private communication) has noted that a correction for non-LTE effects lowers the 7774 abundance by about 0.6-0.8 dex. Corrections of a similar magnituce may apply to the other lines., Corrections of a similar magnitude may apply to the other lines. 0.2 em The Na D lines are prominent features in the specrum (Figure 8)., 0.2 cm The Na D lines are prominent features in the spectrum (Figure \ref{f_na_synthesis}) ). Three contributors are. identifiable: strong stellar D lines. interstellar D lines with several blended components. and the night sky emission features which are not completey removed in the data reduction.," Three contributors are identifiable: strong stellar D lines, interstellar D lines with several blended components, and the night sky emission features which are not completely removed in the data reduction." The interstellar lines are similar as regards strength and velocity with the interstellar D lines, The interstellar lines are similar as regards strength and velocity with the interstellar D lines " (aB)) = lraj + DE (a E) = —D,B. whereD;=0,—£3 is the total time derivative. including Lie derivative along the velocity of the zero angular momentum observers (ZAMOs). V is a covariant derivative and a is the delay funetion (in ggeometry à=Vfl— 2M/r). ("," 0 ( ) = 4 + D_t ( ) = - D_t, where$D_t = \partial _t - {\cal L} _{\vec{\beta}} $ is the total time derivative, including Lie derivative along the velocity of the zero angular momentum observers (ZAMOs), $ \nabla$ is a covariant derivative and $\alpha$ is the delay function (in geometry $\alpha = \sqrt{1-2 M/r}$ ). (" Relations (1)) are valid if the shift Function is divergence-less aud the metric is time-iuuidependent.,Relations \ref{maxw1}) ) are valid if the shift function is divergence-less $\div \vec{\beta}=0$ and the metric is time-independent. For a more general formulation see Ixomissarov(2001.2011)..)," For a more general formulation see \cite{2004MNRAS.350..427K,2011arXiv1108.3511K}. .)" " Taking the total time derivative of the constraiut E-B=0Oand eliminating D,E aud D;H using Maxwell equations. one arrives at the correspoudiug Olun’s law in Ixerr metric (Lyutikov2011a).. eeneralizine the result of Ciruziuov(1999):: j-"," Taking the total time derivative of the constraint $\E \cdot \B =0$ and eliminating $D_t \E$ and $D_t \B$ using Maxwell equations, one arrives at the corresponding Ohm's law in Kerr metric \citep{2011PhRvD..83f4001L}, generalizing the result of \cite{Gruzinov99}: =." Note that this expression does not contain the shift function ?., Note that this expression does not contain the shift function $\vec{\beta}$. See also section 2.2 in for a fully covariaut derivation of the [-current that also does not require time derivatives aic is independent of the shift function., See also section 2.2 in \citet{mckff06b} for a fully covariant derivation of the 4-current that also does not require time derivatives and is independent of the shift function. " During ecollapse iuto abole.. time cilation near the horizon aud the fraume-drageiug of the horizou lead to the ""horizon locking"" coucditiou: objects are dragged iuto corotation with the holes event horizon.⋅ which⋅ has a frequency⋅ associated⋅ with it ⋅⋅⋅of Quy22ac/(2rse)Hs=οκaod10radsPog1 αν Where « ds the dimensionless Werr parameter."," During collapse into a, time dilation near the horizon and the frame-dragging of the horizon lead to the “horizon locking” condition: objects are dragged into corotation with the hole's event horizon, which has a frequency associated with it of $ \Omega_H \approx a c/(2 r_{\rm Sc}) = 9 \times 10^3 {\rm rad s^{-1}} P_{\rm NS,-3}^{-1} $ , where $a$ is the dimensionless Kerr parameter." The herr parameter of the resulting uunay become fairly large.," The Kerr parameter of the resulting may become fairly large," Iu the following sections. we will assune a ucutral fraction of hvdrogen. yp~10.P at z~20 for calculations of spectra and colors of GRD afterglows.,"In the following sections, we will assume a neutral fraction of hydrogen, $x_{\rm HI} \sim 10^{-6}$ at $z\sim 20$ for calculations of spectra and colors of GRB afterglows." Before such calculations. we show. here. that «yp~10 is possible at a very hiel-: Iu seueral. the neutral fraction. ays). ds spatially variable.," Before such calculations, we show, here, that $x_{\rm HI}\sim 10^{-6}$ is possible at a very $z$ In general, the neutral fraction, $x_{\rm HI}(z)$, is spatially variable." However. we discuss onlv its mean value for siuplicity.," However, we discuss only its mean value for simplicity." The averaged μι is determined by the UV inteustv of the background radiation and the inhomogeneity of the hydrogen παπα” density at the redshift 7., The averaged $x_{\rm HI}$ is determined by the UV intensity of the background radiation and the inhomogeneity of the hydrogen number density at the redshift $z$. Even at very ligh-: universe. the recombination time-scale is πιο. less than the IIubble time-scale.," Even at very $z$ universe, the recombination time-scale is much less than the Hubble time-scale." Thus. we assume the ionization equilibrimu.," Thus, we assume the ionization equilibrium." " In that case. the neanneutral fraction for a highly ionized medium (ie. μι 1) is given bv μιzmCuyoTg. where €—(ui)(np? i the cbhuupiug factor. ay is the nunber density of hwdrogen nuclei. à ids the recombination coefficient. aud Ty=[σονουν is the III photoionization rate where s, is the photon nuuber density per frequency."," In that case, the meanneutral fraction for a highly ionized medium (i.e. $x_{\rm HI} \ll 1$ ) is given by $x_{\rm HI} \approx C n_{\rm H} \alpha/\Gamma_{\rm HI}$, where $C=\langle n_{\rm H}^2 \rangle/\langle n_{\rm H} \rangle^2$ is the clumping factor, $n_{\rm H}$ is the number density of hydrogen nuclei, $\alpha$ is the recombination coefficient, and $\Gamma_{\rm HI}=\int \sigma_{\rm LC}(\nu) c n_\nu d\nu$ is the HI photoionization rate where $n_\nu$ is the photon number density per frequency." " Therefore. the UW backerouud intensity is required to estimate ayy, even if we know the chuupiug factor from the model of the cosinological structure formation."," Therefore, the UV background intensity is required to estimate $x_{\rm HI}$ even if we know the clumping factor from the model of the cosmological structure formation." Tow much photons are required to control the hydrogenneutral fraction in a very low level?, How much photons are required to control the hydrogenneutral fraction in a very low level? Approximately. the III photoionization rate is estimated to be Typ~σιπω with rion beiug the umuber density of ionizing photons.," Approximately, the HI photoionization rate is estimated to be $\Gamma_{\rm HI} \sim \sigma_{\rm L}c n_{\rm ion}$ with $n_{\rm ion}$ being the number density of ionizing photons." ence. we fiud where the case B recombination rate à=2.73410.3? cn? st is adopted (COsterbrock1980," Hence, we find where the case B recombination rate $\alpha=2.73\times10^{-13}$ $^3$ $^{-1}$ is adopted \citep{ost89}." "], Now. we are interested in a very hieh redshift universe (2~ 20)."," Now, we are interested in a very high redshift universe $z\sim20$ )." In there. the chuupine factor is an order of unity.," In there, the clumping factor is an order of unity." Therefore. we find that oulv one photon per a hwdrosen nuclei is sufficient to keep ayy~10.9.," Therefore, we find that only one photon per a hydrogen nuclei is sufficient to keep $x_{\rm HI} \sim 10^{-6}$." Then. we exanüne how mnmuchn stars are required to uaiutaiu the photon density.," Then, we examine how much stars are required to maintain the photon density." " Since a proton recoubines with an electron in a certain time-scale. continuous supply of ionizing photons is needed to keep nm,Dp."," Since a proton recombines with an electron in a certain time-scale, continuous supply of ionizing photons is needed to keep $n_{\rm ion} \sim n_{\rm H}$." Siuce he recombination time-scale is ~μα for μιm1. the required photon enüssvitv per uuit volume is estimated O be EonMona~ayoLte.," Since the recombination time-scale is $\sim 1/n_{\rm H}\alpha$ for $x_{\rm HI} \ll 1$, the required photon emissivity per unit volume is estimated to be $\epsilon_{\rm ion}\sim n_{\rm ion}n_{\rm H}\alpha \sim Cn_{\rm H}^2\alpha^2/x_{\rm HI}\sigma_{\rm L}c$." Ou the other mane. the emissivity is given by Crierej=fccrepsen(ll:)5m where fos is the escape fraction of Lyman contiuuuua roni primordial galaxies. epe is the Lyman contiuuu Xioton enüssiwitv per unit stellar mass. aud pagg is the star formation density per unit tine per unit comoving voluuc.," On the other hand, the emissivity is given by $\epsilon_{\rm ion}=f_{\rm esc}\epsilon_{\rm LC}\rho_{\rm SFR}(1+z)^3$, where $f_{\rm esc}$ is the escape fraction of Lyman continuum from primordial galaxies, $\epsilon_{\rm LC}$ is the Lyman continuum photon emissivity per unit stellar mass, and $\rho_{\rm SFR}$ is the star formation density per unit time per unit comoving volume." Therefore. the required star formation deusitv is Although the photon cnüssvitv at hieh-: is very uucertain because we dont kuow the stellar mass distribution. we estimate the euussivity bv Starburst 99 model (Leithereretal.1999) by assunune the Salpeter mass function with various mass ranecs.," Therefore, the required star formation density is Although the photon emissivity at $z$ is very uncertain because we don't know the stellar mass distribution, we estimate the emissivity by Starburst 99 model \citep{lei99} by assuming the Salpeter mass function with various mass ranges." The estimated values of epe are sununnuarized iu Table 1.The Pop III stars are likely to have a top-heavy mass function (c.e..Nakamura&Umoenmura2001).," The estimated values of $\epsilon_{\rm LC}$ are summarized in Table 1.The Pop III stars are likely to have a top-heavy mass function \citep[e.g.,][]{nu01}." . Hence. the case of 10100. AL. in Table Loamayv be suitable.," Hence, the case of 10–100 $M_\sun$ in Table 1 may be suitable." Iu this case. the required star formation density to maintain tu~LO8 ds ~0.05 AZ. t 7 (comoving) when fine00 and €=I.," In this case, the required star formation density to maintain $x_{\rm HI}\sim10^{-6}$ is $\sim 0.05$ $M_\sun$ $^{-1}$ $^{-3}$ (comoving) when $f_{\rm esc}=0.1$ and $C=1$." I: this star formation deusitv possible?, Is this star formation density possible? ) The latest observations suggest that the star formation density retains a levelof~ 0.3 AL. | ? from: ~ 1to t (Caavaliscoetal.2003)., The latest observations suggest that the star formation density retains a level of $\sim 0.1$ $M_\sun$ $^{-1}$ $^{-3}$ from $z\sim 1$ to $z\sim 6$ \citep{gia03}. . Such a level of star formation may be kept toward more hieh-: universe., Such a level of star formation may be kept toward more $z$ universe. Moreover. a seniaualvtie model shows 0.010.0 AL. | ? at Do20 depending on the assuued star formation efficiency (Somerville&Livio2003).," Moreover, a semianalytic model shows 0.01–0.1 $M_\sun$ $^{-1}$ $^{-3}$ at $z\sim 20$ depending on the assumed star formation efficiency \citep{som03}." ". Thus. we can sufficieutlv expect ~0.05 AZ, + 7 and then. sgg~10 at zc20."," Thus, we can sufficiently expect $\sim 0.05$ $M_\sun$ $^{-1}$ $^{-3}$, and then, $x_{\rm HI}\sim10^{-6}$ at $z\sim20$." In addition. we note that the escape fraction iav be much larger than 0.1 assumed above if the Pop IIT stars are formed in low-mass lalos.," In addition, we note that the escape fraction may be much larger than 0.1 assumed above if the Pop III stars are formed in low-mass halos." Let us discuss the observed spectra of the CRB atterglows in the NIR bands., Let us discuss the observed spectra of the GRB afterglows in the NIR bands. To do so. an afterglow spectral model is required.," To do so, an afterglow spectral model is required." We adopt a simple afterglow model: the svuchrotron radiation from the relativistic shock (Sari.Piau.&Naravan1998)., We adopt a simple afterglow model; the synchrotron radiation from the relativistic shock \citep{sar98}. . More specifically. we adopt equations (1).(5) iu Ciardi&Loeb(2000) who take iuto account the effect of the cosmological redshift.," More specifically, we adopt equations (1)–(5) in \cite{ciardi00} who take into account the effect of the cosmological redshift." The adopted parameters are the magnetic energy fraction of ep=0.1. the electrou cucrey fraction of e.=0.2. the spherical shock energy of E=1077 ere. the ambicut gas umber density of η=10 . aud the power-law iudex of the electron energy distribution p—2.5.," The adopted parameters are the magnetic energy fraction of $\epsilon_{\rm B}=0.1$, the electron energy fraction of $\epsilon_{\rm e}=0.2$, the spherical shock energy of $E=10^{52}$ erg, the ambient gas number density of $n=10$ $^{-3}$, and the power-law index of the electron energy distribution $p=2.5$." First we cousider the observed afterglow spectra in the hypothetical perfectly neutral universe for comparison., First we consider the observed afterglow spectra in the hypothetical perfectly neutral universe for comparison. Iu Figure 1l. we show the expected afterglow spectra iLk cr ueutral universe observed 1 hour after the burst i—- observers frame.," In Figure 1, we show the expected afterglow spectra in the neutral universe observed 1 hour after the burst in the observer's frame." Due to the Lya line absorption. the coutiuuuni bluer than the Lvo liue in the source framehe observed svaveleusthi 1216[1| τμ] ιά)} is completely damped.," Due to the $\alpha$ line absorption, the continuum bluer than the $\alpha$ line in the source frame(the observed wavelength $1+z_{\rm S}$ ] ) is completely damped." Thus. we can flud the Lya break clearly.," Thus, we can find the $\alpha$ break clearly." From the observed wavelength of the Lyra break. we can determine the redshift of the GRBs.," From the observed wavelength of the $\alpha$ break, we can determine the redshift of the GRBs." If we observe the afterglow through a filter. the radiation from the source with the redshift higher than the characteristic redshift of the filter uunot be detected because of the Lvo break.," If we observe the afterglow through a filter, the radiation from the source with the redshift higher than the characteristic redshift of the filter cannot be detected because of the $\alpha$ break." For example. the effect starts from τωτε8 for the J-band aud the source with τα211 cannot be scen through the filter. i.e. 7out.," For example, the effect starts from $z_{\rm S}\simeq 8$ for the $J$ -band and the source with $z_{\rm S}\ga 11$ cannot be seen through the filter, i.e. $J$." " These characteristic redshifts are summarized in Table 2,", These characteristic redshifts are summarized in Table 2. However. we have a chance to see the source hevoud the drop-out redshift if the uuiverse is highly ionized as we will show later.," However, we have a chance to see the source beyond the drop-out redshift if the universe is highly ionized as we will show later." Next we exanuue what is observed if the very 2 universe ds ionized completely as proposed by (20038a.b)..," Next we examine what is observed if the very $z$ universe is ionized completely as proposed by \cite{cen03a,cen03b}. ." Let us set the neutral fraction. ο. of the παάνοδο in the redshift range 15<2<20 to be very small and «yp~d for 2<15 aud +> 20. That is. we assunie that the Pop III stars ionized the universe at 2=20 aud the sudden chanee of the IME due to the transition frou the Pop III to II was occurred at := 15.," Let us set the neutral fraction, $x_{\rm HI}$ , of the universe in the redshift range $15\leq z < 20$ to be very small and $x_{\rm HI} \sim 1$ for $z < 15$ and $z \geq 20$ That is, we assume that the Pop III stars ionized the universe at $z=20$ and the sudden change of the IMF due to the transition from the Pop III to II was occurred at $z=15$ ." The neutral fraction is determined bv the background UV intensity produced by the Pop III stars., The neutral fraction is determined by the background UV intensity produced by the Pop III stars. However. the intensity is," However, the intensity is" Gravitational lensing is now recognised as a valuable probe of the mass distribution in intermediate recshilt (2E 0.4) galaxy clusters independent of any assumptions about the nature of the lensing material (see reviews by Fort AMellier. 1995. Naravan Bartelmann 1997. Mellier 1999. Bartelmann Schneider 1999).,"Gravitational lensing is now recognised as a valuable probe of the mass distribution in intermediate redshift $z < 0.4$ ) galaxy clusters independent of any assumptions about the nature of the lensing material (see reviews by Fort Mellier 1995, Narayan Bartelmann 1997, Mellier 1999, Bartelmann Schneider 1999)." For lenses at such redshifts. uncertainties arising from the redshift distribution of background sources are minimized and the angular scales of both weak and stronglv-Iensed features are well-suited for precise studies.," For lenses at such redshifts, uncertainties arising from the redshift distribution of background sources are minimized and the angular scales of both weak and strongly-lensed features are well-suited for precise studies." On small angular scales in super-critical systems. multiplv-lensed. arces. can provide useful absolute mass estimates provided. spectroscopic redshifts ancl geometric constraints on the location of the various critical lines are available (e.g. Ixneib 1994. 1996).," On small angular scales in super-critical systems, multiply-lensed arcs can provide useful absolute mass estimates provided spectroscopic redshifts and geometric constraints on the location of the various critical lines are available (e.g. Kneib 1994, 1996)." Phe most promising progress in constraining the mass on large scales has come from weak shear measurements (e.g. Fischer 1999: Hoekstra 1908: Clowe 1998). for which sophisticated inversion techniques have been developed: (e.g. lxalser Squires 1993: Ixalser. 1995)., The most promising progress in constraining the mass on large scales has come from weak shear measurements (e.g. Fischer 1999; Hoekstra 1998; Clowe 1998) for which sophisticated inversion techniques have been developed (e.g. Kaiser Squires 1993; Kaiser 1995). Llowever. cluster mass determinations based on weak shear signals are not without limitations.," However, cluster mass determinations based on weak shear signals are not without limitations." Firstly. the mass reconstruction [rom weak shear is non-trivial because of boundary elfects due to the finite field of the cata.," Firstly, the mass reconstruction from weak shear is non-trivial because of boundary effects due to the finite field of the data." To counter this ellect. several linite-leld methods have been proposed (e.g. Seitz Schneider 1996).," To counter this effect, several finite-field methods have been proposed (e.g. Seitz Schneider 1996)." Secondly. since the shear arises from thegradien! of the gravitational potential. the mass reconstruction is only known to within an additive," Secondly, since the shear arises from the of the gravitational potential, the mass reconstruction is only known to within an additive" finders and so it is interesting to ask whether or not (sub)halo properties recovered by different halo finders are consistent.,finders and so it is interesting to ask whether or not (sub)halo properties recovered by different halo finders are consistent. " In this paper we have compared and contrasted the results of two halo finders, andAHF,, that use fundamentally different approaches to identifying subhaloes."," In this paper we have compared and contrasted the results of two halo finders, and, that use fundamentally different approaches to identifying subhaloes." " We have taken a simple test problem, the identification of a NFW subhalo embedded in a more massive NFW halo, and compared the performance of and in recovering the mass of the subhalo at different radii within its host."," We have taken a simple test problem, the identification of a NFW subhalo embedded in a more massive NFW halo, and compared the performance of and in recovering the mass of the subhalo at different radii within its host." " As shown usingSUBFIND,, halo finders that identify subhaloes as overdensities will have a strong dependence on the local density."," As shown using, halo finders that identify subhaloes as overdensities will have a strong dependence on the local density." This is demonstrated in the strong radial dependence in the fraction of a model subhalo recovers., This is demonstrated in the strong radial dependence in the fraction of a model subhalo recovers. " As the subhalo gets closer to the centre of the halo, the background density from the halo is rising."," As the subhalo gets closer to the centre of the halo, the background density from the halo is rising." " With a higher background density and the same density for the subhalo, the overdensity will be less leading to a smaller subhalo being recovered."," With a higher background density and the same density for the subhalo, the overdensity will be less leading to a smaller subhalo being recovered." " By the time the subhalo is in the centre of the halo, which corresponds to the densest point, the overdensity becomes negligible leading to no saddle point and the subhalo is no longer detected."," By the time the subhalo is in the centre of the halo, which corresponds to the densest point, the overdensity becomes negligible leading to no saddle point and the subhalo is no longer detected." " While the size of the overdensity recovered roughly corresponds to the tidal radius of the subhalo, it has been shown that not all subhaloes are stripped down to this size when they pass through a halo."," While the size of the overdensity recovered roughly corresponds to the tidal radius of the subhalo, it has been shown that not all subhaloes are stripped down to this size when they pass through a halo." " The authors of are aware of these issues (see84.1ofSpringeletal.2008) and post-process, but where this effect is not taken into account it could have profound consequences on substructure studies."," The authors of are aware of these issues \citep[see \S4.1 of][]{Springel08} and post-process, but where this effect is not taken into account it could have profound consequences on substructure studies." The radial dependence of locating subhaloes as overdensities will have a large effect on measures of tidal stripping., The radial dependence of locating subhaloes as overdensities will have a large effect on measures of tidal stripping. " As a subhalo plunges into a halo, the halo finder will reduce the size of the subhalo due to the increase in density."," As a subhalo plunges into a halo, the halo finder will reduce the size of the subhalo due to the increase in density." " If this is not considered, then it will appear the subhalo is undergoing a larger amount of stripping as it falls through the halo than it actually underwent."," If this is not considered, then it will appear the subhalo is undergoing a larger amount of stripping as it falls through the halo than it actually underwent." " Stripping will be further complicated by the fact it occurs in the outer region of the subhalo, an area that is not included in the truncated subhalo that is recovered."," Stripping will be further complicated by the fact it occurs in the outer region of the subhalo, an area that is not included in the truncated subhalo that is recovered." This can lead to confusion when comparing the recovery of andSUBFIND., This can lead to confusion when comparing the recovery of and. ". indicates that most of the stripping occurs as the subhalo passes through the centre of the halo and not during the infall, but has been shown to have inefficient unbinding causing it to retain a larger fraction of particles."," indicates that most of the stripping occurs as the subhalo passes through the centre of the halo and not during the infall, but has been shown to have inefficient unbinding causing it to retain a larger fraction of particles." " Meanwhile indicates a more gradual process, but the effects of truncation will cause the recovered subhaloes to always be lower estimates of the size."," Meanwhile indicates a more gradual process, but the effects of truncation will cause the recovered subhaloes to always be lower estimates of the size." Further studies will need to be made to determine how dramatic the effect of stripping is on an infalling subhalo., Further studies will need to be made to determine how dramatic the effect of stripping is on an infalling subhalo. The radial dependence in recovery will also have important implications for the subhalo mass distribution., The radial dependence in recovery will also have important implications for the subhalo mass distribution. 'Two subhaloes that have identical mass can be recovered with different sizes based on position., Two subhaloes that have identical mass can be recovered with different sizes based on position. " This will lead to large subhaloes being recovered as smaller ones, in turn, leading to subhalo mass distributions biased towards the low mass end."," This will lead to large subhaloes being recovered as smaller ones, in turn, leading to subhalo mass distributions biased towards the low mass end." " Whilst most subhaloes that reside in the inner region of the halo will have undergone a large amount of stripping and will be smaller anyway, the effect of truncation still needs to be considered alongside the underlying physics."," Whilst most subhaloes that reside in the inner region of the halo will have undergone a large amount of stripping and will be smaller anyway, the effect of truncation still needs to be considered alongside the underlying physics." T'hese issues highlight that the recovered mass identified using the overdensity method is not a good property to consider when studying subhaloes., These issues highlight that the recovered mass identified using the overdensity method is not a good property to consider when studying subhaloes. " This is true even as far out as the virial radius of the halo, where the mass can be underestimated by around 25 per cent."," This is true even as far out as the virial radius of the halo, where the mass can be underestimated by around 25 per cent." A more stable quantity to consider is the peak in the circular velocity profile., A more stable quantity to consider is the peak in the circular velocity profile. T'his is located much closer to the centre of the subhalo and so will be less affected by truncation and the particular choice of the definition for an, This is located much closer to the centre of the subhalo and so will be less affected by truncation and the particular choice of the definition for an The search algorithm vielded many objects for subsequent analvsis. but none are confirmed 5Ne Ia. Many of the objects are known variable stars. ancl the others correspond to an object visible on the DSS.,"The search algorithm yielded many objects for subsequent analysis, but none are confirmed SNe Ia. Many of the objects are known variable stars, and the others correspond to an object visible on the DSS." Therefore. we conclude that each candidate is a variable star.," Therefore, we conclude that each candidate is a variable star." The search program is effective because many known (and possibly many unknown) variable stars were found. aud some of these objects have light curves that very closely resemble the SN Ia template.," The search program is effective because many known (and possibly many unknown) variable stars were found, and some of these objects have light curves that very closely resemble the SN Ia template." The Monte Carlo simulations imdicate (hat over half of the simulated SN Ia peaking during observation of a field were detected., The Monte Carlo simulations indicate that over half of the simulated SN Ia peaking during observation of a field were detected. Since the filter is effective and detection rates were caleulated. finding zero SNe la outside ISB galaxies is significant and can be used to place limits on the prevalence of LSB galaxies and displaced stars.," Since the filter is effective and detection rates were calculated, finding zero SNe Ia outside HSB galaxies is significant and can be used to place limits on the prevalence of LSB galaxies and displaced stars." Upper limits on the number of SNe Ia in LSB galaxies in (he data set were determined using Poisson statistics., Upper limits on the number of SNe Ia in LSB galaxies in the data set were determined using Poisson statistics. Since we observed no SNe Ia. it was necessary {ο use single-sidecd statistics.," Since we observed no SNe Ia, it was necessary to use single-sided statistics." There is a chance of observing 0 SNe In in LSB galaxies if the expected value is 1.84 5Ne Ia. so <1.84 SNe Ia is the single-sided lo confidence limit.," There is a chance of observing 0 SNe Ia in LSB galaxies if the expected value is 1.84 SNe Ia, so $\le 1.84$ SNe Ia is the single-sided $1\sigma$ confidence limit." Similarly. there is a chance of observing 0 SNe In in LSB galaxies if the expected value is 3.00. so the confidence limit is 3.00 SNe la. For each field. the product of the detection rate (from the Monte Carlo simulations) aud the total space and time searched vields an effective detection region.," Similarly, there is a chance of observing 0 SNe Ia in LSB galaxies if the expected value is 3.00, so the confidence limit is 3.00 SNe Ia. For each field, the product of the detection rate (from the Monte Carlo simulations) and the total space and time searched yields an effective detection region." 5unuming this over all fields gives the total effective detection region (3.33x10* Mpc* days)., Summing this over all fields gives the total effective detection region $3.33 \times 10^7$ $^3$ days). We assume (hat SNe Ia occur at the same rate (number of SNe la per L5. ) in LSBs as is observed in the local Universe.," We assume that SNe Ia occur at the same rate (number of SNe Ia per $L_{B,\odot}$ ) in LSBs as is observed in the local Universe." One objection (o (is assumption is that LSB galaxies mav have binary fractions and/or star formation rates that differ significantly [rom Chose of IISB galaxies., One objection to this assumption is that LSB galaxies may have binary fractions and/or star formation rates that differ significantly from those of HSB galaxies. However. binary formation is a local process ((Tohline2002).. so. even (hough LSBs may have lower star formation rates than Προς (hupex&Bothun1997).. the low stellar density of LSB galaxies will not affect the binary fraction.," However, binary formation is a local process \citep{toh02}, so, even though LSBs may have lower star formation rates than HSBs \citep{imp97}, the low stellar density of LSB galaxies will not affect the binary fraction." Though it was originally thought that LSBs are generally bluer (han HISDs (Impey&Bothun1997).. the CCD survey ol O'Neiletal.(1997) found LSBs with colors ranging from very blue to very red. suggesting that the previous lack of red LSBs was due to a selection effect.," Though it was originally thought that LSBs are generally bluer than HSBs \citep{imp97}, the CCD survey of \citet{one97} found LSBs with colors ranging from very blue to very red, suggesting that the previous lack of red LSBs was due to a selection effect." Thus the stellar population ol LSBs is likely similar to that of HIISDs. which also suggests that the SN Ia rates are similar.," Thus the stellar population of LSBs is likely similar to that of HSBs, which also suggests that the SN Ia rates are similar." Furthermore. the HSB Type Ia supernova rate can be divided into a contribution from old progenitors aud a contribution from voung progenitors (Mannucciοἱal.2005).," Furthermore, the HSB Type Ia supernova rate can be divided into a contribution from old progenitors and a contribution from young progenitors \citep{man05}." . The old progenitor contribution is independent of the star formation rate ancl accounts for most of the SNe Ia in ellipticals. 50 percent in S0a/b. 20 percent in 5bc/d. and a few percent in irnregulars.," The old progenitor contribution is independent of the star formation rate and accounts for most of the SNe Ia in ellipticals, 50 percent in S0a/b, 20 percent in Sbc/d, and a few percent in irregulars." This contribution should also be present in LSBs., This contribution should also be present in LSBs. The voung progenitor contribution is proportional to the SFR. and (thus may be less important in LSBs.," The young progenitor contribution is proportional to the SFR, and thus may be less important in LSBs." Therefore, Therefore "Principally. (he ion velocity v; and the neutral velocity v,, in the molecular clouds. should be determined by solving separate fluid equations of these species. include their coupling by collision processes.","Principally, the ion velocity $\textbf{v}_i$ and the neutral velocity $\textbf{v}_n$ in the molecular clouds, should be determined by solving separate fluid equations of these species, include their coupling by collision processes." However. in the time-scale considered here (see. Fig. 2)).," However, in the time-scale considered here (see, Fig. \ref{timescale}) )," two fluids of ion and neutral are approximately coupled together wilh a drift velocity given bv which is obtained by assuming (hat (he pressure aud gravitational forces on the ehiarged (hud component are negligible compared to the Lorentz force because of the low ionization fraction., two fluids of ion and neutral are approximately coupled together with a drift velocity given by which is obtained by assuming that the pressure and gravitational forces on the charged fluid component are negligible compared to the Lorentz force because of the low ionization fraction. " Llere. in a good approximation we choose p—p,+p;22py."," Here, in a good approximation we choose $\rho=\rho_n+\rho_i\approx\rho_n$." In this way. we can use the basic equations as were given by Shu (1992): where Az&2.16x10?T!?J.«LINtain! is the thermal conduction coefficient in molecular clouds (Lane 19836). and other variables and parameters have (heir usual meanings.," In this way, we can use the basic equations as were given by Shu (1992): where $K \approx 2.16 \times 10^{-2} T^{1/2} \mathrm{J}. \mathrm{s}^{-1} . \mathrm{K}^{-1} . \mathrm{m}^{-1}$ is the thermal conduction coefficient in molecular clouds (Lang 1986), and other variables and parameters have their usual meanings." The energy equation (11)) contains a source term —2pVv. which describes the work is done by expansion or contraction of the medium.," The energy equation \ref{ebenerg}) ) contains a source term $-\frac{5}{2}p\nabla \cdot \textbf{v}$, which describes the work is done by expansion or contraction of the medium." Thus. we note that the sell-gravitating heating term (4)) must be excluded from the net cooling function 9.," Thus, we note that the self-gravitating heating term \ref{hearGR}) ) must be excluded from the net cooling function $\Omega$." The time evolution of magnetic fielcl itself maa then be obtained [rom the approximation that it freezes only in the plasma of ions and electrons., The time evolution of magnetic field itself may then be obtained from the approximation that it freezes only in the plasma of ions and electrons. In. (his way. we obtaim a nonlinear diffusion equation as follows," In this way, we obtain a nonlinear diffusion equation as follows" which is close to the thresholds of 0.7—1.5 g (or 71110 pc?) required to form stars of 10-200(?).,which is close to the thresholds of 0.7–1.5 g (or 110 $^{-2}$ ) required to form stars of 10–200. . It is important to point out that these authors were interested in clouds where no massive stars have yet formed while G11.11P1 shows already signposts of star formation activity., It is important to point out that these authors were interested in clouds where no massive stars have yet formed while G11.11P1 shows already signposts of star formation activity. " We have calculated a density profile power-law index of 1.6 from interferometric observations at 1 and 3 mm; similar values, in the range between 1.5 and 2, for cores in the IRDC G28.34+0.06, have been reported by and for embedded protostellar sources in the protocluster IRAS 05358+3543 as well."," We have calculated a density profile power-law index of 1.6 from interferometric observations at 1 and 3 mm; similar values, in the range between 1.5 and 2, for cores in the IRDC G28.34+0.06, have been reported by and for embedded protostellar sources in the protocluster IRAS 05358+3543 as well." found a velocity gradient of the CH3OH maser emission and explained it as the maser spots being located in a Keplerian disk., found a velocity gradient of the $_3$ OH maser emission and explained it as the maser spots being located in a Keplerian disk. " Interestingly, the spread of the maser components is in the North-South direction which is perpendicular to the CH3OH 2,—1, emission that we propose is originated by an outflow (in the East-West direction)."," Interestingly, the spread of the maser components is in the North-South direction which is perpendicular to the $_3$ OH $2_{k} \rightarrow 1_{k}$ emission that we propose is originated by an outflow (in the East-West direction)." The spread of the masing spots is translated into a radius of ~450 AU for a hypotetical disk in G11.11P1., The spread of the masing spots is translated into a radius of $\sim$ 450 AU for a hypotetical disk in G11.11P1. Note that candidate disks in high-mass protostars have masses in the range 0.2-40 and radii of 0000 AU(?)., Note that candidate disks in high-mass protostars have masses in the range 0.2–40 and radii of 000 AU. ". Our interferometric data set is capable of imaging the biggest disk structures, but not those inferred in?."," Our interferometric data set is capable of imaging the biggest disk structures, but not those inferred in." . G11.11P1 has been cataloged by as a “possible” massive young stellar object (YSO) outflow candidate., G11.11P1 has been cataloged by as a “possible” massive young stellar object (YSO) outflow candidate. " This categorization was based on the angular extent of the extended excess 4.5 um emission, i.e., the extent of green emission in a three-color RGB image."," This categorization was based on the angular extent of the extended excess 4.5 $\mu$ m emission, i.e., the extent of green emission in a three-color RGB image." More evidence pointing to the presence of outflows comes from the non-Gaussian methanol line profiles, More evidence pointing to the presence of outflows comes from the non-Gaussian methanol line profiles In the following. the average symbol <> is omitted. subscript s stands for source. and subseript ο for calibration noise diode.,"In the following, the average symbol $<>$ is omitted, subscript $s$ stands for source, and subscript $c$ for calibration noise diode." " To measure total power in the R and L polarizations. the VV,νο ViVi=VI are made. According to measureme"," To measure total power in the R and L polarizations, the measurements $\widetilde V_R\widetilde V_R^*=V_R^2$ and $\widetilde V_L\widetilde V_L^*=V_L^2$ are made." ntsEq.(," According to Eq.," 8).. introducing= andthe square law detector gain‘ (the scalar quantity g) and recalling that Eq., introducing the square law detector gain (the scalar quantity $g$ ) and recalling that one obtains Eq. " can be expressed in terms of the Stokes parameters or in terms of source linearly polarized flux 75, and phase differences.", can be expressed in terms of the Stokes parameters or in terms of source linearly polarized flux $I_{lps}$ and phase differences. When the Teal calibration is applied. à common post-processing procedure allows one to transform the voltage at the output of the total power devices (TP) into kelvin. as follows The Teal is usually fully linearly polarized and characterized by V.=OK.," When the Tcal calibration is applied, a common post-processing procedure allows one to transform the voltage at the output of the total power devices (TP) into kelvin, as follows The Tcal is usually fully linearly polarized and characterized by $V_{c}=0 K$." This simplifies the involved calculations., This simplifies the involved calculations. By comparing the measured signal with that of the noise diode. the receiver gain fluctuations are removed.," By comparing the measured signal with that of the noise diode, the receiver gain fluctuations are removed." In addition. the Teal calibration procedure calibrates the source strength measurements in terms of antenna temperatures. in kelvin.," In addition, the Tcal calibration procedure calibrates the source strength measurements in terms of antenna temperatures, in kelvin." Discarding the terms of order > 3 one obtains, Discarding the terms of order $\geq$ 3 one obtains not fill the entire shocked. region (of radial length. A’). rut decays to a negligible value at some distance. bA’ (b< 1) behind the shock which energize the emitting luicl.,"not fill the entire shocked region (of radial length $\Delta')$, but decays to a negligible value at some distance $b \Delta'$ $b < 1$ ) behind the shock which energize the emitting fluid." " This implies a reduction of the svynchrotron Dux {ον (equation 23)) by a factor b. which must be compensated » increasing the number of electrons iN, (equation 24)) w a factor b as the product. DE is fixed by the peak- of the svnchrotron spectrum. (equation. 20))."," This implies a reduction of the synchrotron flux $F_{p,sy}$ (equation \ref{ffpsy}) ) by a factor $b$, which must be compensated by increasing the number of electrons $N_e$ (equation \ref{Ne}) ) by a factor $b^{-1}$, as the product $B\Gamma$ is fixed by the peak-energy of the synchrotron spectrum (equation \ref{BG}) )." " The Compton parameter Y and the minimum electron. Lorentz actor 5, remain the same. because they are the 5-rav-to- optical fluences ratio (equation 25)) and the square-root of the 5-rav-to-optical peak-energies ratio (equation 16)). respectively. hence the optical thickness 7. of all electrons (within and outside the region filled with magnetic field) is unchanged."," The Compton parameter $Y$ and the minimum electron Lorentz factor $\gamma_p$ remain the same, because they are the $\gamma$ -ray-to-optical fluences ratio (equation \ref{Y}) ) and the square-root of the $\gamma$ -ray-to-optical peak-energies ratio (equation \ref{gp}) ), respectively, hence the optical thickness $\tau_e$ of all electrons (within and outside the region filled with magnetic field) is unchanged." Consequently. the emission. radius rx(Non)? (equation ⊀− 28)) increases: by a factor⋅ b. ⊥⊐⊳∖," Consequently, the emission radius $r \propto (N_e/\tau_e)^{1/2}$ (equation \ref{taue}) ) increases by a factor $b^{-1/2}$." "⋪This means that the time faa.xr when the jet οedge is seen (equation 36)) ⋅⋅⊀increases by the same factor⋅ 61"" and that [arge-angle emission can last longer than given in equation (43)).", This means that the time $t_{edge} \propto r$ when the jet edge is seen (equation \ref{tedge}) ) increases by the same factor $b^{-1/2}$ and that large-angle emission can last longer than given in equation \ref{ttedge}) ). " As for sell-absorption. a decaving magnetic field means that the column density of the electrons embedded: in the magnetic field the electrons which absorb. the svochrotron flux) is a fraction b of the total electron column density. hence z, of equation (47)) is multiplied b and the up-scatterecl self-absorption energy uieXΤα bv b*7."," As for self-absorption, a decaying magnetic field means that the column density of the electrons embedded in the magnetic field the electrons which absorb the synchrotron flux) is a fraction $b$ of the total electron column density, hence $\tau_a$ of equation \ref{taua}) ) is multiplied $b$ and the up-scattered self-absorption energy $\epsilon_{a,ic} \propto \tau_a ^{3/5}$ by $b^{3/5}$." " The dependence of z. on the filling [actor b is slightly. cdillerent. ifthe Lorentz factor is at. the lower limit implied by the condition 7,22.65, (which lead to equation 33)) and the magnetic field. at the upper limit corresponding to equation. (20))."," The dependence of $\tau_e$ on the filling factor $b$ is slightly different ifthe Lorentz factor is at the lower limit implied by the condition $\gamma_c \simg 2.6\, \gamma_p$ (which lead to equation \ref{Gm}) ) and the magnetic field at the upper limit corresponding to equation \ref{BG}) )." " Lf the electron. radiative cooling is svnchrotron dominated (Y« 1) then the time electrons spend in the magnetic field and cool becomes bfx (equation 32)) while. if scatterings dominate (Y 1). the electron cooling timescale (equation 31)) becomes /.(5,)/b because the intensity of the svnchrotron emission to be up-scattered is b times lower."," If the electron radiative cooling is synchrotron dominated $Y < 1$ ) then the time electrons spend in the magnetic field and cool becomes $b t_\Delta$ (equation \ref{tDelta}) ) while, if scatterings dominate $Y > 1$ ), the electron cooling timescale (equation \ref{tc}) ) becomes $t_c(\gamma_p)/b$ because the intensity of the synchrotron emission to be up-scattered is $b$ times lower." " Thus. in either case. the condition ex2.665, for electron cooling during the burst. leads to Fou)22.6bIx. consequently the lower limit on the Lorentz [actor E (equation 22 33)) decreases by a factor b' and the upper Limit on D resulting from equation (20)) increases by a [actor b.47°)"," Thus, in either case, the condition $\gamma_c \simg 2.6\, \gamma_p$ for electron cooling during the burst leads to $t_c(\gamma_p) > 2.6\, b\, t_\Delta$, consequently the lower limit on the Lorentz factor $\Gamma$ (equation \ref{Gm}) ) decreases by a factor $b^{-1/6}$ and the upper limit on $B$ resulting from equation \ref{BG}) ) increases by a factor $b^{-1/6}$." " [t follows that. if the magnetic field strength D ds at its upper limit. εν of equation (51)) gets multiplied by a factor 6!Lo which is close to the 57"" factor inferred above for the case when E above its lower limit."," It follows that, if the magnetic field strength $B$ is at its upper limit, $\epsilon_{a,ic}$ of equation \ref{eaic}) ) gets multiplied by a factor $b^{7/10}$, which is close to the $b^{3/5}$ factor inferred above for the case when $\Gamma$ above its lower limit." ‘Thus. for the upeseattered: self-absorption. energy is lowered. by a factor 10 and the model fux at to 2 keV. becomes compatible with BeppoSAX observations of CRB 990123.," Thus, for the up-scattered self-absorption energy is lowered by a factor 10 and the model flux at to 2 keV becomes compatible with BeppoSAX observations of GRB 990123." " Parametecrizing 6=0.0864,5. we Lined that the GRB emission is produced at the lower limit on the outflow Lorentz factor is and the upper limit on the magnetic field is The sub-pulse duration of equation (32)) is now £x77οqsLit7bDral sS therefore⋅ the source intrinsic:. luctuations are mareinally resolved and. the observed luctuation amplitude of about requires that jj2100. which is the canonical value chosen in the above equations."," Parameterizing $b = 0.03\, b_{-1.5}$, we find that the GRB emission is produced at the lower limit on the outflow Lorentz factor is and the upper limit on the magnetic field is The sub-pulse duration of equation \ref{tDelta}) ) is now $t_\Delta \le 0.25\; x_1^{-5/3}\, \eta_2^{-1/6}\, b_{-1.5}^{-5/6}$ s, therefore the source intrinsic fluctuations are marginally resolved and the observed fluctuation amplitude of about requires that $\eta \simeq 100$, which is the canonical value chosen in the above equations." " tequiring that the sub-pulse duration fx, does not exceed he EWLLM duration of a GRB pulse. which is /.=10 s. eads to with ye1 because. for fy2fo. the GRB pulse should be a single emission episode."," Requiring that the sub-pulse duration $t_\Delta$ does not exceed the FWHM duration of a GRB pulse, which is $t_\gamma \simeq 10$ s, leads to with $\eta \simg 1$ because, for $t_\Delta \simeq t_\gamma$, the GRB pulse should be a single emission episode." The comoving-frame electron. density of the shocked Iuid is where ¢ is the shock compression factor., The comoving-frame electron density of the shocked fluid is where $\zeta$ is the shock compression factor. Pherefore. the magnetic field energy. is a fraction ∪⇂∎↿⇂⊔⋅∢⋅⊔⋖⋅↓⋅⋏∙≟∙∖⇁∠⇂∢⊾⊔⊳∖⊀∐∙∖⇁⊲↓⊔⇂↓↕⋖⊾⊳∖↓↕⋯∼↳⋖⋅∠⇂∐⊔⊀⊔⇂⊳∖∖⋎↓↕∢⊾↓⋅⋖⋅↓∖↙⊲↓⊳∖ the Lorentz [actor of the shock energizing the GltD-emitting Iluid measured in the frame of the vet unshocked. plasma.," Therefore, the magnetic field energy is a fraction of the energy density in the shocked fluid, where $\Gamma'$ is the Lorentz factor of the shock energizing the GRB-emitting fluid measured in the frame of the yet unshocked plasma." Lf the GRB ejecta were not initially highly. magnetized then a sub-cquipartition magnetic field (2g< 0.5) requires that bO03.P(p/Dteft.," If the GRB ejecta were not initially highly magnetized then a sub-equipartition magnetic field $\varepsilon_B < 0.5$ ) requires that $b > 0.03\, x_1^{13/6}\, (\Gamma'-1)^{-1} \zeta^{-1}$." " For a relativistic shock with I""— few and &=4E"". this condition becomes which is close to that obtained by requiring that ὃν<10 s (equation 561)."," For a relativistic shock with $\Gamma'\sim$ few and $\zeta = 4\Gamma'$, this condition becomes which is close to that obtained by requiring that $t_\Delta \siml 10$ s (equation \ref{bmin1}) )." Thus. we find that the magnetic field length-scale is à fraction b=10 ol the thickness of the shocked gas.," Thus, we find that the magnetic field length-scale is a fraction $b = 10^{-3.5}-10^{-1.5}$ of the thickness of the shocked gas." For the comovine-frame density given in equation (57)). the plasma skin-depth in the shocked. gas is ↿↓⋯⊳∖↿↓∐⋅⊔↓⋜↧⋏∙≟⊔∢⊾↿⊲⊔⇍∐⋖⋅↓∠⇂∠⇂⋯↛⋜↧∙∖⇁⇂∢⊾⊔⋏∙≟↿↓↥−⊳∖≼∙⋜↧⇂⋖⋅⋡∣↗↿∖∆∣∪⊳⊀↓⊳∖ 5.10* times larger than the plasma skin-depth.," For the comoving-frame density given in equation \ref{nco}) ), the plasma skin-depth in the shocked gas is thus the magnetic field decay length-scale, $b(\Delta'/\zeta)$, is $5\times 10^5 - 10^7$ times larger than the plasma skin-depth." Lastly. we note that radius at which the expansion of the ejecta is allected by the interaction with the cireumburst medium. obtained by using the GRB ejecta Lorentz factor E instead of the Lorentz factor of the shocked medium. LI. in equation (38)). is which is close to the radius r-. where the burst emission is produced (equation 53)).," Lastly, we note that radius at which the expansion of the ejecta is affected by the interaction with the circumburst medium, obtained by using the GRB ejecta Lorentz factor $\Gamma$ instead of the Lorentz factor of the shocked medium, $\tilde{\Gamma}$ , in equation \ref{adb}) ), is which is close to the radius $r_\gamma$ where the burst emission is produced (equation \ref{rr}) )." " ""his shows that. if the burst mechanism were internal shocks in a variable wind. the dynamics of these internal shocks is. allectec by the deceleration of the outflow. anc. perhaps. a large number of collisions are between ejecta shells and. the decelerating"," This shows that, if the burst mechanism were internal shocks in a variable wind, the dynamics of these internal shocks is affected by the deceleration of the outflow and, perhaps, a large number of collisions are between ejecta shells and the decelerating" Rueinskis absolute brightness calibration (Rucinski1993) to caleulate M. distances and thus memberships.,"Rucinski's absolute brightness calibration \citep{Ruc93} to calculate $_V$, distances and thus memberships." The method estimates M from the period. unreddened colour. aud svslem metallicity via: For all our EcB systems. we have adopted |Fe/I1I]|—-0.76 and E(V-1)—0.05. 1996).," The method estimates $_V$ from the period, unreddened colour, and system metallicity via: For all our EcB systems, we have adopted [Fe/H]=-0.76 and E(V-I)=0.05 \citep{Harris96}." . Fig.21 shows the derived distance modulus of all EcD lor which we have complete colour information and have periods P«lId: such systems can be regarded. as contact svslenms., \ref{Ruccal} shows the derived distance modulus of all EcB for which we have complete colour information and have periods $<$ 1d; such systems can be regarded as contact systems. " The derived distance modulus (DM) of 47 Tue from this plot is 13.14220.25. which is in agreement with (he estimate of 13.21 presented by Harris(1996)... ancl (hat derived by Percival.Salaris.vanWk.&Kilkenny(2002).. using main sequence fitting. of (m—M),=13.37444."," The derived distance modulus (DM) of 47 Tuc from this plot is $\pm$ 0.25, which is in agreement with the estimate of 13.21 presented by \citet{Harris96}, and that derived by \citet{Per2002}, using main sequence fitting, of $(m-M)_V = 13.37^{0.10}_{-0.11}$." From Fig.21.. it is clear that we have detected 10 eclipsing binaries that are likely members of 47 Tuc.," From \ref{Ruccal}, it is clear that we have detected 10 eclipsing binaries that are likely members of 47 Tuc." V95 and. V26 appear to be foreground members of the Galactic halo. whereas V20 is a likely member of the Small Magellanic Cloud (EHLarries. 2003).," V95 and V26 appear to be foreground members of the Galactic halo, whereas V20 is a likely member of the Small Magellanic Cloud \citep{Harries03}." . Interesünelv. Vill and V75 both have distance moduli which lie inbetween 47 Tuc and the SAIC.," Interestingly, V11 and V75 both have distance moduli which lie inbetween 47 Tuc and the SMC." It is interesting to note the very small amplitude οἱ variation associated with the foreground EcB V26. perhaps indicating low mass components.," It is interesting to note the very small amplitude of variation associated with the foreground EcB V26, perhaps indicating low mass components." To estimate the total number of variable stars present in the WEIT field we consider how many of (INaluzuyetal. 1998)s sample we missed due to telescope offsets ancl gaps between our CCDs., To estimate the total number of variable stars present in the WFI field we consider how many of \citep{Kal98}' 's sample we missed due to telescope offsets and gaps between our CCDs. We recovered 31 of the 42 variables presented in (hat paper., We recovered 31 of the 42 variables presented in that paper. Using (his result. we estimate that we missed ~26% of the variables we are capable of detecting.," Using this result, we estimate that we missed $\sim$ $\%$ of the variables we are capable of detecting." We therefore expect that in total there are 126411 detectable variable stars present in (he field., We therefore expect that in total there are $\pm$ 11 detectable variable stars present in the field. A significant number of Small Magellanie Cloud (SAIC) RR Lyrae stars were found, A significant number of Small Magellanic Cloud (SMC) RR Lyrae stars were found it further.,it further. Doing so csscutially returus us to the results of ?.. who held the data to the highest standards of quality coutrol.," Doing so essentially returns us to the results of \citet{stark}, who held the data to the highest standards of quality control." Their eimipirical result is cousisteut with Gr=3.9L4 0.07)., Their empirical result is consistent with $x = 3.94 \pm 0.07$ ). Iu. triis to extend the sample. I have iucluded some. but not all. of the data your ?7..," In trying to extend the sample, I have included some, but not all, of the data from \citet{begum}." These are difficult observational targets that are inevitably less reliable than the data discussed by ?.., These are difficult observational targets that are inevitably less reliable than the data discussed by \citet{stark}. " Tudeed. only three of the twoeuty-uine galaxies of ?. inect 1ο quality requirements of ὃν,"," Indeed, only three of the twenty-nine galaxies of \citet{begum} meet the quality requirements of \citet{stark}." As discussed in ?.. Dreject ibout half the sample as having unreliable inclinations.," As discussed in \citet{btfseb}, I reject about half the sample as having unreliable inclinations." An example of just how difficult it can be to measure i6 inclination of these objects is elven by the case of IIohuberg II (Fig. 3)).," An example of just how difficult it can be to measure the inclination of these objects is given by the case of Holmberg II (Fig. \ref{HoII}) )," which has rather better data than 1ο majority of Commparably low mass galaxies., which has rather better data than the majority of comparably low mass galaxies. However. inclination estimates for it varv from 317 to 15 (7) to 55° or even SÍ? at large radii (2)..," However, inclination estimates for it vary from $31^{\circ}$ to $45^{\circ}$ \citep{THINGS} to $55^{\circ}$ or even $84^{\circ}$ at large radii \citep{BC}." I do not make use of data with such large disparities in their inclination estimates., I do not make use of data with such large disparities in their inclination estimates. Iu. order to expand the size of the sample as they do. 7? unust invariably do so.," In order to expand the size of the sample as they do, \citet{FS11} must invariably do so." It therefore comes as no surprise— that they fud a larger scatter aud higher as these are the expected results of incorporating less accurate data.," It therefore comes as no surprise that they find a larger scatter and higher $\chi^2$, as these are the expected results of incorporating less accurate data." Returning to the issue of the scatter. one of the xiliaut aspects of the program of ? is that it optionally allows one to fit for the intrinsic scatter.," Returning to the issue of the scatter, one of the brilliant aspects of the program of \citet{benfit} is that it optionally allows one to fit for the intrinsic scatter." Using his option returns a best fit intrinsic scatter of zero., Using this option returns a best fit intrinsic scatter of zero. Zero is the preferred amount of intrinsic scatter the xograun returus irrespective of whether I restrict the slope and normalization to the MOND values or leave hem free., Zero is the preferred amount of intrinsic scatter the program returns irrespective of whether I restrict the slope and normalization to the MOND values or leave them free. Weiners program. provides uo imdepoeudeut substantiation of the claim of finite iutriusie scatter made wo., Weiner's program provides no independent substantiation of the claim of finite intrinsic scatter made by \citet{FS11}. I value intellectual honesty very. highly., I value intellectual honesty very highly. IfI had. found any serious error iu mv work. I would be eager to resolve the discrepancy aud sav so.," If I had found any serious error in my work, I would be eager to resolve the discrepancy and say so." Perliaps Eve qissed somethiug. but I do not see what.," Perhaps I've missed something, but I do not see what." Stepping back from the details. ?. fud esseutiallv the same result as I do: au acceleration scale consistent with MOND with very Little intrinsic scatter in the BTFR.," Stepping back from the details, \citet{FS11} find essentially the same result as I do: an acceleration scale consistent with MOND with very little intrinsic scatter in the BTFR." They justcout like it., They justdon't like it. Tam happy to consider nunodels that make a legitimate effort to explain the data., I am happy to consider models that make a legitimate effort to explain the data. 7. and 7. fall short ofthis standard., \citet{gnedin11} and \citet{FS11} fall short of this standard. Iideed. they do no even attempt to micet it.," Indeed, they do no even attempt to meet it." The point is that MOND provides an economical description of salaxv scale kinematics., The point is that MOND provides an economical description of galaxy scale kinematics. The simple formula proposed by AGlerom is the force law in rotating galaxies., The simple formula proposed by Milgrom is the force law in rotating galaxies. This i what we need to explain. iu oor an other theory.," This is what we need to explain, in or an other theory." It is not easy to understand how this simple formula follows from the complex physics of galaxy formation inACDAL., It is not easy to understand how this simple formula follows from the complex physics of galaxy formation in. If it were. there would already be a well established model for it.," If it were, there would already be a well established model for it." Iustead. the literature is littered with mutuallv inconsistent models that persistently fail to describe galaxy data as well as MOND.," Instead, the literature is littered with mutually inconsistent models that persistently fail to describe galaxy data as well as MOND." The DTFR connects the observed barvouic mass to the characteristic circular velocity., The BTFR connects the observed baryonic mass to the characteristic circular velocity. This relation vetween elobal quantities is just one manifestation of MONDian phenomenology., This relation between global quantities is just one manifestation of MONDian phenomenology. There is also a point bv volut mapping between the observed distribution of xuwvous and the observed rotation curve. includiug all he bumps aud wieeles iu both.," There is also a point by point mapping between the observed distribution of baryons and the observed rotation curve, including all the bumps and wiggles in both." This is a reiteration of he well established observational fact that MIOND fits he rotation curves of galaxies (?).., This is a reiteration of the well established observational fact that MOND fits the rotation curves of galaxies \citep{SMmond}. . One can write this as a scaling relation 7 from he rotation curve that Newtomlan eravity predicts for he observed barvonic components V4(r) to the actual observed rotation curve Ver): As Dvo written it hore (sec.c.g.22). gy=Vpfris the Newtonian acceleration produced by the observed stars and sas as deternüned bv πισα solutiou of the Poisson equation.," One can write this as a scaling relation $\nu$ from the rotation curve that Newtonian gravity predicts for the observed baryonic components $V_b(r)$ to the actual observed rotation curve $V_c(r)$: As I've written it here \citep[see, e.g.,][]{MSclusters,M08}, $g_N = V_b^2/r$ is the Newtonian acceleration produced by the observed stars and gas as determined by numerical solution of the Poisson equation." There is no approximation (6.8. exponential disks): the actual observed surface density is used. Ποπιαπιο bulge. disk. aud gas. with all their bumps and wigeles.," There is no approximation (e.g., exponential disks); the actual observed surface density is used, including bulge, disk, and gas, with all their bumps and wiggles." For reasons not preseutlv uudoerstood. the siuple. smooth functiou ν maps from the observed barvon distribution to the observed rotation curve.," For reasons not presently understood, the simple, smooth function $\nu$ maps from the observed baryon distribution to the observed rotation curve." Ouly the observed barvous are required as input. with no reference to the dyvaiiauicallvy dominant dark matter.," Only the observed baryons are required as input, with no reference to the dynamically dominant dark matter." Stated this wax. equation | is merely a restatement of MOND.," Stated this way, equation \ref{MDaccscaling} is merely a restatement of MOND." Iowever. the scaling relation still holds even if MOND is incorrect. as it is known to fit the majority of rotation curves.," However, the scaling relation still holds even if MOND is incorrect, as it is known to fit the majority of rotation curves." There is only one tiny bit of leeway., There is only one tiny bit of leeway. Computing the barvouic rotation curve requires knowledge of the mass-to-leht ratio of the stars. (, Computing the baryonic rotation curve requires knowledge of the mass-to-light ratio of the stars. ( Note that this does not apply to the gas. but one can in principle have separate mass-to-light ratios for the bulge and disk.),"Note that this does not apply to the gas, but one can in principle have separate mass-to-light ratios for the bulge and disk.)" This stellar miass-to-leht ratio ii the one fit parameter of MOND rotation curve fits., This stellar mass-to-light ratio is the one fit parameter of MOND rotation curve fits. Since we are now considering the case where such fits are just a scaling relation. not a fundamental law of nature. there is no need for this to be the correct niass-to-liehlit ratio.," Since we are now considering the case where such fits are just a scaling relation, not a fundamental law of nature, there is no need for this to be the correct mass-to-light ratio." We can generalize the relation to account for this by defiuing the ratio which is the ratio of the actual stellar mass-to-lieht ratio to thatrequired to obtain à MOND fit., We can generalize the relation to account for this by defining the ratio which is the ratio of the actual stellar mass-to-light ratio to thatrequired to obtain a MOND fit. We can now write This imass-discrepanceyacceleration relation is purely clupirical aud ecuerally valid (?).., We can now write This mass-discrepancy–acceleration relation is purely empirical and generally valid \citep{MDacc}. It is equivalent to MOND in the case of Q=I. but it holds even when MOND does not.," It is equivalent to MOND in the case of ${\cal Q} = 1$, but it holds even when MOND does not." This encapsulates the fact that it is usually. possible to obtain a reasonable fit to rotation curves with MOND., This encapsulates the fact that it is usually possible to obtain a reasonable fit to rotation curves with MOND. The MOND inass-to-light ratios are fairly reasonable in terms of stellar populations (7).. so prestunably Q is not very different from unity. though it could be.," The MOND mass-to-light ratios are fairly reasonable in terms of stellar populations \citep{MDacc}, so presumably ${\cal Q}$ is not very different from unity, though it could be." Note that this cuipirical foruulatiou uced not apply to non-rotating svstems: perhaps it is a scaling relation specific to disk galaxies., Note that this empirical formulation need not apply to non-rotating systems; perhaps it is a scaling relation specific to disk galaxies. While we need notexplain MOND in ACDAL.. we do necd to explain the data.," While we need notexplain MOND in , we do need to explain the data." The data for disk galaxies are eucapsulated by equation 7.., The data for disk galaxies are encapsulated by equation \ref{MDacc}. . A satisfactory model would, A satisfactory model would associated with the NGC 4839 group. must be in front of the cluster (moving in).,"associated with the NGC 4839 group, must be in front of the cluster (moving in)." If the relie is indeed associated with the infalling wall of galaxies. then it would explain why the models of Enflin et al. (," If the relic is indeed associated with the infalling wall of galaxies, then it would explain why the models of lin et al. (" 1998) underestimated its fractional polarization: we are viewing the relic almost edge on.,1998) underestimated its fractional polarization; we are viewing the relic almost edge on. However. similar o Enflin et al. (," However, similar to lin et al. (" 1998). we claim that the correspondence between the radio relic and the infalling wall of galaxies is evidence for this being a true large-scale infall shock and not an outwardly propagatiiag merger shock.,"1998), we claim that the correspondence between the radio relic and the infalling wall of galaxies is evidence for this being a true large-scale infall shock and not an outwardly propagating merger shock." The polarization properties of the exended relic (Fig. 21).," The polarization properties of the extended relic (Fig. \ref{gbt_pol}) )," namely that only the outside edge of the relic is polarized. is consistent with recent numerical simulations showing that relic emission consists of two regions (Paul et a.," namely that only the outside edge of the relic is polarized, is consistent with recent numerical simulations showing that relic emission consists of two regions (Paul et al." 2010)., 2010). At the shock location. first-order Fermi acceleration dominates (and is polarized due to shock compression/alignment of the magnetic fields).," At the shock location, first-order Fermi acceleration dominates (and is polarized due to shock compression/alignment of the magnetic fields)." The post-shock region is increasingly dominated by second-order Fermi acceleration from MHD turbulence. and is ikely depolarized due to small-scale tangling of the field.," The post-shock region is increasingly dominated by second-order Fermi acceleration from MHD turbulence, and is likely depolarized due to small-scale tangling of the field." High-frequency and resolution spectro-polarimetric observations of sufficient depth to detect the extended relic and solve for Faraday rotation are needed in order to confirm this paradigm., High-frequency and resolution spectro-polarimetric observations of sufficient depth to detect the extended relic and solve for Faraday rotation are needed in order to confirm this paradigm. These optical and polarization data suryport the identification of the extended Coma relic as the only ΝTpe scale infall shock currently known., These optical and polarization data support the identification of the extended Coma relic as the only Mpc scale infall shock currently known. However. further investigation. especially with numerical simulations. is needed in order test the plausibility of this claim.," However, further investigation, especially with numerical simulations, is needed in order test the plausibility of this claim." The sharp synchrotron front seen in Figure 3. is unique among classical GRHs., The sharp synchrotron front seen in Figure \ref{wsrt_mos} is unique among classical GRHs. We will first compare the front to published and archival X-ray information. then examine possible origins for the synchrotron emission.," We will first compare the front to published and archival X-ray information, then examine possible origins for the synchrotron emission." Finally. we will examine the global radio vs. X-ray correlation of the radio halo in the context of GRH origin models.," Finally, we will examine the global radio vs. X-ray correlation of the radio halo in the context of GRH origin models." Many deep X-ray observations have been taken of the Coma cluster with telescopes such as ROSAT. XMM. Chandra. and Suzaku.," Many deep X-ray observations have been taken of the Coma cluster with telescopes such as ROSAT, XMM, Chandra and Suzaku." X-ray soft (Bonamente et al., X-ray soft (Bonamente et al. 2009) and hard excesses (e.g.. Eckert et al.," 2009) and hard excesses (e.g., Eckert et al." 2008) have been claimed in the Western infall region. which have been attributed to non-thermal IC emission.," 2008) have been claimed in the Western infall region, which have been attributed to non-thermal IC emission." The non-thermal nature of the excess has been ruled-out/challenged by Wik et al. (, The non-thermal nature of the excess has been ruled-out/challenged by Wik et al. ( 2009) using Suzaku. though they contirm higher temperatures in the western region just interior to the synchrotron front.,"2009) using Suzaku, though they confirm higher temperatures in the western region just interior to the synchrotron front." Neumann et al. (, Neumann et al. ( 2003) also found an excess above a in the west. just interior to the synehrotron front.,"2003) also found an excess above a beta-model in the west, just interior to the synchrotron front." The exact Kinematics of this western X-ray structure is not clear., The exact kinematics of this western X-ray structure is not clear. Adami et al. (, Adami et al. ( 2005) argue that the northern and southern portions of the structure have different histories. with galaxy groups GI2 and GI4 associated with the south part of the structure. and appearing to be infalling from the rear.,"2005) argue that the northern and southern portions of the structure have different histories, with galaxy groups G12 and G14 associated with the south part of the structure, and appearing to be infalling from the rear." Fig., Fig. 8 shows archival ROSAT PSPC observations with our »oint-souree. subtracted WSRT contour image overlaid (4x3’ resolution)., \ref{xray_diff} shows archival ROSAT PSPC observations with our point-source subtracted WSRT contour image overlaid $4^{\prime}\times 3^{\prime}$ resolution). There is a striking alignment of an apparent X-ray edge (Markevich et al., There is a striking alignment of an apparent X-ray edge (Markevich et al. in preparation) in the ROSAT image with he synchrotron edge in the Southern portion of the front., in preparation) in the ROSAT image with the synchrotron edge in the Southern portion of the front. The correlation in the South makes it likely that a shock front is responsible for both features. and the relativistic electrons were oroduced by shock-(reyacceleration.," The correlation in the South makes it likely that a shock front is responsible for both features, and the relativistic electrons were produced by shock-(re)acceleration." The correlation is lost in the orthern region. where the synchrotron extends farther than the diffuse X-rays.," The correlation is lost in the Northern region, where the synchrotron extends farther than the diffuse X-rays." A deep XMM-Newton mosaic of the Coma cluster (Schuecker et al., A deep XMM-Newton mosaic of the Coma cluster (Schuecker et al. 2004: Wik et al., 2004; Wik et al. 2009) yielded a spatially resolved temperature map., 2009) yielded a spatially resolved temperature map. Higher signal/noise fits were taken of the boxed regions indicated in Fig., Higher signal/noise fits were taken of the boxed regions indicated in Fig. 8 (Alexis Finoguenov. private communication) which found [6.8. 0.6. 16.3. 2.9. 0.24. 2.46. 0.21] keV for boxes [l. 2. 3. 4]. respectively.," \ref{xray_diff} (Alexis Finoguenov, private communication) which found $\pm$ 0.6, $\pm$ 2.9, $\pm$ 0.24, $\pm$ 0.21] keV for boxes [1, 2, 3, 4], respectively." The factor of 2 increase in temperature across the Southern front toward the cluster is further evidence for the presence of a shock in this region., The factor of 2 increase in temperature across the Southern front toward the cluster is further evidence for the presence of a shock in this region. The Northern region. however. shows the opposite sign. with the temperature being much higher the synchrotron front.," The Northern region, however, shows the opposite sign, with the temperature being much higher the synchrotron front." This. coupled with the poor correspondence between the synchrotron and X-ray surface-brightness profiles in the North. means that either the Western front is not a single shock structure or there are projection effects operating in the Northern region.," This, coupled with the poor correspondence between the synchrotron and X-ray surface-brightness profiles in the North, means that either the Western front is not a single shock structure or there are projection effects operating in the Northern region." Given the complex three-dimensional dynamics of the cluster. it is quite possible for part of the synchrotron front Gin this case. the North) to be confused by unrelated X-ray brightness and temperature effects.," Given the complex three-dimensional dynamics of the cluster, it is quite possible for part of the synchrotron front (in this case, the North) to be confused by unrelated X-ray brightness and temperature effects." The general rise in temperature towards the northwest is most easily explained by shock-heating. either from an infall/accretion shock or an outward-propagating shock.," The general rise in temperature towards the northwest is most easily explained by shock-heating, either from an infall/accretion shock or an outward-propagating shock." Outward) propagating shocks can arise from merger events. or they could be currently driven by a subcluster/group leaving the cluster after passing through the core.," Outward propagating shocks can arise from merger events, or they could be currently driven by a subcluster/group leaving the cluster after passing through the core." " The alternative to shock heating at the cluster periphery would be that the material was pre-heated up to 10-15 keV in the infalling filamentary structure before accreting onto the cluster,", The alternative to shock heating at the cluster periphery would be that the material was pre-heated up to 10-15 keV in the infalling filamentary structure before accreting onto the cluster. Gas in filaments is normally in the range of 10? « T 107 K. that is. a temperature less than | keV. It is implausible for gas in filaments to be heated to 160 keV or higher by structure formation shocks (e.g. Ryu Kang 2009).," Gas in filaments is normally in the range of $^{5}$ $<$ T $<$ $^{7}$ K, that is, a temperature less than 1 keV. It is implausible for gas in filaments to be heated to 10 keV or higher by structure formation shocks (e.g., Ryu Kang 2009)." Those temperatures, Those temperatures The atomic diffuse hydrogen is πιό:| integrating along the line of sight from the GRD to a radius of 20 kpc from the galactic: center.,The atomic diffuse hydrogen is summed integrating along the line of sight from the GRB to a radius of 20 kpc from the galactic center. The III contribution ranges therefore from+ a null value to —7+E212 LO--cimP7. with. a pick at about 5+0σα 7. not sufficient to obscure the afterglow.," The HI contribution ranges therefore from a null value to $7\cdot10^{22}$ $^{-2}$, with a pick at about $5\cdot10^{20}$ $^{-2}$ not sufficient to obscure the afterglow." On the other haud the encounter of a single cloud yields values O “NIL of about 510220. 2 (MC) or 5-10755 7? (DC) largely cuonel to completely ysorh the optical afterelow., On the other hand the encounter of a single cloud yields values of NH of about $5\cdot10^{22}$ $^{-2}$ (GMC) or $5\cdot10^{23}$ $^{-2}$ (DC) largely enough to completely absorb the optical afterglow. The total amount of NID is computed and catalogued for the whole 500 CRBs set and for the subset of 91 nuclemr bursts., The total amount of NH is computed and catalogued for the whole 500 GRBs set and for the subset of 91 nuclear bursts. Iu Fie., In Fig. 1. the histogram of the total NII distribution is shown for the two populaions., \ref{fignh} the histogram of the total NH distribution is shown for the two populations. To better appreciate the difference a cumulative distribution for a siualler rauge of cohuun deusities is reported aside., To better appreciate the difference a cumulative distribution for a smaller range of column densities is reported aside. Tio alnount of dark CRBs due to dus absorption can now be estimated. once we have fixed the ΠαΊος magnitude of our elescopes in the various passbands and the typical apparent niiwnitude of GRB aftergows.," The amount of dark GRBs due to dust absorption can now be estimated, once we have fixed the limiting magnitude of our telescopes in the various passbands and the typical apparent magnitude of GRB afterglows." We associate randomly to cach CRB a jet opening απο]ο 0 following the lav X0 “that we have extrapolated from the known, We associate randomly to each GRB a jet opening angle $\theta$ following the law $\propto\theta^{-0.85}$ that we have extrapolated from the known "either the ROI has occurred, transferring radial motions to tangential, or the motions are dominated by the initial isotropic velocity dispersion imposed by the initial conditions.","either the ROI has occurred, transferring radial motions to tangential, or the motions are dominated by the initial isotropic velocity dispersion imposed by the initial conditions." " In the latter case, any increase in radial velocity dispersion due to infalling shells is counteracted by the increase in tangential velocities as particles attempt to conserve angular momentum in response to being pulled inward by the infalling material."," In the latter case, any increase in radial velocity dispersion due to infalling shells is counteracted by the increase in tangential velocities as particles attempt to conserve angular momentum in response to being pulled inward by the infalling material." " Therefore, both the large and small radius behavior suggest that the behavior of G(r) increasing from 0 to 1 should be quite typical, as we indeed find."," Therefore, both the large and small radius behavior suggest that the behavior of $\beta(r)$ increasing from 0 to 1 should be quite typical, as we indeed find." " Although the overall shape of 6(r)=0—1 is similar among all halos, we do see a slight signature of the ROI in the steepness with which G(r) increases."," Although the overall shape of $\beta(r)=0\rightarrow1$ is similar among all halos, we do see a slight signature of the ROI in the steepness with which $\beta(r)$ increases." " The σ halos have noticeably steeper transitions from (ή)=0— 1, which could possibly be a result of the initial velocity dispersion dominating the core isotropy rather than the ROI."," The $\sigma$ halos have noticeably steeper transitions from $\beta(r) = 0 \rightarrow 1$ , which could possibly be a result of the initial velocity dispersion dominating the core isotropy rather than the ROI." " It is important to point out that a triaxial halo core cannot be purely isotropic, though it appears so in Figure 8.."," It is important to point out that a triaxial halo core cannot be purely isotropic, though it appears so in Figure \ref{fig:beta_sigmas}." " This is due to our use of spherical radial bins to analyze a non-spherical system, and the fact that the standard-resolution halos do not have enough particles in the central region to properly resolve the orbital motions."," This is due to our use of spherical radial bins to analyze a non-spherical system, and the fact that the standard-resolution halos do not have enough particles in the central region to properly resolve the orbital motions." An examination the Cartesian velocity dispersion tensor of the central regions confirms that the core is nearly but not exactly isotropic., An examination the Cartesian velocity dispersion tensor of the central regions confirms that the core is nearly but not exactly isotropic. " Our use of B(r) as a measure of anisotropy is still very useful, however, as it effectively tracks large-scale changes in anisotropy with radius,as can be seen from the figures."," Our use of $\beta(r)$ as a measure of anisotropy is still very useful, however, as it effectively tracks large–scale changes in anisotropy with radius,as can be seen from the figures." We track the time evolution of the anisotropy profile in Figure 9 for the high-resolution Oc halo., We track the time evolution of the anisotropy profile in Figure \ref{fig:beta_red} for the high–resolution $0\sigma$ halo. The characteristic shape of the profile develops very early on as particles at small radii collapse and undergo mixing., The characteristic shape of the profile develops very early on as particles at small radii collapse and undergo mixing. " At the first timestep shown, the ROI has just begun, causing the innermost particles to enter box orbits, while the rest of the halo is still dominated by radial infall (red dotted line)."," At the first timestep shown, the ROI has just begun, causing the innermost particles to enter box orbits, while the rest of the halo is still dominated by radial infall (red dotted line)." " The near-isotropic core develops quickly and grows as more particles reach the center; by 1.6 Gyr, the ROI has operated on much of the center of the halo (green dashed line)."," The near-isotropic core develops quickly and grows as more particles reach the center; by 1.6 Gyr, the ROI has operated on much of the center of the halo (green dashed line)." The outermost regions consist of radially infalling material throughout the evolution of the halo., The outermost regions consist of radially infalling material throughout the evolution of the halo. Note that the high-resolution halo has enough particles to resolve the orbital motions at the core., Note that the high-resolution halo has enough particles to resolve the orbital motions at the core. " The B(r) profile tends toward zero at small radii but an anisotropic component remains, due to the triaxiality of the halo."," The $\beta(r)$ profile tends toward zero at small radii but an anisotropic component remains, due to the triaxiality of the halo." " The time evolution of the anisotropy profiles of the higher—o halo is comparable to those of the “cold” halo, in that the cores of the halos become isotropic at early times."," The time evolution of the anisotropy profiles of the $\sigma$ halo is comparable to those of the “cold” halo, in that the cores of the halos become isotropic at early times." " However, while these halos appear to develop similarly, the core isotropy comes about differently for each halo; the higher—o halos have pre-existing isotropic orbits in the central region, preventing instabilities during collapse and maintaining a central isotropic core."," However, while these halos appear to develop similarly, the core isotropy comes about differently for each halo; the $\sigma$ halos have pre–existing isotropic orbits in the central region, preventing instabilities during collapse and maintaining a central isotropic core." " In contrast, the Oo halo develops its isotropic core via the ROI."," In contrast, the $\sigma$ halo develops its isotropic core via the ROI." " Therefore, the characteristic shape of the anisotropy profile is independent of the shape of the halo, and can be formed either when there is an existing isotropic velocity dispersion, or via such a mechanism as the ROI if the halo is dynamically cold."," Therefore, the characteristic shape of the anisotropy profile is independent of the shape of the halo, and can be formed either when there is an existing isotropic velocity dispersion, or via such a mechanism as the ROI if the halo is dynamically cold." " This finding explains the results of Luetal.(2006),, who find that the universal y~—1 inner halo density slope is formed for a variety of initial velocity dispersion distributions (i.e. radial, isotropic), particularly during an early ""fast accretion"" phase."," This finding explains the results of \citet{Lu06}, who find that the universal $\gamma\sim-1$ inner halo density slope is formed for a variety of initial velocity dispersion distributions (i.e. radial, isotropic), particularly during an early “fast accretion” phase." Our Gaussian initial conditions are such that ~90% of the halo mass has a freefall time within of the median., Our Gaussian initial conditions are such that $\sim 90\%$ of the halo mass has a freefall time within of the median. Thus our halos are likely to fall in the “fast accretion” regime of Luetal.(2006)., Thus our halos are likely to fall in the “fast accretion” regime of \citet{Lu06}. ". Note, however, that unlike Luetal. we do not need to posit an additional source of isotropization(2006) for a core to be produced."," Note, however, that unlike \citet{Lu06} we do not need to posit an additional source of isotropization for a core to be produced." The necessary isotropization occurs naturally either through the ROI or the conservation of angular momentum., The necessary isotropization occurs naturally either through the ROI or the conservation of angular momentum. " Halos with various velocity dispersions show similar structural properties, whether or not they undergo the ROI."," Halos with various velocity dispersions show similar structural properties, whether or not they undergo the ROI." Figure 10 plots the fully evolved density and phase— density profiles of each standard-resolution halo., Figure \ref{fig:den_psd_sigmas} plots the fully evolved density and phase--space density profiles of each standard–resolution halo. 'There is a noticeably shallower core in both the density and phase-space density profiles with higher o., There is a noticeably shallower core in both the density and phase–space density profiles with higher $\sigma$. " This effect was first reported by Merritt&Aguilar(1985) and is not surprising, considering the higher initial angular momenta characteristic of systems with large oy."," This effect was first reported by \citet{Merritt85} and is not surprising, considering the higher initial angular momenta characteristic of systems with large $\sigma_\phi$." It is also important to recall from our tests in 822 that these medium-resolution simulations may not completely capture the properties of the halo core., It is also important to recall from our tests in 2 that these medium–resolution simulations may not completely capture the properties of the halo core. " So, while these results certainly make intuitive sense, high-resolution simulations are needed for confirmation within 0.05rooo."," So, while these results certainly make intuitive sense, high–resolution simulations are needed for confirmation within $0.05r_{200}$." " 'The evolution of the density and phase-space density profiles with time are shown in Figure 11 for the high-resolution, zero dispersion halo."," The evolution of the density and phase–space density profiles with time are shown in Figure \ref{fig:den_psd_red} for the high–resolution, zero dispersion halo." Each profile is normalized to the virial radius at each corresponding timestep., Each profile is normalized to the virial radius at each corresponding timestep. The basic shape of each profile is formed after 1.5 Gyr of evolution and grows outward with radius as the halo collapses., The basic shape of each profile is formed after 1.5 Gyr of evolution and grows outward with radius as the halo collapses. The outermost radii have yet to collapse at the present time., The outermost radii have yet to collapse at the present time. The final density profile (top, The final density profile (top this model that are roughly 300 times more stringent thaw those from the THA survey. and these coustraints would extend to 2~L. Simularly tight hits can be placed ou the 250-S model. but this time extending out to a redshift of 6.,"this model that are roughly 300 times more stringent than those from the IfA survey, and these constraints would extend to $z \sim 4.$ Similarly tight limits can be placed on the 250-S model, but this time extending out to a redshift of 6." Iu fact. even very faint like 150-W would be scusitively probed out to 2~2.5. In the ceutral panels we adopt a lint of Jyp=30. corresponding to the depth of the planned (7.5 deg?) SNAP decp-field survey.," In fact, even very faint like 150-W would be sensitively probed out to $z \sim 2.5.$ In the central panels we adopt a limit of $J_{\rm AB} = 30$, corresponding to the depth of the planned (7.5 $^2$ ) deep-field survey." Iu this case. both the 200-I and 250-S inodels would be well studied out to :z5. aud the 150-W inodel would be easily detectable out to zI despite its overall low DIuniuositv aud relatively short lifetime.," In this case, both the 200-I and 250-S models would be well studied out to $z \gtrsim 5,$ and the 150-W model would be easily detectable out to $z \sim 4$ despite its overall low luminosity and relatively short lifetime." Finally. in the lower panel. we consider an even redder 21 dee? survey with a limiting maeuitude of Aag=28.7. as appropriate for two mouths of observations frou the yoalization ofJ," Finally, in the lower panel, we consider an even redder 24 $^2$ survey with a limiting magnitude of $K_{\rm AB} = 28.7,$ as appropriate for two months of observations from the realization of." DEAL As the A baud is centered at 22000A.. such observations naturally push to even higher redshifts.," As the $K$ band is centered at $22000$, such observations naturally push to even higher redshifts." Thus while reaching a liitine AB magnitude only slightly lieher than the 700 dee?SNAP survey. such a 21 deg? is able to place the most stringent of auv of the surveysconsidered: constraining the 150-W model out to.~1 and the more luninous models to +~6 aud bevoud.," Thus while reaching a limiting AB magnitude only slightly higher than the $700$ $^2$ survey, such a 24 $^2$ is able to place the most stringent of any of the surveysconsidered: constraining the 150-W model out to $z \sim 4$ and the more luminous models to $z \sim 6$ and beyond." As cosimological curichiment is essentially a local process. certain environnientfs are naturallv more favorable for imetal-free. star formation.," As cosmological enrichment is essentially a local process, certain environments are naturally more favorable for metal-free star formation." In SSF03. we showed that the transition from metaltee to Population II stars was heavily dependent on the efficiency with which metals where mixed into the intergalactic medium.," In SSF03, we showed that the transition from metal-free to Population II stars was heavily dependent on the efficiency with which metals where mixed into the intergalactic medium." " This efficiency depended in turu ou the enerev iuput into galactic outflows powered byPPSNe. which was parameterized by the ""energy iuput per unit primordial gas mass” EH, defined as the product of the fraction of eas iu cach primordial object that is converted into stars (41111, the munhber of per unit mass of nietal-free stars formed (NT). the average kinetic energv por pair-production supernova (Cu) aud the fraction of the total kinetic energv channeled into the resulting galaxy outflow μα)."," This efficiency depended in turn on the energy input into galactic outflows powered by, which was parameterized by the “energy input per unit primordial gas mass” ${\cal E}_{\rm g}^{III}$, defined as the product of the fraction of gas in each primordial object that is converted into stars $f_\star^{III}$ ), the number of per unit mass of metal-free stars formed ${\cal N}^{\pm}$ ), the average kinetic energy per pair-production supernova ${\cal E}_{\rm kin}$ ), and the fraction of the total kinetic energy channeled into the resulting galaxy outflow $f_{\rm wind})$." Tucorporating such outflows iuto a detailed analytical model of structure. formation leads to the approximate relation that. bv mass. the fraction of the total star formation in metal-free stars at 5= Lis Foti.=W~etyd where. as above. EF is du units of 107! eres per M. of eas (sce Figure 3 of ΕΟΟ for details).," Incorporating such outflows into a detailed analytical model of structure formation leads to the approximate relation that, by mass, the fraction of the total star formation in metal-free stars at $z=4$ is (z=4), where, as above, ${\cal E}^{\pm}$ is in units of $10^{51}$ ergs per $\msun$ of gas (see Figure 3 of SSF03 for details)." Extrapolating the results in SSFO3 to :=0 gives EI=0)(, Extrapolating the results in SSF03 to $z=0$ gives (z=0). eli l4n5yDhese fractions can be related to the unederlving population of stars bv adopting fiducial values of ffl!=0.1 for the star formation efficiency which is consistent with the observed star formation rate density at intermediate aud high redshifts (Scannapieco. Ferrara. \ladau 2002): fy.=0.3 for the wiud efficiency. which is consistent with the chwart ealaxv outflow simulatious of Mori Ferrara. Madau (2002): and IN*=0.001. for the uumiber of per nuit solar mass of prinordial stars formed. which is the value asuned in §L.," These fractions can be related to the underlying population of stars by adopting fiducial values of $f_\star^{III} = 0.1$ for the star formation efficiency, which is consistent with the observed star formation rate density at intermediate and high redshifts (Scannapieco, Ferrara, Madau 2002); $f_w = 0.3$ for the wind efficiency, which is consistent with the dwarf galaxy outflow simulations of Mori, Ferrara, Madau (2002); and $N^{\pm} = 0.001$, for the number of per unit solar mass of primordial stars formed, which is the value assumed in 4." This eives FA! values of 0.3(€ian)! at. =[andO.l(Eu) bat. =0. respectively.," This gives $F_\star^{III}$ values of $0.3 ({\cal E}_{\rm kin})^{-1}$ at $z=4$ and $0.1 ({\cal E}_{\rm kin})^{-1}$ at $z=0,$ respectively." Or. in other star formation at +=0 by mass could be in metal-free.," Or, in other words, for typical energies of $30 \times 10^{51}$ ergs per, $\sim 1\%$ of the star formation at $z=4$ and $\sim 0.3 \%$ of the star formation at $z=0$ by mass could be in metal-free." Tn Figure 6 we show estimates of the number of SNe per dee? per dzyear over the wide range of models considered in SSEUS. extrapolating to 2=0. In all cases we asstuue that 1 PPSN forms per 1000 solar masses of metaltree stars. and for comparison we show the simple low-redshift estimates taken iu the previous section.," In Figure 6 we show estimates of the number of SNe per $^2$ per dz over the wide range of models considered in SSF03, extrapolating to $z=0.$ In all cases we assume that 1 PPSN forms per 1000 solar masses of metal-free stars, and for comparison we show the simple low-redshift estimates taken in the previous section." While the values in these mocels are uncertain. they nevertheless serve to illustrate two nmuportaut points.," While the values in these models are uncertain, they nevertheless serve to illustrate two important points." First. even at the low redshifts probed by current surveys. the simple ranee of VAIS formation rates considered in 811 lie well within the theoretically interesting range.," First, even at the low redshifts probed by current surveys, the simple range of VMS formation rates considered in 4 lie well within the theoretically interesting range." Iudeed for the weakest feedback cases several 2~1 should have already. been secu within the HA Deep survey., Indeed for the weakest feedback cases several $z \sim 1$ should have already been seen within the IfA Deep survey. " Secondly. due to the decrease in dr/dz asa function of redshift. as well as the tine dilatiou effect. the peak of οΑαdidt is not iu the :>10 range targeted bv the Telescope, but rather at more moderate redshifts."," Secondly, due to the decrease in $dr$ $dz$ as a function of redshift, as well as the time dilation effect, the peak of $dN_{\rm deg}/{dz dt}$ is not in the $z \gtrsim 10$ range targeted by the , but rather at more moderate redshifts." This micans that the coustraiuts obtained from JDEA-tvpe survevs are likely to reach comparable Bits to higher efforts., This means that the constraints obtained from -type surveys are likely to reach comparable limits to higher-redshift efforts. In fact. it is extremely uulikelv that," In fact, it is extremely unlikely that" spectroscopic redshift of our host galaxy (see fourth column of Table 3)).,spectroscopic redshift of our host galaxy (see fourth column of Table \ref{synfitresults}) ). We have checked the possible impact that the poorly determined. U-band magnitude (error 0.3 mag) might have in the determination of the photometric redshift., We have checked the possible impact that the poorly determined U-band magnitude (error 0.3 mag) might have in the determination of the photometric redshift. Thus. we have repeated all the fits displayed in Table 3 excluding the U-band host magnitude.," Thus, we have repeated all the fits displayed in Table \ref{synfitresults} excluding the U-band host magnitude." " The derived photometric redshifts differ less than 2'4 (achieved for the SOL-MiSc79-Fit86 subfamily of templates) from the ones obtained with the entire CDVRIZJ,N.CL-band SED.", The derived photometric redshifts differ less than $2\%$ (achieved for the SOL-MiSc79-Fit86 subfamily of templates) from the ones obtained with the entire $UBVRIZJ_sK_sCL$ -band SED. This small. variation is the result of the weighted calculation of V2/d0of. which weights each band according to the square of its corresponding photometric error inverses (see Hyperz manual. Bolzonella et al. 2002)).," This small variation is the result of the weighted calculation of $\chi^2/dof$, which weights each band according to the square of its corresponding photometric error inverses (see Hyperz manual, Bolzonella et al. \cite{Bolz02}) )." In the same manner the impact of the U- magnitude on rest of the inferred variables (galaxy type. metallicity. age. template. Agen) is also negligible for the further discussion (the maximum impact corresponds to a variation of one 4qoe grid step. 0.03 mag).," In the same manner the impact of the U-band magnitude on rest of the inferred variables (galaxy type, metallicity, age, template, $A^{global}_{\rm V}$ ) is also negligible for the further discussion (the maximum impact corresponds to a variation of one $A^{global}_{\rm V}$ grid step, 0.03 mag)." The reliability of our empirical templates fits have been also tested., The reliability of our empirical templates fits have been also tested. Leaving the redshift as a free parameter. (and filtering the spurious local νο/dof minimum frequently found at += 0). only the Stb2 template yields a reasonable photometric redshift (27.=1.272. consistent within the expected redshift dispersion of A:~ (0.1).," Leaving the redshift as a free parameter, (and filtering the spurious local $\chi^2/dof$ minimum frequently found at $z=0$ ), only the Stb2 template yields a reasonable photometric redshift $z=1.272$, consistent within the expected redshift dispersion of $\Delta z \sim 0.1$ )." The rest of templates. specially the early and mid types. give redshifts inconsistent with the spectroscopic one.," The rest of templates, specially the early and mid types, give redshifts inconsistent with the spectroscopic one." This fact supports that the Stb2 empirical template (see Sect. 4.2.3)), This fact supports that the Stb2 empirical template (see Sect. \ref{ext}) ) is the optimum one to reproduce our data., is the optimum one to reproduce our data. The absolute B-band magnitude of the host at +=1.118 is Afp0.00.1.," The absolute $B$ -band magnitude of the host at $z=1.118$ is $M_B = -20.6\pm0.1$." Lilly et al. (1995)), Lilly et al. \cite{Lill95}) ) show that 15 depends on the colour and the redshift of the galaxy., show that $M^{\star}_B$ depends on the colour and the redshift of the galaxy. " This luminosity evolution is specially relevant for blue galaxies at +~1 (like the GRB 000418 host galaxy). where 15, ranges from —21.22 to 22.92 (rescaling the 3M, valuesof Lilly et al. (1995))"," This luminosity evolution is specially relevant for blue galaxies at $z \sim 1$ (like the GRB 000418 host galaxy), where $M^{\star}_B$ ranges from $-21.22$ to $-22.93$ (rescaling the $M^{\star}_B$ valuesof Lilly et al. \cite{Lill95}) )" to our cosmology)., to our cosmology). Although the 375 value of blue galaxies is very uncertain. the trivariate luminosity function (LF) of Lilly et al. (1995))," Although the $M^{\star}_B$ value of blue galaxies is very uncertain, the trivariate luminosity function (LF) of Lilly et al. \cite{Lill95}) )" " suggests that the value of 35, of blue galaxies is <20.6.", suggests that the value of $M^{\star}_B$ of blue galaxies is $ < -20.6$. Therefore. we conclude that the host is likely a subluminous galaxy.," Therefore, we conclude that the host is likely a subluminous galaxy." Several characteristics of the GRB 000418 host galaxy are difficult to reconcile. in. particular: a high reddening ts expected for sub-mm luminous galaxies (see Le Floc’h et al.," Several characteristics of the GRB 000418 host galaxy are difficult to reconcile, in particular: a high reddening is expected for sub-mm luminous galaxies (see Le Floc'h et al." 2003)., 2003). However. we find that GRB 000418 occurred in a blue host galaxy with a low/moderate extinction; ANMal | AUAe SERQQJSFRpv050.," However, we find that GRB 000418 occurred in a blue host galaxy with a low/moderate extinction; $^{local}_{\rm V}$ / $^{global}_{\rm V} \sim 1$; $_{mm}$ $_{UV} \sim 50$." Below we discuss several scenarios that could help to reconcile these observations., Below we discuss several scenarios that could help to reconcile these observations. The Sub-mnvradio emission could. trace an. obscured population. of massive stars that could be undetectable at optical/NIR wavelengths., The Sub-mm/radio emission could trace an obscured population of massive stars that could be undetectable at optical/NIR wavelengths. This has been suggested in the case of the host galaxy of the dark GRB 000210 (Gorosabel et al. 2003)., This has been suggested in the case of the host galaxy of the dark GRB 000210 (Gorosabel et al. \cite{Goro03}) ). Given that SER; ΕΙ 0.02. the probability that the progenitor belongs to the obscured population is ~984 (assuming that the probability of making a GRB ts only proportional to the SFR and not other parameters as e.g. the metallicity).," Given that $_{UV}$ $_{mm}$ $\sim 0.02$, the probability that the progenitor belongs to the obscured population is $\sim 98\%$ (assuming that the probability of making a GRB is only proportional to the SFR and not other parameters as e.g. the metallicity)." However. opposite to the case of GRB 000210. GRB 000418 was not dark. so its progenitor either had to belong to the remaining ~2( unobscured stellar population or the GRB destroyed the dust along the line of sight.," However, opposite to the case of GRB 000210, GRB 000418 was not dark, so its progenitor either had to belong to the remaining $\sim 2\%$ unobscured stellar population or the GRB destroyed the dust along the line of sight." Another possibility is that the radio/sub-mm emission comes from a high nuclear radio supernovae rate (>1 SN yr|) or from the activity associated with an AGN., Another possibility is that the radio/sub-mm emission comes from a high nuclear radio supernovae rate $>1$ SN $^{-1}$ ) or from the activity associated with an AGN. " Thus. the radio/mm emission would not invoke an optically hidden stellar population and the discrepancy between SFR;-\-and SFR,,,,,; would be naturally solved."," Thus, the radio/mm emission would not invoke an optically hidden stellar population and the discrepancy between $_{UV}$and $_{mm}$ would be naturally solved." An appreciable amount of starbursts (~—104) contain compact radio cores (Kewley et al. 1999))., An appreciable amount of starbursts $\sim 40\%$ ) contain compact radio cores (Kewley et al. \cite{Kewl99}) ). These compact radio cores nay be originated by obscured AGN or by complexes of luminous radio supernovae from an active nuclear starburst (Smith et al. 1998a))., These compact radio cores may be originated by obscured AGN or by complexes of luminous radio supernovae from an active nuclear starburst (Smith et al. \cite{Smit98a}) ). The GRB 000418 host galaxy would resemble the case of Arp 220. an active star forming galaxy (SFR ~50.—100AZ.. 1) which shows a compact radio core (Smith et al. 1998b)).," The GRB 000418 host galaxy would resemble the case of Arp 220, an active star forming galaxy (SFR $\sim 50-100~M_{\odot}$ $^{-1}$ ) which shows a compact radio core (Smith et al. \cite{Smit98b}) )." The additional radio source detected by Berger et al. (2003)), The additional radio source detected by Berger et al. \cite{Berg03}) ) could also be related to AGN activity (e.g. the hot spot of a radio jet)., could also be related to AGN activity (e.g. the hot spot of a radio jet). The analysis of optical/NIR observations presented ΠΠ. this paper confirms that the GRB 000418 host is a starburst galaxy., The analysis of optical/NIR observations presented in this paper confirms that the GRB 000418 host is a starburst galaxy. This result has been independently achieved by fitting synthetic and empirical templates to the photometric points., This result has been independently achieved by fitting synthetic and empirical templates to the photometric points. This conclusion is also consistent with the morphological information derived from the HST/STIS images. where the host is seen as a blue compact galaxy with no evidence for more widespread star formation.," This conclusion is also consistent with the morphological information derived from the HST/STIS images, where the host is seen as a blue compact galaxy with no evidence for more widespread star formation." The more natural scenario would be a nuclear starburst that harbour a young population of stars where the GRB was originated., The more natural scenario would be a nuclear starburst that harbour a young population of stars where the GRB was originated. " The reported offset of the afterglow respect to the galaxy nucleus (0.023+0.061""; or a projected distance of 0.202+0.561 kpe) is consistent with this hypothesis (Bloom et al. 2002))."," The reported offset of the afterglow respect to the galaxy nucleus $0.023\pm0.064^{\prime \prime}$; or a projected distance of $0.202\pm0.564$ kpc) is consistent with this hypothesis (Bloom et al. \cite{Bloo02}) )." The synthetic SED fits are consistent with a young stellar population., The synthetic SED fits are consistent with a young stellar population. The predicted host galaxy extinction. stellar age and star formation rate depend on the assumed extinction law.," The predicted host galaxy extinction, stellar age and star formation rate depend on the assumed extinction law." Two synthetic SED solutions are consistent with our photometric. points:. i). age 2 5946. Myr. A777lobal=0.15↽. 0.03. SER;\~SM. +. progenitorE mass = ~7M .; ii) age," Two synthetic SED solutions are consistent with our photometric points: i) age = $59 \pm 6$ Myr, $A^{global}_{\rm V} = 0.15 \pm 0.03$ , $_{UV} \sim 8 M_{\odot}$ $^{-1}$ , progenitor mass = $ \sim 7 M_{\odot}$ ; ii) age" Two synthetic SED solutions are consistent with our photometric. points:. i). age 2 5946. Myr. A777lobal=0.15↽. 0.03. SER;\~SM. +. progenitorE mass = ~7M .; ii) ageg," Two synthetic SED solutions are consistent with our photometric points: i) age = $59 \pm 6$ Myr, $A^{global}_{\rm V} = 0.15 \pm 0.03$ , $_{UV} \sim 8 M_{\odot}$ $^{-1}$ , progenitor mass = $ \sim 7 M_{\odot}$ ; ii) age" by the correction term. 0.1. & log (0g /300 2) where qp is the hydrogen density (see σοςἩν for more details).,"by the correction term, 0.1 $\times$ log $n_{\rm H}$ /300 $^{-3}$ ) where $n_{\rm H}$ is the hydrogen density (see SSCK for more details)." We apply these relations to the data of Rodríeeuez-Axdila et al. (, We apply these relations to the data of guez-Ardila et al. ( 2000).,2000). For the objects whose gas density is not eiven in Rodrigenez-Ardila et al. (, For the objects whose gas density is not given in guez-Ardila et al. ( 2000) (CTS ID31.03. CTS M02.30. CTS JL105. CTS COS.0L. 2d LIT 2107-097). we assume the eas density to be 300 cu7.,"2000) (CTS H34.03, CTS M02.30, CTS J14.05, CTS G03.04, and 1H 2107-097), we assume the gas density to be 300 $^{-3}$." The average and median values of the derived 12 | log sseusy and 12) | log μου are given in Table 2., The average and median values of the derived 12 + log $_{\rm SSCK1}$ and 12 + log $_{\rm SSCK2}$ are given in Table 2. Here the effect of the dust extinction is corrected by adopting the values of Aj presented by Rodrigenez-Ardila et al. (, Here the effect of the dust extinction is corrected by adopting the values of $A_V$ presented by guez-Ardila et al. ( 2000) aud the extinction curve of Cardelli. Clayton. Mathis (1989).,"2000) and the extinction curve of Cardelli, Clayton, Mathis (1989)." There is no teudeucv that the NLSIs are metal vich compared to the BLS as implied by some earlier studies., There is no tendency that the NLS1s are metal rich compared to the BLS1 as implied by some earlier studies. To the contrary. the derived oxveeu. abundauces iav be larger iu the sample of BLSIs than in the sample of NLS1s.," To the contrary, the derived oxygen abundances may be larger in the sample of BLS1s than in the sample of NLS1s." We show the relationships between the FWIAL of the broad component of the Πα ciission aud the derived oxygen abundances in Fieure 3., We show the relationships between the FWHM of the broad component of the $\alpha$ emission and the derived oxygen abundances in Figure 3. The object with a huger EWIIM of the Πα emission. seenis to be more oxveen abundant when equation (1) is applied. though this tendency is not sienificant.," The object with a larger FWHM of the $\alpha$ emission seems to be more oxygen abundant when equation (1) is applied, though this tendency is not significant." Ou the other hand. such a tendency is not seen when equation (2) is applied.," On the other hand, such a tendency is not seen when equation (2) is applied." Do the above results presented iu 83.2 sueeest that the NLR of NLSIs is not metal rich compared to that of DLS1s7, Do the above results presented in 3.2 suggest that the NLR of NLS1s is not metal rich compared to that of BLS1s? Receuth. Vérrou-Cotty. Verron. Concaalves (2001) pointed out that the broad component of permitted lues in the optical spectra of NLSIs is well fitted bv a Lorentzian profile and thus the decomposition of the narrow component of permitted lines from the broad colmponent by Rodrigeuez-Ardila et al. (," Recently, Vérron-Cetty, Vérron, Gonçaalves (2001) pointed out that the broad component of permitted lines in the optical spectra of NLS1s is well fitted by a Lorentzian profile and thus the decomposition of the narrow component of permitted lines from the broad component by guez-Ardila et al. (" "2000) may be inaccurate, since the broad components of permitted lines were fitted by a Caussian profile ly Rodrigenez-Ardila et al. (","2000) may be inaccurate, since the broad components of permitted lines were fitted by a Gaussian profile by guez-Ardila et al. (" 2000) (μου also Moran. Halperu. Uelfaud 1996: Leighly et al.,"2000) (see also Moran, Halpern, Helfand 1996; Leighly et al." 19995: Goncaalves. Véerron. Vérron-Cetty 1999: Suleutic et al.," 1999b; Gonçaalves, Vérron, Vérron-Cetty 1999; Sulentic et al." 2102)., 2002). If lis claim ds the case. the fiux ratio of [N AG5S3/IIo usse nay be iuappropriate for t1e inetallicitv diagnostics because the selection of the fitting function for the road component of permitted lines affecs the measurcinent of not only the broad component but also the narrow component of permitted lines.," If this claim is the case, the flux ratio of [N $\lambda$ $\alpha_{\rm narrow}$ may be inappropriate for the metallicity diagnostics because the selection of the fitting function for the broad component of permitted lines affects the measurement of not only the broad component but also the narrow component of permitted lines." Tudeed. the derived oNVOOL anmucdaucc of the NLR gas of the NLSIs aud the DLSl1s bv using equations (1) aud (2) should be suspectec if we take accoit of the following two facts.," Indeed, the derived oxygen abundances of the NLR gas of the NLS1s and the BLS1s by using equations (1) and (2) should be suspected if we take account of the following two facts." First. most of the derived oxveen abundauces Sugeest very sub-solar iuetallicitics.," First, most of the derived oxygen abundances suggest very sub-solar metallicities." This is) especially remarkable when equation (1) is adopted: he inediau value of the derived oxvecu abundances correspouds to Z=0.322..., This is especially remarkable when equation (1) is adopted: the median value of the derived oxygen abundances corresponds to $Z \simeq 0.32 Z_{\odot}$. Second. the derived oxveen abuudanuces we not consisteut to cach other.," Second, the derived oxygen abundances are not consistent to each other." That is. the average and median values of tje derived oxvecu abunudances are systematically differcut: the oxveen abundances derived by using equation (2) are arecr than that WV using equation (1) by ~0.3 dex.," That is, the average and median values of the derived oxygen abundances are systematically different: the oxygen abundances derived by using equation (2) are larger than that by using equation (1) by $\sim$ 0.3 dex." This «lifference is more clearly shown iu Figure L in which we copare the two kiids of the iuferred oxygen abundances.," This difference is more clearly shown in Figure 4, in which we compare the two kinds of the inferred oxygen abundances." Alhough SSCs also imentioned that the oxveen abiuudauce derived by equation (2) tends to be higher than the oue derived by equaion (1) by —0.11 dex. the difference in f10 sample of Rodvigeuez-Ardila et al. (," Although SSCK also mentioned that the oxygen abundance derived by equation (2) tends to be higher than the one derived by equation (1) by $\sim$ 0.11 dex, the difference in the sample of guez-Ardila et al. (" 2000) is much lareer thin that reted bv SSCT.,2000) is much larger than that reported by SSCK. This may imply that the methods proposed by SSCIy are lnappropriae to estimate the eas metallicities of NLRs. at least for Sls.," This may imply that the methods proposed by SSCK are inappropriate to estimate the gas metallicities of NLRs, at least for S1s." Thus it secus to be safe to avoid using the LALTOW COMpoucl of periitted Imes for the investigation of the gas properties of NLRs in Sls., Thus it seems to be safe to avoid using the narrow component of permitted lines for the investigation of the gas properties of NLRs in S1s. has been distorted bevond recoguition bw noise aud coarse aueular resolution. ifs mass function iav still be consistent with the stellar TIME within the uncertainties.,"has been distorted beyond recognition by noise and coarse angular resolution, its mass function may still be consistent with the stellar IMF within the uncertainties." We believe that this behavior of the clamp mass function reflects the deeper origins of the shape of the clump aud stellar mass functions., We believe that this behavior of the clump mass function reflects the deeper origins of the shape of the clump and stellar mass functions. The stellar IME is frequently described as a Salpeter-like power-law., The stellar IMF is frequently described as a Salpeter-like power-law. This interpretation is somewhat outdated: it reflects the lanited range of stellar masses included in Salpeters original stellar IAIF., This interpretation is somewhat outdated; it reflects the limited range of stellar masses included in Salpeter's original stellar IMF. " More recent measurements of the stellar IME show that. when it is extended to low stellu asses. well below the turnover nass, if adopts a lognormal form (Chabricr 2003).. so1uetiues approxiniaed by four or five power- segments of which the Sal)eter power-law is but onc."," More recent measurements of the stellar IMF show that, when it is extended to low stellar masses, well below the turnover mass, it adopts a lognormal form \citep{chabrier03}, sometimes approximated by four or five power-law segments of which the Salpeter power-law is but one." The Salpeter )ower law apjxurs nierelv to be a good approxiuation to the lognorual IMFE. over a restricted range of stellar masses. perlaps 110M.," The Salpeter power law appears merely to be a good approximation to the lognormal IMF over a restricted range of stellar masses, perhaps 1–10." .. Several auttors have showu that a lognorimal stellar IMP arises naturallv as a consequence of the Central Luuit Theorem of calculus (Larson1973:Zinuecker198I:Adams&Fatuzzo 1996).," Several authors have shown that a lognormal stellar IMF arises naturally as a consequence of the Central Limit Theorem of calculus \citep{larson73,z84,af96}." . When a sufficicutly large uunuber of indepeudent physical processes or variables Hact together to produce the stellar IME. it naturally ends towards a lognormal form.," When a sufficiently large number of independent physical processes or variables act together to produce the stellar IMF, it naturally tends towards a lognormal form." The larger the ΠΟ) 6ft independent variables used ia models of the origin 6ft the IME. the more closely the TIAIF approaches the ognormal form (Adams&Fatuzzo1996).," The larger the number of independent variables used in models of the origin of the IMF, the more closely the IMF approaches the lognormal form \citep{af96}." . The same reasoning applies to the clump nass tuuction for two reasous: first. a large muuber of independent factors must act to set the distribution of chump masses aud. second. it is that distribution of clamp nasses Which must ultimatev give rise to the IME.," The same reasoning applies to the clump mass function for two reasons: first, a large number of independent factors must act to set the distribution of clump masses and, second, it is that distribution of clump masses which must ultimately give rise to the IMF." Reid&Wilson(2006b) showed hat chuup mass functioIs neasured from dust contiaWn maps are typically well nt by lognormal functions., \citet{rw06b} showed that clump mass functions measured from dust continuum maps are typically well fit by lognormal functions. Tus result holds true despite he huge varicty of different methods of acquiring t data anc extracting the chups used iu producing f various dass functions., This result holds true despite the large variety of different methods of acquiring the data and extracting the clumps used in producing the various mass functions. Iu Fiigure LL. we show that t uass functions first shown iu Figure | are all well w lognormal distributions.," In Figure \ref{fig:logncmfs}, we show that the mass functions first shown in Figure \ref{fig:resnoisedmfs} are all well fit by lognormal distributions." " This is easier to see when ottius COMES, which show ""every clump in the sample."," This is easier to see when plotting CCMFs, which show every clump in the sample." A lognormal DCME corres]»»uds to an error function., A lognormal DCMF corresponds to an error function. " We believe that the high quiditv of the lognormal fits to he simulated chump mass f""uctious sugeest that they. oo. are being biased toward this fori. by the cumulative"," We believe that the high quality of the lognormal fits to the simulated clump mass functions suggest that they, too, are being biased toward this form by the cumulative" Rapid rotation is a characteristic feature of massive and intermediate mass stars that has a significant and yet poorly understood impact on their structure and evolution.,Rapid rotation is a characteristic feature of massive and intermediate mass stars that has a significant and yet poorly understood impact on their structure and evolution. It 1s a current challenge of stellar physics to obtain observational constraints that will improve the modeling of the physical processes induced by rotation., It is a current challenge of stellar physics to obtain observational constraints that will improve the modeling of the physical processes induced by rotation. Seismology should play a particular role in this context as it is the only way to directly probe stellar interiors., Seismology should play a particular role in this context as it is the only way to directly probe stellar interiors. At present. however. the oscillation spectra of rapidly rotating stars can not be unambiguously interpreted.," At present, however, the oscillation spectra of rapidly rotating stars can not be unambiguously interpreted." One difficulty resides in the modeling of the effects of rapid rotation on the oscillation modes., One difficulty resides in the modeling of the effects of rapid rotation on the oscillation modes. There has been some recent progress in this field notably in the description of the organization of p-modes spectra (Ligniéres&Georgeot.2009)., There has been some recent progress in this field notably in the description of the organization of p-modes spectra \citep{lingor}. . Even if we understand the basic properties of the frequency spectrum. the mode identification process remains a difficult task.," Even if we understand the basic properties of the frequency spectrum, the mode identification process remains a difficult task." In particular. in the p-mode frequency range. the large rotational splittings between modes of different azimuthal number mix the frequencies of different multiplets.," In particular, in the p-mode frequency range, the large rotational splittings between modes of different azimuthal number mix the frequencies of different multiplets." One possible solution to this problem would be to observe a rapidly rotating pulsating star seen pole-on., One possible solution to this problem would be to observe a rapidly rotating pulsating star seen pole-on. Cancellation effect in disk-integrated light would then select axisymmetric modes. non-axisymmetric modes being cancelled out.," Cancellation effect in disk-integrated light would then select axisymmetric modes, non-axisymmetric modes being cancelled out." Such a selection effect would considerably simplify the observed spectrum and thus the mode identification process., Such a selection effect would considerably simplify the observed spectrum and thus the mode identification process. Vega is known to be a rapidly rotating star and reveals a nearly pole on inclination., Vega is known to be a rapidly rotating star and reveals a nearly pole on inclination. This has been shown by analyzing the spectroscopic and interferometric signatures of the surface gravity darkening (Gulliveretal..1994:Peterson2006).," This has been shown by analyzing the spectroscopic and interferometric signatures of the surface gravity darkening \citep{gulli,peterson}." ". The spectroscopic and interferometric approaches provide a similar inclination angle 1 = 5-7 degrees. although they differ in the reported equatorial velocities. vey=245415km .and va~ 175 from the spectroscopic analysis of Gulliveretal.(1994) and Takedaetal. (2008). respectively. and a significantly larger value. v4,~ 275kms!.. from interferometry (Petersonetal..2006:Aufdenberg 2006)."," The spectroscopic and interferometric approaches provide a similar inclination angle i = 5-7 degrees, although they differ in the reported equatorial velocities, $_{\rm eq} = 245 \pm 15$ and $_{\rm eq} \sim$ 175 from the spectroscopic analysis of \citet{gulli} and \citet{Ta08}, , respectively, and a significantly larger value, $_{\rm eq} \sim$ 275, from interferometry \citep{peterson,aufden}." . As a seismic target. Vega also presents the important advantage that its fundamental parameters are very accurately determined. particularly when compared with other rapidly rotating stars.," As a seismic target, Vega also presents the important advantage that its fundamental parameters are very accurately determined, particularly when compared with other rapidly rotating stars." As reviewed by Gray(2007).. Vega was used since more than 150 years as a photometric and. spectrophotometric standard star. the historic reason being most likely its brightness and near-zenith position for european and north american observatories.," As reviewed by \citet{Gr07}, Vega was used since more than 150 years as a photometric and spectrophotometric standard star, the historic reason being most likely its brightness and near-zenith position for european and north american observatories." This particular role of Vega can be considered surprising. since several authors report photometric variability of at least 1—2%. but with no evidence of periodic variations.," This particular role of Vega can be considered surprising, since several authors report photometric variability of at least $1-2 \%$, but with no evidence of periodic variations." A previous study of spectroscopic variability. has been conducted by Goraya&Singh(1983) who described a variability of Ha althought it was not confirmed in subsequent studies (Charlton&Meyer.1985)., A previous study of spectroscopic variability has been conducted by \citet{goraya} who described a variability of $\alpha$ althought it was not confirmed in subsequent studies \citep{charlton}. . The location of Vega in the HR diagram is roughly that of main-sequence AO stars. but bluewards of the ὁ Scuti instability strip. therefore stellar oscillations are in principle not expected.," The location of Vega in the HR diagram is roughly that of main-sequence A0 stars, but bluewards of the $\delta$ Scuti instability strip, therefore stellar oscillations are in principle not expected." However. Fernie(1981) concluded that historie radial velocity curves and photometric variability tend to indicate episodical 6 Scuti type pulsation. with a frequency close to the fundamental radial order of Fi~ for Vega’s parameters as known at that time.," However, \citet{fernie} concluded that historic radial velocity curves and photometric variability tend to indicate episodical $\delta$ Scuti type pulsation, with a frequency close to the fundamental radial order of $_{\rm fund} \sim $ for Vega's parameters as known at that time." The most recent determination of fundamental stellar parameters byTakedaetal.(2008) led him to conclude that this rapid rotator has parameters strongly varying from pole to equator.," The most recent determination of fundamental stellar parameters by\citet{Ta08} led him to conclude that this rapid rotator has parameters strongly varying from pole to equator," CMsin;>LOM yt) The minii masses and orbital periods of the plaucts in this svstems are stuular to those of ¢ Andromedae. but with the immer aud outermost compoucuts reversed.,"$\msini > 10 \mearth$ ) The minimum masses and orbital periods of the planets in this systems are similar to those of $\upsilon$ Andromedae, but with the inner and outermost components reversed." " For the three planets of IHP 11510 we fiud: AMsin;= 3.9. 1.2. aud 0.6Mjay- and P= ""6.67.icai L17.7. and 952 d."," For the three planets of HIP 14810 we find: $\msini =$ 3.9, 1.2, and 0.6, and $P=$ 6.67, 147.7, and 952 d, respectively." We find modest | ant ecceutricities respectivelyfor all 3 compoucuts (0.11. 0.16. and 0.17. respectively).," We find modest but significant eccentricities for all 3 components (0.14, 0.16, and 0.17, respectively)." Table 1| contains a suumiary of the stellar properties of TMP 11810 (= BD120 518). which sits at 53 pec (x=18.1d1.3.vauLeeuwen2009) and has V—8.5.," Table \ref{star} contains a summary of the stellar properties of HIP 14810 (= BD+20 518), which sits at 53 pc \citep[$\pi = 18.7 \pm 1.3$,][]{Hipparcos2} and has $V=8.5$." We have performed an LTE aualvsis of our template spectra for TIP E1810 and derived its mass. auc radius using the methods described in Valenti&Fischer(2005).., We have performed an LTE analysis of our template spectra for HIP 14810 and derived its mass and radius using the methods described in \citet{SPOCS}. Although IIIP 11510 is a solar mass star (AL=0.99ML; ). its inetallicitv (ΤοI= (0.26) and evolutionary status (AAA=0.63 nae. as calculated in Wrieht (2001))) give ita type of C5Π».," Although HIP 14810 is a solar mass star $M = 0.99 \Msol$ ), its metallicity $\feh = +0.26$ ) and evolutionary status $\Delta M_{\rm V} = 0.63$ mag, as calculated in \citet{Wright04b}) ) give it a spectral type of G5." Its low rotation (0sins~0.50.554 kins 1)) spectralaud Ca II Ανν activity levels (ο=0.16 measured with the methods described in Wrightet (2001))) ave consistent with it beiug au old star (age ~ὃ Cyr).," Its low rotation $v \sin i \sim 0.5 \pm 0.5$ km ) and Ca II H K activity levels $S = 0.16$, measured with the methods described in \citet{Wright04}) ) are consistent with it being an old star (age $\sim 8$ Gyr)." This combined with its relatively siuall distance from the main sequence make it a particularly good radial velocity target. since 1f is expected to exhibit very low levels of jitter(Wright2005).," This combined with its relatively small distance from the main sequence make it a particularly good radial velocity target, since it is expected to exhibit very low levels of jitter \citep{Wright05}." .? We began observations of TIP 11810 in 2005 as part of the N2IS survey (Fischeretal.2005) at Keck Observatory using WIRES (Vogtetal.1991). and our usual iodine technique (Butleretal.1996) to achieve typical iuterual (random) errors of 0.81.1l, We began observations of HIP 14810 in 2005 as part of the N2K survey \citep{Fischer05} at Keck Observatory using HIRES \citep{Vogt94} and our usual iodine technique \citep{Butler96b} to achieve typical internal (random) errors of 0.8–1.4. o The presence of the innenuost planet aud the laree resuiduals to its orbital fit mspired the California Planet Search consortium] to continue regular observations of this system at Keck., The presence of the innermost planet and the large resuiduals to its orbital fit inspired the California Planet Search consortium to continue regular observations of this system at Keck. ποetal.(2007) the inner two planets of TIP 11810. though with a rather poor fit for the e component due to the poor plase coverage aud the unaccouuted-for effects of the d. componcut.," \citet{Wright07} the inner two planets of HIP 14810, though with a rather poor fit for the $c$ component due to the poor phase coverage and the unaccounted-for effects of the $d$ component." Also colmplicating the fit was what is now obviously a spurious data poiut. acquired during carly dusk when siguificaut contanunation from the Solar spectrun likely produced an erroneous radial velocity measurement.," Also complicating the fit was what is now obviously a spurious data point, acquired during early dusk when significant contamination from the Solar spectrum likely produced an erroneous radial velocity measurement." We have applied a more rigorous data reteution scheme (based solely on the measured internalerrors'.. not deviations from a ΠΕ) to the data set presented in Table 2..," We have applied a more rigorous data retention scheme (based solely on the measured internal, not deviations from a fit) to the data set presented in Table \ref{vels}." These velocities and uncertaimties supersede our previously published values for this star. as we contiuue to refine our data reduction pipeline (Wrightetal.2009).," These velocities and uncertainties supersede our previously published values for this star, as we continue to refine our data reduction pipeline \citep{Wright09}." . Note that the times given in the table are in heliocentric Julian davs. aud the quoted errors are our iuterual (raudoni) errors. With no “jitter” included.," Note that the times given in the table are in heliocentric Julian days, and the quoted errors are our internal (random) errors, with no “jitter” included." By 2007. residuals to a 2-planetfit clearly showec coherent structure indicative of an outer companion.," By 2007, residuals to a 2-planetfit clearly showed coherent structure indicative of an outer companion." As Figure d shows. by late 2008. these residuals appoeare o describe one complete orbit of à P—950 d planet width modest eccentricity (6~0.2).," As Figure \ref{fig} shows, by late 2008, these residuals appeared to describe one complete orbit of a $P \sim 950$ d planet with modest eccentricity $e \sim 0.2$ )." We have performice a Moute Carlo false aliii probability (FAP) analvsis of he complete set of residuals to determine the likelihooc bat an orbital fit of this quality could have been arrives at-- bv chance., We have performed a Monte Carlo false alarm probability (FAP) analysis of the complete set of residuals to determine the likelihood that an orbital fit of this quality could have been arrived at by chance. This method is very similar to the FAP πι Butleretal.(2006):Wight(2007):Butleretal.(2009):Tloward (2009).. and we refer the reader to those works for more details.," This method is very similar to the FAP analyses in \citet{Butler06,Wright07,Butler09,Howard09}, and we refer the reader to those works for more details." After μήλο the data iun 21-hour intervals and subtracting he best 2-planet fit. we τούτος these residuals 1000 ines (that is. we kept the times of observation the same or each trial. but at cach time assigned a new velocity and velocity uncertainty pair raucdomly drawn from the entire set. with replacement).," After binning the data in 24-hour intervals and subtracting the best 2-planet fit, we redrew these residuals 1000 times (that is, we kept the times of observation the same for each trial, but at each time assigned a new velocity and velocity uncertainty pair randomly drawn from the entire set, with replacement)." We then added the nominal orbital solution for the e componcut back iuto these new residuals aud performed a thorough search for the best-fit 2-planet orbital solution to eachof these 1000 realizations of the data., We then added the nominal orbital solution for the $c$ component back into these new residuals and performed a thorough search for the best-fit 2-planet orbital solution to each of these 1000 realizations of the data. We measure the FAP as the fraction of these realizations for which we fiud a solution superior or equivalent in fit quality to the nominal solution., We measure the FAP as the fraction of these realizations for which we find a solution superior or equivalent in fit quality to the nominal solution. Note that this is an extremely conservative test of the FAP of the new planet. d. because we have not restricted the pariuneter search for the FAP trials to long period or low eccentricity planets.," Note that this is an extremely conservative test of the FAP of the new planet, $d$, because we have not restricted the parameter search for the FAP trials to long period or low eccentricity planets." The best-fit solutions found for the artificial data sets are thus often at short periods (P< 3d) and/or high ecceutricites ©20.7 (seethedis-cussioninButleretal. 2009)., The best-fit solutions found for the artificial data sets are thus often at short periods $P<3$ d) and/or high eccentricites $e > 0.7$ \citep[see the discussion in][]{Butler09}. . Nonetheless. even with this large parameter space available. we find that none of our 1000 realizations ment a better ft than the actual data. vielding an FAP ULIRGs.," On the other hand, $z$ starbursts often have different morphologies than those observed of $z$ ULIRGs." Local starbursts including ULIRGs are vpically compact. with radi of à few huudred parsecs and vertical scales heights of less than a huudred yarsees(Solomonetal.1997:Downes&Solomon1998).," Local starbursts including ULIRGs are typically compact, with radii of a few hundred parsecs and vertical scales heights of less than a hundred parsecs \citep{Solomon97,Downes98}." . These properties do not hold for subiillioeter galaxies (SAGs). very bright (L=1042L 2) starbursts at zm2 nostly poweredby star-formation and not AGNs (c.g. 2009).," These properties do not hold for submillimeter galaxies (SMGs), very bright $L \ga 10^{12} \Lsun$ ) starbursts at $z \approx 2$ mostly powered by star-formation and not AGNs \citep[e.g.,][]{Pope06,Valiante07,Watabe09}." ". SMCis are ο. several kpc iu diameter (several nues- lavecr than low-: ULIRGs)(οιον,Chapmanctal.etal.2009:Younger 2010).. and have much lower surface densities than their low-: counterparts of the &ue huuinositv (Taccouetal.2006.. havebut see Walteretal. 2009))."," SMGs are usually several kpc in diameter (several times larger than $z$ ULIRGs) \citep[e.g.,][]{Chapman04,Biggs08,Younger08,Iono09,Younger10}, and have much lower surface densities than their $z$ counterparts of the same luminosity \citealt{Tacconi06}, but see \citealt{Walter09}) )." Subuuillimeter ealaxies large random velocities compared to their rotation speeds. implying scale heights of 5hzz1 kpcCTacconietal.2006:Ctenzelal.2008:Lawet 2009).," Submillimeter galaxies have large random velocities compared to their rotation speeds, implying scale heights of $h \approx 1~\kpc$ \citep{Tacconi06,Genzel08,Law09}." ".. At hieh redshift. we therefore must consider a class ofradially... with X,=0.¢an3 (σπα21]M.kpe“vr 1j da scale heights of h—1kpc. in addition to the 4=100pe ""couipact starbursts” typical of local ULIRGSs considered in LTO."," At high redshift, we therefore must consider a class of, with $\Sigma_g \ge 0.1~\gcm2$ $\Sigma_{\rm SFR} \ga 2 - 4~\Msun \kpc^{-2} \yr^{-1}$ ) but scale heights of $h = 1~\kpc$, in addition to the $h = 100~\pc$ “compact starbursts” typical of local ULIRGs considered in LTQ." huportautlv. puffv starbursts will have ai ΒΙΑΙΟ voluue deusity for a given aud μπα.," Importantly, puffy starbursts will have a smaller volume density for a given $\Sigma_g$ and $\Sigma_{\rm SFR}$." " Since broenisstrahlung. ionization. X,pion. aud possilly svuchrotron losses— all depeud on the volume— deusity instead of surface density. these loss processes lay all be weaker iu puffy starbursts Like ολων,"," Since bremsstrahlung, ionization, pion, and possibly synchrotron losses all depend on the volume density instead of surface density, these loss processes may all be weaker in puffy starbursts like SMGs." " With these losses suppressed. the lügh-X, conspiracy will become unbalanced. and the FRC can be broken."," With these losses suppressed, the $\Sigma_g$ conspiracy will become unbalanced, and the FRC can be broken." These starbursts can cither be radio-brisht or radio-cdin. depending on their magnetic field) streneths.," These starbursts can either be radio-bright or radio-dim, depending on their magnetic field strengths." " Since the scale height is so large aud the volume deusity is relatively low for SAICs. we can deterimiue whether 5 scales with X, or p with these galaxies. breaking the degeneracy iu LTO."," Since the scale height is so large and the volume density is relatively low for SMGs, we can determine whether $B$ scales with $\Sigma_g$ or $\rho$ with these galaxies, breaking the degeneracy in LTQ." " Because X,=2ph. if B increases with p. then the magnetic field in putty starbursts will be weak and svuchrotron radio enmuüsson will be dim conipared to compact starbursts with the sanie X,."," Because $\Sigma_g = 2 \rho h$, if $B$ increases with $\rho$, then the magnetic field in puffy starbursts will be weak and synchrotron radio emission will be dim compared to compact starbursts with the same $\Sigma_g$." Tlowever. if B increases with X. the maguetic field will be strong aud svuchrotrou radio cussion will be bright in putty starbursts compared to compact starbursts witli the same My.," However, if $B$ increases with $\Sigma_g$ , the magnetic field will be strong and synchrotron radio emission will be bright in puffy starbursts compared to compact starbursts with the same $\Sigma_g$." We amodel galaxies and starbursts as uniform disks of gas. with scale height 5. star formation rate surface Xapg. aud gas surface density Mg.," We model galaxies and starbursts as uniform disks of gas, with scale height $h$, star formation rate surface $\Sigma_{\rm SFR}$, and gas surface density $\Sigma_g$." We solve the diffusion-loss equation to find the steady-state equilibiuu CHR spectra iu galaxies aud starbursts., We solve the diffusion-loss equation to find the steady-state equilibrium CR spectra in galaxies and starbursts. lujectiou. escape. aud cooling losses all compete at cach energv to determine the final CR spectrum (see LTO for details).," Injection, escape, and cooling losses all compete at each energy to determine the final CR spectrum (see LTQ for details)." The relevaut scale height is the height of the volume i which CRs are coufued aud produce svuchrotron radiation., The relevant scale height is the height of the volume in which CRs are confined and produce synchrotron radiation. " Normal galaxiesy. (X,x0.01o@ci? or Myer&0.06M.Ispeντ 1) have large radio halos with hczolπρο which we adopt as the CRscale height. even though the gas disk is much thinner."," Normal galaxies $\Sigma_g \le 0.01~\gcm2$ or $\Sigma_{\rm SFR} \la 0.06~\Msun \kpc^{-2} \yr^{-1}$ ) have large radio halos with $h \approx 1~\kpc$, which we adopt as the CRscale height, even though the gas disk is much thinner." " Compact starbursts are much smaller, with fo100pe (e.g.Solomonetal.1997:Downes& 1998): we use this as their scale height because they are probably good cuough calorimeters to prevent most of the CR clectrous/positrous from escaping out into the ealactic haloes at high cnongl surface deusities (X,Z0.1gcm3 or Mupgg2LM.kpeE ly "," Compact starbursts are much smaller, with $h \approx 100~\pc$ \citep[e.g.,][]{Solomon97,Downes98}; we use this as their scale height because they are probably good enough calorimeters to prevent most of the CR electrons/positrons from escaping out into the galactic haloes at high enough surface densities $\Sigma_g \ga 0.1~\gcm2$ or $\Sigma_{\rm SFR} \ga 2 - 4~\Msun \kpc^{-2} \yr^{-1}$ )." "The CR disk scale height for 2our prototvpical puffv πανταστη, tle SAIC. is not vet directlv measured. but it mast be at least the eas scale height. if the star formation is distributed throughout the eas."," The CR disk scale height for our prototypical puffy starbursts, the SMGs, is not yet directly measured, but it must be at least the gas scale height, if the star formation is distributed throughout the gas." The eas scale height for SAICs is kinematically inferred to be 5z1kpe (e.g...Tacconietal.2006:Cenzelet2008:Law 2009)... which we adopt as the CR scale height of putty starbursts.," The gas scale height for SMGs is kinematically inferred to be $h \approx 1~\kpc$ \citep[e.g.,][]{Tacconi06,Genzel08,Law09}, , which we adopt as the CR scale height of puffy starbursts." " Our models spau the cutive observed range in X, for galaxies aud starbursts. from 0.001&can.7 to 10gcin7."," Our models span the entire observed range in $\Sigma_g$ for galaxies and starbursts, from $0.001~\gcm2$ to $10~\gcm2$." Combined with the scale height. 5all determunes the rate ofinjection. escape. and cooling at energies.," Combined with the scale height, $\Sigma_g$ determines the rate of injection, escape, and cooling at all energies." The total rate of injection per unit volume is proportional to the volumetric star-formation rate. Msp/(25h).," The total rate of injection per unit volume is proportional to the volumetric star-formation rate, $\Sigma_{\rm SFR} / (2h)$." " The observed Schinidt law directly connects X, aud μεν. 1959).", The observed Schmidt law directly connects $\Sigma_g$ and $\Sigma_{\rm SFR}$ \citep{Schmidt59}. . We cousider both XaggxXL! (IKeunicutt1998.hereafterI8) aud MorrX XUI(Bouchéetal.2007. D07).. using the normalizations given bv KOS and DOT respectively.," We consider both $\Sigma_{\rm SFR} \propto \Sigma_g^{1.4}$ \citep[][hereafter K98]{Kennicutt98} and $\Sigma_{\rm SFR} \propto \Sigma_g^{1.7}$ \citep[][hereafter B07]{Bouche07}, , using the normalizations given by K98 and B07 respectively." The DOT relation was explicitlv derived for high-: galaxies. includiug SMs.," The B07 relation was explicitly derived for $z$ galaxies, including SMGs." Protons aud clectrous are iujected mto our model galaxieswith au enerev spectrum £ ον in this paper. we use p=2.2 inaliiost. all Escape. svuchrotrou. luverse Compton. brenisstrahbluues. and ionization losses are included for clectrous and positrons. along with escape. ionization. and pion losses for protous.," Protons and electrons are injected into our model galaxieswith an energy spectrum $E^{-p}$ ; in this paper, we use $p = 2.2$ inalmost all Escape, synchrotron, Inverse Compton, bremsstrahlung, and ionization losses are included for electrons and positrons, along with escape, ionization, and pion losses for protons." Diffusive escape tines are, Diffusive escape times are "ssystem properties are discussed in ??,, and we discuss the results in ??.","system properties are discussed in , and we discuss the results in ." ". The NICMOS grism observations were designed to gather high cadence time series of the bright, V=11.2, star dduring transits of the planet ((HST program 10998)."," The NICMOS grism observations were designed to gather high cadence time series of the bright, V=11.2, star during transits of the planet (HST program 10998)." Gaps in the time series due to Earth occultation necessitate piecing together observations from more than one transit., Gaps in the time series due to Earth occultation necessitate piecing together observations from more than one transit. " HST observed a transit event on 110, 2008 UT (2454506.6 JD) and again three transits later on 221, 2008 UT (2454518.4 JD)."," HST observed a transit event on 10, 2008 UT (2454506.6 JD) and again three transits later on 21, 2008 UT (2454518.4 JD)." Each visit consists of five HST orbits., Each visit consists of five HST orbits. " The first-order spectrum of ffrom the G141 grism (1.1€Ax19 pm)) is positioned on the lower left quadrant (quad 1) of the NIC3 NICMOS detector, and it does not cross any amplifier boundaries Figure "," The first-order spectrum of from the G141 grism $1.1\leq \lambda \leq 1.9$ ) is positioned on the lower left quadrant (quad 1) of the NIC3 NICMOS detector, and it does not cross any amplifier boundaries (see Figure )." "The zeroth-order spectrum lies on the (seelower right 1)).quadrant (quad 2), and it enables accurate tracking of the spectrum's position."," The zeroth-order spectrum lies on the lower right quadrant (quad 2), and it enables accurate tracking of the spectrum's position." No other stars contribute significant flux in the NIC3 field of view., No other stars contribute significant flux in the NIC3 field of view. The Pupil Alignment Mechanism was set at —0.53 mm to defocus the Point Spread Function (PSF)., The Pupil Alignment Mechanism was set at $-0.53$ mm to defocus the Point Spread Function (PSF). Defocusing spreads the light over more pixels which improves operational efficiency by delaying saturation and improves precision by averaging nonuniform pixel response (Xu&Mobasher2003)., Defocusing spreads the light over more pixels which improves operational efficiency by delaying saturation and improves precision by averaging nonuniform pixel response \citep{XU03}. ". The detector is read out in MULTIACCUM mode with the STEPS sequence and NSAMP=11, resulting in an overall exposure time 39.953 s for a singe MULTIACCUM exposure."," The detector is read out in MULTIACCUM mode with the STEP8 sequence and NSAMP=11, resulting in an overall exposure time 39.953 s for a single MULTIACCUM exposure." " Including overheads, the exposure cadence is 49 s between MULTIACCUM exposures."," Including overheads, the exposure cadence is 49 s between MULTIACCUM exposures." There are ~57 exposures per HST orbit., There are $\sim$ 57 exposures per HST orbit. A single direct image in the F166N filter at the beginning of each HST visit provides the reference position of the target for determining the wavelength calibration., A single direct image in the F166N filter at the beginning of each HST visit provides the reference position of the target for determining the wavelength calibration. We reduced the data using both custom procedures and publicly-available procedures written in IDL., We reduced the data using both custom procedures and publicly-available procedures written in IDL. The reduction begins from the raw science file (araw) rather than the calibrated science file (.ccal)., The reduction begins from the raw science file raw) rather than the calibrated science file cal). " In summary, the procedure for reducing an image consists of starting from the last-read minus zeroth-read image of a MULTIACCUM image, applying a wavelength dependent flat field, and then correcting bad pixels through bicubic spline interpolation."," In summary, the procedure for reducing an image consists of starting from the last-read minus zeroth-read image of a MULTIACCUM image, applying a wavelength dependent flat field, and then correcting bad pixels through bicubic spline interpolation." " These data reduction steps are described next, and the resulting images are used to perform broad-band photometry in"," These data reduction steps are described next, and the resulting images are used to perform broad-band photometry in." " To determine the wavelength dependent flat field and to correct for systematic trends in the photometric time series (see ?7?)), we map the position of the spectrum on the detector."," To determine the wavelength dependent flat field and to correct for systematic trends in the photometric time series (see ), we map the position of the spectrum on the detector." " To measure the spectrum location, we fit a Gaussian to calculate the centroid of the spatial profile for 5 pixel intervals along the dispersion axis."," To measure the spectrum location, we fit a Gaussian to calculate the centroid of the spatial profile for 5 pixel intervals along the dispersion axis." A linear fit to the centroids versus position along the dispersion axis yields the slope of the spectrum on the detector., A linear fit to the centroids versus position along the dispersion axis yields the slope of the spectrum on the detector. " The lower left panel in Figures show the spectrum slope as a function of image number within an orbit for the first and second visit, respectively."," The lower left panel in Figures show the spectrum slope as a function of image number within an orbit for the first and second visit, respectively." " Each color represents an orbit, and the color code to identify an orbit is given in the lower right panel of the figure."," Each color represents an orbit, and the color code to identify an orbit is given in the lower right panel of the figure." The spectrum slope variation within an orbit is much smaller than the change between orbits., The spectrum slope variation within an orbit is much smaller than the change between orbits. We measure relative shifts in x and y pixel coordinates of the spectrum by cross correlation of the zeroth-order spectrum with respect to a reference image (11-th image in the second orbit of the first visit)., We measure relative shifts in x and y pixel coordinates of the spectrum by cross correlation of the zeroth-order spectrum with respect to a reference image (11-th image in the second orbit of the first visit). The zeroth-order position shifts are projected to the first-order spectrum’s dispersion relation position., The zeroth-order position shifts are projected to the first-order spectrum's dispersion relation position. " The projection, 62=—Acosa and óy=—Asina, takes into account the spectrum slope, a, and the pixel distance between the zeroth-order light and dispersion relation’s reference position, A=167.93 pix."," The projection, $\delta x=-\Delta\cos{\alpha}$ and $\delta y=-\Delta \sin{\alpha}$, takes into account the spectrum slope, $\alpha$, and the pixel distance between the zeroth-order light and dispersion relation's reference position, $\Delta=167.93$ pix." The top panels in Figure and Figure show the relative x and y pixel coordinate shifts of the dispersion relation's reference position as a function of the image number within an orbit., The top panels in Figure and Figure show the relative x and y pixel coordinate shifts of the dispersion relation's reference position as a function of the image number within an orbit. The dispersion reference position is repositioned within 0.5 pixel between visits and typically 0.2 pixel within a visit., The dispersion reference position is repositioned within 0.5 pixel between visits and typically 0.2 pixel within a visit. " We follow the procedure outlined in Gilliland&Ar-ribas(2003) to determine the wavelength dependent flat field, and the wavelength of each pixel is determined using the dispersion relation given in Pirzkaletal.(2009)."," We follow the procedure outlined in \citet{GIL03} to determine the wavelength dependent flat field, and the wavelength of each pixel is determined using the dispersion relation given in \citet{PIR09}." . The centroid of the direct image taken at the beginning of each visit determines the reference position of the dispersion relation., The centroid of the direct image taken at the beginning of each visit determines the reference position of the dispersion relation. A flat field is calculated for each image taking into account the reference position shifts and the spectrum slope variations., A flat field is calculated for each image taking into account the reference position shifts and the spectrum slope variations. " The individual flat fields are averaged over an orbit, and the resulting orbit averaged flat field is normalized on quad 1 where the first-order spectrum is located."," The individual flat fields are averaged over an orbit, and the resulting orbit averaged flat field is normalized on quad 1 where the first-order spectrum is located." The orbit averaged flat field is applied to all images within that orbit., The orbit averaged flat field is applied to all images within that orbit. " We use four methods to identify the dark, warm, and cosmic ray impacted pixels."," We use four methods to identify the dark, warm, and cosmic ray impacted pixels." We begin with the standard bad pixel mask for the NIC3 camera 2002)., We begin with the standard bad pixel mask for the NIC3 camera \citep{SOS02}. " Second, we identify pixels that significantly(Sosey vary beyond their empirically determined sample standard deviation throughout an orbit."," Second, we identify pixels that significantly vary beyond their empirically determined sample standard deviation throughout an orbit." " Third, warm pixels (> 100 DN) in the region for determining the background level are identified for correction."," Third, warm pixels $>$ 100 DN) in the region for determining the background level are identified for correction." " Fourth, pixels that deviate by > 80 from the Poisson and read noise expectation in both forward and backward differences are identified for correction."," Fourth, pixels that deviate by $>$ $\sigma$ from the Poisson and read noise expectation in both forward and backward differences are identified for correction." " On average, each image has 177 pixels (1.1%)) for correction on quad 1."," On average, each image has 177 pixels ) for correction on quad 1." We replace affected pixels by the value of a bicubic spline fitted to surrounding pixels., We replace affected pixels by the value of a bicubic spline fitted to surrounding pixels. " In addition to the spectrum position and slope, we make use of the G141 filter wheel telemetry to correct for systematic trends in the photometric time series."," In addition to the spectrum position and slope, we make use of the G141 filter wheel telemetry to correct for systematic trends in the photometric time series." The filter wheel telemetry indicates that the G141 grism position does not return to the same state in between orbits., The filter wheel telemetry indicates that the G141 grism position does not return to the same state in between orbits. " The filter wheel telemetry for each visit (Chris Long, private communication) is given as a function of orbit in the lower right panel of Figuresὃ."," The filter wheel telemetry for each visit (Chris Long, private communication) is given as a function of orbit in the lower right panel of Figures." ". There are two preferred telemetry states of the G141 grism (70.6 and ~0.3 fractional telemetry position), and within each of these telemetry states the telemetry do not exactly repeat but have small variations."," There are two preferred telemetry states of the G141 grism $\sim$ 0.6 and $\sim$ 0.3 fractional telemetry position), and within each of these telemetry states the telemetry do not exactly repeat but have small variations." " In the first visit (Figure 2)), the filter wheel telemetry anti-correlates with the spectrum slope; The filter wheel telemetry position of 0.6 (orbits 1 3) correspond to low spectrum slope, and the filter wheel telemetry position of 0.3 (orbits 2, 4, 5) corresponds to the higher spectrum slope."," In the first visit (Figure ), the filter wheel telemetry anti-correlates with the spectrum slope; The filter wheel telemetry position of 0.6 (orbits 1 3) correspond to low spectrum slope, and the filter wheel telemetry position of 0.3 (orbits 2, 4, 5) corresponds to the higher spectrum slope." " In the second visit, the correspondence of filter wheel telemetry and spectrum slope is not as clear."," In the second visit, the correspondence of filter wheel telemetry and spectrum slope is not as clear." structure depends. on the adiabatic index LE.,structure depends on the adiabatic index $\Gamma$. In these numerical experiments. we employ. a purely aciabatie LOS with unique A and E.," In these numerical experiments, we employ a purely adiabatic EOS with unique $K$ and $\Gamma$." Ehe values of A and E are chosen to correspond to density regimes of interest in the crust. e.g. degenerate non-relativistic electron gas 10°. degenerate relativistic electron gas 10Zp/(gcm7)<10/7 and degenerate neutron gas 1077Zopílgcm3)SS10.," The values of $K$ and $\Gamma$ are chosen to correspond to density regimes of interest in the crust, e.g. degenerate non-relativistic electron gas $10^{5} \lesssim \rho/(\mathrm{g} \ \mathrm{cm}^{-3}) \lesssim 10^{7}$ , degenerate relativistic electron gas $10^{7} \lesssim \rho/(\mathrm{g} \ \mathrm{cm}^{-3}) \lesssim 10^{12}$ and degenerate neutron gas $10^{12} \lesssim \rho/(\mathrm{g} \ \mathrm{cm}^{-3}) \lesssim 10^{16}$." In an ideal electron gas. which is approximately isothermal. raciation and Lattice pressures dominate. but this occurs at much lower densities p10!&em5 which are irrelevant to the mountain problem.," In an ideal electron gas, which is approximately isothermal, radiation and lattice pressures dominate, but this occurs at much lower densities $\rho \lesssim 10^{4} \ \mathrm{g} \ \mathrm{cm}^{-3}$, which are irrelevant to the mountain problem." Table 1. displavs the magnetic mountain models we compute here. with the details of their respective EOS.," Table \ref{table:eos} displays the magnetic mountain models we compute here, with the details of their respective EOS." " Á ds a function of mean molecular weight per electron. fe=omaf(maY). according to the sealing Aoκf6 where may, is the mean barvon rest mass. mp is the atomic mass unit. and 3. is the mean number of electrons. per barvon."," $K$ is a function of mean molecular weight per electron, $\mu_{e} = m_{b}/(m_{u}Y_{e})$, according to the scaling $K \propto \mu_{e}^{-4/3}$, where $m_{b}$ is the mean baryon rest mass, $m_{u}$ is the atomic mass unit, and $Y_{e}$ is the mean number of electrons per baryon." " Under the assumption of svmmetric nuclear matter. we take jj.=2 and m,= and hence A is a constant. (i.e. independent. of p)."," Under the assumption of symmetric nuclear matter, we take $\mu_{e} = 2$ and $m_{b} = m_{u}$ and hence $K$ is a constant (i.e. independent of $\rho$ )." This form of the EOS describes well a completely degenerate. ideal Fermi eas (?)..," This form of the EOS describes well a completely degenerate, ideal Fermi gas \citep{shapiro1983}." " llence we use it to model degenerate relativistic electrons (n=3..V4/3.N-—4.93104deng|?32 enm?) degenerate. non-relativistic electrons (n.=3/2.1.—5/3.⋅N⊳⋅⋅ΞX16«10712dyn&n6'3 em) and degenerate non-relativistic neutrons (n=3/2.Vo5/3.N-5.3810°9dvng2653 cnm"")."," Hence we use it to model degenerate relativistic electrons $n=3, \ \Gamma=4/3, \ K=4.93\times10^{14} \ \mathrm{dyn} \ \mathrm{g}^{-4/3} \ \mathrm{cm}^{2}$ ), degenerate non-relativistic electrons $n=3/2, \ \Gamma=5/3, \ K=3.16\times10^{12} \ \mathrm{dyn} \ \mathrm{g}^{-5/3} \ \mathrm{cm}^{3}$ ) and degenerate non-relativistic neutrons $n=3/2, \ \Gamma=5/3, \ K=5.38\times10^{9} \ \mathrm{dyn} \ \mathrm{g}^{-5/3} \ \mathrm{cm}^{3}$ )." " We assume the following neutron star paranieters throughout/ this paper. except where stipulated: otherwise: Al,=LAM.Ry10°em. and es=16«1077Gene (with oy=B,Rin f2. where D, is the polar magnetic field streneth before accretion begins)."," We assume the following neutron star parameters throughout this paper, except where stipulated otherwise: $M_{\ast} = 1.4 \mathrm{M}_{\sun}, \ R_{\mathrm{in}} = 10^{6} \ \mathrm{cm}$, and $\psi_{\ast} = 1.6 \times 10^{24} \ \mathrm{G} \ \mathrm{cm}^{2}$ (with $\psi_{\ast} = B_{\ast} R_{\mathrm{in}}/2$ where $B_{\ast}$ is the polar magnetic field strength before accretion begins)." " Phe fiducial value of the magnetic field. B,=10177€. is chosen in accord with population synthesis models. which predict natal magnetic of μον101G Lot?(??7).."," The fiducial value of the magnetic field, $B_{\ast} = 10^{12.5} \ \mathrm{G}$, is chosen in accord with population synthesis models, which predict natal magnetic fields of $10^{12}-10^{13} \ \mathrm{G}$ \citep{hartman1997, arzoumanian2002, faucher-giguere2006}." The adiabatie Cirad.Shafranoy formalism in Section 2.. and the numerical solver described in Appendix X... must reproduce the results of PMOA in the isothermal limit (i.c. noow.cd.K C2).," The adiabatic Grad–Shafranov formalism in Section \ref{section_2}, and the numerical solver described in Appendix \ref{appendix:pseudocode}, must reproduce the results of PM04 in the isothermal limit (i.e. $n \to \infty, \ \Gamma \to 1, \ K \to c_{\mathrm{s}}^{2}$ )." In this limit. the isocdensity contours and magnetic field lines of an adiabatic mountain with LEl must converge to those plotted. in figs 4. 5 and 9 in PMOA for identical acereted masses.," In this limit, the isodensity contours and magnetic field lines of an adiabatic mountain with $\Gamma \to 1$ must converge to those plotted in figs 4, 5 and 9 in PM04 for identical accreted masses." As there is no unique wav to continuously transform an acdiabatie EOS into an isothermal EOS. we test the adiabatic/isothermal correspondence by taking the limit CAD).s(62.1) in three cilferent wavs below.," As there is no unique way to continuously transform an adiabatic EOS into an isothermal EOS, we test the adiabatic/isothermal correspondence by taking the limit $(K, \Gamma) \to (c_{\mathrm{s}}^{2}, 1)$ in three different ways below." " We apply these three approaches to the case AZ,=1.0 starting from a relativistic degenerate. electron EOS (model € in Table. 132)."," We apply these three approaches to the case $M_{\mathrm{a}} = 1.0 \times 10^{-5} \mathrm{M}_{\sun}$ , starting from a relativistic degenerate electron EOS (model C in Table \ref{table:eos}) )." " This EOS: prevails over a large logarithmic range of densities in a realistic stellar crust. LO""p/(gem7)107: see Section 5]] and. gives way to an isothermal EOS in the upper atmosphere (p«105&em7)."," This EOS prevails over a large logarithmic range of densities in a realistic stellar crust $10^{7} \lesssim \rho/(\mathrm{g} \ \mathrm{cm}^{-3}) \lesssim 10^{12}$; see Section \ref{section_5}] ] and gives way to an isothermal EOS in the upper atmosphere $\rho < 10^{4} \ \mathrm{g} \ \mathrm{cm}^{-3}$ )." We find that all three approaches converge correctly to the DP=1 results of PMÓA after ~32107 iterations., We find that all three approaches converge correctly to the $\Gamma = 1$ results of PM04 after $\sim 3\times10^{3}$ iterations. Fie., Fig. l displavs the mass ellipticitv. magnetic dipole moment. and gric-averaged c residual. (relative to the E=1 result) as a function of E for approaches (i) (red ciamoncds). (ii) (green rectangles) and (iii) (blue triangles).," \ref{fig:convergence} displays the mass ellipticity, magnetic dipole moment, and grid-averaged $\psi$ residual (relative to the $\Gamma = 1$ result) as a function of $\Gamma$ for approaches (i) (red diamonds), (ii) (green rectangles) and (iii) (blue triangles)." As indicated by Fig. L..," As indicated by Fig. \ref{fig:convergence}," the rate of convergence towards the isothermal results dillers between models., the rate of convergence towards the isothermal results differs between models. Phe abnormally. ugh dipole moment for case (i) at P=1.06 in Fig., The abnormally high dipole moment for case (i) at $\Gamma = 1.06$ in Fig. 1. is caused by insullicient. resolution in ϐ and can be prevented w scaling the erid logarithmically in ϐ to handle the steep magnetic field gradients at the equator., \ref{fig:convergence} is caused by insufficient resolution in $\theta$ and can be prevented by scaling the grid logarithmically in $\theta$ to handle the steep magnetic field gradients at the equator. We defer this project o future work., We defer this project to future work. We compute the mass enclosed within the computational/ grid as a function.— of iteration number.— o track the mass lost through the outer boundary.," We compute the mass enclosed within the computational grid as a function of iteration number, to track the mass lost through the outer boundary." In every convereccl equilibrium. the total mass in the final state is always within 4 per cent (and typically within 1 per cent) of the initial mass.," In every converged equilibrium, the total mass in the final state is always within $4$ per cent (and typically within $1$ per cent) of the initial mass." The iterative solver also preserves the divergence-free nature of the magnetic field. with |V-B]=0 to machine precision everywhere on the grid.," The iterative solver also preserves the divergence-free nature of the magnetic field, with $|\nabla \cdot \bmath{B}| = 0$ to machine precision everywhere on the grid." In this section. we compute Cirad.Shafranoy equilibria for several aciabatic EOS using the method described in Section 2 and validated in Section 3..," In this section, we compute Grad–Shafranov equilibria for several adiabatic EOS using the method described in Section \ref{section_2} and validated in Section \ref{section_3}." Fable 1. lists the parameters of each EOS. corresponding to different depth. intervals within the stellar crust (see. Section 5)).," Table \ref{table:eos} lists the parameters of each EOS, corresponding to different depth intervals within the stellar crust (see Section \ref{section_5}) )." The scalings of the magnetic dipole moment ye and mass cllipticity € with accreted mass AM are studied. in Sections 4.1. and 4.2.. respectively.," The scalings of the magnetic dipole moment $\mu$ and mass ellipticity $\epsilon$ with accreted mass $M_{\mathrm{a}}$ are studied in Sections \ref{section_4:dipole_moment} and \ref{section_4:ellipticity}, respectively." The maximum density and local magnetic fiel streneth are computed in Sections 4.3. and 4.4.. respectively.," The maximum density and local magnetic field strength are computed in Sections \ref{section_4:maximum_magnetic_field} and \ref{section_4:maximum_density}, respectively." In Section 4.5.. we compare the equilibrium. density anc magnetic Ποια distributions for adiabatic and. isotherma magnetic mountains.," In Section \ref{section_4:hydromagnetic_structure}, we compare the equilibrium density and magnetic field distributions for adiabatic and isothermal magnetic mountains." For cach model in Table 1.. we stop our simulations once [c/c] is less than 5 per cent averagec over the ericl (see Appendix A)).," For each model in Table \ref{table:eos}, we stop our simulations once $|\Delta \psi/\psi|$ is less than $5$ per cent averaged over the grid (see Appendix \ref{appendix:pseudocode}) )." As accretion proceeds and the initial dipolar magnetic ficld lines are distorted. magnetic cnerey is transferred from the dipole to higher order multipole moments.," As accretion proceeds and the initial dipolar magnetic field lines are distorted, magnetic energy is transferred from the dipole to higher order multipole moments." " The northsouth antisvmmetry. of D, precludes the existence of even multipoles.", The north–south antisymmetry of $B_{r}$ precludes the existence of even multipoles. Fig., Fig. " 2. displavs the magnetic dipole moment ye (normalized. by its initial. or surface.value) as a Function of the accreted mass AL, for models E in Table"," \ref{fig:dipole_mass} displays the magnetic dipole moment $\mu$ (normalized by its initial, or surface,value) as a function of the accreted mass $M_{\mathrm{a}}$ for models A–E in Table" 2005).,. . The first polarimetric observations toward 11333 were carried out by Vrbaetal.(1976) and Turnsheketal.(1980)., The first polarimetric observations toward 1333 were carried out by \citet{Vrba76} and \citet{TTC80}. . Tamuraetal.(1988) conducted K-band polarimetric observations towards the center of the NGC 1333 reflection nebula., \citet{Tamura88} conducted $K$ -band polarimetric observations towards the center of the NGC 1333 reflection nebula. A larger polarimetric survey covering the full Perseus complex was carried out by Goodmanetal.(1990)., A larger polarimetric survey covering the full Perseus complex was carried out by \citet{Goodman90}. ". These observations show that there is a bimodal distribution of polarization P.A., indicating that there are two large scale magnetic field components along the line of sight."," These observations show that there is a bimodal distribution of polarization P.A., indicating that there are two large scale magnetic field components along the line of sight." " 11333 444A (hereafter 44A), a low-mass protostellar system, has become the textbook case of a collapsing magnetized core: high angular submm polarimetric observations have revealed that the magnetic field has an hourglass morphology at scales of few hundred AUs (Girartetal.1999,2006)."," 1333 4A (hereafter 4A), a low-mass protostellar system, has become the textbook case of a collapsing magnetized core: high angular submm polarimetric observations have revealed that the magnetic field has an hourglass morphology at scales of few hundred AUs \citep{Girart99, Girart06}." ". This is the magnetic field morphology predicted by theoretical models based on magnetically controlled molecular core collapse (e.g.,Shuetal. 2001)."," This is the magnetic field morphology predicted by theoretical models based on magnetically controlled molecular core collapse \citep[e.g.,][]{Shu87,Mouschovias01}." ". Indeed, the synthetic polarization maps constructed using models of collapsing magnetized cores (Galli&Shu1993;etal.2006) reproduced quite well the observations in IRAS 4A (Gongalvesetal.2008)."," Indeed, the synthetic polarization maps constructed using models of collapsing magnetized cores \citep{Galli93,Shu06} reproduced quite well the observations in IRAS 4A \citep{Goncalves08}." ". In this context, it is worth mentioning that it is still a question of ongoing debate whether magnetic fields or interstellar turbulence plays a major role in the dynamical evolution of a molecular cloud (e.g.,Crutcheretal.2009;Mouschovias&Tassis2010)."," In this context, it is worth mentioning that it is still a question of ongoing debate whether magnetic fields or interstellar turbulence plays a major role in the dynamical evolution of a molecular cloud \citep[e. g.,][]{Crutcher09, Mouschovias10}." ". In this paper, we report on one of the first scientific results obtained with the near-IR camera LIRIS (Long-slitIntermediateResolutionInfraredSpectrograph:Acosta-Pulidoetal.2003;Manchadoetal.2004) in its polarimetric mode."," In this paper, we report on one of the first scientific results obtained with the near-IR camera LIRIS \citep[Long-slit Intermediate Resolution Infrared Spectrograph:][]{Acosta03,Manchado04} in its polarimetric mode." The observations were done using the J-band filter toward stars located relatively close to IRAS 4A (~ 4’-8’)., The observations were done using the $J$ -band filter toward stars located relatively close to IRAS 4A $\sim 4'$ $8'$ ). " The fields were selected to avoid the most active star-forming portion of the NGC 1333 cloud, so the measured polarized light is mainly due to dichroic absorption."," The fields were selected to avoid the most active star-forming portion of the NGC 1333 cloud, so the measured polarized light is mainly due to dichroic absorption." " In order to ascertain the quality of the near-IR data, we also provide complementary R-band linear polarimetry obtained with the Observatórrio do Pico dos Dias toward the same region."," In order to ascertain the quality of the near-IR data, we also provide complementary $R$ -band linear polarimetry obtained with the Observatórrio do Pico dos Dias toward the same region." The scientific goal of this work is to compare the magnetic field, The scientific goal of this work is to compare the magnetic field MMB again suggests an oval structure iu theLe domain (?)..,MMB again suggests an oval structure in the domain \citep{green10mmb2}. Although readily accounted for by a ring with an apparent expanding velocity. inodelling aud theoretical interpretation lavour elliptical orbits/streatulites.," Although readily accounted for by a ring with an apparent expanding velocity, modelling and theoretical interpretation favour elliptical orbits/streamlines." Here we investigate this by firstly fitting the 3-kpe arm taser distributiou with an elliptical model with constant. angular momenttun aud. secoucdly. a circular ring model incorporatile ea component of racial velocity outwards from the Galactic centre.," Here we investigate this by firstly fitting the 3–kpc arm maser distribution with an elliptical model with constant angular momentum and, secondly, a circular ring model incorporating a component of radial velocity outwards from the Galactic centre." We fit only to the 3-kpe arm maser population as the tudivicual sources towards the tangent points are clepeudenut on the spiral arm mocel and rotation curve (as discussed iu the Appendix)., We fit only to the 3–kpc arm maser population as the individual sources towards the tangent points are dependent on the spiral arm model and rotation curve (as discussed in the Appendix). We first consider the case of an ellipse. with a ratio of seni-miuor to seiui-uiajor axes of (2?).. au orientation between 25° aud 507 and a coustaut augular momentum of between 300 and ! |.," We first consider the case of an ellipse, with a ratio of semi–minor to semi–major axes of 0.50--0.80 \citep{peters75,sevenster99}, , an orientation between $^{\circ}$ and $^{\circ}$ and a constant angular momentum of between 300 and $^{-1}$ $^{-1}$." We assume the tangential velocity at any given point on the ellipse is given by the angular momentum divided by the Galactocentrie radius of that point., We assume the tangential velocity at any given point on the ellipse is given by the angular momentum divided by the Galactocentric radius of that point. The best fit is found for a semi-major axis of L1 kpc. an axis ratio of 0.51 (a semi-iminor axis of kkpc). au orientation of 38° and a rotational velocity of + (a mean circular velocity of 1).," The best fit is found for a semi–major axis of 4.1 kpc, an axis ratio of 0.54 (a semi–minor axis of kpc), an orientation of $^{\circ}$ and a rotational velocity of $^{-1}$ (a mean circular velocity of $^{-1}$ )." This accounts for of the 3-kpe arm sources aud is shown (with a radial thickness of 0.5 kpe) overlaid on the maser distribution in rellyclistributiouring.., This accounts for of the 3–kpc arm sources and is shown (with a radial thickness of 0.5 kpc) overlaid on the maser distribution in \\ref{lvdistributionring}. The ellipse cau approximate the parallel sections of the 3-kpc aruis well. but does not associate tlie masers at positive longitudes (71257) with high velocities.," The ellipse can approximate the parallel sections of the 3–kpc arms well, but does not associate the masers at positive longitudes $>$ $^{\circ}$ ) with high velocities." The effect ou the level of association with varying parameters of the elliptical ring mocel is shown in the left panels of Figure 7.., The effect on the level of association with varying parameters of the elliptical ring model is shown in the left panels of Figure \ref{paramvary2}. In this Figure. each pixel within a pauel represents au ellipse model for a given set of parameters (Semi-major aud —niuor axes. orientation and augular momentum) and the colour scale represents the fraction of masers associated with the mocel.," In this Figure, each pixel within a panel represents an ellipse model for a given set of parameters (Semi–major and –minor axes, orientation and angular momentum) and the colour scale represents the fraction of masers associated with the model." Extencling the allowed range of angular momenta does not improve the fit. with tlie best fits coufined within a limited rauge of ~100kkiuss | t about 300 to. ! +. dependent on the orientation of the ellipse.," Extending the allowed range of angular momenta does not improve the fit, with the best fits confined within a limited range of $\sim$ $^{-1}$ $^{-1}$ about 300 to $^{-1}$ $^{-1}$, dependent on the orientation of the ellipse." Extendiug the leneth range of the axes gives much poorer fits below 3.5 kpe. but has comparable association at longer radii (although as uoted radii larger than 1.5 kpc are increasingly unrealistic as they result in tangential velocities exceediug the terminal velocities).," Extending the length range of the axes gives much poorer fits below 3.5 kpc, but has comparable association at longer radii (although as noted radii larger than 4.5 kpc are increasingly unrealistic as they result in tangential velocities exceeding the terminal velocities)." Varying the orieutation of the ellipse below 20° produces poorer fits., Varying the orientation of the ellipse below $^{\circ}$ produces poorer fits. The ellect of changing the orientation aud the angular momentum is somewhat linked in theLo domain. with a stnaller orientation but larger angular momentum produciug similar results to a larger orientation but sinaller angular iunoimentuim.," The effect of changing the orientation and the angular momentum is somewhat linked in the domain, with a smaller orientation but larger angular momentum producing similar results to a larger orientation but smaller angular momentum." Decreasing tlie ratio of semi-minor to semi-major axes below 0.5 (Le. increasiug tlie level of ellipticity) produces a much poorer fit and increasiug the ratio of axes much beyond 0.5 (makiug the ring increasiugly. circular) introduces the ueed for the radial iotiou of the circular ring scenario., Decreasing the ratio of semi–minor to semi–major axes below 0.5 (i.e. increasing the level of ellipticity) produces a much poorer fit and increasing the ratio of axes much beyond 0.8 (making the ring increasingly circular) introduces the need for the radial motion of the circular ring scenario. If the unassociated sources described at the start of Section ?? are iucluded in the fitting. then the best fit to the combined source sample is for a semi-iuajor axis of L2 kpe. an axis ratio of 0.53 (a semi-iuinor axis of kkpc). an orientation of 28° and a rotational velocity of | (a mean circular velocity of 1).," If the unassociated sources described at the start of Section \ref{lvintro} are included in the fitting, then the best fit to the combined source sample is for a semi–major axis of 4.2 kpc, an axis ratio of 0.53 (a semi–minor axis of kpc), an orientation of $^{\circ}$ and a rotational velocity of $^{-1}$ (a mean circular velocity of $^{-1}$ )." This accounts for of the sources., This accounts for of the sources. Thevariation in the fraction of sources associated with the ring models when iuclucdiug the unassociated sources is shown iu the right pauels of Figure 7.., Thevariation in the fraction of sources associated with the ring models when including the unassociated sources is shown in the right panels of Figure \ref{paramvary2}. . In the barvon mass conservation across the shock front. we also consider some mass loss (equivalently the loss of mass-accretion rate) associated with the outflows that are blown awav as winds/jets.,"In the baryon mass conservation across the shock front, we also consider some mass loss (equivalently the loss of mass-accretion rate) associated with the outflows that are blown away as winds/jets." From equation (15)) we have Clearly. (he mass-accretion rate depends on the measurement of entropy Jy which must increase across the shock because of the heat generated (second. law of thermodvuamics).," From equation \ref{eq:mdot2}) ) we have Clearly, the mass-accretion rate depends on the measurement of entropy $K$ which must increase across the shock because of the heat generated (second law of thermodynamics)." llowever. in the presence of both energy dissipation ancl mass loss a( the shock front. a fraction of total energy. (including mass and thermal energies) can be released from the flow surface. quickly reducing the rise of A.," However, in the presence of both energy dissipation and mass loss at the shock front, a fraction of total energy (including mass and thermal energies) can be released from the flow surface, quickly reducing the rise of $K$." This hypothesis is justifiable when cooling processes are verv efficient. allhough it is bevond the scope of this work to discuss the details of (hese mechanisms.," This hypothesis is justifiable when cooling processes are very efficient, although it is beyond the scope of this work to discuss the details of these mechanisms." Hlence. for simplicity. we assume that the entropy will roughly. remain unchanged at the shock Iront as a result from partial heat loss of the shocked flow.," Hence, for simplicity, we assume that the entropy will roughly remain unchanged at the shock front as a result from partial heat loss of the shocked flow." Thus. we sel A4=Avyhy and require Ay>Mà.," Thus, we set $K_1 = K_1 \equiv K_0$ and require $\dot{M}_1 \ge \dot{M}_2$." " Similarly (0 energy. dissipation. let us define the nass loss and ils fractionas where 0 $ 0.7 keV were used in order to separate out emission from the additional, highly variable, soft component seen after this time." We have constrained the interstellar column to be [Nj]js=(2.450.6)x1074 7 throughout (Iiellmingοἱal.L986) but we let the additional column from the overlving red. giant wind. [Vyfi. be a free parameter up to and including Observation 7.," We have constrained the interstellar column to be $[N_H]_{IS} = (2.4 \pm 0.6) \times 10^{21}$ $^{-2}$ throughout \citep{hje86} but we let the additional column from the overlying red giant wind, $[N_H]_W$, be a free parameter up to and including Observation 7." μη. was then fixed at 1.8x10?! 7 thereafter as the new soft X-ray emission component began to dominate the emission at low energies., $[N_H]_W$ was then fixed at $1.8 \times 10^{21}$ $^{-2}$ thereafter as the new soft X-ray emission component began to dominate the emission at low energies. Spectral fits al several epochs using a solar abundance model are shown in Figure 6.., Spectral fits at several epochs using a solar abundance model are shown in Figure \ref{spectra}. We note that elemental abundanince enhancements were required by Bode&Ixahn(1985) in their model and also by Snijders(1937) and from IUE observations of the 1985 outburst., We note that elemental abundance enhancements were required by \citet{bod85} in their model and also by \citet{sni87} and \citep{sho96} from IUE observations of the 1985 outburst. ILowever. we choose solar abundances until we have performed detailed analvses of the evolution of the shell (as described further in the Discussion section below).," However, we choose solar abundances until we have performed detailed analyses of the evolution of the shell (as described further in the Discussion section below)." We also note that these single temperature fits. as may be reasonably expected. fail to reproduce all of the spectral detail and should not be overly interpreted at this stage.," We also note that these single temperature fits, as may be reasonably expected, fail to reproduce all of the spectral detail and should not be overly interpreted at this stage." In the first three epochs. (Observations 1. 2a and 2b) the Fe Ix line was clearly detected al around 6.7 keV. as expected for the fitted plasma temperatures.," In the first three epochs, (Observations 1, 2a and 2b) the Fe K line was clearly detected at around 6.7 keV, as expected for the fitted plasma temperatures." In the first (wo epoclis. there was also obvious excess emission al lower energies in (he line compared to the single temperature mekal model fit.," In the first two epochs, there was also obvious excess emission at lower energies in the line compared to the single temperature mekal model fit." This could be characterised by an additional line at 6.4 keV which suggests X-rav reflection [rom a cold (or moderately ionised) gas as seen in some AGN and magnetic CVs (Beardmoreetal.1995:Done1995).," This could be characterised by an additional line at 6.4 keV which suggests X-ray reflection from a cold (or moderately ionised) gas as seen in some AGN and magnetic CVs \citep{bea95,don95}." . We consider scattering in the red giant wind more likely in this ease. a situation well documented in a number of supereiant X-rav binaries (e.g. vanderMeer(2005) ancl references therein).," We consider scattering in the red giant wind more likely in this case, a situation well documented in a number of supergiant X-ray binaries (e.g. \citet{van05} and references therein)." The equivalent width of this line (~70 eV in Observation 2a) is consistent with fInorescent emission by the surrounding gas with a column density ~6x107 7 (Alakashinia1935)., The equivalent width of this line $ \sim 70$ eV in Observation 2a) is consistent with fluorescent emission by the surrounding gas with a column density $\sim 6\times 10^{22}$ $^{-2}$ \citep{mak85}. . Figures 7 and 8 illustrate the results lor important parameters derived [rom the fits., Figures \ref{NH} and \ref{vs} illustrate the results for important parameters derived from the fits. For example. Figure 7 shows a monotonic decline in Vj]u: with time. in a manner qualitatively expected as the forward shock traverses the overlving wind.," For example, Figure \ref{NH} shows a monotonic decline in $[N_H]_W$ with time, in a manner qualitatively expected as the forward shock traverses the overlying wind." The forward shock velocity. vy. has been derived from the best fit plasma temperature and Equation 3D above.," The forward shock velocity, $v_s$, has been derived from the best fit plasma temperature and Equation 3 above." It can also immediatelv be seen that the implied shock velocities are of the same order as those derived, It can also immediately be seen that the implied shock velocities are of the same order as those derived We want to relate the eccentricities of a virialised triaxial object with those of its seed.,We want to relate the eccentricities of a virialised triaxial object with those of its seed. " As there are two eccentricities, we need two equations."," As there are two eccentricities, we need two equations." These equations must obviously report on properties involving the shape of these systems., These equations must obviously report on properties involving the shape of these systems. One of such properties is the volume of ellipsoidal isodensity contours., One of such properties is the volume of ellipsoidal isodensity contours. " The ratio between the volumes of the ellipsoids encompassing a given mass in the final and initial systems must be equal, to leading order in the deviation from spherical symmetry, to the ratio between the volumes of the corresponding spheres encompassing identical mass,"," The ratio between the volumes of the ellipsoids encompassing a given mass in the final and initial systems must be equal, to leading order in the deviation from spherical symmetry, to the ratio between the volumes of the corresponding spheres encompassing identical mass,." " To write the member on the right of equation (45)) we have taken into account that the mass of an ellipsoidal isodensity contour with semiaxes, a, b and c, labelled by R ;. coincides, owing to the relations (5)) and (6)) arising from the definition (4)) of the labelling radius, with UMthe mass of the sphere with radius R, "," To write the member on the right of equation \ref{emass}) ) we have taken into account that the mass of an ellipsoidal isodensity contour with semiaxes, $a$ , $b$ and $c$, labelled by $R$ _0^R, coincides, owing to the relations \ref{ellips}) ) and \ref{norm}) ) arising from the definition \ref{R1}) ) of the labelling radius, with the mass of the sphere with radius $R$, ." "On the other hand, the function rp(r) in equation (45)) is the solution, for the boundary condition rp(0)= 0, of the differential equation that follows from differentiation of equation (47)) holding for spheres with identical mass in the initial and final systems."," On the other hand, the function $r\p(r)$ in equation \ref{emass}) ) is the solution, for the boundary condition $r\p(0)=0$ , of the differential equation, that follows from differentiation of equation \ref{mass}) ) holding for spheres with identical mass in the initial and final systems." " For simplicity in the notation, we omit from now on the explicit dependence of rp on r."," For simplicity in the notation, we omit from now on the explicit dependence of $r\p$ on $r$." We stress that equation (45)) is only valid to leading order in the deviations from spherical symmetry., We stress that equation \ref{emass}) ) is only valid to leading order in the deviations from spherical symmetry. This does not mean that the volume of each ellipsoid is approximated by that of the corresponding sphere. (, This does not mean that the volume of each ellipsoid is approximated by that of the corresponding sphere. ( "By doing this, we would lose the information on the shape of the system.)","By doing this, we would lose the information on the shape of the system.)" What we approximate is the whole ratio between the volumes of both ellipsoids by the ratio between the volumes of the corresponding spheres., What we approximate is the whole ratio between the volumes of both ellipsoids by the ratio between the volumes of the corresponding spheres. " Were the axial ratios of the ellipsoid conserved over the evolution of the system, the relation (45)) wouldbe exact."," Were the axial ratios of the ellipsoid conserved over the evolution of the system, the relation \ref{emass}) ) wouldbe exact." " Actually, the axial ratios vary during virialisation."," Actually, the axial ratios vary during virialisation." But thisvariationis of, But thisvariationis of Ausseretal. (2001))).,\citet{NDB01}) ). There are disagreements in detail. for instance over the size of the bias parameter between dark and huninous matter. but the overall picture shows no greal difficulties.," There are disagreements in detail, for instance over the size of the bias parameter between dark and luminous matter, but the overall picture shows no great difficulties." " The problem of the formation of individual galaxies is nich complicated by the inclusion of radiation and gas effects. and it is bevond the scope of this paper even to outline the subfield,"," The problem of the formation of individual galaxies is much complicated by the inclusion of radiation and gas effects, and it is beyond the scope of this paper even to outline the subfield." For our purposes it suffices to note that dark matter and laminous matter are not distributed— the same wav on galactic scales. the dark halo being larger than any directly detectable part of a galaxy. though the two parts appear to be concentric.," For our purposes it suffices to note that dark matter and luminous matter are not distributed the same way on galactic scales, the dark halo being larger than any directly detectable part of a galaxy, though the two parts appear to be concentric." On scales smaller (han large-scale structure and larger (han galaxies we (hen expect lo see a transition., On scales smaller than large-scale structure and larger than galaxies we then expect to see a transition. Dark matter should depart significantly [rom huninous matter in ils distribution. while retaining a similar concentration around the densest points.," Dark matter should depart significantly from luminous matter in its distribution, while retaining a similar concentration around the densest points." Exactly how this happens should Cell us something about dark matter itself., Exactly how this happens should tell us something about dark matter itself. Unfortunately. studying structures in which the density contrast is highly nonlinear is nathematically difllieuli.," Unfortunately, studying structures in which the density contrast is highly nonlinear is mathematically difficult." One approach is to use galaxy clusters. which should be virialized (or nearly so).," One approach is to use galaxy clusters, which should be virialized (or nearly so)." Another is to find a region in which observational data are abundant ancl of veh quality. and in which peculiar velocities indicate dynamical vouth.," Another is to find a region in which observational data are abundant and of high quality, and in which peculiar velocities indicate dynamical youth." Were (the motions should be simpler than in a denanmically old system. while al the same (ime even small notions should be visible.," Here the motions should be simpler than in a dynamically old system, while at the same time even small motions should be visible." Such a region is (he Local Volume. within about 10 megaparsecs /Mpc).," Such a region is the Local Volume, within about 10 megaparsecs (Mpc)." In the Volume there are radial velocities accurate to one or a few km + [or hundreds ol galaxies. and (recently) distances good to or better for a large fraction.," In the Volume there are radial velocities accurate to one or a few km $^{-1}$ for hundreds of galaxies, and (recently) distances good to or better for a large fraction." Using these data. the present study aims to compare (he distribution aud motion of luminous matter. in an effort to show something of the location of gravitating matter.," Using these data, the present study aims to compare the distribution and motion of luminous matter, in an effort to show something of the location of gravitating matter." Data for 149 galaxies in the Local Volume were collected. [rom the literature ancl are presented in Table (1)) (ordered by Supergalactic longitude L. as are the rest of the data tables in this paper).," Data for 149 galaxies in the Local Volume were collected from the literature and are presented in Table \ref{data1}) ) (ordered by Supergalactic longitude $L$, as are the rest of the data tables in this paper)." The main eriterion for inclusion was a distance known to or better. along with a reliable radial velocity.," The main criterion for inclusion was a distance known to or better, along with a reliable radial velocity." The criterion lor distance uncertaintv was rather restrictive. and in fact it is possible to derive some kinematic or dvnamic properties of the Volume with a larger set of poorer data (as done in. for instance. Whiting(2003) or IXarachentsev&Makarov(200101. or anv work on large-scale structive).," The criterion for distance uncertainty was rather restrictive, and in fact it is possible to derive some kinematic or dynamic properties of the Volume with a larger set of poorer data (as done in, for instance, \citet{WH03} or \citet{KM01}, or any work on large-scale structure)." Bul the focus here is on the details of the peculiar velocity, But the focus here is on the details of the peculiar velocity around an AO spectrabtvpe stir. with the minimum particle size of the distribution artificially cut off at sizes between 5 aud 230san. (,"around an A0 spectral-type star, with the minimum particle size of the distribution artificially cut off at sizes between 5 and $30~\micron$. (" Note that we normally calculate the blow-out mass self-cousisteutlv as described in Paper L) We plot these SEDs in the middle paucl of Figure 13..,Note that we normally calculate the blow-out mass self-consistently as described in Paper I.) We plot these SEDs in the middle panel of Figure \ref{fig:synth}. The offsets between the SEDs become apparent for wavelengths shorter than 200san. while for longer wavelengths. the emission profiles agree aud have a common pseudo Ravleigh-Jeaus slope.," The offsets between the SEDs become apparent for wavelengths shorter than $200~\micron$, while for longer wavelengths, the emission profiles agree and have a common pseudo Rayleigh-Jeans slope." Finally. we explore the depeudence of the SED ou the slope ofthe quasi steady-state particle-imass distribution.," Finally, we explore the dependence of the SED on the slope of the quasi steady-state particle-mass distribution." The bottom pancl of Figure 13. shows svuthetic SEDs ecnerated for a debris rug at 25 AU around an AQ spectral type star. with a ΙΙΙ particle cut-off size at 5yuan. but with particle mass distribution slopes between Lal and 1.99.," The bottom panel of Figure \ref{fig:synth} shows synthetic SEDs generated for a debris ring at 25 AU around an A0 spectral type star, with a minimum particle cut-off size at $5~\micron$, but with particle mass distribution slopes between 1.81 and 1.99." These plots show that the slope of the Ravleigh-Jeans part of the emission is ereathy iuflueuced by the particle size distribution slope., These plots show that the slope of the Rayleigh-Jeans part of the emission is greatly influenced by the particle size distribution slope. In fact. it depends alinost solely on this slope. with the temperature of the eraius having wuld effects at large orbital distances.," In fact, it depends almost solely on this slope, with the temperature of the grains having mild effects at large orbital distances." We also performed our tests with cirty-ice optical constants (Preibischetal.1993). aud found very similar results. showing that our results are also iudepeudoenut on particle types assumed.," We also performed our tests with dirty-ice optical constants \citep{preibisch93} and found very similar results, showing that our results are also independent on particle types assumed." The absorption efficiency curves can be simplified aud deseribed as where e is a scaling coustaut for the power-law part of the function., The absorption efficiency curves can be simplified and described as where $x$ is a scaling constant for the power-law part of the function. Fitting the silicate absorption efficiency functions. we find Using this simplified absorption efficiency model and assundue that all particles contribute to the Ravleigh-Jeans tail of the SED with their own BRavleieli-Jeaus Cluission. we estimate the cuutted flux density at long waveloneths as Tere we assumed a} parameter that is independent of the particle size.," Fitting the silicate absorption efficiency functions, we find Using this simplified absorption efficiency model and assuming that all particles contribute to the Rayleigh-Jeans tail of the SED with their own Rayleigh-Jeans emission, we estimate the emitted flux density at long wavelengths as Here we assumed a $\beta$ parameter that is independent of the particle size." " The variable Caja is the προς density scaling (sce Paper D. ky, is the Boltzmann coustaut. T is the temperature of the dust erains (which we also assume to be particle size independent). aud. D is the distance of the system from the observer."," The variable $C_{\rm disk}$ is the number density scaling (see Paper I), ${\rm k}_{\rm b}$ is the Boltzmann constant, $T$ is the temperature of the dust grains (which we also assume to be particle size independent), and $D$ is the distance of the system from the observer." " The quautity i, is the quasisteady-state particle size distribution slope. aud can be calculated from the mass distribution slope as Yqση 2."," The quantity $\eta_a$ is the quasisteady-state particle size distribution slope, and can be calculated from the mass distribution slope as $\eta_a = 3 \eta - 2$ ." Tuteerating these functions. we eet," Integrating these functions, we get" Thus. a detailed study of two such advancecl SNRs represeuts a significant step forward in our understanding of the long-term fate of these objects.,"Thus, a detailed study of two such advanced SNRs represents a significant step forward in our understanding of the long-term fate of these objects." " We also note that δω is siguificantly ereater than Paya, for this remnant. sugeesting sole pressure-diiveu expansion even at these late ages."," We also note that $P_\mathrm{hot}$ is significantly greater than $P_\mathrm{shell}$ for this remnant, suggesting some pressure-driven expansion even at these late ages." N-vav cluission from aappears to trace the fhüluuecuts. again sugecsting that this eas is recently shock heated.," X-ray emission from appears to trace the filaments, again suggesting that this gas is recently shock heated." The appearance of two distinct shells alone with two expansion patterns in the echelle spectrum which correlate with the optical shells suggests a bilobed structure for the SNR., The appearance of two distinct shells along with two expansion patterns in the echelle spectrum which correlate with the optical shells suggests a bilobed structure for the SNR. The near edge of the SNR seems to be chcountering deuscr material as evidenced by the A-rav onadssion correspouding to that shock wave and the stronger eecnissiou convergiue to svstende velocity ou that edge., The near edge of the SNR seems to be encountering denser material as evidenced by the X-ray emission corresponding to that shock wave and the stronger emission converging to systemic velocity on that edge. The observed expausion velocity of 55 Hs quite low and gives an age of 125 kyr., The observed expansion velocity of 55 is quite low and gives an age of 125 kyr. The correspouding ratio E/n=6«107 ere em? does not agree as well with the observed value of 1.6«1079 cre cai., The corresponding ratio $E/n=6\times10^{49}$ erg $^3$ does not agree as well with the observed value of $1.6\times10^{50}$ erg $^3$. Towever. the thermal cucrey of the hot gas was estimated asstuing filling of an entire cllipsoidal shell. whereas we see X-ray Cluission from ouly the eastern half.," However, the thermal energy of the hot gas was estimated assuming filling of an entire ellipsoidal shell, whereas we see X-ray emission from only the eastern half." Furthermore. if this is a bilobed structure which is not aligned with the line of sight. we are onlv measuring a projected. component of the true expansion velocity.," Furthermore, if this is a bilobed structure which is not aligned with the line of sight, we are only measuring a projected component of the true expansion velocity." Both of these cousideratious would brine the two nunubers into closer agreement., Both of these considerations would bring the two numbers into closer agreement. We calculate that the viewing angele of the bilobed expansion would need to be 107 iu order for the two numbers to agree., We calculate that the viewing angle of the bilobed expansion would need to be $\sim40^\circ$ in order for the two numbers to agree. We also note that if the observed. elliptical region of N-ray cinissiou were actually a circular disce. a viewing angle of ~545° would cause it to appear as it does.," We also note that if the observed elliptical region of X-ray emission were actually a circular disc, a viewing angle of $\sim55^\circ$ would cause it to appear as it does." This viewing anele would imply a true expansion velocity of 97 wwhich corresponds to au age of 70 kyr., This viewing angle would imply a true expansion velocity of 97 which corresponds to an age of 70 kyr. However. if the renmuant is indeed cucouutering cdenser naterial. it may have undergone a more abrupt (uon-adiabatic) deceleration. aud again. this expansion velocity is outside the expected range of he Sedov-Taxlor phase. uctting a vounecr age for a given observed radius aud expansion velocity.," However, if the remnant is indeed encountering denser material, it may have undergone a more abrupt (non-adiabatic) deceleration, and again, this expansion velocity is outside the expected range of the Sedov-Taylor phase, netting a younger age for a given observed radius and expansion velocity." The uncertaiuntwv in the properties of this SNR uakes it dificult to choose accurate parameters for the simulations., The uncertainty in the properties of this SNR makes it difficult to choose accurate parameters for the simulations. Moreover. our simmilations are spherically svinietric. which is clearly not the case for this remuaut.," Moreover, our simulations are spherically symmetric, which is clearly not the case for this remnant." Sunulatious run over a range of reasonable parameters all result in fits with ages <50 kyr. lending support to the above consideration.," Simulations run over a range of reasonable parameters all result in fits with ages $< 50$ kyr, lending support to the above consideration." We have presented a inultiwavelength study of three recently discovered SNRs in the LMC. featuring new oobservations.," We have presented a multi-wavelength study of three recently discovered SNRs in the LMC, featuring new observations." We fit backeround spectra from cach observation with a detailed model inchiding soft proton contamination. imstrunental lines. the οσα]. hot bubble. aud extragalactic Ccommponcuts.," We fit background spectra from each observation with a detailed model including soft proton contamination, instrumental lines, the local hot bubble, and extragalactic components." These fits gave consistent values for the background uwanmeters across the Έτος observations., These fits gave consistent values for the background parameters across the three observations. We then ft source spectra with thermal plaza models. and compare the fits to simmlated spectra.," We then fit source spectra with thermal plasma models, and compare the fits to simulated spectra." We analytically estimated the plysical properties of he SNRs., We analytically estimated the physical properties of the SNRs. iis confirmed as au SNR due to its |SII|/IIa ratio. velocity expansion pattern. aud soft N-rav cluission. although we caunot fully characterise that cutission.," is confirmed as an SNR due to its [SII]/Ha ratio, velocity expansion pattern, and soft X-ray emission, although we cannot fully characterise that emission." aappears from our findings to be a large. relatively old SNR. simular to SNR 709.," appears from our findings to be a large, relatively old SNR, similar to SNR $-$ 709." It has fairly disorganized expansion and X-ray enudsson that appears to be due to a combination of recently shocked materi aud olcler “fossil” radiation., It has fairly disorganized expansion and X-ray emission that appears to be due to a combination of recently shocked material and older “fossil” radiation. aappears to be encountering higher density material to one side aud shows sigus of a bipolar expansion econmetry., appears to be encountering higher density material to one side and shows signs of a bipolar expansion geometry. Although we were able to obtain good fits to its spectrum. the age is difficult to determine precisely due to uncertainties m its ecometry and euvironuent.," Although we were able to obtain good fits to its spectrum, the age is difficult to determine precisely due to uncertainties in its geometry and environment." The authors would like to acknowledee David IIeulev for helpful comunenuts and assistance iu the couversion of the simulated spectra to Nspec models., The authors would like to acknowledge David Henley for helpful comments and assistance in the conversion of the simulated spectra to Xspec models. Cerro Tololo Inter-American Observatory CCTIO) is operated by the Association of Universities for Research in Astronomy Inc. (AURA). under a cooperative agreement with the National Science Foundation (NSF) as part of the National Optical Astronomy Observatories (NOAQ).," Cerro Tololo Inter-American Observatory (CTIO) is operated by the Association of Universities for Research in Astronomy Inc. (AURA), under a cooperative agreement with the National Science Foundation (NSF) as part of the National Optical Astronomy Observatories (NOAO)." We eratefully, We gratefully In Table 3. the best fit. parameters for the absorbing column clensity and the δ15 keV and line [uxes (obtainec with model 2: the results on the line fluxes are similar if model 3 is adopted) are summarized.,In Table \ref{time_res} the best fit parameters for the absorbing column density and the 8–15 keV and line fluxes (obtained with model 2; the results on the line fluxes are similar if model 3 is adopted) are summarized. Lt is interesting to note that the fluxes of the lines are correlated with the [Lux of he continuum: the only exception is the Compton shoulder. out the errors are pretty large.," It is interesting to note that the fluxes of the lines are correlated with the flux of the continuum; the only exception is the Compton shoulder, but the errors are pretty large." This applies in. particular or the spectra corresponding to Interval 2 (pre-burst) aux 3 (post-burst)., This applies in particular for the spectra corresponding to Interval 2 (pre-burst) and 3 (post-burst). The ratios of the iron line Luxes between he post- and pre-burst phases (1.8£0.2. and .2.415Ube for. Ίνα and Wet. respectively) are comparable with the average S15 keV continuum (ux ratio between the same intervals (2.41+ 0.04).," The ratios of the iron line fluxes between the post- and pre-burst phases $1.8 \pm 0.2$ and $2.4 \pm^{0.8}_{1.3}$ for $\alpha$ and $\beta$, respectively) are comparable with the average 8–15 keV continuum flux ratio between the same intervals $2.41 \pm 0.04$ )." Vo further explore the relation. between. the emission line and the continuum fluxes. in Fig.," To further explore the relation between the emission line and the continuum fluxes, in Fig." 5. the ight curves for the S15 keV. (which is dominated. by the continuum) and the 66.6 keV (dominated by the iron Ka ine) are shown., \ref{fig3_mg} the light curves for the 8–15 keV (which is dominated by the continuum) and the 6–6.6 keV (dominated by the iron $\alpha$ line) are shown. The line varies on time scales as short as 1000 s. implyingIn that the size of the emittingὃν regiono cannot »¢ larger than about 1077 em. consistent with a scenario in which the absorbing matter is e.g. due to the stream of material owing through the Lagrangian point in a Roche Lobe overllow. to eventually form an accretion disc.," The line varies on time scales as short as 1000 s, implying that the size of the emitting region cannot be larger than about $\times10^{13}$ cm, consistent with a scenario in which the absorbing matter is e.g. due to the stream of material flowing through the Lagrangian point in a Roche Lobe overflow, to eventually form an accretion disc." The line flux follows the variations of the continuum. but not precisely. as it is clear from the linetocontinuum. Hux ratio (lower panel of Fig. 5)).," The line flux follows the variations of the continuum, but not precisely, as it is clear from the line–to–continuum flux ratio (lower panel of Fig. \ref{fig3_mg}) )," suggesting that on these time scales also the properties of the cold matter. ie. the covering factor and/or the average column density. change.," suggesting that on these time scales also the properties of the cold matter, i.e. the covering factor and/or the average column density, change." We have performed a detailed analysis of the NATALNewton observation of LGR. J16318-4848. in order to characterize the properties of the matter responsible for the obscuration along the line-of-sight and for the emission of Fe and Ni lines.," We have performed a detailed analysis of the XMM–Newton observation of IGR J16318-4848, in order to characterize the properties of the matter responsible for the obscuration along the line-of-sight and for the emission of Fe and Ni lines." Our results can be summarized as follows: a) the line of sight material has a column density. of about 107! em2 b) from the value of the Fe We line EW and Compton Shoulder. an average column densitv of a few c1075 em7 (indicating cdishomogeneous or blobby material) and a covering factor of about 0.1.0.2 are estimated: c) the small value of the Compton reflection component suggests a [lat configuration of the matter. with a large inclination angle: d) the iron νὰ line varies on time scales as short as 1000 s. implving a size of the emitting region not exceeding ~310 em.," Our results can be summarized as follows: a) the line of sight material has a column density of about $\times10^{24}$ $^{-2}$; b) from the value of the Fe $\alpha$ line EW and Compton Shoulder, an average column density of a few $\times10^{23}$ $^{-2}$ (indicating dishomogeneous or blobby material) and a covering factor of about 0.1–0.2 are estimated; c) the small value of the Compton reflection component suggests a flat configuration of the matter, with a large inclination angle; d) the iron $\alpha$ line varies on time scales as short as 1000 s, implying a size of the emitting region not exceeding $\sim3\times10^{13}$ cm." The lux of the line roughly follows the variations of the continuum. but not exactly. suggesting a variation of the geometrical properties of the emitting region on similar time scales.," The flux of the line roughly follows the variations of the continuum, but not exactly, suggesting a variation of the geometrical properties of the emitting region on similar time scales." Finally. a few words on the putative “transient” nature of this source.," Finally, a few words on the putative “transient"" nature of this source." A reanalysis of an archival 1994 ASCA observation (Murakami et al., A reanalysis of an archival 1994 ASCA observation (Murakami et al. 2003) points to a Dux variation of a factor of just a few in about 8.5 vears., 2003) points to a flux variation of a factor of just a few in about 8.5 years. Phe comparison between the flux measured by INTEGRAL in the 1540 keV. and by NMM-Newton in the 515 keV is not conclusive. given the large uncertainties associated with the determination of the intrinsic [lux in such an absorbed," The comparison between the flux measured by INTEGRAL in the 15--40 keV and by XMM-Newton in the 5–15 keV is not conclusive, given the large uncertainties associated with the determination of the intrinsic flux in such an absorbed" where Vy is the initial Lorentz factor of the ejecta and La ds the Lorentz factor of the ejecta at the optical Lash peak time.,where $\Gamma_0$ is the initial Lorentz factor of the ejecta and $\Gamma_A$ is the Lorentz factor of the ejecta at the optical flash peak time. " Then the random minimum Lorentz [actor sini of the electrons in the reverse shock region is: The formulas of v,,, at the reverse shockwere given bv Sari & Piran (1999b).", Then the random minimum Lorentz factor $\gamma_{min}$ of the electrons in the reverse shock region is: The formulas of $\nu_m$ at the reverse shockwere given by Sari $\&$ Piran (1999b). We here add the correction for recshi, We here add the correction for redshift. " The observed Dux at £j, can be obtained by assuming that all the electrons in the reverse shock region contribute thesame average power per unit ⋠⋅frequeney i∕ at £u. which. is ⋠⋠given by Po∕=EREX where Bo/=Liye.32am."," The observed flux at $\nu_m$ can be obtained by assuming that all the electrons in the reverse shock region contribute thesame average power per unit frequency $P'_{\nu_m}$ at $\nu_m$, which is given by $P'_{\nu_m}=\frac{\sqrt{3}e^{3}B'}{m_e{c^2}}$, where $B'=\Gamma_{A}c{\sqrt{32\pi{nm_p}\epsilon_B}}$." Adding one factor of P4 to transform to the observer frame and accounting For the redshift. we have: where No ds the total number of radiating electrons in the ejecta shell. anc d;=2e(11zVl|z)/Huo is the luminosity distance.," Adding one factor of $\Gamma_{A}$ to transform to the observer frame and accounting for the redshift, we have: where $N_e$ is the total number of radiating electrons in the ejecta shell, and $d_L=2c(1+z-\sqrt{1+z})/H_0$ is the luminosity distance." " Please note that IN, here is cülferent from the AN, adopted in the forward shock region. which is the total number of swept-up electrons by the forward external shock."," Please note that $N_e$ here is different from the $N_e$ adopted in the forward shock region, which is the total number of swept-up electrons by the forward external shock." " We consider IN, here to be the total number of electrons contained in the barvonic Load: where £2 is the total energy in 5-ravs.", We consider $N_e$ here to be the total number of electrons contained in the baryonic load: where $E_{\gamma}$ is the total energy in $\gamma$ -rays. Substituting the expression of δὲ and z=1.6 into Eq.(10). we get Please note that this formula always holds whether the ejecta is jet-like or spherical. because the beaming factor in Eq.(10) and (11) will cancel out cach other in the jet-like case.," Substituting the expression of $P'_{\nu_m}$ and $z=1.6$ into Eq.(10), we get Please note that this formula always holds whether the ejecta is jet-like or spherical, because the beaming factor in Eq.(10) and (11) will cancel out each other in the jet-like case." According to the jump condition of the shock. the Lorentz factor of the shocked shell should be approximately equal to that of the shocked ISM (Piran 1999).," According to the jump condition of the shock, the Lorentz factor of the shocked shell should be approximately equal to that of the shocked ISM (Piran 1999)." The Lorentz factor of the forward shocked LSAL can be obtained. fron the standard. afterglow model (e. @ Sari. Piran & Naravan 1998): For £3»—5 and n—0.01. we get ‘Taking the above inferred value cg3.1LO7. from the FEqs.(9). (12). and (14) with the conditions: 10H11 and £.. Ldn we finally get: Please note that here the value ο<0.6. inferred from the optical Hash data is consistent with that inferred independently from the afterglow information.," The Lorentz factor of the forward shocked ISM can be obtained from the standard afterglow model (e. g. Sari, Piran $\&$ Narayan 1998): For $E_{52}\sim5$ and $n\sim0.01$, we get Taking the above inferred value $\epsilon_B\sim3.1\times10^{-3}$, from the Eqs.(9), (12), and (14) with the conditions: $\nu_m\leq5\times10^{14}$ Hz and $F_{\nu_m}\sim1$ Jy, we finally get: Please note that here the value $\epsilon_e\leq0.6$ inferred from the optical flash data is consistent with that inferred independently from the afterglow information." " On the other hand. if we substitute the value ¢=0.57 into IE5q.(9). we find that the peak frequeney of the reverse shock £5», is almost located at the optical band."," On the other hand, if we substitute the value $\epsilon_e=0.57$ into Eq.(9), we find that the peak frequency of the reverse shock $\nu_m$ is almost located at the optical band." In addition. our inferred initial Lorentz factor Vy is six times larger than that obtained by Sari & Piran (19995). who have used the ambient density 7 of GIUDOTOS0S.," In addition, our inferred initial Lorentz factor $\Gamma_0$ is six times larger than that obtained by Sari $\&$ Piran (1999b), who have used the ambient density $n$ of GRB970508." Consequently. at the time the reverse shock has just. passed through the ejecta shell. its Lorentz factor was Dy.=an4.," Consequently, at the time the reverse shock has just passed through the ejecta shell, its Lorentz factor was $\Gamma_{rs}=\frac{ \Gamma_0}{\Gamma_A}\sim{4}$." This indicates that the reverse shock had become relativistic before it crossed. the entire shell., This indicates that the reverse shock had become relativistic before it crossed the entire shell. This Met is. also dillerentlun from⋅ that obtained.. by SarimM & Piran. (1990b). who found the Lorentz factor of the reverse shock of CGI1LDB990123 was only near one.," This result is also different from that obtained by Sari $\&$ Piran (1999b), who found the Lorentz factor of the reverse shock of GRB990123 was only near one." However we argue that our result is reasonable according to the criterion presented. by Sari & Piran (1995) (also see Ixobavashi et al., However we argue that our result is reasonable according to the criterion presented by Sari $\&$ Piran (1995) (also see Kobayashi et al. 1998)., 1998). " Thev defined a dimensionless parameter £ constructed from f£. A and Vy: where /=(—3)""? is the Sedov length. A=οὐ is the width of the shell (O1 is the duration of GRB) and Vy is the initial Lorentz factor of the ejecta."," They defined a dimensionless parameter $\xi$ constructed from $l$, $\Delta$ and $\Gamma_0$: where $l=(\frac{E}{nm_p{c^2}})^{1/3}$ is the Sedov length, $\Delta=c\delta{T}$ is the width of the shell $\delta{T}$ is the duration of GRB) and $\Gamma_0$ is the initial Lorentz factor of the ejecta." LE «1. the reverse shock becomes relativistic before it crosses the shell: otherwise (£> 1). the reverse shock remains Newtonian or at best mildly relativistic during the whole energy extraction process.," If $\xi<1$, the reverse shock becomes relativistic before it crosses the shell; otherwise $\xi>1$ ), the reverse shock remains Newtonian or at best mildly relativistic during the whole energy extraction process." For GIUB990123. we find £~0.3«I.," For GRB990123, we find $\xi\sim0.3<{1}$." So the reverse shock of 6120001239 had become relativistic before it crossed the shell. consistent with our calculated. result.," So the reverse shock of GRB990123 had become relativistic before it crossed the shell, consistent with our calculated result." We have constrained some intrinsic parameters. such as the magnetic cnerey density fraction (cg). the electron energy density fraction ες). the isotropic energy. in the acliahatic Forward shock £z» and the ambient density ο.," We have constrained some intrinsic parameters, such as the magnetic energy density fraction $\epsilon_{B}$ ), the electron energy density fraction $\epsilon_e$ ), the isotropic energy in the adiabatic forward shock $E_{52}$ and the ambient density $n$." " Due to the lack of the value of the self-absorption frequency £. we made an assumption that ο, of CID990123 is the same as that of CGIUD970508. then astonishinely [lind that the inferred. value ol cg is also nearly equal to that of CGIUB970508."," Due to the lack of the value of the self-absorption frequency $\nu_a$, we made an assumption that $\epsilon_e$ of GRB990123 is the same as that of GRB970508, then astonishingly find that the inferred value of $\epsilon_B$ is also nearly equal to that of GRB970508." This result favours the argument proposed by WXG99 that the magnetic energv fraction and the electron. density fraction may be universal parameters., This result favours the argument proposed by WG99 that the magnetic energy fraction and the electron density fraction may be universal parameters. Another two important intrinsic parameters οἱ CGIUD990123. are. also. inferred. from the optical flash information: the initial Lorentz factor Vy ancl the Lorentz actor Ly at the prompt optical emission peak time of the ejecta., Another two important intrinsic parameters of GRB990123 are also inferred from the optical flash information: the initial Lorentz factor $\Gamma_0$ and the Lorentz factor $\Gamma_A$ at the prompt optical emission peak time of the ejecta. They. are: Py= 1200. EP4= 300.," They are: $\Gamma_0=1200$ , $\Gamma_A=300$ ." Our inferred. value of je Vy dis six times larger than that obtained by Sari & iran C1999b). who used the ambient density » inferred for GIUD970508.," Our inferred value of the $\Gamma_0$ is six times larger than that obtained by Sari $\&$ Piran (1999b), who used the ambient density $n$ inferred for GRB970508." A larger initial Lorentz factor is reasonable in consideration of the huge energy. of this burst., A larger initial Lorentz factor is reasonable in consideration of the huge energy of this burst. The Lorentz actor of the reverse shock at the optical Lash peak time, The Lorentz factor of the reverse shock at the optical flash peak time explanation for this aunnual variation.,explanation for this annual variation. Iu the next section we consider further refinements aud additious to the model which can explain the long period over which slower modulations are observed., In the next section we consider further refinements and additions to the model which can explain the long period over which slower modulations are observed. Iu the preceding section we assumed that the sciutillation pattern was isotropic., In the preceding section we assumed that the scintillation pattern was isotropic. Auisotropic sciutles could be produced bv either an extended anisotropic source or a anisotropic scattering inediun., Anisotropic scintles could be produced by either an extended anisotropic source or an anisotropic scattering medium. An anisotropic scintillation pattern would leave a distinctive trace in the form of an anual variation of the timescale., An anisotropic scintillation pattern would leave a distinctive trace in the form of an annual variation of the timescale. This would happen as the Earth moves around the Sun. aud we cut the pattern at varving angeles through the anisotropic pattern. thereby introducing an annual variation in the timescale of modulations.," This would happen as the Earth moves around the Sun, and we cut the pattern at varying angles through the anisotropic pattern, thereby introducing an annual variation in the timescale of modulations." Tu the absence of any peculiar velocity of the scattering plasina. the Earth would cut through the scintillation pattern of J1819]3815 at the same angle. but moving in differen directions. approximately every six mouths.," In the absence of any peculiar velocity of the scattering plasma, the Earth would cut through the scintillation pattern of J1819+3845 at the same angle, but moving in different directions, approximately every six months." Thus. for this source im the ahseuce of any peculiar scatterie asina. the lenethening of the timescale would occur about every six nonths.," Thus, for this source in the absence of any peculiar scattering plasma, the lengthening of the timescale would occur about every six months." It is therefore clear that source structure cannot be theonly expluiation of the observed changes im timescale., It is therefore clear that source structure cannot be the explanation of the observed changes in timescale. With he addition of a peculiar. velocity of the scattering medi. however. the periods of: slow modulatious no longer occur every six qmouths.," With the addition of a peculiar velocity of the scattering medium, however, the periods of slow modulations no longer occur every six months." It is therefore possible that both a peculiar plasina velocity aud source structure combine to produce the observed annual variation in timescale., It is therefore possible that both a peculiar plasma velocity and source structure combine to produce the observed annual variation in timescale. We modelled au anisotropy in the scintillation pattern as an ellipsoid. introducing two new paraimecters: the position angle aud axial ratio of the sciutles.," We modelled an anisotropy in the scintillation pattern as an ellipsoid, introducing two new parameters: the position angle and axial ratio of the scintles." Using these extra parameters we agall pertorned a V ΠΕΕΜ over a wide rauge of paraicter space., Using these extra parameters we again performed a $\chi^2$ minimization over a wide range of parameter space. The resulting yest fits are significantly improved over the fits withou the anisotropy term (reduced X? is 1.5 for f: 5.2 for #*: 7.1 for Ü), The resulting best fits are significantly improved over the fits without the anisotropy term (reduced $\chi^2$ is 1.5 for $t$ ; 5.2 for $t^\star$; 7.1 for $t^\prime$ ). Fig., Fig. 9 shows the probability contours., \ref{fig:chi2} shows the probability contours. Althoueh the fit Was naproved. eoo solutions were available over a rauge of parameters.," Although the fit was improved, good solutions were available over a range of parameters." It was found that the position angle aud Vdeo Were relatively well-coustraimed. but the axial ratio iid vga Were poorly coustraimed.," It was found that the position angle and $_{\rm dec}$ were relatively well-constrained, but the axial ratio and $_{\rm RA}$ were poorly constrained." " Tn Paper II we directly measured the velocity of he scattering plastua using the time delay of signals arriving at two telescopes: vg,=32.540.5 kkmns: Valor[15.5+1 This result lies within the jurow region of permussible va Vace space determined roni these vearly mouitoring observations (see Fig 9))."," In Paper II we directly measured the velocity of the scattering plasma using the time delay of signals arriving at two telescopes: $_{\rm RA}=-32.5 \pm 0.5 $ km/s; $_{\rm dec}= +15.5 \pm 1$ This result lies within the narrow region of permissible $_{\rm RA}$ $_{\rm dec}$ space determined from these yearly monitoring observations (see Fig \ref{fig:chi2}) )." Coustraimine the velocity to be within the 3-0 errors of lis measurement. we re-ran the fit aud determined a xobabilitv profile for the shape aud position of the ellipse.," Constraining the velocity to be within the $\sigma$ errors of this measurement, we re-ran the fit and determined a probability profile for the shape and position of the ellipse." This is shown in Fie., This is shown in Fig. Ίθαα. aud the results are listed iu Table L.," \ref{fig:fitfinal}a a, and the results are listed in Table \ref{tab:fit}." " The best fit (at vga=33.5 kan£s: vq aufs) has axial ratio 11,:30j at position augle 8237 CN through Ej."," The best fit (at $_{\rm RA}=-33.5$ km/s; $_{\rm dec}=+13.5$ km/s) has axial ratio $^{-8}_{(+>30)}$ at position angle $^\circ \pm 4^\circ$ (N through E)." Use of the timescales obtained frou the ocak separation gives a simular result. although tle formal ft ix very 2001.," Use of the timescales obtained from the peak separation gives a similar result, although the formal fit is very poor." The introduction of two more parameters has clearly nuproved the fit sufficiently to justify their use. as can be directly seen in Fig. 10..," The introduction of two more parameters has clearly improved the fit sufficiently to justify their use, as can be directly seen in Fig. \ref{fig:fitfinal}." We also note that the dates onwhich the observations display very little variation over 6 hours. and which therefore had no calculated timescale," We also note that the dates onwhich the observations display very little variation over 6 hours, and which therefore had no calculated timescale" 12.6.,12.6. Subsequent analyses comparing independent data sets rave confirmed that this criterion is an excellent predictor of intrinsic vs. possible noise peaks. as long as it is not applied ο very small cata sets or at low frequencies. where the errors of measurement are far from random.," Subsequent analyses comparing independent data sets have confirmed that this criterion is an excellent predictor of intrinsic vs. possible noise peaks, as long as it is not applied to very small data sets or at low frequencies, where the errors of measurement are far from random." In the present study. the noise was calculated by averaging the amplitudes (oversampled by a factor of 20) over 5 ed.+ regions centered around the frequeney. uncer consideration.," In the present study, the noise was calculated by averaging the amplitudes (oversampled by a factor of 20) over 5 $^{-1}$ regions centered around the frequency under consideration." The spectral window of the 1994 data (Fig., The spectral window of the 1994 data (Fig. 3) is quite clean because the data were collected on three continents. thereby avoiding serious regular day-time observing gaps.," 3) is quite clean because the data were collected on three continents, thereby avoiding serious regular day-time observing gaps." Nevertheless. the Led. + aliasing should still be kept in mind. since modes with very small amplitudes might hide in the alias peaks.," Nevertheless, the 1 $^{-1}$ aliasing should still be kept in mind, since modes with very small amplitudes might hide in the alias peaks." The power spectrum of 67. Tau was computed. [rom frequeney values of zero to the Nyquist frequenev., The power spectrum of $\theta^2$ Tau was computed from frequency values of zero to the Nyquist frequency. . The highest power levels were found in the 10 to 16 ced! region., The highest power levels were found in the 10 to 16 $^{-1}$ region. An additional band of power was found in the 26 to 30 region and will be examined in a later section., An additional band of power was found in the 26 to 30 $^{-1}$ region and will be examined in a later section. The power spectra in the S8 to 16 region are presented in Fig., The power spectra in the 8 to 16 $^{-1}$ region are presented in Fig. 3., 3. The second panel from the top shows the dominant three frequencies. which have been found in all other photometric campaigns as well.," The second panel from the top shows the dominant three frequencies, which have been found in all other photometric campaigns as well." Phe next panel shows the power spectrum after prewhitening of the main three frequencies., The next panel shows the power spectrum after prewhitening of the main three frequencies. “Three additional peaks are detected: without any problems., Three additional peaks are detected without any problems. The power spectrum of the cata after. prewhitening six frequencies (Data - 6£) presents a small problem: the dominant peak may be double., The power spectrum of the data after prewhitening six frequencies (Data - 6f) presents a small problem: the dominant peak may be double. The peak at 11.770 +. called. [7. is strong and its frecqucney casily determined.," The peak at 11.770 $^{-1}$, called $_7$, is strong and its frequency easily determined." Removal of this mode leaves another peak at 11.730 cd.3 at a lower amplitude., Removal of this mode leaves another peak at 11.730 $^{-1}$ at a lower amplitude. The frequency separation of 0.04 cd.+ is at the limit of frequency. resolution of the present data set., The frequency separation of 0.04 $^{-1}$ is at the limit of frequency resolution of the present data set. This prevents us from applying the powerful phasingamplitude test to distinguish between two independent close frequencies and the artifacts caused by a single frequency with variable amplitudes. (see Breeer Bischof 2002)., This prevents us from applying the powerful phasing--amplitude test to distinguish between two independent close frequencies and the artifacts caused by a single frequency with variable amplitudes (see Breger Bischof 2002). Fortunately. it is not necessary here to prove the existence of a trequeney doublet: both frequencies have been seen before in the WIRE data (Paper HE). while the weaker component in the 1994 data. was already. detected. in the 1950 data (Paper HD).," Fortunately, it is not necessary here to prove the existence of a frequency doublet: both frequencies have been seen before in the WIRE data (Paper III), while the weaker component in the 1994 data was already detected in the 1986 data (Paper II)." We therefore accept the reality of the two close requeneies. [> and fs.," We therefore accept the reality of the two close frequencies, $_7$ and $_8$." Three additional frequencies ave found in the 1994 data., Three additional frequencies are found in the 1994 data. Further peaks are below the statistical threshold. (bottom iiel of Fig., Further peaks are below the statistical threshold (bottom panel of Fig. 3)., 3). The adopted frequencies ancl amplitudes are shown in ‘Table 2., The adopted frequencies and amplitudes are shown in Table 2. The uncertainties in amplitude: were caleulated rom the standard formulae given in Dreger ct al. (, The uncertainties in amplitude were calculated from the standard formulae given in Breger et al. ( 1999). owed on the assumption. of random. observational errors and no aliasing.,"1999), based on the assumption of random observational errors and no aliasing." The uncertainties of the aniplitucles of [7 and [x are larger because these two modes are very close in pequency., The uncertainties of the amplitudes of $_7$ and $_8$ are larger because these two modes are very close in frequency. Because the separation of two frequencies is at the resolution limit of the present data set. the computed. size of the amplitude of one mode is somewhat allectec by the srescnee of the other mode (the so-called. pumping ellect).," Because the separation of two frequencies is at the resolution limit of the present data set, the computed size of the amplitude of one mode is somewhat affected by the presence of the other mode (the so-called pumping effect)." These amplitucles are therefore marked with a colon., These amplitudes are therefore marked with a colon. The new solution fits the observed data well. as shown in Figs.," The new solution fits the observed data well, as shown in Figs." 1 and 2., 1 and 2. Phe good fit is also demonstrated. by the value of the average residual per single measurement of 2.7 numag in e and 2 mmag in y., The good fit is also demonstrated by the value of the average residual per single measurement of $\pm$ 2.7 mmag in $v$ and $\pm$ 3.2 mmag in $y$ . nearly two vears after the burst.,nearly two years after the burst. Bursts like CRBs 160611. 061121. or even 080319D. (Alanganoctal.2007:Pageetal.2007:Racusiu2008.respectively) were even brighter m X-rays at about 100 s after the mast than GRD 060729. but their plateau phascs are senificautlv shorter than that of GRB 060729.," Bursts like GRBs 060614, 061121, or even 080319B \citep[][respectively]{mangano07, page07, racusin08} were even brighter in X-rays at about 100 s after the burst than GRB 060729, but their plateau phases are significantly shorter than that of GRB 060729." " Thev herefore faded more rapidly than CRB 060729 at late ics,", They therefore faded more rapidly than GRB 060729 at late times. Analysis and mode ofthe N-rav afterelow of CRB 160729 show that this withlingburst happened in a teuuous wiud., Analysis and modeling of the X-ray afterglow of GRB 060729 show that this burst happened in a tenuous wind. This i$ consistent the collapsar picture of long GRBs., This is consistent with the collapsar picture of long GRBs. During the carly plateau phase. the energy in the external shock increased. by two orders of magnitude.," During the early plateau phase, the energy in the external shock increased by two orders of magnitude." A reanalysis of the ART lisht curve together with the three detections by iu 2007 reveal a temporal break at ~1.3 Ms after the burst., A reanalysis of the XRT light curve together with the three detections by in 2007 reveal a temporal break at $\sim1.3$ Ms after the burst. The decay slope stecpened from a=1.32 toa =1.61 around this break aud the X-ray spectra hardened in the meanwhile. indicating this break is a cooling break (the cooling frequency of svuchrotrou radiation crosses the N-rav baud).," The decay slope steepened from $\alpha=1.32$ to $\alpha=1.61$ around this break and the X-ray spectrum hardened in the meanwhile, indicating this break is a cooling break (the cooling frequency of synchrotron radiation crosses the X-ray band)." There is another light curve break at ~1.3 vear after the burst tentatively indicated bv the last two detections., There is another light curve break at $\sim 1.3$ year after the burst tentatively indicated by the last two detections. Thisbreak coincides with a possible spectral softening. sugecsting that thebreak may be of spectral origin. though a livcodvuamic origin (jet break) is also possible.," This break coincides with a possible spectral softening, suggesting that the break may be of spectral origin, though a hydrodynamic origin (jet break) is also possible." If due to a jet break. then the nuplied halfopenius angle is 0;~LL.," If due to a jet break, then the implied half-opening angle is $\theta_j \sim 14^{\circ}$." If due to a spectral break. such a spectral softenime could be the result of a very steep power-law distribution of shock-accclerated electrous responsible for the svuchrotrou radiation.," If due to a spectral break, such a spectral softening could be the result of a very steep power-law distribution of shock-accelerated electrons responsible for the synchrotron radiation." Iu this case. with no evidence for a jet break up to 612 davs after the burst bv. the jet halfopeniug augle umst be 0;>157 aud the jet energv E;223.107523 erg.," In this case, with no evidence for a jet break up to 642 days after the burst by the jet half-opening angle must be $\theta_j>15^{\circ}$ and the jet energy $E_j>3\times10^{52}$ erg." SuchJ a large jet. energy Προς-. that the central engine must be a fast-rotating massive black hole. not a maguctar.," Such a large jet energy implies that the central engine must be a fast-rotating massive black hole, not a magnetar." Ou oobservatious preseuted here have shown again how important lis for late-time observations of CRB ταν afterelows., Our observations presented here have shown again how important is for late-time observations of GRB X-ray afterglows. hhas already been essential for the detection aud nou-detection of jet breaks in the X-ray AR of the short-duration CRBs 050721 and 051221À (Caupeetal.2006:Burrowsctal.2006.respectively )..," has already been essential for the detection and non-detection of jet breaks in the X-ray afterglows of the short-duration GRBs 050724 and 051221A \citep[][respectively]{grupe06,burrows06}." We want to thank Sandy Patel and. Clhirvssa Ikouveliotou for providing the data for the huninosities of aand bbursts. Hala Eid for fitting the late-time Πο curve with the Beuerimann ct al.," We want to thank Sandy Patel and Chryssa Kouveliotou for providing the data for the luminosities of and bursts, Hala Eid for fitting the late-time light curve with the Beuermann et al." model. aud Enc Feigelsou for useful discussion about statistics.," model, and Eric Feigelson for useful discussion about statistics." We thank the referee for his/her sugeestions/conmuents which have helped to lunprove our paper siguificautly., We thank the referee for his/her suggestions/comments which have helped to improve our paper significantly. We are oxtremely thankful to the whole tteaun for successfully planning and perforuuus the observations of CRB 060729., We are extremely thankful to the whole team for successfully planning and performing the observations of GRB 060729. XFW thanks Peter.. Nenji Toma. Derek Fox. Autouine Cucchiara. and Yizhoue Fan for their helpful discussion.," XFW thanks Peter, Kenji Toma, Derek Fox, Antonino Cucchiara, and Yizhong Fan for their helpful discussion." This worHK was also partially supported bv NASA NNX OsALLOCaa (NEW). National Natural Science Foundation of China (erants 10221001. 10103002. 10503012. 10621303. 10633010. and. 10873002). aud National Basic Research Program of China (973 Program 2009€D82[800) CNYW. and EWL).," This work was also partially supported by NASA NNX 08AL40G (XFW), National Natural Science Foundation of China (grants 10221001, 10403002, 10503012, 10621303, 10633040, and 10873002), and National Basic Research Program of China (973 Program 2009CB824800) (XYW, XFW, and EWL)." " Swift is supported at Penn State by ARN,NASA contract NAS5-00136.", Swift is supported at Penn State by NASA contract NAS5-00136. " LTThisLOLS, research has becu supported by SAO erauts SV A12 (D.G. aud CC.) aud C€s-9056 X (D.C)"," This research has been supported by SAO grants SV4-74018, A12 (D.G. and G.G.) and G08-9056 X (D.G.)" Weywot’s orbit could liowever. be explained if another satellite of similar mass once existed about Quaoar.,"Weywot's orbit could however, be explained if another satellite of similar mass once existed about Quaoar." Dynamical interactions could allow the two satellites to scatter off oue-auotlier. euniplacing Weswot on its eccentric orbit aud removing the second satellite from the system.," Dynamical interactions could allow the two satellites to scatter off one-another, emplacing Weywot on its eccentric orbit and removing the second satellite from the system." idee au οude estimate (Croldrveich&Peale1966) implies that the circularization time scale oL Weswots orbit is approximately the age of the Solar system. implying that. if uuperturbed. ouce Wevywot Is on an eccentric orbit. it will remain that way.," Indeed an order-of-magnitude estimate \citep{Goldreich1966} implies that the circularization time scale of Weywot's orbit is approximately the age of the Solar system, implying that, if unperturbed, once Weywot is on an eccentric orbit, it will remain that way." Civen the existence of other collisionally formed. Kuiper belt binaries. this formation mechanism seems plausible.," Given the existence of other collisionally formed Kuiper belt binaries, this formation mechanism seems plausible." Another mechanism that might explain the properties of the Quaoar-Meywot system is a hit-and-run collision. first proposed by AsphaugLIetal.(2006).," Another mechanism that might explain the properties of the Quaoar-Weywot system is a so-called hit-and-run collision, first proposed by \citet{Asphaug2006}." . In such a scenario. an originally ice-rich aud differentiated) Quaoar has a graziug ---upact with a body roughly 2-3 times as massive.," In such a scenario, an originally ice-rich and differentiated Quaoar has a grazing impact with a body roughly 2-3 times as massive." The result is a complete shattering aud scattering of Quaoar's icy mantle. leaving its core bounc. aud relatively intact.," The result is a complete shattering and scattering of Quaoar's icy mantle, leaving its core bound, and relatively intact." During such an impact. the prevalence of three-bocly interactious between the ejecta allows παν ejecta pairs to become bound with mutually eccentric orbits.," During such an impact, the prevalence of three-body interactions between the ejecta allows many ejecta pairs to become bound with mutually eccentric orbits." Such a collision could explain Quaoar's unusually high density aud Weywot’s eccentric orbit., Such a collision could explain Quaoar's unusually high density and Weywot's eccentric orbit. This scenario requires the primordial Ixuiper belt to be significantly more massive than the present for such a collision to be likely., This scenario requires the primordial Kuiper belt to be significantly more massive than the present for such a collision to be likely. If this scenario were prevalent in the early Ixuiper belt. it would suggest that a large fraction of small Ixuiper belt objects are the mineral-less. low-deusity icy ejected mautle fragimeuts of large differentiated bodies.," If this scenario were prevalent in the early Kuiper belt, it would suggest that a large fraction of small Kuiper belt objects are the mineral-less, low-density icy ejected mantle fragments of large differentiated bodies." " As well we should [iud a few large 1000 kim bodies with hieh ~3ecmoE ""densities that were originally the cores of those larger dillerentiated planetesiuials.", As well we should find a few large $\sim 1000$ km bodies with high $\sim 3 \dense$ densities that were originally the cores of those larger differentiated planetesimals. We would like to thank Hal Levison. Eric Asphaug. Darin Ragozzine. aud Alex Parker for their iusiehtFul ciscussious.," We would like to thank Hal Levison, Eric Asphaug, Darin Ragozzine, and Alex Parker for their insightful discussions." This material is based upon work supported by NASA under eraut NNCOSCLO2C. Support for program HST-Go-011169.9-A was provided by NASA through a grant [rom the Space Telescope Science Institute. which is operated by the Association of Universities [or Research in Astronomy. Πιο. under NASA contract NAS 5-26555.," This material is based upon work supported by NASA under grant NNG05GI02G. Support for program HST-Go-011169.9-A 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." 151X galaxies possess a characteristic spectral signature defined by strong hydrogen. Balmer absorption lines (110. Le. 113) combined with a lack of optical emission lines such as OL] 3727 (Dressler Gunn 1983).,"E+A galaxies possess a characteristic spectral signature defined by strong hydrogen Balmer absorption lines $\delta$ , $\gamma$, $\beta$ ) combined with a lack of optical emission lines such as [OII] $3727 \ang$ (Dressler Gunn 1983)." Phe Balmer absorption lines are Aimprinted in the galaxy spectrum by A stars. indicating the presence of a voung («E Gyr old) stellar population.," The Balmer absorption lines are imprinted in the galaxy spectrum by A stars, indicating the presence of a young $< 1$ Gyr old) stellar population." Hlowever. the absence of OL] 3727A emission suggests that star formation is no longer ongoing.," However, the absence of [OII] $3727 \ang$ emission suggests that star formation is no longer ongoing." The inference is that these galaxies have previously. undergone à burst of star formation. which has recently been truncated rather suddenly (Dressler Gunn 1983: Couch Sharples 1987).," The inference is that these galaxies have previously undergone a burst of star formation, which has recently been truncated rather suddenly (Dressler Gunn 1983; Couch Sharples 1987)." For this reason. these systems are also known as “post-starburst galaxies.," For this reason, these systems are also known as `post-starburst galaxies'." The physical mechanisms governing the triggering and cessation of this starburst are not vet fully understood. but undoubtedly rellect the interaction of the galaxy with its environment.," The physical mechanisms governing the triggering and cessation of this starburst are not yet fully understood, but undoubtedly reflect the interaction of the galaxy with its environment." In general. this can occur through interaction with other galaxies (mergers or tical gravitational ellects) or. for those galaxies residing in clusters. through elfects specific to that environment: involving either the hot intracluster gas (ram-pressure elfects) or the cluster gravitational potential.," In general, this can occur through interaction with other galaxies (mergers or tidal gravitational effects) or, for those galaxies residing in clusters, through effects specific to that environment; involving either the hot intracluster gas (ram-pressure effects) or the cluster gravitational potential." " ""Theoretical. modelling. of all these scenarios is not. vet complete. although it is known that à major galaxy. merger can produce the characteristic LE|A) spectral signature (Bekki. Shiova Couch 2001)."," Theoretical modelling of all these scenarios is not yet complete, although it is known that a major galaxy merger can produce the characteristic E+A spectral signature (Bekki, Shioya Couch 2001)." In practice. more than one of the above mechanisms is probably responsible for the overall population of E|A galaxies. with different mechanisms operating in dilferent environments.," In practice, more than one of the above mechanisms is probably responsible for the overall population of E+A galaxies, with different mechanisms operating in different environments." As such. these galaxies are an interesting probe of environmental inlluences. on ealaxy evolution.," As such, these galaxies are an interesting probe of environmental influences on galaxy evolution." The population of I2]X galaxies. exhibits dramatic evolution with redshift., The population of E+A galaxies exhibits dramatic evolution with redshift. These galaxies are. commonplace in intermecdiate-redshift clusters. where they were. first identified and studied (Dressler Gunn. 1983): IZ. and 7X. representing respectively the assumed. morphology and the dominant stellar lines of the spectrum. although high-resolution Hubble Space Telescope (LIST) imaging of such. clusters later revealed that these galaxies were predominantly earlv-tvpe disk svstems (Couch et 11998: Dressler ct 14999).," These galaxies are commonplace in intermediate-redshift clusters, where they were first identified and studied (Dressler Gunn 1983): `E' and `A' representing respectively the assumed morphology and the dominant stellar lines of the spectrum, although high-resolution Hubble Space Telescope (HST) imaging of such clusters later revealed that these galaxies were predominantly early-type disk systems (Couch et 1998; Dressler et 1999)." Whilst. E|}A galaxies are prevalent in intermeciate-redshilt clusters P'Tran et 22003). they only constitute about 1 per cent of 10 menmibers of nearby clusters (Fabricant. MeClintock Dautz 1991).," Whilst E+A galaxies are prevalent in intermediate-redshift clusters Tran et 2003), they only constitute about 1 per cent of the members of nearby clusters (Fabricant, McClintock Bautz 1991)." As a fraction of the overall zero-recishift galaxy population. |A objects comprise significantly less than 1 per cent. (Zabludolt et 11996).," As a fraction of the overall zero-redshift galaxy population, E+A objects comprise significantly less than 1 per cent (Zabludoff et 1996)." μις rarity has rendered. environmentallv-unbiased: studies of low-recdshilt LE}A galaxies in statistically significant numbers cillicult until the recent advent of large-scale galaxy surveys., This rarity has rendered environmentally-unbiased studies of low-redshift E+A galaxies in statistically significant numbers difficult until the recent advent of large-scale galaxy surveys. Vhe first such study was that. of Zabludoll. et ((1996) who identified 21 low-recshilt (0.05 85°), we need to measure the thickness of a dusty torus to confirm whether NIR-faint quasars are really super-Eddington AGNs (rhpx> 10?).","by sub-Eddington AGNs with extremely thin tori (i.e., $\theta_{\rm torus}>85^{\circ}$ ), we need to measure the thickness of a dusty torus to confirm whether NIR-faint quasars are really super-Eddington AGNs $\dot{m}_{\rm BH} \geq 10^{2}$ )." " Based on the kinematics of cold molecular gas in a torus, it would be possible to evaluate the thickness of a torus by ALMA, because the ratio of velocity dispersion and rotational velocity indicates the scale height of the torus (see Wada&Norman 2005))."," Based on the kinematics of cold molecular gas in a torus, it would be possible to evaluate the thickness of a torus by ALMA, because the ratio of velocity dispersion and rotational velocity indicates the scale height of the torus (see \citealt{WN02,WT05}) )." " On the other hand, Jiangetal.(2010) interpreted these two objects as dust-free quasars."," On the other hand, \citet{Ji10} interpreted these two objects as dust-free quasars." " However, this seems to contradict the observations, which suggests that NIR-faint quasars possess super-metallicity as do other z~6 quasars and high-z AGNs (e.g., Pentericci 2009))."," However, this seems to contradict the observations, which suggests that NIR-faint quasars possess super-metallicity as do other $z\sim 6$ quasars and $z$ AGNs (e.g., \citealt{Pe02,Fr03,Ju09,HF93,Na06a,Na06b,Ma09}) )." " Also, Haoetal.(2010) recently reported quasars with unusually faint NIR emission at z= 1.5-3, when the universe was 2-4 Gyr old."," Also, \citet{Ha10} recently reported quasars with unusually faint NIR emission at $z=1.5$ $3$, when the universe was 2–4 Gyr old." " Thus, it seems likely that NIR-faint quasars are exclusively dust-free AGNs."," Thus, it seems likely that NIR-faint quasars are exclusively dust-free AGNs." " As an alternative scenario, a large fraction of gas in a dusty torus would be ejected from host galaxies as a result of strong radiation pressure from the brightest AGNs, such as quasars (Ohsuga&Umemura1999,2001;Watabe&Umemura 2005)."," As an alternative scenario, a large fraction of gas in a dusty torus would be ejected from host galaxies as a result of strong radiation pressure from the brightest AGNs, such as quasars \citep{OU99,OU01,WU05}." ". In this case, NIR-faint quasars may be explained as being quasars without dusty tori around the SMBH."," In this case, NIR-faint quasars may be explained as being quasars without dusty tori around the SMBH." This possibility could be confirmed by investigating the presence of dusty tori in NIR-faint quasars using ALMA., This possibility could be confirmed by investigating the presence of dusty tori in NIR-faint quasars using ALMA. " In the local universe, NLS1s are thought to be AGNs of a high Lboraisc/Lgaa system."," In the local universe, NLS1s are thought to be AGNs of a high $L_{\rm bol, disc}/L_{\rm Edd}$ system." " One NLS1 (Ark 564) shows no NIR emission (Rodríguez-Ardila&Mazzalay2006),, which is consistent with our predictions."," One NLS1 (Ark 564) shows no NIR emission \citep{RM06}, which is consistent with our predictions." " However, most NLS1s tend to have NIR emission similar to or stronger than that of ordinary Seyfert galaxies (e.g. Ryanetal. 2007))."," However, most NLS1s tend to have NIR emission similar to or stronger than that of ordinary Seyfert galaxies (e.g. \citealt{Ry07}) )." One of the reasons for the discrepancy between our predictions and the observations is that NLS1s with apy>10? may be absent (or their fraction is very small)., One of the reasons for the discrepancy between our predictions and the observations is that NLS1s with $\dot{m}_{\rm BH}\geq 10^{2}$ may be absent (or their fraction is very small). " However, some NLS1s have a high mass accretion rate with mag>10? (e.g., 2008))."," However, some NLS1s have a high mass accretion rate with $\dot{m}_{\rm BH}\geq 10^{2}$ (e.g., )." " Another possibility is that these discrepancies may suggest misalignment between the accretion discs and the dusty torus, as mentioned in 83.1."," Another possibility is that these discrepancies may suggest misalignment between the accretion discs and the dusty torus, as mentioned in $\S 3.1$." " Lastly, we note the possibility of contamination of hosts and circumnuclear starbursts in the NIR band, if the host luminosity is comparable to or exceeds the AGN luminosity, as in Seyfert galaxies."," Lastly, we note the possibility of contamination of hosts and circumnuclear starbursts in the NIR band, if the host luminosity is comparable to or exceeds the AGN luminosity, as in Seyfert galaxies." " Although it may be hard to find many NLS1s with low Intr,acn/Lpoi,disc in current observations, in future studies it is worth examining this issue by NIR (rest frame) observations with high spatial resolution."," Although it may be hard to find many NLS1s with low $L_{\rm NIR,AGN}/L_{\rm bol,disc}$ in current observations, in future studies it is worth examining this issue by NIR (rest frame) observations with high spatial resolution." " In this work, we propose a new method to search for candidate galaxies in which super-Eddington growth occurs."," In this work, we propose a new method to search for candidate galaxies in which super-Eddington growth occurs." " In particular, taking account of the dependence of the polar angle on the radiation flux of accretion flows, we investigate the properties of reprocessed ΤΗ, emission (as well as NIR emission) from the inner edge of the dusty torus."," In particular, taking account of the dependence of the polar angle on the radiation flux of accretion flows, we investigate the properties of reprocessed IR emission (as well as NIR emission) from the inner edge of the dusty torus." " As a result, we find that a relatively low ratio of AGN IR (as well as NIR) luminosity and disc luminosity is a genuine property that can be used for exploring for candidates of super-Eddington AGNs with rngu>10?."," As a result, we find that a relatively low ratio of AGN IR (as well as NIR) luminosity and disc luminosity is a genuine property that can be used for exploring for candidates of super-Eddington AGNs with $\dot{m}_{\rm BH}\geq 10^{2}$." This method is especially powerful for searching for high-z super-Eddington AGNs because the direct measurement of meu is difficult for high-z AGNs compared with nearby AGNs., This method is especially powerful for searching for $z$ super-Eddington AGNs because the direct measurement of $\dot{m}_{\rm BH}$ is difficult for $z$ AGNs compared with nearby AGNs. The following are the main results of the present paper: We appreciate the useful comments of the anonymous referees that reviewed this paper., The following are the main results of the present paper: We appreciate the useful comments of the anonymous referees that reviewed this paper. We are grateful to M. Umemura and T. Nagao for useful comments and, We are grateful to M. Umemura and T. Nagao for useful comments and A fundamental problem in the study of stellar evolution is the loss of aneular momentum in stars as they evolve [rom the birthline to the imaiu-sequeuce.,A fundamental problem in the study of stellar evolution is the loss of angular momentum in stars as they evolve from the birthline to the main-sequence. Early observations of T Tauri stars, Early observations of T Tauri stars "core"" to southeast of the site of stellar ejection.",core' to southeast of the site of stellar ejection. Zapata et al. (, Zapata et al. ( "2010) propose that the ""hot-core. may be blocking portions of the outflow in this direction.",2010) propose that the `hot-core' may be blocking portions of the outflow in this direction. The bulk of the [ls emission is located to the northwest. consistent with more of the original core being blown-out in this direction.," The bulk of the $_2$ emission is located to the northwest, consistent with more of the original core being blown-out in this direction." The ejected stars moving south likely plow through the remaining dense material., The ejected stars moving south likely plow through the remaining dense material. source I and possibly BN and n. are surrounded by circumstellar disks (Rodriguez. Zapata. IIo 2008).," Source I and possibly BN and n, are surrounded by circumstellar disks (Rodriguez, Zapata, Ho 2008)." A polarized. infrared bipolar reflection nebula can be traced over from DN.," A polarized, infrared bipolar reflection nebula can be traced over from BN." Simpson et al. (, Simpson et al. ( 2006) argue that the polarization is produced by clichroic absorption by magneticallv aligned dust in a foreground dust lane.,2006) argue that the polarization is produced by dichroic absorption by magnetically aligned dust in a foreground dust lane. Jiang et al. (, Jiang et al. ( 2005) presentecd-adaptive optics-assisted polarimetric nearinfrared images of the BN object and found a polarization pattern indicating illumination [from BN.,2005) presented-adaptive optics-assisted polarimetric near-infrared images of the BN object and found a polarization pattern indicating illumination from BN. The nebula is bipolar with a svmmetry axis oriented al PA zs and a dark band parallel to DNs proper motion., The nebula is bipolar with a symmetry axis oriented at PA $\approx$ and a dark band parallel to BN's proper motion. The dark lane may be a “cisk-shacdow” (e.g. Pontoppidan Dullemond 2005) produced by opaque material close to (he central star: thus (he silhouette only provides an upper-bound on the disk outer radius.," The dark lane may be a “disk-shadow"" (e.g. Pontoppidan Dullemond 2005) produced by opaque material close to the central star; thus the silhouette only provides an upper-bound on the disk outer radius." Such a disk must be oriented close to edge-on with an axis nearly orthogonal to DNs proper motion., Such a disk must be oriented close to edge-on with an axis nearly orthogonal to BN's proper motion. Raclio source I is also surrounded by a nearly edge-on disk with an axis orthogonal to ils apparent proper motion., Radio source I is also surrounded by a nearly edge-on disk with an axis orthogonal to its apparent proper motion. The elongated 7 mm continuum emission associated with source ] has been interpreted as à nearly edge-on disk rendered visible bv collisional ionization ancl l[ree-Iree opacity (Greenhill et al., The elongated 7 mm continuum emission associated with source I has been interpreted as a nearly edge-on disk rendered visible by collisional ionization and $^-$ free-free opacity (Greenhill et al. 1998: Reid et al., 1998; Reid et al. 2007)., 2007). The disk has a radius of about 50 AU and an axis oriented towards PA zz457., The disk has a radius of about 50 AU and an axis oriented towards PA $\approx$. The thermal SiO emission at 86 GlIIz (Plambeck el al., The thermal SiO emission at 86 GHz (Plambeck et al. 2009) and 22 GlIIz ΠΟ masers on scales of a few thousand AU indicate the presence of a very compact bipolar outflow with an age of only a few hundred vears blowing towards the northeast and southwest along the suspected disk axis (Wrieht et al., 2009) and 22 GHz $_2$ O masers on scales of a few thousand AU indicate the presence of a very compact bipolar outflow with an age of only a few hundred years blowing towards the northeast and southwest along the suspected disk axis (Wright et al. 1995: Matthews et al., 1995; Matthews et al. 2008: Deuther Nissen 2008: Plambeck et al., 2008; Beuther Nissen 2008; Plambeck et al. 2009)., 2009). Although source n is suspected to be surrounded. by a disk. its orientation remains uncertain.," Although source n is suspected to be surrounded by a disk, its orientation remains uncertain." Elongation in mid-infrared images suggest an axis towards the north-northeast. close to the axis of the elongation or double structive seen al radio wavelengths (Shupine et al. (," Elongation in mid-infrared images suggest an axis towards the north-northeast, close to the axis of the elongation or double structure seen at radio wavelengths (Shuping et al. (" 2004).,2004). Acceleration of the stars during the interaction that ejected them would have stripped, Acceleration of the stars during the interaction that ejected them would have stripped that the supra-thermal electron distribution well away from the shock front differs from that shown in Fig. l..,"that the supra-thermal electron distribution well away from the shock front differs from that shown in Fig. \ref{fig:fp}," because the efficient Coulomb losses wash-out the non-relativistic thermal electrons., because the efficient Coulomb losses wash-out the non-relativistic supra-thermal electrons. There is à variant of the model where mildly relativistic electrons (with Lorentz factors > 30) comprising a putative long-lived cosmic ray electron population in the ICM are re-accelerated by the MHD-shocks., There is a variant of the model where mildly relativistic electrons (with Lorentz factors $\gtrsim30$ ) comprising a putative long-lived cosmic ray electron population in the ICM are re-accelerated by the MHD-shocks. The energy efficiency problem is alleviated in that model in comparison with the case of only direct particle injection from the thermal plasma., The energy efficiency problem is alleviated in that model in comparison with the case of only direct particle injection from the thermal plasma. However. in this paper we concentrate mostly on the diagnostic of non-relativistic electrons and thus we consider only a direct injection model.," However, in this paper we concentrate mostly on the diagnostic of non-relativistic electrons and thus we consider only a direct injection model." For our example. we take the case of M=2.2.," For our example, we take the case of $M=2.2$." In our decomposition using the genetic algorithm we have taken rn=32 Maxwellians., In our decomposition using the genetic algorithm we have taken $n=32$ Maxwellians. The relative differences of the approximation compared to the exact electron distribution is shown in Fig. 2.., The relative differences of the approximation compared to the exact electron distribution is shown in Fig. \ref{fig:eldis}. The temperatures and relative normalisations of the solution are shown in Fig. 3., The temperatures and relative normalisations of the solution are shown in Fig. \ref{fig:decomp}. We have also used the analytical approximation (13)) and binned it into similar temperature bins as the solutions from the genetic algorithm., We have also used the analytical approximation \ref{eqn:lapsol}) ) and binned it into similar temperature bins as the solutions from the genetic algorithm. We have adjusted all models in the spectral fitting package SPEX that involve emission or absorption from a hot plasma., We have adjusted all models in the spectral fitting package SPEX that involve emission or absorption from a hot plasma. All these models now include an option to account for the presence of supra-thermal electrons., All these models now include an option to account for the presence of supra-thermal electrons. They have an additional parameter. which is the name of a file containing the temperatures and relative emission measures of the Maxwellian components.," They have an additional parameter, which is the name of a file containing the temperatures and relative emission measures of the Maxwellian components." As SPEX does not use pre-calculated tables but calculates spectra on the fly. all relevant rates (ionisation. recombination. excitation) are simply calculated by adding the contributions from the Maxwellian components.," As SPEX does not use pre-calculated tables but calculates spectra on the fly, all relevant rates (ionisation, recombination, excitation) are simply calculated by adding the contributions from the Maxwellian components." Obviously. this process is done in two steps: first the composite multi-Maxwellian electron distribution is used to determine the ionisation balance. and using the resulting non-equilibrium ion concentrations. we calculate the X-ray spectrum for the non-equilibrium electron. distribution.," Obviously, this process is done in two steps: first the composite multi-Maxwellian electron distribution is used to determine the ionisation balance, and using the resulting non-equilibrium ion concentrations, we calculate the X-ray spectrum for the non-equilibrium electron distribution." It is tacitly assumed here that we consider a time-independent. steady situation.," It is tacitly assumed here that we consider a time-independent, steady situation." Por the example given in the previous section. only a few dozen Maxwellian components are needed.," For the example given in the previous section, only a few dozen Maxwellian components are needed." This allows fast and accurate evaluation of the spectrrum. without the need to make simplifications to the atomic physics.," This allows fast and accurate evaluation of the spectrum, without the need to make simplifications to the atomic physics." The most important effects of non-thermal electrons on the spectrum is then a shift of the ronisation balance towards higher ionisation. the production of a non-thermal Bremsstrahlung tul on the continuum spectrum. and enhanced satellite line emission.," The most important effects of non-thermal electrons on the spectrum is then a shift of the ionisation balance towards higher ionisation, the production of a non-thermal Bremsstrahlung tail on the continuum spectrum, and enhanced satellite line emission." These satellite lines (for instance in the Fe-K band) can be detected easily with high-resolution. spectrometers that will fly on future missions such as Astro-H and IXO., These satellite lines (for instance in the Fe-K band) can be detected easily with high-resolution spectrometers that will fly on future missions such as Astro-H and IXO. Their relevance as indicators for the presence of non-thermal electrons was already indicated by ?.., Their relevance as indicators for the presence of non-thermal electrons was already indicated by \citet{gabriel1979}. " To illustrate the effects of such a supra-thermal electro25 distribution on data. we simulated an XMM-Newton EPIC/p> spectrum extracted from a circular region with a radius of ccentred on the core of a bright cluster with a 0.3—10 keV luminosity of Ly=6.3x10°"" W within the extraction region. at a assumed redshift of z=0.055."," To illustrate the effects of such a supra-thermal electron distribution on data, we simulated an XMM-Newton EPIC/pn spectrum extracted from a circular region with a radius of centred on the core of a bright cluster with a $0.3-10$ keV luminosity of $L_{\mathrm{X}}=6.3\times10^{37}$ W within the extraction region, at an assumed redshift of $z=0.055$." In the simulation of the spectrum. we assumed the above mentioned post-shock downstream electron distribution for the Mach number of M=2.2 and pre-shock temperature of ΚΤ=8.62 keV (105 K).," In the simulation of the spectrum, we assumed the above mentioned post-shock downstream electron distribution for the Mach number of $M=2.2$ and pre-shock temperature of $kT=8.62$ keV $10^8$ K)." We assume a deep 100 ks observation., We assume a deep 100 ks observation. The resulting spectrum has very high statistics. which should in principle allow to detect any non-isothermality of the plasma.," The resulting spectrum has very high statistics, which should in principle allow to detect any non-isothermality of the plasma." The best fit temperature of the simulated spectrum is 17.86+0.10 keV (210° κ). consistent with the post-shock temperature of the plasma given," The best fit temperature of the simulated spectrum is $17.86\pm0.10$ keV $2\times10^8$ K), consistent with the post-shock temperature of the plasma given" llere (yy denotes the Dirac bispinor for barvons D wilh vacuum mass 25 and the isospin operator is Lty.,Here $\psi_B$ denotes the Dirac bispinor for baryons $B$ with vacuum mass $m_B$ and the isospin operator is ${\mbox {\boldmath t}}_B$. The scalar selfl-interaction term (Doguta≼↼≱&Bochner19177). is densitv for. hvperon-hivperon interaction (Z4) is given. by 7o o As nucleons do not couple with strange mesons. goon=gg0.," The scalar self-interaction term \citep{Bog} is The Lagrangian density for hyperon-hyperon interaction ${\cal L}_{YY}$ ) is given by As nucleons do not couple with strange mesons, $g_{\sigma^* B} = g_{\phi B} = 0$." " Similarly we (reat the (anti)kaon-barvon interaction in the same footing as the interaction,", Similarly we treat the (anti)kaon-baryon interaction in the same footing as the baryon-baryon interaction. The Lagrangian density for (anti)kaons in the minimal coupling scheme is (Glendenning&Schalfn," The Lagrangian density for (anti)kaons in the minimal coupling scheme is \citep{Gle98,Gle99,Bani1,Bani2}, where the covariant derivative is $D_\mu = \partial_\mu + ig_{\omega K}{\omega_\mu} + ig_{\phi K}{\phi_\mu} + i g_{\rho K} {\mbox{\boldmath t}}_K \cdot {\mbox{\boldmath $ $}}_\mu$ and the effective mass of (anti)kaons is $m_K^* = m_K - g_{\sigma K} \sigma - g_{\sigma^* K} \sigma^*$." er-Dielich1998., We perform this calculation in the mean field approximation \citep{Ser}. . 1999:BanikDandyopadh," The mean meson fields in the condensed phase are denoted by $\sigma$ , $\sigma^*$, $\omega_0$, $\phi_0$ and $\rho_{03}$ ." yay:2001a.b)..," The expressions for mean fields can be found in Ref. \citep{Bani2,DR3}." where the covari, The in-medium energy of $K^-$ mesons for $s$ -wave ${\vec k}=0$ ) condensation is given by where $\mu_{K^-}$ is the chemical potential of $K^-$ mesons and the isospin projection is $I_{3K^-} = -1/2$. "ant derivative is D,=O,4-/gyoyd-gonGpUy Ont!pg ond "," The chemical potential for baryons $B$ is given by where effective baryon mass is $m_B^{*K}=m_B - g_{\sigma B}\sigma - g_{\sigma^* B} \sigma^*$ and isospin projection for baryons $B$ is $I_{3B}$." the ellective mass of (an," We obtain the mean fields in the hadronic phase putting source terms for $K^-$ mesons equal to zero in corresponding equations of motion \citep{Bani2,DR3}." ti and We describe the mixed phase of hadronicand A/— condensed matter usingthe Gibbs conditions for thermodynamic equilibrium along with global charge and barvon numberconservation laws (Glendenning1992;Glendenning&5chaffner-Dielich. 1999)..," The total energy density and pressure in the antikaon condensed phase are given by and We describe the mixed phase of hadronicand $K^-$ condensed matter usingthe Gibbs conditions for thermodynamic equilibrium along with global charge and baryon numberconservation laws \citep{Gle92,Gle99}. ." "this is not a necessary condition for the scenario, since the scattering event can generate mutual inclination.","this is not a necessary condition for the scenario, since the scattering event can generate mutual inclination." " The transition from non-resonant motion to that characterized by Kozai cycles is depicted in Figure 6, where orbital parameters prior to the second planet’s ejection are shown as gray dots and the resonant motion is shown as a black curve."," The transition from non-resonant motion to that characterized by Kozai cycles is depicted in Figure 6, where orbital parameters prior to the second planet's ejection are shown as gray dots and the resonant motion is shown as a black curve." " Note the similarity of resonant motion computed numerically, to that computed analytically, shown in Figure 3."," Note the similarity of resonant motion computed numerically, to that computed analytically, shown in Figure 3." " In this paper, we have addressed the issue of how planetesimals could preserve relative velocities that are slow enough to allow planet accretion to take place, in binary stellar systems."," In this paper, we have addressed the issue of how planetesimals could preserve relative velocities that are slow enough to allow planet accretion to take place, in binary stellar systems." " Particularly, we focused on highly inclined systems where Kozai resonance with the perturbing stellar companion have been thought to disrupt the protoplanetary disk and inhibit planet formation (Marzarietal.,2009).."," Particularly, we focused on highly inclined systems where Kozai resonance with the perturbing stellar companion have been thought to disrupt the protoplanetary disk and inhibit planet formation \citep{2009A&A...507..505M}." " Here, we have shown, from analytical considerations, that fast apsidal precession, which results from the disk self-gravity, wipes out the Kozai resonance and ensures rigid precession of the disk’s nodal reference plane."," Here, we have shown, from analytical considerations, that fast apsidal precession, which results from the disk self-gravity, wipes out the Kozai resonance and ensures rigid precession of the disk's nodal reference plane." It is useful to consider the domain of applicability of the criteria discussed here., It is useful to consider the domain of applicability of the criteria discussed here. " Namely, the trade-off between stellar binary separation and the perturbing companion’s mass should be quantified."," Namely, the trade-off between stellar binary separation and the perturbing companion's mass should be quantified." The region of parameter space (binary separation a vs disk mass to perturber mass ratio) where self-gravity suppresses secular excitation from the binary companion is delineated in Figure 7., The region of parameter space (binary separation $\tilde{a}$ vs disk mass to perturber mass ratio) where self-gravity suppresses secular excitation from the binary companion is delineated in Figure 7. The red curve shows the dividing line between disk-dominated and stellar companion-dominated apsidal precession (as in section 2)., The red curve shows the dividing line between disk-dominated and stellar companion-dominated apsidal precession (as in section 2). " The three purple curves illustrate the disappearance of the Kozai separatrix, for various choices of maximal inclination (as in section 3)."," The three purple curves illustrate the disappearance of the Kozai separatrix, for various choices of maximal inclination (as in section 3)." The black curve delineates the boundary between rigid precession of the disk’s mid-plane and a warped structure (as in section 4)., The black curve delineates the boundary between rigid precession of the disk's mid-plane and a warped structure (as in section 4). " As can be deduced from Figure 7, for distant stellar companions (@1000 AU), the required total disk mass is of order Mai,~1-10M, (depending on the perturber's mass), considerably less than or comparable to, the total mass of the minimum mass solar nebula."," As can be deduced from Figure 7, for distant stellar companions $\tilde{a} \sim 1000$ AU), the required total disk mass is of order $M_{\mathrm{disk}} \sim 1$ $M_J$ (depending on the perturber's mass), considerably less than or comparable to, the total mass of the minimum mass solar nebula." " This implies that generally, protoplanetary disks in binary stars can maintain roughly circular, unwarped and untwisted structures."," This implies that generally, protoplanetary disks in binary stars can maintain roughly circular, unwarped and untwisted structures." " Consequently, we can conclude that planetary formation in wide binary systems is qualitatively no different from planetary formation around single stars."," Consequently, we can conclude that planetary formation in wide binary systems is qualitatively no different from planetary formation around single stars." " After the formation of planets is complete and the gaseous nebula has dissipated, the Kozai effect can continue to be inhibited as a result of orbital precession induced by planet-planet interactions."," After the formation of planets is complete and the gaseous nebula has dissipated, the Kozai effect can continue to be inhibited as a result of orbital precession induced by planet-planet interactions." " However, as the numerical experiment presented here suggests, if a planetary system experiences a transient dynamical instability that leaves the planets on sufficiently well-separated orbits, the planets can start undergoing Kozai cycles."," However, as the numerical experiment presented here suggests, if a planetary system experiences a transient dynamical instability that leaves the planets on sufficiently well-separated orbits, the planets can start undergoing Kozai cycles." " An evolutionary sequence of this kind can explain the existence of orbital architectures characterized by highly eccentric planets, such as those of HD 80606 and 16 Cygni B (EggletonandKiseleva-Eggleton,WuandMurray, 2003).."," An evolutionary sequence of this kind can explain the existence of orbital architectures characterized by highly eccentric planets, such as those of HD 80606 and 16 Cygni B \citep{2001ApJ...562.1012E, 2003ApJ...589..605W}." " The work presented here resolves, at least in part, a pressing dynamical issue of planetary formation in highly inclined binary systems."," The work presented here resolves, at least in part, a pressing dynamical issue of planetary formation in highly inclined binary systems." " As an avenue for further studies, the analytical results presented here should be explored numerically in grater detail."," As an avenue for further studies, the analytical results presented here should be explored numerically in grater detail." " Particularly, hydrodynamic simulations, such as those presented by Fragneretal.(2011) can be used to quantitatively map out the parameter space that allows for planetary systems to form successfully."," Particularly, hydrodynamic simulations, such as those presented by \cite{2011A&A...528A..40F} can be used to quantitatively map out the parameter space that allows for planetary systems to form successfully." The study presented here has further consequences beyond an explanation of planet formation in wide binary systems., The study presented here has further consequences beyond an explanation of planet formation in wide binary systems. " Particularly, the model of instability-driven evolution of newly-formed systems into the Kozai resonance has substantial implications for orbital misalignment with the parent star's rotation axis."," Particularly, the model of instability-driven evolution of newly-formed systems into the Kozai resonance has substantial implications for orbital misalignment with the parent star's rotation axis." " In fact, Kozai cycles with tidal friction produce a particular distribution of orbit-spin axis angles (FabryckyandTremaine, 2007)."," In fact, Kozai cycles with tidal friction produce a particular distribution of orbit-spin axis angles \citep{2007ApJ...669.1298F}." ". This distribution differs significantly from that produced by the planet-planet scattering scenario (Nagasawaetal.,2008)..", This distribution differs significantly from that produced by the planet-planet scattering scenario \citep{2008ApJ...678..498N}. " This distinction has been used to statistically infer the dominant process by which misaligned hot Jupiters form (MortonandJohnson,2011)..", This distinction has been used to statistically infer the dominant process by which misaligned hot Jupiters form \citep{2011ApJ...729..138M}. " However, the model presented here suggests that the two distributions should be intimately related, as planet-planet scattering provides the initial condition from which Kozai cycles originate."," However, the model presented here suggests that the two distributions should be intimately related, as planet-planet scattering provides the initial condition from which Kozai cycles originate." " Consequently, a quantitative re-examination of the orbit-spin axis misalignment angle distribution, formed by Kozai cycles with tidal friction that originate from a scattered orbital architecture, and subsequent comparison of the results with observations of the Rossiter-McLaughlin effect will likely yield new insights into dynamical evolution histories of misaligned hot Jupiters."," Consequently, a quantitative re-examination of the orbit-spin axis misalignment angle distribution, formed by Kozai cycles with tidal friction that originate from a scattered orbital architecture, and subsequent comparison of the results with observations of the Rossiter-McLaughlin effect will likely yield new insights into dynamical evolution histories of misaligned hot Jupiters." from the radio spectrum (see Sect.,from the radio spectrum (see Sect. 4.2). to the relic region.," 4.2), to the relic region." Both fits give consistent results and point to a thermal origin of the X-ray emission. since the combined fit gives a non-thermal component contribution consistent with zero.," Both fits give consistent results and point to a thermal origin of the X-ray emission, since the combined fit gives a non-thermal component contribution consistent with zero." " À spectral fit with only a non-thermal component of a=2.2 does not provide an acceptable fit. giving a higher reduced y and a nH value of 9x10°"" em7. ie. an order of magnitude higher than the observed value of 9x101 em (Dickey Lockman 1990)."," A spectral fit with only a non-thermal component of $\alpha=2.2$ does not provide an acceptable fit, giving a higher reduced $\chi^2$ and a nH value of $9\times 10^{20}$ $^{-2}$, i.e. an order of magnitude higher than the observed value of $9\times 10^{19}$ $^{-2}$ (Dickey Lockman 1990)." Moreover. a thermal-model fit applied to the region NE of the relic provides a gas temperature fully consistent with that of the relic region.," Moreover, a thermal-model fit applied to the region NE of the relic provides a gas temperature fully consistent with that of the relic region." The relatively high reduced y value ir this region can be explained by residuals in the instrumental background subtraction. which are amplified by the vignetting correction.," The relatively high reduced $\chi^2$ value in this region can be explained by residuals in the instrumental background subtraction, which are amplified by the vignetting correction." The non-thermal emission in the relic region. if at all detectable with XMM-Newton. would be much lower than the thermal emission.," The non-thermal emission in the relic region, if at all detectable with XMM-Newton, would be much lower than the thermal emission." We calculate the upper limit of this non-thermal component in two ways: a) spectral fitting. which gives a maximum flux in the 0.3 — 10 keV band of 2.5x107 erg em s!. and b) imaging analysis.," We calculate the upper limit of this non-thermal component in two ways: a) spectral fitting, which gives a maximum flux in the 0.3 $-$ 10 keV band of $2.5\times 10^{-13}$ erg $^{-2}$ $^{-1}$, and b) imaging analysis." For the latter. since no excess X-ray emission directly related to the relic is detected. we can calculate how much of this emission can be “hidden”.," For the latter, since no excess X-ray emission directly related to the relic is detected, we can calculate how much of this emission can be “hidden”." " Assuming Poisson statistics. we estimate that this is 3.2»107? erg cm? s!, which is in excellent agreement with the value obtained from the spectral analysis."," Assuming Poisson statistics, we estimate that this is $3.2\times 10^{-13}$ erg $^{-2}$ $^{-1}$, which is in excellent agreement with the value obtained from the spectral analysis." We adopt as an upper limit of the non-thermal component the more conservative value. 1.8. 3.2x107 ergem™ sol.," We adopt as an upper limit of the non-thermal component the more conservative value, i.e. $3.2\times 10^{-13}$ erg $^{-2}$ $^{-1}$." The results of this paper can be summarized as follows: a) There is extended X-ray emission in and around the Coma relic region. which is connected to the sub-group around NGC 4839.," The results of this paper can be summarized as follows: a) There is extended X-ray emission in and around the Coma relic region, which is connected to the sub-group around NGC 4839." The group is on its first infall onto the cluster. with velocity ~ 1700 km sl. as suggested from optical data by Colless Dunn (1996). and as further demonstrated by the effects of ram pressure stripping detected from XMM-Newton data that indicate the infall direction (Neumann et al.," The group is on its first infall onto the cluster, with velocity $\sim$ 1700 km $^{-1}$, as suggested from optical data by Colless Dunn (1996), and as further demonstrated by the effects of ram pressure stripping detected from XMM-Newton data that indicate the infall direction (Neumann et al." 2001)., 2001). b) The best-fit gas temperatures in the region of the relic and in its vicinity (NE region) are very similar. around 3.3 keV. This value is lower than the 4.4+0.4 keV found in the main body of the NGC 4839 sub-group (Neumann et al.," b) The best-fit gas temperatures in the region of the relic and in its vicinity (NE region) are very similar, around 3.3 keV. This value is lower than the $4.4\pm0.4$ keV found in the main body of the NGC 4839 sub-group (Neumann et al." 2001). although the difference is marginally significant.," 2001), although the difference is marginally significant." However. what is most remarkable is that we do not detect any high temperature gas. which could indicate the presence of a shock at the location of the Coma relic.," However, what is most remarkable is that we do not detect any high temperature gas, which could indicate the presence of a shock at the location of the Coma relic." ϱ) The emission of the relic is largely dominated by thermal emission., c) The emission of the relic is largely dominated by thermal emission. This is deduced by the spectral fit analysis and is also supported by the following arguments: 1) the X-ray emission is connected to the hot gas of the NGC 4839 sub-group. and 10) there are no distinct X-ray features connected to the radio relic itself.," This is deduced by the spectral fit analysis and is also supported by the following arguments: i) the X-ray emission is connected to the hot gas of the NGC 4839 sub-group, and ii) there are no distinct X-ray features connected to the radio relic itself." We can only set a flux upper limit of 3.2»107 erg em sl in the 0.3-10 keV band for the non-thermal component., We can only set a flux upper limit of $3.2\times 10^{-13}$ erg $^{-2}$ $^{-1}$ in the 0.3-10 keV band for the non-thermal component. A brief discussion of the implications of our results follows., A brief discussion of the implications of our results follows. According to current models. the relativistic electrons radiating in radio relics are expected to be accelerated by shocks originating from cluster mergers.," According to current models, the relativistic electrons radiating in radio relics are expected to be accelerated by shocks originating from cluster mergers." In a fully ionized. plasma. à shock with compression factor C and Mach number M can accelerate particles to a power law distribution in momentum. with slope 6=(C+2)/(C—1)2(M7D/OQT4-- (Drury 1983).," In a fully ionized plasma, a shock with compression factor $C$ and Mach number $M$ can accelerate particles to a power law distribution in momentum, with slope $\delta = (C+2)/(C-1) = 2(M^2+1)/(M^2-1)$ (Drury 1983)." The spectral index « of the radio emission is thus related to the Mach number of the shock by the relation: a=(M+3)/2(M7—1).," The spectral index $\alpha$ of the radio emission is thus related to the Mach number of the shock by the relation: $\alpha = (M^2 + 3) / 2(M^2 - 1)$ ." In this framework. the Coma relie with spectral index e = 1.18 should originate from particles accelerated by a shock of Mach number M - 2.," In this framework, the Coma relic with spectral index $\alpha$ = 1.18 should originate from particles accelerated by a shock of Mach number M $\sim$ 2." " In the case of a monoatomic gas. the ratio between the post-shock and pre-shock temperatures T. and Τι is given by 72/7,=(8M—IM+3)/16M"" (see. for example. Sarazin 2002)."," In the case of a monoatomic gas, the ratio between the post-shock and pre-shock temperatures $T_2$ and $ T_1$ is given by $T_2/T_1 = (5M^2 - 1) (M^2 + 3)/16M^2$ (see, for example, Sarazin 2002)." This implies that the temperature jump across a shock of Mach number M ~ 2 ts 2.1. which is not observed in our data.," This implies that the temperature jump across a shock of Mach number M $\sim$ 2 is 2.1, which is not observed in our data." The above calculations refer to the simplest case., The above calculations refer to the simplest case. " More rigorously, one should consider a) the effect of electron ageing on the observed steep radio spectrum. b) the influence of magnetic field on the shock parameters. c) the case of re-acceleration of relativistic particles. leading to possibly higher Mach numbers."," More rigorously, one should consider a) the effect of electron ageing on the observed steep radio spectrum, b) the influence of magnetic field on the shock parameters, c) the case of re-acceleration of relativistic particles, leading to possibly higher Mach numbers." No temperature gradient is detected between the region of the relic (1) and the pre-shock region (2)., No temperature gradient is detected between the region of the relic (1) and the pre-shock region (2). This cannot be due to projection effects., This cannot be due to projection effects. In fact the high resolution radio images of the relie show a sharper brightness decrease on the western (outer) edge (Giovannini et al., In fact the high resolution radio images of the relic show a sharper brightness decrease on the western (outer) edge (Giovannini et al. 1991). and the infall path of the NGC 4839 group to the cluster in a two-body model lies at about (ο the line of sight (Colless Dunn 1996).," 1991), and the infall path of the NGC 4839 group to the cluster in a two-body model lies at about to the line of sight (Colless Dunn 1996)." Thus. a strong inclination. of the shock with respect to the sky plane. which would spread the observed temperature jump over a larger region. should be ruled out.," Thus, a strong inclination of the shock with respect to the sky plane, which would spread the observed temperature jump over a larger region, should be ruled out." The identification of region (2) as the pre-shock region relies on the assumption that the group is on its first passage into the cluster core., The identification of region (2) as the pre-shock region relies on the assumption that the group is on its first passage into the cluster core. This is a widely accepted scenario (see beginning of Discussion)., This is a widely accepted scenario (see beginning of Discussion). Nevertheless. the low temperature at the relic location is a significant result in itself. in particular because it is lower than that of the NGC 4839 group. thus indicating the lack of high temperature shocked gas in the relic region.," Nevertheless, the low temperature at the relic location is a significant result in itself, in particular because it is lower than that of the NGC 4839 group, thus indicating the lack of high temperature shocked gas in the relic region." This result favors the hypothesis that turbulence may be the major mechanism responsible for the physical origin of the radio relic emission., This result favors the hypothesis that turbulence may be the major mechanism responsible for the physical origin of the radio relic emission. During its infall onto the Coma cluster. the sub-group around NGC 4839 encounters a region of relativistic particles connected to a magnetic field.," During its infall onto the Coma cluster, the sub-group around NGC 4839 encounters a region of relativistic particles connected to a magnetic field." The interaction between the ionized moving plasma and the magnetic field would imply energy transfer from the ICM to the relativistic particles., The interaction between the ionized moving plasma and the magnetic field would imply energy transfer from the ICM to the relativistic particles. As for the origin of relativistic particles. Enblin et al. (," As for the origin of relativistic particles, lin et al. (" 1998) suggested that they could be produced by the tailed radio galaxy NGC 4789. located to the SW of the relic.,"1998) suggested that they could be produced by the tailed radio galaxy NGC 4789, located to the SW of the relic." The energy for particle acceleration comes from the kinetic energy of the X-ray gas. which is subsequently slowed down.," The energy for particle acceleration comes from the kinetic energy of the X-ray gas, which is subsequently slowed down." We see indications that the X-ray gas slows down: for example. the gas of the sub-group is lagging behind the galaxies of the," We see indications that the X-ray gas slows down: for example, the gas of the sub-group is lagging behind the galaxies of the" deteriuued frou the EKer-phase model (cf Table 1)) iu this narrow filter reflects this evolution.,determined from the Ker-phase model (cf Table \ref{tbl:params}) ) in this narrow filter reflects this evolution. The analysis of this C161 data demonstrates the validity of the Ixer-phase approach. by positively detecting a companion whose existence was known beforehaud.," The analysis of this GJ164 data demonstrates the validity of the Ker-phase approach, by positively detecting a companion whose existence was known beforehand." This <10:1 contrast detection was however expected to be casy. despite the stall aneular separation of the detection (0.6 A/D).," This $<10:1$ contrast detection was however expected to be easy, despite the small angular separation of the detection (0.6 $\lambda/D$ )." Typical NICMOS datasets ou a given target usually consist of four frames only., Typical NICMOS1 datasets on a given target usually consist of four frames only. The SAO 179809 dataset is then a representativo example aud the statistics of its Isex-phase (6= 19.77) can be used in a Moute-C'arlo simulation to determine contrast detection liits., The SAO 179809 dataset is then a representative example and the statistics of its Ker-phase $\sigma=19.7^{\circ}$ ) can be used in a Monte-Carlo simulation to determine contrast detection limits. Because the supliug of the (a. ¢)-plaue exhibits no eap. the sensitivity does not depend on the the position angle relative to the central star.," Because the sampling of the $(u,v)$ -plane exhibits no gap, the sensitivity does not depend on the the position angle relative to the central star." Oue can however expect it to be a function of angular separation., One can however expect it to be a function of angular separation. A total of 10.000 simulations were performed per point iu the angular separation/coutrast plane to produce the seusitivity map displaved in Fig. 5..," A total of 10,000 simulations were performed per point in the angular separation/contrast plane to produce the sensitivity map displayed in Fig. \ref{fig:sensi}." The map highlehts the 90. 99 and 99.9 confidence level detection thresholds.," The map highlights the 90, 99 and 99.9 confidence level detection thresholds." The% technique looks promising: for such a dataset. at 0.5 A/D. a SOL coutrast detection appears possible at the 99 confidence level.," The technique looks promising: for such a dataset, at 0.5 $\lambda/D$, a 50:1 contrast detection appears possible at the 99 confidence level." The seusitivitv iuereases and peaks at 180 as. which uusurprisiuglv corresponds to the location of the first zero of the diffraction for the centrally obstructed telescope (about 1.1 A/D). aud reaches ~200:1.," The sensitivity increases and peaks at 180 mas, which unsurprisingly corresponds to the location of the first zero of the diffraction for the centrally obstructed telescope (about 1.1 $\lambda/D$ ), and reaches $\sim$ 200:1." Classical closure-plhase appears to be one special case of a wider family of observable quantities that are inumne to phase noise aud non-conmmon path errors., Classical closure-phase appears to be one special case of a wider family of observable quantities that are immune to phase noise and non-common path errors. Tn the high Strehl regime. it was demonstrated that closurc-phase like quantities. called Iscer-phases. cau be extracted froimi focal plane muases. aud provide hnieh quality “interferometric evade” information on a source. even when the pupil is redundant.," In the high Strehl regime, it was demonstrated that closure-phase like quantities, called Ker-phases, can be extracted from focal plane images, and provide high quality “interferometric grade” information on a source, even when the pupil is redundant." The Ίναphase technique was successfully applied to a series of archive NICMOS images. clearly detecting a 1011 contrast colpanion at a separation of 0.5A/D.," The Ker-phase technique was successfully applied to a series of archive NICMOS images, clearly detecting a 10:1 contrast companion at a separation of $0.5 \lambda/D$ ." Non-calibrated I&cr-pliase appears scusitive to the presence of 200:1 contrast companion at angular separation LA/D., Non-calibrated Ker-phase appears sensitive to the presence of 200:1 contrast companion at angular separation $1 \lambda/D$. Re-analvsis of other comparable NICMOS datasets with lis technique nieht very well lead to the detection of oxeviouxlv undetected objects in the direct ucighborhood of nearby stars., Re-analysis of other comparable NICMOS datasets with this technique might very well lead to the detection of previously undetected objects in the direct neighborhood of nearby stars. Uulike closure-phases. which are extremely robust to aree wavefrout errors. the use of Ier-pliases is however ‘or now restricted to the ligh-Strehl regiae. aud will ouly become relevant to eround based observations. when extreme AO svstems become available.," Unlike closure-phases, which are extremely robust to large wavefront errors, the use of Ker-phases is however for now restricted to the high-Strehl regime, and will only become relevant to ground based observations, when extreme AO systems become available." There is jevertheless hope to be able to extend the application of Ixer-phases ο not-soavell corrected ΑΟ images. using additional differential techuiques.," There is nevertheless hope to be able to extend the application of Ker-phases to not-so-well corrected AO images, using additional differential techniques." One possibility. consists in using integral field spectroscopy. to follow iu the Fourier plane. the evolution of the complex visibilities as a function of waveleneth.," One possibility, consists in using integral field spectroscopy, to follow in the Fourier plane, the evolution of the complex visibilities as a function of wavelength." With enoush resolution and spectral coverage. this indeed allows to ideutifv the phasors contributing to the power coutaiued at one spatial frequeucy.," With enough resolution and spectral coverage, this indeed allows to identify the phasors contributing to the power contained at one spatial frequency." The singular value decomposition of the transfer matrix used to create IKer-phase relations can also be used to produce a pseudo inverse to the matrix. and in some cases. allows to inverse the relation linking the (ανο) phases to the pupil phases.," The singular value decomposition of the transfer matrix used to create Ker-phase relations can also be used to produce a pseudo inverse to the matrix, and in some cases, allows to inverse the relation linking the $(u,v)$ phases to the pupil phases." This means that under certain conditions. a single monochromatic focal plane nage can also be useful for wavefrout sensing purposes.," This means that under certain conditions, a single monochromatic focal plane image can also be useful for wavefront sensing purposes." This is particularly interesting since the measurement is happening at the level of the final science detector. which therefore allows to calibrate nou-conmion path errors.," This is particularly interesting since the measurement is happening at the level of the final science detector, which therefore allows to calibrate non-common path errors." The application of the formalisin to wavefrontscusing will be the object of a future publication., The application of the formalism to wavefrontsensing will be the object of a future publication. The physies of the LPAI effect is clearly relevant in calculating the energy loss for last color charges in QCD media.,The physics of the LPM effect is clearly relevant in calculating the energy loss for fast color charges in QCD media. These media are not regular crystals. so that the cancellation becomes only partial.," These media are not regular crystals, so that the cancellation becomes only partial." Let us consider the effect here in a heuristic fashion: for details of the actual calculations. see [66.67]..," Let us consider the effect here in a heuristic fashion; for details of the actual calculations, see \cite{Baier,Zak}." " The time /,. needed for the emission of a gluon after the scattering of a quark (see Fig. 20))", The time $t_c$ needed for the emission of a gluon after the scattering of a quark (see Fig. \ref{4_4}) ) is given bv in the rest svstem of the scattering center. where P? measures how [ar the intermediate quark state is olf-shell: on-shell quarks and gluons are assumed to be massless. and E/VP? is the -[actor between the lab frame and the proper lrame of the intermediate quark.," is given by t_c = =, in the rest system of the scattering center, where $P^2$ measures how far the intermediate quark state is off-shell; on-shell quarks and gluons are assumed to be massless, and $E/\sqrt{P^2}$ is the $\gamma$ -factor between the lab frame and the proper frame of the intermediate quark." For gluons with Ay22hyp. we thus gel ," For gluons with $k_L >> k_T$, we thus get t_c." If the passing color charge can interact wilh several scattering centers during the formation lime of a gluon. the corresponding amplitudes interfere destructively. so that in ellect after (he passage of n centers over (he coherence length z.. only one gluon is emitted. in contrast (o {he emission of » gluons in the incoherent regime.," If the passing color charge can interact with several scattering centers during the formation time of a gluon, the corresponding amplitudes interfere destructively, so that in effect after the passage of $n$ centers over the coherence length $z_c$, only one gluon is emitted, in contrast to the emission of $n$ gluons in the incoherent regime." Nevertheless. in both cases each scattering leads to a Myp-kick of the charge. so that after a random walk past à centers. A57n.," Nevertheless, in both cases each scattering leads to a $k_T$ -kick of the charge, so that after a random walk past $n$ centers, $k_T^2 \sim n$." " Hence where A is the mean free path of the charge in the medium. so that 2,/AÀ>1 counts the number of scatterings."," Hence k_T^2 ^2 }, where $\lambda$ is the mean free path of the charge in the medium, so that $z_c/ \lambda >1$ counts the number of scatterings." At each scattering. the transverse kick received is measured by (he mass of the eluon exchanged between the charge and the scattering center. i.e. bv the screening mass i of the medium.," At each scattering, the transverse kick received is measured by the mass of the gluon exchanged between the charge and the scattering center, i.e., by the screening mass $\mu$ of the medium." From we have," From \\ref{9b} we have z_c ," The main results of the satellite search are. sumnmarised in Table 1..,The main results of the satellite search are summarised in Table \ref{tab_ttype}. The total number of central galaxies searched was 143. approximately one-third of which were found to ↓⋯∖⇁⋖⊾⋜↧↓∢⋅⋜↧⊳∖⇂∪⊔⋖⋅⋜↧⊳∖⊳∖⋯⋰↓⋜⋯⋅∠⇂↓⊀↓⊔∢⊾⊣⋅⊔↓⊲↓∏⊲↓⊔," The total number of central galaxies searched was 143, approximately one-third of which were found to have at least one associated line-emitting galaxy." ⋏∙≟⋏∙≟⋜↧↓⋜∟∖∙∖⇁⊳↻⇂⋅⇂↓∐⊾⊳∖⋖⊾ 47 central hosts. 37 have only a single satellite. T have two satellites. 2 have three satellites and one (NGC. 3074) has five satellites: thus the 47 central galaxies host a total of 62 satellites.," Of these 47 central hosts, 37 have only a single satellite, 7 have two satellites, 2 have three satellites and one (NGC 3074) has five satellites; thus the 47 central galaxies host a total of 62 satellites." The Z-tvpes of the central galaxies for each of the 62 is shown as the dotted line in Fig. 1:, The $T$ -types of the central galaxies for each of the 62 is shown as the dotted line in Fig. \ref{fig:thist}; this matches the type distribution for all galaxies searched within statistical. uncertainties. Le. there is no evidence for anv galaxy ἵνρο having systematically more or fewer satellites than the average.," this matches the type distribution for all galaxies searched within statistical uncertainties, i.e. there is no evidence for any galaxy type having systematically more or fewer satellites than the average." The mean and median recession velocities of the satellite-hosting ealaxics are 2038 and 2543 km s1 respectively. somewhat larger than the corresponding values for the whole sample of 143 galaxies (2539 and 2217 kms ly," The mean and median recession velocities of the satellite-hosting galaxies are 2938 and 2543 km $^{-1}$ respectively, somewhat larger than the corresponding values for the whole sample of 143 galaxies (2539 and 2217 km $^{-1}$ )." This indicates that the dominant. incompleteness is likely to be due to the smaller effective. search area. for the nearer svstems. rather than missing faint satellites at larger distances.," This indicates that the dominant incompleteness is likely to be due to the smaller effective search area for the nearer systems, rather than missing faint satellites at larger distances." In any case. the recession velocity distributions of the overall and satellite-hosting samples are only marginally diferent. with a Ixolmogorov-Smirnov test showing a chance that they could be drawn from the same paren distribution.," In any case, the recession velocity distributions of the overall and satellite-hosting samples are only marginally different, with a Kolmogorov-Smirnov test showing a chance that they could be drawn from the same parent distribution." Our ρα imaging and the catalogued recession velocities were used to determine the total luminosities of the central hosts., Our $R$ -band imaging and the catalogued recession velocities were used to determine the total luminosities of the central hosts. Phe mean value for the 47 satellite-hosting galaxies was 1.53 10 L.. almost identical to our adopte luminosity for the MW. thus confirming that this is à &ooc sample for deriving satellite properties of AIW-like centra galaxies.," The mean value for the 47 satellite-hosting galaxies was $\times$ $^{10}$ $_{\odot}$, almost identical to our adopted luminosity for the MW, thus confirming that this is a good sample for deriving satellite properties of MW-like central galaxies." We now move to a consideration of the properties of the Seellites that were detected. with the principal aim in the present paper of identifying those that can be considere similar to the LMC or SAIC.," We now move to a consideration of the properties of the satellites that were detected, with the principal aim in the present paper of identifying those that can be considered similar to the LMC or SMC." A more detailed discussion of. for example. SE rates. evidence for starbursts or suppressec SE. continuum and. emission-line morphologies. and the overall satellite galaxy luminosity function will be presente in a future paper (C. E. Ivory et ab.," A more detailed discussion of, for example, SF rates, evidence for starbursts or suppressed SF, continuum and emission-line morphologies, and the overall satellite galaxy luminosity function will be presented in a future paper (C. F. Ivory et al.," in preparation)., in preparation). The first satcllite property to consider is. projectec separation. measured from the A-bane centroid of the hos to that of the satellite.," The first satellite property to consider is projected separation, measured from the $R$ -band centroid of the host to that of the satellite." Figure 2 shows the distribution of these values for the 62 satellites. with the dotted. line corresponding to all satellites. and 10 solid line to jus those with central ealaxies more distant than 30 Alpe.," Figure \ref{fig:satsep} shows the distribution of these values for the 62 satellites, with the dotted line corresponding to all satellites, and the solid line to just those with central galaxies more distant than 30 Mpc." The latter thus excludes those svstems with significan incompleteness for outlving satellites cue to the smaller projected area surveved., The latter thus excludes those systems with significant incompleteness for outlying satellites due to the smaller projected area surveyed. The mean ancl median. projecte separations of the satellites from their central galaxies are Sl and 66 kpe respectively. rising to 98 and 90 kpe for," The mean and median projected separations of the satellites from their central galaxies are 81 and 66 kpc respectively, rising to 98 and 90 kpc for" For each cluster halo. we fit the ?.NFW.. the ?.M.. and the ?.JS analytic density profiles.,"For each cluster halo, we fit the \citet[][NFW]{nfw_97}, the \citet[][M]{moore_etal98}, and the \citet[][JS]{jing_suto00} analytic density profiles." For a general profile of the form the NFW. M. and JS profiles have values of (o. 0). y (d. 3. 1). (1.5. 3. 1.5). and (1. 3. 1.5). respectively.," For a general profile of the form the NFW, M, and JS profiles have values of $\alpha$, $\beta$, $\gamma$ ): (1, 3, 1), (1.5, 3, 1.5), and (1, 3, 1.5), respectively." In what follows. we will define the concentration of à halo as €—Fiso£F-o and ey=raro. where r_> is the radius where the logarithmic slope of the best fit profile is equal to -2. riso is the radius within which the average density 1s equal to 180 times the matter density of the universe. and 7; 1s the virial radius defined using the redshift-dependent virial overdensity (5:180 at z>| and z340 at z2 0).," In what follows, we will define the concentration of a halo as $c_{-2}\equiv r_{180}/r_{-2}$ and $c_{\rm v}\equiv r_{\rm vir}/r_{-2}$, where $r_{-2}$ is the radius where the logarithmic slope of the best fit profile is equal to -2, $r_{180}$ is the radius within which the average density is equal to 180 times the matter density of the universe, and $r_{\rm vir}$ is the virial radius defined using the redshift-dependent virial overdensity $\approx 180$ at $z>1$ and $\approx 340$ at $z=0$ )." To convert from (Migo.riso) to (My. rir) we use the fitting formulas of ?.., To convert from $M_{180}$ $r_{180}$ ) to $M_{\rm vir}$ $r_{\rm vir}$ ) we use the fitting formulas of \citet{hu_kravtsov03}. For the general profile of Eq.( 6)).," For the general profile of Eq.( \ref{eq:nuker}) )," " the radius 7-5 is given by where r, 1s the scale radius of the corresponding analytic profile.", the radius $r_{-2}$ is given by where $r_s$ is the scale radius of the corresponding analytic profile. " Thus. 722r, (NEW). 75z0.637; (M). 72=0.59, (IS)."," Thus, $r_{-2}=r_{s}$ (NFW), $r_{-2} \approx 0.63 r_{s}$ (M), $r_{-2} = 0.5 r_{s}$ (JS)." In other words. c»=ewpw. ο7I.59ey. and ο=2eys. if the best fit is found to be the NFW. the M. or the JS profile. respectively.," In other words, $c_{-2}=c_{\rm NFW}$, $c_{-2} \approx 1.59 c_{\rm M}$, and $c_{-2}=2 c_{\rm JS}$, if the best fit is found to be the NFW, the M, or the JS profile, respectively." We present the resulting concentration indices at zz0meolumn 7 of Table 2.., We present the resulting concentration indices at $z=0$ in column 7 of Table \ref{tab:z}. There is a number of factors that may affect the fits of analytic profiles to the profiles of the simulated clusters: the choice of binning. the merit function. the range of radii used in the fitting. the weights assigned to the data points. etc.," There is a number of factors that may affect the fits of analytic profiles to the profiles of the simulated clusters: the choice of binning, the merit function, the range of radii used in the fitting, the weights assigned to the data points, etc." For example. for the merit functions sensitive to the number of bins. such às 47. the choice of binning and bin weights are extremely important.," For example, for the merit functions sensitive to the number of bins, such as $\chi^2$, the choice of binning and bin weights are extremely important." In the following analysis. we use equal-size logarithmic bins in order to give more statistical weight to the inner regions of the halos.," In the following analysis, we use equal-size logarithmic bins in order to give more statistical weight to the inner regions of the halos." The number of bins ts thirty for late epochs., The number of bins is thirty for late epochs. For early epochs the number of bins is reduced to ensure that each bin contains a sufficiently large number (>100) of particles., For early epochs the number of bins is reduced to ensure that each bin contains a sufficiently large number $>100$ ) of particles. We take as bin center the average radius of all particles in a bin., We take as bin center the average radius of all particles in a bin. We checked that the fits are robust when varying the number of bins around the adopted value., We checked that the fits are robust when varying the number of bins around the adopted value. We find. however. that the choice of binning affects the quality of the fit.," We find, however, that the choice of binning affects the quality of the fit." For example. for a large number of bins the resulting profiles are quite noisy.," For example, for a large number of bins the resulting profiles are quite noisy." Our choice of binning minimizes the noise., Our choice of binning minimizes the noise. We weight the data points by the poisson noise in the number of particles of each bin., We weight the data points by the poisson noise in the number of particles of each bin. The presence of substructure may substantially bias fits of smooth analytic profiles., The presence of substructure may substantially bias fits of smooth analytic profiles. In particular. substantial amount of substructure is present in the outer regions of halos and the profiles in these regions are often non-monotonic exhibiting “bumps”.," In particular, substantial amount of substructure is present in the outer regions of halos and the profiles in these regions are often non-monotonic exhibiting “bumps”." To minimize the bias. we fit the profiles using only the bins from à minimum resolved radius (see 5 5.2)) up to the radius within which the average density 1s equal to 500 times the density of the universe. rsqo.," To minimize the bias, we fit the profiles using only the bins from a minimum resolved radius (see $\S $ \ref{conver_study}) ) up to the radius within which the average density is equal to 500 times the density of the universe, $r_{500}$." This choice is motivated by the results of ? who find that the material within this radius is generally relaxed and in hydrostatic equilibrium., This choice is motivated by the results of \citet{evrard_etal96} who find that the material within this radius is generally relaxed and in hydrostatic equilibrium. We find that for the clusters in our sample rsoo/riso0.37 at z20., We find that for the clusters in our sample $r_{500}/r_{180}\simeq 0.36-0.37$ at $z=0$. To the same end. the density profiles of CL9 and 10 were obtained by averaging the z20 and z0.05 outputs.," To the same end, the density profiles of CL9 and 10 were obtained by averaging the $z=0$ and $z \approx 0.05$ outputs." This renders the profiles less noisy and improves the quality of the obtained fits., This renders the profiles less noisy and improves the quality of the obtained fits. The averaging does not change the best fit parameters significantly., The averaging does not change the best fit parameters significantly. It is important to understand that the formal quality of the fit may depend on the merit function.as well as the kind of binning and. weighting used.," It is important to understand that the formal quality of the fit may depend on the merit function,as well as the kind of binning and weighting used." " In the following analysis. we fit the analytic profiles for the parameters p, and r, by minimizing"," In the following analysis, we fit the analytic profiles for the parameters $\rho_{s}$ and $r_{s}$ by minimizing" at phases 0.61.0 due to the area of enhanced. emission rotating into our line of sight.,at phases $0.6-1.0$ due to the area of enhanced emission rotating into our line of sight. For an excellent. overview of CVs. see 2? and ?..," For an excellent overview of CVs, see \citet{warner1995a} and \citet{hellier2001}." The light curves of eclipsing CVs can be quite complex. with the accretion disc. white dwarf and bright spot all being eclipsed in rapid succession.," The light curves of eclipsing CVs can be quite complex, with the accretion disc, white dwarf and bright spot all being eclipsed in rapid succession." When observed with time resolutions of the order of a few seconds. this eclipse structure allows the svstem: parameters to be determined to a high degree of precision with relatively [ew assumptions (2)..," When observed with time resolutions of the order of a few seconds, this eclipse structure allows the system parameters to be determined to a high degree of precision with relatively few assumptions \citep{wood1986}." Over the last eight. vears our group has used the high-speed. three-colour cameraULERACAM (7). to obtain such time-resolution.," Over the last eight years our group has used the high-speed, three-colour camera \citep{dhillon2007} to obtain such time-resolution." The ability to image in three different wave-bancs simultaneously makes an ideal tool to study the complex. highly variable light curves of CVs.," The ability to image in three different wave-bands simultaneously makes an ideal tool to study the complex, highly variable light curves of CVs." Using data. we have obtained: svsten parameters for several short period svstems (e.g. Feline et al.," Using data, we have obtained system parameters for several short period systems (e.g. Feline et al." 2004a. 2004b: Littlefair et al.," 2004a, 2004b; Littlefair et al." 20062. 2007. 2008). including the first svstem accreting from a sub-stellar donor (Littlefair et al.," 2006a, 2007, 2008), \nocite{feline2004a, feline2004a, feline2004b, littlefair2006a, littlefair2007, littlefair2008} including the first system accreting from a sub-stellar donor (Littlefair et al." 2006h)., 2006b). Despite extensive study over recent. decades. there are still several outstancding issues with evolutionary theories of CVs that have wide ranging implications for all close binary systems.," \nocite{littlefair2006b} Despite extensive study over recent decades, there are still several outstanding issues with evolutionary theories of CVs that have wide ranging implications for all close binary systems." The secular evolution of €Vs is driven by angular momentum losses from the binary orbit., The secular evolution of CVs is driven by angular momentum losses from the binary orbit. In the standard model. svstems with orbital periods below ~180 minutes are thought to lose angular momentum via. gravitational radiation.," In the standard model, systems with orbital periods below $\sim$ 130 minutes are thought to lose angular momentum via gravitational radiation." Xngular momentum losses sustain mass transfer and subsequently drive the system to shorter orbital periods. until the point where the donor star becomes degenerate (ος.?).," Angular momentum losses sustain mass transfer and subsequently drive the system to shorter orbital periods, until the point where the donor star becomes degenerate \citep[e.g.][]{paczynski1981}." llere. the donor star is driven out of thermal equilibrium and begins to expand in response to mass-Ioss. driving the system to longer orbital periods.," Here, the donor star is driven out of thermal equilibrium and begins to expand in response to mass-loss, driving the system to longer orbital periods." " We therefore expect to observe a period. cut-olf around. {δν2:6510 minutes. dubbed the ""period. minimum"". in addition to à build up of svstems at this minimum period (the. ""period spike”: Ixolb Baralle Phe period spike has recently been identified. by 2.. whose study of SDSS CVs found an accumulation of systems with orbital periods. between SO and SG minutes."," We therefore expect to observe a period cut-off around $P_{orb} \simeq 65-70$ minutes, dubbed the “period minimum”, in addition to a build up of systems at this minimum period (the “period spike”; Kolb Baraffe \nocite{kolb1999} The period spike has recently been identified by \citet{gaensicke2009}, whose study of SDSS CVs found an accumulation of systems with orbital periods between 80 and 86 minutes." This is significantly longer than expected., This is significantly longer than expected. A larger than expected orbital period implies that the orbita separation is larger than expected. nd thus the radii of the donor star must also be larger than expected in order to remain Roche-lobe filling.," A larger than expected orbital period implies that the orbital separation is larger than expected, nd thus the radii of the donor star must also be larger than expected in order to remain Roche-lobe filling." Recent observations bv 7. suppor this. suggesting that the donor stars in short. period. CVs are roughly LO percent larger than predicted by the models of 7..," Recent observations by \citet{littlefair2008} support this, suggesting that the donor stars in short period CVs are roughly 10 percent larger than predicted by the models of \citet{kolb1999}." " ""Phe reason why the donor stars appear oversize. remains uncertain.", The reason why the donor stars appear oversized remains uncertain. Possible explanations include some form of enhanced angular momentum loss (c.g.2???) which woulc increase mass loss and drive the donor stars further from thermal equilibrium. or missing stellar physics in the form of magnetic activity coupled with the cllects of rapid rotation (eg.2).," Possible explanations include some form of enhanced angular momentum loss \citep[e.g.][]{patterson1998, kolb1999, willems2005} which would increase mass loss and drive the donor stars further from thermal equilibrium, or missing stellar physics in the form of magnetic activity coupled with the effects of rapid rotation \citep[e.g.][]{chabrier2007}." " One way to determine why the donor stars appear oversized is to compare the shape of the observed. donor mass-period relationship (Af, £,5). and by implication. pmuass-radius (As Rs) relationship. to the models of 7.. calculated. with enhanced angular momentum loss or modified stellar physics."," One way to determine why the donor stars appear oversized is to compare the shape of the observed donor mass-period relationship $M_{2}-P_{orb}$ ), and by implication, mass-radius $M_{2}-R_{2}$ ) relationship, to the models of \citet{kolb1999}, calculated with enhanced angular momentum loss or modified stellar physics." These. models. in. principle. make different predictions. for the shape of the mass-period relationship and the position of the period minimum.," These models, in principle, make different predictions for the shape of the mass-period relationship and the position of the period minimum." Both the shape of the mass-period relationship and the position of the period minimum: are dependent on the ratio &= Tuf/Tku. Where may and zig are the mass-Ioss ancl thermal timescales of the donor star respectively.," Both the shape of the mass-period relationship and the position of the period minimum are dependent on the ratio $\kappa = \tau_{M}/\tau_{KH}$ , where $\tau_{M}$ and $\tau_{KH}$ are the mass-loss and thermal timescales of the donor star respectively." Initially. ασ». and the donor is able to contract in response to niass-," Initially, $\kappa$$\gg$ 1, and the donor is able to contract in response to mass-loss." As the system evolves to. shorter. orbital periods both timescales increase. although. the thermal timescale increases much faster than the mass-oss timescale.," As the system evolves to shorter orbital periods both timescales increase, although the thermal timescale increases much faster than the mass-loss timescale." This results in «# decreasing with orbital period., This results in $\kappa$ decreasing with orbital period. When the two timescales become comparable. the donor is unable to contract rapidly enough to maintain thermal equilibrium ancl becomes oversized for a given. mass.," When the two timescales become comparable, the donor is unable to contract rapidly enough to maintain thermal equilibrium and becomes oversized for a given mass." Since conor expansion does not occur until the thermal and. mass-loss timescales become comparable. if. enhanced. angular momentum loss is responsible for the oversized. CV donors. the svstems below the period gap would not be expected: to be far from thermal equilibrium.," Since donor expansion does not occur until the thermal and mass-loss timescales become comparable, if enhanced angular momentum loss is responsible for the oversized CV donors, the systems below the period gap would not be expected to be far from thermal equilibrium." In. contrast. star spots would inhibit the convective processes in all CV donors below the period gap (assuming of course that spot »operties are similar at all masses).," In contrast, star spots would inhibit the convective processes in all CV donors below the period gap (assuming of course that spot properties are similar at all masses)." Alodels that. include he effects of enhanced angular momentum loss ancl star spot coverage therefore begin to diverge significantly in AI ancl A» at orbital periods of 100 minutes., Models that include the effects of enhanced angular momentum loss and star spot coverage therefore begin to diverge significantly in $\dot{M}$ and $M_{2}$ at orbital periods of 100 minutes. We can distinguish tween these models if ve have a sample of CVs that covers a wide range of orbital periods and whose component masses ancl radii are known to a high degree of precision (e.g. Mo00537. 1., We can distinguish between these models if we have a sample of CVs that covers a wide range of orbital periods and whose component masses and radii are known to a high degree of precision (e.g. $\sigma$$M_{2}$$\sim0.005M_{\odot}$ ). Unfortunately we lack enough precise masseracdii determinations for svstems with orbital periods between 95 ancl 130 minutes., Unfortunately we lack enough precise mass-radii determinations for systems with orbital periods between 95 and 130 minutes. To overcome this shortage we observed eclipses of three €Vs below the period gap: C'TC'V. J1800-3052. C'ECV. 2354-4700. and. SDSS J115207.00|404047.8 (hereafter C'ECV. 1300. οον) 2354 and SDSS 1152).," To overcome this shortage we observed eclipses of three CVs below the period gap: CTCV J1300-3052, CTCV J2354-4700 and SDSS J115207.00+404947.8 (hereafter CTCV 1300, CTCV 2354 and SDSS 1152)." ο 2354 and οΕΟΝ 1300 were discovered as part of the Calánn-Tololo Survey follow up (2).., CTCV 2354 and CTCV 1300 were discovered as part of the Calánn-Tololo Survey follow up \citep{tappert2004}. During the ollow up. both systems were found to be eclipsing with orbital periods of 94.4. ancl 128.1 minutes. respectively.," During the follow up, both systems were found to be eclipsing with orbital periods of 94.4 and 128.1 minutes, respectively." Basie. non-time resolved. spectroscopic data was obtained or cach system.," Basic, non-time resolved, spectroscopic data was obtained for each system." The spectrum. of CECV. 1300. showed eatures typical of the three main components in. CVs: strong emission lines from the accretion disc. broad. shallow absorption features from the white chwarl and red continuum ancl absorption bands from the donor.," The spectrum of CTCV 1300 showed features typical of the three main components in CVs: strong emission lines from the accretion disc, broad, shallow absorption features from the white dwarf and red continuum and absorption bands from the donor." CTCV. 2354. was found to contain strong emission lines of LE and Hoe. generally typical of a dwarf nova in quiescence.," CTCV 2354 was found to contain strong emission lines of H and He, generally typical of a dwarf nova in quiescence." SDSS 1152 was identified as a CV by 7., SDSS 1152 was identified as a CV by \citet{szkody2007}. The svstem shows broad. double-peaked. Balmer emission lines. which are characteristic of a high-inclination. accreting binary.," The system shows broad, double-peaked, Balmer emission lines, which are characteristic of a high-inclination accreting binary." Follow up work by ο found the svstem to have an orbital period of 97.5 minutes., Follow up work by \citet{southworth2010} found the system to have an orbital period of 97.5 minutes. In this paper we present Dight curves of οον 1300 (ον. CECV. 2354. Gg) and SDSS 1152 Clg). and in cach case attempt to determine the system parameters via light curve modelling.," In this paper we present light curves of CTCV 1300 $u'g'r'i'$ ), CTCV 2354 $u'g'r'$ ) and SDSS 1152 $u'g'r'$ ), and in each case attempt to determine the system parameters via light curve modelling." In. addition. we also present an updated analysis of all eclipsing svstenis previously published by our group: OU. Vir (Feline et. al.," In addition, we also present an updated analysis of all eclipsing systems previously published by our group: OU Vir (Feline et al." 2004a). NZ Evi and DV UMa (Feline et al.," 2004a), \nocite{feline2004a} XZ Eri and DV UMa (Feline et al." 2004b). SDSS J1702|3229 (Littlefair et al.," 2004b), \nocite{feline2004b} SDSS J1702+3229 (Littlefair et al." 20062) DSS J1035|0551 (Littlefair et al.," 2006a), \nocite{littlefair2006a} SDSS J1035+0551 (Littlefair et al." 2006b. 2008). SDSS 150722|523039E (??)ον SDSS JO908|3300. SDSS J1227|5189.). SDSS J14333|1011. SDSS J150115501 and SDSS J1502|33343 (2)..," 2006b, 2008), \nocite{littlefair2006b, littlefair2008} SDSS J150722+523039 \citep{littlefair2007, littlefair2008}, SDSS J0903+3300, SDSS J1227+5139, SDSS J1433+1011, SDSS J1501+5501 and SDSS J1502+3334 \citep{littlefair2008}." Our primary reason for doing so was the introduction of a new analysis utilising Markov. Chain Monte Carlo (AICAIC) techniques and an updated bright spot model., Our primary reason for doing so was the introduction of a new analysis utilising Markov Chain Monte Carlo (MCMC) techniques and an updated bright spot model. Phe MCMC analysis is more reliable at converging to a best fit than the downhill simplex algorithm used: previously. while the new bright," The MCMC analysis is more reliable at converging to a best fit than the downhill simplex algorithm used previously, while the new bright" mean flat field nuage was formed from many exposures to a tunesten lamp shiuiug off a reflector iu the come iad was usec to rectify the yixcLto-pixel variations.,mean flat field image was formed from many exposures to a tungsten lamp shining off a reflector in the dome and was used to rectify the pixel-to-pixel variations. The skv fat was eniploved. to map the response of the system in the cross dispersion direction. tli15 correcting aiv vienettius 1i the optical xvsteui or variation in «it trausimission.," The sky flat was employed to map the response of the system in the cross dispersion direction, thus correcting any vignetting in the optical system or variation in slit transmission." Tie exposures of the Noon axl Areou lamps were enploved o fit the known wavelengths of the comparison ines aud the spectra were rebinned into channels of constant waveleustji width bv fitting thir order polvuonials., The exposures of the Neon and Argon lamps were employed to fit the known wavelengths of the comparison lines and the spectra were rebinned into channels of constant wavelength width by fitting third order polynomials. Figre 2 shows the long slit spectra centred on PNà55601 orned by averagiug (with cosmic rav rejection) the first four exposures on April 03 (Table 2)., Figure 2 shows the long slit spectrum centred on 5601 formed by averaging (with cosmic ray rejection) the first four exposures on April 03 (Table 2). The other two PN (5619 and 5621) are clearly visible from their |O III] line euissiou., The other two PN (5619 and 5621) are clearly visible from their [O III] line emission. In addition there are a nmnunber of continuuni sources detected. sole of which are probadv stellar clusters in NGC 5128.," In addition there are a number of continuum sources detected, some of which are probably stellar clusters in NGC 5128." There in a faut red sar displaced less than one secing disc from the PNZE55601 aud. visible in Fie., There is a faint red star displaced less than one seeing disc from the 5601 and visible in Fig. 2., 2. The bright contiuuuu source closest to PNZ555619 was the one used in attempting to correct for differential refraction slit losses., The bright continuum source closest to 5619 was the one used in attempting to correct for differential refraction slit losses. " Spectra of the PN. aud the referenceΣο Με, Were extracted from cach image using optimal weielting after subtracting the imean sky from the vicinity of t1ο objects."," Spectra of the PN, and the reference star, were extracted from each image using optimal weighting after subtracting the mean sky from the vicinity of the objects." The atmospheric extiicfion was corrected for cach exposure aud absolute fhx calibration applied from the observation of the spectropiotonietrie standard., The atmospheric extinction was corrected for each exposure and absolute flux calibration applied from the observation of the spectrophotometric standard. T backeround contained a substanial contribution of galaxy helt. especially for 100: so it was necessary to restrict the background region o be close to the PN (wihi typically at least three times as niuiv pixels iu the sk as in the extracted PN).," The background contained a substantial contribution of galaxy light, especially for 4001 so it was necessary to restrict the background region to be close to the PN (with typically at least three times as many pixels in the sky as in the extracted PN)." After extraction ind removal of cosunic ravs. the individual spectra were flux calibrated.," After extraction and removal of cosmic rays, the individual spectra were flux calibrated." The spectra of the reference coutiuuui source fiLL cach exposure were compared., The spectra of the reference continuum source from each exposure were compared. The spectra srowed a very aree difference., The spectra showed a very large difference. Spectra taken before transit of the sar indicated au upward correction to the blue fluxes and a downward correction to red fuxes relative to he sSpectruni aken at the lowest aiass., Spectra taken before transit of the star indicated an upward correction to the blue fluxes and a downward correction to red fluxes relative to the spectrum taken at the lowest airmass. " For the spec‘a taken afer ransit of the star a dowisvard correction to the bτο Huxes and an upward correction to red fhNCS, relative o the spectrum taken at the lowest airinass. was fouIck."," For the spectra taken after transit of the star a downward correction to the blue fluxes and an upward correction to red fluxes, relative to the spectrum taken at the lowest airmass, was found." Ἠοπονο apvius such corrections to the extracted PN spectra eave inconsistent liue fluxes in the seuse flat he correction factors were too steep with wavelength aud resul5 in discordant spectra from before and after neridiau passage., However applying such corrections to the extracted PN spectra gave inconsistent line fluxes in the sense that the correction factors were too steep with wavelength and resulted in discordant spectra from before and after meridian passage. The explanation for the derivation of such 1urealistically large corrections is unclear., The explanation for the derivation of such unrealistically large corrections is unclear. The contiuuuni source could be extended (c.g. be a cluster iu NGC 5128 itself) aud have ditfereut. colours iu differcut rOeglons: rowever this seems unlikelv since exactly t1ο same behaviour was exhibited by the reference spectra for the oher targets., The continuum source could be extended (e.g. be a cluster in NGC 5128 itself) and have different colours in different regions; however this seems unlikely since exactly the same behaviour was exhibited by the reference spectra for the other targets. The most probable explanation i that the slit rotates slightlv during the course of t observations so that the flux received in the slit track across the nuage m opposite directious on either side of the meridian. cxagecrating the effects of differential atmospheric extinction.," The most probable explanation is that the slit rotates slightly during the course of the observations so that the flux received in the slit tracks across the image in opposite directions on either side of the meridian, exaggerating the effects of differential atmospheric extinction." It was found that the line ratios of the extracted (aud extiuctiou corrected) PN spectra did not vary systematically with airmass bevond the errors of nieasurenmen., It was found that the line ratios of the extracted (and extinction corrected) PN spectra did not vary systematically with airmass beyond the errors of measurement. In addition the Ine ratios in the exracted spectra did not differ from those of the broad sli exposure of PN455601 ]o» iore than the errors. although fix determiation of the Ta lilC Was luupered. by the broadened skv lines.," In addition the line ratios in the extracted spectra did not differ from those of the broad slit exposure of 5601 by more than the errors, although flux determination of the $\alpha$ line was hampered by the broadened sky lines." " Since euission lines were onlv cleected over the wavelength rauge £50) toOAL. aud the differenial atmospheric refractioLis y* over this Yaise for an airniass of l.L. then in 1.5 seclis with a 1.5"" slit the «iffereutial fux loss was at juiaxinuuu (see Fie."," Since emission lines were only detected over the wavelength range 4500 to, and the differential atmospheric refraction is $''$ over this range for an airmass of 1.4, then in $''$ seeing with a $''$ slit the differential flux loss was at maximum (see Fig." l of Jacoby Ivaler 1993))., 1 of Jacoby Kaler \cite{jaka}) ). Tlis overall ouly siuall losses iu spectrophotometric integrity of the combined spectra shotId result., Thus overall only small losses in spectrophotometric integrity of the combined spectra should result. The fiuxed sjvectra for each PN were averaged (using weights based ο1 exposure time) on at se by case basis excludiug the last exposure at hiehest annuass to orm the final PN spectra., The fluxed spectra for each PN were averaged (using weights based on exposure time) on a case by case basis excluding the last exposure at highest airmass to form the final PN spectra. The extracted spectrun of the jet filament weis treaed similarly., The extracted spectrum of the jet filament was treated similarly. Figure 3 shows the mean specra of the five PN observed in Cen-A. The red star coutiuuuu under PN355601 could not be effectively subtracted., Figure 3 shows the mean spectra of the five PN observed in Cen-A. The red star continuum under 5601 could not be effectively subtracted. The emission lines were iuteractivelv fitted by. Cassiai aud the flux in the lines are listed in Tables 3 aud { for each PN aud the filament., The emission lines were interactively fitted by Gaussians and the flux in the lines are listed in Tables 3 and 4 for each PN and the filament. Iu Table 3 the hue flux data or the three brielter PN are collected., In Table 3 the line flux data for the three brighter PN are collected. The errors 1 Tade 3 take iuto account the continua uuder the line aud t16 photon noise im the skv-subtracted spectra: the errors ou the IL? flux have been propagated to the other line flux errors., The errors in Table 3 take into account the continuum under the line and the photon noise in the sky-subtracted spectra; the errors on the $\beta$ flux have been propagated to the other line flux errors. The measured signal-to-noise ou the [O Ine fiux for the brightest PN 5601) is 55., The measured signal-to-noise on the [O line flux for the brightest PN (5601) is 55. The reddening COYICCjon was calculated by comparing the observed IIo /ILj ratio to the Case D valο using the Seaton (1979)) Galactic reddening law aud is listed in Table 3., The reddening correction was calculated by comparing the observed $\alpha$ $\beta$ ratio to the Case B value using the Seaton \cite{seat}) ) Galactic reddening law and is listed in Table 3. The dereddened line fluxes (the error on the extinetion was lot propagaed to the dereddeued. lue errors) together with the observed IT. flux are listed in Table 3., The dereddened line fluxes (the error on the extinction was not propagated to the dereddened line errors) together with the observed $\beta$ flux are listed in Table 3. Tn Table l1 the fluxes are preseuted for the two fainter PN aud he filament near 11902., In Table 4 the fluxes are presented for the two fainter PN and the filament near 1902. The errors are substautiallv arecr than for the data presented in Table 3. since the PN are fainter: for example for PN3:55619. the signal-to-noise on the measurement of the |O line is 9.," The errors are substantially larger than for the data presented in Table 3, since the PN are fainter; for example for 5619, the signal-to-noise on the measurement of the [O line is 9." The five PN observed in NGC 5128 show spectra chtirely typical of PN: the spectra are not obviously distinguishable from those of Galactic PN., The five PN observed in NGC 5128 show spectra entirely typical of PN; the spectra are not obviously distinguishable from those of Galactic PN. Although the signal-to-noise is not high. the range of line fixes. absolute," Although the signal-to-noise is not high, the range of line fluxes, absolute" It is normally considered physically reasonable that the stars closest to centre of a galaxy. close to the bottom of the potential well. should have the highest velocity dispersions.,"It is normally considered physically reasonable that the stars closest to centre of a galaxy, close to the bottom of the potential well, should have the highest velocity dispersions." In other words. a radial plot of velocity dispersion across a galaxy should peak on the nucleus.," In other words, a radial plot of velocity dispersion across a galaxy should peak on the nucleus." This prediction. however. would be predicated on the isotropy of the stellar orbits in a spheroid in equilibrium under gravity with its mass centrally concentrated.," This prediction, however, would be predicated on the isotropy of the stellar orbits in a spheroid in equilibrium under gravity with its mass centrally concentrated." As the angular resolution of spectroscopic data has improved. detailed measurements on nearby galaxies have shown in some galaxies an unexpected drop in the stellar velocity dispersion as the nucleus is approached. a phenomenon referred to as a dispersion drop or o-drop (Emsellem et al.," As the angular resolution of spectroscopic data has improved, detailed measurements on nearby galaxies have shown in some galaxies an unexpected drop in the stellar velocity dispersion as the nucleus is approached, a phenomenon referred to as a dispersion drop or $\sigma$ -drop (Emsellem et al." 2001: Emsellem 2004))., 2001; \cite{EM04}) ). One of the first known examples of this phenomenon can be found in Jarvisetal.(1988). later results include those reported by Jarvis&Peletier(1991).. Bottema (1993). Van der Marel (1994). Bertola et al. (," One of the first known examples of this phenomenon can be found in \cite{JA88}, later results include those reported by \cite{JA91}, Bottema (1993), Van der Marel (1994), Bertola et al. (" "1996). Bottema Gerritsen (1997). Fisher (1997). Simien Prugniel (1997a. b. and ο), Hérraudeau Simien (1998). Simien Prugniel (1998). Hérraudeau et al. (","1996), Bottema Gerritsen (1997), Fisher (1997), Simien Prugniel (1997a, b, and c), Hérraudeau Simien (1998), Simien Prugniel (1998), Hérraudeau et al. (" "1999), Simien Prugniel (2000). Emsellem et al. (","1999), Simien Prugniel (2000), Emsellem et al. (" 2001). Simien Prugniel (2002). de Zeeuw et al. (,"2001), Simien Prugniel (2002), de Zeeuw et al. (" 2002). Aguerri et al. (,"2002), Aguerri et al. (" 2003). Márrquez et al.(2003). Shapiro et al. (,"2003), Márrquez et al.(2003), Shapiro et al. (" 2003). Chung Bureau (2004). Faleónn-Barroso et al. (,"2003), Chung Bureau (2004), Falcónn-Barroso et al. (" 2006). Ganda et al. (,"2006), Ganda et al. (" 2006). Emsellem et al. (,"2006), Emsellem et al. (" 2006). and Dumas et al. (,"2006), and Dumas et al. (" 2007).,2007). The frequency of o-drops in galaxy populations has still not been determined with precision. but estimates currently go as high as of dise. galaxies (from the previously cited articles).," The frequency of $\sigma$ -drops in galaxy populations has still not been determined with precision, but estimates currently go as high as of disc galaxies (from the previously cited articles)." They have been found in à wide variety of galaxy types in both active and non-active galaxies., They have been found in a wide variety of galaxy types in both active and non-active galaxies. A few cases have been observed in lenticular and elliptical galaxies (Emsellem 2006)., A few cases have been observed in lenticular and elliptical galaxies (Emsellem 2006). Explanations have been proposed for this phenomenon with theoretical arguments and also using numerical simulations., Explanations have been proposed for this phenomenon with theoretical arguments and also using numerical simulations. For dise galaxies a scenario has been proposed in. which the stellar population in a o-drop galaxy was formed from a circumnuclear rapidly rotating dynamically cool gaseous component., For disc galaxies a scenario has been proposed in which the stellar population in a $\sigma$ -drop galaxy was formed from a circumnuclear rapidly rotating dynamically cool gaseous component. The stars inherit the velocity pattern of the gas from which they form. so their velocity dispersion is lower than that of the older. ‘underlying’ stars.," The stars inherit the velocity pattern of the gas from which they form, so their velocity dispersion is lower than that of the older, `underlying' stars." A young stellar population dominates an older population in luminosity. so the resulting spectrum Is dominated by the lower velocity dispersion. of the younger stars (see. e.g.. Wozniaketal.2003.. also Allard et al.," A young stellar population dominates an older population in luminosity, so the resulting spectrum is dominated by the lower velocity dispersion of the younger stars (see, e.g., \cite{WO03}, also Allard et al." 2005. 2006).," 2005, 2006)." This effect can be enhanced by a falling velocity dispersion of the gas towards the centre of a galaxy. due to a strong accumulation of gas in a dissipative disc that would cool the gas in a cold component (i.e.. a cold dise as shown in Faleónn-Barroso et al.," This effect can be enhanced by a falling velocity dispersion of the gas towards the centre of a galaxy, due to a strong accumulation of gas in a dissipative disc that would cool the gas in a cold component (i.e., a cold disc as shown in Falcónn-Barroso et al." 2006)., 2006). Hydro/N-body simulations (Wozniak&Champavert 2006)) have shown that a c-drop ean form in less than MMyr. but that its lifetime can exceed GGyr if the nuclear zone is continually fed with gas to sustain star formation.," $N$ -body simulations \cite{WO06}) ) have shown that a $\sigma$ -drop can form in less than Myr, but that its lifetime can exceed Gyr if the nuclear zone is continually fed with gas to sustain star formation." This continued formation of stars is required to maintain a Jong term o-drop. which in turn is required for the observed large o-drop fraction among the galaxy population.," This continued formation of stars is required to maintain a long term $\sigma$ -drop, which in turn is required for the observed large $\sigma$ -drop fraction among the galaxy population." When star formation ceases. dynamical relaxation will cause the o-drop to dissipate in a time-scale that goes from few hundred Myr for short-lived o-drops (circumnuclear volume feeding during less than MMvr) to the order of GGyr or even more for long-lived c-drops (see Fig.," When star formation ceases, dynamical relaxation will cause the $\sigma$ -drop to dissipate in a time-scale that goes from few hundred Myr for short-lived $\sigma$ -drops (circumnuclear volume feeding during less than Myr) to the order of Gyr or even more for long-lived $\sigma$ -drops (see Fig." 2 in Wozniak&Champavert 2006))., 2 in \cite{WO06}) ). Although this model is considered not only. plausible but probable. there are a number of alternatives.," Although this model is considered not only plausible but probable, there are a number of alternatives." À massive. concentrated dark matter halo could remove kinetic. energy from the stellar component.," A massive, concentrated dark matter halo could remove kinetic energy from the stellar component." Numerical simulations of this effect can be found in Athanassoula Misiriotis (2002). their Fig.," Numerical simulations of this effect can be found in Athanassoula Misiriotis (2002), their Fig." 13., 13. In this model the nassive halo gives rise to a strong bar. and the c-peak is suppressed compared with galaxies having smaller halos.," In this model the massive halo gives rise to a strong bar, and the $\sigma$ -peak is suppressed compared with galaxies having smaller halos." However. these numerical simulations are only done with particles (stars) and do not take into account the effects of gas concentration in the galactic centre.," However, these numerical simulations are only done with particles (stars) and do not take into account the effects of gas concentration in the galactic centre." " It has also been argued (Dressler&Richstone 1990)) that a o-drop might be a symptom of the absence of a central supermassive black hole. but vanderMarel(1994) argues against this that a cause might even be the widening of spectral line wings in the presence of a black hole. giving rise to an apparent reduction Ino,"," It has also been argued \cite{DR90}) ) that a $\sigma$ -drop might be a symptom of the absence of a central supermassive black hole, but \cite{MA94} argues against this that a cause might even be the widening of spectral line wings in the presence of a black hole, giving rise to an apparent reduction in $\sigma$." In this article we present a statistical study of 20 of these o-drop galaxies. and match the sample with a control sample to see if we can identify characteristics which distinguish the overall morphologies of the «-drop hosts.," In this article we present a statistical study of 20 of these $\sigma$ -drop galaxies, and match the sample with a control sample to see if we can identify characteristics which distinguish the overall morphologies of the $\sigma$ -drop hosts." In Section 2 we explain the sample selection criteria. and give a brief description of the resulting samples.," In Section 2 we explain the sample selection criteria, and give a brief description of the resulting samples." In Section 3, In Section 3 Whittet el al. (,Whittet el al. ( 1987).,1987). Models of spherical envelopes which account for the observed spectral energy distributions of Herbig Be stars all predict strong silicate emission (Berilli et. al., Models of spherical envelopes which account for the observed spectral energy distributions of Herbig Be stars all predict strong silicate emission (Berilli et al. 1992. Miroshnichenko et al.," 1992, Miroshnichenko et al." 1997)., 1997). In order to explain the suppression of the silicate emission feature in a BO star. the inner radius of the envelope must be about 0.02 pe (Natta et al.," In order to explain the suppression of the silicate emission feature in a B0 star, the inner radius of the envelope must be about 0.02 pc (Natta et al." 2000)., 2000). This is inconsistent with our diffraction-limited mid-infrared images. which show that the bulk of flux from IRSI arises from à true point source. re. the radius of the emitting region is « 400 AU.," This is inconsistent with our diffraction-limited mid-infrared images, which show that the bulk of flux from IRS1 arises from a true point source, i.e. the radius of the mid-infrared emitting region is $\rm <$ 400 AU." We estimate the star formation efficiency SFE = Μες Με in the central region ISOSS J 2029843559-FIRI., We estimate the star formation efficiency SFE = $_{stars}$ / $_{tot}$ in the central region ISOSS J 20298+3559-FIR1. Με includes the masses of the diffuse component. the dense core and all young stellar objects.," $_{tot}$ includes the masses of the diffuse component, the dense core and all young stellar objects." We have determined the masses for the near-infrared objects IRS2..5 from the absolute mass relation by Carpenter et al. (, We have determined the masses for the near-infrared objects IRS2..5 from the absolute magnitude-mass relation by Carpenter et al. ( 1993).,1993). Concerning the masses of the Class 0 sources SMMI and SMM3 we assume that they loose 50 of their envelopes during their further evolution (Bachiller et., Concerning the masses of the Class 0 sources SMM1 and SMM3 we assume that they loose 50 of their envelopes during their further evolution (Bachiller et. al., al. 1996)., 1996). The mass of all young stellar objects is then M... 20 ..., The mass of all young stellar objects is then $_{stars}$ = 20 $_{\odot}$. " Adding the mass of gas and dust in FIR to the stellar masses we obtain Mj, = 140 ..", Adding the mass of gas and dust in FIR1 to the stellar masses we obtain $_{tot}$ = 140 $_{\odot}$. This results in a star formation efficiency of about 14%., This results in a star formation efficiency of about 14. . To compare: The SFE is about 2-9 for the Taurus complex (Cohen Kuhi 1979) and 1-9 in Orion A+B (Carpenter 2000)., To compare: The SFE is about 2-9 for the Taurus complex (Cohen Kuhi 1979) and 1-9 in Orion A+B (Carpenter 2000). ISOSS J 2029843559-FIRI clearly has at least the efficiency of these low- and high-mass star forming regions., ISOSS J 20298+3559-FIR1 clearly has at least the efficiency of these low- and high-mass star forming regions. We have identified the young star forming region ISOSS J 2029843559 performing a cross-correlation of cold compact far-infrared sources from the ISOPHOT 170 jim Serendipity Survey database with the 2MASS. MSX and IRAS surveys.," We have identified the young star forming region ISOSS J 20298+3559 performing a cross-correlation of cold compact far-infrared sources from the ISOPHOT 170 $\mu$ m Serendipity Survey database with the 2MASS, MSX and IRAS surveys." Multi-wavelength follow-up observations of this region yield: We thank the referee. Debra Shepherd. for useful comments.," Multi-wavelength follow-up observations of this region yield: We thank the referee, Debra Shepherd, for useful comments." The ISOPHOT Data Center at MPIA is supported by Deutsches Zentrum fürr Luft- und Raumfahrt e.V. (DLR) with funds of Bundesministerium fürr Bildung und Forschung. grant No.," The ISOPHOT Data Center at MPIA is supported by Deutsches Zentrum fürr Luft- und Raumfahrt e.V. (DLR) with funds of Bundesministerium fürr Bildung und Forschung, grant No." 500I0201., 50QI0201. OK thanks the Wernher von Braun-Stiftung zur Fórrderung der Weltraumwissenschaften e.V. for financial support., OK thanks the Wernher von Braun-Stiftung zur Förrderung der Weltraumwissenschaften e.V. for financial support. This study made use of the SIMBAD database operated at CDS. Strasbourg. France.," This study made use of the SIMBAD database operated at CDS, Strasbourg, France." HIRES images were provided by the Infrared. Processing and Analysis Center., HIRES images were provided by the Infrared Processing and Analysis Center. This publication makes use of data products from the Two Micron All Sky Survey. which is a joint project of," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of" a Solar mass. while lower mass fragments form stars later in the evolution due to the compression of gas to higher densities as it [alls into existing stellar clusters (77)..,"a Solar mass, while lower mass fragments form stars later in the evolution due to the compression of gas to higher densities as it falls into existing stellar clusters \citep*{BatBonBro2002a,BonClaBat2008}." Low and intermediate mass stars located in the centre of forming clusters continue to accreted from the infalline σας and come high-mass stars (e.g.77).," Low and intermediate mass stars located in the centre of forming clusters continue to accreted from the infalling gas and become high-mass stars \citep*[e.g.][]{ BonVinBat2004, SmiLonBon2009}." This produces a mass ‘unction that resembles the stellar IME at all points during he evolution with a continuous source of low mass stars orming with a decreasing subset of these accreting to ever ueher masses., This produces a mass function that resembles the stellar IMF at all points during the evolution with a continuous source of low mass stars forming with a decreasing subset of these accreting to ever higher masses. Phe high-mass end of the EME is somewha latter than Salpeter (2)., The high-mass end of the IMF is somewhat flatter than Salpeter \citep{Maschbergeretal2010}. Phis leaves room for the acdcditiona ohvsies of feedback. [rom massive stars and. the expectec decrease in efficiency. of massive star formation., This leaves room for the additional physics of feedback from massive stars and the expected decrease in efficiency of massive star formation. Note tha ov the massive stars attain their high-mass status through ongoing accretion over relatively long time-periods (7). such hat their feedback could only alfect the cloud after much of he star formation has occurred., Note that by the massive stars attain their high-mass status through ongoing accretion over relatively long time-periods \citep{BonVinBat2004} such that their feedback could only affect the cloud after much of the star formation has occurred. The cloud. produces a variety of outcomes in terms of he distribution of stellar masses. clustered and distributec modes of star formation as well as the clliciency of. the star formation process.," The cloud produces a variety of outcomes in terms of the distribution of stellar masses, clustered and distributed modes of star formation as well as the efficiency of the star formation process." These all depenc largely on the initial. conditions of the cloud. and in particular to how eravitationally bound. the cloud. is. locally., These all depend largely on the initial conditions of the cloud and in particular to how gravitationally bound the cloud is locally. The density eracient that is imposed along the major axis. in conjunction with a constant specific kinetic energy of the eas. results in a local variation of the gravitational binding.," The density gradient that is imposed along the major axis, in conjunction with a constant specific kinetic energy of the gas, results in a local variation of the gravitational binding." Measured in terms of the critical mass per unit length to be bound. this variation extends from Al/£L=0.6 Cunbound) to MfL=1.4 (bound with the cloud overall having a AZ/L=1.," Measured in terms of the critical mass per unit length to be bound, this variation extends from $M/L=0.6$ (unbound) to $M/L=1.4$ (bound with the cloud overall having a $M/L=1$." The evolution produced a number of high density clusters as well as a distributed. population of stars., The evolution produced a number of high density clusters as well as a distributed population of stars. The clusters form preclominanthy in the (upper) bound regions of the cloud., The clusters form predominantly in the (upper) bound regions of the cloud. The clusters form. through the fragmentation. of local overdense filamentary structures that arise due to the turbulence. especially where such filaments intersect.," The clusters form through the fragmentation of local overdense filamentary structures that arise due to the turbulence, especially where such filaments intersect." Stars fall into local potential wells ancl form small-N clusters which quickly grow by accreting other stars (ancl eas) that [low along the filaments into the cluster potential., Stars fall into local potential wells and form small-N clusters which quickly grow by accreting other stars (and gas) that flow along the filaments into the cluster potential. Phe merger of, The merger of "Ultra-luminous X-ray (ULX) sources are ;»oint like. nonnuclear sources observed at other galaxies. with observed luminosities greater than the Eddington luminosity for a IOM,. stellar mass black hole (BH). with LyzI0 ergs| (Fabpiano[989)..","Ultra-luminous X-ray (ULX) sources are point like, nonnuclear sources observed at other galaxies, with observed luminosities greater than the Eddington luminosity for a $10\,{\rm M}_{\odot}$ stellar mass black hole (BH), with $L_{X}{\ge}10^{39}$ ${\rm erg\,s^{-1}}$ \citep{f1}." The true nature of these objects is still open to debate (Miller&Col-bert 2004)., The true nature of these objects is still open to debate \citep{mc1}. . One fundamental issue is whether the emission is isotropic or beamed along our line-of-sigh., One fundamental issue is whether the emission is isotropic or beamed along our line-of-sight. A possible scenario for geometrical beaming involves super-Eddington accretion during phases of thermal-timescale mass ransfer (King2002)., A possible scenario for geometrical beaming involves super-Eddington accretion during phases of thermal-timescale mass transfer \citep{k1}. . Alternatively. if the emission is isotropic and the Eddington limit is not violated. ULX must be fuelled by accretion onto Intermediate-BH UMBH). with masses in the range 100-100000. M. (Colbert&Mushotzky1999).," Alternatively, if the emission is isotropic and the Eddington limit is not violated, ULX must be fuelled by accretion onto Intermediate-MassBH (IMBH), with masses in the range 000 ${\rm M}_{\odot}$ \citep{cm1}." .. Currently. here is no agreement regarding the nature of these sources.," Currently, there is no agreement regarding the nature of these sources." It is [xyssible that some ULX appear very luminous because of a combination of moderately high mass. mild beaming and mild super-Eddingon emission.," It is possible that some ULX appear very luminous because of a combination of moderately high mass, mild beaming and mild super-Eddington emission." It is also possible that ULX are an inhomogeneous po»ulation. comprised of both a subsample of IMBH and moderately beamed stellar mass black holes (Fabbiano&White2006:MillerColbert2004...," It is also possible that ULX are an inhomogeneous population, comprised of both a subsample of IMBH and moderately beamed stellar mass black holes \citep{f2,mc1}." NGC 5408 ΧΙ. HOLM II X-1. M 81 X-9 (which is in the companion-dwarf galaxy Holmberg IX. hereafter called HOLM IX X-1). the ULX in NGC 1313 and M 81 X-6 are ULX located in dwarf (NGC 5408 X-1. HOLM II X-1 and HOLM IX ΧΙ) and spiral (NGC 1313 Κι. NGC 1313 X and M 81 X—6) galaxies. respectively.," NGC 5408 X–1, HOLM II X–1, M 81 X–9 (which is in the companion-dwarf galaxy Holmberg IX, hereafter called HOLM IX X–1), the ULX in NGC 1313 and M 81 X–6 are ULX located in dwarf (NGC 5408 X–1, HOLM II X–1 and HOLM IX X–1) and spiral (NGC 1313 X–1, NGC 1313 X–2 and M 81 X–6) galaxies, respectively." All these ULX peak in X-ray luminosity above Ly=Dxl0 eres!. thus being excellent targets for testing spectral models to the data.," All these ULX peak in X-ray luminosity above $L_{X}=1{\times}10^{40}$ ${\rm erg\,s^{-1}}$, thus being excellent targets for testing spectral models to the data." They are nearby and located at distances of D—3.7.3.63.4.50 MMpe (Karachentsev2002:Stobbartetal.&DiStefano 20081). for NGC 5408 ΧΙ HOLM IX X-1. NGC 1313 ΧΙ. M81 X-6 and HOLM II X-1 respectively.," They are nearby and located at distances of $D=4.8,3.5,3.7,3.63,4.50$ Mpc \citealt{karachentsev02,stobbart06,liu08}) ), for NGC 5408 X–1, HOLM IX X–1, NGC 1313 X–1, M 81 X–6 and HOLM II X–1 respectively." NGC 5408 X-1 is among the few ULX for which mmHz) Quasi-Periodic Oscillations (ΟΡΟ) have been found (Strohmayeretal.2007:Dewangan 2006).," NGC 5408 X–1 is among the few ULX for which mHz) Quasi-Periodic Oscillations (QPO) have been found \citealt{stroh1,dewangan06}) )." NGC S408 X-1 exhibits X- timing and spectral properties analogous to those exhibited by Galactic stellar-mass black hole in the orpower-law state (Remillard&McClintock2006).. but with the characteristic variability timescales (QPO and break frequencies) consistently scaled down (Strohmayeretal.," NGC 5408 X-1 exhibits X-ray timing and spectral properties analogous to those exhibited by Galactic stellar-mass black hole in the or state \citep{remi1}, but with the characteristic variability timescales (QPO and break frequencies) consistently scaled down \citep{stroh1}." 2007).. For NGC 5408 X-1 the inferred characteristic size for the X-ray emitting region is = 100 times larger than the typical inner disk radii of Galactic black holes., For NGC 5408 X–1 the inferred characteristic size for the X-ray emitting region is ${\approx}$ 100 times larger than the typical inner disk radii of Galactic black holes. The highest signal-to-noise spectra of ULX can often be fitted by composite models of a thermal disk together with a hard-powerlaw tail. with a low measured disk temperature of 0.2 kkeV (Milleretal.2003. 2004)).," The highest signal-to-noise spectra of ULX can often be fitted by composite models of a thermal disk together with a hard-powerlaw tail, with a low measured disk temperature of ${\approx}0.2$ keV \citealt{miller03,miller04}) )." IIf such factors are entirely due to a higher black hole mass. they impy an IMBH with 47x100—10000 M...," If such factors are entirely due to a higher black hole mass, they imply an IMBH with $M{\approx}100-10\,000$ ${\rm M}_{\odot}$ ." Bothtle morphology and flux of the optical high-excitation nebulae detected around some ULX orobably rule out strong beaming as the origin of the X-ray emission (Pakull&Mirioni2003: 20071).," Both the morphology and flux of the optical high-excitation nebulae detected around some ULX probably rule out strong beaming as the origin of the X-ray emission \citealt{pakull03,kaaret04,soria1,abolmasov07}) )." Figure 2. shows the carly evolution.,Figure \ref{fig:ebfign2} shows the early evolution. Iutially the ucine energv shows laree oscilatious. simaly because he blacs hole particles are not bouud to each other ut orbi within the parent eaaxy in highv eccentric orbits.," Initially the binding energy shows large oscillations, simply because the black hole particles are not bound to each other but orbit within the parent galaxy in highly eccentric orbits." As their orbits shri. threπιο] dvuauical friction. he ampitude of the oscillations becomes snaller. aud eventualv the two black holes )|ecolue boulid.," As their orbits shrink through dynamical friction, the amplitude of the oscillations becomes smaller, and eventually the two black holes become bound." We can see hat the early evolution of the black hole binary. fore the specific binding energy reaches l. is aluost indepencent of N.," We can see that the early evolution of the black hole binary, before the specific binding energy reaches $-1$, is almost independent of $N$ ." Towever. afer Ey reaches —2. the evolution timescale shows a strong dependence ou the ΗΤΟ ¢ot particles.," However, after $E_b$ reaches $-2$, the evolution timescale shows a strong dependence on the number of particles." " To quantitatively evaluate the dependence. of the judenimg rate ou the number of particles. we calculate he hardening rate οὐ, defined as Here. At=fq9ty where fy audfq are the times at which Ej reached the values Fyy aud Eno|AE; respectively."," To quantitatively evaluate the dependence of the hardening rate on the number of particles, we calculate the hardening rate $\beta$ , defined as Here, $\Delta t = t_1 -t_0$ where $t_0$ and$t_1$ are the times at which $E_b$ reached the values $E_{b,0}$ and $E_{b,0}+\Delta E_b$, respectively." " We use AL,=0.5 for all values of Ej."," We use $\Delta E_b=-0.5$ for all values of $E_{b,0}$." Figure 3. shows the result. for Ejíó=1.3.D.7.," Figure \ref{fig:defig} shows the result, for $E_{b,0}=-1,-3,-5,-7$." " When £,=1. the hardening rate is aliiost indepeudout of Αν"," When $E_b=-1$, the hardening rate is almost independent of $N$." Towever. as the binary becomes harder. 3 decreases. and the decrease is larger for larecr Nv.," However, as the binary becomes harder, $\beta$ decreases, and the decrease is larger for larger $N$." Thus. the hardening rate ο) for large values of |E4| shows a strong dependence on the ummber of particles NV.," Thus, the hardening rate $\beta$ for large values of $|E_b|$ shows a strong dependence on the number of particles $N$." This result is exactly what is expected from the simple loss-coue argument: after the loss cone is depleted. 3 should be inversely proportional to the relaxation time. which is proportional to IN.," This result is exactly what is expected from the simple loss-cone argument: after the loss cone is depleted, $\beta$ should be inversely proportional to the relaxation time, which is proportional to $N$." Note that we used a constaut softening. for which the Coulomblogarithi does not depend on NV.," Note that we used a constant softening, for which the Coulomblogarithm does not depend on$N$ ." Tt the loss-cone argument would be correct. writing οκ would let 5 approach unity for huge οποιο V.," If the loss-cone argument would be correct, writing $\beta \propto N^{-\gamma}$ would let $\gamma$ approach unity for large enough $N$ ." in the R-band images.,in the $R$ -band images. This position is fully consistent with the outcome of the NOT observation (Jakobsson et al., This position is fully consistent with the outcome of the NOT observation (Jakobsson et al. 2010) and the enhanced Swift//XRT position (Evans et al., 2010) and the enhanced /XRT position (Evans et al. 2010)., 2010). " In order to separate the two objects, we first used DAOPHOT (Stetson 1987) to obtain the average point spread function (PSF) in each image."," In order to separate the two objects, we first used DAOPHOT (Stetson 1987) to obtain the average point spread function (PSF) in each image." " Then, we used this PSF model to match the afterglow and nearby faint source."," Then, we used this PSF model to match the afterglow and nearby faint source." " Both sources are pointlike, and with this procedure we were able to obtain accurate magnitudes of the optical afterglow."," Both sources are pointlike, and with this procedure we were able to obtain accurate magnitudes of the optical afterglow." " The 2.5-m NOT (longitude=17°53’06.3” W, latitude=28?45'26.2"" N, altitude=2382 m) began observing 1100219A starting on 2010 Feb 20, at 00:11:58.5 UT, about 9 hr after the trigger."," The 2.5-m NOT $\mathrm{longitude} = 17\degr 53\arcmin 06.3\arcsec$ W, $\mathrm{latitude} = 28\degr 45\arcmin 26.2\arcsec$ N, $\mathrm{altitude} = 2382$ m) began observing 100219A starting on 2010 Feb 20, at 00:11:58.5 UT, about 9 hr after the trigger." " After correcting the raw images for the effect of CCD flat and bias, we carried out the R-band photometry using DAOPHOT through the selected unsaturated objects in the images to be consistent with the GMG observation."," After correcting the raw images for the effect of CCD flat and bias, we carried out the $R$ -band photometry using DAOPHOT through the selected unsaturated objects in the images to be consistent with the GMG observation." " Since the NOT observations were carried out under better seeing conditions ( 1.4), the GRB afterglow and the nearby faint object are resolved."," Since the NOT observations were carried out under better seeing conditions $\sim 1.4\arcsec$ ), the GRB afterglow and the nearby faint object are resolved." , For Cluster Analysis we have used (wo methods: one is based on Mixture Models and the other is a partitioning method.,For Cluster Analysis we have used two methods: one is based on Mixture Models and the other is a partitioning method. The mixture model method provides a parametric approach to the clustering problem proposed by Qui Tamhane (2007)., The mixture model method provides a parametric approach to the clustering problem proposed by Qui Tamhane (2007). Here the Expectation-Maxinization (EM) algoritlim is used to compute the maximun likelihood estimators (MLEs) of the parameters of the model., Here the Expectation-Maximization (EM) algorithm is used to compute the maximum likelihood estimators (MLEs) of the parameters of the model. These parameters include mixing proportions. which may be thought of as the prior probabilities of different clusters: then (he maximum posterior (Daves) rule for clustering has been used.," These parameters include mixing proportions, which may be thought of as the prior probabilities of different clusters; then the maximum posterior (Bayes) rule for clustering has been used." The partiüoning method. known as Ix&-means algorithm. is one of the most popular method of clustering developed by MacQueen(1967).," The partitioning method, known as K-means algorithm, is one of the most popular method of clustering developed by MacQueen(1967)." This method is distribution-free in nature. but cannot provide any estimate of misclassification error probabilities of observations.," This method is distribution-free in nature, but cannot provide any estimate of misclassification error probabilities of observations." Qui Tambhane (2007) proved that the mixture model method is a better method of clustering since il vields smaller expected misclassilication rates., Qui Tamhane (2007) proved that the mixture model method is a better method of clustering since it yields smaller expected misclassification rates. To find the optimum munber of clusters (i.e. the value of IX) we have used the method developed by Sugar James (2003)., To find the optimum number of clusters (i.e. the value of K) we have used the method developed by Sugar James (2003). In the present work we have also used the Levenbere-Marquardt algorithm to compute the rotation amplitudes and position angles of the axes of rotation ol different. groups obtained from cluster analvsis., In the present work we have also used the Levenberg-Marquardt algorithm to compute the rotation amplitudes and position angles of the axes of rotation of different groups obtained from cluster analysis. They are listed in last (wo columns at the beginning of each eroup of Table 2 as well as in Table 4., They are listed in last two columns at the beginning of each group of Table 2 as well as in Table 4. All the above mentioned methods are cliseussecl in brief in the appendices., All the above mentioned methods are discussed in brief in the appendices. We took advantage of the method of Lick indices (Faber 1973. Worthev οἱ al.," We took advantage of the method of Lick indices (Faber 1973, Worthey et al." 1994) to disentangle effects of age and metallicity on integrated spectra of elobular clusters., 1994) to disentangle effects of age and metallicity on integrated spectra of globular clusters. A three-dimensional. interpolation. and 4L7 minimization. routine. by Sharina.. Afanasiev," A three-dimensional interpolation and $\chi^2$ minimization routine by Sharina, Afanasiev" A three-dimensional. interpolation. and 4L7 minimization. routine. by Sharina.. AfanasievB," A three-dimensional interpolation and $\chi^2$ minimization routine by Sharina, Afanasiev" A three-dimensional. interpolation. and 4L7 minimization. routine. by Sharina.. AfanasievB.," A three-dimensional interpolation and $\chi^2$ minimization routine by Sharina, Afanasiev" should be pointed out that their. frequency. bands: are overlapping.,should be pointed out that their frequency bands are overlapping. The comparison of the data has. confirmed our above-mentioned. conclusions., The comparison of the data has confirmed our above-mentioned conclusions. All this does not means that we have something against the development. of onc-dipole raclioastronomy and space missions. and rather we want to note their real performance capabilities.," All this does not means that we have something against the development of one-dipole radioastronomy and space missions, and rather we want to note their real performance capabilities." “Phe importance of such one-clipole radio telescopes can scarcely be overestimated for monitoring of solar bursts in Racio and Space Services., The importance of such one-dipole radio telescopes can scarcely be overestimated for monitoring of solar bursts in Radio and Space Services. To cach its own., To each its own. In this context we believe that the erounc-basec support. by large. racioastrononiv instruments will be very useful for the space missions in the sequel., In this context we believe that the ground-based support by large radioastronomy instruments will be very useful for the space missions in the sequel. The WAVIZS instrument is a joint ellort of the Paris-Meudon Observatory. the Universitv of Minnesota. ane the Cocdedare Space Flight Center.," The WAVES instrument is a joint effort of the Paris-Meudon Observatory, the University of Minnesota, and the Goddard Space Flight Center." "these calculations. we use the potential curves without this interaction,","these calculations, we use the potential curves without this interaction." These profiles (Fig. 2)), These profiles (Fig. \ref{profile}) ) were used in the calculation of models and provide a fairly good fit for the red wing: the blue wing is mostly outside the SDSS wavelength range., were used in the calculation of models and provide a fairly good fit for the red wing; the blue wing is mostly outside the SDSS wavelength range. Nevertheless. the current analysis is only a first attempt with a number of shortcomings: By iteration through trial and error we have determined aand abundances and calculated a model. which gives a fairly good fit to the spectrum and photometry of the most feature-rich object. SDSS091642540.," Nevertheless, the current analysis is only a first attempt with a number of shortcomings: By iteration through trial and error we have determined and abundances and calculated a model, which gives a fairly good fit to the spectrum and photometry of the most feature-rich object, SDSS0916+2540." The parameters for this object are == 5500K. log[|Mg/He| = -6.9. log[Ca/He] = -7.6.," The parameters for this object are = 5500K, $\log$ [Mg/He] = $-6.9$ , $\log$ [Ca/He] = $-7.6$ ," In Table 5.. we present the kinematical and structural parameters for the observed clusters.,"In Table \ref{param3}, we present the kinematical and structural parameters for the observed clusters." Column 3 gives the heliocentric radial. velocity (km/s) with the observational (internal) uncertainty; column 4. the radial velocity relative to the local standard of rest: column 5. the concentration parameter (c.= log(refro)): a ο denotes a core-collapsed cluster: columns 6 and 7. the core and the half mass radii in aremin: column 8. the logarithm of the core relaxation time. in years; and column 9 the logarithm of the relaxation time at the half mass radius.," Column 3 gives the heliocentric radial velocity (km/s) with the observational (internal) uncertainty; column 4, the radial velocity relative to the local standard of rest; column 5, the concentration parameter $c = \log (r_{\rm t}/r_{\rm c})$ ); a 'c' denotes a core-collapsed cluster; columns 6 and 7, the core and the half mass radii in arcmin; column 8, the logarithm of the core relaxation time, in years; and column 9 the logarithm of the relaxation time at the half mass radius." Column 10. the central surface brightness in Vy and column 11. the logarithm of central luminosity density (Solar luminosities per cubic parsec).," Column 10, the central surface brightness in $V$; and column 11, the logarithm of central luminosity density (Solar luminosities per cubic parsec)." "burning, time dependent diffusion of the elements and other physical processes that take place in the course of the evolution of a star.","burning, time dependent diffusion of the elements and other physical processes that take place in the course of the evolution of a star." " BK@11 perform “fast white dwarf asteroseismology”, where they guess and parameterize the internal chemical composition profiles and build static models."," 11 perform “fast white dwarf asteroseismology”, where they guess and parameterize the internal chemical composition profiles and build static models." That method allows them a fuller exploration of parameter space., That method allows them a fuller exploration of parameter space. " For KIC 8626021, they find very good fits (hotter than what the preliminary spectroscopy suggests) but also conclude that their internal Oxygen composition profiles are in poor agreement with stellar evolution calculations."," For KIC 8626021, they find very good fits (hotter than what the preliminary spectroscopy suggests) but also conclude that their internal Oxygen composition profiles are in poor agreement with stellar evolution calculations." They suggest further studies to see what the physical parameters of models that agree with stellar evolution calculations would be., They suggest further studies to see what the physical parameters of models that agree with stellar evolution calculations would be. " In essence, this is the kind of study we present here."," In essence, this is the kind of study we present here." " While our best fit models are evidently different, we concur with the conclusion that KIC 8626021 is hotter (and more massive) than suggested by the initial spectroscopic study."," While our best fit models are evidently different, we concur with the conclusion that KIC 8626021 is hotter (and more massive) than suggested by the initial spectroscopic study." " The conclusion that this star is residing at the blue edge of the DBV instability strip appears to be robust, and calls for the necessity of a new and improved spectroscopic determination of its effective temperature."," The conclusion that this star is residing at the blue edge of the DBV instability strip appears to be robust, and calls for the necessity of a new and improved spectroscopic determination of its effective temperature." In Section 2 we present some details about our models and methods., In Section \ref{modeling} we present some details about our models and methods. " In Section 3,, we use the average period spacing of KIC 8626021’s period spectrum to draw some conclusions about its mass and effective temperature."," In Section \ref{avgspacing}, we use the average period spacing of KIC 8626021's period spectrum to draw some conclusions about its mass and effective temperature." We contrast our models to the grid of models computed by BK@11., We contrast our models to the grid of models computed by 11. " In Section 4,, we present our best fit models."," In Section \ref{best-fit}, we present our best fit models." " Again, we contrast our results with those of BK@11."," Again, we contrast our results with those of 11." " In Section 5 we discuss the discrepancies between the results coming from spectroscopy and from asteroseismology, and the differences between our asteroseismological results and those of BK@11."," In Section \ref{discussion} we discuss the discrepancies between the results coming from spectroscopy and from asteroseismology, and the differences between our asteroseismological results and those of 11." We conclude in Section 6.., We conclude in Section \ref{conclusions}. The evolutionary DB white dwarf models employed in this work were presented in Althaus et al. (, The evolutionary DB white dwarf models employed in this work were presented in Althaus et al. ( 2009a) and we refer to that paper for details.,2009a) and we refer to that paper for details. " Briefly, the models were computed with the LPCODE stellar evolutionary code we employed in our previous studies on the formation of PG 1159 and extreme horizontal branch stars (Althaus et al."," Briefly, the models were computed with the LPCODE stellar evolutionary code we employed in our previous studies on the formation of PG 1159 and extreme horizontal branch stars (Althaus et al." 2005; Miller Bertolami Althaus 2006; Miller Bertolami et al., 2005; Miller Bertolami Althaus 2006; Miller Bertolami et al. " 2008), hot DQ white dwarfs (Althaus et al."," 2008), hot DQ white dwarfs (Althaus et al." 2009b) as well as the formation and evolution of He-core white dwarfs with high metallicity progenitors (Althaus et al., 2009b) as well as the formation and evolution of He-core white dwarfs with high metallicity progenitors (Althaus et al. 2009c)., 2009c). " The LPCODE evolutionary code considers a simultaneous treatment of non-instantaneous mixing and burning of elements, which is of primary importance for the calculation of chemical abundance changes during the short-lived evolutionary stages characteristic of unstable burning episodes, like the born-again stage, from which our starting H-deficient white dwarf configurations are derived."," The LPCODE evolutionary code considers a simultaneous treatment of non-instantaneous mixing and burning of elements, which is of primary importance for the calculation of chemical abundance changes during the short-lived evolutionary stages characteristic of unstable burning episodes, like the born-again stage, from which our starting H-deficient white dwarf configurations are derived." Nuclear reaction rates are from Caughlan Fowler (1988) and Angulo et al. (, Nuclear reaction rates are from Caughlan Fowler (1988) and Angulo et al. ( 1999).,1999). " The Ca, y)!°O reaction rate was taken from Angulo et al. ("," The $^{12}$ $(\alpha, \gamma)^{16}$ O reaction rate was taken from Angulo et al. (" "1999), which is about twice as large as that of Caughlan Fowler (1988).","1999), which is about twice as large as that of Caughlan Fowler (1988)." " A moderate, diffusive overshooting in the core and in the envelope is allowed during pre-white-dwarf evolution."," A moderate, diffusive overshooting in the core and in the envelope is allowed during pre-white-dwarf evolution." " For the white dwarf regime, we considered the following main physical ingredients."," For the white dwarf regime, we considered the following main physical ingredients." " Neutrino emission rates for pair, photo, and bremsstrahlung processes are those of Itoh et al. ("," Neutrino emission rates for pair, photo, and bremsstrahlung processes are those of Itoh et al. (" 1996).,1996). " For plasma processes, we use the treatment presented in Haft et al. ("," For plasma processes, we use the treatment presented in Haft et al. (" 1994).,1994). " Radiative opacities are those of the OPAL project (Iglesias Rogers 1996), including C- and O-rich composition."," Radiative opacities are those of the OPAL project (Iglesias Rogers 1996), including C- and O-rich composition." We adopted the conductive opacities of Cassisi et al. (, We adopted the conductive opacities of Cassisi et al. ( 2007).,2007). This prescription covers the whole regime where electron conduction is relevant., This prescription covers the whole regime where electron conduction is relevant. " For the high density regime, we used the equation of state of Segretain et al. ("," For the high density regime, we used the equation of state of Segretain et al. (" "1994), which accounts for all the important contributions for both the liquid and solid phases.","1994), which accounts for all the important contributions for both the liquid and solid phases." " For the low-density regime, we used an updated version of the equation of state of Magni Mazzitelli (1979)."," For the low-density regime, we used an updated version of the equation of state of Magni Mazzitelli (1979)." Convection was treated in the formalism of the mixing-length theory as given by the ML2 parameterization (Tassoul et al., Convection was treated in the formalism of the mixing-length theory as given by the ML2 parameterization (Tassoul et al. 1990)., 1990). All of our white dwarf sequences were computed in a consistent way with the evolution of the chemical abundance distribution caused by element diffusion along the whole cooling phase., All of our white dwarf sequences were computed in a consistent way with the evolution of the chemical abundance distribution caused by element diffusion along the whole cooling phase. " In particular, we considered gravitational settling and chemical diffusion of *He, '?C, °C, ΙΑΝ, and !60."," In particular, we considered gravitational settling and chemical diffusion of $^{4}$ He, $^{12}$ C, $^{13}$ C, $^{14}$ N, and $^{16}$ O." where the range of -Bsin? comes [rom the range of 10'<.éI|x10!vr of the observed SNe rate (Maozeta2011) aud equation (10)).,where the range of $\eta = B \sin \delta$ comes from the range of $ 10^7 \la t \la 10^{10} \yr$ of the observed SNe rate \citep{Maozetal2011} and equation \ref{eq:taub}) ). In this paper we examined the delay time from 1jerger {ο explosiou of the core-degenerate (CD) scenario for SNe Ia. A key iugrecient in tliis scenario is that the mereer occurs while the more lnassive clegenerae component is tlie co‘e of an AGB sar or a planetary nebulae. e.g.. at the eud of the common eivelope pliase or shortly after Such a merger where the more massive WD is still hot. hence larger. is inore likely to avoid au early oll-ceuter iguition of carbon (Yoonetal.2007): an early off-ceuter i[n]enition leads to à Nehgo WD instead of to à SN Ia. The problem of off-center car»on ignition dujug mereer of cold WDs is the most severe problem of tie double degenerate (DD scenario for SNe Ia (Howell2011).," In this paper we examined the delay time from merger to explosion of the core-degenerate (CD) scenario for SNe Ia. A key ingredient in this scenario is that the merger occurs while the more massive degenerate component is the core of an AGB star or a planetary nebulae, e.g., at the end of the common envelope phase or shortly after Such a merger where the more massive WD is still hot, hence larger, is more likely to avoid an early off-center ignition of carbon \citep{Yoon2007}; an early off-center ignition leads to a NeMgO WD instead of to a SN Ia. The problem of off-center carbon ignition during merger of cold WDs is the most severe problem of the double degenerate (DD) scenario for SNe Ia \citep{Howell2011}." . The CD scenario avolls this problem., The CD scenario avoids this problem. The rerinant of the core-degenerate merger is a rapidly rotating WD., The remnant of the core-degenerate merger is a rapidly rotating WD. If its mass is super-critica it will explode alter spiuniug-down toa critical angular velocity Q. (Yoou&Lauger2005).. Iu section 2 we exainiued the spiuning-down ine by the commonly used gravitational waves inechauism.," If its mass is super-critical it will explode after spinning-down to a critical angular velocity $\Omega_c$ \citep{Yoon2005}, In section \ref{sec:gradiation} we examined the spinning-down time by the commonly used gravitational waves mechanism." Altheeh this mechanisiu is snow to be very efficient in spiuniug down neutrou stars. we found that this mechanisin is not elficient in spiulng down WDs (eq. ὃ )).," Although this mechanism is know to be very efficient in spinning down neutron stars, we found that this mechanism is not efficient in spinning down WDs (eq. \ref{eq:taus}) )." It can be efficient only, It can be efficient only (we refer to their Appendix A for a more detailed description).,(we refer to their Appendix A for a more detailed description). The idea behind this method is that the exact contribution to each ring from the external part can be calculated by integrating the volume emission c(r)., The idea behind this method is that the exact contribution to each ring from the external part can be calculated by integrating the volume emission $\epsilon (r)$. Then. the normalization of the power law shape of c(r) is fixed by the requirement of matching the total surface brightness of the last ring.," Then, the normalization of the power law shape of $\epsilon(r)$ is fixed by the requirement of matching the total surface brightness of the last ring." This correction can be expressed as an additional term to eq.€1)). which is proportional to the surface brightness of the last ring: deproj-dgeS| Λα... Here. f; is a geometrical factor which is uniquely specified by the values of the limiting radii of the j-th ring and by the exponen a. Eq.(22))," This correction can be expressed as an additional term to \ref{eq:deproj}) ), which is proportional to the surface brightness of the last ring: S_j = S'_j + f_j, Here, $f_j$ is a geometrical factor which is uniquely specified by the values of the limiting radii of the $j$ -th ring and by the exponent $\alpha$. \ref{eq:deproj_edge}) )" must be actually interpreted as a set of 2/V equations. which corresponds to the separate deprojection of the tSZ and of the X-ray signal. each performed for ;N radial bins.," must be actually interpreted as a set of $2N$ equations, which corresponds to the separate deprojection of the tSZ and of the X–ray signal, each performed for $N$ radial bins." The geometrical deprojection is then performed by inverting each se of AN equations. starting from the outermost bin and proceeding inward.," The geometrical deprojection is then performed by inverting each set of $N$ equations, starting from the outermost bin and proceeding inward." " This procedure provides the radial profiles of η,7). anc of n2A(L). whose combination finally gives the 3D profiles of electron number density and of temperature."," This procedure provides the radial profiles of $n_eT_e$ and of $n_e^2 \Lambda(T)$, whose combination finally gives the 3D profiles of electron number density and of temperature." We emphasize that the temperature so obtained is the actual electron temperature and no the deprojected spectroscopic temperature. usually obtained from the fitting of X-ray spectra.," We emphasize that the temperature so obtained is the actual electron temperature and not the deprojected spectroscopic temperature, usually obtained from the fitting of X–ray spectra." Given the iterative nature of this procedure. the uncertainty associated to each ring propagates not only to the corresponding 3D shell. but also to all the inner shells.," Given the iterative nature of this procedure, the uncertainty associated to each ring propagates not only to the corresponding 3D shell, but also to all the inner shells." For this reason. it is very difficult with this method to have a rigorous derivation of the statistical uncertainties associated to the deprojected profiles.," For this reason, it is very difficult with this method to have a rigorous derivation of the statistical uncertainties associated to the deprojected profiles." " This is particularly true for the X—ray profiles. that also involve a ""erivative of the cooling function with respect to the temperature."," This is particularly true for the X–ray profiles, that also involve a derivative of the cooling function with respect to the temperature." The commonly adopted solution is based on realizing MonteCarlo simulations. over which to compute the errors (e.g.2)..," The commonly adopted solution is based on realizing MonteCarlo simulations, over which to compute the errors \citep[e.g.][]{2002A&A...391..841E}." Furthermore. errors associated to different radial bins are not independent.," Furthermore, errors associated to different radial bins are not independent." This is due to the fact that the projected signal in a given ring is contributed by several shells., This is due to the fact that the projected signal in a given ring is contributed by several shells. The resulting covariance in the signals recovered in different shells is not provided by this deprojection method., The resulting covariance in the signals recovered in different shells is not provided by this deprojection method. This is a rather important point on which we will come back in Section 4., This is a rather important point on which we will come back in Section 4. This technique is based on performing the deprojection by maximizing a likelihood function. which is computed by comparing the observed tSZ and X-ray profiles with the ones obtained by projecting the onion-skin model in the plane of the sky.," This technique is based on performing the deprojection by maximizing a likelihood function, which is computed by comparing the observed tSZ and X–ray profiles with the ones obtained by projecting the onion–skin model in the plane of the sky." This approach offers more than one advantage with respect to the geometrical deprojection. described in the previous section.," This approach offers more than one advantage with respect to the geometrical deprojection, described in the previous section." First. the deprojection of both X-ray and tSZ profiles is performed simultaneously. directly obtaining the whole density and temperature profiles and their errors.," First, the deprojection of both X–ray and tSZ profiles is performed simultaneously, directly obtaining the whole density and temperature profiles and their errors." Second. besides the variance. it is also possible to compute the correlation matrix for all parameters. without any extra computational cost.," Second, besides the variance, it is also possible to compute the correlation matrix for all parameters, without any extra computational cost." Finally. i is possible to introduce in the likelihood extra terms in order to improve the accuracy and robustness of the technique.," Finally, it is possible to introduce in the likelihood extra terms in order to improve the accuracy and robustness of the technique." As we shal describe in the following. we adopt a regularization technique. which is based on imposing a suitable constraint to the likelihood function. to smooth out spurious oscillations in the recovered profiles induced by the covariance in the parameter estimate.," As we shall describe in the following, we adopt a regularization technique, which is based on imposing a suitable constraint to the likelihood function, to smooth out spurious oscillations in the recovered profiles induced by the covariance in the parameter estimate." The definition of the likelihood is the most important par of the whole procedure., The definition of the likelihood is the most important part of the whole procedure. " We define a joint likelihood for the tSZ profile. Z,57. and for the X-ray surface brightness profile. £x. also including a term associated to the regularization constraint. C...reg?"," We define a joint likelihood for the tSZ profile, $\mathcal{L}_{tSZ}$, and for the X–ray surface brightness profile, $\mathcal{L}_{Xray}$, also including a term associated to the regularization constraint, $\mathcal{L}_{reg}^\lambda$." Since these three terms are independent. the total likelihood is given by the product of the individual ones:L," Since these three terms are independent, the total likelihood is given by the product of the individual ones:." e For both the tSZ and the X-ray profiles. the take the Gaussian form for the likelihood. ; where O; are the values of the profiles. in the /-th bin. measured from the maps. while AZ;(.r) are the model-predicted profile values. as obtained for the set ο: of parameters.," For both the tSZ and the X–ray profiles, the take the Gaussian form for the likelihood, = - ^2 = - } _i ( ) ^2, where $O_i$ are the values of the profiles, in the $i$ -th bin, measured from the maps, while $M_i(x)$ are the model–predicted profile values, as obtained for the set $x$ of parameters." Finally. ; is the uncertainty on the measured values O;.," Finally, $\sigma_i$ is the uncertainty on the measured values $O_i$." While the Gaussian expression is adequate for the tSZ signal. its application for the X-ray. instead of the Poisson distribution. requires the number of photons sampling the surface brightness map in each radial shell to be large enough to neglect the Poisson noise.," While the Gaussian expression is adequate for the tSZ signal, its application for the X–ray, instead of the Poisson distribution, requires the number of photons sampling the surface brightness map in each radial shell to be large enough to neglect the Poisson noise." " As we shall discuss in the following. even in the outermost rings. we always have at least 20 photons in the ""noisy"" X-ray maps."," As we shall discuss in the following, even in the outermost rings, we always have at least 20 photons in the “noisy” X–ray maps." For the regularization constraint. we adopt the Philips-Towmey regularization method (2.andreferencestherein)...," For the regularization constraint, we adopt the Philips-Towmey regularization method \citep[][and references therein]{1995A&AS..113..167B}." This method has been already used also by ? to deproject X-ray imaging and spectral data., This method has been already used also by \cite{2006A&A...459.1007C} to deproject X–ray imaging and spectral data. The method consists of minimizing the sum of the squares of the 4/”-order derivatives around each data-point. so as to smooth out oscillations in the profiles.," The method consists of minimizing the sum of the squares of the $k^{th}$ -order derivatives around each data-point, so as to smooth out oscillations in the profiles." Here we choose to minimize the second-order derivative. since we aim to eliminate fluctuations in the profiles. but not the overall gradient.," Here we choose to minimize the second–order derivative, since we aim to eliminate fluctuations in the profiles, but not the overall gradient." As we shall discuss in the following. such oscillations are due either to genuine substructures or to noise which propagates from adjacent bins in the deprojection.," As we shall discuss in the following, such oscillations are due either to genuine substructures or to noise which propagates from adjacent bins in the deprojection." " The local derivative of the function .r; at the /-th radial interval is computed by fitting it value and the values at the adjacent points. c;, and.r; 1). with a second order polynomial."," The local derivative of the function $x_i$ at the $i$ -th radial interval is computed by fitting it value and the values at the adjacent points, $x_{i-1}$ and $x_{i+1}$ ), with a second order polynomial." " Let +; be the value of the equally—spaced cluster-centrie distances. at which the profiles are sampled. and A, the spacing."," Let $r_i$ be the value of the equally–spaced cluster–centric distances, at which the profiles are sampled, and $\Delta_r$ the spacing." " Then. the regularization likelihood can be cast in the form )) -- 5Ali, The quantity between parenthesis in the line formula is the exact value of the local second-order derivative around ο,"," Then, the regularization likelihood can be cast in the form ) = - )^2 - )^2 The quantity between parenthesis in the line formula is the exact value of the local second–order derivative around $r_i$." All the constant factors are included in the coefficient A. which is called theparameter.," All the constant factors are included in the coefficient $\lambda$, which is called the." The choice of its value is determined by the compromise one wants to achieve between the fidelity to the data Gow A) and the regularity of the solution thigh A}., The choice of its value is determined by the compromise one wants to achieve between the fidelity to the data (low $\lambda$ ) and the regularity of the solution (high $\lambda$ ). A small A value will give an inefficient regularization. while a too high A will force the profile to a straight line. especially if the signal-to-noise ratio. S/N. is low.," A small $\lambda$ value will give an inefficient regularization, while a too high $\lambda$ will force the profile to a straight line, especially if the signal-to-noise ratio, S/N, is low." We apply the regularization constraint only to the temperature profile. which is that generally showing large oscillations. while the density protile has always a rather smooth shape.," We apply the regularization constraint only to the temperature profile, which is that generally showing large oscillations, while the density profile has always a rather smooth shape." The sum in eq.(5)) starts from 7=3 since we prefer to exclude the innermost point from the regularization procedure., The sum in \ref{eq:like_reg}) ) starts from $i=3$ since we prefer to exclude the innermost point from the regularization procedure. than star-formation.,than star-formation. It is still unclear. though. whether the low-level racio emission (at mJy ane sub-m.v lux densities) observed in many ellipticals is due to weak AGNs or residual star-Lormation activity (Wrobel IIeeschen 1991: Ho 1999: Llopkins et al.," It is still unclear, though, whether the low-level radio emission (at mJy and sub-mJy flux densities) observed in many ellipticals is due to weak AGNs or residual star-formation activity (Wrobel Heeschen 1991; Ho 1999; Hopkins et al." 2000)., 2000). Fherefore. in the following analysis the radio emission may need to be considered as an upper Init to the SER. of the host galaxy.," Therefore, in the following analysis the radio emission may need to be considered as an upper limit to the SFR of the host galaxy." We define the ratio. 2. between total radio (1.4CGLIz) Hux density. letal51757 and L-bancl luminosity (LLumamel 1981) The f? parameter is independent of distance and estimates he ratio between radio power and optical luminosity.," We define the ratio, $R$, between total radio GHz) flux density, $S^{total}_{1.4}$ and $B$ -band luminosity (Hummel 1981) The $R$ parameter is independent of distance and estimates the ratio between radio power and optical luminosity." lt iw been demonstrated: that the λος racio power is woportional to the mean optical luminositw of galaxics (ΟΙ 1981)., It has been demonstrated that the mean radio power is proportional to the mean optical luminosity of galaxies (Hummel 1981). The 7? parameter also takes into account his elfect. providing5 an estimate of the excess radio emission in galaxies due to star-formation or AGN activity.," The $R$ parameter also takes into account this effect, providing an estimate of the excess radio emission in galaxies due to star-formation or AGN activity." The A? xwameter is plotted against the galaxy age in Figure 2.., The $R$ parameter is plotted against the galaxy age in Figure \ref{fig_r}. Galaxies with evidence for strong ACN activity based on either their optical spectroscopic features. (Veron-Cetty Veron 1998) or their radio morphology (c.g. radio lobes: if jiigh resolution radio maps are available) are excluded from subsequent statistical analvsis., Galaxies with evidence for strong AGN activity based on either their optical spectroscopic features (Veron-Cetty Veron 1998) or their radio morphology (e.g. radio lobes; if high resolution radio maps are available) are excluded from subsequent statistical analysis. This ensures that the trends investigated. more reliably reflect. the evolution of star-ormation processes., This ensures that the trends investigated more reliably reflect the evolution of star-formation processes. Εις piecemeal method for excluding AGN systems is not. completely reliable. and a number he remaining old. (> 3GCGvr) ellipicals in the sample iive Comparatively high radio emission (22> 1.5).," This piecemeal method for excluding AGN systems is not completely reliable, and a number of the remaining old $>3$ Gyr) ellipticals in the sample have comparatively high radio emission $R>1.5$ )." While voung (« Σαιντ) post-merger systems with similarly eh & values show strong evidence or the presence of starburst activity (Ixcel Wu 1995). this is much less typical of evolved. elliptical. galaxies.," While the young $<1$ Gyr) post-merger systems with similarly high $R$ values show strong evidence for the presence of starburst activity (Keel Wu 1995), this is much less typical of evolved elliptical galaxies." The majority of these older systems have radio Bux clensities at he 1JJw level and are likely to belong to the “classic” AGN radio population. although in the absence of unambiguous spectroscopic or morphological classification. they have been retained in the following analysis.," The majority of these older systems have radio flux densities at the Jy level and are likely to belong to the “classic” AGN radio population, although in the absence of unambiguous spectroscopic or morphological classification, they have been retained in the following analysis." With these caveats in münd. anc despite the many non-detections. there is evidence for a decline in the star-lormation rates (traced by racio emission) [rom carly merecr-remnants {ο old. ellipticals.," With these caveats in mind, and despite the many non-detections, there is evidence for a decline in the star-formation rates (traced by radio emission) from early merger-remnants to old ellipticals." ‘This can be demonstrated by estimating the mean 2 parameter within clilferent age bins using survival analysis techniques implemented in the package (LaVallex. Isobe Feigelson 1992: Isobe. Feigelson Nelson 1986).," This can be demonstrated by estimating the mean $R$ parameter within different age bins using survival analysis techniques implemented in the package (LaValley, Isobe Feigelson 1992; Isobe, Feigelson Nelson 1986)." Because of the many upper limits. ancl the probable (albeit unintentional) ineusion of several AGN svstems. the mean IH values in the last three bins are likely to be overestimates of the level of star-formation present.," Because of the many upper limits, and the probable (albeit unintentional) inclusion of several AGN systems, the mean $R$ values in the last three bins are likely to be overestimates of the level of star-formation present." This reinforces the sugeestion that the intensity of star-lormation processes decreases with galaxy age., This reinforces the suggestion that the intensity of star-formation processes decreases with galaxy age. Also shown in Figure 2. are simple mocels that assume that the galaxy. SER. follows an exponential decay. of the form where / is the time since the onset of the star-formation and 7 is the e-folding parameter., Also shown in Figure \ref{fig_r} are simple models that assume that the galaxy SFR follows an exponential decay of the form where $t$ is the time since the onset of the star-formation and $\tau$ is the e-folding parameter. For this SER. law the population svnthesis code of Bruzual Charlot (19093) with a Salpeter IME is used. to. predict the galaxy B- luminosity evolution., For this SFR law the population synthesis code of Bruzual Charlot (1993) with a Salpeter IMF is used to predict the galaxy $B$ -band luminosity evolution. " Additionally. to estimate the €CGllz radio luminosity (54,4). we assume that £1.) is directly. proportional to the model galaxy SER."," Additionally, to estimate the GHz radio luminosity $L_{1.4}$ ), we assume that $L_{1.4}$ is directly proportional to the model galaxy SFR." Following Condon (1992) ancl assuming a Salpeter LME we find where the SER is estimated from equation 6..., Following Condon (1992) and assuming a Salpeter IMF we find where the SFR is estimated from equation \ref{eq_1}. Models with e-plding⋅. parameter τzz.21010 vyrs can reproduce the observed range of radio emission. with the exception of powerful radio ellipticals. dominated by AGNs.," Models with e-folding parameter $\tau\approx2\times10^8-1\times10^9$ yrs can reproduce the observed range of radio emission, with the exception of powerful radio ellipticals, dominated by AGNs." Lt should be noted that our aim is not to find the best fit to the observed: trend but. to. demonstrate. that. simple. models assuming a burst of star-formation that declines with time can reproduce both the observed. trend. and the the range of f? parameters from. carly merger-remnants to evolved ellipticals., It should be noted that our aim is not to find the best fit to the observed trend but to demonstrate that simple models assuming a burst of star-formation that declines with time can reproduce both the observed trend and the the range of $R$ parameters from early merger-remnants to evolved ellipticals. Indeed. the adopted: model does. no include important processes such as recycling. and heating of the eas.," Indeed, the adopted model does not include important processes such as recycling and heating of the gas." Actditionally. the radio emission of some cllipticals in the present sample are likely to be dominated. by ACGNSs rather than SEI.," Additionally, the radio emission of some ellipticals in the present sample are likely to be dominated by AGNs rather than SFR." Consequently. the adopted: model with TO2.10110n vyrs ds D.likely to represent a lower Chyeope.," Consequently, the adopted model with $\tau\approx2\times10^8-1\times10^9$ yrs is likely to represent a lower envelope." Moreover. the spectroscopic ages for the galaxies in the present sample assume an instantaneous burst. of," Moreover, the spectroscopic ages for the galaxies in the present sample assume an instantaneous burst of" “traditional” O-star mass loss rates.A/.. have arisen owing to the preclictions of clumped wind models (see recent Potsdam Workshop. Hamann 22008. and references therein).,"“traditional” O-star mass loss rates, have arisen owing to the predictions of clumped wind models (see recent Potsdam Workshop, Hamann 2008, and references therein)." Abbott ((1981) showed that inhomogeneous winds lead (ο an enhancement in densitv- scquared enission processes such asΠα... infrared and radio Iree-Iree. which means that the inferred wwoulc be overestimated (see also Puls 22006).," Abbott (1981) showed that inhomogeneous winds lead to an enhancement in density- squared emission processes such as, infrared and radio free-free, which means that the inferred would be overestimated (see also Puls 2006)." " Although a clear picture of these elumpy structures is still being developed. the “clamping factor (fi) is believed to be 2 4 to 5. ancl the reduction in sscales with /f,, (see General Discussion in Hamann 22003)."," Although a clear picture of these clumpy structures is still being developed, the so-called “clumping factor” $f_{cl}$ ) is believed to be $\approx$ 4 to 5, and the reduction in scales with $\sqrt f_{cl}$ (see General Discussion in Hamann 2008)." The derived {from diagnostics that ave linearly dependent on density. (e.g... analyses of unsaturated UV resonance line profiles) are expected to be independent of clumping effects (Puls 22006) and supposedly should provide more reliable vvalues.," The derived from diagnostics that are linearly dependent on density (e.g., analyses of unsaturated UV resonance line profiles) are expected to be independent of clumping effects (Puls 2006) and supposedly should provide more reliable values." In fact. analvses of the rresonance line doublet. (AA 1118. 1128 Aj) obtained. fromFUSE observations led to the conclusion that traditional anre overestimated by a factor of 10 or more (Massa 22003. hereafter MO3: Fullerton 22006: herealter FOG).," In fact, analyses of the resonance line doublet $\lambda \lambda$ 1118, 1128 ) obtained from observations led to the conclusion that traditional are overestimated by a factor of 10 or more (Massa 2003, hereafter M03; Fullerton 2006; hereafter F06)." Such reductions have Eur-reaching consequences., Such reductions have far-reaching consequences. For example. HHirschi (2008) concluded that the well known evolutionary (racks of massive stars could survive rrecluetions by a factor of 2. but not by a [actor of 10 or more.," For example, Hirschi (2008) concluded that the well known evolutionary tracks of massive stars could survive reductions by a factor of 2, but not by a factor of 10 or more." Resolution of this pproblem is also of particular importance with regards to the observed. X-ray. emission line properties obtained from Chandra and XMAM—Neiton observations., Resolution of this problem is also of particular importance with regards to the observed X-ray emission line properties obtained from $Chandra$ and $XMM-Newton$ observations. Waldron Cassinelli (2007) analvzed theLLETGS N-ray line properües for a large number of OB stars. and (wo of their conclusions are directly relevant to this iissue.," Waldron Cassinelli (2007) analyzed the X-ray line properties for a large number of OB stars, and two of their conclusions are directly relevant to this issue." 1) All of the resolved. N-rav. emission lines are verv broad. (.e.. HWIIM range of 300 to 1000 19). svanmetric. and the majority have minimal line-shifts.," 1) All of the resolved X-ray emission lines are very broad (i.e., HWHM range of 300 to 1000 ), symmetric, and the majority have minimal line-shifts." Although Waldron Cassinelli (2001) were the first to demonstrate that these X-ray line profiles could in [act be easilv explained bv a significant reduction inAM... this was inconsistent with the then accepted observedM.. and they suggested a clumpy or non-svmnmetric wind structure as a possible explanation.," Although Waldron Cassinelli (2001) were the first to demonstrate that these X-ray line profiles could in fact be easily explained by a significant reduction in, this was inconsistent with the then accepted observed, and they suggested a clumpy or non-symmetric wind structure as a possible explanation." " 2) The racial locations of the He-like fir (forbidden. intercombination. resonance) line sources. as derived [rom their //; line ratios. (wpically range from 1.2 to LO22... aud these distances are well correlated with their respective stellar wind X-ray continuum optical depth unity radii which we shall refer to as (he ""X-ray continuum optical depth unity"," 2) The radial locations of the He-like $fir$ (forbidden, intercombination, resonance) line sources, as derived from their $f/i$ line ratios, typically range from 1.2 to 10, and these distances are well correlated with their respective stellar wind X-ray continuum optical depth unity radii which we shall refer to as the “X-ray continuum optical depth unity" over the posterior redshift distribution for each galaxy.,over the posterior redshift distribution for each galaxy. " We write this as pg(z|zj,) as a shorthand for the redshift probability distribution given all the photometric information available for galaxy g: (ki,κ.)= h πο ο pa(|e) daz"" pu(z""|zn.) ar"" , where r=r(z’)."," We write this as $p_g(z|z_g)$ as a shorthand for the redshift probability distribution given all the photometric information available for galaxy $g$ : (k_1,k_2)= _h (k_1 (k_2 z' p_g(z'|z_g) z” p_h(z”|z_h) ” , where $r'=r(z')$." " This is the covariance of the full 3D shear field constructed only from a sum over the individual tracer galaxy population, and including all uncertainty that may be present from photometric redshift estimates."," This is the covariance of the full 3D shear field constructed only from a sum over the individual tracer galaxy population, and including all uncertainty that may be present from photometric redshift estimates." In this formalism we can retain individual posteriors., In this formalism we can retain individual posteriors. " Since we do not want the data vector to depend on the cosmological parameters (and consequently violating the conditions of the Fisher matrix analysis), we must assume a fiducial cosmology to translate a photo-z to a distance ré."," Since we do not want the data vector to depend on the cosmological parameters (and consequently violating the conditions of the Fisher matrix analysis), we must assume a fiducial cosmology to translate a photo-z to a distance $r_0^g$." " However as long as this choice, for each galaxy, is the same as those used in the actual sum over data (equation 1)) then the estimator will be unbiased."," However as long as this choice, for each galaxy, is the same as those used in the actual sum over data (equation \ref{1}) ) then the estimator will be unbiased." " For clarity we can re-express the covariance as series of matrices (ki,ko) Y, dezpo2""ze) ώμο (ki;7) where A?=AQA”."," For clarity we can re-express the covariance as series of matrices (k_1,k_2) _g z'p_g(z'|z_g) ] ) where ${\mathcal A}^2=\Delta\Omega\ell^2_i\ell^2_j\frac{4}{\pi^2c^2}A^2$." Equation (11)) is a discrete case of the equations in Section—5 2.5 of Heavens et al. (, Equation \ref{CGU}) ) is a discrete case of the equations in Section 2.5 of Heavens et al. ( 2006).,2006). " The ij refer to y combinations (see Appendix A), not redshift bins — this is a continuous 3D estimator."," The $ij$ refer to $\gamma$ combinations (see Appendix A), not redshift bins – this is a continuous 3D estimator." " If we do not have individual posterior distributions, or wish to ignore the individual galaxy redshift error distributions, we can simplify pg(z|z9) to a global p(z|zp) so all galaxies at fixed photometric redshift are assumed to have the same distribution of true redshifts."," If we do not have individual posterior distributions, or wish to ignore the individual galaxy redshift error distributions, we can simplify $p_g(z|z_g)$ to a global $\bar p(z|z_p)$ so all galaxies at fixed photometric redshift are assumed to have the same distribution of true redshifts." " In this regime the the G matrix is modified only so that jo(kir(2p))n(zp)B(2' )Ue(r(2'),k)(12) where p(z|zp) is the redshift probability distribution at photometric redshift zp, and n(zp) is the number density of galaxies as a function of redshift."," In this regime the the $G$ matrix is modified only so that (k_1r(z_p)) (r(z'),k') where $\bar p(z|z_p)$ is the redshift probability distribution at photometric redshift $z_p$ , and $n(z_p)$ is the number density of galaxies as a function of redshift." Equation (12)) is in agreement with Castro et al. (, Equation \ref{Gcont}) ) is in agreement with Castro et al. ( 2003) and Heavens et al. (,2003) and Heavens et al. ( 2006).,2006). " By including the individual galaxies in equation (11)) we automatically take into account all overlap between photometric redshift posteriors, all outliers in the sample and have the best estimate for the covariance of the data vector."," By including the individual galaxies in equation \ref{CGU}) ) we automatically take into account all overlap between photometric redshift posteriors, all outliers in the sample and have the best estimate for the covariance of the data vector." Of course the outliers have only been properly accounted for only if the p(z|zp) is a correct estimate of the probability of a galaxy being anoutlier; we leave an investigation into the effect of errors on the p(z|z) for futurestudy., Of course the outliers have only been properly accounted for only if the $p(z|z_p)$ is a correct estimate of the probability of a galaxy being anoutlier; we leave an investigation into the effect of errors on the $p(z|z_p)$ for futurestudy. It is instructive to compare the fuidamental plane relations of the 5—rav population with the best-lits inlerred from the radio MSP population in GC's.,It is instructive to compare the fundamental plane relations of the $\gamma-$ ray population with the best-fits inferred from the radio MSP population in GCs. IIui et al. (, Hui et al. ( 2010) have found that the slopes of log. and [Fe/II] inferred. from the radio GC MSPs population are 0.69+0.11 and 0.72z0.11 respectively.,2010) have found that the slopes of $\log\Gamma_{c}$ and $\left[{\rm Fe/H}\right]$ inferred from the radio GC MSPs population are $0.69\pm0.11$ and $0.72\pm0.11$ respectively. Within these quoted uncertainties. the slope of the [Fe/1] relation for the radio population is found to intersect with the 26 error contours for (he corresponding parameters of the ο--ταν fundamental plane relations (ie. ay and (343).," Within these quoted uncertainties, the slope of the $\left[{\rm Fe/H}\right]$ relation for the radio population is found to intersect with the $2\sigma$ error contours for the corresponding parameters of the $\gamma-$ ray fundamental plane relations (i.e. $a_{8}$ and $a_{11}$ )." On the other hand. the logaritlimic slope of the D. relation for the radio population is only mareinally overlapped with the rims of the 30 error contours for the corresponding parameters inferred from the 5—rav. population (i.e. e» ancl αγ).," On the other hand, the logarithmic slope of the $\Gamma_{c}$ relation for the radio population is only marginally overlapped with the rims of the $3\sigma$ error contours for the corresponding parameters inferred from the $\gamma-$ ray population (i.e. $a_{2}$ and $a_{5}$ )." We have also idenüfied possible positive correlations with various πο photon fields which have sienilicances compatible with those for the encounter rate and the metalicity., We have also identified possible positive correlations with various soft photon fields which have significances compatible with those for the encounter rate and the metalicity. These correlations are not expected Irom the magnetospheric model., These correlations are not expected from the magnetospheric model. Together with the uncertainty of the sustainability of the outergaps in the MSPs in GCs (see 811). our finding [further motivate the exploration of alternative explanations for the origin of the observed -rav [rom GC's.," Together with the uncertainty of the sustainability of the outergaps in the MSPs in GCs (see 1), our finding further motivate the exploration of alternative explanations for the origin of the observed $\gamma$ -ray from GCs." Abdo et al. (, Abdo et al. ( 2010a) have argued that the 5-rav. emission is magnetospheric in nature because of the hard photon indices aud (he eutoll energies inferred [rom the phenomenological model is consistent with the values expected from the magnetospheric model.,2010a) have argued that the $\gamma$ -ray emission is magnetospheric in nature because of the hard photon indices and the cutoff energies inferred from the phenomenological model is consistent with the values expected from the magnetospheric model. On the other hand. Cheng et al. (," On the other hand, Cheng et al. (" 2010) have recently found that the ICS model can also describe the observed 5 —ray spectra of all the GCs discovered by Abdo et al. (,2010) have recently found that the ICS model can also describe the observed $\gamma-$ ray spectra of all the GCs discovered by Abdo et al. ( 2010a) very well.,2010a) very well. Simply based on the model fitting. we were not able to discriminate (hese two scenarios unambiguously.," Simply based on the model fitting, we were not able to discriminate these two scenarios unambiguously." llowever. different [rom the case of (he magnetospheric model. positive correlation between the enerev densitv of the soft photon fields are expected in a ICS scenario as the ICS power is directly. proportional to soft photon energy density.," However, different from the case of the magnetospheric model, positive correlation between the energy density of the soft photon fields are expected in a ICS scenario as the ICS power is directly proportional to soft photon energy density." The energy clensity of the backeround soft photon field depends on the location of the ‘luster., The energy density of the background soft photon field depends on the location of the cluster. We notice (hese y-ray GC's are possibly resided in the Galactic bulge aud. (therefore ihey are also metal-rich clusters., We notice these $\gamma$ -ray GCs are possibly resided in the Galactic bulge and therefore they are also metal-rich clusters. This results in a natural correlation between (he metalicity nd the soft photon energy density with a significance >95%., This results in a natural correlation between the metalicity and the soft photon energy density with a significance $>95\%$. Therefore. it is non-trivial to —isentanele (he effects of these (wo parameters.," Therefore, it is non-trivial to disentangle the effects of these two parameters." In anv case. our investigation stronglv suggests that either the metalicitv or the soft photon energv clensitv has to be the new parameter. in addition to D. in determining the observed 5-rav luminosities.," In any case, our investigation strongly suggests that either the metalicity or the soft photon energy density has to be the new parameter, in addition to $\Gamma_{c}$, in determining the observed $\gamma$ -ray luminosities." This inference is supported bv comparing (he results reported bv Abdo et al. (, This inference is supported by comparing the results reported by Abdo et al. ( 20108) and Tam et al. (,2010a) and Tam et al. ( 2010).,2010). Apart from the 3 conlirmed cases. Abdo οἱ al. (," Apart from the 8 confirmed cases, Abdo et al. (" 2010a) have also reported 5 non-detections which include three upper-limits and two other cases with (he 5 —rav emission slightly offset. from the respective GC cores.,2010a) have also reported 5 non-detections which include three upper-limits and two other cases with the $\gamma-$ ray emission slightly offset from the respective GC cores. With the LAT data of a longer exposure. Tam et al. (," With the LAT data of a longer exposure, Tam et al. (" 2010) have found a larger number of 5-rav. GCs,2010) have found a larger number of $\gamma$ -ray GCs the verv fact that planetesimal formation mav involve a threshold phenomenon. namely (he existence of a nontrivial critical surface density. “i.e7rp. implies that low-metallicity svstenms should be much less likely to form planets than hieh-metallicity svstenis. a correlation which seems already (o be present in the empirical literature (Gilliland οἱ al.,"the very fact that planetesimal formation may involve a threshold phenomenon, namely the existence of a nontrivial critical surface density, $\Sigma_{\rm p,c} \sim \eta r \rho_{\rm g}$, implies that low-metallicity systems should be much less likely to form planets than high-metallicity systems, a correlation which seems already to be present in the empirical literature (Gilliland et al." 2000. Laughlin 9000).," 2000, Laughlin 2000)." This paper is organized as follows., This paper is organized as follows. In relsec:prop we present the basic properties of our disk models., In \\ref{sec:prop} we present the basic properties of our disk models. Alter reviewing the techniques of Sekiva(1998) [or deriving density distributions of well-coupled particles in relsecitech.. we physically interpret. in relsecisat.. the midplane density. singularities which occur in these profiles as evidence (hat midplane turbulence can only stir a finite amount of material.," After reviewing the techniques of \citet{sek98} for deriving density distributions of well-coupled particles in \\ref{sec:tech}, we physically interpret, in \\ref{sec:sat}, the midplane density singularities which occur in these profiles as evidence that midplane turbulence can only stir a finite amount of material." This allows us. in (o caleulate the solid/gas enhancements required for GI in various model disks.," This allows us, in \\ref{sec:enh} to calculate the solid/gas enhancements required for GI in various model disks." We show that aerodynanmie drift can concentrate particles of a given size racially in the disk on cosmogonically interesting time scales in relsec:single.. and we eeneralize to distributions of particle sizes in relsec:dist..," We show that aerodynamic drift can concentrate particles of a given size radially in the disk on cosmogonically interesting time scales in \\ref{sec:single}, , and we generalize to distributions of particle sizes in \\ref{sec:dist}." In relsec:eolsal we evaluate whether (his concentration mechanism provides enough enhancement to induce GI., In \\ref{sec:gotsat} we evaluate whether this concentration mechanism provides enough enhancement to induce GI. Closing remarks are made in relsec:clise.., Closing remarks are made in \\ref{sec:disc}. If any aceretion ancl its associated turbulence occurs in the disk. we assume that they are conlined to the top aud bottom surlace lavers of the disk (Ganunie1996).," If any accretion and its associated turbulence occurs in the disk, we assume that they are confined to the top and bottom surface layers of the disk \citep{gam96}." . Because the deeper (nidplane) lavers of the disk are then heated only by. radiation [rom above or below. we can then model the gaseous component as being in hvdrostatic equilibrium with a verlically isothermal distribution of temperature. while the radialdistributions for the," Because the deeper (midplane) layers of the disk are then heated only by radiation from above or below, we can then model the gaseous component as being in hydrostatic equilibrium with a vertically isothermal distribution of temperature, while the radialdistributions for the" latitudes that the warm gas is broadly distributed in velocity relative (ο the widths of the cool clouds.,latitudes that the warm gas is broadly distributed in velocity relative to the widths of the cool clouds. So over the velocity range of a single absorption line component we can approximate the warm gas contribution as a linear function of velocity. Le. Tip=ty4aye and 75.5=by+be or for the total with απ. ay. by. by. cy. ancl ey all constants.," So over the velocity range of a single absorption line component we can approximate the warm gas contribution as a linear function of velocity, i.e. $T_{w,f} = a_0 + a_1 v $ and $T_{w,b} = b_0 + b_1 v $ or for the total with $a_0$ , $a_1$, $b_0$, $b_1$, $c_0$, and $c_1$ all constants." Then we have simply where c» is the cool cloud temperature reduced by the background. continuum. and €--—DogDoadua is the fraction of the warm gas which is behind the cloud (0xe <1).," Then we have simply where $c_2$ is the cool cloud temperature reduced by the background continuum, $c_2 = (T_{cool} - T_{cont})$ and $\epsilon \equiv \frac{T_{w,b}} {T_{w,f} + T_{w,b}}$ is the fraction of the warm gas which is behind the cloud $0 \leq \epsilon \leq 1$ )." Here we will assume € is constant across the velocity width of each absorption line component. though in general it max be a function of velocity.," Here we will assume $\epsilon$ is constant across the velocity width of each absorption line component, though in general it may be a function of velocity." " Note that the continuum brightness. Zion, is not the brightness temperature 7). of the background source towards which we measure the absorption. but the diffuse continuum in the directions of the nearby pointines which give the interpolated emission spectrum."," Note that the continuum brightness, $T_{cont}$, is not the brightness temperature $T_c$ of the background source towards which we measure the absorption, but the diffuse continuum in the directions of the nearby pointings which give the interpolated emission spectrum." Given the observed. absorption and emission spectra. we can perform a simple least-squares fit to the data in order to determine (he values of ej. οι. and e» in equation 14.," Given the observed absorption and emission spectra, we can perform a simple least-squares fit to the data in order to determine the values of $c_0$, $c_1$, and $c_2$ in equation 14." The independent variables are ο and ur. ancl (he dependent variable. Z5. we will call y [or simplicity.," The independent variables are $v$ and $x$, and the dependent variable, $T_B$, we will call $y$ for simplicity." The solution is obtained by minimizing the value of 4? in the same way as for polynomial fitting. which leads to a matrix inversion problem where the elements of the malvix ave moments of various combinations of c. c. ancl y.," The solution is obtained by minimizing the value of $\chi^2$ in the same way as for polynomial fitting, which leads to a matrix inversion problem where the elements of the matrix are moments of various combinations of $v$, $x$, and $y$." For example. where (he sunm is taken over all spectral channels. /= 1 (o n. covered by a distinct absorption feature (which presumably corresponds to a single cool phase temperature).," For example, where the sum is taken over all spectral channels, $i=$ 1 to $n$, covered by a distinct absorption feature (which presumably corresponds to a single cool phase temperature)." The parameter e is carried through all the calculations explicitly. so (hat results can be found for anv selected value of e.," The parameter $\epsilon$ is carried through all the calculations explicitly, so that results can be found for any selected value of $\epsilon$." " The advantage of this approach. compared with the Gaussian [its discussed above. is that (here is no ambiguity in the results: the unique solution is found directly. withno iteration and no need for a ""ist guess"" mput bvhand."," The advantage of this approach, compared with the Gaussian fits discussed above, is that there is no ambiguity in the results; the unique solution is found directly withno iteration and no need for a “first guess” input byhand." The equations needed to find (his best fit are given in (he appendix., The equations needed to find this best fit are given in the appendix. hence we conclude that the estimated values of Y! are consistent with each other. and they are independent of the stancarel solar model used as reference.,"hence we conclude that the estimated values of $\yims$ are consistent with each other, and they are independent of the standard solar model used as reference." If standard solar models based on AGSO5 composition are used to derive the relation between Yi; and Yi. we get Aqu;=0.903 instead of 0.836.," If standard solar models based on AGS05 composition are used to derive the relation between $\yim$ and $\ysm$ , we get $K_{\rm (I,S)}=0.903$ instead of 0.836." We have used C598 and AC805 for this comparison in an attempt to bracket what the real solar abundance probably is., We have used GS98 and AGS05 for this comparison in an attempt to bracket what the real solar abundance probably is. These (wo compilations represent the two ends of the currently. accepted range of values for solar photospheric abundancesὃ, These two compilations represent the two ends of the currently accepted range of values for solar photospheric abundances. "ν, Therefore. we also expect that our estimates of Aq, for the GS98-C and AGSO5-Op cases represent the (wo extremes of the possible range of values for this equantitv."," Therefore, we also expect that our estimates of $K_{\rm(I,S)}$ for the GS98-C and AGS05-Op cases represent the two extremes of the possible range of values for this quantity." Replacing κι=0.903 in Eq.," Replacing $K_{\rm (I,S)}=0.903$ in Eq." 10 and again using the standard solar models [rom Serenellietal.(2009).. we get the Y?! values listed in the last. column of Table 3..," \ref{eq:final} and again using the standard solar models from \citet{ssm09}, we get the $\yims$ values listed in the last column of Table \ref{tab:results}." " A comparison of the Y? results obtained with the two values ofAqu, for each SSM shows that the uncertainty in the determination of ἄν has a very minor effect in the predicted Y! values."," A comparison of the $\yims$ results obtained with the two values of$K_{\rm (I,S)}$ for each SSM shows that the uncertainty in the determination of $K_{\rm (I,S)}$ has a very minor effect in the predicted $\yims$ values." The largest difference is found for the AGSS09ph model. [or which AYP=0.0017. a [actor of ~4 smaller than cyiini estimated above.," The largest difference is found for the AGSS09ph model, for which $\Delta \yims= 0.0017$, a factor of $\sim 4$ smaller than $\sigma_{\yims}$ estimated above." We have shown that the predicted Y! values have a very small dependence on (he solar model used to determine il., We have shown that the predicted $\yims$ values have a very small dependence on the solar model used to determine it. The choice of standard solar models [ον deriving the exponent Ius(LA) also introduces a small scatter in the resulting5 Y! values.," The choice of standard solar models for deriving the exponent $K_{\rm(I,S)}$ also introduces a small scatter in the resulting $\yims$ values." Therefore. we averageoS all values Y? presented in Table 3.B to determine the final result and also use the scatter to define the svstematic uncertainty of the method.," Therefore, we average all values $\yims$ presented in Table \ref{tab:results} to determine the final result and also use the scatter to define the systematic uncertainty of the method." The final result Chat we obtain is where the first part of the uncertainty includes contributions from helioseismology ancl solar input. parameters. and the second one is the systematic uncertainty of the method as defined above.," The final result that we obtain is where the first part of the uncertainty includes contributions from helioseismology and solar input parameters, and the second one is the systematic uncertainty of the method as defined above." We have tested the robustness of this result bv applving Equation (10)) to a variety of solar models. stancdarcl and non-standard. ie. including additional physics not considered in SSMs.," We have tested the robustness of this result by applying Equation \ref{eq:final}) ) to a variety of solar models, standard and non-standard, i.e. including additional physics not considered in SSMs." As a first consistency check. we have applied Equation 10. to the two large sets of 55Ms computed by BSBOG used to assess the validity of the power-law expansions obtained in 2..," As a first consistency check, we have applied Equation \ref{eq:final} to the two large sets of SSMs computed by BSB06 used to assess the validity of the power-law expansions obtained in \ref{sec:powerlaws}." " Averaging all results for the AGSO5-Op Monte Carlo set presented in BSBOG. we find yim—9978040.0043 and for theGS98-Cons set we get Y?!=0,2783£ 0.0041. ie. results fully consistent with the basic derivation of Y! and its uncertainty based on the four SSAIs"," Averaging all results for the AGS05-Op Monte Carlo set presented in BSB06, we find $\yims= 0.2780 \pm 0.0043$ and for theGS98-Cons set we get $\yims= 0.2783 \pm 0.0041$ , i.e. results fully consistent with the basic derivation of $\yims$ and its uncertainty based on the four SSMs" requirement for such a reprocessed compouent is also supported by the observation of a luoresceuce line [rom neutral iron (e.e..Ebisawaetal.1096).,"requirement for such a reprocessed component is also supported by the observation of a fluorescence line from neutral iron \citep[e.g.,][]{ebisawa96}." . Assuimit£& a geometry consistiug of an optically thin corona above an optically-thick accretion disk. Haaretetal.(1993). showed that the moclel was consistent. with data from ENOSAT. SIGMA (Salottietal.1992) ancl OSSE (CGrabelskyal.1993). . sugeestineg a much higher coronal electron temyerature (AT)~150 keV) aud au even stnaller optical depth (7~ 0.3) than suggestedMOD by Componization models alone.," Assuming a geometry consisting of an optically thin corona above an optically-thick accretion disk, \citet{haardt93} showed that the model was consistent with data from EXOSAT, SIGMA \citep{salotti92} and OSSE \citep{grabelsky93}, suggesting a much higher coronal electron temperature $kT_e \sim 150$ keV) and an even smaller optical depth $\tau \sim 0.3$ ) than suggested by Comptonization models alone." The reflection component was also incorporated into an accretion disk corona (ADC) model by Doveetal.(1997).., The reflection component was also incorporated into an accretion disk corona (ADC) model by \citet{dove97b}. In this case. the eeometry cousisted of a hot inner splerica corona wilh an exterior accretion clisk.," In this case, the geometry consisted of a hot inner spherical corona with an exterior accretion disk." Reasonable comparisous with the broad-baud spectrum from 1 keV. up to several hundred. keV were emoustrated with an electrou temperature of AT.90 keV and au optical depth of 71.5., Reasonable comparisons with the broad-band spectrum from 1 keV up to several hundred keV were demonstrated with an electron temperature of $kT_e \sim 90$ keV and an optical depth of $\tau \sim 1.5$. A similar model was used by Cüerliuskietal.(1997). to fit à combined Cünga-OSSE spectrum. but they found that. with fixed normalization between the Cinega aud OSSE spectra. a second Comptonization Component was needed to unprove the |Hoc the highest euergies. (," A similar model was used by \citet{gierlinski97} to fit a combined Ginga-OSSE spectrum, but they found that, with fixed normalization between the Ginga and OSSE spectra, a second Comptonization component was needed to improve the fit at the highest energies. (" It las been pointed out by Poutanen(2000).. however. that a sinele emperature Comptoulzation moclel fits the Ciuga-OSSE data quite well if the relative normalization between the two spectra is left as a [ree paraimeter: see Figure 6 of Poutanen (1998)..),"It has been pointed out by \citet{poutanen2000}, however, that a single temperature Comptonization model fits the Ginga-OSSE data quite well if the relative normalization between the two spectra is left as a free parameter; see Figure 6 of \citet{poutanen98a}. .)" Mossaleuko.Collinar&Schóulelder(1998) also developed a multi-component model to explain the spectrum from soft. X-rays iuto the ~-ray 'elon., \citet{moskalenko98} also developed a multi-component model to explain the spectrum from soft X-rays into the $\gamma$ -ray region. Iu this case. a central spherical coroua surrouuds he black hole itself. outside of which is he optic:ully-thick accretion disk. with a much hotter outer corona surrounding the entire system.," In this case, a central spherical corona surrounds the black hole itself, outside of which is the optically-thick accretion disk, with a much hotter outer corona surrounding the entire system." The we of two-compouent Comptonizatiou models to improve spectral fits is motivated by he reasolable assuimptiou that the Comptonization region will not be isothermal., The use of two-component Comptonization models to improve spectral fits is motivated by the reasonable assumption that the Comptonization region will not be isothermal. A simple model may not be very physical. however. since it implicitly assumes that there are wo clistict non-interacting regions in which Comptonization is taking place.," A simple two-temperature model may not be very physical, however, since it implicitly assumes that there are two distinct non-interacting regions in which Comptonization is taking place." A more realistic approach. would be to asstune a contiuuum of Comptouization parameters., A more realistic approach would be to assume a continuum of Comptonization parameters. argued at a thermally-stratified black hole atinosphere «‘ould act to ανάσα the spectrum., \citet{skibo95b} argued that a thermally-stratified black hole atmosphere could act to harden the spectrum. They slinulatec a 1uodel involving a high-euergy spherical core surrounded by au optically thick accretion disk., They simulated a model involving a high-energy spherical core surrounded by an optically thick accretion disk. Ifte inner core of the high-euerey region were hot enctel. then a hard tail extending tuto the MeV region might be produced.," If the inner core of the high-energy region were hot enough, then a hard tail extending into the MeV region might be produced." A similar model was used to interpret the first combined spectra results [rom the BATSE and COMPTEL experiments on CGRO (Lineetal.1997)., A similar model was used to interpret the first combined spectral results from the BATSE and COMPTEL experiments on CGRO \citep{ling97} . Therma stratificaion is also an essential concept in the trausition disk model of Misra&Melia(1996)., Thermal stratification is also an essential concept in the transition disk model of \citet{misra96}. . This 1οςel involves large thermal gradieuts in the inuer region of au optically thick accretion disk., This model involves large thermal gradients in the inner region of an optically thick accretion disk. These er«lients represent a trausitiou between the cold optically thick disk and the lot plasina which exists near the inner part of the disk., These gradients represent a transition between the cold optically thick disk and the hot plasma which exists near the inner part of the disk. This moclel has been used to provide a good Π to spectra ii the 2-500 keV energy baud (Misraetal.1997.1998).," This model has been used to provide a good fit to spectra in the 2–500 keV energy band \citep{misra97,misra98}." . Doveetal.(1997). also incorporated thermal s(ratification into the structure of the inner corona of their moclel., \citet{dove97b} also incorporated thermal stratification into the structure of the inner corona of their model. The ret effect of thermal gradients is to produce a nou-Maxwellian electron energy distribution., The net effect of thermal gradients is to produce a non-Maxwellian electron energy distribution. A hieh eierey tail in the electrou distribution leads. via the the inverse Compton process. to a Ligh energy tail in the photon distribution.," A high energy tail in the electron distribution leads, via the the inverse Compton process, to a high energy tail in the photon distribution." Several moclels hasre sought to explain hard-tail emissious by iuvokiug some Lid of nonthermal process to generate a high euergy (possibly relativistic), Several models have sought to explain hard-tail emissions by invoking some kind of nonthermal process to generate a high energy (possibly relativistic) aud colour offsets which represen ose expected [rom {1e real observations.,and colour offsets which represent those expected from the real observations. Values of P(A>Nai) rear OQ indicate that the functiolal oll is a poor representation of the data., Values of $P(\Delta>\Delta_{obs})$ near 0 indicate that the functional form is a poor representation of the data. To determine ift Je Lore coiplicated LE fictional Oris are statistically warranted. we utilize he log-likelihood tes \92ogL-.," To determine if the more complicated LF functional forms are statistically warranted, we utilize the log-likelihood test $\chi^2=-2\log\frac{L'}{L}$." The logarithin o‘the ratio of maximum likelihoods of the simple aud more Complicated ftuctions. L aud L'. are clistributed as a chi-squared variable with a iumber of degrees of reedoim οςtal to the difference iu f‘ee parameters between the two fuuctional orms.," The logarithm of the ratio of maximum likelihoods of the simple and more complicated functions, $L$ and $L'$, are distributed as a chi-squared variable with a number of degrees of freedom equal to the difference in free parameters between the two functional forms." A table of \7 \alues Cal οι sed to determine the significauce of the tinprovement in the LF it between the two fituctional forms. (?).., A table of $\chi^2$ values can be used to determine the significance of the improvement in the LF fit between the two functional forms. \citep{Kotz1983}. Presented in Taje L are the best-fit parameters for the three different LF forms. aud of each fit.," Presented in Table \ref{tab:fits} are the best-fit parameters for the three different LF forms, and $P(\Delta>\Delta_{obs})$ of each fit." Tie. best-fit: power-law slope to the FOsb data-set. a=0.58. is moderately shallower han. but is consistent with the best-fit a0.65 from ?..," The best-fit power-law slope to the F08b data-set, $\alpha=0.58$, is moderately shallower than, but is consistent with the best-fit $\alpha=0.65$ from \citet{Fraser2008}." The fit however. is a poor description of the claa as evideuced by the low P(A>No)<0.02.," The fit however, is a poor description of the data as evidenced by the low $P(\Delta>\Delta_{obs})<0.02$." The best-lit of the rolling power-law to the FOS) data-set is (a.a’.Nu)=(0.8.—0.06.0.52).," The best-fit of the rolling power-law to the F08b data-set is $(\alpha,\alpha',\Sigma_{23})=(0.8,-0.06,0.82)$." The maxijun likelilood value of this fit is increased. by: more than two orders of inaguitude over the power-law whicl warratts tle inclusion o ‘a third degree of [reedom. aud the fit is au acceptable cescriptioi of the FOSD sample. with P(A>obsj=0.1.," The maximum likelihood value of this fit is increased by more than two orders of magnitude over the power-law which warrants the inclusion of a third degree of freedom, and the fit is an acceptable description of the F08b sample, with $P(\Delta>\Delta_{obs})= 0.4$." The best-fit of he LF giver by Equation L. (log.d.a4.02.205)=(23.56.0.76.0.18.2 L9). is an acceptable fit to the data with PEA>App.)=0.1.," The best-fit of the LF given by Equation \ref{eq:Fraser2008}, $(\log A,\alpha_1,\alpha_2,m_b) = (23.56,0.76,0.18,24.9)$ , is an acceptable fit to the data with $P(\Delta>\Delta_{obs}) = 0.4$." " The uaximun likelihood value is iucreased by more than two orders of magit«cle over the sower-law with a log-likelihood chi-scπας, v7>=431Lid. aud by a factor of 2 over the olliug power-law with 4?L"," The maximum likelihood value is increased by more than two orders of magnitude over the power-law with a log-likelihood chi-square, $\chi^2 = 11.7$, and by a factor of 2 over the rolling power-law with $\chi^2=1.4$." b We find that the best-fit from Equation | 1s preferred over the power-law at greater than the 3-sigu| level., We find that the best-fit from Equation \ref{eq:Fraser2008} is preferred over the power-law at greater than the 3-sigma level. This lit is prelerred Over the roline power-law at S8O% signilicance., This fit is preferred over the rolling power-law at $\sim 80\%$ significance. Thus we lind that oth the rolling power-aw aud broken power-law of Equation | provide equally adequate descri»tions of tie. FOSD saidle., Thus we find that both the rolling power-law and broken power-law of Equation \ref{eq:Fraser2008} provide equally adequate descriptions of the F08b sample. l ote: he Àonte-C'arlo simulations we have cone to calculate P(A>App.) have also deimoustraed hat oum average. the best-lit. LF pa‘ammeters cletermined Crom our maximu likeihood technique 'eprocuce {e input parameters of tje simulatious for all LF fuuctionals forms we have conside'ecd lere.," Note: the Monte-Carlo simulations we have done to calculate $P(\Delta>\Delta_{obs})$ have also demonstrated that on average, the best-fit LF parameters determined from our maximum likelihood technique reproduce the input parameters of the simulations for all LF functionals forms we have considered here." " When je obserrations of ? a'e excluded [rom the FOSb sample. the best-fit, power-law las yaaimeters (0.1105)=(0.65.23.12). which is nearly identical to that found from by ?.."," When the observations of \citet{Bernstein2004} are excluded from the F08b sample, the best-fit power-law has parameters $(\alpha,m_o)=(0.65,23.42)$, which is nearly identical to that found from by \citet{Fraser2008}." The ls a locerately adequate descri»tion of the observatious with PEA>App.)=0.1., The power-law is a moderately adequate description of the observations with $P(\Delta>\Delta_{obs}) =0.1$. This result lllits that the Ixuiper belt LF exhibits a break within the maguitude range of the FOSb sample. )L to fitstle survey data with (2?)<ο.27 clo not explic‘itly require a broken or rolling power-law dlescriptiou.," This result hints that the Kuiper belt LF exhibits a break within the magnitude range of the F08b sample, but fits to the survey data with $m(R)\lesssim27$ do not explicitly require a broken or rolling power-law description." Pulsar Wine Nebulae are perhaps the most cficicnt astrophysical particle accelerators iu our ealaxy.,Pulsar Wind Nebulae are perhaps the most efficient astrophysical particle accelerators in our galaxy. The best studied PWN. the Crab Nebula. accelerates clectrous wp to ~10/9 eV despite the rapid svuchrotron losses of these particles in its 160 4G magnetic field (Aharonianctal. 20013).," The best studied PWN, the Crab Nebula, accelerates electrons up to $\sim10^{16}$ eV despite the rapid synchrotron losses of these particles in its $160$ $\mu$ G magnetic field \citep{hegra_crab}." ". The recent detections| of exteuded TeV cussion from several PWNe. ducludius 5-02 (Ahavonianctal,2005b) aud JIL825-137 (Aharoniοἳ—al.20050) with the ILE.S.S. imstruneut sugeest that such objects are copious TeV οταν cutters."," The recent detections of extended TeV emission from several PWNe, including $-5$ \citep{hess_msh1552} and J1825-137 \citep{hess_j1825} with the H.E.S.S. instrument suggest that such objects are copious TeV $\gamma$ -ray emitters." " Tn this] contest,.Inu a+ PWN2 A“yar provide⋅ry] ma natural+ explanation for the GC TeV cunission."," In this context, a PWN may provide a natural explanation for the GC TeV emission." Tere we discuss. in detail. the case of the new PWN candidate €123359.95-0.01.," Here we discuss, in detail, the case of the new PWN candidate 359.95-0.04." The X-ray nebula [ 3359.95-0.0vas discovered in deep Chandra observations of the Galactic Centre(Wanectal...6) ancl lies at a projected distance to Ser A* of no0.3 pe., The X-ray nebula 359.95-0.04 was discovered in deep Chandra observations of the Galactic Centre \citep{wang} and lies at a projected distance to Sgr $^{\star}$ of 0.3 pc. " The nebula exhibits a COL with a projected size of 0,07. & 0.3 taypc.", The nebula exhibits a cometary morphology with a projected size of 0.07 $\times$ 0.3 pc. The overall euergy spectiuun of this object is nuon-theriaal. with a power-law index of hninosity1.91purely.Mi and an unabsorbed 210 keV X-ray ‘Ofz10°! erg/s. The Chandra data reveal a softening of spectral index with distance from the “lead” of the nebula. a possible signature of cooling of clectrous away from the accelerator.," The overall energy spectrum of this object is purely non-thermal, with a power-law index of $1.94^{+0.17}_{-0.14}$ and an unabsorbed 2–10 keV X-ray luminosity of $\approx10^{34}$ erg/s. The Chandra data reveal a softening of spectral index with distance from the “head” of the nebula, a possible signature of cooling of electrons away from the accelerator." Wangetal.(2006) have sugeested that the head of the nebula coutains a voune pulsar aud that €13359.95-0.01 is likely à. rzu-pressure-confincd PWN., \citet{wang} have suggested that the head of the nebula contains a young pulsar and that 359.95-0.04 is likely a ram-pressure-confined PWN. 3359.95-0.01 lies within the confidence error circle of the οταν source JJl715-290., 359.95-0.04 lies within the confidence error circle of the $\gamma$ -ray source J1745-290. The possible comuection between these two objects was pointed out by Waugetal.men(2006).. who discuss in some detail the important aspects involved in the relationship between the X-ray and ray cuission.," The possible connection between these two objects was pointed out by \citet{wang}, who discuss in some detail the important physical aspects involved in the relationship between the X-ray and $\gamma$ -ray emission." One of our aims here is to ake a full time-dependent calculation to investigate more deeply the likelihood of au association of these two objects., One of our aims here is to make a full time-dependent calculation to investigate more deeply the likelihood of an association of these two objects. A major difficulty in such an association is the ~O.1° angular resolution of ILE.S.S. Iu this scenario. the rav signal would be poiut-like anc non-variable and the ouly available information for modelling is. the spectral data in. the N-ray- and ο παν bands.," A major difficulty in such an association is the $\sim0.1^{\circ}$ angular resolution of H.E.S.S. In this scenario, the $\gamma$ -ray signal would be point-like and non-variable and the only available information for modelling is the spectral data in the X-ray and $\gamma$ -ray bands." However. the N-rav morphology. provides sole clues to the enviroment of the PWN.," However, the X-ray morphology provides some clues to the environment of the PWN." For exaniple. the fact that X-ray spectimm softens rather than hardens away from the (ional) oulsur position indicates that the N-rav cmitting electrous are cooled by svuchrotron radiation (or IC radiation in the Thompson regime) rather than x IC radiation in the Wwlein-Nishina (IKN) regime as nüeht be expected im the dense GC radiation fields.," For example, the fact that X-ray spectrum softens rather than hardens away from the (nominal) pulsar position indicates that the X-ray emitting electrons are cooled by synchrotron radiation (or IC radiation in the Thompson regime) rather than by IC radiation in the Klein-Nishina (KN) regime as might be expected in the dense GC radiation fields." " This fact alone places a lower limit on the uagnetie feld in the PWN of ~100 µία, Due to IN suppression. it is Likely that ie dominant target for IC radiation at a few TeV is the far infrared backerouud."," This fact alone places a lower limit on the magnetic field in the PWN of $\sim100$ $\mu$ G. Due to KN suppression, it is likely that the dominant target for IC radiation at a few TeV is the far infrared background." Matching ιο flux of 290 at these energies with a nonünal FIR radiation energy deusitv of 5000 eV cur? (Davidsonetal.1992) requires a B- of heldzz105 iC. Inthe case that 290 and 6623359.95-0.01 are associated. this value oovides a lower linüt on the average magnetic field iu the PWN.," Matching the flux of $-$ 290 at these energies with a nominal FIR radiation energy density of 5000 eV $^{-3}$ \citep{davidson} requires a $B$ -field of $\approx\,105$ $\mu$ G. In the case that $-$ 290 and 359.95-0.04 are associated, this value provides a lower limit on the average magnetic field in the PWN." Fie., Fig. 3. shows a model spectral," \ref{f3} shows a model spectral" Galactic Nuclei (AGNs) sub class of BL Lacertae objects. characterized by a non thermal spectrum extending up to high energies and by a rapid flux variability at nearly all wavelenghts.,"Galactic Nuclei (AGNs) sub class of BL Lacertae objects, characterized by a non thermal spectrum extending up to high energies and by a rapid flux variability at nearly all wavelenghts." To date about 30 BL Lacs have been detected at very high energies (VHE. E7100 GeV) and Mrk421 is the closest one (z 2 0.031).," To date about 30 BL Lacs have been detected at very high energies (VHE, $>$ 100 GeV) and Mrk421 is the closest one (z = 0.031)." Its relatively small distance makes it one of the best studied TeV gamma ray sources., Its relatively small distance makes it one of the best studied TeV gamma ray sources. Since its discovery this object played a significant role in the discussion concerning both the emission processes in AGNs and the attenuation of TeV gamma rays in the extragalactic space., Since its discovery this object played a significant role in the discussion concerning both the emission processes in AGNs and the attenuation of TeV gamma rays in the extragalactic space. It is now widely recognised that the BL Lae radiation originates 1n a relativistic jet pointing at a small angle to the line of sight and that it is amplified by relativistic effects. explaining both the strong high energy emission and its rapid variability.," It is now widely recognised that the BL Lac radiation originates in a relativistic jet pointing at a small angle to the line of sight and that it is amplified by relativistic effects, explaining both the strong high energy emission and its rapid variability." Usually the BL Lacs energy density spectra have two broad band components. the first one peaking in the infrared to X-ray region. the second one in the MeV-TeV range (Sambrunaetal.1996:Fossati1998).," Usually the BL Lacs energy density spectra have two broad band components, the first one peaking in the infrared to X-ray region, the second one in the MeV-TeV range \citep{Sam96,Fos98}." . Mrk421 is classified as a High-energy peaked BL Lae (HBL). showing the peaks in the X-ray and VHE regions. respectively (Padovani&Giommi1905).," Mrk421 is classified as a High-energy peaked BL Lac (HBL), showing the peaks in the X-ray and VHE regions, respectively \citep{Pad95}." The low energy component is commonly believed to originate as synchrotron emission from relativistic electrons gyrating in the magnetic field of the jet plasma. while the origin of the second one is still unclear.," The low energy component is commonly believed to originate as synchrotron emission from relativistic electrons gyrating in the magnetic field of the jet plasma, while the origin of the second one is still unclear." Many models propose that gamma rays are produced in Inverse Compton scattering of synchrotron (Synchrotron Self-Compton. SSC) or ambient photons (external. Compton. EC) off the same electron population that producesthe synchrotron radiation (Ghisellinietal.1998:Dermer1992).," Many models propose that gamma rays are produced in Inverse Compton scattering of synchrotron (Synchrotron Self-Compton, SSC) or ambient photons (external Compton, EC) off the same electron population that producesthe synchrotron radiation \citep{Ghi98,Der92}." ". Alternatively. in the ""hadronic"" models. gamma rays are emitted as sychrotron radiation of extremely energetic protons. or by secondary particles produced by protons interacting with some target material (Mückeetal.2003)."," Alternatively, in the “hadronic” models, gamma rays are emitted as sychrotron radiation of extremely energetic protons, or by secondary particles produced by protons interacting with some target material \cite{Muc03}." . Flaring activity of Mrk421] at VHE energies has been observed with variability time scales ranging from minutes to months. and many multiwavelength campaigns have revealed a strong correlation of gamma rays with X-rays. that can be easily interpreted in terms of the SSC model (Fossatietal.2008:Wagner2008).," Flaring activity of Mrk421 at VHE energies has been observed with variability time scales ranging from minutes to months, and many multiwavelength campaigns have revealed a strong correlation of gamma rays with X-rays, that can be easily interpreted in terms of the SSC model \citep{Fos08,Wag08}." . In. addition some data have shown significant. variations of the Τον spectrum slope during different activity phases. and an evident correlation between the spectral hardness and the flux intensity (Krennrichetal.2002).," In addition some data have shown significant variations of the TeV spectrum slope during different activity phases, and an evident correlation between the spectral hardness and the flux intensity \citep{Kre02}." . The simultaneous observation at different wavelengths ts of great importance since may provide unique information about the source properties and the radiation processes., The simultaneous observation at different wavelengths is of great importance since may provide unique information about the source properties and the radiation processes. À set of measurements (Donnarummaetal.2009) covering 12 decades of energy. from optical to TeV gamma rays. was performed during the strong flaring activity in the first half of June 2008 by different detectors: WEBT (optical R-band). UVOT (UV). RXTE/ASM (soft X-rays). SWIFT (soft and hard X-rays). AGILE (hard X-rays and gamma rays) and the Cherenkov telescopes VERITAS and MAGIC (VHE gamma rays).," A set of measurements \citep{Don09} covering 12 decades of energy, from optical to TeV gamma rays, was performed during the strong flaring activity in the first half of June 2008 by different detectors: WEBT (optical R-band), UVOT (UV), RXTE/ASM (soft X-rays), SWIFT (soft and hard X-rays), AGILE (hard X-rays and gamma rays) and the Cherenkov telescopes VERITAS and MAGIC (VHE gamma rays)." These data allowed for a deep analysis of the broad band energy spectrum às well as for the study of time correlations among the fluxes in different energy ranges., These data allowed for a deep analysis of the broad band energy spectrum as well as for the study of time correlations among the fluxes in different energy ranges. In this period two flaring episodes were reported. the first one on June 4-8. observed from optical to TeV gamma rays. the second one. larger and harder. on June 10-14. observed from optical to 100 MeV gamma rays.," In this period two flaring episodes were reported, the first one on June 4-8, observed from optical to TeV gamma rays, the second one, larger and harder, on June 10-14, observed from optical to 100 MeV gamma rays." Using the multifrequeney data. Donnarumma et al. (," Using the multifrequency data, Donnarumma et al. (" 2009) derived the Spectral Energy Distribution (SED) for June 6. that shows the typical two humps shape.,"2009) derived the Spectral Energy Distribution (SED) for June 6, that shows the typical two humps shape." In the framework of the SSC model. according to the authors. the second hump intensity. that reached a flux of about 3 < 107!! photons em s! at energies E. 7400 GeV (1.e. about 3.5 times the Crab Nebula emission in the same energy range) seems to indicate that the variability is due to the hardening/softening of the electron spectrum. and not to the increase/decrease of the electron density.," In the framework of the SSC model, according to the authors, the second hump intensity, that reached a flux of about 3 $\times$ $^{-11}$ photons $^{-2}$ $^{-1}$ at energies E $>$ 400 GeV (i.e. about 3.5 times the Crab Nebula emission in the same energy range) seems to indicate that the variability is due to the hardening/softening of the electron spectrum, and not to the increase/decrease of the electron density." Their model predicts for the second flare the Inverse Compton hump slightly shifted towards higher energies and a VHE flux a factor 72 larger with respect to the first one., Their model predicts for the second flare the Inverse Compton hump slightly shifted towards higher energies and a VHE flux a factor $\geq$ 2 larger with respect to the first one. Unfortunately there were no VHE data included in their multiwavelength analysis after June 8 because the moonlight hampered the Cherenkov telescopes measurements., Unfortunately there were no VHE data included in their multiwavelength analysis after June 8 because the moonlight hampered the Cherenkov telescopes measurements. The VHE observation was actually made for such a very important flaring episode by the ARGO-YBJ experiment., The VHE observation was actually made for such a very important flaring episode by the ARGO-YBJ experiment. The ARGO-YBJ experiment. located atthe Yangbajing Cosmic Ray Laboratory (Tibet. P.R. China. 4300 πι α.ς.Ι..," The ARGO-YBJ experiment, located atthe Yangbajing Cosmic Ray Laboratory (Tibet, P.R. China, 4300 m a.s.l.," " 30 067 38"" N. 907 31° 50° E) since December 2007 is performing a continuous monitoring of the sky in the declination band from -107 to 707."," $^{\circ}$ 06' 38” N, $^{\circ}$ 31' 50” E), since December 2007 is performing a continuous monitoring of the sky in the declination band from $^{\circ}$ to $^{\circ}$." In this paper we present our observation of Mrk42] in flaring state during 2008., In this paper we present our observation of Mrk421 in flaring state during 2008. After à summary of the data collected during the most active phase (February-June). we focus our discussion on the results obtained for the June flares in the framework of the Donnarumma et al. (," After a summary of the data collected during the most active phase (February-June), we focus our discussion on the results obtained for the June flares in the framework of the Donnarumma et al. (" 2009) findings.,2009) findings. The ARGO-YBJ detector is constituted by a central carpet —T4« 78 nr. made of a single layer of Resistive Plate Chambers (RPCs) with ~92% of active area. sorrounded by a partially instrumented (~20%) area up to —100 «110 nr.," The ARGO-YBJ detector is constituted by a central carpet $\sim$ $\times$ 78 $^2$, made of a single layer of Resistive Plate Chambers (RPCs) with $\sim$ $\%$ of active area, sorrounded by a partially instrumented $\sim$ $\%$ ) area up to $\sim$ $\times$ 110 $^2$." The apparatus has a modular structure. the basic data acquisition element being acluster «7.6 m). made of 12 RPCs 125 n).," The apparatus has a modular structure, the basic data acquisition element being acluster $\times$ 7.6 $^2$ ), made of 12 RPCs $\times$ 1.25 $^2$ )." Each chamber is read by 80 strips of «61.8 env. (the spatial pixels). logically organized in 10 independent pads of 55.6 .61.8 em* which are individually acquired and represent the time pixels of the detector.," Each chamber is read by 80 strips of $\times$ 61.8 $^2$ (the spatial pixels), logically organized in 10 independent pads of $\times$ 61.8 $^2$ which are individually acquired and represent the time pixels of the detector." The full detector is made of 153 clusters for a total active surface of ~6600 m (Aiellietal.2006)., The full detector is made of 153 clusters for a total active surface of $\sim$ 6600 $^2$ \citep{Aie06}. . ARGO-YBJ operates in two independent acquisition modes: themode and the (Atellietal.2008)., ARGO-YBJ operates in two independent acquisition modes: the and the \citep{Aie08}. .. In. the following we refer —to the data recorded in shower mode., In the following we refer to the data recorded in shower mode. A simple. yet powerful. electronic logic has been implemented to build an inclusive trigger (Aloisioetal.2004).," A simple, yet powerful, electronic logic has been implemented to build an inclusive trigger \cite{Alo04}." .. This logic is based on a time correlation. between the pad signals depending on their relative distance., This logic is based on a time correlation between the pad signals depending on their relative distance. In this way. all the shower events giving à number of fired pads 5 Neg in the central carpet in a time window of 420 ns ρωgenerate the trigger.," In this way, all the shower events giving a number of fired pads $_{pad}\ge$ $_{trig}$ in the central carpet in a time window of 420 ns generate the trigger." " This trigger can work with high efficiency down to N,,;,220. keeping negligible the rate of random coincidences."," This trigger can work with high efficiency down to $_{trig}$ =20, keeping negligible the rate of random coincidences." The time of each fired pad in a window of 2 jrsee around the trigger time and its location. are recorded and used to reconstruct the position of the shower core and the arrival direction of the primary particle (DiSciascioetal.2007)., The time of each fired pad in a window of 2 $\mu$ sec around the trigger time and its location are recorded and used to reconstruct the position of the shower core and the arrival direction of the primary particle \cite{DiS07}. . In order to perform the time calibration of the 18360 pads. a software method has been developed (Atellietal. 2009a)..," In order to perform the time calibration of the 18360 pads, a software method has been developed \cite{Aie09a}. ." " The detector is in stable data taking with the trigger condition N,,;.=20 and a duty cycle = 85%."," The detector is in stable data taking with the trigger condition $_{trig}$ =20 and a duty cycle $\geq 85\%$ ." The trigger rate Is ~3.6 KHz with a dead time of 4%., The trigger rate is $\sim$ 3.6 kHz with a dead time of $\%$ . The angular resolution and the pointing accuracy of the, The angular resolution and the pointing accuracy of the or onlv marginally consistent.,or only marginally consistent. Our result for NCC 1636 is comparable to that determined by6... lower than the interred flux by a factor of z1.1.," Our result for NGC 4636 is comparable to that determined by, lower than the inferred flux by a factor of $\simeq 1.4$." Thus. if ADAF sources associated with central black holes exist iu these ealaxies. they cau only account for oulv a fraction of the hard power-law x-ray cussion observed in the galaxies spectra.," Thus, if ADAF sources associated with central black holes exist in these galaxies, they can only account for only a fraction of the hard power-law x-ray emission observed in the galaxies' spectra." The observations were obtained from the TEASARC data archive. and are summarized in Table 1.," The observations were obtained from the HEASARC data archive, and are summarized in Table 1." " The observations were subjected to the ""dewobblius"" recipe described in the User Guide (11998) in order to imuprove the spatial resolution of the IIBI nuage.", The observations were subjected to the “dewobbling” recipe described in the User Guide \markcite{PRG98}1 1998) in order to improve the spatial resolution of the HRI image. This procedure groups the IIRI photous by phase bius of the telescopes 102 sec wobble period. determines a separate iuaee for cach of these phase bins. aud. then reassenibles the images to a common image centroid.," This procedure groups the HRI photons by phase bins of the telescope's $402$ sec wobble period, determines a separate image for each of these phase bins, and then reassembles the images to a common image centroid." We have checked whether this scheme recovers the //IIRI poiut source response function: in the case of NCCs 1399 and 1636. point sources within a few arciuiu of the IIRI field center appear to have a corrected FWIIM of ~ο.," We have checked whether this scheme recovers the /HRI point source response function: in the case of NGCs 1399 and 4636, point sources within a few arcmin of the HRI field center appear to have a corrected FWHM of $\simeq 6$." Therefore we have used this FEWIIM for the couvolution of the model galactic surface brightuess. iucliding a central point source (see 83).," Therefore we have used this FWHM for the convolution of the model galactic surface brightness, including a central point source (see 3)." Iu the case of NGC 1696. there Is no point source of suffiieut streneth within the IIRI nuaee field to check the recovery of the IRI resolution. so we have assed a 67FWIA for model fitting.," In the case of NGC 4696, there is no point source of sufficient strength within the HRI image field to check the recovery of the HRI resolution, so we have assumed a FWHM for model fitting." The effective observation times are calculated frou the. good time intervals covered by the list of wobble plases used to compose the dewobhled image., The effective observation times are calculated from the good time intervals covered by the list of wobble phases used to compose the dewobbled image. Using the dewobbled images. we extract azimuthally-averaged counts per TERT pixel in 21 2.5’ wide aunulae centered on the galaxies.," Using the dewobbled images, we extract azimuthally-averaged counts per HRI pixel in 24 $2.5$ wide annulae centered on the galaxies." The x-ray centers are determined bv the peak of x-ray coutours of the surface brielitucss of the ealaxv core., The x-ray centers are determined by the peak of x-ray contours of the surface brightness of the galaxy core. We note that in the cases of NGCx 1399 and 1636 the Νταν position agrees within ~2 of their optical centers (tle putative ceutral black tole position). while the x-ray peal for NGC 1696 is within ~ 6”of both the HIST position for the nucleus and the location of the nuclear radio source (Sparks. xivate conuuunication OODea 1991).," We note that in the cases of NGCs 1399 and 4636 the x-ray position agrees within $\simeq 2$ of their optical centers (the putative central black hole position), while the x-ray peak for NGC 4696 is within $\simeq 6$ of both the HST position for the nucleus and the location of the nuclear radio source (Sparks, private communication; \markcite{ODea94}O O'Dea 1994)." This may © Consistent with the pointing accuracy. however if the x-ray poak is not associate with the true galactic micleus. the upper lait to the flux from an ADAF associated with a nuclear black hoe ds mich smaller than he value we determine from our model that we clescribe low.," This may be consistent with the pointing accuracy, however if the x-ray peak is not associated with the true galactic nucleus, the upper limit to the flux from an ADAF associated with a nuclear black hole is much smaller than the value we determine from our model that we describe below." From cach annulus we subtract a backerouncd determined frou a πάς aunuhs at radius of ~12%., From each annulus we subtract a background determined from a wide annulus at radius of $\sim$. The pixel brightuess iun a elven almils is assigned to the uean radius of the anuulus., The pixel brightness in a given annulus is assigned to the mean radius of the annulus. Bacseroumd point sources are removed where necessary., Background point sources are removed where necessary. " The| datapoints are fit to a J-profile inodel for the extended galactic x-ray surface ποοσα, Sy=Syg(lo|por?/62yUT. and a ceutral central point source. both convolved with the dewobbled TRI point source response function of ( BBrown and Breeman 1999)."," The datapoints are fit to a $\beta$ -profile model for the extended galactic x-ray surface brightness, $S_X = S_{X0} (1 + r^2/r_c^2)^{3\beta - 1/2}$, and a central central point source, both convolved with the dewobbled HRI point source response function of \markcite{BrBr99}B Brown and Bregman 1999)." This composite model is a simple representation of the essential question that we wish to answer: to what extent must a central point source be included with extended emission to describe the galactic surface brightness?, This composite model is a simple representation of the essential question that we wish to answer: to what extent must a central point source be included with extended emission to describe the galactic surface brightness? Note that the profile iodol may be ess than ideal to describe the extended euission - if caunot account for asvinmmetry and substructure NCC 1696) - however. we are not attempting to find the best model o describe the elobal x-ray cussion. but a measure as to he point-source like behavior of the center compared to a flat cunission “core”.," Note that the $\beta$ -profile model may be less than ideal to describe the extended emission - it cannot account for asymmetry and substructure NGC 4696) - however, we are not attempting to find the best model to describe the global x-ray emission, but a measure as to the point-source like behavior of the center compared to a flat emission “core”." Cuven the core-like behavior of the enission at sinall racii aud the power-law like behavior at arge radii. the profile model is a reasonable proposition as a gross description of the extended cinission of the ealaxies.," Given the core-like behavior of the emission at small radii, and the power-law like behavior at large radii, the $\beta$ -profile model is a reasonable proposition as a gross description of the extended emission of the galaxies." The Jj-profle | point source model best fit results. and the confidence upper limits to the couut rates from a central point source in cach ealaxy are listed iu Table 2.," The $\beta$ -profile + point source model best fit results, and the confidence upper limits to the count rates from a central point source in each galaxy are listed in Table 2." These are determined by increasing the maguitude of fixed poiut source until the fit for the remaiming .- profile parameters viclds a Ay?>6.61 above the best fit., These are determined by increasing the magnitude of fixed point source until the fit for the remaining $\beta$ -profile parameters yields a $\Delta \chi^2 \geq 6.64$ above the best fit. The maxima point source streneth determined iu precisely the same manner for the undewobbled nuages is substantially lower for all three galaxies. bv factors of 1.57.," The maximum point source strength determined in precisely the same manner for the undewobbled images is substantially lower for all three galaxies, by factors of $1.5 - 7$." Plots of the surface briehtuess for all three galaxies. along with the profiles of the best fit models and those with the upper iit of ceutral point source brightness. are ceive in feures 1-3.," Plots of the surface brightness for all three galaxies, along with the profiles of the best fit models and those with the upper limit of central point source brightness, are given in figures 1-3." Figures 6 shows the 2-10 keV flux aud. photon iudex L for the power-law components determined by ADF2000 Gueluding confidence linits on a single interesting parameter) compared to our upper hints for the flux determined from the URI count rates for a ceutral point source. as a function of E.," Figures 4-6 shows the 2-10 keV flux and photon index $\Gamma$ for the power-law components determined by ADF2000 (including confidence limits on a single interesting parameter) compared to our upper limits for the flux determined from the HRI count rates for a central point source, as a function of $\Gamma$." These PIMMS estimates are shown for the column absorption densities eiven by the maxim value of either Stark (11992) or the best- values derived from aualvsis of PSPC spectra (Davis and White, These PIMMS estimates are shown for the column absorption densities given by the maximum value of either Stark \markcite{Star92}1 1992) or the best-fit values derived from analysis of PSPC spectra (Davis and White Vesta is the largest basaltic filly differentiated asteroid.,Vesta is the largest basaltic fully differentiated asteroid. Remote visible aud ucar-iufrared spectroscopy indicates the presence of basaltic muncralogy on Vesta’s surface and the possible presence of other components (MeCordetal.1970:Larson&Fiuk1975:Cattery 1907).," Remote visible and near-infrared spectroscopy indicates the presence of basaltic mineralogy on Vesta's surface and the possible presence of other components \citep{mcc70,lar75,gaf97}." A Lhuee nmuuber of small asteroids that show a simular surface composition. he so-called V-type asteroids. populates the inner main belt (Binzel&Xu1993:Dufhtudetal. 2001).," A large number of small asteroids that show a similar surface composition, the so-called V-type asteroids, populates the inner main belt \citep{bin93,duf04}." . V-tvpe asteroids have climeusious ess than a few tens of lan that cannot sustain differcutiation processes. therefore they 1st have con. originated from oue -or more- mich larecr. differentiated parent body.," V-type asteroids have dimensions less than a few tens of km that cannot sustain differentiation processes, therefore they must have been originated from one -or more- much larger, differentiated parent body." Thus. it has been sugeested that Vesta is tle parent body for V-ypes (MeCordetal.1970).," Thus, it has been suggested that Vesta is the parent body for V-types \citep{mcc70}." ". To support this scenario. apart from the aforementioned compositional αματν, if has been shown that may V-tvpes and Vesta beloug to a huge asteroid family (Alarzarietal.1996:Nesvoru*ctal. 2008)."," To support this scenario, apart from the aforementioned compositional similarity, it has been shown that many V-types and Vesta belong to a large asteroid family \citep[][]{mar96,nes08}." . To reinforce this luk. a 160 kan wide crater has been detected on Vesta (Thomasetal.1997).," To reinforce this link, a 460 km wide crater has been detected on Vesta \citep{tho97}." . Another interesting aspect concerning Vesta and V-tvpes is that their visible aud near-infrared spectra have been fouud to be similar to those of a particular suite of meteorites. uamely the howardite. eucrite and diogenite achoudrites (IIEDs:MeCord.et.al1970:Cousolinagno&Drake1977:Takeda1997:2001).," Another interesting aspect concerning Vesta and V-types is that their visible and near-infrared spectra have been found to be similar to those of a particular suite of meteorites, namely the howardite, eucrite and diogenite achondrites \citep[HEDs;][]{mcc70,con77,tak97,dra01}." . Qu. the other lud. it is also clear that neither all V-tvpes nor IIEDs are compatible with being derived frou Vesta: therefore. it is suspected that they originate from multiple differeutiated parent bodies (Yamaguchietal.2002:Wiechert200 1).," On the other hand, it is also clear that neither all V-types nor HEDs are compatible with being derived from Vesta; therefore, it is suspected that they originate from multiple differentiated parent bodies \citep{yam02,wie04}." . Iu this respect. it is significant that a few V-tvpes have been discovered bevoud the 3:1 mean motion resonance (Lazzaroetal.2000:Duffard&Roig2009) which cannot be related to Vesta on dynamical basis (Roigetal.2008:Nesvorux2008) and -at least in the case of Maguva-: also on compositional basis (ITardersenctal.2001).," In this respect, it is significant that a few V-types have been discovered beyond the 3:1 mean motion resonance \citep{laz00,duf09} which cannot be related to Vesta on dynamical basis \citep{roi08,nes08} and -at least in the case of Magnya- also on compositional basis \citep{har04}." . Despite the ecueral scenario described above is larecly accepted. there are some observations that remain unexplained.," Despite the general scenario described above is largely accepted, there are some observations that remain unexplained." First of all. V-tvpes generally exhibit strouecr absorption bands than Vesta aud steeper continuum both in the visible pijoteqs1998) and in the 0.L-1.6 rreeion (Burbineetal.2001).," First of all, V-types generally exhibit stronger absorption bands than Vesta and steeper continuum both in the visible \citep{hir98} and in the 0.4-1.6 region \citep{bur01}." . The reason for these discrepancies is not vet clear., The reason for these discrepancies is not yet clear. Possible causes are indicated im composition/texture differences or due to the effects of some alteration process (c.g.Burbineetal.2001).. like for instance those that have been demonstrated to cause optical alteration onu silicate-vich S-type asteroids (Jeclickeetal.2001:Marchi2006a).," Possible causes are indicated in composition/texture differences or due to the effects of some alteration process \citep[e.g.][]{bur01}, like for instance those that have been demonstrated to cause optical alteration on silicate-rich S-type asteroids \citep{jed04,mar06a}." . However. on S-types the 1 aud 2 aabsorption bands tend to become shallower by increasing space weathering (ie. increasing spectral slope). while this effect is not observed ou V-types.," However, on S-types the 1 and 2 absorption bands tend to become shallower by increasing space weathering (i.e. increasing spectral slope), while this effect is not observed on V-types." V-type asteroids that have reddest slopes also show strong 1 aud 2 absorption bands (e.g.Durbineetal.2001)., V-type asteroids that have reddest slopes also show strong 1 and 2 absorption bands \citep[e.g.][]{bur01}. . Vesta is found to be most comparable to howardites with a fine-erained size distribution (c.g.Pietersetal.2006)., Vesta is found to be most comparable to howardites with a fine-grained size distribution \citep[e.g.][]{pie06}. .. Ou the other haud. the laboratory experiments conducted on IIEDs and pyroxeues confirm that V-type materials should alter uudoer the effects of ion bombardment aud wmicrometeorite mipacts; in a wav simular to S-types. although the alteration timescale is) likely somehow reduced (Tirol&al.2006).," On the other hand, the laboratory experiments conducted on HEDs and pyroxenes confirm that V-type materials should alter under the effects of ion bombardment and micrometeorite impacts, in a way similar to S-types, although the alteration timescale is likely somehow reduced \citep{hir98,mar05a,ver06}." Iu this paper we present a comprehensive model of space weathering of caudidate V-tvpoes detected via SDSS photometry (Roig&Gil-IIutton2006)., In this paper we present a comprehensive model of space weathering of candidate V-types detected via SDSS photometry \citep{roi06}. . The preseut aualvsis als to investigate whether or not V-tvpe surfaces are affected by space weathering processes., The present analysis aims to investigate whether or not V-type surfaces are affected by space weathering processes. We identify several interesting facts that support the presence of space weathering alteration. although its behavior appears cistinct to what found on Iu doing so. our findings disclose interesting aspects of surface properties of Vesta and V- that are useful also in the context of the NASA Dawn nissjon (Russelletal.2007) for what concerns mission planning aud Vestas data interpretation.," We identify several interesting facts that support the presence of space weathering alteration, although its behavior appears distinct to what found on In doing so, our findings disclose interesting aspects of surface properties of Vesta and V-types that are useful also in the context of the NASA Dawn mission \citep{rus07} for what concerns mission planning and Vesta's data interpretation." surface of the gearwheel plate. and of a return fiber starting from the bottom surface of the gearwheel plate and reaching the IR detector at room temperature (silicon pin photodiodes OSRAM model BPX 61).,"surface of the gearwheel plate, and of a return fiber starting from the bottom surface of the gearwheel plate and reaching the IR detector at room temperature (silicon pin photodiodes OSRAM model BPX 61)." So the gearwheel interrupts the three optical fibers pairs., So the gearwheel interrupts the three optical fibers pairs. Eight groups of | mm tter holes are drilled through the gearwheel plate in 8 positions. corresponding to the 8 selected rotation angles of the waveplate.," Eight groups of 1 mm ter holes are drilled through the gearwheel plate in 8 positions, corresponding to the 8 selected rotation angles of the waveplate." Each pattern reproduces in binary code the index k of the angle 6)).," Each pattern reproduces in binary code the index $k$ of the angle $\,$ \ref{fig:6}) )." The operation of the system is similar to that of an absolute optical encoder: we detect and identify each integration position analyzing the signals transmitted through (or blocked by) the gearwheel., The operation of the system is similar to that of an absolute optical encoder: we detect and identify each integration position analyzing the signals transmitted through (or blocked by) the gearwheel. The gap (about 3 mm) in the optical fibers. due to the thickness of the gearwheel. introduces a significant light loss.," The gap (about 3 mm) in the optical fibers, due to the thickness of the gearwheel, introduces a significant light loss." This is recovered by modulating at kHz the IR emitters and recovering their signal by means of a synchronous demodulator.," This is recovered by modulating at $\,$ kHz the IR emitters and recovering their signal by means of a synchronous demodulator." A block diagram of the readout electronics is reported in Fig.6..," A block diagram of the readout electronics is reported in $\,$ \ref{fig:6}." For gaps smaller than 10mm (which is our Operating condition) the output signal is highly stable: global variations range from 0.5% to 2% depending on the amplification gain.," For gaps smaller than $\,$ mm (which is our operating condition) the output signal is highly stable: global variations range from $\%$ to $\%$ depending on the amplification gain." A detection test. made with the insertion of a mm diaphragm (the same diameter of the holes in the gearwheel) between the fibers. leaves unchanged the signal to noise ratio.," A detection test, made with the insertion of a $\,$ mm diaphragm (the same diameter of the holes in the gearwheel) between the fibers, leaves unchanged the signal to noise ratio." We have carried out a number of qualification tests on the key components of this system., We have carried out a number of qualification tests on the key components of this system. The CWR. mounted on the cold stage of the photometer. will work with its axis approximately vertical.," The CWR, mounted on the cold stage of the photometer, will work with its axis approximately vertical." During its rotation we need to avoid shifts of the HWP., During its rotation we need to avoid shifts of the HWP. We have verified that the shift of the rotation axis with respect to the aperture stop is limited to < 0.13 mm when the CWR is rotated from a vertical axis configuration to an horizontal one., We have verified that the shift of the rotation axis with respect to the aperture stop is limited to $\lesssim$ 0.13 mm when the CWR is rotated from a vertical axis configuration to an horizontal one. This shift is completely acceptable. and has been obtained by means of suitable belleville washers pressing on the thrust bearing of the gearwheel.," This shift is completely acceptable, and has been obtained by means of suitable belleville washers pressing on the thrust bearing of the gearwheel." The accuracy and repeatability of the rotation angles of the HWP has been tested using a laser reflected on a small mirror mounted on the gearwheel., The accuracy and repeatability of the rotation angles of the HWP has been tested using a laser reflected on a small mirror mounted on the gearwheel. For all positions. from the histogram of many measurements we find that the c dispersion of the position angle is always well below 1* 1)) satisfying the experimental requirements ??)).," For all positions, from the histogram of many measurements we find that the $\sigma$ dispersion of the position angle is always well below $^{\circ}$ $\,$ \ref{tab:1}) ) satisfying the experimental requirements $\,$ \ref{p req}) )." Optical fibers have been tested sunk in liquid nitrogen; in this confiigeurrattion. the transmitted signal shows an increase of about 38%.," Optical fibers have been tested sunk in liquid nitrogen; in this tion, the transmitted signal shows an increase of about $\%$." Tests with a He leak-detector have excluded significant outgassing from the optical fibers and the flexible U-joint., Tests with a He leak-detector have excluded significant outgassing from the optical fibers and the flexible U-joint. The thermal conductivity of the optical fibers has been measured in the temperature range (4-300)K. Fiber specimens. running between the base temperature and a controlled higher temperature. have been mounted inside a test cryostat.," The thermal conductivity of the optical fibers has been measured in the temperature range $\div$ $\,$ K. Fiber specimens, running between the base temperature and a controlled higher temperature, have been mounted inside a test cryostat." We estimated the thermal conductivity from the power required to heat one side of the fibers. keeping the other side at 4K. The conductivity of the support system and the radiative heat leak have been properly taken into account.," We estimated the thermal conductivity from the power required to heat one side of the fibers, keeping the other side at 4K. The conductivity of the support system and the radiative heat leak have been properly taken into account." The estimated conductive thermal load from K to the first thermal shield of the cryostat. where they will be placed. carried by three pairs of fibers. em long. is mW. The fiberglass driveshaft (length. mm. inner and outer diameter 2mm and mm. respectively). carries à conductive thermal load. from room temperature to liquid Helium. of mW. So the total static heat load resulting from our system (driveshaft plus optical fibers) is about mW. well within the experimental requirements ??)).," The estimated conductive thermal load from $\,$ K to the first thermal shield of the cryostat, where they will be placed, carried by three pairs of fibers, $\,$ cm long, is $\,$ mW. The fiberglass driveshaft (length $\,$ mm, inner and outer diameter $\,$ mm and $\,$ mm, respectively), carries a conductive thermal load, from room temperature to liquid Helium, of $\,$ mW. So the total static heat load resulting from our system (driveshaft plus optical fibers) is about $\,$ mW, well within the experimental requirements $\,$ \ref{p req}) )." The operation of the CWR at cryogenic temperatures has been tested inside a labborrattorry eryostat cooled by a Pulse Tube cooler (PT)., The operation of the CWR at cryogenic temperatures has been tested inside a ry cryostat cooled by a Pulse Tube cooler (PT). Key temperatures are read by four silicon diode thermometers mounted on the two stages of the PT. the CWR lid and the top of the CWR vertical cylinder.," Key temperatures are read by four silicon diode thermometers mounted on the two stages of the PT, the CWR lid and the top of the CWR vertical cylinder." A data aequisition/switch unit reads the thermometers., A data acquisition/switch unit reads the thermometers. The optical fibers. 2m long. cross the coldest environment and reach the K stage after thermalization on the intermediate PT stage.," The optical fibers, $\,$ m long, cross the coldest environment and reach the $\,$ K stage after thermalization on the intermediate PT stage." A Mylar shield encloses them avoiding conductive loads due to the contact with the K shield.," A Mylar shield encloses them avoiding conductive loads due to the contact with the $\,$ K shield." " A co-axial magnetic coupling transmits the motor torque through the vacuum shell of the cryostat, a stainless steel non-magnetic containment barrier allows complete insulation of the inner magnetic hub from the outer one without any contact.", A co-axial magnetic coupling transmits the motor torque through the vacuum shell of the cryostat; a stainless steel non-magnetic containment barrier allows complete insulation of the inner magnetic hub from the outer one without any contact. The dissipated power is measured comparing the heating of the K environment. induced by the CWR movement. to the ones produced by two power wirewound resistors. mounted on the CWR lid.," The dissipated power is measured comparing the heating of the $\,$ K environment, induced by the CWR movement, to the ones produced by two power wirewound resistors, mounted on the CWR lid." During this test the intermediate PT stage reached K: the low temperature one (4xI) K. the CWR lid (641) K and the CWR cylinder (6+1) K. The torque required to rotate the system was lower than 0.08 N-m. With the CWR thermalized at cryogenic temperature. we have performed a number of scans during which the electronic system read all the predetermined positions.," During this test the intermediate PT stage reached $(68\pm1)\,$ K; the low temperature one $(4\pm1)\,$ K, the CWR lid $(6\pm1)\,$ K and the CWR cylinder $(6\pm1)\,$ K. The torque required to rotate the system was lower than 0.08 $\cdot$ m. With the CWR thermalized at cryogenic temperature, we have performed a number of scans during which the electronic system read all the predetermined positions." lower-redshift B: K galaxies (which have similar SFRs; e.g. Daddietal.2008)).,lower-redshift $z$ K galaxies (which have similar SFRs; e.g. \citealp{daddi08}) ). " Our results for both LAEs rule out the presence of extreme Iline luminosities, such as those seen in sub-mm galaxics or hyperluminous IR quasars (c.g. Greve2003;Carillietal. 2007))."," Our results for both LAEs rule out the presence of extreme line luminosities, such as those seen in sub-mm galaxies or hyperluminous IR quasars (e.g. \citealp{greve05,walter03,carilli07}) )." LAEs thus appear to either contain significantly lower quantities of cold molecular gas or have significantly higher CO-to-H» conversion factors than sub-mm ealaxies or FIR-bright quasar hosts., LAEs thus appear to either contain significantly lower quantities of cold molecular gas or have significantly higher $_2$ conversion factors than sub-mm galaxies or FIR-bright quasar hosts. " The latter possibility cannot be ruled out as the CO-to-H» conversion factor 15 likely to depend on metallicity (c.g. Maloney&Black19885), and quasar host ealaxies and sub-mm galaxies appear to be dusty, metal-rich systems."," The latter possibility cannot be ruled out as the $_2$ conversion factor is likely to depend on metallicity (e.g. \citealp{maloney88}) ), and quasar host galaxies and sub-mm galaxies appear to be dusty, metal-rich systems." " Finally, it is clear that molecular gas must be present in LAEs to fuel the observed star-formation activity and dust reddening."," Finally, it is clear that molecular gas must be present in LAEs to fuel the observed star-formation activity and dust reddening." " In cases where the CO line emission is optically thick and thermalized, the flux density in the CO lines scales xvexJr. where ο 1s the rotational quantum number of the upper level."," In cases where the CO line emission is optically thick and thermalized, the flux density in the CO lines scales $\propto \nu^2 \propto J_{\rm U}^2$, where $J_{\rm U}$ is the rotational quantum number of the upper level." " This suggests that, despite the sensitive limits obtained here, the οι>5 CO lines may provide a more effective avenue to probe the molecular gas content of high-: LAEs, with planned facilities like the Expanded Very Large Array (EVLA) and the Atacama Large Millimetre Array (ALMA)."," This suggests that, despite the sensitive limits obtained here, the $J_{\rm U} \ge 5$ CO lines may provide a more effective avenue to probe the molecular gas content of $z$ LAEs, with planned facilities like the Expanded Very Large Array (EVLA) and the Atacama Large Millimetre Array (ALMA)." " For example, for optically-thick, thermalized emission, ALMA would be able to detect the lline from a >=6.5 star-forming galaxy with Mi,=3x10""M. in 3 hours of on-source integration time."," For example, for optically-thick, thermalized emission, ALMA would be able to detect the line from a $z = 6.5$ star-forming galaxy with $M_{\rm H_2} = 3 \times 10^9 \: M_{\odot}$ in $3$ hours of on-source integration time." " Unfortunately. the high kinetic temperatures and densities required to raise the CO molecules to the high-./ excitation states are unlikely to be present in ""normal"" star-forming galaxies like the LAEs."," Unfortunately, the high kinetic temperatures and densities required to raise the CO molecules to the $J$ excitation states are unlikely to be present in “normal” star-forming galaxies like the LAEs." " For example, Fig."," For example, Fig." 9 of Aoetal.(2008) shows that the CO line intensities are sub-thermal at ο>5 in almost all galaxies (including ULIRGs and sub-mm galaxies) with observations of these lines., 9 of \citet{ao08} shows that the CO line intensities are sub-thermal at $J_{\rm U} \ge 5$ in almost all galaxies (including ULIRGs and sub-mm galaxies) with observations of these lines. " The sole exception is the lensed quasar APM0827945255, where a combination of AGN heating and very high gas densities appears to yield the high CO excitation (Webetal.2007)."," The sole exception is the lensed quasar APM08279+5255, where a combination of AGN heating and very high gas densities appears to yield the high CO excitation \citep{weiss07}." . This implies that it is likely to be difficult to detect the high- CO lines from 26 LAEs even with ALMA., This implies that it is likely to be difficult to detect the $J$ CO lines from $z \gtrsim 6$ LAEs even with ALMA. The 155m fine-structure transition of ionized carbon may hence prove the best candidate for mapping the large-scale structure of high-2 star-forming galaxies, The $158 \mu$ m fine-structure transition of ionized carbon may hence prove the best candidate for mapping the large-scale structure of $z$ star-forming galaxies cells along the radial and polar axes as specified by the thickness of the ring iu those directions.,cells along the radial and polar axes as specified by the thickness of the ring in those directions. " An obvious result taken from Figure 2 is the strong siuiluitv in the carly"" exponential growth aud lae time saturation profiles of|th magnetized and λαοjetizec rui.", An obvious result taken from Figure \ref{fig:mode53} is the strong similarity in the early exponential growth and late time saturation profiles of both magnetized and unmagnetized runs. But there are also several other poiuts of interest nu Figure 2.., But there are also several other points of interest in Figure \ref{fig:mode53}. For exiuupe. the m=1 mode saurates after about five «vuanudceal times to a level that is wel ow those of the m2 aud { modes (abou three Oreles of magnitude beow jg= 2. and two orders OW 11) la their yeakss). as is characteristic of ! bar mode.," For example, the $m=1$ mode saturates after about five dynamical times to a level that is well below those of the $m=2$ and 4 modes (about three orders of magnitude below $m=2$ , and two orders below $m=4$ at their peaks), as is characteristic of the bar mode." Since the odd modes tend to cucaoulate miuerical errors such astie center of nass clrift aud loss of angular monieitu. it Is encouraging to see the «xd nodes saturate iu time and the characteristic even modes o dominate the Fourlor sctia iu convincing fashion.," Since the odd modes tend to encapsulate numerical errors such as the center of mass drift and loss of angular momentum, it is encouraging to see the odd modes saturate in time and the characteristic even modes to dominate the Fourier spectrum in convincing fashion." We lave tracked the nass center in our caleulations :uic Not the result for a cw vpical cases in Figure 3.., We have tracked the mass center in our calculations and plot the result for a few typical cases in Figure \ref{fig:com}. The carly drift iu the ceut ero uns quickly saturates witiu a few dynamical times. aud the ceuter of mass thereater rendus mostly statioary.," The early drift in the center of mass quickly saturates within a few dynamical times, and the center of mass thereafter remains mostly stationary." The total late-time caift iu he position of the star mass center is very sinall. ~0.0la¢ for the GI? ervids. effectively confined to less thau ha a cell width iu the cenral most highly resolved (ualga+ zoning) portion of the exid.," The total late-time drift in the position of the star mass center is very small, $\sim 0.01\varpi_E$ for the $64^3$ grids, effectively confined to less than half a cell width in the central most highly resolved (smallest zoning) portion of the grid." The ceuter of mass positlon is preserved even bet erin the hieliresolution 96° τι being confined to within one quarter of a cell wi ~0400252;," The center of mass position is preserved even better in the high-resolution $96^3$ runs, being confined to within one quarter of a cell width, $\sim 0.0025\varpi_E$." Although we do not show the results here. we have verified that the modal histories iu the magnetized ruus are very simular to the uninagnetized results also for the P= 2 and 3 caxss. anc both sets look like the P=5/5 results in Figure 2..," Although we do not show the results here, we have verified that the modal histories in the magnetized runs are very similar to the unmagnetized results also for the $\Gamma=$ 2 and 3 cases, and both sets look like the $\Gamma=5/3$ results in Figure \ref{fig:mode53}." The only major difference that we have observed aud attributed to he equation of state is asvetcmatic shift (or delay) im time required for the even bar modes to cuter the exponeutial erowtl phase., The only major difference that we have observed and attributed to the equation of state is a systematic shift (or delay) in time required for the even bar modes to enter the exponential growth phase. This is cliscussecl further in the paragraphs below iu the coutest of eravitational wave enmüssious., This is discussed further in the paragraphs below in the context of gravitational wave emissions. The ineffectiveness of toroidal magnetic fields is denostrated agadn bv two additional calculations iu which we variel JpBaan to generate different initial Ποια amplitudes :oa factor of five reduction in ruu TOS3Bh500. aud a teu-fold increase iu run TCG»3D10.," The ineffectiveness of toroidal magnetic fields is demonstrated again by two additional calculations in which we varied $\beta_{B,\text{min}}$ to generate different initial field amplitudes: a factor of five reduction in run TG53B500, and a ten-fold increase in run TG53B10." Iu both cases. twoidal fields do not affect significantly ic growth or evelopment of the bar mode. in spite of the field iuuplification observed in Figures | and 5 which plot the total inteerated maguctic energv an 1ο local feld :uplitude. respectively. as a function of nue.," In both cases, toroidal fields do not affect significantly the growth or development of the bar mode, in spite of the field amplification observed in Figures \ref{fig:fieldenergy} and \ref{fig:shellamp} which plot the total integrated magnetic energy and the local field amplitude, respectively, as a function of time." The fiek wuplitude in Fieure 5 1 calculate as al aziuutha average inside a circular annulus in 1 equatorial ane at radi O.65ap (the initial center of the toroidal field loop) aud O.2a.¢.," The field amplitude in Figure \ref{fig:shellamp} is calculated as an azimuthal average inside a circular annulus in the equatorial plane at radii $\varpi_E$ (the initial center of the toroidal field loop) and $\varpi_E$." Note the fiek auplitucde is alreuly saturated aud does not evolve much at the initial configuration radius (oop= ü.65zeg). but erows substantiaIv at iunaller racii.," Note the field amplitude is already saturated and does not evolve much at the initial configuration radius $r_\mathrm{loop}=0.65\varpi_E$ ), but grows substantially at smaller radii." Eventually. the fiele auplitude aud eucrey saturate in time at all radii to rougeilv thesame value.," Eventually, the field amplitude and energy saturate in time at all radii to roughly thesame value." This behavior is seen in al of the cases we rave tried. meludiug the smallest Πο]," This behavior is seen in all of the cases we have tried, including the smallest field" lere. the first product is over the set of data points with detections. Ayj.¢. and the second product is over the set of data points with unon-detections. Au...,"Here, the first product is over the set of data points with detections, ${\cal A}_{det}$, and the second product is over the set of data points with non-detections, ${\cal A}_{cens}$." The couditional distribution PAY;loj.Ü.cus) aud the marginal distribution ple;Joes) for the Gaussian mixture model are both given iu L1 aud’ 13..," The conditional distribution $p(y_j|x_j,\theta,\psi_{obs})$ and the marginal distribution $p(x_j|\psi_{obs})$ for the Gaussian mixture model are both given in \ref{s-normreg} and \ref{s-multreg}." Ifthe data points are measured without error and oue asses the normal reeression model. ης0)=N(jla|bo.a7). then Equation 12. becomes the censored data likclihood function described iu Isobeetal.(1986).," If the data points are measured without error and one assumes the normal regression model, $p(\eta|\xi,\theta) = N(\eta|\alpha + \beta \xi,\sigma^2)$, then Equation \ref{eq-censlik} becomes the censored data likelihood function described in \citet{isobe86}." . A MEE for censored regression with measurement errors is then obtaiued by maximizing Equation (12))., A MLE for censored regression with measurement errors is then obtained by maximizing Equation \ref{eq-censlik}) ). " Iu this section I describe a Bayesian method for computing estimates of the regression parameters. 0, and their uncertainties."," In this section I describe a Bayesian method for computing estimates of the regression parameters, $\theta$, and their uncertainties." The Bayesian approach calculates the posterior probability distribution of the model paralcters. given the observed data. aud therefore is accurate for both small and large sample sizes.," The Bayesian approach calculates the posterior probability distribution of the model parameters, given the observed data, and therefore is accurate for both small and large sample sizes." The posterior distribution follows from Baye’s formula as ptf.μοι)Xρθραg|0.0). where ptf.0) is the prior distribution of the parameters.," The posterior distribution follows from Baye's formula as $p(\theta,\psi|x,y) \propto p(\theta,\psi) p(x,y|\theta,\psi)$, where $p(\theta,\psi)$ is the prior distribution of the parameters." I describe some Markov Chain methods for drawing raucom variables frou. the posterior. which can then be used to estimate quantities such as standard errors and coufideuce intervals on ϐ and c.," I describe some Markov Chain methods for drawing random variables from the posterior, which can then be used to estimate quantities such as standard errors and confidence intervals on $\theta$ and $\psi$." Gelinanetal.(200L) is a good reference on Bayesian methods. aud Loredo(1992) eives a review of Bayesian methods inteuded for astronomers.," \citet{gelman04} is a good reference on Bayesian methods, and \citet{loredo92} gives a review of Bayesian methods intended for astronomers." Further details of Markov. Chain simulation. including methods for making the simulations more efficient. can be found in Gelmanetal.(2001).," Further details of Markov Chain simulation, including methods for making the simulations more efficient, can be found in \citet{gelman04}." Iu order to ensure a proper posterior for the Gaussian mixture model. it is necessary to invoke a proper prior deusitv on the mixture paraueters (Roeder&Wasserman1997).," In order to ensure a proper posterior for the Gaussian mixture model, it is necessary to invoke a proper prior density on the mixture parameters \citep{roeder97}." . P adopt a unuiforii prior ou the reeression parameters (0.2.07). and take z1.....ay~Diichlet(l.....1).," I adopt a uniform prior on the regression parameters $(\alpha, \beta, \sigma^2)$, and take $\pi_1,\ldots,\pi_K \sim {\rm Dirichlet}(1,\ldots,1)$." The Dirichlet deusitv is a multivariate extension of the Beta density. aud the Divichlet(1.....1) prior adopted in this work is equivalent to a uniformi» prior. ou 7. under the constraiut. MKπες.1.," The Dirichlet density is a multivariate extension of the Beta density, and the ${\rm Dirichlet}(1,\ldots,1)$ prior adopted in this work is equivalent to a uniform prior on $\pi$ , under the constraint $\sum_{k=1}^K \pi_k = 1$." TheY prior: ou µ auc 77D (or T) adopted inB thisB work is. very similar+ to that advocated by auc Carrolletal.(1999)., The prior on $\mu$ and $\tau^2$ (or $T$ ) adopted in this work is very similar to that advocated by \citet{roeder97} and \citet{carroll99}. . T adopt a normal prior ou the individual jj with mea 440 aud variance u? (or covariance matrix C)., I adopt a normal prior on the individual $\mu_k$ with mean $\mu_0$ and variance $u^2$ (or covariance matrix $U$ ). This reflects our prior belief that the distribution of $ is more likely to be fairly uniniodal. aud thus that we expect it to be more likely that the individual Gaussians will be close together than far apart.," This reflects our prior belief that the distribution of $\xi$ is more likely to be fairly unimodal, and thus that we expect it to be more likely that the individual Gaussians will be close together than far apart." If there is ouly oue covariate. then T adopt a scaled inverse-\? prior ou the individua TÉ with scale parameter (7 aud one deeree of frecdou otherwise if there are p1 covariates I adopt an mverse-Wishart prior on the individual 7; with scale matrix W and p deerces of freedom.," If there is only one covariate, then I adopt a scaled $\chi^2$ prior on the individual $\tau_k^2$ with scale parameter $w^2$ and one degree of freedom, otherwise if there are $p > 1$ covariates I adopt an inverse-Wishart prior on the individual $T_k$ with scale matrix $W$ and $p$ degrees of freedom." This reflects our prior expectation that the varices for the individual Gaussian compoucuts should be simular. but the low number of degrees of freedom accomodates a large range of scales.," This reflects our prior expectation that the variances for the individual Gaussian components should be similar, but the low number of degrees of freedom accomodates a large range of scales." " Both the Gaussian micas and variances- are assumed to be independent. in. theirH priorH distribution.B aud the ""livper-parauietersH pg.ueD Cor Cj. and «7 (or J) are left uuspeciied."," Both the Gaussian means and variances are assumed to be independent in their prior distribution, and the `hyper-parameters' $\mu_0, u^2$ (or $U$ ), and $w^2$ (or $W$ ) are left unspecified." By leaving the parameters for the prior distribution uuspoecified. they becomes additional paraiieters in the statistical model. aud therefore are able to adapt to the data.," By leaving the parameters for the prior distribution unspecified, they becomes additional parameters in the statistical model, and therefore are able to adapt to the data." Since the hyper-paraieters are left as free parameters they also require a prior deusity., Since the hyper-parameters are left as free parameters they also require a prior density. Tassie a uniform prior on. py aud w? (or VW)., I assume a uniform prior on $\mu_0$ and $w^2$ (or $W$ ). Tf there is one covariate. then ΠΠ a scaled inverse-\? prior for à with scale parameter «7? aud oue degree of frecdou otherwise if there are unltiple covariate we assume a inverse-Wishart prior for C with scale matrix Τ and p degrees of freedom.," If there is one covariate, then I assume a scaled $\chi^2$ prior for $u^2$ with scale parameter $w^2$ and one degree of freedom, otherwise if there are multiple covariate we assume a inverse-Wishart prior for $U$ with scale matrix $W$ and $p$ degrees of freedom." The prior on 4? (or C) reflects the prior expectation that the dispersion of the Gaussian compoucuts about their mean fiy shouldbe ou, The prior on $u^2$ (or $U$ ) reflects the prior expectation that the dispersion of the Gaussian components about their mean $\mu_0$ shouldbe on et al..,"et al.," 2002: Sone et al..," 2002; Song et al.," 2009) aud theoretical modelings (oe. Wane ct al..," 2009) and theoretical modelings (e.g., Wang et al.," 1998: Suess et al.," 1998; Suess et al.," 1999: Chen et al.," 1999; Chen et al.," 2001. 2002: IIu et ab.," 2001, 2002; Hu et al.," 2003: Li et aL.," 2003; Li et al.," 2006)., 2006). In this short discussion. we simply make use of the solar wind conditions obtained by Chen Iu (2001).," In this short discussion, we simply make use of the solar wind conditions obtained by Chen Hu (2001)." " Ouly two distauces are considered. (1) at 5 R.. the solav wind velocity c4,=100 kin and p=l1os10? ? and (2) at LO Ro. tee=200 kii s| and» —ὃς10! em7."," Only two distances are considered, (1) at 5 $R_\odot$, the solar wind velocity $v_{sw} = 100$ km $^{-1}$ and $n = 1\times10^5$ $^{-3}$ , and (2) at 10 $R_\odot$, $v_{sw} = 200$ km $^{-1}$ and $n = 2\times10 ^4$ $^{-3}$." " With these assuuiptions. it is straightforward to deduce e; aud thus ey, at the plasima rest frame. and hen calculate the value of the magnetic field strength D, at the above two distances in the region surrouncdiug he plasma sheet."," With these assumptions, it is straightforward to deduce $c_k$ and thus $v_{Ae}$ at the plasma rest frame, and then calculate the value of the magnetic field strength $B_e$ at the above two distances in the region surrounding the plasma sheet." " Were we only present our calculations of B, with the measurements associated with the second olase point P2. whose speeds ave 110 kins 3 at SR. and 360 kins | at 10 Ro. as read from Fieure 5."," Here we only present our calculations of $B_e$ with the measurements associated with the second phase point P2, whose speeds are 410 km $^{-1}$ at $R_\odot$ and 360 km $^{-1}$ at 10 $R_\odot$, as read from Figure 5." It is found that the maeuetic field streueth declines. from 1015 Gat 5b. Ro to 0.01 Cat LOR... indicating a sheltlhy super-radial expansion of the magnetic flux tube from 5 o 10 R..," It is found that the magnetic field strength declines from 0.045 G at 5 $R_\odot$ to 0.01 G at 10 $R_\odot$, indicating a slightly super-radial expansion of the magnetic flux tube from 5 to 10 $R_\odot$." These values are consistent with the results eiven by τουσ! corona aud solar wind models (e.g... Li et al..," These values are consistent with the results given by recent corona and solar wind models (e.g., Li et al.," 2006)., 2006). A more complete seismological study. together with sophisticated wmuecrical MIID simiulatious of CME-streamer interactious to shed amore liebt ou the excitation and propagation of the waves. should be couducted imn future.," A more complete seismological study, together with sophisticated numerical MHD simulations of CME-streamer interactions to shed more light on the excitation and propagation of the waves, should be conducted in future." The SOIIO/LASCO data used here are produced bv a consortium of the Naval Research Laboratory (USA). Max-Plauck-Iustitut finr Acronomie (Cormauy). Laboratoire d'Astrononude Spatiale (France). aud the Universtv of Dinüusghzan (UR).," The SOHO/LASCO data used here are produced by a consortium of the Naval Research Laboratory (USA), Max-Planck-Institut fürr Aeronomie (Germany), Laboratoire d'Astronomie Spatiale (France), and the University of Birmingham (UK)." The CALE catalog cluploved in our study is generated and maintained at the CDAW Data Ceuter by NASA aud The Catholic University of Aierica in cooperation with the Naval Research Laboratory., The CME catalog employed in our study is generated and maintained at the CDAW Data Center by NASA and The Catholic University of America in cooperation with the Naval Research Laboratory. SOTO is a project of international cooperation between ESA and NASA., SOHO is a project of international cooperation between ESA and NASA. This work was supported bv erauts NNSEC. £0771091.. 05252011. LOS9O162. LO90LOLT. NSBRSF C2006CBs0630lL. auc A Foundation for the Author of National Excellent Doctoral Dissertationof PR China (2007B21).," This work was supported by grants NNSFC 40774094, 40825014, 40890162, 40904047, NSBRSF G2006CB806304, and A Foundation for the Author of National Excellent Doctoral Dissertationof PR China (2007B24)." We think Isai Lin and Chenugloug Shen for their assistance in data manipulations., We thank Kai Liu and Chenglong Shen for their assistance in data manipulations. power-law model. without evidence for thermal accretion disc components (Bergheaetal. 2008)). similar to MCG-05-23-016.,"power-law model, without evidence for thermal accretion disc components \cite{Berghea08}) ), similar to MCG--05--23--016." In some cases ULX show a dise component. e.g. the observation of two ULX in revealed soft components which are well fitted by multicolor dise blackbody models with color temperatures of KT=[50eV.," In some cases ULX show a disc component, e.g. the observation of two ULX in revealed soft components which are well fitted by multicolor disc blackbody models with color temperatures of $kT \simeq 150 \rm \, eV$." An alternative model for the accretion process onto black holes has been proposed by Courvoisier Tiirrler (2005). in which the aceretion flows consist of different elements (clumps) which have velocities that may differ substantially.," An alternative model for the accretion process onto black holes has been proposed by Courvoisier Türrler (2005), in which the accretion flows consist of different elements (clumps) which have velocities that may differ substantially." AS aconsequece. collisions between these clumps will appear when the clumps are close to the central object. resulting in radiation.," As a consequence, collisions between these clumps will appear when the clumps are close to the central object, resulting in radiation." In the case of MCG—05—23-016. this model results in low-energetic collisions. which is also indicated by the missing variability in the UV band as seen by Swifr/UVOT. where these collisions should cause flux variations.," In the case of MCG–05–23–016, this model results in low-energetic collisions, which is also indicated by the missing variability in the UV band as seen by /UVOT, where these collisions should cause flux variations." Low mass AGN like MCG -05-23-016 operating at high Eddington rate might be an early state in the evolution towards high-mass black holes as seen in quasars., Low mass AGN like MCG –05–23–016 operating at high Eddington rate might be an early state in the evolution towards high-mass black holes as seen in quasars. As the highest measured redshift of à quasar to date is z=6.43 (Willott et al., As the highest measured redshift of a quasar to date is $z = 6.43$ (Willott et al. 2007). we can assume that these objects with black hole masses of M>10*M.. appear in the Universe around zo7.," 2007), we can assume that these objects with black hole masses of $M > 10^8 \rm \, M_\odot$ appear in the Universe around $z \sim 7$." df we assume the formation of the first heavy black holes with M~109M. at redshift ς=10. we indeed need high mass aceretion rates.," If we assume the formation of the first heavy black holes with $M \sim 10^6 \rm \, M_\odot$ at redshift $z = 10$, we indeed need high mass accretion rates." An object like MCG -05-23-016. if we consider its mass to be indeed M«5x109M... with a constant Eddington ratio of {οει=0.8 and starting black hole mass of M(z=10)10*M. would reach a mass of Μις7)=4x105M...," An object like MCG –05–23–016, if we consider its mass to be indeed $M \lae 5 \times 10^6 \rm \, M_\odot$, with a constant Eddington ratio of $L_{bol}/L_{Edd} = 0.8$ and starting black hole mass of $M(z=10) = 10^6 \rm \, M_\odot$ would reach a mass of $M(z=7) = 4 \times 10^8 \rm \, M_\odot$." However. this would require not only the existence of a super massive black hole with M~109M. at redshift z=10. but also a high accretion rate over a time span of 3x10? yrs.," However, this would require not only the existence of a super massive black hole with $M \sim 10^6 \rm \, M_\odot$ at redshift $z = 10$, but also a high accretion rate over a time span of $3 \times 10^8$ yrs." But even at a duty cycle of only 20% for AGN activity at z>7. objects like MCG —-05-23-016 can evolve to 105M... and it has to be taken into account that the duty cycle of AGN is likely to be larger in the high-redshift Universe (Wang et al.," But even at a duty cycle of only $20\%$ for AGN activity at $z \ge 7$, objects like MCG –05–23–016 can evolve to $10^8 \rm \, M_\odot$, and it has to be taken into account that the duty cycle of AGN is likely to be larger in the high-redshift Universe (Wang et al." 2008)., 2008). On the other hand. it has to be considered that the environment in which the AGN grows at redshifts ς>7 might be significantly different than the one we observe MCG 23-016 at in the local Universe.," On the other hand, it has to be considered that the environment in which the AGN grows at redshifts $z>7$ might be significantly different than the one we observe MCG --05--23--016 at in the local Universe." The Seyfert 1.9 galaxy MCG-05-23-016 shows evidence for a variable reflection component. variable plasma temperature and high-energy cut-off energy.," The Seyfert 1.9 galaxy MCG–05–23–016 shows evidence for a variable reflection component, variable plasma temperature and high-energy cut-off energy." The combined data set presented here shows a low reflection component (R« 0.3) compared to previous studies which show a value as high às R=|., The combined data set presented here shows a low reflection component $R < 0.3$ ) compared to previous studies which show a value as high as $R = 1$. The data require a high-energy cut-off at 72 keV. but one observation shows an undisturbed power-law up to E>100keV.," The data require a high-energy cut-off at 72 keV, but one observation shows an undisturbed power-law up to $E > 100 \rm \, keV$." Tighter constraints on the hard X-ray spectrum and the effect of Compton reflection will be only achievable with focusing optics. as they will be provided by the future missions," Tighter constraints on the hard X-ray spectrum and the effect of Compton reflection will be only achievable with focusing optics, as they will be provided by the future missions" the digitized Second Palomar Observatory Skv Survey (Lopesetal.2001) and the maxBCG technique using the SDSS photometric data to select candidates for eravitational arcs search (Estradactal.2007)..,the digitized Second Palomar Observatory Sky Survey \citep{2004AJ....128.1017L} and the maxBCG technique using the SDSS photometric data to select candidates for gravitational arcs search \citep{2007ApJ...660.1176E}. We analyze cleaned event files version 2.5 of the three. CCD chips (NIS 0. 1. and 3) with both 5 « 5 and 3 <3 editing aud normal clocking modes after reprocessing with the standard selection criteria: the energv correction byspi. the removal of hot/flickcrine pixels byeleensis.," We analyze cleaned event files version 2.5 of the three CCD chips (XIS 0, 1, and 3) with both 5 $\times$ 5 and 3 $\times$ 3 editing and normal clocking modes after reprocessing with the standard selection criteria: the energy correction by, the removal of hot/flickering pixels by." The exposure corrected image shown in Figure 2aa exhibits the preseuce of a diffuse N-rav halo with an πορτα morphology. namely. a new object.," The exposure corrected image shown in Figure \ref{fig:HR}a a exhibits the presence of a diffuse X-ray halo with an irregular morphology, namely, a new object." . We denote three peaks as peak A. D aud € as shown in Figure 2aa. The gravitational ceuter of is likely located near the peak A because of the presence of the BCG (see also the optical image by Digitized Sky Survey (DSS) iu Fig. [2]|," We denote three peaks as peak A, B and C as shown in Figure \ref{fig:HR}a a. The gravitational center of is likely located near the peak A because of the presence of the BCG (see also the optical image by Digitized Sky Survey (DSS) in Fig. \ref{fig:HR}] ]" c )., c ). " Computing the hardness ratio map shown in Figure 2bb. we found ""the hot spot” from the peaks D toward C. The definition of the harducss ratio is IIR—(IlS)/(IE|S) with the hard (I) and soft (S) baud images of the combined froutdilhuuiuated (FT) and backilluuinated (DI) images. where the energy ranee of ID and S are 1.1-2.0 keV and 0.11.1 keV. The combination of the regular morphology aud the preseuce of the hot spot is a conuuon feature in the mereing cluster (e.g.Duetetal.2005:Ferrarict 2006).."," Computing the hardness ratio map shown in Figure \ref{fig:HR}b b, we found “the hot spot” from the peaks B toward C. The definition of the hardness ratio is $\mathrm{HR \equiv (H-S)/(H+S)}$ with the hard (H) and soft (S) band images of the combined front-illuminated (FI) and back-illuminated (BI) images, where the energy range of H and S are 1.1-2.0 keV and 0.4-1.1 keV. The combination of the irregular morphology and the presence of the hot spot is a common feature in the merging cluster \citep[e.g.][]{2005A&A...432..809D,2006A&A...446..417F}." We now ineasure the spectroscopic temperature., We now measure the spectroscopic temperature. All spectral fittings were performed with ASPEC 12.6.0 (Arnaud1996) with Suzaku Calibration Database., All spectral fittings were performed with XSPEC 12.6.0 \citep{1996ASPC..101...17A} with Suzaku Calibration Database. We exclude data having a revised cutoff rigidity (COR2) less than 6 GW., We exclude data having a revised cutoff rigidity (COR2) less than 6 GV. Using.sshnmerfgen. we created two different the Aucillary Respouse Files (ARFs). AP and A' assundue the observed NIS image in the energv range of l-1 keV aud uniform sky cussion. which are applied to the eroup componcut aud the cosnic A-aav backeround (CNB) plus other diffuse galactic colmpoucuts. respectively (shisakictal.2007).," Using, we created two different the Ancillary Response Files (ARFs), $\mathrm{A^B}$ and $\mathrm{A^U}$ assuming the observed XIS image in the energy range of 1-4 keV and uniform sky emission, which are applied to the group component and the cosmic X-ray background (CXB) plus other diffuse galactic components, respectively \citep{2007PASJ...59S.113I}." To determine the foreground and backeround model. we choose TCRB as a fiducial offset (Fig. |l]| ," To determine the foreground and background model, we choose TCRB as a fiducial offset (Fig. \ref{fig:pos}] ] (" Gight).,right). We also analyzed APLI2 offset aud FIL as references although these two regions are close to À2112 and possibly include leakage., We also analyzed A2142 offset and FIL as references although these two regions are close to A2142 and possibly include leakage. " After exchiding a ceutral target of TCRD aud several poiut-like sources. we siauultaneouslv ft the spectra of the FI aud DI chips by the two-temperature modelapeco. wherepow mdicates the power law of the| CNB with the photon iudex P=1.11 (fsx:Isushino 2002).. aud the CNB intensity ον, is the thermal chussion model with T2Tj (APEC:Suüthetal.2001) interpreted as the transabsorption euissiou (TAE:INuutz&Snowden2000). from outside of the Calaxy. such as the Galactic Talo euission.«peco assuues the thermal enussion with 7=T5 from inside of the Galaxy. such as the local hot bubble aud we fix the Calactic absorption Gphabs) using the neutral hydrogen column deusitv Vy provided by IEalberlaetal.(2005).."," After excluding a central target of TCRB and several point-like sources, we simultaneously fit the spectra of the FI and BI chips by the two-temperature model:, where indicates the power law of the CXB with the photon index $\Gamma=1.41$ \citep[fix; ][]{2002PASJ...54..327K}, and the CXB intensity $S_\mathrm{CXB}$, is the thermal emission model with $T=T_1$ \citep[APEC;][]{2001ApJ...556L..91S} interpreted as the transabsorption emission \citep[TAE;][]{2000ApJ...543..195K} from outside of the Galaxy, such as the Galactic Halo emission, assumes the thermal emission with $T=T_2$ from inside of the Galaxy, such as the local hot bubble and we fix the Galactic absorption ) using the neutral hydrogen column density $N_{\mathrm{H}}$ provided by \citet{2005A&A...440..775K}." We use the data in the euerev range of 0.1 - 5.0 keV and 0.5 - 5.0 keV for the BI aud FI chips., We use the data in the energy range of 0.4 - 5.0 keV and 0.5 - 5.0 keV for the BI and FI chips. The best fit values are given in Table 1.., The best fit values are given in Table \ref{tab:spec}. The CNB intensity of TCRD is cousisteut with the results by ASC'A. Scexpaa(6.38+1.05)10Sereem2stsr!keV.1 (905€statisticalsystematicerror:Iushineetal.2002)..," The CXB intensity of TCRB is consistent with the results by ASCA, $S_\mathrm{CXB,asca}=(6.38 \pm 0.07 \pm 1.05) \times 10^{-8} \, \mathrm{erg \, cm^{-2} s^{-1} sr^{-1} keV^{-1}}$ \citep[90 \% statistical and systematic error; ][]{2002PASJ...54..327K}." We extract the spectra of the overall region of the eroup within the radius of 0.6 \Ipe =6.6 around the BCG., We extract the spectra of the overall region of the group within the radius of 0.6 Mpc $=6.6^\prime$ around the BCG. The hot spot was excluded with the radius of 0.2Mpc based on the hardness ratio map (Fig |2]] e).," The hot spot was excluded with the radius of $0.2 \, \mathrm{Mpc}$ based on the hardness ratio map (Fig \ref{fig:HR}] ] c)." " We fit the spectra by the thermal emission model (apec,) with the two temperature model provided by the offset observation:apeco.", We fit the spectra by the thermal emission model ${\it apec_g}$ ) with the two temperature model provided by the offset observation:. We use the fiducial offset (Τοπο) for the temperatures of the ealactic components aud leave normalizatious as free parameters and fx D=αν and Sexpausa for the normalization of the CNB.," We use the fiducial offset (TCRB) for the temperatures of the galactic components and leave normalizations as free parameters and fix $\Gamma=1.41$ and $S_\mathrm{CXB,asca}$ for the normalization of the CXB." We compute the systematics originated from the uncertainty of the CXD intensity bv extrapolating the results of CINGA with the field of views © (Ποποetal.2010) and the temperatures of the galactic commpoucuts assuming that the errors are £0.05 keV and +£0.02 keV for the TAE and the local component., We compute the systematics originated from the uncertainty of the CXB intensity by extrapolating the results of GINGA with the field of views $\Omega$ \citep{2010PASJ...62..371H} and the temperatures of the galactic components assuming that the errors are $\pm 0.05 $ keV and $\pm 0.02$ keV for the TAE and the local component. Although it is difficult to estimate the real fluctuations. the results of the other offset observations are within the assmned crrors.," Although it is difficult to estimate the real fluctuations, the results of the other offset observations are within the assumed errors." The spectra with the fitted lines are shown in Figure 3 and the best-fit parameters are sunumuarized in Table l., The spectra with the fitted lines are shown in Figure \ref{fig:spec} and the best-fit parameters are summarized in Table \ref{tab:spec}. The spectroscopic teniperature Is Lolps keV aud the corresponding που is 0.59Mpce using Vilsblininetal(2006).. which approximately corresponds to the overall region.," The spectroscopic temperature is $1.6_{-0.1}^{+0.4} $ keV and the corresponding $R_{500}$ is $0.59 \, \mathrm{Mpc}$ using \citet{2006ApJ...640..691V}, , which approximately corresponds to the overall region." The group probably escaped from the detection ofthe RASS due to its mareiual fux (3.5105«10λαο for 0.5-2.0 keV) compared with the RASS flux limit ~3.10Pere/s/em?.," The group probably escaped from the detection of the RASS due to its marginal flux $3.5^{+0.3}_{-0.2} \times 10^{-13} \, \mathrm{erg/s/cm^2}$ for 0.5-2.0 keV) compared with the RASS flux limit $\sim 3 \times 10^{-13} \, \mathrm{erg/s/cm^2}$." The bolometric uuninosityv 2.110 erg/sis consistent with the observed Lx-TI relation for T=1.6 keV (e.g.Mulchaey.20000.," The bolometric luminosity $2.4 \times 10^{43} \, \mathrm{erg/s}$ is consistent with the observed $L_\mathrm{X}$ $T$ relation for $T=1.6$ keV \citep[e.g.][]{2000ARA&A..38..289M}." As shown in Figure 2cc. we divide three shells around he BCG center to R=0.6 Mpc with the width of L2Mpce=2.2%.," As shown in Figure \ref{fig:HR}c c, we divide three shells around the BCG center to $R=0.6$ Mpc with the width of $0.2 \mathrm{Mpc} = 2.2^\prime$." The sae analysis was done for the lee shells aud the hot spot., The same analysis was done for the three shells and the hot spot. We exclude the hot spot reeion iu the analysis of the three shells., We exclude the hot spot region in the analysis of the three shells. The fitting cluperatures and metalicitics are provided in Table 1.., The fitting temperatures and metalicities are provided in Table \ref{tab:spec}. . The half decrement of temperature from the ceuter to Foy aud the abuudance profile agree well with a previous systematic study of eroups (Rasmussen&Pouman2007:Sunetal. 2009).," The half decrement of temperature from the center to $R_{500}$ and the abundance profile agree well with a previous systematic study of groups \citep{2007MNRAS.380.1554R,2009ApJ...693.1142S}." . The hot spot has significantly higher enperature (1ο κο) than that of surrounding shells. even than the central temperature within A=0.2 A\Ipc and relatively ligh metallicity which is comparable to hat ofthe center.," The hot spot has significantly higher temperature $T \sim 4$ keV) than that of surrounding shells, even than the central temperature within $R=0.2$ Mpc and relatively high metalicity which is comparable to that of the center." The main systematic source of 47 is the slight inconsistenev of the DI aud FI chips below -0.5 τον likely due to the Nou. N-vayv Backeround (NXB) subtraction., The main systematic source of $\chi^2$ is the slight inconsistency of the BI and FI chips below $E < 0.8$ keV likely due to the Non X-ray Background (NXB) subtraction. However we confirmed this effect does nof change the result by ucelecting E«0.8 keV. We believe hat future update of the NND calibration will improve lis incousisteucy., However we confirmed this effect does not change the result by neglecting $E < 0.8$ keV. We believe that future update of the NXB calibration will improve this inconsistency. The observation of aeroup with several N-rav peaks Is nof so conunon so far., The observation of agroup with several X-ray peaks is not so common so far. Forinstance. Mulchaev.ctal. compiled 109 nearby groups observed by ROSAT and found only 5 seroups have bimodal X-rav peaks and others have rather a single peak.," Forinstance, \citet{2003ApJS..145...39M} compiled 109 nearby groups observed by ROSAT and found only 5 groups have bimodal X-ray peaks and others have rather a single peak." While, While (han ils reverse is acceptable but not preferable for determining quench behavior via the time-scale approach (in which it assumed that ΕΕΟΕΑΡ until «quenching occurs).,than its reverse is acceptable but not preferable for determining quench behavior via the time-scale approach (in which it assumed that $k_{f}[\textrm{H}][\textrm{H}_{2}\textrm{CO}][\textrm{M}]=k_{r}[\textrm{CH}_{3}\textrm{O}][\textrm{M}]$ until quenching occurs). In the context of applving the Yungetal.(1983). kinetic scheme to IID Ls89733b. it would be more appropriate to calculate Τομ) for the reverse reaction ο2hIbCO+II because it is the characterization of CI; quenching that is the main objective.," In the context of applying the \citet{yung1988} kinetic scheme to HD 189733b, it would be more appropriate to calculate $\tau_{chem}$ $_{4}$ ) for the reverse reaction $\textrm{CH}_{3}\textrm{O} \xrightarrow{\textrm{M}} \textrm{H}_{2}\textrm{CO} + \textrm{H}$ because it is the characterization of $_4$ quenching that is the main objective." Nevertheless. we recommend the use of the OIL+CHITI; reactions o+CI2MCII;OIL (23ec) and OIE+Cll;-—CIHSOIIIE (2700) instead of CIO.-IbCO+Il as (he rate-limiline step for methane destruction in hot-Jupiter atmospheres. based upon a comparison of available CII;—CO reaction pathways and recent updates to reaction kinetics (Mosesοἱal.2011).," Nevertheless, we recommend the use of the $\textrm{OH} + \textrm{CH}_{3}$ reactions $\textrm{OH} + \textrm{CH}_{3} \xrightarrow{\textrm{M}} \textrm{CH}_{3}\textrm{OH}$ \ref{ch4mech}c c) and $\textrm{OH} + \textrm{CH}_{3} \rightarrow \textrm{CH}_{2}\textrm{OH} + \textrm{H}$ \ref{ch4bypass}c c) instead of $\textrm{CH}_{3}\textrm{O} \xrightarrow{\textrm{M}} \textrm{H}_{2}\textrm{CO} + \textrm{H}$ as the rate-limiting step for methane destruction in hot-Jupiter atmospheres, based upon a comparison of available $\textrm{CH}_{4}\rightarrow \textrm{CO}$ reaction pathways and recent updates to reaction kinetics \citep{moses2011}." ". Using the reaction schemes (23)) and (27)) described above. we can now test revisions to the time-scale approach for estimating the quenched CIL, mole fraction in the atmosphere ol HD 189733b."," Using the reaction schemes \ref{ch4mech}) ) and \ref{ch4bypass}) ) described above, we can now test revisions to the time-scale approach for estimating the quenched $_{4}$ mole fraction in the atmosphere of HD 189733b." " Considering both OllCI; pathwavs forming the CO bond as a combined rate-limiting step provides a good estimate of the chemical lifetime lor CIL;. given bv The vertical mixing (ime scale (7,,;,) is given by equation (22))."," Considering both $\textrm{OH} + \textrm{CH}_{3}$ pathways forming the C–O bond as a combined rate-limiting step provides a good estimate of the chemical lifetime for $_{4}$, given by The vertical mixing time scale $\tau_{mix}$ ) is given by equation \ref{eq:tmix}) )." " Using the procedure of Smith(1998).. we obtain L~OAL to 0.641 for CIL, quenching kinetics in the atmosphere of HIIDI89733b. depending upon the adopted. A.. value (cf.Cooper&ShowmanHID 209453b).."," Using the procedure of \citet{smith1998}, we obtain $L\sim0.4H$ to $0.6H$ for $_{4}$ quenching kinetics in the atmosphere of HD189733b, depending upon the adopted $K_{zz}$ value \citep[cf.][for HD 209458b]{cooper2006}." " A summary of results [rom our time-scale approach for A..=10*—10!"" em? + is given in Table 2.. which shows L/L values [or CHI; quenching via for different Μι. values in the atmosphere of ILD 189733b."," A summary of results from our time-scale approach for $K_{zz}=10^{7}-10^{10}$ $^{2}$ $^{-1}$ is given in Table \ref{tab: CH4 quench}, which shows $L/H$ values for $_{4}$ quenching via for different $K_{zz}$ values in the atmosphere of HD 189733b." Note that the time-scale arguments generally compare verv well (to within ~1O0% of) with the results of the thermochemical kinetics and transport model., Note that the time-scale arguments generally compare very well (to within $\sim$ of) with the results of the thermochemical kinetics and transport model. " We therefore confirm the analytical approach of and conclude that the (nme-scale approach provides a simple vel accurate wav to describe CII, quench chemistry in hot-Jupiter alimospheres — again. provided that the chemical time scale Το is caleulated using the appropriate rate-limiting step(£6e.. reactions 22cc. and 2766) and that (he mixing time scale τη, is calculated using the appropriate vertical mixine leneth £L (Smith 1998).."," We therefore confirm the analytical approach of \citet{prinn1977} and conclude that the time-scale approach provides a simple yet accurate way to describe $_{4}$ quench chemistry in hot-Jupiter atmospheres — again, provided that the chemical time scale $\tau_{chem}$ is calculated using the appropriate rate-limiting step, reactions \ref{ch4mech}c c and \ref{ch4bypass}c c) and that the mixing time scale $\tau_{mix}$ is calculated using the appropriate vertical mixing length $L$ \citep{smith1998}. ." IIowever. the Uime-scale approximation beeins to break clown al verv high A.. values (e.g.. 10 5 ↽ ↼⋅⋅ ⊔≺∢∐↓−⋟∖⊽↓∶⋟∖⊽≼↲≼↲⊡≸≟⋅≡↽⊰∣⋝∣⋝∐⊔∏∐⋅∐↻↓⋖↽∖⋚," However, the time-scale approximation begins to break down at very high $K_{zz}$ values (e.g., $10^{11}$ $^{2}$ $^{-1}$; see Fig. \ref{figure:methane}) )" ≤∍↙≡↽⊰⋮↽⊰∣↽≻↕⊔⋯⇂≼↲↥⋟∖⇁∶≀↕↴∐∐∪∏≸↽↔↴∐ CO begins to depart from equilibrium once Το>744. the nearly isothermal behavior of (he atmosphere in this region (cl," in our HD 189733b models: although CO begins to depart from equilibrium once $\tau_{chem}>\tau_{dyn}$, the nearly isothermal behavior of the atmosphere in this region (cf." Fig. 1)), Fig. \ref{figure:profiles}) ) " gives 7:4,v744, Over a wide range of altitudes above the quench level. so that there is noclear transition between the equilibrium and quench regimes."," gives $\tau_{chem}\sim\tau_{dyn}$ over a wide range of altitudes above the quench level, so that there is noclear transition between the equilibrium and quench regimes." In these cases. a kinetics and diffusion modeling approach is preferable for," In these cases, a kinetics and diffusion modeling approach is preferable for" ‘The processed imagesn are shown in figures5 ?2.— οοι with optical contours taken from Digitisede Sky Survey data superimposed.,"The processed images are shown in figures \ref{ugc711} – \ref{ugc1459}, with optical contours taken from Digitised Sky Survey data superimposed." Ι1 For each galaxy observed. images were taken centred on the galaxy. (target field) and ollset from it (à control field). in cach of the filters LW2 (6.755m)) and LW3 (—14.550m))," For each galaxy observed, images were taken centred on the galaxy (target field) and offset from it (a control field), in each of the filters LW2 $\sim$ ) and LW3 $\sim$ )." The following points may be noted concerning the images:, The following points may be noted concerning the images: "model we have assumed, Ts catches up with Ty. at a redshift of about eight, when the coupling due to Lya and collisions become significant enough to tie T, to the local Ty.","model we have assumed, $\mathrm{T_s}$ catches up with $\mathrm{T_k}$ at a redshift of about eight, when the coupling due to $\alpha$ and collisions become significant enough to tie $\mathrm{T_s}$ to the local $\mathrm{T_k}$." " As an alternative probe to investigate the influence of Lya-coupling coupling, in Fig.17 we plot the power spectra, now of the kinetic (solid line) and the spin (dashed line) temperatures at four different redshifts."," As an alternative probe to investigate the influence of $\alpha$ -coupling coupling, in \ref{fig:powspectemp} we plot the power spectra, now of the kinetic (solid line) and the spin (dashed line) temperatures at four different redshifts." There are a few interesting attributes to this figure., There are a few interesting attributes to this figure. Firstly we see that at all scales ς is considerably lower than Τι. at the onset of reionization (z~ 12)., Firstly we see that at all scales $\mathrm{T_s}$ is considerably lower than $\mathrm{T_k}$ at the onset of reionization $z \approx 12$ ). This scenario changes rapidly as Ts approaches Ty., This scenario changes rapidly as $\mathrm{T_s}$ approaches $\mathrm{T_k}$. Note that it is only towards the end of reionization (z=6) that T is identicalto Γι at all scales., Note that it is only towards the end of reionization (z=6) that $\mathrm{T_s}$ is identicalto $\mathrm{T_k}$ at all scales. The pecularity observed is that all scales in Ts do not approach Τι simultaneously., The pecularity observed is that all scales in $\mathrm{T_s}$ do not approach $\mathrm{T_k}$ simultaneously. " As seen from the top two panels of the figure at z=10 and z=8, Ts approaches Ty at large scales (small k values)."," As seen from the top two panels of the figure at $z=10$ and $z=8$, $\mathrm{T_s}$ approaches $\mathrm{T_k}$ at large scales (small $k$ values)." And then subsequently at small scales towards the end of reionization., And then subsequently at small scales towards the end of reionization. " This is because the central parts of the ionized bubble around the source was highly ionized and because Joοςxur, the spin temperature obtains extremely low values."," This is because the central parts of the ionized bubble around the source was highly ionized and because $J_o \propto \mathrm{x_{HI}}$, the spin temperature obtains extremely low values." " Now, as you go further away from the source, the IGM is becomes neutral, but Jo from the source and the secondary Lyo photons is high enough to couple the spin temperature to the kinetic temperature."," Now, as you go further away from the source, the IGM is becomes neutral, but $\mathrm{J_o}$ from the source and the secondary $\alpha$ photons is high enough to couple the spin temperature to the kinetic temperature." " Thus, the large scales (large volumes outside the ionized bubble) get ""matched"" first followed by the small scales, when the IGM is hot and collisions become important."," Thus, the large scales (large volumes outside the ionized bubble) get “matched” first followed by the small scales, when the IGM is hot and collisions become important." " Here we briefly compare the output of our simulation with that of Santosetal.(2008), wherein a semi-analytical scheme is developed to look at ionization and heating during the epoch of reionization."," Here we briefly compare the output of our simulation with that of \citet{santos08}, wherein a semi-analytical scheme is developed to look at ionization and heating during the epoch of reionization." Fig.18 shows the comparison between our simulations which has now been performed for the case of a power- source starting at 100eV to facilitate a balanced comparison with the 100eV case of Santosetal.(2008)., \ref{fig:compare} shows the comparison between our simulations which has now been performed for the case of a power-law source starting at 100eV to facilitate a balanced comparison with the 100eV case of \citet{santos08}. . Plotted in this figure are the average gas temperature (solid line and crosses) and volume filling factor of X-ray radiation (dashed line and filled hexagons)., Plotted in this figure are the average gas temperature (solid line and crosses) and volume filling factor of X-ray radiation (dashed line and filled hexagons). The lines correspond to our simulation and points to Santosetal. (2008)., The lines correspond to our simulation and points to \citet{santos08}. ". Their case with the normalization factor f,=10, and photon energies of 100.0 eV shows similar trends."," Their case with the normalization factor $f_x = 10$, and photon energies of 100.0 eV shows similar trends." Because we start reionization a bit later (z— 12) the temperature is a bit lower initially., Because we start reionization a bit later $ z = 12 $ ) the temperature is a bit lower initially. Their model is qualitatively different because the X-ray emissivity is tied to their star-formation rate., Their model is qualitatively different because the X-ray emissivity is tied to their star-formation rate. " Otherwise, the manner in which heating is implemented to similar to the one described in our case albeit without terms involving compton heating/cooling."," Otherwise, the manner in which heating is implemented to similar to the one described in our case albeit without terms involving compton heating/cooling." These effects though are important towards the central regions of the source (Thomas&Zaroubi 2008).., These effects though are important towards the central regions of the source \citep{thomas08}. . The focus of this paper was three-fold., The focus of this paper was three-fold. 1) to introduce an extension to in order to incorporate heating (including X-ray heating), 1) to introduce an extension to in order to incorporate heating (including X-ray heating) "ou this IIubble diagram of a local 1, Galaxy is also shown for comparison. for the two sets of cosmological paraueters used in this paper.","on this Hubble diagram of a local $L^*$ galaxy is also shown for comparison, for the two sets of cosmological parameters used in this paper." In the. IIDE-S there are some objects well above the L lines: most of them are objects with P(tnor)=0. shown as triaugles.," In the HDF-S there are some objects well above the $L^*$ lines: most of them are objects with $P(z_{\rm phot})=0$, shown as triangles." Nearly half of these objects are classified by SExtractor as stars in the Vanzella et al. (2001)), Nearly half of these objects are classified by SExtractor as stars in the Vanzella et al. \cite{vanzella}) ) catalogue., catalogue. When we fit their SEDs with stellar templates (Pickles 1998)) aud quasar spectra (according to the method described bv Tatziminaoeglou et al. 20003).," When we fit their SEDs with stellar templates (Pickles \cite{pickles}) ) and quasar spectra (according to the method described by Hatziminaoglou et al. \cite{evanthia}) )," oulv one of these objects has colors fully consistent with a liehly reddeued star., only one of these objects has colors fully consistent with a highly reddened star. " In all the other cases, these objects are not well fitted ucither with the standard SEDs for ealaxics nor with the stellar or quasar"," In all the other cases, these objects are not well fitted neither with the standard SEDs for galaxies nor with the stellar or quasar" "the guide star, and if the stellar position happened to fall exactly onto the center of a pixel.","the guide star, and if the stellar position happened to fall exactly onto the center of a pixel." " Therefore, stars are always described by local kernels convolved with the PSF."," Therefore, stars are always described by local kernels convolved with the PSF." Examples of local kernels are illustrated by the small insets in the left image in refFig:deconv.., Examples of local kernels are illustrated by the small insets in the left image in \\ref{Fig:deconv}. " If the guide star PSF has been used for deconvolution as in the example presented here, then the most compact kernels are found near the guide star, while the kernel is considerably more complex at distances larger than the isoplanatic angle."," If the guide star PSF has been used for deconvolution as in the example presented here, then the most compact kernels are found near the guide star, while the kernel is considerably more complex at distances larger than the isoplanatic angle." How can deconvolution help to improve photometry in the presence of anisoplanatic effects?, How can deconvolution help to improve photometry in the presence of anisoplanatic effects? " As we have seen, local PSF extraction is necessary in the presence of anisoplanacy."," As we have seen, local PSF extraction is necessary in the presence of anisoplanacy." " The main problem with local PSF extraction, however, occurs in obtaining accurate estimates of the wings of the PSFs."," The main problem with local PSF extraction, however, occurs in obtaining accurate estimates of the wings of the PSFs." " After deconvolution of the image with the guide star PSF, stars in the FOV appear in the shape of the local kernels at the corresponding positions."," After deconvolution of the image with the guide star PSF, stars in the FOV appear in the shape of the local kernels at the corresponding positions." The sizes of these kernels are considerably smaller than the size of the original PSF., The sizes of these kernels are considerably smaller than the size of the original PSF. " Hence, crowding is reduced."," Hence, crowding is reduced." " If we now perform the local PSF fitting algorithm, which was described in the preceding section, on the devonvolved image, the stars can be fit with the local kernels."," If we now perform the local PSF fitting algorithm, which was described in the preceding section, on the devonvolved image, the stars can be fit with the local kernels." " Because of the reduced crowding and the increased S/N of the point sources in the deconvolved image, the estimation of the local kernels can be achieved with high accuracy."," Because of the reduced crowding and the increased S/N of the point sources in the deconvolved image, the estimation of the local kernels can be achieved with high accuracy." " In this way, we can realize local PSF fitting and circumvent the problem of having to truncate the locally extracted PSFs."," In this way, we can realize local PSF fitting and circumvent the problem of having to truncate the locally extracted PSFs." This method will therefore lead to improved photometry of both the point sources and the diffuse background light., This method will therefore lead to improved photometry of both the point sources and the diffuse background light. The photometric uncertainties in the local PSF fitting photometry for the image of dither position 3 after prior LW deconvolution (using the guide star PSF) are shown in refFig:dphotlinloc.., The photometric uncertainties in the local PSF fitting photometry for the image of dither position 3 after prior LW deconvolution (using the guide star PSF) are shown in \\ref{Fig:dphotlinloc}. . " When comparing with refFig:dphotloc,, one can see that the LW deconvolution prior to local PSF fitting leads to reduced scatter and generally lower PSF uncertainty."," When comparing with \\ref{Fig:dphotloc}, one can see that the LW deconvolution prior to local PSF fitting leads to reduced scatter and generally lower PSF uncertainty." " The formal uncertainties, on the other hand, appear to be slightly increased (they have been scaled by a factor of 3, see refsec:simulation))."," The formal uncertainties, on the other hand, appear to be slightly increased (they have been scaled by a factor of $3$, see \\ref{sec:simulation}) )." The residuals related to point sources are not extended and appear to be homogeneous across the FOV (right panel of refFig:residlinloc))., The residuals related to point sources are not extended and appear to be homogeneous across the FOV (right panel of \\ref{Fig:residlinloc}) ). " We note that deconvolution violates to a certain degree a basic assumption of PSF fitting, which is that the noise for each pixel is independent of that of adjacent pixels."," We note that deconvolution violates to a certain degree a basic assumption of PSF fitting, which is that the noise for each pixel is independent of that of adjacent pixels." Deconvolution will lead inevitably to covariances between the pixels., Deconvolution will lead inevitably to covariances between the pixels. " A variety of tests show that linear deconvolution does not lead to any significant bias, but care must be taken when assessing the uncertainties in the measured quantities adequately."," A variety of tests show that linear deconvolution does not lead to any significant bias, but care must be taken when assessing the uncertainties in the measured quantities adequately." This issue will be discussed in refsec:noise.., This issue will be discussed in \\ref{sec:noise}. " In the following subsection, we examine the effects of deconvolution by working on artificial images."," In the following subsection, we examine the effects of deconvolution by working on artificial images." We study the question of which deconvolution technique (LW or LR) is most closely suited to our purpose., We study the question of which deconvolution technique (LW or LR) is most closely suited to our purpose. In order to compare the performance of the various methods of photometry described above we created a simulated image., In order to compare the performance of the various methods of photometry described above we created a simulated image. The anisoplanatic effect was modeled by using local PSFs to create the artificial image., The anisoplanatic effect was modeled by using local PSFs to create the artificial image. " For this purpose, the local kernels extracted from the LR deconvolved image from dither position 3 (see left panel in refFig:deconv)) were used."," For this purpose, the local kernels extracted from the LR deconvolved image from dither position 3 (see left panel in \\ref{Fig:deconv}) ) were used." The kernels were extracted in a grid pattern from 256x ppixel? subframes separated by steps of ppixels., The kernels were extracted in a grid pattern from $256\times256$ $^{2}$ subframes separated by steps of pixels. An individual kernel was produced for each source by interpolatingthe kernels from the four grid points closest to, An individual kernel was produced for each source by interpolatingthe kernels from the four grid points closest to "In local (e.g. Galactic, LMC, SMC) sight-lines, the DDIB is typically 2—3 times stronger than the DDIB (e.g., York et al.","In local (e.g. Galactic, LMC, SMC) sight-lines, the DIB is typically 2–3 times stronger than the DIB (e.g., York et al." 2006a and references therein)., 2006a and references therein). The one exception is the unusual SMC wing sight-line towards Sk 143 where the DDIB has an EW less than half that of the DDIB (Weltyetal. 2006).., The one exception is the unusual SMC wing sight-line towards Sk 143 where the DIB has an EW less than half that of the DIB \citep{WeltyD_06a}. . Yorketal.(2006a) also found that in the one DLA sight-line with a bband detection out of the 7 studied by Lawton et al. (, \citet{YorkB_06a} also found that in the one DLA sight-line with a band detection out of the 7 studied by Lawton et al. ( "in preparation), the EW of the ffeature was also constrained to be less than the EW of the Iline.","in preparation), the EW of the feature was also constrained to be less than the EW of the line." Yorketal.(2006a) suggested that these unusual line ratios could be an indication of an ISM that is more protected from the ambient UV radiation field., \citet{YorkB_06a} suggested that these unusual line ratios could be an indication of an ISM that is more protected from the ambient UV radiation field. " In the 11-selected absorber towards J0013—0024, we constrain the EW of the DDIB to be at least ~20% weaker than the bband."," In the -selected absorber towards $-$ 0024, we constrain the EW of the DIB to be at least $\sim$ weaker than the band." " The DIB ratios in this absorber are therefore consistent with those in the DLA detection of Yorketal.(2006a) and the SMC wing sight-line Sk 143 but inconsistent with other local sight-lines, including starburst galaxies (Heckman&Lehnert2000) and the Magellanic Clouds (Weltyetal.2006).."," The DIB ratios in this absorber are therefore consistent with those in the DLA detection of \citet{YorkB_06a} and the SMC wing sight-line Sk 143 but inconsistent with other local sight-lines, including starburst galaxies \citep{HeckmanT_00b} and the Magellanic Clouds \citep{WeltyD_06a}." " In the Galaxy, many DIBs show correlations with aand NN(Nar) (e.g.Herbig1993,1995).."," In the Galaxy, many DIBs show correlations with and $N$ ) \citep[e.g.][]{HerbigG_93a,HerbigG_95a}." In Table 2 we tabulate the EWs of theΝα doublet for our II-selected absorbers., In Table \ref{dib_table} we tabulate the EWs of the doublet for our -selected absorbers. " However, we do not calculate the column density because, if the lines are strong enough to be detected in our moderate resolution spectra, they are likely to be saturated."," However, we do not calculate the column density because, if the lines are strong enough to be detected in our moderate resolution spectra, they are likely to be saturated." " The Galactic correlations of aand N (Nar) with the DDIB, which isone of the tightest of the DIB relations, is shown in Fig. 2.."," The Galactic correlations of and $N$ ) with the DIB, which isone of the tightest of the DIB relations, is shown in Fig. \ref{ebmv_fig}." We also show data for the Magellanic Clouds (Weltyetal.2006) and DLAs (Yorketal.2006a;; Lawton et al., We also show data for the Magellanic Clouds \citep{WeltyD_06a} and DLAs \citealt{YorkB_06a}; Lawton et al. " in preparation), where it can be seen that the DIBs are weak for their ccompared with the Galactic correlation."," in preparation), where it can be seen that the DIBs are weak for their compared with the Galactic correlation." " As shown in Fig. 2,,"," As shown in Fig. \ref{ebmv_fig}," the DIBs in extra-galactic sight-lines are also weak for their column densities., the DIBs in extra-galactic sight-lines are also weak for their column densities. " These departures from the Galactic relations are probably due to a combination of effects including ambient radiation field, metallicity and dust-to-gas ratios 2006).."," These departures from the Galactic relations are probably due to a combination of effects including ambient radiation field, metallicity and dust-to-gas ratios \citep{CoxN_06a}." " Assuming that the Galactic relation provides a lower limit for the column density, DIB detections may be useful for constraining iin the absence of oobservations."," Assuming that the Galactic relation provides a lower limit for the column density, DIB detections may be useful for constraining in the absence of observations." " For example, Wild&Hewett(2005) and Wildetal.(2006) have argued that absorbers represent the high column density end of the DLA distribution."," For example, \citet{WildV_05a} and \citet{WildV_06a} have argued that absorbers represent the high column density end of the DLA distribution." " Our detection of the DDIB in the zaps=0.1556 absorber towards J0013—0024 supports this hypothesis, and we derive log > 20.9 for this absorber."," Our detection of the DIB in the $z_{\rm abs} = 0.1556$ absorber towards $-$ 0024 supports this hypothesis, and we derive $\log$ $\ge$ 20.9 for this absorber." " Unlike correlations with aand N 1), Weltyetal.(2006) have shown that the DDIB strength follows a single relationship with iin both Galactic and Magellanic Cloud sight-lines."," Unlike correlations with and $N$ ), \citet{WeltyD_06a} have shown that the DIB strength follows a single relationship with in both Galactic and Magellanic Cloud sight-lines." (20062) found that the single DLA DDIB detection towards AO 0235+164 fell on the same relationship., \citet{YorkB_06a} found that the single DLA DIB detection towards AO $+$ 164 fell on the same relationship. It is not yet clear whether the apparent universality of this correlation is driven by a tight physical connection between dust properties and DIB formation (Coxetal.2007) or whether it is coincidence of different physical drivers working in different directions (Cox&Spaans 2006).., It is not yet clear whether the apparent universality of this correlation is driven by a tight physical connection between dust properties and DIB formation \citep{CoxN_07a} or whether it is coincidence of different physical drivers working in different directions \citep{CoxN_06a}. . " However, if thelis applicable to QSO absorbers, we can use our DIB detection limits to constrain their reddening."," However, if theis applicable to QSO absorbers, we can use our DIB detection limits to constrain their reddening." Weltyetal.(2006) derive a, \citet{WeltyD_06a} derive a An estimate of the residual distortion error can be eained from the relative positions of stellar like objects preseut in both the WFCL and URC data.,An estimate of the residual distortion error can be gained from the relative positions of stellar like objects present in both the WFC1 and HRC data. The errors in neasuue the positions themsclves cam be mininuized by averaging the differeuces across as many objects as possible., The errors in measuring the positions themselves can be minimized by averaging the differences across as many objects as possible. We identified 7 stellar like objects common to the PINS 1519-79 data (the PINS 1315|12 field is relatively eniptv) aud ceutroided their positions., We identified 7 stellar like objects common to the PKS 1549-79 data (the PKS 1345+12 field is relatively empty) and centroided their positions. Each stellar object was then paired with the remaining six objects. and the offset between the pairs were recorded (21 total offsets).," Each stellar object was then paired with the remaining six objects, and the offset between the pairs were recorded (21 total offsets)." The dispersion in the relative offsets between these objects in the WECTI aud URC images. which we adopt as our astrometric uncertainty. was found to be ~O03.," The dispersion in the relative offsets between these objects in the WFC1 and HRC images, which we adopt as our astrometric uncertainty, was found to be $\sim0\farcs03$." Iu addition to the astrometric uncertainties. the obscured nature of the central cugines can be an added source of error for the relative aliguiments of the AGN and radio cores: the measured peak in emission line fiux may not correspond to the position of the ACN.," In addition to the astrometric uncertainties, the obscured nature of the central engines can be an added source of error for the relative alignments of the AGN and radio cores; the measured peak in emission line flux may not correspond to the position of the AGN." " In the following two sections we will attempt to minimize this effect. however. for this process to be a significant source of eror it nist act at a distauce of >0703 (100 pe) from the estimated position of the ceutral ACN,"," In the following two sections we will attempt to minimize this effect, however, for this process to be a significant source of error it must act at a distance of $>0\farcs03$ (100 pc) from the estimated position of the central AGN." The very. central region (1700) of PISS 1519-79 ([OIII cCluission line) is presented in Figure 5((a)., The very central region 0) of PKS 1549-79 ([OIII] emission line) is presented in Figure \ref{fig:1549rad}( (a). Wo sce a relatively hieh surface brightuess concentration to he north-east. with a lower surface brightuess fan of Cluission extending toward the south-west.," We see a relatively high surface brightness concentration to the north-east, with a lower surface brightness fan of emission extending toward the south-west." Based ou existing optical and near-IR spectra we do not expect to © able to detect the reddened AGN in the TRC |OIII oeΠάθος, Based on existing optical and near-IR spectra we do not expect to be able to detect the reddened AGN in the HRC [OIII] images. ", Towever. we know from the modeling preseutec x II06 that the quasar nucleus should be detected iu the Ilo coutiuuunu nage."," However, we know from the modeling presented by H06 that the quasar nucleus should be detected in the $\alpha$ continuum image." Therefore. we have assunued that 1ο centroid of the concentration of pixels at the center fthe WECL Πα coutiuuuu image eives the true quasar vosition relative to the reference stars conunon to both ιο WECT and URC fields.," Therefore, we have assumed that the centroid of the concentration of pixels at the center of the WFC1 $\alpha$ continuum image gives the true quasar position relative to the reference stars common to both the WFC1 and HRC fields." " When translated to the IRC oenages the WFECI position is found to lie at the poiut uarked with au ""N in Figure 5((a).", When translated to the HRC images the WFC1 position is found to lie at the point marked with an “X” in Figure \ref{fig:1549rad}( (a). It is with this point rat we align the radio core., It is with this point that we align the radio core. The estimated astrometric ucertaintv is outlined with dotted lines (£0703)., The estimated astrometric uncertainty is outlined with dotted lines $\pm0\farcs03$ ). The radio map in panel (b) of Figure 5. (thin contours) is that presented by II06., The radio map in panel (b) of Figure \ref{fig:1549rad} (thin contours) is that presented by H06. The data were collected in 1988 at ~3 GIIz using a the Southern Henmisphere. VLBI Expernucut. SITEVE (Prestonetal.1981).," The data were collected in 1988 at $\sim3$ GHz using a the Southern Hemisphere VLBI Experiment, SHEVE \citep{pre84}." . The beam size ds 7.3&2.7 mas at a PA ofLY., The beam size is $7.3\times2.7$ mas at a PA of. The westeru-most kuot shows a flat ρούτα across 2.5-8. GIIz and is considered the core., The western-most knot shows a flat spectrum across 2.3-8.4 GHz and is considered the core. The Πα ACN position1 has subsequently been aligned with this., The $\alpha$ AGN position has subsequently been aligned with this. A steep spectrmu jet is seen to extend to the east at a PA of ~907., A steep spectrum jet is seen to extend to the east at a PA of $\sim90\degr$. The jet beuds through approximately607.. indicative of orieutation change. aud exhibits a eap which max be attributed to evelie emission processes.," The jet bends through approximately, indicative of orientation change, and exhibits a gap which may be attributed to cyclic emission processes." II0G estimate au upper nuit of/«55? for the inclination. with respect to the liue of sight. for this jet.," H06 estimate an upper limit of $i<55\degr$ for the inclination, with respect to the line of sight, for this jet." Figure 5b((b) also. demonstrates the comparative morplologics between the radio structure (thin contours) and the cussion (thick lines)., Figure \ref{fig:1549rad}( (b) also demonstrates the comparative morphologies between the radio structure (thin contours) and the [OIII] emission (thick lines). The emission line map shows [OTTno evidence for bi-conical features., The emission line map shows no evidence for bi-conical features. Ellipse fitting to the |OITI| data is preseuted in Figure 6.. where the PAs of knots alone the jet. with respect to the radio core. are also plotted.," Ellipse fitting to the [OIII] data is presented in Figure \ref{fig:1549pas}, where the PAs of knots along the jet, with respect to the radio core, are also plotted." We see excellent agreeineut iotween the ΟΠΗ coutimmiun and [OTT emission line PAs., We see excellent agreement between the [OIII] continuum and [OIII] emission line PAs. Simularitv in the enüssjon Dine aud continu norphology could be attributed to dust obscuration. scattered AGN light. (Tadhunteretal.1992)... nebular coutinuuni (Dicksonetal.1995).. or a mixture of all hrec.," Similarity in the emission line and continuum morphology could be attributed to dust obscuration, scattered AGN light \citep{tad92}, nebular continuum \citep{dic95}, or a mixture of all three." In addition. to the optical enuission-contiuuuu alieument. there is an overlap in the very iuner regions οπου the radio structure aud the [OTH] enission.," In addition to the optical emission-continuum alignment, there is an overlap in the very inner regions between the radio structure and the [OIII] emission." However. this radio-optical agreement deteriorates as the jet curves around.," However, this radio-optical agreement deteriorates as the jet curves around." The jet also extends past the highest smface brightness region of the ΟΠΗ cussion., The jet also extends past the highest surface brightness region of the [OIII] emission. The τον. central region of the western nucleus iu PIS 1315)12 (OTI chussion line) is preseuted iu Figure 7a)., The very central region of the western nucleus in PKS 1345+12 ([OIII] emission line) is presented in Figure \ref{fig:1345rad}( (a). A north-west to south-east elongation is clearly apparent., A north-west to south-east elongation is clearly apparent. As in the case of PINS 1519-79. we do rot expect to be able to directlv detect the AGN in the ΟΠΗ images. nor at optical wavelengths.," As in the case of PKS 1549-79, we do not expect to be able to directly detect the AGN in the [OIII] images, nor at optical wavelengths." However. we can assume that the quasar nucleus will be detected in je W-band.," However, we can assume that the quasar nucleus will be detected in the K-band." Therefore. we have retrieved a NICALOS F222\1 nuage for this source from theLSTarchive.," Therefore, we have retrieved a NICMOS F222M image for this source from the." It was taken as part of programme #77219 PI: Scoville. 1e finer details of which are preseuted in Scovillectal.2000).," It was taken as part of programme 7219 PI: Scoville, the finer details of which are presented in \citet{scov00}." . By determining the relative offset of the eastern micleus with that of the westerm uucleus in both the cnussion line images aud the NIB. we can place a better constraint ou the position of the radio core.," By determining the relative offset of the eastern nucleus with that of the western nucleus in both the emission line images and the NIR, we can place a better constraint on the position of the radio core." Following us we have indicated in Figure 7((a) the position of 16 NIB. peak with respect to the eastern nucleus ou the WRC emission line map., Following this we have indicated in Figure \ref{fig:1345rad}( (a) the position of the NIR peak with respect to the eastern nucleus on the HRC emission line map. It is here we assume the radio core to fall., It is here we assume the radio core to fall. The radio map in panel (b) of Figure 7. (thin coutours) isa 1.5 GIIz map obtained from a global VLBI (111) experiueut (Morgautietal.2001) overlaid onto the siuoothed contours of the TRC emission line map (thick lues), The radio map in panel (b) of Figure \ref{fig:1345rad} (thin contours) is a 1.3 GHz map obtained from a global VLBI (HI) experiment \citep{mor04} overlaid onto the smoothed contours of the HRC emission line map (thick lines). The radio data were collected in 2001 where the bean size was 6.6«L2 mas at a PA of-H07., The radio data were collected in 2001 where the beam size was $6.6\times1.2$ mas at a PA of. . The radio core has been identified at 5 CGIIz bv Staughelliuictal.(1997). from the relatively fat spectrum., The radio core has been identified at 5 GHz by \citet{stang97} from the relatively flat spectrum. However. simular to the fiudiues of Nianeetal.(2002).. this core is rot clearly defined in the 1.3 Giz map. aud is likely self absorbed.," However, similar to the findings of \citet{xia02}, this core is not clearly defined in the 1.3 GHz map, and is likely self absorbed." Therefore. in order to register the 1.3 (αν map @vlich shows more extended. lower surface xiehtuess features than the 5 CGIIz map) against the optical cussion line images. we have aligned the 5 CIIz nap with the 1.3 GITz map based on the positions of the southern coupoucuts of the jet where optical depth effects are likely to be less of an issuc.," Therefore, in order to register the 1.3 GHz map (which shows more extended, lower surface brightness features than the 5 GHz map) against the optical emission line images, we have aligned the 5 GHz map with the 1.3 GHz map based on the positions of the southern components of the jet – where optical depth effects are likely to be less of an issue." Then. knowing he true position of the radio core in the 1.3 GIIz map. we can place it onto the ciission line image.," Then, knowing the true position of the radio core in the 1.3 GHz map, we can place it onto the emission line image." Ellipse fitting to the [OMT] data is shown in Figure 8.., Ellipse fitting to the [OIII] data is shown in Figure \ref{fig:1345pas}. As radio cunission is detected either side of the nucleus. we have prescuted the PA of both the uortheru aud southern jets with respect to the radio core. using knots in both the 1.3 aud 5 (11 maps.," As radio emission is detected either side of the nucleus, we have presented the PA of both the northern and southern jets with respect to the radio core, using knots in both the 1.3 and 5 GHz maps." We can see that there is excellent agreement with the radio aud [OTH] across a range of radii but there is significant divergence as the jet extends past the high surface brielituess regions aud bees to bend.," We can see that there is excellent agreement with the radio and [OIII] across a range of radii, but there is significant divergence as the jet extends past the high surface brightness regions and begins to bend." As with PKS 1519-79. we can also see," As with PKS 1549-79, we can also see" " ∐↸∖↕↕∐↑↕⋜↧↕↸⊳∪⋯∐↕∪∐↴∖↴↕⋟∪↥⋅↻↥⋅∪∪↴∖↴↑↸∖∐⋜∐⋅↸⊳∪∐⋜∏≻↴∖↴↸∖⋜⋯≼↧∐⋯⋅↖↽ re]η, (2). ~2% (??). 22). 77). (???).. lnüas"," \citealt{motte,ts98,onishi}] \citep{wk97} $\sim$ \citep{zuckerman,kt07}. \citealt{m02,mrk06}) \citealt{jijina,km09}) \citep{thompson,murray,andrews}," sive stars (0.g.. ?7?7)). the lot eas shock heated bv stellar winds aud supernovae (ce... 273). and protostellar outflows/jets (e.c... 27777)).," massive stars (e.g., \citealt{whit,dale}) ), the hot gas shock heated by stellar winds and supernovae (e.g., \citealt{yorke,hc09}) ), and protostellar outflows/jets (e.g., \citealt{quill,cunningham,li,naka,wang}) )." Each of these moechanisuis has been considered individually in the literature. but no observational⋅ analyses have ever compared the velative∙ contribution of all these components within WIT regions.," Each of these mechanisms has been considered individually in the literature, but no observational analyses have ever compared the relative contribution of all these components within HII regions." Iu this. paper. we mves.igate: the role of: the stellar Feedback. nacchetnistis isted above in the giaut un region 230. Doradus iu the nearby Larec Alaecllanic (' (LA‘'," In this paper, we investigate the role of the stellar feedback mechanisms listed above in the giant HII region 30 Doradus in the nearby Large Magellanic Cloud (LMC)." Several.Tey ...IuHITs of: theH EMC' mk»σεν ifa ne trs Utle 5 proxuuity (0-50 Ax ensures ο...individual poiut sources can be resolved while maintainingHe theH capabilitymnili- oft mappingn13 theο diffux1-Wal af sub-pe escales., Several properties of the LMC make it a favorable target: the LMC's proximity $\sim$ 50 kpc) ensures individual point sources can be resolved while maintaining the capability of mapping the diffuse emission at sub-pc scales. " Additionally, the LMC has nolecularan a face-on orientation and a low coluun density (a few «107 2) that limits line-of-sight confusion,"," Additionally, the LMC has a face-on orientation and a low column density (a few $\times$ $^{21}$ $^{-2}$ ) that limits line-of-sight confusion." Given these advantages. the LMC (and thas 30 Doradus) has been surveyed atf aly wavelengths at high spatial ane we can exploit these data To compare resolution.observationally all the feedback nmuechanisnis and how they vary position acr 30 Doradus.," Given these advantages, the LMC (and thus 30 Doradus) has been surveyed at many wavelengths at high spatial resolution, and we can exploit these data to compare observationally all the feedback mechanisms and how they vary with position across 30 Doradus." " The text is withstructured. as SS 5L.l gives reevaut on the source, 08 follows:Doradus. aud. describes why this backgroundsonree ds a good case” for our analyses."," The text is structured as follows: $\S$ 1.1 gives relevant background on the source, 30 Doradus, and describes why this source is a good “test case” for our analyses." " Iu 52. we present the uultivavelongth“test data uilized in our work assess the yaunical of all the possible stellar tofeedback πουαντι»,"," In $\S$ 2, we present the multiwavelength data utilized in our work to assess the dynamical role of all the possible stellar feedback mechanisms." 63 outlinesrole how we utilize these ages to calculate the pressures associated with each feedback component across 30 Doradus., $\S$ 3 outlines how we utilize these images to calculate the pressures associated with each feedback component across 30 Doradus. 51 eives the results from our analyses. and 85 discusses the iunlicatiouspuc of our £ndines. μαποιαΊο ‘evidence of A-rav. gas leakage ⊓↴∙↸∙from the Π region (55.1) aud the role of radiation pressure in ΠΤΙregion dynamics (55.3).," $\S$ 4 gives the results from our analyses, and $\S$ 5 discusses the implications of our findings, including evidence of X-ray gas leakage from the HII region $\S$ 5.1) and the role of radiation pressure in HIIregion dynamics $\S$ 5.3)." Additionally. we articulate the different wavs one can defue radiationpressure.and howthesedefinitions can," Additionally, we articulate the different ways one can define radiationpressure,and howthesedefinitions can" We have presened a discussiot of the staidard formalism for unclerstaucing atmospheric energetics. explicitly accouuting [or rictioual heatiug rou the cissipatiou of kinetic energy.,"We have presented a discussion of the standard formalism for understanding atmospheric energetics, explicitly accounting for frictional heating from the dissipation of kinetic energy." The ;»otential energy of he atinospliere is divided into the component that can be converted iuto sinetic energy (tlie “available” potenial energy. APE) and the component associated with uniform Changes iu lemperatt1'e (the πιnavalable” potenial energy. UPE).," The potential energy of the atmosphere is divided into the component that can be converted into kinetic energy (the “available"" potential energy, APE) and the component associated with uniform changes in temperature (the “unavailable"" potential energy, UPE)." Uuilorm frictional heating will eed the UPE. while ¢illerenti:il heaing (from aiv source) will feed APE.," Uniform frictional heating will feed the UPE, while differential heating (from any source) will feed APE." Frictional heating can je salely 1ieglected f‘om the elereetics of the atiuospiere. (to some level of precision) if it is: 1) »edomiuautly uuilor1l. ΟΥ 2) its diferential heating is much less than the radiative clilferential jeating aud it contribος minimally to the generation of APE.," Frictional heating can be safely neglected from the energetics of the atmosphere (to some level of precision) if it is: 1) predominantly uniform, or 2) its differential heating is much less than the radiative differential heating and it contributes minimally to the generation of APE." We give local ex)'ess]ons Or energy generation. conversion. aud dissipation in Equations -22)).," We give local expressions for energy generation, conversion, and dissipation in Equations \ref{eq:finalu}- \ref{eq:finaleg}) )." APE is generated in regions with positive correlations between temperature aud heating (when hoter-than-ave'age LEGIONS :wre heated atd colder-than-average regious are cooled)., APE is generated in regions with positive correlations between temperature and heating (when hotter-than-average regions are heated and colder-than-average regions are cooled). li order o deerniue if frictioial heating 1iatters for tje energeltles of an atmosphere. we must ideutify 20.511e «das mechanisms auc estinate their sreneths ancl spatial variations.," In order to determine if frictional heating matters for the energetics of an atmosphere, we must identify possible drag mechanisms and estimate their strengths and spatial variations." We cau then take eloba inteerals of Eqations (19--2 2)) to deterine if the APE generation from frictional hieallug is a significant fraction of the raclialive APE generation., We can then take global integrals of Equations \ref{eq:finalu}- \ref{eq:finaleg}) ) to determine if the APE generation from frictional heating is a significant fraction of the radiative APE generation. Given the many unkuowns relaed to uodeliug 100 Jupiter atiuosplieres. One may coisider that [rictional APE generation is no longer jeglieible once it exceeds ~LO% of he radiative APE eeneraion.," Given the many unknowns related to modeling hot Jupiter atmospheres, one may consider that frictional APE generation is no longer negligible once it exceeds $\sim$ of the radiative APE generation." This is equivalent to saying tha he heat eigine efficiency. of he ali1osphere wil be altered by more than1055., This is equivalent to saying that the heat engine efficiency of the atmosphere will be altered by more than. . As an exercise and test of this formaisin. we calculate APE aud UPE generation rates lor iuuerical models that incluce drag as a kLuetic euergv siuk ut dotοἱ return the energy as leat.," As an exercise and test of this formalism, we calculated APE and UPE generation rates for numerical models that include drag as a kinetic energy sink but do not return the energy as heat." We used the previosly pubed uunueκ.‘al inodels by Rauscher&Menou(2010) and al. (2010a).. which lave icleL‘al set-ups nuit a range of representative drag strengths.," We used the previously published numerical models by \citet{RM10} and \citet{Perna2010a}, which have identical set-ups but a range of representative drag strengths." We [οι that i these inodels tle spa correlatious between temperatre aud heating rates are such t in all cases tle [rictional heaing Wwe)iuld have worked to decrease tle οobal generation of APE ( equivaently. he atiiospliere 51eat enegiie efficiency). at a [acto of of T. T. aud for the moclels with weak. ineciuin. aud stro180 drag. res»ectively.," We found that in these models the spatial correlations between temperature and heating rates are such that in all cases the frictional heating would have worked to decrease the global generation of APE (or, equivalently, the atmosphere's heat engine efficiency), at a factor of of 1, 7, and for the models with weak, medium, and strong drag, respectively." This provides al estimate of the drag strength at which frictional heaing can sighilicantly alter the energetics oftje circulation. with the caveat that this result is strongly depeuclent ou the spatial form we chose fo ‘the applied drag.," This provides an estimate of the drag strength at which frictional heating can significantly alter the energetics of the circulation, with the caveat that this result is strongly dependent on the spatial form we chose for the applied drag." Iu these models crag tLinescaes were horizoutaly coustant: drag mechanisms hat have fae)ereater spatial variation can liave more elfect on the energetics at weaker drag strengtlis., In these models drag timescales were horizontally constant; drag mechanisms that have greater spatial variation can have more effect on the energetics at weaker drag strengths. Twouel this analysis we were also able to estimae the rate of numerical dissipation iu these models., Through this analysis we were also able to estimate the rate of numerical dissipation in these models. " Any atinospheric dissipation of kinetic energy (uuiuerical or pliysical) must. be balanced by a non-zero global beating rate. in order to generate he Al""E that is converted to kinetic energy (Equation 8))."," Any atmospheric dissipation of kinetic energy (numerical or physical) must be balanced by a non-zero global heating rate, in order to generate the APE that is converted to kinetic energy (Equation \ref{eq:balance}) )." In these moclels the ouly source of heatihe Is raciative aud so this heating must be uou-zero. although it meaus that tle atmosphere is uot in global radiative equilibrium.," In these models the only source of heating is radiative and so this heating must be non-zero, although it means that the atmosphere is not in global radiative equilibrium." Compariug the uet radiative heating rate to a representative valie for the ineiclent stellar flix. we estimate," Comparing the net radiative heating rate to a representative value for the incident stellar flux, we estimate" (2005).. when one corrects the underlving Iunction αλ [ον random orbit inclinations. the index is essentially unchanged. and for an index of —1 it is exactly unchanged.,", when one corrects the underlying function $dN/dM$ for random orbit inclinations, the index is essentially unchanged, and for an index of $-1$ it is exactly unchanged." In this paper. we define (he iniüal mass function (AIF) for highlv-irradiated. ας somewhat differently than the IME for stars. the latter referring to the stellar birth function.," In this paper, we define the initial mass function (IMF) for highly-irradiated EGPs somewhat differently than the IMF for stars, the latter referring to the stellar birth function." Since the majority (~75%)) of detected EGPs have orbital radii >0.07 AU. they cannot have sullerecl significant mass loss [rom atmospheric escape over (heir lifetime.," Since the majority $\sim75$ ) of detected EGPs have orbital radii $> 0.07$ AU, they cannot have suffered significant mass loss from atmospheric escape over their lifetime." " We reler to the latter class as ""field EGPs.", We refer to the latter class as “field” EGPs. " Our hypothesis is (hat hishlv-urvadiated EGDPs are not formeclsitu. but are remnants of field EGPs that have migrated inward to small orbital radii during the ~10"" to LO’ vears that the star's initial planet-Iorming nebula persists."," Our hypothesis is that highly-irradiated EGPs are not formed, but are remnants of field EGPs that have migrated inward to small orbital radii during the $\sim10^6$ to $10^7$ years that the star's initial planet-forming nebula persists." " Let the IMF denote the initial mass function for highly-irradiated EGDPs at age /~10° to 10* vr in a mass range e0.2 AM,«M<~5 AL). when these EGPs start their atmospheric erosion."," Let the IMF denote the initial mass function for highly-irradiated EGPs at age $t\sim10^6$ to $10^7$ yr in a mass range $\sim0.2$ $M_J < M <\sim5$ $M_J$, when these EGPs start their atmospheric erosion." This IME max well differ [rom the observed mass function for field EGPs. since the mieration nechanism could have a mass dependence.," This IMF may well differ from the observed mass function for field EGPs, since the migration mechanism could have a mass dependence." One prediction of the IMF for hiehly-irradiated EGPs (DelPopoloetal.2005) suggests a depletion of planets with M>4 4M; but that ower-mass EGPs migrate inward reaclily (see also Trillingοἱal.(1998) and (2002)))., One prediction of the IMF for highly-irradiated EGPs \citep{del05} suggests a depletion of planets with $M>4$ $M_J$ but that lower-mass EGPs migrate inward readily (see also \citet{tri98} and \citet{tri02}) ). In this paper we make (he provisional assuniption that the IAIF has the same index as (he mass functionfor field EGDPs., In this paper we make the provisional assumption that the IMF has the same index as the mass functionfor field EGPs. Figure 1 shows our assumed IMF /(€A/.0) (heavy solid line). arbitrarily normalized to unity al AM=1 Aj.," Figure 1 shows our assumed IMF $f(M,0)$ (heavy solid line), arbitrarily normalized to unity at $M=1$ $M_J$." " We assume that EGPs born at à~ several to several x10 AU are deposited at smaller orbital radii a~ [fewx10? AU within the first [ewx10"" vears of the parent stars lifetime.", We assume that EGPs born at $a\sim$ several to several $\times 10$ AU are deposited at smaller orbital radii $a\sim$ $\times 10^{-2}$ AU within the first $\times 10^6$ years of the parent star's lifetime. To map the IME onto a time-dependent. ensemble of eroding ECDs. we fix the distance from the star at one of the four standard distances studied in (2006).. ranging from 0.023 to 0.057AU.," To map the IMF onto a time-dependent ensemble of eroding EGPs, we fix the distance from the star at one of the four standard distances studied in \citet{hub06}, ranging from 0.023 to 0.057AU." We then randomly choose an exoplanet of initial mass My trom the IME and allow it to lose mass as a function of time / using either the Watsonetal.(1981). or the DaralTeetal.(2004). prescription., We then randomly choose an exoplanet of initial mass $M_0$ from the IMF and allow it to lose mass as a function of time $t$ using either the \citet{wat81} or the \citet{bar04} prescription. It is necessary to impose a low-mass cutoff to the IMFE., It is necessary to impose a low-mass cutoff to the IMF. As shown by (2006).. hvdrogen-rich. EGPs with masses <0.2 M; and initial entropies corresponding to isolated EGDPs al ~10° vears of age. have such large radii that their aàiospheres are tidally unbound (independent of (he mass-loss rate). ancl so we restrict our analysis to Vy>0.2 AM.," As shown by \citet{hub06}, hydrogen-rich EGPs with masses $\le0.2$ $M_J$ and initial entropies corresponding to isolated EGPs at $\sim10^6$ years of age, have such large radii that their atmospheres are tidally unbound (independent of the mass-loss rate), and so we restrict our analysis to $M_0 \ge 0.2$ $M_J$ ." We have svuthesizecl time-dependent mass functions (41.1) for EGPs al the four orbital radii investigated by Hubbardοἱal. (2006)..," We have synthesized time-dependent mass functions $f(M,t)$ for EGPs at the four orbital radii investigated by \citet{hub06}. ." Figure 1 shows resulting mass functions at /=5 , Figure 1 shows resulting mass functions at $t=5$ orbital period.,orbital period. According to Schüsler&Solanski(1992). the presence of spots at high latitudes in such a situation can be explained by the dynamo mechanism for rapid rotators.," According to \citet{Schusler}, the presence of spots at high latitudes in such a situation can be explained by the dynamo mechanism for rapid rotators." The inclination of the orbit was estimated to be ;= 72°. which means that both the primary and the secondary minima are due to partial eclipses.," The inclination of the orbit was estimated to be $i\approx72^\circ$ , which means that both the primary and the secondary minima are due to partial eclipses." The third component (probably physically attached to the eclipsing pair) contributes approximately to the total light., The third component (probably physically attached to the eclipsing pair) contributes approximately to the total light. Such a strong third light effect has a serious impact on the estimation of the basic system parameters and is particularly important for estimating the degree of overcontact and the orbital inclination., Such a strong third light effect has a serious impact on the estimation of the basic system parameters and is particularly important for estimating the degree of overcontact and the orbital inclination. We estimated the physical parameters of four binary systems — QX And. RW Com. MR Del. and BD+7°3142 - from the analysis of new. high quality CCD light curves in the B. V. and R filters. and from the results of recent high-resolution spectroscopic studies.," We estimated the physical parameters of four binary systems – QX And, RW Com, MR Del, and ${\rm BD+7^o3142}$ - from the analysis of new, high quality CCD light curves in the B, V, and R filters, and from the results of recent high-resolution spectroscopic studies." This is the summary of our findings., This is the summary of our findings. Suberoups Sa iux0|. 5b form structures with a small velocity dispersion. but extending over about 7 Alpe. a size which appears rather large for these groups to be members of two backeround clusters: the exeut and the velocity dispersion of 5e are even larger (Fig. 2).,"Subgroups 5a and 5b form structures with a small velocity dispersion, but extending over about 7 Mpc, a size which appears rather large for these groups to be members of two background clusters; the extent and the velocity dispersion of 5c are even larger (Fig. \ref{xyg4569}) )." While the Serna Cerhal (1996) method. feds dvuinndcal sub-structures for the oher erow» along the line of sight. the same method reveals no substructures iu eroup 6. except for two pairs of galaxies: erou6 therefore appears well defined oth in velocity distribution and in space.," While the Serna Gerbal (1996) method finds dynamical sub-structures for the other groups along the line of sight, the same method reveals no substructures in group 6, except for two pairs of galaxies; group 6 therefore appears well defined both in velocity distribution and in space." Eighteeu egalaxies are included in an ellipse with a major and miuor axes of about 8 aud 3 AIpc. sugeesting that this is a poor. itfuse and low mass cluster (Fig. 2)).," Eighteen galaxies are included in an ellipse with a major and minor axes of about 8 and 3 Mpc, suggesting that this is a poor, diffuse and low mass cluster (Fig. \ref{xyg4569}) )." Finally. Έπος suyeyoups are apparently found iu structure 9. θα. ar SD having very πια! velocity dispersions but spaning a rather large spatial region.," Finally, three subgroups are apparently found in structure 9, 9a and 9b having very small velocity dispersions but spanning a rather large spatial region." The overall velocity field iu group 9 shows an interesting pateru ooking like a velocity eradieut (Fig. 3))., The overall velocity field in group 9 shows an interesting pattern looking like a velocity gradient (Fig. \ref{vg9}) ). This coud be a filament nore or less aligned along the line of sieht., This could be a filament more or less aligned along the line of sight. A raus-welocity classification applied to cac1 group ΟΠΗΣ that eroup l| and possibly group 9 appear to have three substructures (two clear breaks in the curves). eroup 5 jns three or four substructures and eroup 6 has no clear substructure except perhaps for the two or three first galaxies which arο probably infalliug objects.," A rank-velocity classification applied to each group confirms that group 4 and possibly group 9 appear to have three substructures (two clear breaks in the curves), group 5 has three or four substructures and group 6 has no clear substructure except perhaps for the two or three first galaxies which are probably infalling objects." To SULUMATIZe. groups L aud 9 clearly apCar as filaments or at least elongated structures along the line of sight. bit not really massive clusters.," To summarize, groups 4 and 9 clearly appear as filaments or at least elongated structures along the line of sight, but not really massive clusters." This analysis is confirmed bv the iso-velocitv οςfours of eroup 9., This analysis is confirmed by the iso-velocity contours of group 9. " The continuous velocity oeradieunt could be interpreed as the result of a uxveer, with the infalling eroups iot pertectly aligned along the li16 of sight."," The continuous velocity gradient could be interpreted as the result of a merger, with the infalling groups not perfectly aligned along the line of sight." Croup 6 has a low velocity dispersion au dis probably a poor cluster., Group 6 has a low velocity dispersion and is probably a poor cluster. Group 5Γ exhibits two low velocity clispersion sub-structures aud aanoderately high velocity cliispersion eroup (5e). but the munber of galaxies iu De is too low to provide a robust estimation and we assume that this structure is uot a cluster.," Group 5 exhibits two low velocity dispersion sub-structures and a moderately high velocity dispersion group (5c), but the number of galaxies in 5c is too low to provide a robust estimation and we assume that this structure is not a cluster." We will now discuss the dynamical state of the main structure ou the line of sight: the cluster itself (group 3)., We will now discuss the dynamical state of the main structure on the line of sight: the cluster itself (group 3). We displav in Fig., We display in Fig. | the superposition of the optical inaee of the cluster with ROSAT PSPC X-ray aud radio isocontours., \ref{image} the superposition of the optical image of the cluster with ROSAT PSPC X-ray and radio isocontours. The Xa:w contours are quite smooth. with no obvious substructures.," The X-ray contours are quite smooth, with no obvious substructures." However. there aypears to be an excess of N-rav oenadssion towards the north west. iu the direction where there is also au excess of cnussion line ealaxies (Gee below).," However, there appears to be an excess of X-ray emission towards the north west, in the direction where there is also an excess of emission line galaxies (see below)." A radio source is visible south cast of the cluster. probabIv associated with a galaxy.," A radio source is visible south east of the cluster, probably associated with a galaxy." " The cluster ccorresponds to structure 3) in Table L:: it has a BWT mcan velocity of 9885 ku/s anda elobal velocity dispersion of 715 Καιήν, The correspouding velocity interval is [7813.11860 kan/s| aud inclues 211 ealaxies."," The cluster corresponds to structure 3 in Table \ref{tab9groupes}; it has a BWT mean velocity of 9885 km/s and a global velocity dispersion of 715 km/s. The corresponding velocity interval is [7813,11860 km/s] and includes 274 galaxies." Note that the cD galaxy has a velocivof 9851 kan/s. close to the mean cluster velocity. aud is located very close the X-ray cussion ceuter. sueecsting fiat the cD is at the bottom of the cluster eravitationa potential well.," Note that the cD galaxy has a velocity of 9831 km/s, close to the mean cluster velocity, and is located very close the X-ray emission center, suggesting that the cD is at the bottom of the cluster gravitational potential well." This is an mdicatiou of a quiesceut historv of the cluster (see e.g. Zabludoff et al., This is an indication of a quiescent history of the cluster (see e.g. Zabludoff et al. 1993. Oceerle ITil 1991).," 1993, Oegerle Hill 1994)." The wavelet recoustruction of the velocity distribution of sshown in Fig., The wavelet reconstruction of the velocity distribution of shown in Fig. 5 (271 galaxies) suggests he xesence of a certain amount of sustructure., \ref{pdfin} (274 galaxies) suggests the presence of a certain amount of substructure. The sample was analyzed with 256 points. aud the two sinallest scales were excluded.," The sample was analyzed with 256 points, and the two smallest scales were excluded." " The corresponding velocity distribution is τοσαΙστ it shows: a tiny feaure at ~s8300 km/s:oa hain asvuuuetric poak im the [8560. 1070) lan/s| range containing 232 ealaxics. with a BWT iuean velocity of 9769 kis. and a DWT velocity «ispersion of 518 kms: rote that this velocity structure is not quie centered ou he velocity of the cD ealaxy: a sinaller ]veal at 109[0 aufs with 36 galaxies in the |10700. 11861) ans] range,"," The corresponding velocity distribution is non-gaussian; it shows: a tiny feature at $\sim$ 8300 km/s; a main asymmetric peak in the [8500, 10700 km/s] range containing 232 galaxies, with a BWT mean velocity of 9769 km/s, and a BWT velocity dispersion of 518 km/s; note that this velocity structure is not quite centered on the velocity of the cD galaxy; a smaller peak at 10940 km/s with 36 galaxies in the [10700, 11860 km/s] range." If we only keep the largest scales. we are lef with a rather sviunietrie velocity distribution showing au excess at high velociies.," If we only keep the largest scales, we are left with a rather symmetric velocity distribution showing an excess at high velocities." This excess corresponds to the peak at 10910 laus. which contains a sinall πο. of galaxies (sce sectioji L1.," This excess corresponds to the peak at 10940 km/s, which contains a small number of galaxies (see section 4.4)." These structures are also found by applying a rank.velociv classification. which gives two breaks elohal consistent with those found by analyzing the chasted velocity distribution.," These structures are also found by applying a rank-velocity classification, which gives two breaks globally consistent with those found by analyzing the cluster velocity distribution." Such breaks probably indicate substructures with velocitics coherent with the finer analysis based ou he wavelet techiniqte., Such breaks probably indicate substructures with velocities coherent with the finer analysis based on the wavelet technique. However. the miver of galaxies involved in these structures is small. aud he velocity disributiou iu the main cluster therefore appears to be quite sinooth. sugeesting that Abell 196 Is quite well relaxed.," However, the number of galaxies involved in these structures is small, and the velocity distribution in the main cluster therefore appears to be quite smooth, suggesting that Abell 496 is quite well relaxed." Tn order to coufirin fje state of relaxation of Avell 196. we have applied a Serna Gerba (1996). analysis o the sulounuple of 96 ealaxies located within a radius of 1s00 arcsec around he cD aud with maeguiticles R<17.0: within this lumited sample. the coueteness of he redshift catalogue is aud this type of analysis is expected to give robus results.," In order to confirm the state of relaxation of Abell 496, we have applied a Serna Gerbal (1996) analysis to the subsample of 96 galaxies located within a radius of 1800 arcsec around the cD and with magnitudes $\leq$ 17.0; within this limited sample, the completeness of the redshift catalogue is and this type of analysis is expected to give robust results." Note that ealaxies iu his regioi with iieasured velocities but withort published naenuituces were discardec., Note that galaxies in this region with measured velocities but without published magnitudes were discarded. Results are cisplaved in Fig. 6.., Results are displayed in Fig. \ref{sernaamas}. " At the extreme lower right of the figure. we can see the very tiel pair made by the cD (32280. 12.2) anda satellite oealaxv (2905, R=15.6. in the Iniret et al."," At the extreme lower right of the figure, we can see the very tight pair made by the cD 280, R=12.2) and a satellite galaxy 292, R=15.6, in the Durret et al." 19995 catalogue): this coufirus hat the ¢D is at he bottoni of the chster poteutial we1., 1999b catalogue): this confirms that the cD is at the bottom of the cluster potential well. We also observe a structure of 11 brighto galaxies (10 ealaxies with R< 1h.5. plus one with R=!6.8) highly couceitrated in space around the cD (tical ¢istance to the cD: 216 arcsec. with a dispersion of," We also observe a structure of 11 bright galaxies (10 galaxies with $\leq$ 15.8, plus one with R=16.8) highly concentrated in space around the cD (mean distance to the cD: 216 arcsec, with a dispersion of" Tn order to assess the extent ο Which previous surveys may have been biased due to dust. we caleulate the πα” density. (+). and neutral gas lass density. Όρει. of CORALS ⇁⋅,"In order to assess the extent to which previous surveys may have been biased due to dust, we calculate the number density, $n(z)$, and neutral gas mass density, $\Omega_{DLA}$, of CORALS DLAs." " Bil⊀⋃⊳⊥−↕≻⊔↴∖↴⋅↖↖≼∖∱⋯≼⋯⋯↑↕∪≼∙⋂↻∟↼∖∕⊔⇠↴∶−≻⋮↱⊐∩↴⋃⋡⇄∣⊥ (Qaj=LOO, 0) over he redshiff rauge 1.5LabseeMi5. in good aerecment with the latest resiIts from |0].. κου Figure 1."," We find that $\log \Omega_{\rm DLA} h_{65} = -2.59^{+0.17}_{-0.24}$ $\Omega_M = 1.0, \Omega_{\Lambda} = 0$ ) over the redshift range $1.8 < z_{abs} < 3.5$, in good agreement with the latest results from \cite{per}, see Figure 1." Perhaps most importantly. we do not fud amy evideuce for a previously uudetected population of high columm density absorbers.," Perhaps most importantly, we do not find any evidence for a previously undetected population of high column density absorbers." " Siuilbulv. the nuuber deusitv of CORALS DLAs W(t}=Ulqus at πιa mean. absorption redshift (2,5,=2.37 is larger than previous surveys (e.g. | ή."," Similarly, the number density of CORALS DLAs $n(z) = 0.31^{+0.09}_{-0.08}$ at a mean absorption redshift $\langle z_{abs} \rangle= 2.37$ is larger than previous surveys (e.g. \cite{lsl00}) )." However. the difference is significant only at around the lo level.," However, the difference is significant only at around the $\sigma$ level." Overall. we couchide that previous surveys may have underestimated 062) aud οει by at most a factor of two.," Overall, we conclude that previous surveys may have underestimated $n(z)$ and $\Omega_{DLA}$ by at most a factor of two." metallicity (e.g. MI3. M3 ete.),"metallicity (e.g. M13, M3 etc.)." The large modifications in the structure of the self-consistent model atmospheres in the line-formation region as compared to homogeneous ones can give rise to detectable observational effects., The large modifications in the structure of the self-consistent model atmospheres in the line-formation region as compared to homogeneous ones can give rise to detectable observational effects. As will be discussed below. the diffusion process not only causes abundance stratification of the elements but can also lead to visible effects related to the photometric colors and spectroscopic gravities of hot BHB stars.," As will be discussed below, the diffusion process not only causes abundance stratification of the elements but can also lead to visible effects related to the photometric colors and spectroscopic gravities of hot BHB stars." The results of these theoretical models are compared below to established anomalies of hot BHB stars., The results of these theoretical models are compared below to well-established anomalies of hot BHB stars. The vertical stratitication of Fe in our stratified model atmospheres is shown in Fig. 2.., The vertical stratification of Fe in our stratified model atmospheres is shown in Fig. \ref{fig:Fe_3dexmax_teff}. The results presented in this figure clearly show that the gradient of the Fe abundance (as a function of optical depth in the atmosphere) in the range -4 — log ts000 — -2 decreases with the increase of 7., The results presented in this figure clearly show that the gradient of the Fe abundance (as a function of optical depth in the atmosphere) in the range -4 $\preceq$ log $\tau_{5000}$ $\preceq$ -2 decreases with the increase of $T_{\rm eff}$. Since this range of optical depth is where a lot of the iron lines are formed. such a tendancy can be verified with spectroscopic studies.," Since this range of optical depth is where a lot of the iron lines are formed, such a tendancy can be verified with spectroscopic studies." Figure 3. compares the slopes of the detected Fe abundance gradients or lack thereof for a large number of BHB stars (Khalack et al., Figure \ref{fig:Slope_Fe} compares the slopes of the detected Fe abundance gradients or lack thereof for a large number of BHB stars (Khalack et al. 2007. 2008 and 2010) to those predicted by the theoretical model atmospheres of LeBlanc et al. (," 2007, 2008 and 2010) to those predicted by the theoretical model atmospheres of LeBlanc et al. (" 2009).,2009). In these observational studies. the vertical stratification of iron was gauged by determining the abundance of individual lines formed at various optical depths.," In these observational studies, the vertical stratification of iron was gauged by determining the abundance of individual lines formed at various optical depths." The dots in this figure represent individual hot BHB stars while —ye solid line is a quadratic fit of the observed abundance slopes., The dots in this figure represent individual hot BHB stars while the solid line is a quadratic fit of the observed abundance slopes. The filled diamonds connected by a dashed line give the linear slopes of Fe abundance in the theoretical models., The filled diamonds connected by a dashed line give the linear slopes of Fe abundance in the theoretical models. These slopes are those of the linear fit of the abundance stratification of iron for the atmospheric layers in the range -5 log tsono -2 for each Τμ., These slopes are those of the linear fit of the abundance stratification of iron for the atmospheric layers in the range -5 $<$ log $\tau_{5000}$ $<$ -2 for each $T_{\rm eff}$. These layers correspond to the atmospheric depths where most of the Fe lines are formed and where iron stratification is detected (see Figure | of Khalack et al., These layers correspond to the atmospheric depths where most of the Fe lines are formed and where iron stratification is detected (see Figure 1 of Khalack et al. 2010)., 2010). Figure 3. shows that the observed slopes of the Fe abundance decreases with Zr for hot BHB stars and eventually becomes undectectable at Zi~ 14000 K. in agreement with the theoretical results of the models of LeBlane et al. (," Figure \ref{fig:Slope_Fe} shows that the observed slopes of the Fe abundance decreases with $T_{\rm eff}$ for hot BHB stars and eventually becomes undectectable at $T_{\rm eff}\simeq$ 14000 K, in agreement with the theoretical results of the models of LeBlanc et al. (" 2009) shown in Fig. 2..,2009) shown in Fig. \ref{fig:Fe_3dexmax_teff}. These results may serve as additional proof that elemental stratification due to atomic diffusion occurs in the atmospheres of hot BHB stars., These results may serve as additional proof that elemental stratification due to atomic diffusion occurs in the atmospheres of hot BHB stars. BHB stars in globular clusters exhibit several photometric anomalies namely photometric jumps and gaps., BHB stars in globular clusters exhibit several photometric anomalies namely photometric jumps and gaps. This section aims to interpret them in the light of self-consistent stratified model atmospheres., This section aims to interpret them in the light of self-consistent stratified model atmospheres. Grundahl et al. (, Grundahl et al. ( 1999) observed a photometric jump in the (1.4. v) color-magnitude diagram for the horizontal branch sequence in several globular clusters.,"1999) observed a photometric jump in the $u, u-y$ ) color-magnitude diagram for the horizontal branch sequence in several globular clusters." This jump consists of a shift towards brighter stars of the horizontal-branch sequence with respect to canonical models. and occurs for stars with Zi higher than approximately 11500. K. Therefore. there exists a difference (for 7p= 11500 K) between the observed and predicted colors.," This jump consists of a shift towards brighter stars of the horizontal-branch sequence with respect to canonical models, and occurs for stars with $T_{\rm eff}$ higher than approximately 11500 K. Therefore, there exists a difference (for $T_{\rm eff} \succeq $ 11500 K) between the observed and predicted colors." The PHOENIX model atmospheres including elemental stratitication of Hui-Bon-Hoa. LeBlane Hauschildt (2000) were," The PHOENIX model atmospheres including elemental stratification of Hui-Bon-Hoa, LeBlanc Hauschildt (2000) were" obtained after applying a uniform correction of mmag to all the median and also no correction at all are not significantly different.,obtained after applying a uniform correction of mag to all the median and also no correction at all are not significantly different. " We thus adopt a simple scheme that closely approximates the actual situation, applying a correction of -0.016 mag to the median E(B—V) estimates of the absorber samples with MgIIEW <3.0 aand no correction to the median E(B—V) estimates for MgIIEW >3.0AA."," We thus adopt a simple scheme that closely approximates the actual situation, applying a correction of -0.016 mag to the median $E(B-V)$ estimates of the absorber samples with EW $\leq3.0$ and no correction to the median $E(B-V)$ estimates for EW $>3.0$." . The amount of dust in aabsorption systems is generally found to increase as a function of the EEW (??)..," The amount of dust in absorption systems is generally found to increase as a function of the EW \citep{2006MNRAS.367..945Y, 2008MNRAS.385.1053M}." " This increase has important implications for the understanding of galaxy evolution, as EW for the saturated absorbers measures the velocity spread in the gas and there is a strong dependence of EW on the level of associated star-formation activity (?).."," This increase has important implications for the understanding of galaxy evolution, as EW for the saturated absorbers measures the velocity spread in the gas \citep{2006MNRAS.367..945Y} and there is a strong dependence of EW on the level of associated star-formation activity \citep{2009arXiv0912.3263M}." " The accuracy of the E(B—V)smc’® estimate for each absorber was ensured by removing all spectra with a poor fit to the SMC extinction curve, i.e. Dias>0.04 (Section ??))."," The accuracy of the $E(B-V)_{\mathrm{SMC}}$ estimate for each absorber was ensured by removing all spectra with a poor fit to the SMC extinction curve, i.e. $D_{\mathrm{max}}^{\mathrm{smc}}>0.04$ (Section \ref{sub:Evaluating-the-method}) )." We chose the SMC curve as the reddening properties of aabsorbers are found to be well characterised by an SMC-type extinction law (see Section ??))., We chose the SMC curve as the reddening properties of absorbers are found to be well characterised by an SMC-type extinction law (see Section \ref{dusttype}) ). The dependence of dust content on EEW is shown in Fig. 7.., The dependence of dust content on EW is shown in Fig. \ref{cap:fullebvew}. " The median E(B—V)swoc is calculated for absorbers with EWs in the intervalsAA,, AA,,AA,,AA,, AA,, and AA."," The median $E(B-V)_{\mathrm{SMC}}$ is calculated for absorbers with EWs in the intervals, , and ." . The equivalent median E(B—V)swc values incorporating the bias corrections in Equation 7 are also shown., The equivalent median $E(B-V)_{\mathrm{SMC}}$ values incorporating the bias corrections in Equation \ref{cap:fullebvew} are also shown. " The error bars have been calculated using the ‘bootstrap’ method but, at low W2""?9. the errors are limited by systematic uncertainties at the level of ~0.005."," The error bars have been calculated using the `bootstrap' method but, at low $W_{0}^{2796}$, the errors are limited by systematic uncertainties at the level of $\sim0.005$ ." The line in Fig., The line in Fig. 7 corresponds to the best fitting power-law to the median bias-corrected E(B—V)swc values of the form where A=(8.0+3.0)x1074 and a=(3.480.3) and the model is applicable for 1.0ο30 C. An alternative cstimate of the coronal physical paralucters cau be provided in the context of the loop model calculated by Rosneretal.(1978).," If the corona is confined by magnetic fields, the required average field strength is thus $B>\sqrt{8\pi P}\gtrsim 15-30$ G. An alternative estimate of the coronal physical parameters can be provided in the context of the loop model calculated by \citet{rtv78}." . Iu this model the loop temperature. density. aud pressure are related Toeο K. where it is asset that the loop apex temperature is similar to the mean coroual temperature.," In this model the loop temperature, density, and pressure are related by$T\approx 1.4\times 10^3\,(P\ell)^{1/3}$ K, where it is assumed that the loop apex temperature is similar to the mean coronal temperature." The loop leugth. f. is deterxiumed by the observed ταν luminosity. (©2.210 C. in good agreement with the value inferred above by assuniue a uniformi coronal structure."," The pressure inferred from using $\ell\sim H$ is $P\approx 60$ dyne $^{-2}$, and the magnetic field required for confinement is thus $B\gtrsim 40$ G, in good agreement with the value inferred above by assuming a uniform coronal structure." We now turn to the radio euission., We now turn to the radio emission. " The bremesstrabhme contribution in the radio baud is Ενz0.03 jJ. orders of maguitude lower than even the baseline quiesceut enission. which from several fiare-free regious of the radio light curve is found to be F,(s.5)=208+18 p Jy."," The bremsstrahlung contribution in the radio band is $F_\nu\approx 0.03$ $\mu$ Jy, orders of magnitude lower than even the baseline quiescent emission, which from several flare-free regions of the radio light curve is found to be $F_\nu (8.5)=208\pm 18$ $\mu$ Jy." The 30 limit on the fraction of circular polarization of the quiescent Coumpoucnt is à.«25%., The $3\sigma$ limit on the fraction of circular polarization of the quiescent component is $r_c<25\%$. Both the τις aud deeree of circular polarization are similar to those measured iu previous observations refseciobs)). mdicatiug that the quiesceut coniponent is stable on a imulti-vear timescale.," Both the flux and degree of circular polarization are similar to those measured in previous observations \\ref{sec:obs}) ), indicating that the quiescent component is stable on a multi-year timescale." Based on the brghtuess of the radio ciission compared to the predicted thermal ciissiou. and its long term stability. we couchide that it is most likely due to evrosvuchrotron raciation.," Based on the brightness of the radio emission compared to the predicted thermal emission, and its long term stability, we conclude that it is most likely due to gyrosynchrotron radiation." " We follow the typical asstuuption that the nmüldlv relativistic electrons. which produce the radio euüsson. follow a power Luv distribution. Nis)X5$"" for 5>σι with p~3 typical for M aud L dawarts (Cudeletal.19935:Bergeretal.2005:Osten2006b)."," We follow the typical assumption that the mildly relativistic electrons, which produce the radio emission, follow a power law distribution, $N(\gamma)\propto\gamma^{-p}$ for $\gamma>\gamma_m$, with $p\sim 3$ typical for M and L dwarfs \citep{gsb+03,brr+05,ohb+06}." ". The evrosvuchrotron enission spectrum is determined by the size of the emission region (22). the deusitv of radiating electrons (09, ). aud the magnetic feld streneth (2) according to (Dulk&1982): where 0 is the angle between the magnetic field aud the line of sieht."," The gyrosynchrotron emission spectrum is determined by the size of the emission region $R$ ), the density of radiating electrons $n_e$ ), and the magnetic field strength $B$ ) according to \citep{dm82}: where $\theta$ is the angle between the magnetic field and the line of sight." " From previous observations of Ht appears that the peak of the quiesceut omission spectrum 15 ÓÁ, Cz (Ostenetal.20065).", From previous observations of it appears that the peak of the quiescent emission spectrum is $\nu_m\approx 5$ GHz \citep{ohb+06}. .. Using he linüt 5r.« we infer a magnetic Bold strength. Dxl0Tl Ci. for 0—20.sQ.," Using the limit $r_c<25\%$, we infer a magnetic field strength, $B \lesssim 10-740$ G, for $\theta=20-80^\circ$." " With this range we Bud R~(OR8)«1050 cin. and a.~1001,3.<102"" C the latter range is for 0=80° to 207."," With this range we find $R\sim (0.8-8)\times 10^10$ cm, and $n_e\sim 100-1.3\times 10^{10}$ $^{-3}$; the latter range is for $\theta=80^\circ$ to $20^\circ$." A comparison o the coronal density estimated from X-rays inclicates 0—20.30%. aud honce R—few«10! cin and Bew«107 G. The inferred field streugth is cousisteut with he value required for coufiuement of the X-ray ciittineg coronal plasima as derived above.," A comparison to the coronal density estimated from X-rays indicates $\theta\sim 20-30^\circ$, and hence $R\sim {\rm few}\times 10^{10}$ cm and $B\lesssim {\rm few}\times 10^2$ G. The inferred field strength is consistent with the value required for confinement of the X-ray emitting coronal plasma as derived above." Finally. we turn to the observed Tea cussion.," Finally, we turn to the observed $\alpha$ emission." The light curveexhibits clear sinusoidal behavior with a rauge of equivalent widths of 1.55.5 ((Figure 1))., The light curveexhibits clear sinusoidal behavior with a range of equivalent widths of $1.5-5.5$ (Figure \ref{fig:all}) ). The simcoal behavior mdicates that the line is likely modulated by the rotation of rather than fares. and the cinission is thus persisteut in origin. at least on the timescale of our observation.," The sinusoidal behavior indicates that the line is likely modulated by the rotation of rather than flares, and the emission is thus persistent in origin, at least on the timescale of our observation." Walkowiczetal.(2001)— determined a multiplicative factor. \=fxosoo/fiat. to convert Ta EW to LiifLia. For513-16516..," \citet{whw04} determined a multiplicative factor, $\chi\equiv f_{\lambda 6560}/f_{\rm bol}$, to convert $\alpha$ EW to $L_{\rm H\alpha}/L_{\rm bol}$." the observed FoK=L3 mag indicates logy=—5.3. which matches the average value for spectral type M8.5 (Walkowiezctal.2001).," For, the observed $I-K=4.3$ mag indicates ${\rm log}\chi\approx -5.3$, which matches the average value for spectral type M8.5 \citep{whw04}." . Thus. for the full auge of EWs we fud οσοι/Lig)& Loto 5.1.," Thus, for the full range of EWs we find ${\rm log}(L_{\rm H\alpha}/L_{\rm bol})\approx -4.6$ to $-5.1$." This covers the typical range of Wa euission observed from AIS.5 dawarts (Westetal.2001)... as well as the range of EWs frou past observations of this source rofseciobs)).," This covers the typical range of $\alpha$ emission observed from M8.5 dwarfs \citep{whw+04}, as well as the range of EWs from past observations of this source \\ref{sec:obs}) )." We return to the implications ofthe sinusoidal variations m refsec:halpha.., We return to the implications of the sinusoidal variations in \\ref{sec:halpha}. . Since the Nay and Πα cinission appear το be persistent. wecaneain insight iuto the plivsical processes in the outer atinosphere by examining the enerev scalein each baud.," Since the X-ray and $\alpha$ emission appear to be persistent, wecangain insight into the physical processes in the outer atmosphere by examining the energy scale in each band." Iu carly dMe stars there is evidence that the quiescent chromosphere is heated by dowuward directed coronal N-ray emission (Cram 1982). , In early dMe stars there is evidence that the quiescent chromosphere is heated by downward directed coronal X-ray emission \citep{cra82}. . Nearly half of the absorbed energy will be radiatively lost in the Dahner lues. primarily Πα (Cram 1982)..," Nearly half of the absorbed energy will be radiatively lost in the Balmer lines, primarily $\alpha$ \citep{cra82}. ." Tere we find that the ratio Ly/2:2 isin rough agreement with this overall, Here we find that the ratio $L_{\rm H\alpha}/L_X\approx 2$ is in rough agreement with this overall IC process aud then consider the amisotropic scattering effect and pair production absorption effect ou the received IC fiux in section 3 anc | respectively.,IC process and then consider the anisotropic scattering effect and pair production absorption effect on the received IC flux in section 3 and 4 respectively. Finally we eive the conchisious., Finally we give the conclusions. We consider the inverse Compton (IC) scattering of shock breakout N-ravs after the cud of the prompt gamuna-rav chussion but before the sharp X-ray decay. nuncly πο 1000 sec to 3000 sec after the GRB trigger.," We consider the inverse Compton (IC) scattering of shock breakout X-rays after the end of the prompt gamma-ray emission but before the sharp X-ray decay, namely from 1000 sec to 3000 sec after the GRB trigger." During this time. the N-rav enuüssion detected bySwift NRT cau be divided iuto two components. one beime a thermal compoucut aud the other a non-therial one (Campana et al. 2006).," During this time, the X-ray emission detected by XRT can be divided into two components, one being a thermal component and the other a non-thermal one (Campana et al, 2006)." The thermal X-ray component becomes increasiuelv dominant aud las a Iuniuositv of~Ἰθήόσος 1., The thermal X-ray component becomes increasingly dominant and has a luminosity of$\sim10^{46} \rm erg s^{-1}$ . After 3000 s. the N-ray eniission uudereoes a sharp decay aud au X-ray afterglow decaying as à powcr law in fime emerges later.," After $\sim 3000$ s, the X-ray emission undergoes a sharp decay and an X-ray afterglow decaying as a power law in time emerges later." The underline afterglow fiux extrapolated from the late power-law decaving afterelow is more than 30 times lower than the thermal N-rav cussion. and is not chough to account for the non-thermal euission of the previous phase.," The underlying afterglow flux extrapolated from the late power-law decaying afterglow is more than 30 times lower than the thermal X-ray emission, and is not enough to account for the non-thermal emission of the previous phase." This carly nou-thermal comiponeut could come from the shock breakout itself or from the extended internal shock cussion., This early non-thermal component could come from the shock breakout itself or from the extended internal shock emission. " The maeuetic field cucrey density iu the forward shock frame is lower than that of the breakout N-ray emission if the equipartition factor ερ\gamma_c$, which implies that most of the energy of the afterglow shocked electrons during the shock breakout period would go into the IC emission." " As the forward shock propagates in the surrounding medi. the energv that goes into the newly shocked electrous per unit observers time is £,=2«Loe.LEsgf,tere (Wang. Li 2006)."," As the forward shock propagates in the surrounding medium, the energy that goes into the newly shocked electrons per unit observer's time is $L_e=2\times10^{46}\epsilon_{e,-1} E_{50}t_3^{-1} \rm erg$ (Wang, Li 2006)." The bolometric hWuuinositv Lye of the IC emission is equal to L.. so the total energy loss of the shocked electrons during the time from 1000 sec to 3000 sec is about Eye.2.10%.4Esyere and the total IC cussion fluence is where D=LISAIpe ois the distance of GRDBOGU218/SN2006a3.," The bolometric luminosity $L_{IC}$ of the IC emission is equal to $L_e$, so the total energy loss of the shocked electrons during the time from 1000 sec to 3000 sec is about $ E_{IC}\simeq 2\times10^{49} \epsilon_{e,-1}E_{50} \rm erg$ and the total IC emission fluence is where $D=145{\rm Mpc}$ is the distance of GRB060218/SN2006aj." " The observed IC £F, flux peaks at where AL=Od6IeV is the black body temperature of the thermal spectrum of the shock breakout enission (Campana et al.", The observed IC $\nu F_\nu$ flux peaks at where $kT\simeq0.16{\rm KeV}$ is the black body temperature of the thermal spectrum of the shock breakout emission (Campana et al. 2006)., 2006). " The IC energy spectrunt(zP,) las indices of 1/2 aud (p2)/2 before aud after the break at στον respectively,"," The IC energy $\nu F_{\nu}$ ) has indices of $1/2$ and $-(p-2)/2$ before and after the break at $\varepsilon_{IC,p}$ respectively." The upeoiiug GLAST LAT detector has au effective detection area of 105eni. so it cau detect the sub-Ge¥ to CieV photous with the above fux. aud may even identify the peak euerev of this IC cussion.," The upcoming GLAST LAT detector has an effective detection area of $10^4\rm cm^2$, so it can detect the sub-GeV to GeV photons with the above flux, and may even identify the peak energy of this IC emission." The jet afterglow clectrous may also produce high energv cluission through the selfsvuchrotron Compton process (Zhane 2001)., The jet afterglow electrons may also produce high energy emission through the self-synchrotron Compton process (Zhang 2001). However. based ou the assuuptiou that the extrapolated svuchrotrou flux during the carly afterglow is >30 times lower than the shock breakout N-vav fux. the selt-sxuchrotron Compton flux is then lower by tle same factor.," However, based on the assumption that the extrapolated synchrotron flux during the early afterglow is $>30$ times lower than the shock breakout X-ray , the self-synchrotron Compton flux is then lower by the same factor." After the shock breaks out of the optically thick wiucl. its enission drops very sharply. aud the jet afterglow eiission becomes donminaut.," After the shock breaks out of the optically thick wind, its emission drops very sharply, and the jet afterglow emission becomes dominant." The remaining enerew. LE ye. of the jet continucs to power the power-law decaving afterglow at later times.," The remaining energy, $E-E_{IC}$ , of the jet continues to power the power-law decaying afterglow at later times." The jet is likely to cuter iuto the sub- phase around f-—LO?10° secfor a low burst energv. aud the power decay rate should transition frou," The jet is likely to enter into the sub-relativistic phase around $t\sim 10^5-10^6$ secfor a low burst energy, and the power decay rate should transition from" maps to calculate their cross-correlation.,maps to calculate their cross-correlation. The resulting cross-correlation maps obtained for each projection of the magnetic vector are plotted in Fig. 8.., The resulting cross-correlation maps obtained for each projection of the magnetic vector are plotted in Fig. \ref{fig:cross}. " For the radial and azimuthal field components, a correlation parameter close to unity is achieved for a phase shift close to zero (at least if we ignore the intermediate-latitude domain of the azimuthal component), confirming that the maps computed from both independent data sets carry similar information (using the preferred rotation period proposed above)."," For the radial and azimuthal field components, a correlation parameter close to unity is achieved for a phase shift close to zero (at least if we ignore the intermediate-latitude domain of the azimuthal component), confirming that the maps computed from both independent data sets carry similar information (using the preferred rotation period proposed above)." " The correlation is also very good for the meridional field projection above latitude 60 degrees, but is much lower at low and intermediate latitudes (which is expected for a star with a low inclinaison angle, as stated in Sect. 2.3))"," The correlation is also very good for the meridional field projection above latitude 60 degrees, but is much lower at low and intermediate latitudes (which is expected for a star with a low inclinaison angle, as stated in Sect. \ref{sect:procedure}) )." " The absence of any significant phase shift between both epochs suggests that the surface differential rotation, if any, is probably very weak on Vega, so that the photospheric magnetic structure was not significantly distorted by a latitudinal shear within 1 year."," The absence of any significant phase shift between both epochs suggests that the surface differential rotation, if any, is probably very weak on Vega, so that the photospheric magnetic structure was not significantly distorted by a latitudinal shear within 1 year." " Using 4 independent high-resolution spectropolarimetric data sets of Vega collected over more than one year with two different instruments, we confirm the detection of circularly-polarized signatures first reported by LO9."," Using 4 independent high-resolution spectropolarimetric data sets of Vega collected over more than one year with two different instruments, we confirm the detection of circularly-polarized signatures first reported by L09." " The shape and amplitude of the signal show no significant differences between the successive observing runs, giving further support to a stellar origin of the signal."," The shape and amplitude of the signal show no significant differences between the successive observing runs, giving further support to a stellar origin of the signal." " The lack of any detection in the diagnostic null spectrum, and the higher amplitude of the signature obtained while selecting photospheric spectral lines with a higher Landé factor, are strong evidences for a photospheric magnetic origin of this signal."," The lack of any detection in the diagnostic null spectrum, and the higher amplitude of the signature obtained while selecting photospheric spectral lines with a higher Landé factor, are strong evidences for a photospheric magnetic origin of this signal." Periodic variations of the signal are observed in our data and are consistent with a rotation period of 0.732+0.008 d. This period is close to the value of ~0.733 d proposed by Takeda et al. (, Periodic variations of the signal are observed in our data and are consistent with a rotation period of $0.732 \pm 0.008$ d. This period is close to the value of $\approx 0.733$ d proposed by Takeda et al. ( 2008) from a careful modelling of individual spectral lines and the SED.,2008) from a careful modelling of individual spectral lines and the SED. " This period is consistently recovered using two independent spectropolarimetric data sets, although this is not the only possible value if the different sets are considered individually."," This period is consistently recovered using two independent spectropolarimetric data sets, although this is not the only possible value if the different sets are considered individually." We do not find such repeated evidence in favor of the alternate value of «0.524 d proposed by Aufdenberg et al. (, We do not find such repeated evidence in favor of the alternate value of $\approx 0.524$ d proposed by Aufdenberg et al. ( 2006) from interferometric observations.,2006) from interferometric observations. The data adjustment is also slightly degraded while using the value of «0.663 d derived by Hill et al. (, The data adjustment is also slightly degraded while using the value of $\approx 0.663$ d derived by Hill et al. ( 2010) from high resolution spectra.,2010) from high resolution spectra. " We infer that the stellar spin is close to a solid-body rotation, as suggested by the lack of evidence for any significant distortion of the magnetic field distribution over one year."," We infer that the stellar spin is close to a solid-body rotation, as suggested by the lack of evidence for any significant distortion of the magnetic field distribution over one year." New, New Table 3 iicludes some basic orbital parameters based upon intergatiou of the orbits in two moclels «X the Galaxy's potential.,Table \ref{tabfield2} includes some basic orbital parameters based upon intergation of the orbits in two models of the Galaxy's potential. These integratious were made by Dana Dinescu. aud full details ο “the integration routine tay be found in Dinescuetal.," These integrations were made by Dana Dinescu, and full details of the integration routine may be found in \citet{dana}." (1999).. The orbits were integrated in Galactic poential moclels given by Johustouetal.(1995) all Piiczvüski(1990)., The orbits were integrated in Galactic potential models given by \citet{jsh95} and \citet{pac90}. . The two potentials vielc similar orbital parameters aud only the orbital parameters [rom the »otentlal are shown iu Table 3.., The two potentials yield similar orbital parameters and only the orbital parameters from the \citet{pac90} potential are shown in Table \ref{tabfield2}. . The orjtal parameters listed in Table 3 are: L. tde 2-COMpolent o ‘the angular momeutum (a conserved quantity). pericelltric (Rapp) and apocentri (Hips) radii. te anim distauce [rom the plale Tour. the eccenricity of the orbits e aud t inclination auge with respet to the Galactic plane V.," The orbital parameters listed in Table \ref{tabfield2} are: $L_z$ the $z$ -component of the angular momentum (a conserved quantity), pericentric $R_{per}$ ) and apocentric $R_{apo}$ ) radii, the maximum distance from the plane $z_{max}$, the eccentricity of the orbits $e$ and the inclination angle with respet to the Galactic plane $\Psi$." The stars iu Table 3 all wave —0.11<[Fe/H;—0.25 and iu tus uetallicity range oue fin both thiu and thick disk sta* iu the local solar ieighiborhood., The stars in Table \ref{tabfield2} all have $-0.14\le \feh \le -0.25$ and in this metallicity range one finds both thin and thick disk stars in the local solar neighborhood. The dispersiou iu the kinematiCs of the thi and thick disk mase dtiupossible to «elinitavily assign a siiele star to either the t or thick «isk., The dispersion in the kinematics of the thin and thick disk make it impossible to definitavily assign a single star to either the thin or thick disk. For example. i the 1iiu disk o(W.)=20 kin/s while in he thick disk o(1)= kin/s (Exvardssonetal.1993).," For example, in the thin disk $\sigma(W) = 20$ km/s while in the thick disk $\sigma(W) = 40$ km/s \citep{Edv93}." . Tlus. the W veocity of HD 11330 (WV=—25.1. kms) impli that it cotId be member of te thic sor thin disk.," Thus, the $W$ velocity of HD 41330 $W = -25.1$ km/s) implies that it could be member of the thick or thin disk." By cousicering all of the kinematic and orbit: paralete5s (Il. O. W. L.. €ad V) one can classify a star as either a thin or thick disk star. beari180 in mind tat these classificaticus will never be accurate.," By considering all of the kinematic and orbital parameters $\Pi$, $\Theta$, $W$, $L_z$, $e$ and $\Psi$ ) one can classify a star as either a thin or thick disk star, bearing in mind that these classifications will never be accurate." In gener:i. thin clisk stars have sinall LL aud W velocities. Oz220 ans. L.2:1700 kpe lan/s. τρως25Q3 ikdC. eX0.2 and small values of V.," In general, thin disk stars have small $\Pi$ and $W$ velocities, $\Theta \approx 220$ km/s, $L_z \approx 1700$ kpc km/s, $z_{max} \la 0.3$ kpc, $e \la 0.2$ and small values of $\Psi$." In Table 3 we have iudicated the most propobable classificiation of each star (thin or thick disk)alone., In Table \ref{tabfield2} we have indicated the most propobable classificiation of each star (thin or thick disk). HD 52711 aud 210918 are prototypical thick disk stars with rotation (O) velocities significantly different than he LSR. a low z-comiponeut to their orbital angular uomentum (L.) aud a high eccentricity.," HD 52711 and 210918 are prototypical thick disk stars with rotation $\Theta$ ) velocities significantly different than the LSR, a low $z$ -component to their orbital angular momentum $L_z$ ) and a high eccentricity." " Li contrast. HD 207129 is a prototypical thin disk star with a rotation velocity aud L- similar to the LSR. a low eccent‘Ici. a stuall 2,44. and a simall arele to the Galactic plane."," In contrast, HD 207129 is a prototypical thin disk star with a rotation velocity and $L_z$ similar to the LSR, a low eccentricity, a small $z_{max}$ and a small angle to the Galactic plane." Three stars which are likely thin clisk stars (HD 15335. 202628 and 207129) have similar ages ol ~6.1 Gyr.," Three stars which are likely thin disk stars (HD 15335, 202628 and 207129) have similar ages of $\simeq 6.4$ Gyr." TIe oldest sars which appear to be thin disk stars are HD 32923 (10.040.5 Gvi) al HD 11330 (9.3£0.6 Gyr., The oldest stars which appear to be thin disk stars are HD 32923 $10.0\pm 0.5$ Gyr) and HD 41330 $9.3\pm 0.6$ Gyr). Both of these stars have rotation velocities aud L. similar to tje LS and low eccentricities., Both of these stars have rotation velocities and $L_z$ similar to the LSR and low eccentricities. " The z,,4; οἱ these stars is not too large (0.16 aud 0.29 kpc) given tlat thi disk stars have >0.325 kpe scaleheight exponentials (Majewski1993).", The $z_{max}$ of these stars is not too large (0.46 and 0.29 kpc) given that thin disk stars have $\ge 0.325$ kpc scaleheight exponentials \citep{maj}. . The angle o “their orbits the Galacic plea ϱ(Ψ3.15 and 211 are somewhat larger than typical for this disk stars but not extremely so.," The angle of their orbits to the Galactic plane $\Psi = 3.45^{\degr}$ and $2.14^{\degr}$ ) are somewhat larger than typical for thin disk stars but not extremely so." Asa result. we believe that it is likey that at least one of these two stars is a true member o ‘the tlin disk.," As a result, we believe that it is likely that at least one of these two stars is a true member of the thin disk." These stars are ocatecl ina 'eejon of the CMD where the clerived ages are relatively jnselisiive to the metallicities. colors and asolute magnitudes.," These stars are located in a region of the CMD where the derived ages are relatively insensitive to the metallicities, colors and absolute magnitudes." Cousequentlv.tle derived ages have very suall error bars.," Consequently,the derived ages have very small error bars." Averagiug the ages ol these two stars together we find that the oldest. soijewhat metal-poor thin disk st:us in the soar neighborhood have an age of 9.7250.6 Gyr.," Averaging the ages of these two stars together we find that the oldest, somewhat metal-poor thin disk stars in the solar neighborhood have an age of $9.7\pm 0.6$ Gyr." The two sla‘s with kinematic and o‘pital paramelers ost represeutive of the thick clisk (HD 52711 anc 210918) have quite different agesof 6.7dFE1.0 Gyr and 11.7+1.1 Gyr., The two stars with kinematic and orbital parameters most representive of the thick disk (HD 52711 and 210918) have quite different agesof $6.7\pm 1.0$ Gyr and $11.7\pm 1.1$ Gyr. The older age, The older age therein).,. .. Beyond that. there are permitted. lines such as the Balmer-series lines that are verv broad Ceopyyuar>LO? kkniss +) due to eravitationally-induced motions.," Beyond that, there are permitted lines such as the Balmer-series lines that are very broad $v_{\rm FWHM}>10^3$ $^{-1}$ ) due to gravitationally-induced motions." " The characteristic size of this ""broad. line region"" (BLE) apparently scales with the intrinsic Luminosity of the host QSO (and therefore with the mass ofthe central black hole: Ixaspictal.1996:Wandel 1999)). such that in luminous QSOs (as opposed to. e.g. Sevífert Ts). the size of the BL is on the order of six light-months (or ~0.3 ppc)."," The characteristic size of this `broad line region' (BLR) apparently scales with the intrinsic luminosity of the host QSO (and therefore with the mass ofthe central black hole; \citealt{kaspi:96a, wandel:99}) ), such that in luminous QSOs (as opposed to, e.g., Seyfert 1's), the size of the BLR is on the order of six light-months (or $\sim0.3$ pc)." According to long-term studies of QSOs. the typical (rest-frame) Hux variations in the QSO continuum are on the order of (though occasional Uuctuations as high as 50s are possible: Ulrichctal. 19972). while the BLR variations are smaller by a factor of 24 (Maozetal.1994).," According to long-term studies of QSOs, the typical (rest-frame) flux variations in the QSO continuum are on the order of (though occasional fluctuations as high as $\sim50\times$ are possible; \citealt{ulrich:97}) ), while the BLR variations are smaller by a factor of 2–4 \citep{maoz:94}." . 1n the observed frame. these timescales are stretehed by an additional factor of 22).," In the observed frame, these timescales are stretched by an additional factor of $z_s$ )." There is some evidence for anti-correlations between the rest-ultraviolet continuum flux and the equivalent. width of certain emission lines (Baldwin1977: Greenetal. 2001)). which may also be related. to. the correlation between the central black hole mass and the continuum Iux (Wandel1999).," There is some evidence for anti-correlations between the rest-ultraviolet continuum flux and the equivalent width of certain emission lines \citealt{baldwin:77}; \citealt{green:01}) ), which may also be related to the correlation between the central black hole mass and the continuum flux \citep{wandel:99}." ". Phe general trend claimed. is that the more luminous QSOs have less pronounced. broad-line. emission line components. the ccentral-Iux. ratio is small. /anc the rest-ultraviolet and -optical mumultiplet emission lines are more prominent. obfuscating the ""true local continuum level that underlies these emission lines."," The general trend claimed, is that the more luminous QSOs have less pronounced broad-line emission line components, the central-flux ratio is small, and the rest-ultraviolet and -optical multiplet emission lines are more prominent, obfuscating the `true' local continuum level that underlies these emission lines." There is strong (brightening) evolution with recdshift observed in the luminosity function. of QSOs. so that in general. high-redshift optically-selectec QSOs are less likely to have strong eemission.," There is strong (brightening) evolution with redshift observed in the luminosity function of QSOs, so that in general, high-redshift optically-selected QSOs are less likely to have strong emission." The QSO templates from the Large Bright QS&O Survey (LBQS: Francisctal.1992)) and the Sloan Digital Sky Survey (SDSS: VandenBerketal.2001)) are compiled from objects over a broad range of redshifts. relatively few ab zcd (where the rest-optical window around us still visible).," The QSO templates from the Large Bright QSO Survey (LBQS; \citealt{francis:92}) ) and the Sloan Digital Sky Survey (SDSS; \citealt{vandenberk:01}) ) are compiled from objects over a broad range of redshifts, relatively few at $z<1$ (where the rest-optical window around is still visible)." Therefore. the rregion in these templates is drawn from objects that are relatively local ancl of lower luminosity. and so gencrally show a misleacingly large rratio. if they are to be applied to higher-redshift considerations.," Therefore, the region in these templates is drawn from objects that are relatively local and of lower luminosity, and so generally show a misleadingly large ratio, if they are to be applied to higher-redshift considerations." The only definite way to determine the characteristics of a particular system is by direct observations in the rest-optical., The only definite way to determine the characteristics of a particular system is by direct observations in the rest-optical. For example. in the case of | 231 at z;=3.62. AMuravamaetal.(1999). fine that the comission is relatively weak compared to112.. similar to Iower-redshift QSOs.," For example, in the case of $+$ 231 at $z_s=3.62$, \citet{murayama:99} find that the emission is relatively weak compared to, similar to lower-redshift QSOs." Consider a case where the spectrum of all images in an Einstein Cross are obtained. in à. wavelength range where both NLR and BLK— emission features are visible at high signal-to-noise gO) andwithsuf ficientspectralresolitionloctearlyresolvet heshape 200 +).," Consider a case where the spectrum of all images in an Einstein Cross are obtained, in a wavelength range where both NLR and BLR emission features are visible at high signal-to-noise $>\!\!>$ 10), and with sufficient spectral resolution to clearly resolve the shapes of the lines $v_{res}$ $200$ $^{-1}$ )." " ""The NLR emission lines are usec to normalise the spectra to each other. and we wish to attempt o ciisentangle the substructure signature [rom other ellects."," The NLR emission lines are used to normalise the spectra to each other, and we wish to attempt to disentangle the substructure signature from other effects." There are several systematic errors to consider., There are several systematic errors to consider. As each lensed image ollows a cüllerent line of sight through the lensing galaxy. if the gas and dust in the galaxy are sullicienthy patchy or position dependent. it is possible that there will x: dillerential reddening that may allect the measured continuum slope and relative emission line Iuxes.," As each lensed image follows a different line of sight through the lensing galaxy, if the gas and dust in the galaxy are sufficiently patchy or position dependent, it is possible that there will be differential reddening that may affect the measured continuum slope and relative emission line fluxes." Falcoetal.(1999) measured {ποV) in 23 lens galaxies using UST broadband colours. under the (optimistic) assumption hat variability and microlensing were not important.," \citet{falco:99} measured the $\Delta\,E(B-V)$ in 23 lens galaxies using HST broadband colours, under the (optimistic) assumption that variability and microlensing were not important." In recent. broacdband-magnitude-based. substructure estimates. he colour corrections estimated by the above work were applied. which. in light of the possibility. of microlensing. may introduce unquantifiably svstematic errors for any one svstem.," In recent broadband-magnitude-based substructure estimates, the colour corrections estimated by the above work were applied, which, in light of the possibility of microlensing, may introduce unquantifiably systematic errors for any one system." In the spectroscopic approach. choosing NLA ancl DLI emission lines that are close in wavelength. the dillerential reddening is very small.," In the spectroscopic approach, choosing NLR and BLR emission lines that are close in wavelength, the differential reddening is very small." Taking the median value of jàNECD1)= 004mmag in the Falcoctal.(1990). opticallv-selected: sample. and. assuming a MWti- extinction law (Cardellietal.1989).. we estimate that lux ratio between aand for ος—3 and τι=1 will vary by less than and can herefore be ignored.," Taking the median value of $\Delta\,E(B-V)=0.04$ mag in the \citet{falco:99} optically-selected sample, and assuming a MWG-type extinction law \citep{cardelli:89}, we estimate that flux ratio between and for $z_s=3$ and $z_l=1$ will vary by less than and can therefore be ignored." For comparison. between πα the variation will be about1.," For comparison, between and the variation will be about." 44.. Some microlensing by stars probably occurs in most lenses. but it is most clearly seen in quaclruple enses (Witt.Mao&Schechter1995.andcitations thereof)..," Some microlensing by stars probably occurs in most lenses, but it is most clearly seen in quadruple lenses \citep*[][and citations thereof]{witt:95}. ." Microlensing.e events last months or vers. much. longeroO han the time delay between images. but. (especially at caustic crossings. which can oceur quickly) can magnily," Microlensing events last months or years, much longer than the time delay between images, but (especially at caustic crossings, which can occur quickly) can magnify" "Recent X-ray observations have revealed (hat some clusters of galaxies have ""cold fronts” which may have been formed as a result of them undergoing a major/minor merger (Owers el",Recent $X$ -ray observations have revealed that some clusters of galaxies have “cold fronts” which may have been formed as a result of them undergoing a major/minor merger (Owers et since (he svstem 15 axisvnuuetric. only i=0 harmonics. nothing but Legendre polynomials. show up.,"Since the system is axisymmetric, only $m=0$ harmonics, nothing but Legendre polynomials, show up." " The coefficients. ay. can be caleulated by the orthogonality of the Legendre polvuonuals: The position of the shock surface. 2,(0). is estimated [vom (he iso-entropic surlace of s= 5n the following analvses."," The coefficients, $a_{\ell}$, can be calculated by the orthogonality of the Legendre polynomials; The position of the shock surface, $R_{\rm s}(\theta)$, is estimated from the iso-entropic surface of $s=5$ in the following analyses." The temporal evolutions of the average shock radius are obtained from the 6=0 component in the above decomposition and |ARRoy)=[lao—Roo)(aoa! ave plotted in Fig.4," The temporal evolutions of the average shock radius are obtained from the $\ell = 0$ component in the above decomposition and $|\Delta R_{\rm s}/R_{\rm s,0}|=|(a_{0}-R_{\rm s,0})/R_{\rm s,0}|$ are plotted in Fig.," ". where 2,0 is the initial shock radius."," where $R_{\rm s,0}$ is the initial shock radius." As can be seen [rom the figure. after the shock surface oscillates for about LOO ms as in the svimimetric simulations. it begins (o increase.," As can be seen from the figure, after the shock surface oscillates for about 100 ms as in the symmetric simulations, it begins to increase." " For the models with L,=3.0.5.5-10°erg/s. the shock surface is settled in ~50 ms {ο a quasi-steacky state with a radius ~ 1056 Larger than the initial value. ancl keeps oscillating around it thereafter."," For the models with $L_{\nu} = 3.0, 5.5\cdot 10^{52}~\mbox{erg/s}$, the shock surface is settled in $\sim50$ ms to a quasi-steady state with a radius $\sim10$ % larger than the initial value, and keeps oscillating around it thereafter." " In the case of L,=6.0-10erg/s. on the other hand. a continuous increase of the average shock radius is found. which will eventually lead. to the explosion mentioned above."," In the case of $L_{\nu} = 6.0\cdot 10^{52}~\mbox{erg/s}$, on the other hand, a continuous increase of the average shock radius is found, which will eventually lead to the explosion mentioned above." " It is emphasized that even lor (he model with no negative entropy-gracdient (L,—3.0-10° erg/s). the exponential increase of the shock radius occurs during the same period."," It is emphasized that even for the model with no negative entropy-gradient $L_{\nu} = 3.0\cdot 10^{52}~\mbox{erg/s}$ ), the exponential increase of the shock radius occurs during the same period." This demonstrates clearly that the instability has nothing to with the convection al least for this model., This demonstrates clearly that the instability has nothing to with the convection at least for this model. The relative contributions of SASI and convection for other models will be discussed in the next section., The relative contributions of SASI and convection for other models will be discussed in the next section. In this section. we diseuss both the linear ancl nonlinear growths of the instability in ereater detail.," In this section, we discuss both the linear and nonlinear growths of the instability in greater detail." As reported in(2003). the most remarkable feature of SASI is the dominance of the modes with /=1.2 in the instability.," As reported in, the most remarkable feature of SASI is the dominance of the modes with $\ell=1, 2$ in the instability." Tlence we start with the analvsis of the models with £6=1 single-mode velocity perturbation imposed initially., Hence we start with the analysis of the models with $\ell=1$ single-mode velocity perturbation imposed initially. Fig., Fig. shows the temporal evolutions of the (=1 and (=2 modes., shows the temporal evolutions of the $\ell=1$ and $\ell=2$ modes. " Although the result for L,=5.510°?erg/s is plotted as a reference case. the qualitative feature is common to other models."," Although the result for $L_{\nu} = 5.5\cdot 10^{52}~\mbox{erg/s}$ is plotted as a reference case, the qualitative feature is common to other models." As can be clearly seen. (he evolution is divided into two phases.," As can be clearly seen, the evolution is divided into two phases." The initial phase lasting for ~100 ms represents the linear phase. where the amplitude of each mode grows exponentially.," The initial phase lasting for $\sim 100$ ms represents the linear phase, where the amplitude of each mode grows exponentially." It is noted that even for the single-mode perturbation. the second harmonics is generated by the nonlinear coupling aud grows exponentially also.," It is noted that even for the single-mode perturbation, the second harmonics is generated by the nonlinear coupling and grows exponentially also." In the, In the Iu the present cosmological paradigm.ACDM.. most of the imass-cnerey of the universe is du invisible conrponeuts: dark matter and dark cnerev.,"In the present cosmological paradigm, most of the mass-energy of the universe is in invisible components: dark matter and dark energy." Cenerically speaking. dark imatter could mean any non-unünous eravitating mass. barvouic or not.," Generically speaking, dark matter could mean any non-luminous gravitating mass, baryonic or not." For our cosmological uodel to work. the dark matter must specifically be dynamically cold aud nou-harvouic.," For our cosmological model to work, the dark matter must specifically be dynamically cold and non-baryonic." We have arrived at the oparadieni for very good reasons that do not require repetition here., We have arrived at the paradigm for very good reasons that do not require repetition here. " Ilowever. to date alb evidence for dark iatter remains astronondcal in nature. resting ""uudeaneutalh: ou the assmuption that πο new eravitational physics occurs when extrapolating the force aw by eight orders of magnitude frou precision solar system tests to extragalactic svstenis."," However, to date all evidence for dark matter remains astronomical in nature, resting fundamentally on the assumption that no new gravitational physics occurs when extrapolating the force law by eight orders of magnitude from precision solar system tests to extragalactic systems." The persistent xesence of mass discrepancies in extragalactie svstenis welt therefore also be iuterpreted as a £ülure of this asstuuptiou., The persistent presence of mass discrepancies in extragalactic systems might therefore also be interpreted as a failure of this assumption. We come then to a fundamental dichotomy of attitudes hat differcut scicutists bring to the problem., We come then to a fundamental dichotomy of attitudes that different scientists bring to the problem. A common one is that ilias πο many SIHCCOSSCS that it beo correct., A common one is that has so many successes that it be correct. Consequently. nou-barvouic cold dark iuatter exist.," Consequently, non-baryonic cold dark matter exist." This is the attitude I brought to the problem., This is the attitude I brought to the problem. llowever. another valid attitude is the a. hypothetical new particle generally presumed to exist in à hwpothetical new dark sector of particle plivsies.," However, another valid attitude is the a hypothetical new particle generally presumed to exist in a hypothetical new dark sector of particle physics." Until the existence of these particles is confirmed in the laboratory. rronidns au unconfirmed Lypothesis built on a good but unproven supposition.," Until the existence of these particles is confirmed in the laboratory, remains an unconfirmed hypothesis built on a good but unproven supposition." Which of these attitudes oue brings to the problem inevitably colors one’s interpretation of auv eiven set of data., Which of these attitudes one brings to the problem inevitably colors one's interpretation of any given set of data. Rotating galaxies obey a relation between their rotation velocity aud luuinosity (7).. or more generally. their barvonic mass (2) of the form with the slope typically found to be in the range 3x:X oL.," Rotating galaxies obey a relation between their rotation velocity and luminosity \citep{TForig}, or more generally, their baryonic mass \citep{btforig} of the form with the slope typically found to be in the range $3 \le x \le 4$ ." Though widely used in distance scale work. the physical basis of this relation remains unclear.," Though widely used in distance scale work, the physical basis of this relation remains unclear." Starting from) Newtons uuiversal law of eravitv. 2 obtained where “ois the mass surface deusitv.," Starting from Newton's universal law of gravity, \citet{aaronson} obtained where $\Sigma$ is the mass surface density." This suffices if. as believed at the time. disk galaxies all share esseutiallv he same surface briehtuess (7) so that X— constant.," This suffices if, as believed at the time, disk galaxies all share essentially the same surface brightness \citep{freeman70} so that $\Sigma \sim$ constant." I first eucountered this problem in the context of ow surface brightuess (LSB) galaxies. which explicitly violate the required coustancy of X.," I first encountered this problem in the context of low surface brightness (LSB) galaxies, which explicitly violate the required constancy of $\Sigma$." I had. at the time. developed my own (perfectly conventional) theory for the corluation of LSB ealaxics.," I had, at the time, developed my own (perfectly conventional) theory for the formation of LSB galaxies." Motivated by observations of the stellar populations of LSB galaxies (?) that sugeestedCoco that LSB ealaxies were less evolved aud xxhaps had a later start in Πίο than their higher surface brightuess brethreu. I hwpothesized that their ow stellar densities followed from residing in low density dark iatter halos.," Motivated by observations of the stellar populations of LSB galaxies \citep{LSBpops} that suggested that LSB galaxies were less evolved and perhaps had a later start in life than their higher surface brightness brethren, I hypothesized that their low stellar densities followed from residing in low density dark matter halos." Though I arrived at this idea independently. a simular idea had been previously ciseussed by ?..," Though I arrived at this idea independently, a similar idea had been previously discussed by \citet{DS}." Iu oder parlance. IE associated low surface brightuess ealaxies with late forming dark matter halos.," In modern parlance, I associated low surface brightness galaxies with late forming dark matter halos." This hypothesis made two predictions: (1) that LSB ealaxics should be less strongly clustered than TSB galaxies. aud," This hypothesis made two predictions: (1) that LSB galaxies should be less strongly clustered than HSB galaxies, and" »ofile structure depends on the pulse intensity: in stronger »ulses. the leading component (the precursor) is much more pronounced and arrives somewhat earlier. whereas the rest ofthe pulse (the main pulse) is markedly weaker an retains its position in the pulse window.,"profile structure depends on the pulse intensity: in stronger pulses, the leading component (the precursor) is much more pronounced and arrives somewhat earlier, whereas the rest of the pulse (the main pulse) is markedly weaker an retains its position in the pulse window." Ixrishnamohan&Downs(1983) have suggested. that the precursor component originates in a separate emission region. at higher altitudes in the magnetosphere.," \citet{kd83} have suggested that the precursor component originates in a separate emission region, at higher altitudes in the magnetosphere." Phen its location in the pulse ofile can be explained in terms of rotational aberration., Then its location in the pulse profile can be explained in terms of rotational aberration. —owever. if the emission regions of the precursor and. the =nain pulse are completely independent. it is cillicult to understand. the observed. intensity. recistribution between jese components. which is controlled by the total intensity of the pulse.," However, if the emission regions of the precursor and the main pulse are completely independent, it is difficult to understand the observed intensity redistribution between these components, which is controlled by the total intensity of the pulse." We suggest that the precursor component results from. 1e induced scattering of the main pulse into the background (seealsoPetrova2008b)., We suggest that the precursor component results from the induced scattering of the main pulse into the background \citep[see also][]{p08b}. . The main pulse emission is scattered olf the particles. which participate in the resonant absorption and. consequently. perform relativistic helical motion.," The main pulse emission is scattered off the particles, which participate in the resonant absorption and, consequently, perform relativistic helical motion." The induced scattering transfers the radio intensity from the main pulse to the precursor component., The induced scattering transfers the radio intensity from the main pulse to the precursor component. It will be shown that stronger induced: scattering entails larger intensities of the resultant radio pulse and also its earlier arrival., It will be shown that stronger induced scattering entails larger intensities of the resultant radio pulse and also its earlier arrival. Thus. it is the process that can account for the the racio profile structure of the Vela pulsar and its intensity-dependent: variations.," Thus, it is the process that can account for the the radio profile structure of the Vela pulsar and its intensity-dependent variations." The high-energy profile of the Vela. pulsar has. the ollowing structure (Ixanbach.ctal.L094;Gouilles.1998:2002:Shibanovοἱal.2003:Romaniet 2005).," The high-energy profile of the Vela pulsar has the following structure \citep{he1,g98,he5,h02,he2,he4,he3}." . Phere are wo main peaks separated by about a half of the pulsar »eriod., There are two main peaks separated by about a half of the pulsar period. None of them coincide with the radio pulse. aud »eak 1 lags it by ~907 in pulse phase.," None of them coincide with the radio pulse, and peak 1 lags it by $\sim 90^\circ$ in pulse phase." In the optical and μαoft. X-ray profiles. peak 1. noticeably shifts with frequency oward the radio pulse position. whereas at higher energies he components keep their positions fixed.," In the optical and soft X-ray profiles, peak 1 noticeably shifts with frequency toward the radio pulse position, whereas at higher energies the components keep their positions fixed." Ciouilfes(1998) has discovered. an additional. component of the optical olile. which coincides with the radio pulse and. extends o the earlier. pulse. phases.," \citet{g98} has discovered an additional component of the optical profile, which coincides with the radio pulse and extends to the earlier pulse phases." In the soft. X-ray range. the component is also present. and one can ciscern its two peaks. one of which (peak 3) precedes the radio pulse and another one (peak +) coincides with it (Hardingctal.2002).," In the soft X-ray range, the component is also present, and one can discern its two peaks, one of which (peak 3) precedes the radio pulse and another one (peak 4) coincides with it \citep{h02}." . The component is most pronounced at a few tenths keV. and vanishes above a few keV. In the observations of Lommenetal. (2007).. the X-ray profile is integrated over the range of 216 keV. and this component looks às a trough. but still interacts with the radio pulse.," The component is most pronounced at a few tenths keV and vanishes above a few keV. In the observations of \citet{l07}, the X-ray profile is integrated over the range of 2–16 keV, and this component looks as a trough, but still interacts with the radio pulse." In the present paper. we explain the trough at. keV energies and iis connection to the radio pulse.," In the present paper, we explain the trough at keV energies and its connection to the radio pulse." Por this purpose we turn to one more mechanism — the spontaneous scattering olf the spiraling particles. — which deposits the racio photons into the high-energy range.," For this purpose we turn to one more mechanism – the spontaneous scattering off the spiraling particles, – which deposits the radio photons into the high-energy range." The radio photon reprocessing to high energies implies a physical connection between the radio and high-energv emissions. which can manifest itself in the simultaneous fluctuations in these ranges.," The radio photon reprocessing to high energies implies a physical connection between the radio and high-energy emissions, which can manifest itself in the simultaneous fluctuations in these ranges." Phe luctuations are believed to result. from. the variations of the physical conditions in the magnetosphere., The fluctuations are believed to result from the variations of the physical conditions in the magnetosphere. In our model. the radio pulse participates in both the spontaneous and induced scatterings. and it will be shown that the interplay between these processes in the course of the pulse-to-pulse Huctuations of the plasma parameters can account for the X-ray radio connection observed in the Vela »ulsar.," In our model, the radio pulse participates in both the spontaneous and induced scatterings, and it will be shown that the interplay between these processes in the course of the pulse-to-pulse fluctuations of the plasma parameters can account for the X-ray – radio connection observed in the Vela pulsar." The plan of the paper is as follows., The plan of the paper is as follows. Section 2 is devoted o the theory of spontaneous scattering olf the spiraling xwiicles., Section 2 is devoted to the theory of spontaneous scattering off the spiraling particles. The spectral and angular. distributions of the scattered. power are examined. and compared with those of he svnehrotron radiation of the scattering particles., The spectral and angular distributions of the scattered power are examined and compared with those of the synchrotron radiation of the scattering particles. The details of induced. scattering of the radio waves below the resonance are given in Sect., The details of induced scattering of the radio waves below the resonance are given in Sect. 3., 3. In Sect., In Sect. 4 we apply our ormalism to the Vela pulsar., 4 we apply our formalism to the Vela pulsar. Ehe radio profile formation is considered in Sect., The radio profile formation is considered in Sect. 4.1. the high-energy emission is acdressed in Sect.," 4.1, the high-energy emission is addressed in Sect." 4.2. and the observational manifestations of the X-ray radio connection are investigated. in Sect.," 4.2, and the observational manifestations of the X-ray – radio connection are investigated in Sect." 4.3., 4.3. Our results are cliscussed and summarized in Sect., Our results are discussed and summarized in Sect. 5., 5. The cross-section for the magnetized scattering. by the particle at rest was first obtained in Canutoetal.(1971)., The cross-section for the magnetized scattering by the particle at rest was first obtained in \citet{c71}. . In application to the pulsar magnetosphere. the scattering in a strong magnetic [field by the particles streaming relativistically along the magnetic lines was examined in Blancllord&Seharlemann(1976):LyubarskiiPetrova(1996).," In application to the pulsar magnetosphere, the scattering in a strong magnetic field by the particles streaming relativistically along the magnetic lines was examined in \citet{bs76,lp96}." . Wilson&Rees(1978). have considered the magnetized induced scattering in the pulsar wind., \citet{wr78} have considered the non-magnetized induced scattering in the pulsar wind. Let us consider the radio wave scattering. oll the xwiicles performing relativistic helical motion in the magnetic field of a pulsar., Let us consider the radio wave scattering off the particles performing relativistic helical motion in the magnetic field of a pulsar. Deep in the magnetosphere the xwlicles stream relativistically along the open magnetic ines., Deep in the magnetosphere the particles stream relativistically along the open magnetic lines. " In the vicinitv of the radio emission region. he magnetic field is so strong that. any perpendicular momentum. of the particles is almost immediately. lost. via svnchrotron re-emission and the radio wave frequency. in he particle rest frame is much less than the electron evrolrequency. wip,&wer=eBime (here 110050. dis the particle velocity in units of e. ϐ is the wavevector ilt to the magnetic field. 7 is the particle Lorentz-Lactor. 2m(d yy, "," In the vicinity of the radio emission region, the magnetic field is so strong that any perpendicular momentum of the particles is almost immediately lost via synchrotron re-emission and the radio wave frequency in the particle rest frame is much less than the electron gyrofrequency, $\omega\eta\gamma\ll\omega_G\equiv eB/mc$ (here $\eta\equiv 1-\beta\cos\theta$, $\beta$ is the particle velocity in units of $c$, $\theta$ is the wavevector tilt to the magnetic field, $\gamma$ is the particle Lorentz-factor, $\gamma\equiv(1-\beta^2)^{-1/2}$ )." As the magnetic field strength rapidly: decreases with distance from the neutron star. Dxr in the outer magnetosphere the radio waves pass through the exclotron resonance. q=we. where they are subject to resonant absorption.," As the magnetic field strength rapidly decreases with distance from the neutron star, $B\propto r^{-3}$, in the outer magnetosphere the radio waves pass through the cyclotron resonance, $\omega\eta\gamma=\omega_G$, where they are subject to resonant absorption." As a result of this process. the incident. racio emission is partially absorbed: ancl the particles acquire transverse momenta.," As a result of this process, the incident radio emission is partially absorbed and the particles acquire transverse momenta." In the resonance region. the magnetic Ποιά is weak enough. and the spontaneous synchrotron re-enission does not prevent the momentum. growth.," In the resonance region, the magnetic field is weak enough, and the spontaneous synchrotron re-emission does not prevent the momentum growth." As is shown in Petrova(2002.2003).. the particle evration becomes relativistic at the very bottom of the resonance region. and further on the transverse and total momenta of the particles continue growing.," As is shown in \citet{p02,p03}, the particle gyration becomes relativistic at the very bottom of the resonance region, and further on the transverse and total momenta of the particles continue growing." Pulsar radio emission is essentially broadband: and. correspondingly. the resonance region is sulliciently extended.," Pulsar radio emission is essentially broadband and, correspondingly, the resonance region is sufficiently extended." Over most part of this region there is a significant amount of the photons with frequencies well below the resonance. ay)€ο=eDBfsme.," Over most part of this region there is a significant amount of the photons with frequencies well below the resonance, $\omega\eta\ll\Omega\equiv eB/\gamma mc$." We are interested. in the scattering. of the uncler-resonance radio emission. olf the relativistic spiraling particles., We are interested in the scattering of the under-resonance radio emission off the relativistic spiraling particles. In our case the incident radiation presents the transverse electromagnetic waves polarized. either. in the plane of the ambient magnetic, In our case the incident radiation presents the transverse electromagnetic waves polarized either in the plane of the ambient magnetic "amplitude,phase ciagrams. which we will call A/o plots.","amplitude/phase diagrams, which we will call $\phi$ plots." Llere we will show a few of the more significant ones., Here we will show a few of the more significant ones. The ET of run. 86316. contains only Ist) harmonic DNOs and 87311 is predominantly. Ist harmonic., The FT of run S6316 contains only 1st harmonic DNOs and S7311 is predominantly 1st harmonic. In. order o compare their behaviour with that of the fundamental (which would have been strongly present only an hour or so xXore the start of these runs as seen in 86059 in Table 2)) we give in Figs., In order to compare their behaviour with that of the fundamental (which would have been strongly present only an hour or so before the start of these runs – as seen in S6059 in Table \ref{dno4tab2}) ) we give in Figs. 4 and 5. phase diagrams structured in the same manner as the ‘oak panel diagram! of 86059 shown in igure 10 of Paper L These show that the general behaviour of fundamental ancl Ist harmonic DNOs are. essentially identical: short-livecl increases. ancl decreases of. period. or hase superposed on the steady increase in mean period., \ref{dno4fig4} and \ref{dno4fig5} phase diagrams structured in the same manner as the `oak panel diagram' of S6059 shown in figure 10 of Paper I. These show that the general behaviour of fundamental and 1st harmonic DNOs are essentially identical: short-lived increases and decreases of period or phase superposed on the steady increase in mean period. ST311 is. however. relatively more coherent than 856316. with smaller deviations from the secular increase or period.," S7311 is, however, relatively more coherent than S6316, with smaller deviations from the secular increase or period." Run 861358 is predominantly. Ist harmonic and is the first to show noticeable scatter in period., Run S6138 is predominantly 1st harmonic and is the first to show noticeable scatter in period. To examine this at greater resolution we give a phase diagram in Lig. 6..," To examine this at greater resolution we give a phase diagram in Fig. \ref{dno4fig7}," where the run has been divided into two equal parts and the phases are measured relative to periods 25.77 s and 30.50 s respectively., where the run has been divided into two equal parts and the phases are measured relative to periods 25.77 s and 30.50 s respectively. In the upper panel there is the quasi-parabolic variation with phase changing by several eveles. which is the signature of a steadily increasing period. but in the lower panel there is variation (with a range ~ one evele) around a constant. phase. showing no svstematic increase in. period over the 3.7 hi span of time.," In the upper panel there is the quasi-parabolic variation with phase changing by several cycles, which is the signature of a steadily increasing period, but in the lower panel there is variation (with a range $\sim$ one cycle) around a constant phase, showing no systematic increase in period over the 3.7 h span of time." There is no noticeable dilference in the gross light curve behaviour between the two halves of the run (the second. half of which is shown in figure 2 of Paper LL). but we note that optical [ux is largely determined bv aceretion in the outer parts of the disc. whereas the," There is no noticeable difference in the gross light curve behaviour between the two halves of the run (the second half of which is shown in figure 2 of Paper II), but we note that optical flux is largely determined by accretion in the outer parts of the disc, whereas the" EW values for H.j~25-30 Α.. quite similar to that measured in ΕΜ: (43.Α.. Terlevich et al. 19910).,"EW values for $\beta^*\sim$ 25-30, quite similar to that measured in UM448 (43, Terlevich et al. \citeyear{ter91}) )." Therefore. for the hybrid objects the 11. luminosities and equivalent widths expected from stellar photoionization are consistent with those measured for HIT galaxies.," Therefore, for the hybrid objects the $\beta^*$ luminosities and equivalent widths expected from stellar photoionization are consistent with those measured for HII galaxies." We must not forget that the continuum emitted by type 2 quasars is not necessarily stellar so that the measured level is an upper limit to the stellar continuum level and the EW values discussed above for H.3” relative to the stellar continuum are lower limits., We must not forget that the continuum emitted by type 2 quasars is not necessarily stellar so that the measured level is an upper limit to the stellar continuum level and the EW values discussed above for $\beta^*$ relative to the stellar continuum are lower limits. A more strict analysis would require a quantification. of other possible contaminants. such as scattered light from the hidden AGN.," A more strict analysis would require a quantification of other possible contaminants, such as scattered light from the hidden AGN." Polarimetric information would be needed to characterize the nature of the continuum., Polarimetric information would be needed to characterize the nature of the continuum. Lacking this information. we can only say hat the continuum level detected from the hybrid objects. where he stellar contribution is probably highest. is consistent with that expected from H-7.," Lacking this information, we can only say that the continuum level detected from the hybrid objects, where the stellar contribution is probably highest, is consistent with that expected from $\beta^*$." While this is a simplistic exercise and one cannot expect all ype 2 quasars to have identical spectra of the stellar ionized gas. it suggests nevertheless that adding a varying contribution of stellar johoetoionized gas works in the right direction to solve most of the oroblems affecting the standard AGN sequence.," While this is a simplistic exercise and one cannot expect all type 2 quasars to have identical spectra of the stellar ionized gas, it suggests nevertheless that adding a varying contribution of stellar photoionized gas works in the right direction to solve most of the problems affecting the standard AGN sequence." The temperature oroblem remains and a more sofisticated scenario with a range of gas densities or the presence of a matter bounded component might be a viable solution., The temperature problem remains and a more sofisticated scenario with a range of gas densities or the presence of a matter bounded component might be a viable solution. Some studies suggest that the [OIIT]JA3007 emission line is an unbiased indicator of the intrinsic optical-UV luminositiy of both type | quasars and radio galaxies. (, Some studies suggest that the $\lambda$ 5007 emission line is an unbiased indicator of the intrinsic optical-UV luminositiy of both type 1 quasars and radio galaxies. ( Simpson 1998).,Simpson 1998). According ο the results above. it is possible that [ONT] has a strong stellar contribution in a fraction of type 2 quasars.," According to the results above, it is possible that [OIII] has a strong stellar contribution in a fraction of type 2 quasars." Let us estimate the Traction of [ONT] flux originated by stars in the hybrid objects., Let us estimate the fraction of [OIII] flux originated by stars in the hybrid objects. " We know that: using 35 in the range 3.2-3.9 as measured for the hybrid objects. Got =2.9 (Cas for UM448) and ""m —O0.8 (since c4) and rearranging. ao~S9-72%.."," We know that: using $\frac{[OIII]^{tot}}{H\beta^{tot}}$ in the range 3.2-3.9 as measured for the hybrid objects, $\frac{OIII^*}{H\beta^*}$ =2.9 (as for UM448) and $\frac{H\beta^*}{H\beta^{tot}}$ =0.8 (since $x$ =4) and rearranging, $\frac{[OIII]^*}{[OIII]^{tot}}\sim$." This suggests that there could be a fraction of type 2 quasars in which [OTT] is not a reliable indicator ofAGN power., This suggests that there could be a fraction of type 2 quasars in which [OIII] is not a reliable indicator of AGN power. Other type of studies should be performed to investigate this issue more carefully (e.g. Simpson 1998 ))., Other type of studies should be performed to investigate this issue more carefully (e.g. Simpson \citeyear{sim98}) ). We have compared the optical emission lines ratios of type 2 quasars from. Zakamskaetal.(2003) with standard AGN photoionization model predictions. Seyfert 2s. HIT galaxies. and narrow line FRII radio galaxies.," We have compared the optical emission lines ratios of type 2 quasars from \cite{zak03} with standard AGN photoionization model predictions, Seyfert 2s, HII galaxies, and narrow line FRII radio galaxies." Moderate to high ionization narrow line radio galaxies and Seyfert 2s are indistinguishable from type 2 quasars based on their optical line ratios., Moderate to high ionization narrow line radio galaxies and Seyfert 2s are indistinguishable from type 2 quasars based on their optical line ratios. The standard AGN photoionization models. valid for other type 2 AGNs. can reproduce successfully the loci and trends of type 2 quasars in some of the main diagnostic diagrams.," The standard AGN photoionization models, valid for other type 2 AGNs, can reproduce successfully the loci and trends of type 2 quasars in some of the main diagnostic diagrams." On the other hand. these models are not exempt of problems and the discrepancies with the data are the same encountered for other type 2 AGNs.," On the other hand, these models are not exempt of problems and the discrepancies with the data are the same encountered for other type 2 AGNs." The comparison between models and data suggests that a range of ionization and probably physical properties must exist within the type 2 quasar sample., The comparison between models and data suggests that a range of ionization and probably physical properties must exist within the type 2 quasar sample. An internal range of cloud properties (e.g. varying density) must also exist in individual objects., An internal range of cloud properties (e.g. varying density) must also exist in individual objects. This is only natural. as one cannot expect identical gas and continuum properties (e.g. ionizing luminosity) in all quasars. or ensembles of identical clouds in individual objects.," This is only natural, as one cannot expect identical gas and continuum properties (e.g. ionizing luminosity) in all quasars, or ensembles of identical clouds in individual objects." Realistic models must take this into account., Realistic models must take this into account. Possible solutions which have been extensively discussed in the literature are locally optimally emitting clouds. a mixture of matter and ionization bounded clouds. dusty. radiation-pressure dominated models or a mixture of clouds with different ( values.," Possible solutions which have been extensively discussed in the literature are locally optimally emitting clouds, a mixture of matter and ionization bounded clouds, dusty, radiation-pressure dominated models or a mixture of clouds with different $U$ values." The relevant role plaved by AGN photoionization is nof surprising. since Zakamskaetal.(2003). selected objects with properties characteristic of active galaxies.," The relevant role played by AGN photoionization is not surprising, since \cite{zak03} selected objects with properties characteristic of active galaxies." However. based on the lack of correlation between [OTT] and radio luminosities. other authors have suggested that an important fraction of type 2 quasars might not be dominated by AGN activity but by star formation (Vir Lal Ho 2007:: see also Kim et al. 2006).," However, based on the lack of correlation between [OIII] and radio luminosities, other authors have suggested that an important fraction of type 2 quasars might not be dominated by AGN activity but by star formation (Vir Lal Ho \citeyear{vir07}; see also Kim et al. \citeyear{kim06}) )." We have found that stellar photoionization is obvious in a small fraction of objects (3 out of 50) which are characterized by low [ONT] luminosities and large [OITII/TOIIT] ratios compared with most type 2 quasars in the sample., We have found that stellar photoionization is obvious in a small fraction of objects (3 out of 50) which are characterized by low [OIII] luminosities and large [OII]/[OIII] ratios compared with most type 2 quasars in the sample. 1n this work. we have used two sets of mock galaxy samples as simulations of data from DES ancl VIS.,"In this work, we have used two sets of mock galaxy samples as simulations of data from DES and VHS." In this section we briclly describe the way in which these cata samples are generated., In this section we briefly describe the way in which these data samples are generated. Both catalogues are gencrated using Monte Carlo methods after assuming relevant redshift. magnituce and type distributions.," Both catalogues are generated using Monte Carlo methods after assuming relevant redshift, magnitude and type distributions." The first mock catalogue is that of 7? and 7? - DIS5vr hereafter., The first mock catalogue is that of \citet{DES:photoz} and \citet{Lin:DESsims} - DES5yr hereafter. It adopts the galaxy magnituce-recdshift distribution. derived. from. the luminosity. functions of. 2 and ? and a type distribution derived. using data from the GOODS/IIDE-N field (7277) and the CWW template SEDs (2)...," It adopts the galaxy magnitude-redshift distribution derived from the luminosity functions of \citet{Lin:LF} and \citet{Poli:LF} and a type distribution derived using data from the GOODS/HDF-N field \citep{Capak:HDF-N,Wirth:GOODS-N,Cowie:GOODS-N} and the CWW template SEDs \citep{CWW:templates}." X IHlux-limited. sample is constructed with 0